Hi Geoff

Thanks for your quick reply on putting drills. Much appreciated as always.

Question

1. A ball released from a standard USGA stimpmeter runs down the ramp and travels across a flat section of Green 1 for 9.5 feet

2. The same ball released from the stimpmeter travels this time across a flat section of Green 2 for 12 feet

3. In both cases I presume the exit speed of the ball from the ramp onto the grass is the same only the grass height is different

4. Is it possible from knowing the length of the ramp from notch to exit point to calculate the speed of the ball (Speed X) as it exits the ramp? Has anyone timed accurately how long it takes a ball to reach the exit point when the stimpmeter is tipped sufficiently to release the ball from the notch and therefore the speed of exit of the ball?

5. Is the following assumption correct? A ball leaving a putter at impact at the same speed as that calculated in point 4 (Speed X) will travel 9.5 feet on Green 1 and 12 feet on Green 2. (Give or take a small margin for skidding before the ball starts rolling)

6. If the speed of the ball at impact is doubled, it is right to assume that the ball will now travel 19 feet on Green 1 and 24 feet on Green 2?

Is my thinking correct or am I missing something?

Kind regards

Neville Walker
Oz

Dear Neville,

Your physics is pretty correct. Let me address the issues separately. (Your points / questions are here in Italics.)

1. A ball released from a standard USGA stimpmeter runs down the ramp and travels across a flat section of Green 1 for 9.5 feet

2. The same ball released from the stimpmeter travels this time across a flat section of Green 2 for 12 feet

3. In both cases I presume the exit speed of the ball from the ramp onto the grass is the same only the grass height is different

COMMENT: Yes, pretty much. In physics, what actually differs is the "coefficient of friction" of the green. This is a number that represents many factors, including grass height, grain, mositure, chemicals on the surface, and really even air resistance and humidity. But the biggest factor and the commonly understood meaning is grass height. Both surfaces are assumed to be not only "flat" is shape or contour but also "level" to gravity.

4. Is it possible from knowing the length of the ramp from notch to exit point to calculate the speed of the ball (Speed X) as it exits the ramp? Has anyone timed accurately how long it takes a ball to reach the exit point when the stimpmeter is tipped sufficiently to release the ball from the notch and therefore the speed of exit of the ball?

COMMENT: Sure. Arthur Weber has written for the USGA Green Section an article entitled Green Speed Physics (pdf document) that calculates a speed of the golf ball off the bottom of the ramp of 95.5 inches per second. His otherwise very nice paper, however, has a mistake embedded in the calculations, in that he uses 12.6 inches for the beginning height of the ball, and the actual height is only 10.6 inches. Let me re-do his calculations.

First, what exactly is a Stimpmeter?



A Stimpmeter is an inclined plane or ramp that is 36 inches long, with a notch for the golf ball 30 inches from the bottom end, such that raising the back end of the ramp to a height of 12.6 inches and an angle of 20.5 degrees causes the ball to tip out of the notch and start rolling down the ramp. See USGA Stimpmeter Instruction Book. The golf ball notch is 10.5 inches above the ground at release, from Pythagorean geometry, 30 inches * sine(20.5 degrees) = 10.5 inches.

An inclined plane is simply a mechanism for spreading out the WORK of raising a WEIGHT to a HEIGHT. The milder the angle of the ramp, the more spread out the WORK and the less FORCE required to be applied over time to move the WEIGHT up to the increased HEIGHT. If you want to raise a bowling ball five feet off the ground, its a lot easier to roll it up a gently sloped ramp than it is to hoist it straight up, and carrying a suitcase up a flight of stairs is harder on steep stairs than on a long, more gently sloped flight of stairs. The point is that the ENERGY to raise the WEIGHT a given HEIGHT does not at all depend upon the angle of length of the ramp, but only on the HEIGHT. Galileo sorted all this out about 400 years ago. Students at Rice University in Texas have reproduced Galileo Inclined Plane Experiment.

