PDA

View Full Version : About WW2 fighter aircraft firing power


Rob Philips
7th September 2008, 22:16
About WW2 fighter aircraft firing power


What exactly is the firing power of a WW2 fighter aircraft? This is a subject that has seen debate and confusion. In this thread the subject is summarized, and expanded, as I believe that it may be possible to improve upon common opinion.


Definitions

Caliber is the bore diameter of the barrel, expressed in millimeters or inches. Firing rate is the number of rounds fired per minute. Fighter aircraft armament in WW2 is usually of the machine gun or automatic cannon type, meaning automatic projection of projectiles as long as the trigger is squeezed. The division between machine guns and cannon is usually made at a caliber of 15 or 20 mm.

Vo is the muzzle velocity, expressed in meters per second, the speed at which the projectile leaves the muzzle. This velocity declines with range, faster with light projectiles and slower with heavier ones.

Projectile weight is expressed in grams or grains.

Kinetic energy is the product of velocity and weight. A high kinetic energy, resulting from high muzzle velocity and/or high projectile weight, means a high capability to do damage to a target.


Opinions

1. Firing power is sometimes seen only in terms of gun caliber. 9mm is bigger and therefore better than 7,5mm. This is not enough. A high speed 7,5mm projectile can have more kinetic energy than a 9mm projectile, meaning that it shall be able to do more damage.

2. Firing power is sometimes seen as the sum of machine guns available. The Dutch Fokker G1 fighter aircraft had an at that time unprecedented eight machine guns, looking most impressive indeed. However, it can be demonstrated that the kinetic energy delivered at targets was a mere 50% of the kinetic energy delivered by two machine guns and one cannon in an Me.109, that would soon become its opponent.

3. Firing power is more commonly seen as the product of projectile weight and firing rate. A hundred 7,62mm, 7,92mm or .303" rounds of 15 grams each, if projected in a second, deliver a mass of 100 x 15 = 1.500 grams per second on the target. Twenty 20mm rounds of say 100 grams each, if projected in a second, deliver a mass of 20 x 100 = 2.000 grams per second on the target. 2.000 is more than 1.500, so that 20mm cannon has a higher firepower than that 7,62 to 7,92mm machine gun.

I wonder if this notion of firepower can stand the test of scrutiny. The theory assumes that the target is indeed hit, and that was one of the problems in WW2 fighter combat.

We shall not consider the following improvements of WW2 fighter armament. These improvements were highly relevant, but they are difficult to quantify:

- introduction of explosive and incendiary substances to the projectiles

- introduction and improvements of aiming aids

- introduction of rocket munitions

After WW2, these improvements were superseded by self-aiming rocket projectiles, leading to a one shot - one kill situation that was unheard of during WW2. Furthermore, cyclic firing rates were vastly improved with new implementations of the old Gatling multi-barrel machine gun or cannon system.


4. Pattern density added to opinion 3

In order to hit a target in WW2 aerial combat, you need to have a high fire power as defined above, meaning a lot of kinetic energy on target, but also a firing pattern that increases the chance of scoring hits. If a fighter would carry a 90mm gun, then surely one hit would be enough to destroy the opposing fighter aircraft. But 90mm guns could not be made to fire at 900 rounds per minute. 20 rounds per minute was the achievement of such guns at the end of the war. And if they could, the aircraft could not carry the weight of ammunition needed for a few seconds of firepower. On the other end of the scale, WW2 fighters would be able to carry a multitude of the number of projectiles, if scaled down in caliber, such as in hunting shells, but these munitions would not have the kinetic energy and the range required to do the job. The practical solutions were in fact trade-offs between technological possibilities of the day.

The excursion into the ammunition range from 2mm hunting pellets to 90mm shells shows the missing factor in the firing power definition given above: projectile spread. Or better: kinetic energy delivered per square meter of space. Assuming sufficient pattern density to achieve effective damage at all, then the aircraft with the largest shot pattern had the better chance to achieve hits in the lightning fast aerial combat of WW2 fighter aircraft.

Projectile spread from a multi-gun platform results from three factors:

1. Adjustment, also called synchronisation, of the individual guns.

2. Differences between individual rounds of ammunition.

3. Barrel, and especially muzzle, wear. A worn barrel leads to less accuracy, which may not be a bad thing in this case.

The adjustment of the guns is by far the most important factor here. Unfortunately for this proposed theory, there is hardly any data about WW2 fighter aircraft gun synchronisation. Some services, or some Squadrons, or even some individual pilots, had the guns synchronised to hit at say 150 meters, others at other distances. But this figure does not tell us a lot about the spread. Were the guns adjusted to catch the size of the opponents silhouette at that distance, or did the projectiles meet at one point at that distance, or was the pattern adjusted to something wider than this? I would be interested to hear from anybody who has real knowledge about this.

It seems that the best scoring pilots were the ones who engaged from the closest distances. That did away with most of the considerations above: kinetic energy would be maximal, gun synchronisation would have much less influence, and pattern density would be as high as available.

Regards,

Rob

Pilot
8th September 2008, 00:11
Just short note- smaller caliber have larger rate of fire and larger calliber have smaller. In other way energy input was different and better for large calliber. There was varius way to find compromise. One of them was mixed armament with machine guns and cannons.

I like your post :)

Rob Philips
8th September 2008, 00:47
Thanks, Srecko. Usually, but not always, rate of fire is higher in smaller caliber automatic weapons, as a result of less weight of cartridge and breech block metal that needs to be moved. One of the WW2 developments was to increase the rate of fire for aircraft armaments, all calibers, for instance by reducing the weight of the breech block, by increasing the recoil spring force, by different lock mechanisms, and any combination of these. Machine guns for fighter aircraft would evolve in the direction of 1.200 rpm, whilst the army versions of these guns had 800 rpm.

After the war, a .22LR Gatling gun driven by an electric motor was made, that sported a much higher firing power than any of the WW2 aircraft machine guns, as a result of the >20.000 rpm (rounds per minute) firing rate. I believe that this gun was never used operationally, but it serves to demonstrate the technical point.

