The penetration of projectiles of different forms into various styles of armor has been very thoroughly studied and many attempts have been made to bring the subject down to mathematical formulæ. These formulæ are based on several suppositions, and agree very closely with results obtained in actual experiments, but there are so many varying conditions that it is extremely doubtful if any formulæ will ever be written that will properly express the penetration. Many different forms have been given to the heads of projectiles, as flat, ogival, hemispherical, conoidal, parabolic, blunt trifaced, etc. The flat headed projectile has the shape of a right cylinder, and acts like a punch, driving the material of the armor plate in front of it. These projectiles are especially valuable when firing at oblique armor, for they will bite or cut into the armor when striking at an angle of thirty degrees. The ogival head acts more as a wedge, pushing the metal aside, and generally will give more penetration in thick solid plates than the flat headed projectile. The ogival head is usually designed by using a radius of two calibers. The hemispherical, conoidal, parabolic and blunt trifaced all give more or less of the wedging effect. The blunt trifaced has all the good qualities of the ogival of two calibers. It bites at a slightly less angle, and the three faces start cracks radiating from the point of impact. Forged steel is the best material for armor-piercing projectiles, but many are made of chilled cast iron, on account of its great hardness and cheapness. The best weight for a projectile is found by the formula w = d³ (0.45 to 0.5) w being the weight in pounds, d the diameter in inches and 0.45 to 0.5 having been determined by experiment. With a light projectile we get a flat trajectory, and accuracy at short ranges is increased. With a heavy projectile the resistance of the air has less effect and the projectile is advantageously employed at long ranges. In the following formulæ, used in calculating the penetration of projectiles in rolled iron armor, g = the force of gravity. w = the weight of projectile in pounds. d = the diameter of projectile in inches. v = the striking velocity in feet per second. P = the penetration in inches. Major Noble, R.A., gives _________________ 1.6 / w v² P = /\ / ---------------- \/ [pi] g d 11334.4 [TEX: P = \sqrt[1.6]{\frac{w \ v^2}{\pi \ g \ d \ 11334.4}}] U.S. Naval Ordnance Proving Ground uses ________________ 2.035/ w v² P = /\ / --------------- \/ [pi] g d 3852.8 [TEX: P = \sqrt[2.035]{\frac{w \ v^2}{\pi \ g \ d \ 3852.8}}] Col. Maitland gives w v² P = ------------ g d² 16654.4 [TEX: P = \frac{w \ v^2}{g \ d^2 \ 16654.4}] Maitland's latest formula, now used in England, is _ v /w P = ----- \/ - - 0.14 d 608.3 d