British Tank Gun Accuracy

From various British War Office (WO) documents and I don't have copies of the originals.  A few are from images of photos of the original printed pages.

1. WO 291/238 AORG Report No.256 "The Importance of Gun Dispersion in A.P. Shooting"
(Assumed to be using 90%)
6pdr    APCBC    dispersion at 1000yds             5.2mins - tangent (5.2/60) x 1000 / 1.22 =
1.24 yd.      *[1.05 yd]
75mm Mk.V APCBC dispersion at 1000yds      3.0mins  - tangent (3/60) x 1000 / 1.22 =
0.71 yd.        *[0.60 yd]
17pdr APCBC dispersion at 1000yds                 5.2mins - tangent (5.2/60) x 1000 / 1.22 =
1.24 yd.      *[1.05 yd]
17pdr APDS dispersion at 1000yds                  12.0mins - tangent (12/60) x 1000 / 1.22 =
2.86 yd.       *[2.4  yd]
* Alternately using the BA program to find dispersion that results in 90% hit chance of dispersion sized target.
Or covert by method #4 page 41 of British 90% zone radii to German 50% zone width divide by 1.5.
Note- 17pdr dispersion is assumed to include fouling from aluminum residue by using APDS rounds.
2. AORG Memo No. 514:
1000 yds                        mean  dispersion
6 pdr Mark IV APCBC: 1.5 minutes  -  tangent (1.5/60) x 1000 x 1.69 =
0.737 yd
17 pdr     APCBC:          1.0 minutes -  tangent (1.0/60) x 1000 x 1.69 =
0.492 yd

3. Weapon Research Committee: accuracy of anti-tank guns and rigidity of gun barrels", 1948 [PRO piece number WO 195/10134],
Gun         Ammunition    m.v. (f.p.s.) Ave m.d. of strike     
6-pr 7 cwt
   APCBC        2725             0.9'   -  tangent (0.9/60) x 1000 x1.69 = 0.442 yd
Mks 4 and 5 
 DS            3850              2.3'   -  tangent (2.3/60) x 1000 x1.69 = 1.13 yd
17-pr
           APCBC       2900              0.8'   -  tangent (0.8/60) x 1000 x1.69 = 0.393 yd
Mks 1-5 and 7
DS           3950              2.0'   -  tangent (2.0/60) x 1000 x1.69 = 0.98 yd
77mm
           APCBC       2575              0.7'  -  tangent (0.7/60) x 1000 x1.69 = 0.344 yd
                          DS
         3400              1.2'  -  tangent (1.2/60) x 1000 x1.69 = 0.59 yd

There are a number of documents on shooting percentages.  This will need the Ballistic Accuracy calculator to model the dispersion.
4. WO 291/238 AORG Report No.256 "The Importance of Gun Dispersion in A.P. Shooting"
Theoretical chances of a hit on a 2-ft high target representing a hull-down tank at 1,000 yards.
Gun   ammo      2nd shot  calc. dispersion
6-pdr  HV            38%         
0.76 yd
77mm  APCBC   56%           
0.55 yd
17 pdr APDS      17%           
1.29 yd
Standard range error is 250 yd at 1000 or 25% s.d. or 19.95% mean error.
Gun      First shot               calc.  dispersion
77mm       11%                     
0.64 yd
17 pdr      15%                     
0.47 yd

5. 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   Calc. From dispersion of:
Churchill IV 6pdr APCBC 150rnds  74%     73%       62%           
0.5 yd.
Churchill IV 6pdr APDS 90rnds       74%     50%       37%           
0.76 yd
Sherman 17pdr APC 100rnds           88%     66%       52%           
0.59 yd 
Sherman 17pdr APDS 40rnds           42%     21%       14%           
1.44 yd
Comet   77mm APC   40rnds            98%     86%       76%           
0.38 yd

6. WO 291/1263, Firing Trials, 17pdr Sherman
"Table VI has been constructed which shows the probability of a hit on a target 5' wide by 2' high
(representing a Panther turret) at various ranges using both types of round."
Range (yards)             APC %                           AP/DS %
1000                          45.3   [
0.335 yd]           14.9   [0.7 yd]    (assuming 17% mean ranging error)

7. WO 291/180, Accuracy of anti-tank gunnery
Ranges in yards, target assumed to be Pz VI size.
Probability (%) of hitting static hull-down target after first round:
Gun            500          1000
6 pdr            85             43     - 
0.7 yds
17 pdr          88             51     - 
0.6 yds

8. Table "D."    28 Dec. '44   No. Q. 2.908
Range At Which There is a 50 Per Cent. Chance of Obtaining Hits.   Hulldown target = 2' x 5'
Hulldown                                Q.F.  6-pr  7 cwt.                                       Q.F. 17-pr         

                                             APCBC              DS                                  APCBC       DS

First shot                         500 yds [0.84]      500 yds [1.06]      600 yds [0.28]       500 yds[1.15]
Subsequent hits                800 yds.[
0.77]      600 yds [1.02]      900 yds[0.68]       600 yds [1.02]                                             

(Note. This also includes jump and throw off.)
The British seem to think the average mean range estimation error with a telescope sight was 20-25%.

Nick Moran, the Chieftain,  found some documents of dispersion tests at Aberdeen Proving Ground. link
9. The US tested the 17 pdr to determine the dispersion of APCBC and APDS.   They tested at 500 yds., 1000 yds, and 2000 yds.  They found that mean dispersion at 1000 yds deflection: .233 mils, elevation: .219 mils.  Now this works out to a 50% zone of .387 yds / .364 yds at 1000 yds.  Now this would be great except they moved the center of the target to the center of the spread.   This means that jump and throw-off have to be included in the calculation to compare it to German and Russian deflection numbers.  To do this we have to look ahead one page to the Post War reports

where a random jump or laying error is included with the ballistic dispersion.  This is a bit tedious to do with a calculator so I wrote a program for it.  Assume the jump/throw-off/laying error has a s.d. of .167 mils as is found here:. Link PDF
Then the calculation goes:
A= tan(1.25331x 0.233 x 0.05625). B= tan(0.167 x 0.05625).
C= squareroot(A2+B2) x 1000 x 1.349.
Result 50% zone def:
.446 yd / ele: .425 yd at 1000 yds.
APDS 50% zone:  .5mils/.92 mils    = .
859 yds / 1.543 yds
10. The US also checked their tests  for the 90mm and 76mm guns.

Following the same reasoning for this data:
.115 mil /.142 mil for the 90mm  50% zone   =
.292 yds / .323 yds
.112 mil and .110  mil for the 76mm 50% zone =
.289 yds / .287 yds

The Dispersion program can be downloaded here:  Download