WORLD WAR 2 FIGHTER ARMAMENT EFFECTIVENESS

© Anthony G   Williams & Emmanuel Gustin (with acknowledgements to Henning Ruch)

 Revised 28 June 2004

The comparative effectiveness of fighter guns in the Second World War is a subject of perennial fascination (and a great deal of argument) among technical military historians. This is an attempt to take a fresh and objective look at the evidence in order to draw up comparative tables of cartridge destructiveness, gun power and gun efficiency. The effectiveness of typical day fighter armament fits is also considered.

CARTRIDGE DESTRUCTIVENESS

There are two types of energy that may be transmitted to the target; kinetic and chemical. The kinetic energy is a function of the projectile weight and the velocity with which it hits the target. This velocity in turn depends on three factors: The muzzle velocity, the ballistic properties of the projectile, and the distance to the target. There are therefore two fixed elements in calculating the destructiveness of a projectile, its weight and chemical (high explosive or incendiary) content, and one variable element, its velocity. The key issue is the relationship between these three factors.

A high muzzle velocity will provide a short flight time, which is advantageous in increasing the hit probability and extending the effective range, and will also improve the penetration of AP rounds. However, it might not add much to destructiveness, as unless an AP projectile hits armour plate (and not much of the volume of an aircraft was protected by this), a higher velocity just ensures that a neater hole is punched through the aircraft; the extra kinetic energy is wasted. Also, if the projectile is primarily relying on HE blast or incendiary effect, the velocity with which it strikes the target is almost immaterial. Provided that it hits with sufficient force to penetrate the skin and activate the fuze, the damage inflicted will remain constant. In contrast, AP projectiles lose effectiveness with increasing distance.

It is sometimes argued that a projectile with a high muzzle velocity and a good ballistic shape (which reduces the rate at which the initial velocity is lost) provides a longer effective range. To some extent this is true, but the greatest limitation on range in air fighting in the Second World War was the difficulty in shooting accurately. The problem of hitting a target moving in three dimensions from another also moving in three dimensions (and probably at a different speed and on a different heading) requires a complex calculation of range, heading and relative speed, while bearing in mind the flight time and trajectory of the projectiles. Today, such a problem can easily be solved by a ballistic computer linked to a radar or laser rangefinder, but at the time we are examining, the "radar" was the human eyeball and the "ballistic computer" the human brain. The range, heading and speed judgements made by the great majority of pilots were notoriously poor, even in training. And this was without considering the effects of air turbulence, G-forces when manoeuvring, and the stress of combat. These factors limited the effective shooting range to around 400 m against bombers (longer in a frontal attack) and against fighters more like 250 m.

For all of these reasons muzzle energy (one half of the projectile weight multiplied by the square of the velocity) has not been used to calculate kinetic damage as this would overstate the importance of velocity. Instead, momentum (projectile weight multiplied by muzzle velocity) was used as an estimate of the kinetic damage inflicted by the projectile. It might be argued that even this overstates the importance of velocity in the case of HE shells, as noted above, but the effect of velocity in improving hit probability is one measure of effectiveness which needs acknowledging, so it is given equal weighting with projectile weight.

Chemical energy is generated by the high explosive or incendiary material carried by most WW2 air-fighting projectiles. First, there is the difference between HE and incendiary material, which were often mixed (in very varying proportions) in the same shell. HE delivers instant destruction by blast effect (plus possibly setting light to inflammable material within its blast radius), incendiaries burn on their passage through the target, setting light to anything inflammable they meet on the way. The relationship between the effectiveness of HE and incendiary material is difficult to assess. Bearing in mind that fire was the big plane-killer, there appears to be no reason to rate HE as more important, so they have been treated as equal.

