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

Drag ∝ v²

Air resistance and drag oppose motion. Change velocity, frontal cross-sectional area and surface, and watch the drag force respond. Double the speed and drag goes up four times.

Drag force0N · opposes motion
Velocity0m/s
If speed doubled0N · ×4

Model: drag force = ½ × fluid density × drag coefficient × frontal area × velocity². You will not be asked for this equation in the exam, but it shows why velocity has the biggest effect. Surface and helmet effects are illustrative.

Air · ρ = 1.2 kg/m³
Athlete:
Surface:

Pick an athlete, then try the Double the speed button.

The key idea, drawn live

Drag rises with velocity squared

The curve shows drag against velocity for the athlete you picked. It gets steeper as speed rises: twice the velocity gives four times the drag. A smaller frontal area or smoother surface flattens the whole curve.

Part 2 · Lift and the Bernoulli principle

Tilt the discus

A discus is shaped like an aerofoil. Increase its angle of attack and air travelling over the top goes further and faster than air underneath. Faster air means lower pressure, so a pressure gradient pushes the discus upwards: a lift force. Go too far and the airflow breaks away (stall).

Object:
0°15°30°45°
Lift force0N · upwards
Drag force0N · opposes motion
Discus weight19.6N · 2 kg discus

Lift rising

Discus at 25 m/s. Lift rises with angle of attack up to a point, then the airflow separates from the upper surface: lift falls and drag rises sharply. The stall angle here comes from a simplified model, not a measured value. Lift doesn't need to beat weight: it reduces the net downward force, so the discus stays in the air longer.

Part 3 · Challenge

Beat the clock

Same rider, same 350 W of power, 1 km on the flat. The only thing you can change is how much air resistance they meet. Beat the target time in each round.

Round 1/3Score 0Target 81.5 s

Predict first: which single change will save the most time?

Position:
Helmet:
Kit:

Round 1: beat 81.5 s.

Quick-fire · Name the factor

AQA names four factors that affect air resistance and drag. Which one is each example mainly changing?

…

Pick an answer.

Correct 0/0
01 · AQA definitions

Learn these word for word

Air resistance
A force that opposes the direction of motion of a body travelling through the air.
Drag
A force that opposes the direction of motion of a body travelling through water. The word is also commonly used for air.
Bernoulli
Bernoulli principle Air molecules exert less pressure the faster they travel, and more pressure when they travel slower.
Lift
Lift force An additional force created by a pressure gradient forming on opposing surfaces of an aerofoil moving through a fluid. It acts at right angles to the direction of motion.
Angle
Angle of attack The most favourable angle of release for a projectile to optimise lift: the angle at which the aerofoil (e.g. a discus) is tilted relative to the airflow.
Downforce
Downward lift force Created by an inverted aerofoil (e.g. a racing car spoiler): higher pressure above, lower pressure below, so the force acts downwards.

Factors that increase or reduce air resistance and drag:

  • Velocity The greater the velocity, the greater the air resistance or drag. Velocity has the biggest effect because drag depends on velocity squared.
  • Frontal cross-sectional area The larger the frontal area, the greater the air resistance. A cyclist in a tuck presents a smaller area than one sitting upright.
  • Streamlining and shape An aerodynamic, tapered shape lets air flow smoothly around the body, reducing air resistance (e.g. teardrop helmet, bobsleigh shape).
  • Surface characteristics A smooth surface (skinsuit, shaved body hair, full-body swimsuit) reduces drag compared with loose or rough clothing.

Water vs air. Water is about 800 times denser than air, so a swimmer meets far more drag than a runner moving at the same speed. That is why swimmers work so hard on streamlining.

02 · Mechanism

How a discus gets lift

  • The discus is released with an angle of attack so it acts like an aerofoil.
  • Air travelling over the top surface has further to travel, so it moves faster, creating lower pressure above.
  • Air travelling underneath has a shorter distance, travels slower and creates higher pressure below.
  • The pressure gradient (high below, low above) creates an upward lift force.
  • Lift keeps the discus in the air for longer, increasing the horizontal distance travelled.
  • If the angle of attack is too large, airflow separates from the upper surface, lift decreases and drag increases (stall), reducing distance.

