Part Two: Criteria for the evaluation of a “600 m” round
Terminal ballistic considerations
“Sufficient” terminal effectiveness is very easy to achieve with rifle bullets, regardless of calibre, and
even a tiny 4.6 mm solid brass (non-fragmenting) bullet impacting at more than 600 m/s could produce
a severe wound (better than a 5.56 mm M193 fragmenting bullet), as shown in Figure 44.
Figure 44: High speed film of 4.6 x 36 mm type 614 solid brass bullet impacting a 20% ballistic gelatine
bloc (15 x 17 x 38 cm), impact from the left side of the bloc. Left picture, bullet yawing inside the bloc;
Right picture, maximum temporary cavity size.
At the beginning of the 20th century, it was demonstrated that a 3 g steel sphere impacting a human
target at 240 m/s (86 J) could easily penetrate and break even the biggest bones of the human body
and inflict lethal wounds xxxvi so a “minimum” level of effectiveness is very easy to achieve but trying to
define a level of “sufficient” terminal effectiveness is like opening the proverbial Pandora box.
Medical (anatomopathology) studies (i.e., examination of bullet path and tissue damage) involving
shooting living animal (dogs or goats) revealed only minor differences between bullets of various
calibres and impact energy, to the extent that “from wound examination alone, it was never possible to
distinguish the calibre of rifle or machinegun bullets nor the size of explosive shells. It was frequently
impossible to judge with any accuracy whether the wound had been produced by a bullet or grenade
shell or bomb fragment” xxxvii.
Leaving the medical field to instrumented studies (tissues simulant) leads us to two different
approaches (if we leave aside shooting at vessels filled with water). The oldest one is to follow the
bullet during impact (energy deposition and temporary cavity) while the other is to look at the final
state of the gelatine bloc (permanent cavity and “cracks” due to non-elastic deformation).
Kinetic energy (“force vive”) was probably the first criterion used to “scientifically” (or at least
“mathematically”) evaluate bullet terminal effectiveness. The relationship between kinetic energy loss
and hydraulic pressure in closed vessels filled with water was established at the beginning of the 20th
century, and later the same relationship was established between kinetic energy loss and temporary
cavities in ballistic gelatine (Figure 45).
Figure 45: Relation between kinetic energy loss in the first 15 cm of uncalibrated ballistic gelatine and
maximum temporary cavity.
Unfortunately, most studies performed before the ‘90s measured energy deposit only in the first 15 cm
of bullet travel in non-calibrated ballistic gelatine (models were developed and validated for high-
velocity fragments then “extended” to bullets), and the validity of those studies, results and models
derived from them, could be questioned xxxviii.
The KE deposit model used during the ‘60s and ‘70s was later superseded by the EKE model that
uses energy deposit in the first 38 cm of bullet path, combined with a probability law (the probability of
a bullet to be inside the target body after “x” cm of bullet travel, see Figure 46) xxxix. While this model
addresses some issues found in the previous KE model, others (like energy “consumed” by bullet
deformation or fragmentation and not transferred to the ballistic medium, or the very shallow
penetration considered against unprotected ballistic bloc) are still unsolved.
For example, a 5.56 mm or 7.62 mm bullet aimed toward the spinal cord and impacting a standing
human at right angle need to penetrate an equivalent of 40 cm to 60 cm of NATO ballistic gelatine to
reach the spinal cord 90% of the time xl. This result could be compared with the distribution probability
used in the EKE model that nearly do not take into account kinetic energy deposit after 25 cm of
penetration into said NATO ballistic gelatine (see Figure 46).
Figure 46: Probability to cause immediate incapacitation as a function of the Distance of Penetration
(DOP) in NATO ballistic gelatine xl, and distribution probability used in the EKE model.
Finally, it should be noted that the mathematic equation selected for describing missile effectiveness is
sensitive to energy deposit only in a very narrow range of energy (between 0 and 200 J, see Figure 47
for the “Defence” and “Assault <30 s” criteria).
Figure 47: Relationship between EKE and P(i/h) for the “Defence” and “Assault <30 s” cases.
This range is useful for discriminating high velocity fragments and FMJ handgun bullets, but it’s much
more difficult to discriminate between rifle bullets.
According to the “defence” criteria, a bullet delivering an EKE of 500 J (handgun power level) will have
a p(I/H) of ~45%), compared to ~50% for a bullet delivering 3000 J (full-power rifle, six times as much).
Most hunters will probably disbelieve that the difference of terminal effectiveness between a full-power
rifle round and a handgun round (both using expanding bullets) is 50% compared to 45%, but this very
small difference in effectiveness could be easily explained if one considers that this model 1)- is based
on random impact (so impacts to extremities play a major role compared to impacts to the torso or
abdomen), and 2)- while using “kinetic energy” as a driver it is in fact a “medical” model based on
several (first 10, then 16 later) “functional loss” or “disability” classes xli, xlii (see Figure 48).
Figure 48: Extract of the sixteen functional groups and disability classes, based on hits to extremities xlii.
For example, in the above table a soldier “losing” one leg (N,T) or two legs (T,T), but with no wounds
to the arms (N,N), torso or head is classified as a “group IV” (losing one leg) or “group V” (losing two
legs) disability class, and in the “defence” scenario an incapacitation rating of 50% is applied. Said
differently, if you shoot in the legs 100 soldiers with .50 BMG bullets, the model predicts that 50
soldiers will still be able (and willing) to return fire.
With the same wound and disability class (group V), but in the “assault” scenario, an incapacitation
rating of 100% is applied because the soldier can’t move anymore, so ironically the “Expected Kinetic
Energy” model is a strong function of the shooting scenario and respective human body areas, but
finally a weak function of the kinetic energy.
With a methodology that does not set a lower practical limit to bullet diameter and weight, it’s not
difficult to understand why the current 5.56 mm was considered only an interim cartridge pending the
development of high velocity “micro-calibres” (lower than 5 mm) and saboted flechettes during the ‘70s
that promised significant ammunition weight reduction without a decrease of terminal performance.
Setting an energy level sufficient to inflict a lethal wound is debatable but a value of 82 J is commonly
found in the literature and according to Figure 47, this value is well above the level needed to inflict a
wound that will significantly reduce soldier’s effectiveness. This value will be used in the following part.
The work of M.L. Fackler xlii i led to the use of calibrated ballistic gelatine of a different composition and
temperature (10% gelatine at 4°C compared to 20% gelatine at 10°C) and the examination of the
bullet track and real damage done to the gelatine block. Contrary to models based on kinetic energy,
this approach explains why hunting arrows (or a blow from a slashing weapon of sufficient size, as
informally demonstrated by the infamous “Cold Steel” video channel) could kill, with less than 90 J, as
efficiently as a soft-point hunting bullet delivering more than 3000 J.
While sound, the main limitation of this model that relies on tissue simulant quality and size (the
measured temporary cavity changes with the size of the gelatine bloc) is that nearly all the previous
work done back from the ‘60s needs to be done again.
In addition to those considerations related to defeating non-protected soldiers, one could expect that
opposing force will be equipped with some kind of ballistic protection.