The comparison between kinetic and chemical energy is the most difficult and complicated subject to tackle. This complexity is revealed by the example of a strike by a delay-fuzed HEI cannon projectile. This will first inflict kinetic damage on the target as it penetrates the structure. Then it will inflict chemical (blast) damage as the HE detonates. Thirdly, the shell fragments sent flying by the explosion will inflict further kinetic damage (a thin-walled shell will distribute lots of small fragments, a thick-walled shell fewer but larger chunks), and finally the incendiary material distributed by the explosion may cause further chemical (fire) damage.

There will therefore always be a degree of arbitrariness in any attempt to compare kinetic and chemical energy, as it all depends on exactly where the projectile strikes, the detail design of the projectile and its fuze, and on the type of aircraft being attacked. To allow a simple comparison, we will reduce all these factors to an increase in effectiveness directly proportional to the chemical content of the projectile. We assign to projectiles that rely exclusively on kinetic energy an effectiveness factor of 100%. For projectiles with a chemical content, we increase this by the weight fraction of explosive or incendiary material, times ten. This chosen ratio is based on a study of many practical examples of gun and ammunition testing, and we will see below that it at least approximately corresponds with the known results of ammunition testing.

To illustrate how this works: a typical cannon shell consists of 10% HE or incendiary material by weight. Multiplying this by ten gives a chemical contribution of 100%, adding the kinetic contribution of 100% gives a total of 200%. In other words, an HE/I shell of a given weight that contains 10% chemicals will generate twice the destructiveness of a plain steel shot of the same weight and velocity. If the shell is a high-capacity one with 20% chemical content, it will be three times as destructive. If it only has 5% content, the sum will be 150%, so it will be 50% more destructive, and so on.

The following table for the most common cartridges and loadings used in aircraft guns shows the consequences of these assumptions and calculations. The first few columns should be self-explanatory, as these are basic statistics about the ammunition. HE(M) means Minengeschoss, or high-capacity mine shell. The 'DAMAGE' column shows the results of the calculations described above. To run through an example, let us look at the case of the 7.7x56R (.303") incendiary. The projectile (a "De Wilde") weighs 9.8 g, (which equals 0.0098 kg) and was fired at 747 m/s. Multiplying these gives 747 x 0.0098 = 7.3206, so you have a momentum factor of 7.32. As the bullet contains 5% by weight of incendiary material, the momentum is multiplied by 1.5 to give a destructive power score of 10.98 - rounded to 11.

The last column - 'POWER' - takes into account that different types of ammunition, with different destructiveness scores, were commonly loaded into an ammunition belt or magazine. Many cannon shells were also available with tracers, which reduced the weight of HEI mix. This column therefore shows an average score for the different types to give an overall destructiveness assessment for that calibre. For convenience, the result is divided by ten and rounded to the nearest whole number (except for HMGs), which helpfully leaves the least powerful cartridges, the rifle calibre rounds, scoring 1.

TABLE 1: CARTRIDGE DESTRUCTIVENESS

 

CARTRIDGE	TYPE	ROUND WEIGHT	MV M/SEC	PROJECTILE WEIGHT GM	% HEI CONTENT	DAMAGE	POWER
7.7x56R	AP /  I	24	762  /  747	11.3  /  9.8	-  /  5	8.6  /  11	1
7.92x57	AP-v	24	865	11.5	-	10	1
13x64B	AP  /  HE	76 /  72	710  /  750	38.5  /  34	-  /  3.5	27  /  34	3.2
12.7x81SR	AP  /  HE	82	760  /  770	35.4  /  33	-  /  2.2	27  /  31	3
12.7x99	API	112	890	43	2	46	4.6
12.7x108	API	125	840	48	4.2	57	5.7
15x96	AP  /  HE	166  /  151	850  /  960	72  /  57	-  /  4.9	61  /  82	7.8
20x72RB	HE	200	600	128	6	123	12
20x80RB	API  /  HEIT  /  HE(M)	182  /  162	585  /  585  /  700	117  /  115  /  92	3.1  /  3.2  /  22	90  /  89  /  206	14
20x82	API  /  HET  /  HE(M)	205  /  183	720  /  720  /  800	117  /  115  /  92	3.1  /  3.2  /  22	110  /  109  /  236	16
20x94	AP  /  HE	250  /  213	700  /  730	112  /  79	-  /  12	78  /  127	11
20x99R	API  /  HEI	183	750  /  790	96  /  95	2  /  6	86  /  120	11
20x101RB	HE	222	750	128	6	154	15
20x110RB	HE	240	830	122	8	182	18
20x110	HE (Mk II  / Mk V)	257	860  /  830	130	8	201  /  194	20
20x125	HE	290	820	127	7	177	18
23x152B	API  /  HE	467	880  /  880	200  /  200	3  /  7	228  /  300	26
30x90RB	HE (M)	480	505	330	25	580	58
30x184B	HE (M)	780	860	330	25	990	99
37x145R	HE	900	610	608	7.4	645	64
37x195	HE	1570	900	735	6	1060	106
40mm CL	HE	587	246	585	8.7	269	27

