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William Armstrong, internal EOC note on guns and armour

Experiments have shown that the best way of measuring the efficaciousness of a gun is to examine the penetrative power in terms of the force exerted, in foot-tons, compared to the circumference of the round, in inches. Thus the penetration power and the resistance may be expressed in foot-tons per inch; a gun of forty foot-tons per inch will penetrate the same armour as another gun of forty foot-tons per inch. Thus we may also compare armours by their foot-tons per inch in resistive power.
This may also be expressed in terms of a thickness of good wrought iron, rolled and of the best quality, as this is the most effective means of resisting shot and shell yet devised for the thickness it bears, but it would be better to keep in mind foot-tons per inch - armour of one country may be inferior to that of another, but a foot-ton is a foot-ton and an inch is an inch.
So long as the foot, the ton and the inch are the normal British measures, of course.

We must conclude that, in future, the thickness of armour must increase. Thus it is not right for us to continue to build the same guns, the same shells, but it is right for us to continually press to increase the power of the guns.
For a comparison, we must consider the armour of the past. The Erebus, with four inches of rolled iron and poorly backed, has roughly 38 foot tons per inch with the angle of her sides in account; the French Gloire's hammered plates are 16 but when backed become 40. The 4.5 inch rolled plates of the Warrior are about 28, but when backed become 61.
The new Bellerophon is about 90 foot tons per inch in the whole system. To place this in relative difference, the 25 inches of oak of the old ships of the line was but 16 foot tons per inch - there is a great improvement in the efficacy of wood as a shield when it is fronted by iron.
It has been shown by direct experiment that the resistance of single armour plates varies as the square of the thickness, but that for a "laminate" of plates bolted together or left resting together this does not apply - thus, eight inches of one inch plates is not nearly so strong as a single eight inch plate (though it is stronger than eight times the strength of a one inch plate).

Now, to how this is calculated. The penetrating power in foot-pounds per inch is the weight in pounds of the shot, times the square of the velocity in feet per second, divided by twice the effect of gravity and by the circumference of the shot in inches.
The weight in foot-tons per inch is this number divided through by 2,240.

Thus, for a seventy-two pound shot which travels at 1,700 feet per second with a diameter of eight inches - the old 68 pounder gun - the "work" is about fifty-eight foot tons per inch, and so we may see that the design of the Warrior was well thought of - it resists the guns of the time.
For a more modern gun such as our own guns of the last few years, compare the two seven inch guns, the 110 pounder and the 120 pounder. The 110 pounder could handle but an initial velocity of 1,100 feet per second, and so the work done was but 42 foot-tons per inch; the new gun has 1,525 feet per second, and the work done is 88 foot-tons per inch.
If a gun could be built that would handle the same great velocity of the old 68 pounder gun of 112 cwt - to whit, over 2,000 feet per second - then the work that might be done is nearly one hundred and sixty foot-tons per inch. We can see that the great want for the construction of a fine gun is a fine system of metallurgy, and that the great want for fine armour is the same.

It is amusing to imagine how the late American War might have gone had we had the guns of today only a few years ago. The best estimates for the resistance of "Monitor" are that the turret may have resisted with fifty or sixty foot-tons per inch, and so the 120-pounder would put shot right through the turret even at far range. (For all the values given are for the initial velocity of the gun.)

Thus I think the importance of the larger gun is not the "racking" effect, but the "punching" effect - for a gun of common proportion, the circumference goes up linearly with the bore, but the size of the powder chamber and the mass of the round go up as the cube of the bore. A gun of 14 inches, with the same initial velocity as the 120 pounder (due to the same ratio of the powder charge and the round), would be expected to fire a projectile of nearly half a ton and to have a penetration of three hundred and fifty-four foot tons per inch - a power which would not be ably resisted by even a single plate of fifteen inches (unbacked) - if such a plate may be achieved.
A larger gun is of no worth if it cannot thus increase the density of the energy of the round! We must not fall into the American trap of seeing mere mass as the key to defeating armour.