Re: trebuchet

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

One doesn't often see the trebuchet mentioned in physics texts, yet it is
a very interesting mechanism, and suggests some questions worthy of
discussion here.

The trebuchet, invented at least as early as the 13th century, is
generally acknowledged to be the most powerful of all mechanical siege
engines. It has a counterweigted arm at one end and a sling at the other.
During the 45 degree swing of the arm, the weight on the sling moves
through a curve which increases its radius by, perhaps, a factor of 2,
before it releases from the curved pin which holds it.

They were used to sling projectiles beyond arrow range, exceeding 300
yards, but probably not more than 350 yards. The counterweight was about
20,000 lbs. The largest trebuchet had arms of about 50 feet, to sling
stones of 300 pounds, according to Payne-Gallway.

Villard de Honnecourt, a 13th century French engineer, described a
trebuchet with an 8x12x12 foot box of sand as counterweight. If full, this
would weigh over 80 tons. Accounts of this era were often exaggerated.

So, here's the question for physicists. Why does this articulated-arm
engine convert energy to the projectile so much more efficiently than
rigid-arm engines? Modern trebuchets (often seen at Medieval fairs) have
achieved efficiencies as high as 64%, according to the literature, with
100 lb projectiles and a range of over 600 feet and a mass ratio
(counterweight/projectile) of 20.

I think it's no coincidence that Honnecourt also made the first known
overbalanced wheel proposal for a perpetual motion machine. Of course it
didn't work. But it used the articulated arm principle to move a mass from
small to large radius--very much like the trebuchet. Was he thinking that
this motion increased energy? Or that it increased efficiency so much that
the efficiency could be greater than 100%? Alas, the literature on history
of physics seems to be silent on this point, and since this history is
written by historians, not physicists, it doesn't address this question
about efficiency, nor the connection to the perpetual motion machine
proposals.

But if you are going to introduce the trebuchet into a physics course, I
suppose you'd feel obligated to delve into the history of it, and also do
the physics of it by analysis of the energy and angular momentum changes
in the device during the swing. Otherwise, why do the experiment? Good
luck, for it isn't simple. Perhaps someone will do the general
mathematical analysis and post the results here.

It might be very instructive to construct rigid-arm and trebuchet devices
of the same scale and compare their performance with different mass
ratios, different arm/sling ratios, different angles of release, etc.

While the trebuchet was a formidable device, slinging boulders and even
dead horses into the enemy stronghold, it had a very great disadvantage.
The forms used in medieval times couldn't be accurately aimed, for the
release point was variable, affecting the range by a large amount.

If there's a medieval fair in your area, have your students visit it to
examine a full-sized trebuchet and see it in action.

        -- Donald

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



On Thu, 11 Feb 1999, Pete Joenks wrote:

> Does anyone have any plans to build a small scale Trebuchet catapult?
> Most of the pages I find on the search engines are for huge machines.  I
> kind of want this to be a class project for all my class or if managable
> enough a project for small groups.
>
> Thanks
>
> Pete