Placement of Center of Gravity
for Best Spin and Launch Angle
Dave Tutelman  August 16, 2013
The work I have done analyzing vertical gear effect
tells the golfer where to hit the ball on the clubface for maximum
distance. But it doesn't tell the club designer where to place the
Center of Gravity (CG) of the clubhead, to make it as easy as possible
for the golfer to hit the ball on a favorable clubface spot. This
article addresses that question, as well as how CG location figures into custom fitting the driver.
In March of 2013, Jeff Summitt^{[1]}
emailed me about a clubhead design problem. (Jeff is the Chief
Technical Officer for Hireko, and he designed most of the clubheads in
my bag.) Rather than paraphrase the problem, let me quote a bit of
Jeff's note.
We know that the lower the CG, the higher the ball will go with all
else equal. Manufacturers (even Hireko) tout drivers to have a
high launch with low spin to help optimize distance. We know
there are limits to that, but bear with me for a second. If you
read or hear from the manufacturers, many will say that moving the CG
rearward will reduce spin, while others now are saying the opposite.
So... does moving the CG rearward reduce or increase spin? Good question!
Here is what is covered in this article, page by page:
 What causes the changes of spin and
launch angle, and how does CG location affect them? Here it is
discussed from an intuitive and visual perspective. We're not getting
quantitative yet.
 I present a spreadsheet for computing spin and launch angle
as we vary the CG location, and graphs of performance plotted by the
spreadsheet.
 The
spreadsheet gave us some surprising numberical results. In particular,
reduced backspin often did not result in increased distance. Sometimes,
in fact, the distance dropped. Here we summarize what we have learned, figure out why the distance sometimes dropped, then apply it to proper driver fitting.

The final page is the math and physics used in the spreadsheet; you can skip it if this is not your thing.
Visual explanation
My previous work on
vertical gear effect has a naive answer; moving it rearward reduces
spin, at least if you hit the ball high on the clubface as you are
supposed to. Let's explain that. Backspin on a golf ball comes from two
different effects at impact:
 The loft of the club provides a glancing blow, which causes backspin.
 The rotation of the clubhead  gear effect  will add backspin
if the hit is below the center and add topspin if the hit is above the
center.
A high hit on the clubface means the gear effect topspin is subtracted
from the loft backspin, for a lower net total backspin. The higher on
the clubface you hit the ball, the more the gear effect will reduce the
backspin.
To see how the CG placement creates gear effect topspin, let's borrow a diagram from that article.
The gear effect spin is proportional to C y, the multiplication of:
 C, the depth of the CG from the face, times
 y, the height above (or, if negative, below) the CG.
The left picture ("Naive analysis") makes it pretty clear.
 Moving the CG lower increases y, and thus increases the gear effect topspin.
 Moving the CG rearward increases C, also increasing gear effect topspin.
Case closed, right?
Not exactly. See the picture on the right ("Force aligned..."). C and y should really be measured in a direction aligned with the launch angle. When we do that, we still increase C by moving the CG rearward. But consider: a pure horizontal rearward movement of the CG will actually decrease y. Let's look at this a little more closely.
This picture^{[2]} shows what happens to y
as we move the center of gravity rearward. The green arrow is the line
of the ball's initial flight, extended in both directions from the
point of impact on the face. The red, blue, and yellow circles are
three possible positions of the CG, all at the same height (as
indicated by the horizontal dotted line). Note that the three CG
positions are much further apart than a club designer can actually
accomplish; this is exaggerated to make a point.
Each CG position has a line of correponding color drawn from the CG to the green arrow. That line is the y for that CG position. The C is the length of green arrow between the clubface and the position where the yline intersects it. Let's look at each one:
 The red CG is the most forward position. The red yline can be multiplied by C to estimate the gear effect topspin.
 If we move the CG rearward to the blue position, the yline shrinks most of its value, while C increases somewhat. y shrinks by a larger percentage of its value than C increases, so C times y
sees a net decrease. Thus the gear effect topspin is less, so the total
backspin is higher. In this case, moving the CG rearward increased the
total spin.
 If we continue moving the CG rearward to the yellow position, y has become negative. The reason is that the green extended launch line is now below the CG. The consequence is that C times y
is negative, meaning that the gear effect spin is backspin. So the
total backspin continues to increase as the CG is moved rearward.
This might not happen with all clubhead designs nor with all impact
positions on the face. Sometimes moving the CG rearward increases spin
and sometimes it decreases it. Let's see what we can surmise, however. See the
pictures below for a visual demonstration of these rules of thumb.
 The lower the CG of the clubhead, the more likely it is that moving the CG rearward will reduce total backspin.
 The higher on the face the ball strikes, the more likely it is that moving the CG rearward will reduce total backspin.
As we can see from the diagrams, either lowering the CG or raising the ball strike point increases the value of y. Therefore, a given change in rearward position of the CG makes a smaller percentage decrease in y. (That is, the actual value of y changes as it did before  but that is on top of a larger value of y to begin with. Thus the percentage change is smaller.)
Now remember that the gear effect is proportional to the product of C and y. From the diagram we see that, as we move the CG to the rear:
 The value of C increases.
 The value of y decreases.
So, if the percentage increase in C is bigger than the percentage decrease in y,
we can get favorable gear effect and reduced backspin.
Reality check: when we
get to numerical results, we will discover that it takes a lot
of #1 and #2 so that rearward CG motion will reduce total backspin. For
realistic designs, rearward CG motion results in higher backspin. For
the designs we evaluate, reducing backspin involves moving the CG
forward, not backward. Even then, the spin improvement is small, and
disappears high on the face.
Launch angle
Along
with the change in spin is a change in launch angle. Remember that the
gear effect spin is due to the clubhead's rotation. If impact results
in a positive y,
then the clubface rotates upward. This will provide a higher loft
during impact than was present when impact started. So we should expect
the launch angle to be higher, probably by some amount proportional to
the face rotation during impact.
The image shows the face rotating upwards, "geared" to the ball's spin. The rate at which the face rotates is:
 Proportional to the gear effect spin. Not the total spin, just that due to gear effect.
 Proportional to the distance from the face to the clubhead's CG  which is C. The ratio of C to the radius of the golf ball is analogous to the gear ratio of a pair of spur gears. In a set
of mating spur gears, the tooth pitch is the same in both gears, so the
gear ratio is the same as the ratio of the pitch diameters. And the
gear ratio determines the ratio of rotational speed.