Comments on Table 1

Clearly, the resulting scores can only be approximate, and in particular will vary depending on the particular mix of types included in an ammunition belt. The power calculation takes a typical mix of ammunition, where known. They also take no account of the fact that some incendiary mixtures, and some types of HE, were more effective than others were. However, they do provide a reasonable basis for comparison. There is no point in trying to be too precise, as the random factors involved in the destructive effects were considerable.

If we compare the values with the few data known from ballistic tests, we have some indications that the factors assumed in the calculations are realistic. The 20x80RB M-Geschoss and the 20x110 (Hispano) HE were rated as about equal; the greater blast effect of the M-Geschoss was countered by the greater penetration and kinetic damage inflicted by the Hispano. They do indeed emerge with similar scores. Also, the Luftwaffe reckoned that it took about four or five times as many 20 mm shells to destroy a heavy bomber as it did 30 mm rounds. The power relationship here is 3.6 times for the MK 108 and 6.2 times for the MK 103, which neatly brackets this observation.

Cartridge illustrations

These photos illustrate the different cartridges listed above (with the exception of the 40mm CL). The first PHOTO includes rounds from 7.7x56R to 20x101RB; the second PHOTO starts with the 20x101RB and finishes with the 37x195.

GUN POWER AND EFFICIENCY

The cartridge destructiveness table above only shows the relative effect of one hit. When comparing the guns that fired the cartridges, other factors come into play, namely the rate of fire (RoF) and the gun weight.

To calculate the destructive power of the gun, the 'POWER' factor from the above table has been multiplied by the RoF, expressed in the number of rounds fired per second. This gives the relative 'GUN POWER' figures in the table below. It is important to note that all of the RoF figures are for unsynchronised guns; the exception is the 12.7 mm UB (Soviet Berezin) where the lower RoF figure is for a synchronised gun (which it commonly was in fighters), the higher for unsynchronised. The effects of synchronisation on other guns varied considerably; for German weapons, which used an efficient electrical system, the reduction in RoF was around 10%. For other systems it typically varied between 20 and 40%.

To judge how efficient the gun was, the 'GUN POWER' result is divided by the weight of the gun in kilograms to provide the 'GUN EFFICIENCY' score in the last column. This is, in effect, a measure of the power-to-weight ratio of the gun and ammunition combination.

TABLE 2: GUN POWER AND EFFICIENCY

 

