Introduction to Sports Biomechanics: Analysing Human Movement ...

INTRODUCTION TO SPORTS BIOMECHANICS
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FORCE–TIME GRAPHS AS MOVEMENT PATTERNS
Consider an international volleyball coach who wishes to assess the vertical jumping
capabilities of his or her squad members. Assume that this coach has access to a force
plate, a device that records the variation with time of the contact force between a person
and the surroundings (see below). The coach uses the force plate to record the force–
time graph exerted by the players performing standing vertical jumps (see, for example,
Figure 5.2). These graphs provide another movement pattern for both the qualitative
and the quantitative movement analyst; our world is exceedingly rich in such patterns.
Each player’s force–time graph, after subtracting his or her weight, is easily converted to
an acceleration–time graph (Figure 5.12(a)) as acceleration equals force divided by the
player’s mass, where the acceleration is that of the jumper’s centre of mass.
Qualitative evaluation of a force–time or acceleration–time pattern
In Chapter 2, we saw how important it is for a qualitative analyst to be able to interpret
movement patterns such as displacement or angle time series. Force–time or acceleration–time
patterns are far less likely to be encountered by the qualitative movement
analyst and are not so revealing about other kinematic patterns – velocity and displacement.
However, if you are prepared to accept that the velocity equals the area between
the horizontal zero-acceleration line – the time (t) axis of the graph – and the acceleration
curve from the start of the movement at time 0 up to any particular time, and that
areas below the time axis are negative and those above positive, then several key points
on the velocity–time graph follow. Ignore, for the time being, the numbers on the
vertical axes of Figure 5.12.
At time A in Figure 5.12(a), the area (−A 1) under the time axis and above
the acceleration–time curve from 0 to A reaches its greatest negative value, so the
vertical velocity of the jumper’s centre of mass also reaches its greatest negative value
there, corresponding to a zero acceleration. We can then sketch the velocity graph
in Figure 5.12(b) up to time A.
At time B in Figure 5.12(a), the area under the acceleration–time curve from A
to B and above the time axis is +A 1 – the same magnitude as before but now
positive. So the net area between the acceleration–time curve and the time axis
from 0 to B is −A 1 + A 1 = 0. The vertical velocity of the jumper’s centre of mass at B
is, therefore, zero; we can now sketch the vertical velocity curve from A to B in
Figure 5.12(b).
From B to C the area between the acceleration–time curve and the time axis is
positive, so the area (A 2) reaches its greatest positive value at C. Now we can sketch
the vertical velocity curve from B to C in Figure 5.12(b).
Finally, from C to take-off at D (time T), we have a small negative area, A 3, and the
vertical velocity decreases from its largest positive value by this small amount before
take-off, as in Figure 5.12(b).