Talk:Sloped armour

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Contents 1 Angles 2 Picture 3 Efficient use of space 4 Excuse me

[edit] Angles

At thirty degrees to the horizontal the effect is about fifty percent.

Is that the equivalent of 50% thicker armour, 50% greater chance of deflection, 50% greater deflecting force? This needs an explanation and a reference source. —Michael Z. 2005-11-9 00:01 Z

None of the above. I just rewrote most of the article, but the last two paragraphs still need some work. Ergbert 19:48, 24 March 2006 (UTC)

Sorry, but the "fallacies" you removed are in fact correct. The increase of slope offers no direct weight advantage because of LOS increase. That is the common fallacy made :o).--MWAK 09:10, 23 June 2006 (UTC)

In fact it DOES "offer direct weight advantage". For example, steel plate sloped @60degs has 2x LOS thickness, but can have up to 2.6x effective protection level (of the equivalent vertical armor plate). However, exact level depends on the shape of the projectile. Pointed (ballistic caped) ones are affected stronger - main reason is that kinetic energy is distributed upon a larger area of impact. Warning: that's true for (post-)WW2 era steel armor, nowadays things became a lot more complicated. 195.98.64.69 03:53, 12 June 2007 (UTC)

Yes, but that's an indirect advantage :o). What I meant was the effect implied by the increase in LOS thickness as such. We are thus not in disagreement. However the effect can at sixty degrees result in a factor much larger than 2.6 if the projectile is light enough.--MWAK 06:36, 12 June 2007 (UTC)

The article said nothing about protection at a given areal density -- it specifically referred to protection at a given normal thickness. Most of what you put in just isn't true, so I'm removing it again and clarifying what I wrote previously. Ergbert 03:44, 23 July 2006 (UTC)

Yes, the version you wrote had these defects :o). But I must admit that the present wording is much more precise. However, could you point out why you believe that the following points are untrue or shouldn't be explicitly mentioned:

1. There is a conceptual difference to be made between deflection in general and the special case of ricochet.
2. The shape of the penetrator and especially its length-diameter ratio influences the degree of deflection; older bullet-shaped rounds were more easily deflected.
3. Because the point of impact is also a friction point for bullet-shaped rounds the effect of "turning into the plate" negates deflection at angles below 45 degrees.
4. For bullet-shaped rounds the highest increment of deflection is around 67 degrees.
5. There is such an effect called the "back plate effect", a function of T-D ratio; for modern long-rod penetrators its easier to penetrate a plate at sixty degrees to the vertical than a vertical plate of the same area density, for the reason that the deformation of the penetrator leads to a different T-D ratio.
6. The reason why ceramic tiles benefit less from sloping is mainly their large face defeat component.
7. Modern tank design doesn't strive for deflection anymore simply because modern penetrators are difficult to deflect; for WWII tanks the benefits of deflection were the main reason to implement the principle of sloped armour, not the surface-volume ratio.

These, I think, are points so fundamental and generally accepted that it surprises me that anyone could consider them contentious. Could it also be that you have been focussed too much on modern developments? Deflection is unimportant for modern penetrators but was a major defeat mechanism in early WWII. --MWAK 06:54, 23 July 2006 (UTC)

1. What exactly do you mean by "deflection"? I have some texts on armor penetration from circa WWII and I don't recall them making that distinction (and if "deflection", as opposed to ricochet, was then the most important advantage of sloped armor (What about shattering of brittle penetrators? That's certainly mentioned.), I think they would've).
2. Shape and L:d ratio do affect ricochet, but the results for shape not only differ, but reverse, in different situations, and I did mention L:d ratio. There are also different sorts of bullet shapes.
3. "Increment of deflection" is something I have never encountered in all my reading on the subject...67 degrees is close to the ideal obliquity for deflecting WWII-era carbide-cored and APC shot (60-65 degrees), however, so maybe that's what you mean? AP shot is best defeated at only about 30 degrees obliquity, however.
4. The back plate/surface effect is why penetrators turn into the plate; it isn't responsible for the total destruction of armor.
5. Interface defeat seems to be pretty uncommon. Sloped ceramics are less effective at a given area density due to their earlier fracturing.
6. Sloped armor is still widely used today, and ricochet is still very much possible and likely a major reason for heavily sloped armor. Ergbert 04:09, 24 July 2006 (UTC)

I'll try to answer your points and (hopefully) make myself more clear:

1. Ricochet is a apecial case of deflection as a round doesn't have to "bounce off" the armour; even when it "gets stuck", it might still be deflected and this will affect penetration. Apart from problems in producing thick armour plates, the main reason to implement sloped armour was to benefit from deflection in general. You discuss the mathematical analysis first, but the article should first give the functional reason for the design concept and then give the mathematics — and mainly to point out there is no direct weight benefit, a mistake most people seem to make.
2. I agree, but it should be made explicit in the text that older penetrator shapes in general were much more prone to deflection, whereas for modern penetrators it's often easier to penetrate through armour that is sloped. See point four.
3. My wording was confusing. What I meant was that the derivative function peaks around 67 degrees. Between zero and 45 degrees the differential gains by increasing the slope are negligable, but then quickly start to increase. After 67 degrees (this is merely the theoretical optimum within a simplified model; actual numbers may vary) they again decline. This however does not mean that the ideal obliquity is to be found there, unless by "ideal" you mean: giving the ideal mix of deflection and surface-volume effects. After all, the shallower the angle, the better the deflection. That AP shot would be best defeated by thirty degrees armour is only true when the backplate effect is strongly relevant, i.e. with very large WWII rounds hitting armour that would, when sloped while keeping a given area density, be thinner than a quarter of the diameter of the round — or, if APDSFS is included in "AP" — with modern penetrators (at very long distances as their trajectory is so flat).
4. The backplate effect is often associated with 88 mm Tiger rounds punching out entire slabs of sloped T-34 armour that would have been able to resist them without it. Certainly the modern penetrator can't bring about such catastrophic failure. Nevertheless the main mechanism causing at sixty degrees a lesser protection than LOS thickness, is the backplate effect. This is counterintuitive. A round with such a small diameter simply shouldn't benefit from it. But when the tip of the penetrator bends upwards, this gives the same effect as a large diameter: it overloads the tensile strength of the remaining armour just the way a large round would, be it mainly in one axis. The rotation effects are secondary. Tate's article, though a classic, is very dated on this point.
5. Indeed I know of no ceramic able to effect a interface defeat against a large caliber penetrator :o). But even when penetration occurs, there has been a face defeat component of the total protection rendered, simply by the dwell caused by the surface resistance. And precisely because of the subsequent fracturing you mention, that feace defeat component is so important. We seem to refer to two aspects of one and the same effect and thus be in agreement ;o).
6. Well, ricochet with long rod penetrators is possible at only very shallow angles. Tate was even a tad optimistic. Only the Merkava seems to be designed with deflection in mind. That doesn't mean sloped armour isn't important any more — far from it. But it is used to deform and, above all, break the penetrator.--MWAK 14:03, 1 August 2006 (UTC)

"Back plate/surface effect", "interface defeat"? Sounds like this article and/or armor-piercing shot and shell need some work so the rest of us can read up and follow the conversation. —Michael Z. 2006-07-24 05:57 Z

I just created a short article on interface defeat. I hope it's long enough to be helpful. For the back surface effect, I'd prefer to find a good, reliable source that clearly defines it before I try to explain it. Ergbert 20:44, 24 July 2006 (UTC) Update: I added a mention of it to penetration (weapons). Ergbert 21:44, 24 July 2006 (UTC)

I partially rewrote the article emphasizing some points that, I believe, are as such not contentious between us, but might not be readily apparent to the average reader.--MWAK 07:31, 8 August 2007 (UTC)

Likewise. The fallacy in this section "Increasing the LOS-thickness is not however the motive for applying sloped armour in armoured vehicle design. The reason for this is that it offers no weight benefit. To maintain a given mass of a vehicle, the area density would have to remain equal and this implies that the LOS-thickness would also have to remain constant while the slope increases, which again implies that the normal thickness decreases. In other words: to avoid increasing the weight of the vehicle, plates have to get proportionally thinner while their slope increases. " is, I hope, evident. You can get a real effective thickness increase against a horizontal projectile by turning a box on it's end. The diagram I replaced included triangular 'end caps' to make the armour horizontal at top and bottom. As the length increases, the cross sectional area of these end caps become negligible relative to the area of the rest of the plate and, in any case, is incorporated into adjacent armour plates. Dhatfield (talk) 13:27, 24 April 2008 (UTC)

Yes, you obviously can get a an effective thickness increase for the same plate thickness — but not for the same weight. In the diagram you inserted blocks C and D have the same mass, but not blocks A and B. You try to get around this simple truth by reffering to the "end caps" as if they indeed were negligable, but you seem to have become confused: obviously when the inclination increases their mass proportionally increases with it. The incorporation within adjacent armour plates is irrelevant for a LOS hit --MWAK (talk) 14:56, 24 April 2008 (UTC)

Blocks A and B are identical, therefore identical in volume and mass. The CAD program I used renders the one in the foreground bigger, but they are the same in terms of dimensions. I can re-render so that the effect is not so noticeable, but 3D rendering will always make foreground objects larger. I could swop them so that the sloped one looked smaller. As the inclination increases, the 'end caps' do become larger but that is really irrelevant. For a fair comparison there should be no end caps in either case so that they are identical - as in my picture. Dhatfield (talk) 15:17, 24 April 2008 (UTC)

The picture and text were misleading. I have uploaded a better picture. Dhatfield (talk) 16:29, 24 April 2008 (UTC)

I apologise: I only observed the picture for a fraction of a second before I allowed my exasperation to get the better of me and make me write a protest :o). But the protest is still well justified. Blocks A and B have the same mass but also in principle the same protection value: the average area density on the LOS is equal. B only offers a better protection in the middle of the area to be protected. As you say — and if a block is simply rotated — for a fair comparison no end caps should be present. Meaning that where they lack, protection is sacrificed, obviously exactly proportional to the protection gained in the middle. Of course, in a special case the protection offered by B would be superior: if a penetrator could penetrate 30 units of armour anyway, but not 42.4. And there is the special case the, let us say, "top" and "bottom" plates would be as thick as the block and then your argument of incorporation within these plates would indeed be valid — another mistake I made. But in fact this special case never holds, for all tanks rather have much thinner top and bottom plates.

