Golf Swing Physics
Guest article by Rod White
Golf has always been a game of technology, with a long history of
improvements to golf balls and clubs. However it is easy to be
sceptical of the impact technology has had – surely coaching and swings
have improved too.
On this page we look at some of the effect of some of the recent
technological changes on golf driving distances.
The pink curve on the graph shows the mean driving distance for PGA
tour professionals for every year between 1980 and 2008. The two curves
side show the average plus and minus 1 standard deviation (a measure of
the variation amongst the golfers). The dots show the average driving
distance for the longest driver of the year.
The graphs show a consistent increase of about 40m with much of that
occurring between 1995 and 2005. How much of that gain is due to
we should expect from the simple model we developed earlier, the
driving distances are more or less independent of club head mass. As
the club-head mass increases, the swing efficiency increases (more
kinetic energy transferred the clubhead), and the collision efficiency
The chart shows that there is a maximum between 170 and 180 g,
but it is
a very broad peak. That is, you have to get a long way from the peak
before it makes a lot of difference. Any club head mass between
and 240 g yields the same distance within about 4 m.
The optimal mass not only gives the greatest distance, it also means
that the same club will do for almost all golfers (which is good news
for the club manufacturers).
optimum mass indicated in the figure is still a little short of the
195 g to
205 g typical of modern drivers. There are a couple of reasons
Firstly, muscles work better at slower speeds, favouring a slightly
club and slower swing. Secondly, the driven pendulum model used to
graph assumes a constant shoulder torque. In reality it will take a
for the shoulder torque to build so that more of the work is done at
the end of
the swing where it is not transferred efficiently, and the lower
in a heavier optimum mass. Finally,
value I chose for the effective mass of the golfer’s arms is a nominal
that had been used previously by other researchers, a 20% increase in
is sufficient to account for the difference.
length used in the graph is defined
point where the arms and the club hinge, and can be a couple of inches
than the full length of the club.
have already mentioned the increase in efficiency that accompanies
increased shaft length. In fact, increasing the shaft length increases
driving distances through two effects:
The total work done by the golfer is downswing angle x shoulder torque,
and clubs with a longer shaft take a longer time to swing out, and
results in a greater down-swing angle, and hence greater work done by
the golfer. However, a natural release swing (with no wrist
torque) becomes anatomically impossible with long shafts. For the
average male golfer, most of the modern standard length drivers (45-46”)
are a little long, although this depends a lot on the golfer's grip and
the location of the centre of the hinge at the wrists.
- An increased downswing angle – which means that more
work is done by the golfer, and
- The improved efficiency of the swing – a greater
fraction of the work done by the golfer is transferred to the
number of professional golfers have observed that their driving
accuracy improves with shorter shafts. This is probably due to a
reduction in the use of the hands.
By far the
largest contribution to increased driving distances has come about from
the improved Coefficient of Restitution (CoR) of the club-ball
collision. At the time of the introduction of the solid core
ball, the CoR of most balls was in the low 0.7 range. As rubbers
improved, the CoR improved markedly. During this time, manufacturers
had to compromise between a soft skin (better spin control) and
distance (with a harder, longer wearing skin). Nowadays it is
possible to achieve the maximum CoR permitted under the rules while
still having a soft skin.
The rules have two tests on balls, one based on ball velocity after a
well defined impact with a solid steel object moving at a prescribed
speed. This limits the CoR of the ball (in collision with solid steel)
to about 0.79. The second limits the driving distance with a specified
With the development of metal drivers, it became possible to build
large thin club faces with a resonant frequency low enough that they
would flex and store energy during impact. This "trampoline effect"
reduces the compressive forces on the ball, and therefore reduces the
energy dissipated in the collision. As a consequence of the trampoline
effect, the CoR for the combined club-ball
collision has risen to about 0.83 -- where it is now limited by rule.
This means, since the 1970’s the improved CoR has resulted in a
20m increase in driving distances for the average golfer.
of the major technological advances has been the change from stainless
steel shafts to graphite shafts.. The effect is due to an improvement
in the swing efficiency.
