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    Has there ever been any operational analysis done on grenade usage and effectiveness similar to the work done on small arms?


    John D Salt

    Yes, and I have just typed quite a long reply which has been blown into the ether with a 403 error.

    I am now in far too bad a temper to type it all out again tonight.

    All the best,



    Ah no!!!


    John D Salt

    I am not aware of much OA work on grenade effectiveness, nor, for that matter, on small arms. The following snippets are from my collection of WW2 bits. There was also, I recall, a piece on the effectiveness of the Belgian PRB controlled-fragmentation grenade in an ancient copy of International Defence Review by a Colonel Crevecoeur, but that is I think on a shelf in Wales at the moment, and I am in Swindon.

    The usual methods of assessing the effectiveness of fragmenting munitions would seem to apply to grenades, with the advantage that static detonations are less misleading than with artillery shells because the contribution of projectile motion to fragment velocity is presumably negligible. However, unless the pattern of fragmentation is isotropic, grenade orientation will obviously have an effect.

    Because grenades are not required to withstand the firing stresses of artillery shells or mortar bombs, they can have more efficient charge : casing ratios — more explosive, less steel. As far as I am aware grenade fillings in WW2 tended to be simlar to arty fillings. The British had a fondness for ammonal and baratol, and the Germans and Russians seem to have used straight TNT instead of the cheaper (and only marginally less effective) amatol. The US, while rich enough to afford TNT as a standard shell filling, weirdly seem to have filled a lot of their Mk II grenades with EC powder, a low explosive.

    WW2 grenades as far as I know were all naturally fragmenting, so one would expect a negative exponential distribution of fragment sizes — a small number of big fragments, a medium number of medium fragments, and a huge number of tiny fragments. More recent controlled-fragmentation grenades assure a more even fragment population (and hence a more sharply-defined lethal area) by using notched wire, or by placing small ball-bearings or steel cubes in an explosive matrix.

    There are formulae for predicting fragment sizes and velocities, but I never seem to be able to find all the data I need to feed them. Modelling fragment retardation in air is not straightforward, as fragments tend to be of irregular shape and unstable. What one counts as an “effective fragment” is also something of a moveable feast, but a traditional method of testing involves counting the number of “throughs” on one-inch thick pine boards placed at different ranges from the grenade. Obviously, target posture has a significant effect on vulnerability, but in general figures quoted for “area of effect”, “lethal area”, “vulnerable area” or whatever else you want to call it are based on the area over which one would expect 50% of standing men to collect at least one effective fragment.

    With all that in mind, my sources tell me:

    WO 190/706 “German Infantry Weapons” credits the Stielgranate 24 with a “radius of splintering effect” of 20 yards, as against 12 yards from the 5cm mortar.

    WO 291/150 “WP as an anti-personnel weapon” gives the “incendiary area” of the 77 Grenade (filled 8oz WP) as 800 square feet against troops in the open on hard ground, as against 700 square feet for the 2-in mortar (filled 5oz WP).

    WO 291/472 “Performance and handling of HE grenades” is my best source, and gives details on throwing distances and fragmentation effectiveness from trials conducted with a small number of grenades.

    Taking an average of 18 throws (3 throws by 6 men), the average miss distances, in feet, for the 36 Grenade (Mills bomb) were:

    			15 yds	20 yds	30 yds	40 yds
    Guards	Range		13	11	14	12
    	Line		5	4	10	10
    Devons	Range		–	26	11	14
    	Line		–	9	8	11

    For stick grenades, “the stick does not seem to increase the maximum accurate throw, but it does prevent rolling”. Average errors and length of roll, in feet, are given as:

    				Range	Line	Roll
    	Mills 36		15	8	9
    	Time-fuzed stick	8	8	3

    Maximum lengths of throw, in yards, for various British grenades were:

    	Grenade		Standing	Lying
    	70		33		31
    	71		28		23
    	36		30		26

    Comparison of lengths of throw, in yards, for British and US grenades:

    			Standing	In the open	Crouching 	Lying in the open
    		 	behind cover			behind cover
    British 36		31				21	
    US fragmentation	31				21	
    British 69				32				26
    US offensive				28				26

    I assume that “US fragmentation” refers to the Mk II grenade, and “US offensive” to the Mk III.

    The following table shows the expected chance of incapacitation at different distances from a grenade. The USA grenade was given an experimental TNT filling for these tests. Only one German grenade was available, so this was fragmented on its base and the results used to calculate the expected results “as thrown”, the orientation of a thrown grenade being significant in affecting its burst pattern.

    The 36 grenade, it is stated. “has a very irregular burst”.