The picture is also very deceptive in that a block of a given length and thickness has only one position in which it would after rotation precisely cover the full area to be protected. Any less rotation and the area density would decrease because the edges would project beyond it; any more rotation and it would at once be obvious holes begin to appear that would necessitate a thinning of the block to stretch it out — a proportional thinning, keeping the area density equal, showing sloping has no weight benefit!--MWAK (talk) 16:55, 24 April 2008 (UTC)

If I may venture a guess: you had been thinking in terms of point protection. But a tank is very much a set of points ;o).--MWAK (talk) 18:01, 24 April 2008 (UTC)

The point I am trying to make with the picture (obviously badly, I will work on it further) is simply that of trigonometry. As the armour plate increases in slope, the horizontal LOS thickness increases. That is very simple. If you take the example blocks A&B and expand each one out into a plate, the same principle applies. D, with exactly that same mass and internal volume as C has a 45 degrees slope (relative to the horizontal) on all sides and the interior of D is better protected than C (with respect to fire from the horizontal), despite being otherwise identical. Dhatfield (talk) 18:24, 24 April 2008 (UTC)

Yes, obviously the LOS thickness increases — but only in the middle of the area to be protected. So if you wanted to protect only a single point and have a certain armour plate to do it with, you'd better angle that plate. But in vehicle design the mission is to protect, not just a single point, but a certain area. Angling then will not assist in increasing the area density. You could also consider it this way: given a certain protective mass, no rearrangement of whatever kind of that mass could possibly influence the area density. By definition.

Your statement "If you take the example blocks A&B and expand each one out into a plate, the same principle applies. D, with exactly that same mass and internal volume as C has a 45 degrees slope (relative to the horizontal) on all sides and the interior of D is better protected than C (with respect to fire from the horizontal), despite being otherwise identical" confuses three different cases: the first is not a simple application of the same principle and for the second your statement, if "C" and "D" would be replaced with "A" and "B" and "interior" by "area to be protected", would be simply false. Obviously to provide the same area with a constant LOS thickness block A would not have to be expanded and B would, so B would become heavier and not have the same mass and internal volume as A (case 1). If you do not expand (case 2) — then the mass and volume are equal, but the average protection (the area density) is equal too. That B in case 2 offers a 45° slope on all points is true, but the question is whether it offers the same increased LOS thickness on all points — and it does not: you would have to add those "end caps" (in fact adding the end caps is what "expanding into a plate" means). And at this point I very much fear your reaction will be: "Ah, but we have already determined those end caps are irrelevant". But we have done no such thing. You seem to have confused yourself by concluding from the fact that they should be absent to ensure that A and B have the same mass, that they do not need to be considered to determine the protection offered. This is, however, a non sequitur. By angling you simply concentrate more of the mass in front of the centre of the area to be protected. This is done at the expense of the marginal areas above and below the centre. If the rotation is completed, bringing your presumed general angling benefit to its optimum, the centre is protected by the full prior height of the block; and two gaping holes have appeared. Would you then still claim this is irrelevant and the protection can simply be equated to that height?

Now you might retort by "Ah, but with expansion I meant creating a connection between the glacis and the top and bottom plates. They will compensate for the deficiency". Now this aspect creates a situation much more complex than the idealisation of the basic principle of angling. But true enough; they might. However, this simply means assuming the top and bottom plates provide a sufficient extra mass. In a fair comparison, that mass should already have been present when determining the protection value offered by the unrotated block A. It is thus not valid to add that mass only to block B to compensate for the deficiency. Now a special case might hold: if the top and bottom plate are very thick a certain amount of redundant mass would be present, that would, as it were, be put to good use by angling the block. True. But this is only a special case. And worse: it is a special case that in the actual world has no instantiation. For no operational armoured vehicle ever had such thick top and bottom plates. Tanks are preferably not built with redundant mass. And if you would make them only thick enough just behind (or below in front of) the glacis, just enough to compensate; why, they would then be those "end caps" ;o)

However, there is also a third case: that of "C" and "D". It is very true that the volume in block D is much better protected than that in block C. But again not as a simple application of the principle. In D you have two angling plates in front, the lower one comforming to the bottom plate of C. So in the special case, again, that the bottom plate would be as thick as the front plate, which, again, in reality never is the case, you had better move that mass to the front. In this case this can be simply done by rotating the cube, which creates those two frontal angling plates. But the angling as such is immaterial: you might as well have kept the cube in the same position and made the bottom thinner and the front thicker and thereby moved the mass. In fact within the context of a frontal LOS hit, this would even be considerably superior, as the rotation increases the area to be protected!

