Measure the angle between the spanned and drawn bow, with the point where the string connects to the prod making the base, and the drawn bowstring making one side. This angle is α. Next measure the angle of where the drawn string is held by the nut. This is β. You will also need the draw weight of the bow. This is W.
The equation is: W=2F(cosα)(cosβ)
For this bow W is 70, α is 42°, and β is 58°. Working it out** we get:
The Force is 88.8 LbF (pounds of force) We’ll need to change that to the SI unit of
Newtons (N) by multiplying it by 4.448, so 88.8×4.448=394.98 Newtons.
Once you have the force in Newtons, you can figure out the energy in Joules.
E in energy in Joules, F is the Force in Newtons, and X is the draw length in Meters, in this case 6” which is 15.5 cm, or .155 meters.
Now we can calculate velocity. E=1/2 MV^2 E is 30.61, M is the mass of the projectile, in this case 15 grams, or .015 Kg and V is in Meters per second.
The projectile will have a calculated velocity of 66.13 M/s or ±217 FPS
We need to remember that this does not account for drag/wind resistance, or friction from the bow channel or other factors like this. It will however, give you a pretty good approximation of what to expect. This also works best with a plain old curved bow, recurves get more tricky, and this won’t work with compound bows.
** Make sure your calculator is set to DEG not RAD (radians) or the whole thing will be screwy. On the Google calculator the toggle is on the upper left just under the number line. On most calculators there is a button, and the display will say DEG or RAD.
Now, to test this experimentally.