Sloped armour Sloped armour is armour that is neither in a vertical nor a horizontal position . Such " angled " armour is often mounted on tank s and other armoured fighting vehicle s ( AFVs ) . Sloping an armour plate makes it harder to penetrate for antitank - weapons , such as armour - piercing shells ( kinetic energy penetrator s ) and rockets , if they take a more or less horizontal path to their target , as is often the case . The better protection is caused by three main effects . Firstly , 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 ) has to be pierced ; increasing the armour slope improves , for a given plate thickness , the armour ' s 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 ( in this case relative to the horizontal ) : the relative armour mass used to protect that area . If we increase the horizontal thickness by increasing the slope while keeping the plate thickness constant , we need a longer and thus heavier armour plate to protect a certain area . This improvement of protection is simply equivalent to the increase of area 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 a more efficient envelopment of a certain vehicle volume by armour . In general , more rounded forms have a lesser surface relative to their volume . As in an armoured vehicle that surface has to be covered by heavy armour , a more efficient form can lead to a substantial weight reduction or a thicker armour for the same weight . Sloping the armour can lead to a better approximation of an ideal rounded form . 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 . However , these effects are strongly dependent on the precise armour materials used and the qualities of the projectile hitting it : sloping might even lead to a better penetration . 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 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 the mass . Sloped armour provides increased protection for armoured fighting vehicle 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 ; 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 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 from perpendicular ity to the projectile ' s travel ( assumed to be in the horizontal plane ) or : where 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 penetrator s 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 . 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 onset ) 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 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 , the strength of the armour material becomes negligible – as by the impact both projectile and armour will melt and behave like fluid 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 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 of HEAT 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 Armoured 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 a 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 deflects at an angle of 2formula _ 5 ( where formula _ 5 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 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 formula _ 5 ) , 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 , it is easy to calculate the proportion of energy absorbed by the target if it is hit by 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 projected to the target depends on the angle of slope : where However , in practice the AP - shells were powerful enough that the forces involved reach the plastic deformation 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 . As such this means that approximately half the deflection can be assumed ( just formula _ 5 rather than 2formula _ 5 ) 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 formula _ 5 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 formula _ 5 in the formula is now higher than the angle of the armour slope . The value of the appropriate real formula _ 5 ' 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 recorded uses of sloped armour was on early Confederate ironclad s , such as CSS Virginia , 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 by the Soviet tank design team of the Kharkov Locomotive Factory , led by Mikhail Koshkin . It was a technological response to the more effective anti - tank 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 and Tiger differ clearly from post 1941 vehicles like for example the Panther , the Tiger II , the Jagdpanzer and the Hetzer , 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 , 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 penetrator is so difficult . These tanks have a more blocky appearance . Examples include the Leopard 2 and M1 Abrams . An exception is the Israeli Merkava .