## Engineering Question #9365

Mary, a 21 year old female from the Internet asks on December 22, 2016,

Scientists, if you had to calculate armor penetration for medieval armors, what formula would you use?

- The formula would be used to determine if a projectile penetrates an armor and by how much.

- It would only consider relatively low velocity projectiles like arrows and bolts, and the melee weapons like swords and spears (not firearms!)

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### John Jones answered on December 23, 2016

Many people care passionately about this question. Some typical discussion can be found at myArmoury.com and vikingsword.com

Among the relevant parameters are:

1. Mass of the projectile
2. Velocity of the projectile
3. Hardness of the projectile tip (typically measured in Vickers pyramid number, Hv)
4. Thickness of the armour
5. Hardness of the armour plate (also typically measured in Vickers pyramid number, Hv)
6. Resilience of the armour; this measures its ability to spring back into shape, or elasticity. Glass, for example, can be quite hard, but it doesn't make good armour, because it lacks resilience. Rubber, on the other hand, is resilient but not hard, and is again not the best choice for armour.

More difficult to pin down is the angle at which the projectile strikes the armour. Armour is designed with curved surfaces, to encourage strikes to glance off. The test reported in this link uses head-on impact with a flat plate, so its results may be pessimistic (from the target's point of view). If you're the target, your survival chances will also be affected by what you're wearing under the armour.

There is no formula that takes all this into account, nor is there enough empirical data to curve-fit or test such a formula. The best practical solution may be to take an experimental result from Bane's report as a starting point, then use the following formula to obtain a new result from that reference result:

Penetration depth = Reference Penetration * (Velocity/Ref Velocity)^1.4283 * (Diameter/Ref. Diameter)^1.0714 * (Weight/Diameter^3)^0.7143 * (Ref. Weight/Ref. Diameter^3)^0.7143

(This is Commandant Jacob de Marre's formula for penetration depth of naval shells into ship's armour plate.)

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