Shoes and Energy
Date: Winter 2011-2012
A company named Athletic Propulsion Labs designed a basketball shoe that they claim makes a player jump higher. The shoe has "Load and Launch" technology built into the front sole of the shoe that is some sort of spring mechanism. The way I see it, this mechanism cannot allow a player to jump higher because only an external force can produce motion. The spring mechanism is internal to the body (including the player, shoes, socks uniform) that is launched into the air and an internal force cannot produce motion. Despite this, the shoe has been tested and found to provide additional lift. The shoe has actually been banned by the NBA because it provides an unfair advantage to players who wear them. How could this shoe possibly work?
The problem is with the idea that only an external force can produce motion.
That is not quite right. It is true that you cannot change your
pushing against something else, but it is not true that you cannot do the
The springs work because they store the energy of a player's downward motion
and release that energy to push the player upward. Kangaroos, and other good
hoppers, do the same thing with tendons in their legs.
I do not understand your "only external forces" principle as you apply it.
By your usage, the leg muscles would be internal too,
but we know they push the body into the air...
If some player wore shoes with 4-inch-long helical compression springs
poking down from the bottom of the fore-soles,
could you imagine that helping? I think I could.
I think maybe the principle applies to a single rigid body
but not to flexible, jointed (multi-part), dynamic (having time-changing forces) bodies.
If there was a strong metal bracket clamped to the center of mass (around the waist)
reaching down underneath the shoes and all they contain,
then the player's lower half would be a rigid body
and his legs could not make him jump
and all the shoes with springs in the world would not help.
To propel him into the air, something would have to get underneath the bracket,
between bracket-bottom and the floor, and make expansive force there.
That would be force external to the rigid body.
The poor guy wearing the bracket might still be able to jump about 1/4 inch high
by bending at the waist then snapping up straight.
If he was a true athlete. (Not me.)
Throwing his arms upward would be a big part of it too.
So maybe we should extend the bracket upward to grab his neck and arms too.
Then he is really a rigid body and only external forces could move him,
and that prediction from principle matches one's intuition quite easily.
Anyway, I see two kinds of spring this shoe could contain:
1) a pancake-like compression spring between top and bottom of the fore-sole
2) a lever spring with its flexure at the heel,
which would need to somehow grab the ankles or shins to make torque around the heel,
applying that torque to the front of the foot with respect to the heel.
2b) a compression-like spring from fore-foot to someplace on the shin or higher
arranged so it's force-axis is less than 45 degrees from vertical,
would be pretty much the same thing as (2)
You can see videos of inventions like this on the web;
a sweeping L-shaped spring that runs from below the foot, around behind the heel,
up to some point on back of the shin near the knee, also having some attachment to the heel.
This is very effective, even dramatic; guys wearing them go galloping around with big easy bounds.
These would be clearly unfair for both high-jumping and running competitions.
I am not sure how they can get a force-point to the shin or upper ankle as in (2) or (2b)
all packed into a basketball shoe, unless it has an extremely high top.
So I am vaguely guessing that your shoe must be more like (1) inside.
But I have not seen it yet.
A model to replace the rigid-body model?
Consider each long bone a rigid body, with energy applied between them by muscles.
Unfortunately it is a complicated model;
it does not give you an external-forces principle for the body as a whole.
But it does let you think some about jumping.
The foot is made of many small bones,
so maybe the length of the foot is an elastically bendable passive body, a flexy plank-foot,
with some muscle running from the shin and heel to the mid-foot, to pull it up or down.
I guess I would neglect toes altogether. But I am a beginner at modelling this.
I think within 5 years you will be able to find freeware
with which you can set up and try such machine-models or body-models graphically.
getting both pictures and crude numbers.
It'll make it easier to check out your mental models.
Somebody has such software today, but far from free.
Once you weed through the advertising hype, it appears that the intended principle of operation behind these shoes is no different than the super flexible poles that pole jumpers use. That is, energy is stored during one phase of the jump, and then released at the moment of the jump which adds propulsion to the jump.
But with high jumping, the large flexible pole can store a huge amount of energy at the start of the jump, and release it at just the right moment to add this energy to the jumper, helping him to jump higher.
But things are vastly different with a shoe. Stated simply, any mechanism small enough to fit in a shoe, is simply not going to store significant amounts of energy. This series of before and after photos.... http://www.nicekicks.com/2010/10/athletic-propulsion-labs-review-jury/ ...clearly shows that there is essentially no performance difference between ordinary shoes and the APL shoes.
So this appears like a marketing gimmick that is based on reasonable theory, but in practice, the added energy (if any is added at all) is too insignificant to make any difference in performance. But that won't stop non-scientific folks from rushing to buy these shoes.
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Update: June 2012