### Re: Force of a Bullet vs. Force of an Arrow

Date: Wed Oct 1 13:05:57 2003
Posted By: Gareth Evans, Industrial R&D practitioner and manager ( retired )
Area of science: Physics
ID: 1064447204.Ph
Message:
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Question:  A modern bullet vs. a medieval arrow which would have more
strength behind it? Wouldn’t it be the bullet since it's made of metal
while the arrow is simply made of wood?

Dear Krystina,  thank you for your question.  It is not an easy one since
there are so many things to consider in both the case of bullets and of
arrows.  I’m no expert in armaments but I’ll point out some of the things

You used the words “force” and “strength” and although we know what you
mean, we should take some care to use measures of the behaviour of arrows
and bullets which would let us compare the two on a fair basis.  Let’s be
honest, both bullets and arrows are used to cause damage, usually to
animals including humans so we need a measure of this capability to cause
damage.  In order to cause damage the projectile must use its kinetic
energy, the energy it need to travel at speed, to split crush and deform
the material being hit.  Often we use the ability of the bullet or arrow
to penetrate a solid material.  At least that is a good starting point.

Let’s look at bullets first.  They are propelled by an explosion within
the gun barrel and the expanding gases force the bullet down the barrel
and out towards the target.  Guns often need to be carried easily so the
size of the cartridges and bullets is a compromise between causing the
maximum damage and being easy to handle.  The kinetic energy of the bullet
( and arrow ) is  ½ x M x V ^2 where M is the mass, and V the velocity.
The mass depends on the size and density of the bullet and the velocity
depends on things like the amount of explosive, the mass of the bullet and
the design of the gun.

Arrows on the other hand are projected by a bow which has been drawn by
the archer’s muscles.  This web-site has some interesting information
about the history of the long-bow:-
http://www.history-magazine.com.

We can define energy as the force applied times the distance over which
the force is applied.  In the case of a bow, the archer pulls back the
string using at first a small force but as the bow bends the force needed
to pull further builds up.  Some say that a medieval bow could require
160lbs “draw strength” which is the force needed for the last part of the
draw where most of the energy is stored up. On release of the string, most
of the stored energy is transferred to the arrow. Arrows could be up to 3
feet long so even though they were made largely of wood this weight of
wood plus the weight of the normally metal arrow-head could be much
greater than a rifle bullet.  This is a factor which results in the arrows
traveling more slowly than bullets which usually travel faster than sound.

Once the projectile is on its way, it can only lose energy through air
resistance.  This energy loss is important because it is the energy on
impact not the firing energy that counts. The bullet and arrow are again
very different.  Because the arrow travels more slowly, the air resistance
due to pushing air out of the way is lower.  On the other hand the shaft
and particularly the flights will cause frictional drag.  ( The fact that
the drag due to the flight is greater than the tip is how flights keep the
arrow straight ! )

The final amount of energy depends on these losses and therefore of course
how far the projectile travels before impact.  I should think arrows lose
a smaller fraction of their energy.  This may help to explain why arrows
can penetrate solid materials so well.

Another factor is their shape.  The arrow-head is very sharp, that is it
has a very small cross sectional area at the tip.  The size builds up
slowly and this is good for air resistance and particularly good for
penetrating solids.  Arrows shot by the famous Welsh bowmen at around the
time of Henry the Fifth in Britain could penetrate solid oak, four inches
thick and poke through by over six inches.

Hope that helps even though there is no clear winner – at least not as
clear as Henry was against the French thanks to the Welsh ( how did you
guess I was Welsh ? ).

maybe on the Web, about typical bullet masses and velocities, and
typical arrow masses and velocities, the kinetic energy could be
compared.]

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