The protection generally considered on the battlefield is the 3.5 mm NATO steel plate. The impact
energy needed to perforate such plate is a function of the bullet diameter (to the power 3/2).
= !. "
For common “soft” core bullets (lead, brass, common steel), a value of 41.6 could be used for the
parameter k and the table below summarize the energy requirement at 600 m.
Bore & bullet diameter
“soft core” bullet
Energy needed to defeat
the 3.5 mm plate
Energy needed to
produce a lethal wound
required at 600 m
5.56 mm (.224”)
6 mm (.243”)
6.35 mm (.257”)
6.5 mm (.264”)
6.8 mm (.277”)
7 mm (.284”)
7.62 mm (.308”)
In order to increase the efficiency of existing cartridges against personal protections, more efficient
bullets than FMJ were designed and for those bullets using an “arrow like” heat treated steel insert a
value of only 14 could be used for the parameter k (hence reducing significantly the energy needed to
defeat the steel plate), but since they lose around 50% of their weight during plate perforation (jacket
stripping) the required energy to produce a lethal wound should be increased to 164 J instead of 82 J
(so the fragment representing half the bullet weight will still have 82 J after plate perforation).
The reduction of the energy needed to defeat the steel plate and produce significant wound greatly
opens the “solution space” towards the smaller bores.
Bore & bullet diameter
“semi AP” bullet
Energy needed to defeat
the 3.5 mm plate
Energy needed to
produce a lethal wound
required at 600 m
5.56 mm (.224”)
6 mm (.243”)
6.35 mm (.257”)
6.5 mm (.264”)
This requirement is sufficient to guarantee that a bullet that will defeat a protected soldier at 600 m will
also defeat an unprotected soldier at 800 m.
While better protections (NIJ level III & IV) are available today, this point should not be overstressed
because those protections are designed to cover mainly the torso (representing only ~16% of the
wounds) and that if they are tailored to stop full-power rifle lead-core FMJ and (most) steel-core AP
bullets respectively, they are defeated by APHC bullets with tungsten carbide inserts at a distance
higher than a hundred meters.
The specific weight needed to achieve multi shot level III ballistic protection is between 40 kg/m²
(composite plate) and 50 kg/m² (AR500 steel plate).
Composite plates with the same specific weight could also achieve a level IV ballistic protection but
against only one hit, and in order to resist multiple hits, an AR500 steel plate would need a (quite
impractical) specific weight in the vicinity of 80 kg/m².
At the higher end of the threat spectra, the first generation of NAMMO 5.56 mm and 7.62 mm APHC
rounds could repeatedly defeat 12 mm (specific weight of 95 kg/m²) and 15 mm of RHA (specific
weight of 120 kg/m²), respectively, at a distance of 100 m, so even with the constant progress of
ceramic materials a practical “all around” protection against such threat is highly unlikely in near term
So, if heavy ballistic vests are very useful to reduce the ratio of soldiers killed versus the number of
soldiers wounded, they would probably have a very limited impact on the number of casualties caused
by small-arms fire.
The time of flight to the target should be as short as possible and wind drift should be minimised. The
bullet drop (vertical plane) and wind drift (horizontal plane) in average wind conditions (~5 m/s) are
combined in a single number called “Combined Distance from Centre” (CDFC). This way, “flat-
shooting” bullets (generally light weight, high drag, launched at high muzzle velocity) could be easily
compared with “wind buckling” bullets (generally heavy weight, low drag, launched at a lower muzzle
The vertical drop (Z) equals to "
#.$.(%&')² (with g the gravitational constant, and ToF the time of flight
to the target), and the Didion formula for wind drift (Y) is *.(%&' + ,
-/), with W the wind speed and ,
the time of flight in vacuum conditions.
Since g equals 9.81 m/s², then g/2 (4.905) is very close to the average wind velocity measured in
France (4.5 m/s) or the “10 mph” used by US shooters, and so, for comparison purpose, the CDFC
could be practically reduced to 01%&'23 (%&' + ,
Contrary to the previous requirement (impact energy), not exceeding the CDFC of the current
7.62 x 51 mm M80 bullet at 600 m and 800 m can’t be easily reduced to a single distance requirement,
Combined Distance from Centre
Point of aim
Point of impact
but with few exceptions (high BC bullets launched at low muzzle velocity), a round that matches the
M80 CDFC at 800 m also matches the M80 CDFC at 600 m.
Suppression, or the “Crack & Splash” effectiveness
The importance of suppression effects for small-arms fire was pointed out in the first part of this article,
but without quantification or evaluation.
Since the “1 m” criterion does not account for specific bullet characteristics, using acoustic (bullet
relative “loudness”) and visual (impacts) criteria is a way to improve suppression evaluation.
Limited results are available in the literature, but some could be found in xliv and xlv.
In the first report, the acoustic and visual signature of several rounds are compared, including the
XM645 “flechette” round fired from the XM19, the 5.56 mm M193 fired from the M16, the 7.62 x 39 mm
fired from the AK, the 7.62 x 51 mm fired from the M60, the .45 ACP fired from the M1A1 SMG and the
.50 BMG fired from the M2 HMG.
Those results will serve to identify physical parameters that could be used to build a relative scale for
suppression, accounting for both acoustic and visual stimuli.
Results from the second report will be used to correlate this relative scale to real life “threatening”
This scale will be used in the third part (theoretical study), along bullet time of flight (trajectory
parameters), retained energy, heat flux and impulse, to try to narrow the “solution space” for optimal
Acoustic index, the “Crack” part
Live fire test performed at a distance of 150 m revealed that:
- the mean dangerousness of both the XM19 and the M1A1 SMG were rated significantly lower
than other weapons, the XM19 being rated significantly lower than the M1A1,
- subjects failed to discriminate the AK from the M60, and the AK from the M16 (“From Table 5-
14 it can be seen that only the comparisons of the AK47 with the M60 (+0.16) and the AK47
with the M16 (+0.23) fail to reach the ICI of 0.38 necessary for the demonstration of a
significant difference in the mean perceived dangerousness for the two weapons”), but the
difference between the M16 and the M60 could be considered significant (a ICI of 0.39 was
achieved between those two weapons).
- the .50 BMG scored the highest mean dangerousness value, but the result was not found “off
scale” compared to other weapons,
- mean dangerousness decreased linearly with the miss distance (minimum miss distance
considered was 2 m).
A relationship between kinetic energy and perceived mean dangerousness was established, but the
remaining velocities at 150 m for the various rounds quoted are in some cases suspiciously low (2200
fps for both the M16 and the M60).
More recently xlvi, investigations were made to properly measure bullet noise between Mach 0.5 and
Peak pressure for 4 bullets diameter (.224”; .308”; .338” and .510”) sharing the same shape (the exact
G7 shape) was measured at a distance of 61 cm from the bullet path (Figure 49).
Figure 49: measured peak pressure of bullets following the G7 shape, fired at different velocities.
The peak value reached in the supersonic domain corresponds to a sound value between 155 dB and
163 dB, which is similar to the noise range of some stun grenades.
