Introduction to Sports Biomechanics: Analysing Human Movement ...

Drag forces
CAUSES OF MOVEMENT – FORCES AND TORQUES
If an object is symmetrical with respect to the fluid flow, such as a non-spinning soccer
ball, the fluid dynamic force acts in the direction opposite to the motion of the object
and is termed a drag force. Drag forces resist motion and, therefore, generally restrict
sports performance. They can, however, have beneficial propulsive effects, as in
swimming and rowing. To maintain a runner in motion at a constant speed against a
drag force requires an expenditure of energy equal to the product of the drag force and
the speed. If no such energy is present, as for a projectile, the object will decelerate at a
rate proportional to the area presented by the object to the fluid flow (the so-called
‘frontal’ area, A) and inversely proportional to the mass of the body, m. The mass to area
ratio (m/A) is crucial in determining the effect that air resistance has on projectile
motion. A shot, with a very high ratio of mass to area, is hardly affected by air resistance
whereas a cricket ball, with only 1/16th the mass to area ratio of the shot, is far more
affected. A table tennis ball (1/250th the mass to area ratio of the shot) has a greatly
altered trajectory.
Pressure drag
Pressure drag, or wake drag, contributes to the fluid resistance experienced by, for
example, projectiles and runners. This is the major drag force in most sports and is
caused by boundary layer separation leaving a low-pressure wake behind the object. The
object, tending to move from a low-pressure to a high-pressure region, experiences a
drag force. The pressure drag can be reduced by minimising the disturbance that the
object causes to the fluid flow, a process known as ‘streamlining’. An oval shape, similar
to a rugby ball, has only two-thirds of the pressure drag of a spherical ball with the same
frontal area. The pressure drag is very small on a streamlined aerofoil shape, such as the
cross-section of a glider wing. Streamlining is very important in motor car and motor
cycle racing, and in discus and javelin throwing. Swimmers and skiers can reduce the
pressure drag forces acting on them by adopting streamlined shapes. The adoption of a
streamlined shape is of considerable advantage to downhill skiers.
If we increase the speed of an object through a fluid – such as a ball through the
air – we find a dramatic change in the drag as the boundary layer flow changes from
laminar to turbulent. As this transition occurs at the critical Reynolds number, the
drag decreases by about 65%. Promoting a turbulent boundary layer is an important
mechanism in reducing pressure drag if the speed is close to the value necessary to
achieve the critical Reynolds number. At such speeds, which are common in ball sports,
roughening the surface promotes turbulence in the boundary layer, encouraging this
decrease in drag. The nap of tennis balls and the dimples on a golf ball are examples of
roughness helping to induce boundary layer transition, thereby reducing drag. Within
the Reynolds number range 110 000–175 000, which corresponds to ball speeds off the
tee of 45–70 m/s, the dimples on a golf ball cause the drag coefficient to decrease
proportionally to speed. The drag force then increases only proportionally to speed,
rather than speed squared, benefiting the hard-hitting player.
Many sport balls are not uniformly rough. Then, within a speed range somewhat
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