Gun precision / dispersion

[fsimon]

Richelieu 380mm/45
Richelieu had delay coils for the center guns of each turret fitted in 1947-1948 when a tighter dispersion pattern was desired in order to take the maximum advantage of radar fire control. During tests at Mers el-Kébir in May 1948, the measured average dispersion at 26,500 meters was 525m without the firing delay and 300m with a 0.06 second firing delay (at this time the guns had all fired more than 200 shells without refit).
525m for 26.5km battery dispersion divided by 1.692 = 310m apparent mean dispersion giving true mean dispersion for n8 = 310m x 1.069 = 331m equaling 1.25% of range.
True mean dispersion 1.25% @ 20km = 250m during WW2
Average range pattern @ 20km:
8 guns: 270m x 3.85 = 963m
4 guns: 270m x 2.89 = 723m
300m for 26.5km battery dispersion divided by 1.692 = 177m apparent mean dispersion giving true mean dispersion for n8 = 177m x 1.069 = 189m equaling 0.71% of range.
True mean dispersion 0.71% @ 20km = 143m after WW2
Average range pattern @ 20km:
8 guns: 155m x 3.85 = 549m
4 guns: 155m x 2.89 = 413m

[fsimon]

True mean dispersion.JPG (108.97 KiB) Viewed 22422 times

[fsimon]

The different values for Bismarck and Scharnhorst at 20 and 25km are not derived via the percentage of range, but via the graphs of gkdos 100a and W.A.39,16.
These graphs show, that the percentage of dispersion is not konstant over range. The percentage is larger at shorter ranges, smaller at medium ranges and increases again at very large ranges. Bismarck's guns had the smallest dispersion in percent of range at ca. 20° elevation. At 20° elevation these guns had a range of ca. 28.5km.
The numbers for the UK 15"/42 are derived of practice shootings inside of 16km. I suspect that dispersions in percent of range were smaller for these guns as well at ranges between 20 and 25km.

[TTTT]

Thanks for your hard work!

Try to explain to an average dumkopf what "True mean dispersion" means.

[fsimon]

I am a dumkopf myself and would not rely too much on the data I wrote as many other factors are involved in chances to hit a naval target. The number of events used to gather those numbers is small. This makes all of this not very meaningful.

True mean dispersion can be understood as the statistical average of the dispersions in range (or deflection) of an infinite number of shots, all assumed to have been fired under conditions as nearly the same as possible and excluding wild shots.

Best regards
Frank

[hans zurbriggen]

Hello Mr.TTTT,
you write: 'Thanks, interesting to hear about the 28cm guns - it makes sense. They seem to have done rather good in actual combat, though.'.
Possibly 'large' dispersion of Scharnhorst's guns helped to hit HMS Glorious @ 24 km, as suggested by Mr. Jurens.

Hello Mr. fsimon,
thanks so much for all calculations and comparison table.

hans

[fsimon]

Dispersion is only one factor in the equation. A correct mean point of impact is another important factor. What could have resulted in Scharnhorst hitting Glorious were the flat trajectory of Scharnhorst's bullets resulting in a large danger zone, the large height of Glorious, the short time of flight of Scharnhort's projectiles, the accurate ranging of sharnhorsts radar and optical range finders, the remote control of Scharnhorsts guns with stabilistion in elevation and "Seitenvorzündwerk" in azimuth, an advanced fire control computer and pure chance.

Frank

[fsimon]

Danger Zones.JPG (161.81 KiB) Viewed 22384 times

[fsimon]

Time of flight.JPG (121.71 KiB) Viewed 22383 times

[TTTT]

Thanks, gentlemen. As Mr.Jurens and FSimon have pointed out, "accuracy" is clearly much more than just dispersion.

A couple of questions.

"The Bureau of Ordnance expected the nine-gun patterns given by the 16-inch batteries mounted aboard the Washingtons, South Dakotas and Iowas to be slightly larger than the eight-gun pattern sizes for the old 16-inch guns mounted aboard Colorado, Maryland and West Virginia. Specifically, eight old guns were expected to yield an average range pattern of 1.8% of range while nine new guns would give a 1.9% pattern."

FSimon, from your numbers it seems that The Bureau of Ordnance were wrong about this, as the triple turrets seem to have less dispersion than the old twins of the Colorados? Or are the datas to limited to make a conclusion?

