08.11.
22, 12:12 Effects and Weight of Fire
BRITISH ARTILLERY IN WORLD WAR 2
EFFECTS & WEIGHT OF FIRE
The Weapon of Artillery
Updated 6 June 2014 WHAT IS WEIGHT OF FIRE?
Weight of fire concerns the quantity, density and intensity of
CONTENTS artillery fire used to attack a target. In essence it is about the
effectiveness ('doing the right thing') and efficiency ('doing the
WHAT IS WEIGHT OF FIRE?
thing right') of artillery fire at the target end. The British
BRITISH RESEARCH IN WORLD undertook lots of research into this during World War 2 and in
WAR 2 1943 the War Office established the Fire Effect Committee.
The Effects of HE Shells
Fragmentation BRITISH RESEARCH IN WORLD WAR 2
The Effects of Terrain Broadly, research proceeded in two phases, initially theoretical
The Effects of Target Posture investigations, experiments and trials in UK. Then field studies
by 1 Operations Research Section (ORS) in Italy and 2 ORS with
BATTLEFIELD EFFECTS
21 Army Group in NW Europe. There are indications of some
Quantitative Effects work in the Burma theatre but this seems to have been
Equivalence Between Calibres bequeathed to the Indian Government. Studies examined hostile
What it Means on the Ground and fratricidal artillery fire, and friendly fire on subsequently
CALCULATING WEIGHT OF FIRE captured positions. Both sections had several artillery officers.
AND FINDING THE RESULTS OF The morale effects were a particular concern and there was a lot
FIRE analysis trying to separate this effect from the others, without
Area of Effect much success.
How many shells must hit the
target to get the results?
Initial work concentrated on HE fragmentation, the theoretical
AoE Shape
effectiveness of shells and the vulnerability of particular targets.
How many shells must be
fired?
This being combined into usable data as ‘area of effect’ (AoE),
How good are the
originally called 'vulnerable areas', for each combination of shell
calculations? and target type. This led to such things as the definition of a
AFTER WORLD WAR 2
casualty and, in contrast to the US, UK adopted a probability
approach. For example, “a 50% military loss occurs when a
wound causes a disability lasting approximately 6 days” – the 100% loss was a 45-day disability.
This is a very good analytical approach and possibly valuable at the operational level but perhaps
less useful as a tactical guide to units in the field.
As an example of target vulnerability research, the mean presentation area of a human body
across a variety of postures was calculated as 4.2 ft sq with vulnerable organs occupying 43% of
the total at the front and 36% at the back. Similar approaches can be used for equipment targets.
The Effects of HE Shells
The physical effects from High Explosive (HE) shells are caused by three things, in descending
order of significance:
https://nigelef.tripod.com/wt_of_fire.htm 1/11
08.11.22, 12:12 Effects and Weight of Fire
Fragments or 'splinters' from the shell casing when it is shattered by the shockwave created
by the detonating explosive filling, often erroneously called 'shrapnel'. These fragments rely
on kinetic energy for their effect. A key point is that a high proportion of these fragments are
wasted (they go up in the air or straight into the ground).
Blast can be significant with very large calibre shells and all shells if they detonate in a
confined space or very close (inches not yards) to a vulnerable hard target. Blast is the
pressure wave created by the expanding gases released from the fractured shell casing, it
causes overpressure, which in turn causes damage. When a shell penetrates the ground the
gas pressure created by the detonation displaces material to form a crater.
Flash from the heated gases, generally insignificant for artillery HE weapons, the blast and
splinters will usually do more damage but flammable materials may catch fire.
Fragmentation
Shrapnel was widely used in World War 1, but not in World War 2, it was invented at the end of the
18th Century. In its 20th Century form a time fuze detonated a propelling charge in a carrier shell
with a low angle of descent to fire a few hundred balls (called bullets) forwards and downwards in a
narrow cone, like a shotgun. However, by WW2 HE shells, which had started appearing at the
beginning of the century, had replaced shrapnel. Like shrapnel bullets, shell fragment kinetic
energy is the product of a fragment's mass and velocity (½(mass × velocity2)), given equal initial
velocity heavier fragments travel further because they have greater 'carrying power'.