I agree that mixing calibers was one way to achieve compromises, the way in which the Germans led the field.

Regards,

Rob

Juha
8th September 2008, 00:58
Hello
Tony Williams' pages are a good introduction to this matter.
See:http://www.geocities.com/CapeCanaveral/Hangar/8217/fgun/fgun-in.html

Juha

Rob Philips
8th September 2008, 01:42
Thanks, Juha. Very well researched article, which is what we expect if Tony Williams is the source. Curiously, fire power or firing power is not defined in this article, and not expressed in the tables given. However, when discussed, the type 3 in my post, projectile weight times firing rate, is intended. Two other expressions are mentioned, the Q and the M factor. Both consider the weight of the weapon as well, and therefore express the efficiency of the weapon. My proposal to include kinetic energy and pattern density cannot be found in these pages. I believe that this article represents the visions of gun manufacturers, whilst I am looking for user visions too. Users mounted multiple guns in flying gun platforms. The difference is between firing range data, and aerial combat data, technological data versus tactical data.

There is one remark in these pages, that points into the direction that I would like to go. It is a remark made by Adolf Galland, stating that the Me.109 armament of two machine guns and one cannon was not good enough for the average pilot. Why? Not because the projected weight was insufficient, but because the pattern was not dense enough. A denser pattern would have led to more results achieved by aviators with average marksman skills.

Regards,

Rob

Juha
8th September 2008, 02:07
One important point is the effectiveness of different ammo types, for ex. German Minen HE, API etc. Tony analyses this in his WWII Guns book.

Other is how the guns were sighted, at what distance their bullets/shells converged.

Juha

Harri Pihl
8th September 2008, 11:28
IMHO the ability to hit the moving target is a key factor on firing power, therefore the aspects which affect the hitting probability have large influence on firing power. The best known example of this is the velocity of the projectiles; 50% increase in muzzle velocity increase hitting probability by five times according to some sources.

Rob Philips
8th September 2008, 12:44
Thanks, gentlemen. I excluded HE & I ammunitions from the discussion as it is very difficult to quantify their effects. It is clear that adding explosives to a round increases its effectiveness by a large margin. Have checked what Tony Williams has to say about this, on the site mentioned by Juha. Explosive power is mentioned, of course, but not quantified. Perhaps we can include into the equasion the kinetic energy of an exploding round. But first comes the ability to hit the target at all.

I introduced "sighting" of the guns, as expressed by Juha, as "pattern density" into the equasion. Harri hits the mark I'm trying to make, with "the ability to hit a moving target". Projectile velocity is less of a factor here than you might believe. Projectile velocities are about 800 to 900 meters per second at the muzzle, reducing to say 700 after 150 meters. 700 meters per second translates to 2.520 km/h, about four times faster than the top speeds of the aircraft involved. Max. muzzle velocity of conventional projectiles coming out of rifled barrels is limited; this cannot be increased easily. If a Vo could be raised to say 1.000 m/s, or 3.600 km/h, reducing to say 850 m/s after 150 meters, or 3.060 km/h, then that would be about 5 times faster than the fastest aircraft, lessening the projectile flight time to target by a factor 5/4 = 1,25 only. This would translate to a smaller leading angle in the deflection shooting required in aerial combat, but that would be all. I would be interested to hear how, as Harri said, some sources calculate an increase of hitting probability by a factor 5, if muzzle velocity is increased by 50% - if that would be possible. I would also be interested in a definition of "hitting probability", as that would indeed be the key notion in this matter.

Have once done experiments to determine the max Vo that can be obtained from a rifled barrel. Using custom made plastic projectiles, used for their light weight, with .223 cartridges fired from an AR 15 rifle, cartridges loaded to the brim to obtain max. propelling force, a max. Vo of about 1.500 m/s was achieved. This was found to be a limit, that could not be exceeded with these means. Vo's of WW2 aircraft machine guns are all below 900 m/s.

Regards,

Rob

Juha
8th September 2008, 14:04
Rob, there are books which explains the effects of different HE, API etc rounds and those effects are very significant, that’s why ball rounds were not very common late war years even if they many times had better kinetic energy than HE rounds.

On hitting, you leave away very important factor, gravity drop. Higher muzzle velocity means flatter flight path and made hitting easier.

And some WWII aircraft guns had muzzle velocities as low as appr 520m/s.

Juha

Harri Pihl
8th September 2008, 14:13
Rob,
Check your PM.

Rob Philips
8th September 2008, 14:31
Thanks, Juha. Surely you are correct in stating that gravity drop is a relevant factor. It increases with low muzzle velocities, long firing ranges and low projectile weights. It complicates the difficulties of deflection shooting. This would ideally be taken into account by the gun sight. Hitting probability is not yet well defined, but I am talking about the situation that a target is indeed in the sight, but nevertheless not hit, or not hit effectively.

To obtain some idea about the differences in effectiveness of explosive and non-explosive rounds of aircraft ammunition, I can offer the following:

The example is the Hispano Suiza 20mm cannon, widely used in fighter aircraft in WW2. The cartridge is 110mm long, rimless. A HE (High Explosive) projectile weighs 130 grams, and carries 6 grams of TNT. A solid non-explosive projectile weighs 150 grams. Both are fired at a muzzle velocity of 850 m/s. TNT has a detonation speed of 7.000 m/s.

Kinetic energy (Joules) = 0,5 x projectile weight (kg) x the square of the muzzle velocity (m/s)

The muzzle energy of the non-explosive round is calculated as follows:
0,5 x 0,150 x 850 x 850 = 54.188 Joules, or 54 kiloJoules

The muzzle energy of an exploding round is calculated as follows:
0,5 x 0,124 x 7.000 x 7.000 = 3.038 kJ
To this should be added the kinetic energy of the round directly prior to explosion:
0,5 x 0,130 x 850 x 850 = 47 kJ
Total = 3.085 kJ

Meaning that the explosive round has 3.085/54 = 57 times the energy of the non-explosive round.

