V^2 = \frac{a}{w} \{ 3507 \ E^2 \times 2265464 \ e^{1.4} \}

V = the velocity of the projectile in feet per second.
a = the diameter of the projectile in inches.
w = the weight of the projectile in pounds.
E = the thickness of the backing in inches.
e = the thickness of the plate in inches.

Using the above formula we can make out a table as follows:

 -------+-------+-------------+-------+-------+------+---------+

Plate. |Backi'g| Gun, service| w, | a, | V. | Energy, |

Inches.|Inches.| shot. |Pounds.|Inches.| f. 8.| Impact. |

| | | | | | f. tons.|

-------+-------+-------------+-------+-------+------+---------+

6 | 36 | 6" B.L.R. | 100 | 5.96 | 1389 | 1337 |

7 | 36 | 6" " | 100 | 5.96 | 1528 | 1619 |

8 | 36 | 8" " | 250 | 7.96 | 1213 | 2550 |

9 | 36 | 8" " | 250 | 7.96 | 1308 | 2966 |

10 | 36 | 8" " | 250 | 7.96 | 1399 | 3390 |

11 | 36 | 8" " | 250 | 7.96 | 1489 | 3839 |

12 | 36 | 10" " | 500 | 9.96 | 1247 | 5386 |

13 | 36 | 10" " | 500 | 9.96 | 1315 | 5987 |

14 | 36 | 10" " | 500 | 9.96 | 1381 | 6608 |

15 | 36 | 12" " | 850 | 11.96 | 1215 | 8699 |

16 | 36 | 12" " | 850 | 11.96 | 1269 | 9710 |

17 | 36 | 12" " | 850 | 11.96 | 1332 | 10454 |

18 | 36 | 12" " | 850 | 11.96 | 1374 | 11124 |

19 | 36 | 12" " | 850 | 11.96 | 1425 | 11965 |

20 | 36 | 12" " | 850 | 11.96 | 1476 | 12837 |

-------+-------+-------------+-------+-------+------+---------+ 

No projectile or fragment of the plate or projectile must get wholly through the plate and backing. The plate must not break up or give such cracks as to expose the backing, previous to the third shot.

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 formulae. These formulae 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 formulae 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 formulae, 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

P = \sqrt[1.6]{\frac{w \ v^2}{\pi \ g \ d \ 11334.4}}

U.S. Naval Ordnance Proving Ground uses

P = \sqrt[2.035]{\frac{w \ v^2}{\pi \ g \ d \ 3852.8}}

Col. Maitland gives

P = \frac{w \ v^2}{g \ d^2 \ 16654.4}

Maitland's latest formula, now used in England, is

P = \frac{v}{608.3} \sqrt{\frac{w}{d}}   0.14 \ d

General Froloff, Russian army, gives

P = \frac{w \ v}{d^2 \ 576}

for plates less than two and one-half inches thick, and

P = \frac{w \ v}{d^2 \ 400}   1.5

for plates more than two and one-half inches thick.

If θ be the angle between the path of the projectile and the face of the plate, then v in the above formulae becomes v sin θ.

When we come to back the plates, their power to resist penetration becomes greater, and our formula changes. The Gavre formula, given above, is used to determine the velocity necessary for a projectile to pass entirely through an iron plate and its wood backing.

Compound and steel armor are said to give about 29 per cent. more resisting power than wrought iron, but in one experiment at the proving ground, at Annapolis, a compound plate gave over 50 per cent. more resisting power than wrought iron.

The Italian government, after most expensive and elaborate comparative tests, has decided in favor of the Creusot or Schneider all-steel plates, and has established a plant for their manufacture at Terni, near Rome.

The French use both steel and compound plates; the Russians, compound; the Germans, compound; the Swedes and Danes use both. Spain has adopted and accepted the Creusot plate for its new formidable armored vessel, the Pelayo; and China too has recently become a purchaser of Creusot plates.

Certain general rules may be laid down for attacking armor. If the armor is iron, it is useless to attack with projectiles having less than 1,000 feet striking velocity for each caliber in thickness of plate. It is unadvisable to fire steel or chilled iron filled shells at thick armor, unless a normal hit can be made. When perforation is to be attempted, steel-forged armor-piercing shells, unfilled, should be used. They may be filled if the guns are of great power as compared to the armor. Steel and compound armor are not likely to be pierced by a single blow, but continued hammering may break up the plate, and that with comparatively low-powered guns.

Wrought iron must be perforated, and hard armor, compound or steel, must be broken up. Against wrought iron plates the projectile may be made of chilled cast iron, but hard armor exacts for its penetration or destruction the use of steel, forged and tempered. Against unarmored ships, and against unarmored portions of ironclads, the value of rapid-firing guns, especially those of large caliber, can hardly be overestimated.

The relative value of steel and compound armor is much debated, and at present the rivalry is great, but the weight of evidence and opinion seems to favor the all-steel plate. The hard face of a compound plate is supposed to break up the projectile, that is, make the projectile expend its energy on itself rather than upon the plate, and the backing of wrought iron is, by its greater ductility, to prevent the destruction of the plate. It seems probable that these two systems will approach each other as the development goes on. An alloy of nickel and steel is now attracting attention and bids fair to give very good results.

The problem to be solved, as far as naval armor is concerned, is to get the greatest amount of protection with the least possible weight and volume, and this reduction of weight and volume must be accomplished, in the main, by reducing the thickness of the plates by increasing the resisting power of the material. In the compound plate great surface hardness is readily and safely attained, but it has not yet been definitely determined what the proper proportionate thickness of iron and steel is.

A considerable thickness of steel is necessary to aid, by its stiffness, in preventing the very ductile iron from giving back to such an extent as to distort the steel face and thus tear or separate the parts of the plate. The ductile iron gives a very low resisting power, its duty being to hold the steel face up to its work. If now we substitute a soft steel plate in the place of the ductile iron, we will get greater resisting power, but our compound plate then becomes virtually an all-steel one, only differing in process of manufacture. The greatest faults of the compound plate are the imperfect welding of the parts and the lack of solidity of the iron. When fired at, the surface has a tendency to chip.

In the all-steel plate we have the greatest resisting power throughout, but there are manufacturing difficulties, and surface hardness equal to that of the compound plate has not been obtained. The manufacturing difficulties are being gradually overcome, and artillerists are in high hopes that the requisite surface hardness will soon be obtained.

The following may be stated as well proved:

1. That steel armor promises to replace both iron and compound.

2. That projectiles designed for the piercing of hard armor must be made of steel.

3. That the larger the plate, the better it is able to absorb the energy of impact without injury to itself.

4. That the backing must be as rigid as possible.