--MWAK (talk) 06:34, 25 April 2008 (UTC)

You make a very good point and I had to think this through carefully again. Please take a look at Figure 2. I increased the dimensions of the plates perpendicular to the normal and measured the volumes of all the components in this hypothetical situation: the end cap volume for a 30mm plate is 35110cm^3 each and the plate volume is 291600cm^3. Therefore each end cap weighs 8% of the weight of the plate. To get equivalent weight overall, we must thin the plate by 16%. If we thin the plate (to 23mm) and recalculate the LOS thickness by the formula on the main page, it is 32.5mm. That is nearly, bit not exactly, 30mm. Therefore, it is not true to say that there is no added LOS thinkness due to sloping in this case. Longer sections in the vertical (relative to their thickness) have less thinning due to end caps, and very short, thick sections (such as A and B) are thinned to the point where the LOS thickness is reduced. Mitigating against this are the thin top and bottom plates that do take some of the end cap additional mass but I agree that the glacis plate is much thicker so this effect is limited. On the other hand there are the considerations of normal fracture of ceramic plates and bending of rods so that normal (rather than LOS) thickness is important. I agree that due to factors specifically relevant to modern AFV design (shape of interior compartment, height restrictions, thin top and bottom plate), AFV designers would not view sloping of armour as a method to reduce armour weight for LOS thickness reasons only. I will try to write a section that explains this. Dhatfield (talk) 09:56, 25 April 2008 (UTC)

Well, there can, by definition, for a given mass not be any added LOS thickness. I think your calculation is off the mark because of using approximations. You refer to volumes; but these would be dependent on the plate width, which is immaterial. If we limit ourselves to the cross-section, it is obvious that the ratio of the cross-section of the "end caps" to the cross-section of the remainder of the plate, depends on the plate length, which is variable. Should we limit ourselves to the special case in which a 30 mm plate after a rotation of 45° again exactly covers the area to be protected, this plate would be about 72,4 mm long (thus not a very realistic case :o); the cross-section of the end caps would add about 41%. The plate would therefore have to be thinned to 21,213 etc, etc. mm. If we reverse the classic cosinus-rule the end result is exactly 30 mm. Ergo: no added LOS thickness. --MWAK (talk) 07:45, 26 April 2008 (UTC)

I'm afraid I don't follow your example. "...it is obvious that the ratio of the cross-section of the "end caps" to the cross-section of the remainder of the plate, depends on the plate length, which is variable." In which case we cannot make general statements regarding whether sloping necessarily results in weight saving (for a given LOS thickness) or not. It must vary on a case by case basis (specifically thickness to length ratio). Not so? Dhatfield (talk) 16:27, 28 April 2008 (UTC)

Not so: the combination of the end caps and the plate length variation ensures an exact trade-off. The length increases tangentially with the angling; to keep the cross-section surface constant — which is a given: the question is whether angling offers a protection benefit for a given mass — the surface normal has to decrease accordingly. How could it possibly be otherwise? However, for any plate with a thickness greater than zero, there is the added complication that at first the angling will make the front and back faces protrude beyond the area to be protected. The greater the relative thickness the more important this effect. This is what I have tried to tell you: your black cuboids have precisely the proportions to make the length irrelevant for a 45° angle, but this is only one special case and therefore deceptive. --MWAK (talk) 18:30, 28 April 2008 (UTC)

In Figure 3, I have sheared or sheared a given solid through 30 and 60 degrees. The volumes of all three is the same, as is the LOS thickness, but the normal thickness decreases. Is this the point you are trying to make? Dhatfield (talk) 21:11, 28 April 2008 (UTC)

For my first two sentences, probably yes — if the top of the rotated plates is to be interpreted as a horizontal surface.--MWAK (talk) 04:52, 29 April 2008 (UTC)

The shearing effect of constant LOS thickness and decreasing normal thickness on sloping only applies if you assume that you are trying to protect a constant vertical height. In AFV design you are not trying to do that at all. You are trying to protect an internal volume. The shape of that internal volume is dictated by what you want to put into the tank. Consider a driver and assistant seated behind and under the glacis plate - the shape of their bodies conforms to a sloped plate. Frankly, I find you discussions hard to understand and you are more persistent than I am so your opinion will appear on the main page, but I would urge you to stay away from sweeping statements. Dhatfield (talk) 13:17, 10 May 2008 (UTC)

Well, it not so much applies regarding protecting a certain height, but a certain area as opposed to certain volume. It is very true that sloped armour is often more efficient for the latter purpose and in the article I indicated this superior efficiency as the main reason in modern armoured vehicle design to apply sloped armour. However, this issue is different from the one constituted by the simple fact that sloping a plate increases the LOS-thickness. I assumed we had reached consensus that any weight benefit offered by this simple principle is illusory — and thus adjusted the article confident to express, not my personal, but our shared opinion.--MWAK (talk) 18:10, 10 May 2008 (UTC)

