TENNIS MOVIES
You shouldnÕt
use a heavy racquet if you have a light arm. You can see why in these 300 fps double
pendulum movies. An adult forearm
weighs about 1.5 kg. I used a 406 g forearm
here. A 52 g ÒracquetÓ is then OK but a 272 g racquet is too heavy for this very
light arm. Note the double pendulum legs in the background!
Film of a 100 mph
kick serve shows double pendulum action of the forearm and the racquet. When the upper
arm slows down, it exerts a torque on the forearm and causes the forearm to rotate faster.
When the forearm slows down, it exerts a torque on the racquet and causes
the racquet to
rotate faster. That way, rotational energy is transferred from one segment
to the next in
sequence. Does the racquet rotate the wrist or does the wrist rotate the
racquet? Double
pendulum calculations show that in golf, the club rotates the wrist after
the wrist relaxes. In
tennis, the player needs to use the wrist to rotate the racquet.
The force on
the arm can be reduced by using softer strings or hitting the ball at the sweet spot. The
result here shows that the centre of percussion is NOT a sweet spot since the axis
of rotation is through the wrist regardless of the impact point. See also impact at throat where the axis is close to
the butt end of the handle.
The explanation of Movie 4 is probably that the racquet rotates by only
1 or 2 degrees during the first half of the collision so the ball compresses in
a direction perpendicular to the strings. It then expands back along the same
path, the resultant force, R, on the ball being perpendicular to the original
position of the string plane (see drawing). The force
on the ball has a component N perpendicular to the strings and a static
friction force component F parallel to the strings. That also explains the
rotation of the ball after it bounces.
Compare MovieA with MovieB. The
incident speed (22 m/s) spin (3900 rpm) and angle (40
deg) is the same but the bounce is quite different since the impact point is
different. If the racquet rotates then the ACOR is low ie low perpendicular
bounce speed.
That happens with most tennis shots, even with the pros. Note change in spin
direction. That is how topspin is generated, viewed in the racquet
reference frame.
The Tennis Racquet Theorem. Racquets flip over when tossed in the air. So do books and a packet of
cornflakes. But tennis racquets work best. Watch in
slow motion.
Low speed tennis ball bounce filmed at 1000 frames/s
High speed tennis ball filmed at 3000
frames/sec, bouncing on a clay court to measure the court ÒspeedÓ. Bounce
2 is on a grass court.
Measuring the
friction force F and the normal reaction force N on a
ball bouncing off a glass block. Ball incident without spin Ball incident with spin
How to measure the balance point of a tennis racquet (ie the location of the centre of mass).
How to measure the swing weight of a
tennis racquet (ie the moment of inertia about an axis
10 cm from the end of the handle). ItÕs easier to
first measure about a different axis.
How to measure the ACOR of a tennis
racquet. ACOR = (outgoing ball speed/incoming
ball speed) when the racquet is at rest. The ACOR
is lowest at the tip and largest in the throat
region.
Real racquets donÕt vibrate enough to
see the vibrations. Here is a vibrating cardboard racquet
with two strings. The node point in the ÒmiddleÓ of the
strings can be seen, as well as the node points at 2
and 10 oÕclock (towards bottom end of racquet).