Regards,

Rob

Rob Philips
8th September 2008, 15:17
Thanks, Harri, most interesting. Your material describes the Janecek invention, presented to the BSA company, who presented it to the Ministry of Aircraft Productions in Febr. 1941. The invention is a variation of the squeeze bore principle, designed to obtain higher muzzle velocities.

The basics are as follows. To drive a projectile to a very high speed, you need a lot of propellant. Using that, you also need a long barrel, so that the propellant can be burnt completely into propelling gases. Long barrels can become impractical, and this is where the invention kicks in. If you restrain a projectile, by narrowing the bore towards the muzzle, you create more time for the propellant to burn. This requires two things:
1. a tapered barrel, which is difficult to produce, and
2. squeezable projectiles, which are not too difficult to make.
The Janecek invention deals with the first requirement in a simple way: use a normal barrel, and add a choke to the muzzle. A relatively simple accessory, with which standard gun barrels can be transformed into high velocity ones. Or so the claim goes. Quite comparable to the choke applied to the muzzle of 12 gauge hunting guns.

Then the document continues, trying to sell the idea. For this a calculation of "hit probability" is introduced, and, as could be expected, this calculation demonstrates that hit probability is proportional to muzzle velocity. That's where the statement appears, that a 50% higher muzzle velocity leads to a hit probability that is five times higher. Elsewhere in the document the calculation leads to a factor eight. I believe that the exercize is executed quite well, but we must realize that this is a marketing exercize. The entire calculation is based on an assumed capability of the target to perform lateral movements, of deviating from a straight line of flight so as to avoid being hit. The outcome of the calculation shall depend on what is agreed about such lateral movement capabilities.

In any case, the British did not buy it. Neither the invention, nor its sales talk. I assume that the choke idea could not as easily be implemented to existing guns as was believed. We know that the squeeze bore principle was made operational and succesful by the Germans. They had to surmount the difficulties of producing a tapered bore to get the idea to work. They did so to obtain very high muzzle velocities, meaning very high kinetic energies, which were desirable for armour piercing applications. As far as I know, the Germans did not implement that technology in fighter aircraft armament, let alone that an increased hit probability would have been a reason for doing so.

Nevertheless, a most interesting find.

Regards,

Rob

Harri Pihl
8th September 2008, 15:48
Rob,
The point here is the relation between muzzle velocity and hitting probability regardless the Janacek's invention being bought or not. We do know that allies stayed on relatively high velocity weapons, say HS 404 and M53, because their air targets were generally small and agile fast moving fighters while the axis went towards higher caliber low velocity weapons, say MK 108 and rockets, because the main threat was the slow and large bombers.

Harri Pihl
8th September 2008, 16:06
And regarding a "marketing exercize"; there is no question if Janacek was selling his invention. However, he atleast tried to take account a key factor which is not accounted in some other comparisons at all.

PeterVerney
8th September 2008, 16:50
This is a very, very complex subject. In fact the variables are too great to have been properly computed in WWII conditions. Having done many hours of cine gun assesments, listened to lectures, and sat beside or behind pilots on practice or live firing sorties, I used to take a great deal of interest in this.
Mixed armament is a no no to start with because of the differing ballistics of the rounds
Then there is the pilot skill in flying the aircraft correctly when squeezing the tit. If the old turn and bank indicator is not correct, i.e. if there is slip or skid, then the gunsite is not correctly aligned. After that comes variation in the ammo itself, and I could be here all day.

Juha
8th September 2008, 18:02
Hello Rob
WWII era reflector sight gives only right solution if the range was estimated correctly (that happened seldom, usually range was underestimated many time grossly) and wings were level, any kind of bank bought a need for sideway correction. And as Peter noted any kind of skid ruined the solution. Because flatter flight path of shot/shell lessened the effects of errors, it increased the possibility of hit. Of course lessening the firing distance did the same.

On the effects of explosive component of a shell. It is no use to try to invent wheel again. And I doubt that we have ability to do that. In any case it was over 30 years ago when I last time made rough calculations on effects of certain amount of certain explosive to certain bridge and the amounts were tens or hundreds kilos, so entirely different ball game. And anyway I have only vague recollections on some general principles used in those calculations. So much better solution is that you try to find out some formula made by experts and use it.

Juha

Rob Philips
8th September 2008, 19:48
Thanks, Juha. I agree that a flatter trajectory decreases the effects of errors, and therefore increases the chance of a hit. I did not agree with the quantification of that statement, in that a 50% higher Vo would give a 5 times higher probability of a hit. That would depend upon a definition of "hit probability", and we do not yet have a good one.

About reverting to the experts: if you could point me to a work on the subject, I'd be interested. We are not talking about civil explosive demolition here, where charges can be calculated to do a certain job under known conditions. In military explosive manuals, you'll find much less theory, and much more empirical data, based on substances and applications as they become available. In military applications, the bigger blast is usually seen as the better one. In civil explosive demolition the opposite is the way to go.

Ammo parameters in our case are given. Energies can be calculated, based on these parameters. The explosive can be seen as a propellant, that projects the fragmented shell bits initially (Vo of explosion) with the speed of the explosion. Therefore, I felt safe to use the energy formula that is used for non-explosive projectiles: E = 0,5xWeightxVsquare. I'm not claiming absolute accuracy here, I offered a comparison of the energy delivered at the target of a solid and an explosive round with the parameters as stated. This data is not found in the ammo manuals, and that's the reason to give it a try. If there is an error in my reasoning, I would like to know which. In any case, hit probability is not effected by the presence or absense of explosives in a projectile, so it really is a sideline here. Hit effectiveness however is greatly effected by the use of explosive rounds.

To Peter: mixing calibers in aircraft armament is a way to achieve compromises, and surely this way introduces new issues resulting from differences in exterior ballistics. That the matter is highly complicated is fully understood. I'm inclined to decide whether it is too complicated only after having given it a try.

To Harri: I understand the point made, and appreciate the effort to come to a quantification of "hit probability". I was not convinced by the result of that effort. The fact that the Germans evolved to low Vo large caliber aircraft armament most likely has to do with bombers being their main targets, as you said, but there may be no direct connection with the achievement of hits here, and more with delivering of the energy levels that could destroy a bomber. That meant shooting with the highest amounts of High Explosive as technology allowed at the time. Not because the bombers were slow, but because more energy on target was needed to bring them down.

