# Archery

LANGJ@mail.syntron.com LANGJ at mail.syntron.com
Mon Mar 27 13:04:36 PST 1995

```	 Quibbling about physics?  Yes!

>	 Firstly, (1) F = M * a -- that is, force = mass x acceleration
>	 (not velocity).

>	 >>>>> Please recheck this.  Using this equation if an object hits
>	 you at a constant velocity (ie:  a = 0) then it hits with no
>	 force.  I find it hard to believe that the non-accelerating piano
>	 at a constant 30 MPH is going to hit softer than the bottle rocket
>	 going from 0 MPH to whatever.	<<<<<

1] A Thistle Missile (TM) that hits at any constant velocity slows
down abruptly (we hope).  Deceleration (negative acceleration)
still fits the equation.

2] The factor that we are chiefly concerned about is the kinetic
energy of a projectile.  That value is one half M * V squared.

3] When a missile is fired from a bow, the energy stored in the
bow, accelerates the arrow/quarrel as the bow relaxes.
> The F = m * a equation applies here, with the acceleration
a = F/m.
The force is not easily derived.  The force(weight) of the bow at
full draw may be known, but the force diminishes as the bow
relaxes.  The rate of diminution is dependant of the moment of
inertia of the bow (which depends on its shape), the elastic
constant of the bow (which depends on the material from which it
is constructed), and the moment arm of the bow (which depends on
its length and curvature).  The result is a nasty partial
differential equation of at least second order (which will vary
from one bow to the next).  I would prefer to accept the empirical
regulations on bows used by the marshallate.
A "standard bow" will impart a standard value of kinetic energy to
an arrow.

4] The effects of drag on a projectile only become significant
after the projectile has traveled some distance.  Our primary
concern should be close range.  If it's safe at close range, it'll
be safe at 100 yds.

5] The effects of the impact of an arrow/quarrel depend on its
kinetic energy, the area that the energy covers, and the amount of
energy required to compress the padding between you and the arrow.

6] Finally, arrows (unlike swords) may travel hundreds of feet from
a combat zone, into an area occupied by unarmored individuals.

bran
[langj at mail.syntron.com]

(I wondered if I'd ever get a chance to use all the stuff they
taught in those "core distribution" courses.)

```