GUN	CARTRIDGE	RoF RPS	CARTRIDGE POWER	GUN POWER	GUN WEIGHT KG	GUN EFFICIENCY
Browning .303	7.7x56R	20	1	20	10	2.1
MG 17	7.92x57	20	1	20	12	1.75
MG 131	13x64B	15	3.2	48	17	2.82
Breda-SAFAT	12.7x81SR	12	3	36	29	1.24
12.7mm Scotti	12.7x81SR	12	3	36	22	1.64
Ho-103	12.7x81SR	15	3	45	23	1.96
.50 Browning M2	12.7x99	13	4.6	60	29	2.1
12.7mm UB	12.7x108	13 - 17	6	74  - 97	25	3  -  3.9
MG 151	15x96	12	7.8	94	42	2.2
20mm Type 99-1	20x72RB	8	12	108	24	4.5
MG-FF	20x80RB	8	14	126	28	4.5
MG 151/20	20x82	12	16	192	42	4.6
20mm Ho-5	20x94	14	10	154	37	4.2
20mm ShVAK	20x99R	13	11	143	42	3.4
Berezin B-20	20x99R	13	11	143	25	5.7
20mm Type 99-2	20x101RB	8	15	120	35	3.4
HS.7 and 9	20x110RB	6.5	18	117	48	2.4
Hispano II	20x110	10	20	200	50	4
Hispano V	20x110	12.5	20	250	42	6
Ho-1  /  Ho-2	20x125	7	18	126	45	2.8
VYa-23	23x152B	9	26	234	68	3.4
MK 108	30x90RB	10	58	580	60	9.7
MK 103	30x184B	7	99	693	141	4.9
37mm M4	37x145R	2.5	64	160	96	1.7
NS-37	37x195	4	106	424	170	2.5
Ho-301	40mm CL	7.5	27	202	132	1.5

Comments on Table 2

Two factors not included are gun reliability and total ammunition weight. The former is simply not available in most cases. The latter involves too many variables. First, the ammunition supply for most guns varied according to the installation. Furthermore, in searching for comparators, there would be the problem of which measures to take: the weight of the number of rounds fired per second, or the weight of the number required to inflict a certain amount of damage? There would be a case for either of these, but they would produce very different results. This issue is however addressed in the next table.

The lower rate of fire of many of the larger guns tends to reduce their power advantage over the smaller calibres. However, in power-to-weight ratio, larger guns are generally better performers (the slow-firing American 37 mm M4 and low-velocity IJA Ho-301 excepted).

Most of the Soviet guns show up as being remarkably efficient, with scores of around 4, but the Hispano and the MG 151/20 also show up well, as do the simple MG-FF and Japanese Type 99 API blowbacks because of their light weight.

The American Browning .50 M2 is an undistinguished performer, particularly when compared with its closest competitor, the 12.7 mm Berezin. The relatively small incendiary content in the .50 API (0.9 g instead of 2 g) gives the Soviet round a flying start, which it adds to by its usefully higher rate of fire, then finishes off in style by being lighter as well, and thereby almost twice as efficient overall. The Browning also makes an interesting comparison with the Japanese Ho-5, which was basically the M2 slightly scaled up to take 20 mm cartridges.

It may appear that this low score of the .50 M2 is in disagreement with the satisfactory experience the USAAF had with this weapon. The answer to this apparent contradiction is that the .50 M2 proved very effective against fighters and (not too sturdy) bombers, if installed in sufficient numbers. Six or eight guns were specified as standard armament, resulting in a destructive power total of 360 or 480, at the cost of a rather high installed weight. Most American fighters were sufficiently powerful to have a high performance despite this weight penalty. Incidentally, the mediocre efficiency score of the .50 M2 is not only an effect of the low chemical content of its projectiles. Even if only the kinetic energy were considered, the efficiency of this gun would remain inferior to that of the UBS, B-20, ShVAK or Hispano, although better than that of the MK 108 or MG-FFM. To sum up, the preferred US armament fit was effective for its purpose, but not very efficient by comparison with cannon.

A further validation of the calculations is provided by the outcome of tests by the USN, which stated that the 20 mm Hispano was about three times as destructive as the .50 M2. In the above table, the ratio between their scores is 3.3.