    Distance 	USA grenade	German stick grenade
    (feet)	36 gren	Normal 	TNT 	On base	As thrown
    		filling	filling
    3				97%	83%
    6				92%	75%
    9				70%	45%
    10	45%	20%	40%		
    20	17%	7%	18%		
    30	13%	2%	10%		
    40	10%	0.5%	5%		
    50	–				
    60	3.0%				
    70	1.4%				
    80	0.7%				

    The lethal area of the 36 grenade is given as 1550 sq ft on meadow land, and that of the USA grenade 350 sq ft. The lethal area of the 36 grenade is calculated as 2000 sq ft on perfectly flat ground, which would correspond to 1500 sq ft on normal ground. On perfectly smooth ground, incapacitation probabilities are stated as being 84% at 10 feet, falling to 14% at 30 feet.

    “The conclusions with regard to the 69 grenade were:–
    (i) A direct hit would be lethal
    (ii) Apart from the concussive effect and flying stones there seems to be little probability of injury beyond a radius of a few feet.”

    The above presumably refers to the 69 grenade without fragmentation jacket, as screen test results give expected incapacitation probabilities as follows:

    Grenade			4 feet	8 feet	12 feet
    70			85%	39%	20%
    71			98%	63%	36%
    36			73%	29%	14%
    69 (segmented jacket)	96%	56%	31%
    69 (plain jacket)	91%	44%	23% 

    The average percentage chances of incapacitation at 10 to 20 feet are given as 33% for the 36 grenade, and 25% for the US rifle grenade M9A1, an anti-tank grenade with good anti-personnel characteristics.

    WO 291/543 “Note on an experiment with Grenades 36 on dummy targets at Birmingham”, says:

    “One of the main effects of a grenade 36, indoors, is blast. Our methods do not, however, allow us to assess this effect quantitatively.”

    “Personnel within 3 feet of the burst stand a very small chance of escaping incapacitation if not otherwise protected. Ordinary doors and planks afford little protection, ceiling and floor together are good, and even a thin brick wall gives absolute cover against this weapon.”

    “A man would seem to stand a more than even chance of escaping incapacitation if 5 feet or more away from the burst. A fuller trial in the open at the School of Infantry (by AORG 6) showed a risk rate falling from 45% ten feet from the grenade to 17% twenty feet from the grenade.”

    http://www.lonesentry.com/articles/sovgrenades/ gives throwing distances and burst radii of various Soviet grenades of WW2.

    Overall there does not appear to be a great deal of information available, so if anyone has any further numerical data, please contribute.

    All the best,


    • This reply was modified 4 years, 6 months ago by John D Salt.

    Thanks very much for taking the time to write that out, it was fascinating.  One question (forgive my ignorance), what do “range”, “line” and “roll” indicate in the miss distances – is it range = y-axis error, line = x-axis error, roll = further deviation from POI?


    John D Salt

    If you take the grenade to have been thrown along the Y axis, then, yes, that’s what I would interpret it as.

    Obviously not all kinds of ground would permit much of a roll, but looking at the roll distances quoted and the way effect diminishes from the point of burst, it seems that the stick grenade seems offers a non-negligeable advantage in terms of accuracy.

    Now I wonder if anyone has considered making grenades in the form of Weebles[tm], both to reduce rolling and to ensure an upright orientation for the grenade when it bursts?

    All the best,



    Haha! Nice.

    More seriously, I wonder if grenade accuracy follows the same broad pattern of reduction as experienced with small arms in TESEX/live-firing situations and in real operations.  I don’t think I have ever seen the subject mentioned. Nor a discussion of any suppressive effects.



    Jemima Fawr

    Excellent stuff as always, John.

    My wargames blog: http://www.jemimafawr.co.uk/

    John D Salt

    I wonder if grenade accuracy follows the same broad pattern of reduction as experienced with small arms in TESEX/live-firing situations and in real operations. I don’t think I have ever seen the subject mentioned. Nor a discussion of any suppressive effects.

    I am now making stuff up out of my head, and not relying on any quantitative sources — what follows is opinion, not fact.

    I would have thought that hand grenades might stand a good chance of avoiding many of the tendencies that limit the effectiveness of small-arms in close combat. Throwing things at the bad guys is an established threat behaviour in apes and monkeys, and the human shoulder joint is exceptionally well-evolved for the task. The ability to aim small-arms precisely can be limited by large doses of adrenalin causing loss of close vision and fine motor control, neither of which are necessary for throwing — indeed gross motor control may be improved. The fact that the grenade is an area weapon, and need not strike its target directly, might also tend to reduce any loss of performance caused by excitement. Even in the last extremes of the red mist, when you are so worked up your vision is beginning to grey out, it is still quite instinctive to throw something at someone who is annoying you — you just need to be sure you remember to take the pin out first (not always the case in the stress of action, I believe). So I would expect grenade-throwing performance to be degraded much less than shooting performance by the same amount of stress. Since a grenade can be flung over the parapet of a trench with some hope of doing some good, it is possible to imagine defenders being completely suppressed from the point of view of small arms, but still capable of grenade action.

