Sloped armor

Sloped armour is armour that is neither in a vertical nor a horizontal position. Such "angled" armour is often mounted on tanks and other armoured fighting vehicles (AFVs), as well as naval vessels such as battleships and cruisers. Sloping an armour plate makes it harder to penetrate for antitank-weapons, such as armour-piercing shells (kinetic energy penetrators) 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 you increase the horizontal thickness by increasing the slope while keeping the plate thickness constant, you 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.

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Wikipedia