 This topic has 3 replies, 2 voices, and was last updated 2 years, 5 months ago by John D Salt.

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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://paulatrydes.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 5580mm 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 61K BR167 58 51 40 30 23 45mm 19K BR240 60 54 45 36 29 45mm m37 53K BR240 69 62 50 40 31 45mm M42 BR240 73 67 55 45 36 57mm m43 ZiS2 BR271 127 121 111 102 93 57mm m43 ZiS2 BR171 123 113 97 82 69 57mm m43 ZiS2 BR271K 115 99 72 52 36 76mm m27 BR350A 28 26 23 21 18 76mm m39, 42 BR350SP 80 75 66 59 51 76mm m31, 38 AA BR350A 105 100 89 79 70 85mm 52K BR367 122 118 109 101 94 85mm m43 D53 BR365 121 116 106 97 89 85mm m43 D53 BR365K 118 109 94 80 68 100mm m44 BS3 BR412 176 163 141 120 102 107mm m40 M60 B420 138 134 124 115 107 122mm m43 D25 BR471 158 148 128 111 96 152mm m38 how M10 m1915/28 78 76 71 66 62 152mm m10/34 ML20 BR540 131 126 116 108 100
Conclusion:
The penetration figures given are produced on a consistent basis, using a modern and dimensionallyconsistent 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 53K 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 subcalibre projectiles produced obvious nonsense, with downrange 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 subcalibre 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 subcalibre 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.
12/04/2022 at 19:35 #171406WhirlwindParticipantJohn, 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!!!
13/04/2022 at 01:33 #171409John D SaltParticipantTa — 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 25pounder.
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 timeofflight 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 17pr 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,
John.

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