The person in the image above is enjoying a totally silent flight under a triangle. How does this work?
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The triangle is a Rogallo wing, invented by Gertrude and Francis Rogallo in 1948. The Rogallo wing is made of fabric and supported by a very light frame, which holds the fabric in two triangular sections whose cross section becomes conical when filled with air. The resulting shape provides lift, and the flyer changes his body position to change the flight direction from left to right. As depicted below, these glider aircraft have been used to monitor the migratory flight of geese and Demoiselle cranes.
The most important characteristic of any wing is its lift/drag ratio (L/D), which determines its glide angle. For the Rogallo wing, L/D ratios of 9:1 to 14:1 are attainable, resulting in them being safe and fun to fly.
See more for yourself about hang gliders: http://www.willswing.com/articles/Hang-Glider-Design-and-Performance.pdf
A major pioneer of manned flight was Otto Lilienthal, who spearheaded wing design in gliders thirty years before the Wright brothers. Lilienthal developed a correct shape for an airplane wing but died in a crash of his glider, when gusts overcame his ability to move his body fast enough to counteract the change in wind direction. You can read more about him and his innovations at the link below.