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Sloped armour is armour that is neither in a vertical nor a horizontal position. Such angled armour is typically mounted on
tank A tank is an armoured fighting vehicle intended as a primary offensive weapon in front-line ground combat. Tank designs are a balance of heavy firepower, strong armour, and good battlefield mobility provided by tracks and a powerful ...
s and other
armoured fighting vehicle An armoured fighting vehicle (AFV) is an armed combat vehicle protected by armour, generally combining operational mobility with offensive and defensive capabilities. AFVs can be wheeled or tracked. Examples of AFVs are tanks, armoured cars, ...
s (AFVs), as well as
naval vessels A naval ship is a military ship (or sometimes boat, depending on classification) used by a navy. Naval ships are differentiated from civilian ships by construction and purpose. Generally, naval ships are damage resilient and armed with w ...
such as
battleship A battleship is a large armour, armored warship with a main artillery battery, battery consisting of large caliber guns. It dominated naval warfare in the late 19th and early 20th centuries. The term ''battleship'' came into use in the late 1 ...
s and
cruiser A cruiser is a type of warship. Modern cruisers are generally the largest ships in a fleet after aircraft carriers and amphibious assault ships, and can usually perform several roles. The term "cruiser", which has been in use for several ...
s. Sloping an armour plate makes it more difficult to penetrate by anti-tank weapons, such as armour-piercing shells (
kinetic energy penetrator A kinetic energy penetrator (KEP), also known as long-rod penetrator (LRP), is a type of ammunition designed to penetrate vehicle armour using a flechette-like, high- sectional density projectile. Like a bullet or kinetic energy weapon, thi ...
s) and rockets, if they follow a more or less horizontal trajectory to their target, as is often the case. The improved protection is caused by three main effects. First, a projectile hitting a plate at an angle other than 90° has to move through a greater thickness of armour, compared to hitting the same plate at a right-angle. In the latter case only the plate thickness (the normal to the surface of the armour) must be pierced. Increasing the armour slope improves, for a given plate thickness, the level of protection at the point of impact by increasing the thickness measured in the horizontal plane, the angle of attack of the projectile. The protection of an area, instead of just a single point, is indicated by the average horizontal thickness, which is identical to the
area density The area density (also known as areal density, surface density, superficial density, areic density, mass thickness, column density, or density thickness) of a two-dimensional object is calculated as the mass per unit area. The SI derived unit is ...
(in this case relative to the horizontal): the relative armour
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different ele ...
used to protect that area. If the horizontal thickness is increased by increasing the slope while keeping the plate thickness constant, a longer and thus heavier armour plate is required to protect a certain area. This improvement in protection is simply equivalent to the increase of areal density and thus mass, and can offer no weight benefit. Therefore, in armoured vehicle design the two other main effects of sloping have been the motive to apply sloped armour. One of these is the more efficient envelopment of a certain vehicle volume by armour. In general, more rounded shapes have a smaller surface area relative to their volume. In an armoured vehicle that surface must be covered by heavy armour, so a more efficient shape leads to either a substantial weight reduction or a thicker armour for the same weight. Sloping the armour leads to a better approximation of the ideal rounded shape. The final effect is that of deflection, deforming and ricochet of a projectile. When it hits a plate under a steep angle, its path might be curved, causing it to move through more armour – or it might bounce off entirely. Also it can be bent, reducing its penetration.
Shaped charge A shaped charge is an explosive charge shaped to form an explosively formed penetrator (EFP) to focus the effect of the explosive's energy. Different types of shaped charges are used for various purposes such as cutting and forming metal, ini ...
warheads may fail to penetrate or even detonate when striking armour at a highly
oblique angle In Euclidean geometry, an angle is the figure formed by two rays, called the '' sides'' of the angle, sharing a common endpoint, called the ''vertex'' of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles ...
. However, these desired effects are critically dependent on the precise armour materials used in relation to the characteristics of the projectile hitting it: sloping might even lead to better penetration. The sharpest angles are usually designed on the frontal
glacis A glacis (; ) in military engineering is an artificial slope as part of a medieval castle or in early modern fortresses. They may be constructed of earth as a temporary structure or of stone in more permanent structure. More generally, a glacis ...
plate, because it is the hull direction most likely to be hit while facing an attack, and also because there is more room to slope in the longitudinal direction of the 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 the horizontal plane, 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 Sheep shearing is the process by which the woollen fleece of a sheep is cut off. The person who removes the sheep's wool is called a '' shearer''. Typically each adult sheep is shorn once each year (a sheep may be said to have been "shorn" o ...
the mass. Sloped armour provides increased protection for
armoured fighting vehicle An armoured fighting vehicle (AFV) is an armed combat vehicle protected by armour, generally combining operational mobility with offensive and defensive capabilities. AFVs can be wheeled or tracked. Examples of AFVs are tanks, armoured cars, ...
s 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 A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the c ...
