On the subject of trebuchets...

G

Goistein

Junior Member
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Oct 8, 2006
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This would either belong in here of math odds and ends, but here is probably better. I have a trebuchet to be built, it's kind of like a seesaw, with something to be thrown on one end, and a counterweight on the other. I'll ignore friction for the time being. So the formula for Torque is given in terms of the weights of the beam, the current angle and both end objects. Inertia is constant.

*==========^==========*
(spacespace)|
(spacespace)|

It looks like that a bit. So I'll let m3 and m4 be the two weights, and m1 and m2 be thee mass of the two parts of the beam, left to right. l1 and l2 are the lengths. x is the angle it's at, from the beam to the vertical, 90 being the angle in the picture. v is the angular velocity, and a is angular acceleration. t is time. And m4 is the object being thrown, so the beam will turn counter clockwise.

Torque=T=9.8sin(x)[(m3)(l1)-(m4)(l2)+((l1)/2)(m1)-((l2)/2)(m2)]
Inertia=I
a=T/I
T/I can really be simplified to k*sin(x)
dv/dt=a
dx/dt=v

So k*sin(x)=x`` which probably isn't solvable if I'm right. But I really hope not, but if I am, can it be solved?

Also, there's been ideas of the object being in a sling attached by a string, to somehow increase the centrifugal force. I would have a hard time illustrating this, but I have no idea for the equations in that case. Wheels have also been suggested, which even further complicate this. So hopefully someone can help. Thank you!

to see what a trebuchet looks like, go to

http://www.trebuchet.com/
 
Either, whether or not x``=sin(x) is solvable, or what the equations are for the variations. It might take some background knowledge on physics.
 
Goistein said:
Either, whether or not x``=sin(x) is solvable, or what the equations are for the variations. It might take some background knowledge on physics.
Click to expand...

kx = sin(x) cannot be solved in closed-form

You can estimate the answer by using various numerical schemes - such as Newton-Raphson method.
 
OK, thank you! I was able to get equations to predict movements when two objects are attached to a string and one moves while the other is stationary. However, now I've got to deal with an already moving object, which although isn't much of a problem, how exactly would it work if the object moves too fast and tension is put on the string. A bit like an overshot pendulum, but with the vertex also moving.
 
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