# Is the trajectory of a ball with friction calculable?

1. ### anotheruser

4
I have written a simulation for school that simulates balls being thrown under the influence of friction.

To check if my results are correct, do you know if it is possible to calculate the trajectory?

I can use the friction formulas of either stokes or newton. Is it possible to calculate how far a ball will fly for either of those?

Wikipedia shows formulas for a free fall, but I don't think that suffices, as there is only one coordinate that changes in that case.

2. ### xxChrisxx

2 words. Drag and lift.

Balls produce lift when spinning, see Magnus effect.
A sphere has an inherent drag, and you can find the answer to that from 'drag on a sphere'. Both lift and drag will be influenced greatly by Reynolds number. If this is modelling something real then you are going to have turbulent flow, so stokes' equations are out.

How have you modelled this?

Last edited: Aug 25, 2010
3. ### anotheruser

4
the program I wrote simulates the trajectory in realtime by dividing time in fragments and iterating. In each iteration, the simulation applies the acceleration the ball would experience to its speed and its speed to its location. For sufficiently small iteration lengths the simulation is precise enough.

The drag force is included (along with gravity and lift), the spin is not. I have decided not to include it to make it simpler for myself. Also, the drag coefficient is assumed to be constant throughout the simulation (if newton's formula is used). I don't use Reynold's number at all. Is that important? It works just fine without it.

Back to my question: to compare my simulation's results with something, is it possible to calculate the tryjectory directly (for either stokes' or newton's formula for drag)? I'm guessing not, but I want to make sure.

4. ### xxChrisxx

That's all fine, there are different levels of complexity for a model like this, all are valid, you just need to list the assumptions made (in this case a constant drag coefficient).

It's not possible to calculate the trajectory in any other way than you are doing it. If there was an easy equation to do this, there would be no point in doing a numerical?

I did something very similar using excel back in Uni.

5. ### anotheruser

4
Good to hear this. I knew it was impossible for stokes' law, but thought that some sites explained it for newton's. I didn't understand any of it, though, so I wanted to make sure.

Thanks for confirming my assumptions.

6. ### mugaliens

584
Interestingly enough, a spinning sphere has less drag that a non-spinning one.

7. ### xxChrisxx

The Cd also drops significantly after a critical Re number, after this the Cd value stays vitually constant.

When spinning there is also an induced drag component, meaning that to kick a ball the furthest the launch angle is less than 45 degrees, about 37 seemed to give the best results iirc.

Interesting, but not really relevent to the OP's question.