Make your own stimpmeter, and the science behind it

I had been playng golf for about twenty years but just began regular putting practice when I joined my first men's club last year. Between the two public courses that I sneak out to for putting practice,  one feels like a shag carpet and the other feels like glass. I've been seeing signs reading   "Current Stimp xx.x feet" for years and decided to build my own Stimpmeter.

A Stimpmeter is an inclined ramp that can be any length, with a starting point for the golf ball 30 inches from the bottom end. The key specific is that ramp must be set to a precise 20.5 degree angle. For the math nerds, the golf ball is 10.5" abouve the ground at release, 30" * sine(20.5 degrees) = 10.5". Tada!

The only other specification for the Stimpmeter is that the ball must only contact the ball at two points 1/2" apart. When you see the professional measuring the green with a real Stimp, it looks like a wide piece of material bent at a very subtle angle. The angle is set to meet the two point contact spec. Anyway, I am starting off this project with an alternate configuration. I lucked out and found a 1/2"id (inner diameter) 8' long piece of alluminum sliding glass door channel. I'll delve more into the physics of possible contact friction between the two profiles later, but first, a little about what we are making: 

 

The Physics

 
(Skip to the pictures if you want to jump to the build)

 

The potential energy, or stored energy (PE) is the energy stored in the golf ball's weight (W) at whatever the distance it is from the ground (H)

PE = W*H

Obviously the higher the ball is, the more distance it has to gain speed during its ride down.

Using the Stimpmeter specs and a USGA conforming golf ball, the numbers are PE = 1.62oz * 10.5". Thus PE = 1.62 * 10.5 = 17.01 in/oz ("inch ounces") of POTENTIAL ENERGY the ball has with the Stimpmeter set at 20 degrees.

Now to calulate the conversion of "POTENTIAL ENERGY" to "Kinetic Energy" which will yeild a new component, VELOCITY!

KE=PE*cosineANGLE

The VEOLICTY (V) of the ball at the bottom of the ramp is determined by the KE, which in turn depends on the WEIGHT, HEIGHT and ANGLE of the ramp. V=SQR[2*15.93*384/1.62], or SQR[7,552] = 86.90 inches / second velocity at the bottom of the ramp.

Did I mention I'm a 20+ handicap player?
I'm a 20+ handicap player with a shop and some math skills
BOO YA!

So the ball rolls for 0.69 seconds and leaves the ramp traveling at 86.9 inches per second (which is about 16.5 revolutions per second) and will ultimately be stopped by the green's "coefficient of friction," where all "Stimp 10" measured greens should stop at exactly 10' from the ramp. Well kinda. The USGA allows +/- 8" from six readings, three going one way then another three rolls going back from the oposite direction.

Lastly we need to calculate friction

f = 15.93 in-oz(Kinetic ENERGY) / 1.62 oz(ball weight) * S(VELOCITY) (*12 in/ft to convert Stimp in feet to Stimp in inches)

f = .82 ft / S (back to S in feet), or f = .82 ft / S ft

I've skipped the irrelevant expressions for the actual green/ball's real "resultant-friction" variable because it involves the compressability of the grass, the variable depth of the ball at varying speeds, the collisions difference of the ball/grass based on grain direction etc. I say irrelevant because we will replicate what old man Stimpson dictated in his design and make sure we get consistant readings.

 

A 5% green slope and a Stimpmeter reading of 13 is the point at which a golf ball will continue to roll, fun fact.

Ok lets do this.