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Help needed from the grognards: Physics behind penetration

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Playing Combat Mission has rekindled my interest in 20mm miniatures once again. I am fascinated by the concept of armor penetration, kinectic energy, velocity etc., but I don't know enough to understand it. I know there must be a formula out there that will allow me to create a chart whereby I can determine the chance of my tank's survivability. How much does an oblique angle impact penetration? At what rate does muzzel velocity diminish? I have located an interesting web-site that details a formula, but I can't make it work. http://www.wargamer.org/GvA/background/pentypes11.html. It has a lot of information regarding mass of a projectile, velocity, angle, thickness of armor and diameter of the projectile. I am trying to write some miniature armor rules. Can anyone help here? It will also assist me in understanding CM with respect to armored engagements. I thought I recalled a thread with some technical stats on this subject, but my search came up empty. Thanks, John

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Rexford, that's great news. I will be the first to seek it out. In the meantime, how does one determine penetration requirments for sloped armor or armor at oblique facings? The formula given on the sight I mentioned is terribly difficult for me..."at higher angles than 30 degrees, the power of the cosine will increase, leading to a further decrease in penetration." That's some deep stuff. The constant in the formula is n=1.43. A standard four function calculator won't begin to handle it. I'm anxious to see your booklet. The web-site also uses velocity at the point of impact. Gracious sakes, how does one determine that? Most velocity stats are muzzle based. How can we know the diminishing velocity over distance? Velocity is also influenced by the type of ammunition fired. I can use the muzzle velocity for the formula at ranges of 100 meters, but when the distance increases, what is the velocity at impact going to be, at...say 500 meters? Does your booklet cover that? John

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Dear John,

I run the web site that you mentioned. I have 98% completed a new article on the effect of obliquity on penetration. I am awaiting confirmation of some data that I am using from Lorrin Bird, but I hope to have it up soon.

Impact velocity vs muzzle velocity - this is the subject of a separate article, nowhere near complete. Again awaiting some Krupp data. Typical values of velocity loss range from 50 m/s per km range (modern APFSDS) to, say, 300 m/s per km range as a worst case. It does vary with range, but not by much.


US 90mm HVAP loses roughly 160m/s per km.

US 90mm APC loses roughly 80m/s per km.

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"at higher angles than 30 degrees, the power of the cosine will increase, leading to a further decrease in penetration." That's some deep stuff.

John - think back to trig. Old SOHCAHTOA has just reared its ugly head. On a direct hit, the incidence angle is 0 degrees. The cosine of 0 is 1 and thus the full effect of the velocity of the shell, the weight of the shell, and the armor come into play. At any other angle (varying degrees of a "glancing blow") energy is lost according to the cosine of the incidence angle. The "30 degree rule" is an arbitrary cut-off that describes the way the cosine function works. The best way to look at this is in a table:

Cos(0) = 1 = direct hit and full force.

Cos(10) = .98 = only 2% energy lost to angle.

Cos(20) = .94 = only 6% energy lost.

Cos(30) = .87 = 13%

Cos(40) = .77

Cos(60) = .5

Cos(90) = 0 but then, you cant hit something when you are 90 degrees off.

To transmit your kinetic energy (and any additional nasty suprises) to the target you want to lose as little as possible in the incidence angle. And for angles less than 20 you are stull getting good bang for your buck.

Of course, after wolrd war II, FMC decided that ablative armor is a pretty good idea. That way, any non direct hit would just knock away outer layers of metal. They even came up with a way for direct hits. Rather than allow the projectile to determine the size of the contact patch (and small radius high velocity rounds have great penetration) they decided to explosively eject an outer layer of armor that gets hit and then pushed back into the tank body, but then the contact patch is the size of the ejected outer laywer instead of the projectile. The much larger surface area was quite nice.

Er, back to the topic. The loss of projectile velocity due to air friction is how tank guns are rated: ie kills 5inch armor at 500 feet. Interesting things like higher density shells (carry more inertia), rifling, gravity (always nice to shoot downhill) all add to longer effective kill ranges.

You also asked a question about the loss of shell velocity in the muzzle. Since the shell is being ejected by expanding gas, just use Boyle's Law along the length of the barrel. Really long barrels have much greater volume and thus can actually slow a shell. But then things like recoil and rifling are trade offs that are made in shell velocity (and also, material science in that the shell charge could be so great that the barrel itself simply shatters when firing the "hot" load).