Since from basic Pythagorean geometry we know that any one angle and any one length of a hypotenuse of a right triangle corresponds to one and only one triangle with adjacent and opposite sides (and the opposite side is the same as the back-end HEIGHT of a Stimpmeter), then it is obvious that a Stimpmeter is just a device for always giving a golf ball the same ENERGY on every roll, since that LENGTH and ANGLE always corresponds with the same HEIGHT.

The relevant physics formulas are the following:

1. PE = W*H

The Potential Energy (PE) is the ENERGY stored in the golf ball's WEIGHT (W) by raising it higher than it is on the ground a certain HEIGHT (H).

For the Stimpmeter and a golf ball, the numbers are PE = 1.62 ounces (oz) * 10.5 inches. Thus PE = 1.62 * 10.5 = 17.01 in-oz of ENERGY with the Stimpmeter raised.

2. KE=PE*cosineANGLE, or KE=W*H*cosineANGLE

The Kinetic Energy of the ball off the bottom of the ramp is the PE reduced by part of the ANGLE of the ramp's tilt.

For a Stimpmeter and ball, the numbers are KE = 17.01 * cosine(20.5 degrees). This KE = 17.01 in-oz * 0.9367 = 15.93 in-oz. The difference between PE and KE (17.01 - 15.93) of 1.08 in-oz is just the bounce at the bottom that dissipates or wastes some of the PE.

3. KE = 0.5 W V^2 / g and V = SQR[2*KE*g/W]

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, as seen in formulas 1 and 2 above. The variable "g" is earth's constant of acceleration form gravity's force, and is usually taken to be 32.2 feet per second per second (velocity increases each second by this amount of added velocity). In units of "inches per second per second," this is 32.2 * 12, or 384 inches per second per second (in/s/s).

For the Stimpmeter and golf ball, the numbers are V=SQR[2*15.93*384/1.62], or SQR[7,552] = 86.90 inches / second velocity at the bottom of the ramp. [Weber gets 95+ inches per second, too high, since he erroneously uses 12.6 as the release HEIGHT.]

To figure how long in TIME it takes to roll down the ramp, which is always the same, the formula is simply DISTANCE = SPEED * TIME. Here, SPEED is the average VELOCITY while rolling down the ramp. Since the ball starts at 0 inches per second velocity in the notch, and smoothly accelerates to a peak VELOCITY at the bottom or end of the roll off the ramp of 86.9 inches per second, the average velocity or SPEED is one half 86.9, or 43.45 inches per second. The DISTANCE is 30 inches. So the TIME = DISTANCE / SPEED, or T = 30 in / 43.45 in/s, for a total roll time of 0.69 seconds. If you silently mouthed "one mississippi" after the ball starts rolling, then ball would exit the bottom of the ramp after about "one missip..."

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).

To convert the Stimpmeter reading into the green's "coefficient of friction," where all Stimp 9 greens have the identical "coefficient of friction," the formula is:

5. KE = W*S*f

KE is Kinetic Energy of the ball off the Stimpmeter, W is WEIGHT of the ball, S is Stimpmeter of the green (e.g., 9, 10.5, etc.), and f is the "coefficient of friction" of the green.

The numbers are 15.93 in-oz = 1.62 oz. S f. Thus, rearranging to see the relationship between Stimp and f,

f = 15.93 in-oz / 1.62 oz * S (*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

So, for a Stimp of 10, the green has a "coefficient of friction" of 0.082. For a Stimp 5, f = 0.165 or twice as high.

