phsstpok's Rule For Trebuchets

A simple formula or rule of thumb for determining a number of values associated with the design of Hinged Counterweight Trebuchets.

This writeup assumes that the reader is already more or less familiar with how a trebuchet works, but is interested in pushing it to the limit.

This message was posted to the old version of the Catapults Message Board, (hosted and moderated by Ron Toms) in response to a question about determining the appropriate mass of projectile for a trebuchet of given dimensions..

Subject Re: The projectile
Posted by phsstpok on 2002-14-05 02:32

Too light a missle leaves more energy in the machine which must be disipateted through the frame. At the far end of too light is a dry fire (no missle at all) which can be very hard on the frame.

You're right that there comes a point where lighter missles won't go much, if any, farther than heavier missles. For my own experiments I used one and two liter soda bottles filled with water and varied the amount of water in them as well as sling lengths and pin angles.

As for what you should throw. All machines are a little different and there is no definite answer. Here is a rough guideline for HCW machines. Multiply the beam ratio by twenty. Divide your counter weight by the result and that will give a good starting point for your missle weight.

(bold emphasis added by me)

Since the person who posted it uses the handle "phsstpok", without capatalisation, I'll continue to write it that way. His handle, by the way, was borrowed (with a minor spelling change) from the character "Phssthpok", in Larry Niven's science fiction novel Protector.

URL of that posting:

(If the above diagam does not look quite right, select the text and paste it into a text editor, using a mono-spaced typeface such as Courier)

Generally, you design a trebuchet with the idea of obtaining the maximum range or distance at which you can throw the payload. Common sense suggests that if you add more counterweight mass, you will obtain a greater range. You will, but only up to a point where it is no longer practical to add more CW mass.

The reason for that upper practical limit is that as the CW mass increases, (assuming that the mass of the beam is negligible) the mass of the payload becomes negligible, and for all intents and purposes the CW is in "free-fall", accelerating downward at 9.8 meters per second^{2, as if it was simply dropped
off a cliff}. It does not matter how much mass you add to the counterweight, it will not fall any faster than free-fall. Since the counterweight cannot fall any faster, the arm will not pivot any faster, the sling won't whip around any faster, and the payload won't be thrown any faster. Since the velocity of the payload does not increase, neither will the range.

As I've said, it's simply a "rule of thumb". The mass of the beam itself does have some effect, because it is not some ideal massless beam, it has inertia. No matter how small the payload mass is, the beam itself still has to be brought from rest to rotation, which takes some energy. I suppose if you found the centre of gravity of the beam and treated that as some additional mass tied onto the beam somewhere between the main axle and the release pin, but unless the beam mass was something like, oh, maybe greater than 10% of the CW mass, it's probably not worth calculating. Suffice it to say that it's not taken into consideration for phsstpok's Rule.

You have selected (or have been given) a particular CW mass, a payload, and a beam length. Where do you place the hole for the main axle?

There is a small trebuchet competition, You are allowed a maximum height of 1 meter, when it's in the cocked position, and the supplied ammo will be tennis balls.