American Tank Gun Accuracy Cont.

Propelled,122mm, Model 1944... [PDF] The US/UK zones are only half that of the Ger/Rus of the same percents.  This is why converting from a 90% UK zone to a 50% German zone the dimensions are divided by 1.22 rather than 2.44.  For mean deviation and standard deviations this may apply as well.  But, I am not convinced yet.  Maybe next revision I'll have more information on this point.

Next I will turn the
Ballistic Accuracy Calculator on some of the accuracy data in order to find the dispersion that it is using.
12. WO 291/751 AORG Memo No.427, 24th Nov 1944, "Comparative Dispersion of Tank Guns"

Probability of a hit when firing for effect on a target 2' high by 5' wide (M.P.I. assumed on centre of target) at 
                                                           500yds;   800yds;    1000yds; 1500yds:      Calc 50% Disp. at 1000 yds
Sherman        75mm  M3   M61 150rnds  100%     96%         90%     73%                 
Sherman        76mm  APC M62 40rnds    100%    100%        96%     92%                 

13. WO 291/238, The Importance of Gun Dispersion in AP Shooting AORG report number 256.
Theoretical chances of a hit on a 2-ft high target representing a hull-down tank at 1,000 yards.
This also says the standard average range estimation error is 250 yds at 1000.  Does that mean std. Deviation error is 25% ?

Second shot corrected:  1000yds               Calc 50% Disp. at 1000 yds.
75mm M3        M61         70%                   
76mm         APCBC          82%                 

14. Table "D."    28 Dec. '44   No. Q. 2.908
Range At Which There is a 50 Per Cent. Chance of Obtaining Hits.
Hulldown                  Q.F.  75mm  APCBC    Hulldown target = 2' x 5'                     
Calc 50% Disp. at 1000 yds
First shot                  400 yds                         17% mean ranging error and dispersion           0.65 yd.
Subsequent hits        900 yds.                                        Dispersion only                                0.625 yd.
(Note. This also includes jump and throw off.)
If you thought things were clear on the subject of percentage definition differences between US/UK and Ger/Rus I remembered a magazine article.

15. In Warship International , No. 3, 1991, Evolution of Battleship Gunnery in the US Navy, 1920 - 1945 by W. J. Jurens The Dispersion Rectangle appears.  It seems the US Navy defines the 50% dispersion zone center at mean point of impact different than the Army.

From Russian Archive the US 76mm on the M18 Hellcat had a dispersion "At a range of 1200 meters, average horizontal deviation is 0.16 meters

The Dispersion Rectangle (reproduced from article)

and vertical deviation is 0.1 meters."  As this is Soviet radius multiply by 2 to find the 50% zone i.e diameter  Giving .32m horizontal by .2m  vertical.   Or at 1000m 0.267m x 0.167m

It may seem the dispersion of the US 75mm and 76mm guns is much better than that of other nations.  And that may be true of pure dispersion from the center point of a collection of hits at 1000 yds.  However, other factors will cause this center to be off center the target.  In particular the M4 linkage on the periscope sight has slack such that after a some firing it produces an additional dispersion of up to 4 mils in both planes. Source: War Department Report of the New Weapons board, April 1944 [PDF] page 58 f.

Aiming differences of HVAP for vehicles based on jump, muzzle brake and other factors of 76mm and 3" guns. link