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    Avatar photoJohn D Salt

    Minor celebrations may be in order, as I have, for the first time, reproduced a set of official penetration tables using the same method as the original. Most official penetration tables give embarrassingly little information about the method and assumptions used, but the Russians, thank goodness, are, or used to be, a little more open about such things.

    Since the official formula used is by no means my favourite of the formulae in my collection, I have recalculated using my favourite, Dehn’s penetration formula.

    Now read on.


    1. Extract official penetration figures from official Soviet source documents, helpfully posted at


    2. Using the Soviet version of the de Marre formula for critical velocity (also given at the above page) and the stated K value of K=2400, calculate residual velocities from the stated penetration.

    Vcrit = K * (d^0.75/sqrt(m))*(e^0.7/sin(a))


    Vcrit is the critical velocity for penetration, in m/s
    K is a plate quality constant, set to 2400 for cemented armour
    d is the diameter (calibre) of the projectile, in decimetres
    m is the mass of the projectile, in kg
    e is the thickness of armour just penetrated,in decimetres
    a is the striking angle measured from the horizontal, in degrees

    The worked example on the source web page, drawn from an official artillery course, contains an error. Drivel in official publications can remain undetected for years, until someone actually tries it.

    3. Average the velocities given for 90 and 60 degree impact, and fit an exponential trend line to series of velocities at different ranges, forcing an intercept at the muzzle velocity. The average r^2 figure for these fitted curves was 0.994.

    4. Using the exponential decay formula generated from the velocity figures, produce residual velocity figures for the ranges desired.

    5. Apply Dehn’s penetration formula using the known projectile calibre and mass, and assuming target armour of density 7850 kg/m^2 (typical for steel) and with ultimate tensile strength 970 Megapascals (typical of current RHA and representative of German WW2 rolled plate of 55-80mm thickness).


    Expected penetration in mm at normal impact, Dehn's formula.
    Target plate density 7850 kg/m^2, ultimate tensile strength 970 Mpa.
                                                          range (m)	
    Weapon                  Round           250     500    1000    1500    2000
    37mm m39 AA 61-K	BR-167		 58	 51	 40	 30	 23
    45mm 19-K		BR-240		 60	 54	 45	 36	 29
    45mm m37 53-K		BR-240		 69	 62	 50	 40	 31
    45mm M-42		BR-240		 73	 67	 55	 45	 36
    57mm m43 ZiS-2		BR-271	        127	121	111	102	 93
    57mm m43 ZiS-2		BR-171		123	113	 97	 82	 69
    57mm m43 ZiS-2		BR-271K		115	 99	 72	 52	 36
    76mm m27		BR-350A		 28	 26	 23	 21	 18
    76mm m39, 42		BR-350SP	 80	 75	 66	 59	 51
    76mm m31, 38 AA		BR-350A		105	100	 89	 79	 70
    85mm 52-K		BR-367		122	118	109	101	 94
    85mm m43 D-53		BR-365		121	116	106	 97	 89
    85mm m43 D-53		BR-365K		118	109	 94	 80	 68
    100mm m44 BS-3		BR-412		176	163	141	120	102
    107mm m40 M-60		B-420		138	134	124	115	107
    122mm m43 D-25		BR-471		158	148	128	111	 96
    152mm m38 how M-10	m1915/28	 78	 76	 71	 66	 62
    152mm m10/34 ML-20	BR-540		131	126	116	108	100


    The penetration figures given are produced on a consistent basis, using a modern and dimensionally-consistent penetration formula, with stated assumptions of plate strength and density. They are based on velocity figures deduced from official figures, but it is not known how the official velocities were derived. The muzzle velocity of 835 m/s for the 45mm 53-K seems odd, and the ability of some 57mm rounds to retain velocity at range seems hard to believe.

    This is the first time I have found the method used to produce official penetration tables, and confirmed it by calculation. It is unfortunate that identical calculations done for sub-calibre projectiles produced obvious nonsense, with down-range velocities greater than the muzzle velocity. A likely explanation is that the same formula was used, but with a different K value, probably about 1600, in contradiction to statements made in the original documents.

