View Full Version : Re: PP126: F-V PARADOX

Yves Roy
10-22-1999, 02:00 AM
Dear all, as suggested by Dr. Siff, I am sending this reply to the entire

As few people have already address the question with regard to the effect
of drag force upon objects of same size but different masses, I rather
would like to comment this issue on the basis of the F-V relationship

The force-velocity relationship is about muscle force and muscle shorthing
velocity. To address this relationship, you must first be able to control
the active state of the muscle (must be the same for all conditions).
Then, you can either use different muscle loadings (which must be constant
throughout the measurement), and look upon the resulting shorthening
velocity, or control the shorthening velocity (constant...), and look upon
the resulting muscle force output. One should be cautious to relate muscle
loading with an external load (weight), and muscle's shorthening velocity
with the velocity of the object. Such assumptions are true only in certain

with regards to the throwing example:

1) Active state needs time to rise. With light "baseballs", active state
does not have time to rise to maximal level (which I believe is the
intention of the thrower), because muscles will start to shorten as soon as
the force applied overcomes the resistance. A baseball throw uses the
stretch-shorthening cycle, and therefore there are no constraints upon the
initial conditions (i.e., static condition, 100% of active state). Muscle
force will thus be affected by the shorthening velocity of the muscle
(lower output force). For the sake of simplicity, I voluntarily ommit to
consider the stretch phase. Thus the impulse on the load (ball) will be
smaller as compare to if 100% of active state was reached. This is a true
application of the F-V relationship. I do not agree with those who
mentionned that the lightest baseballs (same size) should be the ones
reaching the largest velocity when the ball leaves the hand, and that
after, only air resistance (drag force) explains the difference in the
distance of throws. Rather, the ball having the smallest mass which will
still permits the muscle to reach 100% of the active state is the one which
will have the largest velocity (and thus go farther). As suggest by Dr.
Siff, this mass will be optimal, and not minimal.

2) The F-V relationship is about constant muscle loading... not constant
load weights. The work done when throwing is not strictly against gravity
(which would be the required condition to assume that the external load
equates with muscle loading, at constant velocity). Thus the constant
weight used in the example does not translate into a constant loading of
the muscle, nor a constant velocity of shorthening.

3) One must be carefull when using a performance such as throwing distance
to assess the F-V relationship. The F-V experiments from which the
relationship was presented, considered one muscle (I should say one bundle
or one single fiber...). I do not think that F-V can be assess the way it
was presented, because the performance criteria invloves the interplay of
many muscles acting at different time during the movement.

In summary, the conditions are in no way representative of those of the
classic F-V experiments. However, the F-V relationship still can be use to
explain why the lightest ball is not the one that will go farther,
irrespectively of the effect of air resistance.

Yves Roy

At 05:58 1999-10-21 EDT, you wrote:
>For newcomers to this forum, these P&Ps are Propositions, not facts or
>dogmatic proclamations. They are intended to stimulate interaction among
>users working in different fields, to re-examine traditional concepts, foster
>distance education, question our beliefs and suggest new lines of research or
>approaches to training. We look forward to responses from anyone who has
>views or relevant information on the topics.
>Here is an apparent paradox which concerns the force-velocity relationship
>which describes how force and velocity are interdependent in human movement.
>The relationship between force and velocity is seemingly well known. Maximum
>force is developed at (or close to, according to more recent research) zero
>velocity, i.e. under isometric conditions. Maximum velocity is attainable
>only if the load to be overcome is very small.
>In other words, velocity and force are inversely proportional to one another
>and the graph of force vs velocity is a typical hyperbola, crudely sketched
>below (if this transmits accurately over the Internet).
> | *
> | *
> | *
> | *
> | *
> | *
> 0 |________________*______ VELOCITY
>Let us now keep this theory in mind as we prepare to throw a series of balls
>all having the same size, say, about that of a baseball. The lightest weighs
>50gm and the heaviest 5kg. Our experiment is to find out which mass of ball
>can be thrown the furthest.
>You will find, apparently contrary to the theory, that the lightest ball will
>not be thrown the furthest. The honour will be bestowed upon a ball that is
>somewhere in between the lightest and heaviest balls. You can try this for
>yourself by throwing a normal table tennis ball and throwing a series of
>table tennis balls filled with sand, lead shot and fillings of other
>densities through a small hole drilled into it. Explain this apparent
>Does the above graph not indicate that the lighter the ball, the further it
>will be thrown? We cannot attribute any difference to air resistance,
>because the balls have the same area and surface characteristics.
>Will this be the same with lifts such as the squat, bench press, deadlift,
>curl or tricep pushdown or will one be able to accelerate and move to
>greatest velocity a light empty bar or broomstick?
>Will this still be the case if we use a tennis ball serving or baseball
>pitching machine to project balls of different mass, but identical size? How
>will your answer relate to the famous force-velocity curve?
>Contemplation on this problem may well assist unrelenting slow training
>believers in understanding the necessity for ballistic and neural system
>training, as well as the limitations of applying the laws of physics or
>physiology independently of one another in trying to fathom the nuances of
>applied strength science.
>Your comments are welcome.
>Dr Mel C Siff
>Denver, USA
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