The outstanding performer is clearly the German 30 mm MK 108, which achieves ten times the destructiveness of the .50 M2 for only twice the weight. It makes a particularly interesting comparison with the MK 103, which fired the same M-Geschoss projectiles. The MK 103 gains an advantage because of its higher velocity, but loses most of it due to its lower rate of fire, then is finally eclipsed in efficiency because of its much greater weight. No surprise that the Luftwaffe considered the MK 108 their premier air-fighting gun despite its low muzzle velocity. The Me 262 jet fighter, with four of these guns clustered in the nose, completely outclassed the firepower of every other WW2 fighter.

FIGHTER FIREPOWER

Finally, a consideration of how the firepower of day fighters compared with each other, and in particular how it increased during the war. The aircraft have been grouped in early-war, middle-war and late-war fighters, and have been chosen to be representative of their period.

TABLE 3: FIGHTER FIREPOWER

 

Name	Armament	Weight (kg)	AmmoPower	GunPower	Time to fire 2320
1939 - 1941
Morane-Saulnier MS.406	1 x HS.7 (e) 2 x MAC 1934	91	1680	163	(14.2)
Messerschmitt Bf 109E-4	2 x MG 17 (s) 2 x MG-FFM	149	3680	286	8.1
Fiat G.50 Freccia	2 x Breda-SAFAT 12.7 (s)	107	1800	54	(43.0)
Hawker Hurricane Mk.I	8 x Browning .303	144	2672	160	14.5
Supermarine Spitfire Mk.VC	2 x Hispano Mk.II 4 x Browning .303	235	6200	480	4.8
Lavochkin LaGG-3	1 x ShVAK (e) 2 x ShKAS (s)	93	1970	189	(12.3)
Yakovlev Yak-1B	1 x ShVAK (e) 1 x UBS (s)	178	2908	217	10.7
Curtiss P-40C	2 x Browning .5 M2 (s) 4 x Browning .30	230	5456	163	14.3
Brewster F2A-3 Buffalo	2 x Browning .5 M2 (s) 2 x Browning .5 M2	318	8280	202	11.5
Bell P-39D Airacobra	1 x 37 mm M4 2 x Browning .5 M2 (s) 4 x Browning .30 M2	367	7898	323	7.2
Mitsubishi A6M2 Reisen	2 x Type 97 Fixed (s) 2 x Type 99-1	120	2440	238	9.7
Nakajima Ki-43-Ib Hayabusa	1 x Type 89 Fixed (s) 1 x Ho-103 (s)	70	1310	38	(61.1)
1942 - 1943
Messerschmitt Bf 109F-4	1 x MG 151/20 (e)      2 x MG 17 (s)	129	4200	226	10.3
Messerschmitt Bf 109G-6/R6	1 x MG 151/20 (e)      2 x MG 131 (s)            2 x MG 151/20	286	8640	714	3.3
Focke-Wulf Fw 190A-4	2 x MG 151/20 (s)      2 x MG 17 (s)              2 x MG-FFM	310	10080	666	3.5
Macchi C.205V series III Veltro	2 x Breda-SAFAT 12.7 (s)                        2 x MG 151/20	285	8800	438	5.3
Hawker Typhoon Mk.IB	4 x Hispano Mk.II	344	11200	800	2.9
Lavochkin La-5FN	2 x ShVAK (s)	157	4400	220	10.5
Yakovlev Yak-9T	1 x NS-37 (e)              1 x UBS (s)	270	4532	498	4.7
Curtiss P-40E Warhawk	6 x Browning .50 M2	332	6486	360	6.5
Lockheed P-38J Lightning	1 x Hispano M2          4 x Browning .50 M2	429	12200	440	5.3
Republic P-47D Thunderbolt	8 x Browning .50 M2	613	15640	480	4.8
Mitsubishi A6M3a Reisen	2 x Type 97 Fixed (s) 2 x Type 99-2	162	4000	262	8.9
Kawasaki Ki-61-I-KAIb Hien	2 x Ho-103 (s)             2 x Ho-5	280	7000	362	6.4
Nakajima Ki-44-IIc Shoki	2 x Ho-103 (s)             2 x Ho-301	363	2040	459	(5.1)
1944 - 1945
Messerschmitt Me 262A-1a	4 x MK 108	413	20880	2320	1.0
Focke-Wulf Fw 190A-8	2 x MG 131 (s)            2 x MG 151/20 (s)      2 x MG 151/20	431	16160	826	2.8
Focke-Wulf Fw 190A-8/R8	2 x MG 131 (s)            2 x MG 151/20 (s)      2 x MK 108	458	17420	1608	1.4
Supermarine Spitfire Mk.XIVE	2 x Hispano Mk.II       2 x Browning .50 M2	276	7100	520	4.5
Hawker Tempest Mk.V	4 x Hispano Mk.V	374	16000	1000	2.3
Lavochkin La-7	3 x B-20S (s)	147	4290	330	7.0
North American P-51D Mustang	6 x Browning .50 M2	385	8648	360	6.5
Kawanishi N1K2-J Shiden	4 x Type 99-2	255	7800	480	4.8
Kawasaki Ki-84-Ib Hayate	2 x Ho-5 (s)                 2 x Ho-5	291	6600	484	4.8

