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Figure 1: USS West Virginia. She demonstrated some of the best battleship gunnery of the war at Surigao Straits. (Wikipedia)
I just finished reading The Battle of Surigao Strait by Anthony Tully, a battle that saw the final clash of battleships. For a battleship aficionado, the climax of the fight was the contest between two Japanese battleships and six US battleships, where five of the six US battleships had been sunk or heavily damaged during the Pearl Harbor attack – only the USS Mississippi had escaped the carnage of Pearl Harbor. These were old battleships (Table 1), with two having been commissioned during WW1 and the rest shortly after the WW1 ended.
When US folks think of WW2 battleships, they generally focus on the Iowa Class, probably because these ships survived the war and avoided the scrap heap. However, they did not begin deployment until 1944, which was after much of the tough surface combat had passed.
Table 1: US Battleships at Surigao Strait.
| Battleship | Designation | Class | Commissioned |
|---|---|---|---|
| USS Pennsylvania | BB38 | Pennsylvania | 1916 |
| USS Mississippi | BB41 | New Mexico | 1917 |
| USS Tennessee | BB43 | Tennessee | 1920 |
| USS Maryland | BB46 | Colorado | 1921 |
| USS California | BB44 | Tennessee | 1921 |
| USS West Virginia | BB48 | Colorado | 1923 |
Table 1 also shows us that there were four different classes of US battleship at Surigao Strait: New Mexico, Pennsylvania, Colorado, and Tennessee. This seemed like a lot and made me curious about the evolution of US battleships relative to other combatants. Fortunately, Wikipedia has a great table of battleship throw weights (i.e, the weight of a broadside from the main guns). I used Power Query to download and tidy the table, and R to plot the data.
Figure 2 shows the number of battleships classes in service with major combatants. Notice how the US had the largest number of battleship classes. My personal opinion is that the US had so many classes in operation because
- It had a lot to learn about battleships during and after WW1 and the commissioning of new classes shows how the US was working hard to catch up.
- The US operated the old battleships for the entire war because new classes of battleships would not be available until the latter part of the WW2.
Figure 2: Number of Battleship Classes During WW2 By Major Combatants.
An important metric for a battleship is the weight of a broadside. As I read about the Battle of Surigao Strait, it became clear the rate of the broadsides was also import. To understand the broadside weight per minute, I multiplied the rate of fire by the weight of an individual broadside to find the weight of fire per minute.
Figure 3 shows the top ten weights of fire for the different WW2 battleship classes. The Yamato and US 16-inch gun classes clearly dominate this metric.
Figure 3: Weight of Fire Per Minute.
The weight of a broadside depends on the weight of an individual shell. WW2 saw battleships with a wide range of shell calibers (i.e., diameter in inches). I became curious as to how the shell weight varied by caliber. I also fit a cubic curve (Figure 3) to the data to show that shell weight is roughly related to the cube of the caliber, which follows from the dimensional scaling laws.
Figure 3: Battleship Shell Weights Versus Caliber.
My spreadsheet and R markdown document are included here.
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Some questions raised by your interesting article:
When a battleship fires a broadside at sea, aiming for another vessel, are the guns set at different angles so that the shells straddle the target? What is the ratio of shells fired/hits?
Is the rolling displacement of the battleship taken into account when targeting?
Do the guns have to return to the horizontal after each salvo in order to load for the next one?
Are the shells built like a rifle bullet, with the projectile and propellant all enclosed within a casing? How is the shell triggered?
My home town was Portsmouth (in Hampshire, not New Hampshire) and from my bedroom window, I could see dozens of ships moored in the harbour after the end of the war, mostly awaiting a final trip to the scrapyard. Most notable was the battleship "Vanguard" whose keel was laid during the war but was not commissioned until after the war. In 1960 it was towed out for scrap, but as it passed through the very narrow entrance to the harbour, a tow line came loose and it swung around and went aground, nearly demolishing a pub crowded with sightseers. Apparently, it was the most violent action it was ever involved with. Here is a youtube film which includes that event (excuse the plummy accent of the narrator, but once you had to speak like that to get a job with the BBC):
https://www.youtube.com/watch?v=Db6bgu0gs-g
When a battleship fires a broadside at sea, aiming for another vessel, are the guns set at different angles so that the shells straddle the target?