; because horizontal attack is in fact to be expected the ideal becomes an
oblate spheroid A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has ci ...
. 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 the most likely. A simple wedge, such as can be seen in the hull design of the
M1 Abrams The M1 Abrams is a third-generation American main battle tank designed by Chrysler Defense (now General Dynamics Land Systems) and named for General Creighton Abrams. Conceived for modern armored ground warfare and now one of the heaviest t ...
, 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 for a vehicle in a horizontal position can be calculated by a simple formula, applying the cosine rule: it is equal to the armour's normal thickness divided by the cosine of the armour's
inclination Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object. For a satellite orbiting the Ea ...
from
perpendicular In elementary geometry, two geometric objects are perpendicular if they intersect at a right angle (90 degrees or π/2 radians). The condition of perpendicularity may be represented graphically using the '' perpendicular symbol'', ⟂. It c ...
ity to the projectile's travel (assumed to be in the horizontal plane) or: :T_L=\frac where * T_L: Line of sight thickness * T_N: Normal thickness * \theta: 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 Rolled homogeneous armour (RHA) is a type of vehicle armour made of a single steel composition hot-rolled to improve its material characteristics, as opposed to layered or cemented armour. Its first common application was in tanks. After World ...
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 A kinetic energy penetrator (KEP), also known as long-rod penetrator (LRP), is a type of ammunition designed to penetrate vehicle armour using a flechette-like, high- sectional density projectile. Like a bullet or kinetic energy weapon, thi ...
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 1960s, however,
long-rod penetrator A kinetic energy penetrator (KEP), also known as long-rod penetrator (LRP), is a type of ammunition designed to penetrate vehicle armour using a flechette-like, high-sectional density projectile. Like a bullet or kinetic energy weapon, this type ...
s were introduced projectiles that are both very elongated and very dense in mass. On hitting 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. The deformed penetrator also 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 1970s. 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. Sloped armour can also cause projectiles to ricochet, but this phenomenon is much more complicated and as 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 occur) for a long rod projectile, but different formulae may predict different critical ricochet angles for the same situation.


Basic physical principles of deflection

The behaviour of a real world projectile, and the armour plate it hits, depends on many effects and mechanisms, involving their material structure and
continuum mechanics Continuum mechanics is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such mo ...
which are very difficult to predict. Using only a few basic principles will therefore not result in a model that is a good description of the full range of possible outcomes. However, in many conditions, most of these factors have only a negligible effect while a few of them dominate the equation. Therefore, a very simplified model can be created providing a general idea and understanding of the basic physical principles behind these aspects of sloped armour design. If the projectile travels very fast, and thus is in a state of
hypervelocity Hypervelocity is very high velocity, approximately over 3,000 meters per second (6,700 mph, 11,000 km/h, 10,000 ft/s, or Mach 8.8). In particular, hypervelocity is velocity so high that the strength of materials upon impact is v ...
, the strength of the armour material becomes negligible, as by the impact, both projectile and armour will melt and behave like
fluid In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear ...
s, and only its area density is an important factor. In this limiting case, the projectile, after the hit, continues to penetrate until it has stopped transferring its
momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass ...
to the target matter. In this ideal case, only momentum, area cross section, density and LOS-thickness are relevant. The situation of the penetrating metal jet caused by the explosion of the
shaped charge A shaped charge is an explosive charge shaped to form an explosively formed penetrator (EFP) to focus the effect of the explosive's energy. Different types of shaped charges are used for various purposes such as cutting and forming metal, ini ...
of
HEAT In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is ...
