Footnotes for Best Battleship Page: Guns

1. Drawn primarily from John Campbell's Naval Weapons of World War II, but also from Dulin & Garzke, various Warship International issues, and additional unpublished material from Nathan Okun.

2. To a certain extent, weight of broadside is an artificial concept, in that it says nothing about shell quality or armor penetration ability, which really determines how much potentially critical damage one can do to a heavily armored opponent. Shooting lots and lots of shells that don't get through the enemy's belt isn't as effective as shooting one shell that goes kaboom in the other guy's magazine. However, broadside weight does give a rough indication of the raw power of the batteries in question.

3. The Italian 15" was an extraordinarily powerful gun, but achieved its performance at the cost of exorbitant barrel wear (barrel life for this weapon was in the neighborhood of 110-130 'effective full charges'; roughly half that of most other nationalities' 15" guns) and reduced accuracy due to wide salvo spreads. All in all, the tradeoffs probably weren't worth it. Campbell states that the muzzle velocity of these weapons could have been reduced 'with advantage.' On the other hand, the Italians may well have rationalized that the additional barrel wear and reduced life was worth it. After all, (as a friend of mine noted to me once) the Italians would hardly ever be operating terribly far from port, meaning that they could afford more frequent barrel changes because of the proximity of good base facilities. To an American designer (or British, for that matter), accepting higher-power ballistics also meant accepting the possibility of maybe needing to change one's barrels in Northeast Tonga, or some other beastly Pacific sandbox in the middle of No Where, which wasn't really a very palatable option. Hence the more conservative ballistics of American heavy ordnance.

4. It should be noted that firing cycle (minimum time between shots at a 'typical' battle range) is calculated at the base loading angle, which for most ships was between 2 and 5 degrees elevation. In a long-range duel, elevation of the gun to a firing angle of 30-40 degrees would account for several seconds more. Iowa's guns elevated at 12 degrees per second; the fastest of the lot. Most elevated at around 6 degrees per second. (It should be noted that Richelieu alone of these seven vessels could be loaded at any angle.)

Without question the gun whose firing cycle I get the most mail on is Yamato's. Here's how I derived it. The U.S. Naval Technical Mission to Japan issued a report on Japanese ordnance which states that Yamato's firing cycle was 1.5 rounds / minute (i.e. 40 seconds) at maximum elevation. Maximum elevation is 50 degrees, and loading is performed at 3 degrees. This means that the barrel must travel through a total of 47 degrees down, be loaded, and travel 47 degrees back up to maximum elevation, for a total of 94 degrees of travel. Her barrels elevated at 8 degrees per second, meaning that 11.75 seconds would be spent in transit, leaving a total of 28.25 seconds (40-11.75) for loading. This is why I put Yamato's cyclic rate at 30 seconds, and not the 40-45 seconds many of my correspondents have stated as being the true figure. This also jibes nicely with John Campbell's figures, which break as follows:

     Open breech: 2.0-2.5 sec
     Move shell loading bogie forward: 3 sec
     Ram shell: 3 sec
     Withdraw rammer & return bogie: 5 sec
     Move rammer to load position: 3 sec
     Ram shell: 3 sec
     Withdraw rammer: 3sec
     Return charge cylinder and rammer: 3 sec
     Close breech: 2 sec
     Recoil & run-out: 2 sec
     Total: 29.5-30.5 seconds

In addition, it needs to be noted that at ranges above 15,000 yards or so, one would not be able to fire at full speed given the need to watch the fall of shot of previous salvos, which might take as long as a minute to reach their destinations. Firing cycles, then, are somewhat misleading in significance for large-caliber weapons such as these.

5. Campbell cites a firing cycle of 30 seconds. Both Dulin & Garzke's "Axis and Neutral Battleships in World War II" and Breyer's works say18-20 seconds, which is quite fast for a weapon of this size. Again, however, note that practical firing cycles may be lower for the reasons cited previously.

6. Arriving at some quantitative value of 'Gun Power' wasn't easy. Here's my general approach:

Assemble sufficient ballistics data to make some armor penetration calculations.
Calculate the armor penetration of the shells in question.
Assign a basic rating to each shell based on its armor penetration.
Assign a second basic rating for the shell's destructive power after it breaches the armor. This is based on shell weight and burster size.
Combine the two into a final shell rating.
Calculate the number of shells the ship in question could fire during the course of a finite chunk of time; five minutes.
Assign a final gunpower rating which takes into account the shell's penetration and explosive power ratings, and the rate-of-fire (ROF) of the guns.