As could be seen in Figure 49, for a given bullet diameter the measured pressure level is pretty
constant in the whole supersonic domain and a .50” calibre G7 bullet traveling around ~400 m/s (the
remaining velocity of the M33 ball at ~1200 m) will still produce a higher overpressure (0.288 psi or
160 dB) than a .338” G7 bullet (0.257 psi or 159 dB) traveling at 900 m/s (the typical MV of the 338
The same is true with the 7.62 mm and the 5.56 mm G7 bullets, the first one producing more
overpressure at Mach 1.16 (0.190 psi or 156 dB at a distance around ~700 m for the M80 bullet) than
the 5.56 mm at Mach 2.95 (0.173 psi or 155 dB at typical MV of the M193 bullet).
The mathematical expression based on global bullet drag ( !("#.($. %)&+ 1)) proposed in a previous
version of this paper was reviewed in the light of those results and was found insufficient, with too
much sensitivity to bullet diameter and Mach number.
The mathematical model proposed in xlvi for predicting the relationship between bullet characteristics
and overpressure ( ) is restricted to bullet supersonic domain
because the peak pressure is found to be proportional to ('&* 1)(, -
/ ) and the bullet form factor K
used in this formula (not to be confused with the i7 form factor generally used in this paper), instead of
being constant (as presumed from results obtained with artillery projectiles), was found to be a
function of both the Mach number and the bullet diameter.
To avoid those limitations, a simplified and empirical model was developed (the Acoustic Index E2)
which is pretty effective at predicting the measured overpressure of a passing bullet (Figure 50) in the
supersonic domain, but also in the subsonic domain (with less accuracy, particularly in the transonic
Figure 50: correlation between measured passing bullet overpressure and proposed mathematical model
(acoustic index E2).
As a sidenote, in the above formula the distance is elevated to the power (-3/4), so the reduction of the
bullet overpressure as a function of the distance is not proportional. If at a given distance a bullet “A” is
producing 40% more overpressure than bullet “B”, then bullet “A” will produce the same overpressure
as bullet “B” at a distance 56% greater, and an increase of the threatened area by 145%.
With those findings, the proposed mathematical expression for the evaluation of perceived acoustic
ACOUSTIC INDEX E2
'. $. ("#)0 2
With M, the local bullet Mach number (dimensionless), d, the bullet diameter (in mm), i7 the bullet form
factor (dimensionless, G7 table) and CD, the drag coefficient (dimensionless, G7 table) relative to the
Results for some projectiles tested.
(at 150 m)
Relative Acoustic Index
(at 150 m)
Relative Acoustic Index
.223 Remington M193
7.62 x 39 mm
7.62 x 51 mm
Even if the new model is significantly different from the previous one, the overall trend is very similar
but with a slightly better sensitivity. For example, during previously mentioned live fire tests, the
acoustic signature of the 7.62 x 39 mm M43 and the 7.62 x 51 mm M80 were found very similar, which
is supported by the E2 model (0.98 for the M43 versus 1.00 for the M80, compared with 0.89 versus
1.00 with the E1 model). During those same tests, the difference between the 223 Remington M193
and the 7.62 x 39 mm was found significant, a reality also better supported by the E2 model (0.76 for
the M193 versus 0.98 for the M43) than the previous E1 model.
Visual index (impact signature experiments), the splash
Again, live fire tests performed at a distance of 150 m revealed that:
- the M1A1 SMG in the visual signature mode received a higher mean suppression scale value
than did the M16,
- the visual effect of the .50 BMG M2 HMG was so much “off the scale” compared to other
weapons that it was not possible to find a statistically significant difference between the M1A1
SMG, the M16 AR and the M60 MG (the XM19 was not rated),
It was anticipated that the visual signature of impacting bullets would be related to kinetic energy
(because cavity volume in soft soils is directly a function of the kinetic energy), but the rating of the
M1A1 SMG over the M16 suggests that other mechanisms could be involved.
This unexpected observation could be linked to the ricochet characteristics of those very different
bullets, a low velocity, round nose .45 ACP bullet on one hand and a high velocity, spitzer M193 bullet
on the other hand.
The military interest of ricochets is not new (the bullet “E.N.T. n°111” previously described was
discarded in favour of the bullet “E.N.T. n°123” on ground of ricochets requirements) and was also
highlighted in ORO-T-397:
“One factor not recognized in SALVO I and not previously recognized as being significant in
combat rifle effectiveness was isolated in the SALVO II experiment—the importance of the
ricochet characteristics of ammunitions. The best example of this is the difference in hits of
.22-cal duplex ammunition compared with .30-cal duplex ammunition. Here a difference in
total hits recorded of almost 10 percent is due directly to the superior ricochet characteristics
of .22-cal duplex ammunition. This particular effect is worthy of further study.”
Unfortunately, ricochets are now mostly regarded as a firing range safety hazard and ammunition
“safety fan” can’t be used to evaluate the military interest of ricochets, because those safety fans do
not discriminate between rounds that produce dangerous ricochets 30% of the time versus 5% of the
In the absence of a clear indication of the physical effect that produced this rating, momentum (in N.s)
instead kinetic energy will be used for building a Visual Index. This choice is not totally arbitrary
because momentum is a relevant parameter for the physical description of elastic collisions.
VISUAL INDEX E1
With M, the bullet weight (in g) and V the local velocity (in m/s).
Results for some projectiles tested.
(at 150 m)
Relative Visual Index
(at 150 m)
.223 Remington M193
7.62 x 39 mm
7.62 x 51 mm
If the acoustic signature of the .50 BMG bullet was “only” 63% more than the acoustic signature of the
7.62 x 51 mm, the visual signature is 5 times more according to momentum and much higher than all
other visual signatures.
Building a Relative Suppression Index (RSI)
Balancing visual and acoustic signature to obtain a single suppression index is not an easy task,
because if acoustic signature is detected much more often than visual signature by soldiers, visual
signature seems to play a much bigger role if detected xliv. A more practical problem is that adding mm
(acoustic index) and N.s (visual index) doesn’t make sense.
So, the easiest way to build a composite index using acoustic and visual data is to use non-
dimensional values, using the 7.62 mm NATO as the reference case.
Unfortunately, while this scale could be used to compare probable “suppression effectiveness” of two
different rounds, this would not answer the basic question of “what is the average distance at which a
given bullet will be considered dangerous and could be expected to deliver a given suppression
Available data from CDEC xlv resulting from DUCS (“Degradation Under Controlled Stimuli”, April
1975), SASE (“Small Arms Suppression Experiments”) and SUPEX (“Suppression Experiment”)
experiments shows that the relationship between miss distance and “suppression probability” is not
linear (Figure 51).
Figure 51: Suppression probability as a function of miss distance, as found in DAR (Data Analysis) report.
Unfortunately, no indications are given for the distance between the firing line and the “targets”, so we
will make the assumption that this distance was the same as in the previous test (i.e. 150 m).
As can be seen, the miss distance could be very large (several meters) and still effective suppression
(> 50%) could be achieved.
