MadSci Network: Engineering Query:

### Re: What effects will there be if we increase the arm lenght of a trebuchet?

Date: Fri Oct 27 09:53:32 2006
Posted By: Calvin Cole, Faculty, Engineering Physics, Northeastern State University
Area of science: Engineering
ID: 1161872390.Eg
Message:

You should perhaps see my previous answer to the question "How do trebuchets work?" posted here back in December of 2005 for a start. You might also check out www.trebuchet.com, they have a trebuchet simulator program that’s fairly good as well as various books if you really get into this. Some of your questions are a bit intertwined in their answers, 1 and 4 especially. My students and I have some experience at this business. Our big machine stands about 3.6m high at the throwing arm pivot and will put a 16 Lb (7.3Kg) bowling ball about 60m downrange while lofting it to about 30m altitude. They also built a 1.0m tall steel framed machine for investigating the detailed interaction of the many variables for both fixed and swinging counterweight machines. There are, to say the least, some fairly interesting physics and engineering questions involved with the operation of these devices.

So, questions 1 and 4 first. You should know first that a trebuchet properly set up to work efficiently is “tuned” or “timed” so that the ball is released at approximately 45degrees with the counterweight as near the bottom of its swing as possible and with the least velocity still remaining in the arm. The original purpose of a trebuchet was to throw as heavy a projectile as possible a fixed distance (Usually about 200yards) to the castle. See the video “Medieval Siege” produced by NOVA (Annenberg CPB) to understand why. It is difficult to consider the effect of just changing the length of the throwing arm (that part of the arm opposite the part that has the counterweight attached) because without changing sling length, shot weight, counterweight, or release pin angle (if that’s variable for your machine) you will change the timing of the machine. All that said the general effect of increasing the throwing arm length will be to throw lighter projectiles farther if you adjust sling length or release pin angle to achieve a 45degree release. This typically comes at the price of leaving more recoil energy in the throwing arm. It will be swinging more rapidly after release even if you manage to release at the bottom of the swing and this is in some sense energy wasted. Likewise increasing the counterweight would let you throw heavier things the same distance you had been or the same weight farther but only if you adjust the sling length accordingly and only up to a point as you will again start leaving motion in the arm if you don’t change things like the overall size of the machine. Distance is determined by velocity not momentum (see what your science text says about projectile motion) as long as we neglect air friction. Basically the faster you can throw it for the same release angle (which can only be achieved by changing all the variables mentioned above) the farther you can throw it.

If question 5 means what I think it does then it is answered by answering number 4. For the same velocity you get more momentum by having a more massive projectile. (Recall: momentum is the product of mass and velocity) For the same velocity with a more massive ball the effects of head, tail, or cross winds will be less. For instance the only time I witnessed noticeable drift with a bowling ball was about a half a meter sideways drift with a 50KPH gusting crosswind.

Question 3. We haven’t encountered anything we considered to be unexpected or hard to build except for the wheels on the large machine. This was only because we had to make fully functional wooden wheels to meet the period appearance requirements of the medieval village site in which it had to operate. Had we been able to use modern wheels and rims there would have been no difficulty. Just be sure beams, slings, and triggering mechanisms are strong enough for their intended purposes. It can be a bit tricky to get the pouch on the sling the right size and flexibility so as to release the projectile cleanly without spilling it out the side during firing or having it hang up and release late (if at all) from a pouch that is to deep.

Question 2. You can build them any size you like! It just depends on what you want to throw and how far. The bowling ball hurler I’ve been describing is about as small as they actually would have built one for real siege warfare. It uses about 200Kg of counterweight and would have had its throwing arm lengthened to about 6m (we use 3.5m for the heavier balls) to throw 1 or 2 Kg rocks a little more than 200 yards to get them over the walls. The machines trying to destroy the walls with 90Kg balls would have been about 4 times larger with counterweights of 8000 to 12000 Kg. Apparently for a real siege they would build lots of the smaller trebuchets and one or two of the big ones. In the instances when both those laying siege and the besieged both had trebuchets we have first hand accounts that speak of a “rain of rocks day and night”, ouch. I hope this helps. Have fun with the project and be careful if you do build a few.

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