The fragmentation of HE shells and fragment velocity varies depending on the amount and type of
explosive, the design of the shell body and type of steel. Key parameters are the ratio of explosive
weight to shell body weight and the ratio of internal diameter (ie explosive content) to shell wall
thickness.
A fragment of 1/8 oz or more has a 50% probability of being lethal at 200 feet from the point of
burst (providing it hits in the area of a vital organ). Of course actual fragment sizes vary quite a lot,
see Table 1, in part due to the shape of the shell. One indicator is the ratio 'diameter of the shell
cavity'/'thickness of the shell wall', calculating this means ratios through lots of 'slices' of a shell to
find the mean. For 25-pdr this ratio was about 4, the ideal is about 10. Fragments have more air
resistance than streamlined rifle bullets, so lose their velocity more quickly. However, heavier
fragments have more 'carrying power', but bigger fragments means less of them from a particular
size of projectile, which reduces the likelihood of a hit. Nevertheless, fragment's 'un-aerodynamic'
shape means they are very efficient at transferring kinetic energy on impact with a soft material.
By 1941 British research determined that the best size for an anti-personnel splinter was under
1/25 oz (ie about 1 gram), significantly less than the then existing designs. The 1907 criteria,
reputedly developed by France, was a force of 58 ft-lbs to create an incapacitating wound;
however, 58 ft-lbs actually appears to have been the German criteria (8 kg-m (or Newtons)), the
French one being only 4 kg-m, albeit 19 kg-m for horses). British research with small fragments
suggested closer to 5 ft-lbs (0.7 Newtons of force or 6.8 Joules of kinetic energy ) was all that was
needed, and that it was energy not force or momentum that was the key. In contrast research into
anti-aircraft ammunition before WW2 led to the 3.7-inch HAA HE shell being designed to produce
2.5 oz fragments. Larger fragments travel further and have greater effect on 'harder' targets, but
there are less of them. For more details about shells see the Ammunition page. Joules/mm2 are
the modern measure of fragment lethality.
The following table shows the percentage and numbers of fragments of different sizes for different
percentages of HE weight in 25-pdr shells, optimum anti-personnel fragmentation comes from
shells with HE content at least about 25% of total weight, this was not achieved in WW2. However,
the amount of fragmentation varies quite significantly with the power and violence of the explosive
used, which also affects its destructive effects.
Table 1 - Fragment Sizes and Quantities for HE Content
(1 oz = 28.35 grams)
https://nigelef.tripod.com/wt_of_fire.htm 2/11
08.11.22, 12:12 Effects and Weight of Fire
HE content > 2 oz 2 - 1 oz 1 - 1/4 oz 1/4 - 1/8 oz 1/8 - 1/25 oz < 1/25 oz
15% 13% 15% 35% 12% 10% 15%
7% 31% 26% 29% 5% 2% 7%
Expected number of fragments per 10 kg (22 lb) projectile
15% <19 70 168 192 363 >1122
7% <51 57 152 87 80 >572
Most British field artillery shells used standard engineering steel, '19-ton' yield strength; in contrast
the US used '23-ton'. Using normal as opposed to high strength steel made it easier to produce
shells. However, it also meant that shell walls had to be thicker to survive firing stresses
(assuming similar safety margins), which left less volume for explosive filling. One rule of thumb is
that 19 ton steel allows 7% HE fill while 23 ton permits 15%. Table 2 shows the HE percentage in
some World War 2 shells and broadly supports this rule of thumb. Note the weights are fuzed
weights, a fuze typically weighed about 1 lb, contributed little to fragmentation and normally went
into the ground.
Table 2 - Shell and Filling Weights
(1 lb = 0.453 kg)
HE Shell Weight (lbs) HE % Weight
76.2-mm OF-350 14 11.3
25-pdr 25 7.0
3.7-in How 28 9.0
10.5-cm Gr38 33 9.3
105-mm M1 33 14.8
122-mm OF 462 (How) 48 16.9
122-mm OF 471 (Gun) 55 15.2
4.5-in Gun 55 6.9
5.5-in 100-lb 100 10.0
5.5-in 80-lb 82 14.6
15-cm Gr42 95 14.3
152-mm OF-540 (How) 96 14.0
152-mm OF-530 (Gun) 88 15.4
155-mm M107 95 15.8
7.2-in 201 13.9
8-in M106 200 18.5
This table shows the 4.5-inch shell was seriously deficient in explosive power having only about
3.8 lbs of HE, less than 105-mm! However, given that the 4.5-inch Gun was primarily for counter-
battery fire with the goal of damaging equipment then large fragments may not have been such a
bad idea.
