Researching Golf Balls

Hi,

I need to write a essay on golf balls and surprisingly it is more difficult than I thought. Now, this is no normal essay, and is based on the physics of golf ball flight involving Bernoulli's principle, the Magnus effect, Reynolds number, drag coefficients etc. Now the reason I am telling you this is because I hit a dead end with the essay. The essay question is: What effect do dimples have on the aerodynamics of a golf ball? I realized calculating the drag coefficient for different speeds of the golf ball is more difficult than I thought. Here is the formula (Fd is the drag force):

F d = -C d v

where C d is the drag coefficient, v is the velocity of the ball and Fd is the drag force( v x, v y, v z are its components) and the minus sign means that this drag force opposes the ball's motion .

or

F d= 0.5 P v ² C d A

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 able to calculate Reynolds Number for different speeds, and plotting this against the drag coefficient I  should get a graph like this which was taken from the internet:

Here are my final questions:
How do I calculate the drag coefficient if I don't know the value of the drag force of the golf ball (Fd)? I believe this is not the same for different golf balls and at different speeds. I need to get a graph as shown above.

What else can I investigate? (I am doing the IB program which is slightly more advanced than high school, so it cannot be things like using a wind tunnel)

Should I change the title of my essay and investigate something else in relation to golf? (preferably using golf balls as I already bought several expensive ones)

Resources: I have dimpled and dimple-less golf balls and different golf clubs (experiment carried out in golf shop). The way I calculate data such as speed, rpm etc is by using this machine: http://www.golfachiever.com/Web/Technology/LaserTech/laser-tech.html

You have two equations and two unknowns. You just need to use them together to solve for Cd and Fd. So, since Fd = -Cd*V, that means -Cd*V = 0.5P*V^2*Cd*A. Once you solve that equation for Cd, you can then use that value to calculate Fd.

I don't really know what else you could investigate, but you seem to be on a pretty good track with this. Is this not going to yield enough information?

EDIT: I noticed after posting that if you go straight at it like that, Cd divides out. I didn't really think that one through. That obviously won't help you.

It's not the maths that is a difficulty (sorry if I was not clear), it is more about collecting the data for it. The drag force is what I have to find out. This is different for different balls and speeds. I provided the equations so that you understand what I need the drag force for. Apparently it can only be found out using a wind tunnel which I don't have.

Yeah, I can't think of any other way than using a wind tunnel. A couple guys I went to college with built one for a design project. It only cost them about $50, I believe. I don't know exactly what they did because I studied electrical engineering and they were in a mechanical class that I didn't take. But, knowing these guys, I just about guarantee the idea and, most likely, the design, came from somewhere around the internet. You could probably find something like that if that is a possibility for you. It would be perfect for your purposes. It was only about 2' x 1' x 1' or so.

I assume this is for your extended essay? (I was an IB student at one time as well).

Your graph provides some insight into reasons behind dimples. In general, turbulent flow means that drag is less on the ball. What the dimples do is reduce the "critical Reynolds number", which is basically the number at which flow over the object transitions from laminar to turbulent. At very high speeds, the drag coef. on the smooth ball is very low, because we are in the turbulent phase (the right side of the graph where the blue line dips). However, given the restrictions on how much velocity humans can impart on the ball, dimples are required to bring this critical number down.

Given your limited resources, how about investigating the way in which reynolds number changes with balls that claim to "improve distance"? You could talk about the properties of the ball that bring down the critical reynolds number in order to allow amateurs with low swing speeds to impart turbulent flow over the ball.

Also, callaway's new balls have hexagonal dimples. i dunno, those might produce a different graps compared to balls with circular ones.

Yea it is for my extended essay, and thanks for the explanation, clearer than what I found on the internet. I actually didnt make the graph myself, i need to produce one similar to it and that is what I am having difficulties with. Your question you provided also allows me to focus my extended essay a bit more. But the only thing that is concerning me is how to test and explain how different dimples have a different effect. The way the experiment is going to be carried out is by hitting the golf balls with a 7 iron (any suggestion for a different club) at different speeds. I will then calculate reynolds number. However to determine the critical reynolds number I also need the drag coef. which I can't calculate as I dont have the drag force for the golf ball.

Funny enough, I actually found one the other day on the course. I was examining the dimples and realized they were hexagonal. Thought I could use it for my essay.

Producing a wind tunnel is not optimal for my essay. I had a look and it takes too much time to build. I can then see the air flow on the golf balls however I will only get qualitative data then.

That I can understand. The actual tunnel wasn't very expensive to build, but they did have some rather expensive instruments that allowed them to quantify what they were seeing. I didn't think about you probably not having access to instruments like that.

Does the material in which a ball is made of have a significant impact on the flight of the ball, hence affecting reynolds number?

Different materials will either make the ball harder or softer. A harder ball allows for a more efficient transfer of energy from the club, therefore making it travel further. I've never seen a study on how that affects the flight (lift, drag, etc.), but it may be worth looking into. Personally, I don't think it would have a really significant effect, but I can't say for sure.