|MadSci Network: Physics|
Yes and no. You can find the Magnus coefficient without an expressly given Magnus force, however...you need to know a few key items and basically calculate the force :)
The Magnus force is nothing more than the force applied to a rotating object due to the surface pressure differences. So...
First, for a tennis ball, calculate the surface pressure distribution, using the spherical coordinate system rates of rotation and the radial velocity of the ball. Build this into a composite Magnus force.
I never said this would be easy....
To conceptualize this and model a more easily understood equation do the following:
1) Picture the ball rotating, but with no velocity of its own.
2) Picture the air flowing at the ball. (Same result, just easier to grasp)
3) Now, according to my undergrad aerodynamics book, Aerodynamics for Engineers, by Bertin and Smith, Prentice Hall, 1989, Vr=dphi/dr, Vw=(1/r).dphi/dw, Vtheta=(1/(r.sin(w))).dphi/dtheta. Here, phi represents the velocity potential function. That's the general form. If you know the velocity function in terms of r, theta, and w, then perform a surface integral, using Bernoulli's equation in the general form to find the resultant pressure from the spin in the tennis ball (theta and w). This resultant pressure should be your Magnus force. From here, you can easily determine the coefficient.
Thanks for your question and Good Luck! Keep the velocity components seperated during your integrations and you should be fine :) Ken C.
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