Mark Harris mark_harris at
Mon Mar 27 10:39:06 PST 1995

        Reply to:   RE>>archery

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

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.

Looking at equation (2), we see that, for a given V, Dtm < Dmb, because CDtm
CDmb and Atm < Amb.  This implies in equation (3) that a Thistle Missile
less of the thrust of the bow to drag than does a Markland blunt.  However,
note the feedback loop here.  Less drag implies greater velocity, which
increases drag in proportion to the square of the velocity.  Without actual
numbers, it's hard to predict which bolt will have the greater Vm, based on
their aerodynamics.

However, there is another factor involved here, the respective masses of the
bolts.  Mtm > Mmb and TH is inversely proportional to mass.  The difference
masses is probably more important that the differences in drag, so <
Vm.mb (maybe).  Again, without some real numbers, it's hard to say what will

Right. I would expect the mass differances to overwelm the drag differances
between thistle missile vs. Markland blunt. However, I don't think the
was between one crossbow tip vs. another. I think it's more between using the
thistle on the arrow but not the crossbow quarrel. Here the drag may have a
bigger effect. The fact that the arrow will tend to waver or oscillate more
flight may also have an effect.

Equation (4) has another feedback in it.  The slower bolt has less drag per
equation (2) and so loses less of its initial velocity over a given time
period.  But, it takes longer to get there, so there's more time for drag to
slow it down.  Which bolt has the greater terminal velocity?

Yes, at what range it the target getting hit. At Gulf Wars, I believe there
was a different minimum range for crossbows than for bows.

Equation (5) tells us that the more massive bolt has more energy for a given
velocity and the the faster bolt has more energy for a given mass.  Which of
our two bolts has more energy depends on the ratios of the masses and the

I'm not trying to say Savian's analysis is wrong, per se, but that the
situation too complex to say anything without some hard numbers.  Give me a
wind tunnel to measure the CD's and a scale to measure the masses, and then
can make predictions.  Or, get some flight times so we can have velocities to
use with the masses to determine KE.

Savian is correct in stating that the stiffer Thistle Missile will have a
harder impact.  This is because less of its Kinetic Energy is spent
compressing the blunt, thus imparting more energy to the target.

I also agree with Savian that it is hard believe reports of excessive force
from crossbow bolts without seeing the dents they caused.  I've seen plenty
helm-denting sword blows called light (may have even called a few that
for all I know...).

I still think this is the key. Niether the Markland blunt nor the thistle
hit as hard as most sword or spear shots. You face away from me and let me
hit you with a legal arrow shot or a legal spear or sword shot and you tell
which one hits harder. 

Or let me do it with a thistle on an arrow and a thistle on a quarrel and you
identify which blow was which.

Stefan li Rous
Barony of Bryn Gwlad

Feicfidh me' ari's thu',


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