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Ball Position for Maximum Distance

Dave Tutelman - May 14, 2012

In May of 2012, two things happened that motivated me to do this short article:

Charlie Badami called me about trajectory issues he was having, working with long-drive competitor Evan Ogule. We worked for a while with the TrajectoWare Drive software to see what numbers we should be aiming for, then talked about ways to accomplish it. The subject of ball position (including both fore-and-aft position and tee height) was a major topic of discussion.
A Jim McLean video on the Revolution Golf site talked about how to change your driver swing to "hit up on the ball". The essence of the changes were to move the ball forward in the stance, and move the bottom of the arc backwards away from the ball. Like Charlie and Evan's problem, this is an exercise in ball position. It requires adjusting both the fore-and-aft position and tee height.

Charlie and Evan were having a little trouble visualizing where to move the ball for each of the changes we talked about. The telephone is decidedly not a visual means of communication, so I put together a few illustrations and emailed them to Charlie. The illustrations and the obvious follow-up questions led to this article. Let me mention that this turned out to be successful in competition.

Before we get to the meat of the article, where to position the ball for improved driving distance, let's review why ball position (both X and Y position) is a factor in getting the maximum distance from your drives. Actually, there are several reasons:

Hitting up on the ball means you are increasing your angle of attack. There are very few ways to increase launch angle without increasing spin, and this is one of them.
The increased angle of attack needn't all be turned into launch angle. If you use part of it to go to a lower-loft driver, you do two things for your distance: (a) you decrease the backspin imparted to the ball, and (b) you hit the ball less obliquely, giving a slightly higher ball speed.
The only other way to increase launch angle without a proportional increase in backspin is to hit the ball higher on the clubface. Vertical gear effect, along with the face roll (curvature) of the clubhead do good things for distance when your point of impact is high on the face. And again, this is a ball position issue.

It's just Geometry

Let's start out by saying that there is really no physics in this article. It is all geometry. Yes, we use some results from physics, but the actual work of this article is just geometry. By the time I finished my junior year of high school, I had all the math that it took to do this work. (Perhaps not the experience and maturity to know which math to use, but I could do the math.)

So here is the starting point for the geometry of ball position.

The diagram shows a "normal" setup for a typical golfer -- definitely not a long-drive competitor, nor someone who has incorporated Jim McLean's suggestions for the driver. The usual rule of thumb taught to novice golfers is to hit the ball in the middle of the clubface at the bottom of the swing arc.

The arcs in this and the other diagrams are:

Black centerline: the path of the center of the clubface.
Gray dotted line: the upper and lower edges of the clubface.
Red dotted line: The path of a point about a half inch above the center of the clubface.

With a good swing, the clubhead traces an arc in the vicinity of impact. Even if you are not trying for the middle of the face at the bottom of the arc, you should still make a good swing with a similar arc. This article is about how to change the impact conditions without changing that swing, or with intentional, controlled changes in the swing arc. The secret to that is proper ball position, relative to the bottom of the arc.

Angle of Attack

When you get to the point where you want to drive for distance and are willing and able to practice technique to accomplish it, the first thing you discover is that you want a high launch angle and low spin. (See my article on launch optimization for more on this.) But you can't accomplish both a higher launch angle and lower spin by messing with equipment, unless the equipment is really ill fitted for you to begin with. (Again the article on launch optimization discusses this.) The way to do it is the old-fashioned way; you earn it by perfecting your technique.

The first and most obvious way to increase launch angle while lowering spin is to increase the angle of attack. In other words, hit the ball on the upswing. That allows a lower-loft driver with no sacrifice of launch angle. And, of course, a lower-loft driver means lower spin.

The diagram shows how to increase the angle of attack without hurting the arc of the swing. You need to move the ball forward in the stance, to where the clubhead is moving on the upswing. You don't want to change the swing or distort your movements to cause an upward hit; just make the same good, sound swing, but catch the ball on the upward path of the arc.

But the diagram shows us something else as well: the ball must be teed higher. If you wait to hit the ball until the clubhead is traveling upward, the arc demands that the clubhead is already higher than grass-top level. The ball must be teed high enough so that the center of the face is impacting the ball. If you don't tee upwards, you'll catch the ball with the bottom of the face; any gains from angle of attack are lost (and then some) because of lousy impact.

Angle of Attack
Move ball forward
Tee ball higher

1º
1 1/2"
0

2º 2 1/2"
1/20"

3º 4"
1/10"

4º 5"
1/6"

5º 6 1/2"
1/4"

6º 8"
3/8"

7º 9"
1/2"

8º 10"
3/4"

9º 11 1/2"
7/8"

10º 12 3/4"
1 1/8"

Here is a table of where to position the ball for any particular angle of attack. It is based on:

A long-drive competitor's club, which would be the maximum 48" long. (For a shorter club, just scale down the Ball Position values proportional to the length. For typical drivers in the 45"-48" range, this will not result in a change worth worrying about.)
A 55º lie angle at impact, typical for drivers. Therefore the clubhead is traveling left as well as up at impact. Dealing with this is not something ball position can solve. It is an alignment or perhaps a swing technique issue. For instance, you may have to operate from a closed stance.
The hands are moving at 1/5 the speed of the clubhead. (This comes from Steven Nesbit's kinematic study, and was checked by playing with the SwingPerfect computer program.)
The zero ball position is the position (including tee height) that you should tee the ball for a center-face hit at the bottom of the swing arc. The table shows how much to move the ball forward and upward from this position.

