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Re: Drag coefficient of 2012 Game Piece
The best solution may just be to have a look-up table to be honest. I've already derived equations of motion, and you end up with a system of second-order nonlinear equations which would have to be solved numerically. It's something probably a little too advanced to teach high-schoolers how to do, and it may also be a little too much for the CPU to handle (with any reasonable accuracy).
For the curious:
m * p_dd = -K * sqrt(p_d^2 + h_d^2) * p_d
-m * h_dd = m*g + K * sqrt(p_d^2 + h_d^2) * h_d
where:
m = mass of ball
p = x-distance
h = negative y-distance (coordinate frame unit vector pointed down. positive h is downward)
K = rho * S * C_D/2
rho = density of air
S = Cross-sectional area of ball
C_D = Drag Coefficient
?_d = ? dot (as in first time-derivative)
?_dd = ? double-dot (as in second time-derivative)
It can also be expressed in terms of Speed, V, and flight path angle, gamma as a single order system of nonlinear eqations.
m * V_d = -m * g * sin(gamma) - K * V^2
-m * V * gamma_d = m * g * cos(gamma)
Expressing that way is "prettier," but is less useful.
Last edited by Michael Hill : 09-01-2012 at 13:44.
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