5. Is the following assumption correct? A ball leaving a putter at impact at the same speed as that calculated in point 4 (Speed X) will travel 9.5 feet on Green 1 and 12 feet on Green 2. (Give or take a small margin for skidding before the ball starts rolling)

COMMENT: Yes. The ENERGY imparted by a putter to a ball depends on the MASS of the putter head and the SPEED (i.e., Velocity) of the clubhead at impact. The resulting SPEED of the ball is a combination of the MASS of the clubhead and its SPEED and the MASS of the ball and its SPEED (zero to start). In the impact, the putter gives up some SPEED and the ball gains some SPEED (actually, VELOCITY, or SPEED in a given DIRECTION). The "some" is a function of the relative MASSES of putter head and ball, which is typically in the ratio of about 6 to 1. When the resulting SPEED of the ball matches the end-of-ramp SPEED of the ball off a Stimpmeter, then the two balls go the same distance. The "coefficient of friction" of the green operates on the beginning ENERGY of both balls identically, so they roll the same distance so long as they start with the same ENERGY at the beginning.

If you wanted to determine what sort of stroke matched the Stimpmeter, all you have to do is roll a ball off the ramp until it stops at some distance, and then putt a ball with your putter to exactly that same distance. Assuming you have a constant TEMPO for all putting strokes and always use the same putter and ball and impact the ball solidly, the only remaining variable is BACKSTROKE LENGTH. That is, once you find out what BACKSTROKE LENGTH with your putter, ball, and TEMPO matches the roll produced by the ENERGY of a Stimpmeter, you don't need a Stimpmeter any at all. Just reproduce that BACKSTROKE LENGTH with a putt, and the roll of your ball will tell you what the Stimpmeter tells the greenkeeper.

I've modified this with my CORE PUTT technique because the Stimpmeter is an arbitrary level of ENERGY, and in my experience the real trick to making your stroke serve as a Stimpmeter is not matching the Stimpmeter's ENERGY but instead always giving the ball the same level of ENERGY with your stroke. The BACKSTROKE LENGTH doesn't have to match the Stimpmeter to be a reliable indicator of green speed: it simply has to be consistent, used with a consistent TEMPO. As it happens, there is a convenient BACKSTROKE LENGTH that everyone is familiar with, which is the point going back where it feels that if the putter is to continue any farther back, the golfer will have to start lifting the putter. This is just the normal comfort zone for sashaying the shoulders and upper torso rocking up and down, and it pretty much moves the hands from thigh to thigh reliably and consistently, so the putter moves just a little past the rear foot on the backstroke. This BACKSTROKE LENGTH with MY TEMPO does not precisely correspond to the roll that a Stimpmeter produces, but it's close. What matters is that it shows me in an analog fashion what MY CORE STROKE provides for ENERGY and hence roll on THIS GREEN SPEED. This basic "unit" of roll allows me to calibrate my touch to any surface in a natural, analog manner, simply by looking at the result, rather than trying to translate a Stimpmeter number into "touch and feel" somehow. The Stimpmeter may be "science" for the greenkeeper, but my CORE PUTT is "useful science" for the golfer.

6. If the speed of the ball at impact is doubled, it is right to assume that the ball will now travel 19 feet on Green 1 and 24 feet on Green 2?

COMMENT: Yes.

Cheers!

Geoff Mangum
Putting Theorist and Instructor

Geoff Mangum's PuttingZone
Golf's most advanced and comprehensive putting instruction.

Over 710,000 visits and growing strong ...