The pattern of the spread of fragments from an HE shell is shaped mainly by the fragment ejection
angle and velocity (helped by shell rotational velocity), and modified by the terminal velocity and
angle of descent of the projectile. Most fragments from a static shell go in a direction of 90° from
the external face of the shell body. In flight shells 'wobble' and the angle of the external face varies
in relation to the shell's long axis depending on its circular radius head (crh) shape. However, the
angle of descent is never vertical so a proportion of the fragments go into the ground or into the air
and fall to earth by gravity. More generally a typical angle of descent is 25° or less, and depending
on the charge and range, terminal velocity is typically 25% - 35% of fragment velocity the nett
effect (a vector sum) being to send the fragments about 25° forward of their static direction. This
gives a wing shaped pattern of the fragment spread. Of course in all but the hardest ground even
direct action fuzed shells penetrate a short distance, which which means the ground absorbs most
of the forward projected fragments. Figure 1 shows this in generalised plan view for ground burst
https://nigelef.tripod.com/wt_of_fire.htm 3/11
08.11.22, 12:12 Effects and Weight of Fire
shells of World War 2 type. Air-burst shells make use of the fragments projected downwards and
the ideal anti-personal height of burst against troops in the open is 5 - 10 feet, which is difficult to
achieve (even with VT fuzes due to the varying reflectivity of the ground) and was
effectively impossible in WW2. However, higher bursts are more effective against dug-in troops.
Typically, from a stationary Britsh WW2 shell initial fragment velocity was 3000+ ft /sec, although in
some directions they may be substantially less, this is considerably less than the
explosive's velocity of detonation. The proportion of fragments going forwards and backwards can
vary substantially between shell designs, although those going forwards are often very small size;
the base of the shell is usually much thicker that the side walls and often breaks into just a few
large fragments that tend to go back along the trajectory. However, a moving shell has two effects
on fragments, first the terminal velocity, (for 25-pdr varying between 600 and 1000 ft/sec) imparts
forward movement on the fragments. Second, the surface of the spinning shell imparts its
tangental velocity, (for 25-pdr varying between 90 and 230 ft/sec). Fragments fly in straight-lines
out from the shell burst but being un-aerodynamic in shape air resistance quickly retards
them, despite their high velocity. Gravity also pulls them down but by the time this is noticeable
they have lost most of their kinetic energy. Fragments going generally upwards fall to earth with
little kinetic energy left.
Figure 1 - Ground and Air Burst Fragmentation Patterns from the Point of Burst at Different
Angles of Descent
https://nigelef.tripod.com/wt_of_fire.htm 4/11
08.11.22, 12:12 Effects and Weight of Fire
The Effects of Terrain
The effects of terrain are many and varied and can markedly reduce the direct effects of bursting
shells. An impact fuzed shell will send its forward moving fragments into the ground. In soft
ground a shell will penetrate slightly deeper than in hard ground, this means that the crater will
absorb more of the laterally projected fragments. Of course the efficiency of the fuze's
instantaneous mechanism is a factor; inefficient impact fuzes penetrate deeper giving fewer useful
fragments (this was a significant problem in the early part of World War 1 when 'graze' fuzes were
used). Of course penetration of the ground may be required for destructive effects. Graze fuzes,
direct action fuzes with a delay mechanism or direct action fuzes fired with 'cap on' could be used
for this, and graze and 'cap on' was also used against targets behind light cover.
However, very few targets are on football fields. 'Normal' open ground is 'rough', it has natural
folds, small dips and hollows, furrows, ditches, bunds, etc. These all provide troops with protection
from ground bursting weapons, not to mention direct fire projectiles. 'Natural' or 'average’ ground
offers about 5 times as much protection to a prone soldier as an 'unnatural' level surface like a
football field. Then there are the more obvious results of human activity such as buildings and
walls, and military activity, notably trenches. However, air-burst shells direct their fragments into
and behind this natural or artificial protection.
