Sloped armour
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Sloped armour was developed as a defensive measure by the French SOMUA (Société d'Outillage Mécanique et d'Usinage d'Artillerie) right before the outbreak of World War II. It was a technological response to the trend of fitting increasingly bigger guns on battle tanks.
The idea behind sloped armour is that shots fired in a somewhat straight arc towards the vehicle will be deflected and simply bounce off. Sloped armour greatly increases the armour's protective effect compared to conventional armour, even though it's thinner. At 30 degrees to the horizontal the effect is about 50%. Consequently, less steel is needed per tank, and the tank will be tougher for the same weight or more manoeuverable for the same protection.
This effect should not be confused (but very often is) with another effect of sloping the armour: that the Line of Sight (horizontal) thickness of the armour increases also (this gives no weight advantage!). This other effect can be calculated by the cosine rule. At 30 degrees to the horizontal this increase is exactly 100%. Both effects must be multiplied, so a 100 mm armour plate reclined at 60 degrees from the vertical will render a protection equivalent to about 300 mm of vertical plate. Listed single armour protection numbers are often this equivalence value, for knowing only the thickness of the plate is insufficient, one should also know its declination.
The principle itself was well known of old and partially implemented on even the first French tank, the Schneider CA1, but the first tanks to be completely fitted with sloped armour were the French SOMUA S-35 and other French tanks developed at the same time, which had a fully cast hull and turret. It was also used to a greater effect on the famous Russian T-34 battle tank. After the war the principle became very much the fashion, its most pure expression being perhaps the British Chieftain. The latest tank models however use compound or formed armours, trying to deform and abrase the penetrator rather than deflecting it, so they have a more blocky appearance. The Leopard 2 is a case in point.