ORIGINAL: bow_hunter44
V(light arrow) > root m (heavy arrow) divided by root (light arrow) times velocity (heavy arrow). What that inequality states is that if the velocity of the light arrow is the product of the square root of the ratio of the mass of the heavy arrow to the mass of the light arrow times the velocity of the heavy arrow, then the ‘light’ arrow will have more KE than the heavy arrow! In the case of the 500-grain/400-grain arrow comparison, the 400-grain arrow will have more KE than the 500-grain arrow if the velocity of the 400-grain arrow is (root 5)/2 times greater than the velocity of the 500-grain arrow, period, no ifs ands or buts about it!. That statement is not a function of tune of the bow, or spine of the arrow. A ‘light’ arrow with root 5/2 times the velocity of a ‘heavy’ arrow can be flying sideways or turning cartwheels on its merry little path, it will have more KE than the ‘heavy’ arrow (which can also be doing aerial gymnastics as well). The math behind that argument is not integral calculus or Diff. Eq., it is good old friendly ninth grade algebra. If you don’t believe me, then as one of my college professors stated, “Do the math! Do the G.D. math!”
Good Post. Let there be sanity! Aparently some people are incapable of it. As usuall, random facts and theories are made to fit arguments - not the other way around as would better be done. Not one shred of evidence exists ( and I read most of the links!) that indicates a bow ALWAYS gains KE (not to mention momentum!) as more and more mass is added to the projectile. A compound bow is a complex energy system where no two are identical. All systems, in the real world (including various frictional effects, limb resiliance(sp), etc) have
a operating peak efficency. Its that simple. What the virtual work papers showed is what a theoretical system contains. A typical redutio ad absurdum argument.