Sorry, lost my cool a bit there. I like the re-write, except for this paragraph "The mere fact that the LOS-thickness increases by angling the plate is not however the motive for applying sloped armour in armoured vehicle design. The reason for this is that it offers no weight benefit. To maintain a given mass of a vehicle, the area density would have to remain equal and this implies that the LOS-thickness would also have to remain constant while the slope increases, which again implies that the normal thickness decreases. In other words: to avoid increasing the weight of the vehicle, plates have to get proportionally thinner while their slope increases, a process equivalent to shearing the mass." Given that you are protecting an internal volume, not an area, to say "it offers no weight benefit" is misleading, in my opinion. Given certain constraints, the statement is true, but those constraints are generally not true in AFV design, which is what sloped armour is all about. In my opinion, this article is not about the (very artificial) case of shearing a plate while maintaining constant area protection, rather, it is about the use of sloped armour in AFV design. Not so? Dhatfield (talk) 21:19, 11 May 2008 (UTC)

Yes it is. And in the context of AFV-design the two main reasons to apply sloped armour are efficiency in enclosing a certain volume and deflection. However, many popular accounts make the natural mistake to assume that you can easily improve the design of a given AFV by simply taking its armour plates and rotate them, not understanding that for the resultant increase of LOS-thickness a price has to be paid in proportional weight increase. As this mistake is so very common and easy to make, we point it out, at the same time creating a context in which the cosine rule can be mentioned. I have to admit the text as it stands is dangerously ambiguous as "it offers no weight benefit" does not to refer to sloped armour in general but to "the mere fact that the LOS-thickness increases by angling the plate". I will replace the "it" by "this increase".

I also noticed that you mentioned the wedge shape in your last edit as being an ideal. However, it is an ideal for the combination of efficient volume protection and constant deflection over the area to be protected. When looking to the pure case of volume protection efficiency the curvature corresponding to that of an oblate spheroid is still ideal, even in the case of frontal attack. Approximations are the boat-shaped hulls of the M48 and the Swiss Panzer 61; and the turrets of the Soviet T-54/55 and T-62. Of course, for practical reasons this ideal was never attained (if only to increase the deflection at the point of the nose by making it more pointed) and it is not suited for welded plates.--MWAK (talk) 05:58, 12 May 2008 (UTC)

With respect to "At any given area density, ceramic armour is also best when mounted more vertically, as maintaining the same area density requires the armour be thinned as it is sloped and the ceramic fractures earlier because of its reduced normal thickness.^[1]" Is it the area density effect that makes sloped ceramic armour less effective? Dhatfield (talk) 13:39, 24 April 2008 (UTC)

In combination with the fact that cracks tend to propagate perpendicularly.--MWAK (talk) 14:56, 24 April 2008 (UTC)

But is that not falling back on the area density / LOS argument we are having above? Dhatfield (talk) 15:17, 24 April 2008 (UTC)

[edit] Picture

Nice picture Graeme!--MWAK 07:08, 28 June 2006 (UTC)

It came about it while playing with my son's wooden bricks - take two triangular ones slide them past each other and voila! GraemeLeggett 08:44, 28 June 2006 (UTC)

[edit] Efficient use of space

Another motive is the fact that sloping armour is a more efficient way of enveloping a certain volume with armour; it thus reduces a vehicle's internal volume, removing space that would go unused, thereby minimizing the vehicle's size and thus mass.

Neither the logic of this sentence nor the theory behind it make sense. It also seems to contradict the earlier assertion that sloped armour "offers no weight benefit".

How is sloping armour "a more efficient way of enveloping a certain volume", and how does efficiency reduce internal volume? (Is this backwards logic meaning that reduced volume is more efficient?) What is "space that would go unused"?

And yes, reducing volume necessarily reduces size and mass, but "smaller" and "more efficient" are not synonyms. In fact, it means that a vehicle would have to be larger to have the same internal volume, which sounds less efficient to me. The odd-shaped spaces under sloped armour are probably more difficult to utilize.

There may be something to say on this topic regarding AFV design, but I'm removing this until we figure it out. —Michael Z. 2007-10-01 17:55 Z

Yes, the sentence should be changed, but not everything about it is wrong:

1. Efficient here mainly means "light"; in tank design you want to minimise the weight of a vehicle for a given level of armour protection. The lightest way of enveloping a certain volume is of course by means of a sphere. A sphere is obviously a very "sloped" object and by applying sloped armour a tank better approximates this ideal form. This why the M48 looks the way it does :o).
2. The article nowhere states that sloping armour offers no weight benefit; it states that the fact that by sloping you can use thinner plates to obtain the same LOS-thickness offers no weight benefit. There certainly is a weight benefit, caused by a more efficient form and (in some cases) by deflection.
3. The sentence doesn't state that efficiency reduces volume but that sloping reduces volume and thus sloping is more efficient.
4. However, you do have a very good point in that the "thus" is misplaced. There are two separate aspects: one that for a given volume and armour protection a sloped form is lighter; the other that for a given set of dimensions (height, length and width) a sloped form compared to some blockier shapes has a smaller volume and by this virtue then is lighter also. Whether it can thus be called more efficient depends on the importance of the absolute volume of the vehicle. If that importance is low, e.g. with the Mark I that simply needed a certain length to cross trenches and a proportionate width and height, then a sloped form is more efficient as the volume as such is less important; it then indeed removes unused space. However if you must place a certain desired weapon system within the vehicle and are also constrained by size limitations, such as a maximum width imposed by railway transport or a maximum height imposed by considerations of vulnerability reduction, it might well be more efficient to have a more squat form within the given dimensions. In practice the first aspect is more important than possible absolute space requirements within the second aspect; using a wedge-form prevents odd-shaped spaces.
5. The sentences thus should be :

Another motive is the fact that sloping armour is a more weight-efficient way of enveloping a certain volume with armour; it also for a given set of dimensions potentially reduces a vehicle's internal volume; if thereby removing possible unused space, this further minimises the vehicle's mass.

--MWAK 19:58, 1 October 2007 (UTC)

That still doesn't make sense, although I'm still trying to wrap my head around all of it. I think we may be trying to summarize two or more factors in a single statement.

Sure, if you start with a boxy tank that's full of unused space, you can add sloped armour to improve protection and decrease weight. But making a smaller boxy tank accomplishes that too, so this does not demonstrate any benefit of sloped armour.

But since the benefits of sloped armour and reduced size/weight have been recognized in the 1930s, no one designs a tank than way. You start with a fixed volume based on the design requirements (e.g., room for power train, suspension, four crew, a gun and 30 rounds), and design a functional shape that encloses the volume.

Given a fixed volume, will sloped armour of the same thickness make the vehicle lighter or heavier?—simple logic says heavier, because you are going further away from the optimal sphere, cube, or cuboid towards more complex geometry. But given the same volume, will sloped armour of the same protection level make the vehicle lighter, heavier, or the same?—I don't know. —Michael Z. 2007-10-01 22:57 Z

The last question could also be restated with sloped armour of the same weight rather than the same protection level (presuming that volume and weight of interior components are fixed). —Michael Z. 2007-10-01 23:47 Z

The point is that the cube is not optimal; it has much more surface for a given volume than a sphere. By sloping you go from the cube to the sphere, so to say. Complexity as such is irrelevant. A dodecahedron (my favourite solid :o) is more complex then a cube but still more weight-efficient. Therefore by sloping armour for a given volume and protection level the vehicle can be made lighter; or for a given volume and weight can be better protected.--MWAK 07:38, 2 October 2007 (UTC)

Yes, truncating the corners of a cube reduces its volume and gets closer to a sphere. But we are not doing that. We are not reducing the volume.

But to make a tank hull you start with an oblong box of a fixed volume. Then you stretch its front into a wedge, making it longer. If you slope the sides, you have to make it wider to account for the lost space. You end up with a flatter shape of the same volume. It becomes less efficient. To me, the boxy Tiger looks more spherical than the stretched-out T-34.

Anyway, we should base this on some reference. —Michael Z. 2007-10-03 05:29 Z

I think I see what you mean. We should make a distinction between two cases:

1. Firstly the general case that a sphere is the most weight-efficient means of enveloping a certain volume and that thus a more spherical form is superior in this respect. You can truncate a cube and make its dimensions somewhat larger, thus maintaining the volume but reducing the surface. Such a truncated cube is more weight-efficient. Such a form would ideally not have a constant slope. If we apply an infinite number of truncations, the result will be a curved armour. The turrets of many tanks from the fifties and the hull of the M48 are very good examples.
2. But then, as you say: tanks are in fact not spherical. Indeed not any sloping will be weight-efficient. What about the special case — that is in fact quite common for tanks — that the hull has more or less the form of a cuboid with a sloped plate at the front end? At first blush such a shape seems less efficient. This is not simply because it makes the vehicle at some places longer or wider: if you slope one side but keep the same volume, this indeed increases absolute dimensions: some part of the tank is getting longer; however the top (supposing you recline the plate) is getting shorter. The inefficiency resides in the fact that it may make the vehicle more "pointed" and such sharp angles are obviously less "spherical". In fact however for two reasons a negative design effect does not occur:
3. If we change the angle of the frontplate by rotating it around its central horizontal axis from the vertical to a more sloped position, the vehicle volume remains equal but the surface increases. Nevertheless there will be no weight penalty — on the condition that we keep the areal density constant along the LOS. Yes, we do now have a larger surface to defend and, even worse, this surface is less well armoured. But that is to say: perpendicular to the plate. As in reality the penetrators move more or less on the horizontal plane only, we can in this instance happily disregard the general case effect. All we care about is whether incoming shells can be stopped and the sloped armour, despite increasing the surface, offers the same protection for a given weight (even without any deflection effect).
4. The second reason is that tanks have in fact not one but two sloped plates at the front, the bottom one truncating the point formed by the upper one (or vice versa). If well designed this should negate most surface increase or ideally lead to small decrease.
5. In the case of the T-34 the upper side and front armour truncate each other at the top; and the lower side armour again cuts off the large corner point that might possibly have been created by using sloped armour on two axes. It is a pretty efficient design. The Tiger, though applying some sloped armour, has some very ineffcicient forms, especially the gun mantle.--MWAK 12:33, 3 October 2007 (UTC)

Okay, #3 makes sense. I even drew a section of the glacis plate out on graph paper. I'm not positive that the angled plate with the same horizontal thickness will be exactly lighter to offset its increased length, but the difference is probably not very significant, and probably more than compensated for by ricochet effect.