    The grenade is, though, a mainly offensive weapon, and I expect it is mostly used after questions of suppression have been determined and the firefight won. When the attackers get close enough to start grenading the defenders’ fire trenches, which I assume they could not very well do without keeping the defenders’ heads down, most times I would think it is all over bar the shouting. As long as the supply of grenades holds out, the attackers can with a little organisation systematically clear the enemy position (“aufrollen” or “bombing along”). Grenades are less use to the defender, as pointed out in something I was reading recently (Stephen Bull’s book on Stosstrupp tactics, I think), because with fuze delays of typically 3 or 4 seconds an attacker may have moved a fair distance (in comparison with the fairly small lethal radius) before the grenade goes off, whereas a defender in a trench has not the same freedom of movement.

    One way or another, then, I do not expect that grenades are subject to as much combat degradation as small arms (always assuming you remember the pin), nor do I think they have the same opportunities for suppressive effect.

    All the best,


    John D Salt

    More detail on various grenades is available in FM 3-23-30, “Grenades and Pyrotechnic Signals”, available from various places on the intertubes including http://pentagonus.ru/_ld/1/199_FM-3-23.30-Gren.pdf

    Unfortunately this site does not have any facility for uploading spreadsheets, so I shall describe the few simple bits of numerical manipulation I did on the data from this source, having first typed it all in.

    The first thing to investigate was throwing range against grenade weight. It makes sense that you should be able to throw a lighter grenade a bit further. A linear trend line plotted against the available data gave a tremendously bad coefficient of determination, but for the sake of a rough and ready rule of thumb I would be prepared to believe something like 43 metres, less 0.015 of the grenade’s mass in grams. This is probably fairly meaningless anyway, as I am sure such variation will be swamped by the variation of throwing ability between individuals.

    The next thing was to see if any correlation could be found between filling weight and effective burst radius. I had previously developed a reasonably good expression to find 25-pounder equivalent weight from filling weight for WW2 artillery shell, based on figures drawn from an OR paper on the bombardment of Wesel. Trying something similar for grenades produced not only a poor coefficient of determination, but a perverse trend line; it seemed that burst radius decreased with increasing charge weight. Looking at the grenade characteristics, this could be partially explained by the presence of some well-filled offensive grenades with fibre or plastic bodies, and some smaller grenades with pre-formed fragments but smaller charges. There would also have been non-negligible differences in brisance between the various different fillings — PETN I think packs a bit more oomph than TNT or Composition B. Anyhow, no simple relation was apparent for grenades in the way it was for WW2 artillery shell.

    Finally, and perhaps most usefully, I produced a calculator to work out the probability of a target being hit at different ranges by fragments spreading isotropically from a point source (the exploding grenade). To do this I defined three input variables: The number of fragments, the target area (in square metres), and the range step (in metres, 1 seems convenient). It is then easy for each row in the spreadsheet to write the following formulae:

    Cell A — The range. The first entry is equal to the range step; subsequent ones are the previous entry plus the range step.
    Cell B — Surface area of a sphere at this range. This is 4 times pi times the square of the range (cell A).
    Cell C — Fragment density, in frags per square metre. This is the number of fragments divided by the surface area of the sphere (cell B).
    Cell D — Expected number of hits. This is the fragment density (Cell C) multiplied by the target area.
    Cell E — Probability of hit. This is calculated using Koopman’s exponential search formula: 1 – EXP(-Cell D)

    All very easy, as it is to draw a chart of range against P(hit). Obviously there are some simplifying assumptions. No account is taken of the loss of velocity of fragments, which are assumed to remain effective up to the maximum range considered. No allowance is made of the masking effect of terrain, which becomes appreciable at surprisingly short ranges. The assumption of isotropic fragmentation is probably not justified for most designs of grenade.

    Representative numbers I used were 1000 for the number of fragments (I believe about right for the notched wire from a US M26 or British L2) and a target size of 0.37 square metres (the STANAG number for a standing man). This gave the following results:

     2m     100%
     4m      84%
     6m      56%
     8m      37%
    10m      26%
    15m      12%
    20m       7%
    25m       5%
    30m       3%
    40m       2%
    50m       1%

    I suspect that this overrates the long-range probabilities, because fragments will have been slowed down considerably, but I need to find a good simple fragment retardation formula from somewhere.

    All the best,


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