From the paper. "Experiments have shown that the coefficients of restitution of impact between a golf ball and a clubhead is a smoothly declining (nearly linear) function of clubhead speed (Chou, et. al., 1994; Cochoran, 1998; Lemons, 1998)." This is the work he replicated without giving us clear indication why he chose to do so. Upon reflection, my best guess is that his intent was to update the experiment with modern balls. However, he made no explanation of why it would be necessary to do that.
You misunderstand the purpose of the study. The author knows good and well what the COR versus clubhead speed curve for modern Tour golf balls look like. He presents that as background. Then he goes on to perform tests to show the curve of distance versus clubhead speed for modern Tour golf balls. And he explains at length that distance is a function of both COR and aerodynamics. He wants to be able to make a statement that draws a soup-to-nuts conclusion about the distance that modern Tour golf balls travel with high clubhead speeds. I think he made that case pretty succinctly and adequately.
Personally, I think the study was a waste of resources. There is nothing in his COR or aerodynamics results that he didn't go would be there before he started (as would any of a couple hundred professionals in the golf equipment business as well as many well-informed laymen). Yet for political reasons, the USGA obviously thought a complete study was necessary to shut up all the bullshit about "exponential" this and "disproportionate" that. What I believe they underestimated was the willingness of know-nothings to ignore anything they don't understand in pursuit of their continued bullshit. But maybe I'm just cynical.
What I would have liked to see was graphs of ball trajectory predicted by the equations that were presented and then ignored, and graphs of ball trajectory as seen in experiments with balls. I would also like to have seen what the model would predict for older balls.
Garland, the equations have unknown parameters that vary by golf ball characterstics. There is no one curve shape predicted by an equation written out with symbols instead of actual parameter values. Once the experiment is done, working backward to get the parameters and then tracing out curves corresponding to those values will get you a curve that looks so much like the empirical curve as makes no difference. Hell, you can't really tell the different balls apart because they're so similar. Nothing would be gained by twice as many almost-identical curves on the plot. The equations he presents aren't something that needs testing, they are known, settled, accepted by anyone who has bothered to become educated on the subject and not needed at all once you have actual experimental data in front of you.
Yes they answered the question posed. So why did they waste my time by making me read the mathematical model that they made no use of?
It is standard in technical literature to give the theoretical background that you are stating as underlying your experiments. It's like quoting Marbury vs. Madison when you go argue a case in front of the Supremes. It simply establishes the frame of reference in which the discussion takes place.
It would be the way science is done. You make a model or hypothesis, explain what it shows, and then you do the experiments to show whether or not the model holds. For this paper the mathematical model was just fluff, a way of saying look at me, I have a Ph. D.!
The formulas they presented were not a hypothesis or a model to be tested. It was the technical underpinnings that someone might need to understand the experimental results. The experimental results were a laborious undertaking to demonstrate a trivial physical relationship. They phrased it like an experiment but it was really more like a demonstration that you would perform in high school physics class where the result is not in question.