Is the trajectory of a ball with friction calculable?

Click For Summary

Discussion Overview

The discussion centers around the calculation of the trajectory of a ball influenced by friction, specifically considering the applicability of Stokes' and Newton's laws of drag. Participants explore the feasibility of deriving a direct calculation for the trajectory, the impact of drag and lift, and the assumptions involved in modeling such a scenario.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant has created a simulation that calculates the trajectory of a ball under friction and seeks to verify if a direct calculation is possible using Stokes' or Newton's formulas.
  • Another participant mentions the importance of drag and lift, referencing the Magnus effect and the influence of Reynolds number on the behavior of the ball.
  • A participant describes their simulation method, which involves iterating over time and applying forces, while noting that they have simplified the model by not including spin and assuming a constant drag coefficient.
  • One participant asserts that the trajectory cannot be calculated directly and emphasizes the necessity of numerical methods for such simulations.
  • Another participant acknowledges the complexity of the model and the validity of different approaches, highlighting the importance of listing assumptions made in the modeling process.
  • There are discussions about the effects of spinning on drag, with some participants noting that a spinning sphere experiences less drag than a non-spinning one and that the drag coefficient changes with Reynolds number.

Areas of Agreement / Disagreement

Participants generally agree that direct calculation of the trajectory is not feasible for the scenario described, particularly under Stokes' law. However, there is some uncertainty regarding the applicability of Newton's law and whether a direct calculation is possible, as one participant expresses confusion about existing explanations.

Contextual Notes

Participants mention various assumptions, such as the use of a constant drag coefficient and the exclusion of spin in the simulation. The discussion also highlights the potential complexity introduced by turbulent flow and the relevance of Reynolds number, which some participants do not incorporate into their models.

anotheruser
Messages
3
Reaction score
0
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.
 
Physics news on Phys.org
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 modeled this?
 
Last edited:
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.
 
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.
 
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.
 
xxChrisxx said:
A sphere has an inherent drag...

Interestingly enough, a spinning sphere has less drag that a non-spinning one.
 
mugaliens said:
Interestingly enough, a spinning sphere has less drag that a non-spinning one.

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 relevant to the OP's question.
 

Similar threads

  • · Replies 77 ·
3
Replies
77
Views
7K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 25 ·
Replies
25
Views
4K
  • · Replies 3 ·
Replies
3
Views
8K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 3 ·
Replies
3
Views
9K
Replies
14
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K