SWEET SPOTS

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SWEET SPOTS
A/Prof Rod Cross Physics Department Sydney
University June 2006
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What is a sweet spot ?
Tennis racquets, baseball bats, cricket bats and
golf clubs all have a sweet spot. It is the
impact point that feels best. Compared with other
impact points, the player feels an almost
complete absence of jarring and vibration in the
handle of the striking implement if the ball is
struck at the sweet spot. Why does this spot
exist, where is it located, how big is it and
does the ball travel any faster when it is struck
at the sweet spot?
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Opinions
Some people say that the sweet spot is located at
the centre of percussion of the striking
implement. Others say it is a node point where
there is no vibration. Some say is the point
where the ball comes off the implement at maximum
speed and hence minimum effort is needed to
strike the ball. Others say that the sweet spot
varies in size according to how clever the
manufacturer has been in designing the implement
or in getting these various points to overlap.
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Vibrations
All objects vibrate back and forth when they are
struck. In general, you can see them vibrate, you
can hear them vibrate and you can feel them
vibrate. A guitar string or a violin string or a
tennis string will vibrate rapidly when it is
struck or plucked or bowed. Heavier objects like
tennis racquets and baseball bats vibrate more
slowly and are harder to hear unless you put your
ear up close. Guitar strings vibrate back and
forth around 1000 times a second. We say that the
vibration frequency is about 1000 Hz. Bats and
racquets vibrate at around 100 Hz to 200 Hz.
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High frequency modes
Even though bats and racquets vibrate at around
100 to 200 Hz, they can also vibrate
simultaneously at higher frequencies, as can a
guitar string. A guitar string has many such
overtones which is why it sounds different to
say a trumpet vibrating at the same basic or
fundamental frequency. The mix of overtones is
different in all musical instruments. In
practice, the only vibration mode of a tennis
racquet of any importance is the fundamental
mode. The ball sits on the strings too long
(about 0.005 seconds) to allow any high frequency
modes to vibrate. The effect is similar to
putting your finger on a guitar string to stop
the string vibrating.
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Node points
When an object vibrates, some parts of the object
vibrate more than others and some parts dont
vibrate at all. Those parts that dont vibrate
are called node points. A guitar string has a
node point at each end where it is tied down. The
most important node points of a bat or racquet
are located about 15 cm (6 in) from each end for
the fundamental mode. An object that is struck
at a node point will not vibrate at all. If you
strike a ball at such a node point you will feel
no vibrations at all in the handle. This point is
a good candidate for the sweet spot of a bat or a
racquet or a club.
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CENTRE OF PERCUSSION
Handle moves to right
Handle moves to left
Handle doesnt move
Impact at tip
Impact at COP
Impact at throat
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SIMPLE BEAM
Before experimenting with bats or racquets it
helps (a lot) to understand the behaviour of
objects with a simple shape such as a rectangular
beam or a cylindrical rod. A beam or rod of
length L has a node point located a distance
0.22L from each end. The COP is located a
distance L/3 from the striking end. If a ball
impacts at the COP then the beam will rotate
about an axis at the end of the handle.
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WOOD BEAM EXPERIMENT
Impact at tip feels worse
Impact at node feels good
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LISTEN TO VIBRATIONS

• Hold at node in handle, with handle close to
  your ear. If you hold the far end of the handle
  (an antinode) the vibrations are strongly damped.

• Impact strings or racquet frame with a ball or
  with the soft end of your finger (not with
  finger-nail).

• This way you can locate the handle and frame
  nodes as well as the node near the middle of the
  strings.

200 Hz (high pitch) very stiff (and light)
racquet 100 Hz (low pitch) very flexible (and
heavy) racquet
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SOME EXPERIMENTS TO DO
Find YOUR sweet spot on a wood beam, a bat and a
racquet. (Mine is at the node point, not the
COP). The node COP points are much closer
together in a baseball bat. Bats vibrate at two
frequencies simultaneously. What differences do
you find when using thick or short (stiff) beams
thin or long (flexible) beams and when using a
stiff ball (eg golf or baseball) vs a soft tennis
ball. Does the sweet spot zone get any bigger?
Stiff racquets are harder to bend so they vibrate
less (and faster or at a higher pitch). Does the
node or the COP point shift when you hold the
handle with your hand? Does the vibration
frequency (pitch) change? Try adding a heavy
weight at the handle end. Does the ball bounce
any faster off the sweet spot? Try bouncing a
ball from a fixed height off a racquet held with
the strings horizontal. The bounce height is
proportional to the rebound speed squared.