# Relation between magnus effect, speed and acceleration

1. Oct 4, 2009

### hkhalil

Hi,

Is it right to assume that, since F = ma, that the magnus force has an impact on the acceleration of the spinning object, which in turn leads to a change in its velocity?

I need to program an application that simulates a corner in soccer. This involves calculating the viscous and Magnus forces applied to the ball. I am just trying to find the relation between these two forces and the acceleration of the ball.

Is it right to sum the viscous friction and the magnus force, as well as the gravitational force, and divide everything by the mass in order to find the acceleration at a time T ?

Thanks

2. Oct 4, 2009

### Pythagorean

Yes, remembering that velocity is direction as well as speed. Also remember that there's a translational velocity as well as a rotational velocity. I always thought of the magnus effect in terms of a golf ball. All the little dimples on the golf ball "grab" the air (because of the ball's rotational motion) and "pulls" the ball.

In reality, there's a lot more turbulent effects that I don't understand going on around the ball that lie in the domain of fluid dynamics.

Well, as with any body, you have to break the forces up into their component forces. When I did this code, we only considered the lift of the magnus force, which would sum with gravity, we didn't consider "hooking" or "slicing" of the ball. But yes, the mass still acts as resistance to the force.

Also, when I did the code, rotational velocity was constant. In reality, I'd assume the magnus force slows down the rotational velocity of the ball as it gains lift (Newton's 3rd).

The http://en.wikipedia.org/wiki/Magnus_effect" [Broken] only considers the lift force on a round object.

Last edited by a moderator: May 4, 2017
3. Oct 4, 2009

### rcgldr

The dimples create a localized turbulence which helps the flow remain attached better and reduced the magnus force.

This article does a better job of explaining detatchment of flow as the most likely cause of Magnus effect:

http://www.geocities.com/k_achutarao/MAGNUS/magnus.html

Last edited by a moderator: May 4, 2017
4. Oct 4, 2009

### Pythagorean

Interesting... that means that a smooth ball feels more magnus force than a dimpled ball? (assuming same mass, and cross-sectional area)

I'd always assumed that the golf balls were intentionally manufactured to take advantage of the magnus effect.

5. Oct 4, 2009