[{"data":1,"prerenderedAt":14036},["ShallowReactive",2],{"blog-posts":3,"blog-navigation":14017},[4,371,1031,1059,1240,1438,1562,1722,1858,2003,2059,2149,2209,2433],{"id":5,"title":6,"body":7,"description":350,"extension":351,"meta":352,"navigation":366,"path":367,"seo":368,"stem":369,"__hash__":370},"blog\u002Fblog\u002F1.Human-Birdflight-Feasibility.md","Human Birdflight",{"type":8,"value":9,"toc":338},"minimark",[10,28,73,78,81,86,137,141,207,211,214,243,247,250,277,281,331],[11,12,13,14,21,22,27],"p",{},"In a land before time, there once was the ",[15,16,20],"a",{"href":17,"rel":18},"https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FQuetzalcoatlus",[19],"nofollow","Quetzalcoatulus",", a huge Pterosaur the size of a Cessna 172. It was estimated to weigh something around ",[15,23,26],{"href":24,"rel":25},"https:\u002F\u002Fdoi.org\u002F10.1152\u002Fajpregu.1994.266.4.R1077",[19],"250 kg"," and have a wingspan of about 5 m. Very impressive, considering the limited force and power density of muscle fibre. Nevertheless, these guys are long long gone.",[11,29,30,31,36,37,42,43,48,49,54,55,60,61,66,67,72],{},"Since the very beginning of civilization, humankind has been longing for the skies. The first reference we found, the babylonian Myth of Etana, is about ",[15,32,35],{"href":33,"rel":34},"https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FEtana",[19],"four and a half thousand years"," old! One of the oldest refrence in western culture is the story of ",[15,38,41],{"href":39,"rel":40},"https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FIcarus",[19],"Icarus and Daedalos"," in ancient Greek mythology. It still has such presence that many people we talked to in the last years instantly thought of that legend, when told about our exoskeleton. Many ",[15,44,47],{"href":45,"rel":46},"https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FTimeline_of_aviation_before_the_18th_century",[19],"attempts"," were made throughout ancient history, but it took until about 1500 CE for the \"first engineer\", ",[15,50,53],{"href":51,"rel":52},"https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FCodex_on_the_Flight_of_Birds",[19],"Leonardo da Vinci",", to analyse the concept of flight in a more rigorous manner. Sadly he didn't solve the mystery back then, but he created detailes schematics and also built prototypes of flying machines.\nAround 1800, craftsmen and engineers started to figure flying out. ",[15,56,59],{"href":57,"rel":58},"https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FGeorge_Cayley#Flying_machines",[19],"Sir George Cayley"," worked out many important aspects of heavier than air flight and constructed a glider in 1804 proven to be worth it's salt. Shortly after, Albrecht Berblinger, the Tailor of Ulm flies his own contraption down German slopes. Both works fail to be taken seriously by their peers. The wall finally breaks down at the end of the 19th century, when Otto Lilienthal and his brother Gustav finally get the gist and build their \"",[15,62,65],{"href":63,"rel":64},"https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FDerwitzer_Glider",[19],"Flugapparat","\" (flying apparatus). They also experimented with flapping flight, but had to realize that humans are not strong enough for this method of propulsion. The Wright Brothers then added an engine and propeller to the outfit and the rest is history. Since then, flying has become ubiquitous with planes nowadays weighting ",[15,68,71],{"href":69,"rel":70},"https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FAirbus_A380#Specifications_(A380-800,_Trent_engines)",[19],"more than five hundred tonnes",". Great! But only half of the dream, the pioneers had back then. Because flying in an aircraft is nice, but it doesn't fulfil this ancient dream of spreading your arms and just flying like a bird! You can't feel the lift on your arms and the wind in your face when sitting in an airplane.",[74,75,77],"h2",{"id":76},"modern-work-in-flapping-flight-and-unsteady-aerodynamics","Modern Work in Flapping Flight and Unsteady Aerodynamics",[11,79,80],{},"Several inventors and scientists have investigated the concept of flapping flight since 1900.\nSelected pieces from the large body of work can be found below.",[82,83,85],"h3",{"id":84},"natural-flyers","Natural Flyers",[87,88,89,98,106,113,121,129],"ul",{},[90,91,92,97],"li",{},[15,93,96],{"href":94,"rel":95},"http:\u002F\u002Fhdl.handle.net\u002F10088\u002F22978",[19],"1962 - Greenewalt"," - Dimensional relationships for flying animals",[90,99,100,105],{},[15,101,104],{"href":102,"rel":103},"https:\u002F\u002Fdoi.org\u002F10.1242\u002Fjeb.80.1.17",[19],"1979 - Rayner"," - Power requirements",[90,107,108,112],{},[15,109,111],{"href":24,"rel":110},[19],"1994 - Marden"," - Power requirements vs. size of birds",[90,114,115,120],{},[15,116,119],{"href":117,"rel":118},"https:\u002F\u002Fdoi.org\u002F10.1242\u002Fjeb.000273",[19],"2007 - Tobalske"," - Biomechanics of bird flight",[90,122,123,128],{},[15,124,127],{"href":125,"rel":126},"https:\u002F\u002Fdoi.org\u002F10.1242\u002Fjeb.038109",[19],"2010 - Berg, Biewener"," - Wing and body kinematics of takeoff and landing flight",[90,130,131,136],{},[15,132,135],{"href":133,"rel":134},"https:\u002F\u002Fdoi.org\u002F10.1242\u002Fjeb.116228",[19],"2015 - Cranell, Tobalske"," - Kinematics and aerodynamics of avian upstrokes during slow flight",[82,138,140],{"id":139},"fluid-dynamics-aerodynamics-aeroelastics","Fluid Dynamics, Aerodynamics, Aeroelastics",[87,142,143,151,159,167,175,183,191,199],{},[90,144,145,150],{},[15,146,149],{"href":147,"rel":148},"https:\u002F\u002Fdigital.library.unt.edu\u002Fark:\u002F67531\u002Fmetadc53413\u002Fm2\u002F1\u002Fhigh_res_d\u002F19800006788.pdf",[19],"1934 - Theodorsen"," - General Theory of Aerodynamic Instability and the Mechanism of Flutter",[90,152,153,158],{},[15,154,157],{"href":155,"rel":156},"https:\u002F\u002Fdoi.org\u002F10.1002\u002Fzamm.19920720208",[19],"1992 - Send"," - The Mean Power of Forces and Moments in Unsteady Aerodynamics",[90,160,161,166],{},[15,162,165],{"href":163,"rel":164},"http:\u002F\u002Fdx.doi.org\u002F10.1103\u002FPhysRevLett.103.118102",[19],"2009 - Pesavento, Wang"," - Flapping Wing Flight Can Save Aerodynamic Power Compared to Steady Flight",[90,168,169,174],{},[15,170,173],{"href":171,"rel":172},"https:\u002F\u002Fdx.doi.org\u002F10.2514\u002F1.29263",[19],"2012 - Platzer et al."," - Flapping Wing Aerodynamics: Progress and Challenges",[90,176,177,182],{},[15,178,181],{"href":179,"rel":180},"https:\u002F\u002Fhdl.handle.net\u002F11370\u002F31931f33-4aa0-4280-892e-93699af0e9b6",[19],"2014 - Thielicke"," - The Flapping Flight of Birds - Analysis and Application",[90,184,185,190],{},[15,186,189],{"href":187,"rel":188},"https:\u002F\u002Fdoi.org\u002F10.1017\u002FS0001924000026105",[19],"2016 - DeLaurier"," - The development of an efficient ornithopter wing",[90,192,193,198],{},[15,194,197],{"href":195,"rel":196},"https:\u002F\u002Fwww.aniprop.de\u002Fsites\u002Fdefault\u002Ffiles\u002Fdlrk2018\u002FDLRK2018_Send_0178_en-US.pdf",[19],"2018 - Send"," - Project BigBird XL: Commercial Use of the  Bending\u002FTorsional Drive",[90,200,201,206],{},[15,202,205],{"href":203,"rel":204},"https:\u002F\u002Fdoi.org\u002F10.1103\u002FPhysRevFluids.6.013101",[19],"2021 -  Zurman-Nasution, Ganapathisubramani, Weymouth"," - Effects of aspect ratio on rolling and twisting foils",[82,208,210],{"id":209},"powered-exoskeletons","Powered Exoskeletons",[11,212,213],{},"This topic is developing fast. A few quotes:",[87,215,216,219,227,235],{},[90,217,218],{},"2001 - Schiele, “Development of a Human Arm Exoskeleton for Space Robotics Telepresence: From Biomechanics to Mechanism Design”, ESA Final Report, EWP – 2161",[90,220,221,226],{},[15,222,225],{"href":223,"rel":224},"https:\u002F\u002Fdoi.org\u002F10.5772\u002F55336",[19],"2013 - Kim et al."," - Lower Limb Exoskeleton",[90,228,229,234],{},[15,230,233],{"href":231,"rel":232},"http:\u002F\u002Fdx.doi.org\u002F10.1016\u002Fj.robot.2015.10.001",[19],"2015 - Gopura et al."," - Overview Paper for exoskeletons",[90,236,237,242],{},[15,238,241],{"href":239,"rel":240},"https:\u002F\u002Fdoi.org\u002F10.1109\u002FAIM.2017.8014123",[19],"2017 - Sui et al."," - upper-limb exoskeleton and mechanisms\nSome names of exoskeletons: Rupert, ESA X-Arm-2, NEUROExos, NREX, Stuttgart Exo-Jacket",[82,244,246],{"id":245},"control-systems","Control systems",[11,248,249],{},"What you need is a bilateral teleoperation system (developed since the 1960s). Or a brain-computer-interface, if you find one. A few hints:",[87,251,252,255,258,266,274],{},[90,253,254],{},"1997 - Zeng, Hemami - An overview of robot force control, Robotica, volume 15, pp 473 –482",[90,256,257],{},"2011 - Haddadi - Stability, Performance, and Implementation Issues in Bilateral Teleoperation Control and Haptic Simulation Systems, PhD Thesis, Queen’s University, Kingston, Ontario, Canada",[90,259,260,265],{},[15,261,264],{"href":262,"rel":263},"https:\u002F\u002Fdoi.org\u002F10.1177\u002F0278364910385730",[19],"2011 - Aguirre-Ollinger et al."," - Impendance control and inertia compensation",[90,267,268,273],{},[15,269,272],{"href":270,"rel":271},"https:\u002F\u002Fdoi.org\u002F10.1007\u002F978-3-319-19557-5",[19],"2015 - Lee, Payandeh"," - Haptic Teleoperation Systems, ISBN 978-3-319-19556-8",[90,275,276],{},"\"A brain-computer interface that evokes tactile sensations improves robotic arm control\" -  Flesher et al., Science 372, 831–836 (2021)",[82,278,280],{"id":279},"recent-work-on-human-flapping-flyers","Recent work on human flapping flyers",[87,282,283,298,307,316],{},[90,284,285,286,291,292,297],{},"In 2006 ",[15,287,290],{"href":288,"rel":289},"https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FJames_DeLaurier",[19],"James DeLaurier"," finished building an ornithopter ",[15,293,296],{"href":294,"rel":295},"https:\u002F\u002Fphys.org\u002Fnews\u002F2006-07-university-toronto-ornithopter.html",[19],"capable of carrying one person",".",[90,299,300,301,306],{},"In 2010, also in Toronto, the ",[15,302,305],{"href":303,"rel":304},"https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FUTIAS_Snowbird",[19],"Snowbird"," lifted off.",[90,308,309,310,315],{},"In 2011, the inventor Douglas C. George published his latest design of the ",[15,311,314],{"href":312,"rel":313},"https:\u002F\u002Fwww.dcgeorge.com\u002F",[19],"Project Falcon",". He calls it \"A Biomimetic, Battery-Powered Robotic Exoskeleton Ornithopter\", which follows a similar idea to Fluglicht.",[90,317,318,319,324,325,330],{},"The fake ",[15,320,323],{"href":321,"rel":322},"https:\u002F\u002Fweb.archive.org\u002Fweb\u002F20120930071507\u002Fhttp:\u002F\u002Fhumanbirdwings.net\u002F",[19],"\"Human Birdwings Project\""," by ",[15,326,329],{"href":327,"rel":328},"https:\u002F\u002Fwww.floriskaayk.com\u002F#view-human-birdwings",[19],"Floris Kaayk"," aka. \"Jarno Smeets\" explored the public reception of human birdflight. It was very well produced on a shoe-string budget and shows excellently how exciting the idea is for many people.",[11,332,333,334],{},"Further reading: ",[15,335,337],{"href":336},"\u002Fblog\u002Ftechnology_details","Technology and Calculations",{"title":339,"searchDepth":340,"depth":340,"links":341},"",2,[342],{"id":76,"depth":340,"text":77,"children":343},[344,346,347,348,349],{"id":84,"depth":345,"text":85},3,{"id":139,"depth":345,"text":140},{"id":209,"depth":345,"text":210},{"id":245,"depth":345,"text":246},{"id":279,"depth":345,"text":280},"Reviewing the literature and history on human birdflight and flapping wings","md",{"subtitle":353,"topic":354,"category":355,"image":356,"authors":357,"tags":361,"date":365},"History and Research","Flying","Technical","\u002Fimages\u002Fimage1_contoured_whitebg_lowres.jpg",[358],{"name":359,"avatar":360},"Peter Jüstel","Team_Platzhalter.png",[362,363,364],"Human birdflight","history","feasibility","2023-11-05",true,"\u002Fblog\u002Fhuman-birdflight-feasibility",{"title":6,"description":350},"blog\u002F1.Human-Birdflight-Feasibility","4grN6PM4dlTWmkcAWOuMSxKHpGkltXGaawF92SCZeT8",{"id":372,"title":373,"body":374,"description":1019,"extension":351,"meta":1020,"navigation":366,"path":1027,"seo":1028,"stem":1029,"__hash__":1030},"blog\u002Fblog\u002F10.Business_Lessons.md","Business Lessons",{"type":8,"value":375,"toc":1002},[376,379,382,386,389,392,407,410,419,422,447,452,495,499,502,516,520,527,534,539,546,553,560,564,567,575,586,589,593,596,599,608,614,617,626,630,633,644,647,650,688,691,694,697,701,704,707,718,722,725,742,746,749,769,772,776,782,786,789,806,809,812,816,819,832,836,866,869,892,896,957,961],[11,377,378],{},"You might think, the challenge in building the wings is in the technology. And it's certainly a challenge! But I'd say, the real challenge and the reason nobody succeeded in building these wings is to get the funds to build them just ONCE. Time of engineers is expensive, and you will need A LOT of it. In fact, the materials required are relatively cheap in comparison. Our estimates run at $6.5 million (in 2024) for one proper flying exoskeleton. Of that, about $5.5 million is just to pay 10 engineers for 5 years. The estimate for the material is about $80k (manufacturing is assumed to be done by the engineers themselves). So where and how do you get starting funds from? Once you managed to get that, it will become more and more obvious how many people love this idea and the market pull will make raising funds way easier.",[11,380,381],{},"I think I found a way so that you won't need the $6.5m upfront. It's a four-step approach building on entertainment as the addressed need. I'll get back to that later. First, let's look at all the possibilities.",[74,383,385],{"id":384},"all-the-business-possiblities","All the business possiblities",[11,387,388],{},"There are a myriad possibilities with the exoskeleton, as it is a platform technology. It's easy to get lost in all the options. Here are some things we thought about.",[11,390,391],{},"With the Exoskeleton:",[393,394,395,398,401,404],"ol",{},[90,396,397],{},"Industry robot teaching",[90,399,400],{},"Teleoperation of robots in hazardous environments (radiation, submarine work, space)",[90,402,403],{},"Powered exoskeletons for heavy work or orthopedic purposes\u002Fortheses (also think of \"Powerarmor\")",[90,405,406],{},"Haptic interface for VR gaming",[11,408,409],{},"With the Exoskid:",[393,411,413,416],{"start":412},5,[90,414,415],{},"Selling the Exoskid",[90,417,418],{},"\"Virtual travelling\" - being a bird at the Grand Canyon, Yosemite, Klimandscharo. Controlling a drone-airplane with VR goggles and your body from your sofa or an attraction booth at the site.",[11,420,421],{},"With the wings:",[393,423,425,428,431,434,441,444],{"start":424},7,[90,426,427],{},"Mountain rescue and\u002For Police patrolling",[90,429,430],{},"Show-robotics for Hollywood",[90,432,433],{},"The wings as a means of general transportation and commuting",[90,435,436,437],{},"The Military - ",[438,439,440],"em",{},"we explicitly decided against this on and you shall burn in hell if you use the information on this page to build something that helps to kill people. I explicitly dissalow this by the power of my copyright and also give anyone else the license to spit on you, sue you, and destroy you for defiling this dream of mankind. The wings shall be a symbol of hope and positivity, not a tool for destruction and power gain.",[90,442,443],{},"A sports league of flying games (think \"Quidditch\")",[90,445,446],{},"Flying experiences and a pilot club",[448,449,451],"h4",{"id":450},"here-are-the-reasons-we-decided-against-1-11","Here are the reasons we decided against 1-11:",[393,453,454,457,460,463,471,474,477,480,483,486,489,492],{},[90,455,456],{},"Training for Industry Robots: The need and the market seemed not interesting\u002Fbig enough and there are better options (e.g. Wandelbots). It also needs a suitable industry partner. And also we didn't care enough.",[90,458,459],{},"Teleoperation for HAZMAT: There are companies in this field, but none are a real big deal. Often there is a certain kind of nimbleness required (like for submarine welding), which would require a nimble exoskeleton+robot for the hand. And there are companies doing only that, so the obstactle and competition seemed too high for the opportunity.",[90,461,462],{},"Powerarmor: There are a few companies building exoskeletons for heavy work support or health. Work support companies usually pivoted to un-powered exoskeletons, so there seems no sufficient need in that sector. Also there seems to be a usability issue preventing workers to actually use the thing (it's too clumsy to put on and off). Health companies usually only focus on one joint or limb, which probably has reasons. Also \"power support\" is no \"teleoperation\" anymore and comes with the fundamental issue that you have to predict the will of the user in the control algorithms. So the \"obstacle vs. potential and fun\" equation didn't look good again.",[90,464,465,466,470],{},"Gaming Exoskeleton: Gaming might actually be a great community and market to get the \"exoskeleton thing\" going! I investigated this quite a bit. Gamers are open to new techology and willing to pay a new experience. And the gaming market is growing steadily. There is a fundamental issue blocking this path, though: for an exoskeleton to be attractive there needs to be games for it. For gamestudios to develop games for exoskeletons there needs to be a widespread adoption of exoskeletons. So figuratively speaking: you would need to drag yourself out of the mud on your own hair. As we are not Baron Münchhausen, and the real thing was capturing us more than the VR worlds, we decided against this route. Anyways, for your pleasure, ",[15,467,469],{"href":468},"\u002FResources","here"," is the pitch and business model canvas I built..",[90,472,473],{},"The Exoskid is probably somewhat interesting for RC-enthusiasts. So one might be able to get a small, profitable business out of this. It would require probably two to three years of work and a bit of re-engineering, as the current status of the design is not sellable or producable on scale. Also the Flysky hacking works only on that Flysky. Most RC-enthusiasts would probably want to use their own transmitter. So the market potential seemed uninteresting and there would be a lot of tinkering and footwork to be done to claim it.",[90,475,476],{},"Virtual Travelling: a couple of companies (even in Dresden) seemed to have tried this one, not managing to get any noteworthy traction with customers. So this hearsay kept us from investigating further down this path.",[90,478,479],{},"Mountain Rescue and Police: This is a possible spin-off when it's built. If one had a good connection to public funders, this might be a viable route. With the Police thing it might get a dark tone though, if they screw it up, or the country is gripped by despotism. This path seemed too buerocracy-ridden, so we passed on it.",[90,481,482],{},"Show-robotics for Hollywood: Disney Robotics and the like might be interested in the wings. This might finance the first prototype enabling next steps without the issue of flight-certification. It would require masterful networking to get to talk to the right person, though. I think Vlad in the Startup House of Palo Alto came up with this idea (creds to him!). So relatively late in our building effort. In the aftermath of our valley trip, it seemed more daunting than finding an Angel for our main approach, so we never followed that road.",[90,484,485],{},"Commuting: in 2024 I met Daniel Wiegand, one of the founders of Lilium (a VTOL Startup). We talked for quite some time and he strongly advised against this path because of buerocracy. To get certified by the EASA and the FAA is ludicrously hard and buerocratic. It might have been what broke their fledging wings in the end (apart from the incredible visionlessness of the German government).",[90,487,488],{},"Military: just no. See above.",[90,490,491],{},"Sports league: That would be spectacular, but it's not really a thing that one creates. It might emerge once there are pilots in the sky, inventing their own kind of games. So no way to start with.",[90,493,494],{},"experiences and pilot club: this might actually work, and is explained in further detail next.",[74,496,498],{"id":497},"the-four-step-approach-to-building-the-business","The four-step approach to building the business",[11,500,501],{},"So what transpired in all the countless talks we had with potential customers is, that the product has to fulfill certain requirements in order to be interesting. Basic requirements are things like safety, attainable cost per use, and the experience being non-virtual but the real thing. Also people were wondering how you would learn this. So here are the four steps for development with revenue on every step:",[393,503,504,507,510,513],{},[90,505,506],{},"thing on a crane",[90,508,509],{},"thing on a Zeppelin",[90,511,512],{},"thing in an arena",[90,514,515],{},"thing in the wild",[82,517,519],{"id":518},"explanation","Explanation",[11,521,522,523,526],{},"See also the pitch and our revenue potential estimates on ",[15,524,525],{"href":468},"this page"," for accompanying pictures and numbers.",[11,528,529],{},[530,531],"img",{"alt":532,"src":533},"Step 1","\u002Fimages\u002FStep1.png",[393,535,536],{},[90,537,538],{},"Build a flying exoskeleton, but \"fake\" the wings first. The wings and the exoskeleton only require 4 degrees of freedom (flapping, aileron, elevator, rudder). And everything is dangling from a crane in the wind. This reduces the development effort a lot, as no proper structural and aerodynamical analysis of the wings has to be performed. But it already gives a feeling for flying like this. This can prove the market and raise attention. Imagine these attractions at the Golden Gate, the Buraj Khalifa in Dubai, or a beach in southern France. One can sell tickets for the ride. Richard Browning\u002FGravity Industries earned it's initial revenue with this.",[11,540,541,545],{},[530,542],{"alt":543,"src":544},"Step 2","\u002Fimages\u002FStep2.png","\n2) Hanging the same thing from a Zeppelin will be even greater, as some travelling is involved. Again, the single flight experience is sold. To lower cost per flight, more than one system could be attached. The Zeppelin itself will draw attention which is worth something. And this combination has the crucial benefit that the wings are not freely flying. Apart from the lower development effort this means: no madly expensive certification has to be endured, while people can still experience flying in the outside world.",[11,547,548,552],{},[530,549],{"alt":550,"src":551},"Step 3","\u002Fimages\u002FBild3_resize.jpg","\n3) This next step involves freely flying in an arena. This again is not a public space and can be secured with nets. Thus, system failure doesn't produce damages and EASA certification is not necessary (private space). The technology can then be further developed along pilot experiences, adding more degrees of freedom and continually improving the system. Watching these guys fly and play in the air is probably exciting (including crashes into the net). If played right, one can make a business out of this and it can lead to a new and amazing sport. In parallel, a pilot club can be founded, as from this point on, proper pilot training will start. Also, all the revenue channels of sports clubs will open up (merchandise, clothing\u002Ffashion, game tickets, etc.). The clothes and gear brand, invoking associations of daring, cutting edge technology, and a positive future, might be the most lucrative part of the business (that can actually be started at any stage of the process).",[11,554,555,559],{},[530,556],{"alt":557,"src":558},"Step 4","\u002Fimages\u002FBild2_final_crop.jpg","\n4) All of the previous steps lay groundwork for this really big throw: flying freely in public space. An inauguration flight from Crete to mainland Greece would be in due order. And then, the applications are endless. Silent commuting above the traffic jam, mountain soaring and rescuing, islandhopping, playing with the clouds, races, steampunk travelling air circus with Zeppelin and flying exosekeletons... let your imagination fly! Eventually the patent will run out and \"security\" might get a hold of it. Anything flying is inherently dual-use, sadly..\nIt might be sensible not to sell the wings, but only lease or rent them, keeping control over maintenance and ownership of the device. This way, it might at least be possible to prevent it from getting into the very very wrong hands.",[82,561,563],{"id":562},"getting-funding","Getting funding",[11,565,566],{},"There are two fundamental challenges in getting funding:",[393,568,569,572],{},[90,570,571],{},"getting into contact with the right people who have the funds",[90,573,574],{},"convincing them to trust you with their funds",[11,576,577,578,580,581,585],{},"For the first point, you can either go nuts in networking, and\u002For have the people find you by being very visible. Both is a lot of fustrating work. You can find a list of investors ",[15,579,469],{"href":468}," in the Dataroom bundle.\nAs mentioned in the ",[15,582,584],{"href":583},"\u002Fblog\u002Fthe_legacy","\"legacy\""," article already, going to hard tech mixer events in California is the fastest way of getting an intro to an investor. But take note that many events are not publicly announced. In our two weeks we also pitched at the Stanford Startup Society and at a Go Global event. Both only accessible via contacts. On these events it's useful to be eye-catching without looking pathetic. For instance having a t-shirt with a striking image or somesuch. There is no \"dresscode\" for these events.",[11,587,588],{},"As a German one should realise that it's ok to just start talking to people and also move on after 5 minutes. This is very relaxed in California. But never forget: \"let's connect!\"",[448,590,592],{"id":591},"approach-of-investors","Approach of investors",[11,594,595],{},"There are many strategies for approaching investors. Some suggest first refining your pitch with less critical investors before presenting to the really important VCs, while others argue against wasting time and collecting confusing feedback from unsuitable investors, recommending instead to go straight to the right people. Which approach is best likely depends on your product and your own personal style.",[11,597,598],{},"There’s a story about Raj: one investor told him, “Your product is crap and your pitch is terrible,” and then a few days later he got his break-through investment with the exact same pitch and product.\nSo when it comes to feedback in conversations, you’ll encounter countless opinions, many of which will contradict each other. It’s crucial to consider the perspective of the person giving the feedback and weigh their input accordingly. Always think for yourself and don’t blindly accept others’ opinions.",[11,600,601,602,607],{},"Useful places to start networking include the ",[15,603,606],{"href":604,"rel":605},"https:\u002F\u002Fhackerdojo.org\u002F",[19],"Hacker Dojo",", which hosts regular pitch sessions, and Noisebridge, a hackerspace with a lot of cool, hands-on people. Circuit Control in Oakland is another option for co-working and networking. Every Wednesday, Stanford offers lectures (ETL – Entrepreneurial Thought Leaders) featuring impressive speakers. Here is picture from the Hacker Dojo with a bunch of German CEOs and CTOs from Germany in the back row:",[11,609,610],{},[530,611],{"alt":612,"src":613},"Hacker Dojo Picture","\u002Fimages\u002FHackerdojo_Pic_von_Svet1.jpg",[11,615,616],{},"On LinkedIn, there are “slutty connectors\". People with thousands of contacts who accept every request. You can search through their networks to find local contacts. While LinkedIn is often seen as spammy these days, reaching out to other founders for warm introductions can still work well. Just make sure your profile and the description line that appears with your name are solid, so you don’t come across as a novice.",[11,618,619,620,625],{},"Joining a startup house or hacker house is worthwhile because you’ll immediately connect with like-minded people who have already spent time in the area. This is a great way to build a foundational network. It helped us alot (thanks, ",[15,621,624],{"href":622,"rel":623},"https:\u002F\u002Fstartuphouse.co\u002F",[19],"Startup House","!)",[448,627,629],{"id":628},"convincing-the-investor","Convincing the investor",[11,631,632],{},"Depending on where you are and who you talk to, the most important aspects for convincing the investor vary. But in my opinion it always comes down to showing:",[87,634,635,638,641],{},[90,636,637],{},"Does the technology work or is it fake? Is the technological risk acceptable? (\"Technology\")",[90,639,640],{},"Is there a market\u002Fneed for the product? If yes, how big is it? (\"Market\")",[90,642,643],{},"Is the team capable of pulling this through? (\"Team\")",[11,645,646],{},"In Germany you have to be triple A in every category to get breadcrumbs. In the US it doesn't have to be that perfect, the focus is on the market (scalability, business model) and the team. And if you meet the right person, none might matter much, if the angel is stoked on the idea and likes you. So don't be discouraged if you haven't got much to show! In the US, many things are possible. But it might take a longer time to get to know the right person.",[11,648,649],{},"In general, the more \"proof\" you can show for the three above points (Technology, Market, Team), the better and the more money you can pitch for. So for instance:",[87,651,652,655,658,661,664,670,673,676,679,682,685],{},[90,653,654],{},"Technology: technological proof of concept (BUT: Investors won't look at your calculations until they hire an assessor to do the due diligence). The more physical proof you can show that the concept works, the better. Make a crunchy video or do a demo.",[90,656,657],{},"Prototype(s)",[90,659,660],{},"Published papers",[90,662,663],{},"Patents, intellectual property",[90,665,666,667,669],{},"How big TAM, SAM and SOM are. It needs to be a billion Dollar market (TAM) for an investor to be interested (as you will only get a slice of that (SOM). Check also ",[15,668,469],{"href":468}," for our calculations.",[90,671,672],{},"Financials: numbers on unit cost and how much money you could make with your business (best: annual recurring revenue). How big the \"traction\" (read: your revenue) already is.",[90,674,675],{},"A concrete plan for what you want the initial 500k for. What milestone (that will be used for raising the next round) will you achieve with this in the next 6-18 month? Think of \"proof of market\" and \"proof of technology(-parts)\".",[90,677,678],{},"\"investing in lines, not in the dots\". This means, you need to show\u002Fpublish consistent progress over time. This reinsures investors that you take it seriously and shows them your pace of progress. (Our 7 years of struggle didn't look to good..)",[90,680,681],{},"Letters of Intent from potential customers. Any kind of tangible proof for the excitement of people about this product (like customer interviews you conducted) and that they are willing to pay the estimated price (\"traction\" again).",[90,683,684],{},"Social credits, so for instance if you can win somebody \"believable\" from the technology's field as an angel. Like the CTO of another aerospace company. Or a scientist with a name in that topic (especially an ivy-league professor). But also the mere fact that you managed to get a warm contact to the investor.",[90,686,687],{},"Team: that every needed expertiese is on board. People in the US are relatively focussed on pre-approval through namedropping, so better have the ivy-league or big, well-known corporates in your CV\u002Fpitch.. Also, everyone needs to be working full time on the start-up, otherwise people don't believe you take it seriously.",[11,689,690],{},"As a rule of thumb, you will need to manage with $500k max in the pre-seed stage (less is better) and will have to give up 10-20% of your shares. The seed round can be somethig between 1 and 10 million, depending on how much substance you managed to build in pre-seed.",[11,692,693],{},"Try to avoid anything that has to do with certification AT ALL COST! It takes an INSANE amount of time and money to get something flying certified and might easily kill your business (this insight comes straight from Lilium's founder Daniel Wiegand). Better focus on a niche like the \"attraction business\" and \"commercials\" for the start and build something that doesn't need to be certified that much (or just go where the regulations are less strict than with the EASA or the FAA, #Dubai). Consider: the necessary certification depends on the country where your HQ is located in (not the country you want to sell the thing in)!",[11,695,696],{},"Technologically, the Exoskid seemed to excite the people in San Francisco the most, but it was not enough. People wanted to see a person\u002Fdummy with wings on the back, even if they are completely fake.",[82,698,700],{"id":699},"red-bull","Red Bull",[11,702,703],{},"This is so obvious that I dedicate a whole section to it. Red Bull would be the ideal inital partner to get this of the ground, as their brand values, marketing, and symbolism align perfectly with the Fluglicht concept and initial business case. There are two problems though. First, they seem to get spammed by tons of people with ideas for crazy flying contraptions and are extremely defensive with cold introductions. We weren't able to talk to them at all, and we tried 4 times over differing routes. Secondly they might consider you as competition and might try to swallow the whole thing before it can grow. So if you want to build a business it might be risky to co-operate with them.",[11,705,706],{},"Alternative possible Sponsors:",[87,708,709,712,715],{},[90,710,711],{},"Disney Robotics",[90,713,714],{},"Dubai",[90,716,717],{},"Jochen Schweitzer",[82,719,721],{"id":720},"finding-a-co-founder","Finding a co-founder",[11,723,724],{},"Best is someone you already worked with (e.g. in a student project) or from your network (pre-aproved). Otherwise put out job advertisments with your local start-up supporters (like Berkeley Skydeck, Circuit Launch, Techstars, Y-combinator, Founder Institute, TiE) or on Linkedin or Fivver. Work on something like a small project together BEFORE founding together! You can only know if someone is a team player after having a couple of disagreements. Talk about:",[87,726,727,730,733,736,739],{},[90,728,729],{},"why do both of you want to do this? What motivates you? (Flying and freedom, getting rich, going down into history\u002Fbecoming immortal, ...?)",[90,731,732],{},"What are the things you like and don't like to do?",[90,734,735],{},"What are your skillsets, what do you want to try\u002Flearn?",[90,737,738],{},"Following form that: what are the respective responsibilies?",[90,740,741],{},"What do you expect from the other person and from the project?