How fast is an arrow?

The speed of an arrow as it leaves the bow can be found in several ways.  From the archer's point of view the two most convenient are based on (a) energy conservation and (b) measurements made on the bow and calibrating the sight.  These two methods are discussed in the note on arrow speed estimation and the results are quoted here for ease for reference.

Energy considerations (recurve and longbow)

    speed = sqr(e*P*g*b/m)

where e is the efficiency of the bow, P the poundage at full draw, g the acceleration due to gravity, b the difference between full draw and bracing height and m the arrow mass in lb.

Arrow flight considerations (any bow)

    speed = sqr(0.5*g*d/A)

where d is the distance from the eye (or peep sight) to the sight pin and A is the scaling of the sight as discussed in the sight calibration note

A full justification of these formulae is given in the arrow speed note together with a couple of examples.