Golf Swing Physics
3. Technique
Guest article by Rod White
--
December 2008
In
the previous sections we explained the principle of
the golf swing, how the unfolding of the club from the cocked position
causes
rotational energy to be transferred from the arms and the body to the
club, and
that this unfolding can be passive requiring no effort from the golfer.
Now that we understand what is happening, let’s look
more closely
at a more realistic model of the golf swing, in the interest of
clarifying technique. In the actual
golf swing,
the golfer is applying torque, throughout the swing, to the inner arm
of the double pendulum -- by using muscles in the torso to turn the
shoulders. The
improved model is a similarly-driven double
pendulum with a few extra features that allow us to investigate aspects
of
technique. It will give us an opportunity to see what sort
of things
the golfer can do with the swing to improve his distance -- or screw
things up altogether.
A Driven
Double Pendulum
The improved model can vary:
- Torque applied to the inner arm of the pendulum, to
model the work done by the golfer via the torso and shoulders
- Torque applied to the outer arm of the pendulum, to
model work done by the golfers hands
- Wrist cock angle
- Release timing, to model the golfer releasing the
club early or late during the first phase of the downswing
- Arm mass
- Arm length
- Club shaft length
- Club head mass
- Coefficient of restitution for the club-ball collision
 For the
moment we will focus on the aspects of technique that have the largest
effect on the effectiveness of the golf swing – we will look at the
technological factors later.
The animation shows the swing of a moderately good amateur golfer with
a sound golf swing.
During
the first part of the downswing,
the golfer holds the club
in a cocked
position and accelerates the shoulders and torso. Initially some
positive wrist torque is required to stop the club from being pulled
into the golfers neck (the hub). Remember the passive, steadily
rotating model on the
previous page? There, a string (providing negative torque) was needed
to keep the
club from swinging outward. Here, during the initial build up of speed,
some sort of "brace" (providing positive torque) is needed prevent the
club
from being pulled inward. The positive torque
required to brace the club falls rapidly as the club accelerates. When
the
positive ‘bracing’ torque falls to zero, the club can be allowed to
swing out -- ending the first phase.
The second
phase of the downswing occurs as the club swings out.
If the golfer lets
the club swing out when the bracing torque falls to zero, then this is
described as a swing with a natural
release. If
the golfer holds the club in the cocked position for a short
while longer, this is described as a late release. If the golfer
releases the
club early, the club will swing in towards the neck for a small moment
and then
swing out. We won’t
look at the effect
of release timing because to a good approximation release timing has no
effect.
During the second phase the golfer continues to turn his body and
arms, but
no torque is applied via the hands – they are no more than a hinge
during this phase.
This model will be the starting point for
all our future calculations. The full numerical model includes a number
of variable factors, as indicated in the list above. The animation
shows the
solution for the swing we have just described.
Important
note:
By
pure coincidence (perhaps), the golf swing can be executed with the
natural release. This is not necessarily true for all stick-and-ball
sports, not even if the stick is a golf club. Consider:
- With baseball swings, the natural swing time is
much shorter because the bat is shorter, and the base-baller must
restrain the bat using negative
wrist torque to stop it from swinging out early.
- With professional long-drive
golfers, the shaft length is longer (up to 50
inches), the natural swing time is
much longer, and a swing with a natural release is anatomically
impossible. Professional long drivers must use positive wrist torque
(forcing the club out) to complete the swing.
- The normal golf swing
does not require positive or negative wrist torque during the second
phase of the downswing; therefore the hands are passive, and the golf
stroke can be more
accurate with fewer muscles involved.
|
How is
the energy transferred?
We have discussed the golf swing in terms of the conservation of energy
and momentum, and showed that the energy is transferred to
the club as the swing unfolds, but what actually happens – where are
the forces that make this happen?
The figure shows a ‘stroboscopic’ view of the golf swing. Have a
close look at the direction of the clubhead midway through the swing –
this is indicated approximately by the red arrow. Now look where the
hands
move at the same time – the blue arrow: in a different
direction!
Obviously the hands and clubhead cannot continue to move in different
directions, they are restrained by the fixed length of the shaft. The
diverging directions
of the club and hands results in a large tension in the shaft.
The tension pulls against the club head causing it to accelerate, and
pulls
against the hands causing them to decelerate. It is the
differing directions of the hands and club that are ultimately
responsible for the energy transfer.