\nSearch for \"co-founder checklist\" to go deeper.",[82,743,745],{"id":744},"other-possible-funding-routes","Other possible funding routes",[11,747,748],{},"Possibilities what still can be done to get funding for building the wings:",[87,750,751,754,757,760,763,766],{},[90,752,753],{},"Build a student team, get sponsoring and just build this thing in a year. You will need at least 20 really motivated people willing to put the work in (including at least one person excited about getting the sponsors and project management).",[90,755,756],{},"Do a Master's thesis, PhD, or research project on the subject. Requires a host institution\u002Fprofessor and a lot of patience\u002Fpersistence.",[90,758,759],{},"Patreon",[90,761,762],{},"Build a crowd and make a crowdfunding campaign",[90,764,765],{},"Produce and market the Exoskid (about 2yrs of work)",[90,767,768],{},"Create a fashion brand around the emotions and values attached to flying like a bird",[11,770,771],{},"and as a whole subgenre:",[82,773,775],{"id":774},"exoskeleton-spin-offs","Exoskeleton spin-offs",[11,777,778,779,781],{},"There are a bunch of markets where haptic interaction with the digital space is interesting. Gaming might be a good first-movers market for that. For some time, I worked on a business case for this, ",[15,780,469],{"href":468}," are the details. The trouble is, that there are few to none (VR-)games that could really use this. It's a chicken-and-egg problem, because as long as there are no exoskeletons, there is no market for the games to include this. But as long as there are no games using exoskeletons, there is no market for exoskeletons.",[82,783,785],{"id":784},"some-more-thoughts","Some more thoughts..",[11,787,788],{},"What you probably need:",[87,790,791,794,797,800,803],{},[90,792,793],{},"A good website",[90,795,796],{},"Social media content production (e.g. of the vision and of you building stuff)",[90,798,799],{},"Connections to Advisors from the industry. Connecting to founders building new aeronautical stuff is very useful.",[90,801,802],{},"Connections to Angel Investors with deep pockets, who are amazed by the idea and willing to fund the initial 500k of development (unless you are a student team and nobody gets paid)",[90,804,805],{},"pitching: start with why, tell a good story",[11,807,808],{},"Professional associations are a great resource for informations on the market and sometimes also for connections.",[11,810,811],{},"The Y-Combinator website and youtube videos are probably the most accurate primer to understand what you need to raise successfully in Silicon Valley.",[74,813,815],{"id":814},"organizing-and-infrastructure","Organizing and Infrastructure",[11,817,818],{},"Here are some tips on useful tools (that are not tracking you):",[87,820,821,824],{},[90,822,823],{},"uberspace.de, Nextcloud.com: cloud infrastructure for shared files, e-mails, and Kanban board. For people capable of using Linux.",[90,825,826,831],{},[15,827,830],{"href":828,"rel":829},"https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FSMART_criteria",[19],"SMART goals",". A useful but not too complicated framework for work planing. Don't try to plan everything in advance, though. That almost never works in an exploratory journey. Make a plan defining who does what and when, try to execute, if it doesn't work iterate the plan.",[74,833,835],{"id":834},"useful-links","Useful links",[87,837,838,845,852,859],{},[90,839,840],{},[15,841,844],{"href":842,"rel":843},"https:\u002F\u002Fshizune.co\u002Fblog\u002Fhow-to-get-warm-introductions-to-investors\u002F",[19],"How to get warm intros",[90,846,847],{},[15,848,851],{"href":849,"rel":850},"https:\u002F\u002Ftechcrunch.com\u002F2023\u002F05\u002F16\u002Fwarm-and-cold-investor-introductions\u002F",[19],"How to get warm intros 2",[90,853,854],{},[15,855,858],{"href":856,"rel":857},"https:\u002F\u002Fwww.linkedin.com\u002Fpulse\u002Fhow-run-strategic-seed-round-process-nick-raushenbush?trk=article-ssr-frontend-pulse_more-articles_related-content-card",[19],"Seed round strategy",[90,860,861],{},[15,862,865],{"href":863,"rel":864},"https:\u002F\u002Fwww.youtube.com\u002Fwatch?v=7G7P-c49Kgs",[19],"More on FOMO in investors",[11,867,868],{},"Also Y-Combinator has a bunch of useful videos. For instance:",[87,870,871,878,885],{},[90,872,873],{},[15,874,877],{"href":875,"rel":876},"https:\u002F\u002Fwww.youtube.com\u002Fwatch?v=zBUhQPPS9AY",[19],"How Startup Fundraising works",[90,879,880],{},[15,881,884],{"href":882,"rel":883},"https:\u002F\u002Fwww.youtube.com\u002Fwatch?v=hUbM-bURoJE",[19],"The Hard Conversations Founders Don't Want to Have",[90,886,887],{},[15,888,891],{"href":889,"rel":890},"https:\u002F\u002Fwww.ycombinator.com\u002Flibrary\u002F2u-how-to-build-your-seed-round-pitch-deck",[19],"How to build your seed round pitch deck",[82,893,895],{"id":894},"investor-lists","Investor lists",[87,897,898,905,912,919,926,933,940,947,954],{},[90,899,900],{},[15,901,904],{"href":902,"rel":903},"https:\u002F\u002Fairtable.com\u002FshrsDIW1FMuA5cI9P\u002FtblaahhCCc2v0065Q\u002Fviwdm9nLc4Aj3sHJO?blocks=hide",[19],"No warm intro required",[90,906,907],{},[15,908,911],{"href":909,"rel":910},"https:\u002F\u002Fdocs.google.com\u002Fspreadsheets\u002Fd\u002F1ebGZ6-ivf_3woBGC4Kz_3217DhjGsefoRu_5iP3nuFQ\u002Fedit#gid=0",[19],"Shai Goldman list",[90,913,914],{},[15,915,918],{"href":916,"rel":917},"https:\u002F\u002Fairtable.com\u002FshrkohpeE2AO2ldeq\u002Ftbl5Q8N7NuW22z5Bt?backgroundColor=cyan&viewControls=on",[19],"Active vc list",[90,920,921],{},[15,922,925],{"href":923,"rel":924},"https:\u002F\u002Fairtable.com\u002FshrSPNzYoSRhJBCbv\u002Ftbl216CjzNssfsDpB?backgroundColor=gray&viewControls=on",[19],"Active pre-seed investors",[90,927,928],{},[15,929,932],{"href":930,"rel":931},"https:\u002F\u002Fairtable.com\u002FshrWjYGLAHKETll5B\u002FtblOCFaxHvjb8etrV",[19],"Pre-seed Family offices",[90,934,935],{},[15,936,939],{"href":937,"rel":938},"https:\u002F\u002Fwww.mountsideventures.com\u002Flist-of-angel-networks",[19],"List of angel networks",[90,941,942],{},[15,943,946],{"href":944,"rel":945},"https:\u002F\u002Fmercury.com\u002Finvestor-db",[19],"Investor database (also contains angels)",[90,948,949],{},[15,950,953],{"href":951,"rel":952},"https:\u002F\u002Fwww.crunchbase.com\u002F",[19],"Crunchbase (Info DB with Investors, Startup, Events, etc.; a lot of paywalls)",[90,955,956],{},"For cold outreach, Apollo.io is a good source for finding email addresses.",[82,958,960],{"id":959},"organizations-and-events","Organizations and Events",[87,962,963,966,969,972,975,978,981,984,987,990,993,996,999],{},[90,964,965],{},"Idea to IPO (Rob Lau)",[90,967,968],{},"Hacker Dojo Mix & Pitch",[90,970,971],{},"Stanford Startup Society",[90,973,974],{},"Stanford ETL",[90,976,977],{},"Meetup",[90,979,980],{},"Eventbrite",[90,982,983],{},"Luma",[90,985,986],{},"Crunchbase events (see above)",[90,988,989],{},"SF Hardware Meetup",[90,991,992],{},"Go Global World",[90,994,995],{},"Berkeley Skydeck",[90,997,998],{},"LA Tech Week",[90,1000,1001],{},"El Segundo (the district of LA) - bunch of tech startups there",{"title":339,"searchDepth":340,"depth":340,"links":1003},[1004,1005,1014,1015],{"id":384,"depth":340,"text":385},{"id":497,"depth":340,"text":498,"children":1006},[1007,1008,1009,1010,1011,1012,1013],{"id":518,"depth":345,"text":519},{"id":562,"depth":345,"text":563},{"id":699,"depth":345,"text":700},{"id":720,"depth":345,"text":721},{"id":744,"depth":345,"text":745},{"id":774,"depth":345,"text":775},{"id":784,"depth":345,"text":785},{"id":814,"depth":340,"text":815},{"id":834,"depth":340,"text":835,"children":1016},[1017,1018],{"id":894,"depth":345,"text":895},{"id":959,"depth":345,"text":960},"Building wings sustainably",{"topic":1021,"category":1021,"authors":1022,"tags":1024,"date":1026},"Blog",[1023],{"name":359,"avatar":360},[1025],"blog","2026-03-01","\u002Fblog\u002Fbusiness_lessons",{"title":373,"description":1019},"blog\u002F10.Business_Lessons","dPlWcSwFRqvU-0jjYPaSHR_1yghoqN8nv2VZqtJzPEA",{"id":1032,"title":1033,"body":1034,"description":1046,"extension":351,"meta":1047,"navigation":366,"path":1055,"seo":1056,"stem":1057,"__hash__":1058},"blog\u002Fblog\u002F11.Vitravian_Simulator.md","Vitravian Simulator",{"type":8,"value":1035,"toc":1044},[1036,1039],[11,1037,1038],{},"As all good pilot trainings include a simulator, we were thinking how that could be realized for Fluglicht. What you see below is a concept drawing from March 2023 for the rig of the \"Vitravian Simulator\". The description is in German, as it originally was not inteded to be published. It's supposed to be a ring-in-ring mechanical design somewhat similar to the Star Gate and enables two or three degrees of freedom of rotation. The ring is not supposed to look like the Star Gate though, but rather like the things in the Tron movies (e.g. the Tron:Legacy lightcycle wheels).",[11,1040,1041],{},[530,1042],{"alt":1033,"src":1043},"\u002Fimages\u002FVitravian_Simulator.jpg",{"title":339,"searchDepth":340,"depth":340,"links":1045},[],"A concept to build a simulator and gaming rig for flying games.",{"subtitle":1048,"topic":1049,"category":355,"authors":1050,"tags":1052,"date":1054},"VR flight experience","Gaming",[1051],{"name":359,"avatar":360},[362,1053],"Simulation","2026-02-04","\u002Fblog\u002Fvitravian_simulator",{"title":1033,"description":1046},"blog\u002F11.Vitravian_Simulator","G9cRmv2eWst40O3qJJGJ1mXlK3vaOQm2n9G9YlpmDsA",{"id":1060,"title":1061,"body":1062,"description":1228,"extension":351,"meta":1229,"navigation":366,"path":1236,"seo":1237,"stem":1238,"__hash__":1239},"blog\u002Fblog\u002F12.Post_Archive.md","Post Archive",{"type":8,"value":1063,"toc":1222},[1064,1069,1075,1079,1082,1085,1088,1091,1094,1098,1104,1108,1111,1114,1117,1120,1123,1127,1133,1137,1140,1143,1146,1149,1152,1155,1158,1160,1162,1164,1166,1168,1172],[1065,1066,1068],"h1",{"id":1067},"_2024-11-01","2024-11-01",[11,1070,1071],{},[530,1072],{"alt":1073,"src":1074},"What if","\u002Fimages\u002FLinkedinpost_What_if_1_ed.jpg",[82,1076,1078],{"id":1077},"what-if-you-could-just-fly-like-a-bird","What if you could just fly like a bird?",[11,1080,1081],{},"Sometimes, when I see a beautiful cloud like this one, I imagine what it would be like to fly along it's flanks and majestically soar high above it's crest. What joy it must bring to bath in sunshine while silently moving through the crisp air...",[11,1083,1084],{},"This is one of the reasons why we founded Fluglicht, where we build a flying exoskeleton to make it happen!",[11,1086,1087],{},"Do you also sometimes think like me when you look to the skies? What clouds do you find the most inspiring?",[11,1089,1090],{},"#fluglicht #freedom #cloud",[11,1092,1093],{},"(NB: if you look closely at the picture, you might notice something funny about the birds..)",[1065,1095,1097],{"id":1096},"_2024-11-11","2024-11-11",[11,1099,1100],{},[530,1101],{"alt":1102,"src":1103},"Hidden Sunshine","\u002Fimages\u002FSunshineHidden11.jpg",[82,1105,1107],{"id":1106},"is-the-future-dead","Is the future dead?",[11,1109,1110],{},"Sometimes when reading the news one might think everything just gets worse day by day. Autumn has this effect on people… even in the third millennium. But is there really no future to look ahead to?",[11,1112,1113],{},"Considering the wonderful book “Factfulness” by Hans Rosling et al., this is just a mental bias. And I would also argue, one can only reach a better future if one has an idea of what this better future could look like.",[11,1115,1116],{},"Today is the 11th day of the 11th month, which in Germany marks the beginning of the “fith season” of the year. You may not be fond of these old traditions, but I think it harbors an interesting idea: when nature “dies” and cold, wet greyness swallows the land, you are quite capable of choosing your own state of mind and your own future. So when you are feeling Autumn in your bones, remember:",[11,1118,1119],{},"There is sunshine hidden in this picture!",[11,1121,1122],{},"#fluglicht #positiveFuture",[1065,1124,1126],{"id":1125},"_2024-06-12","2024-06-12",[11,1128,1129],{},[530,1130],{"alt":1131,"src":1132},"Exoskeletons","\u002Fimages\u002FExoskeletonsRealFake.png",[82,1134,1136],{"id":1135},"can-you-tell-the-real-from-the-fake","Can you tell the real from the fake?",[11,1138,1139],{},"Proper exoskeletons seem like this impossible sci-fi tech. But is this true? So many things have been \"impossible\" in the past. But only very few people guessed right!",[11,1141,1142],{},"The \"good\" people actually try to disprove a hypothesis and can tell you the conditions that make it impossible.",[11,1144,1145],{},"The \"bad\" people usually have tried some things and didn't succeed and now think it is impossible. They are basically just frustrated. A typically human generalization error.",[11,1147,1148],{},"And then there are the \"ugly\" people who didn't even really try to find a solution, but fiercely tell you how impossible things are. Those people are not our customers ;)",[11,1150,1151],{},"Because we want you to feel hope! We want you to feel Fluglicht in your heart and believe in yourself! We can create a better world if we just dare to and if we stick together.",[11,1153,1154],{},"So test your biases and be surprised by the picture above. It displays some of the real and imaginary exoskeletons we came across while researching for Fluglicht. Can you tell which one is real and which one is fake? Tell us in the comments! But mind you: it's not as easy as it looks ;)",[11,1156,1157],{},"#Fluglicht #exoskeleton #hope",[11,1159,297],{},[11,1161,297],{},[11,1163,297],{},[11,1165,297],{},[11,1167,297],{},[82,1169,1171],{"id":1170},"solution","Solution:",[393,1173,1174,1182,1189,1196,1199,1202,1209,1212,1219],{},[90,1175,1176,1177,1181],{},"Fluglicht Exoskid (",[15,1178,1179],{"href":1179,"rel":1180},"https:\u002F\u002Ffluglicht.com\u002Fexoskid",[19]," )",[90,1183,1184,1185,1181],{},"DFKI CAPIO (",[15,1186,1187],{"href":1187,"rel":1188},"https:\u002F\u002Frobotik.dfki-bremen.de\u002Fen\u002Fresearch\u002Frobot-systems\u002Fexoskeleton-active-capio",[19],[90,1190,1191,1192,1181],{},"German Bionic (",[15,1193,1194],{"href":1194,"rel":1195},"https:\u002F\u002Fgermanbionic.com\u002F",[19],[90,1197,1198],{},"Stanley exoskeleton (not offered anymore, stanleyhandling.co.uk )",[90,1200,1201],{},"Skeletonics Gundam \"Costume\"",[90,1203,1204,1205,1181],{},"Skeletonics (",[15,1206,1207],{"href":1207,"rel":1208},"https:\u002F\u002Fwww.skeletonics-us.com\u002F",[19],[90,1210,1211],{},"Fake",[90,1213,1214,1215,1181],{},"The Fallout power armour is actually being built! (",[15,1216,1217],{"href":1217,"rel":1218},"https:\u002F\u002Fwww.youtube.com\u002Fwatch?v=sfR0yZCDDNA",[19],[90,1220,1221],{},"Beautiful, but sadly fake!",{"title":339,"searchDepth":340,"depth":340,"links":1223},[1224,1225,1226,1227],{"id":1077,"depth":345,"text":1078},{"id":1106,"depth":345,"text":1107},{"id":1135,"depth":345,"text":1136},{"id":1170,"depth":345,"text":1171},"Posts on Linkedin that aught to stay accessible.",{"subtitle":1230,"topic":1021,"category":1021,"authors":1231,"tags":1233,"date":1235},"Some goodness worth preserving",[1232],{"name":359,"avatar":360},[1234],"Archive","2026-04-14","\u002Fblog\u002Fpost_archive",{"title":1061,"description":1228},"blog\u002F12.Post_Archive","K8x_oD5uJEdNqRhV_Cl88OboNYYBFikOeQEL92xtgz0",{"id":1241,"title":1242,"body":1243,"description":1428,"extension":351,"meta":1429,"navigation":366,"path":1434,"seo":1435,"stem":1436,"__hash__":1437},"blog\u002Fblog\u002F2.Stuff-We-Love.md","Stuff We Love",{"type":8,"value":1244,"toc":1425},[1245,1248,1317,1321,1416,1419],[11,1246,1247],{},"Lot's of amazing things have been happening in the past few years, that inspire us. In this blogpost we want to share an assorted (and growing) list to boost your horizon on what's possible.",[87,1249,1250,1258,1266,1274,1282,1290,1298],{},[90,1251,1252,1257],{},[15,1253,1256],{"href":1254,"rel":1255},"https:\u002F\u002Fyoutu.be\u002FsX1Y2JMK6g8?t=189",[19],"SpaceX Falcon Heavy Booster Landing",": The thing that kicked us off. Years of professors telling us it's not possible to re-land a rocket on earth and that reusability is a dead end.. And then SpaceX just lands a rocket booster right on that preconception. -> Almost nothing is impossible. It's just our fear of failure holding us back. In fact, a lot of things considered impossible in the past are now state of the art technology.",[90,1259,1260,1265],{},[15,1261,1264],{"href":1262,"rel":1263},"https:\u002F\u002Fwww.youtube.com\u002Fwatch?v=ZtCC3b3TSBo",[19],"Richard Browning's Gravity Industries",": This crazy dude actually built an Ironman suit for flying. Check it out!",[90,1267,1268,1273],{},[15,1269,1272],{"href":1270,"rel":1271},"https:\u002F\u002Fwww.youtube.com\u002Fwatch?v=huIhdVlpFio",[19],"Franky Zapata's Flyboard Air",": Awesomeness from our French neighbors! This time the guy is standing on a deck of jet engines and flies like the Green Goblin in Spiderman.",[90,1275,1276,1281],{},[15,1277,1280],{"href":1278,"rel":1279},"https:\u002F\u002Fwww.youtube.com\u002Fwatch?v=nj-Iwv5NJKg",[19],"Jetman Dubai",": No question, very cool! Probably the fastest (and most stable) jetpowered flyer in this list. Sadly they stopped operations after the crash of the dreamer. But they proved it possible, nonetheless.",[90,1283,1284,1289],{},[15,1285,1288],{"href":1286,"rel":1287},"https:\u002F\u002Fwww.youtube.com\u002Fwatch?v=TWfph3iNC-k",[19],"Wingsuiting"," by people like Jeb Corliss: This is also super fast, and really nothing for the feint hearted!",[90,1291,1292,1297],{},[15,1293,1296],{"href":1294,"rel":1295},"https:\u002F\u002Fwww.youtube.com\u002Fwatch?v=Hz2F_S3Tl0Y",[19],"Red Bull Stratos",": The most insane skydive ever! Felix acutally jumped alle the way from the top of the sky, from outside of the sky, from \"you can't even see the sky anymore\"! Respect.",[90,1299,1300,1305,1306,1311,1312,1316],{},[15,1301,1304],{"href":1302,"rel":1303},"https:\u002F\u002Fwww.youtube.com\u002Fwatch?v=Wfoy_OvNDvw",[19],"Space Walking"," and ",[15,1307,1310],{"href":1308,"rel":1309},"https:\u002F\u002Fwww.youtube.com\u002Fwatch?v=x2adl6LszcE",[19],"walking on the Moon",": This list would not be complete without the final frontier. This is ",[15,1313,1315],{"href":1314},"\u002FTheCrew","freedom, courage, and a positive future"," distilled and bottled up for your pleasure! We need to get back into that spirit.",[74,1318,1320],{"id":1319},"other-cool-stuff","Other cool stuff",[87,1322,1323,1330,1337,1344,1350,1356,1369,1375,1383,1392,1405,1413],{},[90,1324,1325,1326],{},"Bellwether Volar: ",[15,1327,1328],{"href":1328,"rel":1329},"https:\u002F\u002Fwww.youtube.com\u002Fwatch?v=tts81ok5_OY",[19],[90,1331,1332,1333],{},"Jetson ONE: ",[15,1334,1335],{"href":1335,"rel":1336},"https:\u002F\u002Fwww.youtube.com\u002Fwatch?v=FzhREYOK0oo",[19],[90,1338,1339,1340],{},"XTURISMO: ",[15,1341,1342],{"href":1342,"rel":1343},"https:\u002F\u002Fwww.augustman.com\u002Fsg\u002Fgear\u002Ftech\u002Fxturismo-flying-bike-limited-edition\u002F",[19],[90,1345,1346,1347],{},"Manned Ornithopter (maiden flight 2006): ",[15,1348,288],{"href":288,"rel":1349},[19],[90,1351,1352,1353],{},"Snowbird (Bicycle powered ornithopter): ",[15,1354,303],{"href":303,"rel":1355},[19],[90,1357,1358,1359,1364,1365],{},"Smartbird by ",[15,1360,1363],{"href":1361,"rel":1362},"https:\u002F\u002Faniprop.de\u002F",[19],"Dr. Send"," and Festo: ",[15,1366,1367],{"href":1367,"rel":1368},"https:\u002F\u002Fwww.youtube.com\u002Fwatch?v=nnR8fDW3Ilo",[19],[90,1370,1371,1372],{},"Project Falcon by Douglas C. George: ",[15,1373,312],{"href":312,"rel":1374},[19],[90,1376,1377,1382],{},[15,1378,1381],{"href":1379,"rel":1380},"https:\u002F\u002Fwww.boredpanda.com\u002Fpatented-tech-gadgets-3d-renders-simpleghar\u002F",[19],"Boredpanda\u002FSimpleghar",": apparently we are part of the \"Biggest Names in the Tech Industry\" 😂 These guys just created their own renders of our concept without ever talking to us and gave it the name \"Freedom suit\". Funny. And looks cool! Nevertheless, the design would probably not work...",[90,1384,1385,1386,1391],{},"The ",[15,1387,1390],{"href":1388,"rel":1389},"https:\u002F\u002Fyoutu.be\u002FqC5KtatMcUw?t=463",[19],"Unreal Engine 5 Demo"," flying part. Gives me goose-bumps every time.",[90,1393,1394,1395,1305,1400],{},"Hayao Miyzaki's Anime with flying things, like ",[15,1396,1399],{"href":1397,"rel":1398},"https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FCastle_in_the_Sky",[19],"Laputa: Castle in the Sky",[15,1401,1404],{"href":1402,"rel":1403},"https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FThe_Wind_Rises",[19],"The Wind Rises",[90,1406,1407,1408,1412],{},"The Right Stuff: ",[15,1409,1410],{"href":1410,"rel":1411},"https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FThe_Right_Stuff_(film)",[19],", because you've gotta have the right stuff!",[90,1414,1415],{},"Lilienthal Monument in Lichterfelde: for the honour of the one who started it all...",[11,1417,1418],{},"Keep on dreaming!",[11,1420,1421],{},[530,1422],{"alt":1423,"src":1424},"Lilienthal Denkmal Lichterfelde","\u002Fimages\u002FLilienthaldenkmal_Lichterfelde.jpg",{"title":339,"searchDepth":340,"depth":340,"links":1426},[1427],{"id":1319,"depth":340,"text":1320},"Other cool things in the skies",{"topic":1021,"category":1021,"authors":1430,"tags":1432,"date":1433},[1431],{"name":359,"avatar":360},[1025],"2024-04-05","\u002Fblog\u002Fstuff-we-love",{"title":1242,"description":1428},"blog\u002F2.Stuff-We-Love","Jwo6Uy81fUbCRDg5yYBof_ccpnwiNv1RC-cVQcnYVRY",{"id":1439,"title":1440,"body":1441,"description":1550,"extension":351,"meta":1551,"navigation":366,"path":1558,"seo":1559,"stem":1560,"__hash__":1561},"blog\u002Fblog\u002F3.Flysky-Hacking.md","Flysky Hacking",{"type":8,"value":1442,"toc":1543},[1443,1447,1454,1457,1461,1464,1479,1486,1489,1498,1504,1507,1511,1518,1527,1530,1534,1537,1540],[74,1444,1446],{"id":1445},"using-the-flysky-fs-i6x-transmitter-and-fs-ia6b-receiver-connection-with-custom-data","Using the Flysky FS-i6X Transmitter and FS-iA6B Receiver Connection With Custom Data",[11,1448,1449,1450,297],{},"This post describes, how we \"hijacked\" the Flysky transmitter-receiver link with Arduinos to transport our exo data to the skid. If you don't know what an Exoskid is, see ",[15,1451,469],{"href":1452,"rel":1453},"https:\u002F\u002Ffluglicht.com\u002FExoskid",[19],[11,1455,1456],{},"Caution: Don't follow this guide mindlessly! We take no responibility for you breaking your gear. You do this at your own risk (and fun)!",[82,1458,1460],{"id":1459},"setting-up-the-fs-i6x-transmitter","Setting up the FS-i6X Transmitter",[11,1462,1463],{},"Goal: Getting all 16 channels and a bunch of extras from OpenTX onto the FS-i6X.",[11,1465,1466,1467,1472,1473,1478],{},"In principle, you can use your vanilla FS-i6X link, by passing a PPM signal to the trainer port on the back. One just has to be careful, because the FS-i6X usually uses slightly different timings to the standard of the Arduino ",[15,1468,1471],{"href":1469,"rel":1470},"https:\u002F\u002Fgithub.com\u002Fschinken\u002FPPMEncoder",[19],"PPMEncoder"," library. Check out ",[15,1474,1477],{"href":1475,"rel":1476},"https:\u002F\u002Fwww.rcgroups.com\u002Fforums\u002Fshowthread.php?3792327-Controlling-Flysky-FS-I6X-with-an-arduino-via-trainer-port",[19],"this"," thread for details.",[11,1480,1481,1482],{},"The Flysky i6X can be connected to the computer's USB port through the \"Trainer\" socket. Below you find a picture of the pinout of this Mini-DIN-4 port.\n",[530,1483],{"alt":1484,"src":1485},"Flysky Trainer Port Pinout","\u002Fimages\u002FFlysky_i6X_Trainer_Port_Pinout.png",[11,1487,1488],{},"There seems to be some dispute about this pinout on the internets. Except for the \"PPM Out\" we have used all of these pins and can confirm their function. You can buy a USB connector cable to connect to the trainer port. But you can also rig this temporarily by cautiously wedging in some jumper cables. Then you need an old USB cable to strip apart and connect accordingly to the above pinout (search for USB cable colors to figure out which goes where).",[11,1490,1491,1492,1497],{},"Once you have the connection, follow the guide of ",[15,1493,1496],{"href":1494,"rel":1495},"https:\u002F\u002Fgithub.com\u002FOpenI6X\u002Fopentx",[19],"Openi6X"," to install the new firmware. After installation, the buttons are a bit confusing at first. Below is a guide of how to navigate the screens:",[11,1499,1500],{},[530,1501],{"alt":1502,"src":1503},"Openi6X Usage","\u002Fimages\u002FOpeni6X_usage.jpg",[11,1505,1506],{},"Fiddle around with it, until you get your receiver bind (Page 2 at the bottom -> \"Receiver\" [bnd]). Once that is done, you can get data onto the transmitter via the \"PPM in\" pin. These channels are available in the mixer as \"Tr1-16\". You don't need to enable student mode to use the channels, but I suppose one can, to get the first 4 channels as well. We used the first channels to always have the transmitter pilot in the game.",[82,1508,1510],{"id":1509},"connecting-to-the-ia6b-receiver","Connecting to the iA6B Receiver",[11,1512,1513,1514],{},"You can keep on using the PWM outputs of the receiver. You can also use the horizontal iBus output on the top right of the receiver, which is a serial output of all the signals.\n",[530,1515],{"alt":1516,"src":1517},"FS-iA-6B Pinout iBus","\u002Fimages\u002FFS-iA6BOut.png",[11,1519,1520,1521,1526],{},"You can use the ",[15,1522,1525],{"href":1523,"rel":1524},"https:\u002F\u002Fgitlab.com\u002Ftimwilkinson\u002FFlySkyIBus",[19],"FlySkyIBus"," library to decode the signal, if you are using an Arduino on the receiver side as well. There is some triple trouble involved, if you use a SAMD-based Arduino like the Nano 33 IoT that we used (so beware the dragons and just don't do it)!",[11,1528,1529],{},"And there you go! Low latency, 16 channel, long-range remote control. It looks all so easy and clean, now that I've written it all up. But it took us a LONG time to piece together all the information and getting it to work. And it would have taken ages longer without the incredible coolness of all the linked sources, so big creds to them!",[82,1531,1533],{"id":1532},"airplane-wiring-and-firmware","Airplane wiring and firmware",[11,1535,1536],{},"WIP",[11,1538,1539],{},"Some more stuff you need: Here is the wiring diagram of the airplane.",[11,1541,1542],{},"TODO: CAD Daten von Laptop sichern und hier einbinden. Schaltplan Flieger fotografieren und hier ablegen. Kalibration und Datenfluss beim Exoskid erklären (Exoskelett kalibration liefert normierte Daten, Exoskid kalibration versucht Fliegerdetails egal zu machen, sodass normierte Daten funktionieren).",{"title":339,"searchDepth":340,"depth":340,"links":1544},[1545],{"id":1445,"depth":340,"text":1446,"children":1546},[1547,1548,1549],{"id":1459,"depth":345,"text":1460},{"id":1509,"depth":345,"text":1510},{"id":1532,"depth":345,"text":1533},"Detailed description on using the Flysky data link",{"topic":1552,"category":355,"authors":1553,"tags":1555,"date":1433},"Electronics",[1554],{"name":359,"avatar":360},[1556,1557],"FS-i6X","FS-iA6B","\u002Fblog\u002Fflysky-hacking",{"title":1440,"description":1550},"blog\u002F3.Flysky-Hacking","4jjFnXdDBveh6VmsfTlI4Hg0U_9HrZukrL_f5a4FdfM",{"id":1563,"title":1564,"body":1565,"description":1706,"extension":351,"meta":1707,"navigation":366,"path":1718,"seo":1719,"stem":1720,"__hash__":1721},"blog\u002Fblog\u002F3.GPIO_on_Raspberry_Pi_CM5.md","GPIO on a Raspberry Pi CM5",{"type":8,"value":1566,"toc":1699},[1567,1571,1580,1589,1593,1596,1604,1611,1621,1625,1631,1634,1643,1649,1652,1655,1661,1664,1667,1673,1676,1680,1683,1687,1690],[74,1568,1570],{"id":1569},"libgpio-explained-using-gpio-on-a-raspberry-pi-cm5-ioboard-in-python","libgpio explained: using GPIO on a Raspberry Pi CM5 ioboard in Python",[11,1572,1573,1574,1579],{},"Using the GPIO on a Raspberry Pi CM5 ioboard is not straight forward at the time of writing this article. The RPi.GPIO library does not work on a CM5 and libgpio is \"the preferred way of using GPIO\" apparently. The ",[15,1575,1578],{"href":1576,"rel":1577},"https:\u002F\u002Fpypi.org\u002Fproject\u002Fgpiod\u002F",[19],"libgpio python bindings API"," sadly is complicated to use while the documentation is useless. The syntax is not described there, available arguments are not explained, and the example is convoluted and intransparent. Also it seems to me, the API was written in a way that is good to write, but is neither easy to use nor understand. On the plus side, the library exists.",[11,1581,1582,1583,1588],{},"The only way to figure out how to use this library is to read the ",[15,1584,1587],{"href":1585,"rel":1586},"https:\u002F\u002Fgit.kernel.org\u002Fpub\u002Fscm\u002Flibs\u002Flibgpiod\u002Flibgpiod.git\u002Ftree\u002Fbindings\u002Fpython\u002Fgpiod",[19],"doc strings and the source code",". As you don't have the time for that, I'll break it down for you.",[82,1590,1592],{"id":1591},"how-to-use-gpiod","How to use gpiod",[11,1594,1595],{},"There are two things you need to accomplish:",[393,1597,1598,1601],{},[90,1599,1600],{},"configure the pin",[90,1602,1603],{},"access the pin",[11,1605,1606,1607,1610],{},"Let's look at an example for reading a pin state of how to do that. Prerequisites are installing gpiod and running \"usermod -a -G gpio ",[438,1608,1609],{},"your_username","\" in the terminal.",[1612,1613,1618],"pre",{"className":1614,"code":1616,"language":1617,"meta":339},[1615],"language-python","import gpiod\n\nGPIO_CHIP = \"\u002Fdev\u002Fgpiochip4\"    # The chip to use\nBUTTONPIN = 24          # GPIO-number\u002Fline offset\n\nwith gpiod.Chip(path=GPIO_CHIP) as gpiochip:\n    gpioconfig = {\n        \"direction\": gpiod.line.Direction.INPUT,\n        \"bias\": gpiod.line.Bias.PULL_UP,\n        \"edge_detection\": gpiod.line.Edge.NONE\n    } \n    gpiolinesetting = gpiod.LineSettings(**gpioconfig)\n\n    linerequest_config = {\n        \"config\": {BUTTONPIN: gpiolinesetting},\n        \"consumer\": \"some-name-you-can-make-up-freely\"\n    }\n\n    with gpiochip.request_lines(**linerequest_config) as gpiolines:\n        pinstate = gpiolines.get_value(BUTTONPIN).value\n\n    print(pinstate)\n","python",[1619,1620,1616],"code",{"__ignoreMap":339},[448,1622,1624],{"id":1623},"here-is-a-step-by-step-explanation","Here is a step-by-step explanation:",[1612,1626,1629],{"className":1627,"code":1628,"language":1617,"meta":339},[1615],"GPIO_CHIP = \"\u002Fdev\u002Fgpiochip4\"\nBUTTONPIN = 24\n",[1619,1630,1628],{"__ignoreMap":339},[11,1632,1633],{},"These are the chip and the GPIO number used in this example. The chip path can be found by surveying \u002Fdev and maybe trying out the available options. \"pinctrl\" is a useful program to try out the pins, which comes with libgpio.",[11,1635,1636,1637,1642],{},"The pin number can be found on the official(?) ",[15,1638,1641],{"href":1639,"rel":1640},"https:\u002F\u002Fpinout.xyz",[19],"pinout website",". The shell command \"pinout\" should also do that job, but at the time of writing it doesn't work on the CM5. gpiod requires GPIO numbers, not actual pin numbers as with the Arduino. They are called \"line offset\" in libgpio.",[1612,1644,1647],{"className":1645,"code":1646,"language":1617,"meta":339},[1615],"with gpiod.Chip(path=GPIO_CHIP) as gpiochip:\n\n",[1619,1648,1646],{"__ignoreMap":339},[11,1650,1651],{},"This line opens the gpio chip for interaction. As the chip is represented as a character device, it needs to be opened and closed like a normal file. The \"with\" statements makes that more secure.",[11,1653,1654],{},"The next part holds the convoluted configuration:",[1612,1656,1659],{"className":1657,"code":1658,"language":1617,"meta":339},[1615],"    gpioconfig = {\n        \"direction\": gpiod.line.Direction.INPUT,\n        \"bias\": gpiod.line.Bias.PULL_UP,\n        \"edge_detection\": gpiod.line.Edge.NONE\n    } \n    gpiolinesetting = gpiod.LineSettings(**gpioconfig)\n\n    linerequest_config = {\n        \"config\": {BUTTONPIN: gpiolinesetting},\n        \"consumer\": \"some-name-you-can-make-up-freely\"\n    }\n",[1619,1660,1658],{"__ignoreMap":339},[11,1662,1663],{},"The first part defines the configuration of the pin you want to use. Config parameters can be found in site-packages\u002Fgpio\u002Fline.py and site-packages\u002Fgpio\u002Fline_settings.py. To make it complicated, they have to be defined using gpiod.line objects instead of strings and the defined settings have to be wrapped in a class instance afterwards instead of using the dictionary directly. But using **kwargs makes this at least more readable.",[11,1665,1666],{},"The second part connects the configuration to the pin number (aka \"line\"). It is again a dictionary of parameters that will be expanded with **kwargs in the following line request. The first paramter, called \"config\", expects a dict with  line numbers as keys and LineSettings objects as values. So the syntax is: {line number: LineSettingsObject}, where \"line number\" can also be a tuple of numbers to assigns the config to all the specified lines. There is another argument called \"consumer\", which needs to exist for some reason, but is meaningless in basic usage.",[1612,1668,1671],{"className":1669,"code":1670,"language":1617,"meta":339},[1615],"    with gpiochip.request_lines(**linerequest_config) as gpiolines:\n        pinstate = gpiolines.get_value(BUTTONPIN).value\n",[1619,1672,1670],{"__ignoreMap":339},[11,1674,1675],{},"Finally the gpio pins can be used. As the \"lines\" also need to be \"closed\" (gpiod.Chip.release() ) after interaction, this is best done using another \"with\"-statement. Otherwise it will read \"busy\" on the next try.",[82,1677,1679],{"id":1678},"edge-detection","Edge detection",[11,1681,1682],{},"Did not actually work at the time of writing.",[82,1684,1686],{"id":1685},"gpiod-and-async","gpiod and async",[11,1688,1689],{},"When using asyncio, the lines can be polled without blocking the script with sleep statements. For that, the async function polling the pin will need to contain a loop with an async.sleep() statement.",[11,1691,1692,1693,1698],{},"Apparently there is an async watch line value in the C-library (",[15,1694,1697],{"href":1695,"rel":1696},"https:\u002F\u002Fgit.kernel.org\u002Fpub\u002Fscm\u002Flibs\u002Flibgpiod\u002Flibgpiod.git\u002Ftree\u002Fexamples\u002Fasync_watch_line_value.c",[19],"see here",").",{"title":339,"searchDepth":340,"depth":340,"links":1700},[1701],{"id":1569,"depth":340,"text":1570,"children":1702},[1703,1704,1705],{"id":1591,"depth":345,"text":1592},{"id":1678,"depth":345,"text":1679},{"id":1685,"depth":345,"text":1686},"gpiod in python explained",{"topic":1552,"category":355,"authors":1708,"tags":1710,"date":1717},[1709],{"name":359,"avatar":360},[1711,1712,1713,1714,1715,1716],"gpiod","libgpio","Python","Raspberry Pi 5","Raspberry Pi CM5","CM5 ioboard","2025-05-22","\u002Fblog\u002Fgpio_on_raspberry_pi_cm5",{"title":1564,"description":1706},"blog\u002F3.GPIO_on_Raspberry_Pi_CM5","P3Vx5ee2PJE_Axvdo_a7GGYaAA_jvGNBvzEtzR6EjSg",{"id":1723,"title":1724,"body":1725,"description":1848,"extension":351,"meta":1849,"navigation":366,"path":1854,"seo":1855,"stem":1856,"__hash__":1857},"blog\u002Fblog\u002F4.Exoskid-Flight-One.md","Exoskid - Flight One",{"type":8,"value":1726,"toc":1844},[1727,1730,1744,1755,1758,1761,1767,1773,1776,1782,1785,1791,1797,1803,1806,1812,1815,1819,1822,1828,1831,1834,1838,1841],[11,1728,1729],{},"tl;dr:",[87,1731,1732,1735,1738,1741],{},[90,1733,1734],{},"So we built it.",[90,1736,1737],{},"And then we flew it.",[90,1739,1740],{},"And it worked!",[90,1742,1743],{},"And then we crashed it...",[1745,1746,1749,1750],"video",{"className":1747,"controls":366},[1748],"mx-auto","\n  ",[1751,1752],"source",{"src":1753,"type":1754},"\u002Fvideos\u002FFirstflight_cut.webm","video\u002Fwebm",[11,1756,1757],{},"On one of the first sunny days of 2024 after a long period of rain, we, co-founders Peter and Leon along with Martin (another student engineer on the project) are ready to test our first sub-scale prototype named Exoskid. I, Leon, have high expectations for our first test flight and the tension is palpable as we had invested a significant amount of our free time into this project over the past months. Some of our friends are also present to document the test flight with drones and cameras.",[11,1759,1760],{},"After assembling the model, our test pilot Peter puts on the exoskeleton and we performed a quick integration test. The signal transmission from the exoskeleton to the flyer works flawlessly. The tension continues to rise as everyone gets ready for our first launch ever. I hold the airplane with both hands, feeling my hands become a little sweaty despite the cold wind on this rolling hill near Dresden. I nod to Martin, signaling I'm ready to launch.",[11,1762,1763],{},[530,1764],{"alt":1765,"src":1766},"Power Armor Engaged","\u002Fimages\u002FFirstflight_VLCsnap_power_armor.jpg",[11,1768,1769],{},[530,1770],{"alt":1771,"src":1772},"Preflight Punk","\u002Fimages\u002FFirstflight_preflightPunk.jpg",[11,1774,1775],{},"“Okay, let's do it,” Martin answers, followed by a loud “Three…” beginning the countdown. I lean back to gain momentum. Martin pushes the joystick halfway, and I'm surprised at how decent the thrust is already. Will this contraption actually fly or just hit the ground like a rock? “…Two…” A flashback from my last bungee jump comes to mind, making me want to retreat. “...One...” And just like back then, I empower myself with a “#$*@ it, what could go wrong?!” “…Liftoff!” I flex and, as hard as I can, throw the nearly 2 kg flyer into the sky like a spear. Martin gives full throttle. And it actually flies..! a beautiful display of the dihedral as it rushes upwards. Relief spreads through me seeing all our hard work paying off. The first bank turn follows and the relief turns into pure excitement and joy! The fear that I might not hit the correct launch angle or somehow mess up our first flight drops off me like a stone.",[11,1777,1778],{},[530,1779],{"alt":1780,"src":1781},"The First Launch","\u002Fimages\u002FFirstflight_Liftoff_crop.jpg",[11,1783,1784],{},"After a few laps, during which Martin gets a feel for the flight characteristics, it's time for the exoskeleton test: handing over control from Martin on the transmitter to Peter in the exoskeleton. Peter can adjust the dihedral angle of each wing with his arms, the ailerons with his hands, and the elevator and rudder with his feet.",[11,1786,1787],{},[530,1788],{"alt":1789,"src":1790},"Aireal View of Plane","\u002Fimages\u002FFirstflight_FliegerImFlug.png",[11,1792,1793],{},[530,1794],{"alt":1795,"src":1796},"Flying Faces","\u002Fimages\u002FFirstflight_FlyingFaces.jpg",[11,1798,1799],{},[530,1800],{"alt":1801,"src":1802},"Cyberpunk Stylez","\u002Fimages\u002FFirstflight_VLCsnap_cyberpunk_stylez.jpg",[11,1804,1805],{},"The flyer is about 100 meters east over a field at an altitude of about 30 meters when Peter says, \"Okay Martin, switch me in.\" Martin responded, \"Well, let's goooo!\" We watch anxiously from a distance and are shocked to see the Skid doing a nosedive! The entire flyer is diving towards the ground like a falcon! Less than two seconds later, the flyer disappears behind a small hill from our view. It's immediately clear to everyone that this is a \"Rapid Unscheduled Disassembly\" and that the aircraft won't be available for another test soon...",[11,1807,1808],{},[530,1809],{"alt":1810,"src":1811},"Ooops...","\u002Fimages\u002FFirstflight_ooops.png",[11,1813,1814],{},"Special thanks to Andy for the follower drone piloting and footage!",[82,1816,1818],{"id":1817},"results-and-insights","Results and Insights",[11,1820,1821],{},"After retrieving the remnants of the Skid from the field, we reviewed the drone footage. Everyone agrees that, up until the crash, the test flight was a complete success. It demonstrates that the flyer could be launched successfully and could gain altitude quickly and safely with the help of the built-in propeller. The flight stability for this design was relatively high, and banking up to a load factor of 3g was possible.",[11,1823,1824],{},[530,1825],{"alt":1826,"src":1827},"Crash Site","\u002Fimages\u002FFirstflight_crashsite.jpg",[11,1829,1830],{},"The cause of the crash was quickly identified: although we had conducted an integration test before the flight, where Peter in the exoskeleton assumed a body posture leading to stable elevator and dihedral angle positions, Peter's posture had changed slightly after the first few laps. This caused the elevators to force the aircraft into a nose-dive immediately after switching control to the exoskeleton. We had initially agreed that Martin would retain control of the elevator, allowing Peter to focus on steering the flyer with the ailerons first. However, we had forgotten to re-enable this mode after the pre-flight integration test. In summary, our pre-flight excitement led to an oversight, laying the groundwork for this subsequent dual pilot error. So, better write a checklist, next time!",[11,1832,1833],{},"Additionally, we concluded that future test flights should conduct riskier tests at a higher altitude, giving the main pilot enough time to correct any mistakes made by the test pilot wearing the exoskeleton before the flyer hits the ground.",[82,1835,1837],{"id":1836},"next-steps","Next Steps",[11,1839,1840],{},"We will repair the Exoskid in the coming weeks and create a checklist for the next test flight. This should prevent similar errors in the future.",[11,1842,1843],{},"The second test flight attempt will be in the next month. If you want to be there live and in color, you can sign up as a spectator for the second test flight by emailing us. Stick around and watch us make a dent in the Universe!",{"title":339,"searchDepth":340,"depth":340,"links":1845},[1846,1847],{"id":1817,"depth":345,"text":1818},{"id":1836,"depth":345,"text":1837},"The heroic first lift-off story",{"topic":354,"category":1021,"authors":1850,"tags":1852,"date":1853},[1851],{"name":359,"avatar":360},[1025],"2024-01-27","\u002Fblog\u002Fexoskid-flight-one",{"title":1724,"description":1848},"blog\u002F4.Exoskid-Flight-One","d1pXcD-RtUuGAJcK8t6DVNANlp8qCaakTI3835RYJaY",{"id":1859,"title":1860,"body":1861,"description":1993,"extension":351,"meta":1994,"navigation":366,"path":1999,"seo":2000,"stem":2001,"__hash__":2002},"blog\u002Fblog\u002F5.Exoskid-Flight-Two.md","Exoskid - Flight Two",{"type":8,"value":1862,"toc":1991},[1863,1866,1885,1891,1898,1921,1948,1955,1958,1961,1979,1982,1988],[11,1864,1865],{},"tl;dr",[87,1867,1868,1871,1873,1876,1879,1882],{},[90,1869,1870],{},"So we re-built it.",[90,1872,1737],{},[90,1874,1875],{},"And it worked even better!",[90,1877,1878],{},"And we tested all important stuff.",[90,1880,1881],{},"And then we crashed again (material failure..)",[90,1883,1884],{},"Rapid unscheduled disassemblies for the win..",[1745,1886,1749,1888],{"className":1887,"controls":366},[1748],[1751,1889],{"src":1890,"type":1754},"\u002Fvideos\u002FExoskid_cut_2.webm",[11,1892,1893,1897],{},[530,1894],{"alt":1895,"src":1896},"The Crew 1","\u002Fimages\u002FSecondFlight1_crew.JPG","\nMartin, Peter, Leon and Markus on a beautiful April day around the rebuilt Exoskid. A lot of improvements for operation were implemented, like a reproducible and secure way to attach and detach the wings without loosing taring every time. We were really hot to test our improved version. And this time we even had a checklist! So what could possibly go wrong?!?",[11,1899,1900,1904,1908,1912,1916,1917],{},[530,1901],{"alt":1902,"src":1903},"Puttin On the Ritz1","\u002Fimages\u002FSecondFlight1_puttinOnTheRitz0.png",[530,1905],{"alt":1906,"src":1907},"Puttin On the Ritz2","\u002Fimages\u002FSecondFlight2_puttinOnTheRitz1.JPG",[530,1909],{"alt":1910,"src":1911},"Puttin On the Ritz3","\u002Fimages\u002FSecondFlight3_puttinOnTheRitz2.JPG",[530,1913],{"alt":1914,"src":1915},"Exo Ready","\u002Fimages\u002FSecondFlight4_ExoReady.JPG","\nReady to launch! Below you can see almost the full Fluglicht crew with only Chris missing: Martin, Leon, Robin and Peter (left to right).\n",[530,1918],{"alt":1919,"src":1920},"The Crew 2","\u002Fimages\u002FSecondFlight5_theCrew2.JPG",[11,1922,1923,1924,1928,1932,1936,1940,1944],{},"And here we go:\n",[530,1925],{"alt":1926,"src":1927},"Launch 1","\u002Fimages\u002FSecondFlight_launch2.png",[530,1929],{"alt":1930,"src":1931},"Launch 2","\u002Fimages\u002FSecondFlight_launch3.png",[530,1933],{"alt":1934,"src":1935},"Launch 3","\u002Fimages\u002FSecondFlight_launch4.png",[530,1937],{"alt":1938,"src":1939},"Launch 4","\u002Fimages\u002FSecondFlight_launch5.png",[530,1941],{"alt":1942,"src":1943},"Launch 5","\u002Fimages\u002FSecondFlight_launch6.png",[530,1945],{"alt":1946,"src":1947},"Launch 6","\u002Fimages\u002FSecondFlight_launch7.png",[11,1949,1950,1951],{},"Everything went really smooth this time. Martin got the plane on propeller power quite high up to have more buffer for failures. Then he engaged autoflap with almost idle propeller. And the plane happily flapped it's way across the sky! The angle of attack and flapping cycle was designed with the help of Dr. Send, the father of the Festo Smart Bird. His body of research and support made it a lot easier for us to get thrust out of our system.