Comments on Table 3

The armament installations are listed in the second column. In some cases there were several alternative armament installations for the specified type of aircraft; of these one has been chosen. The (e) and (s) in the armament column indicate engine cannon and guns synchronised to fire through the propeller, respectively. Where the rate of fire for the synchronised installation is not known, a reduction of 25% of the unsynchronised rate of fire has been assumed. An exception was made for the MG 131 and MG 151/20 with their electrical priming systems (10%) and the big Browning .50 M2, Ho-103, and Ho-5 (40%), as these weapons reportedly suffered badly when synchronised.

The specified weight is the weight of the bare guns and the ammunition. It does not include belt links, ammunition tanks, gun mounting points and recoil buffers, synchronisation systems and trigger gear, et cetera. Realistic figures for the weight penalty would probably be 30 to 60% higher; for example, values are known of 685 kg for the P-38J and 495 kg for the P-39D.

The ammunition power value is the cartridge power value from Table 1, multiplied by the number of cartridges carried. The gun power value is the sum of the gun powers as in Table 2, but recalculated to take into account the effects of synchronisation.

The final column gives the time in seconds, needed to fire the equivalent of an ammunition power of 2320. The choice of this value is somewhat arbitrary; it was selected simply because the heaviest armed fighter - the Me 262 - was capable of delivering this firepower in one second, so it enables easy comparisons to be made. Not all fighters carried that much ammunition; for those aircraft that did not the time has been put between brackets.

During 1939 - 1941 we see that all fighters of the Axis nations and the USSR have fairly modest firepower. This characteristic is also shared by the Hurricane Mk.I (and of course the Spitfire Mk.IA). Near the end of this period the UK and USA started to build fighters with much more firepower, and by 1942 the Curtiss P-40E and Hawker Typhoon were established in service. With those fighters the armament pattern preferred by these two nations emerged: six .50 M2 guns and four Hispano cannon, respectively. We see that these choices are approximately the same in weight, but the second offers twice the firepower. Armed with six .50 guns in the wings were also the F4F-4, P-51D, and most of the production of the F6F and F4U. Some US fighters - the most important of them was the P-51B - had only four .50 M2 guns, resulting in a firepower value of just 240, well below average after 1941.

In the second period the firepower of Axis fighters is substantially improved, mostly by the introduction of multiple and better 20 mm cannon: the MG 151/20, Ho-5 and Type 99-2. The weight of their armament installations remained fairly low, especially compared with that of the new American fighters, the P-38 and P-47. But the empty weight of these aircraft was 5.8 and 4.5 tons, compared with 2.6 tons for a Bf 109 and 3.5 tons for an Fw 190A, so the weight of the armament was roughly proportional. The Japanese made an interesting attempt to improve the firepower of the Ki-44 by installing the 40 mm Ho-301 cannon, firing caseless ammunition. But the 245 m/s muzzle velocity of these weapons was far too low, and they failed in combat. Not many of these Ki-44-IIc aircraft were built.