Regards,

Rob

Juha
8th September 2008, 20:16
Hello Rob
Tony sometimes post here and anyway his site has also discussion board. Maybe a couple years ago we had conversation here on effects of different fillings of HE and Minen shells and Tomislav had better recollections on explosives than me. If you can suck him into this thread he might give some tips.

Juha

Rob Philips
8th September 2008, 20:25
Thanks, Juha. I know how to reach Tony, and shall ask him what he knows about "hit probability".

Regards,

Rob

Juha
8th September 2008, 20:31
Hello Rob
checked the thread, it's here http://forum.12oclockhigh.net/showthread.php?t=5142
Fairly interesting and also gives some indication how complicated the subject is.

Juha

Harri Pihl
8th September 2008, 22:44
Because flatter flight path of shot/shell lessened the effects of errors, it increased the possibility of hit. Of course lessening the firing distance did the same.

The advantages of high muzzle velocity is not limited to the flat flight path of the projectile and sudden movements of the target (Janacek's point); because the time to reach target is shorter, also the needed lead is shorter and therefore the aiming error will be smaller as well.

Juha
8th September 2008, 22:50
Hello Harri
Yes, of course, but Rob acknowledged that already in his message #8.

Juha

Harri Pihl
8th September 2008, 23:14
To Harri: I understand the point made, and appreciate the effort to come to a quantification of "hit probability". I was not convinced by the result of that effort. The fact that the Germans evolved to low Vo large caliber aircraft armament most likely has to do with bombers being their main targets, as you said, but there may be no direct connection with the achievement of hits here, and more with delivering of the energy levels that could destroy a bomber. That meant shooting with the highest amounts of High Explosive as technology allowed at the time. Not because the bombers were slow, but because more energy on target was needed to bring them down.


I believe that there is fairly direct connection between probability of the hit and muzzle velocity. Janacek's point is just one simple approach based on unknown movement of the target, while we can can disagree on amount of this effect, it is still a valid point. Other advantages being quite clear as well; less room for aiming error.

The Germans had high muzzle velocity weapons, like the MK 103, but these were too bulky for smaller aircraft. And regardless the speed, the bombers were still much larger and less agile targets than fighters so hitting them with low velocity weapons was much easier.

Harri Pihl
8th September 2008, 23:28
Hello Harri
Yes, of course, but Rob acknowledged that already in his message #8.


I don't see that Rob acknowledged aiming error there, just noted smaller lead. The point is that even if we assume that the relative error in lead is the same for low and high muzzle velocity weapon, the absolute aiming error will be lower for high velocity weapon. In practice also relative error will be lower for a high velocity weapon because smaller lead is easier to quess.

Kurfürst
9th September 2008, 00:13
The advantages of high muzzle velocity is not limited to the flat flight path of the projectile and sudden movements of the target (Janacek's point); because the time to reach target is shorter, also the needed lead is shorter and therefore the aiming error will be smaller as well.

... the model remains true if we strictly stay with single-shot weapons.

However, with automatic guns, such as aircraft cannons, a round fired earlier, ie. in case of higher cyclic rate during a given time frame will reach the target earlier, than in a case of a higher velocity round fired at a slower cyclic rate. For practical applications, careful aiming and application of proper lead is less attractive than just let the target 'walked into' a sufficiently dense line of firepower applied - ie. point and shoot. Its a fail-proof method.

There is a reason for using shotguns for hunting small game and birds with a high number of slow pellets instead of .223 bolt action rifles with 1200-1300 m/sec.

Rob Philips
9th September 2008, 00:21
Thanks, gents. Lively topic. We agree that high muzzle velocity is good for the capability to score hits. We are unsure about a quantification of this statement. We agree that the Janecek effort regarding "hit probability" is remarkable, and very relevant, even if we cannot (yet?) agree with the presuppositions of that theory.

We do not agree that hitting bombers was easier with low Vo weapons. I believe that a lower Vo was the trade-off in the wish to bring a lot of explosives to the bomber target, as that required a large caliber, meaning a large projectile that could accomodate a lot of TNT, or whatever mixture of the contemporary explosive compounds. Larger calibers meant lower Vo's, or elso the design of weapons that would become prohibitively heavy for use in aircraft.

The earlier thread mentioned by Juha shows that the explosives used by the combattants of WW2 were rather similar. Detonation speeds from 7.000 to 8.750 m/s. Density differences of up to about 35%. Compounds that were either already available during WW1, or were variants of that, with no major developments to this day - if we limit this statement to explosives based on chemical compounds, the so-called conventional explosives. But all that is not relevant to hitting capability, or probability. It is highly relevant to the capability to do damage. But for that, a hit needs to be scored first.

I like to re-adress attention to what I'm after: an understanding of the probability to achieve hits. This is meant in a way that strictly belongs to weapon technology, not to weapon system technology. The latter would include aiming aids, and human factors such as pilot skills. I proposed to leave that out of the discussion, at least for now, so as not to complicate matters too much in round one.

In an effort to direct the thoughts, I would like to use the comparison with hunting ammo once more. If the target is stationary, and/or if it needs a lot of energy to bring it down, you choose ammo with a single high velocity projectile. If the target is a duck in flight, you choose ammo with submunitions, a 12 gauge cartridge loaded with a lot of size 5 to 7 pellets, that deliver a cloud of projectiles at a certain range. This cloud of pellets enables you to hit the duck, flying at about 70 km/h, at all. You would have virtually no chance to hit it with a single .22LR round, even if your marksman skills were exceptionally good. One .22LR round would definitely kill the duck, whilst one size 6 pellet would not. The .22LR round would probably fly through the duck's body, spending only a portion of its energy in that body, but that would be more than enough to bring down the duck. A size 6 pellet, at a shooting range of 40 meters, would penetrate only skin deep, not nearly enough to kill the duck. Three pellets however would bring down the duck, killing it instantly, as his nervous system cannot survive the sensory overload produced by their impact. Three pellets out of perhaps 150 fired with the shot, in a cloud of about 2 meters in diameter, a cloud with sufficient pellet density to score 3 hits at that max. range of 40 meters.