\n",[530,1952],{"alt":1953,"src":1954},"In flight","\u002Fimages\u002FSecondFlight6_InFlight1.JPG",[11,1956,1957],{},"After successfully testing the flapping propulsion of the plane, Martin contentiously switched to the exoskeleton. And this time, it was not an immediate nosedive. Peter could induce a turn, but for some reason the controls were sluggish, and the plane started to roll. And then it started to suddenly dive and tumble head over toe, leading to a rapid unscheduled disassembly somewhere in the rapeseed field below!",[11,1959,1960],{},"What had happened??",[11,1962,1963,1964,1968,1969,1973,1974,1978],{},"To figure that out, we had to find the wreck in the ocean of yellow. Not an easy task.\n",[530,1965],{"alt":1966,"src":1967},"Rapeseed Ocean","\u002Fimages\u002FSecondFlight1_dokoDesu.jpg","\nBut after 2 hours, the remains were found.\n",[530,1970],{"alt":1971,"src":1972},"The Wreck","\u002Fimages\u002FSecondFlight2_theWreck.jpg","\nThe search party looked horrible afterwards though, and we want to apologize at this point to the farmer for combing his rapeseed...\n",[530,1975],{"alt":1976,"src":1977},"Heroes of the Storm","\u002Fimages\u002FSecondFlight3_destroyedPeople.jpg","\nAnalysis of the plane, the separately found tail, and the ground video revealed that the tail had ripped off mid-flight. Layer delamination due to a crappy PLA filament. Oh, well... Martin had to buy an unknown filament, as the good stuff was empty and sold out. The wings, tail and electronics actually stayed intact due to the cushioned landing in the rapeseed. Only the nacelle and gears were ripped apart. So the plane could be rebuilt from the printer!",[11,1980,1981],{},"Again we faced a frustrating ending to the test, even though we could prove every part of the system. Nevertheless, we didn't let that drag us down and Martin went on to fly his MG6 till sunset.",[11,1983,1984],{},[530,1985],{"alt":1986,"src":1987},"Sunset Flying","\u002Fimages\u002FSecondFlight4_sunsetFlying.jpg",[11,1989,1990],{},"Special thanks also to Andy again for the follower drone flying and footage!",{"title":339,"searchDepth":340,"depth":340,"links":1992},[],"The heroic second lift-off story",{"topic":354,"category":1021,"authors":1995,"tags":1997,"date":1998},[1996],{"name":359,"avatar":360},[1025],"2024-04-30","\u002Fblog\u002Fexoskid-flight-two",{"title":1860,"description":1993},"blog\u002F5.Exoskid-Flight-Two","oxD4HiYk1xPad9yHIa-WMuXBiwjtpLH4AJ-bjfYlt70",{"id":2004,"title":2005,"body":2006,"description":2048,"extension":351,"meta":2049,"navigation":366,"path":2055,"seo":2056,"stem":2057,"__hash__":2058},"blog\u002Fblog\u002F5.F1.Trainer.md","Exoskid - Trainer",{"type":8,"value":2007,"toc":2045},[2008,2012,2015,2021,2024,2030,2033,2036,2039],[74,2009,2011],{"id":2010},"for-better-exoskeleton-control","For better exoskeleton control",[11,2013,2014],{},"After the crash of our second prototype we decided to build a trainer, in order to get a better feeling for the exoskeleton control. The principle is the same as with the Skid. In fact the trainer uses the same electronics and almost identical code as the Skid. In November 2024 we went and extensively tested the system in multiple flights.",[11,2016,2017],{},[530,2018],{"alt":2019,"src":2020},"Trainer in Flight","\u002Fimages\u002FTrainerFlight_inFlight.jpg",[11,2022,2023],{},"We reused a simple \"Trittschalldämmung\"-plane, Martin built for Fluglicht in the haydays of our endeavour. Certainly not the most pretty thing we ever built, but it works! As this RC plane has a low wing loading, it flys rather slow and stable.",[11,2025,2026],{},[530,2027],{"alt":2028,"src":2029},"Plane in Flight","\u002Fimages\u002FTrainerFlight_plane.jpg",[11,2031,2032],{},"This allowed us to extensively test exoskeleton control in the air. It is very intuitive, as we suspected! Doing turns with the arms is straightforward. Tail control with the feet is a bit more tricky. Elevator control by parallel feet movement is intuitive as well. But rudder control from feet angle difference is hard, as one can easily get into slip or accidental elevator moves. But supposedly with some training, one can get this right. Control with the feet is not strictly necessary though, as the co-pilot can fulfill these tasks.",[11,2034,2035],{},"The exoskeleton could use an upgrade though, as it is not very comfortable to wear for longer time and there is no \"zero point\" or restoring force in the controls that can be felt. A thumb button enables reset of the drifting rotary encoders (wrists\u002Faileron control). But it's hard to get a feeling for the amout one has rotated the wrist\u002Faileron without any force feedback. Some kind of resetting spring or indeed force feedback actuators would be highly desirable.",[11,2037,2038],{},"The biggest learning: despite the lack of flapping, it's still an amazing feeling to control the plane with the body! Because of the video goggles and the immediate reaction of the plane to arm movements, it really feels like being up there, flying like a bird! We had great fun, and finally the other team members could try it out as well! In the end, we managed to deplete all our batteries and take home an intact system this time.",[11,2040,2041],{},[530,2042],{"alt":2043,"src":2044},"Traner Preparations","\u002Fimages\u002FTrainerFlight_readyForLiftoff.jpg",{"title":339,"searchDepth":340,"depth":340,"links":2046},[2047],{"id":2010,"depth":340,"text":2011},"Short description of our trainer",{"topic":354,"category":355,"authors":2050,"tags":2052,"date":2054},[2051],{"name":359,"avatar":360},[2053],"Trainer","2026-01-28","\u002Fblog\u002Ff1.trainer",{"title":2005,"description":2048},"blog\u002F5.F1.Trainer","rjAMuK5Ornm6CbPchK_J4sDNRp33EgVfRoWEgVc9gRU",{"id":2060,"title":2061,"body":2062,"description":2139,"extension":351,"meta":2140,"navigation":366,"path":2145,"seo":2146,"stem":2147,"__hash__":2148},"blog\u002Fblog\u002F6.Flying-Dreams.md","Flying Dreams",{"type":8,"value":2063,"toc":2137},[2064,2069,2076,2081,2084,2088,2091,2096,2103,2108,2111],[11,2065,2066],{},[530,2067],{"alt":2068,"src":1074},"Flying in the clouds",[11,2070,2071,2072],{},"2011 - Schredl - Frequency and nature of flying dreams in a long dream series:\n",[15,2073,2074],{"href":2074,"rel":2075},"https:\u002F\u002Fdoi.org\u002F10.11588\u002Fijodr.2011.1.9077",[19],[87,2077,2078],{},[90,2079,2080],{},"people tend to go flying when they have lucid dreams",[11,2082,2083],{},"1991 - Barett - Flying Dreams and Lucidity: An Empirical Study of Their Relationship\nDOI:10.1037\u002Fh0094325",[87,2085,2086],{},[90,2087,2080],{},[11,2089,2090],{},"2014 - Mathes, Schredl - Analysis of a large sample of diary dreams - How typical are these typical dreams?\nDOI:10.1007\u002Fs11818-013-0653-6",[87,2092,2093],{},[90,2094,2095],{},"63% of all people at least once dreamt of flying (Tab. 2 -> TDQ56(%))",[11,2097,2098,2099],{},"2007 - Schredl, Piel - Prevalence of Flying Dreams\n",[15,2100,2101],{"href":2101,"rel":2102},"https:\u002F\u002Fdoi.org\u002F10.2466\u002Fpms.105.2.657-660",[19],[87,2104,2105],{},[90,2106,2107],{},"7.5% of all people regularly dream of flying (=600 mio of 8 billion)",[11,2109,2110],{},"Why we dream about flying (Blogs):",[87,2112,2113,2119,2125,2131],{},[90,2114,2115],{},[15,2116,2117],{"href":2117,"rel":2118},"https:\u002F\u002Fwww.mindbodygreen.com\u002Farticles\u002Fdream-of-flying",[19],[90,2120,2121],{},[15,2122,2123],{"href":2123,"rel":2124},"https:\u002F\u002Fwww.psychologytoday.com\u002Fus\u002Fblog\u002Fthe-superhuman-mind\u002F201611\u002Fwhy-do-we-dream-we-are-flying",[19],[90,2126,2127],{},[15,2128,2129],{"href":2129,"rel":2130},"https:\u002F\u002Fyourdreamyland.com\u002Fflying-in-a-dream\u002F#Flying_Dreams_in_Modern_Times",[19],[90,2132,2133],{},[15,2134,2135],{"href":2135,"rel":2136},"https:\u002F\u002Fpracticalpie.com\u002Fdream-of-flying\u002F",[19],{"title":339,"searchDepth":340,"depth":340,"links":2138},[],"A collection of literature on flying in dreams",{"topic":1021,"category":1021,"authors":2141,"tags":2143,"date":2144},[2142],{"name":359,"avatar":360},[1025],"2024-05-01","\u002Fblog\u002Fflying-dreams",{"title":2061,"description":2139},"blog\u002F6.Flying-Dreams","216ZCEFPlsxZPoShzAkyS8_8qyKF6p5JOQ3VxVNR6sA",{"id":2150,"title":2151,"body":2152,"description":2198,"extension":351,"meta":2199,"navigation":366,"path":2205,"seo":2206,"stem":2207,"__hash__":2208},"blog\u002Fblog\u002F7.Fluglicht_Soundtrack.md","Fluglicht Soundtrack",{"type":8,"value":2153,"toc":2195},[2154,2157,2174,2178],[11,2155,2156],{},"If you want to get into our groove while browsing the website, here are the tracks you need! (ongoing)",[87,2158,2159,2162,2165,2168,2171],{},[90,2160,2161],{},"Dianne Reeves - Sky Islands",[90,2163,2164],{},"Plini - Electric Sunrise (and the rest of Handmade Cities)",[90,2166,2167],{},"Plini\u002FSithu Aye - Solstice",[90,2169,2170],{},"Chrono Trigger Main Theme",[90,2172,2173],{},"Cowboy Bebop - Tank!",[74,2175,2177],{"id":2176},"arena","Arena",[87,2179,2180,2183,2186,2189,2192],{},[90,2181,2182],{},"Daft Punk - Flynn Lives",[90,2184,2185],{},"Daft Punk - Arena",[90,2187,2188],{},"Tantrum Desire - Reach VIP (Team 1)",[90,2190,2191],{},"Tomayasu Hotei - Battle Without Honor or Humanity (Team 2)",[90,2193,2194],{},"Daft Punk - Derezzed",{"title":339,"searchDepth":340,"depth":340,"links":2196},[2197],{"id":2176,"depth":340,"text":2177},"Music to listen to, while browsing the website",{"topic":2200,"category":1021,"authors":2201,"tags":2203,"date":2204},"Music",[2202],{"name":359,"avatar":360},[1025],"2024-05-06","\u002Fblog\u002Ffluglicht_soundtrack",{"title":2151,"description":2198},"blog\u002F7.Fluglicht_Soundtrack","oURAvzVSe7jvKvLzA4RvC06GeSYj-HJfAyeCEcwPruE",{"id":2210,"title":2211,"body":2212,"description":2425,"extension":351,"meta":2426,"navigation":366,"path":583,"seo":2430,"stem":2431,"__hash__":2432},"blog\u002Fblog\u002F8.The_Legacy.md","The Legacy",{"type":8,"value":2213,"toc":2419},[2214,2217,2221,2224,2241,2251,2258,2266,2269,2272,2275,2295,2301,2308,2311,2320,2330,2333,2339,2345,2351,2363,2366,2369,2372,2376,2381,2384,2389,2393,2400,2403,2406,2409,2415],[11,2215,2216],{},"In the edes of the year 2025, we are calling an official end to the Fluglicht project. This is sad, but also the perfect time to reflect on the last 7 years and work out what we have learned! An incredible amount of work has flown into the project and many people will be sad that it ends. But it has to be done, as we have reached the limit of our will to push on and found no-one willing to give us the necessary funds. Nonetheless the idea of human birdflight is immortal. And as we have figured out the way, it is just a matter of time till it will eventually be realised. So if it will not be our work it will be that of others. One day humans shall have wings and be free! This article is meant to lay open our lessons learnt so the journey of Fluglicht can be picked up and continued.",[74,2218,2220],{"id":2219},"history-and-general-lessons","History and General Lessons",[11,2222,2223],{},"Back in 2016 when I, Peter, first had the idea of how to fly like a bird, I would have never expected it to get this far. I was still studying and had worked on a project to build a flying bicycle. The idea came up, after calculating wing areas for this project and I wondered: \"why do we actually not fly like a bird? Is there a technical obstacle that can not yet be solved or anything like that?\" Being a fledging aerospace engineer, I put myself to work and started to calculate. But in these rudimentary numbers I couldn't see any hindrance:",[87,2225,2226,2229,2232,2235,2238],{},[90,2227,2228],{},"the power supply was there (small turboshaft engines),",[90,2230,2231],{},"the material for the wing structure was there (carbon fibre reinforced plastics) and capable of taking the loads,",[90,2233,2234],{},"the actuators to make the wings flap were there (small hydraulic cylinders and\u002For electric motors)",[90,2236,2237],{},"the sensors and fast control systems were there (small computers being the keystone)",[90,2239,2240],{},"the accelerations and aerodynamics weren't too crazy.",[11,2242,2243,2244,2250],{},"So finishing my studies in 2017, I decided to try and ",[438,2245,2246],{},[2247,2248,2249],"strong",{},"make it happen","! First, I made a CAD model of the concept and applied for a patent. I also had some start-up experience and knew what student projects like the car racing teams could acheive. So I jumped into the unknown and moved to Dresden in 2018. Why Dresden you may ask? Well, \"intelligence\" showed it had low cost of living, a lot of free space, a technical university with presumably eager students, and local actors looking for and supporting young founders.",[11,2252,2253,2254,2257],{},"Here is the first ",[2247,2255,2256],{},"lesson"," to learn! What is ACTUALLY crucial to get an audacious project like Fluglicht of the ground is the following:",[87,2259,2260,2263],{},[90,2261,2262],{},"being in a place, where people gather that are ambitious, open minded, and willing to help each other with connections and real effort",[90,2264,2265],{},"being in an environment where money and support flows easily towards those people taking risks to convert big chances.",[11,2267,2268],{},"Dresden was not that place. The overwhelming majority of people here (including students) were risk averse, have a very modest (if not \"depressed\") perspective on life and were highly suspicious of people with big dreams. As a consequence, I had to face general disinterest and even active resistance from many sides. Limited support came from the start-up facilitators who were amazed by the idea and spirit, but couldn't give out any funds due to risk aversion of the national fund-owners.",[11,2270,2271],{},"Extreme risk aversion is a fundamental issue, deeply ingrained in Germany, and is slowly dismantling the economy of this place. But that's a different discussion. Suffice to say, even 35 years after the fall of the Berlin wall, East Germany is still fighting with depression (and I don't mean the economic one). It is an interesting question how one could \"heal\" whole societies from something like that. Or more general also hatred, cowardice, distrust, greed, egoism, powerabuse, and corruption. Part of Fluglicht was the attempt to bring hope and excitement for a positive future back into the hearts of people. Maybe that was at least a partial success, as many people we talked to were amazed by the idea (but unable to help).",[11,2273,2274],{},"In hindsight I probably should just have packed my bags and gone to the USA. MIT, Caltech, Stanford - one of these. Students at these universities regularly surprise the world with novelties. And when we visited in May 2024, people told us that before Covid-19, the funds for crazy ideas in Silicon Valley were flowing in copious amounts. Oh, well...",[11,2276,2277,2278,2282,2283,2285,2286,2291,2292,2294],{},"But back to the story. I managed to gather a small student team with people coming and going. The inital plan was to build the full scale wings as a student team within 2 years relying on sponsoring. In Stuttgart, I witnessed the power of what student teams can accomplish first hand. It didn't go that way. Due to the small size of the team and lack of sponsors, this plan was scrapped in exchange for building what is now the ",[15,2279,2281],{"href":2280},"\u002FExoskid","Exoskid",". There is another ",[2247,2284,2256],{}," right there: the team is key and you have to have people on the team that actually WANT to do the tasks at hand. If for example nobody is keen to do financials and get sponsors, it's unlikely to happen. It's the difference between being capable and ",[15,2287,2290],{"href":2288,"rel":2289},"https:\u002F\u002Fwww.youtube.com\u002Fwatch?v=43RhhwpiSk0",[19],"having the appetite"," to do something.\nAfter about a year, the team stabilised with a few very talented and motivated engineering students at the prototyping. I also got better in project management and leadership. At one point even a sales person joined but there is another ",[2247,2293,2256],{}," there: only take up people into the team that are team players and fit with the rest of the team. In the end it was a complete mess when I ignored my gut feeling. It worked for some time, even though none of the goals were reached. But at one point it just got ugly and I had to throw him out.",[11,2296,2297,2298,2300],{},"And then, the world turned outside-in and Covid-19 happened. At that time, I had taken up a \"part time\" job as research associate (PhD student) and the lock-down actually came as a relief. Having two factually-fulltime jobs for a year brought me into extreme overwork. The day just never felt finished, no matter how much effort I put in. This is another ",[2247,2299,2256],{},": leading something like Fluglicht is no part time job. You've got to burn bright to shine through the haze. This is really tough. Keeping morale up when everything feels like walking through a swamp takes a lot of strength and grit. \"Optimism is true moral courage\" as Shackelton would have said. So, caring for your own mental health is crucial not to wear out.",[11,2302,2303,2304,2307],{},"Despite the general weirdness of a pandemic, the team stuck together and we had a few sessions in the lab with extreme care. Martin started to design and build the airplane for the exoskid. Leon iterated the exoskeleton design, which we then built and fully equipped with sensors and the Arduino. In 2019 we already had an exoskeleton arm that could move our original hydraulic wing model. The system later called Exoskid now should use servo motors on the airplane. There are two ",[2247,2305,2306],{},"lessons"," right there. For one: Teams work a lot better, if everyone mostly works on things they actually enjoy and are interested in. Secondly: the amount of work needs to fit to the available hands. Not the other way around! That was hard to realise and accept when I knew what could have been acheived with a larger group. But once we had the right kind of goal that was acheivable and distributed work the right way, things started to happen a lot faster! SMART Goals help. Over the years, I had also built up some digital infrastructure like a landingpage, cloud, Kanban board and communication system. That also helped.",[11,2309,2310],{},"At the end of 2021 the exoskeleton was almost finished, except for the ankles. The wired connection between Exoskeleton and Skid was working. We could flap the wings and produce some wind in the lab. In 2022 the ankle joint system was designed and four-way-ultimate-pong developed (Pong with four bars, controlled entirely with the Exoskeleton). A lot of microcontroller work was done. We struggled to get a radio channel for the exoskeleton data running. In the end we hacked the Flysky's radio link and fed the signal into the Flysky via the trainer port. Probably wouldn't have happened without our Linux and Embedded guru Chris! But on the whole we wrangled the system until we completed the full system integration test in January 2024.",[11,2312,2313,2314,2316,2317,2319],{},"It was an awesome feeling, when we stepped outside for our fist flight in Febuary! You can read that story ",[15,2315,469],{"href":1854},". The ",[2247,2318,2256],{}," of this experience is: have good communication prepared! Like having a checklist to prevent misunderstandings and errors with the complex system. And have clear communication prepared for when something goes wrong. The crash might not have happened (like this) if we have had that.",[11,2321,2322,2323,2326,2327,2329],{},"We didn't let ourselves be stopped, though. Lean work means \"build, measure, learn\", doesn't it? So we rebuilt the airplane with improvements and went out for the ",[15,2324,2325],{"href":1999},"second run"," in  April. This time, we got much longer flight time but were again cut short on exoskeleton flight time by material failure. The only ",[2247,2328,2256],{}," here is: avoid shitty FDM filament! Or you might find yourself wading through a field of flowering rapeseed for 2 hours trying to find the rapid unscheduled disassembly of your project...",[11,2331,2332],{},"In any case, we collected enough data to take the next step: proper funding. I had worked for a long time on the business model and pitch for Fluglicht. With Leon up as a co-founder, we plunged into an airplane and slapped down in Palo Alto. The Start-Up House catapulted us then back and fourth through the Valley, talking to awesome people like Jim Duchovny (Alef) and Yashar Moradi (MOD), gaining valuable connections (also to Germany), pitching at Stanford Startup Society and to Investors in the Hacker Dojo and at GoGlobal.",[11,2334,2335,2336,2338],{},"It was a wild two weeks in the Bay Area and in LA! The main ",[2247,2337,2256],{}," here was that going out there, getting the idea known, and connecting to people is everything. On these \"mixer\" events found on Meetup, Eventbrite, and Luma, me actually found the real chances (search for e.g. \"mix & pitch\"). This is where the power of the Valley unfolds, because people there are willing to help you by making connections. Also they give great feedback, if asked the right way (#The Mom Test). Almost everything works via this networking, as it is futile to just go to Sand Hill Road and walz into Sequoia Capital (even though that was scay and fun at the same time...)",[11,2340,2341],{},[530,2342],{"alt":2343,"src":2344},"Sand Hill Road Picture","\u002Fimages\u002FCrashing_Sequoia.jpg",[11,2346,2347,2348,2350],{},"The next ",[2247,2349,2256],{}," we learnt was: preparation is everything. Having your introduction and (elevator-)pitches of all length ready will not waste valuable potential (1, 2, 3, 5, 7, 10 min pitches - with and without slides). Also, having a clear goal which investors you want to get a warm intro to and who you need to talk to for that, is critical! Many things come with the flow, when you meet a random person at an event that knows just the right people. But time is limited!",[11,2352,2353,2354,2356,2357,2359,2360,625],{},"In the end we had to realise that two weeks are just not enough when starting from scratch. We already had gotten quite far, but did not have the luck to make the winning connection. The main ",[2247,2355,2256],{}," here is: stay longer in California! It's bloody expensive, but the only place on earth where the real crazy shit has a chance, and where EVERYONE helps the others to achieve. And another important ",[2247,2358,2256],{}," is (again): get the right person for the job. We probably didn't manage to \"sell\" the wings good enough to gain traction with the investors. (NOTE: more on the learnings from the valley in the ",[15,2361,2362],{"href":1027},"business lessons article",[11,2364,2365],{},"Back in Germany, I kept on working on our gained traction and had the pleasure to meet Daniel Wiegand of Lilium (thanks a lot Yashar!). The conversation was very interesting and inspiring but, bottom line, it didn't transpire anything. And to be honest, the Valley trip was my last hope on getting the funds. Nothing in Germany had borne fruit in the last 6 years. And the prospect to go throught the tedium of getting warm intros to all the investors on our list wasn't appealing. We searched for a business co-founder, to no avail. I pushed on to the end of 2024, gaining at least a pitch to an aerospace affine angel investor.",[11,2367,2368],{},"But when this didn't work out, something broke inside. I had to admit to myself that I didn't have the strength to push on, even though a lot of leads were still untouched. So I called Leon and told him, I wanted to stop the project. Not an easy decision, when something has been the pride and joy of ones life for that many years! But in hindsight I can say, it was a good and necessary decision. Admiting defeat is painful and it took me a year to be able to sit down and write this up. But in the end, the death of one project opens up space for something new!",[11,2370,2371],{},"If you are interested in the lessons of technology development and the business development, I wrote two more lengthy articles about that. You can find the links below!",[74,2373,2375],{"id":2374},"technical-lessons","Technical Lessons",[11,2377,2378,2379,297],{},"The deep dive into the technology can be found ",[15,2380,469],{"href":336},[74,2382,373],{"id":2383},"business-lessons",[11,2385,2386,2387],{},"Our lessons learnt for the business part can be found ",[15,2388,469],{"href":1027},[74,2390,2392],{"id":2391},"resumee","Resumee",[11,2394,2395,2396,2399],{},"So after 7 years of struggle, can I answer the question \"is human birdflight possible?\" What is ",[2247,2397,2398],{},"the biggest lesson of them all","?",[11,2401,2402],{},"Yes, human birdflight with a flying exoskeleton can work! From a technical side, there are no fundamental roadblocks. It won't be easy and to get the performance up will take time. But it can be done. The bigger challenge is that it's ludicrously hard to get the funds together to pay the engineers and materials. And the reason is that it's a high risk, uncertain reward endeavour. Few people will be willing to put money in it. THAT is the real reason, why it hasn't been built yet. So the crucial task is, getting it built once and then prove how much love people really harbor for flying like a bird.",[11,2404,2405],{},"Looking back, there is also the question, if it was worth it. Seven years of struggle, many weeks of work to compile all the information here... will it be all for nothing?",[11,2407,2408],{},"Indeed, we didn't make it in the end. But we leant A LOT in that time. It was daunting, straining, uncomfortable, and even painful at times. But also exciting, stimulating, fun and even exhiliarating! I grew alot as a person, especially from the challenging parts. And with the most important information gathered here, I'm hope strongly, all the pain was not in vain. Since aeons men have turned their heads skywards, hearts full of Fluglicht. So if it will not be our work, it will be that of others. I'm certain: this dream will never perish! And one day, humans shall have wings, and they shall fly!",[11,2410,2411],{},[530,2412],{"alt":2413,"src":2414},"GoodByePicture","\u002Fimages\u002FGoodbyeStart.jpg",[448,2416,2418],{"id":2417},"we-are-fluglicht-and-this-is-our-legacy","We are Fluglicht and this is our legacy.",{"title":339,"searchDepth":340,"depth":340,"links":2420},[2421,2422,2423,2424],{"id":2219,"depth":340,"text":2220},{"id":2374,"depth":340,"text":2375},{"id":2383,"depth":340,"text":373},{"id":2391,"depth":340,"text":2392},"Wrapping up Fluglicht",{"topic":1021,"category":1021,"authors":2427,"tags":2429,"date":1026},[2428],{"name":359,"avatar":360},[1025],{"title":2211,"description":2425},"blog\u002F8.The_Legacy","9ol-QQ2h7H410QQc_K3iNY63xBu3Mp6CKldPX4XVwo0",{"id":2434,"title":337,"body":2435,"description":14007,"extension":351,"meta":14008,"navigation":366,"path":336,"seo":14014,"stem":14015,"__hash__":14016},"blog\u002Fblog\u002F9.Technology_Details.md",{"type":8,"value":2436,"toc":13968},[2437,2441,2451,2454,2457,2463,2467,2476,2479,2482,2499,2502,2510,2513,2517,2520,2645,2648,2686,2689,2715,2718,2722,2728,2731,3007,3199,3202,3206,3635,3735,4019,4197,4389,4462,4581,4653,4901,4988,5430,5434,5437,5720,5883,5887,5933,6060,6064,6067,6218,6323,6328,6338,6342,6345,6356,6789,6792,7365,7369,7372,7444,7448,7451,7485,7718,8127,8293,8296,8300,8307,8378,8381,8385,8521,8751,8875,9045,9078,9308,9452,9676,9867,10248,10554,10558,10771,10847,10982,10986,10989,11624,12067,12135,12208,12212,12215,12218,12296,12303,12308,12312,12416,12833,13052,13410,13756,13806,13810,13819,13822,13826,13829,13833,13836,13839,13843,13846,13850,13853,13856,13860,13865,13868,13885,13888,13911,13914,13917,13921,13932,13936,13939,13943,13957,13961],[74,2438,2440],{"id":2439},"how-to-design-a-flying-exoskeleton","How to design a flying Exoskeleton",[11,2442,2443,2447,2448,2450],{},[530,2444],{"alt":2445,"src":2446},"Wing Artwork","\u002Fimages\u002F2019-WingArtworkEd-cut.png","\nOver the years, we have assembled a lot of information and calculations for the design of the flying Exoskeleton. Have a look at ",[15,2449,6],{"href":367}," for a historical introduction and a glimpse at the scientific literature. On our journey we faced many questions like: Does it even fly? How large are the wings? How heavy is it? Can a human control this thing? Is the available material strong enough?",[11,2452,2453],{},"This page shall dive deep into the topic and shed some light on the hard facts and calculations. It will not capture the topic fully, though, as there is much too much to put it here. Nevertheless, it shall provide a forward base for further developments in the future. Some of the most critical and fundamental calculations of our basic design study shall be presented here.",[11,2455,2456],{},"This article requires some prior knowledge and is geared towards engineers.",[11,2458,2459,2460],{},"For literature citations see ",[15,2461,2462],{"href":367},"human birdflight feasibility",[82,2464,2466],{"id":2465},"preliminary-thoughs","Preliminary Thoughs",[11,2468,2469,2470,2475],{},"The basic idea, as described in ",[15,2471,2474],{"href":2472,"rel":2473},"https:\u002F\u002Fpatentscope.wipo.int\u002Fsearch\u002Fen\u002Fdetail.jsf?docId=WO2019192636&_cid=P12-M5MKAQ-47752-1",[19],"the patent",", is to let people fly like a bird through robotic wings attached to a backpack. The wings are controlled with the arms\u002Fbody via an exoskeleton and return the aeroelastic forces back to the pilot via the exoskeleton. Thus, the pilot can feel the air under the wing and \"learn to fly\" in the best possible sense. No direct mechanical connection between the control input (e.g. the arms) and the output at the aerodynamic surfaces (e.g. the wings) should exist. They are coupled via the flight control computer\u002Fthe teleoperation system. This way, the amount of feedback force on the arms and legs\u002Fankles can be adjusted or even turned to zero. The pilot can decide how much feedback is desirable for a good experience.",[11,2477,2478],{},"Further necessary parts of the system are, a power source to drive the robotic actuators and other subsystems, tail robot for aerodynamic control, and safety\u002Femergency systems.",[11,2480,2481],{},"The system will thus consist of:",[87,2483,2484,2487,2490,2493,2496],{},[90,2485,2486],{},"Pilot",[90,2488,2489],{},"Exoskeleton",[90,2491,2492],{},"Backpack housing support subsystems",[90,2494,2495],{},"Wing robots attached to the backpack",[90,2497,2498],{},"Tail wing robot",[11,2500,2501],{},"To generate lift for flight, two options exist analogous to birds. Both options correlate with distinct flight modes:",[393,2503,2504,2507],{},[90,2505,2506],{},"Gliding and flapping flight. Steady forward movement generates dynamic lift at the wings, which requires a minimum true airspeed. Thrust can be generated by flapping the wings.",[90,2508,2509],{},"Fluttering flight. Unsteady dynamic lift generated by wing flapping. Potentially using unsteady aerodynamic effects. Does not require motion of the whole system relative to the air and is thus usable for vertical take-off and landing (VTOL) and hovering.",[11,2511,2512],{},"In the final installment, the system is supposed to be VTOL-capable (just like birds). So it will need to be able to lift its own weight with the thrust generated by fluttering. As this mode drains the most power and puts the highest strains on the mechanical structure, it can be considered a system driver of the final system. Both modes will be investigated in the following.",[82,2514,2516],{"id":2515},"design-process-summary","Design process summary",[11,2518,2519],{},"The process for the preliminary design study is as follows. First, the system's basic dimensions necessary for gliding are determined. Gliding is the first basic flight mode used in steady flight and landing. The process has these steps:",[393,2521,2522,2529,2532,2535],{},[90,2523,2524,2525,2528],{},"Have a rough idea of the system. (see e.g. ",[15,2526,469],{"href":2527},"\u002FflyingExoskeleton",")",[90,2530,2531],{},"Estimate the weight of the components\u002Fstructure plus the pilot.",[90,2533,2534],{},"Estimate the wing geometry and maximum lift coefficient.",[90,2536,2537,2538,2644],{},"Estimate necessary wing area with weight, ",[2539,2540,2543,2572],"span",{"className":2541},[2542],"katex",[2539,2544,2547],{"className":2545},[2546],"katex-mathml",[2548,2549,2551],"math",{"xmlns":2550},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[2552,2553,2554,2567],"semantics",{},[2555,2556,2557],"mrow",{},[2558,2559,2560,2564],"msub",{},[2561,2562,2563],"mi",{},"c",[2561,2565,2566],{},"d",[2568,2569,2571],"annotation",{"encoding":2570},"application\u002Fx-tex","c_d",[2539,2573,2577],{"className":2574,"ariaHidden":2576},[2575],"katex-html","true",[2539,2578,2581,2586],{"className":2579},[2580],"base",[2539,2582],{"className":2583,"style":2585},[2584],"strut","height:0.5806em;vertical-align:-0.15em;",[2539,2587,2590,2594],{"className":2588},[2589],"mord",[2539,2591,2563],{"className":2592},[2589,2593],"mathnormal",[2539,2595,2598],{"className":2596},[2597],"msupsub",[2539,2599,2603,2635],{"className":2600},[2601,2602],"vlist-t","vlist-t2",[2539,2604,2607,2630],{"className":2605},[2606],"vlist-r",[2539,2608,2612],{"className":2609,"style":2611},[2610],"vlist","height:0.3361em;",[2539,2613,2615,2620],{"style":2614},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[2539,2616],{"className":2617,"style":2619},[2618],"pstrut","height:2.7em;",[2539,2621,2627],{"className":2622},[2623,2624,2625,2626],"sizing","reset-size6","size3","mtight",[2539,2628,2566],{"className":2629},[2589,2593,2626],[2539,2631,2634],{"className":2632},[2633],"vlist-s","​",[2539,2636,2638],{"className":2637},[2606],[2539,2639,2642],{"className":2640,"style":2641},[2610],"height:0.15em;",[2539,2643],{},", and a desired stall speed.",[11,2646,2647],{},"With the basic questions answered, further flight modes can be investigated. For propulsive flapping flight, the process is:",[393,2649,2650,2653,2656],{},[90,2651,2652],{},"Decide for a maximum allowable flapping frequency.",[90,2654,2655],{},"Decide for a maximum flapping amplitude.",[90,2657,2658,2659,2663,2664,2669,2670,2675,2676,2681,2682],{},"Calculate thrust, aerodynamic efficiency, optimum wing torsion using the ",[15,2660,2662],{"href":155,"rel":2661},[19],"research of Dr. Send",". For hints on understanding the paper see below and ",[15,2665,2668],{"href":2666,"rel":2667},"https:\u002F\u002Fwww.aniprop.de",[19],"aniprop.de",". For an excel implementation of the paper see ",[15,2671,2674],{"href":2672,"rel":2673},"http:\u002F\u002Fberblinger2.de",[19],"berblinger2.de"," and \"",[15,2677,2680],{"href":2678,"rel":2679},"https:\u002F\u002Fwww.aniprop.de\u002Fsites\u002Fdefault\u002Ffiles\u002Fnatrs03_xlsmodell_send.html",[19],"Physik der schwingenden Platte","\" at aniprop.de. Dr. Send's body of work can be found ",[15,2683,469],{"href":2684,"rel":2685},"https:\u002F\u002Fwww.aniprop.de\u002Fartikel",[19],[11,2687,2688],{},"Further questions can then be answered:",[87,2690,2691,2694,2697,2700,2703,2706,2709,2712],{},[90,2692,2693],{},"What moments and forces are necessary for fluttering?",[90,2695,2696],{},"Are there materials and acutators capable of handling these?",[90,2698,2699],{},"What is the aerodynamic efficiency (gliding angle) of the system?",[90,2701,2702],{},"How to acheive aerodynamic control and stability?",[90,2704,2705],{},"What are the power requirements of flappling and fluttering flight? What systems can provide this?",[90,2707,2708],{},"How long can the system stay in the air? What is the maximum range? How high can it fly?",[90,2710,2711],{},"Is the above made assumption of maximum weight reasonable?",[90,2713,2714],{},"And are humans fast enough to control the system, or is kybernetic augmentation necessary?",[11,2716,2717],{},"Answering these questions can get arbitrarily complex, considering all the different load cases, missions profiles, degrees of freedom, and geometric designs the system might attain. For a preliminary study of feasibility, we had to somewhat limit ourselves.",[74,2719,2721],{"id":2720},"does-it-fly-dimensioning-the-wings","Does it fly? - Dimensioning the Wings",[11,2723,2724],{},[530,2725],{"alt":2726,"src":2727},"Wings CAD half-backview","\u002Fimages\u002FWings_Halb_hintenLinks.png",[11,2729,2730],{},"Bird wings use dynamic lift of an airfoil to enable flight. Lilienthal figured this out and built some of the first commercially available airplanes of the world. The lift is calculated with:",[2539,2732,2735],{"className":2733},[2734],"katex-display",[2539,2736,2738,2791],{"className":2737},[2542],[2539,2739,2741],{"className":2740},[2546],[2548,2742,2744],{"xmlns":2550,"display":2743},"block",[2552,2745,2746,2788],{},[2555,2747,2748,2751,2755,2762,2765,2775,2783,2785],{},[2561,2749,2750],{},"L",[2752,2753,2754],"mo",{},"=",[2558,2756,2757,2760],{},[2561,2758,2759],{},"C",[2561,2761,2750],{},[2752,2763,2764],{},"⋅",[2766,2767,2768,2771],"mfrac",{},[2561,2769,2770],{},"ρ",[2772,2773,2774],"mn",{},"2",[2776,2777,2778,2781],"msup",{},[2561,2779,2780],{},"u",[2772,2782,2774],{},[2752,2784,2764],{},[2561,2786,2787],{},"S",[2568,2789,2790],{"encoding":2570},"L = C_L\\cdot \\frac{\\rho}{2}u^2 \\cdot S",[2539,2792,2794,2816,2877,2997],{"className":2793,"ariaHidden":2576},[2575],[2539,2795,2797,2801,2804,2809,2813],{"className":2796},[2580],[2539,2798],{"className":2799,"style":2800},[2584],"height:0.6833em;",[2539,2802,2750],{"className":2803},[2589,2593],[2539,2805],{"className":2806,"style":2808},[2807],"mspace","margin-right:0.2778em;",[2539,2810,2754],{"className":2811},[2812],"mrel",[2539,2814],{"className":2815,"style":2808},[2807],[2539,2817,2819,2823,2866,2870,2874],{"className":2818},[2580],[2539,2820],{"className":2821,"style":2822},[2584],"height:0.8333em;vertical-align:-0.15em;",[2539,2824,2826,2830],{"className":2825},[2589],[2539,2827,2759],{"className":2828,"style":2829},[2589,2593],"margin-right:0.0715em;",[2539,2831,2833],{"className":2832},[2597],[2539,2834,2836,2858],{"className":2835},[2601,2602],[2539,2837,2839,2855],{"className":2838},[2606],[2539,2840,2843],{"className":2841,"style":2842},[2610],"height:0.3283em;",[2539,2844,2846,2849],{"style":2845},"top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;",[2539,2847],{"className":2848,"style":2619},[2618],[2539,2850,2852],{"className":2851},[2623,2624,2625,2626],[2539,2853,2750],{"className":2854},[2589,2593,2626],[2539,2856,2634],{"className":2857},[2633],[2539,2859,2861],{"className":2860},[2606],[2539,2862,2864],{"className":2863,"style":2641},[2610],[2539,2865],{},[2539,2867],{"className":2868,"style":2869},[2807],"margin-right:0.2222em;",[2539,2871,2764],{"className":2872},[2873],"mbin",[2539,2875],{"className":2876,"style":2869},[2807],[2539,2878,2880,2884,2957,2988,2991,2994],{"className":2879},[2580],[2539,2881],{"className":2882,"style":2883},[2584],"height:1.7936em;vertical-align:-0.686em;",[2539,2885,2887,2892,2953],{"className":2886},[2589],[2539,2888],{"className":2889},[2890,2891],"mopen","nulldelimiter",[2539,2893,2895],{"className":2894},[2766],[2539,2896,2898,2944],{"className":2897},[2601,2602],[2539,2899,2901,2941],{"className":2900},[2606],[2539,2902,2905,2918,2929],{"className":2903,"style":2904},[2610],"height:1.1076em;",[2539,2906,2908,2912],{"style":2907},"top:-2.314em;",[2539,2909],{"className":2910,"style":2911},[2618],"height:3em;",[2539,2913,2915],{"className":2914},[2589],[2539,2916,2774],{"className":2917},[2589],[2539,2919,2921,2924],{"style":2920},"top:-3.23em;",[2539,2922],{"className":2923,"style":2911},[2618],[2539,2925],{"className":2926,"style":2928},[2927],"frac-line","border-bottom-width:0.04em;",[2539,2930,2932,2935],{"style":2931},"top:-3.677em;",[2539,2933],{"className":2934,"style":2911},[2618],[2539,2936,2938],{"className":2937},[2589],[2539,2939,2770],{"className":2940},[2589,2593],[2539,2942,2634],{"className":2943},[2633],[2539,2945,2947],{"className":2946},[2606],[2539,2948,2951],{"className":2949,"style":2950},[2610],"height:0.686em;",[2539,2952],{},[2539,2954],{"className":2955},[2956,2891],"mclose",[2539,2958,2960,2963],{"className":2959},[2589],[2539,2961,2780],{"className":2962},[2589,2593],[2539,2964,2966],{"className":2965},[2597],[2539,2967,2969],{"className":2968},[2601],[2539,2970,2972],{"className":2971},[2606],[2539,2973,2976],{"className":2974,"style":2975},[2610],"height:0.8641em;",[2539,2977,2979,2982],{"style":2978},"top:-3.113em;margin-right:0.05em;",[2539,2980],{"className":2981,"style":2619},[2618],[2539,2983,2985],{"className":2984},[2623,2624,2625,2626],[2539,2986,2774],{"className":2987},[2589,2626],[2539,2989],{"className":2990,"style":2869},[2807],[2539,2992,2764],{"className":2993},[2873],[2539,2995],{"className":2996,"style":2869},[2807],[2539,2998,3000,3003],{"className":2999},[2580],[2539,3001],{"className":3002,"style":2800},[2584],[2539,3004,2787],{"className":3005,"style":3006},[2589,2593],"margin-right:0.0576em;",[11,3008,3009,3010,3038,3039,3109,3110,3140,3141,3170,3171,297],{},"with the lift force ",[2539,3011,3013,3026],{"className":3012},[2542],[2539,3014,3016],{"className":3015},[2546],[2548,3017,3018],{"xmlns":2550},[2552,3019,3020,3024],{},[2555,3021,3022],{},[2561,3023,2750],{},[2568,3025,2750],{"encoding":2570},[2539,3027,3029],{"className":3028,"ariaHidden":2576},[2575],[2539,3030,3032,3035],{"className":3031},[2580],[2539,3033],{"className":3034,"style":2800},[2584],[2539,3036,2750],{"className":3037},[2589,2593],", the lift coefficient ",[2539,3040,3042,3060],{"className":3041},[2542],[2539,3043,3045],{"className":3044},[2546],[2548,3046,3047],{"xmlns":2550},[2552,3048,3049,3057],{},[2555,3050,3051],{},[2558,3052,3053,3055],{},[2561,3054,2759],{},[2561,3056,2750],{},[2568,3058,3059],{"encoding":2570},"C_L",[2539,3061,3063],{"className":3062,"ariaHidden":2576},[2575],[2539,3064,3066,3069],{"className":3065},[2580],[2539,3067],{"className":3068,"style":2822},[2584],[2539,3070,3072,3075],{"className":3071},[2589],[2539,3073,2759],{"className":3074,"style":2829},[2589,2593],[2539,3076,3078],{"className":3077},[2597],[2539,3079,3081,3101],{"className":3080},[2601,2602],[2539,3082,3084,3098],{"className":3083},[2606],[2539,3085,3087],{"className":3086,"style":2842},[2610],[2539,3088,3089,3092],{"style":2845},[2539,3090],{"className":3091,"style":2619},[2618],[2539,3093,3095],{"className":3094},[2623,2624,2625,2626],[2539,3096,2750],{"className":3097},[2589,2593,2626],[2539,3099,2634],{"className":3100},[2633],[2539,3102,3104],{"className":3103},[2606],[2539,3105,3107],{"className":3106,"style":2641},[2610],[2539,3108],{},", the air density ",[2539,3111,3113,3127],{"className":3112},[2542],[2539,3114,3116],{"className":3115},[2546],[2548,3117,3118],{"xmlns":2550},[2552,3119,3120,3124],{},[2555,3121,3122],{},[2561,3123,2770],{},[2568,3125,3126],{"encoding":2570},"\\rho",[2539,3128,3130],{"className":3129,"ariaHidden":2576},[2575],[2539,3131,3133,3137],{"className":3132},[2580],[2539,3134],{"className":3135,"style":3136},[2584],"height:0.625em;vertical-align:-0.1944em;",[2539,3138,2770],{"className":3139},[2589,2593],", the true airspeed ",[2539,3142,3144,3157],{"className":3143},[2542],[2539,3145,3147],{"className":3146},[2546],[2548,3148,3149],{"xmlns":2550},[2552,3150,3151,3155],{},[2555,3152,3153],{},[2561,3154,2780],{},[2568,3156,2780],{"encoding":2570},[2539,3158,3160],{"className":3159,"ariaHidden":2576},[2575],[2539,3161,3163,3167],{"className":3162},[2580],[2539,3164],{"className":3165,"style":3166},[2584],"height:0.4306em;",[2539,3168,2780],{"className":3169},[2589,2593]," and the wing area ",[2539,3172,3174,3187],{"className":3173},[2542],[2539,3175,3177],{"className":3176},[2546],[2548,3178,3179],{"xmlns":2550},[2552,3180,3181,3185],{},[2555,3182,3183],{},[2561,3184,2787],{},[2568,3186,2787],{"encoding":2570},[2539,3188,3190],{"className":3189,"ariaHidden":2576},[2575],[2539,3191,3193,3196],{"className":3192},[2580],[2539,3194],{"className":3195,"style":2800},[2584],[2539,3197,2787],{"className":3198,"style":3006},[2589,2593],[11,3200,3201],{},"As the sharp engineer can see from these equations: even a rock flys if you stick wings to it. The question is just: \"how well?