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Geoff
Thanks for the physics lesson.
The basis of my inquiry concerns my wishing to help blind and vision impaired golfers with distance control on the putting green. This presents some difficulty for them as it takes a long time to develop a sense of distance based solely on feel.
As background when on the green it is customary for the blind player with the guidance of the caddie to walk the distance from hole to ball counting the paces to assess the straight-line distance. The player and caddie then determine (the player through his or her feet and the caddie by observation) what factors may influence the ball's roll such as the putt being uphill and the green being slow. (Most blind and vision impaired golfers play on public courses where the greens are on the slow side).
A straight-line uphill putt of 16 feet may be converted to the equivalent of a 24 feet level putt. My player uses the technique of repeating to himself a mantra such as "give me 24 feet" as a way of reinforcing in his mind the effective distance. He then putts after I have aligned him and waits for my feedback on how far the putt travelled.
Practising putting for distance control can be difficult for the blind and vision impaired golfer as it can't be done easily without outside help. I am interested in devising a gismo that can be used indoors on a carpet based on the concept that if you can measure the ball's speed just after impact (either through radar or laser), this can be converted to the distance the ball will have travelled and then audio-fed to the player.
As the physics of a ball exiting a ramp at a known speed are apparently constant, it should be possible to construct a table of different distances for different ball speeds. Once you have it for one green speed, say 8 on the stimpmeter, the calculation for other green speeds should be straight forward. Is this a correct assumption?
Imagine this situation, the blind player sets the ball down on a pad aligned to the gismo, putts the ball into a cushion a few feet away and then hears that the ball would have travelled 20 feet on the referenced standard green of 8 on the stimpmeter. Through practice the player learns to make strokes that will travel set distances such as 12 feet, 24 feet, and 36 feet. These are like your core putts. Back on the course these core putts are used as a reference for distance control.
Does this make sense to you or am I off track?
Kind regards
Neville
Oz

Dear Neville,

I have been designing practice aids for blind golfers for several years now. I have tried to interest blind golfer associations, but have so far received no interest. I can't disclose my training device in public without patent protection, but will gladly share it with you in conjunction with a nondisclosure agreement.

Cheers!

Geoff Mangum
Putting Theorist and Instructor

Geoff Mangum's PuttingZone
Golf's most advanced and comprehensive putting instruction.

Over 710,000 visits and growing strong ...

518 Woodlawn Ave
Greensboro NC 27401
336.230.0612 home
336.402.1602 cell

Thanks Geoff for your reply.
If I got to build such a gismo it would be at my expense. The time I give to blind golf is on a voluntary basis and where there is a cost involved in putting together a training aid I have to take the risk and then do the fund raising on their behalf to recoup the cost. Not always successful. I am hoping that this will change as the Association for the Blind in Western Australia is building a sports centre and will have to become more organised in helping blind and vision impaired clients (especially juniors)play golf. If they get serious about teaching golf as a sport rather than just using it as occupational therapy, things might change and some money may be directed into adaptive equipment. At the moment money collected for adaptive equipment in the State goes only to those with multiple and severe disabilities and this does not include the disability of blindness.
Kind regards
Neville
Oz

Dear Neville,

The trick to teaching a person with sight impairment how to learn distance control without the assistance of a sighted guide is obviously to make available some form of feedback about the location of the putted ball in relation to the body and target. The most easily used sense is audition, as you well know.

Target first: The training device or apparatus could locate the target (hole) in relation to the body either in a fixed, constant way (as in a putting mat of fixed dimensions), or in a fixable way (adjustable length putting mat) or by virtue of auditory communication from target to body. The cheapest way is to make an adjustable length mat, the length of which is in the control of the golfer.

I would suggest a 20-foot+ putting mat or platform surrounded by rails so that the ball would not roll off, with raisable bars at different distances. The bar could be some sort of thin metal that makes a nice plunk or ping sound when a golf ball rolls slowly against it. The golfer could then raise the metal barrier for, say, 14 feet, and practice cozying the balls against the barrier. A track beneath the platform could have a pulley attached to a draw string that positions the wheel beneath one of the many metal barriers by turning a dial to the set distance, and then levering the bar upward beneath the metal barrier to raise just that one barrier. The golfer could set various distances and putt away. If the platform had a slight tilt to it, all the ball would return by gravity. The top of the barrier could be T-shaped to fit flush with the rest of the surface when not in use. There's probably a way to make holes open and close at various distances as well.

A variant is to make the tilt of the platform adjustable, to make the influence of increasing gravity from increasing tilt mimmick different green speeds.

Another idea is to use a car remote lock device to activate a sound inside the hole from a distance. The golfer could use this on a real practice green for echo-location of the hole. A variant would be to modify one of Fuzzy Zoeller's Putting Pods, which sounds when contacted by a putted ball (one for indoors, and one for use on a real green) so that it also emits a sound in response to a remote car key device. Then, the target makes a sound once when the golfer locates it, and again if his putted ball successfully contacts it.