For the 7.62 mm, a miss distance around 6 m will produce 50% of suppression, compared to around
3 m for the 5.56 mm and the .45 ACP, and 24 m for the .50 BMG (a class of its own, and ~4 times the
miss distance of the 7.62 mm).
Presented differently, at a (presumed) distance of 150 m a single 7.62 mm NATO (24 g cartridge)
could be expected to supress 50% of a group located in a 113 m² area, compared with 28 m² for the
.223 Remington (12 g cartridge) and 1,800 m² for the .50 BMG round (115 g cartridge).
So, if we divide the suppression area by the cartridge weight, we found that at a distance of 150 m,
1 kg of .223 Remington ammunition will provide a 50% suppression effect in a 2,350 m² area, 1 kg of
7.62 mm NATO ammo will cover 4,710 m² (twice as much for the same ammo load) and 1 kg of
.50 BMG will cover 15,700 m².
The miss distance for achieving suppression 90% of the time is much shorter, around 0.7 m for the
7.62 mm NATO, less than 0.5 m for the 5.56 mm and the .45 ACP, and 5 m for the .50 BMG (again, a
class of its own in the realm of kinetic energy small-arms).
During the tests, the miss distance was not measured with an accuracy of 10 cm (the step was
probably closer to 1 m), but it’s the result of a statistical data reduction. According to those results, the
miss distance achieving suppression 90% of the time for the 7.62 mm NATO is around 1 m, very
similar to the old “1 m or 3 ft. rule” and this value will be used for further validation.
Other results available from xliv are given below. The suppressive quality of several weapons (M1A1
SMG, M16A1 rifle, M60 GPMG and M2 HMG) was compared by 8 subjects that rated their acoustic
signature (two consecutive 3 round burst), their visual signature (2 consecutive 3 round burst
impacting at a distance of 15 m in the soil), and the combined visual / acoustic signature (one 3 round
burst fired in the ground and one 3 round burst fired overhead at the same time).
The statistical analysis of this test is presented in Figure 52, with Delphi suppression value for acoustic
mode, visual mode and combined visual and acoustic mode.
Figure 52: Mean Delphi scale suppression values for each weapon for each signature mode.
With this result, the following Relative Suppression Index (RSI) is built using 2 strong (but not totally
- The RSI value of a round delivering an acoustic index of 3.78 (mm) and a visual index of
7.0 (N.s) (7.62 mm NATO at 150 m) is 1 meter,
- The relative weight of the acoustic index is 0.3 and the relative weight of the visual index is
0.7, in order to achieve the best linear correlation (R² = 0.9987, cf. Figure 54) for the scenario
used in the above study that could be qualified as “defence, daylight”, and also the ~4 to 1
distance ratio of the 12.7 mm versus 7.62 mm (24 m vs. 6 m, cf. Figure 51 & Figure 53).
This proposed ratio (70% visual and 30% acoustic) is most probably “scenario dependant” but in the
absence of other reliable data, this ratio will be used for all bullet / calibre / ammunition comparisons.
Figure 53: Threatened range ratio (12.7 mm over 7.62 mm) as a function of the balance of Visual Index and
Acoustic Index into the RSI.
The reduction of this ratio below 65% (visual) and 35% (acoustic) reduce both the linear correlation
and the threatened distance ratio of the 12.7 mm compared with the 7.62 mm. With the new acoustic
index, the previously proposed 60% (visual) and 40% (acoustic) balance leads to a 3.6 to 1 ratio that
does reflect less accurately the difference between the 12.7 mm and the 7.62 mm.
Figure 54: linear correlation between calculated RSI (in m) at 150 m and Delphi suppression value as
found in xliv, for a mix of 30% acoustic and 70% visual.
Model sensitivity and validation, the 5.56 mm M193 vs. the 7,62 mm M43 vs. the 7,62 mm NATO
The change of the Acoustic Index (from E1 to E2) and the balance between acoustic and visual threat
(like selecting 40%+60% with the E1 model -case B- instead of 30%+70% with the E2 model –case C-
for a “defence, daylight” scenario) have a limited effect on the global trends of this study, as shown by
the Figure 55.
Figure 55: Relative Suppression Index (7.62 x 51 mm equals 1 m at 150 m) with a balance of 60% visual
threat and 40% acoustic threat (case B, bottom) and a balance of 70% visual threat and 30% acoustic
threat using the E2 model (case C, top), for various rounds of military interest (50 BMG not shown due to
The two mix proposed (case B or case C) are telling us essentially the same story.
At the weapon’s muzzle and short range, the predicted suppression distance of the 7.62 x 39 mm is
higher than the predicted suppression distance of the 5.56 x 45 mm, which is higher than the predicted
suppression distance of the 45 ACP.
At 600 m, all those 3 rounds are delivering similar suppression effects and any predicted difference
would be probably very difficult to demonstrate.
Whatever the range, those 3 rounds are producing a significantly smaller predicted suppression
distance than the 7.62 x 51 mm, which in turn is delivering a significantly smaller suppression distance
than the 338 Lapua Magnum, while everyone is dwarfed by the 12.7 x 99 mm (not shown due to
At short range, the 6 mm SAW is slightly inferior to the 7.62 x 39 mm, then a close equivalent around
350-400 m, and superior at longer range (particularly around 600 m) to the extent of being a close ,
equivalent to the 7.62 x 51 mm around 800 m.
While absolutely no hypothesis were made about the relative suppression distance of the 5.56 mm
relatively to the suppression distance of the 7.62 mm, this model actually predict that the 5.56 mm is
delivering roughly half the suppression distance of the 7.62 mm at 150 m (58% for case B, 53% for
case C), and that the suppressive effect of the 45 ACP (fired from a M1A1 SMG) is lower than that of
the 5.56 mm (fired from the M16A1), results in total agreement with actual values measured during the
several CDEC experimental studies named previously (see Figure 51).
“High Velocity Small Calibre” assault rifle cartridges (5.45 x 39 mm and 5.56 x 45 mm) could be
expected to deliver only half the “90% suppression distance” (hence a quarter of the effective area) of
the “full power” 7.62 mm (51 mm or 54 mm case length) at any engagement range.
At short range (up to 300 m), the 7.62 x 39 mm shows good suppression behaviour, delivering around
75% of the full-power 7.62 mm, significantly higher than both 5.45 mm (~50%) and 5.56 mm (~55%).
One could see the 5.56 mm NATO capability to deliver half the suppression distance of the 7.62 mm
NATO for half the cartridge weight, or the 7.62 mm NATO capability to deliver one fifth of the
suppression distance of the .50 BMG for one fifth the cartridge weight as a fair deal (at least weight
neutral), but when the fire dispersion is important, bullets could fall short or long, so it’s not the miss
distance (one dimension) that is the driving parameter, but the beaten area (two dimensions, see
Figure 56: Simple representation of a bullet threatened area.
In this representation, the distance D is the calculated suppression distance (90% level)4.
This area could be divided by the cartridge weight to obtain the specific suppression area for 1 kg of
ammo (Figure 57).
Figure 57: Specific suppression area of several military bullets as a function of the range.
4 Another possible methodology to evaluate this threatened area would be to consider that the
threatened area in the horizontal plane is a function of the visual index only, and that the threatened
area in the vertical plane is a function of the acoustic index only.
