Thickness / Diameter Question

[Guest mdc]

Concerning T/D ratios

 

I would assume that this works both ways?

 

If you have 42mm's of armor being fired at by a 37mm gun then your armor would be

equivalent to 42 / 37 = 1.13513514 * 42 = 47.6756757

 

Is this correct?

 

 

Regards

[Catalan]

Is the diameter of the ammunition being fired 37mm?

[Guest mdc]

Is the diameter of the ammunition being fired 37mm?

394909[/snapback]

 

Yes

[Geoff Winnington-Ball]

For a brief moment I thought Tanknet had hit a new low...

[DwightPruitt]

For a brief moment I thought Tanknet had hit a new low... 

394969[/snapback]

 

Only in the Scientific Forum.

[jwduquette1]

Concerning T/D ratios

 

I would assume that this works both ways?

 

If you have 42mm's of armor being fired at by a 37mm gun then your armor would be

equivalent to 42 / 37 = 1.13513514 * 42 = 47.6756757

 

Is this correct?

Regards

394907[/snapback]

 

I can't tell if you’re kidding or not, but no, it doesn't work that way. t/d is simply a ratio. It is normally just an intermediate step used in a larger equation. Like the DeMarre Equation. Due a Google search for "DeMarre Equation" to see its entire form. You'll see t/d (or e/d) is just one part of a much bigger mess.

 

t/d by itself is – amongst other applications – sometimes used as a means of comparing performance of different caliber projectiles to each other. Like an efficiency thing. Which projectile or which armor is doing a better job.

 

For example: Maybe I am looking at some 37mm AP projectile that penetrates 40mm of armor at 30-degrees at a velocity of 2300-fps -- or whatever. And maybe I'm also looking at a 50mm AP projectile that does 54mm at 30-degrees at 2400-fps. I don't really know which one is more efficient by just looking at this jumble of numbers. But I can reduce or normalize this mess into a couple of simple t/d values and immediately see which projectile is more efficient. In this case, the t/d for both projectiles is about 1.08. So I'm comparing apples to apples. You can see that the 50mm AP projectile is less efficient than the 37mm round. Moreover for an identical t/d value the 50mm AP round is penetrating with a velocity of 2400-fps. The 37mm round only needs a striking velocity of 2300-fps to successfully penetrate t/d=1.08.

Edited November 21, 2006 by jwduquette1

[Guest mdc]

I can't tell if you’re kidding or not

 

Actually I wasn’t kidding, I guess I am showing my ignorance on the subject, but if I don’t ask then well I remain ignorant on the subject.

 

I have seen people talking on forums about T/D ratios and how it is used in determining overmatching and also how it reduces the effect of sloped armor.

So if a larger shell hitting a thinner armor has an effect on the penetration process in reducing the amount of effective armor and also leading to a possible overmatch I thought that the opposite must be taken into consideration a smaller shell striking a thicker armor must have a similar effect.

 

Thank you for your response, I will look up the DeMarre Equation.

 

 

Best Regards

[Guest pfcem]

Actually I wasn’t kidding, I guess I am showing my ignorance on the subject, but if I don’t ask then well I remain ignorant on the subject.

 

I have seen people talking on forums about T/D ratios and how it is used in determining overmatching and also how it reduces the effect of sloped armor.

So if a larger shell hitting a thinner armor has an effect on the penetration process in reducing the amount of effective armor and also leading to a possible overmatch I thought that the opposite must be taken into consideration a smaller shell striking a thicker armor must have a similar effect.

 

Thank you for your response, I will look up the DeMarre Equation.

Best Regards

395241[/snapback]

Let me see if I am getting this straight.

 

You're thinking is that a projectile of greater diameter than the thickness of the armor it is penetrating reduces the effective thickness of the armor and are asking if the reverse (smaller diameter projectile vs thicker armor increases effective armor thickness) is true?

[Guest mdc]

Let me see if I am getting this straight.

 

You're thinking is that a projectile of greater diameter than the thickness of the armor it is penetrating reduces the effective thickness of the armor and are asking if the reverse (smaller diameter projectile vs thicker armor increases effective armor thickness) is true?

395327[/snapback]

 

Yes, this is what I have read on some other forums.

