# Sloped armour

Sloped armour

Sloped armour is armour that is neither vertical nor horizontal and is typically mounted on tanks and other armoured fighting vehicles (AFVs). For a given normal to the surface of the armour, its plate thickness, increasing armour slope improves the armour's level of protection of a certain point by increasing the thickness measured in the horizontal plane. The horizontal plane is of interest because it is the usual plane of attack, although urban and irregular warfare is more likely to violate this assumption due to the three dimensional nature of the conflict. Given the specifics of tank armour layout and design and modern arms and armour technology this effect has become less important on the modern battlefield. The horizontal thickness is frequently converted to the area density relative to the horizontal which is a better indicator of its protection capability against kinetic energy penetrators.

This 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, and more efficiently enclosing a certain vehicle volume have been the reasons to apply sloped armour in armoured vehicles design. For a given area density of 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. Shaped charge warheads may fail to penetrate and even detonate when striking armour at a highly oblique angle.

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.

The principle of sloped armour

The cause for the increased protection of a certain point "at a given normal thickness" is the increased line-of-sight ("LOS") thickness of the armour, which is the thickness along a line describing the oncoming projectile's general direction of travel. For a given thickness of armour plate, a projectile must travel through a greater thickness of armour to penetrate into the vehicle when it is sloped. 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 this increase 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.

Sloped armour provides increased protection for armoured fighting vehicles through two primary mechanisms. The most important is based on the fact that to attain a certain protection level a certain volume has to be enclosed by a certain mass of armour and that sloping may reduce the surface to volume ratio and thus allow for either a lesser relative mass for a given volume or more protection for a given weight. If attack were equally likely from all directions, the ideal form would be a sphere; because horizontal attack is in fact to be expected the ideal becomes an oblate spheroid. Angling flat plates or curving cast armour allows designers to approach these ideals. For practical reasons this mechanism is most often applied on the front of the vehicle, where there is sufficient room to slope and much of the armour is concentrated, on the assumption that unidirectional frontal attack is most likely. A simple wedge, such as can be seen in the hull design of the M1 Abrams, is already a good approximation that is often applied.

The second mechanism is that shots hitting sloped armour are more likely to be deflected, ricochet or shatter on impact. Modern weapon and armour technology has significantly reduced this second benefit which initially was the main motive sloped armour was incorporated into vehicle design in the Second World War.

The cosine rule

Even though the increased protection to a point, provided by angling a certain armour plate with a given normal thickness causing an increased line-of-sight ("LOS") thickness, is of no consideration in armour vehicle design, it is of great importance when determining the level of protection of a designed vehicle. The LOS-thickness can be calculated by a simple formula: it is equal to the armour's normal thickness divided by the cosine of the armour's inclination from perpendicularity to the projectile's travel or:

:$T_L=frac\left\{T_N\right\}\left\{cos\left( heta\right)\right\}$

where
* $T_L$: Line of sight thickness
* $T_N$: Normal thickness
* $heta$: Angle of the sloped armour plate from the vertical

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, as the cosine of 60° is ½. 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.

Deflection

Sloping armour can increase protection by a mechanism 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. Also the deformed penetrator tends to act as a projectile of a very large diameter and this stretches out the remaining armour, causing it to fail more easily. If these latter effects occur strongly — for modern penetrators this is typically the case for a slope between 55° and 65° — 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. [cite conference | first = D. | last = Yaziv | coauthors = Chocron, S.; Anderson, Jr., C.E.; Grosch, D.J. | title = Oblique Penetration in Ceramic Targets | booktitle = Proceedings of the 19th International Symposium on Ballistics IBS 2001, Interlaken, Switzerland | pages = 1257-1264]

Sloped armour can also cause projectiles to ricochet, but this phenomenon is much more complicated and ad yet 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, [cite journal | author=Tate, A | title=A simple estimate of the minimum target obliquity required for the ricochet of a high speed long rod projectile | journal=J. Phys. D: Appl. Phys. | year=1979 | volume=12 | pages=1825–1829 | doi=10.1088/0022-3727/12/11/011] but different formulae may predict different critical ricochet angles for the same situation.

Historical application

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. 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, its most pure expression being perhaps the British Chieftain. However, the latest main battle tanks use perforated and composite armour, which attempts to deform and abrade a penetrator rather than deflecting it, as deflecting a long rod penatrator is so difficult. These tanks have a more blocky appearance. Examples include the Leopard 2 and M1 Abrams. An exception is the Israeli Merkava.

Notes

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