All about Gear Effect
Dave
Tutelman 
February 20, 2009
Too many
questions have come up recently that require knowing about
gear effect. Not just handwaving and intuitive explanation, but the
ability to estimate numbers. I can't put it off any longer; I have to
do
the homework.
First
of all, what is gear effect? When you hit a golf club anywhere but the
middle of the face, the clubhead will twist. With drivers and fairway
woods, the twist will impart the opposite twist to the ball. That is,
if the clubhead rotates clockwise, the ball's spin will be
counterclockwise  just like two gears meshing. Sounds a bit arcane,
but it is responsible for all sorts of interesting things, like
adjustable weight screws that claim to cause a draw or fade, and the
advice that a driver's "sweet spot" is high on the face.
This article presents an analysis that allows answering
questions like: 
 How much weight needs to be moved to actually induce a
draw or fade (e.g. the screw weights you see on drivers)?
 Does shaft torque
have any impact on resisting gear effect?
 Can you really get more distance by hitting the ball high
on the clubface?
 Dana
Upshaw reported that he greatly decreased a longdrive
competitor's spin by going to a
flexible tip and lower loft. Vertical gear effect is the only way I
could imagine to get the sort of results that Dana got, but it requires
that the shaft's tip stiffness be a major factor in how much gear
effect there is. So how does shaft stiffness influence vertical gear
effect?
 I am updating my article
on optimizing the launch parameters for real drivers. It
requires knowing whether vertical gear effect provides enough spin
reduction to make a significant difference in distance.
All these questions require a quantitative knowledge about gear effect.
Not precise knowledge perhaps, but at least good ballpark estimates.
This article, after a tutorial introduction
to gear effect, presents the results
of analysis in a summary form. The subsequent pages present the
analysis itself, and detailed answers to the interesting
questions, along with more diagrams and photos.
Introduction to gear effect
Let's start with a brief explanation of what gear effect is. The
explanation is lifted from my tutorial
on golf club physics.
Gear effect is sidespin which is the result of an offcenter
hit with a club whose center of gravity is well back
from the clubface. Without both these conditions, gear effect does not
happen.
Let's see what causes gear
effect. In the picture at the right, we have two offcenter impacts,
one on an iron and the other on a driver. Both are toe impacts, which
means it is to the toe side of the center of gravity of the clubhead.
(The CG is denoted by the fourquadrant blackandwhite circle; it's a
pretty common notation for CG.) What does Newton say about such an
impact? The CG wants to continue moving forward in a straight line, but
there is a force on the clubhead that is off that line. That creates a
torque that wants to twist the club. The result is that the CG keeps
moving forward, but the club rotates around the CG in a clockwise
direction (red arrows).
The CG of the iron is close to the clubface. So, where the clubface and
ball meet, this rotation (the red
arrow) consists of the clubface "falling away" from the
ball. This results in loss of distance (the momentum transfer is not as
complete as it should have been), and perhaps the ball flying somwhat
to the right as the face opens. But there isn't any special effect on
spin.
The driver is a completely different story. Its CG is well behind the
clubface. When the driver head rotates around its CG, the whole face of
the club moves sideways. Look at the direction of the red arrow where the clubface
and ball meet; it is mostly parallel to the clubface, with only a bit
of "falling away".
So the club's face is moving to the right while the
ball is compressed on it. The result is that the ball starts to rotate
so its surface doesn't slide along the clubface; remember it's
compressed so sliding is difficult. This rotation is the blue arrow in the picture. If
the clubhead is rotating clockwise (as in the picture), then the ball
rotates counterclockwise. It's as if the clubhead and ball were a pair
of gears, with their teeth meshing where they meet.
That's why a toe hit with a driver tends to hook. For all the same
reasons, a heel hit with a driver tends to slice. You don't have this
effect with an iron. 
Summary
of results
Here is an executive summary of the results. Click on the topic header
to see more detail than the summary provides.
The picture shows the model we use for the analysis.
 The impact is a distance x
from being through the center of gravity (CG).
 The CG is a distance C
behind the face.
 The ball leaves the clubface with a velocity V_{b}.
 The moment of inertia of the clubhead about its CG is
I_{h}.
With C and x
in inches, V_{b} in
miles per hour, and I_{h} in
gramcm^{2}, the sidespin due to gear effect in RPM
is given by:
s =
58,830 
V_{b}
C x_{
}
I_{h} 
After analyzing how C and I_{h} vary
in current driver
heads, the equation can be further simplified to:
s = 16.4 V_{b} x
with pretty good accuracy for the vast majority of designs.
An interesting byproduct of the analysis, worth noting and using, is
that the force (in pounds) between ball and clubhead is:
F = 9.24 V_{b}