Buildings are a further complication, and their protective properties depend on the amount of
artillery fire directed at them and the material used to build them. The blast effect of shells will
damage buildings, particularly if there are direct hits, and if there are enough hits the building will
be reduced to rubble. However, most masonry or concrete buildings will stop fragments. The flash
of detonation can ignite flammable materials in buildings.
Then there is vegetation. Fragments and blast will strip away foliage and eventually reduce large
trees to shattered trunks. The branches and trunks will absorb many splinters, one test for the 58
ft-lbs criterion was that a fragment penetrated about 1 inch into wood. In heavy bombardments the
blast will move the loose and shattered vegetation on the forest floor to the edge of the impact area
or pile it up against obstacles such as large branches 'cut' from the trees. However, before the
trees are well stripped by shell fire the shells burst in the branches and are effective air-bursts.
Flying debris can be a hazard, particularly rubble in built up areas when large shells are used. In
either soft or hard ground artillery shells do not cause a noticeable hazard from flying spoil and
forest debris usually offers little danger except at close range to the burst.
British research also investigated using artillery fire to cut wire entanglements and clear mines,
wire cutting had been a vital artillery task in WW1 before tanks arrived and trials were conducted in
that war. This work showed that there were some useful effects, blast being quite effective against
some types of Teller mine and shell fragments easily cut wire. However, they were not reliable or
efficient methods due to the natural dispersion of the shells.
The Effects of Target Posture
It's also useful to note how vulnerability changes with target posture because it suggests the
relative amounts of fire needed in different circumstances. The following estimates the relative
risks of becoming a casualty to ground-burst shells on ‘average’ ground:-
Standing 1
Lying 1/
3
Firing from open fire trenches 1/ – 1/
15 50
Crouching in open fire trenches 1/ – 1/
25 100
BATTLEFIELD EFFECTS
The direct effects of an HE shell are one way of looking at the effects of artillery fire. However,
they have to be related to the battlefield.
https://nigelef.tripod.com/wt_of_fire.htm 5/11
08.11.22, 12:12 Effects and Weight of Fire
British operational research scientists in WW2 defined artillery effects on the battlefield stating
them “in order of their ease of achievement”, although they are all happening in some degree
simultaneously. They were:-
To prevent enemy movement and observation, and in cases of greater effect to prevent
“Neutralising”
the effective use of enemy weapons. Effect to last during the bombardment.
To produce, in addition to neutralisation, a lack of will to resist continuing for some time
“Morale”
after the end of the bombardment.
“Lethal” To kill or wound enemy personnel.
“Material” To destroy or damage enemy equipment.
The last two, sometimes called “physical effects,” are much easier to analyse and in the final year
of the war most of the research focused on the first two (“psychological effects”) through operations
analysis. The definition of demoralisation is particularly important; it is specific and is different from
a more general deterioration in morale. There was no information about recovery rates or how
long the effect lasted. There were additional caveats to demoralisation including that fire must be
continuous over the period and that the target troops must not be fully protected against the
bombardment by being in deep or concrete bunkers, etc. Note to that “a lack of will to resist
continuing for some time after the end of the bombardment” is different from the time taken for
neutralised troops to decide that fire has ended and move to their fighting positions.
Of course there are also tertiary effects, notably disruption and delay caused by taking evasive or
protective action, evacuating casualties and repairing damage, and so on. And casualties will
usually reduce, even if only temporarily, the efficiency and effectiveness of the unit suffering them,
and may reduce capability if casualties or damaged equipment are not promptly replaced. Note
that here 'capability' is basically numeric strength in men and equipment and the target of attrition,
efficiency is 'doing the thing right' and effectiveness is 'doing the right thing'. Capability,
effectiveness and efficiency all merge into combat power which reflects the human element and
cohesion (morale, motivation and training), materiel (weapons and equipment) and the intellectual
element (doctrine, concepts, tactics, techniques and procedures).
Quantitative Effects
British researchers put much effort into investigating and quantifying the effects of artillery fire. The
early focus was on physical effects. Later work focused on the much more psychological ones, a
much more challenging problem that was never entirely resolved.
Early work established splinter patterns and their relationship with the angle of descent and the all-
important AoEs for different types of target. Figure 2 shows an example of AoE contours.
