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You\'ve been tapped by a Scorpius
#1
One of the fun we have with our siege weapons is doing the math of the physics behind them.

So after a lot of internal debate if we should consider drag or not in our range equations, I settled by considering using a discrete system and a simple excel sheet for computation (as opposed to solving the diferential equations).

So we came up with a nice simulator that with a given angle will bring up range and impact energy.

For our computations we assumed our exit speed of 120m/s (our theoretical exit speed was of 132m/s but measured with a high speed camera we came up with 120m/s) a Drag Coeficient of 0.35, our section Area is 0.177x 10^-3 m^2, projectile mass is 0.175 kg and we assumed air density at 1 atm 25ºC (1.18kg/m^3).

So at 120m we hit with 1150 J.

For comparison a .357 magnum hits at 60m with 782 J (.008kg at an exit speed of 442 m/s - no drag).

Our bolts will decrease their impact energy to 755J at 293 m. We tap hard...


Now you might be asking why do we bother, our why should you care. First we find it fun, much like shooting them, predicting and analysing the forces involved in a siege weapon is fun.

Second you might find it interesting as well. I'll update ou page this weekend with all the computations and variables as well as an expanded page with the final physics (ballistics), and I'm considering puting a range simulator for fun as well.
Mário - Cerco 21

www.cerco21.com - Looking back to see further ahead.
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#2
I've uploaded our computations, known variables and a very advanced graphic to our site.(History/Physics)

Take a look and if you find anything that might be wrong, please feel free to correct us.
Mário - Cerco 21

www.cerco21.com - Looking back to see further ahead.
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#3
It's VERY wrong to compare energy of a bullet and an arrow.
For example, a typical 0.22lr bullet has WAY more energy than a typical crossbow bolt, but such a bolt will completly penetrate an elk, where a 0.22 will mostly cause only a minor wound.
"Deadliness" is a tricky bussiness. I think that with arrows, it's the ability to get propper penetration that is the real parameter. And that can be determined only through experiments with the specific arrow, at different velocities.
Regards, Yuv.
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#4
It's not "wrong" to compare them - you can't cheat physics, it treats everyone the same. In your example you are talking about penetration ability, not energy.
--------
Ross

[url="http://galeforcearmoury.blogspot.com"] Working on a segmentata.[/url]
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#5
Quote:It's not "wrong" to compare them - you can't cheat physics, it treats everyone the same. In your example you are talking about penetration ability, not energy.

As Ventus says, you can't cheat physics.

It is true that we've compared simply Kinetic Energy (to be easier to understand), to fully compare you have to compute sectional density, momentum, relative friction, deformation etc.

However we feel that to a layman reader that would be way too much physics. I think that we "disclaim" all over the site where we do aproximations or simply disregard certain forces in our theoretical models to measure them in the actual model.

For example momentum (m*v) is extremely important for penetration as all the kinetic penetrators demonstrate by using very high density metals such as Depleted Uranium or Tungsten, or Tungsten core, this increases mass without increasing volume/area so the sectional density is far more favorable. In case of Depleted Uranium it's density overcomes the impact deformation for example.

But your point is taken, we will write "For simplification purposes we've considered Kinetic energy only - as it amounts to most of the damage dealt"
Mário - Cerco 21

www.cerco21.com - Looking back to see further ahead.
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#6
There is no problem with the physics. It does not lie, but it has many aspects, and not all (namely energy) are proportional to LETHALITY.

And I"m not talking about refinements or marginal differences, but of completely different SCALES. For example: A very powerfull crossbow will shoot a 27gram bolt at 100m/s. It will completely penetrate an elk, cutting two 1" channels all the way. All this with "only" 135J.

A 357mag has ROUGHLY the same lethality (probably less), but with 6 times more energy! Crossbow is a practical and common hunting tool for elks and bears, while 357mag is considered marginal for deer.

0.22 will not kill an elk, and is only good for hunting varmints. But it has TWICE the energy of the bolt. How can we say that energy accounts for most of the damage?

I can't give a definitive formula for "deadliness". I think there are very different mechanisms and physical factors. Given 2 IDENTICAL projectiles, the more energetic will usualy be deadlier. But energy figures are useless when comparing bullets and arrows.

Therefore, if the bolt I described above is comparable (lethality wise) to a 357mag, than your arrow, which is faster and way heavier, is by FAR more potent (thou you cant be twice more dead...)

I"m not critisizing your work. on the contrary. I think your creation is more potent than you credit it and yourself for.

BTW, I mentioned "lethality" several times. But on the battlefield, this is NOT an issue. What you realy want is to INCAPACITATE the enemy soldier. It doesn't matter if he dies quickly (from a bullet), slowly (from an arrow) or not at all, as long as he cant fight.
Regards, Yuv.
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#7
I understand your point, I also belive that in an "lethal"* role momentum has more to say than simply kinetic energy ( so a very small bullet with very high speed can have huge amounts of kinetic energy - it's velocity squared, and very little momentum).

* lethal as in "no you are not combat worthy anymore".

One way to assert this would be by shooting it at balistic gel targets? Any other sugestions?
Mário - Cerco 21

www.cerco21.com - Looking back to see further ahead.
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