Ball second. There cirrently exist patents for golf balls that emit sounds either continuosly or in response to a remotely generated signal. These were designed to help golfers find the balls in the rough, but could be adapted to putting. I would really like to see a ball that emits a sound with a frequency that varies with the rolling speed of the ball, so the golfer can not only hear where and how far away the ball is at any point during its roll, but also hear the pattern of speed (fast, then steadily slowing, then dying out to a full stop). Then perhaps the ball could emit a final signal in response to a remote device that tells the golfer the final position.

Another way is to construct a platform that has infrared or laser circuits arrayed across the surface at ball height in a series of lines perpendicular to the long axis of the platform. As the ball rolled thru each light line, breaking the circuit, it would sound a tone. The tones could be sequenced from low to high along the platform,so the golfer could easily detect how far different putts rolled. This paltform could also be tilted for purposes of gravity return of the balls and for mimmicking different green speeds.

There is a device already available that allows the golfer to set a green speed and then make a stroke across a surface with magnets on the putter head that generate a signal read by the device. The device looks like a putting mat, and comes with a putter and two small magnets to attach to the putter head. When the golfer makes a stroke over the mat, either with or without a golf ball, the mat detects the putter head position in the stroke and calculates a number of aspects, such as face squareness, centering of sweetspot, height of sweetspot above surface, and path of putter head in relation to the line of the putt. Given the green speed, it also calculates from the speed of the putter head in the impact area how far the putted ball would roll on that green speed. The device allows the golfer to set the length of the putt, and then he makes a stroke and the device reads out the devloping distance of the roll until the ball comes to a stop. If the ball is putted squarely with the correct distance, so that the line is good enough to find a regulation sized hole at that distance, the device emits a ball-rattle-in-cup sound at the end of the roll. If the ball misses, the device tells how far short or long. A sequential readout provides details about putter face at impact, path, etc. This device currently just shows the information in an LED readout, with the sound of the rattle (and also a puck sound at impact), but could be modified to call out the info in a computerish voice, I'm sure.

Let me know if I can help with this project, as I think anything that helps sighting impaired golfers could not but also help fully sighted golfers.

Cheers!

Geoff Mangum
Putting Theorist and Instructor

Geoff Mangum's PuttingZone
Golf's most advanced and comprehensive putting instruction.

Over 710,000 visits and growing strong ...

518 Woodlawn Ave
Greensboro NC 27401
336.230.0612 home
336.402.1602 cell

Thank Geoff for your ideas. Much appreciated. When the Sports Centre comes on stream I will talk to Association for the Blind and try and raise some funds for adaptive training aids. Last year I managed to organise 12 half-sets of clubs for the juniors. Through various donations I got the heads from one organisation, the grips and shafts from another, and a club fitter kindly assembled them for me.
I was also hoping to get the starting new at golf (SNAG golf) launcher, roller, and velcro covered balls but I believe that the founders of SNAG golf in the States have gone bust.
Kind regards
Neville
Oz

The rolling of a ball down the Stimpneter is slower than the frictionless sliding of a block down the same ramp due to some energy going into making the ball roll. The TRANSLATIONAL velocity of the ball at the bottom of the ramp is not as fast as the above calculations suggest in ITEM 5. The actual formula that accounts for this difference generates a predicted speed at the bottom of the ramp of 76.9 inches / second or 6.35 feet / second, so the AVERAGE velocity down the ramp is 1/2 this, or 38.45 inches / second or 3.175 feet / second over 30 inches. Thus the time down the ramp is 0.78 seconds. It takes the ball about 8/10th of a second to roll from the top of the ramp to the bottom.

The correction to this is posted HERE.

Sorry for the confusion.

Cheers!

Geoff Mangum
Putting Theorist and Instructor
Geoff Mangum's PuttingZone
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geoff@puttingzone.com

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