This max. range of 40 meters is the trade-off. The pellets have a very low weight; they go out at about 350 m/s, and they lose their speed very rapidly. If fired at a wooden door from a distance of one meter, the cloud of pellets is small and very dense, blowing a most impressive hole in that door. If fired at the same door from 50 meters, chances are that the pellets shall produce tiny dents in the woodwork, nothing more spectacular than that.

Surely a WW2 fighter aircraft is not comparable to a duck. But the analogy could be useful, to find out which aircraft armament can be considered as the more effective one for the envisaged job of bringing down adversaries, given the non-guided projectiles of that time, the gun sights that were marvels then, but very poor tools to those who are familiar with computers, and the likelyhood that most pilots were common people, meaning average marksmen.

The 12 gauge tool has a game hunting track record of centuries. Apparently it is most effective. It uses a very rudimentary sight only. It enables marksmen of average skills to score on a regular basis. Which WW2 fighter aircraft armament came nearest to a comparable achievement?

Regards,

Rob

P.s.:

1. This was written & send before I had a chance to read the preceding 3 posts. I used many more words to make the same point as Kurfürst did.

2. Harri demonstrates to be a close reader. Shall try to match that and state that we also agree that muzzle velocity is a factor when talking about aiming error. I'm not sure how important that factor is. That may change as we proceed.

Tony Williams
9th September 2008, 10:42
My attention has been drawn to this one ;)

The link near the start of the thread was to my co-author Emmanuel Gustin's site, not mine. This is my take on WW2 fighter firepower: http://www.quarry.nildram.co.uk/WW2guneffect.htm

As a result of my analyses, this is my view of the "ideal" WW2 fighter armament: http://www.quarry.nildram.co.uk/ideal.htm

There are also other articles on my site concerning aircraft gun armament.

As with all aspects of this, the question of hit probability is complex. High muzzle velocity is certainly a big help, especially against fighters. But there is no point in hitting with insufficient force to achieve much damage. In the Battle of Britain, Luftwaffe bombers sometimes returned to base with hundreds of .303 holes in them. And planes got tougher and harder to shoot down as the war went on.

It's worth considering the German and Russian experience. The Germans had two versions of the MG 151 from which to choose: the high-velocity 15mm and the medium-velocity 20mm. The 15mm would certainly have had a higher hit probability, but it was almost entirely dropped in favour of the 20mm which was far more destructive. The Russians similarly preferred the 20mm ShVAK over the faster-firing, higher-velocity 12.7mm UB.

Rob Philips
9th September 2008, 13:00
Hi Tony,

Thanks for this. I note that "hitting capability" or "hitting probability" is not defined in these articles, as a subject that is said to be too complicated to be dealt with within the scope of these articles, and that pilot skills are the most important factor in any definition of "hitting capability".

I also note your remarkable analysis of the ideal WW2 fighter aircraft armament, based on combinations of features of the best guns & ammo types available then, to which is added an expectation of a possible development of these during that period. Here too, "hitting capability" is not present in the equasions.

Do you consider it possible to design a passable definition of "hitting capability", if we leave pilot skills and aiming aids out of the equasion?

I'm sure that pilot skills are of prime importance here. But it seems passable to leave that out, at least for now, as it would apply to any other measures designed to increase hitting capability.

I believe that a consideration about hitting capability precedes considerations about power of armaments to inflict damage on target. Therefore excursions into the effectiveness of AP versus HE would not be needed at this stage.

If that would strike you as too theoretic, then allow for the use of HE, effectively meaning using 20mm, and then give a go at defining hitting capability.

The relevance of this would be to analyse technological ways that could have helped the average marksman to achieve better results. A historical exercize only, as hardly any of this would apply today.

Regards,

Rob

Rob Philips
9th September 2008, 13:20
In correction of earlier statements in this thread, so as to avoid confusion:

Synchronisation/synchronizing is timing the gun firing so that it can fire through the arc of a rotating propellor.

Harmonisation is adjustment of multiple guns in one aircraft, so that the arcs of fire meet at a certain point in space.

Rob

Tony Williams
9th September 2008, 13:23
There were three ways to improve the hit probability in WW2 (in no particular order):

1. Minimise the time of flight of the projectiles - achieved by a combination of a high muzzle velocity and a good ballistic coefficient of the projectiles. However, other things being equal, increasing the muzzle velocity involves reducing the rate of fire and increasing the weight of gun and ammo, so you can carry less.

2. Increase the rate at which projectiles are fired by increasing the number of guns or speeding up their rate of fire (N.B. The Luftwaffe preferred to fit 2x low-velocity 30mm MK 108 rather than 1x high-velocity 30mm MK 103 for the same weight, because the MK 108 combo put shells into the air at three times the rate). However, that requires a bigger ammo capacity and more weight again.

You will appeciate that Nos. 1 and 2 are in conflict with each other, within any reasonable weight limit. As with virtually everything else, the best solution is a compromise between conflicting factors.

3. Fit gyro sights - which made a huge difference to the hit probability of the average pilot with no weight penalty - brilliant!

A final comment: the hit probability is not the same as the kill probability. Within any given weight limit, an armament designed to maximise the hit probability is likely to have a reduced kill probability because it will be firing smaller and less destructive projectiles.

Juha
9th September 2008, 13:24
Hello Tony
thanks for the correct link. How embarrassing! I googled to Emmanuel’s site by typing “WWII Gun power” and seeing the book covers assumed that it was yours. I even looked vainly for analyze of ammo effectiveness which I remembered to be somewhere in your site but of course didn’t find it. Then I concluded that you have removed it. Really embarrassing.
But you cleared my mistake and so Rob got the info.

Juha

Harri Pihl
9th September 2008, 13:27
Harri demonstrates to be a close reader. Shall try to match that and state that we also agree that muzzle velocity is a factor when talking about aiming error. I'm not sure how important that factor is. That may change as we proceed.

