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Catapults and Power Amplifiers

 

Before thinking about how grasshoppers solve the power problem of muscles, let's think about how humans solve the same problem.

Exactly the same difficulty faces a human who wants to throw something as faces a grasshopper that wants to throw itself (after all, that's what jumping is - throwing oneself using ones legs). A good throw needs a rapid and forceful arm movement, but as we have just said, muscles can produce high force or high speed, but not both.

Humans have solved this problem by using tools, such as the catapult, or bow-and-arrow.

archer

What is going on here?

  1. The archer draws back the bow slowly. This means that her arm muscles can contract with the maximum force of which they are capable.

  2. The energy of the muscle contraction is stored in the bending of the bow.
  3. The archer lets go of the bow string, and ...
  4. The bow springs back, transferring the energy from the bow to the arrow.
  5. The KEY POINT is that although the bow is drawn very slowly, it springs back very quickly. It can do this because it does not suffer from the same trade-off that muscle does; the bow can move with both high force and high speed.
  6. The arrow zooms off towards the target, and the rest is history.

Thus in summary, the archer uses her arm muscles to store energy in the bow slowly, and the bow then transfers this energy to the arrow quickly. In physics terms, the bow is acting as a power amplifier.

This same principle is used in all sorts of devices intended for hurling projectiles (usually sharp and/or heavy, at an enemy, or possibly dinner): the catapult, the bow-and-arrow, the crossbow, the wind-up variety of those Roman seige machines for chucking huge rocks (ballistae), the mechanical clay-pigeon launcher, the air-gun etc., etc.. In each case some form of mechanical spring acts as an intermediate energy store. Muscles are used to load the store at low speed, and the store then spits out the energy at high speed.

So what has all this got to do with grasshoppers? The answer is that grasshoppers developed their very own catapults about 100 million years before humans ever thought of them. This catapult is built into the back legs of every grasshopper.

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