Unusual Golf Ball Behavior: Investigating an Unexplained Force vs Distance Graph

[golfz]

I am almost done in my research on golf balls, however I found something unusual which I can't seem to find an explanation for. After collecting data on a golf swing (golf ball speed, club head speed, backspin, distance etc.) I created a few graphs. Once of them was a force vs distance graph (shown below). Now, the golf balls I tested were rated 72 (Callaway HX Diablo), 88 (Pinnacle lady), 98 (Titleist Pro V1) and a smooth golf ball from Caesar golf.

http://cdn.thesandtrap.com/e/ef/efa9d536_unusual.jpeg

Basically from interpreting the graph, the more compressible golf ball (72) needs more force upon impact than a less compressible ball (98) at low speeds to travel the same distance. However, at higher speeds the 72 rating golf ball needs less force to travel the same distance as the 98 rating golf ball (black line below the green line above 720kg). For the upper portion of the graph, the results make sense, except for the lower portion it doesn't. Does anyone have an idea why the graph looks like it is?

I initially thought of the deformation energy lost to the ball upon impact at low speed, however that would also occur at higher speeds too. Maybe at higher speeds more energy is translated to the kinetic energy of the ball and at lower speeds its lost to the deformation energy of the ball. However I feel that makes no sense at all. I just can't seem to come up with a viable explanation. I also thought the results were wrong but maybe they are not.

Anyone has any suggestions to the reason why the graph looks as it is?

 

[Dickfore]

First of all, what does this graph represent?

 

[kmarinas86]

I am almost done in my research on golf balls, however I found something unusual which I can't seem to find an explanation for. After collecting data on a golf swing (golf ball speed, club head speed, backspin, distance etc.) I created a few graphs. Once of them was a force vs distance graph (shown below). Now, the golf balls I tested were rated 72 (Callaway HX Diablo), 88 (Pinnacle lady), 98 (Titleist Pro V1) and a smooth golf ball from Caesar golf.

http://cdn.thesandtrap.com/e/ef/efa9d536_unusual.jpeg

Basically from interpreting the graph, the more compressible golf ball (72) needs more force upon impact than a less compressible ball (98) at low speeds to travel the same distance. However, at higher speeds the 72 rating golf ball needs less force to travel the same distance as the 98 rating golf ball (black line below the green line above 720kg). For the upper portion of the graph, the results make sense, except for the lower portion it doesn't. Does anyone have an idea why the graph looks like it is?

I initially thought of the deformation energy lost to the ball upon impact at low speed, however that would also occur at higher speeds too. Maybe at higher speeds more energy is translated to the kinetic energy of the ball and at lower speeds its lost to the deformation energy of the ball. However I feel that makes no sense at all. I just can't seem to come up with a viable explanation. I also thought the results were wrong but maybe they are not.

Anyone has any suggestions to the reason why the graph looks as it is?

Given the distances in your charts, I don't know what indoor area you could have available to do this without having winds affect your data.

The impact of winds can be significant:
http://probablegolfinstruction.com/golf-wind.htm

 

[golfz]

Forgot to include that data. The backspin, ball speed, clubhead speed etc was calculated by a simulation program (Golf Achiever), which involves a golfer hitting golf balls on a mat with lasers. The simulation program was programmed there was no wind affecting the flight path of the golf balls. Now the force vs distance graph shows how much force was applied to the ball by the club head(at impact) compared to the distance the ball flew.

The equation I used to calculate the force is: (clubhead speed*9.24)/2.2 (for kg and not lb). I found this as part of another calculation process off a website. Another method to calculate it was found on this thread: https://www.physicsforums.com/showthread.php?t=197752 however it is not useful as I do not have the impact time. I do however have the clubhead weight, ball weight, speed of clubhead before collision and speed of ball after collision, and the impact angle.

 

[Dickfore]

I'm out of this thread.

 

[golfz]

I'm out of this thread.

so its not an easy problem?

 

[Dickfore]

Not really, but these things told me I am wasting my time:

After collecting data on a golf swing (golf ball speed, club head speed, backspin, distance etc.) I created a few graphs.