In a professional golfer's swing, the tension peaks above
500 N (50 kg
equivalent, or over 100 pounds). During this phase of the
swing the rate at which
energy is transferred to the club peaks at about 5 kW (or
almost 7
horsepower).
Now we’ll take a look
at the factors that affect the effectiveness of the swing. The two big
factors
are the wrist cock angle and the wrist torque. Since greater wrist cock
increases the divergence of the trajectories of the hands and the
clubhead, we can
expect greater wrist cock (smaller wrist-cock angle) to improve the
swing. It is less
obvious whether wrist torque -- usually described in golf as "hand
action" -- helps or hurts. Let's look in more detail at the effects of
wrist cock first.
|
Wrist Cock
Angle
 The
figure to the left shows the
clubhead speed versus downswing angle (the angle between the arms and where they were at the beginning of the downswing), for
three different wrist cock
angles (the angle between the arms and the club shaft). Note again
that the wrist-cock angle is
measured
between the arms and the club, so a smaller angle corresponds to
greater wrist
cock, or greater "lag" as it is often called. If there were no wrist cock at all, the angle would be 180 degrees.
As expected, increasing the amount of wrist-cock (reducing the angle between
the arms and shaft) increases the efficiency of the swing. The
key point is that the peak speeds all occur at a very similar
downswing
angle, showing that the swing timing is almost unchanged.
The golfer expends the same effort for all three swings, yet we see a
10% increase in head speed resulting in a 10%
increase in distance – say 20 m for a 200 m drive --
with no extra effort.
|
 The
chart at the right plots the driving distance versus wrist cock angle,
assuming all
other aspects of the swing remain the same and that the ball is hit at
the peak head velocity. The
increase in distance that occurs with a decrease in wrist-cock angle
between 110 and 70 degrees is about 20 m – say 5m for each 10
degrees
wrist cock.
Note again – the distance is gained with no extra effort from
the golfer – the difference is purely one of technique.
For those who are interested, I've estimated the distance from the
clubhead speed using a formula from Cochrane and Stobbs.
D = 3.75 x
ball
speed – 25m
where the ball speed is in meters per second.
|
Wrist
Torque
 Now we
look at the effect of positive wrist torque during the second phase of
the swing. The use of the hands is a very frequent flaw with
amateur golfers. It is not uncommon to see the hands spread far apart
(like a baseball grip), or the right hand adjusted so the thumb is
behind the shaft through impact, or the right forefinger is set down
the shaft. All this is done in the hope of pushing the head faster
through the impact zone.
In fact it has the opposite effect. In this figure, the wrist torque is
expressed as a percentage of the shoulder torque. For the model I’ve
chosen, 10% corresponds to 1 kg.m of wrist torque in the
model. This is
a very large torque, but probably
typical for male beginners who have yet to learn to let the club swing
by
itself.
The graph shows that positive wrist torque causes the club to unfold
early, and therefore
causes the clubhead speed to peak early, and with a lower
velocity. Common symptoms include a pronounced swishing sound
that peaks before impact, drop-kicked shots (club ricochets off the
ground before impact), shots with a high trajectory, and often problems
with big high fades or slices. Researchers who have
tracked the swing speed for golfers with a range of handicaps find that
only golfers
with low single-figure handicaps or better come close to hitting the
ball at
the peak clubhead speed. For most golfers, the club is decelerating
through
impact.
|
 The
chart to the right plots the approximate driving distance versus wrist
torque with almost all other parameters kept the same. Remember that
wrist torque has two effects on clubhead speed. It (a) peaks at a lower
clubhead speed and (b) peaks earlier in the downswing.
- The blue curve
assumes that the golfer changes his swing so impact still occurs at the
peak. We shorten or lengthen the swing so that impact will occur at
maximum clubhead speed. This golfer is then only bitten by (a) above.
- The red curve
assumes that the golfer simply makes the same length swing no matter
what the wrist torque. This golfer is then bitten by both (a) and (b).
Negative wrist torque also costs distance because the clubhead speed
peaks after impact (i.e., impact is at the black line in the curve
above).
Even if we assume that the ball is hit at the peak head velocity (blue
curve), the difference between a beginners swing (10% wrist torque)
and a swing with no wrist torque is about 20 m in distance.
More
typically the
beginner will take the same backswing as a low handicap golfer and lose
the
distance indicated by the red curve – nearly 40 m!