In the final period specialised bomber-killers such as the Fw 190A-8/R8 and Me 262 appeared, with impressively high firepower values due to their MK 108 cannon. These too had a relatively low muzzle velocity, but at 505 m/s this was still sufficient for engaging bombers. Exchanging two MG 151/20 for MK 108 cannon nearly doubles the firepower of the Fw 190A-8. It is also obvious that the armament installations of these fighters are quite heavy, especially for the small Fw 190; the A-8/R8 was heavily armoured as well. The need to destroy heavy bombers had an adverse effect on the performance of German fighters.

An obvious overall tendency is that towards steadily increasing firepower: The average gun power in the three periods is 210, 460 and 870. This comes with a rise in the average weight, which climbs from 175 kg over 300 kg to 340 kg. In the first years of war a third of the selected fighters fails to reach the 2320 ammunition limit, but in the last years they all carry much more than that.

Of course, the projectiles could only inflict damage if they hit the target, and in aerial combat the great majority missed (estimates for an average pilot's hit rate varying between two and five percent). Pilot skill was by far the most important factor in this, in combination with the quality of the gunsight; it was claimed that the gyroscopic sight (which entered UK/USA service in 1944) put deflection shooting within the ability of the average pilot and thereby doubled armament effectiveness. Other factors were the nature of the target (its size and whether or not it was manoeuvring), the steadiness of the fighter as a gun platform, the muzzle velocity of the guns (the higher, the better) and the location of the guns, centre-mounted ones being more efficient than wing-mounted over a wide range of target distances.

Criticisms and Alternatives

The publication of this study has created much interest and comment. Unsurprisingly, the most vocal commentators have been those with criticisms of the methodology used. This section has therefore been added in order to describe and answer the criticisms.

There are four principal criticisms, which are mainly centred on the validity of the comparison between the .50 Browning and the rival cannon. In these tables, the Browning compares rather poorly and this is sometimes, of itself, taken to discredit the entire comparison on the grounds that the USAAF was the most successful air force, so its chosen armament had to be much better than this study suggests. This general point will be returned to later. The specific criticisms are:

1. The kinetic element of destructiveness is measured at the muzzle, not at combat range. The subtext of this argument is that the .50 Browning, having better ballistics than cannon, retains a higher percentage of its destructiveness at long range than cannon.

In fact, while it is true that most cannon shells slow down more quickly than the .50 calibre bullets, it is not true that their destructiveness reduces pro rata. As has already been pointed out in this study, much of the destructiveness of cannon shells lies in their HE/I content, which is not affected at all by the striking velocity as long as it is sufficient to actuate the fuze. So while both .50 bullets and cannon shells lose kinetic effectiveness with range (the cannon shells at a faster rate), in overall destructiveness (kinetic +chemical) most cannon shells actually lose effectiveness more slowly than the bullets.

It is also worth pointing out that most successful attacks in WW2 took place at fairly short ranges at which different projectile ballistics would not have had a major effect on destructiveness. During 1940 the RAF rapidly dropped the harmonisation distance for their fighter guns from 370 to 230m, and were annoyed that the narrow gun bays in the Spitfire's wing prevented them from harmonising the 20mm cannon down to their preferred distance of 180m (at which they did most ammunition effectiveness testing). Although successful attacks at longer ranges were possible, particularly against large, stable targets like heavy bombers (as the Luftwaffe discovered), it seems probable that the great majority of shoot-downs took place between 100 and 300m. This is often not appreciated by players of combat sims, who think that the ability to score routinely at ranges of 1,000m or more in their games reflects WW2 reality – it doesn't!

2. The way of calculating the chemical destructiveness is too crude. It is suggested that instead of just adding an arbitrary percentage to the kinetic destructiveness depending on the percentage weight of HE/I filling, an energy calculation should be produced. This would calculate the kinetic energy of the projectiles (in joules) at some typical combat range, then add to this a calculation of the chemical energy (also in joules) contained within the high explosive (if any).