Let's look at an example (shaded in blue): 6º Angle of Attack, attained by moving the ball forward 8" and teeing it 3/8" higher. Eight inches is quite a bit of ball motion. Most people will not be able to hit the ball that far forward in the stance. So maybe it can't be done. But you might use some of the swing techniques suggested in Jim McLean's video. They move the bottom of the arc backwards. If you could get a 4" backward motion in the bottom of the arc, then you would only need to move the ball 4" forward to get a total of 8". That sounds a lot more doable.

The math used to generate the table is in the Appendix, for those interested.

Height on Clubface

There is another, perhaps even more efficient, way to increase launch angle while reducing spin: hit the ball higher on the clubface. This causes vertical gear effect to reduce the backspin on the ball. Let's review why this should happen, because a lot of folks are confused about this:

The clubhead's loft at impact will impart a certain launch angle and backspin. And it will be backspin; in spite of what TV commentators and self-proclaimed experts say, there is no drive except a worthless total duck-hook that has topspin.
If you hit the ball above the center of gravity for the clubhead, gear effect introduces some topspin. It is never close to the backspin imparted by the loft, but it can be enough to materially reduce the total backspin of the ball. (Conversely, hitting below the center of gravity actually increases the backspin above that due to loft alone.)
At the same time, clubface roll (the vertical curvature of a driver face) means that the ball will encounter more loft when hit higher on the clubface -- so the launch angle will increase as well.

It has been documented by tests and analyzed mathematically: hitting the ball higher on the clubface than the center of gravity will result in longer drives. The optimum position on the clubface is about a half inch (or a bit more) above the center of gravity. This optimum point is relatively independent of the amount of face roll, over a wide range of face roll. But the optimum is less critical at "normal" face rolls of about 10" radius.

How do we accomplish this, while still making our normal swing? Again, it is a matter of where we tee the ball. Let's go back to our diagram with the arcs. This time, we are still using the position for an upwards angle of attack, but we are putting the ball on the red dotted arc -- a half inch above the center of the clubface. This requires teeing the ball a half inch higher. (Actually a little more, according to trigonometry. But, at a 9º angle of attack, the "little more" is less than 1/100 of an inch, so we can safely ignore it.)

Follow-Up

In late June, I got another call from Charlie and Evan. They told me that Evan had qualified for the 2012 World Long Drive Finals in Mesquite. Evan told me that his winning (qualifying) drive in competition had the textbook trajectory. It was much higher than he was used to; at first he thought he had popped it up. But it kept going and going. Then it landed... and it kept bouncing and rolling. That is a sure sign of high launch and low spin.

Then they told me a funny story. That drive had cracked the clubhead, where the top of the face meets the crown. Charlie had not gotten delivery of Evan's reinforced-for-long-drive clubhead, and built him a temporary driver using a Mizuno clubhead with the right specs except for face reinforcement. Afterward, they had to call Mizuno to report the cracked clubhead. Evan told their customer service people, "My engineer said I had to hit it high on the clubface." I told him I'd be proud to take the blame for that.

Conclusion

Two ways to increase driving distance are to hit up on the ball (increase the Angle of Attack) and to hit the ball higher on the clubface. Key to both is the proper ball position. The ball must be positioned further forward in the stance and teed higher. This article covered how much forward and how much higher.

Appendix

Here is the derivation of the equations used to generate the table of ball position. You don't need to understand this, but it is included to allow criticism of my methods.

The illustration is drawn in the plane of the swing. This is not the vertical plane, but rather the plane defined by the lie angle. Therefore, a is not the actual Angle of Attack, and Y is not the actual ball height. But we will correct for this later.

We will also need to correct the shaft length R later. This image assumes zero hand velocity at impact; the clubhead motion is all tangential motion around the hands. Since there is some hand motion in reality (about 1/5 the speed of the clubhead), some correction is necessary.

The key to the calculation is to recognize that the angle of the clubface a changes by the same amount as the angle of the shaft, a pretty reasonable assertion. So it is pretty easy to calculate X and Y.

X = R sin a

Y = R - R cos a = R (1-cos a)

The whole plane shown here is slanted to the lie angle. That foreshortens the ball height (from Y) and the Angle of Attack (from a). The foreshortening factor is the sine of the lie angle. That is, if the plane were perfectly upright (lie angle = 90º), then there would be no foreshortening (sine = 1).

Ball height = Y sin (lie)

Angle of Attack = a sin (lie)

Now let's correct for the assumption of zero hand velocity. In fact, the hands are probably moving very close to one fifth of the clubhead speed. That means that the center of curvature of the clubhead path is "inside" the hand arc. The effective shaft length for the calculation should be the radius of that curvature. Let's figure out the effective club length:

R = R_effective - 1/5 R_effective

... or ...

R_effective = 5/4 R = 1.25 R

That means the calculations use an R_effective of 60" instead of the 48" club length.

These equations were implemented in an Excel spreadsheet, which produced the table and a graph.

Acknowledgements

Of course, my thanks to Charlie Badami and Evan Ogule for putting me onto this problem.

Thanks also to Sun Ung Kim for pointing out a mathematical error (cosine instead of sine for the lie angle correction), which accounts for the Sept 5, 2012 update.

Last modified -- Sept 5, 2012