### Re: What is the Magnus Coefficient of a tennis ball with a top spin?

Date: Wed Nov 15 09:02:46 2000
Posted By: Kenneth Chivers, Grad student, B.S. Aerospace Engineering, In school for MBA:Management of Information Systems, NAWCAD, Lakehurst, NJ
Area of science: Physics
ID: 972664776.Ph
Message:
```
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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