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Muscle Speed

The extensor muscle is very strong, but strength is only half the issue. To get a good jump or kick, the force has to be applied quickly. And muscles are not very good at that.

There are two aspects to the problem:

  1. The muscle would seem to have to develop force quickly. The extensor muscle starts off completely relaxed and then it has to build up force to the maximum that it is capable of, and it has to do this before the animal leaves the ground, or else it will just be wasting force.

  2. The muscle would seem to have to shorten quickly. The leg has to move very quickly, and if the muscle moves the leg, the muscle itself would seem to have to shorten quickly as the leg extends (although not as quickly as the end of the leg itself, due to the lever ratio).

Let us look at these two in turn.

Force Development

If the final take-off velocity is 3 m s-1 the average velocity during leg extension is probably about half that (1.5 m s-1). The total leg length is only 45 mm, so the force has to go from zero to maximum within about 30 ms (that is, thirty thousands of a second!). Can the muscle do that?

muscle force development
The extensor muscle was stimulated electically with a single pulse (blue) or multiple pulses (red), while measuring the force at the end of the tibia.

If the muscle is stimulated with a single pulse it develops its peak force quite quickly, but the force is tiny. If the muscle is stimulated multiple times in quick succession (50 Hz) much more force is developed - about the right amount to drive the acceleration during a jump. However, the force takes about 300 ms to reach its peak, which is about 10 times longer than it takes to extend the leg during take-off. This seems to be a conundrum.

Shortening Rate

A fundamental property of muscle, which has been known for many years (see Hill, 1950, in the Bibliography), is that if you make a muscle contract so as to get high force out of it, then it only shortens very slowly, if at all.

On the other hand, if you make a muscle shorten as quickly as possible, then you don't get much force.

Think of climbing a flight of stairs. If you are carrying a heavy backpack, you stagger up slowly, gasping for breath at every step. If you are not carrrying anything, you bound lightly up, two steps at a time (maybe).

When you are carrying a heavy load your muscles have to contract with a lot of force in order to lift the load, and so they can only contract slowly. When you are not carrying much, then your muscles do not have to produce so much force, and they can contract much more quickly.

The physical property which relates force and rate of shortening is power (which is force multiplied by velocity). If you make a muscle contract at a force and speed which maximises power, then it only contracts with a force of about one-third of the maximum that it is capable of producing.

[Science stuff: energy and power]

A Problem?

So in terms of speed, the extensor muscle seems to fail both on the rate at which it can develop force, and on the rate at which it can shorten. It is perfectly obvious that grasshoppers can jump well, so somehow they must be able to overcome this fundamental muscle limitation. How do they do that?


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