The Science of the Spin

We all know that spin allows us to add unpredictability and increases our margin of error.  On average, an ATP professional player can reach spins of up to 2000 RPM (Rotations Per Minute).  Rafael Nadal can reach over 3200 RPMs!

There are 3 forces acting on a tennis ball as it flies through the air which in combination result in the ball spin:

  • Gravity
  • Aerodynamic drag
  • TheMagnus effect

In science, spin is correlated to the “Magnus Effect” which, in simple terms, relates the effect of the pressure difference across the tennis ball traveling across a medium (e.g. air).

The pressure difference generates a net force that curves the ball towards the low pressure side. For instance:

  • Top spin brings the ball down
  • Back spin bring the ball up hence giving the floating effect which can trick your opponents’ point of contact.

magnuseffect

The above image depicts the spinning of a tennis ball as it flies through the air (the ball is moving into the page and spinning around an axis at an angle of φ from vertical with an angular momentum of ω radians per second).  The spinning motion causes a difference in air pressure between one side of the ball and another – the Magnus effect.

The angle of deviation, θ from the straight line to your intended impact spot, is

eq1

where:

wsis the vertical angular velocity (how fast the ball spins, measured in radians per second)

u is the ball’s initial speed as it leaves the racket

A and B are constants that depend on the drag coefficient of the air and the straight-line distance from the player to the impact point.

The tennis ball trajectory with respect to a straight line at an angle of θ determines the spin effect on the tennis ball:

  • A larger musically likes slice spin results in a wider shot with respect to the angle.

sliceserve

A slice serve occurs when the ball is hit with side spin, causing the tennis ball to curve dramatically to the direction of the spin applied.