\" The better the system aerodynamics, the bigger the wings, the higher the fluid density, and the faster you go, the more lift is generated.",[82,3203,3205],{"id":3204},"how-much-lift-gliding","How much lift? - Gliding",[11,3207,3208,3209,3266,3267,3314,3315,3588,3589,3634],{},"How much lift is needed depends on the weight of the whole system including pilot. As the details of the system are not known yet, we have to estimate. The pilot is assumed to weigh ",[2539,3210,3212,3240],{"className":3211},[2542],[2539,3213,3215],{"className":3214},[2546],[2548,3216,3217],{"xmlns":2550},[2552,3218,3219,3237],{},[2555,3220,3221,3224,3228],{},[2772,3222,3223],{},"80",[3225,3226,3227],"mtext",{}," ",[2555,3229,3230,3234],{},[2561,3231,3233],{"mathvariant":3232},"normal","k",[2561,3235,3236],{"mathvariant":3232},"g",[2568,3238,3239],{"encoding":2570},"80\\,\\mathrm{kg}",[2539,3241,3243],{"className":3242,"ariaHidden":2576},[2575],[2539,3244,3246,3250,3253,3257],{"className":3245},[2580],[2539,3247],{"className":3248,"style":3249},[2584],"height:0.8889em;vertical-align:-0.1944em;",[2539,3251,3223],{"className":3252},[2589],[2539,3254],{"className":3255,"style":3256},[2807],"margin-right:0.1667em;",[2539,3258,3260],{"className":3259},[2589],[2539,3261,3265],{"className":3262,"style":3264},[2589,3263],"mathrm","margin-right:0.0139em;","kg",". For the system we firstly assumed a maximum of ",[2539,3268,3270,3293],{"className":3269},[2542],[2539,3271,3273],{"className":3272},[2546],[2548,3274,3275],{"xmlns":2550},[2552,3276,3277,3290],{},[2555,3278,3279,3282,3284],{},[2772,3280,3281],{},"60",[3225,3283,3227],{},[2555,3285,3286,3288],{},[2561,3287,3233],{"mathvariant":3232},[2561,3289,3236],{"mathvariant":3232},[2568,3291,3292],{"encoding":2570},"60\\,\\mathrm{kg}",[2539,3294,3296],{"className":3295,"ariaHidden":2576},[2575],[2539,3297,3299,3302,3305,3308],{"className":3298},[2580],[2539,3300],{"className":3301,"style":3249},[2584],[2539,3303,3281],{"className":3304},[2589],[2539,3306],{"className":3307,"style":3256},[2807],[2539,3309,3311],{"className":3310},[2589],[2539,3312,3265],{"className":3313,"style":3264},[2589,3263],", as this is roughly what a well-trained person can shoulder. So a total minimum lift of ",[2539,3316,3318,3379],{"className":3317},[2542],[2539,3319,3321],{"className":3320},[2546],[2548,3322,3323],{"xmlns":2550},[2552,3324,3325,3376],{},[2555,3326,3327,3329,3331,3334,3336,3339,3341,3347,3349,3352,3354,3366,3368,3371,3373],{},[2561,3328,2750],{},[2752,3330,2754],{},[2561,3332,3333],{},"G",[2752,3335,2754],{},[2772,3337,3338],{},"140",[3225,3340,3227],{},[2555,3342,3343,3345],{},[2561,3344,3233],{"mathvariant":3232},[2561,3346,3236],{"mathvariant":3232},[2752,3348,2764],{},[2772,3350,3351],{},"9.81",[3225,3353,3227],{},[2766,3355,3356,3359],{},[2561,3357,3358],{"mathvariant":3232},"m",[2776,3360,3361,3364],{},[2561,3362,3363],{"mathvariant":3232},"s",[2772,3365,2774],{},[2752,3367,2754],{},[2772,3369,3370],{},"1374",[3225,3372,3227],{},[2561,3374,3375],{"mathvariant":3232},"N",[2568,3377,3378],{"encoding":2570},"L = G = 140\\,\\mathrm{kg} \\cdot 9.81\\,\\frac{\\mathrm{m}}{\\mathrm{s^{2}}} = 1374\\,\\mathrm{N}",[2539,3380,3382,3400,3418,3445,3573],{"className":3381,"ariaHidden":2576},[2575],[2539,3383,3385,3388,3391,3394,3397],{"className":3384},[2580],[2539,3386],{"className":3387,"style":2800},[2584],[2539,3389,2750],{"className":3390},[2589,2593],[2539,3392],{"className":3393,"style":2808},[2807],[2539,3395,2754],{"className":3396},[2812],[2539,3398],{"className":3399,"style":2808},[2807],[2539,3401,3403,3406,3409,3412,3415],{"className":3402},[2580],[2539,3404],{"className":3405,"style":2800},[2584],[2539,3407,3333],{"className":3408},[2589,2593],[2539,3410],{"className":3411,"style":2808},[2807],[2539,3413,2754],{"className":3414},[2812],[2539,3416],{"className":3417,"style":2808},[2807],[2539,3419,3421,3424,3427,3430,3436,3439,3442],{"className":3420},[2580],[2539,3422],{"className":3423,"style":3249},[2584],[2539,3425,3338],{"className":3426},[2589],[2539,3428],{"className":3429,"style":3256},[2807],[2539,3431,3433],{"className":3432},[2589],[2539,3434,3265],{"className":3435,"style":3264},[2589,3263],[2539,3437],{"className":3438,"style":2869},[2807],[2539,3440,2764],{"className":3441},[2873],[2539,3443],{"className":3444,"style":2869},[2807],[2539,3446,3448,3452,3455,3458,3564,3567,3570],{"className":3447},[2580],[2539,3449],{"className":3450,"style":3451},[2584],"height:1.0404em;vertical-align:-0.345em;",[2539,3453,3351],{"className":3454},[2589],[2539,3456],{"className":3457,"style":3256},[2807],[2539,3459,3461,3464,3561],{"className":3460},[2589],[2539,3462],{"className":3463},[2890,2891],[2539,3465,3467],{"className":3466},[2766],[2539,3468,3470,3552],{"className":3469},[2601,2602],[2539,3471,3473,3549],{"className":3472},[2606],[2539,3474,3477,3526,3534],{"className":3475,"style":3476},[2610],"height:0.6954em;",[2539,3478,3480,3483],{"style":3479},"top:-2.655em;",[2539,3481],{"className":3482,"style":2911},[2618],[2539,3484,3486],{"className":3485},[2623,2624,2625,2626],[2539,3487,3489],{"className":3488},[2589,2626],[2539,3490,3492,3495],{"className":3491},[2589,2626],[2539,3493,3363],{"className":3494},[2589,3263,2626],[2539,3496,3498],{"className":3497},[2597],[2539,3499,3501],{"className":3500},[2601],[2539,3502,3504],{"className":3503},[2606],[2539,3505,3508],{"className":3506,"style":3507},[2610],"height:0.7463em;",[2539,3509,3511,3515],{"style":3510},"top:-2.786em;margin-right:0.0714em;",[2539,3512],{"className":3513,"style":3514},[2618],"height:2.5em;",[2539,3516,3520],{"className":3517},[2623,3518,3519,2626],"reset-size3","size1",[2539,3521,3523],{"className":3522},[2589,2626],[2539,3524,2774],{"className":3525},[2589,3263,2626],[2539,3527,3528,3531],{"style":2920},[2539,3529],{"className":3530,"style":2911},[2618],[2539,3532],{"className":3533,"style":2928},[2927],[2539,3535,3537,3540],{"style":3536},"top:-3.394em;",[2539,3538],{"className":3539,"style":2911},[2618],[2539,3541,3543],{"className":3542},[2623,2624,2625,2626],[2539,3544,3546],{"className":3545},[2589,2626],[2539,3547,3358],{"className":3548},[2589,3263,2626],[2539,3550,2634],{"className":3551},[2633],[2539,3553,3555],{"className":3554},[2606],[2539,3556,3559],{"className":3557,"style":3558},[2610],"height:0.345em;",[2539,3560],{},[2539,3562],{"className":3563},[2956,2891],[2539,3565],{"className":3566,"style":2808},[2807],[2539,3568,2754],{"className":3569},[2812],[2539,3571],{"className":3572,"style":2808},[2807],[2539,3574,3576,3579,3582,3585],{"className":3575},[2580],[2539,3577],{"className":3578,"style":2800},[2584],[2539,3580,3370],{"className":3581},[2589],[2539,3583],{"className":3584,"style":3256},[2807],[2539,3586,3375],{"className":3587},[2589,3263]," is requied for flight. Of course a more light-weight system would be highly desirable. But making it lighter requires more engineering. This is just a first shot and wieght reduction will happen over time. And the idea is anyways to start somewhere and then iterate the design.\nAfter finding geometry, forces and some exemplary parts, we did a rough check on our initial assumption of ",[2539,3590,3592,3613],{"className":3591},[2542],[2539,3593,3595],{"className":3594},[2546],[2548,3596,3597],{"xmlns":2550},[2552,3598,3599,3611],{},[2555,3600,3601,3603,3605],{},[2772,3602,3281],{},[3225,3604,3227],{},[2555,3606,3607,3609],{},[2561,3608,3233],{"mathvariant":3232},[2561,3610,3236],{"mathvariant":3232},[2568,3612,3292],{"encoding":2570},[2539,3614,3616],{"className":3615,"ariaHidden":2576},[2575],[2539,3617,3619,3622,3625,3628],{"className":3618},[2580],[2539,3620],{"className":3621,"style":3249},[2584],[2539,3623,3281],{"className":3624},[2589],[2539,3626],{"className":3627,"style":3256},[2807],[2539,3629,3631],{"className":3630},[2589],[2539,3632,3265],{"className":3633,"style":3264},[2589,3263]," for the whole system and it seemed reasonable.",[82,3636,3638,1305,3707],{"id":3637},"clc_lcl-and-sss",[2539,3639,3641,3658],{"className":3640},[2542],[2539,3642,3644],{"className":3643},[2546],[2548,3645,3646],{"xmlns":2550},[2552,3647,3648,3656],{},[2555,3649,3650],{},[2558,3651,3652,3654],{},[2561,3653,2759],{},[2561,3655,2750],{},[2568,3657,3059],{"encoding":2570},[2539,3659,3661],{"className":3660,"ariaHidden":2576},[2575],[2539,3662,3664,3667],{"className":3663},[2580],[2539,3665],{"className":3666,"style":2822},[2584],[2539,3668,3670,3673],{"className":3669},[2589],[2539,3671,2759],{"className":3672,"style":2829},[2589,2593],[2539,3674,3676],{"className":3675},[2597],[2539,3677,3679,3699],{"className":3678},[2601,2602],[2539,3680,3682,3696],{"className":3681},[2606],[2539,3683,3685],{"className":3684,"style":2842},[2610],[2539,3686,3687,3690],{"style":2845},[2539,3688],{"className":3689,"style":2619},[2618],[2539,3691,3693],{"className":3692},[2623,2624,2625,2626],[2539,3694,2750],{"className":3695},[2589,2593,2626],[2539,3697,2634],{"className":3698},[2633],[2539,3700,3702],{"className":3701},[2606],[2539,3703,3705],{"className":3704,"style":2641},[2610],[2539,3706],{},[2539,3708,3710,3723],{"className":3709},[2542],[2539,3711,3713],{"className":3712},[2546],[2548,3714,3715],{"xmlns":2550},[2552,3716,3717,3721],{},[2555,3718,3719],{},[2561,3720,2787],{},[2568,3722,2787],{"encoding":2570},[2539,3724,3726],{"className":3725,"ariaHidden":2576},[2575],[2539,3727,3729,3732],{"className":3728},[2580],[2539,3730],{"className":3731,"style":2800},[2584],[2539,3733,2787],{"className":3734,"style":3006},[2589,2593],[11,3736,3737,3738,3807,3808,3878,3879,3948,3949,4018],{},"Now that we know the ballpark of the required lift, over which path can we generate it? As the system is unknown its aerodynamics expressed in ",[2539,3739,3741,3758],{"className":3740},[2542],[2539,3742,3744],{"className":3743},[2546],[2548,3745,3746],{"xmlns":2550},[2552,3747,3748,3756],{},[2555,3749,3750],{},[2558,3751,3752,3754],{},[2561,3753,2759],{},[2561,3755,2750],{},[2568,3757,3059],{"encoding":2570},[2539,3759,3761],{"className":3760,"ariaHidden":2576},[2575],[2539,3762,3764,3767],{"className":3763},[2580],[2539,3765],{"className":3766,"style":2822},[2584],[2539,3768,3770,3773],{"className":3769},[2589],[2539,3771,2759],{"className":3772,"style":2829},[2589,2593],[2539,3774,3776],{"className":3775},[2597],[2539,3777,3779,3799],{"className":3778},[2601,2602],[2539,3780,3782,3796],{"className":3781},[2606],[2539,3783,3785],{"className":3784,"style":2842},[2610],[2539,3786,3787,3790],{"style":2845},[2539,3788],{"className":3789,"style":2619},[2618],[2539,3791,3793],{"className":3792},[2623,2624,2625,2626],[2539,3794,2750],{"className":3795},[2589,2593,2626],[2539,3797,2634],{"className":3798},[2633],[2539,3800,3802],{"className":3801},[2606],[2539,3803,3805],{"className":3804,"style":2641},[2610],[2539,3806],{},", are also unknown. An estimate for the profile lift coefficient ",[2539,3809,3811,3829],{"className":3810},[2542],[2539,3812,3814],{"className":3813},[2546],[2548,3815,3816],{"xmlns":2550},[2552,3817,3818,3826],{},[2555,3819,3820],{},[2558,3821,3822,3824],{},[2561,3823,2563],{},[2561,3825,2750],{},[2568,3827,3828],{"encoding":2570},"c_L",[2539,3830,3832],{"className":3831,"ariaHidden":2576},[2575],[2539,3833,3835,3838],{"className":3834},[2580],[2539,3836],{"className":3837,"style":2585},[2584],[2539,3839,3841,3844],{"className":3840},[2589],[2539,3842,2563],{"className":3843},[2589,2593],[2539,3845,3847],{"className":3846},[2597],[2539,3848,3850,3870],{"className":3849},[2601,2602],[2539,3851,3853,3867],{"className":3852},[2606],[2539,3854,3856],{"className":3855,"style":2842},[2610],[2539,3857,3858,3861],{"style":2614},[2539,3859],{"className":3860,"style":2619},[2618],[2539,3862,3864],{"className":3863},[2623,2624,2625,2626],[2539,3865,2750],{"className":3866},[2589,2593,2626],[2539,3868,2634],{"className":3869},[2633],[2539,3871,3873],{"className":3872},[2606],[2539,3874,3876],{"className":3875,"style":2641},[2610],[2539,3877],{}," not higher than 1.5. Birds can acheive ",[2539,3880,3882,3899],{"className":3881},[2542],[2539,3883,3885],{"className":3884},[2546],[2548,3886,3887],{"xmlns":2550},[2552,3888,3889,3897],{},[2555,3890,3891],{},[2558,3892,3893,3895],{},[2561,3894,2563],{},[2561,3896,2750],{},[2568,3898,3828],{"encoding":2570},[2539,3900,3902],{"className":3901,"ariaHidden":2576},[2575],[2539,3903,3905,3908],{"className":3904},[2580],[2539,3906],{"className":3907,"style":2585},[2584],[2539,3909,3911,3914],{"className":3910},[2589],[2539,3912,2563],{"className":3913},[2589,2593],[2539,3915,3917],{"className":3916},[2597],[2539,3918,3920,3940],{"className":3919},[2601,2602],[2539,3921,3923,3937],{"className":3922},[2606],[2539,3924,3926],{"className":3925,"style":2842},[2610],[2539,3927,3928,3931],{"style":2614},[2539,3929],{"className":3930,"style":2619},[2618],[2539,3932,3934],{"className":3933},[2623,2624,2625,2626],[2539,3935,2750],{"className":3936},[2589,2593,2626],[2539,3938,2634],{"className":3939},[2633],[2539,3941,3943],{"className":3942},[2606],[2539,3944,3946],{"className":3945,"style":2641},[2610],[2539,3947],{}," of up to 4 by using unsteady aerodynamic effects. And the ground effect will substantially boost lift near the ground (duh..). But for this first draft, we'll stick to conservative estimates from airplanes and hang-gliders. The profile lift coefficient is not yet a usable number due to the finite length of the wing and a consequential wingtip vortex. To estimate ",[2539,3950,3952,3969],{"className":3951},[2542],[2539,3953,3955],{"className":3954},[2546],[2548,3956,3957],{"xmlns":2550},[2552,3958,3959,3967],{},[2555,3960,3961],{},[2558,3962,3963,3965],{},[2561,3964,2759],{},[2561,3966,2750],{},[2568,3968,3059],{"encoding":2570},[2539,3970,3972],{"className":3971,"ariaHidden":2576},[2575],[2539,3973,3975,3978],{"className":3974},[2580],[2539,3976],{"className":3977,"style":2822},[2584],[2539,3979,3981,3984],{"className":3980},[2589],[2539,3982,2759],{"className":3983,"style":2829},[2589,2593],[2539,3985,3987],{"className":3986},[2597],[2539,3988,3990,4010],{"className":3989},[2601,2602],[2539,3991,3993,4007],{"className":3992},[2606],[2539,3994,3996],{"className":3995,"style":2842},[2610],[2539,3997,3998,4001],{"style":2845},[2539,3999],{"className":4000,"style":2619},[2618],[2539,4002,4004],{"className":4003},[2623,2624,2625,2626],[2539,4005,2750],{"className":4006},[2589,2593,2626],[2539,4008,2634],{"className":4009},[2633],[2539,4011,4013],{"className":4012},[2606],[2539,4014,4016],{"className":4015,"style":2641},[2610],[2539,4017],{},", one has to first define some wing dimensions.",[11,4020,4021,4022,4052,4053,4094,4095,4052,4125,1305,4165,4196],{},"Let's assume a trapezoid wing with a span ",[2539,4023,4025,4039],{"className":4024},[2542],[2539,4026,4028],{"className":4027},[2546],[2548,4029,4030],{"xmlns":2550},[2552,4031,4032,4037],{},[2555,4033,4034],{},[2561,4035,4036],{},"b",[2568,4038,4036],{"encoding":2570},[2539,4040,4042],{"className":4041,"ariaHidden":2576},[2575],[2539,4043,4045,4049],{"className":4044},[2580],[2539,4046],{"className":4047,"style":4048},[2584],"height:0.6944em;",[2539,4050,4036],{"className":4051},[2589,2593]," of ",[2539,4054,4056,4075],{"className":4055},[2542],[2539,4057,4059],{"className":4058},[2546],[2548,4060,4061],{"xmlns":2550},[2552,4062,4063,4072],{},[2555,4064,4065,4068,4070],{},[2772,4066,4067],{},"12",[3225,4069,3227],{},[2561,4071,3358],{"mathvariant":3232},[2568,4073,4074],{"encoding":2570},"12\\,\\mathrm{m}",[2539,4076,4078],{"className":4077,"ariaHidden":2576},[2575],[2539,4079,4081,4085,4088,4091],{"className":4080},[2580],[2539,4082],{"className":4083,"style":4084},[2584],"height:0.6444em;",[2539,4086,4067],{"className":4087},[2589],[2539,4089],{"className":4090,"style":3256},[2807],[2539,4092,3358],{"className":4093},[2589,3263],", cord length ",[2539,4096,4098,4112],{"className":4097},[2542],[2539,4099,4101],{"className":4100},[2546],[2548,4102,4103],{"xmlns":2550},[2552,4104,4105,4110],{},[2555,4106,4107],{},[2561,4108,4109],{},"r",[2568,4111,4109],{"encoding":2570},[2539,4113,4115],{"className":4114,"ariaHidden":2576},[2575],[2539,4116,4118,4121],{"className":4117},[2580],[2539,4119],{"className":4120,"style":3166},[2584],[2539,4122,4109],{"className":4123,"style":4124},[2589,2593],"margin-right:0.0278em;",[2539,4126,4128,4147],{"className":4127},[2542],[2539,4129,4131],{"className":4130},[2546],[2548,4132,4133],{"xmlns":2550},[2552,4134,4135,4144],{},[2555,4136,4137,4140,4142],{},[2772,4138,4139],{},"1.5",[3225,4141,3227],{},[2561,4143,3358],{"mathvariant":3232},[2568,4145,4146],{"encoding":2570},"1.5\\,\\mathrm{m}",[2539,4148,4150],{"className":4149,"ariaHidden":2576},[2575],[2539,4151,4153,4156,4159,4162],{"className":4152},[2580],[2539,4154],{"className":4155,"style":4084},[2584],[2539,4157,4139],{"className":4158},[2589],[2539,4160],{"className":4161,"style":3256},[2807],[2539,4163,3358],{"className":4164},[2589,3263],[2539,4166,4168,4183],{"className":4167},[2542],[2539,4169,4171],{"className":4170},[2546],[2548,4172,4173],{"xmlns":2550},[2552,4174,4175,4180],{},[2555,4176,4177],{},[2561,4178,4179],{},"δ",[2568,4181,4182],{"encoding":2570},"\\delta",[2539,4184,4186],{"className":4185,"ariaHidden":2576},[2575],[2539,4187,4189,4192],{"className":4188},[2580],[2539,4190],{"className":4191,"style":4048},[2584],[2539,4193,4179],{"className":4194,"style":4195},[2589,2593],"margin-right:0.0379em;"," reduction to 0.3. The resulting wing area is gained by",[2539,4198,4200],{"className":4199},[2734],[2539,4201,4203,4256],{"className":4202},[2542],[2539,4204,4206],{"className":4205},[2546],[2548,4207,4208],{"xmlns":2550,"display":2743},[2552,4209,4210,4253],{},[2555,4211,4212,4214,4216,4218,4220,4224,4226,4229,4231,4233,4235,4238,4240,4242,4245,4247],{},[2561,4213,2787],{},[2752,4215,2754],{},[2561,4217,4036],{},[2752,4219,2764],{},[2752,4221,4223],{"stretchy":4222},"false","(",[2561,4225,4109],{},[2752,4227,4228],{},"+",[2561,4230,4179],{},[2561,4232,4109],{},[2752,4234,2528],{"stretchy":4222},[2561,4236,4237],{"mathvariant":3232},"\u002F",[2772,4239,2774],{},[2752,4241,2754],{},[2772,4243,4244],{},"15.3",[3225,4246,3227],{},[2776,4248,4249,4251],{},[2561,4250,3358],{"mathvariant":3232},[2772,4252,2774],{},[2568,4254,4255],{"encoding":2570},"S = b \\cdot ( r + \\delta r )\u002F2 = 15.3\\,\\mathrm{m^{2}}",[2539,4257,4259,4277,4295,4317,4345],{"className":4258,"ariaHidden":2576},[2575],[2539,4260,4262,4265,4268,4271,4274],{"className":4261},[2580],[2539,4263],{"className":4264,"style":2800},[2584],[2539,4266,2787],{"className":4267,"style":3006},[2589,2593],[2539,4269],{"className":4270,"style":2808},[2807],[2539,4272,2754],{"className":4273},[2812],[2539,4275],{"className":4276,"style":2808},[2807],[2539,4278,4280,4283,4286,4289,4292],{"className":4279},[2580],[2539,4281],{"className":4282,"style":4048},[2584],[2539,4284,4036],{"className":4285},[2589,2593],[2539,4287],{"className":4288,"style":2869},[2807],[2539,4290,2764],{"className":4291},[2873],[2539,4293],{"className":4294,"style":2869},[2807],[2539,4296,4298,4302,4305,4308,4311,4314],{"className":4297},[2580],[2539,4299],{"className":4300,"style":4301},[2584],"height:1em;vertical-align:-0.25em;",[2539,4303,4223],{"className":4304},[2890],[2539,4306,4109],{"className":4307,"style":4124},[2589,2593],[2539,4309],{"className":4310,"style":2869},[2807],[2539,4312,4228],{"className":4313},[2873],[2539,4315],{"className":4316,"style":2869},[2807],[2539,4318,4320,4323,4326,4329,4332,4336,4339,4342],{"className":4319},[2580],[2539,4321],{"className":4322,"style":4301},[2584],[2539,4324,4179],{"className":4325,"style":4195},[2589,2593],[2539,4327,4109],{"className":4328,"style":4124},[2589,2593],[2539,4330,2528],{"className":4331},[2956],[2539,4333,4335],{"className":4334},[2589],"\u002F2",[2539,4337],{"className":4338,"style":2808},[2807],[2539,4340,2754],{"className":4341},[2812],[2539,4343],{"className":4344,"style":2808},[2807],[2539,4346,4348,4351,4354,4357],{"className":4347},[2580],[2539,4349],{"className":4350,"style":2975},[2584],[2539,4352,4244],{"className":4353},[2589],[2539,4355],{"className":4356,"style":3256},[2807],[2539,4358,4360,4363],{"className":4359},[2589],[2539,4361,3358],{"className":4362},[2589,3263],[2539,4364,4366],{"className":4365},[2597],[2539,4367,4369],{"className":4368},[2601],[2539,4370,4372],{"className":4371},[2606],[2539,4373,4375],{"className":4374,"style":2975},[2610],[2539,4376,4377,4380],{"style":2978},[2539,4378],{"className":4379,"style":2619},[2618],[2539,4381,4383],{"className":4382},[2623,2624,2625,2626],[2539,4384,4386],{"className":4385},[2589,2626],[2539,4387,2774],{"className":4388},[2589,3263,2626],[11,4390,4391,4392,4461],{},"With the rough geometry defined, one can estimate ",[2539,4393,4395,4412],{"className":4394},[2542],[2539,4396,4398],{"className":4397},[2546],[2548,4399,4400],{"xmlns":2550},[2552,4401,4402,4410],{},[2555,4403,4404],{},[2558,4405,4406,4408],{},[2561,4407,2759],{},[2561,4409,2750],{},[2568,4411,3059],{"encoding":2570},[2539,4413,4415],{"className":4414,"ariaHidden":2576},[2575],[2539,4416,4418,4421],{"className":4417},[2580],[2539,4419],{"className":4420,"style":2822},[2584],[2539,4422,4424,4427],{"className":4423},[2589],[2539,4425,2759],{"className":4426,"style":2829},[2589,2593],[2539,4428,4430],{"className":4429},[2597],[2539,4431,4433,4453],{"className":4432},[2601,2602],[2539,4434,4436,4450],{"className":4435},[2606],[2539,4437,4439],{"className":4438,"style":2842},[2610],[2539,4440,4441,4444],{"style":2845},[2539,4442],{"className":4443,"style":2619},[2618],[2539,4445,4447],{"className":4446},[2623,2624,2625,2626],[2539,4448,2750],{"className":4449},[2589,2593,2626],[2539,4451,2634],{"className":4452},[2633],[2539,4454,4456],{"className":4455},[2606],[2539,4457,4459],{"className":4458,"style":2641},[2610],[2539,4460],{}," for the finite wingspan. Wing stretch is gained by",[2539,4463,4465],{"className":4464},[2734],[2539,4466,4468,4500],{"className":4467},[2542],[2539,4469,4471],{"className":4470},[2546],[2548,4472,4473],{"xmlns":2550,"display":2743},[2552,4474,4475,4497],{},[2555,4476,4477,4480,4482,4488,4490,4492,4494],{},[2561,4478,4479],{"mathvariant":3232},"Λ",[2752,4481,2754],{},[2776,4483,4484,4486],{},[2561,4485,4036],{},[2772,4487,2774],{},[2561,4489,4237],{"mathvariant":3232},[2561,4491,2787],{},[2752,4493,2754],{},[2772,4495,4496],{},"9.41",[2568,4498,4499],{"encoding":2570},"\\Lambda = b^2\u002FS = 9.41",[2539,4501,4503,4521,4572],{"className":4502,"ariaHidden":2576},[2575],[2539,4504,4506,4509,4512,4515,4518],{"className":4505},[2580],[2539,4507],{"className":4508,"style":2800},[2584],[2539,4510,4479],{"className":4511},[2589],[2539,4513],{"className":4514,"style":2808},[2807],[2539,4516,2754],{"className":4517},[2812],[2539,4519],{"className":4520,"style":2808},[2807],[2539,4522,4524,4528,4557,4560,4563,4566,4569],{"className":4523},[2580],[2539,4525],{"className":4526,"style":4527},[2584],"height:1.1141em;vertical-align:-0.25em;",[2539,4529,4531,4534],{"className":4530},[2589],[2539,4532,4036],{"className":4533},[2589,2593],[2539,4535,4537],{"className":4536},[2597],[2539,4538,4540],{"className":4539},[2601],[2539,4541,4543],{"className":4542},[2606],[2539,4544,4546],{"className":4545,"style":2975},[2610],[2539,4547,4548,4551],{"style":2978},[2539,4549],{"className":4550,"style":2619},[2618],[2539,4552,4554],{"className":4553},[2623,2624,2625,2626],[2539,4555,2774],{"className":4556},[2589,2626],[2539,4558,4237],{"className":4559},[2589],[2539,4561,2787],{"className":4562,"style":3006},[2589,2593],[2539,4564],{"className":4565,"style":2808},[2807],[2539,4567,2754],{"className":4568},[2812],[2539,4570],{"className":4571,"style":2808},[2807],[2539,4573,4575,4578],{"className":4574},[2580],[2539,4576],{"className":4577,"style":4084},[2584],[2539,4579,4496],{"className":4580},[2589],[11,4582,4583,4652],{},[2539,4584,4586,4603],{"className":4585},[2542],[2539,4587,4589],{"className":4588},[2546],[2548,4590,4591],{"xmlns":2550},[2552,4592,4593,4601],{},[2555,4594,4595],{},[2558,4596,4597,4599],{},[2561,4598,2759],{},[2561,4600,2750],{},[2568,4602,3059],{"encoding":2570},[2539,4604,4606],{"className":4605,"ariaHidden":2576},[2575],[2539,4607,4609,4612],{"className":4608},[2580],[2539,4610],{"className":4611,"style":2822},[2584],[2539,4613,4615,4618],{"className":4614},[2589],[2539,4616,2759],{"className":4617,"style":2829},[2589,2593],[2539,4619,4621],{"className":4620},[2597],[2539,4622,4624,4644],{"className":4623},[2601,2602],[2539,4625,4627,4641],{"className":4626},[2606],[2539,4628,4630],{"className":4629,"style":2842},[2610],[2539,4631,4632,4635],{"style":2845},[2539,4633],{"className":4634,"style":2619},[2618],[2539,4636,4638],{"className":4637},[2623,2624,2625,2626],[2539,4639,2750],{"className":4640},[2589,2593,2626],[2539,4642,2634],{"className":4643},[2633],[2539,4645,4647],{"className":4646},[2606],[2539,4648,4650],{"className":4649,"style":2641},[2610],[2539,4651],{}," is then estimated with:",[2539,4654,4656],{"className":4655},[2734],[2539,4657,4659,4702],{"className":4658},[2542],[2539,4660,4662],{"className":4661},[2546],[2548,4663,4664],{"xmlns":2550,"display":2743},[2552,4665,4666,4699],{},[2555,4667,4668,4674,4676,4682,4694,4696],{},[2558,4669,4670,4672],{},[2561,4671,2759],{},[2561,4673,2750],{},[2752,4675,2754],{},[2558,4677,4678,4680],{},[2561,4679,2563],{},[2561,4681,2750],{},[2766,4683,4684,4686],{},[2561,4685,4479],{"mathvariant":3232},[2555,4687,4688,4690,4692],{},[2561,4689,4479],{"mathvariant":3232},[2752,4691,4228],{},[2772,4693,2774],{},[2752,4695,2754],{},[2772,4697,4698],{},"1.24",[2568,4700,4701],{"encoding":2570},"C_L = c_L \\frac{\\Lambda}{\\Lambda + 2} = 1.24",[2539,4703,4705,4760,4892],{"className":4704,"ariaHidden":2576},[2575],[2539,4706,4708,4711,4751,4754,4757],{"className":4707},[2580],[2539,4709],{"className":4710,"style":2822},[2584],[2539,4712,4714,4717],{"className":4713},[2589],[2539,4715,2759],{"className":4716,"style":2829},[2589,2593],[2539,4718,4720],{"className":4719},[2597],[2539,4721,4723,4743],{"className":4722},[2601,2602],[2539,4724,4726,4740],{"className":4725},[2606],[2539,4727,4729],{"className":4728,"style":2842},[2610],[2539,4730,4731,4734],{"style":2845},[2539,4732],{"className":4733,"style":2619},[2618],[2539,4735,4737],{"className":4736},[2623,2624,2625,2626],[2539,4738,2750],{"className":4739},[2589,2593,2626],[2539,4741,2634],{"className":4742},[2633],[2539,4744,4746],{"className":4745},[2606],[2539,4747,4749],{"className":4748,"style":2641},[2610],[2539,4750],{},[2539,4752],{"className":4753,"style":2808},[2807],[2539,4755,2754],{"className":4756},[2812],[2539,4758],{"className":4759,"style":2808},[2807],[2539,4761,4763,4767,4807,4883,4886,4889],{"className":4762},[2580],[2539,4764],{"className":4765,"style":4766},[2584],"height:2.1297em;vertical-align:-0.7693em;",[2539,4768,4770,4773],{"className":4769},[2589],[2539,4771,2563],{"className":4772},[2589,2593],[2539,4774,4776],{"className":4775},[2597],[2539,4777,4779,4799],{"className":4778},[2601,2602],[2539,4780,4782,4796],{"className":4781},[2606],[2539,4783,4785],{"className":4784,"style":2842},[2610],[2539,4786,4787,4790],{"style":2614},[2539,4788],{"className":4789,"style":2619},[2618],[2539,4791,4793],{"className":4792},[2623,2624,2625,2626],[2539,4794,2750],{"className":4795},[2589,2593,2626],[2539,4797,2634],{"className":4798},[2633],[2539,4800,4802],{"className":4801},[2606],[2539,4803,4805],{"className":4804,"style":2641},[2610],[2539,4806],{},[2539,4808,4810,4813,4880],{"className":4809},[2589],[2539,4811],{"className":4812},[2890,2891],[2539,4814,4816],{"className":4815},[2766],[2539,4817,4819,4871],{"className":4818},[2601,2602],[2539,4820,4822,4868],{"className":4821},[2606],[2539,4823,4826,4849,4857],{"className":4824,"style":4825},[2610],"height:1.3603em;",[2539,4827,4828,4831],{"style":2907},[2539,4829],{"className":4830,"style":2911},[2618],[2539,4832,4834,4837,4840,4843,4846],{"className":4833},[2589],[2539,4835,4479],{"className":4836},[2589],[2539,4838],{"className":4839,"style":2869},[2807],[2539,4841,4228],{"className":4842},[2873],[2539,4844],{"className":4845,"style":2869},[2807],[2539,4847,2774],{"className":4848},[2589],[2539,4850,4851,4854],{"style":2920},[2539,4852],{"className":4853,"style":2911},[2618],[2539,4855],{"className":4856,"style":2928},[2927],[2539,4858,4859,4862],{"style":2931},[2539,4860],{"className":4861,"style":2911},[2618],[2539,4863,4865],{"className":4864},[2589],[2539,4866,4479],{"className":4867},[2589],[2539,4869,2634],{"className":4870},[2633],[2539,4872,4874],{"className":4873},[2606],[2539,4875,4878],{"className":4876,"style":4877},[2610],"height:0.7693em;",[2539,4879],{},[2539,4881],{"className":4882},[2956,2891],[2539,4884],{"className":4885,"style":2808},[2807],[2539,4887,2754],{"className":4888},[2812],[2539,4890],{"className":4891,"style":2808},[2807],[2539,4893,4895,4898],{"className":4894},[2580],[2539,4896],{"className":4897,"style":4084},[2584],[2539,4899,4698],{"className":4900},[2589],[82,4902,4904,4905],{"id":4903},"stall-speed-uminu_minumin","Stall speed ",[2539,4906,4908,4934],{"className":4907},[2542],[2539,4909,4911],{"className":4910},[2546],[2548,4912,4913],{"xmlns":2550},[2552,4914,4915,4931],{},[2555,4916,4917],{},[2558,4918,4919,4921],{},[2561,4920,2780],{},[2555,4922,4923,4925,4928],{},[2561,4924,3358],{},[2561,4926,4927],{},"i",[2561,4929,4930],{},"n",[2568,4932,4933],{"encoding":2570},"u_{min}",[2539,4935,4937],{"className":4936,"ariaHidden":2576},[2575],[2539,4938,4940,4943],{"className":4939},[2580],[2539,4941],{"className":4942,"style":2585},[2584],[2539,4944,4946,4949],{"className":4945},[2589],[2539,4947,2780],{"className":4948},[2589,2593],[2539,4950,4952],{"className":4951},[2597],[2539,4953,4955,4980],{"className":4954},[2601,2602],[2539,4956,4958,4977],{"className":4957},[2606],[2539,4959,4962],{"className":4960,"style":4961},[2610],"height:0.3117em;",[2539,4963,4964,4967],{"style":2614},[2539,4965],{"className":4966,"style":2619},[2618],[2539,4968,4970],{"className":4969},[2623,2624,2625,2626],[2539,4971,4973],{"className":4972},[2589,2626],[2539,4974,4976],{"className":4975},[2589,2593,2626],"min",[2539,4978,2634],{"className":4979},[2633],[2539,4981,4983],{"className":4982},[2606],[2539,4984,4986],{"className":4985,"style":2641},[2610],[2539,4987],{},[11,4989,4990,4991,5285,5286,5331,5332,1305,5360,5429],{},"With all necessary values estimated, the stall speed can be calculated from the above lift equation to be ",[2539,4992,4994,5049],{"className":4993},[2542],[2539,4995,4997],{"className":4996},[2546],[2548,4998,4999],{"xmlns":2550},[2552,5000,5001,5046],{},[2555,5002,5003,5015,5017,5020,5022,5028,5030,5033,5035],{},[2558,5004,5005,5007],{},[2561,5006,2780],{},[2555,5008,5009,5011,5013],{},[2561,5010,3358],{},[2561,5012,4927],{},[2561,5014,4930],{},[2752,5016,2754],{},[2772,5018,5019],{},"10.9",[3225,5021,3227],{},[2766,5023,5024,5026],{},[2561,5025,3358],{"mathvariant":3232},[2561,5027,3363],{"mathvariant":3232},[2752,5029,2754],{},[2772,5031,5032],{},"39.2",[3225,5034,3227],{},[2766,5036,5037,5043],{},[2555,5038,5039,5041],{},[2561,5040,3233],{"mathvariant":3232},[2561,5042,3358],{"mathvariant":3232},[2561,5044,5045],{"mathvariant":3232},"h",[2568,5047,5048],{"encoding":2570},"u_{min} = 10.9\\,\\frac{\\mathrm{m}}{\\mathrm{s}} = 39.2\\,\\frac{\\mathrm{km}}{\\mathrm{h}}",[2539,5050,5052,5110,5199],{"className":5051,"ariaHidden":2576},[2575],[2539,5053,5055,5058,5101,5104,5107],{"className":5054},[2580],[2539,5056],{"className":5057,"style":2585},[2584],[2539,5059,5061,5064],{"className":5060},[2589],[2539,5062,2780],{"className":5063},[2589,2593],[2539,5065,5067],{"className":5066},[2597],[2539,5068,5070,5093],{"className":5069},[2601,2602],[2539,5071,5073,5090],{"className":5072},[2606],[2539,5074,5076],{"className":5075,"style":4961},[2610],[2539,5077,5078,5081],{"style":2614},[2539,5079],{"className":5080,"style":2619},[2618],[2539,5082,5084],{"className":5083},[2623,2624,2625,2626],[2539,5085,5087],{"className":5086},[2589,2626],[2539,5088,4976],{"className":5089},[2589,2593,2626],[2539,5091,2634],{"className":5092},[2633],[2539,5094,5096],{"className":5095},[2606],[2539,5097,5099],{"className":5098,"style":2641},[2610],[2539,5100],{},[2539,5102],{"className":5103,"style":2808},[2807],[2539,5105,2754],{"className":5106},[2812],[2539,5108],{"className":5109,"style":2808},[2807],[2539,5111,5113,5116,5119,5122,5190,5193,5196],{"className":5112},[2580],[2539,5114],{"className":5115,"style":3451},[2584],[2539,5117,5019],{"className":5118},[2589],[2539,5120],{"className":5121,"style":3256},[2807],[2539,5123,5125,5128,5187],{"className":5124},[2589],[2539,5126],{"className":5127},[2890,2891],[2539,5129,5131],{"className":5130},[2766],[2539,5132,5134,5179],{"className":5133},[2601,2602],[2539,5135,5137,5176],{"className":5136},[2606],[2539,5138,5140,5154,5162],{"className":5139,"style":3476},[2610],[2539,5141,5142,5145],{"style":3479},[2539,5143],{"className":5144,"style":2911},[2618],[2539,5146,5148],{"className":5147},[2623,2624,2625,2626],[2539,5149,5151],{"className":5150},[2589,2626],[2539,5152,3363],{"className":5153},[2589,3263,2626],[2539,5155,5156,5159],{"style":2920},[2539,5157],{"className":5158,"style":2911},[2618],[2539,5160],{"className":5161,"style":2928},[2927],[2539,5163,5164,5167],{"style":3536},[2539,5165],{"className":5166,"style":2911},[2618],[2539,5168,5170],{"className":5169},[2623,2624,2625,2626],[2539,5171,5173],{"className":5172},[2589,2626],[2539,5174,3358],{"className":5175},[2589,3263,2626],[2539,5177,2634],{"className":5178},[2633],[2539,5180,5182],{"className":5181},[2606],[2539,5183,5185],{"className":5184,"style":3558},[2610],[2539,5186],{},[2539,5188],{"className":5189},[2956,2891],[2539,5191],{"className":5192,"style":2808},[2807],[2539,5194,2754],{"className":5195},[2812],[2539,5197],{"className":5198,"style":2808},[2807],[2539,5200,5202,5206,5209,5212],{"className":5201},[2580],[2539,5203],{"className":5204,"style":5205},[2584],"height:1.2251em;vertical-align:-0.345em;",[2539,5207,5032],{"className":5208},[2589],[2539,5210],{"className":5211,"style":3256},[2807],[2539,5213,5215,5218,5282],{"className":5214},[2589],[2539,5216],{"className":5217},[2890,2891],[2539,5219,5221],{"className":5220},[2766],[2539,5222,5224,5274],{"className":5223},[2601,2602],[2539,5225,5227,5271],{"className":5226},[2606],[2539,5228,5231,5245,5253],{"className":5229,"style":5230},[2610],"height:0.8801em;",[2539,5232,5233,5236],{"style":3479},[2539,5234],{"className":5235,"style":2911},[2618],[2539,5237,5239],{"className":5238},[2623,2624,2625,2626],[2539,5240,5242],{"className":5241},[2589,2626],[2539,5243,5045],{"className":5244},[2589,3263,2626],[2539,5246,5247,5250],{"style":2920},[2539,5248],{"className":5249,"style":2911},[2618],[2539,5251],{"className":5252,"style":2928},[2927],[2539,5254,5255,5258],{"style":3536},[2539,5256],{"className":5257,"style":2911},[2618],[2539,5259,5261],{"className":5260},[2623,2624,2625,2626],[2539,5262,5264],{"className":5263},[2589,2626],[2539,5265,5267],{"className":5266},[2589,2626],[2539,5268,5270],{"className":5269},[2589,3263,2626],"km",[2539,5272,2634],{"className":5273},[2633],[2539,5275,5277],{"className":5276},[2606],[2539,5278,5280],{"className":5279,"style":3558},[2610],[2539,5281],{},[2539,5283],{"className":5284},[2956,2891],". This might seem a lot to run with ",[2539,5287,5289,5310],{"className":5288},[2542],[2539,5290,5292],{"className":5291},[2546],[2548,5293,5294],{"xmlns":2550},[2552,5295,5296,5308],{},[2555,5297,5298,5300,5302],{},[2772,5299,3281],{},[3225,5301,3227],{},[2555,5303,5304,5306],{},[2561,5305,3233],{"mathvariant":3232},[2561,5307,3236],{"mathvariant":3232},[2568,5309,3292],{"encoding":2570},[2539,5311,5313],{"className":5312,"ariaHidden":2576},[2575],[2539,5314,5316,5319,5322,5325],{"className":5315},[2580],[2539,5317],{"className":5318,"style":3249},[2584],[2539,5320,3281],{"className":5321},[2589],[2539,5323],{"className":5324,"style":3256},[2807],[2539,5326,5328],{"className":5327},[2589],[2539,5329,3265],{"className":5330,"style":3264},[2589,3263]," on the back. But keep in mind that the ground effect will cut this down to size. The values for ",[2539,5333,5335,5348],{"className":5334},[2542],[2539,5336,5338],{"className":5337},[2546],[2548,5339,5340],{"xmlns":2550},[2552,5341,5342,5346],{},[2555,5343,5344],{},[2561,5345,2787],{},[2568,5347,2787],{"encoding":2570},[2539,5349,5351],{"className":5350,"ariaHidden":2576},[2575],[2539,5352,5354,5357],{"className":5353},[2580],[2539,5355],{"className":5356,"style":2800},[2584],[2539,5358,2787],{"className":5359,"style":3006},[2589,2593],[2539,5361,5363,5380],{"className":5362},[2542],[2539,5364,5366],{"className":5365},[2546],[2548,5367,5368],{"xmlns":2550},[2552,5369,5370,5378],{},[2555,5371,5372],{},[2558,5373,5374,5376],{},[2561,5375,2759],{},[2561,5377,2750],{},[2568,5379,3059],{"encoding":2570},[2539,5381,5383],{"className":5382,"ariaHidden":2576},[2575],[2539,5384,5386,5389],{"className":5385},[2580],[2539,5387],{"className":5388,"style":2822},[2584],[2539,5390,5392,5395],{"className":5391},[2589],[2539,5393,2759],{"className":5394,"style":2829},[2589,2593],[2539,5396,5398],{"className":5397},[2597],[2539,5399,5401,5421],{"className":5400},[2601,2602],[2539,5402,5404,5418],{"className":5403},[2606],[2539,5405,5407],{"className":5406,"style":2842},[2610],[2539,5408,5409,5412],{"style":2845},[2539,5410],{"className":5411,"style":2619},[2618],[2539,5413,5415],{"className":5414},[2623,2624,2625,2626],[2539,5416,2750],{"className":5417},[2589,2593,2626],[2539,5419,2634],{"className":5420},[2633],[2539,5422,5424],{"className":5423},[2606],[2539,5425,5427],{"className":5426,"style":2641},[2610],[2539,5428],{}," correspond to those of hang gliders, which are quite capable of landing and starting with a similar weight (much heavier pilot, though). Also, just like birds, the system is supposed to be able to flutter. That's a different flight mode though, and will be investigated below.",[74,5431,5433],{"id":5432},"curve-radius","Curve radius",[11,5435,5436],{},"For the concept of a stadium sport, the minimum turning radius is important, as the space is limited. This directly follows from u_min, when a maximum g-force is defined via the centripetal force. We'll assume a conservative estimate of a 3g-turn. The radius then follows as:",[2539,5438,5440],{"className":5439},[2734],[2539,5441,5443,5503],{"className":5442},[2542],[2539,5444,5446],{"className":5445},[2546],[2548,5447,5448],{"xmlns":2550,"display":2743},[2552,5449,5450,5500],{},[2555,5451,5452,5465,5467,5491,5493,5496,5498],{},[2558,5453,5454,5457],{},[2561,5455,5456],{},"R",[2555,5458,5459,5461,5463],{},[2561,5460,3358],{},[2561,5462,4927],{},[2561,5464,4930],{},[2752,5466,2754],{},[2766,5468,5469,5484],{},[5470,5471,5472,5474,5482],"msubsup",{},[2561,5473,2780],{},[2555,5475,5476,5478,5480],{},[2561,5477,3358],{},[2561,5479,4927],{},[2561,5481,4930],{},[2772,5483,2774],{},[2555,5485,5486,5489],{},[2772,5487,5488],{},"3",[2561,5490,3236],{},[2752,5492,2754],{},[2772,5494,5495],{},"4",[3225,5497,3227],{},[2561,5499,3358],{"mathvariant":3232},[2568,5501,5502],{"encoding":2570},"R_{min} = \\frac{u_{min}^2}{3g} = 4\\,\\mathrm{m}",[2539,5504,5506,5566,5705],{"className":5505,"ariaHidden":2576},[2575],[2539,5507,5509,5512,5557,5560,5563],{"className":5508},[2580],[2539,5510],{"className":5511,"style":2822},[2584],[2539,5513,5515,5519],{"className":5514},[2589],[2539,5516,5456],{"className":5517,"style":5518},[2589,2593],"margin-right:0.0077em;",[2539,5520,5522],{"className":5521},[2597],[2539,5523,5525,5549],{"className":5524},[2601,2602],[2539,5526,5528,5546],{"className":5527},[2606],[2539,5529,5531],{"className":5530,"style":4961},[2610],[2539,5532,5534,5537],{"style":5533},"top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;",[2539,5535],{"className":5536,"style":2619},[2618],[2539,5538,5540],{"className":5539},[2623,2624,2625,2626],[2539,5541,5543],{"className":5542},[2589,2626],[2539,5544,4976],{"className":5545},[2589,2593,2626],[2539,5547,2634],{"className":5548},[2633],[2539,5550,5552],{"className":5551},[2606],[2539,5553,5555],{"className":5554,"style":2641},[2610],[2539,5556],{},[2539,5558],{"className":5559,"style":2808},[2807],[2539,5561,2754],{"className":5562},[2812],[2539,5564],{"className":5565,"style":2808},[2807],[2539,5567,5569,5573,5696,5699,5702],{"className":5568},[2580],[2539,5570],{"className":5571,"style":5572},[2584],"height:2.3715em;vertical-align:-0.8804em;",[2539,5574,5576,5579,5693],{"className":5575},[2589],[2539,5577],{"className":5578},[2890,2891],[2539,5580,5582],{"className":5581},[2766],[2539,5583,5585,5684],{"className":5584},[2601,2602],[2539,5586,5588,5681],{"className":5587},[2606],[2539,5589,5592,5607,5615],{"className":5590,"style":5591},[2610],"height:1.4911em;",[2539,5593,5594,5597],{"style":2907},[2539,5595],{"className":5596,"style":2911},[2618],[2539,5598,5600,5603],{"className":5599},[2589],[2539,5601,5488],{"className":5602},[2589],[2539,5604,3236],{"className":5605,"style":5606},[2589,2593],"margin-right:0.0359em;",[2539,5608,5609,5612],{"style":2920},[2539,5610],{"className":5611,"style":2911},[2618],[2539,5613],{"className":5614,"style":2928},[2927],[2539,5616,5617,5620],{"style":2931},[2539,5618],{"className":5619,"style":2911},[2618],[2539,5621,5623],{"className":5622},[2589],[2539,5624,5626,5629],{"className":5625},[2589],[2539,5627,2780],{"className":5628},[2589,2593],[2539,5630,5632],{"className":5631},[2597],[2539,5633,5635,5672],{"className":5634},[2601,2602],[2539,5636,5638,5669],{"className":5637},[2606],[2539,5639,5642,5657],{"className":5640,"style":5641},[2610],"height:0.8141em;",[2539,5643,5645,5648],{"style":5644},"top:-2.4413em;margin-left:0em;margin-right:0.05em;",[2539,5646],{"className":5647,"style":2619},[2618],[2539,5649,5651],{"className":5650},[2623,2624,2625,2626],[2539,5652,5654],{"className":5653},[2589,2626],[2539,5655,4976],{"className":5656},[2589,2593,2626],[2539,5658,5660,5663],{"style":5659},"top:-3.063em;margin-right:0.05em;",[2539,5661],{"className":5662,"style":2619},[2618],[2539,5664,5666],{"className":5665},[2623,2624,2625,2626],[2539,5667,2774],{"className":5668},[2589,2626],[2539,5670,2634],{"className":5671},[2633],[2539,5673,5675],{"className":5674},[2606],[2539,5676,5679],{"className":5677,"style":5678},[2610],"height:0.2587em;",[2539,5680],{},[2539,5682,2634],{"className":5683},[2633],[2539,5685,5687],{"className":5686},[2606],[2539,5688,5691],{"className":5689,"style":5690},[2610],"height:0.8804em;",[2539,5692],{},[2539,5694],{"className":5695},[2956,2891],[2539,5697],{"className":5698,"style":2808},[2807],[2539,5700,2754],{"className":5701},[2812],[2539,5703],{"className":5704,"style":2808},[2807],[2539,5706,5708,5711,5714,5717],{"className":5707},[2580],[2539,5709],{"className":5710,"style":4084},[2584],[2539,5712,5495],{"className":5713},[2589],[2539,5715],{"className":5716,"style":3256},[2807],[2539,5718,3358],{"className":5719},[2589,3263],[11,5721,5722,5723,5763,5764,5803,5804,5842,5843,5882],{},"With common soccer fields having a size of ",[2539,5724,5726,5745],{"className":5725},[2542],[2539,5727,5729],{"className":5728},[2546],[2548,5730,5731],{"xmlns":2550},[2552,5732,5733,5742],{},[2555,5734,5735,5738,5740],{},[2772,5736,5737],{},"100",[3225,5739,3227],{},[2561,5741,3358],{"mathvariant":3232},[2568,5743,5744],{"encoding":2570},"100\\,\\mathrm{m}",[2539,5746,5748],{"className":5747,"ariaHidden":2576},[2575],[2539,5749,5751,5754,5757,5760],{"className":5750},[2580],[2539,5752],{"className":5753,"style":4084},[2584],[2539,5755,5737],{"className":5756},[2589],[2539,5758],{"className":5759,"style":3256},[2807],[2539,5761,3358],{"className":5762},[2589,3263]," times ",[2539,5765,5767,5785],{"className":5766},[2542],[2539,5768,5770],{"className":5769},[2546],[2548,5771,5772],{"xmlns":2550},[2552,5773,5774,5782],{},[2555,5775,5776,5778,5780],{},[2772,5777,3223],{},[3225,5779,3227],{},[2561,5781,3358],{"mathvariant":3232},[2568,5783,5784],{"encoding":2570},"80\\,\\mathrm{m}",[2539,5786,5788],{"className":5787,"ariaHidden":2576},[2575],[2539,5789,5791,5794,5797,5800],{"className":5790},[2580],[2539,5792],{"className":5793,"style":4084},[2584],[2539,5795,3223],{"className":5796},[2589],[2539,5798],{"className":5799,"style":3256},[2807],[2539,5801,3358],{"className":5802},[2589,3263],", this seams feasable with a large margin. N.B.: we are aware that this says nothing about corresponding aerodynamics. With a wingspan of ",[2539,5805,5807,5824],{"className":5806},[2542],[2539,5808,5810],{"className":5809},[2546],[2548,5811,5812],{"xmlns":2550},[2552,5813,5814,5822],{},[2555,5815,5816,5818,5820],{},[2772,5817,4067],{},[3225,5819,3227],{},[2561,5821,3358],{"mathvariant":3232},[2568,5823,4074],{"encoding":2570},[2539,5825,5827],{"className":5826,"ariaHidden":2576},[2575],[2539,5828,5830,5833,5836,5839],{"className":5829},[2580],[2539,5831],{"className":5832,"style":4084},[2584],[2539,5834,4067],{"className":5835},[2589],[2539,5837],{"className":5838,"style":3256},[2807],[2539,5840,3358],{"className":5841},[2589,3263],", a turn of ",[2539,5844,5846,5864],{"className":5845},[2542],[2539,5847,5849],{"className":5848},[2546],[2548,5850,5851],{"xmlns":2550},[2552,5852,5853,5861],{},[2555,5854,5855,5857,5859],{},[2772,5856,5495],{},[3225,5858,3227],{},[2561,5860,3358],{"mathvariant":3232},[2568,5862,5863],{"encoding":2570},"4\\,\\mathrm{m}",[2539,5865,5867],{"className":5866,"ariaHidden":2576},[2575],[2539,5868,5870,5873,5876,5879],{"className":5869},[2580],[2539,5871],{"className":5872,"style":4084},[2584],[2539,5874,5495],{"className":5875},[2589],[2539,5877],{"className":5878,"style":3256},[2807],[2539,5880,3358],{"className":5881},[2589,3263]," seems ambitious, with parts of the inside wings not seeing reversed flow...",[74,5884,5886],{"id":5885},"wing-root-moment-gliding","Wing root moment - gliding",[11,5888,5889,5890,5930,5931,1698],{},"Let's have a quick look onto what kind of moment we would have to generate at the wing root, in order to hold the wing in position. We'll assume an elliptical lift distribution. Birds actually seem to use more of a bell-shaped lift distribution with small negative lift on the wing tip due to twist. But the elliptical distribution yields a more conservative estimate. Assuming a double trapezoid wing, the calculationand a double trapezoid wing, the calculation of the lever of ",[2539,5891,5893,5912],{"className":5892},[2542],[2539,5894,5896],{"className":5895},[2546],[2548,5897,5898],{"xmlns":2550},[2552,5899,5900,5909],{},[2555,5901,5902,5905,5907],{},[2772,5903,5904],{},"2.4",[3225,5906,3227],{},[2561,5908,3358],{"mathvariant":3232},[2568,5910,5911],{"encoding":2570},"2.4\\,\\mathrm{m}",[2539,5913,5915],{"className":5914,"ariaHidden":2576},[2575],[2539,5916,5918,5921,5924,5927],{"className":5917},[2580],[2539,5919],{"className":5920,"style":4084},[2584],[2539,5922,5904],{"className":5923},[2589],[2539,5925],{"className":5926,"style":3256},[2807],[2539,5928,3358],{"className":5929},[2589,3263]," (see details in the calculation package ",[15,5932,469],{"href":468},[11,5934,5935,5936,6059],{},"With half of the weight per wing, one arrives at a root moment of ",[2539,5937,5939,5974],{"className":5938},[2542],[2539,5940,5942],{"className":5941},[2546],[2548,5943,5944],{"xmlns":2550},[2552,5945,5946,5971],{},[2555,5947,5948,5956,5958,5961,5963],{},[2558,5949,5950,5953],{},[2561,5951,5952],{},"M",[2772,5954,5955],{},"0",[2752,5957,2754],{},[2772,5959,5960],{},"1648",[3225,5962,3227],{},[2555,5964,5965,5967,5969],{},[2561,5966,3375],{"mathvariant":3232},[3225,5968,3227],{},[2561,5970,3358],{"mathvariant":3232},[2568,5972,5973],{"encoding":2570},"M_0 = 1648\\,\\mathrm{N\\,m}",[2539,5975,5977,6035],{"className":5976,"ariaHidden":2576},[2575],[2539,5978,5980,5983,6026,6029,6032],{"className":5979},[2580],[2539,5981],{"className":5982,"style":2822},[2584],[2539,5984,5986,5990],{"className":5985},[2589],[2539,5987,5952],{"className":5988,"style":5989},[2589,2593],"margin-right:0.109em;",[2539,5991,5993],{"className":5992},[2597],[2539,5994,5996,6018],{"className":5995},[2601,2602],[2539,5997,5999,6015],{"className":5998},[2606],[2539,6000,6003],{"className":6001,"style":6002},[2610],"height:0.3011em;",[2539,6004,6006,6009],{"style":6005},"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;",[2539,6007],{"className":6008,"style":2619},[2618],[2539,6010,6012],{"className":6011},[2623,2624,2625,2626],[2539,6013,5955],{"className":6014},[2589,2626],[2539,6016,2634],{"className":6017},[2633],[2539,6019,6021],{"className":6020},[2606],[2539,6022,6024],{"className":6023,"style":2641},[2610],[2539,6025],{},[2539,6027],{"className":6028,"style":2808},[2807],[2539,6030,2754],{"className":6031},[2812],[2539,6033],{"className":6034,"style":2808},[2807],[2539,6036,6038,6041,6044,6047],{"className":6037},[2580],[2539,6039],{"className":6040,"style":2800},[2584],[2539,6042,5960],{"className":6043},[2589],[2539,6045],{"className":6046,"style":3256},[2807],[2539,6048,6050,6053,6056],{"className":6049},[2589],[2539,6051,3375],{"className":6052},[2589,3263],[2539,6054],{"className":6055,"style":3256},[2807],[2539,6057,3358],{"className":6058},[2589,3263]," for gliding. This fairly large moment will define the main actuator of the wing actuator system. All other actuators can likely be significantly smaller. Indeed, when looking at the reference of birds, the breast is huge in comparison to all other muscles.",[82,6061,6063],{"id":6062},"actuators-to-produce-the-root-moment","Actuators to produce the root moment",[11,6065,6066],{},"We investigated three different types of possible actors. The first are piezoelectric polymer fibers, which are an interesting concept and have been used in some exoskeleton systems. For the main wing actuators, the force density is too low, though. They might be an interesting option for a soft exoskeleton or other low-force applications.",[11,6068,6069,6070,6120,6121,6169,6170,6217],{},"The second option are small hydraulic cylinders. With a cantilever mechanism and ",[2539,6071,6073,6098],{"className":6072},[2542],[2539,6074,6076],{"className":6075},[2546],[2548,6077,6078],{"xmlns":2550},[2552,6079,6080,6095],{},[2555,6081,6082,6085,6087],{},[2772,6083,6084],{},"150",[3225,6086,3227],{},[2555,6088,6089,6091,6093],{},[2561,6090,4036],{"mathvariant":3232},[2561,6092,15],{"mathvariant":3232},[2561,6094,4109],{"mathvariant":3232},[2568,6096,6097],{"encoding":2570},"150\\,\\mathrm{bar}",[2539,6099,6101],{"className":6100,"ariaHidden":2576},[2575],[2539,6102,6104,6107,6110,6113],{"className":6103},[2580],[2539,6105],{"className":6106,"style":4048},[2584],[2539,6108,6084],{"className":6109},[2589],[2539,6111],{"className":6112,"style":3256},[2807],[2539,6114,6116],{"className":6115},[2589],[2539,6117,6119],{"className":6118},[2589,3263],"bar"," pressure, a cylinder of ",[2539,6122,6124,6147],{"className":6123},[2542],[2539,6125,6127],{"className":6126},[2546],[2548,6128,6129],{"xmlns":2550},[2552,6130,6131,6144],{},[2555,6132,6133,6136,6138],{},[2772,6134,6135],{},"2.6",[3225,6137,3227],{},[2555,6139,6140,6142],{},[2561,6141,2563],{"mathvariant":3232},[2561,6143,3358],{"mathvariant":3232},[2568,6145,6146],{"encoding":2570},"2.6\\,\\mathrm{cm}",[2539,6148,6150],{"className":6149,"ariaHidden":2576},[2575],[2539,6151,6153,6156,6159,6162],{"className":6152},[2580],[2539,6154],{"className":6155,"style":4084},[2584],[2539,6157,6135],{"className":6158},[2589],[2539,6160],{"className":6161,"style":3256},[2807],[2539,6163,6165],{"className":6164},[2589],[2539,6166,6168],{"className":6167},[2589,3263],"cm"," diameter is required. This works in principle with existing technology. The drawback is the large oil volume necessary for the whole system. This alone would add about ",[2539,6171,6173,6196],{"className":6172},[2542],[2539,6174,6176],{"className":6175},[2546],[2548,6177,6178],{"xmlns":2550},[2552,6179,6180,6193],{},[2555,6181,6182,6185,6187],{},[2772,6183,6184],{},"10",[3225,6186,3227],{},[2555,6188,6189,6191],{},[2561,6190,3233],{"mathvariant":3232},[2561,6192,3236],{"mathvariant":3232},[2568,6194,6195],{"encoding":2570},"10\\,\\mathrm{kg}",[2539,6197,6199],{"className":6198,"ariaHidden":2576},[2575],[2539,6200,6202,6205,6208,6211],{"className":6201},[2580],[2539,6203],{"className":6204,"style":3249},[2584],[2539,6206,6184],{"className":6207},[2589],[2539,6209],{"className":6210,"style":3256},[2807],[2539,6212,6214],{"className":6213},[2589],[2539,6215,3265],{"className":6216,"style":3264},[2589,3263]," of weight for the main actuators. The actual cylinder and other systems are not the main weight constituent here, as there are versions made of carbon fibre available. Due to the weight, this option seems undesirable.",[11,6219,6220,6221,6226,6227,6276,6277,6322],{},"The third option is electromotors and a transmission system. Motors of a desirable size, weight and power are commercially available (e.g. ",[15,6222,6225],{"href":6223,"rel":6224},"https:\u002F\u002Fwww.hacker-motor-shop.com\u002FQ100-6M-kv168.htm?a=article&ProdNr=19990626&p=8589",[19],"HACKER Motor Q100-6M kv168"," with ",[2539,6228,6230,6254],{"className":6229},[2542],[2539,6231,6233],{"className":6232},[2546],[2548,6234,6235],{"xmlns":2550},[2552,6236,6237,6251],{},[2555,6238,6239,6242,6244],{},[2772,6240,6241],{},"9.3",[3225,6243,3227],{},[2555,6245,6246,6248],{},[2561,6247,3233],{"mathvariant":3232},[2561,6249,6250],{"mathvariant":3232},"W",[2568,6252,6253],{"encoding":2570},"9.3\\,\\mathrm{kW}",[2539,6255,6257],{"className":6256,"ariaHidden":2576},[2575],[2539,6258,6260,6263,6266,6269],{"className":6259},[2580],[2539,6261],{"className":6262,"style":4048},[2584],[2539,6264,6241],{"className":6265},[2589],[2539,6267],{"className":6268,"style":3256},[2807],[2539,6270,6272],{"className":6271},[2589],[2539,6273,6275],{"className":6274,"style":3264},[2589,3263],"kW"," peak power). They require a good amount of transmission in order to not get too big and heavy. We assumed a transmission ratio of about ",[2539,6278,6280,6301],{"className":6279},[2542],[2539,6281,6283],{"className":6282},[2546],[2548,6284,6285],{"xmlns":2550},[2552,6286,6287,6298],{},[2555,6288,6289,6291,6295],{},[2772,6290,5737],{},[2752,6292,6294],{"lspace":6293,"rspace":6293},"0em",":",[2772,6296,6297],{},"1",[2568,6299,6300],{"encoding":2570},"100{:}1",[2539,6302,6304],{"className":6303,"ariaHidden":2576},[2575],[2539,6305,6307,6310,6313,6319],{"className":6306},[2580],[2539,6308],{"className":6309,"style":4084},[2584],[2539,6311,5737],{"className":6312},[2589],[2539,6314,6316],{"className":6315},[2589],[2539,6317,6294],{"className":6318},[2812],[2539,6320,6297],{"className":6321},[2589],". This transmission can be realized using a harmonic drive (or a cycloidal drive) or a multi-stage belt-and-pulley system. The former is relativeley heavy, so a belt system is probably desirable.",[11,6324,6325,6326],{},"The pictures below are also available in larger format ",[15,6327,469],{"href":468},[11,6329,6330,6334],{},[530,6331],{"alt":6332,"src":6333},"Schulterdesign","\u002Fimages\u002FSchulter_Fluegel.jpg",[530,6335],{"alt":6336,"src":6337},"Kolbenstudien","\u002Fimages\u002FKolbenstudien.jpg",[74,6339,6341],{"id":6340},"structure","Structure",[11,6343,6344],{},"Most of the structure will be made of glass and carbon fibre composites for their lightness and strength. Parts requiring isotropic or very hard materials will be made from metals (Titanium, Aluminium, hardend Steel). The wings are supposed to be partitioned in three, just like bird wings. The parts are named accordingly \"humerus\" for the \"upper arm bone\", \"radius\" or \"ulna\" for the \"lower arm bone\", and \"digitus\" for the \"hand\" structure. In birds, the hand is usually reduced to:",[87,6346,6347,6350],{},[90,6348,6349],{},"a thumb remnant, often controlling the thumb feather as a kind of nose-flap,",[90,6351,6352,6353,6355],{},"a prominent \"index finger\" controlling the hand feathers.\nIn birds, the relatively short humerus protrudes from the shoulder in a backwards sweep. At the elbow, the leading edge angles in the upstream direction. Lastly, at the wrist joint, the short digitus bone and hand feathers sweep backwards again. Most of the outer wing is actually just feathers without an internal bone structure. Probably, because this allows for the nice aerodynamics of the hand wing in flapping and fluttering flight. But also because it keeps the inertia of the wing small during flapping\u002Ffluttering and is thus energy efficient. The length ratios of humerus, radius, and hand wing vary between bird species. Usually, humerus and radius make up about 40 percent of the wing length while the hand wing makes up the rest (see data on birds ",[15,6354,469],{"href":468},"). Thus, the bone-less hand section encompasses a sizable portion of the total wingspan.",[11,6357,6358,6359,6644,6645,6715,6716,6788],{},"A general remark of Berg and Rayner on the wing design: \"The best predictor for the moment of inertia is the product of wing mass and the square of wing length: ",[2539,6360,6362,6425],{"className":6361},[2542],[2539,6363,6365],{"className":6364},[2546],[2548,6366,6367],{"xmlns":2550},[2552,6368,6369,6422],{},[2555,6370,6371,6374,6376,6379,6381,6388,6397,6404,6407,6409,6415,6417,6420],{},[2561,6372,6373],{},"I",[2752,6375,2754],{},[2772,6377,6378],{},"0.118",[2752,6380,4223],{"stretchy":4222},[2558,6382,6383,6385],{},[2561,6384,3358],{},[2561,6386,6387],{},"w",[5470,6389,6390,6393,6395],{},[2561,6391,6392],{},"l",[2561,6394,6387],{},[2772,6396,2774],{},[2776,6398,6399,6401],{},[2752,6400,2528],{"stretchy":4222},[2772,6402,6403],{},"1.04",[3225,6405,6406],{}," ",[2752,6408,4223],{"stretchy":4222},[2776,6410,6411,6413],{},[2561,6412,4109],{},[2772,6414,2774],{},[2752,6416,2754],{},[2772,6418,6419],{},"0.997",[2752,6421,2528],{"stretchy":4222},[2568,6423,6424],{"encoding":2570},"I=0.118(m_w l_w^2)^{1.04}\\ (r^2 =0.997)",[2539,6426,6428,6447,6632],{"className":6427,"ariaHidden":2576},[2575],[2539,6429,6431,6434,6438,6441,6444],{"className":6430},[2580],[2539,6432],{"className":6433,"style":2800},[2584],[2539,6435,6373],{"className":6436,"style":6437},[2589,2593],"margin-right:0.0785em;",[2539,6439],{"className":6440,"style":2808},[2807],[2539,6442,2754],{"className":6443},[2812],[2539,6445],{"className":6446,"style":2808},[2807],[2539,6448,6450,6454,6457,6460,6502,6556,6588,6591,6594,6623,6626,6629],{"className":6449},[2580],[2539,6451],{"className":6452,"style":6453},[2584],"height:1.0641em;vertical-align:-0.25em;",[2539,6455,6378],{"className":6456},[2589],[2539,6458,4223],{"className":6459},[2890],[2539,6461,6463,6466],{"className":6462},[2589],[2539,6464,3358],{"className":6465},[2589,2593],[2539,6467,6469],{"className":6468},[2597],[2539,6470,6472,6494],{"className":6471},[2601,2602],[2539,6473,6475,6491],{"className":6474},[2606],[2539,6476,6479],{"className":6477,"style":6478},[2610],"height:0.1514em;",[2539,6480,6481,6484],{"style":2614},[2539,6482],{"className":6483,"style":2619},[2618],[2539,6485,6487],{"className":6486},[2623,2624,2625,2626],[2539,6488,6387],{"className":6489,"style":6490},[2589,2593,2626],"margin-right:0.0269em;",[2539,6492,2634],{"className":6493},[2633],[2539,6495,6497],{"className":6496},[2606],[2539,6498,6500],{"className":6499,"style":2641},[2610],[2539,6501],{},[2539,6503,6505,6509],{"className":6504},[2589],[2539,6506,6392],{"className":6507,"style":6508},[2589,2593],"margin-right:0.0197em;",[2539,6510,6512],{"className":6511},[2597],[2539,6513,6515,6547],{"className":6514},[2601,2602],[2539,6516,6518,6544],{"className":6517},[2606],[2539,6519,6521,6533],{"className":6520,"style":5641},[2610],[2539,6522,6524,6527],{"style":6523},"top:-2.453em;margin-left:-0.0197em;margin-right:0.05em;",[2539,6525],{"className":6526,"style":2619},[2618],[2539,6528,6530],{"className":6529},[2623,2624,2625,2626],[2539,6531,6387],{"className":6532,"style":6490},[2589,2593,2626],[2539,6534,6535,6538],{"style":5659},[2539,6536],{"className":6537,"style":2619},[2618],[2539,6539,6541],{"className":6540},[2623,2624,2625,2626],[2539,6542,2774],{"className":6543},[2589,2626],[2539,6545,2634],{"className":6546},[2633],[2539,6548,6550],{"className":6549},[2606],[2539,6551,6554],{"className":6552,"style":6553},[2610],"height:0.247em;",[2539,6555],{},[2539,6557,6559,6562],{"className":6558},[2956],[2539,6560,2528],{"className":6561},[2956],[2539,6563,6565],{"className":6564},[2597],[2539,6566,6568],{"className":6567},[2601],[2539,6569,6571],{"className":6570},[2606],[2539,6572,6574],{"className":6573,"style":5641},[2610],[2539,6575,6576,6579],{"style":5659},[2539,6577],{"className":6578,"style":2619},[2618],[2539,6580,6582],{"className":6581},[2623,2624,2625,2626],[2539,6583,6585],{"className":6584},[2589,2626],[2539,6586,6403],{"className":6587},[2589,2626],[2539,6589,6406],{"className":6590},[2807],[2539,6592,4223],{"className":6593},[2890],[2539,6595,6597,6600],{"className":6596},[2589],[2539,6598,4109],{"className":6599,"style":4124},[2589,2593],[2539,6601,6603],{"className":6602},[2597],[2539,6604,6606],{"className":6605},[2601],[2539,6607,6609],{"className":6608},[2606],[2539,6610,6612],{"className":6611,"style":5641},[2610],[2539,6613,6614,6617],{"style":5659},[2539,6615],{"className":6616,"style":2619},[2618],[2539,6618,6620],{"className":6619},[2623,2624,2625,2626],[2539,6621,2774],{"className":6622},[2589,2626],[2539,6624],{"className":6625,"style":2808},[2807],[2539,6627,2754],{"className":6628},[2812],[2539,6630],{"className":6631,"style":2808},[2807],[2539,6633,6635,6638,6641],{"className":6634},[2580],[2539,6636],{"className":6637,"style":4301},[2584],[2539,6639,6419],{"className":6640},[2589],[2539,6642,2528],{"className":6643},[2956]," (Fig. 3B; Table 3). This suggests that the mass distribution of the wings of each bird species reflects a similar compromise between reduction in the cost of beating the wings and maintaining a reasonable stiffness and strength. (",[2539,6646,6648,6666],{"className":6647},[2542],[2539,6649,6651],{"className":6650},[2546],[2548,6652,6653],{"xmlns":2550},[2552,6654,6655,6663],{},[2555,6656,6657],{},[2558,6658,6659,6661],{},[2561,6660,3358],{},[2561,6662,6387],{},[2568,6664,6665],{"encoding":2570},"m_w",[2539,6667,6669],{"className":6668,"ariaHidden":2576},[2575],[2539,6670,6672,6675],{"className":6671},[2580],[2539,6673],{"className":6674,"style":2585},[2584],[2539,6676,6678,6681],{"className":6677},[2589],[2539,6679,3358],{"className":6680},[2589,2593],[2539,6682,6684],{"className":6683},[2597],[2539,6685,6687,6707],{"className":6686},[2601,2602],[2539,6688,6690,6704],{"className":6689},[2606],[2539,6691,6693],{"className":6692,"style":6478},[2610],[2539,6694,6695,6698],{"style":2614},[2539,6696],{"className":6697,"style":2619},[2618],[2539,6699,6701],{"className":6700},[2623,2624,2625,2626],[2539,6702,6387],{"className":6703,"style":6490},[2589,2593,2626],[2539,6705,2634],{"className":6706},[2633],[2539,6708,6710],{"className":6709},[2606],[2539,6711,6713],{"className":6712,"style":2641},[2610],[2539,6714],{},": wing mass, ",[2539,6717,6719,6737],{"className":6718},[2542],[2539,6720,6722],{"className":6721},[2546],[2548,6723,6724],{"xmlns":2550},[2552,6725,6726,6734],{},[2555,6727,6728],{},[2558,6729,6730,6732],{},[2561,6731,6392],{},[2561,6733,6387],{},[2568,6735,6736],{"encoding":2570},"l_w",[2539,6738,6740],{"className":6739,"ariaHidden":2576},[2575],[2539,6741,6743,6747],{"className":6742},[2580],[2539,6744],{"className":6745,"style":6746},[2584],"height:0.8444em;vertical-align:-0.15em;",[2539,6748,6750,6753],{"className":6749},[2589],[2539,6751,6392],{"className":6752,"style":6508},[2589,2593],[2539,6754,6756],{"className":6755},[2597],[2539,6757,6759,6780],{"className":6758},[2601,2602],[2539,6760,6762,6777],{"className":6761},[2606],[2539,6763,6765],{"className":6764,"style":6478},[2610],[2539,6766,6768,6771],{"style":6767},"top:-2.55em;margin-left:-0.0197em;margin-right:0.05em;",[2539,6769],{"className":6770,"style":2619},[2618],[2539,6772,6774],{"className":6773},[2623,2624,2625,2626],[2539,6775,6387],{"className":6776,"style":6490},[2589,2593,2626],[2539,6778,2634],{"className":6779},[2633],[2539,6781,6783],{"className":6782},[2606],[2539,6784,6786],{"className":6785,"style":2641},[2610],[2539,6787],{},": wing length)\" Source: Berg, Rayner - 'The moment of inertia of bird wings and the inertial power requirement for flapping flight'; The Journal of Experimental Biology 198, 1655–1664 (1995)",[11,6790,6791],{},"There are a large number of possible loading conditions resulting from the many degrees of freedom, flight modes, and mission profiles. With our small team of engineers, we had to limit ourself to a rudimentary feasibility analysis. Thus, we only estimated, if the largest required forces can be handled by a CFRP beam. That turned out fine. But for some reason, the docuemnt with that calculation got lost (sorry!). And I'm too busy now to do it again (not sorry). I only could find some data we used for the calculation. So if you're up for it, help yourself:",[87,6793,6794,6797,6955,7110,7214],{},[90,6795,6796],{},"Fibre-volumefraction: 50% (Vacuum infusion)",[90,6798,6799,6800],{},"Epoxyde resin density: ",[2539,6801,6803,6834],{"className":6802},[2542],[2539,6804,6806],{"className":6805},[2546],[2548,6807,6808],{"xmlns":2550},[2552,6809,6810,6831],{},[2555,6811,6812,6815,6817],{},[2772,6813,6814],{},"1.15",[3225,6816,3227],{},[2766,6818,6819,6821],{},[2561,6820,3236],{"mathvariant":3232},[2555,6822,6823,6825],{},[2561,6824,2563],{"mathvariant":3232},[2776,6826,6827,6829],{},[2561,6828,3358],{"mathvariant":3232},[2772,6830,5488],{},[2568,6832,6833],{"encoding":2570},"1.15\\,\\frac{\\mathrm{g}}{\\mathrm{cm^{3}}}",[2539,6835,6837],{"className":6836,"ariaHidden":2576},[2575],[2539,6838,6840,6844,6847,6850],{"className":6839},[2580],[2539,6841],{"className":6842,"style":6843},[2584],"height:1.0925em;vertical-align:-0.345em;",[2539,6845,6814],{"className":6846},[2589],[2539,6848],{"className":6849,"style":3256},[2807],[2539,6851,6853,6856,6952],{"className":6852},[2589],[2539,6854],{"className":6855},[2890,2891],[2539,6857,6859],{"className":6858},[2766],[2539,6860,6862,6944],{"className":6861},[2601,2602],[2539,6863,6865,6941],{"className":6864},[2606],[2539,6866,6869,6918,6926],{"className":6867,"style":6868},[2610],"height:0.7475em;",[2539,6870,6871,6874],{"style":3479},[2539,6872],{"className":6873,"style":2911},[2618],[2539,6875,6877],{"className":6876},[2623,2624,2625,2626],[2539,6878,6880],{"className":6879},[2589,2626],[2539,6881,6883,6886],{"className":6882},[2589,2626],[2539,6884,2563],{"className":6885},[2589,3263,2626],[2539,6887,6889,6892],{"className":6888},[2589,2626],[2539,6890,3358],{"className":6891},[2589,3263,2626],[2539,6893,6895],{"className":6894},[2597],[2539,6896,6898],{"className":6897},[2601],[2539,6899,6901],{"className":6900},[2606],[2539,6902,6904],{"className":6903,"style":3507},[2610],[2539,6905,6906,6909],{"style":3510},[2539,6907],{"className":6908,"style":3514},[2618],[2539,6910,6912],{"className":6911},[2623,3518,3519,2626],[2539,6913,6915],{"className":6914},[2589,2626],[2539,6916,5488],{"className":6917},[2589,3263,2626],[2539,6919,6920,6923],{"style":2920},[2539,6921],{"className":6922,"style":2911},[2618],[2539,6924],{"className":6925,"style":2928},[2927],[2539,6927,6929,6932],{"style":6928},"top:-3.4461em;",[2539,6930],{"className":6931,"style":2911},[2618],[2539,6933,6935],{"className":6934},[2623,2624,2625,2626],[2539,6936,6938],{"className":6937},[2589,2626],[2539,6939,3236],{"className":6940,"style":3264},[2589,3263,2626],[2539,6942,2634],{"className":6943},[2633],[2539,6945,6947],{"className":6946},[2606],[2539,6948,6950],{"className":6949,"style":3558},[2610],[2539,6951],{},[2539,6953],{"className":6954},[2956,2891],[90,6956,6957,6958],{},"Carbon fibre density: ",[2539,6959,6961,6992],{"className":6960},[2542],[2539,6962,6964],{"className":6963},[2546],[2548,6965,6966],{"xmlns":2550},[2552,6967,6968,6989],{},[2555,6969,6970,6973,6975],{},[2772,6971,6972],{},"1.77",[3225,6974,3227],{},[2766,6976,6977,6979],{},[2561,6978,3236],{"mathvariant":3232},[2555,6980,6981,6983],{},[2561,6982,2563],{"mathvariant":3232},[2776,6984,6985,6987],{},[2561,6986,3358],{"mathvariant":3232},[2772,6988,5488],{},[2568,6990,6991],{"encoding":2570},"1.77\\,\\frac{\\mathrm{g}}{\\mathrm{cm^{3}}}",[2539,6993,6995],{"className":6994,"ariaHidden":2576},[2575],[2539,6996,6998,7001,7004,7007],{"className":6997},[2580],[2539,6999],{"className":7000,"style":6843},[2584],[2539,7002,6972],{"className":7003},[2589],[2539,7005],{"className":7006,"style":3256},[2807],[2539,7008,7010,7013,7107],{"className":7009},[2589],[2539,7011],{"className":7012},[2890,2891],[2539,7014,7016],{"className":7015},[2766],[2539,7017,7019,7099],{"className":7018},[2601,2602],[2539,7020,7022,7096],{"className":7021},[2606],[2539,7023,7025,7074,7082],{"className":7024,"style":6868},[2610],[2539,7026,7027,7030],{"style":3479},[2539,7028],{"className":7029,"style":2911},[2618],[2539,7031,7033],{"className":7032},[2623,2624,2625,2626],[2539,7034,7036],{"className":7035},[2589,2626],[2539,7037,7039,7042],{"className":7038},[2589,2626],[2539,7040,2563],{"className":7041},[2589,3263,2626],[2539,7043,7045,7048],{"className":7044},[2589,2626],[2539,7046,3358],{"className":7047},[2589,3263,2626],[2539,7049,7051],{"className":7050},[2597],[2539,7052,7054],{"className":7053},[2601],[2539,7055,7057],{"className":7056},[2606],[2539,7058,7060],{"className":7059,"style":3507},[2610],[2539,7061,7062,7065],{"style":3510},[2539,7063],{"className":7064,"style":3514},[2618],[2539,7066,7068],{"className":7067},[2623,3518,3519,2626],[2539,7069,7071],{"className":7070},[2589,2626],[2539,7072,5488],{"className":7073},[2589,3263,2626],[2539,7075,7076,7079],{"style":2920},[2539,7077],{"className":7078,"style":2911},[2618],[2539,7080],{"className":7081,"style":2928},[2927],[2539,7083,7084,7087],{"style":6928},[2539,7085],{"className":7086,"style":2911},[2618],[2539,7088,7090],{"className":7089},[2623,2624,2625,2626],[2539,7091,7093],{"className":7092},[2589,2626],[2539,7094,3236],{"className":7095,"style":3264},[2589,3263,2626],[2539,7097,2634],{"className":7098},[2633],[2539,7100,7102],{"className":7101},[2606],[2539,7103,7105],{"className":7104,"style":3558},[2610],[2539,7106],{},[2539,7108],{"className":7109},[2956,2891],[90,7111,7112,7113,7164,7165],{},"Tensile strength and modulus laminate: ",[2539,7114,7116,7142],{"className":7115},[2542],[2539,7117,7119],{"className":7118},[2546],[2548,7120,7121],{"xmlns":2550},[2552,7122,7123,7139],{},[2555,7124,7125,7128,7130],{},[2772,7126,7127],{},"820",[3225,7129,3227],{},[2555,7131,7132,7134,7137],{},[2561,7133,5952],{"mathvariant":3232},[2561,7135,7136],{"mathvariant":3232},"P",[2561,7138,15],{"mathvariant":3232},[2568,7140,7141],{"encoding":2570},"820\\,\\mathrm{MPa}",[2539,7143,7145],{"className":7144,"ariaHidden":2576},[2575],[2539,7146,7148,7151,7154,7157],{"className":7147},[2580],[2539,7149],{"className":7150,"style":2800},[2584],[2539,7152,7127],{"className":7153},[2589],[2539,7155],{"className":7156,"style":3256},[2807],[2539,7158,7160],{"className":7159},[2589],[2539,7161,7163],{"className":7162},[2589,3263],"MPa",", ",[2539,7166,7168,7192],{"className":7167},[2542],[2539,7169,7171],{"className":7170},[2546],[2548,7172,7173],{"xmlns":2550},[2552,7174,7175,7189],{},[2555,7176,7177,7179,7181],{},[2772,7178,3281],{},[3225,7180,3227],{},[2555,7182,7183,7185,7187],{},[2561,7184,3333],{"mathvariant":3232},[2561,7186,7136],{"mathvariant":3232},[2561,7188,15],{"mathvariant":3232},[2568,7190,7191],{"encoding":2570},"60\\,\\mathrm{GPa}",[2539,7193,7195],{"className":7194,"ariaHidden":2576},[2575],[2539,7196,7198,7201,7204,7207],{"className":7197},[2580],[2539,7199],{"className":7200,"style":2800},[2584],[2539,7202,3281],{"className":7203},[2589],[2539,7205],{"className":7206,"style":3256},[2807],[2539,7208,7210],{"className":7209},[2589],[2539,7211,7213],{"className":7212},[2589,3263],"GPa",[90,7215,7216,7217,7164,7266,7315,7316,297],{},"Compression strength and modulus laminate: ",[2539,7218,7220,7245],{"className":7219},[2542],[2539,7221,7223],{"className":7222},[2546],[2548,7224,7225],{"xmlns":2550},[2552,7226,7227,7242],{},[2555,7228,7229,7232,7234],{},[2772,7230,7231],{},"635",[3225,7233,3227],{},[2555,7235,7236,7238,7240],{},[2561,7237,5952],{"mathvariant":3232},[2561,7239,7136],{"mathvariant":3232},[2561,7241,15],{"mathvariant":3232},[2568,7243,7244],{"encoding":2570},"635\\,\\mathrm{MPa}",[2539,7246,7248],{"className":7247,"ariaHidden":2576},[2575],[2539,7249,7251,7254,7257,7260],{"className":7250},[2580],[2539,7252],{"className":7253,"style":2800},[2584],[2539,7255,7231],{"className":7256},[2589],[2539,7258],{"className":7259,"style":3256},[2807],[2539,7261,7263],{"className":7262},[2589],[2539,7264,7163],{"className":7265},[2589,3263],[2539,7267,7269,7294],{"className":7268},[2542],[2539,7270,7272],{"className":7271},[2546],[2548,7273,7274],{"xmlns":2550},[2552,7275,7276,7291],{},[2555,7277,7278,7281,7283],{},[2772,7279,7280],{},"54",[3225,7282,3227],{},[2555,7284,7285,7287,7289],{},[2561,7286,3333],{"mathvariant":3232},[2561,7288,7136],{"mathvariant":3232},[2561,7290,15],{"mathvariant":3232},[2568,7292,7293],{"encoding":2570},"54\\,\\mathrm{GPa}",[2539,7295,7297],{"className":7296,"ariaHidden":2576},[2575],[2539,7298,7300,7303,7306,7309],{"className":7299},[2580],[2539,7301],{"className":7302,"style":2800},[2584],[2539,7304,7280],{"className":7305},[2589],[2539,7307],{"className":7308,"style":3256},[2807],[2539,7310,7312],{"className":7311},[2589],[2539,7313,7213],{"className":7314},[2589,3263],"\nThe data for laminate strength is from a fibre\u002Ffabric manufacturer's data sheet and is likely very conservative. For reference: the tensile strength of the fibres is stated to be ",[2539,7317,7319,7344],{"className":7318},[2542],[2539,7320,7322],{"className":7321},[2546],[2548,7323,7324],{"xmlns":2550},[2552,7325,7326,7341],{},[2555,7327,7328,7331,7333],{},[2772,7329,7330],{},"3750",[3225,7332,3227],{},[2555,7334,7335,7337,7339],{},[2561,7336,5952],{"mathvariant":3232},[2561,7338,7136],{"mathvariant":3232},[2561,7340,15],{"mathvariant":3232},[2568,7342,7343],{"encoding":2570},"3750\\,\\mathrm{MPa}",[2539,7345,7347],{"className":7346,"ariaHidden":2576},[2575],[2539,7348,7350,7353,7356,7359],{"className":7349},[2580],[2539,7351],{"className":7352,"style":2800},[2584],[2539,7354,7330],{"className":7355},[2589],[2539,7357],{"className":7358,"style":3256},[2807],[2539,7360,7362],{"className":7361},[2589],[2539,7363,7163],{"className":7364},[2589,3263],[74,7366,7368],{"id":7367},"thrust-powered-flight","Thrust - powered flight",[11,7370,7371],{},"In difference to airplanes, birds generate thrust by flapping and morphing their wings. The aerodynamics of this process are necessarily unsteady. It begs the questions: how is the movement pattern supposed to look like? How fast has the wing to flap and with which amplitude?",[11,7373,7374,7375,7443],{},"To understand the basic ways birds move it is useful to study the literature and slow motion videos. In the mode of steady forward flight, birds flap their stretched-out wings roughly ",[2539,7376,7378,7397],{"className":7377},[2542],[2539,7379,7381],{"className":7380},[2546],[2548,7382,7383],{"xmlns":2550},[2552,7384,7385,7394],{},[2555,7386,7387],{},[2776,7388,7389,7391],{},[2772,7390,3281],{},[2752,7392,7393],{"lspace":6293,"rspace":6293},"∘",[2568,7395,7396],{"encoding":2570},"60^{\\circ}",[2539,7398,7400],{"className":7399,"ariaHidden":2576},[2575],[2539,7401,7403,7407,7411],{"className":7402},[2580],[2539,7404],{"className":7405,"style":7406},[2584],"height:0.6741em;",[2539,7408,7410],{"className":7409},[2589],"6",[2539,7412,7414,7417],{"className":7413},[2589],[2539,7415,5955],{"className":7416},[2589],[2539,7418,7420],{"className":7419},[2597],[2539,7421,7423],{"className":7422},[2601],[2539,7424,7426],{"className":7425},[2606],[2539,7427,7429],{"className":7428,"style":7406},[2610],[2539,7430,7431,7434],{"style":5659},[2539,7432],{"className":7433,"style":2619},[2618],[2539,7435,7437],{"className":7436},[2623,2624,2625,2626],[2539,7438,7440],{"className":7439},[2589,2626],[2539,7441,7393],{"className":7442},[2589,2626]," up and down at max. For long distance flights, this amplitude is lower. Presumably to save energy.