Placement of Center of Gravity
for Best Spin and Launch Angle
Dave Tutelman  August 16, 2013
Discussion and implications
BackspinOur 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 350400 rpm.

Forward motion of the CG reduces backspin for center hits. The
reduction is only 160rpm, and this falls off for higherface 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 midface impact, but none for the ideal highface
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 threedimensional, 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 twodimensional colorcoded 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 timeconsuming, 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 highlaunch/lowspin down to
lowlaunch/highspin. 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:
 It moves you toward the ridge, or
 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 195205 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 8º to 22º. 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, 14º gives a carry distance of 188 yards, and 18º 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 15º, 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 2º at impact, and the shaft is bending
forward at 1º, then that 15º optimum dynamic loft becomes
15º  2º 
1º = 12º
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
300400rpm, 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

12º

177
→ 172

5

14º

188
→ 187

1

16º

189
→ 193 
+3

18º

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 12º and 14º
reducing spin costs
distance, while at 16º and 18º 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
highclubface 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 halfinch increase in h (the height of
strike) results in:
 About 900rpm reduction of spin.
 Almost 2º increase in launch angle.
As we did with CG motion, we can map [900rpm, 2º]
onto launch space. Here it is, tacked onto the CG motion we did in the
last exercise.
Loft

Distance
before and after

Distance
change

14º

186
→ 185

1

16º

193
→ 194 
+1

18º

190
→ 197 
+7

The green arrows are motions of [900rpm, 2º]
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 14º 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 18º 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

15º

Moving
CG
down 0.1"

193

16º 
Hitting
0.5"
above center

197

18º 
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 underloft.
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 (15º 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
launchangle and low spinrate. . . 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
centerhits 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:
 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.
 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.
 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 nottoodistant future.

The final page of the article is the mathematical analysis used in the
spreadsheet, for those interested.
Last updated
 Mar 11, 2014