I've tried to stay on my original point on relation between muzzle velocity and hitting probability. However, aiming error is another issue despite connected to the muzzle velocity due to easier aiming.

Things get very complicated when increasing number of factors are accounted; I have not even touch the factors like rate of fire, lenght of the burst and density of projectiles in the target area (dispersion in other words). I have seen probably similar analysis as mentioned by Peter Verney above; as example RAE did analysis on gun camera films (real combat footage from RAF, USAF and GAF and simulated attacks) and studied many factors like aim wander and error, lenght of the burst etc. were measured and analysed.

I think you have couple possibilities here. The easy way is to stay strictly on easily measurable factors like rate of fire, muzzle velocity and energy content and in the end you have probably very similar results as Tony got. The hard way is to try to understand how these more or less random factors like aim wander and error, dispersion, burst lenght etc. affect on different guns.

Harri Pihl
9th September 2008, 13:38
It's worth considering the German and Russian experience. The Germans had two versions of the MG 151 from which to choose: the high-velocity 15mm and the medium-velocity 20mm. The 15mm would certainly have had a higher hit probability, but it was almost entirely dropped in favour of the 20mm which was far more destructive. The Russians similarly preferred the 20mm ShVAK over the faster-firing, higher-velocity 12.7mm UB.

Well, on other side, it's worth considering USAF experience; after all the M53 is by far the most succesfull fighter weapon of the WWII.

There is obviously differences how the Air Forces saw the benefits of the guns. The MG 151 is a good example because USAF did seriously consider to use it (15mm version) while the Germans went towards larger calibers.

In the Russia 20mm ShVAK was older weapon and, at least according to Finnish experience, less problematic than the Berezin.

Rob Philips
9th September 2008, 15:57
Thanks, Harri. In his analysis Tony Williams included factors such as the benefits of mass production of a single weapon type rather than a multitude, and most of all the fact that the US considered their .50 to be, perhaps not the most efficient gun, but a combat proven and adequate one. Benefits of a different nature than can be expressed with gun & ammo technicalities only.

Regarding the complexities of a hitting capability definition: let's go the hard way, and see where we end. If the matter was easy, and with that most likely well known, then I would not have raised it. I agree that equasions with rate of fire, muzzle velocity and energy content shall lead to conclusions that were already nicely summarized by Tony. I do not agree with his proposed calculation of explosive energies, that rather simplifies the matter, but would agree that a more elaborate calculation would probably lead to the same or similar results in a table with comparative data.

In any case, I'm not finding pattern density, or dispersion, anywhere in these considerations. It strikes me that this could be a flaw, that is not present in the world of hunting shell ballistics. Note that "dispersion" has a negative ring to it, as in "deviation from the perfect line". That would be valid at the target practice range, but it might be a desirable feature in aerial combat.

I once witnessed so-called accidental automatic fire coming out of an AR 15 rifle. Obviously the interruptor was modified to produce automatic fire from this civil version of the M16. Three rounds, and all three in a group of 3 cm diameter at a 100 meter range, and on top of that all within the inner circle of the bullseye of the 100 m target. First class accuracy, that would however be pointless in actual combat, where one of these hits would have been quite enough to incapacitate the opponent. This splendid accuracy does not increase the chances of hitting, it merely wastes ammo at the same point of a basically motionless target. The pattern is too dense to make sense under these conditions.

In aerial combat things would be different, as the target is moving fast, in four dimensions. Multiple hits at the same spot with non-explosive rounds could accumulate the damage done. If not at the same spot, which is very unlikely anyway at regular firing ranges, then multiple hits close together could lead to a greater net effect than can be calculated as the sum of the effects of all hits. A wing spar may not yield after a hole has been shot into it. It may not yield after several holes. But it may yield if several holes are shot close together. This is another way of saying that, if we forget about explosives for the moment, pattern density is a factor that needs to be considered. And surely, as stated by Tony in his post of today, this makes sense only if the individual rounds can do damage at all.

Pattern density is presented here as a factor in damage infliction. It is also a factor in my key interest: hitting capability. Perhaps it would be better to speak of "pattern spread" here. The larger the pattern, the easier it is to score hits on a target of a given size on a given distance. The pattern cannot be enlarged beyond the point where the projectile density becomes too low to score hits, and/or to be effective in inflicting damage. There must be an optimum here. My question is: how can we define that optimum? Leaving out explosive rounds, then this optimum is likely to be a trade-off between number of rounds per second, their damage inflicting properties, and their dispersion in a plane vertical to the line of fire.

Regards,

Rob

Tony Williams
9th September 2008, 18:57
Well, on other side, it's worth considering USAF experience; after all the M53 is by far the most succesfull fighter weapon of the WWII.
Better known as the Browning .50 M2...it depends on how you measure success. Certainly US fighters armed with the .50 shot down lots of planes, but there are other factors involved than the quality of the gun: such as the superiority of the aircraft, the superiority of pilot training, superiority in numbers (later) and so on. And of course the fact that few planes carried anything other than the .50 meant it was bound to shoot down a lot of planes. What that doesn't tell you is whether or not they would have been even more successful if armed with a good cannon: personally, I think they would.

I have analysed the US reliance on the .50 here: http://www.quarry.nildram.co.uk/CannonMGs.htm

Tony Williams
9th September 2008, 19:11
I agree that equasions with rate of fire, muzzle velocity and energy content shall lead to conclusions that were already nicely summarized by Tony. I do not agree with his proposed calculation of explosive energies, that rather simplifies the matter, but would agree that a more elaborate calculation would probably lead to the same or similar results in a table with comparative data.
If you look at the final section of my armament effectiveness article, you will see that Henning Ruch suggested a more scientific calculation for chemical energy and the results are tabulated: but this made very little difference to the relative power scores, except to magnify the effectiveness of high-capacity HE shells.

In any case, I'm not finding pattern density, or dispersion, anywhere in these considerations. It strikes me that this could be a flaw, that is not present in the world of hunting shell ballistics. Note that "dispersion" has a negative ring to it, as in "deviation from the perfect line". That would be valid at the target practice range, but it might be a desirable feature in aerial combat.
Pattern density is partly a function of the harmonisation arrangements, but equally so a function of the combined rates of fire of the armament: which also affects the overall armament effectiveness scores in Table 3 of that article.

