<< In Dr. Siff’s example of the twin lifters with body mass of 60 kg, one
athlete, Ted, squats 100 kg. Ted is posited to perform this squat with an
acceleration rate of 1.5 meters/sec^2. The combined weight of the lifter and
the load is 160 kg x 9.8 m/sec^2 or nearly 1570 newtons. That reaction force
thru the platform is necessary to merely stand and perform a constant
velocity lift. To accelerate his body and the load upward at 1.5 m/s^2,
would require an additional 160 kg x 1.5 m/s^2 or 240 newtons (upper limit
calculation of acceleration requirement).
The platform should register a peak force in the neighborhood of the sum or
approximately 1800 newtons
during the lift.>>
***Thanks, Paul, for picking that up. It is a real pleasure to have some
more physicists or engineers wandering into the sporting field to give it a
new dimension.
I gave a figure of 1300Newtons as measured on the force platform. It should
have been 1800N. I clumsily typed in a “3″ instead of an “8″ (after
moderating numerous messages in the early hours of the morning, that may be
understandable).
One small point, though – during squatting, the lifter does not accelerate
his entire body mass upwards, but only the part of the body that is actually
being moved. In Olympic lifting, the lifter may actually leave the platform,
so that comparisons of weightlifters and powerlifters have to take this into
account. The figure that I quoted came from an actual force platform
recording with a 60kg squatter and was not derived from this equation
(although the theoretical and experimental results were quite close for this
simple movement):
Force F = mg + mA = 160 (9.8) + 160 (1.5) = 1808 N
(where g = 9.8m per sec squared in the gravitational acceleration and A is
the upward acceleration imparted by the lifter).
The actual acceleration was 1.37 m per sec squared – I simply gave 1.5 m per
sec sqd as a roughly rounded off order of magnitude for the purposes of
acceleration. During relatively heavier lifts, this acceleration can drop to
below 1 m per sec sq.
<<This is about 3 g’s or three times body wt. This force is still far below
the reaction forces measured by the platform on the twin, Tom, when
performing his ‘plyometric’ feats of running and jumping; but there
are other differences in execution that may bear consideration.
In dynamic situations, where a change in the momentum of the body in question
is the main effect sought, thrust is the requisite factor. (Yes, this is
rocket science actually.) The momentum change depends on this thrust or
impulse applied. [Force x time] gives us the impulse quantity and is
equivalent to the change in momentum of the body under impulse. That is: the
body undergoes a change in momentum of [mass x change in velocity] during
the execution of the impulse (the jump ).
Well, if the squat takes two seconds to perform, that effort is equivalent to
an impulse generation of 1800 newtons x 2 seconds or 3600 newton seconds.
Tom may perform his jump with a .2 second time of foot contact, representing
an impulse generation of 3100 newtons x .2 seconds or 620 newton seconds.
Tom’s effort represents only about 1/5 the impulse generation ability of
Ted’s effort in the squat. >>
PROBLEMS IN USING ‘IMPULSE’
*** As you know, the definition of Impulse comes from the general expression
of Newton’s 2nd Law in differential form, namely (where V is the velocity as
any instant):
F = d (MV)/ dt (Rate of change of momentum)
F = M.dV/dt + V.dM/dt
Since the second term refers to a situation in which mass is changing, it
drops out of calculations for lifting a bar, though in rocket science, the
ejection of mass from the rocket is what provides the propulsion. So, in
fact, we are not strictly speaking about ‘rocket science’. In lifting, the
mass of the combined lifter/bar system is constant. We are left with:
F = M.dV/dt which may be rewritten:
F.dt = M.dV
If the time interval dt is extremely small, as in a true rapid impulse, it
may be replaced by a finite, but still very small value called (delta t),
which I am going to write as T simply because we cannot use Greek symbols in
ordinary email. This approximation is valid only if the time interval is
very small and neither force nor velocity change during the period when
impulse is being generated. So, our approximation becomes
F.T = M.V (where MV simply is the momentum of the moving mass M)
In your analysis, you have applied the definition for impulse to a situation
in which the time of action, T, does not approximate to the differential dt.
Moreover, the force and velocity of the bar are changing throughout the
squat. In other words, we would rather have to consider the integrals of
the functions F.dt or m.dV in order to analyse the situation correctly.
<<The jump peak forces aren’t experienced at the ROM angles encountered at
the bottom of a deep squat and
therefor jump reaction forces can hardly be used as evidence of the safety of
such a squat at equivalent loading (weight) levels. >>
***Quite correct, but we also have to consider at least two other factors in
this regard, namely the mechanical stiffness of the athlete and the damping
ratio of the body, both of which change with athlete and characteristics of
movement.
Possibly, the easiest way to appreciate the effect of these factors is to
liken the body to a car. Among other things, the shock absorbers of a car
determine how shock will be transmitted to the vehicle and how stable the
vehicle will be under different motion conditions. If the mechanical
stiffness of the shock absorbers is high, then any shock will be transmitted
very unattenuated to the vehicle, but the vehicle will be very stable under
sharp cornering conditions.
This is similar to the situation encountered in running and jumping, but not
in squatting, where the knee goes through a large range of movement. In
other words, though it is important to consider what you implied with your
computations about impulse, one also has to consider how much of the impulse
or energy is actually transmitted to the body and its joints. In this
respect, running and jumping are far worse ‘offenders’ than lifting heavy
weights.
Interestingly, the use of shock absorbing running shoes tends to increase the
mechanical stiffness of the body, so that we have the apparent paradox that a
measure implemented to reduce stress on the joints of the body can actually
can achieve the very opposite. Scientists believe that the body attempts to
maintain approximately the same overall stiffness no matter what one wear, so
that any decrease in stiffness offered by shoes results to an increase in
stiffness elsewhere in the body, such as the ankles, knees and hips.
In saying all of this, don’t for one moment think that I support the idea of
action being taken to prevent children participating in running and jumping
sports. I simply contrasted lifting with these activities to point out the
serious oversimplifications being made when claims are made that heavy
lifting is more stressful than other unloaded physical activities.
In fact, research by colleagues of mine seems to show that the incidence of
joint degeneration and osteoporosis in men and women is significantly higher
among those who are sedentary or indulge in milder, non-impulsive
activities. If anyone is interested in this information, I can paste some
relevant sections from “Supertraining” and “Facts & Fallacies of Fitness”
into future letters. The Table of Contents of these books appear at:
http://24.16.71.95/SPORTSCI/JANUARY/textbooks_by_m_c_siff.htm
Dr Mel C Siff