Figure 2 – 25-pdr HE ground-burst, angle of descent 20º - Percentage Casualties to men
standing in the open around the point of burst of the shell.
However, as Figure 1 shows, the shape of the fragment pattern depends on the shell's angle of
descent, while the size of the AoE depends on the type of target and the lethality of the shell.
Nevertheless, data for shells, mortar bombs and aircraft bombs against various targets was
https://nigelef.tripod.com/wt_of_fire.htm 6/11
08.11.22, 12:12 Effects and Weight of Fire
provided and explained in Army Operational Research Group Report No 179 'Lethal and Material
Effects of Gunfire and Bombing on Land Targets - A Record of the Present State of Knowledge' 20
March 1944. It was updated in Report No 234, although the changes mainly concerned aircraft
bombs, including relative areas for the blast effects of aircraft bombs. It also considered the
effectiveness of white phosphorus munitions, best summarised as 'not very'.
Next they produced estimated weights of fire to achieve these effects. These are in terms of 25-
pdr equivalence and shown in the next table.
Table 3 – Intensity and Density
(1 yd = 0.9144 m, 1 lb = 0.453 kg)
Effect 25-pdr Equivalent Effects
0.02 - 0.08 lb/sq yd/hr,
"Neutralising"
enemy in open positions
0.1 lb/sq yd/hr for 4 hrs, or
"Morale"
0.25 lb/sq yd/min for 15 mins (*note)
0.1 lb/sq yd gives
"Lethal" 2% casualties to troops in weapon pits,
20% casualties to troops in open
0.1 lb/sq yd
"Material" gives 1.5% damage to infantry weapons in weapon pits & guns in gun pits,
20% damage to soft skinned vehicles
*Note - The morale and neutralisation data need to be treated with caution; the evidence for
achieving the defined demoralisation in 15 minutes was based on a single operation, at Wesel,
during the Rhine crossings. Before this it was thought that at least 4 hours were needed. There is
also doubt about 25-pdr effect equivalence for neutralisation because there were indications that
neutralisation correlated with the number of rounds fired rather than their lethality.
Equivalence Between Calibres
During World War 2 there were far more calibres than now so one need was relating the effects of
one calibre of shell to another. Using a standard target of 'men crouching in (British standard) slit
trenches', a reasonable approximation of relative effect was the square root of the weight of
explosive filling. Of course this ignores the different power of different explosives and this type of
target is one that is little affected by fragments. However, it is a representative target for an army
on the offensive. It also has logic, a splinter of a given size goes much the same distance no
matter what size shell it came from unless there are very significant differences in the HE
detonation velocity. However, at any given distance from the burst there will be a greater density of
fragments from a larger shell but this density decreases geometrically with distance.
Table 4 – World War 2 25-pdr Equivalence
25-pdr equals 1
Weight 25-pdr Weight 25-pdr Effect
Calibre Shell Origin
(kg) Equivalence Equivalence
76.2-mm 6.2 HE OF-350 SU 0.6 0.9
84-mm 8.2 18-pdr HE UK 0.8 0.7
87.6-mm 11.3 25-pdr HE UK 1.0 1.0
94-mm 8.8 3.7-inch How HE UK 0.8 1.0
105-mm 14.8 10.5-cm HE Gr38 GE 1.3 1.3
105-mm 15.0 HE M1 US 1.3 1.7
114-mm 24.9 4.5-inch Gun HE UK 2.2 1.5
122-mm 21.8 HE-FRAG OF-462 SU 1.9 2.2
122-mm 25.0 HE-FRAG OF-471 SU 2.2 2.2
140-mm 37.2 5.5-inch 80lb HE UK 3.3 2.6
140-mm 45.6 5.5-inch 100lb HE UK 4.0 2.4
150-mm 43.0 15-cm HE Gr42 GE 3.8 2.8
152-mm 43.5 HE-FRAG OF-530 SU 2.8 3.5
https://nigelef.tripod.com/wt_of_fire.htm 7/11
08.11.22, 12:12 Effects and Weight of Fire
152-mm 40.0 HE-FRAG OF-540 SU 2.8 3.8
155-mm 43.1 HE M107 US US 3.8 2.9
183-mm 91.2 7.2-inch How HE UK 8.0 4.0
203-mm 90.7 HE M106 US 8.0 4.6
203-mm 109.1 HE M103 US 9.6 3.5
240-mm 163.3 HE US 13.8 5.3
A notable point is that smaller shells are proportionally more effective than larger ones. However,
the ratios aren't generally supported by the number of fragments derived from their distribution in
Table 1. Of course larger shells can be fired further, their greater explosive content makes them
more effective against more solid targets, if they hit them, and their blast effects are greater.
