I am building a pvc trebuchet for school, can any one answer this question?
Is there an equation to find the optimum length of a throwing arm compared to the wieght (20lbs) used to throw a tennis ball?

ps. no I don't know what it is lol - but other members do :-)

Watched a trebuchet being built on scrapyard challenge last week. I do remember that the length from the pivot point to the weight should be 1/5th of the length from the pivot point to the end of the throwing arm. But did not absorb a weight to length ratio.

They were throwing motor scooters. And used an underarm style rather than the usual overarm treb. unusual but effective. Apparently it eased the strain on the arm.

Check this out - [url]http://andypsionfan.users.btopenworld.com/treb01/trebuchet01.html[/url]
Not sure how accurate his numbers are but this bit seems to make sense

[i]'counter-weight should be 80 to 100 times heavier than the projectile
the angle of the throwing arm should be 45 degrees when cocked
the upper part of the throwing arm should be 3 to 4½ times longer than the lower end (I chose 4 times)
the sling should be three quarters the length of the upper part of the throwing arm (for starters, that is). [/i]'

Hope that helps :-)

Ooh, just found this - [url]http://andypsionfan.users.btopenworld.com/trebdrop.html[/url]
Calculates all the sizes and weights for you :-)

Trebuchet technology isn't as old as the sling, but it has been around for a while. Long enough that some of the mathematical relationships are understood. There's a rule of thumb, called Phsstpok's Rule about the relationship between the leverage ratio (called beam ratio, or BR) and the ratio between and counterweight missile weight (mass ratio, or MR). It states that beam ratio should be 1/20 mass ratio. It does tend to break down at the extremes, though, and in your case (tennis ball is 1/8 pound divided by 20 pounds equals 160:1 mass ratio equivalent to an 8:1 beam ratio) the mass ratio is a little extreme. 6:1 would work better in your case.

This is if your trebuchet uses a counterweight that is suspended from the short side of the lever arm. It it is firmly attached the story is very different. In that case you have what is called a Fixed Counterweight Trebuchet, and a BR in the 2:1 area is the classic formula, though with plenty of CW you can use 2.5:1. The explanation can get a bit complicated.

In either case, for best performance keep the arm light.

well hurlinthom sounds like he knows what he's talking about - pm him :-)

There are a few bods on the forum who have made trebs - dunno if they'd be considered experts or not - I suppose you count the number of trebs built and divide by the number of intact limbs left on the builder - :-)