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EGA118Q1.m contains a script that calculates the motion of a football that is subject to drag and a Magnus force. The governing equation for such a problem is the standard equation for linear dynamic problems:
m a=mdVdt=F For this problem the motion is in two dimensions and so the acceleration, velocity and force are vectors. The code assumes the ball is rotating at an angular velocity of ω=10-t1000 radians s-1 This equation accounts in a simple way for friction effects slowing down the rotation. I’ve used equations I found on the web for the coefficient of lift and drag of a rotating ball.
CL=12+vvspin L=12ρ S v2 CL
CD=0.55+122.2+4.2*vvspin2.50.4 D=12ρ S v2 CD
In these equations v is the forward speed of the ball, vspin=ωR where R is the ball radius and S is the frontal area of the ball, R2. The lift, L, and drag, D, forces are calculated using the equations given above. Remember that drag opposes motion and lift is at right angles to motion. The direction of the Magnus force is shown in Figure 1.
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