The harmonisation arrangements are also affectd by the destructiveness of each hit: the less powerful your ammo, the more important it is to concentrate its fire to achieve acceptable effectiveness. So the RAF had to reduce the harmonisation distance - in other words, tighten the pattern - for its 8x .303 fighters during the BoB, but considered increasing the dispersion of Hispano armament, because only a few hits were needed for a kill.

In aerial combat things would be different, as the target is moving fast, in four dimensions. Multiple hits at the same spot with non-explosive rounds could accumulate the damage done. If not at the same spot, which is very unlikely anyway at regular firing ranges, then multiple hits close together could lead to a greater net effect than can be calculated as the sum of the effects of all hits.
Multiple hits on the same spot are highly improbable, even with a high pattern density. All you have to do is look at camera gun film of ground attack strafing runs, where you can see (especially against naval craft) the shots scattered all around the craft or vehicle, due to the movement and vibration of the plane, aim wander, and the dispersion of each gun. Then add to that the fact the aircraft are moving far more quickly than naval craft or vehicles, and the chances of concentrated hits go down sharply.

There was only one way to ensure a close grouping of hits - and that was to get very, very close before opening fire. And by that I mean 50 metres or less. Not many pilots were capable of that.

Rob Philips
9th September 2008, 20:39
Thanks, Tony. I had read the statements from Henning Ruch. I believe that your suppositions made to make the matter manageable, underestimate the power that is delivered by explosives. However, as said, if these, or other, suppositions are applied consistently to all gun/ammo systems in a comparison, then results are likely to be comparable, and perhaps even quite similar. I cannot prove this as I cannot point to objective measurements of explosive force. The cavity size blasted in gelatin would be an objective measurement, if this would be a practicable technique.

"Pattern density is partly a function of the harmonisation arrangements, but equally so a function of the combined rates of fire of the armament."
Exactly. And added to that factors such as gun platform vibration under firing, delivering a dispersion that did not result from design, but that could nevertheless be used in a weapons system design. Density required shall be controlled by the projectiles employed, as in your .303 machine gun vs. 20mm cannon comparison. Now we are heading towards clarity about desirable pattern densities. This cannot be studied by looking at individual guns and/or ammo's. The entire aircraft with multiple gun and/or cannon and ammo needs to be considered as a system. Or ammo's, plural, if more than one type is to be deployed. The last is what you did, calculating for a repetitive 3 HE + 1 AP ammo arrangement in the belt.

Pattern density shall be maximal at the point where projectile trajectories converge. Before and after that the pattern shall be basically conical in the direction of projectile flight. Harmonisation seems to have been done according to this one-point-convergence strategy, that point being about 300 to 200 yards out, as the fashion of the day had it. Are you aware of other arrangements that may have been used? Meaning harmonisation to parallel trajectories, or perhaps to a circular pattern at the envisaged engagement range?

One other point that you raised in the articles. The presence of tracer is mentioned as undesirable, as it reduces space that could otherwise be filled with HE, and as tracer gave away the fact that somebody was shooting at you. On the other hand, wasn't tracer an excellent aid in deflection shooting, as the pilot could see where the rounds were going, enabling him to let the opponent fly into the pattern, or to chase the pattern into the opponent?

Regards,

Rob

PeterVerney
9th September 2008, 21:36
ISTR that harmonisation of our Mosquitos in 1952 was two guns at 350 yards and two at 250 yards. Giving an idealised firing range of 300 yards. Of course in practise, firing at drogues and at ground targets, there was only time for a quick squirt at about 350 yards with the range rapidly decreasing. Bear in mind that firing on the target was not permitted at less than 30 degrees angle off for fear of ricochets hitting the tug.
When we switched to the Meteor NF with wing mounted guns I think similar harmonisation applied. Incidentally I do remember an incident when a wing commander, eager to get a better score, closed to a lower angle off and bounced a shell clean into one of the tugs engines. Ball ammo of course, but made a horrible mess of the engine and as we only had one aircraft modded to tow a flag that put an end to the fun.
In any instance scores were not marvellous and it was not unknown for a pilot to score a blank while over 15% on air to air was considered reasonable and over 30 very good.

Rob Philips
9th September 2008, 22:10
Thanks, Peter, a most vivid picture of the difficulties encountered in practice. Two point harmonisation added to the list.

Regards,

Rob

Tony Williams
9th September 2008, 23:24
Two-point harmonisation was also used by some US fighters. I have a diagram of a P-47's harmonisation which is exactly the same as Peter described - 250 and 350 yards. I have also read that some pilots set each pair of .50s to converge at a different range. This meant that they never had really concentrated fire at any range, but moderate concentration at all ranges.

Tony Williams
9th September 2008, 23:27
One other point that you raised in the articles. The presence of tracer is mentioned as undesirable, as it reduces space that could otherwise be filled with HE, and as tracer gave away the fact that somebody was shooting at you. On the other hand, wasn't tracer an excellent aid in deflection shooting, as the pilot could see where the rounds were going, enabling him to let the opponent fly into the pattern, or to chase the pattern into the opponent?
The problem was that by the time the tracers reached the target and the pilot could see that they were missing, it could be too late to correct. From the point of view of scoring hits it would be best to aim well ahead of a turning target then let your nose fall away, delivering raking fire. However, if you started by firing ahead of your target its pilot could see the tracers and take violent avoiding action.

Harri Pihl
9th September 2008, 23:53
Better known as the Browning .50 M2...it depends on how you measure success. Certainly US fighters armed with the .50 shot down lots of planes, but there are other factors involved than the quality of the gun: such as the superiority of the aircraft, the superiority of pilot training, superiority in numbers (later) and so on. And of course the fact that few planes carried anything other than the .50 meant it was bound to shoot down a lot of planes. What that doesn't tell you is whether or not they would have been even more successful if armed with a good cannon: personally, I think they would.

