Placement of Center of Gravity

for Best Spin and Launch Angle

Dave Tutelman -- August 16, 2013

Discussion and implications


Backspin

Our numbers are based on a 100mph clubhead speed and CG motions of a tenth of an inch. (Jeff Summitt tells me that 0.1" is a fairly large movement of CG. It can be done with simple shape or thickness changes, but it takes special measures to do much more.) Larger CG movement or faster clubhead speed magnifies the spin effects.

Here are the results:
  • As expected, downward motion of the center of gravity reduces backspin. A 0.1" movement results in a spin reduction of 350-400 rpm.
  • Forward motion of the CG reduces backspin for center hits. The reduction is only 160rpm, and this falls off for higher-face hits. The spin reduction disappears altogether about a half inch above the center of the face. Therefore, a forward movement of the CG provides some small help for the mid-face impact, but none for the ideal high-face impact. It is more to forgive low hits than to power good hits.
  • Rearward motion of the CG did not reduce backspin for any of the configurations tried. (Well, it did, sort of. But it required unrealistically large downward motion of the CG to make it happen. Try it on the spreadsheet yourself, and you will see how much downward CG motion it takes, and how little reward it gives.)

Launch angle

The launch angle changes very little due to CG motion of a tenth of an inch. The changes are negligible compared to manufacturing tolerances, and even measurement precision for driver heads. The changes may increase with more CG motion or clubhead speed, but they will still be small changes.

The changes observed were:
  • Downward motion of the CG raises the launch angle due to gear effect rotation, but the launch angle change is less than a tenth of a degree.
  • Forward motion of the CG lowers the launch angle, because it reduces the centrifugal shaft bend thus reducing dynamic loft. This change is about a tenth of a degree.

Distance... and implications for fitting

To my surprise, the spin reductions were sometimes counterproductive with respect to distance. I wondered about it for a while, and concluded that the explanation lay in where we were operating in "launch space". Launch space is the graph of distance vs both launch angle and spin.

The launch space graph (shown here) is three-dimensional, with launch angle and spin being the horizontal axes and distance the vertical axis. As conventional wisdom leads us to expect, the highest point on the graph is where the launch angle is highest and the spin is lowest. But the converse is not true; the low point of the graph is not low launch and high spin. Rather, it is at high launch and spin, or low launch and spin. There is a diagonal "ridge" of fairly high distance, and falling off the ridge on either side loses distance much faster than simply climbing down the ridge. This is perhaps better seen in a two-dimensional color-coded map of the graph, so let's look at that.


Here is a launch space for an 86mph clubhead speed. That is not the 100mph case we have been using. But creating a launch space map like this is time-consuming, so I'm going to use one I have on hand.

The colors denote classes of distance as they move through the rainbow: red for long distance and purple for short drives. we can see the ridge -- the black dotted line -- that goes from high-launch/low-spin down to low-launch/high-spin. The distance changes rather slowly as you move along the ridge, but falls off rapidly on either side; that is why it is called a ridge.

There is an important fact to be carried away from this: Simply reducing spin does not necessarily increase distance! It only increases distance if:
  1. It moves you toward the ridge, or
  2. It is combined with enough increase of launch angle to move you parallel to the ridge.
If you are below the ridge and reduce spin, carry distance drops like a rock!

Let's get back to our results from moving the center of gravity. There were cases where we reduced spin and lost carry distance at the same time. The combination is no longer astonishing. The driver's loft and clubhead speed must have left us at or below the ridge, where reduced spin hurts rather than helps.

Is there any way to map a driver onto the launch space? Let's do it! We start by mapping just the dynamic loft at the given clubhead speed, keeping everything else neutral:
  • Angle of attack = 0.
  • Clubhead mass = 200 grams (for a modern driver, it is mostly 195-205 grams).
  • Coefficient of restitution = 0.83.
  • Benign ambient conditions: flat fairway close to sea level, warm day with no wind.
  • No gear effect! We'll incorporate gear effect later.
The result is a line, the locus of the loft in launch space. The red balls are labeled with the loft they represent, from 8 to 22. Each loft is placed at the launch angle and spin produced by the driver. You can read the distance from the nearby cells in the launch space map. For instance, 14 gives a carry distance of 188 yards, and 18 about 185 yards.



The important thing to note here is that varying the loft generates a line that crosses the ridge almost at a right angle. It isn't anything like parallel to the ridge; just the opposite, in fact. There is no opportunity here to move along the ridge -- to play with increased launch and decreased spin. Anything you do to the loft changes both launch angle and spin in the same direction.

If we were to use loft alone to optimize the driver, we would choose the point where the locus of lofts intersects the ridge of maximum distance. For this golfer -- who swings at 86mph, remember -- we would use a loft of 15, giving a carry distance of 189 yards.

The loft is the dynamic loft, which includes shaft bend. It may even include any wrist angle the golfer has at impact. For instance, if the golfer has his wrist cupped 2 at impact, and the shaft is bending forward at 1, then that 15 optimum dynamic loft becomes
15 - 2 - 1   =   12
which is the loft that should be designed into the clubhead.

Including gear effect

Let's get back to gear effect, which is the focus of this article. We had to set the stage before we start designing in launch space, but now we are ready.

Let's start with CG motion, which is the major topic of the article. Moving the center of gravity downward by 0.1" reduces spin by 300-400rpm, with minimal change to the launch angle. Let's see what driver launch space looks like with the reduced spin.