\nDuring the downstroke, the wing is twisted forward such that the wing hand (pinion feathers) is turned in the direction of the downward movement. This turns the lift vector forward, producing thrust. During the upstroke, the twist is in the opposite direction, albeit less pronounced. If moved quick enough, the outer wing part actually has inflow coming from slightly above, which results in thrust and downforce on the outer wing part. Birds also move their wings forward and backwards (w.r.t. the direction of flow) during the stroke. This is not strictly necessary to generate thrust, though, and will be ignored for now.",[82,7445,7447],{"id":7446},"flapping-frequency-empirical-research","Flapping Frequency - Empirical Research",[11,7449,7450],{},"How fast should the wings beat? Can a human facilitate that?",[11,7452,7453,7454,7484],{},"To gain an initial estimate of frequency ",[2539,7455,7457,7471],{"className":7456},[2542],[2539,7458,7460],{"className":7459},[2546],[2548,7461,7462],{"xmlns":2550},[2552,7463,7464,7469],{},[2555,7465,7466],{},[2561,7467,7468],{},"f",[2568,7470,7468],{"encoding":2570},[2539,7472,7474],{"className":7473,"ariaHidden":2576},[2575],[2539,7475,7477,7480],{"className":7476},[2580],[2539,7478],{"className":7479,"style":3249},[2584],[2539,7481,7468],{"className":7482,"style":7483},[2589,2593],"margin-right:0.1076em;",", one can look at scaling laws from the literature on birds. Berg and Rayner stated in 1995 two laws:",[87,7486,7487,7588],{},[90,7488,7489],{},[2539,7490,7492,7524],{"className":7491},[2542],[2539,7493,7495],{"className":7494},[2546],[2548,7496,7497],{"xmlns":2550},[2552,7498,7499,7521],{},[2555,7500,7501,7503,7506],{},[2561,7502,7468],{},[2752,7504,7505],{},"∼",[2776,7507,7508,7510],{},[2561,7509,4036],{},[2555,7511,7512,7515,7517,7519],{},[2752,7513,7514],{},"−",[2772,7516,2774],{},[2561,7518,4237],{"mathvariant":3232},[2772,7520,5488],{},[2568,7522,7523],{"encoding":2570},"f \\sim b^{-2\u002F3}",[2539,7525,7527,7545],{"className":7526,"ariaHidden":2576},[2575],[2539,7528,7530,7533,7536,7539,7542],{"className":7529},[2580],[2539,7531],{"className":7532,"style":3249},[2584],[2539,7534,7468],{"className":7535,"style":7483},[2589,2593],[2539,7537],{"className":7538,"style":2808},[2807],[2539,7540,7505],{"className":7541},[2812],[2539,7543],{"className":7544,"style":2808},[2807],[2539,7546,7548,7552],{"className":7547},[2580],[2539,7549],{"className":7550,"style":7551},[2584],"height:0.888em;",[2539,7553,7555,7558],{"className":7554},[2589],[2539,7556,4036],{"className":7557},[2589,2593],[2539,7559,7561],{"className":7560},[2597],[2539,7562,7564],{"className":7563},[2601],[2539,7565,7567],{"className":7566},[2606],[2539,7568,7570],{"className":7569,"style":7551},[2610],[2539,7571,7572,7575],{"style":5659},[2539,7573],{"className":7574,"style":2619},[2618],[2539,7576,7578],{"className":7577},[2623,2624,2625,2626],[2539,7579,7581,7584],{"className":7580},[2589,2626],[2539,7582,7514],{"className":7583},[2589,2626],[2539,7585,7587],{"className":7586},[2589,2626],"2\u002F3",[90,7589,7590],{},[2539,7591,7593,7627],{"className":7592},[2542],[2539,7594,7596],{"className":7595},[2546],[2548,7597,7598],{"xmlns":2550},[2552,7599,7600,7624],{},[2555,7601,7602,7604,7606,7609,7611],{},[2561,7603,7468],{},[2752,7605,2754],{},[2772,7607,7608],{},"1.807",[3225,7610,6406],{},[5470,7612,7613,7615,7617],{},[2561,7614,6392],{},[2561,7616,6387],{},[2555,7618,7619,7621],{},[2752,7620,7514],{},[2772,7622,7623],{},"1.055",[2568,7625,7626],{"encoding":2570},"f = 1.807\\ l_w^{-1.055}",[2539,7628,7630,7648],{"className":7629,"ariaHidden":2576},[2575],[2539,7631,7633,7636,7639,7642,7645],{"className":7632},[2580],[2539,7634],{"className":7635,"style":3249},[2584],[2539,7637,7468],{"className":7638,"style":7483},[2589,2593],[2539,7640],{"className":7641,"style":2808},[2807],[2539,7643,2754],{"className":7644},[2812],[2539,7646],{"className":7647,"style":2808},[2807],[2539,7649,7651,7655,7658,7661],{"className":7650},[2580],[2539,7652],{"className":7653,"style":7654},[2584],"height:1.0611em;vertical-align:-0.247em;",[2539,7656,7608],{"className":7657},[2589],[2539,7659,6406],{"className":7660},[2807],[2539,7662,7664,7667],{"className":7663},[2589],[2539,7665,6392],{"className":7666,"style":6508},[2589,2593],[2539,7668,7670],{"className":7669},[2597],[2539,7671,7673,7710],{"className":7672},[2601,2602],[2539,7674,7676,7707],{"className":7675},[2606],[2539,7677,7679,7690],{"className":7678,"style":5641},[2610],[2539,7680,7681,7684],{"style":6523},[2539,7682],{"className":7683,"style":2619},[2618],[2539,7685,7687],{"className":7686},[2623,2624,2625,2626],[2539,7688,6387],{"className":7689,"style":6490},[2589,2593,2626],[2539,7691,7692,7695],{"style":5659},[2539,7693],{"className":7694,"style":2619},[2618],[2539,7696,7698],{"className":7697},[2623,2624,2625,2626],[2539,7699,7701,7704],{"className":7700},[2589,2626],[2539,7702,7514],{"className":7703},[2589,2626],[2539,7705,7623],{"className":7706},[2589,2626],[2539,7708,2634],{"className":7709},[2633],[2539,7711,7713],{"className":7712},[2606],[2539,7714,7716],{"className":7715,"style":6553},[2610],[2539,7717],{},[11,7719,7720,7721,7749,7750,7819,7820,7856,7857,7892,7893,7931,7932,7982,7983,8030,8031,8078,8079,8126],{},"With the wingspan ",[2539,7722,7724,7737],{"className":7723},[2542],[2539,7725,7727],{"className":7726},[2546],[2548,7728,7729],{"xmlns":2550},[2552,7730,7731,7735],{},[2555,7732,7733],{},[2561,7734,4036],{},[2568,7736,4036],{"encoding":2570},[2539,7738,7740],{"className":7739,"ariaHidden":2576},[2575],[2539,7741,7743,7746],{"className":7742},[2580],[2539,7744],{"className":7745,"style":4048},[2584],[2539,7747,4036],{"className":7748},[2589,2593]," and the wing length ",[2539,7751,7753,7770],{"className":7752},[2542],[2539,7754,7756],{"className":7755},[2546],[2548,7757,7758],{"xmlns":2550},[2552,7759,7760,7768],{},[2555,7761,7762],{},[2558,7763,7764,7766],{},[2561,7765,6392],{},[2561,7767,6387],{},[2568,7769,6736],{"encoding":2570},[2539,7771,7773],{"className":7772,"ariaHidden":2576},[2575],[2539,7774,7776,7779],{"className":7775},[2580],[2539,7777],{"className":7778,"style":6746},[2584],[2539,7780,7782,7785],{"className":7781},[2589],[2539,7783,6392],{"className":7784,"style":6508},[2589,2593],[2539,7786,7788],{"className":7787},[2597],[2539,7789,7791,7811],{"className":7790},[2601,2602],[2539,7792,7794,7808],{"className":7793},[2606],[2539,7795,7797],{"className":7796,"style":6478},[2610],[2539,7798,7799,7802],{"style":6767},[2539,7800],{"className":7801,"style":2619},[2618],[2539,7803,7805],{"className":7804},[2623,2624,2625,2626],[2539,7806,6387],{"className":7807,"style":6490},[2589,2593,2626],[2539,7809,2634],{"className":7810},[2633],[2539,7812,7814],{"className":7813},[2606],[2539,7815,7817],{"className":7816,"style":2641},[2610],[2539,7818],{},". The exponent of the latter equation actually had a 95% fiduciary interval from ",[2539,7821,7823,7840],{"className":7822},[2542],[2539,7824,7826],{"className":7825},[2546],[2548,7827,7828],{"xmlns":2550},[2552,7829,7830,7837],{},[2555,7831,7832,7834],{},[2752,7833,7514],{},[2772,7835,7836],{},"1.29",[2568,7838,7839],{"encoding":2570},"-1.29",[2539,7841,7843],{"className":7842,"ariaHidden":2576},[2575],[2539,7844,7846,7850,7853],{"className":7845},[2580],[2539,7847],{"className":7848,"style":7849},[2584],"height:0.7278em;vertical-align:-0.0833em;",[2539,7851,7514],{"className":7852},[2589],[2539,7854,7836],{"className":7855},[2589]," to ",[2539,7858,7860,7877],{"className":7859},[2542],[2539,7861,7863],{"className":7862},[2546],[2548,7864,7865],{"xmlns":2550},[2552,7866,7867,7874],{},[2555,7868,7869,7871],{},[2752,7870,7514],{},[2772,7872,7873],{},"0.86",[2568,7875,7876],{"encoding":2570},"-0.86",[2539,7878,7880],{"className":7879,"ariaHidden":2576},[2575],[2539,7881,7883,7886,7889],{"className":7882},[2580],[2539,7884],{"className":7885,"style":7849},[2584],[2539,7887,7514],{"className":7888},[2589],[2539,7890,7873],{"className":7891},[2589],". Assuming a wingspan of ",[2539,7894,7896,7913],{"className":7895},[2542],[2539,7897,7899],{"className":7898},[2546],[2548,7900,7901],{"xmlns":2550},[2552,7902,7903,7911],{},[2555,7904,7905,7907,7909],{},[2772,7906,4067],{},[3225,7908,3227],{},[2561,7910,3358],{"mathvariant":3232},[2568,7912,4074],{"encoding":2570},[2539,7914,7916],{"className":7915,"ariaHidden":2576},[2575],[2539,7917,7919,7922,7925,7928],{"className":7918},[2580],[2539,7920],{"className":7921,"style":4084},[2584],[2539,7923,4067],{"className":7924},[2589],[2539,7926],{"className":7927,"style":3256},[2807],[2539,7929,3358],{"className":7930},[2589,3263],", the frequencies become ",[2539,7933,7935,7960],{"className":7934},[2542],[2539,7936,7938],{"className":7937},[2546],[2548,7939,7940],{"xmlns":2550},[2552,7941,7942,7957],{},[2555,7943,7944,7947,7949],{},[2772,7945,7946],{},"0.19",[3225,7948,3227],{},[2555,7950,7951,7954],{},[2561,7952,7953],{"mathvariant":3232},"H",[2561,7955,7956],{"mathvariant":3232},"z",[2568,7958,7959],{"encoding":2570},"0.19\\,\\mathrm{Hz}",[2539,7961,7963],{"className":7962,"ariaHidden":2576},[2575],[2539,7964,7966,7969,7972,7975],{"className":7965},[2580],[2539,7967],{"className":7968,"style":2800},[2584],[2539,7970,7946],{"className":7971},[2589],[2539,7973],{"className":7974,"style":3256},[2807],[2539,7976,7978],{"className":7977},[2589],[2539,7979,7981],{"className":7980},[2589,3263],"Hz"," for the first equation and ",[2539,7984,7986,8009],{"className":7985},[2542],[2539,7987,7989],{"className":7988},[2546],[2548,7990,7991],{"xmlns":2550},[2552,7992,7993,8006],{},[2555,7994,7995,7998,8000],{},[2772,7996,7997],{},"0.2729",[3225,7999,3227],{},[2555,8001,8002,8004],{},[2561,8003,7953],{"mathvariant":3232},[2561,8005,7956],{"mathvariant":3232},[2568,8007,8008],{"encoding":2570},"0.2729\\,\\mathrm{Hz}",[2539,8010,8012],{"className":8011,"ariaHidden":2576},[2575],[2539,8013,8015,8018,8021,8024],{"className":8014},[2580],[2539,8016],{"className":8017,"style":2800},[2584],[2539,8019,7997],{"className":8020},[2589],[2539,8022],{"className":8023,"style":3256},[2807],[2539,8025,8027],{"className":8026},[2589],[2539,8028,7981],{"className":8029},[2589,3263]," (",[2539,8032,8034,8057],{"className":8033},[2542],[2539,8035,8037],{"className":8036},[2546],[2548,8038,8039],{"xmlns":2550},[2552,8040,8041,8054],{},[2555,8042,8043,8046,8048],{},[2772,8044,8045],{},"0.179",[3225,8047,3227],{},[2555,8049,8050,8052],{},[2561,8051,7953],{"mathvariant":3232},[2561,8053,7956],{"mathvariant":3232},[2568,8055,8056],{"encoding":2570},"0.179\\,\\mathrm{Hz}",[2539,8058,8060],{"className":8059,"ariaHidden":2576},[2575],[2539,8061,8063,8066,8069,8072],{"className":8062},[2580],[2539,8064],{"className":8065,"style":2800},[2584],[2539,8067,8045],{"className":8068},[2589],[2539,8070],{"className":8071,"style":3256},[2807],[2539,8073,8075],{"className":8074},[2589],[2539,8076,7981],{"className":8077},[2589,3263],"–",[2539,8080,8082,8105],{"className":8081},[2542],[2539,8083,8085],{"className":8084},[2546],[2548,8086,8087],{"xmlns":2550},[2552,8088,8089,8102],{},[2555,8090,8091,8094,8096],{},[2772,8092,8093],{},"0.387",[3225,8095,3227],{},[2555,8097,8098,8100],{},[2561,8099,7953],{"mathvariant":3232},[2561,8101,7956],{"mathvariant":3232},[2568,8103,8104],{"encoding":2570},"0.387\\,\\mathrm{Hz}",[2539,8106,8108],{"className":8107,"ariaHidden":2576},[2575],[2539,8109,8111,8114,8117,8120],{"className":8110},[2580],[2539,8112],{"className":8113,"style":2800},[2584],[2539,8115,8093],{"className":8116},[2589],[2539,8118],{"className":8119,"style":3256},[2807],[2539,8121,8123],{"className":8122},[2589],[2539,8124,7981],{"className":8125},[2589,3263],") for the second.",[11,8128,8129,8130,8245,8246,297],{},"Another scaling law is by Greenwalt from 1962: ",[2539,8131,8133,8161],{"className":8132},[2542],[2539,8134,8136],{"className":8135},[2546],[2548,8137,8138],{"xmlns":2550},[2552,8139,8140,8158],{},[2555,8141,8142,8144,8146],{},[2561,8143,7468],{},[2752,8145,7505],{},[5470,8147,8148,8150,8152],{},[2561,8149,6392],{},[2561,8151,6387],{},[2555,8153,8154,8156],{},[2752,8155,7514],{},[2772,8157,6814],{},[2568,8159,8160],{"encoding":2570},"f \\sim l_w^{-1.15}",[2539,8162,8164,8182],{"className":8163,"ariaHidden":2576},[2575],[2539,8165,8167,8170,8173,8176,8179],{"className":8166},[2580],[2539,8168],{"className":8169,"style":3249},[2584],[2539,8171,7468],{"className":8172,"style":7483},[2589,2593],[2539,8174],{"className":8175,"style":2808},[2807],[2539,8177,7505],{"className":8178},[2812],[2539,8180],{"className":8181,"style":2808},[2807],[2539,8183,8185,8188],{"className":8184},[2580],[2539,8186],{"className":8187,"style":7654},[2584],[2539,8189,8191,8194],{"className":8190},[2589],[2539,8192,6392],{"className":8193,"style":6508},[2589,2593],[2539,8195,8197],{"className":8196},[2597],[2539,8198,8200,8237],{"className":8199},[2601,2602],[2539,8201,8203,8234],{"className":8202},[2606],[2539,8204,8206,8217],{"className":8205,"style":5641},[2610],[2539,8207,8208,8211],{"style":6523},[2539,8209],{"className":8210,"style":2619},[2618],[2539,8212,8214],{"className":8213},[2623,2624,2625,2626],[2539,8215,6387],{"className":8216,"style":6490},[2589,2593,2626],[2539,8218,8219,8222],{"style":5659},[2539,8220],{"className":8221,"style":2619},[2618],[2539,8223,8225],{"className":8224},[2623,2624,2625,2626],[2539,8226,8228,8231],{"className":8227},[2589,2626],[2539,8229,7514],{"className":8230},[2589,2626],[2539,8232,6814],{"className":8233},[2589,2626],[2539,8235,2634],{"className":8236},[2633],[2539,8238,8240],{"className":8239},[2606],[2539,8241,8243],{"className":8242,"style":6553},[2610],[2539,8244],{},". This yields a frequency of ",[2539,8247,8249,8272],{"className":8248},[2542],[2539,8250,8252],{"className":8251},[2546],[2548,8253,8254],{"xmlns":2550},[2552,8255,8256,8269],{},[2555,8257,8258,8261,8263],{},[2772,8259,8260],{},"0.127",[3225,8262,3227],{},[2555,8264,8265,8267],{},[2561,8266,7953],{"mathvariant":3232},[2561,8268,7956],{"mathvariant":3232},[2568,8270,8271],{"encoding":2570},"0.127\\,\\mathrm{Hz}",[2539,8273,8275],{"className":8274,"ariaHidden":2576},[2575],[2539,8276,8278,8281,8284,8287],{"className":8277},[2580],[2539,8279],{"className":8280,"style":2800},[2584],[2539,8282,8260],{"className":8283},[2589],[2539,8285],{"className":8286,"style":3256},[2807],[2539,8288,8290],{"className":8289},[2589],[2539,8291,7981],{"className":8292},[2589,3263],[11,8294,8295],{},"These frequencies are quite attainable by humans flapping their arms.",[82,8297,8299],{"id":8298},"theory-of-thrust-generation","Theory of Thrust Generation",[11,8301,8302,8303,297],{},"The correct relative amplitudes and phase angles of the flapping movement can be derived using potential theory. This has been worked out since 1935 when Theodorsen wrote his paper on flutter. In 1992 Dr. Wolfgang Send picked up this thread. His work describes a 2-dimensional profile undergoing plunging and rotating motion with potential theory. He calls this the bending\u002Ftorsional drive. Roughly speaking, bending means here the flapping of the wing around its root, while torsion means the changes of the angle of incidence of the wing(part). The theory was successfully applied in the ",[15,8304,8306],{"href":1367,"rel":8305},[19],"Festo Smart Bird",[11,8308,8309,8310,8377],{},"The upshot of the theory is that the wing tip twist has a phase lag of approximately ",[2539,8311,8313,8332],{"className":8312},[2542],[2539,8314,8316],{"className":8315},[2546],[2548,8317,8318],{"xmlns":2550},[2552,8319,8320,8329],{},[2555,8321,8322],{},[2776,8323,8324,8327],{},[2772,8325,8326],{},"90",[2752,8328,7393],{"lspace":6293,"rspace":6293},[2568,8330,8331],{"encoding":2570},"90^{\\circ}",[2539,8333,8335],{"className":8334,"ariaHidden":2576},[2575],[2539,8336,8338,8341,8345],{"className":8337},[2580],[2539,8339],{"className":8340,"style":7406},[2584],[2539,8342,8344],{"className":8343},[2589],"9",[2539,8346,8348,8351],{"className":8347},[2589],[2539,8349,5955],{"className":8350},[2589],[2539,8352,8354],{"className":8353},[2597],[2539,8355,8357],{"className":8356},[2601],[2539,8358,8360],{"className":8359},[2606],[2539,8361,8363],{"className":8362,"style":7406},[2610],[2539,8364,8365,8368],{"style":5659},[2539,8366],{"className":8367,"style":2619},[2618],[2539,8369,8371],{"className":8370},[2623,2624,2625,2626],[2539,8372,8374],{"className":8373},[2589,2626],[2539,8375,7393],{"className":8376},[2589,2626]," with respect to the flapping. So when the wing starts to flap downwards, the chord is horizontal. Half of the downstroke the wing tip points downwards. And at the end of the downstroke, the chord is horizontal again.",[11,8379,8380],{},"As the flow at the wing changes with flapping frequency and amplitude. In order to achieve thrust, the correct movement pattern has to be executed to get the correct incident flow.",[82,8382,8384],{"id":8383},"movement-parameters-and-dimensionless-numbers","Movement Parameters and Dimensionless Numbers",[11,8386,8387,8388,8457,8458,8520],{},"Let's assume first, we would first choose a flapping frequency ",[2539,8389,8391,8418],{"className":8390},[2542],[2539,8392,8394],{"className":8393},[2546],[2548,8395,8396],{"xmlns":2550},[2552,8397,8398,8415],{},[2555,8399,8400,8402,8404,8407,8409],{},[2561,8401,7468],{},[2752,8403,2754],{},[2772,8405,8406],{},"1.2",[3225,8408,3227],{},[2555,8410,8411,8413],{},[2561,8412,7953],{"mathvariant":3232},[2561,8414,7956],{"mathvariant":3232},[2568,8416,8417],{"encoding":2570},"f = 1.2\\,\\mathrm{Hz}",[2539,8419,8421,8439],{"className":8420,"ariaHidden":2576},[2575],[2539,8422,8424,8427,8430,8433,8436],{"className":8423},[2580],[2539,8425],{"className":8426,"style":3249},[2584],[2539,8428,7468],{"className":8429,"style":7483},[2589,2593],[2539,8431],{"className":8432,"style":2808},[2807],[2539,8434,2754],{"className":8435},[2812],[2539,8437],{"className":8438,"style":2808},[2807],[2539,8440,8442,8445,8448,8451],{"className":8441},[2580],[2539,8443],{"className":8444,"style":2800},[2584],[2539,8446,8406],{"className":8447},[2589],[2539,8449],{"className":8450,"style":3256},[2807],[2539,8452,8454],{"className":8453},[2589],[2539,8455,7981],{"className":8456},[2589,3263]," (because that is about the maximum what we could do with our arms). Then a parameter called the reduced frequency ",[2539,8459,8461,8481],{"className":8460},[2542],[2539,8462,8464],{"className":8463},[2546],[2548,8465,8466],{"xmlns":2550},[2552,8467,8468,8478],{},[2555,8469,8470],{},[2776,8471,8472,8475],{},[2561,8473,8474],{},"ω",[2752,8476,8477],{},"∗",[2568,8479,8480],{"encoding":2570},"\\omega^*",[2539,8482,8484],{"className":8483,"ariaHidden":2576},[2575],[2539,8485,8487,8491],{"className":8486},[2580],[2539,8488],{"className":8489,"style":8490},[2584],"height:0.6887em;",[2539,8492,8494,8497],{"className":8493},[2589],[2539,8495,8474],{"className":8496,"style":5606},[2589,2593],[2539,8498,8500],{"className":8499},[2597],[2539,8501,8503],{"className":8502},[2601],[2539,8504,8506],{"className":8505},[2606],[2539,8507,8509],{"className":8508,"style":8490},[2610],[2539,8510,8511,8514],{"style":5659},[2539,8512],{"className":8513,"style":2619},[2618],[2539,8515,8517],{"className":8516},[2623,2624,2625,2626],[2539,8518,8477],{"className":8519},[2873,2626]," can be calculated as follows:",[2539,8522,8524],{"className":8523},[2734],[2539,8525,8527,8579],{"className":8526},[2542],[2539,8528,8530],{"className":8529},[2546],[2548,8531,8532],{"xmlns":2550,"display":2743},[2552,8533,8534,8576],{},[2555,8535,8536,8542,8544,8571,8573],{},[2776,8537,8538,8540],{},[2561,8539,8474],{},[2752,8541,8477],{},[2752,8543,2754],{},[2766,8545,8546,8569],{},[2555,8547,8548,8550,8553,8555,8557,8559,8561,8563,8565,8567],{},[2772,8549,2774],{},[2561,8551,8552],{},"π",[2752,8554,2764],{},[2561,8556,7468],{},[2752,8558,2764],{},[2752,8560,4223],{"stretchy":4222},[2561,8562,2563],{},[2561,8564,4237],{"mathvariant":3232},[2772,8566,2774],{},[2752,8568,2528],{"stretchy":4222},[2561,8570,2780],{},[2752,8572,2754],{},[2772,8574,8575],{},"0.24",[2568,8577,8578],{"encoding":2570},"\\omega^* = \\frac{2\\pi\\cdot f \\cdot (c\u002F2)}{u} = 0.24",[2539,8580,8582,8627,8742],{"className":8581,"ariaHidden":2576},[2575],[2539,8583,8585,8589,8618,8621,8624],{"className":8584},[2580],[2539,8586],{"className":8587,"style":8588},[2584],"height:0.7387em;",[2539,8590,8592,8595],{"className":8591},[2589],[2539,8593,8474],{"className":8594,"style":5606},[2589,2593],[2539,8596,8598],{"className":8597},[2597],[2539,8599,8601],{"className":8600},[2601],[2539,8602,8604],{"className":8603},[2606],[2539,8605,8607],{"className":8606,"style":8588},[2610],[2539,8608,8609,8612],{"style":2978},[2539,8610],{"className":8611,"style":2619},[2618],[2539,8613,8615],{"className":8614},[2623,2624,2625,2626],[2539,8616,8477],{"className":8617},[2873,2626],[2539,8619],{"className":8620,"style":2808},[2807],[2539,8622,2754],{"className":8623},[2812],[2539,8625],{"className":8626,"style":2808},[2807],[2539,8628,8630,8634,8733,8736,8739],{"className":8629},[2580],[2539,8631],{"className":8632,"style":8633},[2584],"height:2.113em;vertical-align:-0.686em;",[2539,8635,8637,8640,8730],{"className":8636},[2589],[2539,8638],{"className":8639},[2890,2891],[2539,8641,8643],{"className":8642},[2766],[2539,8644,8646,8722],{"className":8645},[2601,2602],[2539,8647,8649,8719],{"className":8648},[2606],[2539,8650,8653,8664,8672],{"className":8651,"style":8652},[2610],"height:1.427em;",[2539,8654,8655,8658],{"style":2907},[2539,8656],{"className":8657,"style":2911},[2618],[2539,8659,8661],{"className":8660},[2589],[2539,8662,2780],{"className":8663},[2589,2593],[2539,8665,8666,8669],{"style":2920},[2539,8667],{"className":8668,"style":2911},[2618],[2539,8670],{"className":8671,"style":2928},[2927],[2539,8673,8674,8677],{"style":2931},[2539,8675],{"className":8676,"style":2911},[2618],[2539,8678,8680,8683,8686,8689,8692,8695,8698,8701,8704,8707,8710,8713,8716],{"className":8679},[2589],[2539,8681,2774],{"className":8682},[2589],[2539,8684,8552],{"className":8685,"style":5606},[2589,2593],[2539,8687],{"className":8688,"style":2869},[2807],[2539,8690,2764],{"className":8691},[2873],[2539,8693],{"className":8694,"style":2869},[2807],[2539,8696,7468],{"className":8697,"style":7483},[2589,2593],[2539,8699],{"className":8700,"style":2869},[2807],[2539,8702,2764],{"className":8703},[2873],[2539,8705],{"className":8706,"style":2869},[2807],[2539,8708,4223],{"className":8709},[2890],[2539,8711,2563],{"className":8712},[2589,2593],[2539,8714,4335],{"className":8715},[2589],[2539,8717,2528],{"className":8718},[2956],[2539,8720,2634],{"className":8721},[2633],[2539,8723,8725],{"className":8724},[2606],[2539,8726,8728],{"className":8727,"style":2950},[2610],[2539,8729],{},[2539,8731],{"className":8732},[2956,2891],[2539,8734],{"className":8735,"style":2808},[2807],[2539,8737,2754],{"className":8738},[2812],[2539,8740],{"className":8741,"style":2808},[2807],[2539,8743,8745,8748],{"className":8744},[2580],[2539,8746],{"className":8747,"style":4084},[2584],[2539,8749,8575],{"className":8750},[2589],[11,8752,8753,8754,8815,8816,8844,8845,6294],{},"where ",[2539,8755,8757,8779],{"className":8756},[2542],[2539,8758,8760],{"className":8759},[2546],[2548,8761,8762],{"xmlns":2550},[2552,8763,8764,8776],{},[2555,8765,8766,8768,8770,8772,8774],{},[2561,8767,2563],{},[2752,8769,2754],{},[2561,8771,2787],{},[2561,8773,4237],{"mathvariant":3232},[2561,8775,4036],{},[2568,8777,8778],{"encoding":2570},"c = S\u002Fb",[2539,8780,8782,8800],{"className":8781,"ariaHidden":2576},[2575],[2539,8783,8785,8788,8791,8794,8797],{"className":8784},[2580],[2539,8786],{"className":8787,"style":3166},[2584],[2539,8789,2563],{"className":8790},[2589,2593],[2539,8792],{"className":8793,"style":2808},[2807],[2539,8795,2754],{"className":8796},[2812],[2539,8798],{"className":8799,"style":2808},[2807],[2539,8801,8803,8806,8809,8812],{"className":8802},[2580],[2539,8804],{"className":8805,"style":4301},[2584],[2539,8807,2787],{"className":8808,"style":3006},[2589,2593],[2539,8810,4237],{"className":8811},[2589],[2539,8813,4036],{"className":8814},[2589,2593]," is the average chord length, and ",[2539,8817,8819,8832],{"className":8818},[2542],[2539,8820,8822],{"className":8821},[2546],[2548,8823,8824],{"xmlns":2550},[2552,8825,8826,8830],{},[2555,8827,8828],{},[2561,8829,2780],{},[2568,8831,2780],{"encoding":2570},[2539,8833,8835],{"className":8834,"ariaHidden":2576},[2575],[2539,8836,8838,8841],{"className":8837},[2580],[2539,8839],{"className":8840,"style":3166},[2584],[2539,8842,2780],{"className":8843},[2589,2593]," the free stream velocity.\nThis number relates the downward motion to the forward motion. If this motion is supposed to be aerodynamically efficient and produce thrust, the flapping speed and wing twist have to fit together. This is captured by the approximated relation of the figure of merit ",[2539,8846,8848,8863],{"className":8847},[2542],[2539,8849,8851],{"className":8850},[2546],[2548,8852,8853],{"xmlns":2550},[2552,8854,8855,8860],{},[2555,8856,8857],{},[2561,8858,8859],{},"η",[2568,8861,8862],{"encoding":2570},"\\eta",[2539,8864,8866],{"className":8865,"ariaHidden":2576},[2575],[2539,8867,8869,8872],{"className":8868},[2580],[2539,8870],{"className":8871,"style":3136},[2584],[2539,8873,8859],{"className":8874,"style":5606},[2589,2593],[2539,8876,8878],{"className":8877},[2734],[2539,8879,8881,8914],{"className":8880},[2542],[2539,8882,8884],{"className":8883},[2546],[2548,8885,8886],{"xmlns":2550,"display":2743},[2552,8887,8888,8911],{},[2555,8889,8890,8892,8894],{},[2561,8891,8859],{},[2752,8893,2754],{},[2766,8895,8896,8898],{},[2772,8897,6297],{},[2555,8899,8900,8906,8908],{},[2776,8901,8902,8904],{},[2561,8903,8474],{},[2752,8905,8477],{},[2752,8907,2764],{},[2561,8909,8910],{},"λ",[2568,8912,8913],{"encoding":2570},"\\eta = \\frac{1}{\\omega^* \\cdot \\lambda}",[2539,8915,8917,8935],{"className":8916,"ariaHidden":2576},[2575],[2539,8918,8920,8923,8926,8929,8932],{"className":8919},[2580],[2539,8921],{"className":8922,"style":3136},[2584],[2539,8924,8859],{"className":8925,"style":5606},[2589,2593],[2539,8927],{"className":8928,"style":2808},[2807],[2539,8930,2754],{"className":8931},[2812],[2539,8933],{"className":8934,"style":2808},[2807],[2539,8936,8938,8942],{"className":8937},[2580],[2539,8939],{"className":8940,"style":8941},[2584],"height:2.0074em;vertical-align:-0.686em;",[2539,8943,8945,8948,9042],{"className":8944},[2589],[2539,8946],{"className":8947},[2890,2891],[2539,8949,8951],{"className":8950},[2766],[2539,8952,8954,9034],{"className":8953},[2601,2602],[2539,8955,8957,9031],{"className":8956},[2606],[2539,8958,8961,9012,9020],{"className":8959,"style":8960},[2610],"height:1.3214em;",[2539,8962,8963,8966],{"style":2907},[2539,8964],{"className":8965,"style":2911},[2618],[2539,8967,8969,9000,9003,9006,9009],{"className":8968},[2589],[2539,8970,8972,8975],{"className":8971},[2589],[2539,8973,8474],{"className":8974,"style":5606},[2589,2593],[2539,8976,8978],{"className":8977},[2597],[2539,8979,8981],{"className":8980},[2601],[2539,8982,8984],{"className":8983},[2606],[2539,8985,8988],{"className":8986,"style":8987},[2610],"height:0.6147em;",[2539,8989,8991,8994],{"style":8990},"top:-2.989em;margin-right:0.05em;",[2539,8992],{"className":8993,"style":2619},[2618],[2539,8995,8997],{"className":8996},[2623,2624,2625,2626],[2539,8998,8477],{"className":8999},[2873,2626],[2539,9001],{"className":9002,"style":2869},[2807],[2539,9004,2764],{"className":9005},[2873],[2539,9007],{"className":9008,"style":2869},[2807],[2539,9010,8910],{"className":9011},[2589,2593],[2539,9013,9014,9017],{"style":2920},[2539,9015],{"className":9016,"style":2911},[2618],[2539,9018],{"className":9019,"style":2928},[2927],[2539,9021,9022,9025],{"style":2931},[2539,9023],{"className":9024,"style":2911},[2618],[2539,9026,9028],{"className":9027},[2589],[2539,9029,6297],{"className":9030},[2589],[2539,9032,2634],{"className":9033},[2633],[2539,9035,9037],{"className":9036},[2606],[2539,9038,9040],{"className":9039,"style":2950},[2610],[2539,9041],{},[2539,9043],{"className":9044},[2956,2891],[11,9046,9047,9048,9077],{},"with ratio of amplitudes ",[2539,9049,9051,9065],{"className":9050},[2542],[2539,9052,9054],{"className":9053},[2546],[2548,9055,9056],{"xmlns":2550},[2552,9057,9058,9062],{},[2555,9059,9060],{},[2561,9061,8910],{},[2568,9063,9064],{"encoding":2570},"\\lambda",[2539,9066,9068],{"className":9067,"ariaHidden":2576},[2575],[2539,9069,9071,9074],{"className":9070},[2580],[2539,9072],{"className":9073,"style":4048},[2584],[2539,9075,8910],{"className":9076},[2589,2593],". This ratio connects the amplitudes of flapping and twisting. It is defined as:",[2539,9079,9081],{"className":9080},[2734],[2539,9082,9084,9125],{"className":9083},[2542],[2539,9085,9087],{"className":9086},[2546],[2548,9088,9089],{"xmlns":2550,"display":2743},[2552,9090,9091,9122],{},[2555,9092,9093,9095,9097],{},[2561,9094,8910],{},[2752,9096,2754],{},[2766,9098,9099,9105],{},[2558,9100,9101,9103],{},[2561,9102,5045],{},[2772,9104,5955],{},[2555,9106,9107,9114,9116,9118,9120],{},[2558,9108,9109,9112],{},[2561,9110,9111],{},"α",[2772,9113,5955],{},[2752,9115,2764],{},[2561,9117,2563],{},[2561,9119,4237],{"mathvariant":3232},[2772,9121,2774],{},[2568,9123,9124],{"encoding":2570},"\\lambda = \\frac{h_0}{\\alpha_0 \\cdot c\u002F2}",[2539,9126,9128,9146],{"className":9127,"ariaHidden":2576},[2575],[2539,9129,9131,9134,9137,9140,9143],{"className":9130},[2580],[2539,9132],{"className":9133,"style":4048},[2584],[2539,9135,8910],{"className":9136},[2589,2593],[2539,9138],{"className":9139,"style":2808},[2807],[2539,9141,2754],{"className":9142},[2812],[2539,9144],{"className":9145,"style":2808},[2807],[2539,9147,9149,9153],{"className":9148},[2580],[2539,9150],{"className":9151,"style":9152},[2584],"height:2.3074em;vertical-align:-0.936em;",[2539,9154,9156,9159,9305],{"className":9155},[2589],[2539,9157],{"className":9158},[2890,2891],[2539,9160,9162],{"className":9161},[2766],[2539,9163,9165,9296],{"className":9164},[2601,2602],[2539,9166,9168,9293],{"className":9167},[2606],[2539,9169,9172,9237,9245],{"className":9170,"style":9171},[2610],"height:1.3714em;",[2539,9173,9174,9177],{"style":2907},[2539,9175],{"className":9176,"style":2911},[2618],[2539,9178,9180,9222,9225,9228,9231,9234],{"className":9179},[2589],[2539,9181,9183,9187],{"className":9182},[2589],[2539,9184,9111],{"className":9185,"style":9186},[2589,2593],"margin-right:0.0037em;",[2539,9188,9190],{"className":9189},[2597],[2539,9191,9193,9214],{"className":9192},[2601,2602],[2539,9194,9196,9211],{"className":9195},[2606],[2539,9197,9199],{"className":9198,"style":6002},[2610],[2539,9200,9202,9205],{"style":9201},"top:-2.55em;margin-left:-0.0037em;margin-right:0.05em;",[2539,9203],{"className":9204,"style":2619},[2618],[2539,9206,9208],{"className":9207},[2623,2624,2625,2626],[2539,9209,5955],{"className":9210},[2589,2626],[2539,9212,2634],{"className":9213},[2633],[2539,9215,9217],{"className":9216},[2606],[2539,9218,9220],{"className":9219,"style":2641},[2610],[2539,9221],{},[2539,9223],{"className":9224,"style":2869},[2807],[2539,9226,2764],{"className":9227},[2873],[2539,9229],{"className":9230,"style":2869},[2807],[2539,9232,2563],{"className":9233},[2589,2593],[2539,9235,4335],{"className":9236},[2589],[2539,9238,9239,9242],{"style":2920},[2539,9240],{"className":9241,"style":2911},[2618],[2539,9243],{"className":9244,"style":2928},[2927],[2539,9246,9247,9250],{"style":2931},[2539,9248],{"className":9249,"style":2911},[2618],[2539,9251,9253],{"className":9252},[2589],[2539,9254,9256,9259],{"className":9255},[2589],[2539,9257,5045],{"className":9258},[2589,2593],[2539,9260,9262],{"className":9261},[2597],[2539,9263,9265,9285],{"className":9264},[2601,2602],[2539,9266,9268,9282],{"className":9267},[2606],[2539,9269,9271],{"className":9270,"style":6002},[2610],[2539,9272,9273,9276],{"style":2614},[2539,9274],{"className":9275,"style":2619},[2618],[2539,9277,9279],{"className":9278},[2623,2624,2625,2626],[2539,9280,5955],{"className":9281},[2589,2626],[2539,9283,2634],{"className":9284},[2633],[2539,9286,9288],{"className":9287},[2606],[2539,9289,9291],{"className":9290,"style":2641},[2610],[2539,9292],{},[2539,9294,2634],{"className":9295},[2633],[2539,9297,9299],{"className":9298},[2606],[2539,9300,9303],{"className":9301,"style":9302},[2610],"height:0.936em;",[2539,9304],{},[2539,9306],{"className":9307},[2956,2891],[11,9309,8753,9310,9380,9381,9451],{},[2539,9311,9313,9331],{"className":9312},[2542],[2539,9314,9316],{"className":9315},[2546],[2548,9317,9318],{"xmlns":2550},[2552,9319,9320,9328],{},[2555,9321,9322],{},[2558,9323,9324,9326],{},[2561,9325,5045],{},[2772,9327,5955],{},[2568,9329,9330],{"encoding":2570},"h_0",[2539,9332,9334],{"className":9333,"ariaHidden":2576},[2575],[2539,9335,9337,9340],{"className":9336},[2580],[2539,9338],{"className":9339,"style":6746},[2584],[2539,9341,9343,9346],{"className":9342},[2589],[2539,9344,5045],{"className":9345},[2589,2593],[2539,9347,9349],{"className":9348},[2597],[2539,9350,9352,9372],{"className":9351},[2601,2602],[2539,9353,9355,9369],{"className":9354},[2606],[2539,9356,9358],{"className":9357,"style":6002},[2610],[2539,9359,9360,9363],{"style":2614},[2539,9361],{"className":9362,"style":2619},[2618],[2539,9364,9366],{"className":9365},[2623,2624,2625,2626],[2539,9367,5955],{"className":9368},[2589,2626],[2539,9370,2634],{"className":9371},[2633],[2539,9373,9375],{"className":9374},[2606],[2539,9376,9378],{"className":9377,"style":2641},[2610],[2539,9379],{}," is the flapping amplitude, ",[2539,9382,9384,9402],{"className":9383},[2542],[2539,9385,9387],{"className":9386},[2546],[2548,9388,9389],{"xmlns":2550},[2552,9390,9391,9399],{},[2555,9392,9393],{},[2558,9394,9395,9397],{},[2561,9396,9111],{},[2772,9398,5955],{},[2568,9400,9401],{"encoding":2570},"\\alpha_0",[2539,9403,9405],{"className":9404,"ariaHidden":2576},[2575],[2539,9406,9408,9411],{"className":9407},[2580],[2539,9409],{"className":9410,"style":2585},[2584],[2539,9412,9414,9417],{"className":9413},[2589],[2539,9415,9111],{"className":9416,"style":9186},[2589,2593],[2539,9418,9420],{"className":9419},[2597],[2539,9421,9423,9443],{"className":9422},[2601,2602],[2539,9424,9426,9440],{"className":9425},[2606],[2539,9427,9429],{"className":9428,"style":6002},[2610],[2539,9430,9431,9434],{"style":9201},[2539,9432],{"className":9433,"style":2619},[2618],[2539,9435,9437],{"className":9436},[2623,2624,2625,2626],[2539,9438,5955],{"className":9439},[2589,2626],[2539,9441,2634],{"className":9442},[2633],[2539,9444,9446],{"className":9445},[2606],[2539,9447,9449],{"className":9448,"style":2641},[2610],[2539,9450],{}," is the twisting amplitude",[11,9453,9454,9455,9483,9484,9536,9537,9606,9607,297],{},"If one assumes somewhat efficient thrust production and thus chooses some value for ",[2539,9456,9458,9471],{"className":9457},[2542],[2539,9459,9461],{"className":9460},[2546],[2548,9462,9463],{"xmlns":2550},[2552,9464,9465,9469],{},[2555,9466,9467],{},[2561,9468,8859],{},[2568,9470,8862],{"encoding":2570},[2539,9472,9474],{"className":9473,"ariaHidden":2576},[2575],[2539,9475,9477,9480],{"className":9476},[2580],[2539,9478],{"className":9479,"style":3136},[2584],[2539,9481,8859],{"className":9482,"style":5606},[2589,2593]," (e.g. 0.75), the ratio of amplitudes can be calculated (",[2539,9485,9487,9506],{"className":9486},[2542],[2539,9488,9490],{"className":9489},[2546],[2548,9491,9492],{"xmlns":2550},[2552,9493,9494,9503],{},[2555,9495,9496,9498,9500],{},[2561,9497,8910],{},[2752,9499,2754],{},[2772,9501,9502],{},"5.56",[2568,9504,9505],{"encoding":2570},"\\lambda = 5.56",[2539,9507,9509,9527],{"className":9508,"ariaHidden":2576},[2575],[2539,9510,9512,9515,9518,9521,9524],{"className":9511},[2580],[2539,9513],{"className":9514,"style":4048},[2584],[2539,9516,8910],{"className":9517},[2589,2593],[2539,9519],{"className":9520,"style":2808},[2807],[2539,9522,2754],{"className":9523},[2812],[2539,9525],{"className":9526,"style":2808},[2807],[2539,9528,9530,9533],{"className":9529},[2580],[2539,9531],{"className":9532,"style":4084},[2584],[2539,9534,9502],{"className":9535},[2589],"). And from the ratio of amplitudes, the twisting amplitude ",[2539,9538,9540,9557],{"className":9539},[2542],[2539,9541,9543],{"className":9542},[2546],[2548,9544,9545],{"xmlns":2550},[2552,9546,9547,9555],{},[2555,9548,9549],{},[2558,9550,9551,9553],{},[2561,9552,9111],{},[2772,9554,5955],{},[2568,9556,9401],{"encoding":2570},[2539,9558,9560],{"className":9559,"ariaHidden":2576},[2575],[2539,9561,9563,9566],{"className":9562},[2580],[2539,9564],{"className":9565,"style":2585},[2584],[2539,9567,9569,9572],{"className":9568},[2589],[2539,9570,9111],{"className":9571,"style":9186},[2589,2593],[2539,9573,9575],{"className":9574},[2597],[2539,9576,9578,9598],{"className":9577},[2601,2602],[2539,9579,9581,9595],{"className":9580},[2606],[2539,9582,9584],{"className":9583,"style":6002},[2610],[2539,9585,9586,9589],{"style":9201},[2539,9587],{"className":9588,"style":2619},[2618],[2539,9590,9592],{"className":9591},[2623,2624,2625,2626],[2539,9593,5955],{"className":9594},[2589,2626],[2539,9596,2634],{"className":9597},[2633],[2539,9599,9601],{"className":9600},[2606],[2539,9602,9604],{"className":9603,"style":2641},[2610],[2539,9605],{}," can be calculated, given a flapping amplitude ",[2539,9608,9610,9627],{"className":9609},[2542],[2539,9611,9613],{"className":9612},[2546],[2548,9614,9615],{"xmlns":2550},[2552,9616,9617,9625],{},[2555,9618,9619],{},[2558,9620,9621,9623],{},[2561,9622,5045],{},[2772,9624,5955],{},[2568,9626,9330],{"encoding":2570},[2539,9628,9630],{"className":9629,"ariaHidden":2576},[2575],[2539,9631,9633,9636],{"className":9632},[2580],[2539,9634],{"className":9635,"style":6746},[2584],[2539,9637,9639,9642],{"className":9638},[2589],[2539,9640,5045],{"className":9641},[2589,2593],[2539,9643,9645],{"className":9644},[2597],[2539,9646,9648,9668],{"className":9647},[2601,2602],[2539,9649,9651,9665],{"className":9650},[2606],[2539,9652,9654],{"className":9653,"style":6002},[2610],[2539,9655,9656,9659],{"style":2614},[2539,9657],{"className":9658,"style":2619},[2618],[2539,9660,9662],{"className":9661},[2623,2624,2625,2626],[2539,9663,5955],{"className":9664},[2589,2626],[2539,9666,2634],{"className":9667},[2633],[2539,9669,9671],{"className":9670},[2606],[2539,9672,9674],{"className":9673,"style":2641},[2610],[2539,9675],{},[2539,9677,9679],{"className":9678},[2734],[2539,9680,9682,9733],{"className":9681},[2542],[2539,9683,9685],{"className":9684},[2546],[2548,9686,9687],{"xmlns":2550,"display":2743},[2552,9688,9689,9730],{},[2555,9690,9691,9697,9699,9701,9703,9705,9707,9709,9711,9713,9715,9717,9719,9721,9723,9726,9728],{},[2558,9692,9693,9695],{},[2561,9694,5045],{},[2772,9696,5955],{},[2752,9698,2754],{},[2561,9700,8552],{},[2561,9702,4237],{"mathvariant":3232},[2772,9704,7410],{},[2752,9706,2764],{},[2772,9708,2774],{},[2561,9710,4237],{"mathvariant":3232},[2772,9712,5488],{},[2752,9714,2764],{},[2561,9716,4036],{},[2561,9718,4237],{"mathvariant":3232},[2772,9720,2774],{},[2752,9722,2754],{},[2772,9724,9725],{},"2.09",[3225,9727,3227],{},[2561,9729,3358],{"mathvariant":3232},[2568,9731,9732],{"encoding":2570},"h_0 = \\pi\u002F6 \\cdot 2\u002F3 \\cdot b\u002F2 = 