ECOR 2606 Lecture Notes - The Skydivers, Parachuting, Terminal Velocity
28 Sep 2014
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Apply engineering knowledge to get desired output in terms of known inputs. Problem: a skydiver jumps from a balloon (hence no initial velocity). Downward force due to gravity: fg = mg. Upward force due to air resistance: fd = cdv2. An analytical solution can be obtained fairly easily: tv gm c d tanh d gc tm. But suppose that the math was a little too scary . In this case we could resort to using numerical methods. The following becomes exact as t approaches zero. dv dt v t v i t i. For small t it"s not exact but if t is made small enough it"s a good approximation. Rearranging and substituting for dv/dt gives v i v i. 1 dv dt t v i g d c vm i. Starting from the known initial conditions (t1 = 0, v1 = 0), this formula and some assumed t can be used to calculate v2, v3, v4 and so on.
