Geoff, when you said

"The greater the mass of the putter head, the more "send" the same stroke gives the ball in comparison to a lighter putter, so a shorter stroke is used for the same putt on the same green in comparison to a lighter putter used with the same tempo on that ..."

For the masses of golf balls (46 grams) and putters (putterheads over 300 grams) I believe that that is basically not the case.

If you model the impact of a putter and ball as simply free body impact of the putterhead and ball, then you have two relevant equations of motion - COR equation and conservation of momentum. And you have two unknowns (velocity of the ball after impact and velocity of the putter after impact).

Solving those for the velocity of the ball as a function of the initial velocity of the putter gives you

VB = VPi*(1+C)*MP/(MP +MB)

where MP is mass of the putterhead, MB is the mass of the ball, VPi is the initial velocity of the putterhead at impact, and C is the coefficient of restitution.

For even relatively light putterheads (low 300 grams) MP is going to be around 8x bigger than MB. So the velocity of the ball is going to be pretty much independent of the mass of the putterhead - at least for conventional/modern putters.

Does this look correct to you? There certainly are a few assumptions buried in this analysis. Once I decided that this is true I added around 60 grams of weight to my relatively light putter, as there didn't seem to be any "feel" to be gained here.

Thanks.

dave

... this message (Putterhead Weight) was posted (yesterday) as a response to the Putter Fitting thread and it showed up there after I posted it. Yet right now it appears as a new thread, except that I can't edit it. This seems wrong - kinda' like my putting the other day

dave

Dear avid,

I moved it because your question was independently important and on a different topic from the other "putter fitting" thread.

Geoff

Dear Dave,

The ratio of putter head mass to ball mass (45 grams) in available putter designs today runs in the range of 7 to 11 -- 320-375 grams to 45 grams for conventional putters (7.1 to 8.3), 360-400 grams to 45 grams for belly putters (8 to 8.8), and 400-500 grams to 45 grams for long putters (8.8 to 11.1). Here is a detailed discussion of this subject on a previous Flatstick Forum post.

Applying these ratios to the same backstrokes and tempos on the same level green, we get these different "send" distances using different putter head weights with the same putt stroke:

First, to get the coeficient of friction, the basic formula relating Stimpmeter reading (S) to grass friction (f) is f = 0.828 / S. [This is a correction of Weber in his paper where he mistakenly uses 12.5 inches instead of 10.6 inches for the starting height of the ball on a Stimpmeter. Weber derives the formula f = 0.983 / S.] Choosing a Stimp 10 green for our comparison, the coefficient of friction of the green is 0.083.

Your formula: VB = VPi*(1+C)*MP/(MP +MB) requires us to use an initial putter head velocity. The velocity off the bottom of the Stimpmeter is a good one to use for the putter head, and that is 76.9 inches per second. [Your C is my f.]

7:1 -- VB = 76.9 * (1.083) * 7 / (7+1)
7:1 -- VB = 83.283 * 7/8
7:1 -- VB = 72.87 inches per second

8:1 -- VB = 83.283 * 8/9
8:1 -- VB = 74.03 inches per second

9:1 -- VB = 83.283 * 9/10
9:1 -- VB = 74.95 inches per second

10:1 -- VB = 83.283 * 10/11
10:1 -- VB = 75.71 inches per second

11:1 -- VB = 83.283 * 11/12
11:1 -- VB = 76.34 inches per second

Using this set of VBs to calculate distance of roll across level green, the formula is:

Distance = VB^2 * [1.62 / (2 * 32.2 * 12)]
Distance = VB^2 * 0.0021

Thus,

7:1 Distance = 11.13 feet * 12 = 133.6 inches
8:1 Distance = 11.49 feet * 12 = 137.9 inches (+ 4.3 in)
9:1 Distance = 11.78 feet * 12 = 141.4 inches (+ 3.5 in)
10:1 Distance= 12.02 feet * 12 = 144.2 inches (+ 2.8 in)
11:1 Distance= 12.22 feet * 12 = 146.6 inches (+ 1.6 in)

As you can see, the difference in putter head weight results in more send in the increase from 7 to 8 times ball mass than does the increase from 8 to 9 or 9 to 10 or 10 to 11. This just reflects the progression of the fractions 7/8, 8/9, 9/10, 10/11, 11/12.

The overall range of "send" from 7 to 11 is 13 inches for one "Stimp's worth" of putter head velocity at impact.

This also means that for an 11-foot putt, the above backstroke and putter head velocity at impact for a 7:1 putter head is essentially correct, whereas the backstroke length and putter head velocity at impact for a long putter with an 11:1 ratio putter head will have to be somewhat shorter. Heavier head with same tempo = shorter stroke.

The "feel" in this difference in send that you refer to has to be the vibrational "feel" and this will vary with the putter head mass, shaft, shaft length, and handle (and probably the hoseling also). But if all things were held equal, with the same shaft, hosel, length and handle, with only the putter head mass varying, the "feel" of a light putter at impact will transfer (I think) bigger vibrations that are not damped out as much as the smaller vibrations of the more massive putter head.

My observation is that "touch" or distance control is more about timing than about feel. All of the above putting strokes will have the same tempo and the same putter head velocity at impact, and the same acceleration pattern under gravity (alone), in my approach to touch. Because in gravity, the mass of the object is irrlevant to the acceleration experienced in gravity (Galileo and the leaning Tower of Pisa), in order for the different-mass putters all to arrive at the bottom of the stroke with 76.9 inches per second velocity, they all have exactly the same backstroke length, exactly the same free-fall pattern of acceleration, and the exact same moment of impact. So. prior to impact, the "feel" is really all about "timing."

Cheers!

Geoff Mangum
Putting Theorist and Instructor
Geoff Mangum's PuttingZone
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Geoff, thanks for the additional information and explanation for the 'wandering post'.

I had simply looked at the impact of adding 60 grams to my putterhead. For a given initial (fixed) putterhead velocity, it is only a couple percent of change in initial ball velocity. Given that (for me) a good day of lag putting is an average error of around 8% (bad days can be much worse), it seemed to me that my own ability was a far bigger variable.

Maybe a good goal would be to get good enough at lagging so that the mass of my putterhead really matters

dave