Here's some Maths! about ironclad penetration, as calculated at the time.
1) Does low velocity or high velocity work better for the same energy?
The energy or "work" was calculated for two projectiles (this done in 1864) and matched. They took the 10.5" 12 ton gun, and fired it at an iron plate with 50 lbs charge and 170 lbs spherical steel shot, then took the same gun and fired it with 40 lbs and a 300 lb hemispherical headed steel elongated shot - the result was that the "work" was identical, 2,898 foot tons.
2) If the work is proportional to the diameter of the round, how does this affect the penetration?
The 100-lber gun was fired with a 15.4 lbs charge and the 7" RML fired with a 13.5 lb charge, resulting in a "work" of 128 foot-tons per inch of diameter.
The results of this experiment showed that the resistance (in foot-tons) of a plate when struck by a projectile of constant diameter varied as the square of the plate's thickness, for unbacked and solid plate.
It also (critically) showed that the resistance was constant per inch of diameter of the projectile.
The resistance of the Warrior target was (counting the backing) 61 foot-tons per inch against steel-headed hemispherical rifle shot; for Lord Warden it was more like 89 foot-tons per inch. (The 8" Parrott could just about produce 64 foot-tons per inch, so just about penetrates Warrior - see page one of the thread!)
The unbacked plate resisted at only about 28 foot-tons per inch, so the backing is very important and more than doubles the resistance of the plate.
For wrought iron balls attacking wrought iron the Fairbairn formula holds up pretty well.
T/D = (0.0007692)[(W/D^3)V^2]^0.5
For the 11" Dahlgren
V (fps) T (penetration, in)
800 2.32
900 2.61
1000 2.90
1100 3.19
1200 3.48
1300 3.77
1400 4.06
1500 4.35
1600 4.63
At 1,600 fps the 11" will just pierce an unbacked 4.5" plate.
The 15" does this at just over 1,000 fps.
The Dahlgren 9" does this:
V (fps) T (penetration, in)
800 1.95
900 2.19
1000 2.43
1100 2.68
1200 2.92
1300 3.16
1400 3.41
1500 3.65
1600 3.89
1700 4.14
1800 4.38
1900 4.62
Both the 9" and 11" were massively overcharged by Dahlgren and he got about 1,400 fps out of them.
Using steel shot, which deforms better and thus transfers more energy, the Noble formula is preferred.)
11"
V (fps) T (penetration, in)
800 3.81
900 4.29
1000 4.77
1100 5.25
1200 5.72
1300 6.20
1400 6.68
1500 7.15
1600 7.63
1700 8.11
1800 8.58
1900 9.06
So an unbacked plate would be pierced at around 950 fps, but Warrior (equiv to a 6.64" unbacked plate) at around 1,400 fps - so with steel shot and double charges, the 11" could just about penetrate Warrior (though at that powder load it's an interesting question whether Warrior or the 11" breaks first).
For the 9":
V (fps) T (penetration, in)
800 3.20
900 3.60
1000 4.00
1100 4.40
1200 4.80
1300 5.21
1400 5.61
1500 6.01
1600 6.41
1700 6.81
1800 7.21
1900 7.61
Against Warrior there is no possibility even with a steel shot of generating enough velocity.
For the 68 pdr with a 68 lb common shot:
V (fps) T (penetration, in)
800 1.80
900 2.03
1000 2.26
1100 2.48
1200 2.71
1300 2.93
1400 3.16
1500 3.38
1600 3.61
1700 3.83
1800 4.06
1900 4.29
With steel:
V (fps) T (penetration, in)
800 3.06
900 3.44
1000 3.82
1100 4.20
1200 4.58
1300 4.97
1400 5.35
1500 5.73
1600 6.11
1700 6.49
1800 6.88
1900 7.26
2000 8.01
The 68 lber 95 cwt developed 2040 fps over the first 40 yards when fired with the "far" charge. Since 11" laminate is (assuming equivalent metal quality) about equal to an 8" unbacked plate, this would allow a one-shot of a Passaic class monitor at very close range. Thus, believe it or not, my battle written on page one should have had the Warrior completely cripple the Monitor with the first 68 pounder shot fired with battering charge...
For the 100 pdr Somerset (all steel shot):
V (fps) T (penetration, in)
800 3.39
900 3.82
1000 4.24
1100 4.67
1200 5.09
1300 5.51
1400 5.94
1500 6.36
1600 6.79
1700 7.21
1800 7.63
1900 8.06
The Somerset gun could produce 1,700 to 1,800 fps quite easily at very close range.
The 300 pounder Armstrong (actually fired a 164 lb steel ball as a smoothbore, but if rifled would have fired 300 lb shot) was much better:
V (fps) T (penetration, in)
800 4.02
900 4.53
1000 5.03
1100 5.53
1200 6.03
1300 6.54
1400 7.04
1500 7.54
1600 8.05
1700 8.55
1800 9.05
1900 9.55
This got around 1,750 fps at the muzzle.
ED: using the 15" Dahlgren it has a penetration velocity against Warrior of 1600 fps for iron shot and 1000 fps for steel shot (assuming both are 440 lb).
Double ED: since the 15" Dahlgren's steel ball is 484 lb, it has a penetration velocity vs. Warrior of c. 900 fps.
Interestingly, we also have the "initial velocity" for many Dahlgren guns based on USN tables - this is not muzzle velocity, but velocity over first second of flight - thus, we can calculate penetration at 150-250 yards. They show that, for the standard charges and excluding cast-steel rounds:
The best penetration by the 20" is when firing iron shot and with a 100 lbs charge - it penetrates approx. 6.8 inches at this range.
For the 15" it can penetrate 5.1 inches with a 50 lb charge.
For the 13", 4.3 inches with a 70 lbs charge.
11" has 20 lbs of charge and penetrates 3.1 inches.
The 10" uses 12.5 lbs and penetrates 2.7".
The 9" uses 13 lbs of powder and penetrates 2.6 inches.
The 8 inch penetrates 2.2 inches, using 9 lbs of powder.
And the long 32 pounder penetrates about 2.2 inches, using 9 lbs of powder as well.
This excludes the use of massive overcharge, of course - but the Dahlgren 11" using the 30lb charges would only last for about 20 rounds. (Same for the 15" with the 60lb charge - these are guns being badly overstrained!)