Hi!
I have developed a functioning interval timer using a pair of break beam sensors 2" apart. The idea is that I putt a golf ball through the sensors and the program calculates the distance that the golf ball would roll, given that initial velocity.
The only initial velocity-to-actual distance relationship that I know of is that an average golf green will provide about ten feet of roll to a golf ball initially launched at 6 feet per second. This data is available due to a machine called a Stimp meter- a simple track at a fixed angle that rolls golf balls at 6 fps and the distance that the ball travels is given as the Stimp rating, e.g. a Stimp Rating of 10.0 means the ball rolled out ten feet.
What I can't figure out is the math to translate the initial velocities that i'm measuring with my machine (accurately, it would seem) and HOW FAR THE BALL WILL ROLL ON VARIOUS GREENS given their stimp rating.
I've tried using 10/6 as my stimp in the formula (initial velocity * stimp) and while that obviously gives a perfect answer under one condition (the machine is set to a stimp of 10.0 and the ball is struck at 6 fps) I don't think it is accurate when I change the stimp to 7.0 or 13.0 (the range of golf greens one encounters in the world) OR when I strike the ball harder or softer.
Any ideas how to go about making the formula that accounts for rolling friction and returns
a) more accurate readings at a stimp rating of 10.0 and a range of initial velocities and
b) more accurate readings when the stimp rating is changed
I get the feeling this is not going to be linear but I have no real math training.
Tbryden:
Hi!
I have developed a functioning interval timer using a pair of break beam sensors 2" apart. The idea is that I putt a golf ball through the sensors and the program calculates the distance that the golf ball would roll, given that initial velocity.[....]
What I can't figure out is the math to translate the initial velocities that i'm measuring with my machine (accurately, it would seem) and HOW FAR THE BALL WILL ROLL ON VARIOUS GREENS given their stimp rating.
I have never played golf but a couple of thoughts occur to me.
To emulate the Stimp rating you need a formula that relates the Rating, the Distance and the Initial Velocity. I suspect it is not a linear relationship. Do you have graphs that show the Distance / Velocity for several different Stimp ratings? I think having those is essential.
Assuming you have the graphs and can produce a suitable formula how do you plan to use it? Is it your intention is to enter a particular Stimp rating (to simulate a particular green) and then practice your putting to get different distances?
...R
PS. I presume the Stimp rating is for a perfectly flat and level playing surface. From occasionally watching golf on TV they seem to be few and far between. But maybe if you can manage distance you can then concentrate on the other things.
I do have such a graph, and it shows that the relationship is not linear.
My goal is to do the following:
- Allow the user to select a stimp rating to practice on. For example, 10.0, which is a somewhat medium speed.
- When the user putts a golf ball through the pair of break beam sensors, the velocity is determined. I have this tested and working.
- I need a formula to multiply the fps of the golf ball by some coefficient of friction (as determined by the stimp rating the user enters in) to predict a distance rolled on flat ground. Since it is a practice device, I only intend to simulate flat ground at this point.
- I have a table of coefficients of friction that relate to basically the entire range of expected stimp values:
Stimp Coefficient
5.0 0.197
6.0 0.164
8.5 0.116
11.0 0.089
12.5 0.079
- When the Stimp coefficients of friction are graphed, it's not linear. It's a curve.
So I need one formula that will translate feet per second into distance traveled using coefficient of friction (or just modeling the curved graph of the values) so that I get accurate distances at all reasonable initial velocities- from about 2 feet per second to about 15 feet per second, at least.
As a non-mathematician, the more I'm learning, the further I feel from the answer
Look at the energy. What is the kinetic energy of the ball at 6fps? Does it lose a constant amount of energy for each foot that it rolls? Does a ball hit twice as hard roll four times the distance?
I'm sure your carpet at home will make a better test surface than an actual golf green.
Tbryden:
4. I have a table of coefficients of friction that relate to basically the entire range of expected stimp values:Stimp Coefficient
5.0 0.197
6.0 0.164
8.5 0.116
11.0 0.089
12.5 0.079
- When the Stimp coefficients of friction are graphed, it's not linear. It's a curve.
I can think of two approaches.
You should be able to figure out the formula to produce that curve using a spreadsheet and a knowledge of curve-fitting, It might be a square law or exponential.
OR
you could interpolate between the above values. For example if the Stimp is between 5 and 6 apportion the values between 0.197 and 0.164 in a linear fashion.
...R