How to Calculate the Launch Velocity of a Trebuchet Projectile?

[LoLzAsian]

Ok, so for my high school physics assignment i need to analyse the physics of a trebuchet but i need help calculating the velocity at which the projectile would be launched when released, can you please give me a detailed outline of the procedure including all formulas used?

 

[Drakkith]

What does your book say about it? Surely it has all the information you need if you were assigned this.

 

[LoLzAsian]

I'm only given the measurements of the trebuchet, counter-weight, & Projectile, I don't need the problem solved for me I just need an outline of the procedure in calculating the velocity at which the projectile will be launched at.

 

[Drakkith]

Yes I realize that, but part of the work is figuring out how these things fit together. Can you name some of the major steps you know you need to do?

 

[LoLzAsian]

I know the torque that counter-weight undergoes and the transfer of energy is a key to solving the problem but I'm having trouble adjusting to that a trebuchet is both a lever and a sling and I'm not sure what calculations are needed to do this.

 

[voko]

All you really need to visualize are the initial and the final position of the mechanism, where the final is when the projectile separates. Then use conversation of energy.

 

[Drakkith]

I know the torque that counter-weight undergoes and the transfer of energy is a key to solving the problem but I'm having trouble adjusting to that a trebuchet is both a lever and a sling and I'm not sure what calculations are needed to do this.

Can you treat the sling as a lever?

 

[LoLzAsian]

Can you treat the sling as a lever?

The sling is not treated as a lever, the trebuchet is basically a lever that in turn powers a sling, thus accelerating the projectile at a massive rate.

 

[K^2]

The purpose of a sling in a trebuchet is to improve energy transfer. Ultimately, you don't need to worry about it, unless you are actually designing a trebuchet.

You have two conservation laws. Trebuchet will conserve energy and it will conserve angular momentum. That gives you two equations in two unknowns, the unknowns being the final velocities of projectile and counterweight. Write down both equations and solve them together. Angular momentum conservation is a linear equation, so use it for substitution into the energy conservation equation, which should yield a single quadratic equation for final velocity of the projectile.

It's pretty straight forward. Just make sure your signs are consistent.

 

[CAF123]

Consider also the rotational kinetic energy of the arm/wooden piece that swings and it's conversion to gravitational potential energy.

 

[A.T.]

Google "trebuchet calculator". Some sites provide the theory and source code.

 

[LoLzAsian]

i was thinking that first i would use a free-body diagram to break down the individual components( for both lever and sling mechanism) then i can work out the force required to move the projectile which i can then subtract from the force exerted by the counter-weight as energy lost , then once i work out how convert that into a velocity at the other end that would give me the rate at which the projectile would be traveling vertically during launch, that would also be the tangental veloctiy which needs to be converted to radians per second as the projectile is moving both vertically as well as in a circle which would give me the speed which it would be traveling within the circle, i could then do a vector sum incorporating the angle of release to find its velocity when launched.

 

[voko]

i was thinking that first i would

A very laborious effort. Just use the conservation laws, as suggested by many posters above.

 

[LoLzAsian]

Can you please provide an example?

 

[LoLzAsian]

The purpose of a sling in a trebuchet is to improve energy transfer. Ultimately, you don't need to worry about it, unless you are actually designing a trebuchet.

You have two conservation laws. Trebuchet will conserve energy and it will conserve angular momentum. That gives you two equations in two unknowns, the unknowns being the final velocities of projectile and counterweight. Write down both equations and solve them together. Angular momentum conservation is a linear equation, so use it for substitution into the energy conservation equation, which should yield a single quadratic equation for final velocity of the projectile.

It's pretty straight forward. Just make sure your signs are consistent.

Can you please provide an example?

 

[K^2]

I jumped the gun on angular momentum conservation earlier. It's not conserved, as there is external source of torque, which is why the thing works in the first place. So we're down to one conservation law, which is good to establish limiting cases, but not to do actual computations.

I know how to account for the sling dynamically. If you have access to Mathematica, I can write up a notebook that does numerical computations. But as far as simple solution you can do yourself, I'm not sure I have anything yet. I'm going to put a bit more thought into it, and get back to you if I come up with anything.

 

[LoLzAsian]

A very laborious effort. Just use the conservation laws, as suggested by many posters above.

that's what i originally thought of using but I'm not sure if that will allow for the range of difference in length on both sides that provides leverage. if i thought that would work i wouldn't be asking for help

 

[A.T.]

Trebuchet Mechanics:
http://www.algobeautytreb.com/trebmath35.pdf

Softwares:
http://www.algobeautytreb.com/
http://ronleigh.com/ivytech/_ref-trebuchet-range.htm