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I'm trying to design a parachute that minimizes the descent velocity, but I'm not sure what shape I should use.

From what I've read, ellipse-shaped parachutes are too aerodynamic and minimize drag, while squares are good enough to maximize drag, but I've read this from very unreliable sources and unfortunately I've never taken a fluid dynamics course so I'm not sure if those answers are right.

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Well, obviously, this is for one of my university courses, this is nothing serious. Basically, we have to get our parachutes to stay afloat for more than a predetermined time. – user1002327 Aug 16 '12 at 0:20

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You want your parachute not to be a parachute, but a wing. The difference is that it has horizontal velocity, and the air flows smoothly over the top and bottom surfaces.

In addition, you want to minimize drag, because sink rate is proportional to drag. The main way to minimize drag is to minimize speed. So it needs forward speed, but no more than necessary.

Check out paragliders, because that's what they do. I've seen these things in action. They stay up a long time.

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Let me see if I understand. Paragliders keep the descent speed low and add a horizontal velocity component that doesn't affect the descent speed, right? I'm mainly concerned about the time it stays afloat, but adding an extra component is fine too. – user1002327 Aug 16 '12 at 1:39
@user1002327: It's the same as in any aircraft. For the given weight and wing area, there is a speed that's too slow, called the "stall speed", where the wing ceases flying and becomes a parachute. The speed that gives maximum time aloft is just above stall speed. You adjust the speed by trimming the weight more or less forward. – Mike Dunlavey Aug 16 '12 at 1:50

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