The Mechanics of Squash by Neil Martin, Yale University '14
May 3, 2016
- Squash is a game of physical chess. The winner is the player who most
effectively maneuvers an opponent around the court without making an
error. A skilled player will vary their shots, but the player who
displays the greatest mastery over shrewd angles will find the best
results.
To achieve this mastery, it is
vital that players adopt the correct technical aspects of racket work,
movement and spacing. While many club players have absorbed the advice
of their nearby professional, such as; “get low to the ball”; “bend
your knees”; and “don’t get too close”, these catch-phrases will have
more impact if the underlying physics concepts are absorbed.
Physics can aid understanding at all levels of the game, from basic
understanding of angles, to the more complex application of Isaac
Newton’s Equations of Motion.
For instance, when asked
what constitutes a good straight drive, common knowledge is that a
drive should be ‘tight’ to the sidewall; traveling from the front wall
to the back wall as close or ‘tight’ to the sidewall as possible.
Accomplishing this implicitly uses the Law of Reflection that the angle
at which the ball meets the front wall relative to the perpendicular to
the wall, is the same at which the ball will rebound. Thus, to hit a
tight straight drive, you must be striking a ball that was already
relatively tight. Unfortunately, this will not always be possible. In
fact, the ball is regularly struck from a more central position on the
court. If a player aims their drive too close to the sidewall
from a central position, the ball will rebound into the middle of the
court from the sidewall. Rather than visualize the ball being ‘tight’,
it is more effective to hit your shot further from the side wall to
ensure the ball travels to the back of the court rather than striking
the side wall and rebounding into the middle.
We can also
consider the physics of an effective volley. As a ball is struck, both
horizontal and vertical forces act upon it. Gravity causes the ball to
drop with an acceleration of approx. 9.8 m/s2. Therefore, as the ball
gets closer to the floor, its downward velocity grows and it becomes
more difficult to strike. For example, a ball will fall 7.7 inches in
the first 0.2 seconds, but 23 inches in the following 0.2
seconds! Thus, there is a clear advantage to step up and volley
before the ball has time to gain downward velocity. In addition, for a
player lobbing from the front of the court, the greater the height
used, the more effective that lob is likely to be.
The
previous cases have illustrated how physics can help explain the best
strategy for a shot. Another example occurs when a player seeks to
minimize the vertical motion of the ball, such as when playing a drop
shot or a boast, so that the ball bounces as low as possible. To
minimize vertical motion, a player must strike the ball at the point
just above the tin (19”) with a flat racket motion from preparation
until follow through, rather than the conventional “U”-shaped swing
from high to low and back to high. If this is achieved, the drop will
have minimal bounce and be extremely difficult to retrieve. Conversely,
if a drop shot is struck from a standing position, the swing will be
“U” shaped. Since the concept of equal angles of approach and rebound
also applies in the vertical direction, a U swing will result in
greater vertical force being transferred to the ball. This ball will
take longer to reach the front wall, will have an upward rebound
trajectory, and will bounce higher from the floor on impact.
As
mentioned earlier, coaches discourage their players from striking the
ball too close to their body and often allude to the concept of
spacing. It is intuitive that striking the ball too close to the body
(often by over-running the ball) will hinder the full swing and result
in a poor shot. But physics tells us additional advantages of enhanced
space to the ball.
A player’s swing can be understood as a
transfer of rotational energy (RE) of the swinging racket to forward
ball motion. The formula for RE is RE = ½I2 where denotes angular
velocity, and “I” denotes the moment of inertia which relates to the
force generated through the mass of your racket (m) and the space
between you and the ball (r) by the formula I = mr2. Thus RE =
½mr22. Hence, the force is greatest if mass, velocity, and radius
are maximized. While we do not have much control over the mass,
and can affect the swing velocity only to some extent, maximizing the
space between the body and the ball is, in practice, the most
significant factor. Therefore, the optimum swing should be with a
straight arm and racket extended, creating the maximum radius, and
moment of inertia, and therefore imparting the maximum energy to the
ball. For some players, correcting their swing can double the radius
(quadrupling RE).
There has been a huge growth in squash
recently and many players take to local clubs for advice. This article
has tried to show that a greater understanding of the mechanics of the
sport will allow players to make their own technical choices and play
to their strengths.
