Introduction to Sports Biomechanics: Analysing Human Movement ...

INTRODUCTION TO SPORTS BIOMECHANICS
but it does provide a simple example of qualitatively interpreting curvature. To summarise
(see also Figure 3.7):
When the curvature is positive, the acceleration is positive, and the gradient and
velocity are increasing; this is why we called valley-type curvature positive.
When the curvature is negative, so is the acceleration, and the gradient and velocity
are decreasing; this is why we called hill-type curvature negative.
Where the curvature and acceleration change from positive to negative, the acceleration
is instantaneously zero; the velocity stops increasing and starts decreasing.
Where the curvature and acceleration change from negative to positive, the
acceleration is instantaneously zero; the velocity stops decreasing and starts
increasing.
For an elite sprinter, we might find a straight horizontal portion on the displacement–
time graph where the curvature was zero. The curvature would change from positive
to zero at the start of that portion of the graph and from zero to negative at its end. The
acceleration during that portion of the graph would be zero and the gradient, the
velocity, would be constant.
When you have the above information about what the changes in gradient and
curvature on a displacement–time graph represent for velocity and acceleration then,
with experience, you will find that you can roughly – and non-numerically – sketch the
velocity and acceleration patterns to obtain further movement patterns for qualitative
analysis. All quantitative analysis packages will do this too, and provide more accurate
velocity and acceleration patterns; these can also be analysed qualitatively through their
shape as well as quantitatively.
Figure 3.8 Hypothetical centre of mass displacement (continuous black curve), velocity (dashed black curve) and acceleration
(blue curve) variation with % race time for a novice sprinter.
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