Area presented by a human target

[John D Salt]

Rules writers who muck about with hit probability calculations need to know the size of the target being shot at.
Even people who don’t need to know that might well want to know what the difference in vulnerability is between, say, a standing soldier and a prone one.
To either these ends, a good thing to know would be the presented area of a human target; since humans can change their posture, it would also be useful to know how this changes when someone is kneeling, lying, or shooting over the parapet of a slit trench.
It is a source of perpetual disappointment to me that simple questions like these are so awkward to answer. It’s not that there are no answers available (although they take a bit of digging), it’s that the answers one comes up with vary so alarmingly — more than can be explained by variation in the size of humans, anyway. The 10th percentile American male is only about 10% shorter than the 90th (which if other dimensions vary by the same percentage one might imagine corresponds to about 20% less presented area). The figures I have for the area of a standing man vary from a high of 0.675 square metres to a low of 0.37, which is 45% less. Agreement on the degree to which changing posture varies the target area is similarly dreadful.
Still, for what it’s worth, I present the numbers I have accumulated over the years, with some more recently dug up. Not every source gives a figure for every posture. Where different areas are given for frontal and flanking aspects, the frontal aspect has been used. The first table shows target areas, given in square metres, obviously. The second table shows in percentage terms how presented area reduces compared to a standing target. In case it matters, source 1 (dating from 1899) is the closest to the average across all sources.
The STANAG (source 6) gives unusually little benefit for all the non-standing postures. In rough terms, the others offer a reduction in target area of between a fifth and a third for prone targets, and between an eighth and a quarter for targets in slit trenches.
Given that most anti-personnel fire is distributed sufficiently randomly that hit probability should be pretty much proportional to target size, do your favourite wargames rules reflect differences of that order in the vulnerability of troops standing, lying, or in slit trenches?

Source		 1	 2&3	 4	 5	 6	 7	 8
Standing	0.4753	0.37	0.39	0.64	0.37	0.675	0.5
Kneeling	0.3248		0.195	0.45	0.32	0.426	0.37
Prone		0.1612		0.093	0.2	0.27	0.232	0.1
Slit trench	0.119	0.046		0.1	0.15	0.186	 

Source		 1	 2&3	 4	 5	 6	 7	 8
Standing	100%	100%	100%	100%	100%	100%	100%
Kneeling	 68%		 50%	 70%	 86%	 63%	 74%
Prone		 34%	 	 24%	 31%	 73%	 34%	 20%
Slit trench	 25%	 12%	 	 16%	 41%	 28%	

Sources:

1. H. Nimier and Ed. Laval, Les Projectiles des Armes de Guerre: Leur action vulnérante, p.101, Félix Alcan, Paris, 1899
2. WO 291/476, Comparison of rifle, Bren and Sten, 1944
3. WO 291/471, Weight of small-arms fire needed for various targets, 7 May 1944
4. James F Dunnigan, The Information Gap: Some Problems in Tabletop Realism, p. 22, Strategy & Tactics no. 13, May-June 1968
5. GRAU firing table No. 61, Firing tables for 5.54 and 7.62mm weapons against ground targets, USSR Ministry of Defence, Moscow, 1977
6. STANAG 4512, Dismounted Personnel Target, North Atlantic Treaty Organization, Brussels, 10 Nov 1995
7. Captain Stephen C Small, US Army retd., Small arms and asymmetric threats, p.38, Military Review, Nov-Dec 2000
8. Alan Catovic, Berko Zecevic, Jasmin Ter, Analysis of terminal effectiveness for several types of HE projectiles and impact angles using coupled numerical-CAD technique, New Trends in Research of Energetic Materials, Czech Republic, 2009

[irishserb]

I tend to reduce it to more of a base probability of hit being modified by type and or magnitude of cover.  And, the base probability has to be built out of more data than simply cross sectional area v. weapon’s grouping at range on the range.

I mean some soldiers are vetaran snipers, warm and well fed, other times they are green, using an unfamiliar weapon from the dead guy in front of them, hungry, tired, freezing and lost their glasses.  Their groupings probably arean’t the same.  And even if both are 50th percentile within their racia,l cultural, and whatever other groups, they may not represent the same size target in in the same pose.

But, yes, I do like rules to try to invest some element from this type of data.

And I don’t mean any of this in an argumentative way.  Reading my type sounds a lot drier than the tone and inflection of my typing.

