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- 20/07/2021 at 19:27 #159158John D SaltParticipant
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.

Method:

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

https://paul-atrydes.livejournal.com/254413.html

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))

where

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 degreesThe 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).

Results:

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

Conclusion:

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,

John.

21/07/2021 at 03:12 #159161John D SaltParticipantIf 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,

John.

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