In this case, the set of hypothesis would be that a bullet with a visual index of 7.0 will have a horizontal
suppression distance (90% level) of 1 m, and that a bullet with an acoustic index of 3.64 will have a
vertical suppression distance (90% level) of 1 m. The total threatened area is the sum of both
horizontal and vertical half-disc.
S = π.D²
This intensive parameter (suppression area divided by ammo weight) is telling us a very different story
about bullets “soft power” on the battlefield, compared with the more traditional “hitting power”
At a distance of 200 m, the specific area suppressed by the 5.56 mm NATO is around 70 m²/kg,
compared with 120 m²/kg for the “full power” 7.62 mm NATO so that means that in theory you could
expect to expend 40% less ammunition weight to achieve the same suppression area using a
7.62 mm NATO MG than using a 5.56 mm NATO MG.
The “full power” 7.62 mm maintains this ~2 to 1 ratio up to 600 m (60 m²/kg versus 30 m²/kg) then the
gap starts to increase and at 800 m the advantage of the 7.62 mm is now 5 to 1.
If you add the fact that since all gas-powered MGs have roughly the same rate of fire (so that in a
given timeframe a 7.62 mm MG will fire twice as much ammunition weight than a 5.56 mm MG), at the
end of the day (between 0 and 600 m) a “full power” 7.62 mm MG will achieve the same suppression
effect as a 5.56 mm version, using only half the ammunition load and 4 times faster. At longer range
the difference is even more balanced against the 5.56 mm.
While still highly speculative, this suppression criteria at least offers an explanation as to why, contrary
to all predictions based on “hard power” (terminal ballistics) indicators, the 5.56 x 45 mm never
managed to effectively replace the 7.62 x 51 mm (hence the current movement in western armies to
reintroduce 7.62 mm LMG and DMR at the fire team level), and also the unexpected longevity of the
7.62 x 39 mm that is, despite unimpressive external and terminal ballistics, still so widely encountered
on nearly every battlefield 40 years after its official replacement.
Another interesting point is that the 6 x 45 mm SAW, designed to deliver effective fire up to 800 m,
seems to duplicate (at least on paper and using this criteria) the 7.62 mm NATO suppression
effectiveness at this distance. While not a clear and definitive demonstration, this point sustains the
view that the Relative Suppression Index, as defined previously, is a useful index if one wants to be
able to replace the current 7.62 mm NATO without limiting itself to shortening the cartridge case by a
Looking at the upper part of the scale, the .338 Lapua Magnum (or the ballistic equivalent .338 Norma
Magnum), while not really a substitute for the mighty .50 BMG, seems to deliver significantly better
performances than the current ubiquitous 7.62 mm GPMG to warrant significant interest if chambered
in a lightweight MG, a kind of modern reincarnation of the pre-WWII experimental 9x66 mm MAS MG
that used a 20 g bullet launched at 780 m/s.
We’ve seen that using a “conditional hit probability” (hit without being hit) seems to be a way to
account for “incoming fire effects”, so the same approach could be used to calculate the “suppression
probability”, then the “hit without being suppressed” conditional probability.
Using this methodology and the proposed miss distance for 90% suppression, we can compare the
probability of hitting an IPSC target (direct hit) and the probability of hitting inside the “90%
suppression circle” (achieving direct hit or suppression of the target, Figure 58).
Figure 58: Predicted hit probability of an IPSC target in the absence of incoming fire (blue curve),
predicted suppression probability (red curves) for the 5.56 mm (dots and dash), 7.62 mm (solid), .338LM
(dash) and predicted hit probability in battlefield conditions (“under fire”, black curves) against 5.56 mm,
7.62 mm and .338LM suppressive fire.
Computations were run using Applied Ballistics Analysis software, a “low confidence” scenario and a
“worst case” of 25 MoA (~7.5 mils, 3 seconds target exposure time) extreme spread for the weapon
system (as found in ORO-T-160).
The comparison of the blue curve and the black curves on Figure 58 is a vivid illustration of the military
effect of, and interest in, suppressive fire, the hit probability (effectiveness) of opposing soldiers being
At a range of ~200 m, the opposing force hit probability decreased from 23% (without suppressive fire)
to 11% against 5.56 mm suppressive fire, or 3% against 7.62 mm suppressive fire and finally 0.3%
against .338” Lapua Magnum suppressive fire.
Using a 10 MoA dispersion (5 seconds target exposure time) and the previous hypothesis, we obtain
the following results (Figure 59).
Figure 59: Predicted hit probability of an IPSC target in the absence of incoming fire (blue curve),
predicted suppression probability (red curves) for the 5.56 mm (dots and dash), 7.62 mm (solid), .338LM
(dash) and predicted hit probability in battlefield conditions (“under fire”, black curves) against 5.56 mm,
7.62 mm and .338LM fire.
The reduction of fire dispersion from 25 MoA to 10 MoA do not change the general shape of the
various curves, but tends to increase the “optimum engagement range”, from 200 m to 400 m (against
5.56 mm NATO suppressive fire), and from ~400 m to ~600 m against 7.62 mm NATO suppressive
By construction, the RSI(90%) value of the 7.62 mm NATO bullet is 1.00 m at 150 m and the quoted
effective range of this round against point target, when fired from a bipod, is generally 800 m which
cover the full supersonic range of this round.
The calculated RSI(90%) value of this round at Mach 1.1 is 0.62 m and the area “suppressed” by a
kilogram of 7.62 mm NATO ammunition is 50 m².
Longer effective ranges (1100 m and up to 1800 m when T&E mechanism is present) could be found
in the context of tripod-mounted MGs (delivering high volume of fire) but those values are probably not
relevant to LMGs and IWs fire.
For comparison purpose, the calculated RSI(90%) of the 6 x 45 mm SAW is 0.49 m at 600 m (50 m²
per kg) and 0.42 m at 800 m (36 m² per kg), in essence delivering the same suppression effects as the
7.62 mm NATO at 800 m and 1000 m respectively, in a more compact and lighter package.
Given those results, it is safe to assume that a value close to 0.50 m is probably needed in the context
of bipod-mounted LMGs or Individual Weapons, or a value of 50 m² per kg of ammo if one wants to
properly take the opportunity to reduce unitary cartridge weight.
The chart below details the maximum distance at which the 7.62 mm NATO, the 6 mm SAW and the
5.56 mm NATO are achieving a RSI(90%) of 0.5 m or 50 m per kg of ammunition.
50 m² per kg
7.62 mm NATO
6 mm SAW
5.56 mm NATO
The area of the IPSC target used by AB Analytics WEZ software for the evaluation of the hit probability
is 2775 cm² (0.2775 m²), that’s nearly the same area as a 0.30 m radius circle, so when the RSI(90%)
falls below ~0.30 m, the 90% suppression probability and the hit probability are nearly equal and the
interest for using a 90% suppression distance is lost, but for analysis of long range fire one could still
choose a lower suppression probability (75% or even 50%) and use the bigger suppression radius.