The club-ball collision time for a typical drive is below 0.0005
seconds. During this time, the kinetic energy must be carried from all
parts of the clubhead to the ball. You can envisage this happening as a
compression wave in the metal clubhead carrying the energy
forward. The same is true for the first few inches of the
shaft. However, most of the kinetic energy in the shaft cannot be
carried into the head and to the ball because the speed of the wave,
carrying the energy from the shaft, is too slow. So the great majority
of the shaft's mass is not involved in momentum transfer to the ball.
This means that all of
the work done by the golfer to put kinetic energy into the shaft is
wasted -- it does not participate in energy transfer to the ball -- and
reducing the mass of the shaft will make the stroke more efficient.
Reducing the shaft mass from about 130 g (steel
about 60 g in modern lightweight shafts has resulted in an
driving distance of about 10m.
Note: contrary to common claims, the flex of a shaft has no
effect on the club head speed, and there is little energy stored in the
flex of the shaft that can be recovered at impact – this is all
advertising BS. The shaft flex
does however affect the loft of the club at impact. The huge
(50 kg for
a professional) tension in the shaft pulls at the heel of the clubhead.
However, the centre of mass of the club
head is a few inches away from the heel, near the centre of the head,
and with a high swing
speed the centre of mass tends to line up with the shaft.
The shaft therefore bends towards the target and
toe down a few centimeters. This effect provides club manufacturers
with a way
expanding the range of lofts on their clubs. A flexible shaft will
enhance loft by as much as 5 degrees, while a stiff shaft only about 2
degrees. Tip-stiff shafts also reduce this effect, and tip-flexible
shafts emphasize it. Golfers with a slow
swing speed require drivers with a high loft (14-15 degrees say) to
achieve the greatest distance, whereas golfers with a high swing speed
achieve optimum distances with a lower loft (as low as 9 degrees).
So there you have it! The great distances produced by
good golfers using modern equipment are due to both technique and
technology. The important factors we have discussed are:
the transfer of momentum and rotational energy from your turning body
and arms to the clubhead and then to the ball. Don't try to impose your
will on the club, but rather allow the energy to flow to it. (This is
not some new-age proverb. As we saw, it is classical physics.)
Particular techniques to use include:
on the mechanical aspects of technique,
as we describe it above, is often unhelpful when you are playing. Our
work better if we can establish an emotional connection to the correct
swing. When you’re
practicing at the
range, practice by first swinging the club about your shoulders as
are going to throw the club – don’t use your hands: remember how it
the rhythm and the feel in your muscles. Now when you stand over the
ball, remember the rhythm and feelings as you throw the club through
zone. When you hit a good shot, pause and enjoy it, and remember the
that feeling so you can recall it during your pre-shot routine on the
- Start the downswing with the club (and even the arms)
"folded" close to the body.
- Keep them folded there as late as you can into the
downswing. That means the first part of the downswing is just rotation, with
nothing from the hips up moving relative to any other part.
not apply wrist torque to swing the club out or forward into the ball.
You may think you are increasing the clubhead speed with "hand action",
but the physics
shows that it does exactly the opposite.
speed is maximized by using the lightest, longest shaft you can
control. But keep in mind the modern driver shafts are too long for the
average golfer to swing without use of the hands, which means a
tendency to lose control under mental pressure. Like some pros, you may
backing off on the length and making sure of a consistent center-face
impact is a better strategy for both average distance
drivers with the larger heads and flexible face have a higher
Coefficient of Restitution than older drivers, and are a little more
tolerant of off center hits. Update your driver if you have not already
done so. If you already have a 460 cc driver, there is
to be gained.
be tempted by drivers with a low loft. The optimum loft for modern
drivers with a low centre of mass and low spin rate, is a higher than
for the older drivers. Few golfers need a loft below 10.5 degrees these
days. Also, as your swing improves with less use of the hands, the less
the club will be ahead of the hands at impact, and the lower the
- Don't worry excessively
about clubhead weight. Choose it so you swing the club comfortably and
consistently. Any commercially available driver head today is close
enough to the mechanically optimum weight that you aren't losing any
Last modified - Apr 10, 2010