[Guest pfcem]

Yes, this is what I have read on some other forums.

395334[/snapback]

As jwduquette1 has pointed out, it does not work that way.

[Mobius]

Let me see if I am getting this straight.

 

You're thinking is that a projectile of greater diameter than the thickness of the armor it is penetrating reduces the effective thickness of the armor and are asking if the reverse (smaller diameter projectile vs thicker armor increases effective armor thickness) is true?

395327[/snapback]

Isn't that the nature of a x/y relationship? You increase one factor it reduces and you increase the other it increases. Mathematically it can be no other way.

But you just can't increase something like the diameter without a corresponding increase in mass or the equations won't work.

Though you have to start somewhere, so the question would be "compared to what?".

Edited November 22, 2006 by Mobius

[Guest pfcem]

Isn't that the nature of a x/y relationship?  You increase one factor it reduces and you increase the other it increases.  Mathematically it can be no other way.

But you just can't increase something like the diameter without a corresponding increase in mass or the equations won't work.

Though you have to start somewhere, so the question would be "compared to what?".

395608[/snapback]

No. Changing (increasing or decreasing) x does nothing to y (or visa versa). It does change the value of x/y though.

[Mobius]

No.  Changing (increasing or decreasing) x does nothing to y (or visa versa). It does change the value of x/y though.

395685[/snapback]

So when you increase x x/y stays the same?

[Guest pfcem]

So when you increase x x/y stays the same?

395766[/snapback]

Did you even read what I posted?

 

Changing x does change the value of x/y but does not change y.

 

The value of x/y (or t/d in this case) is not a constant. As jwduquette1 pointed out it is "simply a ratio" used as part of a larger equation.

 

While it is true that projectiles with different t/d values are effected more or less by different factors such as slop of the armor (or more accurately, the angle of impact), mdc's thinking that it is mathematically represented by the value of t/d (hense the idea that if t increases that d increases proportionally to t) is not correct.

[Paul Lakowski]

Your looking at this the wrong way around. Start from a 'semi infinite' target. This is a target whos thickness is so great the projectile can't penetrate. The resultant depth of penetration is refered to as "Penetration". In actual fact its the thickness of plate that prevents the 'back plate effect' from contributing anything measurable to the penetration.

 

[note: "back plate effect" is the effect of shockwaves bouncing of the rear of the plate , thereby weakening the rear portion of the plate. Some times it leads to failure of the plate through plugging cracking etc etc. A similar effect occurs if the target plate is not very wide in relation to the diameter of the projectile. For AP types this weakening occurs when the ratio is less than 4 plate d to 1 projectile D , but with modern rods is anywhere from 20 plate d to 30 plate d to 1 projectile D.]

 

Any way if you reduce the thickness of the plate , progressively the impact of this back plate effect increases in relation to the penetration. So effective penetration increases. Eventually if you reduce the plate thickness enough the projectile will completely perforate the plate. This is then refered to as perforation. From that point on if you reduce the thickness of the plate the energy needed to penetrate or length of projectile needed to penetrate is reduced. At some point the ultra thin plate offers almost no resistance at all.

 

T/d is critical to understanding why some projectiles 'penetrate' one thickness but can 'perforate'an even greater thickness. The rule of thumb is perforation is 1 diameter more than penetration for rod projectiles and this is independant of angle, so at 60o its effectively 2 d extra penetration etc etc. The angle rule of thumb works for flat rod projeciles up to about 70o region, but not sure how much more than this it works at. Projectiles with sharp noses have the oposite effect so that advantage is reduced with increasing angle...which is why virtually all modern penetrators are flat nose or stepped configuration.

 

Unfortunately I the 'armsandarmor.net' is not functioning otherwise I would up load some papers. "itsuneek", any luck with the problem?

[jwduquette1]

Your looking at this the wrong way around. Start from a 'semi infinite' target. This is a target whos thickness is so great the projectile can't penetrate. The resultant depth of penetration is refered to as "Penetration". In actual fact its the thickness of plate that prevents the 'back plate effect' from contributing anything measurable to the penetration. 