What it Means on the Ground
Putting Tables 3 and 4 together reveals how many shells of different calibres are needed to
achieve the different effects per 10,000 yds², ie 100 × 100 yds.
Table 5 - Density and Intensity per 100 × 100 yds
(8631 sq m)
Effect 25-pdr 5.5-in
“Neutralising”
8 - 32 rds/hr 3 - 12 rds/hr
enemy in open positions
40 rds/hr for 4 hrs, or 16 rds/hr for 4 hrs, or
“Morale”
100 rds/min for 15 mins 39 rds/min for 15 mins
“Lethal”
2% casualties to troops in weapon pits, 40 rds 16 rds
20% casualties to troops in open
“Material”
1.5% damage to infantry weapons in
40 rds 16 rds
weapon pits & guns in gun pits, 20%
damage to soft-skinned vehicles
An often asked question is about the effect of indirect artillery fire on tanks. One example helps, in
1944 the German IX Corps in Italy reported that artillery fire was the largest single cause of its
tanks losses, it seems that this was usually from medium and heavy guns controlled by air OPs.
The second largest source was German destruction of damaged or broken-down tanks to prevent
their capture (mechanical reliability was not a feature of German tanks - but perhaps some of this
was due to the Special Operations Executive's campaign of insaisissable sabotage). Other tanks,
anti-tank, air attack and mines were well below the first two as the causes of tank losses.
CALCULATING WEIGHT OF FIRE AND FINDING THE RESULTS OF FIRE
Calculating density (rounds per 100 yd square) or intensity (rounds per 100 yd square per minute),
involves two main steps:
Finding the number of rounds to achieve the effect.
Finding how many rounds to fire so that the necessary number hit the target.
Alternatively the same approach can be used to work out what results would have been for a given
amount of fire. The first step being to find how many shells probably hit the target and then what
their result was.
Additional considerations include duration of intensity, the distribution of aim-points and the number
of guns required. The calculations are not absolute, like all gunnery they depend on statistics and
probability theory. However, before doing any calculations the data, AoE, has to be available for
the expected target types and their postures. Further data is also required as will be seen below.
Area of Effect
https://nigelef.tripod.com/wt_of_fire.htm 8/11
08.11.22, 12:12 Effects and Weight of Fire
Figure 1, above, showed how AoE varies with the angle of descent and how a low angle pattern
with its conspicuous ‘butterfly’ wings becomes more rounded as the angle steepens.
The AoE becomes more circular as the angle of descent increases and the number of
effective fragments increases because fewer are going into the ground or upwards before
falling ineffectually.
Next, the AoE reflects a probability of effect in the area, not that any target element in the
area will suffer the effect and that none outside it will.
Finally, the AoE definition may assume that a target in the open is on flat ground without any
undulations, etc, providing cover against ground burst shells.
Unless direct hits are sought, HE air-burst is more effective than ground-burst for two reasons: for
a given angle of descent there are more useful splinters, particularly at lower angles, and because
the splinters strike downwards, instead of horizontally, they reach into holes and hollows. Clearly,
the extent of increased effectiveness will depend on the target. Post World War 2 trials found that
against dug-in targets proximity (VT) fuzed shells varied from about 1.2 to 2.5 times as effective as
ground-burst. However, some data from the war indicated that air-burst could be as much as 10
times as effective as ground-burst.
One important aspect of air-burst is the height of burst (HOB), 30 feet was considered about
optimal against troops in trenches and if the bursts are too high then the effectiveness of the
splinters is significantly reduced. Getting this HOB by predicting the fuze length of 'time' fuzes,
whether clockwork or powder burning, was virtually impossible so HOB had to be ranged. Even
with ranging the fuze to fuze variations and consequential spead of burst heights meant that there
would be groundbursts. The benefit of VT was its correct and consistent HOB without ranging it.
Of course against troops in the open ' daisy-cutters' are best but there was no prospect of
achieving this with WW2 fuzes.
