Introduction to Sports Biomechanics: Analysing Human Movement ...

INTRODUCTION TO SPORTS BIOMECHANICS
LINEAR MOTION AND THE CENTRE OF MASS
A sprint coach might want to know how long it takes one of his or her novice athletes
to reach maximum horizontal velocity, often referred to as running speed, and what
happens thereafter, when running a 100-m race. To do this, we would need to record
the position of the athlete’s centre of mass (we will return to how we can do this in
Chapter 5) at equal intervals of time – we can do the latter using a video camera. Let us
assume for now that the movements of a particular point that we mark on the pelvis
closely approximate those of the centre of mass; we could obtain the positions of
this point from biomechanical software packages for qualitative video analysis, such
as siliconCOACH (siliconCOACH Ltd, Dunedin, New Zealand; http://
www.siliconcoach.com) and Dartfish (Dartfish, Fribourg, Switzerland; http://
www.dartfish.com). This example is a curvilinear movement, but we make it rectilinear
by ignoring the vertical movements of the sprinter and focusing only on the horizontal
ones. Our geometrical pattern in this case represents the horizontal path taken by the
centre of mass during the time of the race and might look something like Figure 3.6,
a pattern of the centre of mass movement – its horizontal displacement – over time.
It is often said that a picture is worth a thousand words, so let us see what we can
deduce from the movement pattern of Figure 3.6, which, as we saw above, is known as a
‘time series’, because we are looking at the pattern over time. But first, a few important
terms.
The time-series graph of Figure 3.6, which is a special kind of pattern, is called a
displacement–time graph – this, for all important purposes, is the same as a position–
time graph. The rate of change of displacement or position with time is known as
velocity; the rate of change of velocity with time is called acceleration. We can find
important information about velocities and accelerations from a displacement–time
graph qualitatively, without recourse to any mathematics, if we accept two extremely
important relationships:
Figure 3.6 Hypothetical horizontal displacement of the centre of mass with time for a novice sprinter.
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