There was enough variation between individual shots that multiple shots were usually fired at each range setting. Three guns were often fired at a time to ensure that an errant splash round could be detected (2 out of 3 at the same range). Here is a desciption of the ladder salvo used for ranging by the US Navy from the Navweaps website:
The US Navy procedures are discussed a bit on this web page.
The Royal Navy used a procedure that involved firing a salvo with half the guns at a specific range (Friedman, Naval Firepower). The other half were then available for a correction. You want more than two guns in a salvo because a two gun salvo with an errant shot will create an ambiguity as to which splash reflected the correct range.
The Germans also used a half-salvo approach.
I should mention that all the countries first fired salvos to get the deflection correct, then they corrected for range.
What is the ratio of shells fired/hits?
This question gets the battleship crowd stirred up. Here is a table from a forum discussion that I think is reasonable. There are many other examples using battle data, but it has proven to be difficult to separate out the hits from multiple ships and I do not trust the results.
vs Bismarck-Type
Is the rolling displacement of the battleship taken into account when targeting?
Yes, but different ships used different approaches. The US Navy had a stable vertical reference and Remote Power Control in both elevation and azimuth for directing the guns. This allowed them to cancel out the roll electromechanically. If I recall correctly, the UK and Germans had stable verticals, but did not have RPC for elevation (example).
Do the guns have to return to the horizontal after each salvo in order to load for the next one?
Certainly for US battleships. Here is a quote from a forum discussion.
Are the shells built like a rifle bullet, with the projectile and propellant all enclosed within a casing?
No. Large bore guns normally use bag charges (for example, USS North Carolina used as many as six 90 lb bags). The Germans did use a system with one cased charge and the rest bagged.
How is the shell triggered?
Do you mean fired from the gun? As far as firing goes, a primer charge is loaded. The primer is detonated, which initiates the powder train that detonates the bags.
I thought you may be interested in this bit of maths related news.
https://www.quantamagazine.org/mathematician-solves-computer-science-conjecture-in-two-pages-20190725/
Thank you for the reference. Very well written article on a tough problem.
mark
Mark, I downloaded your Broadside.zip file but had problems reading in the *.csv files in R after I extracted them from your Broadside workbook. For instance, some of the column names were wrong. I'm still learning about R and would like to run your Broadside.RMD file. Please provide the *.csv files as separate files. Thanks
Hi Ronan,
Sorry for the omission. Try the update.
mark
Mark, thanks. I was able to the R file to work. I also had to modify the "read_csv" command to "read.csv" to get the plots.
As always, I appreciate you sharing this interesting info. Just playing with the math and using your Iowa vs Bismark hit table, at 10,000 yards with a 10.5% chance of a hit, you'd need 7 shots to have a combined 53% chance of getting a hit. With a 2.7% chance of a hit at 30,000 yards, you'd need 26 shots to get a combined 51% chance of a hit.
The basic formula for a hit with p being the probability of a hit and n being the number of shots fired is 1-(1-p)^n
Sorry for the issues. The read_csv command is from the readr package, a part of the tidyverse. I may have had it in my environment, but not in my library list. I will check later tonight.
The probabilities you are computing are pretty consistent with what was actually seen. Many shells were fired to get a hit. They typically carried ~100 shells per main gun (Iowa carried a ~130 shells per gun). So you can see where it was important to use your shells wisely.
I hope all is well with you. I am just beginning to get back to blogging. Starting a consulting business and dealing with family issues has been very time-consuming. Thanks for continuing to read and contribute.
mark
I should also mention that I finally got an SSL certificate. If you type in https://mathscinotes.com, you will see that you no longer get a warning about the site not being secure. That is why you may have received some email this week as I fumbled around adding the certificate this week.
mark
Hi Mark, I've been out of town for a bit. My wife and I went to a vintage dance in Chattanooga, TN. Dances covered were from the 1890s to the 1930s. We're basically doing fine except that with age our bodies creak a little more than they did when we were younger.
I didn't know how many shells per gun that our battleships carried. Thanks for sharing.
Looking forward to your blogging.
Great stuff, Mark. I've read a number of your posts in the past c0uple of days, particularly related to naval artillery problems. I have not seen one yet where you derive the differential equations for the trajectory. Why is that, or did I just overlook it? I look forward to more; thanks for posting all this.
Sam
Great analysis. During the Battle of Manila Bay in 1898 (pre-radar) the US hit rate was 220 of 5,859 rounds fired. Goes to show you how important volume of fire is, too.