# Golf ball aerodynamics

Hi,
How do you calculate the drag coeficient of a golf ball without the use of a wind tunnel. I have been researching this for hours and have not found a solution. The equation for the drag coefficient involves a value for drag which I cannot find out. I need to find the drag force to find the drag coefficient. I am stuck with finding out the drag force.

Fd= 0.5Pv²CdA

Where P is the density of the air, v is the velocity of the ball relative to the air, A is the cross-sectional area and Cd is the drag coefficient (the value to be found).

I am sure there is a method besides using a wind tunnel. I have a machine which can caluclate initial velocity, rpm, air density etc. It even simulates the distance the ball would fly. Does anyone know how I would be able to calculate it so that I could get a graph like this: Related Classical Physics News on Phys.org
Gold Member
The problem is that the equation you cite is an empirical relationship and Cd is typically found by conducting experiments or CFD. You could get a reasonable estimate if you were to do a potential flow analysis on the ball as long as you know the separation points, but that would require experiments or a boundary layer solver. It isn't a simple task.

so there is no way to find it out without a wind tunnel or the method you suggested. Is there another formula that I can use?

Unfortunately, you can't just use a "plug-and-chug" method here. It's just not that simple.

are there any other methods that I can use to obtain a similar graph for analysis. I would like to analyze the air flow around a golf ball.

Gold Member
Again, you will need to actually look at fluid flow equations, not just the simple empirical correlations. Because the drag on a golf ball is dictated by the separation points, you will need some method to determine where those occur. That will require a boundary layer solver. Of course, the whole point of the dimples is to trip the flow to turbulence to delay the separation, so you will need to know at what point the flow becomes turbulent. That would likely require experimental observation as there is no general method to predict transition. Finally, you would need the pressure distribution on the ball, which could be found simply using potential flow. If you had all these pieces, you could pretty quickly come up with an answer, but you still need that one experimental stage.

In other words, no matter what the problem is complicated and will require some sort of experiment. Luckily for you, there have been many experiments already carried out on golf balls...

Thanks for your reply. So I have been researching this topic for hours on end and realised I had a problem. Firsty you mention fluid flow equations. For example does this include the following:
Fres=-C1vr+C2v2r2
Which can be used to find the terminal velocity in a fluid. Secondly, what is a boundary layer solver? Didn't get much from google.

Thirdly, finding the separation points is completely new to me. Is this determined experimentally in a wind tunnel such as the air flow separation from laminar to turbulent?
I was able to calculate Reynolds number for different speeds of the golf ball however I am struggling to find the drag force, like you mentioned, an experiment it needed. Unfortunately this cannot be done as I dont have a wind tunnel at my disposal. Is there a different method to use? I have this machine to obtain data: http://www.golfachiever.com/Web/Technology/LaserTech/laser-tech.html" [Broken]

I have also found out that
'Physical Parameters
GolfAchiever's Proprietary Algorithms include Ball Flight Aerodynamics defined by four physical variables: Friction Coefficient, Magnus Coefficient, Spin Time Constant, and K-Azimuth' If its possible to calculate such information without a wind tunnel, isnt it possible for me to do the same with the data displayed?

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Unfortunately this is a very difficult problem. There is no way to calculate the drag on a golf ball analytically without some kind of experimental data. By "flow equations" Boneh3ad means the Navier Stokes Equations which describe the motion of a fluid. These equations cannot be solved analytically except in a few simple cases. They can be solved numerically but this is very difficult especially on a bluff body when turbulence and separation are present.

Your best bet is to use the empirical equation. Fd= 0.5Pv²CdA and a chart like the one you showed to determine the drag coefficient Cd for the given Reynolds number.

Gold Member
Unfortunately this is a very difficult problem. There is no way to calculate the drag on a golf ball analytically without some kind of experimental data. By "flow equations" Boneh3ad means the Navier Stokes Equations which describe the motion of a fluid. These equations cannot be solved analytically except in a few simple cases. They can be solved numerically but this is very difficult especially on a bluff body when turbulence and separation are present.

Your best bet is to use the empirical equation. Fd= 0.5Pv²CdA and a chart like the one you showed to determine the drag coefficient Cd for the given Reynolds number.
Or if the Navier-Stokes are too daunting (as they should be; doing a DNS is not really feasible) then you could couple a potential flow analysis with a boundary layer solver to get a pretty darn close estimate. The problem is you need to know how to do that and you need to know where the flow goes turbulent.

By boundary layer solver, I mean a computer program that solves the boundary layer equations at a grid of points to generate a flow field for the boundary layer around the golf ball.

A separation point is a point where the local velocity very close to the surface in the boundary layer has actually reversed, causing the boundary layer to effectively separate from the surface and a recirculating bubble to form under it. This leads to very low pressures compared to the front end of the object and therefore increases the drag by a very large amount. The point of the dimples is to trip the boundary layer to turbulence because a turbulent boundary layer doesn't separate as easily.

I was considering doing as you suggested. I actually wished to compare the data from different type of golf balls, hence I would get different curves as the dimples on the golf balls would be different. In fact I found another way to analyse the physics of this. I will look at the club-ball impact relationship. The kinetic energy of the clubhead translates into the kinetic energy of the ball, however the ball first undergoes compression and the restores its original shape (the restoration coefficient). I wished to analyse this in relationship to the rpm of the ball and the speed of the clubhead. Any information regarding the restoration coefficient?

By boundary layer solver, I mean a computer program that solves the boundary layer equations at a grid of points to generate a flow field for the boundary layer around the golf ball.
You got any computer program which does this?

Or if the Navier-Stokes are too daunting (as they should be; doing a DNS is not really feasible) then you could couple a potential flow analysis with a boundary layer solver to get a pretty darn close estimate. The problem is you need to know how to do that and you need to know where the flow goes turbulent.
This is also not a simple task. Even assuming you knew where the flow transitioned you would have to incorporate a turbulence model and the boundary layer equations are no longer valid near the separation point and in the separated region. So you would have to go back to the Navier Stokes equations.

You got any computer program which does this?
To my knowledge there is no computer program capable of this sort of analysis that an inexperienced user could just start using. Even for someone with a decent fluid mechanics background this would take some time if they have never done computational work before.

would you advise me do steer away from such a topic? Is the analysis of the club-ball impact reasonable to research for an IB student?