In this section I use the force concepts from the first part of the Top Speed analysis and
the wind drag data from the second part to continue the speedskating technique analysis.
The result is a scaling law for basic skating parameters. This scaling procedure shows
how to increase one's top speed.
The following panel of figures shows our stick skater
with stroke length "Y" in the sideways direction " y". He moves with velocity V in the " x"
direction. His speed is constant at his present top speed because his forward thrust
force [F*sin(Angle)] is balanced by a backward wind drag force [Fdrag].
The far right figure shows two complete strokes of the right leg. Each stroke takes a time "t"
and his stroke frequency is:
f=1/t.
As shown in part 2, the drag varies as velocity squared so I define the wind drag force
:
Fdrag = k*V*V
where V = |V|.
Now if we require force balance (thrust=drag) at top speed we find:
F*sin(Angle) = k*V*V.
Assuming that he is at high speed so that the skate angle "Angle" is small, I approximate
sin(Angle)~tan(Angle)=Y/V*t = f*Y/V so the force balance equation becomes
:
F*f*Y/V = k*V*V
or
:
F*f*Y = k*V**3
which has a simple (tri)
linear parameter scaling for the
skater's applied force, stroke frequency, and stroke distance:
F~V
f~V
Y~V
In words, for example, if you need to increase your top speed V by 10% to be the fastest
skater in the world you will achieve your goal if you can accomplish a 10% increase in your
leg strength, a 10% increase in your stroke frequency, and a 10% increase in your stroke
length.
This analysis ignored some other variables including: the grip performance of the wheels,
how you move your leg and ankle during the stroke (both in space and time), and whether you use a slap-skate
or klap-skate etc. My analysis assumed that you apply constant force F during your stroke.
If an analysis can be accomplished using more parameters it is likely that the improvement per
parameter need be even less than linear.