2.09\\,\\mathrm{m}",[2539,9734,9736,9791,9813,9831,9852],{"className":9735,"ariaHidden":2576},[2575],[2539,9737,9739,9742,9782,9785,9788],{"className":9738},[2580],[2539,9740],{"className":9741,"style":6746},[2584],[2539,9743,9745,9748],{"className":9744},[2589],[2539,9746,5045],{"className":9747},[2589,2593],[2539,9749,9751],{"className":9750},[2597],[2539,9752,9754,9774],{"className":9753},[2601,2602],[2539,9755,9757,9771],{"className":9756},[2606],[2539,9758,9760],{"className":9759,"style":6002},[2610],[2539,9761,9762,9765],{"style":2614},[2539,9763],{"className":9764,"style":2619},[2618],[2539,9766,9768],{"className":9767},[2623,2624,2625,2626],[2539,9769,5955],{"className":9770},[2589,2626],[2539,9772,2634],{"className":9773},[2633],[2539,9775,9777],{"className":9776},[2606],[2539,9778,9780],{"className":9779,"style":2641},[2610],[2539,9781],{},[2539,9783],{"className":9784,"style":2808},[2807],[2539,9786,2754],{"className":9787},[2812],[2539,9789],{"className":9790,"style":2808},[2807],[2539,9792,9794,9797,9800,9804,9807,9810],{"className":9793},[2580],[2539,9795],{"className":9796,"style":4301},[2584],[2539,9798,8552],{"className":9799,"style":5606},[2589,2593],[2539,9801,9803],{"className":9802},[2589],"\u002F6",[2539,9805],{"className":9806,"style":2869},[2807],[2539,9808,2764],{"className":9809},[2873],[2539,9811],{"className":9812,"style":2869},[2807],[2539,9814,9816,9819,9822,9825,9828],{"className":9815},[2580],[2539,9817],{"className":9818,"style":4301},[2584],[2539,9820,7587],{"className":9821},[2589],[2539,9823],{"className":9824,"style":2869},[2807],[2539,9826,2764],{"className":9827},[2873],[2539,9829],{"className":9830,"style":2869},[2807],[2539,9832,9834,9837,9840,9843,9846,9849],{"className":9833},[2580],[2539,9835],{"className":9836,"style":4301},[2584],[2539,9838,4036],{"className":9839},[2589,2593],[2539,9841,4335],{"className":9842},[2589],[2539,9844],{"className":9845,"style":2808},[2807],[2539,9847,2754],{"className":9848},[2812],[2539,9850],{"className":9851,"style":2808},[2807],[2539,9853,9855,9858,9861,9864],{"className":9854},[2580],[2539,9856],{"className":9857,"style":4084},[2584],[2539,9859,9725],{"className":9860},[2589],[2539,9862],{"className":9863,"style":3256},[2807],[2539,9865,3358],{"className":9866},[2589,3263],[2539,9868,9870],{"className":9869},[2734],[2539,9871,9873,9949],{"className":9872},[2542],[2539,9874,9876],{"className":9875},[2546],[2548,9877,9878],{"xmlns":2550,"display":2743},[2552,9879,9880,9946],{},[2555,9881,9882,9888,9890,9910,9912,9915,9917,9925,9927,9937,9939],{},[2558,9883,9884,9886],{},[2561,9885,9111],{},[2772,9887,5955],{},[2752,9889,2754],{},[2766,9891,9892,9898],{},[2558,9893,9894,9896],{},[2561,9895,5045],{},[2772,9897,5955],{},[2555,9899,9900,9902,9904,9906,9908],{},[2561,9901,8910],{},[2752,9903,2764],{},[2561,9905,2563],{},[2561,9907,4237],{"mathvariant":3232},[2772,9909,2774],{},[2752,9911,2754],{},[2772,9913,9914],{},"0.59",[3225,9916,3227],{},[2555,9918,9919,9921,9923],{},[2561,9920,4109],{"mathvariant":3232},[2561,9922,15],{"mathvariant":3232},[2561,9924,2566],{"mathvariant":3232},[3225,9926,6406],{},[2752,9928,9929],{},[9930,9931,9932,9934],"mover",{"accent":2576},[2752,9933,2754],{},[2752,9935,9936],{},"^",[3225,9938,6406],{},[2776,9940,9941,9944],{},[2772,9942,9943],{},"33.9",[2752,9945,7393],{"lspace":6293,"rspace":6293},[2568,9947,9948],{"encoding":2570},"\\alpha_0 = \\frac{h_0}{\\lambda \\cdot c\u002F2} = 0.59\\,\\mathrm{rad}\\ \\mathrel{\\hat=}\\ 33.9^{\\circ}",[2539,9950,9952,10007,10136,10205],{"className":9951,"ariaHidden":2576},[2575],[2539,9953,9955,9958,9998,10001,10004],{"className":9954},[2580],[2539,9956],{"className":9957,"style":2585},[2584],[2539,9959,9961,9964],{"className":9960},[2589],[2539,9962,9111],{"className":9963,"style":9186},[2589,2593],[2539,9965,9967],{"className":9966},[2597],[2539,9968,9970,9990],{"className":9969},[2601,2602],[2539,9971,9973,9987],{"className":9972},[2606],[2539,9974,9976],{"className":9975,"style":6002},[2610],[2539,9977,9978,9981],{"style":9201},[2539,9979],{"className":9980,"style":2619},[2618],[2539,9982,9984],{"className":9983},[2623,2624,2625,2626],[2539,9985,5955],{"className":9986},[2589,2626],[2539,9988,2634],{"className":9989},[2633],[2539,9991,9993],{"className":9992},[2606],[2539,9994,9996],{"className":9995,"style":2641},[2610],[2539,9997],{},[2539,9999],{"className":10000,"style":2808},[2807],[2539,10002,2754],{"className":10003},[2812],[2539,10005],{"className":10006,"style":2808},[2807],[2539,10008,10010,10013,10127,10130,10133],{"className":10009},[2580],[2539,10011],{"className":10012,"style":9152},[2584],[2539,10014,10016,10019,10124],{"className":10015},[2589],[2539,10017],{"className":10018},[2890,2891],[2539,10020,10022],{"className":10021},[2766],[2539,10023,10025,10116],{"className":10024},[2601,2602],[2539,10026,10028,10113],{"className":10027},[2606],[2539,10029,10031,10057,10065],{"className":10030,"style":9171},[2610],[2539,10032,10033,10036],{"style":2907},[2539,10034],{"className":10035,"style":2911},[2618],[2539,10037,10039,10042,10045,10048,10051,10054],{"className":10038},[2589],[2539,10040,8910],{"className":10041},[2589,2593],[2539,10043],{"className":10044,"style":2869},[2807],[2539,10046,2764],{"className":10047},[2873],[2539,10049],{"className":10050,"style":2869},[2807],[2539,10052,2563],{"className":10053},[2589,2593],[2539,10055,4335],{"className":10056},[2589],[2539,10058,10059,10062],{"style":2920},[2539,10060],{"className":10061,"style":2911},[2618],[2539,10063],{"className":10064,"style":2928},[2927],[2539,10066,10067,10070],{"style":2931},[2539,10068],{"className":10069,"style":2911},[2618],[2539,10071,10073],{"className":10072},[2589],[2539,10074,10076,10079],{"className":10075},[2589],[2539,10077,5045],{"className":10078},[2589,2593],[2539,10080,10082],{"className":10081},[2597],[2539,10083,10085,10105],{"className":10084},[2601,2602],[2539,10086,10088,10102],{"className":10087},[2606],[2539,10089,10091],{"className":10090,"style":6002},[2610],[2539,10092,10093,10096],{"style":2614},[2539,10094],{"className":10095,"style":2619},[2618],[2539,10097,10099],{"className":10098},[2623,2624,2625,2626],[2539,10100,5955],{"className":10101},[2589,2626],[2539,10103,2634],{"className":10104},[2633],[2539,10106,10108],{"className":10107},[2606],[2539,10109,10111],{"className":10110,"style":2641},[2610],[2539,10112],{},[2539,10114,2634],{"className":10115},[2633],[2539,10117,10119],{"className":10118},[2606],[2539,10120,10122],{"className":10121,"style":9302},[2610],[2539,10123],{},[2539,10125],{"className":10126},[2956,2891],[2539,10128],{"className":10129,"style":2808},[2807],[2539,10131,2754],{"className":10132},[2812],[2539,10134],{"className":10135,"style":2808},[2807],[2539,10137,10139,10142,10145,10148,10155,10158,10161,10199,10202],{"className":10138},[2580],[2539,10140],{"className":10141,"style":4048},[2584],[2539,10143,9914],{"className":10144},[2589],[2539,10146],{"className":10147,"style":3256},[2807],[2539,10149,10151],{"className":10150},[2589],[2539,10152,10154],{"className":10153},[2589,3263],"rad",[2539,10156,6406],{"className":10157},[2807],[2539,10159],{"className":10160,"style":2808},[2807],[2539,10162,10164],{"className":10163},[2812],[2539,10165,10168],{"className":10166},[2589,10167],"accent",[2539,10169,10171],{"className":10170},[2601],[2539,10172,10174],{"className":10173},[2606],[2539,10175,10177,10186],{"className":10176,"style":4048},[2610],[2539,10178,10180,10183],{"style":10179},"top:-3em;",[2539,10181],{"className":10182,"style":2911},[2618],[2539,10184,2754],{"className":10185},[2812],[2539,10187,10188,10191],{"style":10179},[2539,10189],{"className":10190,"style":2911},[2618],[2539,10192,10196],{"className":10193,"style":10195},[10194],"accent-body","left:-0.25em;",[2539,10197,9936],{"className":10198},[2589],[2539,10200,6406],{"className":10201},[2807],[2539,10203],{"className":10204,"style":2808},[2807],[2539,10206,10208,10212,10216],{"className":10207},[2580],[2539,10209],{"className":10210,"style":10211},[2584],"height:0.7241em;",[2539,10213,10215],{"className":10214},[2589],"33.",[2539,10217,10219,10222],{"className":10218},[2589],[2539,10220,8344],{"className":10221},[2589],[2539,10223,10225],{"className":10224},[2597],[2539,10226,10228],{"className":10227},[2601],[2539,10229,10231],{"className":10230},[2606],[2539,10232,10234],{"className":10233,"style":10211},[2610],[2539,10235,10236,10239],{"style":2978},[2539,10237],{"className":10238,"style":2619},[2618],[2539,10240,10242],{"className":10241},[2623,2624,2625,2626],[2539,10243,10245],{"className":10244},[2589,2626],[2539,10246,7393],{"className":10247},[2589,2626],[11,10249,10250,10350,10351,10420,10421,10553],{},[2539,10251,10253,10279],{"className":10252},[2542],[2539,10254,10256],{"className":10255},[2546],[2548,10257,10258],{"xmlns":2550},[2552,10259,10260,10276],{},[2555,10261,10262,10268,10270,10272,10274],{},[2558,10263,10264,10266],{},[2561,10265,9111],{},[2772,10267,5955],{},[2752,10269,2764],{},[2561,10271,2563],{},[2561,10273,4237],{"mathvariant":3232},[2772,10275,2774],{},[2568,10277,10278],{"encoding":2570},"\\alpha_0 \\cdot c\u002F2",[2539,10280,10282,10338],{"className":10281,"ariaHidden":2576},[2575],[2539,10283,10285,10289,10329,10332,10335],{"className":10284},[2580],[2539,10286],{"className":10287,"style":10288},[2584],"height:0.5945em;vertical-align:-0.15em;",[2539,10290,10292,10295],{"className":10291},[2589],[2539,10293,9111],{"className":10294,"style":9186},[2589,2593],[2539,10296,10298],{"className":10297},[2597],[2539,10299,10301,10321],{"className":10300},[2601,2602],[2539,10302,10304,10318],{"className":10303},[2606],[2539,10305,10307],{"className":10306,"style":6002},[2610],[2539,10308,10309,10312],{"style":9201},[2539,10310],{"className":10311,"style":2619},[2618],[2539,10313,10315],{"className":10314},[2623,2624,2625,2626],[2539,10316,5955],{"className":10317},[2589,2626],[2539,10319,2634],{"className":10320},[2633],[2539,10322,10324],{"className":10323},[2606],[2539,10325,10327],{"className":10326,"style":2641},[2610],[2539,10328],{},[2539,10330],{"className":10331,"style":2869},[2807],[2539,10333,2764],{"className":10334},[2873],[2539,10336],{"className":10337,"style":2869},[2807],[2539,10339,10341,10344,10347],{"className":10340},[2580],[2539,10342],{"className":10343,"style":4301},[2584],[2539,10345,2563],{"className":10346},[2589,2593],[2539,10348,4335],{"className":10349},[2589]," is the arc length, of the wing twist at a radius of c\u002F2. ",[2539,10352,10354,10371],{"className":10353},[2542],[2539,10355,10357],{"className":10356},[2546],[2548,10358,10359],{"xmlns":2550},[2552,10360,10361,10369],{},[2555,10362,10363],{},[2558,10364,10365,10367],{},[2561,10366,5045],{},[2772,10368,5955],{},[2568,10370,9330],{"encoding":2570},[2539,10372,10374],{"className":10373,"ariaHidden":2576},[2575],[2539,10375,10377,10380],{"className":10376},[2580],[2539,10378],{"className":10379,"style":6746},[2584],[2539,10381,10383,10386],{"className":10382},[2589],[2539,10384,5045],{"className":10385},[2589,2593],[2539,10387,10389],{"className":10388},[2597],[2539,10390,10392,10412],{"className":10391},[2601,2602],[2539,10393,10395,10409],{"className":10394},[2606],[2539,10396,10398],{"className":10397,"style":6002},[2610],[2539,10399,10400,10403],{"style":2614},[2539,10401],{"className":10402,"style":2619},[2618],[2539,10404,10406],{"className":10405},[2623,2624,2625,2626],[2539,10407,5955],{"className":10408},[2589,2626],[2539,10410,2634],{"className":10411},[2633],[2539,10413,10415],{"className":10414},[2606],[2539,10416,10418],{"className":10417,"style":2641},[2610],[2539,10419],{}," also can be considered an arc length, and thus can be calculated from the deflection angle (",[2539,10422,10424,10457],{"className":10423},[2542],[2539,10425,10427],{"className":10426},[2546],[2548,10428,10429],{"xmlns":2550},[2552,10430,10431,10454],{},[2555,10432,10433,10435,10437,10439,10447],{},[2561,10434,8552],{},[2561,10436,4237],{"mathvariant":3232},[2772,10438,7410],{},[2752,10440,10441],{},[9930,10442,10443,10445],{"accent":2576},[2752,10444,2754],{},[2752,10446,9936],{},[2776,10448,10449,10452],{},[2772,10450,10451],{},"30",[2752,10453,7393],{"lspace":6293,"rspace":6293},[2568,10455,10456],{"encoding":2570},"\\pi\u002F6 \\mathrel{\\hat=} 30^{\\circ}",[2539,10458,10460,10512],{"className":10459,"ariaHidden":2576},[2575],[2539,10461,10463,10466,10469,10472,10475,10509],{"className":10462},[2580],[2539,10464],{"className":10465,"style":4301},[2584],[2539,10467,8552],{"className":10468,"style":5606},[2589,2593],[2539,10470,9803],{"className":10471},[2589],[2539,10473],{"className":10474,"style":2808},[2807],[2539,10476,10478],{"className":10477},[2812],[2539,10479,10481],{"className":10480},[2589,10167],[2539,10482,10484],{"className":10483},[2601],[2539,10485,10487],{"className":10486},[2606],[2539,10488,10490,10498],{"className":10489,"style":4048},[2610],[2539,10491,10492,10495],{"style":10179},[2539,10493],{"className":10494,"style":2911},[2618],[2539,10496,2754],{"className":10497},[2812],[2539,10499,10500,10503],{"style":10179},[2539,10501],{"className":10502,"style":2911},[2618],[2539,10504,10506],{"className":10505,"style":10195},[10194],[2539,10507,9936],{"className":10508},[2589],[2539,10510],{"className":10511,"style":2808},[2807],[2539,10513,10515,10518,10521],{"className":10514},[2580],[2539,10516],{"className":10517,"style":7406},[2584],[2539,10519,5488],{"className":10520},[2589],[2539,10522,10524,10527],{"className":10523},[2589],[2539,10525,5955],{"className":10526},[2589],[2539,10528,10530],{"className":10529},[2597],[2539,10531,10533],{"className":10532},[2601],[2539,10534,10536],{"className":10535},[2606],[2539,10537,10539],{"className":10538,"style":7406},[2610],[2539,10540,10541,10544],{"style":5659},[2539,10542],{"className":10543,"style":2619},[2618],[2539,10545,10547],{"className":10546},[2623,2624,2625,2626],[2539,10548,10550],{"className":10549},[2589,2626],[2539,10551,7393],{"className":10552},[2589,2626],") times the radius of the representative wing profile (2\u002F3 wing length). The resulting angle of the wing twist is even higher than the flapping angle, which seems counter-intuitive. But keep in mind that for aerodynamic velocities, not the angle is important but the distance traversed.",[82,10555,10557],{"id":10556},"caveats","Caveats",[11,10559,10560,10561,10630,10631,10700,10701,10770],{},"As the theory is derived in 2D, transferring the concept to a 3 dimensional wing has pitfalls. Due to kninematics, every radius yields a different ",[2539,10562,10564,10581],{"className":10563},[2542],[2539,10565,10567],{"className":10566},[2546],[2548,10568,10569],{"xmlns":2550},[2552,10570,10571,10579],{},[2555,10572,10573],{},[2558,10574,10575,10577],{},[2561,10576,5045],{},[2772,10578,5955],{},[2568,10580,9330],{"encoding":2570},[2539,10582,10584],{"className":10583,"ariaHidden":2576},[2575],[2539,10585,10587,10590],{"className":10586},[2580],[2539,10588],{"className":10589,"style":6746},[2584],[2539,10591,10593,10596],{"className":10592},[2589],[2539,10594,5045],{"className":10595},[2589,2593],[2539,10597,10599],{"className":10598},[2597],[2539,10600,10602,10622],{"className":10601},[2601,2602],[2539,10603,10605,10619],{"className":10604},[2606],[2539,10606,10608],{"className":10607,"style":6002},[2610],[2539,10609,10610,10613],{"style":2614},[2539,10611],{"className":10612,"style":2619},[2618],[2539,10614,10616],{"className":10615},[2623,2624,2625,2626],[2539,10617,5955],{"className":10618},[2589,2626],[2539,10620,2634],{"className":10621},[2633],[2539,10623,10625],{"className":10624},[2606],[2539,10626,10628],{"className":10627,"style":2641},[2610],[2539,10629],{},". For aerodynamically optimal thrust generation, the resulting ",[2539,10632,10634,10651],{"className":10633},[2542],[2539,10635,10637],{"className":10636},[2546],[2548,10638,10639],{"xmlns":2550},[2552,10640,10641,10649],{},[2555,10642,10643],{},[2558,10644,10645,10647],{},[2561,10646,9111],{},[2772,10648,5955],{},[2568,10650,9401],{"encoding":2570},[2539,10652,10654],{"className":10653,"ariaHidden":2576},[2575],[2539,10655,10657,10660],{"className":10656},[2580],[2539,10658],{"className":10659,"style":2585},[2584],[2539,10661,10663,10666],{"className":10662},[2589],[2539,10664,9111],{"className":10665,"style":9186},[2589,2593],[2539,10667,10669],{"className":10668},[2597],[2539,10670,10672,10692],{"className":10671},[2601,2602],[2539,10673,10675,10689],{"className":10674},[2606],[2539,10676,10678],{"className":10677,"style":6002},[2610],[2539,10679,10680,10683],{"style":9201},[2539,10681],{"className":10682,"style":2619},[2618],[2539,10684,10686],{"className":10685},[2623,2624,2625,2626],[2539,10687,5955],{"className":10688},[2589,2626],[2539,10690,2634],{"className":10691},[2633],[2539,10693,10695],{"className":10694},[2606],[2539,10696,10698],{"className":10697,"style":2641},[2610],[2539,10699],{}," would need to be gradual along the wing. In our technical system, the wing twist is not gradual, but only realized by rotating the outer wing part. Thus, a representative radius is chosen, for which the angle ",[2539,10702,10704,10721],{"className":10703},[2542],[2539,10705,10707],{"className":10706},[2546],[2548,10708,10709],{"xmlns":2550},[2552,10710,10711,10719],{},[2555,10712,10713],{},[2558,10714,10715,10717],{},[2561,10716,9111],{},[2772,10718,5955],{},[2568,10720,9401],{"encoding":2570},[2539,10722,10724],{"className":10723,"ariaHidden":2576},[2575],[2539,10725,10727,10730],{"className":10726},[2580],[2539,10728],{"className":10729,"style":2585},[2584],[2539,10731,10733,10736],{"className":10732},[2589],[2539,10734,9111],{"className":10735,"style":9186},[2589,2593],[2539,10737,10739],{"className":10738},[2597],[2539,10740,10742,10762],{"className":10741},[2601,2602],[2539,10743,10745,10759],{"className":10744},[2606],[2539,10746,10748],{"className":10747,"style":6002},[2610],[2539,10749,10750,10753],{"style":9201},[2539,10751],{"className":10752,"style":2619},[2618],[2539,10754,10756],{"className":10755},[2623,2624,2625,2626],[2539,10757,5955],{"className":10758},[2589,2626],[2539,10760,2634],{"className":10761},[2633],[2539,10763,10765],{"className":10764},[2606],[2539,10766,10768],{"className":10767,"style":2641},[2610],[2539,10769],{}," is calculated. Dr. Send also analyses in his 1992 paper a 3D version of his theory and remarks that looking at the flow section by section is an acceptable approach.",[11,10772,10773,10774,10846],{},"Further on, the flapping amplitude can be chosen freely (to a certain extent). In Dr. Send's model, the approximation of small angles (e.g. ",[2539,10775,10777,10806],{"className":10776},[2542],[2539,10778,10780],{"className":10779},[2546],[2548,10781,10782],{"xmlns":2550},[2552,10783,10784,10803],{},[2555,10785,10786,10789,10792,10794,10796,10798,10801],{},[2561,10787,10788],{},"tan",[2752,10790,10791],{},"⁡",[2752,10793,4223],{"stretchy":4222},[2561,10795,9111],{},[2752,10797,2528],{"stretchy":4222},[2752,10799,10800],{},"∝",[2561,10802,9111],{},[2568,10804,10805],{"encoding":2570},"\\tan(\\alpha) \\propto \\alpha",[2539,10807,10809,10837],{"className":10808,"ariaHidden":2576},[2575],[2539,10810,10812,10815,10819,10822,10825,10828,10831,10834],{"className":10811},[2580],[2539,10813],{"className":10814,"style":4301},[2584],[2539,10816,10788],{"className":10817},[10818],"mop",[2539,10820,4223],{"className":10821},[2890],[2539,10823,9111],{"className":10824,"style":9186},[2589,2593],[2539,10826,2528],{"className":10827},[2956],[2539,10829],{"className":10830,"style":2808},[2807],[2539,10832,10800],{"className":10833},[2812],[2539,10835],{"className":10836,"style":2808},[2807],[2539,10838,10840,10843],{"className":10839},[2580],[2539,10841],{"className":10842,"style":3166},[2584],[2539,10844,9111],{"className":10845,"style":9186},[2589,2593],") has been used in a few places. Large angles can and will therefore lead to inaccuracies.",[11,10848,10849,10850,8078,10917,297],{},"Also, choosing an aerodynamic efficiency as input does not mean, that this efficiency will actually be reached. This will have to be tested. In his work, Dr. Send described also that the best efficiency actually was reached with a slightly larger phase lag of ",[2539,10851,10853,10872],{"className":10852},[2542],[2539,10854,10856],{"className":10855},[2546],[2548,10857,10858],{"xmlns":2550},[2552,10859,10860,10869],{},[2555,10861,10862],{},[2776,10863,10864,10867],{},[2772,10865,10866],{},"95",[2752,10868,7393],{"lspace":6293,"rspace":6293},[2568,10870,10871],{"encoding":2570},"95^{\\circ}",[2539,10873,10875],{"className":10874,"ariaHidden":2576},[2575],[2539,10876,10878,10881,10884],{"className":10877},[2580],[2539,10879],{"className":10880,"style":7406},[2584],[2539,10882,8344],{"className":10883},[2589],[2539,10885,10887,10891],{"className":10886},[2589],[2539,10888,10890],{"className":10889},[2589],"5",[2539,10892,10894],{"className":10893},[2597],[2539,10895,10897],{"className":10896},[2601],[2539,10898,10900],{"className":10899},[2606],[2539,10901,10903],{"className":10902,"style":7406},[2610],[2539,10904,10905,10908],{"style":5659},[2539,10906],{"className":10907,"style":2619},[2618],[2539,10909,10911],{"className":10910},[2623,2624,2625,2626],[2539,10912,10914],{"className":10913},[2589,2626],[2539,10915,7393],{"className":10916},[2589,2626],[2539,10918,10920,10938],{"className":10919},[2542],[2539,10921,10923],{"className":10922},[2546],[2548,10924,10925],{"xmlns":2550},[2552,10926,10927,10935],{},[2555,10928,10929],{},[2776,10930,10931,10933],{},[2772,10932,5737],{},[2752,10934,7393],{"lspace":6293,"rspace":6293},[2568,10936,10937],{"encoding":2570},"100^{\\circ}",[2539,10939,10941],{"className":10940,"ariaHidden":2576},[2575],[2539,10942,10944,10947,10950],{"className":10943},[2580],[2539,10945],{"className":10946,"style":7406},[2584],[2539,10948,6184],{"className":10949},[2589],[2539,10951,10953,10956],{"className":10952},[2589],[2539,10954,5955],{"className":10955},[2589],[2539,10957,10959],{"className":10958},[2597],[2539,10960,10962],{"className":10961},[2601],[2539,10963,10965],{"className":10964},[2606],[2539,10966,10968],{"className":10967,"style":7406},[2610],[2539,10969,10970,10973],{"style":5659},[2539,10971],{"className":10972,"style":2619},[2618],[2539,10974,10976],{"className":10975},[2623,2624,2625,2626],[2539,10977,10979],{"className":10978},[2589,2626],[2539,10980,7393],{"className":10981},[2589,2626],[82,10983,10985],{"id":10984},"how-much-thrust-can-be-produced","How much Thrust can be produced?",[11,10987,10988],{},"Not much could be found on this, but in one place Dr. Send gives the formula:",[2539,10990,10992],{"className":10991},[2734],[2539,10993,10995,11092],{"className":10994},[2542],[2539,10996,10998],{"className":10997},[2546],[2548,10999,11000],{"xmlns":2550,"display":2743},[2552,11001,11002,11089],{},[2555,11003,11004,11012,11014,11021,11023,11029,11035,11037,11039,11041,11043,11045,11047,11049,11051,11069,11072,11074,11077,11079,11081],{},[9930,11005,11006,11009],{"accent":2576},[2561,11007,11008],{},"F",[2752,11010,11011],{},"ˉ",[2752,11013,2754],{},[2558,11015,11016,11018],{},[2561,11017,11008],{},[2561,11019,11020],{},"D",[2752,11022,4228],{},[2766,11024,11025,11027],{},[2561,11026,2770],{},[2772,11028,2774],{},[2776,11030,11031,11033],{},[2561,11032,2780],{},[2772,11034,2774],{},[2752,11036,2764],{},[2561,11038,2787],{},[2752,11040,2764],{},[2561,11042,8552],{},[3225,11044,6406],{},[2752,11046,4223],{"stretchy":4222},[2772,11048,6297],{},[2752,11050,7514],{},[2766,11052,11053,11063],{},[2558,11054,11055,11057],{},[2561,11056,9111],{},[2558,11058,11059,11061],{},[2561,11060,7953],{},[2772,11062,5955],{},[2558,11064,11065,11067],{},[2561,11066,9111],{},[2772,11068,5955],{},[2561,11070,11071],{},"sin",[2752,11073,10791],{},[2561,11075,11076],{},"κ",[2752,11078,2528],{"stretchy":4222},[2752,11080,2764],{},[5470,11082,11083,11085,11087],{},[2561,11084,9111],{},[2772,11086,5955],{},[2772,11088,2774],{},[2568,11090,11091],{"encoding":2570},"\\bar{F} = F_D + \\frac{\\rho}{2}u^2 \\cdot S \\cdot \\pi\\ (1-\\frac{\\alpha_{H_0}}{\\alpha_0}\\sin \\kappa) \\cdot \\alpha_0^2",[2539,11093,11095,11145,11201,11307,11325,11352,11565],{"className":11094,"ariaHidden":2576},[2575],[2539,11096,11098,11102,11136,11139,11142],{"className":11097},[2580],[2539,11099],{"className":11100,"style":11101},[2584],"height:0.8201em;",[2539,11103,11105],{"className":11104},[2589,10167],[2539,11106,11108],{"className":11107},[2601],[2539,11109,11111],{"className":11110},[2606],[2539,11112,11114,11123],{"className":11113,"style":11101},[2610],[2539,11115,11116,11119],{"style":10179},[2539,11117],{"className":11118,"style":2911},[2618],[2539,11120,11008],{"className":11121,"style":11122},[2589,2593],"margin-right:0.1389em;",[2539,11124,11126,11129],{"style":11125},"top:-3.2523em;",[2539,11127],{"className":11128,"style":2911},[2618],[2539,11130,11133],{"className":11131,"style":11132},[10194],"left:-0.1667em;",[2539,11134,11011],{"className":11135},[2589],[2539,11137],{"className":11138,"style":2808},[2807],[2539,11140,2754],{"className":11141},[2812],[2539,11143],{"className":11144,"style":2808},[2807],[2539,11146,11148,11151,11192,11195,11198],{"className":11147},[2580],[2539,11149],{"className":11150,"style":2822},[2584],[2539,11152,11154,11157],{"className":11153},[2589],[2539,11155,11008],{"className":11156,"style":11122},[2589,2593],[2539,11158,11160],{"className":11159},[2597],[2539,11161,11163,11184],{"className":11162},[2601,2602],[2539,11164,11166,11181],{"className":11165},[2606],[2539,11167,11169],{"className":11168,"style":2842},[2610],[2539,11170,11172,11175],{"style":11171},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[2539,11173],{"className":11174,"style":2619},[2618],[2539,11176,11178],{"className":11177},[2623,2624,2625,2626],[2539,11179,11020],{"className":11180,"style":4124},[2589,2593,2626],[2539,11182,2634],{"className":11183},[2633],[2539,11185,11187],{"className":11186},[2606],[2539,11188,11190],{"className":11189,"style":2641},[2610],[2539,11191],{},[2539,11193],{"className":11194,"style":2869},[2807],[2539,11196,4228],{"className":11197},[2873],[2539,11199],{"className":11200,"style":2869},[2807],[2539,11202,11204,11207,11269,11298,11301,11304],{"className":11203},[2580],[2539,11205],{"className":11206,"style":2883},[2584],[2539,11208,11210,11213,11266],{"className":11209},[2589],[2539,11211],{"className":11212},[2890,2891],[2539,11214,11216],{"className":11215},[2766],[2539,11217,11219,11258],{"className":11218},[2601,2602],[2539,11220,11222,11255],{"className":11221},[2606],[2539,11223,11225,11236,11244],{"className":11224,"style":2904},[2610],[2539,11226,11227,11230],{"style":2907},[2539,11228],{"className":11229,"style":2911},[2618],[2539,11231,11233],{"className":11232},[2589],[2539,11234,2774],{"className":11235},[2589],[2539,11237,11238,11241],{"style":2920},[2539,11239],{"className":11240,"style":2911},[2618],[2539,11242],{"className":11243,"style":2928},[2927],[2539,11245,11246,11249],{"style":2931},[2539,11247],{"className":11248,"style":2911},[2618],[2539,11250,11252],{"className":11251},[2589],[2539,11253,2770],{"className":11254},[2589,2593],[2539,11256,2634],{"className":11257},[2633],[2539,11259,11261],{"className":11260},[2606],[2539,11262,11264],{"className":11263,"style":2950},[2610],[2539,11265],{},[2539,11267],{"className":11268},[2956,2891],[2539,11270,11272,11275],{"className":11271},[2589],[2539,11273,2780],{"className":11274},[2589,2593],[2539,11276,11278],{"className":11277},[2597],[2539,11279,11281],{"className":11280},[2601],[2539,11282,11284],{"className":11283},[2606],[2539,11285,11287],{"className":11286,"style":2975},[2610],[2539,11288,11289,11292],{"style":2978},[2539,11290],{"className":11291,"style":2619},[2618],[2539,11293,11295],{"className":11294},[2623,2624,2625,2626],[2539,11296,2774],{"className":11297},[2589,2626],[2539,11299],{"className":11300,"style":2869},[2807],[2539,11302,2764],{"className":11303},[2873],[2539,11305],{"className":11306,"style":2869},[2807],[2539,11308,11310,11313,11316,11319,11322],{"className":11309},[2580],[2539,11311],{"className":11312,"style":2800},[2584],[2539,11314,2787],{"className":11315,"style":3006},[2589,2593],[2539,11317],{"className":11318,"style":2869},[2807],[2539,11320,2764],{"className":11321},[2873],[2539,11323],{"className":11324,"style":2869},[2807],[2539,11326,11328,11331,11334,11337,11340,11343,11346,11349],{"className":11327},[2580],[2539,11329],{"className":11330,"style":4301},[2584],[2539,11332,8552],{"className":11333,"style":5606},[2589,2593],[2539,11335,6406],{"className":11336},[2807],[2539,11338,4223],{"className":11339},[2890],[2539,11341,6297],{"className":11342},[2589],[2539,11344],{"className":11345,"style":2869},[2807],[2539,11347,7514],{"className":11348},[2873],[2539,11350],{"className":11351,"style":2869},[2807],[2539,11353,11355,11359,11541,11544,11547,11550,11553,11556,11559,11562],{"className":11354},[2580],[2539,11356],{"className":11357,"style":11358},[2584],"height:1.9436em;vertical-align:-0.836em;",[2539,11360,11362,11365,11538],{"className":1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the average (Thrust-)Force ",[2539,11628,11630,11648],{"className":11629},[2542],[2539,11631,11633],{"className":11632},[2546],[2548,11634,11635],{"xmlns":2550},[2552,11636,11637,11645],{},[2555,11638,11639],{},[9930,11640,11641,11643],{"accent":2576},[2561,11642,11008],{},[2752,11644,11011],{},[2568,11646,11647],{"encoding":2570},"\\bar{F}",[2539,11649,11651],{"className":11650,"ariaHidden":2576},[2575],[2539,11652,11654,11657],{"className":11653},[2580],[2539,11655],{"className":11656,"style":11101},[2584],[2539,11658,11660],{"className":11659},[2589,10167],[2539,11661,11663],{"className":11662},[2601],[2539,11664,11666],{"className":11665},[2606],[2539,11667,11669,11677],{"className":11668,"style":11101},[2610],[2539,11670,11671,11674],{"style":10179},[2539,11672],{"className":11673,"style":2911},[2618],[2539,11675,11008],{"className":11676,"style":11122},[2589,2593],[2539,11678,11679,11682],{"style":11125},[2539,11680],{"className":11681,"style":2911},[2618],[2539,11683,11685],{"className":11684,"style":11132},[10194],[2539,11686,11011],{"className":11687},[2589],", the drag ",[2539,11690,11692,11710],{"className":11691},[2542],[2539,11693,11695],{"className":11694},[2546],[2548,11696,11697],{"xmlns":2550},[2552,11698,11699,11707],{},[2555,11700,11701],{},[2558,11702,11703,11705],{},[2561,11704,11008],{},[2561,11706,11020],{},[2568,11708,11709],{"encoding":2570},"F_D",[2539,11711,11713],{"className":11712,"ariaHidden":2576},[2575],[2539,11714,11716,11719],{"className":11715},[2580],[2539,11717],{"className":11718,"style":2822},[2584],[2539,11720,11722,11725],{"className":11721},[2589],[2539,11723,11008],{"className":11724,"style":11122},[2589,2593],[2539,11726,11728],{"className":11727},[2597],[2539,11729,11731,11751],{"className":11730},[2601,2602],[2539,11732,11734,11748],{"className":11733},[2606],[2539,11735,11737],{"className":11736,"style":2842},[2610],[2539,11738,11739,11742],{"style":11171},[2539,11740],{"className":11741,"style":2619},[2618],[2539,11743,11745],{"className":11744},[2623,2624,2625,2626],[2539,11746,11020],{"className":11747,"style":4124},[2589,2593,2626],[2539,11749,2634],{"className":11750},[2633],[2539,11752,11754],{"className":11753},[2606],[2539,11755,11757],{"className":11756,"style":2641},[2610],[2539,11758],{},", the phase lag of twisting to flapping ",[2539,11761,11763,11777],{"className":11762},[2542],[2539,11764,11766],{"className":11765},[2546],[2548,11767,11768],{"xmlns":2550},[2552,11769,11770,11774],{},[2555,11771,11772],{},[2561,11773,11076],{},[2568,11775,11776],{"encoding":2570},"\\kappa",[2539,11778,11780],{"className":11779,"ariaHidden":2576},[2575],[2539,11781,11783,11786],{"className":11782},[2580],[2539,11784],{"className":11785,"style":3166},[2584],[2539,11787,11076],{"className":11788},[2589,2593],", and the maximum angle of the inflow ",[2539,11791,11793,11839],{"className":11792},[2542],[2539,11794,11796],{"className":11795},[2546],[2548,11797,11798],{"xmlns":2550},[2552,11799,11800,11836],{},[2555,11801,11802,11812,11814],{},[2558,11803,11804,11806],{},[2561,11805,9111],{},[2558,11807,11808,11810],{},[2561,11809,7953],{},[2772,11811,5955],{},[2752,11813,2754],{},[2766,11815,11816,11834],{},[2555,11817,11818,11824,11826,11828,11830,11832],{},[2558,11819,11820,11822],{},[2561,11821,5045],{},[2772,11823,5955],{},[2752,11825,2764],{},[2772,11827,2774],{},[2561,11829,8552],{},[2752,11831,2764],{},[2561,11833,7468],{},[2561,11835,2780],{},[2568,11837,11838],{"encoding":2570},"\\alpha_{H_0} = \\frac{h_0\\cdot 2\\pi\\cdot f}{u}",[2539,11840,11842,11938],{"className":11841,"ariaHidden":2576},[2575],[2539,11843,11845,11849,11929,11932,11935],{"className":11844},[2580],[2539,11846],{"className":11847,"style":11848},[2584],"height:0.6807em;vertical-align:-0.2501em;",[2539,11850,11852,11855],{"className":11851},[2589],[2539,11853,9111],{"className":11854,"style":9186},[2589,2593],[2539,11856,11858],{"className":11857},[2597],[2539,11859,11861,11921],{"className":11860},[2601,2602],[2539,11862,11864,11918],{"className":11863},[2606],[2539,11865,11867],{"className":11866,"style":2842},[2610],[2539,11868,11869,11872],{"style":9201},[2539,11870],{"className":11871,"style":2619},[2618],[2539,11873,11875],{"className":11874},[2623,2624,2625,2626],[2539,11876,11878],{"className":11877},[2589,2626],[2539,11879,11881,11884],{"className":11880},[2589,2626],[2539,11882,7953],{"className":11883,"style":11476},[2589,2593,2626],[2539,11885,11887],{"className":11886},[2597],[2539,11888,11890,11910],{"className":11889},[2601,2602],[2539,11891,11893,11907],{"className":11892},[2606],[2539,11894,11896],{"className":11895,"style":11489},[2610],[2539,11897,11898,11901],{"style":11492},[2539,11899],{"className":11900,"style":3514},[2618],[2539,11902,11904],{"className":11903},[2623,3518,3519,2626],[2539,11905,5955],{"className":11906},[2589,2626],[2539,11908,2634],{"className":11909},[2633],[2539,11911,11913],{"className":11912},[2606],[2539,11914,11916],{"className":11915,"style":11511},[2610],[2539,11917],{},[2539,11919,2634],{"className":11920},[2633],[2539,11922,11924],{"className":11923},[2606],[2539,11925,11927],{"className":11926,"style":11523},[2610],[2539,11928],{},[2539,11930],{"className":11931,"style":2808},[2807],[2539,11933,2754],{"className":11934},[2812],[2539,11936],{"className":11937,"style":2808},[2807],[2539,11939,11941,11945],{"className":11940},[2580],[2539,11942],{"className":11943,"style":11944},[2584],"height:1.2772em;vertical-align:-0.345em;",[2539,11946,11948,11951,12064],{"className":11947},[2589],[2539,11949],{"className":11950},[2890,2891],[2539,11952,11954],{"className":11953},[2766],[2539,11955,11957,12056],{"className":11956},[2601,2602],[2539,11958,11960,12053],{"className":11959},[2606],[2539,11961,11964,11978,11986],{"className":11962,"style":11963},[2610],"height:0.9322em;",[2539,11965,11966,11969],{"style":3479},[2539,11967],{"className":11968,"style":2911},[2618],[2539,11970,11972],{"className":11971},[2623,2624,2625,2626],[2539,11973,11975],{"className":11974},[2589,2626],[2539,11976,2780],{"className":11977},[2589,2593,2626],[2539,11979,11980,11983],{"style":2920},[2539,11981],{"className":11982,"style":2911},[2618],[2539,11984],{"className":11985,"style":2928},[2927],[2539,11987,11988,11991],{"style":6928},[2539,11989],{"className":11990,"style":2911},[2618],[2539,11992,11994],{"className":11993},[2623,2624,2625,2626],[2539,11995,11997,12038,12041,12044,12047,12050],{"className":11996},[2589,2626],[2539,11998,12000,12003],{"className":11999},[2589,2626],[2539,12001,5045],{"className":12002},[2589,2593,2626],[2539,12004,12006],{"className":12005},[2597],[2539,12007,12009,12030],{"className":12008},[2601,2602],[2539,12010,12012,12027],{"className":12011},[2606],[2539,12013,12015],{"className":12014,"style":11489},[2610],[2539,12016,12018,12021],{"style":12017},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[2539,12019],{"className":12020,"style":3514},[2618],[2539,12022,12024],{"className":12023},[2623,3518,3519,2626],[2539,12025,5955],{"className":12026},[2589,2626],[2539,12028,2634],{"className":12029},[2633],[2539,12031,12033],{"className":12032},[2606],[2539,12034,12036],{"className":12035,"style":11511},[2610],[2539,12037],{},[2539,12039,2764],{"className":12040},[2873,2626],[2539,12042,2774],{"className":12043},[2589,2626],[2539,12045,8552],{"className":12046,"style":5606},[2589,2593,2626],[2539,12048,2764],{"className":12049},[2873,2626],[2539,12051,7468],{"className":12052,"style":7483},[2589,2593,2626],[2539,12054,2634],{"className":12055},[2633],[2539,12057,12059],{"className":12058},[2606],[2539,12060,12062],{"className":12061,"style":3558},[2610],[2539,12063],{},[2539,12065],{"className":12066},[2956,2891],[11,12068,12069,12070,12134],{},"Dr. Send writes: \"The coupled flapping and rotational motion of a wing is capable of overcoming the steady-state drag generated by the wing when the angle of the instantaneous inflow due to the flapping motion is greater than the angle due to the rotational motion.\nThe mechanism is particularly effective when the flapping motion leads the rotational motion by ",[2539,12071,12073,12090],{"className":12072},[2542],[2539,12074,12076],{"className":12075},[2546],[2548,12077,12078],{"xmlns":2550},[2552,12079,12080,12088],{},[2555,12081,12082],{},[2776,12083,12084,12086],{},[2772,12085,8326],{},[2752,12087,7393],{"lspace":6293,"rspace":6293},[2568,12089,8331],{"encoding":2570},[2539,12091,12093],{"className":12092,"ariaHidden":2576},[2575],[2539,12094,12096,12099,12102],{"className":12095},[2580],[2539,12097],{"className":12098,"style":7406},[2584],[2539,12100,8344],{"className":12101},[2589],[2539,12103,12105,12108],{"className":12104},[2589],[2539,12106,5955],{"className":12107},[2589],[2539,12109,12111],{"className":12110},[2597],[2539,12112,12114],{"className":12113},[2601],[2539,12115,12117],{"className":12116},[2606],[2539,12118,12120],{"className":12119,"style":7406},[2610],[2539,12121,12122,12125],{"style":5659},[2539,12123],{"className":12124,"style":2619},[2618],[2539,12126,12128],{"className":12127},[2623,2624,2625,2626],[2539,12129,12131],{"className":12130},[2589,2626],[2539,12132,7393],{"className":12133},[2589,2626],".\"",[11,12136,12137,12138,12207],{},"It makes sense that something like the \"incidence angle\" between the flapping wing and the instantaneous inflow dictates thrust. But it is also insteresting, that the wing twist ",[2539,12139,12141,12158],{"className":12140},[2542],[2539,12142,12144],{"className":12143},[2546],[2548,12145,12146],{"xmlns":2550},[2552,12147,12148,12156],{},[2555,12149,12150],{},[2558,12151,12152,12154],{},[2561,12153,9111],{},[2772,12155,5955],{},[2568,12157,9401],{"encoding":2570},[2539,12159,12161],{"className":12160,"ariaHidden":2576},[2575],[2539,12162,12164,12167],{"className":12163},[2580],[2539,12165],{"className":12166,"style":2585},[2584],[2539,12168,12170,12173],{"className":12169},[2589],[2539,12171,9111],{"className":12172,"style":9186},[2589,2593],[2539,12174,12176],{"className":12175},[2597],[2539,12177,12179,12199],{"className":12178},[2601,2602],[2539,12180,12182,12196],{"className":12181},[2606],[2539,12183,12185],{"className":12184,"style":6002},[2610],[2539,12186,12187,12190],{"style":9201},[2539,12188],{"className":12189,"style":2619},[2618],[2539,12191,12193],{"className":12192},[2623,2624,2625,2626],[2539,12194,5955],{"className":12195},[2589,2626],[2539,12197,2634],{"className":12198},[2633],[2539,12200,12202],{"className":12201},[2606],[2539,12203,12205],{"className":12204,"style":2641},[2610],[2539,12206],{}," impacts the thrust quadratically. Presumably, because the more the wing is twisted, the stronger the lift vector is rotated into the flight direction.",[74,12209,12211],{"id":12210},"fluttering-flight","Fluttering flight",[11,12213,12214],{},"This flight mode is somewhat different to normal flapping. The flapping angle becomes quite large and forward motion of the system is small. Most of the inflow on the wing is produced by the active flapping.",[11,12216,12217],{},"In this mode, effects of unsteady aerodynamics are very pronounced. The periodic and strong change of angle of attack produces vortex interactions behind the wing that change the flow at the wing. Bumblebees and Hummingbirds use this effect very strongly, basically pushing themselves off their shed vortices.\nIn fluttering, stall is delayed, as disturbances in the flow don't necessarily have enough time to traverse the airfoil fast enough to separate the flow. This can yield very high lift coefficients of up to 4.