Other Things in Archery:
DIMENSIONAL EFFECTS
Why do larger bows, like the longbow, shoot farter than short bows? Simple answer-- they are bigger. Complex answer:
Scaling laws. Considering the reasons to use a smaller bow.
1.) It is lighter.
2.) It is easier to use.
This is why this bow would be used for hunting, when a larger bow just wouldn't be profitable. The distance at which you could hit a target hunting with sufficient accuracy requires a smaller bow than a military longbow (which is shot for distance, not for accuracy). But why would a smaller bow fire a shorter distance with lethal force?
1.) A smaller bow has a smaller draw length.
2.) A smaller bow, if scaled down accurately, would have limbs with a lower tensile strength.
Assuming a shorter draw, the arrows would have to be shorter, and therefore, lighter. It is safe to assume that a scaled down bow would fire equally scaled down arrows with the same speed as a larger bow would fire equally large arrows.
The problem that arises from this is aerodynamics.
An object moving through a viscous fluid (or any fluid, air being one) experiences drag. This is a force(F) proportional to velocity (v) and cross-section (A). F = KAv. "K" being the viscosity of the fluid.
Another factor involved is the mass of the object. This comes in to play as F = ma. Now, that leaves us with KAv = ma, "a" being the negative acceleration caused by the fluid. Considering that "K" and "v" would be standard for our arrows of any size, the only variables would be "m", "A", and "a". An arrow scaled down to 1/2 would have 1/2 the cross-section, but 1/4 the mass, which means that an arrow of 1/2 the size would have 4 times the negative acceleration, which means that it would leave the bow at the same speed, but would slow down faster.
Not to mention penetration. If mass were 1/4, momentum would also be 1/4, so, in theory, it would only be able to penetrate 1/4 as deeply. Either that or use blunt tips to stun or injure the target.
That was that.