Kite Flying — credits and provenance ==================================== WHAT THIS IS An independent reimplementation of the steady-state physics of a kite on a flexible tether. Nothing here is copied from any other kite simulator: no code, no art, no data. Every asset ships in this bundle and the page loads nothing from any other site. The app calls no language model and spends no credits. THE SUBJECT Kite flying is a practice roughly 2,500 years old and in the public domain. Wikipedia records the invention claimed in China for the 5th-century-BC philosophers Mozi and Lu Ban, who flew wooden kites called muyuan, and a kite used to carry a rescue message by 549 AD. Accounts reached Europe with Marco Polo late in the 13th century; Benjamin Franklin published his kite experiment in 1752. The kite drawn on screen is a bowed tailless diamond of the type developed in the late 1880s by WILLIAM ABNER EDDY (28 January 1850 - 26 December 1909) and patented as US 646375, granted 27 March 1900. The box kite referred to in the text is LAWRENCE HARGRAVE's, of 1893. Both are long out of patent. The 2014 altitude record of 16,009 ft cited in the app is Robert Moore's team, with a 12 m^2 delta carrying a box centre cell. WHAT DIFFERS FROM A REAL KITE - Steady state only. The wind is uniform in height, steady and horizontal. Real wind has a boundary layer and gusts; a gust is a transient this model cannot represent, and the documented NASA statement that a kite "moves vertically" on a gust describes exactly that transient rather than a new equilibrium. - Two dimensions. The kite sits in the vertical plane through the wind. A real kite yaws, rolls, hunts and can be flown across the wind window. - The kite is a flat plate with a single aerodynamic centre and no stall. Past roughly 15 degrees the thin-plate lift model is outside the range its own sources claim for it. - The bridle model is a free two-dimensional pivot about a single tow point. It has no keel and no tail, and it disagrees with one hobby source about which way to move the tow point; the app says so in its About panel rather than tuning the disagreement away. - Line stretch is ignored: the tether is inextensible. SOURCES USED, WITH WHAT EACH ONE SUPPLIED NASA Glenn, Beginner's Guide to Kites - the force balance Pv + W - L = 0, Ph - D = 0, tan b = Pv/Ph. https://www.grc.nasa.gov/www/K-12/airplane/kitefor.html NASA Glenn, Kite Lift Equations - Clo = 2*pi*a, AR = s^2/A, Cl = Clo/(1 + Clo/(pi*AR)). https://www.grc.nasa.gov/www/K-12/airplane/kitelift.html NASA Glenn, Kite Drag Equations - Cdo = 1.28*sin(a), Cd = Cdo + Cl^2/(.7*pi*AR). https://www.grc.nasa.gov/www/K-12/airplane/kitedrag.html Leloup, Roncin, Bles, Leroux, Jochum, Parlier, "Estimation of the Lift-to-Drag Ratio Using the Lifting Line Method: Application to a Leading Edge Inflatable Kite", chapter 19 of Airborne Wind Energy (2013) - the massless-kite statement T + Fa = 0, the glide angle eps = arctan(D/L), and the only measured kite polar quoted here (Flexifoil Blade III, CL = 0.776, CD = 0.128 +/- 0.012). https://crea.ecole-air-espace.fr/wp-content/uploads/2020/03/2013ch19_awe22_leloup.pdf Sadeh and Saharon, "Turbulence Effect on Crossflow Around a Circular Cylinder at Subcritical Reynolds Numbers", NASA Contractor Report 3622 (1982) - subcritical cylinder drag coefficients between 1.10 and 1.31 for the flying line. https://ntrs.nasa.gov/api/citations/19830005116/downloads/19830005116.pdf "Study on Wind Load Distribution and Aerodynamic Characteristics of a Yawed Cylinder", Buildings 15(23):4390 - the independence (cross-flow) principle, and its stated limits. https://doi.org/10.3390/buildings15234390 "Refining the airborne wind energy system power equations with a vortex wake model", Wind Energy Science 8:1639 (2023), citing Trevisi, Gaunaa and McWilliam (2020) - the equivalent tether drag coefficient C_D,t = C_Dperp * d * L / (4A). https://wes.copernicus.org/articles/8/1639/2023/ Wikipedia, "Catenary" - the cable equation and the closed form the dragless limit must reproduce. https://en.wikipedia.org/wiki/Catenary Emmakites braided Dacron line specifications - line diameters and masses per metre. https://www.emmakites.com/products/50-200lb-braided-dacron-kite-line Kitesite Australia - braided Dyneema diameters and mass per metre. https://www.kitesite.com.au/kiterecord/dyneema.html Wikipedia, "Kite", "William Abner Eddy", "Box kite" - history, dates, patent number. https://en.wikipedia.org/wiki/Kite my-best-kite.com, "How Does A Kite Fly? A Tale Of Four Forces" - the flyer-facing statement that longer lines lower the flight angle. https://www.my-best-kite.com/how-does-a-kite-fly.html American Kitefliers Association, "How Do Kites Fly?" - the tow-point rule this model disagrees with. https://www.kite.org/about-kites/how-do-kites-fly/ RECONSTRUCTED, BECAUSE NO SOURCE COULD BE FOUND - The frame-and-bridle parasite drag coefficient (default 0.03). Exposed as a control. Without it the thin-plate model has no best angle of attack at all. - Lift and drag curves for the Eddy diamond, the Hargrave box kite and the sled. No fetchable source publishes them; Hoerner's Fluid-Dynamic Drag is not online and the delta-kite papers in MDPI Energies and Wiley Wind Energy were unreachable. Every polar in this app comes from the flat-plate model instead. - The centre-of-gravity and tow-point stand-off fractions used by the bridle model. TWO PUBLISHED RESULTS THIS APP CONTRADICTS, WITH ARITHMETIC 1. NASA's finite-wing lift correction, Cl = Clo/(1 + Clo/(pi*AR)), is not the Prandtl lifting-line result it resembles. Lifting line corrects the lift-curve SLOPE, giving Cl = 2*pi*a/(1 + 2/AR) with a constant denominator; NASA's puts the coefficient where the slope belongs, so its correction fades away as a goes to zero. The two agree only at a = 1 radian. Both models ship, with the gap measured in the app. 2. The AWE equivalent tether drag coefficient C_D,t = C_Dperp*d*L/(4A) does not reproduce the exact tether solution for a kite parked in a steady wind, because its quarter comes from a crosswind kite whose tether sees a linear speed ramp. The app measures the error in both directions. NAMES AND TRADEMARKS Product, material and company names mentioned in this app and in these credits (Dacron, Dyneema, Flexifoil Blade III, Emmakites, Kitesite Australia, NASA KiteModeler) belong to their respective owners and are used only to identify the source of a published figure. This app is not affiliated with, endorsed by or sponsored by any of them, and it uses no logos or artwork from them. LICENCE This reimplementation is released under the MIT licence; see LICENSE.txt.