Ballistics Data

I don't have official range tables for the guns in question (although I'm working on it). So I grabbed the next best thing; the ballistic data from Campbell's "Naval Weapons of World War II", which presents data for most of the large-caliber weapons of the war. However, some of it is in meters, some of it in yards, and I wanted it all in yards. So, I used a nifty program called CurveExpert to fit a 3rd-degree polynomial curve to the data points for each individual gun. With the equation for those lines in hand, I was then able to get very accurate values for both the fall angle and velocity values for these shells at any given range. So I calculated these values at increments of 5000 yards, out to a maximum range of 40,000 yards. [Yes, some of these guns can throw a shell to 45,000 yards, but I decided not to go out that far. It's almost impossible to hit anything out there anyway, and I felt that including a 40,000 yard set of figures would be a somewhat artificial.] [Note: King George V can only throw a shell to 35,000 yards; Bismarck only to 39,000 yards, and these values were used as needed] The values I arrived at are presented below:

Range (yds.) Yamato Iowa Bismarck Richelieu King George V Vittorio Veneto South Dakota
0 2557 ft/sec
@ 0o
2500 ft/sec
@ 0o
2691 ft/sec
@ 0o
2723 ft/sec
@ 0o
2474 ft/sec
@ 0o
2790 ft/sec
@ 0o
2300 ft/sec
@ 0o
5000 2329 ft/sec
@ 2.6o
2286 ft/sec
@ 2.6o
2407 ft/sec
@ 1.9o
2477 ft/sec
@ 2.3o
2180 ft/sec
@ 2.9o
2528 ft/sec
@ 1.1o
2091 ft/sec
@ 3o
10000 2116 ft/sec
@ 5.8o
2076 ft/sec
@ 5.9o
2148 ft/sec
@ 5o
2247 ft/sec
@ 4.8o
1924 ft/sec
@ 6.8o
2292 ft/sec
@ 3.5o
1900 ft/sec
@ 6.8o
15000 1926 ft/sec
@ 9.7o
1893 ft/sec
@ 9.9o
1922 ft/sec
@ 9.2o
2042 ft/sec
@ 8o
1715 ft/sec
@ 11.7o
2085 ft/sec
@ 7.2o
1734 ft/sec
@ 11.8o
20000 1767 ft/sec
@ 14.4o
1741 ft/sec
@ 14.8o
1736 ft/sec
@ 14.4o
1867 ft/sec
@ 12o
1559 ft/sec
@ 17.8o
1910 ft/sec
@ 12o
1604 ft/sec
@ 17.8o
25000 1647 ft/sec
@ 20.1o
1628 ft/sec
@ 20.7o
1598 ft/sec
@ 20.5o
1728 ft/sec
@ 17.7o
1464 ft/sec
@ 25.5o
1770 ft/sec
1520 ft/sec
@ 25.3o
30000 1573 ft/sec
@ 27o
1564 ft/sec
@ 27.4o
1515 ft/sec
@ 27.5o
1631 ft/sec
@ 23.5o
1437 ft/sec
@ 34.9o
1668 ft/sec
@ 24.5o
1492 ft/sec
@ 34.3o
35000 1552 ft/sec
@ 35o
1558 ft/sec
@ 36.4o
1494 ft/sec
@ 35.1o
1582 ft/sec
@ 31.6o
1486 ft/sec
@ 46.2o
1608 ft/sec
@ 31.7o
1530 ft/sec
@ 45o
40000 1593 ft/sec
@ 44.5o
1618 ft/sec
@ 46.6o
1527 ft/sec
@ 41.6o
1586 ft/sec
@ 41.5o
- 1592 ft/sec
@ 39.4o

Armor Penetration

Once those range tables were in place, it was time to calculate some armor penetration values. I wasn't content with the existing data on armor penetration that can be found in the open literature. Most of these figures are based on the US Navy Empirical formula, which dates from the 1930s. I felt, in light of the fact that science and the study of ballistics hasn't stood still since the end of World War II, that more accurate information should be available. I found what I was looking for in Nathan Okun, a civilian fire-control systems programmer for the US Navy who has spent much of his life researching the effects of large caliber naval shells on armor. Nathan graciously sent me much information, as well as the latest cut of his face-hardened armor program.

I used Nathan Okun's Face-Hardened Armor Penetration calculator to crank out penetration values for the given ranges against vertical (belt) plates. In each case, I fired the guns using their native shells (i.e. Richelieu fires her original French shells, not the ones manufactured for her by Crucible Steel corporation after she was refitted in the United States in 1943). The plate armor I used was British CA, the best in the world at the time.