 

[note: "back plate effect" is the effect of shockwaves bouncing of the rear of the plate , thereby weakening the rear portion of the plate. Some times it leads to failure of the plate through plugging cracking etc etc. A similar effect occurs if the target plate is not very wide in relation to the diameter of the projectile. For AP types this weakening occurs when the ratio is less than 4 plate d to 1 projectile D  , but with modern rods is anywhere from 20 plate d to 30 plate d to 1 projectile D.]

 

Any way if you reduce the thickness of the plate , progressively the impact of this back plate effect increases in relation to the penetration. So effective penetration increases. Eventually if you reduce the plate thickness enough the projectile will completely perforate the plate. This is then refered to as perforation. From that point on if you reduce the thickness of the plate the energy needed to penetrate or length of projectile needed to penetrate is reduced. At some point the ultra thin plate offers almost no resistance at all.

 

T/d is critical to understanding why some projectiles 'penetrate' one thickness but can 'perforate'an even greater thickness. The rule of thumb is perforation is 1 diameter more than penetration for rod projectiles and this is independant of angle, so at 60o its effectively 2 d extra penetration etc etc. The angle rule of thumb works for flat rod projeciles up to about 70o region, but not sure how much more than this it works at. Projectiles with sharp noses have the oposite effect so that advantage is reduced with increasing angle...which is why virtually all modern penetrators are flat nose or stepped configuration.

 

Unfortunately I the 'armsandarmor.net' is not functioning otherwise I would up load some papers.  "itsuneek", any luck with the problem?

395822[/snapback]

 

I think it is important to make a distinction between rigid, non-deforming projectile penetration mechanics and hydrodynamic deforming\eroding rod penetration\perforation lest some folks become confused. Moreover, there is no need to add an additional term to existing rigid projectile penetration equations such as DeMarre or the USN 1931 Equation in order to account for back surface effects. These equations are already “perforation†or “complete penetration†equations.

 

Regards

JD

[jwduquette1]

I think most of us are typically interested in either the thickness penetrated or the limit velocity associated with a given thickness of plate. Empirically developed relationships for determining rigid projectile complete-penetration often take the following generalized form:

 

T/D = V[(0.5/K)(W/D^A)]^B

T = plate thickness

D = projectile diameter

W = projectile weight

V = limit velocity

K = is an empirical coefficient

“A†and “B†are exponents

 

Most of us would probably want to rearrange this form of the equation into something that we can use to solve directly for either "T" or "V". If we want thickness completely penetrated "T" we might resolve the above into the form:

 

T= DV[(0.5/K)(W/D^A)]^B

 

Plate thickness that will be completely penetrated “T†is than the dependent variable (our “Y†value so to speak).

 

If we are talking about a specific projectile –for example 3†M79 AP – weight and diameter become constants. D will always be 3-inches and W will always be 15-lbs. Velocity “V†is than our independent variable (our “X†value so to speak). When every value of the variable “X†is associated with one and only one value of another variable “Y†we say that “Y†is a function of “Xâ€. This is typically written as y = f (x).

 

For 3†M79 AP our y = f(x) is:

 

T = f(V)

 

For each assumed value of “Vâ€, there is one unique plate thickness “T†that will be determined from the function T = f(V).

[Gille]

T= DV[(0.5/K)(W/D^A)]^B

 

As I understand it this is the form of equation for penetration at 0 degree angle of impact.

 

How is that generalised for a projectile striking at an angle, say A?

[Gille]

Just to go on, from reading I understand the basic form of the slope multiplier equation for effective thicknesses is of this form:

 

1/(Cos A)^C

 

where C is an empirically determined co-efficient, the values of which I have seen ranging from about 1.4 to 1.7, and no allowance is made for overmatching effects.

 

So to apply that, if a plate of thickness 75mm is hit by a 75mm round at say 30 degrees, then the slope multiplier is (using C=1.6):

 

1/(cos 30)^1.6 = 1.26

 

so that plate would resist penetration as well as a vertical plate of thickness

 

1.26*75 = 95mm

 

If that 75mm thick plate was instead hit at 30 degrees by:

 

- a 40mm round

 

- a 122mm round

 

then as I understand it in real life testing in the first case the effective armor would be > 95mm (ie slope multiplier > 1.26) and in the second the effective armor would be < 95mm (ie slope multiplier < 1.26)

 

The question is then how to work the t/D ratio into the slope multiplier formula so as to account for these results?

