Notes · Physical EducationUK · A-Levels

Fluid Mechanics

This chapter examines how the fluids a performer moves through - air and water - affect performance. It explains drag and its two components, the factors that determine its size and how performers reduce it, and the lift force produced by the Bernoulli principle, including the aerodynamic lift on a discus or ski-jumper, the downforce on a racing car and the Magnus effect that makes a spinning ball swerve or dip.

3 sections~12 min reading time3 competenciesLevel Standard 2 · Advanced 1

T·0777 / 17

Exam profile

AO1 · Describe drag, lift and the Bernoulli principleAO2 · Apply the concepts of drag and lift to named sporting situationsAO3 · Analyse and evaluate how performers manipulate drag and lift to improve performance

Operators:describeexplainapplyanalyseevaluate

basic level

AS-Level requires the meaning of drag and the factors affecting it.

higher level

The full A-Level requires the Bernoulli principle and the analysis of lift and the Magnus effect in named sporting situations.

Depth

Text

Contents · 3 sections

Fluid Mechanics

Air and water resistance (drag)#

StandardAQA 7582 3.2.3.3DfE GCE PE - fluid mechanics: drag

Forces on a cyclist at constant velocity

Fig. 1A cyclist at steady speed on the flat: the forward driving force balances the backward drag (air resistance), and the upward reaction balances the weight.

When a performer moves through a fluid (air or water) the fluid exerts a resistive force called drag, which acts opposite to the direction of motion and so tends to slow the performer down. Water is far denser than air, so drag is much greater and much more important in swimming than in running; but at high speeds, and for cyclists, sprinters and downhill skiers, air resistance is also a substantial force that limits performance. Reducing drag is therefore a central concern in many sports.

Drag has two components. Surface drag (skin friction) arises from the friction between the fluid and the surface of the body and its equipment - it depends on the roughness or smoothness of the surface and is reduced by smooth suits, shaved skin or waxed skis. Form drag (pressure drag) arises from the pressure difference between the front and the back of the body as it pushes the fluid aside, creating a high-pressure region in front and a low-pressure turbulent wake behind; it depends on the shape and frontal area of the body and is usually the larger component for a bluff (non-streamlined) shape.

The size of the drag force is governed by four main factors: the velocity of the performer (drag rises steeply, approximately with the square of the velocity, so it becomes far more important at high speed), the frontal (cross-sectional) area presented to the fluid (a larger area gives more drag), the shape (a streamlined shape gives much less form drag than a bluff one) and the surface characteristics (a smoother surface gives less surface drag). The density of the fluid also matters, which is why drag is so much greater in water.

These factors explain why drag rises so sharply with speed and why it dominates the effort of a fast cyclist or sprinter. Because drag increases with roughly the square of velocity, doubling the speed roughly quadruples the drag, so at racing speeds a large share of a cyclist's power goes into overcoming air resistance. This is why elite performers work so hard to reduce it - through position, equipment and surface - which is the subject of the next section. Being able to name the two components of drag and the factors that determine its size, and to apply them to a named sport, is the foundation of this topic.

F_{drag} \propto \rho \, A \, v^2

Factors affecting drag

Drag increases with the fluid density (rho), the frontal area (A) and approximately the square of the velocity (v); shape and surface set the constant of proportionality.

Worked example

Why speed dominates drag

A cyclist doubles their speed on a flat road. Using the relationship between drag and velocity, estimate how the air-resistance force changes, and explain the consequence for the power they must produce.

State the relationship
Drag is approximately proportional to the square of the velocity, so if velocity doubles, drag increases by a factor of 2 squared = 4.
Effect on force
The air-resistance force therefore roughly quadruples when the speed is doubled.
Effect on power
Because power to overcome drag is force multiplied by velocity, and both the force (x4) and the velocity (x2) have risen, the power needed rises by roughly a factor of 8 - which is why small increases in top speed require large increases in effort.

Result: Doubling the speed roughly quadruples the drag force and increases the power needed to overcome it about eightfold - so reducing drag is critical at high speed.