For deck plates, which are composed of homogeneous armor, I couldn't use the face-hardened program. And unfortunately, Nathan hasn't worked out a final homogenous armor penetration formula yet - it is a very complex phenomena. Instead, he sent me the official US Navy armor penetration plates for all the guns in question (except Yamato's 18.1"). From these I was able to plot the armor penetration of the shells. I am not completely satisfied with this data -- among other things, there were no plates for either the Japanese 18.1"/45 or the British 14"/45, so I had to extrapolate these figures from the curves of similar guns. But until Nathan completes his homogeneous program, it will have to do.

It is important to note that better high muzzle-velocity does not necessarily equate to better performance against horizontal deck armor. For instance, guns like Richelieu's and Vittorio Veneto's have tremendous ballistics at short range, but they are comparatively lousy at penetrating deck armor. Why? Because these guns fire their shells at very flat trajectories, and shells coming in at flat trajectories tend to ricochet. It's very tough to get any sort of penetration at obliquities above 70-degrees. This means that flat trajectory weapons don't start getting effective deck penetration until they are much farther away and their shells start coming in at a decent fall angle. The end result is that guns that have poorer ballistics make up for it (to a certain extent) at longer ranges against deck armor because they must fire their guns at higher elevations for a given range, and therefore loft their shells higher, and consequently hit decks with the benefit of gravitic acceleration from a greater height. The battleship that benefits most from this is South Dakota. Her 16"/45 has a muzzle velocity of only 2300 ft./sec., and thus she has to heave her shells very high to get them out to range. But her shell weighs 2700 lbs, and thus has better deck penetration than Yamato or anybody else. Note, too, that the Americans worked out the ballistics and range tables for firing the Iowa's 16"/50 weapons with reduced charges (three charges instead of four) which would still allow for great range (given the 50-caliber barrel), but would also require greater elevation for a given range, and thus provide greater striking power against deck armor. I have not tried calculating these figures, but they would tend to make the 16"/50 even more powerful against deck armor, and would make the Iowa a very formidable long-range foe. Anyway, here are the figures I arrived at:

Armor Penetration at Range (yds.):
Yamato Iowa Bismarck Richelieu King George V Vittorio Veneto South Dakota
0 32.7" / - 30.4" / - 30.4" / - 29.6" / - 26.5" / - 27.7" / - 27.5" / -
5000 28.5" / - 26.6" / - 26.1" / - 25.8" / - 22.2" / - 24.3" / - 23.8" / -
10000 24.6" / - 23" / - 22.2" / - 22.3" / - 18.4" / - 21.2" / - 20.5" / -
15000 21.1" / - 19.9" / - 18.7" / - 19.2" / - 15.4" / - 18.5" / - 17.6" / -
20000 18.2" / - 17.3" / - 15.8" / - 16.5" / - 13.1" / 3.2" 15.6" / - 15.3" / 4.4"
25000 15.8" / 5.5" 15.2" / 5.2" 13.6" / 4.2" 14.2" / 4.3" 11.3" / 4.5" 13.3" / 4.7" 13.4" / 5.8"
30000 13.9" / 7.1" 13.5" / 6.6" 11.8" / 5.5" 12.4" / 5.4" 9.8" / 6.2" 11.4" / 5.9" 11.7" / 7.6"
35000 12.3" /9.5" 11.9" / 8.5" 10.3" / 7.1" 10.8" / 6.9" 8.3" / 7.7" 9.8" / 7.6" 9.9" / 10.4"
40000 10.7" / 11.7" 10.3" / 11.1" 9.1" / 9.3" 9.2" / 9.0" - / - 8.3" / 9.6" - / -
Aggregate Penetration 211.5" 199.5" 184.0" 185.7" 146.7" 177.6 167.8"

Destructive Power

Okay, now we also need to quantify the amount of damage the shell causes after it gets past the plate. This is basically a function of the size (weight) of the shell, i.e. Bigger Shell = Bigger Kaboom. Simple enough, right? Actually, though, the size of the explosion is based on the size of the explosive burster charge in the shell. Most battleship burster charges were in the neighborhood of 2.5% of the shell's weight. British, German, and French heavy APC conformed to these specs. Italian shells were in the neighborhood of 2.0%, and American and Japanese shells were in the 1.5% range, meaning that while the American shells were the best armor penetrators in the world, pound for pound, they also did less damage on the other side of the plate due to a smaller KaBoom. According to a physicist friend of mine, KaBoom (i.e. force) is related to the energy of the explosion (which is roughly given by the explosive weight) to the .4 power. In other words, a 1000lb. bomb explodes with (2)1.4 of a similar bomb half its size, or 1.32 times the force. So I calculated the size of the bursters for all the shells, and normalized them relative to each other by taking their .4 root. Note: I am aware that some of these bursters used more powerful explosives than others, however, I didn't want to get into that, for largely the same reason that I didn't want to mess around with quantifying dud rates. However, Nathan's information suggests explosive power as follows:      TNT = 1.00 "power" (German, Italian)      Japanese TNA = 1.05 (approx.)      U.S. explosive "D" = .95 (apporx.)      British Shellite = .96 (approx.)      All Picric Acid = 1.10 (approx.)      Guncotton = .5 (approx.)      Black Powder = .33-.5 (approx.)