Edited November 25, 2006 by Gille

[jwduquette1]

As I understand it this is the form of equation for penetration at 0 degree angle of impact.

 

How is that generalised for a projectile striking at an angle, say A?

396625[/snapback]

 

My intent was to keep it simple, and at the same time define what a function is, as well as define what the dependent and independent variables are within a function.

 

As you have indicated in your above post, an obliquity term can and was introduced into various forms of full caliber -- non-deforming projectile -- penetration equations. It was not always done in this manner. Sometimes a look-up table was used to convert the zero obliquity results into either an equivalent thickness at obliquity, or equivalent limit velocity at obliquity. I suppose both approaches have merit. To me, inclusion of the obliquity term directly into the empirical relationship is far more elegant than plodding through a set of look-up tables. However, it is not always so simple to capture the nuances of obliquity effects with one simple term within an equation. Empirical data does not always lend itself readily to application of a simple regression equation.

But in terms of what I was talking about earlier the generalized form of the DeMarre equation might look something like this:

 

T/D = K D^A [ (W/D^ (V/C)^E Cos^D(Ob)]^F

 

The only new terms are:

 

Ob = Obliquity

C = The DeMarre Coefficient

 

There are a couple of additional exponents. The DeMarre coefficient was specific to a particular projectile. However DeMarre did develop a look-up chart of DeMarre coefficients. This is tucked into a set of papers I have at home somewhere.

 

Let’s say we are again interested in a specific projectiles ability to obtain a complete penetration (or perforation if you like) over a range of potential targets. As we are interested in thickness penetrated we rearrange the DeMarre into:

 

T = D K D^A [ (W/D^ (V/C)^E Cos^D(Ob)]^F

 

If our projectile of choice is again 3†M79 AP, than weight and caliber are held constant at 3†and 15-lbs respectively. Assuming we are using the look up chart to determine our DeMarre coefficient, we have two independent variables and one dependent variable, and we write this as z = F(x,y).

 

Plate thickness penetrated “T†is our dependent variable, and limit velocity “V†and plate obliquity “Ob†are the independent variables. “T†is a function of “V†and “Obâ€, and we write: T = F(V,Ob). For each unique combination of “V†and “Ob†there is one unique solution “Tâ€.

 

As to your question:

Gille Said:  “…how to work the t/D ratio into the slope multiplier formula so as to account for these results?â€

 

I’m not sure I understand. If this is the general form of our equation

 

T/D = K D^A [ (W/D^ (V/C)^E Cos^D(Ob)]^F

 

You can rearrange it via algebra into whatever form you like, and examine whatever specific "dependent variable" you want. If you wish to make T/D an independent variable and examine its effects on say limit velocity “Vâ€; velocity becomes the dependent variable. You need to reaarange the equation such that “V†ends up on the left side of the equation and T/D ends up on the right side of the equation. Our function than becomes:

 

V = F(T/D, Ob)

 

If a specific projectile is being examined than D is a constant, and our function becomes:

 

V = F(T, Ob)

 

As you will quickly surmise, the algebra is not so fun when solving for “Vâ€. But it can be done if you use a bit of elbow grease.

Edited November 28, 2006 by jwduquette1

[Gille]

JW

 

What I'm trying to understand in a qualitative sort of way is what (if any) variables other than obliquity influence the relative effectiveness of sloped versus unsloped armor.

 

if I start with the generalised De Marre equation:

 

T/D = K D^A [ (W/D^ (V/C)^E Cos^D(Ob)]^F

 

and solve for thickness of armor penetrated in absolute terms:

 

T = K D^A+1 [(W/D^ (V/C)^E Cos^D(Ob)]^F

 

which indicates that T is a function of D, W, V and Ob, with constants K, A, B, C, E and F

 

Then if I consider the ratio for a particular shell hitting at a fixed impact velocity of:

 

T(at obliquity Ob)/T(obliquity zero)

 

Then almost all of the terms cancel out and I get (if my algebra is right):

 

T(obliquity Ob)/T(obliquity zero) = Cos^DF(Ob)

 

which would indicate that the relative penetration of a shell against sloped armor as compared to vertical armor is a function of D and Ob.