For example, according to Figure 51 the radius of the 50% suppression probability seems to be
around 5 to 6 times the radius of the 90% suppression probability, so between 1.5 m to 1.8 m (7 m² to
10 m per round) when the 90% suppression radius of a given round is falling below 0.3 m, probably
effective enough from a military point of view for harassing fire, but very far from IWs, DMRs or LMGs
Small arms are internal combustion systems with limited efficiency (generally between 20% and 40%).
Heat not converted into kinetic energy or rotational energy (between 60% and 80% of the overall
energy) will be used to heat the weapon chamber and barrel, or will remain in the combustion products
(increasing the weapon muzzle signature with flash and blast).
According to the “Powley computer”, the thermal efficiency of both the 5.56 mm SS-109 and 7.62 mm
M80 bullets when fired from a 20” (508 mm) barrel is around ~31%, so that means that the amount of
“wasted heat” (thermal load) is a little higher than 3900 J for the 5.56 mm round (1700 J of bullet
muzzle energy) and 7450 J for the 7.62 mm round (3300 J of bullet muzzle energy).
Heat flux (wasted heat divided by bore area) for both rounds is around 15.5 kJ/cm².
If we extended those calculations to more well-known cartridges (also using the Powley computer and
a uniform 508 mm barrel length), we obtain the following results.
Figure 60: Thermal flux for different civilian cartridges.
Without much surprise, at the “low end” of the scale (<<15 kJ/cm²) we find the wildcats 6.5 mm TCU
and 6-223 Remington, cartridges that use the small .223 Remington case necked up to 6 mm or
6.5 mm. The .300 AAC Blackout and the 7.62 x 40 mm WT, not shown here, would exhibit even lower
Those rounds could be of historical interest since the casehead of the .223 Remington is the same
(9.6 mm) that that of the .351 WSL, and the unfortunate 8 mm Ribeyrolles (8 x 35 mm SR) could be
seen as a kind of necked-up, low-pressure “8 mm AAC Blackout”.
At the other side of the scale (>30 kJ/cm²) we find “high intensity” cartridges like the .220 Swift, .240
Weatherby and the .264 Winchester Magnum that have a well established reputation of being “barrel
burners” even for civilian applications. The barrel length of 508 mm used for those computations does
not do justice to the big 7 mm Remington Magnum in terms of barrel life, but is a clear indication that a
lot of wasted heat will flow through the barrel and that one could expect a large muzzle report. In the
case of the .264 Winchester Magnum fired from a 508 mm tube, you will achieve both low barrel life
and large muzzle report.
Between those two extremes, we have the “comfortable” 15-20 kJ/cm² zone where we could find
military cartridges and civilian equivalents (.223 Remington, .308 Winchester and 7-08), and the 25-
30 kJ/cm² zone with high velocity cartridges (.243 Winchester and .22-250 Remington) that represents
what is generally considered the “high-end” of the usable range.
According to results obtained with the “Powley Computer”, the 7 x 59 mm of the 1909 automatic rifle
program, with a cartridge length of 79.3 mm, a case length of 58.9 mm and a case capacity of 4.5 cm3
(3.6 g of powder) could launch a 7.6 g steel bullet (7.24 mm diameter and 27.4 mm length) at a muzzle
velocity of 1030 m/s (4030 J of muzzle energy) out of an extra-long (for now) 715 mm barrel length,
when loaded at a standard chamber pressure of 48 000 CUP (330 MPa).
Those predicted results are very similar to what was actually achieved in 1913.
The calculated thermal efficiency is 28.8% and is equal to a thermal load of 9960 J (33% more than
the current 7.62 mm M80 ball) and a thermal flux of 24.5 kJ/cm² (60% higher).
Depending on the applications, cartridges in the 20-25 kJ/cm² range could be used but the failure of
the 7 x 59 mm as a military round is an indication that a heat flux lower than 20 kJ/cm² is a safer bet
(and closer to 15 kJ/cm² even better).
Even if the 7.62 mm NATO (~11.5 N.s) was originally designed to be fired from semi-auto “lightweight”
IWs, the ammunition impulse does not really allow its use in a ~4 kg IW (free recoil energy of 16 J).
The interest of a low-recoil, light rifle seems pretty well demonstrated in the context of sport shooting,
where target locations are known and the limiting time is the time needed to point, shoot and reload.
In a context closer to military application, with several people trying to manoeuver, spot and engage
elusive targets without shooting at each other, the benefits of a low-recoiling rifle seems to be less
During the CDCEC-SAWS study xlvi i, several 9 men squads trialled a mix of different weapons in order
to achieve the maximum effectiveness, as measured by target effects and sustainability.
The IWs used were the M14 (7.62 x 51 mm), the AK (7.62 x 39 mm), the Stoner M63 and the M16A1
(both firing the 223 Remington cartridge).
While this study definitively worth an in-depth review (some have already be writtenxlviii ), only the main
results will be exposed here, and the reader will reach his own conclusions.
Individual weapons mixes
If we remove the AK from the individual weapon mixes (due to a small number of previously used rifles
and no support, the evaluation of the AK rifle was not performed to the same standard as the other
rifles), the 3 “rifle squads” configurations used in the CDCEC-SAWS were:
- The “UA” mix consisting in nine M14 rifles and 1290 rounds. 7 riflemen with a load of 100
rounds (ball ammo) per rifle and 2 riflemen with 295 rounds (tracers) per rifle, 20 rounds
magazines, semi-auto fire.
- The “SA” mix consisting in nine Stoner rifles and 2352 rounds, 7 riflemen with a load of 180
rounds (ball ammo) per rifle and 2 riflemen with 546 rounds (ball & tracer) per rifle, 30 rounds
magazines, 2 rounds burst.
- The “CA” mix consisting in nine M16A1 rifles and 3618 rounds, 7 riflemen with a load of 300
rounds (ball ammo) per rifle and 2 riflemen with 759 rounds (ball & tracer) per rifle, 30 rounds
magazines, 2 rounds burst.
The number of rounds was adjusted to achieve a common rifle squad weight of ~86 kg per squad.
Situations & measured parameters
The various scenarios relevant to IWs were:
- The “situation 1: Rifle Squad In Line Assault” designed to “evaluate rifle squad weapons mixes
in marching fire against targets in foxholes at ranges of 148 to 15 meters”, duration was
- The “Situation 2: Rifle Squad as Base of Fire Supporting the Assault” designed to “evaluate
rifle squad weapon mixes firing supporting fire from hastily prepared foxholes. Range from the
foxholes to enemy targets was from 269 to 326 meters”, duration was 4 minutes (2 minutes for
target array “X” and 2 minutes for target array “Y”).
- The “situation 4: Rifle Squad in Approach to Contact” designed to “evaluate the rifle squad
mixes in standing quickfire at briefly exposed visible targets. This situation, in which firers
were time stressed, was designed especially to evaluate the pointing characteristics of small
arms”, duration was between 25 minutes and 30 minutes.
