Exactly! What you want is for the top of the arm to move as far as possible during the tie the weights fall. Making the arm longer will make the arm more further in the same amount of time. Greater distance over the same amount of time = greater velocity. Greater velocity = greater distance. Don't forget that you want to launch at an angle of 45° for greatest range, but you can tune that part once everything is built and stable. Torque = radius *cross* force. For your purpose, *cross* can mean *times*. If you were to have the beam horizontal, and placed the beam such that the counterweights were placed 1 foot away from the pivot, 100lbs would balance out a 10 lb weight10 feet away. For a 14 foot beam, if your counterweights are let's say 2 feet away from the pivot (this is reasonable I believe), then you'll ned 120 lbs to counteract the 10 lbs at the opposite end (12 feet from pivot). I'm not sure what ratio is optimal for trebuchets, but I think I read a 4:1 ratio is optimal. If that's the case, then you'll need only 500 pounds to launch your projectile. If you want even greater range, then add more weight or add more weight and increase the length of the arm. I'm a bit too bust to calculate the exact estimated speed with which the projectile would be launched with, but assuming the weights fall 1/2 meter (it'll actully be more but I don't feel like whipping out converters and such), and an acceleration due to gravity of 10 m/s (rounded up). Distance = 1/2 a t^2 (simplified since initial velocity is 0). So 0.5m 5 m/s^2 t^2. 0.5 / 5 = t^2, so t = 0.316 seconds Now... let's say our beam starts off tilted so that the weights are positioned 30° above the horizontal. The tip of the throwing arm will be 30° below the horizontal. Let's say that's exactly where the projectile is. If it launches at 45°, then it will have travelled 75°. Change in angle over change in time is equal to the angular velocity. Angular velocity us equal to v/r. So we have 75° = 1.31 radians. So... 1.31 rad / 0.316s = v/r. With r being 10 feet (approx 3 meters), velocity of the tip will be 12.4 m/s. I *think* I did this all correctly. Of course this is with a massless arm and it doesn't take into account the projectile weight or the counterweight weights. The acceleration isn't really 9.8m/s^2 here (or 10 as I rounded it) since the projectile will be counteracting it. So instead of 9.8m/s^2, it will be less. The calculations become messy b/c torque has to be involved, but I'll get into that in a few days if nobody else does. The range as such would be about 50 feet, I believe. That estimate seems far too low. Can anyways point out where/what I did wrong? The range should be v^2 sin(2theta)/g, which would be v^2 sin (90) / g. It should be about 15 meters and change, or roughly 50 feet. Hmm... of course the projectile will be attached via a sling (right?) so that will also greatly increase the velocity as it increases the radius between he projectile and the pivot. If you add another 1 meter of rope extending to a sling, you'll get an extra 30+ or so feet out of the range. Additionally, you're goingto use more than 0.5m for the counterweight length, so that should increase the acceleration time. Before you do anything else, sit down and crunch these numbers. I've given you most of the equations you need. What you have to do is figure out the range you need (300 feet?) and the beam lengths you need for it. I figure your acceleration will not be 9.8 but maybe 8.0 or so after compensating? Since you're doing this for physics, calculate the torques and by how much it takes away from the downward force of the counterweight, and that should give you your true acceleration. EDIT: I just saw the last posts after I posted this so I didn't see the corrected beam values. I'm too lazy to recaluclate everything, but these values should still offer a *rough* estimate.