Last year (4th grade) my son's science fair entry was based on a 
trebuchet.  His question was what would be the effect on the distance a 
projectile would be thrown with different pivot points and counter 
weights.  This provide me the excuse to build my first simple trebuchet 
complete with an adjustible arm.  While researching the project we ran 
across an university engineering department (a Kansas institution I 
believe) website that discusses the physics and engineering involved in 
this family of siege engines. 

It was there that I learned about the engineering and physics reasons 
behind the canter counter weight and free wheeling carriage.  The basic 
idea, as I understand it, is that the straighter that the weight falls 
the more of the potential energy is utilized in throwing the projectile 
and less is lost to changing the counter weights angular momentum to 
subscribe an arc.

I've been hankering to build a slightly larger model utilizing these 
features ever since. 



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