Typical mistakes

Treating drag as constant with speed - it rises steeply (approximately with the square of velocity), so it matters far more at high speed.
Confusing surface drag (friction along the surface) with form drag (the front-to-back pressure difference).

Active revision

Explain why air resistance becomes a much greater problem for a track cyclist as their speed increases, referring to the two components of drag.

Active recall

Recall the key points — then reveal.

Sources: GCE AS and A level subject content for physical education (Department for Education) · AQA A-level Physical Education 7582 specification (AQA)

Factors affecting drag and streamlining#

StandardAQA 7582 3.2.3.3DfE GCE PE - reducing drag

Streamlined versus bluff shape

Fig. 2A streamlined, tapering shape lets air flow around it with a small wake (low form drag); a bluff shape leaves a large low-pressure turbulent wake (high form drag).

Because drag limits performance in fast and in aquatic sports, performers work systematically to reduce each of the factors that increase it, and the most powerful of these is streamlining the shape. A streamlined shape has a smooth, tapering profile that lets the fluid flow around it with little separation, keeping the wake small and so reducing form (pressure) drag. A cyclist adopting a low, tucked aerodynamic position, a swimmer holding a long, flat streamline off the wall and a downhill skier crouching into an egg position are all reducing form drag by streamlining.

Reducing the frontal (cross-sectional) area presented to the fluid cuts drag directly, and it usually goes hand in hand with streamlining: the cyclist's tuck and the skier's crouch both make the body narrower to the oncoming air as well as smoother. A sprinter or speed skater leaning forward, and a swimmer keeping their body high and flat in the water, all present a smaller area to the fluid.

Reducing the surface drag (skin friction) is the other main strategy, achieved by making the surface of the body and equipment as smooth as possible. Swimmers wear smooth, low-friction suits and caps and remove body hair; cyclists and skiers use smooth, close-fitting clothing; and equipment is designed with low-friction surfaces. In some cases a carefully textured surface (such as the dimples on a golf ball) actually reduces overall drag by keeping the airflow attached longer and shrinking the turbulent wake - a reminder that the aim is to reduce total drag, not simply to make everything smooth.

The key evaluative idea is that reducing drag involves trade-offs and diminishing returns, and it must be balanced against other demands. A more streamlined cycling position may reduce a rider's power output or comfort; an extreme swimming streamline cannot be held while breathing or stroking; and equipment that reduces drag may be expensive or restricted by the rules. Because drag rises with the square of velocity, the gains from reducing it are greatest at high speed, so the effort of streamlining is most worthwhile for the fastest performers. Applying the factors to explain how a named performer minimises drag, and weighing the trade-offs, is the analytical skill here.

Worked example

Analysing a downhill skier's aerodynamics

Explain how a downhill skier minimises drag to maximise their speed, referring to shape, frontal area and surface.

Shape (form drag)
The skier adopts a low, tucked 'egg' position that streamlines the body, reducing the wake and so the form drag.
Frontal area
The tuck also reduces the frontal area presented to the oncoming air, which directly reduces drag.
Surface (skin drag)
A smooth, close-fitting speed suit and waxed skis reduce surface (skin-friction) drag.
Why it matters
Because drag rises with the square of speed, these reductions have the greatest effect at the skier's high racing speeds, where drag would otherwise dominate.

Result: The tuck streamlines the shape and cuts frontal area (reducing form drag), while a smooth suit and waxed skis cut surface drag - most valuable at the skier's high speeds.

Typical mistakes

Assuming a perfectly smooth surface is always best - a textured surface (e.g. golf-ball dimples) can reduce total drag by shrinking the wake.
Describing streamlining without linking it to form drag and frontal area - it works by reducing both.

Active revision

Explain three ways a competitive swimmer reduces drag, identifying which component of drag each addresses.

Active recall

Recall the key points — then reveal.

Sources: GCE AS and A level subject content for physical education (Department for Education) · AQA A-level Physical Education 7582 specification (AQA)

Lift, the Bernoulli principle and the Magnus effect#

AdvancedAQA 7582 3.2.3.3DfE GCE PE - the Bernoulli principle and lift

The Magnus effect on a topspin ball

Fig. 3Topspin drags air faster under the ball (lower pressure) than over it (higher pressure), so the net Magnus force is downward and the ball dips.

