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The Soviet T-34 tank has sloped armour on all sides of its hull.

Sloped armour is armour that is mounted at a non-vertical and non-horizontal angle, typically on tanks and other armoured fighting vehicles. For a given normal to the surface of the armour, its plate thickness, increasing armour slope improves the armour's level of protection by increasing the thickness measured on a horizontal plane, while for a given area density of the armour the protection can be either increased or reduced by other sloping effects, depending on the armour materials used and the qualities of the projectile hitting it. The increased protection caused by increasing the slope while keeping the plate thickness constant, is due to a proportional increase of area density and thus mass, and thus offers no weight benefit. Therefore the other possible effects of sloping, such as deflection, deforming and ricochet of a projectile, have been the reasons to apply sloped armour in armoured vehicles design. The sharpest angles are usually seen on the frontal glacis plate, both as it is the hull side most likely to be hit and because there is more room to slope in the longitudinal direction of a vehicle.

An illustration of sloped armour. A comparison of a vertical slab of armour on the left and a section of armour sloped at an angle of 45 degrees on the right. The horizontal distance through the armour (black arrows) is the same, but the normal thickness of the sloped armour (green arrow) is less. It can be seen that the actual cross-sectional area of armour, and hence its mass, is the same in each case; for a given mass the normal would have to decrease if the slope is increased.

The cause for the increased protection at a given normal thickness is the increased line-of-sight (LOS) thickness of the armour, which is the thickness along a line parallel to the oncoming projectile's general direction of travel (horizontal or vertical). The LOS thickness is equal to the armour's normal thickness divided by the cosine of the armour's inclination from perpendicularity to the projectile's travel. For example, armour sloped sixty degrees back from the vertical presents to a projectile travelling horizontally a line-of-sight thickness twice the armour's normal thickness. When armour thickness or rolled homogeneous armour equivalency (RHAe) values for AFVs are provided without the slope of the armour, the figure provided generally takes into account this effect of the slope, while when the value is in the format of "x units at y degrees", the effects of the slope are not taken into account.

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.

However, beyond the change in line-of-sight thickness, sloping armour has other effects on the level of protection it provides, which can offer a weight benefit. Sloping armour can cause additional protection-enhancing effects such as shattering of a brittle kinetic energy penetrator or a deflection of that penetrator away from the surface normal, even though the area density remains constant. These effects are strongest when the projectile has a low absolute weight and is short relative to its width. Armour piercing shells of the Second World War, certainly those of the early years, had these qualities and sloped armour was therefore rather efficient in that period. In the sixties however long-rod penetrators were introduced, projectiles that are both very elongated and very dense in mass. Hitting a sloped thick homogeneous plates such a long-rod penetrator will, after initial penetration into the armour's LOS thickness, bend toward the armour's normal thickness and take a path with a length between the armour's LOS and normal thicknesses. If the latter effect occurs, better protection would be provided by vertically mounted armour of the same area density. Another development decreasing the importance of the principle of sloped armour has been the introduction of ceramic armour in the seventies. 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]

Sloped armour can also cause projectiles to ricochet, but this phenomenon is much more complicated and not fully predictable. High rod density, impact velocity, and length-to-diameter ratio are factors that contribute to a high critical ricochet angle (the angle at which ricochet is expected to onset) for a long rod projectile,^[2] but different formulae may predict different critical ricochet angles for the same situation.

Research into the effects of sloping armour plate was first conducted in the 1930s by the French SOMUA, and by the Soviet tank design team of the Kharkov Locomotive Factory. It was a technological response to the more effective anti-tank guns being put into service at this time.

Sloped armour on the front of Soviet T-54 tank, here cut open for demonstration purposes

The principle itself was well known of old and had been in use on warships and partially implemented on the first French tank, the Schneider CA1 in the First World War, but the first tanks to be completely fitted with sloped armour were the French SOMUA S35 and other contemporary French tanks like the Renault R35, which had fully cast hulls and turrets. It was also used to a greater effect on the famous Soviet T-34 battle tank. Sloped armour became very much the fashion after World War II, although not every tank designed since the war makes much use of it.

1. ^ Yaziv, D.; Chocron, S.; Anderson, Jr., C.E.; Grosch, D.J.. "Oblique Penetration in Ceramic Targets". Proceedings of the 19^th International Symposium on Ballistics IBS 2001, Interlaken, Switzerland: 1257-1264. 
2. ^ Tate, A (1979). "A simple estimate of the minimum target obliquity required for the ricochet of a high speed long rod projectile". J. Phys. D: Appl. Phys. 12: 1825–1829.