How do i calculate the energy lost by my catapult

[Buggsy GC]

I Have built a catapult for a 1st year engineering assignment, I know catapult are extremely energy inefficient and my theoretical catapult calculations prove that, but i don't know how to calculate the exact energy of my projectile as it hits the ground again, I can measure the projectiles real life height, distance, weight and time but I am a bit lost on the formula to find the joules of the projectile as it land. In summery I want to be able to calculate how energy inefficient my catapult in transferring energy to its projectile.

 

[scottdave]

If you have a projectile, which is heavy and appears streamlined, you could model a path which ignores air resistance to get the projectile to the target. You may be able to test how much air resistance if you are able to drop test the projectile from a tall height and measure the time. Physics labs have equipment to measure this accurately.
You can calculate the initial velocity of the projectile as it leaves necessary to hit a certain distance. Knowing the mass, you can calculate initial kinetic energy. Are you wanting to know if there is energy loss to the air, or energy loss within the actual catapult? If it is the catapult, then you can do some experiments to find the spring constant, and figure out how much potential energy you are putting into it.

 

[Buggsy GC]

If you have a projectile, which is heavy and appears streamlined, you could model a path which ignores air resistance to get the projectile to the target. You may be able to test how much air resistance if you are able to drop test the projectile from a tall height and measure the time. Physics labs have equipment to measure this accurately.
You can calculate the initial velocity of the projectile as it leaves necessary to hit a certain distance. Knowing the mass, you can calculate initial kinetic energy. Are you wanting to know if there is energy loss to the air, or energy loss within the actual catapult? If it is the catapult, then you can do some experiments to find the spring constant, and figure out how much potential energy you are putting into it.

The energy lost by the catapult, I calculated the spring constant and the theoretical time and distances I calculated are large than those in reality by a factor for 10 roughly

 

[scottdave]

So I would assume very little air resistance, if my projectile is heavy, relative to its size, and smooth (something like a small steel ball). Then based on height and distance, you should be able to fit a parabola and calculate what the initial velocity is. from that you can calculate initial kinetic energy. Figure how much energy you put in (1/2)*k*x^2, then find the difference.