How many shells must hit the target to get the results?
The first step in weight of fire planning is calculating the number of shells to achieve the required
effect on the target. For example:
A target has 10 elements in an area 150 yds × 150 yds (22,500 yds2), the aim is to inflict a
particular level of damage on any 4 of them (40%) and the AoE for this damage is 10 yds
radius (314 yds2).
Then N = P/100 × S/A, where N is the number of shells to be fired, P is the required
percentage of damaged target elements, S is the target’s area and A is the AoE. Here N =
29 (density 13 rounds per 100 yd square).
However, this simple model assumes that no target element will be hit effectively more than once.
This is statistically reasonable up to about 10% casualties, higher than this more shells need to be
fired to compensate for ‘overhitting’, if 100% casualties are sought then the calculations must be
for about 400%. In the above example N should be 36 for 40% casualties. A second assumption
is that fire will be evenly distributed across the target, and in reality this was almost never the case
in World War 2. British practice was for a troop's guns to fire parallel and approximately in a
straight line at right angles to their line of fire, of course the range probable error (PER) distributed
the shells along each gun's line of fire but their 'average' impact was in a straightish line
(depending on the accuracy of their relative calibration and assuming they were all firing with
propellant from the same lot). The overall spread improved when several widely separated
regiments attacked a target. See the 'Errors and Mistakes' page for more information about
spread.
For example, modern thinking suggests that 30% casualties results in a target being militarily
'destroyed'. The fine print of definitions and whether or not this is true are not considered further!
However, using the figures in Table 5, and the target of 'casualties to troops in weapon pits',
suggest that for each 100 yds × 100 yds then 40 × 15 = 600 25-pdr shells were required.
Compensating this for overhitting raises the number to 690.
https://nigelef.tripod.com/wt_of_fire.htm 9/11
08.11.22, 12:12 Effects and Weight of Fire
When this is compared to the 8 - 32 shells per hour for neutralisation, then the implications of
neutralisation versus destruction becomes clear, even without making allowance for shells that
miss the target or are ineffective (see below). Conversion factors in Table 4 can be used to convert
to other types of shell.
AoE Shape
Another necessary adjustment is for the shape of the AoE. This varies with angle of descent,
which in turn varies with range and propelling charge size. The problem of AoE shape is one of
the keys to accurately estimating the extent of the effect on the target, and this was barely touched
in the World War 2 work.
How many shells must be fired?
The second calculation step is to increase the theoretical number of shells to compensate for some
of them missing the target or being ineffective. There are several causes of this. The first three
concern 'accuracy' in a general sense.
Target Location Error – there is always some inaccuracy, although it's small for targets that have
been effectively ranged (adjusted).
Accuracy of Fire – there are many possible causes of predicted fire inaccuracy - the distance
between where the shells were aimed and their mean point of impact. However, their magnitude at
the target is closely related to range. The work of the ORS identified lack of accuracy (errors) in
predicted fire as a major problem, with incorrect muzzle velocities being particularly significant.
Dispersion – the PEs in range and line, their size varies with range and charge. Round to round
variations in MV are the primary source of the first but there are various others including laying
accuracy. However, the importance of range dispersion depends on the size of the target and the
relationship between the line of fire and the target axis. Against larger target areas whose long
axis is parallel to the line of fire dispersion may be a good thing, particularly at shorter ranges.
Slope – depending on the relationship between the direction of the slope of the ground and the line
of fire, shells may fall outside the target area or not fully cover it. 1 ORS in Italy seem to have been
the only group to incorporate this, no doubt because of its importance in the Italian terrain.
Angle of Descent - the shape of the AoE varies with the angle of descent and is relative to the line
of fire. So the line of fire and the shape of the effect may have more or less effect depending on
the layout of the target, the relationship between the line of fire and the target's axis and the
amount of dispersion. Of course the angle of descent assumes horizontal ground, sloping ground
with alter the effective angle of descent for fragmentation distribution purposes.
Blinds – there will always be some shells that don't explode.
Protective Qualities of Terrain - this is complicated and does not seem to have been included in
WW2 calculation. It also depends on the type of target.