Here is
a graph of the hook
or slice spin due to gear effect,
for values of ball speed V_{b}
from 80mph to 200mph. (If you prefer to think in terms of clubhead
speed, here is a conversion table.)
If you use this spin to look
at the trajectory,
you must also take into account the face bulge radius. For instance, a
toe hit will provide hook spin via gear effect, but bulge will cause
the ball to start to the right, and to have some slice spin that will
subtract from the gear effect hook spin. 
If
you strike the ball above or below the center of gravity, gear effect
will occur in a vertical direction. Let us start with the assumption
that there is no reason to expect this to be substantially different
from horizontal gear effect. So, if the vertical miss is y
and the moment of inertia in the vertical plane is I_{v},
then the gear effect spin is given by:
s =
58,830 
V_{b}
C y_{
}
I_{v} 
Some approximate calculations suggest that, for most driver heads, I_{v}
will be some fraction of I_{h},
probably between .5 and .66 of I_{h}.
Consequently, the spin due to vertical gear effect is between 1.5 and 2
times the spin due to horizontal gear effect, for the same amount of
miss. (Of course, there isn't as much room on the clubface to miss
vertically as horizontally.)
As with horizontal gear effect, we can approximate the spin for most
drivers. The vertical approximation is:
s = 25 V_{b} y
Vertical gear effect is the
major reason that golfers are told that the "sweet spot" of a driver is
above the center of the clubface. Better golfers (and perhaps
all
golfers) will get more total distance from a higher launch angle at the
same time as lower backspin. Vertical gear effect can reduce backspin
without reducing launch angle  in fact, it may even be accompanied by
an increase in launch angle. The reason for reduced backspin is that
the gear effect from a
highface hit will
produce topspin. The ball does not experience a net
topspin; the backspin due to loft is much too great for this. But the
topspin is subtracted from the backspin, reducing the backspin.
Assuming a properly fit driver, the result is increased carry distance
as well as increased roll after landing. A sample calculation
shows, for a 150mph ball speed, a gain of 8 yards of carry and a
reduction in angle of descent of 6° for a hit 0.6" above the center,
compared with a hit in the center of the clubface.
The
only big surprise here is how big the spin due to vertical gear effect
is. Strikes that are extremely high and low on the clubface (but still
on the face) can result in 15003000rpm of gear effect spin  much
more than most people believe. So which is true, the model or what some
people believe? The
model has been validated using data from Hotstix
published in Golf Magazine.

We
see drivers on the market today with weight screws that claim to
control the trajectory of the drive. The TaylorMade R7 family was the
original driver to offer weight screws, and is still the best known.
The latest R7 is advertised to be able to make a 35yard difference
between maximum fade and maximum draw, just by placement of the weight
screws. (The screws allow moving 15 grams between the heel and the toe,
the biggest weight shift of any R7 model so far.)
Does this
claim have any validity? For years, I have been saying it does not 
that weight screws do not move the center of gravity of the clubhead
enough to produce a noticeable difference in performance. I was not
alone in this view; Tom Wishon has been most vocal that you need 3040
grams of "discretionary weight" to see the difference.
Now we
have a mathematical model that allows us to predict the effect of
moving the weight. What does it tell us? It turns out that Tom and I
were wrong. There is a noticeable draw/fade effect from moving even as
small a weight as 15 grams. Here are my conclusions:
 The
size of the draw/fade varies a lot with ball speed. Not only does the
spin vary with ball speed (we know that from the equation for gear
effect spin), but also the time and distance the ball is in the air
letting the shot curve.
 In order to achieve the 35 yards that
TaylorMade advertises, you need a clubhead speed about the average of
the Tour players  115mph.
 What about the likely target of the
advertising: the hacker who hits the ball with an 85mph clubhead speed
and usually hits a high, 40yard slice. Unfortunately, this golfer will
only see a 6yard improvement to that slice, and a golfer like that is
unlikely to even notice such a small improvement relative to the slice
that remains.

It turns out to be fairly easy to show that even very torquestiff
shafts have negligible limiting influence on gear effect.
The
reason is that impact lasts such a short time that the clubhead only
has an opportunity to rotate about 2º during that time. Even with a
very "low torque" shaft with a 2º rating, that only produces one
footpound of torque in
the shaft. Meanwhile, the ball is imposing more than 80 times that
torque on the clubhead. So the inertia of the clubhead is absorbing
about 99% of the ball's torque, and the shaft only about 1%. Therefore
the
difference between that lowtorque shaft and a torsionally very "loose"
shaft is going to make a 1% or less difference in the gear effect
spin.

