# 'Piercing Power'

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#### Nevermore

I'm not exactly a physicist, but I do understand most things.
I'm looking for a formula that will give how far into a material a projectile can travel given it's mass, speed, area and the object's density. Is this possible?

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#### Jonathan

I think you need to know the density of the pierced substance, and I think from there the equation is simple, but I can't remember it.

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#### eNtRopY

For a viscous material, the problem is super easy. Just sum the forces.

m1*a = k*(m1-m2)*v
m1*(d^2/dt^2)*x = k*(m1-m2)*(d/dt)*x

Here,

a = acceleration of object
v = velocity of object
x = position of object
m1 = mass of object
m2 = mass of material that object displaces
k = constant of resistance to motion of object in a medium

To incorporate density, just remember that

D = m/V

where, D = density and V = volume.

In order to solve this problem, you will need to specify whether or not the object falling under the influence of a central field potential and if we know the initial velocity.

eNtRopY

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#### eNtRopY

Tryo, he asked for an explicit expression which describes relationships. Have you ever performed the Milikin Oil Drop experiment in class? The situation is very similiar... it involves the calculation of the velocity of an object penetrating a medium.

You can model the physics of the controlling mechanisms of Nevermore's scenario very well using first principles. Furthermore, you can add assume the object is shaped like a sphere, and use a single correction factor to make the analytical result match the observed results.

eNtRopY

N

Thanks.

#### Heathcliff

Newton analyzed penetration of a projectile into a medium as a transfer of momentum from the projectile to the medium. Assuming the medium is being thrown aside at about the same velocity as the projectile velocity, the projectile will stop when the mass of the material thrown aside equals the mass of the projectile, very approximately.

Thus the (length of the hole)/(length of projectile) = (density of the projectile)/(density of the medium)

Or, penetration = constant x (length of projectile)

where constant = the ratio of densities, projectile to medium

So for penetration you want something long and dense. Velocity is less of a consideration. This theory works best for fluids. The case of a projectile hitting a solid involves more factors, such as hardness, fragility, etc.

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#### Heathcliff

Newton was not analyzing inelastic collisions, but penetration into a fluid such as water or air, and his analysis is correct as an approximation and works quite well.

The shockwave from a supersonic bullet is a pressure wave. If a pressure acts on a large area it will create a force that can maybe knock something over in extreme cases, but I fail to see how this would be a factor in penetration. Cavitation likewise.

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#### Heathcliff

Of course cavitation is a problem with propellers, but what does this have to do with the price of tea in China?

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#### Loren Booda

The Reynolds number gives a practical, quantitative and dimensional perspective on problems involving fluid-like flow.

#### Heathcliff

Well, I don't pretend to be an expert on ballistics. If someone can add something meaningful, like cavitation further reduces penetration of a bullet in water by such and such a percent, or pushing air in front of a supersonic bullet reduces its range by such and such a percent it would add something to the conversation, were it couple with an explanation.

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#### Heathcliff

My intuition tells me cavitation is insignificant as a factor in penetration and shockwaves?--well I'm willing to listen to what someone has to say, but since someone can't answer I remain unrefuted.

I went back through this thread, any your first post was quite good, Tyro. I agree with you that a good professional analysis of ballistics requires taking into account a myriad of factors.

But at the same time I think the factors of length and density for penetration are the main factors and make a good approximation. Spear guns for underwater, depleted uranium darts for penetrating tank armor, and this sort of thing.

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#### Heathcliff

Originally posted by Tyro

Spear guns having good penetration underwater? Are you kidding? Just a few tens of feet? Great job proving my point. Spear guns have low velocity projectiles which rely on mass instead of velocity for their kinetic energy. They therefore don't cavitate, if at all, compared to a bullet. RAMICS projectiles are supersonic but have stable cavitation envelopes. Normal bullets are supersonic but have unstable cavitation envelopes.
[/B]
I've tried to shoot many a fish with 22 calibre bullets and they don't go very far at all (the bullets, that is--dont' think I ever hit a fish). Maybe a couple feet. This would be in accordance with the teachings of Newton--long = penetration. Spear goes far; bullet falls short.
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"The RAMICS Super Cavitating Projectile is fired from a standard 20mm rapid-fire gun mounted on the helicopter. Spin stabilized in air, the projectile is designed to enter the water at oblique angles to the surface. Upon water entry, its shape and speed produce a cavitation envelope in which the projectile rides at very low drag.

"The Rapid Airborne Mine Clearance System (RAMICS) mission is to rapidly neutralize near surface, floating and shallow bottom mines providing safe transit and ..."
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Oh, dear, It seems the military still doesn't understand the principles behind penetration. Note that they are shooting "near surface, floating, and shallow..." They should be using spears in accordance with the teachings of Isaac Newton.

