Hello, I am a high school student who has been given an assignment to build a trebuchet using the principles that we have learned in class already (gravity, gravitational and kinetic energy, projectiles and such).
How would you figure out the length of the arm to optimize the range?
From research and general physics knowledge, I am aware that the projectile must be shot at a 45 degree angle and that the counterweight vs projectile ratio for mass should be significantly big (10 to 1ish).
I know how it should work but I don't really know how to plan for it. Is there a way to mathematically determine the optimum arm length, sling length, and such? How might you make sure that the projectile is released at a 45 degree angle?
We have already built a trebuchet based on a plan we saw on the internet, but it ended up being way too small.
A bigger trebuchet would yield great range, right? Since you can add a greater counterweight and also increase the height of the counterweight further? Does the height of the counterweight affect range at all?