They are some great articles on the net about balistics, but perhaps the best resource would be to look up the hyper velocity gun. The truly mosterous guns that Germany built in France to shoot at England had valves all along the length of the *very* long barrels to insert more fuel and thus get more expanding gas for the projectile.

Man, there are just so many factors here. I would still like to point out that even if you built a megalithic tank with a ton of armor, shells that don't penetrate can still kill the tank in that the concosuive air wave in the tank can kill the personell. And then loads like magnesium of phospehrous rounds that cause the tank metal to heat unevenly and thus tear itself apart are nasty suprises for penetration.

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Slope effects are a function of the T/D ratio for a particular type of ammo, such as APCBC (T is armor thickness, D is projectile diameter for steel rounds). Why T/D?

When a hammer hits a thick wall it may bounce off without a dent, whereas the same force may blow a plug of material out of a thin wall. The thicker the wall relative to the projectile diameter, the more material pushing back on the shot and the harder it is to penetrate.

When 50mmL42 APC from PzKpfw III in Russia hit KV side turret wall, they bounced off without a visible dent. T/D was very high and too much material to even push the surface very far.

Rounds penetrate sloped armor by pushing out a plug and following the plug down through the armor. This is very difficult to model with physics but easier to model using published penetration data. Analysis of tests shows that T/D and angle are the factors that matter.

U.S. Army Technical Manual TM-9-1907 has penetration data vs. angle and range for APCBC and HVAP. British NPL report has slope equations for AP, as does TM-9-1907.

We have U.S. test of 122mm APBC with flat nose, based on captured IS-2m gun and turret from Berlin. Really low slope effect since projectile doesn't have a nose and noses:

1. bend on impact, absorbing energy

2. hit the walls as projectile moves thru plug, using energy

The only real way to predict slope effect is to analyze penetration data and plot results vs. T/D for particular angles.

When Panther 75mmL70 APCBC hits 63mm at 60° from vertical (30° from horizontal), slope multiplier is 3.1!!!!!!!!

This means that a round that can penetrate 190mm at 0° (vertical armor) can also penetrate 63mm at 60° from vertical at same velocity. Both armors will have same equivalent thickness.

This is how slope effect or multipliers are calculated from penetration data, find penetration at 500m vs. 0° vertical, find penetration at 500m vs. 60°, divide 0° penetration by 60° penetration and that is the multiplier that converts 60° penetration to 0°. Note T/D ratio for 60° penetration and plot slope effect at 60° vs. T/D ratio.

If slope effect = T/(cosine(angle)) raised to 1.43 then 60° slope effect is 2.69, which is too low for Panther vs. T/D = 0.84 (63/75).

Most of the slope multipliers in published documents are based on a single data point, such as slope effect at 500m, because it is hard work plotting multiplier vs. T/D and results cannot be easily presented to non-technical types. British reports state that slope effect is function of many factors including plate thickness and projectile diameter.

We plotted slope effect vs. T/D vs. angle for different ammo types using equations fit thru data, and it takes about 12 graphs to do everything including tungsten rounds.

The spreadsheet takes data on projectile, armor thickness and compound angle (result of lateral and vertical angles taken together to form a single angle) and cranks out the slope effect and then compares everything to penetration at 0° and range, and says whether it penetrates or not.

Since penetration data is based on 50% success when penetration at 0° = equivalent armor resistance at 0°, penetrations can occur when penetration is less than resistance and shots can bounce when penetration exceeds resistance.

Think of it this way, penetration and armor resistance calculations represent AVERAGE values and variations occur in almost all projectiles and armor. Three hits on the same armor in different areas with similar angles can result in three different results.

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You guys are terrific! Please let me know when your publication is ready. I spoke with a physics teacher at the school where I work today. He was very interested in the concept and, not being a WWII enthusiast, hadn't contemplated the topic at great length. He did, however, lend me a T1-83 calculator that enables me to plug the numbers into the formulas you spoke of. With this calculator, I can multiply the projectile's mass times the velocity squared, times the diameter of the projectile raised to the 1.43 power, divided by "C" the constant of 2.5, divided by the shell's diameter cubed...all raised to the 1/1.43 power to determine "T" or thickness of the armor perforated. My problem arises when I have to consider not only the slope of the armor, but also the angle of attack. Also, in what way does the distance impact penetration? The muzzle velocity doesn't change for all practical purposes although air friction plays its role, but rather the angle at which a shell strikes due to gravity and a falling shot. Is not the angle more important than the velocity? In attempting to create a game that works, I will have to fudge on a chart. Otherwise, any poor devil who attempts to determine armor penetration will have to calculate the darn thing with a sophisticated machine. Well, that's where I hope your work will help. You guys obviously know what you're talking about. Thanks for the feedback, and let me know when it's available.