    Further work:

    If anyone has any better data on velocity decay of WW2 ATk projectiles, or any knowledge of how the Russians calculated penetration for sub-calibre projectiles, I’m all ears.

    All the best,


    Avatar photoJohn D Salt

    If anyone has any better data on velocity decay of WW2 ATk projectiles, or any knowledge of how the Russians calculated penetration for sub-calibre projectiles, I’m all ears.

    Of course the obvious thing to do is to get velocity decay information for US ammunition from the curves drawn in “Handbook of Ballistic and Engineering Data” 1950 vols 1 and 2 and “Terminal Ballistic Data”, and then do the same curve fitting trick.

    So here is a table of penetration for US guns. Note that, as the assumptions of target plate density and ultimate tensile strength are the same, these figures are directly comparable with those already given for Russian guns.

    Expected penetration in mm at normal impact, Dehn's formula.
    Target plate density 7850 kg/m^2, ultimate tensile strength 970 Mpa.
                                         range (m)	
    Weapon		Round	250	500	1000	1500	2000
    37mm M6		M51	 68	 63	 53	 44	 37
    37mm AA M1A2	M49	 35	 28	 18	 11	  7
    40mm AA M1,2	M81,A1	 54	 48	 38	 30	 23
    57mm M1		M70	 91	 78	 56	 40	 28
    57mm M1		M86	100	 92	 80	 68	 58
    75mm M2		M61A1	 64	 60	 53	 46	 40
    75mm M3		M61A1	 75	 70	 62	 54	 48
    76mm M1A2,M5	M79	107	 97	 80	 65	 53
    90mm M3		T33	144	139	129	120	111
    90mm M3		M77	125	113	 91	 73	 58
    90mm M3		M82(l)	144	139	128	118	109
    90mm M3		M82(e)	135	129	120	110	102

    If anyone has velocity decay data for the 75mm M72 and 76mm M62 rounds, I’d like to add them.

    Oh, and all British, German, Italian and Japanese guns.

    All the best,


    Avatar photoWhirlwind

    John, very many thanks for posting this (and sorry I am just getting around to reading it!).  Given our recent quick discussion on the Panzer III with additional frontal plate, interesting what a difference 60mm vs 30mm makes looking at Soviet guns too – and how that 76mm would make like difficult to impossible for the Panzerwaffe in 1941.  And as you mention, those are some very impressive figures for that 57mm!!!

    Avatar photoJohn D Salt

    Ta — it’s good to know I’m not talking entirely to myself.

    Progress since posting these figures has been very much a question of one step forward, two steps back, trip over the parapet and plunge off the bridge screaming.

    I made contact with a nice man at Bovington who sent me, for a modest fee, scans of official firing tables for WW2 British and US tank guns held in their library. I also managed to obtain a hard copy of the AP firing tables for the 25-pounder.

    So far, so good.

    Unfortunately, it turns out that whoever compiles these tables was much more interested in angle of departure and angle of fall than they were in residual velocity. The good news is that I have got the maths necessary to find the trajectory height anywhere along its path given those two items; the bad news is that this doesn’t tell me anything about how fast the projectile is moving along that path. It is possible to make an estimate on the assunption that the projectile is accelerating downwards at 9.8 m/s/s under gravity, but, unfortunately, these estimates are, to use a mathematical term, utter piffle.

    Worse yet, some of the entries in the tables are obviously wrong. In a few cases, the time-of-flight given at close range is wrong, being obviously too short even if the projectile kept up its muzzle velocity the whole way. There is one case in the 75mm M3 table where the angle of departure is given as more than the angle of arrival, which is obviously impossible for an unpowered projectile.

    My confidence in the reliability of the data was also not reinforced by a note in the 17-pr range table saying “Range Table based on practice of 23rd June, 1942”, which suggests to me that the evidential basis for all this stuff is even more painfully thin than I had previously imagined.

    Still, at least there are records, even of they are a bit dodgy. I have yet to turn up any range tables for the Italians, Japanese and French.

    All the best,


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