# Efficiency in trebuchet design

1. Feb 3, 2010

### Ketman

The medieval trebuchet is a missile-throwing device, with a heavy counterweight on the short end of a beam that pivots about an axle fixed to a supporting frame. A sling is attached to the long end, and when properly "tuned" by adjusting its length, it will release the missile at exactly the moment the counterweight is directly under the axle, and will bring it to a halt by taking all the kinetic energy developed. Disregarding friction, there is a 100% transfer.

It's been observed that trebuchets throw further if the frame is on wheels, though the reasons given by constructors are a bit vague. I can see that that backward swing of the counterweight will exert a forward pull on the frame, which if allowed to roll forward will add to the propulsive force on the missile. On the other hand, if the machine is fixed to the ground, then instead of transferring some of its KE to the frame, the counterweight holds onto it and transfers it to the missile via the beam alone. Provided the beam is brought to a halt, there is still a theoretical 100% transfer of KE to the missile, or so it seems to me. What I mean is, I can't see where energy is being lost when the machine is fixed. It must be, since practical experiments show the wheeled-base machine to throw further, but I can't see why. What's the solution?

2. Feb 3, 2010

### Zula110100100

Not really sure, but are you taking into account the centripetal force into the original PE of the device?

Could it have anything to do with the reactive-centrifugal force that is applied to the shaft and eventually the bottom of the device being the same in either case in the non-wheeled version it is canceled by friction I guess and in the wheeled one it goes into KE of the whole device forward and so on..

3. Feb 3, 2010

### turin

I would guess that the issue is with conservation of momentum. In a fixed design, the heavy weight "recoils" against the Earth, and so there is an undesirable (though unnoticeable) momentum transfer to the Earth. If the recoil is instead made against the rest of the trebuchet, then the entire machine obtains some forward momentum, which is also (partially) transferred into the missile. Do you happen to know what % gains are typically achieved by the wheeled version vs. an identical fixed version? Based on my argument, I wouldn't expect a very high % gain.

4. Feb 3, 2010

### gmax137

Have you seen this in real life? The examples I watched at punkin chunkin did NOT do this, rather the counterweight would oscillate after the shot.

5. Feb 4, 2010

### turin

Although these guys probably represent the most enthusiastic group of trebuchet builders, I wonder how much thought they give to theoretical yield vs. "I rec'n we c'n win it with a bigger weight." Did the mythbusters make a trebuchet? Maybe I'm thinking of a different group.

However, I do find it hard to believe that 100% of the PE of the weight can be converted into KE of the missile.

6. Feb 4, 2010

### Ketman

Yes, I was thinking along those lines, the idea that the earth just absorbs the forces from a fixed-base machine, so they disappear into a sort of mush. The earth isn't a rigid surface, after all. But there was an international team that built a replica of Edward I's "Warwolf" trebuchet that destroyed the walls of Stirling Castle in the Middle Ages. They built small models first, and according to them, the wheeled version throws as much as 1/3 further. That's a huge difference, much more than can be explained by absorption.

7. Feb 4, 2010

### Ketman

Yes, especially those that use the hinged-counterweight, or HCW. The other kind is the fixed counter-weight - FCW. With the FCW, you have some chance of tuning the machine so that the weight comes to a halt. But with the HCW, the weight hangs several feet below the tip of the beam, so inevitably it starts swinging when the action begins, and there's no way you can tune it out. There is always residual KE that leaves the weight still swinging afterwards. Despite that, the accepted view is that the HCW is superior. The problem is, I don't know how you set up equal starting conditions to make a valid comparison. For the same length of arm at the long end, the HCW obviously needs a higher axle for the weight to clear the ground, or else a shorter arm at the short end. You can never make a level playing field. I intend eventually to build models to test all designs, but at the moment I have my doubts about the HCW as being more efficient than the FCW.

8. Feb 4, 2010

### A.T.

The level playing field could be: the same amount of input energy (potential energy of the counter weight).

But it depends what you see a the "cost". It could be also size.

9. Feb 5, 2010

### Ketman

Yes, fixing the starting PE value, and the weights of the counterweight and missile would be the obvious way. But the configurations in terms of arm ratio and angle would end up different. More importantly, for the same PE, the HCW system needs a higher axle, and therefore a more robust frame. In pure physics we don't bother too much about that, but in practice the constructional cost has to be a big factor in deciding how efficient the system is.

