Tebuchet With a Sling
This trebucht model is the most efficient. The kinetic energy of the projectile can be given by the same equation- KEproj=DPEcw+DPEb+DPEproj-KEcw-KEb. This time, however, KEb can also be zero, since the projectile is not directly attached to it. Both the beam and the counterweight can stall. If they both stall at the release point, the model can be surprisingly efficient. Also, if you use a non-uniform beam, DPEb can also be zero, or positive.
(This fact isn't taken into account in the efficiency equations, so don't be mislead if your trebuchet has an efficiency greater than 100%...)
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