Searching the SDMB, I know at least one person is familiar with the floating-arm trebuchet. (A trebuchet is a catapult that uses a see-saw counter balance & sling to hurl stuff.) I know that hinging the counter weight to make its drop closer to vertical increases range. I know that, according to google searches, putting the machine on wheels to even more closely approximate a vertical drop for the counter weight improves range by about 33%. (I’m not going back to find the cite, sorry.) But I cannot figure out how much farther a modern floating-arm trebuchet would do over a historical trebuchet, for parameters that are roughly comparable.
Obviously, there are design choices that are going to change the results and prevent a perfect answer. With that in mind, I’m asking, for similar projectiles, weights, and amounts of wood (I guess), how much farther can a floating-arm trebuchet toss an object? Roughly speaking.
Roughly speaking, the answer seems to be “a lot more” - one comparison I’ve come across was a 3-foot beam FAT with 9# of weight threw a golf ball 245 feet. The only machine to throw a ball farther at that event was a regular 19-foot treb with 200# of weight, and the throw was 305 feet.
Roughly 20 times less counterweight and one-sixth beam length on the FAT yielded only a roughly 20% penalty in throw distance.
If you scaled that 3-foot FAT up to 19 feet, I don’t think it would throw a golf ball a quarter-mile, but it would be far enough that you’d need a lot of empty land.
Another thing to consider is that a treb ought to be built for, and tuned to a particular projectile. You can’t just go off and double the counterweight (for example) and expect your distance to double. If anything, the distance might be less. On mine (a small standard treb), a bad projectile/weight mis-match tends to result in throws measured in inches, rather than feet or yards.