Dave Tutelman  --  February 20, 2009

 Too many questions have come up recently that require knowing about gear effect. Not just hand-waving 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 counter-clockwise -- 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:
1. How much weight needs to be moved to actually induce a draw or fade (e.g.- the screw weights you see on drivers)?
2. Does shaft torque have any impact on resisting gear effect?
3. Can you really get more distance by hitting the ball high on the clubface?
4. Dana Upshaw reported that he greatly decreased a long-drive 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?
5. 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 off-center 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 off-center 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 four-quadrant black-and-white 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 counter-clockwise. 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.

Horizontal gear effect

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 Vb.
• The moment of inertia of the clubhead about its CG is Ih.
With C and x in inches, Vb in miles per hour, and Ih in gram-cm2, the sidespin due to gear effect in RPM is given by:
 s  =  58,830 Vb C x Ih
After analyzing how C and Ih vary in current driver heads, the equation can be further simplified to:
s  =  16.4 Vb x
with pretty good accuracy for the vast majority of designs.

An interesting by-product of the analysis, worth noting and using, is that the force (in pounds) between ball and clubhead is:
F  =  9.24 Vb
Here is a graph of the hook or slice spin due to gear effect, for values of ball speed Vb 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.

Vertical Gear Effect

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 Iv, then the gear effect spin is given by:
 s  =  58,830 Vb C y Iv
Some approximate calculations suggest that, for most driver heads, Iv will be some fraction of Ih, probably between .5 and .66 of Ih. 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 Vb 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 high-face 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 1500-3000rpm 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.

Application: Do weight screws produce draws and fades?

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 35-yard 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 30-40 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, 40-yard slice. Unfortunately, this golfer will only see a 6-yard improvement to that slice, and a golfer like that is unlikely to even notice such a small improvement relative to the slice that remains.

Application: Does shaft torque limit the gear effect?

It turns out to be fairly easy to show that even very torque-stiff 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 foot-pound 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 low-torque shaft and a torsionally very "loose" shaft is going to make a 1% or less difference in the gear effect spin.

Application: Does shaft tip stiffness limit vertical gear effect?

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.

Application: What is the role of roll?

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 high-face 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 low-face 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 high-speed 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

 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: