Is there an equation to find the optimum release point of a catapult?

Question

Is there an equation to find the optimum release point of a catapult?

Answer 1

Your 'optimum release point' is the point at which the payload will be released and hit the target.  You'll find this is best determined by trial-and-error.  

Answer 2

A catapult has at least 5 variables to contend with in your design.

The weight of the projectile,

Position of the projectile on the pivot arm,

The position of the striking plate that the arm hits,

The starting position of the arm and

The elasticity of the rubber band.

The Problem Statement you should start with is "How far do you want your projectile to travel?"

Then set up a DOE (Design of Experiments) to determine the optimum settings for each of the above characteristics or variables. Start with two levels for each and consider three Interactions. Where an interaction is where two variables are considered one. This will become apparent in the results.

The use of DOE produces exactly the results, the equation for optimum release point, you are seeking. This equation will dictate the specific level of each variable. It will also tell you which variable and interaction between two or more variables has the most impact to the out come.

If you have access to Mini Tab the experiment calculation and set-up is a cinch. Otherwise, you need to do all the calculating by hand, the way I was taught several years ago.

Good Luck!

Answer 3

Global Spec not only provides an interactive calculator on their website, they also explain the equations of the trebuchet (catapult)

Check out this website and have a ball!