Is the reason that Scharnhorst is behind Bismarck and Richelieu in "the race to the target" that her lighter shell loses velocity faster?

[fsimon]

The bureau of Ordnance is talking about the pattern size of a nine gun salvo of the new guns and an eight gun salvo of the old guns. The pattern of nine guns would be larger with the TMD of both guns beeing practically similar. I also think the numbers resulting in the 1.8% and 1.9% pattern sizes were derived from shootings with a mixture of AP and HC rounds and mixture of charges, while the TMD I used for the new guns only apply to shootings with full charge AP rounds.
Pattern size depends on number of guns shot per pattern. TMD is independent thereoff.

As to Scharnhorst, I would think so as you wrote.

As I said, I am a dummkopf. The experts on this topic are Mr Jurens, Mr Fischer and delcyros and Thoddy.

Best regards,
Frank

[Bill Jurens]

As others have pointed out already, small values of dispersion in and of themselves -- which at best, being largely statistical animals, do tend to vary quite significantly from shoot to shoot -- are not in and of themselves very predictive of hitting probability unless they are combined with one's ability to get the mean point of impact centered on the target. The most accurate rifle in the world is of little use if the user is blind, or nearly so. Similarly, the best marksman on the planet is not going to hit very much if his weapon is not performing predictably. In most detailed target shooting analyses, one measures both true mean dispersion (which can only be approximated if the number of shots is small) and one's ability to center the pattern on the target. The net result of most of this is that dramatic variations in hits per gun per minute are by no means uncommon from target-shoot to target-shoot. Results obtained from any single practice are unlikely to produce much that is of any statistical significance regarding how well the ship might perform at any given point in the future. That's not to say that the results obtained in single-shoot target practices are of no use at all, but unless the results differ rather dramatically, comparing the results of one-off practices, particularly if conditions vary between the practices one is comparing, are of much analytical utility.

A good down-to-earth illustration of this may be gleaned from Bismarck's performance at Denmark Strait, and later on during her final engagement only a few days later. The guns and the fire control equipment were, by and large identical in both instances, but on 24 May Bismarck did very well indeed, whereas on 28 May her performance was relatively abysmal. An 'n' of one doesn't count for much...

Bill Jurens

[Steve Crandell]

I believe full salvos (in the US case nine guns) made it easier to determine MPI on a late war PPI display.

[Bill Jurens]

That's sort of true. Technically the precision of the mean point of impact is independent of the number of shots in the pattern. As pattern size goes up, however, the random statistical 'drift' of the m.p.i. becomes less and less important, so plotting the trajectory of the m.p.i. becomes easier. With 3 shots, the m.p.i. can drift a lot from salvo to salvo just due to random variations in the impact points. With 100 shots in a salvo -- impossible I know, but just used here as an example -- the drift of m.p.i. from one 100 shot group to the next 100 shot group would be quite small.

Bill Jurens

[fsimon]

To get the mean point of impact (MPI) on target, one important factor is to get the correct range and range rate. While bearing can be measured relatively easily by optical means, measuring range is a difficult task. Radar on the other hand can measure range relatively accurate while measuring bearing by radar involves some tricks.
I tried to gather information on how those measurements were done by the major battleship types. Here is what I found:

Brad Fisher on optical ranging: “The total systematic mean range error for an Iowa class battleship at 20kyds might be around ± 172yds (two 26.5ft Mk 48, two 46ft Mk 53 and one 46ft Mk 52), 269yds at 30,000yds. Direct stereo-spotting accuracy can be assessed against the baseline instrument unit of error. Generally 1.5e is consistent from a trained spotter. (158yds at 20Ky, 355yds at 30Ky for the Mk 48 rangefinder) Note the much larger error at long range and this is why doctrine called for bracket and halve technique for adjusting fire via optics.”
Minimum system error: (58.2 × R²)/(B × M)
R = Range in km
B = Baselength in m
M = Magnification
Total optical ranging error = 1.5 times the minimum system error.

Example @ 20km:
Hood 30ft (9.14m) RF: (58.2 x 400) / (9.14 x 25) = 23280 / 228.5 = 101.88; x 1.5e =152.8m