When is lifting an Advantage? In response to Ron's 10/9 post.

Below is the message I sent to Jack Mortland and Elaine Ward:

Dear Jack and Elaine,

This is in response to the article by Ron Daniel that appeared in both
of your publications.

Towards the end of the article Ron made the comment ""Again, traditional
physics says as soon as the walker in not on the ground pushing, he or
she is starting to lose forward velocity.  That is why a hurdler, when
clearing a hurdle works very hard on getting the lead foot down on the
ground as soon as possible rather than continuing a nice long float." 
The only force acting on a walker or runner while in the air is the
force of air resistance.  It is easy to show (see addendum below) that
velocity loss while in the air is negligible for both the walker and the
hurler.  In fact, the walker would only loose 0.0079 ft/sec while off
the ground for the 0.02 sec, the estimated maximum time for which a
"float" would be invisible to the judges.

Actually, the hurdler does not slow down appreciably either.  The reason
a hurdler gets his lead leg down as quickly as possible is not because
of deceleration do to air resistance, but because he wants to make
contact as close under his center of mass as possible and avoid the
braking which would occur if contact was made in front of the center of

Then I began to think about the problem of walking as fast as possible
within the constraints of the rules of race walking.  Starting from
velocity equals stride frequency times stride length and because of
geometric constraints imposed by the contact rule, we might  conclude at
first that the only way to increase speed is to increase stride
frequency.  The legs are of fixed length and must form a triangle with
the ground, although moving the hips fore and aft and up and down does
provide some leeway.  However, often walkers are not able to take
advantage of their full geometric limits, to say nothing of any flight
phase undetectable to the eye of the judges.  In 1953 A. V. Hill
determined that the force of muscular contraction is inversely
proportional to the speed of muscular contraction.  Therefore, at high
stride frequencies the push to the rear by the walker decreases.  The
vertical component of force must always balance the walker's weight. 
The vertical component of force decreases and the horizontal component
increases as the angle of the trailing leg decreases relative to the
ground during extension to the rear.  It is impossible for the walker to
extend beyond the point where the vertical component of force is less
than the walker's weight.  Thus, it can be seen that at high stride
frequencies, stride length to the rear can be compromised.

What happens when a walker attempts to maintain a high stride frequency
with an insufficient push-off?  The walker, because he cannot support
himself at full extension, takes a step with a very short posterior
segment.  Another consequence of this situation can be the athlete
snatching his trailing foot off the ground without full extension to the
rear.  This often occurs before the advancing foot contacts the ground,
resulting in a loss of contact (that should be) easily visible to the

Therefore, a walker should never attempt to walk at a stride frequency
which would compromise push-off, because the loss of velocity due to
shortened stride length more than negates velocity gains produced by the
increased frequency, and also for questions of legality.  One of the
hallmarks of a world class walker, perhaps the singular most important
characteristic, is a powerful full extension to the rear, still
performed at a high stride rate.  The push-off at full extension, if
strong enough, will also produce a low flight phase that will be
undetectable by the judges but still extend the stride.

>From the above discussion is would seem that walkers should train to
develop force at high rates of muscular contraction in the hip and ankle
extensors through appropriate training.


For the range of velocities found in track and field the force of air
resistance on an object is given well by the formula

    F = (1/2)(sigma)(rho)Av**2,

where sigma is the drag coefficient of the object, rho is the density of
air, A is the cross sectional area of the object, and v is the velocity
of the object with respect to the air.  The human body is not very
streamlined; it approximates a flat board moving through the air, and
thus sigma is approximately = 1.  The density of air at sea level is
about 1.20 kg/m**3.  The height of a typical male elite 20k walker is
approximately 1.65 m and his average width is probably about 0.42 m,
giving a cross section of about 0.7 m**2.  Walking at a 1:20:00 pace for
20k, his velocity is 4.17 m/sec.  Using these values, the air resistance
is seen to be 7.22 N.  A typical mass for an elite male walker would be
60 kg.  Assuming a flight phase of 0.02 sec, which would be
invisible to the eye, the decrease in velocity during the flight phase
would be 0.0024 m/sec, a totally insignificant amount.  Even if the
walker were to be walking into a very stiff wind, the loss of velocity
would be no more than three or four times this quantity, still

In fact, when we repeat the above analysis for the case of the high
hurdler, we arrive at a similar conclusion.  A typical elite male 110 m
hurdler is about 1.85 m tall and has an average width of about 0.45 m. 
Because he lays out over the hurdle during clearance, his average cross
section over the hurdle is probably only about 2/3 his cross section
when running erect.  This would give a cross section of 0.592 m**2.  If
he runs a time of 13.00 sec, he has an average speed (allowing 0.80 sec
for the start) of 9.02 m/s.  (Amazing that a 110 hurdler is only going a
little over twice as fast as a 20k walker!)  The hurdler therefore
experiences an air resistance of about 28.88 N.  80 kg would be a
typical mass for an elite hurdler.  If we accept the traditional rule of
thumb for time lost per hurdle clearance of 0.2 sec, we find that an
elite hurdler decelerates approximately 0.072 m/sec additional beyond
that lost in a normal sprint stride.  This amount is also small, even if
we would consider the effects of running into a headwind.


Wayne T. Armbrust, Ph.D.
Computomarx (TM)
3604 Grant Ct.
Columbia MO 65203-5800 USA
(573) 445-6675 (voice & FAX)
"Know the difference between right and wrong...
Always give your best effort...
Treat others the way you'd like to be treated..."
- Coach Bill Sudeck (1926-2000)

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