Very intriguing reading doublelunginum! A couple of thoughts....
ORIGINAL: doublelunginem
If you take Bow A and shoot a 350, 400, 450, 500, etc grain arrow through a chrono and calculate the KE, yes, the KE will go up, but only to a point. The reason for this is because Bow A has a set amount of POTENTIAL energy at full draw (the area under the draw curve). The heavier the arrow, the more efficient the energy transfer, but the only way to transfer ALL of the bows potential energy into an arrow is for the string to come to a COMPLETE stop once the arrow is released....same must be true of the limbs, cams, and cables. This would mean that ZERO energy even makes it to the Riser (wouldnt need ANY dampening products).
When you nail this idea down (100% efficiency = perpetual motion machine = wealth beyond your wildest dreams!), please keep your old friend bow_hunter44 in mind!! If I happen upon the solution, I will reciprocate, I promise!!
My theory is that at some point in the test (as the arrow weights go up), the bow reaches it's maximum efficiency or energy transfer and once you go heavier than that, thevelocity begins to drop exponentially. This makes sense because we now have a fixed maximum KE....In the KE formula, Velocity is squared, therefore when KE is fixed and mass goes up, then Velocity decreases exponentially.
Yup. At some point the mass of the arrow would be so great that its inertia would make it the proverbial "immovable object".
It is at this peak in the "curve" of speed vs. weight that KE is maximized. I am not sure that this is EXACTLY what is taking place, but I do know that as I tested my bow with different weighted arrows, there was a point at which KE plateau'd out and then began to drop. As soon as it plateaus, I suggest going with the lightest arrow/highest velocity for that KE.
I would be VERY interested to see where this point on the graph corresponds to other charactersitics,like momentum,of the system. As Arthur suggests (very astute man is Arthur!), perhaps a doublegraph on the same coordinate plane. Mass and velocity on the X and Y axis, then plot KE and momentum. The point you reference (where KE peaks and starts to go down) would be the vertex of the KE parabola. If the momentum line (y = mx + b, since momentum is a linear function) and the KE parabola were to intersect at the vertex of the KE parabola!!! hmmmmmmm..... If you think you smell wood burning, it is just me thinking!
Come to think of it, the momentum line would have to reach a maximum as well. One wonders where that point would be, and how that point would correspond to the KE parabola??
Who said that physics wasn't fun!!
Damn you doublelunginem! My poor little head will be slowly (slowly being the operative word!) grinding away on physics problems all day!! Oh man - I just had an idea for my physics class!!!! It will be, shall we say, challenging"! I take the "damn you doublelunginum back"!! Thanks man!!!