- The “situation 5: Rifle Squad as a Base of Fire Supporting the Advance” designed to “evaluate
the technique of distributed fire used throughout the sector, with point fire used when targets
were seen or weapon simulators gave specific cues to a target's location.” Two groups of
targets were used, the first one located 379 m to 445 m from the firers, the second one
located 477 m and 560 m from the firers. Duration was 4 minutes (2 minutes for target array
“X” and 2 minutes for target array “Y”).
- The “situation 7: Rifle Squad in Defence Against Attack” designed to “evaluate rifle fire from
hastily prepared foxholes at enemy targets appearing at ranges from 345 meters to 45
meters.” This scenario was played twice with the UA mix firing semi-auto and the SA and CA
mixes firing fully-auto, and a second time with half the UA, SA and CA mixes firing fully-auto
(and half firing semi-auto). Duration was 8.5 minutes.
Those scenarios were “played” by at least 6 squads in order to calculate a significant mean value.
Effectiveness was evaluated along various parameters:
- Targets hit and total hits (self-explaining, some targets could be hit more than once before
- Near-misses (impacts in a semi-circular zone 2 m around the main target),
- Cumulative Exposure Time (CET). This parameter needs some explanations. Each target of
an array was programmed to be exposed for a predetermined period that was identical for
each squad in a given tactical situation, hitting targets reduced the exposure time of this
target, and hitting fast reduced the CET even more. CET of the target system is a primary
measure of fire effectiveness; it reflects both the number of targets in a group that were hit and
the timeliness in which they are hit. The lower the CET value, the higher the fire effectiveness.
- Sustainability. The measure of sustainability used in the CDCEC-SAWS is the percentage of
ammunition remaining for a given weapon mix when the squad weapon system weight
constraint (starting system weight), tactical situation, and record run time are held constant for
all squad mixes. The maximum number of rounds that could be safely fired by each weapon
before cook-off problems arose was not taken into account for evaluating sustainability, which
greatly diminish the relevance of this parameter.
The mean number of rounds fired by each IW weapon system for each situation is given below.
It should be noticed that due to the uneven number of rounds carried among each squad, after firing
around 900 rounds (UA mix), only 2 weapons could still be expected to fire at the end of situation 2.
The same situation could happen for the SA mix after firing 1620 rounds (also probably encountered
during situation 2) and for the CA mix after firing 2700 rounds (probably not encountered).
The various weapon mixes were rated (first, second, third) based on the mean CET results along with
the statistical analysis.
For example, in situation 5 the SA mix ranked first, UA ranked second but with a “p” factor of 0.22 the
difference is not statistically significant (the lower the “p” factor, the higher the confidence that the
difference is statistically significant).
CA ranked third with a “p” factor of 0.02, so the SA weapon mix performed significantly better than the
CA weapon mix in this situation.
As could be seen, the UA mix performed pretty well during those 5 situations and never ranked at the
By comparison, the SA mix performed first in two situations (1 & 5, but not significantly better than the
UA mix that ranked second), but also ranked last in three situations (2, 4 & 7).
The CA mix performed first in two situations (4 & 7, but again not significantly better than the UA mix
that ranked second) but also ranked last in 2 situations (1 & 5) which involved high intensity firing and
high thermal stress.
Of those 5 scenario, two (situation 1 and situation 4) were devoted to close range
engagements, situation 4 being expressly devoted to the evaluation of weapons point firing.
For situation 1, the mean CET was 24.8 ±1 minute for the SA (stoner) system, 25.5 ±1.2 minute for
the UA (M14) system and 25.8 ±1.4 minute for the CA (M16A1) system.
The scenario lasted for 2 minutes, and during this time the UA squad fired up to 850 rounds (or 94
rounds per rifle, close to the allocation of 100 rounds per rifles for 7 rifles), the CA squad fired up to
1418 rounds (or 157 rounds per rifle) and the SA squad fired a mean 1536 rounds (or 171 rounds per
rifle, again close to the allocation of 180 rounds per rifles for 7 rifles). It was a pretty intensive firing,
even more if you take into account the fact that the squad have to move (an average 100 m distance
was covered in 2 minutes), shoot and reload.
All 3 systems were pushed to their thermal limits (or beyond), but the “light and low recoiling” 5.56 mm
systems did not showed a significant “point & hit” advantage over the “heavy and hard recoiling”
7.62 mm, as shown in the statistical analysis (“F test”) provided in the study.
According to this analysis, the only significant differences (p score <0.06) were that:
- the SA (Stoner) system scored more near miss (a mean 470 for 1150 rounds fired) than the
CA (M16A1, a mean 394 for 1042 rounds fired) and UA (M14, a mean 313 for 677 rounds
- the SA system scored more hits (4.5 ±0.8) than the CA system (3.0 ±2.0) (difference between
the SA and UA mixes was not significant),
- the “sustainability” of the CA system was significantly higher than both SA and UA systems,
so compared with the SA system, the CA system could simply be viewed as unable to shoot
a significant proportion of the ammo carried.
Results for the “Situation 4” designed to “evaluate the rifle squad mixes in standing quickfire at
briefly exposed visible targets. This situation, in which firers were time stressed, was designed
especially to evaluate the pointing characteristics of small arms” (as found in the study report) were
hardly more demonstrative.
The mean CET (for the 12 events of this scenario) was 1.97 ±0.2 minute for the CA (M16A1) system,
2.04 ±0.1 minutes for the UA (M14) system and 2.11 ±0.1 minutes for the SA (Stoner) system.
Squads needed 25 to 30 minutes to perform this scenario, and the total cumulative exposure time for
all 40 targets was 180 seconds. During this time the UA squad fired up to 399 rounds, the CA squad
fired up to 1064 rounds and the SA squad fired up to 990 rounds. Thermal stress was probably much
lower during this 25 minutes scenario than during the 2 minutes of situation1.
The mean number of targets hit (30.4 for the CA mix, 30.0 for the UA mix and 29.2 for the SA mix) was
also more or less constant for the 3 systems and again, the M14 ranked in-between the two 5.56 mm
systems but the difference was not found significant.
The situation is even more blurred if we look at the sub-scenario shown in “Table c -- Rank order of
weapon mixes and associated standard scores for the ambush situation (ten enemy targets at a range
of 21 to 34 meters)”.
Figure 61: Results of the “ambush” event.
Even in this sub-scenario, the difference between the SA, CA and UA mixes does not sustain the idea
that a light, low recoiling rifle is inherently superior to a heavy recoiling rifle in a military context (as
opposed to a sporting context).
At the end of the day, the methodology used during the CDCEC-SAWS greatly favoured systems
using the lightest cartridge.
If the ammo load was effectively expended (like in the case of the Stoner rifle and a weight of 3.6 kg
unloaded), then the system would score a large number of near-miss (and then achieve a good rank in
“target effect”), if the system won’t shoot the ammo due to thermal issues (like the M16A1 and a
weight of 3.0 kg unloaded) then the system will still achieve a large “sustainability rating”.
If the CDCEC-SAWS study showed the interest of carrying as much ammo as possible for a given
system weight, it was hardly a clear and definitive demonstration of any intrinsic military advantage of
a light-recoiling round.