\nIf the tips of both wings get very close when the down-\u002Fupstroke start, a kind of sucking effect can be induced between the wings. This yields extra thrust and reduces the starting vortex shed.",[11,12219,12220,12221,12285,12286,12290,12291,12295],{},"Larger birds usually lift off in a rather shallow angle. Probably due to power limitations of the flight muscles. When medium sized birds lift off (VTOL), they use a different flight pattern. The wrist and wing folding becomes important. On the backstroke they fold the inner wing (shoulder and elbow) and tilt their hand backwards up to ",[2539,12222,12224,12241],{"className":12223},[2542],[2539,12225,12227],{"className":12226},[2546],[2548,12228,12229],{"xmlns":2550},[2552,12230,12231,12239],{},[2555,12232,12233],{},[2776,12234,12235,12237],{},[2772,12236,8326],{},[2752,12238,7393],{"lspace":6293,"rspace":6293},[2568,12240,8331],{"encoding":2570},[2539,12242,12244],{"className":12243,"ariaHidden":2576},[2575],[2539,12245,12247,12250,12253],{"className":12246},[2580],[2539,12248],{"className":12249,"style":7406},[2584],[2539,12251,8344],{"className":12252},[2589],[2539,12254,12256,12259],{"className":12255},[2589],[2539,12257,5955],{"className":12258},[2589],[2539,12260,12262],{"className":12261},[2597],[2539,12263,12265],{"className":12264},[2601],[2539,12266,12268],{"className":12267},[2606],[2539,12269,12271],{"className":12270,"style":7406},[2610],[2539,12272,12273,12276],{"style":5659},[2539,12274],{"className":12275,"style":2619},[2618],[2539,12277,12279],{"className":12278},[2623,2624,2625,2626],[2539,12280,12282],{"className":12281},[2589,2626],[2539,12283,7393],{"className":12284},[2589,2626]," to the wing surface. This allows them to push air downwards during the backstroke, increasing the lift produced. See e.g. ",[15,12287,1477],{"href":12288,"rel":12289},"https:\u002F\u002Fwww.youtube.com\u002Fwatch?v=uAIZrRAR31Y",[19],"\nThe small feathers on the back of the wing also help prevent stall in this extreme flight mode, as they prevent flow inversion by lifting a little off the surface. This can be very well seen in ",[15,12292,1477],{"href":12293,"rel":12294},"https:\u002F\u002Fwww.youtube.com\u002Fwatch?v=VTVigNA3KCY",[19]," slow motion footage. Here is some slow motion footage by the BBC and the Slow Mo Guys:",[1745,12297,1749,12299],{"className":12298,"controls":366},[1748],[1751,12300],{"src":12301,"type":12302},"\u002Fvideos\u002FBirdSlowMo.mp4","video\u002Fmp4",[11,12304,12305,12306,297],{},"Due to all of these strange effects, thrust generation and power requirements of fluttering is hard to calculate. We made a (probably wrong) attempt that didn't consider any of the complex aerodynamics but just the rotation of the wing. This only delivered a possibly useful value for the working point of the lift force (3\u002F4 of the wing length). You can find the calculation ",[15,12307,469],{"href":468},[74,12309,12311],{"id":12310},"power-requirements-power-systems","Power requirements & power systems",[11,12313,12314,12315,12361,12362,12409,12410,12415],{},"To supply enough power to the system, several options exist. For powered flapping flight, a larger LiPo Battery might suffice. In this flight mode, mainly potential energy gain and drag have to be compensated. The more energy hungry fluttering flight can be supplied with small shaft power engines (\"Turboprops\") with about ",[2539,12316,12318,12340],{"className":12317},[2542],[2539,12319,12321],{"className":12320},[2546],[2548,12322,12323],{"xmlns":2550},[2552,12324,12325,12337],{},[2555,12326,12327,12329,12331],{},[2772,12328,8344],{},[3225,12330,3227],{},[2555,12332,12333,12335],{},[2561,12334,3233],{"mathvariant":3232},[2561,12336,6250],{"mathvariant":3232},[2568,12338,12339],{"encoding":2570},"9\\,\\mathrm{kW}",[2539,12341,12343],{"className":12342,"ariaHidden":2576},[2575],[2539,12344,12346,12349,12352,12355],{"className":12345},[2580],[2539,12347],{"className":12348,"style":4048},[2584],[2539,12350,8344],{"className":12351},[2589],[2539,12353],{"className":12354,"style":3256},[2807],[2539,12356,12358],{"className":12357},[2589],[2539,12359,6275],{"className":12360,"style":3264},[2589,3263],", weighing ",[2539,12363,12365,12388],{"className":12364},[2542],[2539,12366,12368],{"className":12367},[2546],[2548,12369,12370],{"xmlns":2550},[2552,12371,12372,12385],{},[2555,12373,12374,12377,12379],{},[2772,12375,12376],{},"2.9",[3225,12378,3227],{},[2555,12380,12381,12383],{},[2561,12382,3233],{"mathvariant":3232},[2561,12384,3236],{"mathvariant":3232},[2568,12386,12387],{"encoding":2570},"2.9\\,\\mathrm{kg}",[2539,12389,12391],{"className":12390,"ariaHidden":2576},[2575],[2539,12392,12394,12397,12400,12403],{"className":12393},[2580],[2539,12395],{"className":12396,"style":3249},[2584],[2539,12398,12376],{"className":12399},[2589],[2539,12401],{"className":12402,"style":3256},[2807],[2539,12404,12406],{"className":12405},[2589],[2539,12407,3265],{"className":12408,"style":3264},[2589,3263]," per engine (e.g. ",[15,12411,12414],{"href":12412,"rel":12413},"https:\u002F\u002Fwww.chiefaircraft.com\u002Fjc-71147-0000.html",[19],"Jetcat SPT10","). They are similar to what Gravity uses to propel its jet suit. The lift generation of the flying exoskeleton is a lot more efficient, though, and can provide much longer flying times per litre fuel.",[11,12417,12418,12419,12422,12423,12470,12471,7856,12499,12539,12540,12587,12588,7856,12617,12736,12737,12784,12785,12832],{},"The ballpark of power requirements can also be estimated from the examples of flapping flyers. There exists a large body of research on power requirements of birds, bats, moths and even pre-historic flyers. One example from the last category is ",[438,12420,12421],{},"Quetzalcoatlus Northropi",", the largest known Pterodactyl dinosaur. Data for those beasts from the lost world are obviously questionable. But it is estimated to have lifted ",[2539,12424,12426,12449],{"className":12425},[2542],[2539,12427,12429],{"className":12428},[2546],[2548,12430,12431],{"xmlns":2550},[2552,12432,12433,12446],{},[2555,12434,12435,12438,12440],{},[2772,12436,12437],{},"250",[3225,12439,3227],{},[2555,12441,12442,12444],{},[2561,12443,3233],{"mathvariant":3232},[2561,12445,3236],{"mathvariant":3232},[2568,12447,12448],{"encoding":2570},"250\\,\\mathrm{kg}",[2539,12450,12452],{"className":12451,"ariaHidden":2576},[2575],[2539,12453,12455,12458,12461,12464],{"className":12454},[2580],[2539,12456],{"className":12457,"style":3249},[2584],[2539,12459,12437],{"className":12460},[2589],[2539,12462],{"className":12463,"style":3256},[2807],[2539,12465,12467],{"className":12466},[2589],[2539,12468,3265],{"className":12469,"style":3264},[2589,3263]," into the air, having a wingspan of ",[2539,12472,12474,12487],{"className":12473},[2542],[2539,12475,12477],{"className":12476},[2546],[2548,12478,12479],{"xmlns":2550},[2552,12480,12481,12485],{},[2555,12482,12483],{},[2772,12484,6184],{},[2568,12486,6184],{"encoding":2570},[2539,12488,12490],{"className":12489,"ariaHidden":2576},[2575],[2539,12491,12493,12496],{"className":12492},[2580],[2539,12494],{"className":12495,"style":4084},[2584],[2539,12497,6184],{"className":12498},[2589],[2539,12500,12502,12521],{"className":12501},[2542],[2539,12503,12505],{"className":12504},[2546],[2548,12506,12507],{"xmlns":2550},[2552,12508,12509,12518],{},[2555,12510,12511,12514,12516],{},[2772,12512,12513],{},"11",[3225,12515,3227],{},[2561,12517,3358],{"mathvariant":3232},[2568,12519,12520],{"encoding":2570},"11\\,\\mathrm{m}",[2539,12522,12524],{"className":12523,"ariaHidden":2576},[2575],[2539,12525,12527,12530,12533,12536],{"className":12526},[2580],[2539,12528],{"className":12529,"style":4084},[2584],[2539,12531,12513],{"className":12532},[2589],[2539,12534],{"className":12535,"style":3256},[2807],[2539,12537,3358],{"className":12538},[2589,3263],". From the standpoint of our own analysis, the resulting wing loading seems a bit much, leading to very high stall speeds and thus, landings. Maybe these giants could only land by diving into bodies of water and lift off from cliffs. In any case, the power requirement for lift-off was estimated by Marden in 1994 to be about ",[2539,12541,12543,12566],{"className":12542},[2542],[2539,12544,12546],{"className":12545},[2546],[2548,12547,12548],{"xmlns":2550},[2552,12549,12550,12563],{},[2555,12551,12552,12555,12557],{},[2772,12553,12554],{},"13",[3225,12556,3227],{},[2555,12558,12559,12561],{},[2561,12560,3233],{"mathvariant":3232},[2561,12562,6250],{"mathvariant":3232},[2568,12564,12565],{"encoding":2570},"13\\,\\mathrm{kW}",[2539,12567,12569],{"className":12568,"ariaHidden":2576},[2575],[2539,12570,12572,12575,12578,12581],{"className":12571},[2580],[2539,12573],{"className":12574,"style":4048},[2584],[2539,12576,12554],{"className":12577},[2589],[2539,12579],{"className":12580,"style":3256},[2807],[2539,12582,12584],{"className":12583},[2589],[2539,12585,6275],{"className":12586,"style":3264},[2589,3263],". Birds nowadays seem to require about ",[2539,12589,12591,12605],{"className":12590},[2542],[2539,12592,12594],{"className":12593},[2546],[2548,12595,12596],{"xmlns":2550},[2552,12597,12598,12603],{},[2555,12599,12600],{},[2772,12601,12602],{},"20",[2568,12604,12602],{"encoding":2570},[2539,12606,12608],{"className":12607,"ariaHidden":2576},[2575],[2539,12609,12611,12614],{"className":12610},[2580],[2539,12612],{"className":12613,"style":4084},[2584],[2539,12615,12602],{"className":12616},[2589],[2539,12618,12620,12647],{"className":12619},[2542],[2539,12621,12623],{"className":12622},[2546],[2548,12624,12625],{"xmlns":2550},[2552,12626,12627,12644],{},[2555,12628,12629,12632,12634],{},[2772,12630,12631],{},"50",[3225,12633,3227],{},[2766,12635,12636,12638],{},[2561,12637,6250],{"mathvariant":3232},[2555,12639,12640,12642],{},[2561,12641,3233],{"mathvariant":3232},[2561,12643,3236],{"mathvariant":3232},[2568,12645,12646],{"encoding":2570},"50\\,\\frac{\\mathrm{W}}{\\mathrm{kg}}",[2539,12648,12650],{"className":12649,"ariaHidden":2576},[2575],[2539,12651,12653,12657,12660,12663],{"className":12652},[2580],[2539,12654],{"className":12655,"style":12656},[2584],"height:1.3534em;vertical-align:-0.4811em;",[2539,12658,12631],{"className":12659},[2589],[2539,12661],{"className":12662,"style":3256},[2807],[2539,12664,12666,12669,12733],{"className":12665},[2589],[2539,12667],{"className":12668},[2890,2891],[2539,12670,12672],{"className":12671},[2766],[2539,12673,12675,12724],{"className":12674},[2601,2602],[2539,12676,12678,12721],{"className":12677},[2606],[2539,12679,12682,12699,12707],{"className":12680,"style":12681},[2610],"height:0.8723em;",[2539,12683,12684,12687],{"style":3479},[2539,12685],{"className":12686,"style":2911},[2618],[2539,12688,12690],{"className":12689},[2623,2624,2625,2626],[2539,12691,12693],{"className":12692},[2589,2626],[2539,12694,12696],{"className":12695},[2589,2626],[2539,12697,3265],{"className":12698,"style":3264},[2589,3263,2626],[2539,12700,12701,12704],{"style":2920},[2539,12702],{"className":12703,"style":2911},[2618],[2539,12705],{"className":12706,"style":2928},[2927],[2539,12708,12709,12712],{"style":3536},[2539,12710],{"className":12711,"style":2911},[2618],[2539,12713,12715],{"className":12714},[2623,2624,2625,2626],[2539,12716,12718],{"className":12717},[2589,2626],[2539,12719,6250],{"className":12720,"style":3264},[2589,3263,2626],[2539,12722,2634],{"className":12723},[2633],[2539,12725,12727],{"className":12726},[2606],[2539,12728,12731],{"className":12729,"style":12730},[2610],"height:0.4811em;",[2539,12732],{},[2539,12734],{"className":12735},[2956,2891]," bodyweight (Tobalske 2003). This would mean a power requirement of ",[2539,12738,12740,12763],{"className":12739},[2542],[2539,12741,12743],{"className":12742},[2546],[2548,12744,12745],{"xmlns":2550},[2552,12746,12747,12760],{},[2555,12748,12749,12752,12754],{},[2772,12750,12751],{},"7",[3225,12753,3227],{},[2555,12755,12756,12758],{},[2561,12757,3233],{"mathvariant":3232},[2561,12759,6250],{"mathvariant":3232},[2568,12761,12762],{"encoding":2570},"7\\,\\mathrm{kW}",[2539,12764,12766],{"className":12765,"ariaHidden":2576},[2575],[2539,12767,12769,12772,12775,12778],{"className":12768},[2580],[2539,12770],{"className":12771,"style":4048},[2584],[2539,12773,12751],{"className":12774},[2589],[2539,12776],{"className":12777,"style":3256},[2807],[2539,12779,12781],{"className":12780},[2589],[2539,12782,6275],{"className":12783,"style":3264},[2589,3263]," for the Flying Exoskeleton, assuming the upper bound. Another estimate for the minimum required power, based on the mass of the flyer, arrives at ",[2539,12786,12788,12811],{"className":12787},[2542],[2539,12789,12791],{"className":12790},[2546],[2548,12792,12793],{"xmlns":2550},[2552,12794,12795,12808],{},[2555,12796,12797,12800,12802],{},[2772,12798,12799],{},"3.5",[3225,12801,3227],{},[2555,12803,12804,12806],{},[2561,12805,3233],{"mathvariant":3232},[2561,12807,6250],{"mathvariant":3232},[2568,12809,12810],{"encoding":2570},"3.5\\,\\mathrm{kW}",[2539,12812,12814],{"className":12813,"ariaHidden":2576},[2575],[2539,12815,12817,12820,12823,12826],{"className":12816},[2580],[2539,12818],{"className":12819,"style":4048},[2584],[2539,12821,12799],{"className":12822},[2589],[2539,12824],{"className":12825,"style":3256},[2807],[2539,12827,12829],{"className":12828},[2589],[2539,12830,6275],{"className":12831,"style":3264},[2589,3263]," for sustained flight (scaling law by J.M.V. Rayner 1979).",[11,12834,12835,12836,12980,12981,13051],{},"Using aerodynamic reference values from hang gliders, one can also estimate the power required for sustained forward flight. The glide ratio ",[2539,12837,12839,12870],{"className":12838},[2542],[2539,12840,12842],{"className":12841},[2546],[2548,12843,12844],{"xmlns":2550},[2552,12845,12846,12867],{},[2555,12847,12848,12851,12853,12859,12861],{},[2561,12849,12850],{},"ϵ",[2752,12852,2754],{},[2558,12854,12855,12857],{},[2561,12856,2759],{},[2561,12858,15],{},[2561,12860,4237],{"mathvariant":3232},[2558,12862,12863,12865],{},[2561,12864,2759],{},[2561,12866,6387],{},[2568,12868,12869],{"encoding":2570},"\\epsilon = C_a\u002FC_w",[2539,12871,12873,12891],{"className":12872,"ariaHidden":2576},[2575],[2539,12874,12876,12879,12882,12885,12888],{"className":12875},[2580],[2539,12877],{"className":12878,"style":3166},[2584],[2539,12880,12850],{"className":12881},[2589,2593],[2539,12883],{"className":12884,"style":2808},[2807],[2539,12886,2754],{"className":12887},[2812],[2539,12889],{"className":12890,"style":2808},[2807],[2539,12892,12894,12897,12937,12940],{"className":12893},[2580],[2539,12895],{"className":12896,"style":4301},[2584],[2539,12898,12900,12903],{"className":12899},[2589],[2539,12901,2759],{"className":12902,"style":2829},[2589,2593],[2539,12904,12906],{"className":12905},[2597],[2539,12907,12909,12929],{"className":12908},[2601,2602],[2539,12910,12912,12926],{"className":12911},[2606],[2539,12913,12915],{"className":12914,"style":6478},[2610],[2539,12916,12917,12920],{"style":2845},[2539,12918],{"className":12919,"style":2619},[2618],[2539,12921,12923],{"className":12922},[2623,2624,2625,2626],[2539,12924,15],{"className":12925},[2589,2593,2626],[2539,12927,2634],{"className":12928},[2633],[2539,12930,12932],{"className":12931},[2606],[2539,12933,12935],{"className":12934,"style":2641},[2610],[2539,12936],{},[2539,12938,4237],{"className":12939},[2589],[2539,12941,12943,12946],{"className":12942},[2589],[2539,12944,2759],{"className":12945,"style":2829},[2589,2593],[2539,12947,12949],{"className":12948},[2597],[2539,12950,12952,12972],{"className":12951},[2601,2602],[2539,12953,12955,12969],{"className":12954},[2606],[2539,12956,12958],{"className":12957,"style":6478},[2610],[2539,12959,12960,12963],{"style":2845},[2539,12961],{"className":12962,"style":2619},[2618],[2539,12964,12966],{"className":12965},[2623,2624,2625,2626],[2539,12967,6387],{"className":12968,"style":6490},[2589,2593,2626],[2539,12970,2634],{"className":12971},[2633],[2539,12973,12975],{"className":12974},[2606],[2539,12976,12978],{"className":12977,"style":2641},[2610],[2539,12979],{}," of those flyers is about 15. One can assume a ",[2539,12982,12984,13002],{"className":12983},[2542],[2539,12985,12987],{"className":12986},[2546],[2548,12988,12989],{"xmlns":2550},[2552,12990,12991,12999],{},[2555,12992,12993],{},[2558,12994,12995,12997],{},[2561,12996,2759],{},[2561,12998,15],{},[2568,13000,13001],{"encoding":2570},"C_a",[2539,13003,13005],{"className":13004,"ariaHidden":2576},[2575],[2539,13006,13008,13011],{"className":13007},[2580],[2539,13009],{"className":13010,"style":2822},[2584],[2539,13012,13014,13017],{"className":13013},[2589],[2539,13015,2759],{"className":13016,"style":2829},[2589,2593],[2539,13018,13020],{"className":13019},[2597],[2539,13021,13023,13043],{"className":13022},[2601,2602],[2539,13024,13026,13040],{"className":13025},[2606],[2539,13027,13029],{"className":13028,"style":6478},[2610],[2539,13030,13031,13034],{"style":2845},[2539,13032],{"className":13033,"style":2619},[2618],[2539,13035,13037],{"className":13036},[2623,2624,2625,2626],[2539,13038,15],{"className":13039},[2589,2593,2626],[2539,13041,2634],{"className":13042},[2633],[2539,13044,13046],{"className":13045},[2606],[2539,13047,13049],{"className":13048,"style":2641},[2610],[2539,13050],{}," of 0.75 for distance flight (s. e.g. Berblinger2 paper by Dr. Send). The power reqired then follows from the drag force:",[2539,13053,13055],{"className":13054},[2734],[2539,13056,13058,13117],{"className":13057},[2542],[2539,13059,13061],{"className":13060},[2546],[2548,13062,13063],{"xmlns":2550,"display":2743},[2552,13064,13065,13114],{},[2555,13066,13067,13069,13071,13081,13083,13089,13091,13093,13095,13101,13103,13106,13108],{},[2561,13068,7136],{},[2752,13070,2754],{},[2766,13072,13073,13079],{},[2558,13074,13075,13077],{},[2561,13076,2759],{},[2561,13078,15],{},[2561,13080,12850],{},[2752,13082,2764],{},[2766,13084,13085,13087],{},[2561,13086,2770],{},[2772,13088,2774],{},[2752,13090,2764],{},[2561,13092,2787],{},[2752,13094,2764],{},[2776,13096,13097,13099],{},[2561,13098,2780],{},[2772,13100,5488],{},[2752,13102,2754],{},[2772,13104,13105],{},"3.66",[3225,13107,3227],{},[2555,13109,13110,13112],{},[2561,13111,3233],{"mathvariant":3232},[2561,13113,6250],{"mathvariant":3232},[2568,13115,13116],{"encoding":2570},"P = \\frac{C_a}{\\epsilon}\\cdot \\frac{\\rho}{2}\\cdot S \\cdot u^3 = 3.66\\,\\mathrm{kW}",[2539,13118,13120,13138,13253,13330,13348,13392],{"className":13119,"ariaHidden":2576},[2575],[2539,13121,13123,13126,13129,13132,13135],{"className":13122},[2580],[2539,13124],{"className":13125,"style":2800},[2584],[2539,13127,7136],{"className":13128,"style":11122},[2589,2593],[2539,13130],{"className":13131,"style":2808},[2807],[2539,13133,2754],{"className":13134},[2812],[2539,13136],{"className":13137,"style":2808},[2807],[2539,13139,13141,13145,13244,13247,13250],{"className":13140},[2580],[2539,13142],{"className":13143,"style":13144},[2584],"height:2.0463em;vertical-align:-0.686em;",[2539,13146,13148,13151,13241],{"className":13147},[2589],[2539,13149],{"className":13150},[2890,2891],[2539,13152,13154],{"className":13153},[2766],[2539,13155,13157,13233],{"className":13156},[2601,2602],[2539,13158,13160,13230],{"className":13159},[2606],[2539,13161,13163,13174,13182],{"className":13162,"style":4825},[2610],[2539,13164,13165,13168],{"style":2907},[2539,13166],{"className":13167,"style":2911},[2618],[2539,13169,13171],{"className":13170},[2589],[2539,13172,12850],{"className":13173},[2589,2593],[2539,13175,13176,13179],{"style":2920},[2539,13177],{"className":13178,"style":2911},[2618],[2539,13180],{"className":13181,"style":2928},[2927],[2539,13183,13184,13187],{"style":2931},[2539,13185],{"className":13186,"style":2911},[2618],[2539,13188,13190],{"className":13189},[2589],[2539,13191,13193,13196],{"className":13192},[2589],[2539,13194,2759],{"className":13195,"style":2829},[2589,2593],[2539,13197,13199],{"className":13198},[2597],[2539,13200,13202,13222],{"className":13201},[2601,2602],[2539,13203,13205,13219],{"className":13204},[2606],[2539,13206,13208],{"className":13207,"style":6478},[2610],[2539,13209,13210,13213],{"style":2845},[2539,13211],{"className":13212,"style":2619},[2618],[2539,13214,13216],{"className":13215},[2623,2624,2625,2626],[2539,13217,15],{"className":13218},[2589,2593,2626],[2539,13220,2634],{"className":13221},[2633],[2539,13223,13225],{"className":13224},[2606],[2539,13226,13228],{"className":13227,"style":2641},[2610],[2539,13229],{},[2539,13231,2634],{"className":13232},[2633],[2539,13234,13236],{"className":13235},[2606],[2539,13237,13239],{"className":13238,"style":2950},[2610],[2539,13240],{},[2539,13242],{"className":13243},[2956,2891],[2539,13245],{"className":13246,"style":2869},[2807],[2539,13248,2764],{"className":13249},[2873],[2539,13251],{"className":13252,"style":2869},[2807],[2539,13254,13256,13259,13321,13324,13327],{"className":13255},[2580],[2539,13257],{"className":13258,"style":2883},[2584],[2539,13260,13262,13265,13318],{"className":13261},[2589],[2539,13263],{"className":13264},[2890,2891],[2539,13266,13268],{"className":13267},[2766],[2539,13269,13271,13310],{"className":13270},[2601,2602],[2539,13272,13274,13307],{"className":13273},[2606],[2539,13275,13277,13288,13296],{"className":13276,"style":2904},[2610],[2539,13278,13279,13282],{"style":2907},[2539,13280],{"className":13281,"style":2911},[2618],[2539,13283,13285],{"className":13284},[2589],[2539,13286,2774],{"className":13287},[2589],[2539,13289,13290,13293],{"style":2920},[2539,13291],{"className":13292,"style":2911},[2618],[2539,13294],{"className":13295,"style":2928},[2927],[2539,13297,13298,13301],{"style":2931},[2539,13299],{"className":13300,"style":2911},[2618],[2539,13302,13304],{"className":13303},[2589],[2539,13305,2770],{"className":13306},[2589,2593],[2539,13308,2634],{"className":13309},[2633],[2539,13311,13313],{"className":13312},[2606],[2539,13314,13316],{"className":13315,"style":2950},[2610],[2539,13317],{},[2539,13319],{"className":13320},[2956,2891],[2539,13322],{"className":13323,"style":2869},[2807],[2539,13325,2764],{"className":13326},[2873],[2539,13328],{"className":13329,"style":2869},[2807],[2539,13331,13333,13336,13339,13342,13345],{"className":13332},[2580],[2539,13334],{"className":13335,"style":2800},[2584],[2539,13337,2787],{"className":13338,"style":3006},[2589,2593],[2539,13340],{"className":13341,"style":2869},[2807],[2539,13343,2764],{"className":13344},[2873],[2539,13346],{"className":13347,"style":2869},[2807],[2539,13349,13351,13354,13383,13386,13389],{"className":13350},[2580],[2539,13352],{"className":13353,"style":2975},[2584],[2539,13355,13357,13360],{"className":13356},[2589],[2539,13358,2780],{"className":13359},[2589,2593],[2539,13361,13363],{"className":13362},[2597],[2539,13364,13366],{"className":13365},[2601],[2539,13367,13369],{"className":13368},[2606],[2539,13370,13372],{"className":13371,"style":2975},[2610],[2539,13373,13374,13377],{"style":2978},[2539,13375],{"className":13376,"style":2619},[2618],[2539,13378,13380],{"className":13379},[2623,2624,2625,2626],[2539,13381,5488],{"className":13382},[2589,2626],[2539,13384],{"className":13385,"style":2808},[2807],[2539,13387,2754],{"className":13388},[2812],[2539,13390],{"className":13391,"style":2808},[2807],[2539,13393,13395,13398,13401,13404],{"className":13394},[2580],[2539,13396],{"className":13397,"style":4048},[2584],[2539,13399,13105],{"className":13400},[2589],[2539,13402],{"className":13403,"style":3256},[2807],[2539,13405,13407],{"className":13406},[2589],[2539,13408,6275],{"className":13409,"style":3264},[2589,3263],[11,13411,13412,13413,4052,13441,13549,13550,13578,13579,4052,13607,297],{},"This further assumes a velocity ",[2539,13414,13416,13429],{"className":13415},[2542],[2539,13417,13419],{"className":13418},[2546],[2548,13420,13421],{"xmlns":2550},[2552,13422,13423,13427],{},[2555,13424,13425],{},[2561,13426,2780],{},[2568,13428,2780],{"encoding":2570},[2539,13430,13432],{"className":13431,"ariaHidden":2576},[2575],[2539,13433,13435,13438],{"className":13434},[2580],[2539,13436],{"className":13437,"style":3166},[2584],[2539,13439,2780],{"className":13440},[2589,2593],[2539,13442,13444,13466],{"className":13443},[2542],[2539,13445,13447],{"className":13446},[2546],[2548,13448,13449],{"xmlns":2550},[2552,13450,13451,13463],{},[2555,13452,13453,13455,13457],{},[2772,13454,12602],{},[3225,13456,3227],{},[2766,13458,13459,13461],{},[2561,13460,3358],{"mathvariant":3232},[2561,13462,3363],{"mathvariant":3232},[2568,13464,13465],{"encoding":2570},"20\\,\\frac{\\mathrm{m}}{\\mathrm{s}}",[2539,13467,13469],{"className":13468,"ariaHidden":2576},[2575],[2539,13470,13472,13475,13478,13481],{"className":13471},[2580],[2539,13473],{"className":13474,"style":3451},[2584],[2539,13476,12602],{"className":13477},[2589],[2539,13479],{"className":13480,"style":3256},[2807],[2539,13482,13484,13487,13546],{"className":13483},[2589],[2539,13485],{"className":13486},[2890,2891],[2539,13488,13490],{"className":13489},[2766],[2539,13491,13493,13538],{"className":13492},[2601,2602],[2539,13494,13496,13535],{"className":13495},[2606],[2539,13497,13499,13513,13521],{"className":13498,"style":3476},[2610],[2539,13500,13501,13504],{"style":3479},[2539,13502],{"className":13503,"style":2911},[2618],[2539,13505,13507],{"className":13506},[2623,2624,2625,2626],[2539,13508,13510],{"className":13509},[2589,2626],[2539,13511,3363],{"className":13512},[2589,3263,2626],[2539,13514,13515,13518],{"style":2920},[2539,13516],{"className":13517,"style":2911},[2618],[2539,13519],{"className":13520,"style":2928},[2927],[2539,13522,13523,13526],{"style":3536},[2539,13524],{"className":13525,"style":2911},[2618],[2539,13527,13529],{"className":13528},[2623,2624,2625,2626],[2539,13530,13532],{"className":13531},[2589,2626],[2539,13533,3358],{"className":13534},[2589,3263,2626],[2539,13536,2634],{"className":13537},[2633],[2539,13539,13541],{"className":13540},[2606],[2539,13542,13544],{"className":13543,"style":3558},[2610],[2539,13545],{},[2539,13547],{"className":13548},[2956,2891],", the wing area ",[2539,13551,13553,13566],{"className":13552},[2542],[2539,13554,13556],{"className":13555},[2546],[2548,13557,13558],{"xmlns":2550},[2552,13559,13560,13564],{},[2555,13561,13562],{},[2561,13563,2787],{},[2568,13565,2787],{"encoding":2570},[2539,13567,13569],{"className":13568,"ariaHidden":2576},[2575],[2539,13570,13572,13575],{"className":13571},[2580],[2539,13573],{"className":13574,"style":2800},[2584],[2539,13576,2787],{"className":13577,"style":3006},[2589,2593]," from above and an air density ",[2539,13580,13582,13595],{"className":13581},[2542],[2539,13583,13585],{"className":13584},[2546],[2548,13586,13587],{"xmlns":2550},[2552,13588,13589,13593],{},[2555,13590,13591],{},[2561,13592,2770],{},[2568,13594,3126],{"encoding":2570},[2539,13596,13598],{"className":13597,"ariaHidden":2576},[2575],[2539,13599,13601,13604],{"className":13600},[2580],[2539,13602],{"className":13603,"style":3136},[2584],[2539,13605,2770],{"className":13606},[2589,2593],[2539,13608,13610,13641],{"className":13609},[2542],[2539,13611,13613],{"className":13612},[2546],[2548,13614,13615],{"xmlns":2550},[2552,13616,13617,13638],{},[2555,13618,13619,13622,13624],{},[2772,13620,13621],{},"1.22",[3225,13623,3227],{},[2766,13625,13626,13632],{},[2555,13627,13628,13630],{},[2561,13629,3233],{"mathvariant":3232},[2561,13631,3236],{"mathvariant":3232},[2776,13633,13634,13636],{},[2561,13635,3358],{"mathvariant":3232},[2772,13637,5488],{},[2568,13639,13640],{"encoding":2570},"1.22\\,\\frac{\\mathrm{kg}}{\\mathrm{m^{3}}}",[2539,13642,13644],{"className":13643,"ariaHidden":2576},[2575],[2539,13645,13647,13650,13653,13656],{"className":13646},[2580],[2539,13648],{"className":13649,"style":11944},[2584],[2539,13651,13621],{"className":13652},[2589],[2539,13654],{"className":13655,"style":3256},[2807],[2539,13657,13659,13662,13753],{"className":13658},[2589],[2539,13660],{"className":13661},[2890,2891],[2539,13663,13665],{"className":13664},[2766],[2539,13666,13668,13745],{"className":13667},[2601,2602],[2539,13669,13671,13742],{"className":13670},[2606],[2539,13672,13674,13717,13725],{"className":13673,"style":11963},[2610],[2539,13675,13676,13679],{"style":3479},[2539,13677],{"className":13678,"style":2911},[2618],[2539,13680,13682],{"className":13681},[2623,2624,2625,2626],[2539,13683,13685],{"className":13684},[2589,2626],[2539,13686,13688,13691],{"className":13687},[2589,2626],[2539,13689,3358],{"className":13690},[2589,3263,2626],[2539,13692,13694],{"className":13693},[2597],[2539,13695,13697],{"className":13696},[2601],[2539,13698,13700],{"className":13699},[2606],[2539,13701,13703],{"className":13702,"style":3507},[2610],[2539,13704,13705,13708],{"style":3510},[2539,13706],{"className":13707,"style":3514},[2618],[2539,13709,13711],{"className":13710},[2623,3518,3519,2626],[2539,13712,13714],{"className":13713},[2589,2626],[2539,13715,5488],{"className":13716},[2589,3263,2626],[2539,13718,13719,13722],{"style":2920},[2539,13720],{"className":13721,"style":2911},[2618],[2539,13723],{"className":13724,"style":2928},[2927],[2539,13726,13727,13730],{"style":6928},[2539,13728],{"className":13729,"style":2911},[2618],[2539,13731,13733],{"className":13732},[2623,2624,2625,2626],[2539,13734,13736],{"className":13735},[2589,2626],[2539,13737,13739],{"className":13738},[2589,2626],[2539,13740,3265],{"className":13741,"style":3264},[2589,3263,2626],[2539,13743,2634],{"className":13744},[2633],[2539,13746,13748],{"className":13747},[2606],[2539,13749,13751],{"className":13750,"style":3558},[2610],[2539,13752],{},[2539,13754],{"className":13755},[2956,2891],[11,13757,13758,13759,13805],{},"Machines can have a much higher force- and powerdensity then biological systems. Applying even ",[2539,13760,13762,13784],{"className":13761},[2542],[2539,13763,13765],{"className":13764},[2546],[2548,13766,13767],{"xmlns":2550},[2552,13768,13769,13781],{},[2555,13770,13771,13773,13775],{},[2772,13772,12602],{},[3225,13774,3227],{},[2555,13776,13777,13779],{},[2561,13778,3233],{"mathvariant":3232},[2561,13780,6250],{"mathvariant":3232},[2568,13782,13783],{"encoding":2570},"20\\,\\mathrm{kW}",[2539,13785,13787],{"className":13786,"ariaHidden":2576},[2575],[2539,13788,13790,13793,13796,13799],{"className":13789},[2580],[2539,13791],{"className":13792,"style":4048},[2584],[2539,13794,12602],{"className":13795},[2589],[2539,13797],{"className":13798,"style":3256},[2807],[2539,13800,13802],{"className":13801},[2589],[2539,13803,6275],{"className":13804,"style":3264},[2589,3263]," of power is not a real issue when using tubo engines. On the other hand, birds and other small flyers can profit more from unsteady aerodynamics, as they move in a different Reynolds-number regime. Also, bird feathers are still hard to reproduce technically (aerodynamics + stiffness). So the Flying Exoskeleton does not necessarily outperform birds off the bat. In any case, these estimated power requirements seem attainable.",[74,13807,13809],{"id":13808},"control","Control",[11,13811,13812,13813,13818],{},"Control can be an issue with a bird-like tail, as it was during the development of the ",[15,13814,13817],{"href":13815,"rel":13816},"https:\u002F\u002Fwww.youtube.com\u002Fwatch?v=kA7PNQiHT1Q",[19],"SmartBird",".\nAs the arms are busy and for the authentic feel, this tail should be controlled with the feet. The exoskeleton at the ankles can detect the angle and transform this into control output to the tail. Bird tails do not split elevator and rudder, but have one aerodynamic surface for both purposes. The tail can rotate along its axis and bob. As a result, the tail can produce moments in any direction around the body center. Birds actually often don't use the tail like a typical elevator, but regulate tilting moment via wing twist. The tail is sometimes even used to create extra lift.",[11,13820,13821],{},"Controlling roll via the arms, pitch and yaw with the feet has been tested by Fluglich using the Exoskid and the Exoskid Trainer. This distribution was indeed found to be intuitive, even though tail control via the feet requires some training. In our setup, the rudder was controlled by the angle-difference of the ankle joints, while the elevator was controlled by the average angle of the two joints.",[74,13823,13825],{"id":13824},"safety-systems","Safety Systems",[11,13827,13828],{},"Despite what every second German out there seems to believe, we have also spent some thoughts on safety. From pilot error or system failure stems arisk of crashing.",[82,13830,13832],{"id":13831},"when-far-enough-above-ground-or-in-stable-flight","When far enough above ground or in stable flight",[11,13834,13835],{},"The wings are supposed to be designed in a way, that they return to a neurally gliding configuration upon power loss. This can be facilitated by wires along the core of the wing skeleton. When power is lost, these wires are tensioned by springs. The wing joints can be designed in a way that they return and be held in the desired position this way. Alternatively there could be inflatable bags inside the joints that get filled by pressurized air cartridges on power loss, acheiving the same effect.",[11,13837,13838],{},"Even with one wing broken or ripped off, the system would still rotate down to the ground like a maple seed. A possible option would be to separate backpack and exoskeleton, ejecting the pilot with a parachute. This can work even relatively close to the ground, if an explosively inflated chute is used (has been only used in drones up to now).",[82,13840,13842],{"id":13841},"close-to-the-ground","Close to the ground",[11,13844,13845],{},"This part is more tricky. If the system is still reactive, the wings could be used to cushion the crash, destroying the wings, but saving the pilot. Other than that, the exoskeleton could contain inflatable \"airbags\" around the body, forming a full body airbag.",[82,13847,13849],{"id":13848},"general-safety-systems","General safety systems",[11,13851,13852],{},"The flight computers and sensors are supposed to be redundant as in commercial airplanes. But many of the critical componens, like the power electronics, can not be made redundant due to weight constraints.",[11,13854,13855],{},"Reaching above the helmet from the backpack there is supposed to be a crash bar protecting the neck in case of a belly landing. The backpack will probably need to contain a fire control system.",[74,13857,13859],{"id":13858},"designing-the-exoskeleton","Designing the Exoskeleton",[11,13861,13862],{},[530,13863],{"alt":2489,"src":13864},"\u002Fimages\u002FWingVisionFront_exocutout.png",[11,13866,13867],{},"The exoskeleton is the human-machine-interface of the system. It has several tasks:",[87,13869,13870,13873,13876,13879,13882],{},[90,13871,13872],{},"measuring and delivering position and forces at the limbs",[90,13874,13875],{},"supporting the legs and the arms against gravity's pull",[90,13877,13878],{},"protecting the pilot from cold and other physical harms",[90,13880,13881],{},"providing a flight information system",[90,13883,13884],{},"implementing matters of design",[11,13886,13887],{},"In its most sophisticated form, the exoskeleton will consist of 7 degrees of freedom (DOF) for each arm, and 3 DOF for each leg. The arms are directly mapped to the DOF of the wings, allowing to control the following angles:",[87,13889,13890,13893,13896,13899,13902,13905,13908],{},[90,13891,13892],{},"dihedral angle (flapping, shoulder 1),",[90,13894,13895],{},"angle of attack (shoulder 2),",[90,13897,13898],{},"wing sweep angle (shoulder 3),",[90,13900,13901],{},"folding the wing elbow (elbow),",[90,13903,13904],{},"folding the wing hand (wrist 1),",[90,13906,13907],{},"dihedral angle of the hand (wrist 2),",[90,13909,13910],{},"angle of attack of the hand (aileron equivalent, lower arm).",[11,13912,13913],{},"The DOF of the ankle controls the tail, as described above. The two additional DOF are used for weight offloading through a lower-limb exoskeleton (knee and hip).",[11,13915,13916],{},"Not all of these angles are necessary for the first prototype. The minimum setup controlling horizontal flapping flight only requires aileron, tail and flapping. This has been realized with the Exoskid.",[82,13918,13920],{"id":13919},"soft-or-hard","Soft or Hard?",[11,13922,13923,13924,13927,13928,13931],{},"If the exoskeleton should be hard or soft, is a matter of debate. The ",[438,13925,13926],{},"soft exoskeleton"," uses the bones of the body as structure and only applies forces via pulleys. This has the advantage of being lightweight. However it has the disadvantage of being imprecise in measuring and applying force and position. This can make it hard to apply proper control theory. The ",[438,13929,13930],{},"hard exoskeleton"," has a structure of its own. It is easier to approach from a control theory side and can be implemented with common engineering tools and materials. Its main disadvantage is biomechanics. As the structure is external to the body, it has to follow the movement of the limbs relatively faithfully in order to not hurt the operator. This can be a significant challenge, especially with the shoulder joint. Nevertheless, due to the ease of manufacture and instrumentation, Fluglicht has decided to build a hard exoskeleton.",[82,13933,13935],{"id":13934},"helmet","Helmet",[11,13937,13938],{},"For navigation and system control, the pilot will wear a helmet with built-in Head-Up-Display in the visor. This will provide typical altitude, attitude, orientation, speed, turning rate, etc. data as known from airplane instrumentation. Perception of movement could also be made available in an intuitive way by virtually projecting an array of dots into the surrounding volume via the visor. This way, the pilot can comprehend movement relative to this dot grid.",[74,13940,13942],{"id":13941},"technological-next-steps","Technological Next Steps",[87,13944,13945,13948,13951,13954],{},[90,13946,13947],{},"Create a CAD model for the full-scale tethered wings prototype and build it. This doesn't need to have an exact aerodynamic and structural design.",[90,13949,13950],{},"Create realistic\u002Fproducible design for the exoskeleton and build it.",[90,13952,13953],{},"Research question: how does a teleoperation system behave, where there is a mechanical connection between master and slave? This feedback route is out of scope for typical teleoperation.",[90,13955,13956],{},"Exoskid: giving the person a feeling for where \"zero deflection\" is, is important as long as there is no force feedback from the aerodynamic forces.",[74,13958,13960],{"id":13959},"how-to-cite-this-article","How to cite this article",[11,13962,13963,13964],{},"P. Jüstel - \"How to design a flying Exoskeleton\", Febuary 2026, ",[15,13965,13966],{"href":13966,"rel":13967},"https:\u002F\u002Ffluglicht.com\u002Fblog\u002Ftechnology_details",[19],{"title":339,"searchDepth":340,"depth":340,"links":13969},[13970,13974,13981,13982,13985,13986,13993,13994,13995,13996,14001,14005,14006],{"id":2439,"depth":340,"text":2440,"children":13971},[13972,13973],{"id":2465,"depth":345,"text":2466},{"id":2515,"depth":345,"text":2516},{"id":2720,"depth":340,"text":2721,"children":13975},[13976,13977,13979],{"id":3204,"depth":345,"text":3205},{"id":3637,"depth":345,"text":13978},"CLC_LCL​ and SSS",{"id":4903,"depth":345,"text":13980},"Stall speed uminu_{min}umin​",{"id":5432,"depth":340,"text":5433},{"id":5885,"depth":340,"text":5886,"children":13983},[13984],{"id":6062,"depth":345,"text":6063},{"id":6340,"depth":340,"text":6341},{"id":7367,"depth":340,"text":7368,"children":13987},[13988,13989,13990,13991,13992],{"id":7446,"depth":345,"text":7447},{"id":8298,"depth":345,"text":8299},{"id":8383,"depth":345,"text":8384},{"id":10556,"depth":345,"text":10557},{"id":10984,"depth":345,"text":10985},{"id":12210,"depth":340,"text":12211},{"id":12310,"depth":340,"text":12311},{"id":13808,"depth":340,"text":13809},{"id":13824,"depth":340,"text":13825,"children":13997},[13998,13999,14000],{"id":13831,"depth":345,"text":13832},{"id":13841,"depth":345,"text":13842},{"id":13848,"depth":345,"text":13849},{"id":13858,"depth":340,"text":13859,"children":14002},[14003,14004],{"id":13919,"depth":345,"text":13920},{"id":13934,"depth":345,"text":13935},{"id":13941,"depth":340,"text":13942},{"id":13959,"depth":340,"text":13960},"Details of our design",{"topic":1021,"category":14009,"authors":14010,"tags":14012,"date":1026},"Technology",[14011],{"name":359,"avatar":360},[14009,14013,2489],"Wings",{"title":337,"description":14007},"blog\u002F9.Technology_Details","fRwykP2bNi17rzzMnHELCfnGrzn8GSD3qtvKOTUv1IM",[14018],{"title":1021,"path":14019,"stem":1025,"children":14020,"page":14035},"\u002Fblog",[14021,14022,14023,14024,14025,14026,14027,14028,14029,14030,14031,14032,14033,14034],{"title":6,"path":367,"stem":369,"children":-1},{"title":1242,"path":1434,"stem":1436,"children":-1},{"title":1440,"path":1558,"stem":1560,"children":-1},{"title":1564,"path":1718,"stem":1720,"children":-1},{"title":1724,"path":1854,"stem":1856,"children":-1},{"title":1860,"path":1999,"stem":2001,"children":-1},{"title":2005,"path":2055,"stem":2057,"children":-1},{"title":2061,"path":2145,"stem":2147,"children":-1},{"title":2151,"path":2205,"stem":2207,"children":-1},{"title":2211,"path":583,"stem":2431,"children":-1},{"title":337,"path":336,"stem":14015,"children":-1},{"title":373,"path":1027,"stem":1029,"children":-1},{"title":1033,"path":1055,"stem":1057,"children":-1},{"title":1061,"path":1236,"stem":1238,"children":-1},false,1782398427596]