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Guest Big Time Software

The really fun part about calculating impact velocity is that as a shell travels through the air, it decelerates at a rate proportional to the square of its current speed, meaning that the faster it's going, the more it decelerates. So a shell actually suffers greater deceleration early in its flight compared to later. This is also why super-speedy tungsten rounds decelerate so much (and part of the reason why their long-range performance isn't so good).


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This is from the Combined Fleet Webpage (Imperial Japanese Navy Website)...There a links to penetration calculators, from a person name Nathan Okun "the Godfather of Terminal Balistics" It's actually kind of cool if you run the programs and do the reading lots of math!



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- Emperor Hirohito (1940)

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Any chance this sort of info will be posted in a form non-mathematicians/physicists will be able to appreciate? Are there any introductory books/articles on ballistics that don't assume much pre-existing math knowledge? I'd like to learn more about this, but my degrees were in the liberal arts smile.gif


War is cruel and you cannot refine it. --Sherman

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U.S. 76mm APCBC steel shell vs HVAP tungsten core.

This is from U.S. penetration data:



HVAP- 232













HVAP loses penetration faster but still ends up with more penetration. HVAP is also more accurate due to flatter trajectory.

The big difference is the slope effect. At 55°, HVAP multiplier is 3.25, APCBC will be lower against armor thickness based on T/D. HVAP slope effect is not influenced by T/D.

HVAP is brittle and tends to break against sloped armor, which is why multiplier is so high.

How does one estimate velocity vs. range, use the DeMarre equation.

If a round has 130mm penetration at 0m and 92mm at 1000m, moving terms around in DeMarre equation indicates that velocity ratio at range is proportional to penetration ratio raised to 0.7 power.

(92/130) raised to 0.7 power is 0.785, so if muzzle velocity is 2600 fps than estimated velocity at 1000m is 0.785 x 2600 fps, or 2041.

We use this all the time and it works reasonably well for almost all ammo, including HVAP but with a little less accuracy (but results still reasonable).

Soviet APBC flat nose rounds have three different velocity regions where the power number changes drastically. Pushing a flat nose through a plate at high velocity is alot easier than at low speed, due to shape, whereas pointed or rounded noses have less drastic changes between high and low velocity (although they still do and using one 0.7 exponent on penetration ratio is a simplification.

We have read all of Okun's work and correspond with him. His work on plates in contact was used to estimate Sherman Jumbo resistance.

If velocity squared in DeMarre equation is equal to plate thickness raised to 1.4 power times a bunch of irritating constants, then taking the square root shows that velocity is proportional to penetration T raised to 0.7 power. This is powerful and lets one estimate striking velocity vs range for almost any round if one om velocity and penetration and penetration data vs. range.

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<BLOCKQUOTE>quote:</font><HR>Originally posted by Big Time Software:

... as a shell travels through the air, it decelerates at a rate proportional to the square of its current speed, ...<HR></BLOCKQUOTE>Not the square, the cube (^3)...




Srategy is the art of avoiding a fair fight...

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<BLOCKQUOTE>quote:</font><HR>Originally posted by Big Time Software:

The really fun part about calculating impact velocity is that as a shell travels through the air, it decelerates at a rate proportional to the square of its current speed, meaning that the faster it's going, the more it decelerates. So a shell actually suffers greater deceleration early in its flight compared to later. This is also why super-speedy tungsten rounds decelerate so much (and part of the reason why their long-range performance isn't so good).


Its because of the viscous nature of air.

Please dont confuse HVAP/AP40 with APDS. HVAP and AP40 will scrub velocity alot quicker than APDS.

Both have accuracy problems from unique attributes/foibles of their designs. HVAP and AP40 would be very dependant on the hard fixed penetrator being centered in the light fixed casing. Any off centered weight and the spinning round would go stupid.

APDS is very dependant on the discarding sabots being equal in mass and leaving the penetrator without imparting a disturbance force. This is a problem in rifled weapons.

If an APDS was fired true and the sabots left neatly, then it would fly nicely and scrub alot less velocity than a solid shot due to its mass to weight ratio.

Both these ammo types for all nationalities would be used at short ranges. I am sure that the germans had a SOP on maximum ranges for them. In certain situations (like firing into the side of a tank) they could be less effective. They had no HE content and made a very small hole and could concievably fly right on through the two sides of the tank.

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