This is a very tough
lesson, yet all of us have experienced the occasion when we relax, try
not to
hit a ball too hard, and hit the best drives of our lives. Learn to
relax, to shorten
your grip, and not to
use your hands.
Many
people have
trouble believing that you do not need to use wrist torque to have an
effective golf swing. But to prove a point,
some stunt golfers use drivers with a section of rubber tube or dog
chain
replacing part of the shaft. They still hit the golf ball a long way --
in fact,
much the same distance as with a proper shaft. With such a flexible
shaft,
there is no way that wrist torque can have any effect.
Another good example is the trebuchet shown in a couple of
the videos on the next page, a medieval siege machine
used to fling rocks into or over castle walls. From the physics point
of view, the trebuchet is an upside-down golfer; the raised weight
represents the torque applied through the shoulders, the long wooden
beam represents the golfer's arms, and the rope sling represents the
shaft of the golf club.
Remember that almost all the energy transfer to the club is due to
tension in the shaft; the shaft does not need to be stiff, because the
vast majority of the force it transmits is along the length of the
shaft. If the club had a perfectly
flexible shaft -- like the rope sling of a trebuchet -- then there is
no way to apply wrist torque to get any action from the clubhead. Yet
the trebuchet was a very effective siege weapon. It was the best, most
powerful catapult in warfare for centuries until it was replaced by
gunpowder-powered
cannons, demonstrating that "wrist torque" isn't all that important.
See the videos on
the next page for visual demonstrations that a trebuchet can
sling things a long way with no "wrist torque" at all.
|
Summary for Technique
Work done
by the golfer builds up kinetic energy in
the torso, shoulders, and arms. This is then transferred via tension in
the
shaft as the club and arms unfold away from the golfer’s body.
- The
good:
the greater the fold (wrist cock) the
more efficient the transfer of energy from the body to the club.
- The
bad: the greater the wrist torque (use of the hands) the
earlier
the club unfolds and the less energy is transferred to the club.
These two
effects,
the negative effect of wrist torque and the positive effect of wrist
cock, account for most of the 70 m difference between the
beginner and
the scratch golfer.
These effects are also
counterintuitive –
not what the beginner golfer expects. This perhaps explains why a good
golf swing is so hard to learn.
Another factor making a good swing hard to learn is that it is mentally
difficult to hold onto the club firmly while not holding the wrists
firmly. It is curious that most people, when asked to throw a golf
club as
far as possible, would swing the club around their shoulders without
using wrist torque, and
this is exactly the action required for a good swing. Swinging a club
loosely around your shoulders as if you were about to throw it will
help to train your brain to not use your hands. I have also found it
helpful to visualise throwing the club through the impact zone. In fact
a full vigorous swing around your shoulders like a baseball swing,
including hip and shoulder movement, captures all of the important
parts of the swing.
One of the benefits of the overlap grip is that it keeps
the combined length of the hands short and the right hand weak
(for a right-handed golfer). This enables the golfers to grip the club
firmly, but limits the ability to apply wrist torque.
Math
note
I
have not given the full equations for the
numerical model here. As I indicated in the introduction, they are too
complicated to yield any insights directly – at least not for me. Also,
they
have to be solved numerically because there is no analytic solution. If
you
want to experiment with the equations, the full version can be found in
Appendix
4 of Jorgensen’s book.
For
the analysis here I neglected gravity,
assumed constant shoulder torque, and assumed constant wrist torque
during the
second phase of the downswing. This allows the equations to be
partially
integrated analytically and reduces the number of dynamic variables in
the
numerical integration from 4 to 2. For
further information see the paper by Pickering and Vickers, or the
supplementary
EPAPS document associated with my paper – it can be found quickly if
you Google
EPAPS, golf swing. To do the integrations you will need a moderately
good numerical
integration algorithm. Applications like Mathcad, Maple, and
Mathematica have
very good integration routines.
References:
Theodore
Jorgensen, "The
Physics of Golf 2nd
Ed", Springer Verlag, New York, 1994)
W.
M. Pickering and G. T. Vickers, “On The
Double Pendulum Model Of The Golf Swing”, Sport.
Eng., 2, 161-172 (1999)
D R White, "On
the efficiency of the golf swing",
Am. J. Phys. 74,
pp. 1088-1094 (2006)
|
Last modified - May 14, 2013
|