10. Feb 5, 2010

### turin

It's obvious; isn't it? For the same total length from pivot to ground, the FCW gives you more leverage, because the force that produces the torque is applied at the CM, whereas the HCW force that produces the torque is applied at the hinge. Why would anyone make an HCW? If you make an HCW, and then fix the hinge so that you now have an "equivalent" FCW version, the FCW version surely produces more torque.

11. Feb 5, 2010

### Ketman

Well, I wouldn't go so far as to say it's obvious. If I answered you in the voice of the average treb designer, I'd say the HCW "falls more vertically" (you could call that a merging of quotes from several sources). But it doesn't really. It's an optical illusion. Ignoring the swinging, the path of its descent is the same circular one as the FCW, but with the radial centre somewhere below the axle, rather than right on it. I'm not impressed by that argument. The reason I myself can imagine the HCW using its PE more efficiently is that it falls without rotation. With a starting angle possibly 30 degrees above the horizontal, a fixed weight will turn through a third of a revolution, so it ends up with a fair amount of rotational energy at the bottom. Some of that can be used, if the machine is on wheels, to drive it forward. But at least half of it is lost while the arm is mostly horizontal, due to the counterweight trying to lift the machine. If it succeeds by ever so small an amount, that's work done to no useful purpose. On the other hand the HCW wastes a lot too, for reasons I gave earlier. I've never seen one that didn't have swing left in it when the arm has reached the vertical. Only a rigorous series of tests on models of both kinds will clear the question up for me.

12. Feb 5, 2010

### turin

The paths are not the same. The HCW path has a smaller radius (smaller by the distance between the counter weight and the hinge). That was my argument.

That's a good point. I didn't even consider the rotational energy of the counterweight itself. I wonder how the final KErot of the counterweight compares to its initial PE. Of course, this problem can be alleviated by reducing the moment of rotational inertia of the weight.

13. Feb 6, 2010

### Ketman

It was mine as well - originally. It's just that A.T. suggested that equal PE might be a good level playing-field to test one system against the other. But as I said, for the same height of drop the HCW needs a bigger machine - higher axle, longer arm. And it's not an insignificant difference either, because it's said that you need a distance from hinge to CM at least half the length of the short arm before you get the "effect". (Don't ask me what they mean by "effect" - I just don't know.) But it all adds up to a constructional problem big enough for it to be my main argument against the HCW. If I were setting the rules for a competition, I'd make axle-height the main restriction, because it's that that determines the basic size and strength of the machine. And then I'd fix the weight of the missile and set a max. on the counterweight. After that it's up to the designer to use those limits to best advantage. If both opt for a starting angle of 45 above the horizontal (which is common enough), the drop-heights they could achieve come out as a little under 3:2 in favour of the FCW, which means nearly 50% more PE. Despite the rotational problem with the FCW, I couldn't see it not winning, could you?

14. Feb 6, 2010

### A.T.

Is this a typical one :

Have you tried any of these simulators:
http://heim.ifi.uio.no/~oddharry/blide/vtreb.html
http://www.algobeautytreb.com/
http://www.trebuchet.com/sim/ [Broken]

I don't know if they include both FCW & HCW. Ideally you wold have such a simulator and run a probabilistic analysis on it, that optimizes all design parameters for certain goal.

EDIT:

http://www.algobeautytreb.com/fortmontecarlo.html

Last edited by a moderator: May 4, 2017
15. Feb 7, 2010

### Ketman

Oh, yeah, the English eccentric. I remember him from a TV program about the team that built the Warwolf treb. They consulted him, or interviewed him anyway, and I remember him being flummoxed by the idea of putting wheels on a treb. He uses a tractor to cock his machine, and when the sheep on his lands hear it starting up they scatter in all directions. They know what's coming.

I've seen all those links you gave on my recent travels. Eventually I might buy Donald Siano's simulator, just to see how accurate it is. But he seems stuck on the HCW as the machine of choice. I've read through his quite long file on the physics of the system, and emailed him a couple of questions asking for clarification. Because, at certain points, just when you want some exactness, he becomes a bit vague, using words like "presumably", or "the dynamics of the system are such that...". But I never got a reply. Strange character. He writes a lot of reviews on Amazon, mostly about books, where he reveals some pretty questionable political views.

Last edited by a moderator: Sep 25, 2014
16. Feb 8, 2010

### turin

I don't know if you can count it as a trebuchet (although apparently some people do), but the F.A.T. (Floating Arm Trebuchet) apparently solves the FCW vs. HCW issue.