 

And since Cos^DF(Ob) is always <1 for Ob>0 that makes sense, penetration is less against sloped armor than vertical.

 

What does seem peculiar to me is that if that is correct, then increasing D will produce lower values of Cos^DF(Ob) which means larger shells have a lower penetration ratio?

[jwduquette1]

JW

 

What I'm trying to understand in a qualitative sort of way is what (if any) variables other than obliquity influence the relative effectiveness of sloped versus unsloped armor.

397185[/snapback]

 

Hey Gille:

 

Many of these sorts of equations include various constraints over which they are intended to produce accurate information. If you go beyond these boundary conditions, you may or may not be getting accurate predictions. One such assumption is that the the projectile is "rigid and non-deforming" during perforation. This is an O.k. assumption at 0-degrees out to say 30-degrees or so -- depending upon the projectile. However, the effects of obliquity -- slope effects if you like -- often include braking or deforming a projectile. Now I don't want to go overboard in stressing this particular aspect, as some of these equations are based upon extensive empirical data bases that can include larger numbers of high obliquity tests. Just be aware that some of the older equations are heavily based upon empirical data within the obliquity range of about 0-degrees to 30-degrees. It’s always good to check actual ballistic test data against equation predicted data to get a feel for what the equation is doing and how accurate it is doing things – particularly at obliquities above about 30-degrees.

 

 

if I start with the generalised De Marre equation:

 

T/D = K D^A [ (W/D^ (V/C)^E Cos^D(Ob)]^F

 

and solve for thickness of armor penetrated in absolute terms:

 

T = K D^A+1 [(W/D^ (V/C)^E Cos^D(Ob)]^F

 

which indicates that T is a function of D, W, V and Ob, with constants K, A, B, C, E and F

 

Then if I consider the ratio for a particular shell hitting at a fixed impact velocity of:

 

T(at obliquity Ob)/T(obliquity zero)

 

Then almost all of the terms cancel out and I get (if my algebra is right):

 

T(obliquity Ob)/T(obliquity zero) = Cos^DF(Ob)

 

which would indicate that the relative penetration of a shell against sloped armor as compared to vertical armor is a function of D and Ob.

 

And since Cos^DF(Ob) is always <1 for Ob>0 that makes sense, penetration is less against sloped armor than vertical.

 

What does seem peculiar to me is that if that is correct, then increasing D will produce lower values of Cos^DF(Ob) which means larger shells have a lower penetration ratio?

397185[/snapback]

 

There are scale effects with full-caliber AP projectiles. What I have seen in various empirical studies of full-caliber AP projectiles is that smaller caliber projectiles will typically penetrate armor less efficiently than larger caliber projectiles. You can see this by normalizing perforation to t/d values and comparing limit velocities of two sets of projectiles with differing calibers. A smaller caliber projectile will invariably require more velocity to penetrate the same t/d ratio.

 

Scaling Effects and the DeMarre Equation: You can convince yourself of this by comparing two projectiles of differing caliber and plotting limit velocity as a function of t/d – V=F(t/d). The figure below is a comparison of 37mm M86 APC vs. 16†Mk8-6 APC. When doing this you may want to stick with projectile comparisons in which W/D^3 are similar. This way the contrasts in projectile weights aren’t masking some of the scale effects. The following figure shows the DeMarre Equations take on scale effects for 37mm M86 APC vs. 16†Mk8-6 APC. As you can see for the same t/d ratios, the larger projectile is penetrating with less effort.

 

Figure: DeMarre Equation Scale Effects

 

Slope effects and the DeMarre Equation: DeMarre handles slopes effects differently than the USN 1931 Equation. Unlike the USN 1931 Equation, the DeMarre Equations slope effects are completely independent of the t/d ratio. See the figure below.

 

Figure: DeMarre Equation Slope Effects

 

I am using the following Form of the DeMarre Equation:

 

T/D = (0.00005021) D^0.07144 [(W/D^3) (V/C)^2 Cos^3(Ob)]^0.71429

 

Best Regards

Jeff

Edited November 27, 2006 by jwduquette1

[DB]

Jeff, more superb stuff, thanks.

 

David