### SWEET SPOTS A/Prof Rod Cross Physics Department Sydney University

```SWEET SPOTS
A/Prof Rod Cross
Physics Department
Sydney University
June 2006
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?
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.
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.
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.
Node points
When an object vibrates, some parts of the object vibrate
more than others and some parts don’t vibrate at all. Those
parts that don’t 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.
CENTRE OF PERCUSSION
Handle
moves
to right
String
Impact at tip
Handle
moves
to left
Impact at throat
Handle
doesn’t
move
Impact at COP
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.
Node
Node
COP
L
Handle
end
WOOD BEAM EXPERIMENT
COP
Impact at node
feels good
Node
Impact at tip
feels worse
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
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.
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