But I don't get #4. If we simply divide the vertical plate into two and angle the glacis and lower front plate in opposite directions, we see that we simply have two instances of #3, which did not add or save any weight or space. If the plates are not symmetrical then some minor adjustment has to be made, but in my second sketch that looks like it would have to either reduce the volume or enlarge the horizontal roof or belly plate.

So the end result is pretty close to the squared box in terms of space efficiency. So it looks to me that the savings in weight is due to the better efficiency of armour due to deflection effect, and not at all due to geometry. —Michael Z. 2007-10-03 17:15 Z

Be positive. It is True ;o). Regarding #4, you're correct in assuming we basically have two instances of #3 here, but you forgot that in #3 the shortening of the top plate is cancelled out by a proportional lenghtening of the bottom plate, whereas in #4 the two half-systems are, as it were, back to back to each other, so this effect doesn't take place. If we take the simple case of the two sloped plates being, looked at from the side, the diagonals of squares halving the front of the rectangle of the hull, these two plates have a length of 1,4 (square root of 2) compared to the length of a vertical plate, but they cause a reduction of the length of the top and bottom plates with a length of 0,5, resulting in a slight gain in general surface-volume efficiency. However, as the sloped plates weigh the same as the vertical plate for a given LOS-protection, the real gain will in fact be the full weight of the reduction of the top and bottom plates. And if the angles increase, so does the reduction. In modern tanks this effect alone reduces the weight of the total vehicle armour package by 3-5%. Not much, but not negligible either.

And keep in mind a reclined front plate is just one special case of sloping in general. The makers of the M48 claimed a 25% vehicle weight reduction (compared to a completely unsloped tank, that is: not the M47 :o) and probably the Swiss achieved about the same.--MWAK 12:19, 4 October 2007 (UTC)

oops, back to remedial geometry for me! Now, does a citable source exist which explains this? —Michael Z. 2007-10-05 19:23 Z

In this detail? Perhaps. Most technical publications take such basic knowledge for granted and most basic publications aren't technical enough...I'll try and find something.--MWAK 06:03, 7 October 2007 (UTC)

I know. It's not critical that it happen immediately, but it would be good to find a source backing some of the fundamental principals we're covering in the article. —Michael Z. 2007-10-08 20:38 Z

[edit] Excuse me

I don't think that that discussion is properly well directed.

One, it's untrue that 'sloped armour' born pratically in '30s. Since the beginnings, with individual armors this was well known, see the medioeval armours. Then there were naval turrets, in all the respects the anchestors of tank tecnology

Apart this, just to understand: T-34 had rougly the same armour of an italian M13 or a german Pz III or IV, and the weight of this latter; How can be supported that his protection did not gave 'weight benefits?'. So sloping armour, must been a huge mistake because after seen T-34 germans started to project Panther and Konigtiger, and all the tanks produced since then have sloped armour at least in the glacis. This lead a less internal volume with a tank with the same size. But the gain about weight efficience, in some manners, is still present. If not, all the sloped tanks had: a more complex and expensive design, less internal space, no efficiency weight-resistence?

Just look to HE and HEAT ammo: many projectiles and missiles are not capable to detonate reliably if they hits over 60 degrees. APDS ammunitions, expecially US early models (before M111 generation) were notoriously with a nasty tendency to bounce. And given a sufficient angle,there is no projectile that can assure the penetration. With some calculations, as example, WWII battleship ammunition capable to pierce vertical armour of 800 mm with 85 angle degrees can just make 40-50 mm horizontal deck with the corrispondent, 5 degrees on the horizontal. It was a well known fact, since no battleship had a horizontal armour comparable with a vertical belt. Simply, this depended by angle of fall.

Moreover, there is effective a twice benefict: let's take Tiger tank: it can have an effective armour, but it was a sort of 'box'. The roof, 26 mm thick, was wided, and perhaps also the bottom. This meant some weight more. Panther, with 80mm well sloped had a better resistance than the vertical armour of Tiger.

Apart this, Panther had another advantage: the multiple angle complex. If someone fired to the Tiger flank, they were 82 mm thick but just vertical: firing to them at 60 degrees and they will began a LOS of 164. But with the Panther, 45 mm flanks were sloped let's say 30 degrees. Applyng to an already sloped (vertical) surface a 60 degrees lateral shot meant to have a tri-axial businnes. If the ammunition was granted to pierce until 65 degrees, with this double angle to face is pratically impossible to pierce, regardless of the theoric capability.