Forgot to include that data. Basic information like the backspin, ball speed, clubhead speed etc was calculated by a simulation program (Golf Achiever), which involves a golfer hitting golf balls on a mat with lasers. The simulation program was set so with no wind affecting the flight trajectory of the golf balls.

The equation I used to calculate the force is: (clubhead speed*9.24)/2.2 (for kg and not lb). However I am not sure how this is calculated in the first place as I got this off a site (still looking for it).

 

[Ken G]

Force seems like an awkward parameter to measure to understand the distance traveled (and kg is not a unit of force, do you mean some kind of weight equivalent at sea level?). Also, you haven't said what those rating numbers mean. For an infinitely hard and elastic golf ball, the speed of the ball would naively relate only to the speed of the golf club head, but even that is only true if the head has way more mass than the ball. In reality we know the head bends back a bit when it hits the ball, so the stiffness of the club shaft comes into play as well. The problem with using "force" to characterize that interaction is that the amount of kinetic energy transferred depends on the distance over which the force is applied, to that depends on the bend of the shaft and the compression of the ball. The larger is that bend and that compression, the larger the distance over which the force will be applied, but the smaller the force. It would be hard to disentangle those factors! Why don't you use clubhead speed as your tracked variable? Also, it is customary to put the variable you control on the x-axis, and the one that comes out of the experiment on the y-axis, so we think of "distance as a function of X" not "force as a function of distance", though this is just a convention and has nothing to do with your question.

It sounds like you are trying to keep the club action controlled, and ask which balls will go farther. That's why you should focus on something the golfer can control, like the club speed, not something that is also affected directly by the ball, like the force. I would say that your curious results stem from looking at a variable that is confused by interactions between the club and the ball, and is not the thing the golfer controls, nor is independent from the attributes of the ball.

ETA: I see from your formula that in fact you are really using club speed, not force at all. (The force will not just be a function of the club speed, it will also depend on the ball.) My tendency would be to look at your data and say "distance depends on club speed" and attribute the rest to experimental uncertainty. There does seem to be some small trend where some balls perform better at low club speeds, but at high club speeds, they all pretty much go the same distance. What more do you want to know than that?

 

[Ken G]

By the way, it surprises me that the smooth ball doesn't go much less distance. It was my impression that such balls experience a large air resistance at high speed.

 

[golfz]

Not really, but these things told me I am wasting my time:

I understand why you think you are wasting your time. I just wanted to communicate my ideas across and did not bother to write with care. With collecting data I actually meant experiement. I am doing an extended essay so it is not that simple. The equation I got off the internet was used as it was a step in another calculation. Considering it was what I needed, I used it without thinking how the author derived the equation. I wished to figure that out at a later point however I failed to do so. I do know how to calculate the impact force however I need the impact time which was a variable not recorded by the golf simulator I used. I guess I can assume it to be 0.0005 seconds for all golf shots.

 

[golfz]

By the way, it surprises me that the smooth ball doesn't go much less distance. It was my impression that such balls experience a large air resistance at high speed.

I believe the cause for that is an error in the simulation program. For each golf ball I did not iindepenantly input the drag coefficient for the golf balls. I believe the program assumed the smooth golf ball had the same drag coefficient as a dimpled golf ball.

 

[golfz]

Force seems like an awkward parameter to measure to understand the distance traveled (and kg is not a unit of force, do you mean some kind of weight equivalent at sea level?). Also, you haven't said what those rating numbers mean. For an infinitely hard and elastic golf ball, the speed of the ball would naively relate only to the speed of the golf club head, but even that is only true if the head has way more mass than the ball. In reality we know the head bends back a bit when it hits the ball, so the stiffness of the club shaft comes into play as well. The problem with using "force" to characterize that interaction is that the amount of kinetic energy transferred depends on the distance over which the force is applied, to that depends on the bend of the shaft and the compression of the ball. The larger is that bend and that compression, the larger the distance over which the force will be applied, but the smaller the force. It would be hard to disentangle those factors! Why don't you use clubhead speed as your tracked variable? Also, it is customary to put the variable you control on the x-axis, and the one that comes out of the experiment on the y-axis, so we think of "distance as a function of X" not "force as a function of distance", though this is just a convention and has nothing to do with your question.