As a side note, exploratory firing during the CDCE-SAWS study demonstrated that the best mode of
fire for the UA mix was semi-auto and 2 round bursts for the SA and CA mixes, supporting the current
trend in western armies to use “controlled pairs” instead of full-auto fire.
Regarding weapon controllability in full-auto firing, reducing the ammo impulse below 5.56 mm level to
simply approach the ideal dispersion pattern envisioned during ORO-T-160 would be a difficult task.
This ideal “diamond pattern” (4 shots) dispersion used to demonstrate the potential increase of hit
probability was 20 inches (ES) at 300 yards, or 1.9 mils.
The mean extreme spread (MES) of a compensated 5.56 mm M16A1 (impulse of 1.2 pound-seconds),
firing 3 shots burst, is 17.6 mils when the shooter is standing and 12.6 mils when the shooter is prone
xlix, very far from the “ideal” value.
The same weapon firing a 4.32 mm round (impulse around 0.57 pound-seconds) produced a MES of
14.7 mils and 10.2 mils respectively, or a nearly linear reduction of the dispersion area with the ammo
The “in burst” dispersion (between the first round and the third round) of the M16 firing the 4.32 mm
cartridge was 14 mils (standing) compared with 12.5 mils for the SPIW firing at 800 rpm, or 9.2 mils for
the SPIW firing at 1500 rpm.
This reduction of the dispersion of a hand-held weapon firing at high rpm was well documented during
the studies made for the FAMAS development, when it was discovered that due to muscular response,
the lowest dispersion would be achieved for a firing frequency lower than 10 Hz (600 rpm) or higher
than 20 Hz (1200 rpm), the highest dispersion of a hand-held rifle would be achieved with a firing
frequency between 14 Hz (840 rpm) and 18 Hz (1080 rpm) l.
All in all, the “best case” MES recorded with the 4.32 mm (.17 SBR) was 9.2 mils when the ideal
pattern dispersion asked for 1.9 mils (and 4 shots).
According to H&K commercial flyer, the MES of the HK G11 firing 3 shots burst is 4.6 mils (standing),
with the best MES scoring around 2.5 mils. While closer to the 1.9 mils goal, such dispersion is still
much higher than the ideal “controlled dispersion” pattern.
If the linear relationship between ammo impulse and dispersion area is true, then in order to achieve
the 1.9 mils ideal dispersion pattern used in ORO-T-160 study (and achieve the predicted increase of
the hit probability), one needs to combine the “high rpm, free linear recoil” of the G11 rifle and a huge
reduction in the ammunition impulse with an impractical goal of 0.9 N.s (.22 LR impulse level).
With the current availability of the .17 WSM round propelling a 1.3 g bullet at 1000 m/s (nearly
duplicating the experimental rimfire 4.5 x 26 mm MKR), dispersion during full-auto fire could be studied
with “off the shelf” components.
If the ammo impulse is a primary factor to calculate weapon free recoil energy (the round impulse
squared divided by twice the weapon weight) this parameter does not take into account the fact that
for the same amount of impulse, the felt recoil (linked to weapon acceleration and not final velocity) is
greatly influenced by the amount of bolt travel.
Since bolt rearward velocity is very similar among automatic rifles (close to 7 m/s), the greater the bolt
travel, the lower the bolt deceleration (and weapon acceleration), so instead of “kicking” the gun will
“push”, even if the final recoil velocity is the same for a given ammo impulse and weapon weight.
For IWs, the weapon cyclic RoF is a close function of the bolt travel. High rpm is produced by short
bolt travel (~85 mm of bolt travel for the FAMAS firing at 1100 rpm, ~108 mm for the M16 firing at
850 rpm and ~135 mm for the FN SCAR and the AK firing at 600 rpm), so a first order parameter to
evaluate the felt recoil is to divide the ammunition impulse by the bolt travel.
The benchmark used for comparative evaluation is the 5.56 mm NATO round fired from the M16
platform (impulse ~6 N.s; bolt travel ~108 mm) or the 7.62 x 39 mm fired from the AK platform
(impulse ~7.5 N.s bolt travel length ~135 mm) because the “felt recoil” is 55.5 kg/s in both case.
At the upper end of the scale, the 7.62 mm NATO fired from a FAL or a G3 (impulse ~11.6 N.s, bolt
travel ~119 mm) is delivering a “felt recoil” of ~97 kg/s (+75%).
Below that, a “felt recoil” of 86 kg/s could be calculated for the 7.62 mm NATO fired from a FN SCAR
(impulse ~11.6 N.s, bolt travel ~135 mm, +55%); 74 kg/s for the 6.8 mm SPC fired from a M16
platform (impulse ~8 N.s, bolt travel ~108 mm, +33%) and at the lower end 37 kg/s for the
5.45 x 39 mm (impulse ~5 N.s, bolt travel ~135 mm, only 2/3 of the benchmark case).
Interestingly, since around 30% of the impulse generated by a 7.62 mm NATO cartridge is produced
by the exhaust of the combustion products, a rifle equipped with a reasonably efficient muzzle brake
(impulse ~8.0 N.s as measured by ballistic pendulum with a very effective muzzle break li, ~8.5 N.s for
a more practical one) will have a “felt recoil” around 60-63 kg/s with 135 mm of bolt travel (8-13%
higher than the benchmark case, and roughly equivalent to a 0.25-0.50 kg weapon weight penalty to
keep the weapon recoil velocity constant) and there is anecdotal evidence that this level of “felt recoil”
is not detrimental to weapon stability.
All in all, it seems that a recoil limit of 8.5 N.s (without muzzle break) is not high enough to reduce the
tactical effectiveness of semi-auto or full-auto fire as long as the weapon cyclic RoF stays around
600 rpm (or lower).
Part Three: Study of a 600 m lightweight round
With the realization that hand-held weapons could be used with a significant military effect
(suppression) up to a much longer range (~600 m and up) than predicted by studies focusing only on
hit probability, we will now “explore the design space” to try to found the “best” (or the least
handicapping) combination of parameters.
The methodology used in this study is very similar to the one presented in CRC-307lii “A
METHODOLOGY FOR SELECTING SMALL-ARMS ROUNDS TO MEET MILITARY
REQUIREMENTS”, but with different design parameters.
Two “design space” will be explored, the first one with a 2.8” cartridge overall length (COAL) fired from
a 508 mm (20”) barrel (rifle or MG), the second with a 2.26” COAL fired from a 406 mm (16”) barrel
The main requirements of a “600 m lightweight round” are:
- to be able to hit and defeat a protected soldier at 600 m (point target) and to deliver accurate
and lethal fire up to 800 m (area target),
- to deliver suppressive effects as close as possible to current 7.62 mm NATO ball,
- to be as light as possible (as a general rule, low cartridge weight means low cartridge impulse
AEBE, so impulse will be used as a weight surrogate).
2.8” COAL design space results
In the previous versions of this paper, 3 bullet lengths (4; 4.5 and 5 calibres) were investigated. Since
the shortest bullet was neither an optimum, it was decided in this release to remove it and include a
5.5 calibres flat-base bullet that will benefit from the increased stability demonstrated by flat-base
bullets compared with boat-tail bullets.