 This topic has 7 replies, 6 voices, and was last updated 1 month ago by John D Salt.

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05/07/2024 at 23:07 #200237Ivan SorensenParticipant
Does anyone have any numbers (and ideally a book to look at) giving some estimates for how many shots a tank or an antitank gun at a given range might expect to fire before one hits the target?
As a follow up question, assuming the target isn’t moving, could it be expected that follow up shots once you are shot in are now going to hit too? I guess what I am wondering here is how much variation there could be between shots, flight path etc.
05/07/2024 at 23:38 #200238Aethelflaeda was framedParticipantYou and every ordinance officer every where. Ordinance range testing will give you a figure but that figure is not going to be the same as on the battlefield.
bore sighting…not bore sighted? Cold day, warmed barrel? Rain, wind? Good consistency in the quality of round and charge or was the round made by POWs under duress? Is someone shooting at you or do you have surprise?
Mick Hayman
Margate and New Orleans06/07/2024 at 02:36 #200241Pieter RoosParticipantThis video is a good start, and gives sources:
06/07/2024 at 02:46 #200242Pieter RoosParticipantThe TLDW (Too Long, Didn’t Watch – but it is worth while and not limited to 88mms) 1040 shots per kill. Any game using individual shots would probably not be acceptable to most players as round after round (die roll after die roll) missed.
06/07/2024 at 07:41 #200247MartinRParticipantTo answer the second part of the OP, yes, the point of strike varies even once ranged in on a target. There are ballistiics formulas which calculate this stuff. The degree of variation is such that at longer ranges they can miss completely.
As to the first, it depends. Simply dividing rounds fired vs hits will give you numbers in the 10 to 40 range as above, but it varies hugely by individual crew. Another interesting thing which comes out of Rowlands “Stress of Battle” (and others) is that the vast number of kills are inflicted by a very small number of crews, the rest just roll around being targets,occasionally blazing away ineffectually in the direction of the enemy. So a crew of “killers” might achieve range levels of accuracy, while the rest never, or very rarely, hit anything.
I am minded of John Foleys Memoir of his Churchill tank troop in Northwest Europe. I can recall precisely two anti tank engagements they took part in, in one they spotted a Stug motoring into a wood and two troops of Churchill spent twenty minutes blindly firing AP shot into the foliage. Eventually they noticed smoke coming from the wood as someone had hit it.
In the other, Foleys gunner scored three hits from three shots in quick succession. Sadly they were at the front of a Tiger 50 yards in front of them. They all bounced off and the Tiger put a round right through the tank from one end to the other with its first shot.
So, pick a number between one shot one hit, and 120 shots, one hit.
"Mistakes in the initial deployment cannot be rectified"  Helmuth von Moltke
08/07/2024 at 21:27 #200359John D SaltParticipantDoes anyone have any numbers (and ideally a book to look at) giving some estimates for how many shots a tank or an antitank gun at a given range might expect to fire before one hits the target?
People have a colossal variety of such numbers; and, remember, the great thing about trying to estimate a probability is that you are never going to be out by more than one.
Obviously, the probability of a hit for any ballistic weapon depends on the range it is firing at, thanks to the Father Dougal principle — small cows look the same as faraway cows, and it is easier to hit a big cow on the arse with a banjo than a small one.
For the sake of a spread of numbers from an actual book, Biryukov and Melnikov’s “Anti Tank Warfare” (Progress Publishers, 1972) contains the rule of thumb that, during the Great Patriotic War, it took typically one or two shots to hit a tank at 300 metres, and 8 to 10 shots to score a hit at 1000 metres. For what it’s worth, they also reckon that it typically needs two or three hits to score a knockout.
As Charles Grant put in in “Battle!”, he had spoken to a WW2 tankie who reckoned you were very lucky if you could spot, identify, and hit a panzer at more than a few hundred metres. The average engagement distance for most theatres was only about a klick. Without giving a source, a US TRADOC bulletin that tries to show the difference in effectiveness between modern (1970s) and WW2 weapons says that an M60 firing 105mm sabot against an exposed tank has a 50% chance of a firstshot hit at 1500 metres, and a WW2vintage Sherman would need 13 rounds from its 75mm to achieve the same probability. A quick bit of maths, on the assumption of statistical independence between shots (almost certainly wrong if the fall of shot is being observed and adjusted) shows that this corresponds to a singleshot hit probability of about 5 per cent, or twenty rounds to produce the expectation of a hit.
