Determinants of Distance
Clubhead Speed and Mass
Here are a few rules of thumb on how the grossest measurements of a
club
affect the distance the ball will travel. The first place I ever saw
these
is a June 1992 posting by Sean D. O'Neil reporting on a talk by James
Paul
(founder of Airflow Research). But, as I've read more on the subject
and
done a little original analysis, I've seen basically the same
information
in all the classic places.

Holding everything else constant, distance is a strong positive
function
of clubhead speed. (I.e. distance increases markedly with clubhead
speed.)

For most golfers, clubhead speed is a negative function of swingweight.
(I.e. clubhead speed decreases as swingweight increases.)

For a given clubhead speed, distance is a weak positive function of
swingweight.
(I.e. if you can get the clubhead speed in spite of the swingweight,
the
extra clubhead mass will increase distance slightly.)
These rules of thumb are consistent with the Golfsmith "philosophy" of
lighter weight for more distance. For instance, quoting from the 1993
Golfsmith
catalog:
"Two basic facts about golf clubs and the
swing:

Greater clubhead speed results in greater distance.

Lighter weight clubs permit greater clubhead speed.
Our relatively simple causeeffect sequence was confirmed for us by
USGA
Technical Director Frank Thomas. If a club is shafted with graphite
'lighter
than steel by two ounces, then all else being equal, clubhead velocity
will increase by up to three feet per second  which will result in
approximately
five yards increase in distance.'"
For the mathematically inclined, distance is a monotonically increasing
function of ball speed. In everyday terms, that means that every time
you increase ball speed you increase distance, all other things being
equal.
Now that we know that the secret is ball speed, the exact formula for ball speed is easily derived
from
freshman college physics, or just pulled from the appendix of Cochran
and
Stobbs' book.
1 + e
Vball = Vclubhead * 
1 + (m/M)
where:
e = 
An efficiency measure of momentum transfer called the Coefficient of Restitution (COR). Typical values are:
 0.67 at the time Cochran & Stobbs' book was written,
with a thentypical ball and a rigid clubface.
 0.78 for a modern ball and a rigid clubface.
 0.83 for a springface driver with the maximum legal COR. (The USGA and R&A have decided to measure and limit COR.)

m = 
Mass of the ball (typically 46 grams or 1.62 ounces). 
M = 
Mass of the clubhead (typically 200 grams or 7 ounces for driver). 
To see how differently the clubhead speed and the clubhead mass effect
the ball velocity, consider that

A 10% increase in clubhead speed with no change in clubhead weight
increases
ball velocity 10%.

A 10% increase in clubhead weight with no change in clubhead speed
increases
ball velocity only 1.7%.
So clubhead speed is about six times as effective as clubhead mass in
producing ball speed, which translates into distance. That supports the
statements at the top of this chapter.
This formula assumes a lowloft club like a driver. The higher the
loft, the more the "leakage" of ball speed, as more of the energy of
impact goes into producing spin instead of speed.
It's interesting to look at some of the things people think are
important
to distance (gauged from recent posts in rec.sport.golf), and compare them with facts:

Square clubface and direction of clubhead travel:
Right on! The
equation assumes that the clubface is square to the direction it is
traveling.
If not (due to improper swing or a lofted clubface), a lot of the
momentum
will be transferred to sidewise motion and spin, instead of ball speed.
 Center impact on the clubface:
Right on! Every club has a "sweet spot" somewhere near the middle of
the face. The equation above assumes you hit the sweet spot. If you
miss it, you lose ball speed. I have seen estimates as high as 7% loss
of distance for every half inch you miss the sweet spot.

Strength or weight of the golfer holding the club: Simply not a factor!
If the golfer
couldn't convert strength and weight into clubhead speed, then there's
nothing that they can do during impact to increase distance. As we saw
in the section on vibrational frequency, the clubhead is swinging free
at this point, with little more connection to the grip than if it were on a
string.
Actually, that's an overstatement. The shaft is
infinitesimally stiffer
than a string. If you do something at the grip during impact, 1/10,000
of that effect will reach the clubhead while the ball is still there.
But
that's all.
In other words, and in summary:

Distance is a strong function of clubhead speed.

Distance is a weak function of clubhead weight.

If you can't swing a heavier clubhead very nearly as fast as a lighter
one, the heavier head will cost you distance.
 If
you can't bring the clubhead into the ball with good impact (center of
clubface, with clubface square to the path of the clubhead), you will
lose more distance than you might imagine.
Loft and Spin
The information here is qualitatively well known.
But recently, I've been able to do a little quantification as well,
using a computer program written by Max Dupilka.
Here are a few surprising facts about how loft affects distance:

Air, while presenting drag to slow the ball, also presents lift to a
ball with backspin.
This keeps it in the air longer, and lets it go much further.
A ball struck by a driver in a vacuum will travel less than 2/3 the
distance it will
in normal earth atmosphere.
 In seeming contradiction, drives go further at
altitude where the air is thinner.
It really isn't a contradiction, though; as air gets thinner, distance
peaks at about
90% of the density at sea level, and drops off pretty sharply at less
than 80% of the
sea level density. The distance peak is only a few percent better than
sea level.
 The more clubhead speed you generate, the lower
you want your driver loft
(down to some reasonable minimum). Conversely, the less your clubhead speed,
the more loft you want on your driver. Now that I've run some curves on
Max's program,
I have a better feel for what's going on here.
First the curves, which show carry distance (no roll) vs
loft,
for several clubhead speeds. Note that the higher the clubhead speed,
the lower the loft that achieves maximum carry.
 For a 120mph clubhead, the maximum carry occurs at 10
degrees of loft.
 For a 80mph clubhead, the maximum carry occurs at 16
degrees.
The reason is that ball speed "amplifies" the lifting effect. Moreover,
a higher clubhead
speed puts more spin on the ball to produce lift. Between the two, a
high clubhead speed
can use lift to keep the ball in the air; it doesn't need as much loft.
Before you dive right in and use these numbers directly
for clubfitting, let me remind you that:

They are for carry only, and don't include roll.
 They don't include shaft flex, which changes the effective loft at impact.
But the effect of loft and lift are clear from the graph.
Golf is Not Artillery
Let me end this section by dispelling a common myth,
based on a misinterpretation of
a wellknown "law" of physics.
As many of us learned in Physics 101, an object travels furthest if
launched at an
angle of 45 degrees. Why does this not seem to apply to the design of
golf clubs?
We all know that a 45º loft is about that of a pitching wedge, and
a 45º launch angle requires considerably more loft than that. From
experience, we all know that clubs with that much loft don't hit
the ball nearly as far as the lowerlofted clubs.
Here is what's happening: The Physics 101 problem assumed that
the ball starts at the same speed,
no matter what
the angle of takeoff. This is a true assumption for artillery, which is
where the problem originated. In artillery, you change the launch angle
by tilting the cannon up or down, which doesn't hurt the "ball speed"
at all.
But, for the golf model, increasing the launch angle usually
involves increasing the loft. As noted above, this causes ballspeed
"leakage", as more of the impact energy is turned into spin instead of
ball speed. By the time you get to a 45º launch angle, you are
hitting a very highlofted wedge with lots of height and rather little
distance.
In order to duplicate the "artillery model" with a golf swing, it would require you
to cause the
45º launch by using a tee more than a foot tall, and hit the ball
with a lowloft
driver on a 45º upswing.
I hope that made sense.
Last modified Oct 6, 2006