ammunition forms a good approximation of this ideal. Therefore, if the angle is not too extreme and the projectile is very dense and fast, sloping has little effect and no relevant deflection takes place. On the other extreme, the more light and slow a projectile is, the more relevant sloping becomes. Typical World War II armour-piercing shells were bullet-shaped and had a much lower velocity than a shaped charge jet. An impact would not result in a complete melting of projectile and armour. In this condition, the strength of the armour material becomes a relevant factor. If the projectile would be very light and slow, the strength of the armour might even cause the hit to result in just an elastic deformation, the projectile being defeated without damage to the target. Sloping will mean the projectile will have to attain a higher velocity to defeat the armour, because on impact on sloped armour, not all kinetic energy is transferred to the target, the ratio depending on the slope angle. The projectile in a process of
elastic collision In physics, an elastic collision is an encounter ( collision) between two bodies in which the total kinetic energy of the two bodies remains the same. In an ideal, perfectly elastic collision, there is no net conversion of kinetic energy into ...
deflects at an angle of 2\alpha (where \alpha denotes the angle between the armour plate surface and the projectile's initial direction), however the change of direction could be virtually divided into a
deceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by t ...
part, when the projectile is halted when moving in a direction perpendicular to the plate (and will move along the plate after having been deflected at an angle of about \alpha), and a process of elastic acceleration, when the projectile accelerates out of the plate (velocity along the plate is considered as invariant because of negligible friction). Thus the maximum energy accumulated by the plate can be calculated from the deceleration phase of the collision event. Under the assumption that only elastic deformation takes place and that the target is solid, while disregarding
friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion of ...
, it is easy to calculate the proportion of energy absorbed by the target if it is hit by a projectile, which, if we also disregard more complex deflection effects, after impact bounces off (elastic case) or slides along (idealised inelastic case) the armour plate. In this very simple model, the portion of the energy transferred to the target depends on the angle of slope: :E_d / E_k = where * E_d: Energy transferred to the target * E_k: Incident kinetic energy of projectile * \alpha: Angle of the sloped armour plate from the projectile's initial direction However, in practice, the AP-shells were powerful enough that the forces involved reach the
plastic deformation In engineering, deformation refers to the change in size or shape of an object. ''Displacements'' are the ''absolute'' change in position of a point on the object. Deflection is the relative change in external displacements on an object. Strain ...
limit and the elasticity of the plate could accumulate only a small part of the energy. In that case, the armour plate would yield and much of the energy and force be spent by the deformation. his means that approximately half the deflection can be assumed (just \alpha rather than 2\alpha) and the projectile will groove into the plate before it slides along rather than bounce off. Plasticity surface friction is also very low in comparison to the plastic deformation energy and can be neglected. This implies that the formula above is principally valid also for the plastic deformation case, but because of the gauge grooved into the plate, a larger surface angle \alpha should be taken into account. Not only would this imply that the energy transferred to the target would thus be used to damage it, it would also mean that this energy would be higher because the effective angle \alpha in the formula is now higher than the angle of the armour slope. The value of the appropriate real \alpha' which should be substituted cannot be derived from this simple principle and can only be determined by a more sophisticated model or simulation. On the other hand, that very same deformation will also cause, in combination with the armour plate slope, an effect that diminishes armour penetration. Though the deflection is under conditions of plastic deformation smaller, it will nevertheless change the course of the grooving projectile which again will result in an increase of the angle between the new armour surface and the projectile's initial direction. Thus the projectile has to work itself through more armour and, though in absolute terms thereby more energy could be absorbed by the target, it is more easily defeated, the process ideally ending in a complete ricochet.


Historical application

One of the earliest documented instances of the concept of sloped armour is in the drawing of Leonardo da Vinci's fighting vehicle. Sloped armour was actually used on nineteenth century early Confederate
ironclad An ironclad is a steam-propelled warship protected by iron or steel armor plates, constructed from 1859 to the early 1890s. The ironclad was developed as a result of the vulnerability of wooden warships to explosive or incendiary shells. Th ...
s, such as
CSS Virginia CSS ''Virginia'' was the first steam-powered ironclad warship built by the Confederate States Navy during the first year of the American Civil War; she was constructed as a casemate ironclad using the razéed (cut down) original lower hull ...
, and partially implemented on the first French tank, the
Schneider CA1 The Schneider CA 1 (originally named the Schneider CA) was the first French tank, developed during the First World War. The Schneider was inspired by the need to overcome the stalemate of trench warfare which on the Western Front prevailed duri ...
in the First World War, but the first tanks to be completely fitted with sloped armour were the French
SOMUA S35 The SOMUA S35 was a French cavalry tank of the Second World War. Built from 1936 until 1940 to equip the armoured divisions of the Cavalry, it was for its time a relatively agile medium-weight tank, superior in armour and armament to its Frenc ...
and other contemporary French tanks like the
Renault R35 The Renault R35, an abbreviation of ''Char léger Modèle 1935 R'' or R 35, was a French light infantry tank of the Second World War. Designed from 1933 onwards and produced from 1936, the type was intended as an infantry support light tank, ...
