Introduction to Sports Biomechanics: Analysing Human Movement ...

Optimum projection conditions
QUANTITATIVE ANALYSIS OF MOVEMENT
In many sports events, the objective is to maximise either the range, or the height of
the apex achieved by the projectile. As seen above, any increase in projection speed
or height is always accompanied by an increase in the range and height achieved by a
projectile. If the objective of the sport is to maximise height or range, it is important to
ascertain the best – the optimum – angle to achieve this. Obviously maximum height
is achieved when all of the available projection speed is directed vertically, when the
projection angle is 90°.
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As we saw above, when the projection height is zero, the range is given by v0 sin2θ/g.
For a given projection speed, v0, the range is a maximum when sin2θ is a maximum,
that is when sin2θ = 1 and 2θ = 90°; therefore, the optimum projection angle, θ, is 45°.
For the more general case of a non-zero projection height, the optimum projection
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angle can be found from: cos2θ = g y0/(v0 + g y0). For a good shot putter, for example,
this would give a value of around 42°.
Although optimum projection angles for given values of projection speed and height
can easily be determined from the last equation, they do not always correspond to those
recorded from the best performers in sporting events. This is even true for the shot put,
for which the object’s flight is the closest to a parabola of all sports objects. The reason
for this is that the calculation of an optimum projection angle assumes, implicitly, that
the projection speed and projection angle are independent of one another. For a shot
putter, the release speed and angle are, however, not independent, because of the
arrangement and mechanics of the muscles used to generate the release speed of
the shot. A greater release speed, and hence range, can be achieved at an angle of about
35°, which is less than the optimum projectile angle. If the shot putter seeks to increase
the release angle to a value closer to the optimum projectile angle, the release speed
decreases and so does the range.
A similar deviation from the optimum projection angle is noticed when the
activity involves the projection of an athlete’s body. The angle at which the body is
projected at take-off can have a large effect on the take-off speed. In the long jump,
for example, take-off angles used by elite long jumpers are around 20°. To obtain the
theoretically optimum take-off angle of around 42°, long jumpers would have to
decrease their normal horizontal speed by around 50%. This would clearly result in
a drastically reduced range, because the range depends largely on the square of the
take-off speed.
In many sporting events, such as the javelin and discus throws, badminton, skydiving
and ski jumping, the aerodynamic characteristics of the projectile can significantly
influence its trajectory. The projectile may travel a greater or lesser distance than
it would have done if projected in a vacuum. Under such circumstances, the calculations
of optimal projection parameters need to be modified considerably to take
account of the aerodynamic forces (see Chapter 5) acting on the projectile.
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