Quoting George Gamow: "It is interesting that the length of penetration does not depend on the initial velocity of the projectile (provided that this velocity is sufficiently high). This is the fact that puzzled the U.S. military experts who were dropping from different heights the explosive missiles which were supposed to burrow deep into the ground before busting up. The penetration did not seem to change with the height from whih he missiles were dropped (thus hitting the ground with different velocities) and the experts were sratching their heads until somebody pointed out to them a theory on that subject in Newton's Principia."

#### Heathcliff

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On supercavitating. I've been hearing for the last few months about the supersonic Russian torpedo. I think they call it a "skiva" or something like that, and its secret is that it has a supercavitating skin that enables it to fly through the water with little drag at supersonic speeds. This is pure horse twaddle of course. A projectile still has to push water out of its path. This has led me to associate the word "supercavitating" with "horse twaddle," perhaps unjustly.

As far as you directing me to reading matter, you have to make your own case. Why on earth would I be interested in reading up on theories I regard as horse twaddle, such as cavitation being a major factor in penetration?
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I think you might be foolhardy to challenge the theories of people with the credentials of Isaac Newton and George Gamow.

Newton's model is a simplistic one not suited for real world calculations, but I'll stick with it until a better case is shown to me. It seems to model correctly the phenomena I am familiar with that were discussed here.

1. It offers an explanation of why spearguns are used underwater while bullets virtually stop dead--I phenomenun I have personally observed.

2. It explains the rationale for using dense long rod penetrators in anti-tank rounds.

3. It explains why bombs dropped from different heights penetrate to the same depth.

It is left to the "one percenters" as Thomas Edison would call them to flesh it out with true engineering calculations.

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#### Janus

Staff Emeritus
Gold Member
In case anyone is wondering, All the editing I did to this thread was to remove personal attacks while trying to keep the points of the discusion intact.

It was not fun! I do not know if I have the patience to do it again. So be forewarned : In the future I just might decide to just delete the entire post, rather then try to salvage any of it.

#### Tyro

Janus, you should have just deleted it. Now I'm doing it for you. Some people are hardly worth my effort, it is like me throwing pearls before swine.

#### Nereid

Staff Emeritus
Gold Member
Tyro and Heathcliff,

Personally, I feel this forum is the poorer for what's just happened, and the loss goes beyond the upset that either of you felt.

I found the breadth of material which Tyro posted to be very interesting. Although I have little interest to dig deeper into the subject, I was frankly amazed at how much complex physics is involved, and am disappointed that I've now no ready reference.

Supercavitation is a well understood physical phenomenon, the closest cousin to cavitation is boiling. A supercavity is the last phase of a whole range of cavitation regimes starting with incipient, cloud/vortex cavitation, sheet cavitation and then finally supercavitation. Cavitation occurs when a fluid is accelerated to the point where the dynamic pressure drop causes the static pressure to fall below the vapor pressure of water (remember Bernoulli's equation). A supercavity is defined as a water vapor cavity that envelops the cavitator and exhibits a length longer than several cavitator lenghts.

Before I go on let us examine drag. There are several factors that cause fluid dynamic drag on a vehicle. Chief among these are friction drag causes by the shear stress in the boundary layer and pressure drag caused by the geometry of the vehicle. Supercavitation allows the engineer to substantially decrease friction drag on the projectile (about a 98% reduction) and since the compliant boundary of the cavity interface assumes the most energy efficient profile pressure drag can also be substantially decreased with carefull design of the cavitator nose.

It is important to distinguish the underwater phase of a supercavitating projectile and the water-entry phase of a supercavitating projectile, very different effects are at play during each phase. During water-entry the viscous effects on the projectile can be neglected since the inertial forces are so large the reason the .22 projectile doesn't hit the fish is because the projectile is subjected to a lrage angular velocity during it's water-entry phase because of the asymmetric pressure distrubution in the nose when it hits the water this, the other reason is that the .22 bullet will start tumbling because the it cannot rectify the moments around it's CG because it has a large diameter relative to it's length. A a L/D of ratio of 13 is good for supercavitating projectiles. The supercavity formed during water-entry is vented to the atmosphere and since it's volume is increasing as the projectile moves into the water the pressure inside drops till the supercavity breaks in the middle forming two cavities. The projectile now moves inside a smaller supercavity which can be supported by the formation of water vapor at the projectile nose. This is true supercavitating flight in which viscous effects are quite important.

This actually works. We have designed a projectile that can hit and penetrate a underwater target at 80 - 100 m below the water surface.

Hope it helps.

#### Nereid

Staff Emeritus
Gold Member

The "we" in the penultimate para suggests you played a part in such (or does 'we' simply mean 'us homo saps'?). If so, you may find this thread of some interest

"'Piercing Power'"

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