Downward lift force. Turn the aerofoil upside down, as with a racing car spoiler. Air underneath now travels further and faster, so pressure is lower below and higher above. The force acts downwards, increasing the normal reaction, so the maximum friction (grip) between the tyres and the track increases and the car can corner faster.

03 · Applied

In sport

PerformerWhat they doFactor or forceEffect
Track cyclistLow, tucked positionFrontal cross-sectional areaLess air resistance, higher speed for the same power
Track cyclistTeardrop helmet, disc wheelsStreamlining and shapeSmoother airflow, less air resistance
SwimmerFull-body suit, shaved body hair, swim capSurface characteristicsLess drag through the water
Downhill skierCrouched tuck, arms in frontFrontal area and streamliningLess air resistance at very high velocity
Discus throwerReleases with an angle of attackLift force (Bernoulli)Longer flight time, greater horizontal distance
Racing carInverted aerofoil spoilerDownward lift forceGreater normal reaction, so more maximum friction (grip) and faster cornering
04 · Diagrams

Getting the diagram marks

  • Show the direction of motion with an arrow.
  • Draw air resistance or drag opposite to the direction of motion.
  • Draw lift at right angles to the direction of motion: upwards for a discus, downwards for a spoiler.
  • Show the airflow lines: closer together and faster on the curved or longer surface, further apart and slower on the other side.
  • Label low pressure on the fast side and high pressure on the slow side. The force acts from high to low pressure.
05 · Exam practice

Try, then check

Question 1 · Identify4 marks

Identify four factors that affect the air resistance acting on a cyclist. For each, explain how it affects air resistance and give one way the cyclist could reduce it.

Show mark scheme
  • Velocity: air resistance increases as velocity increases
  • Frontal cross-sectional area: lower, tucked position / elbows in
  • Streamlining and shape: aerodynamic teardrop helmet / disc wheels / streamlined frame
  • Surface characteristics: smooth Lycra skinsuit / shaved legs
Question 2 · Calculate1 mark

A skier doubles her velocity from 15 m/s to 30 m/s without changing her body position. By what factor does the air resistance acting on her increase?

Show mark scheme
  • Four times (air resistance increases with velocity squared, 2² = 4)
Question 3 · Draw and label3 marks

Draw and label a diagram of a discus in flight to show how a lift force is created.

Show mark scheme
  • Discus drawn with an angle of attack, direction of motion shown, airflow drawn opposite to motion
  • Airflow over the top travels further and faster, labelled low pressure; airflow underneath slower, labelled high pressure
  • Lift force arrow drawn upwards, at right angles to the direction of motion (from high to low pressure)
Question 4 · Explain3 marks

Explain why a discus thrower should not release the discus with too large an angle of attack.

Show mark scheme
  • Increasing the angle of attack increases lift, but only up to a point
  • If the angle of attack is too large, airflow breaks away from the upper surface (stall), so lift decreases
  • Air resistance / drag increases, so the discus slows and horizontal distance is reduced
Question 5 · Explain3 marks

Explain how the spoiler on a racing car helps it go around corners faster.

Show mark scheme
  • The spoiler is an inverted (upside-down) aerofoil
  • Air underneath travels further and faster, giving lower pressure below and higher pressure above (Bernoulli principle)
  • This creates a downward lift force, increasing the normal reaction, so the maximum friction / grip between the tyres and the track increases
Question 6 · Explain5 marks

Using the Bernoulli principle, explain how a discus thrower can increase the horizontal distance the discus travels.

Show mark scheme
  • Bernoulli principle: air molecules exert less pressure the faster they travel and more pressure the slower they travel
  • The discus is released at an angle of attack so it acts as an aerofoil
  • Air over the top travels further and faster, creating low pressure above
  • Air underneath travels a shorter distance, more slowly, creating high pressure below
  • The pressure gradient creates an upward lift force
  • Lift increases flight time, so the discus travels further horizontally
  • Angle of attack must not be too large, or lift falls and drag increases
  • Max 5 marks