The approach to the first three is to enlarge the target area to hold the PEs, typically combining
them using root mean squares. For adjusted fire the first two become a small PE depending on
the adjustment precision. Slope corrections make the target area asymmetric in relation to its
‘centre’. Blinds are a percentage matter.
Finally, considerations of accuracy and particularly dispersion, together with AoE shape come
together with the relationship between the long axis of the target and the line of fire. If the line of
fire is across the axis of a long narrow targets far more rounds will be wasted than if the line of fire
is along the target's axis. This is because most dispersion is along the line of fire.
It will immediately be apparent that predicting compensation for accuracy, dispersion, AoE shape
and slope again depends on where the guns are, and poses a real ‘chicken and egg’ problem if
https://nigelef.tripod.com/wt_of_fire.htm 10/11
08.11.22, 12:12 Effects and Weight of Fire
there is a choice of firing units.
Accuracy and dispersion, including dispersion compensating for inaccuracy, are reviewed in more
detail in the "Errors and Mistakes" page.
How good are the calculations?
A key question is the goodness of the models. British researchers summarised by an example
giving the expected number of casualties as 9%. They then said that it might be as low a 5% or as
high as 15% but not as low as 2 or 3% or as high as 30 or 40%. However, it could be argued that
there is not, even today, a good model capable of handling all the variables and being used to
either estimate the number of rounds required to produce the desired effects or reversible to
estimate the effects for a given number of rounds.
Data quality is also an issue. Physical effects are relatively easy to model and validate, although
the latter may be expensive and apparently similar targets can vary widely in terms of their
vulnerability. Psychological effects are a different matter, realistic experiments and trials are out of
the question on ethical grounds (at least in Western countries, although there are some tantalising
hints that the Soviets may have experimented). Therefore only war provides the data, but is not a
good environment for well managed trials and experiments!
AFTER WORLD WAR 2
The need for more lethal HE shells was an important lesson from WW2. UK fully developed two
new shell designs during the early and late 1960's using higher strength steels. 105-mm Field (for
Abbot) was about 1 kg heavier than the US 105-mm HE (1935 pattern) and was a slight
improvement by having almost 16% HE. 155-mm for FH70 was a large improvement over HE
M107, 26% instead of 15.8%. Of course improvements in fragmentation were also achieved by
changing HE fillings from predominantly TNT to RDX. The 21st century change to plastic bonded
explosives (with a RDX base) is again increasing the explosive power and improving
fragmentation. Some late 20th Century multi-role fuzes, including those adopted by UK, offer
height of burst options in their proximity (VT) function, this makes it possible match the height of
burst setting to the ground so as to achieve the low air-burst or 'daisy-cutter', at 2 or 3
metres, which is best against some types of target.
The training pamphlets covering the application of fire published in the late 1940's and early 1950's
included very simple guidance. The 1948 'Organisation, Command and Employment' pamphlet
provided simplified data on bombardment intensity derived from the WW2 research. However, the
1952 'Engagement of Targets by Observed Fire' espoused the notion of 'immediate neutralization'
achieved by 5% casualties and gave the numbers of rounds required to fall in a 100 yard square to
achieve it. Later training pamphlets ignored the subject apart from stating that the amount of fire
was a matter of experience and judgement. The source of this experience, for a peacetime army
preparing for a war that was expected to last only days, was conveniently ignored.
The matter lapsed until the 1980's when a requirement for weight of fire calculations was included
in the Staff Requirement for BATES (Battlefield Artillery Target Engagement System). This system
adopted the US Superquickie II model for casualties and destructive effects, while neutralisation
intensities were founded on UK WW2 data. The model was simple and originally designed to be
run on an HP-41C programmable handheld calculator. It was a reversible model (casualty % in
& number of shells out or number of shells in & casualty % out), but ignored slope, the protective
properties of the terrain and did not provide a variable shaping factor to represent the angle of
descent, although it did include a 'factor k' (k = kludge). The UK operational researchers had
developed a model for casualty and destructive effects that accurately reflected the angle of
descent. However, it was not reversible and only gave casualty % for the number of rounds fired,
which was not what was needed in the field. It's interesting to note that the Bundeswehr adopted
Superquickie II for neutralisation by calculating 10% casualties and dividing by 60 to give rounds
per minute intensity.
https://nigelef.tripod.com/wt_of_fire.htm 11/11