[John D Salt]

irishserb wrote:

I tend to reduce it to more of a base probability of hit being modified by type and or magnitude of cover.

Well, yes, but where do you get the base P(hit) numbers from?

irishserb wrote:

And, the base probability has to be built out of more data than simply cross sectional area v. weapon’s grouping at range on the range.

Agreed, but only because of that “…on the range” qualification. Range firing hitting rates, as I hope we all know by now, are about two orders of magnitude worse than happens on the battlefield. But you can produce P(hit) numbers from a mere two inputs, the target size and the weapon’s dispersion.

irishserb wrote:

I mean some soldiers are vetaran snipers, warm and well fed, other times they are green, using an unfamiliar weapon from the dead guy in front of them, hungry, tired, freezing and lost their glasses. Their groupings probably arean’t the same. And even if both are 50th percentile within their racia,l cultural, and whatever other groups, they may not represent the same size target in in the same pose.

Snipers can probably shoot well enough that the crude approach I am going to outline here is badly inadequate, but it will do for most battlefield infantry shooting, where accuracy is so poor that “trivial” things like crosswind and sight setting can safely be ignored.

The great thing about the factors affecting dispersion is that they can all be wrapped up into a single overall number. The business of estimating the magnitude of each element of an error budget can get honkingly complex for tank shooting, but for infantry work I think we can use more of a “big handfuls” approach, as other factors tend to be swamped by the soldier’s ability to point the weapon at the target. No matter, you can have as many factors as you like contributing to dispersion, just remember that you combine them by summing the squares and taking the square root.

Join me now on a magical journey of discovery on how to make crude P(hit) estimates from just two numbers, target area and weapon dispersion. Have your spreadsheets ready. There will be a test later. Try to imagine Rachel Riley telling you all this if it helps.

The measure of weapon accuracy I intend to use here is CEP, Circular Error Probable. This is the radius of a circle containing 50% of the projectile impacts. If someone has given you the standard deviation (sigma) of miss distance instead, convert this into a CEP by multiplying by the magic number 1.1774.

The measure of target size is the radius if the target, which is treated as being circular (“assume all chickens to be perfectly spherical”). Again, of someone has given you the target area, convert it to a target radius by doing A = pi * R^2 in reverse, which is R = sqrt(A/pi), where A is the area and R the radius.

Given the target radius, R, and CEP, the P(hit) can be calculated as 1.0 – (0.5^(R/CEP)^2). Why, yes, this is the method they use for nukes.

A worked example: consider a kneeling soldier being shot at from a range of 200 metres.

The weapon dispersion we will set equal to the AMSAA aim error function, which in effect assumes a perfect rifle, but a shooter whose skill-at-arms is in the bottom third of those observed in 8 different US Army experiments. The aim error at 200 metres is expected to be 3.67 mils. This corresponds to 0.734 metres at that range, using the mil relation (multiply the angle in mils by the range in kilometres, 3.67 * 0.2 = 0.734). Those AMSAA swine have given us a sigma, so we convert it to a CEP, 0.734 * 1.1774 = 0.864.

The target area we’ll take from Nimier and Laval, the first of my sources in the initial posting: 0.3248 square metres (one must admire precision to the nearest square centimetre). To convert this to a target radius, sqrt(0.3248/pi) gives 0.322.

P(hit) is then 1.0 – (0.5^(0.322/0.864)^2), which is 0.0918, or a gnat’s tadger north of 9%.

You can do all this on a calculator (how I did the worked example), and it is not at all hard to stick the formulae into a spreadsheet (how I checked it).

Additional sources to show where I got the CEP P(hit) calculation and the AMSAA aim error function, both available from DTIC:

DARCOM-P 706-101, Engineering Design Handbook, Army Weapon Systems Analysis, part 1, US Army Materiel Development and Readiness Command, Alexandria, VA, Nov 1977.

AMSAA Technical Report No. 461, System Error Budgets, Target Distributions and Hitting Performance Estimates for General Purpose Rifles and Sniper Rifles of 7.62x51mm and Larger Calibres, LTC(retd) Jonathan Weaver, May 1990.

irishserb wrote:

And I don’t mean any of this in an argumentative way. Reading my type sounds a lot drier than the tone and inflection of my typing.

Don’t worry, Mr. Picky can pick an argument anyway, and will argue with himself if nobody else wants to play.

All the best,

John.

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