AQA A-level PE · Paper 2 · Biomechanical movement · Fluid mechanics

Magnus force

Spin makes air flow faster past one side of the ball than the other. Faster air means lower pressure, so the ball is pushed from high to low pressure. Pick a spin and hit.

Spin rate0rpm
Magnus force at launch0.00N
Compared with no spin0.0m

Model: real ball masses and sizes. Weight, air resistance and the Magnus force are recalculated 500 times per second of flight.

Tennis · side-on
Sport:
Spin: See the exam diagram for this spin ↓

Predict, then hit:

The exam diagram, drawn live

Slow air, high pressure. Fast air, low pressure.

This is the diagram AQA asks you to draw. It updates with the spin you choose. The side of the ball rotating into the oncoming airflow slows the air down, so pressure there is higher. The Magnus force acts from that side towards the low-pressure side.

Side-on for topspin and backspin. From above for hook, slice and a curling free kick.

01 · AQA definitions

Learn these word for word

Bernoulli
Bernoulli principle Air molecules exert less pressure the faster they travel, and more pressure the slower they travel.
Gradient
Pressure gradient A difference in pressure on opposite surfaces of a body. A force acts from the area of high pressure to the area of low pressure.
Magnus F
Magnus force A force created by a pressure gradient on opposing surfaces of a spinning body moving through the air.
Magnus
Magnus effect The creation of an additional Magnus force on a spinning projectile, which deviates it from its normal flight path.
Spin
How spin is created An eccentric force: a force applied outside the centre of mass of the ball.
  • Topspin: eccentric force applied above the centre of mass. The ball dips and its flight is shortened.
  • Backspin: eccentric force applied below the centre of mass. The ball gains lift, floats and its flight is lengthened.
  • Hook (right-handed golfer): eccentric force applied to the right of the centre of mass. The ball swerves to the left.
  • Slice (right-handed golfer): eccentric force applied to the left of the centre of mass. The ball swerves to the right.

The one rule that gets every diagram right. Find the surface of the ball that is rotating into the oncoming airflow. The air there is slowed, so pressure is high. The opposite surface moves with the airflow, so the air is faster and pressure is low. The Magnus force acts from high to low.

02 · Drawing it

Five steps to full diagram marks

  1. Draw the ball and an arrow for the direction of travel.
  2. Draw the airflow in the opposite direction to travel.
  3. Show the spin with a curved arrow and name it (topspin, backspin, hook or slice).
  4. Label where airflow is slower (high pressure) and faster (low pressure). Bunched lines show faster air.
  5. Draw the Magnus force from high to low pressure, then state the effect on flight (dips, floats, swerves left or right).

Topspin and backspin happen about a horizontal axis, so draw them side-on. Hook, slice and a curling free kick spin about a vertical axis, so draw them as if looking down from above.

03 · Applied

In sport

SpinEccentric forceSlower air · high pressureFaster air · low pressureMagnus forceEffect and example
TopspinAbove centre of massAbove the ballBelow the ballDownwardsBall dips, shorter flight. A tennis forehand can be hit hard and still land in, then kicks forward off the bounce.
BackspinBelow centre of massBelow the ballAbove the ballUpwardsBall floats, longer flight. A golf drive carries further; a tennis or squash slice stays low and checks on the bounce.
HookRight of centre of massRight sideLeft sideTo the leftRight-handed golfer's shot curves right to left. Same spin as a right-footer curling a free kick with the inside of the foot.
SliceLeft of centre of massLeft sideRight sideTo the rightRight-handed golfer's shot curves left to right. Same spin as an outside-of-the-foot pass from a right-footer.

Watch the word "slice". In golf it means sidespin. In tennis and squash a slice shot is hit with backspin.

04 · Spot the mistake

Mark it like an examiner

Each diagram has exactly one mistake. Which part is wrong? There are seven diagrams in a random order, and the same part can be wrong more than once.

05 · Exam practice

Try, then check

Question 1 · Define2 marks

Define the Bernoulli principle and the Magnus force.

Show mark scheme
  • Bernoulli principle: air molecules exert less pressure the faster they travel and more pressure the slower they travel
  • Magnus force: a force created by a pressure gradient on opposing surfaces of a spinning body moving through the air
Question 2 · Identify2 marks

A right-handed golfer hits a drive that curves from right to left. Identify the type of spin and state where the eccentric force was applied to the ball.

Show mark scheme
  • Hook / sidespin
  • Eccentric force applied to the right of the centre of mass
Question 3 · Draw4 marks

Draw and label a diagram to show how backspin affects the flight of a golf ball.

Show mark scheme
  • Direction of travel shown, with airflow in the opposite direction, and backspin shown on the ball
  • Below the ball: airflow slower / higher pressure
  • Above the ball: airflow faster / lower pressure
  • Magnus force acts upwards (from high to low pressure), so the ball stays in the air longer / travels further
Question 4 · Explain5 marks

Using the Bernoulli principle, explain how a tennis player uses topspin to hit a fast shot that still lands in the court.

Show mark scheme
  • Eccentric force applied above the centre of mass creates topspin
  • The top surface of the ball rotates into the oncoming airflow, so airflow above the ball is slower and pressure is higher
  • The bottom surface rotates with the airflow, so airflow below the ball is faster and pressure is lower
  • The pressure gradient creates a Magnus force acting downwards (from high to low pressure)
  • The ball dips / flight path is shortened, so it can be hit harder and still land in
  • Credit beyond the flight points: on landing the ball kicks forward / skids through quickly, giving the opponent less time (max 5)
Question 5 · Apply3 marks

A right-footed player curls a free kick around the wall with the inside of their foot, and the ball swerves from right to left. Explain how the spin causes the swerve.

Show mark scheme
  • Eccentric force applied to the right of the centre of mass gives sidespin (anticlockwise when viewed from above)
  • Airflow on the left side of the ball is faster / lower pressure; airflow on the right side is slower / higher pressure
  • Magnus force acts to the left (from high to low pressure), so the ball swerves left around the wall
Question 6 · Compare3 marks

Compare the flight of a tennis ball hit with topspin and one hit with backspin, at the same speed and angle of release.

Show mark scheme
  • Topspin: Magnus force downwards, so the ball dips and has a shorter flight
  • Backspin: Magnus force upwards, so the ball floats / stays in the air longer
  • So the topspin ball lands shorter and the backspin ball lands further
  • Credit beyond the flight points: on the bounce topspin kicks forward / skids through quickly; backspin checks / slows

The bounces in the simulator are illustrative only.