This question is harder to analyze, and the answer I got is more
equivocal and less satisfying.
The
tip stiffness, according to the analysis, may have a measurable effect
on the spin  but a far smaller effect than Dana Upshaw's anecdotes
report. Dana shows a difference of thousands of rpm as tip stiffness is
varied. My analysis can only account for a few hundreds of rpm. The
limitation due to tip stiffness seems to max out at less than 14% of
the spin. That is more significant than the 1% we got for shaft torque,
but still not a really big deal.

Most
drivers not only have bulge but roll as well. That's curvature of the
clubface in the vertical plane. Does face roll play some important role
in the flight of the golf ball? If so, it is a help or a hindrance?
The
graph shows that roll is a considerable help. Both drivers give the
best distance when impact is about a half inch above the center of the
clubface. (The reason for that is vertical
gear effect.)
Away from this best height, carry distance falls off. But, as the graph
shows, a driver with the best possible face roll will not lose distance
nearly as fast as a flat face. The blue curve has a very sharp peak,
and loses distance rapidly as you move away from the "sweet spot".
According
to the mathematical model, the optimum face roll for drivers is about
an 8" radius
 a little flatter for slower clubhead speeds and a little rounder for
big hitters. Even if the model's assumptions are off, I think it's
unlikely that the optimum roll is more than 12", and probably less.
So
the next time one of the TV golf gurus says, "Today's drivers
are
designed to be hit high on the face," you can answer, "Yeah! They put
loft on them." Seriously! Gear effect has been a fact of life since
golf has been played. And a driver will give maximum distance
when
hit high on the face because of gear effect and loft. That is nothing
new! What is new is that, with fitting and training being done with
launch monitors, we suddenly know that we get
better launch conditions from a highface hit. And now you know why 
and those TV pundits do not.

GRT is Tom Wishon's clubface design with greatly reduced face roll. The analytical model certainly
does not seem to support the concept.
This pair of graphs shows the computational model's output when
comparing the optimum roll with the roll numbers of GRT. Not only does
GRT incur a carry distance penalty for lowface hits, those hits
produce a considerably higher angle of descent. Angle of descent is a
strong indicator of distance after landing, so the the penalty in total
distance will be greater than just the carry distance penalty.
This agrees with my limited personal experience with GRT. It does not agree with what Wishon says his prototype testing showed. 
Conclusion
Gear
effect, both horizontal and vertical, is remarkably important for club
designers and custom fitters. The club or component designer needs to
know about it
in detail. The fitter needs to know about it in principle, in order to
allow the golfer to take advantage of it  or perhaps minimize it for
the golfer who cannot use it to advantage.
Acknowledgements
I'd like to express special thanks to Russ Ryden,
whose highspeed videography was instrumental in figuring out the
effect of shaft tip stiffness on vertical rotation of the clubhead.
Thanks are also due to Richard
Kempton and especially Jeff
Summitt, whose email discussions helped focus my thinking
about the problem. When the discussion turned to face roll and GRT, I got
some very helpful suggestions from Ed Reeder, Malcolm Shepherd, and
Alan Brooks. Thanks, guys!
Notes:
Ball
speed,
clubhead speed, and smash factor
Ball Speed

Smash
Factor 
Clubhead
speed 
1.48
(pro) 
1.40
(decent) 
1.25
(hacker) 
70 
104 
98 
88 
80 
118 
112 
100 
90 
133 
126 
113 
100 
148 
140 
125 
110 
163 
154 
138 
120 
178 
168 
150 
The equations for spin are in terms of ball speed. But
most people tend to think in terms of clubhead speed. Here is a
conversion table based on the simple equation:
BallSpeed =
SmashFactor
* ClubheadSpeed
The "smash factor" is a number based on clubhead characteristics (like
COR and mass) and on the goodness of the ball strike. A clean,
oncenter, squareface strike with a modern driver has a theoretical
maximum
smash factor of 1.5. The tour pros typically have a smash factor in
the mid to high onepointfours, say 1.48. Fairly decent golfers are in
the low onepointfours, and hackers can be 1.25 or even less.
Note
that the 1.50 maximum smash factor assumes a 200g clubhead (typical for
a driver), a 0.83 COR (the legal maximum), and almost no loft
(loft contributes to "unsquareness" of the hit).

Last modified  April 3, 2009