It sounds like you are trying to keep the club action controlled, and ask which balls will go farther. That's why you should focus on something the golfer can control, like the club speed, not something that is also affected directly by the ball, like the force. I would say that your curious results stem from looking at a variable that is confused by interactions between the club and the ball, and is not the thing the golfer controls, nor is independent from the attributes of the ball.

ETA: I see from your formula that in fact you are really using club speed, not force at all. (The force will not just be a function of the club speed, it will also depend on the ball.) My tendency would be to look at your data and say "distance depends on club speed" and attribute the rest to experimental uncertainty. There does seem to be some small trend where some balls perform better at low club speeds, but at high club speeds, they all pretty much go the same distance. What more do you want to know than that?

Those ratings are based on USGA golf ball compression ratings. All golf balls are in this manner, and the higher the number, the less compressible the ball. I myself conducted an experiment to find the COR of the golf balls, except that was for a golf ball dropping on concrete. The smooth golf ball and the 88 rating golf ball had the same COR.

Additionally, the variables you mentioned (such as the flexibility of the club shaft) would have been discussed in the evaluation and been variables in the experiment which are difficult to control and measure. I used impact force on the ball instead of club head speed vs distance as I thought it would be better for analysis. I have made a graph with distance vs club head speed and have got a similar graph. I will post that up shortly.

 

[golfz]

http://cdn.thesandtrap.com/4/4a/4a975260_Untitled5.jpeg
This graph is easier to interpret, however considering it is part of a research project, I thought it would be better to include calculations. Is there any other way I could calculate something out of any of the following vaiables:
Launch Angle, Sidespin, backspin, club speed, ball speed, flight time, distance, and max height (i have whether the shot was off centre or not (toe shot, heel shot, centre shot) and azimuth values, but I don't think these are useful).

 

[Ken G]

To my eye, the variations with ball are not significant, and possibly not even handled self-consistently (as with the smooth ball that does not have the right air drag, the key issue for a smooth ball). I do prefer the use of club speed, because I'm sure your formula for the force doesn't mean anything (it should vary with the compressibility of the ball). So to me, the only useful information I see is a single straight line that connects club speed to distance traveled. If I were you, I'd concentrate on understanding that, just using simple approximations like the speed of the ball being twice the club head speed (the expected result for an incompressible ball with mass much less than the club head). Is distance traveled proportional to ball speed? Not normally-- that would hold if the time aloft did not vary with speed and there was no air resistance. But the time aloft is proportional to ball speed, all else equal, so I'd expect the distance to scale like the square of the ball speed, if no air resistance. Air resistance is worse at high speed, so perhaps that knocks it down into something more like distance proportional to speed. That would seem to be the interesting direction this data is leading, I don't think there's anything reliable here about comparison of the balls.

 

[chrisbaird]

I am almost done in my research on golf balls, however I found something unusual ...has any suggestions to the reason why the graph looks as it is?

I don't mean to burst your bubble, but looking at the original chart, the data variation within a single ball type is much greater than the variation between the average trends of the different ball types. What this leads to is that there is no meaningful difference between the behavior of the different balls according to your data. Simply throwing down regression lines and comparing the lines is misleading. Think of it this way: try drawing trend lines for the different data sets by hand, without the help of some automatic software algorithm, and you find it very hard to draw trend lines that are significantly different without resorting to some preconceived bias. You may have to repeat the measurements with better control of the supposed-to-be-constant effects (such as wind) to get the data point spread down.

 

[chrisbaird]

That reminds me of a research talk I went to once where the speaker presented data that looked like this:

I thought to myself, maybe there's a downward trend, but he needs more data to make sure. Then he showed the data bars to be something like this:

I thought to myself, this data is useless. I could draw just about any trend line through those error bars. He then choose the trend line to be this, because that's what he wanted to find:

I don't think your case is as bad, but you do have to be careful of the same kind of self-delusion.