Loft
Distance
before and after
Distance
change
12 177 → 172
-5
14 188 → 187
-1
16 189 → 193 +3
18 185 → 190 +5
The "sticks" extend the lofts downward in spin by 350rpm. The table to the right shows what happens at four different lofts. At 12 and 14 reducing spin costs distance, while at 16 and 18 it gives the expected result of increasing distance. What accounts for the different results? Simple! The cases that gained distance, the red sticks (representing spin reduction) moved us toward the ridge. The cases that lost distance, the red sticks moved us away from the ridge. If we understand launch space, it is pretty clear what is going on.

The conclusion is that, in order for spin reduction by itself to increase distance, we have to have enough loft to begin with so that we are operating above the ridge of maximum distance. If we do, then moving the CG to reduce spin can give us more distance that just loft alone. In the case of 86mph clubhead speed, we can get up to 189 yards with loft alone. If we apply spin reduction to that point, we actually lose distance. Why? Because we were already on the ridge, and reduced spin moved us away from the ridge. But we can gain distance by "lofting up" beyond the ridge and then reducing spin. This can get us another four yards, to 193 yards, because this time we intersect the ridge higher on its slope.

Please review this until it makes sense. The next step is more of the same, and slightly more complex.

Including high-clubface hits

Let's explore gear effect further. It is possible to increase launch angle at the same time as reducing spin, by hitting the ball higher on the clubface. The launch angle increase comes almost entirely from the curvature of the clubface; that is much more pervasive than anything we get from clubhead rotation during impact.

Good drivers of the ball will consistently hit high on the clubface. How do we design a driver for a skilled player who can take advantage of this?

I went back to the detailed calculations portion of the spreadsheet and determined that a half-inch increase in h (the height of strike) results in:
  • About 900rpm reduction of spin.
  • Almost 2 increase in launch angle.
As we did with CG motion, we can map [900rpm, 2] onto launch space. Here it is, tacked onto the CG motion we did in the last exercise.



Loft
Distance
before and after
Distance
change
14 186 → 185
-1
16 193 → 194 +1
18 190 → 197 +7
The green arrows are motions of [900rpm, 2] in launch space. As before, the table at the right shows the distance change the arrow causes. The arrows are more nearly parallel to the ridge than any of the motions we looked at before (those motions were loft and spin reduction). Because they are more nearly parallel to the ridge, they give more uniformly good resuls.

But still not entirely good results. The arrow for 14 loft (minus the spin reduction stick) was already well below the ridge, and the arrow actually lost a yard of carry distance. But the biggest gain came from the 18 driver, where the arrow got it up to 197yd, a gain of 7yd just from the arrow.

Step
Maximum
distance
Optimum
loft
Loft alone.
No gear effect
189
15
Moving CG
down 0.1"
193 16
Hitting 0.5"
above center
197 18
The moral of the story

If you hit high on the clubface for more distance, you still need to "loft up" to get the most out of it. And you can still lose distance if you under-loft.

Here are the results of our design steps in a table. We were able to get four more yards by moving the CG downward, and another four yards on top of that by hitting high on the clubface. But each of those gains required more loft -- and starting from more loft than you might have guessed (15 for a clubhead speed of 86mph). If you have too little loft at any stage, the changes will hurt distance rather than help.

TaylorMade SLDR



I have little use for most ads that tout technological advances in golf equipment. Most of them are hype and hot air. Not this one, though! After the observations above, I can resonate with TaylorMade's ads for its new SLDR driver. Here are a few excerpts from their web site:

SLDR maximizes distance for all golfers
  • Low forward CG makes SLDR our lowest spinning driver ever
  • SLDR unlocks that distance by enabling the golfer to hit the ball higher with less spin – WHEN THEY ADD LOFT
. . . . .
 
Long distance comes from combining of fast ball speed, high launch-angle and low spin-rate. . .  To launch the ball on a high enough angle to maximize distance, we’ve discovered that most golfers benefit from increasing their loft, some by as much two or three degrees.

My take?
  • Low CG reduces spin. A lot.
  • Forward CG reduces spin a little. Its greatest effect would be on center-hits and lower. But there is indeed some spin reduction there.
  • You really need enough loft for reduced spin to equate to more distance. They got that part right, too.

Next steps

I am posting this article with the knowledge that it begs several important questions:
  1. The distance analyzed here is just carry distance. We know that we get more roll after landing from reduced angle of descent -- which itself comes from reduced spin at launch and reduced launch angle. So, if you look at total distance rather than just carry distance, this will limit the amount you want to loft up.
  2. While the general shape of launch space is the same at all clubhead speeds, it would be very informative to plot a launch space for the sort of speeds generated by Long Drive competitors. This would typically be clubhead speeds about 140mph and ball speeds in excess of 200mph. We would see what the benefit of CG placement is for Long Drive, as well as how much to loft up.
  3. There is probably a different design strategy for using gear effect for the two different sports of Golf and Long Drive. Consider:
    • In golf, you want good driving distance, but your mishits should not be too much worse than your best hits. Two reasons: predictability of the landing point, and forgivingness  for mishits.
    • In Long Drive, you want your best drive to be absolutely as long as possible. You get six tries, and only the best drive counts.
    Given these differences, the strategy for Long Drive is probably to design so the perfect clubface strike gives a result on the ridge, and as far up the ridge as possible. But what about for golf? Where do you want to assume the operating point to be, to give good performance for a great strike but not too degraded performance for a miss?
I hope to get to these questions in the not-too-distant future.



The final page of the article is the mathematical analysis used in the spreadsheet, for those interested.


Last updated - Mar 11, 2014