I would add that the total number of rounds fired divided by the number of targets hit is probably a fairly ropey estimate of the hit probability on a live tank, because a lot of rounds on operations and on realistic exercises are fired at things that, it turns out, are not tanks at all. Even if the enemy has no scheme of decoys and dummies, it is easy for the nervous gunner to mistake an item of farm machinery or a suspiciouslooking midden for an enemy AFV. On an active battlefield one might also expect to meet wrecked AFVs. There is an episode in Shabtai Teveth’s “The Tanks of Tammuz” from the 1967 war where an Israeli armoured brigade wastes a lot of time stalking a black Centurion, wondering if the dark colour scheme indicates a Jordanian vehicle, and ultimately discovers that it is black because it is burnt out.
If you can get the basic data required — and that’s a big if — the mathematics of calculating hit probability is sufficiently straightforward to be done on a single line in a spreadsheet. Copy this into cell G4 of a spreadsheet, go on (I use LibreOffice Calc, but it should work just the same in Excel).
=(NORMDIST((A4/2+C4), 0, E4,1)NORMDIST((A4/2+C4), 0, E4,1))*(NORMDIST((B4/2+D4), 0, F4,1)NORMDIST((B4/2+D4), 0, F4,1))
You will need to fill in the data in cells A4 to F4, in this case, as follows:
A4: Target height
B4: Target width
C4: Vertical offset of aimpoint
D4: Horizontal offset of aimpoint
E4: Standard deviation of vertical dispersion of shot
F4: Standard deviation of horizontal dispersion of shotA fairly usual assumption is that the MPI is correctly aimed at the centre of the target, so the offsets (C4 and D4) will be zero, but this formula allows for offcentre aim points.
Fairly obviously, this method assumes a rectangular target, and assumes that ballistic errors are normally distributed in both planes. If you want to find hit probabilities in a more complex target — say one rectangle for the hull and another for the turret — you can use this formula to work out the p(hit)s for each rectangle using the appropriate offsets, and add them together.
The maths doesn’t care what units you use; I do, and will consider you a candidate for the funny farm if you use anything but SI units. It is customary to give ballistic dispersions in mils (and we don’t really care if they are real milliradians or NATO mils, 6400 to the circle). The fact that a mil subtends one metre at a thousand metres makes it easy to work out what the dispersion will be in metres at the target. So, a cow that is 2 metres wide will seem to subtend 2 mils at 1,000 metres, 1 mil at 2,000 metres, 4 mils at 500 metres, and so on. The important thing is always to be consistent, expressing the dispersion, offset and target dimensions either as mils at the muzzle or (my preference) metres at the target.
There is a little bit more to be said about adding sources of error together, how to allow for rangefinding errors (which needs a model of trajectory shape) and how to twiddle dispersion data annoyingly given in forms other than standard deviations, but in deference to the pervasive numerophobia that is the spirit of the age, I shall leave those on the side of the plate for now.
I would, however, encourage everyone with access to a spreadsheet (which should be approximately everyone) to have a go at using the above formula.
The NATO standard tank target is a rectangle 2.5m by 2.5m. If we assume we are shooting at that with a gun and ammo whose vertical and horizontal dispersions are both 1.25m, and aimed at the centre of the target (both offsets are zero) you should get a calculated P(hit) of 47%. Add a vertical offset of 1 metre and it should drop to 37%.
Let me know if you got it to work.
All the best,
John.
08/07/2024 at 22:44 #200361Guy FarrishParticipantIt does work in Excel! And gives the values you said with the inputs you gave.
Lots of fun playing around with different values in this – no idea what I will use it for, but thanks for an entertaining time!
I am tempted to make spuriously precise hit tables from it to lend an air of gravitas to wobbly home made rule sets!
08/07/2024 at 23:06 #200362John D SaltParticipantI am tempted to make spuriously precise hit tables from it to lend an air of gravitas to wobbly home made rule sets!
Exactly what it is intended for. Also, if anyone disagrees with the numbers you have fed the formula with, you can tell them to produce some better ones. Applicable to pretty much any ballistic weapon, so use it for smallarms and bows and arrows as well. Have endless fun trying to find out why there are such widelydiffering opinions on the presented area of a human target.
All the best,
John.

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