As well as drag, a fluid can exert a lift force - a force perpendicular to the direction of motion - and this is explained by the Bernoulli principle. Bernoulli's principle states that where a fluid flows faster its pressure is lower, and where it flows slower its pressure is higher. If a shape makes the air travel faster over one surface than the other, the pressure difference creates a net force from the high-pressure (slow) side towards the low-pressure (fast) side. This is the origin of aerodynamic lift.

In sport this lift can act upwards or downwards. An object shaped or angled like an aerofoil - a discus, or a ski-jumper's body and skis angled to the airflow - makes the air travel faster over the top than underneath, so the pressure is lower above and higher below, giving an upward lift force that keeps the object in the air longer and increases the distance. The same principle is used in reverse in motor sport: a racing car's inverted-aerofoil wing makes the air travel faster underneath, giving lower pressure below and a downward force (downforce) that presses the tyres onto the track for grip.

The Magnus effect is the lift produced by a spinning ball, and it is the reason a ball can swerve, dip or float. The spin drags the air around with it, so on one side of the ball the surface moves with the airflow and speeds it up (lower pressure), while on the other side it moves against the airflow and slows it down (higher pressure); the resulting pressure difference pushes the ball from the high-pressure side towards the low-pressure side. Topspin makes the air move faster under the ball, giving lower pressure below and a downward Magnus force, so the ball dips steeply (a topspin forehand or a dipping free-kick). Backspin does the reverse, giving a lift that makes the ball float and stay up longer, and sidespin makes it swerve sideways (a curling free-kick or a spinning table-tennis ball).

Understanding lift lets a performer shape a flight path deliberately, and the evaluative point is that a spin or an aerofoil angle changes both lift and drag together. A discus thrower angles the discus to gain lift for distance but must not stall it; a footballer uses topspin to bring a shot down under the bar or sidespin to bend it around a wall; a tennis player uses topspin to hit hard yet keep the ball in. In each case the performer trades some extra drag for the control that lift provides. Applying the Bernoulli principle and the Magnus effect to explain how a named performer manipulates the flight of a body or a ball is the most demanding skill in this chapter.

Worked example

Explaining a dipping topspin shot

A footballer strikes a shot with heavy topspin. Explain, step by step, why the ball dips sharply beneath the crossbar.

The spin drags the air
The topspin drags the surrounding air around with the ball as it flies forward.
Create a velocity difference
Underneath the ball the surface moves in the direction of the airflow, speeding the air up; over the top the surface moves against the airflow, slowing it down.
Apply Bernoulli
By the Bernoulli principle the faster air below is at lower pressure and the slower air above is at higher pressure.
Resulting force
The pressure difference produces a net downward Magnus force, which adds to gravity and makes the ball dip sharply, bringing it down under the bar.

Result: Topspin speeds the air below the ball, so the lower pressure beneath creates a downward Magnus force that makes the ball dip beneath the crossbar.

Typical mistakes

Getting the pressure-velocity relationship backwards - faster-moving fluid has lower, not higher, pressure.
Saying topspin makes a ball rise - topspin gives a downward Magnus force so the ball dips; backspin makes it float.

Active revision

Explain, using the Bernoulli principle and the Magnus effect, how a footballer uses topspin to make a shot dip beneath the crossbar.

Active recall

Recall the key points — then reveal.

Sources: GCE AS and A level subject content for physical education (Department for Education) · AQA A-level Physical Education 7582 specification (AQA)

References & sources

Sources

Department for Education

GCE AS and A level subject content for physical education

AQA

AQA A-level Physical Education 7582 specification

Fluid Mechanics

3 sections~12 min reading time3 competenciesLevel Standard 2 · Advanced 1

Fluid Mechanics

Key points

Why speed dominates drag

Key points

Analysing a downhill skier's aerodynamics

Key points

Explaining a dipping topspin shot

Sources

Fluid Mechanics

Key points

Why speed dominates drag

Key points

Analysing a downhill skier's aerodynamics

Key points

Explaining a dipping topspin shot

Sources