This is also true with early APDS: one of the value about british guns showed that they can pierce let's say with APDS 17 pdr, something like 250mm. Well, at 60 degrees this fallen to around 70, just a bit better than the normal APCBC. This was true for those early high speed projectiles. Now it's not so true, but still, Merkava shows that this is not a lost of time to project 'sloped tanks'. Apart this, a sloped armoured is more likely to have a profile less visible on the ground, thank to a more slim aspect, less rectangular and box-like. Also this helps to improve defence.--Stefanomencarelli 12:51, 24 October 2007 (UTC)

Again: it is merely stated that the fact that thinner armour plating can be used for the same area density offers no weight benefit — after all the area density is the same!

On the other point you are completely correct: as the article states there is a deflection benefit and it is more weight-efficient. And yes, a tri-axial analysis is sadly lacking. We need better sources.--MWAK 20:08, 24 October 2007 (UTC)

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While in the pure 'angular analysis' it's true the fact of sloped armour -no benefits to thiker but not sloped (i.e. 100mm vertical offers cleary the same weight/surface than a 50mm/60°), it's evident that this was not the case in real tank tecnology.

You says that there are needed better sources. This is what i have:

1- Naval weapons of the world, really a lot of stuff all around guns and ballistic:

Naval weapons of the World

with the tecnical aspects (i recomend to read the articles, there is some information) in: Guns and Mountings/ Ammunition/ The Nathan Okun Naval Gun and Armor Data Resource sections, like: Tecnical section

Among the surprisin datas you can find that Iowa guns; [406 mm Mk 7] with 5,7° angle of fall, are capable to pierce 664 mm vertical and... 43mm horizontal armour...with a rate of around 15:1! This could explain why armour, like BMP or even M1 Abrams have so sloped glacis (0ver 70-75°).

2-Some pages about:

-modern armour penetration (mm and degrees included): Mc Kanzie page

-For armour estimation: Armour and projectile performances

-For old guns: The russian battlefield

-And: WWII veicles, here the tab of british guns (much more are available)

Note that 17 PDR has indicated, with APBCB: 172 mm at 0, 132 at 30, 62 at 60 degrees. The APDS: 280-200-...70. The 20PDR had too : 300/240/80. This explain oustanding how sloped armour worked with these early ammo. 17PDR APBCB had a ratio of 2,9:1 reduction to 60° sloped armour, APDS was around 4:1. Far more in both cases, to the theorical 2:1.

3-But above all i have this: Tanknet forum, especially it's possible to look to this: Armour scientific forum. I know the 'usual' wikipedian objection with forums, but believe me, this one really worths to be analyzed. I rate so well Tanknet to have downloaded almost all the discussions. THere you can have datas, talk with experts like Antony G. William, P.Labowsky, TTK Ciar, and many more, and have the help needed to better understand (sources included, they not talk without knowledge) every stuff about armour, modern, ancient, basic principle.

That' all folks.--Stefanomencarelli 10:51, 25 October 2007 (UTC)

The sites you mentioned are very useful and anybody interested in the subject would be well advised to take good note of them, but I was really referring to published sources giving a more general analysis of the subject. Websites make poor footnotes...And even the people posting at Tanknet, though far better informed than the average armour enthusiast, are not armour engineers and often do not seem to fully understand the very interesting articles they make available to a larger public. And those articles are again too technical and limited in scope. You are of course right in asserting that the older types of ammunition were much more liable to deflection.--MWAK 13:25, 25 October 2007 (UTC)

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well, for such tecnical datas you well understand that there is not such glamour bibliography like let's say F-16. I rate that, in the british armour pen. datas:

'British and American Tanks of World War Two, The Complete Illustrated History of British, American, and Commonwealth Tanks 1933-1945, Peter Chamberlain and Chris Ellis, 1969

'World War II Infantry Anti-Tank Tactics, Gordon L Rottman, 2005'

'Cromwell Cruiser Tanks, 1942-1950, David Fletcher & Richard C Harley, 2006'

Are well valuable for a internet site. After all, how many have artillery books in their house?

The Warship.com has both historical sources well referenced, like Campbell, and well referenced and known authors like S.Slade, that i alredy know since 1994 in missile naval warfare field.

I know that much of this stuff is outside the usual for a wiki.article, but atleast we have 'more than enough' to check. Once Wiki article will grow enough in complexity and deepth, i think these things will became much useful as well. Perhaps for that time Wiki.en will have 5,000,000 articles, but i think that it will done. Already some wiki.articles are based on Navweapons.com, just as example.--Stefanomencarelli 17:45, 25 October 2007 (UTC)

Apparently Stefano has been banned for a year for being too abrasive. I'll look into his links and see if there is anything of value. This is unfortunately a topic with esoteric physics that treads very close to classified info, so good info is hard to come by. Dhatfield (talk) 14:51, 24 April 2008 (UTC)