Strength of springs - length of travel vs tension weight

[R_Rose]

I'm trying to design some novel cross bow designs and also trebuchet's with the trebuchet (similar to catapults to those who don't know) using springs or a combination of weight and springs. I'm looking into using linear springs and pullies for the crossbow depending on whether they can be efficient or not.

What I need to know most is how to calculate the energy that can be obtained from a spring and which aspect gives the greatest increase of energy - such as pull weight vs expansion distance. Also, is there a difference in using a compression spring vs tension - can they both give the same results? I was looking at using a number of heavy duty coil truck springs and a block and tackle which can allow for greater distance of movement of the attached rope to compensate for the great compression strength vs short movement of the spring, so the 8" travel of expansion of the spring will translate to 16" or 24" depending upon what pulley system I use. I need to to know how I can calculate expected energy from the different springs that I use.

Another idea that I've had is to use tension springs and pulleys as needed to make for appropriate travel distances of bolt carraige or throwing arm.

Finally we come to bungees which I've come to respect greatly as they can store an awful lot of energy and for their size and weight can be very useful. I have no idea how to calculate energy available in these cords.

If anyone can help me out, I'd greatly appreciate it! Thanks

 

[anorlunda]

cross bow designs and also trebuchet's

I suggest that your hobby is of the kind where empirical science (experimentation) is more applicable than calculations. Since you want to push things to the limit, that means past the edge where simple mathematical models are valid. The nonlinear properties of materials come into play, and there is no simple formula for those.