Re: trebuchet

["Donald E. Simanek" <dsimanek@EAGLE.LHUP.EDU>]

On Sat, 13 Feb 1999, Ludwik Kowalski wrote:

> If I had time I would try to simulate the mechanism (see below)
> with Interactive Physics. It is designed for this kind of simulations
> and allows us to "measure" everything we want. But this would not be
> a reliable way of getting the efficiency. My guess is that in the
> absence of friction (at joints), without air resistance, and for the
> throwing arm (and rope) of negligible mass, the simulated efficiency
> would be 1. By the way, air resistance is not simulated realistically
> in the program.

Good, we don't need to include resistance to get an upper limit on
efficiency. The guess that that the efficiency might be 1 isn't the case
here. There's a "gotcha" which makes this most problem especially
interesting.

In cocking a siege engine, one lifts the counterweight, which gives the
machine potential. energy As the counterweight falls, *some* of that
energy goes to the projectile. Some of it is kinetic energy of the
counterweight at the point the projectile is released. This kinetic energy
of the counterweight is wasted, and accounts for the maximum efficiency
being less than one.

Now if, for a given height of fall of the counterweight, we can, by
modifying the mechanism, make the final KE of the counterweight *less*
than before, then we increase the efficiency. That's just what the *sling*
on the end of the rigid arm of the trebuchet does. But I've already given
away too much of the answer.

There's a parallel in the various baroque modifications of target and
hunting bows these days, using eccentric compound pulleys which are
designed to modify the rate of conversion of potential energy to the
kinetic energy of the arrow. And the germ of this clever idea originated
with engineers who modified the catapult into the trebuchet in the 13th
century or earlier! Still, before we think them too clever, the idea can
be considered to have stemmed from the sling and stone thrown with the
human arm, where the same principle applies. And we, with just a little
physics, can see the commonality of concept, which even the best
historians of science don't seem to have noticed.

To merely tinker a mechanism to make it better is good. But far more
satisfying is to *understand* why it is better, and what underlying
princples account for the difference. That gives us the power to use
those principles in many other ways.

        -- Donald

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Donald E. Simanek
dsimanek@eagle.lhup.edu                 http://www.lhup.edu/~dsimanek
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