There is a lot of merit in this suggestion, which is more scientific in its approach. However, there are some drawbacks also. First, there is the question of what constitutes a typical combat range. And whatever range was selected, the kinetic energy with which the projectiles struck the target would vary considerably depending on whether the engagement was a tail chase, a beam attack or a head-on attack.

Second, there is the comparison between the various HE and incendiary compounds used. Some of the information required as to their chemical energy is difficult to obtain, and in any case the filling of some shells varied through time, in ways which have not always been recorded.

The final response is the simplest: this approach, while affecting the relative scores of some of the projectiles, doesn't actually change the 'order of merit' very much. Basically, the lower-powered AP or small-HE-capacity cannon shells (which derive most of their effectiveness from kinetic energy) tend to show up as less effective than in Table 1, while the high capacity HE shells show up as being more effective. As these types were typically mixed in an ammunition belt, the net result is no significant change in the rankings.

Henning Ruch has done some calculations on the basis of the 'kinetic+chemical energy' equation and compared the results with those in Table 1. If the .50 Browning is taken as the baseline and given a score of 1.00, the following are some results for other rounds: As you will see, the 'total energy' calculation as much as doubles the performance of the high-capacity cannon shells, while almost halving the score of the AP projectiles.

3. The shorter flight time of the .50 bullets, plus the larger number fired for a given weight of armament, greatly improves the hit probability of this armament by comparison with the slower-firing cannon, making shoot-downs more likely.

The first part of this criticism is undoubtedly correct, but the second part does not follow. The relative lack of effectiveness of the .50 bullets mean that it is necessary (on average) to score many more hits to shoot down a plane than with cannon armament. These two factors probably more or less cancel each other out.

As has already been observed, hit probability is also affected by many other things apart from gun performance: the quality of the gunsights, the location of the guns, the stability of the aircraft as the gun platform, and above all, pilot skill. These cannot be taken into account in a study of this type – there are just too many variables.

4. That the calculations understate the effectiveness of cannon in general, and large-calibre cannon in particular. This is partly because while a machine gun bullet relying in kinetic energy has to hit something vital to have an effect (or score so many hits close together that it shreds the structure) - it otherwise just makes small holes - a single cannon strike anywhere on the aircraft can inflict significant damage. It is also argued that a hit by one large cannon shell is more effective than hits by several smaller shells generating the same total damage score, as these will be spread across the aircraft instead of being concentrated at one point.

These points are valid. However, it is also true that cannon shells did not always explode when they hit – the fuze could sometimes fail to function – in which case they were reliant solely on their kinetic damage. Again, it seems likely that this would more or less counteract the criticism.

In Conclusion, while it is admitted that some elements of the calculations – especially concerning the relative weighting given to kinetic and chemical damage – are open to criticism, in practical terms the results stand up quite well. Changing the method of calculation affects some scores but has surprisingly little effect on the overall 'order of merit' of the destructiveness rankings. Where it does have an effect, it is generally to boost the scores of high-capacity HE shells while reducing those of lower-velocity AP cannon shells, which is validated by the Luftwaffe's decision to focus on chemical rather than kinetic energy in developing their aircraft weapons.

To return to the obviously controversial question of the relatively poor performance of the .50 Browning: as has already been stated in this study, "the preferred US armament fit [of six or eight .50 HMGs] was effective for its purpose, but not very efficient by comparison with cannon". It is worth pointing out that for as long as the battery of .50s proved adequate against the targets usually encountered, there were strong arguments in favour of retaining the weapon, as the standardisation of production, supply, maintenance and training provided great logistic benefits by comparison with the plethora of different weapons fielded by the Germans and Japanese in particular. Of course, the USA did make some use of the 20mm Hispano cannon, but this was severely limited by production problems: that is another story, told elsewhere on this website!

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