Shell Destructive Power Yamato Iowa Bismarck Richelieu King George V Vittorio Veneto South Dakota
Burster Size: % of Total Shell Weight 1.5% 1.5% 2.5% 2.5% 2.5% 2.0% 1.5%
Burster Size: lbs. 48.29 40.50 44.10 48.73 39.75 39.02 40.50
Normalized Explosive Power 4.72 4.40 4.55 4.73 4.36 4.33 4.40

Main Battery Output

Battleships fire shells, and thus their offensive power is brought to bear on an opponent in the form of discrete pulses of destruction. It is important to know, therefore, how many shells the ship can fire in a given period of time. One minute seemed too short an interval to be realistic, especially when some of these ships have firing cycles which don't break cleanly across that interval -- I don't like fractional shells. At the same time, I wanted an interval that was tactical in length, rather than representing the entirety of a long engagement. So I chose a time span of five minutes. At least a couple of capital ship actions during the war (Bismarck vs. Hood, Washington vs. Kirishima) were settled in about this length of time. I assigned a Rate Of Fire that was meant to represent the ship's practical output under combat conditions (i.e. suffering casualties, maneuvering, watching for fall of shot, trying to load during rough weather, trying to get a bead on the target in lousy weather or through the smoke of battle, etc.), which will tend to modify the vessel's ROF's downward. At the same time, I felt that the slower-firing vessels (Yamato and Vittorio Veneto) should not be overly penalized. Likewise, the fastest shooter (Bismarck, due to her semi-fixed ammo) should not be overly rewarded. As a consequence, the ROFs I assigned tended to move towards a common medium of around 1.7 rounds per minute.

Rate of Fire Yamato Iowa Bismarck Richelieu King George V Vittorio Veneto South Dakota
ROF Per Minute 1.5 1.7 1.8 1.7 1.7 1.5 1.7
# of Barrels 9 9 8 8 10 9 9
5-minute ROF 68 77 72 68 85 68 77

Final Gunpower Rating

The final gunpower rating is a product of three things:

Aggregate Armor Penetration
Normalized Explosive Power
Main Battery Output: 5-minute ROF

I simply multiplied the three ratings together to get a combined rating, and then normalized them on a scale of '1' to '10.' For instance, Yamato's gun battery scores as follows: (211.53 inches of aggregate penetration * 4.72 normalized explosive power * 68 shells = score: 67829).

Rate of Fire Yamato Iowa Bismarck Richelieu King George V Vittorio Veneto South Dakota
Raw Gunpower 67,829 67,525 60,241 59,751 54,399 52,283 56784
Adjusted Rating 10 10 9 9 8 7.5 8.5

And there you have it. Not a perfect system, by any means, but one which tries to take into account several different factors affecting the performance of a main battery.

7. The tradeoffs the Japanese made for these shells don't seem to have been worth it. The only textbook example of an optimal Type-91 hit was an 8" shell that struck the magazine of the U.S. light cruiser Boise during the Battle of Cape Esperance. In this case, rapid flooding prevented a catastrophic detonation of the magazine. Thus, the shell hit, while causing massive damage to Boise, did not achieve the sort of critical damage the Japanese had sacrificed so much for in terms of raw penetrative power in the design of their Type 91 ammunition. Further, it should be noted that the very long fuze delay times in these sorts of shells (necessary for allowing adequate delay if the shell was transiting underwater to the target) had undesirable effects when the shell struck light plating at flat trajectories (such as superstructures). In these cases, Type-91 shells frequently detonated well after the shell had carried through the target ship and was in mid-air on the other side. In a long-range gunnery duel, plunging fire from a Type-91 shell might conceivably pass through the armor deck and then through the bottom of the target ship before detonation -- again, not a trivial hit, but hardly the optimal amount of damage to be expected from a very large caliber shell penetrating to the vitals of the target.