Javascript Archery Ballistics Calculator Technical Info(Not Finished Yet) Weight of an arrow; W=mg Mass of an arrow ; m=W/g m = W(grn)(1lb/7000grn)/32.22 ft/s^2 The basic relationship being used in all calculations is; Kinetic Energy(KE) = 1/2 * m * v^2 (or one-half times mass(of arrow) times velocity squared) Normally people just say KE = arrow weight divided by 451,000 something or other times velocity squared, here's where it comes from; KE = 1/2 X (arrow weight in grains) X (1 lb/7000grn) X v^2 X (1/32.22) 2 X 7000 X 32.22 = 451,080 grn-ft/s^2 and that's where that number comes from. This formula can be rearranged to solve for arrow speed, if energy input to the arrow from the bow is known by the following. v = sqrt( 2 * KE / m) ( or the square root of 2 times the Kinetic energy divided by mass(of arrow) The difference between method 1 and 2 for calculating arrow speed for a particular setup is due to the way Norb Mullaney performs his tests. In either case, the second equation is massaged slightly to get the values we need. Method 1: v = sqrt( 2 * PDF * SEPDF / m) where m = Arrrow wgt + String addon + virtual mass Method 2: v = sqrt( 2 * PDF * SEPDF * Efficiency/ m) where m = Arrrow wgt + String addon Norb Mullaney uses the virtual mass number to roll-up all the bow inefficiencies, this number is derived from his experimental plots of bow data. The values gotten from this method match his much more closely than if the efficiencies are used, since this number changes depending on arrow weight but the virtual mass number is more affected by draw weight, the way he develops the numbers(they both change though). There's only a couple feet per second difference between the methods and some of that is due to round-off. |