There
is another force which has to do with CG placement, in addition to gear effect, that is changing the loft
of the club. As the club comes
to impact, there is a substantial centrifugal force on the clubhead,
pulling it outward from the center of rotation of the club. This force,
shown red in the picture, acts on the center of gravity of the head. It
is resisted by the pull of the shaft on the clubhead, shown green in
the picture.
The important thing to note here is that the CG is further back than the hosel, so the two forces constitute a turning moment
that wants to rotate the clubhead face up. The further back the CG, the
greater this turning moment. The flex of the shaft allows this to
happen, at least to some extent.

So far, we have been explaining the effects in words. On the next page
we will get quantitative, with a spreadsheet to show how much of an effect this is.
Notes:
 Jeff Summitt is the Chief Technical
Officer for Hireko,
and does their clubhead design as well as running their technical blog
and support forum. Hireko's brands include Dynacraft, Acer, Apollo, and
SK Fiber, among others. So you may not have heard of Hireko, but their
brands are wellrespected in custom clubfitting. (As of this writing in
August 2013, eleven of the clubs in my bag are made with Jeff Summitt
designed clubheads and Hirekobrand or Hirekosold shafts.) Jeff is also known in the
industry for having coauthored (with Tom Wishon) the 1990 book, "The Modern Guide to Shaft Fitting", one of the earlier books that looks at the science of what makes a golf club work.
 This diagram is drawn on top of a picture
of Hireko's XS driver. An appropriate choice, since Jeff raised the
question during a discussion of this new design. Well, actually we were
discussing the XS titanium threemetal. The head was designed to have
an unusually low CG, as this article recommends. I currently have the
XS titanium threemetal in my bag, and it is the best fairway wood I've
ever used.
Last updated  Mar 11, 2014
