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 longdrive 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 foreandaft 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 foreandaft 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
followup 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 lowerloft 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 longdrive 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 oldfashioned
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 lowerloft driver with no sacrifice of launch
angle. And, of course, a lowerloft 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
grasstop 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 longdrive competitor's club, wich 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 centerface 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 selfproclaimed experts say, there
is no drive except a worthless total duckhook that has topspin.
 If you hit the ball above the center of gravity, 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.)

FollowUp
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 reinforcedforlongdrive 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 (1cos 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
