The Virtual Trebuchet

Drawing of a small trebuchet

My Virtual Rockchucker is finally online again, now disguised as a Java applet! Much revised, updated & improved too. The old version, from 1991, was written in Simula. The most prominent upgrades in this release are:

My old model clearly had it's weaknesses, the main throwing arm was massless, and the sling off the wall. A while ago I found the paper 'Mathematics of the Trebuchet' by Donald B. Siano, and was inspired to try again. I now use his 'unconstrained sling' model, and refer you to the paper and his web-page 'The Algorithmic Beauty of Trebuchets' for more details.

I actually made the 'Ballistics computer' to study Napoleonic-era cannonfire, but it works fine with the treb as well! It features a simple target too, so now you can play 'Hit the Monkey' with your treb designs...

Of course there are a few shortcuts in the model... As usual (?) when we deal with mathematical models of physical phenomena, we live in a perfect world without friction, where the idea that wooden beams and structures will bend or rock under the influence of a mere ton or two of stones is ridiculed. There is, however, evidence indicating that this may not be entirely true. E.g. the sound of catapults I have built...

How to use this thing

If you need a briefing, I recommend The Grey Company's page on Simple Weight Powered Trebuchet Theory as an introduction to how a treb actually works.

Enter the desired dimensions, and press the 'Load' button. The applet will now draw the treb you have specified, in the ready to fire position. The vertical bar in the lower left corner is just for scale, it's 1.8 m high. If your design looks awkward, fix it, if it's OK, press the 'Fire' button and dive for cover.

I have made a page of some sample experiments to get you started.

Note that the 'Sliphook angle' adjusts the moment of release of the sling (and projectile).

The Virtual Trebuchet

You need Java!

The results from the trebuchet simulator is passed on to an instance of my 'Ballistic Computer' below. It will enable you to see the trajectory of the virtual rock you just threw (Hey.. where'd it go?)

Ballistic Computer V1.2

You definitely need Java!

The output

The virtual trebuchet: The simulations are run as a series of descrete timesteps, and the positions of the sling, throwing arm (beam) and 'main weight strap' are drawn (in black) at specified intervals. You can change the timestep (Delta T) and the plot frequency. The simulator will always assume that the rock is still in the sling, and stop when the beam is vertical.

Two other positions are also plotted:
The red lines show the situation at the moment of release, i.e. where the rock would have left the sling.
The blue lines indicate the position where the projectile has the highest kinetic energy (speed).

The Ballistics computer: The blue trajectory is that of a perfect sphere of the given weight and density. The drag is found from standard formulas, asuming ground level conditions.

If you click on the 'No Drag' button, you'll get a green curve indicating the trajectory you would get without air resistance.

'Max range' is the distance to the point where the projectile hit the ground, it doesn't matter if you hit the target or not. The 'Momentum' is the projectiles momentum (mass * velocity) at the distance of the target. Ie. it's the punch you'll give the target if you hit it.

Do the results hold water?

Yes and no! You can't design a trebuchet with these programs, and expect identical results in the real world. The models are to simple for that, but they shouldn't be too far of the mark.... I made this simulator to be able to study the effects of alterations in the design parameters.

Tuning a treb to optimal performance

Most people designing catapults seem to use 'optimal' as a synonym for 'maximum range'. I see optimal performance as being able to design & trim a device to hit a given target at a given range, and with enough force to ruin it's day. We are of course talking about elevation here, azimuth corrections just require manpower (and lots of it considering the size of these things).

As in real life the elevation can be adjusted by bending the beams sliphook. You do that by changing the beam/sling angle for which the procectile is supposed to leave the sling. Changes in the dimentions of the treb itself will naturally have dramatic effects on the elevation. To maximise the projectiles velocity and kinetic energy, the design must be trimmed so that the red (release) lines are as close to the blue (max. lines as possible. You should also endeavour to get the trebs's energy ratio as high as possible, we don't want to waste time and energy by hoisting tons of rocks for no good reason.

A note on the energy ratio

My energy ratio is the kinetic energy of the released projectiles ((Mp*Vo*Vo)/2), as a percentage of the total energy used to hoist the mainweight (Mw*g*h). I have seen several such performance indexes but I prefer this one, as it compares the 'usefull output' to the effort needed to prepare the thing for firing. Furthermore there are no dubious range estimates involved.

Features (bugs)

The trebuchet doesn't always automatically trigger the trajectory calculator. Hit both the 'Clear' buttons and try again.

The momentum seems to be somewhat optimistic, I'll look into it.

The trajectory calculator will only consider the y-co-ordinate of the point of release. If you plot several trajectories on top of each other, they may (will) be slightly offset in the x-direction.

There seem to be portability problems on some browsers! The treb doesn't always work properly with Netscape Comunicator, odd results and wrong colors have been reported. If these applets go loco on your browser please mail me a description of the problem.
Netscape Navigator 3.04, 3.01 and 3.01S. should be OK though.

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