Initial Speed of a trebuchet projectile?

Question

ok, so i have a trebuchet, dr=21 inches, R= 10N. It starts horizontal, and stops instantly at vertical. what is the speed of what i am launching the moment it leaves the trebuchet (tell me if i need to put more information, this is a real trebuchet)

Answer 1

The initial speed of the projectile will be the same as the fastest speed at which the end of the arm is moving during its swing. This would normally be at the top of the throw, but the arm can be arrested before the top of the throw - this gives some initial upward velocity that improves the range.

The accelerating force is the counter weight moment divided by the length of the throwing arm, and the acceleration is that force divided by the mass of the projectile. (the weight of the throwing arm can be deducted in calculating the counterweight moment).

Although the force changes, this works like a pendulum, and the math is fairly easy

Answer 2

You could probably work out some kind of answer mathematically if you knew how to figure in all the variations, but it would only be approximate. Check out Siano's "Algorithmic Beauty of the Trebuchet" to get an idea of the calculations involved.

In the real world you never achieve 100% efficiency in translating the potential energy in the raised counterweight into kinetic energy in the missile, generally only about 30 to 40%. Any proper trebuchet uses a sling, so knowing the beam's tip speed doesn't help much with the missile speed.

Answer 3

You haven't given enough information. For one thing define your terms. What is dr and R? To make a rough calculation you would need to know the weight of the counterweight, the weight of the projectile and the distance to the center of rotation for both. I believe a trebuchet also uses a sling, not sure how to do calculations for that...

Answer 4

If you know the angle of launch with the horizontal plane, the weight of the projectile, the height above ground at the release point, and the distance traveled you can then calculate the initial velocity.

Answer 5

as as been said. Not enough info here to answer this.