, which had fully cast hulls and turrets. It was also used to a greater effect on the famous Soviet
T-34 The T-34 is a Soviet medium tank introduced in 1940. When introduced its 76.2 mm (3 in) tank gun was less powerful than its contemporaries while its 60-degree sloped armour provided good protection against anti-tank weapons. The C ...
battle tank by the Soviet tank design team of the Kharkov Locomotive Factory, led by
Mikhail Koshkin Mikhail Ilyich Koshkin ( Russian: Михаи́л Ильи́ч Ко́шкин; 3 December 1898, Brynchagi, Yaroslavl Oblast – 26 September 1940) was a Soviet tank designer, chief designer of the famous T-34 medium tank. The T-34 was the most pr ...
. It was a technological response to the more effective
anti-tank Anti-tank warfare originated from the need to develop technology and tactics to destroy tanks during World War I. Since the Triple Entente deployed the first tanks in 1916, the German Empire developed the first anti-tank weapons. The first dev ...
guns being put into service at this time. The T-34 had profound impact on German WWII tank design. Pre- or early war designs like the
Panzer IV The ''Panzerkampfwagen'' IV (Pz.Kpfw. IV), commonly known as the ''Panzer'' IV, was a German medium tank developed in the late 1930s and used extensively during the Second World War. Its ordnance inventory designation was Sd.Kfz. 161. The Panz ...
and Tiger differ clearly from post 1941 vehicles like for example the
Panther Panther may refer to: Large cats * Pantherinae, the cat subfamily that contains the genera ''Panthera'' and ''Neofelis'' **'' Panthera'', the cat genus that contains tigers, lions, jaguars and leopards. *** Jaguar (''Panthera onca''), found in S ...
, the
Tiger II The Tiger II is a German heavy tank of the Second World War. The final official German designation was ''Panzerkampfwagen'' Tiger ''Ausf''. B,''Panzerkampfwagen'' – abbr: ''Pz.'' or ''Pz.Kfw.'' (English: " armoured fighting vehicle"), ''Ausf.' ...
, the Jagdpanzer and the
Hetzer The ''Jagdpanzer'' 38 ( Sd.Kfz. 138/2), originally the leichter Panzerjäger 38(t), known mostly post-war as ''Hetzer'', was a German light tank destroyer of the Second World War based on a modified Czechoslovakian Panzer 38(t) chassis. Germ ...
, which all had sloped armour. This is especially evident because German tank armour was generally not cast but consisted of welded plates. Sloped armour became very much the fashion after
World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the World War II by country, vast majority of the world's countries—including all of the great power ...
, its most pure expression being perhaps the British
Chieftain A tribal chief or chieftain is the leader of a tribal society or chiefdom. Tribe The concept of tribe is a broadly applied concept, based on tribal concepts of societies of western Afroeurasia. Tribal societies are sometimes categorized a ...
. However, the latest main battle tanks use perforated and
composite armour Composite armour is a type of vehicle armour consisting of layers of different material such as metals, plastics, ceramics or air. Most composite armours are lighter than their all-metal equivalent, but instead occupy a larger volume for the sa ...
, which attempts to deform and abrade a penetrator rather than deflecting it, as deflecting a long rod penetrator is difficult. These tanks have a more blocky appearance. Examples include the
Leopard 2 The Leopard 2 is a 3rd generation main battle tank originally developed by Krauss-Maffei in the 1970s for the West German army. The tank first entered service in 1979 and succeeded the earlier Leopard 1 as the main battle tank of the West Ger ...
and
M1 Abrams The M1 Abrams is a third-generation American main battle tank designed by Chrysler Defense (now General Dynamics Land Systems) and named for General Creighton Abrams. Conceived for modern armored ground warfare and now one of the heaviest t ...
. An exception is the Israeli
Merkava The Merkava ( he, מרכבה, , "chariot") is a series of main battle tanks used by the Israel Defense Forces and the backbone of the IDF's armored corps. The tank began development in 1970, and its first generation, the Merkava mark 1, entere ...
.


References

{{DEFAULTSORT:Sloped Armour Vehicle armour Military technology Naval armour