I'm not arguing wether USAF swould have done better with something else than the M2. I merely replied to your point that the Germans and Russians went towards lower velocity, higher caliber weapons, my point being that the USAF stayed on higher velocity weapon, the M2, and even did consider another high velocity weapon, the 15mm MG 151, which was replaced by lower velocity weapon in Germany. In other words I'm saying that the air forces selected weapons with different standards and the USAF experience is just as relevant as German and Russian experience because the USAF results are undeniable (actually same can't be said about German results).

Infact I agree with you that the USAF might have done better by adopting a cannon like the Hispano or the MG 151. However, it's not the point discused here.

Rob Philips
10th September 2008, 00:54
Thanks, Tony. 3 and 4 point harmonisation added to the list too.

Assume an engagement range of 200 meters. Small caliber projectiles, Vo say 850 m/s, V200 say 650 m/s, Vaverage over that trajectory say 700 m/s, would take 200/700 = 0,29 second only to reach the target. Forgetting about a quantification of the violent evasive action capabilities of the target, and same for the attacker to follow that evasive action, and forgetting about a pattern fired so far forward that the pilot in the target had a reaction time in the >0,5 second area, then would your idea still hold? It would interest me to hear about this from those who have been up there. The point is, or could be, that small caliber rounds flying at such velocities cannot be seen. Neither by the attacker, nor by the pilot in the target aircraft. The flying noise would be such that they could not hear the projectiles in flight either. From my own experiments it follows that a small caliber projectile, meaning <10mm, can be seen, if you are focussed and if lighting conditions are good, only at speeds well below 200 m/s. Poor sample count in this experiment; I assume my eyes to be as sharp and as fast as the eyes of the average guy. This might be a bit different if there is a dense pattern flying around, I don't know. It seems that there is a clear benefit in this type of extremely fast four dimensional shooting, if you can see where the pattern is going. The fighter pilot is there to control the aircraft which is there to carry & aim the guns. It seems that a tracer path offers a more intuitive picture than any gun sight could do, in the days of unguided ammunitions.

Regards,

Rob

Harri Pihl
10th September 2008, 00:55
Regarding the complexities of a hitting capability definition: let's go the hard way, and see where we end. If the matter was easy, and with that most likely well known, then I would not have raised it.


Ok, harmonisation patterns, dispersion etc, are rather easy to calculate so I'll give you some references on aiming which, I believe, is a key factor on hitting probability. I dug up this kind of material from the PRO some time ago and some of these might be the same Peter Verney refered above:

AVIA 6/16177
This is RAE report on aiming simultor but it contain some flight tested data.

DSIR 23/15015
This comparison of various fighters as aiming platform.

AIR 20/12712
Aerial gunnery theory, lots of it...

AVIA 6/17286
Effects of aiming and harmonisation patterns in air to air gunnery.

AVIA 18/1626
Aiming characteristics of fighter aircraft

AIR 77/62
Review of the Aiming errors and firing tactics of Fighter aircraft. This report is particularly good because the sources include for example Luftwaffe gun camera data.

Rob Philips
10th September 2008, 01:09
Thanks, Harri, looks promising. How can I access this material?

Aiming surely is the key factor. No hits without aiming. But I'm looking for technological ways that could possibly make it easier for the average marksman to score hits. No doubt others have given this long and deep thoughts 7 decades ago. It is just that I'm missing something, in the material I have seen so far.

Regards,

Rob

Harri Pihl
10th September 2008, 01:26
http://www.nationalarchives.gov.uk/catalogue/default.asp?j=1

In practice you should go there, digital cameras are allowed... or order the copies (rather expensive).

Rob Philips
10th September 2008, 14:36
Thanks, Harri.

Does any of the forum visitors have any of the documents mentioned by Harri available, as that would be the fast way to obtain the information?

Regards,

Rob

Tony Williams
10th September 2008, 14:51
I'm not arguing wether USAF swould have done better with something else than the M2. I merely replied to your point that the Germans and Russians went towards lower velocity, higher caliber weapons, my point being that the USAF stayed on higher velocity weapon, the M2, and even did consider another high velocity weapon, the 15mm MG 151, which was replaced by lower velocity weapon in Germany. In other words I'm saying that the air forces selected weapons with different standards and the USAF experience is just as relevant as German and Russian experience because the USAF results are undeniable (actually same can't be said about German results).

Infact I agree with you that the USAF might have done better by adopting a cannon like the Hispano or the MG 151. However, it's not the point discused here.
To be precise, the M2 was a moderately high-velocity gun (the muzzle velocity was little more than the 20mm Hispano's) and they rejected an extremely high-velocity one (the T17 - the MG 151 copy - was chambered for the US 15.2x115 round, far more powerful than the MG 151's 15x96).

I suspect that there were two reasons why the US stayed with the .50: it was the only reliable aircraft gun they had, and it proved adequate as long as they fitted at least six of them. That is not exactly a ringing endorsement.

The following extract from a 1944 US evaluation may be of interest:

"As it is now, we have the 50-cal. gun which has reached its peak. The only improvements will be minor. The only good increase is to increase the number of guns. So it seems to be just about the right time to look for a better weapon. There are two possibilities here - the one we have and the one we might get shortly. The one we have is a 20-mm gun. I think very highly of it. In fact, it is one we have here, and it is one in hand. It won't do what the 60 will do, but we haven't got the 60, and we won't have it for a year. So, we are gradually working into all of our aircraft the 20-mm gun. To give you some idea of the 50 versus the 20 and dispel a lot of ideas that have bothered us, I would like to give you a comparison. When somebody goes from four 50's to two 20's, to the layman that means a decrease in fire power. Actually, quite the reverse is true. In the horsepower of the gun, one 20 is equal to three .50-calibers. In the actual rate of fire delivered at the target, one 20 equals three 50's; in kinetic energy at 500 yards, one 20 equals two and one half 50's.[N.B. This takes no account of the effect of the HE content of the 20mm shells]

That adds up to four 20's equaling twelve 50 calibers, judging by those standards. Of course you have other advantages of the 20. You have the much greater penetration of armor. The 20 will go through 3/4 inch of armor at 500 yards, while the .50 cal, will go through only .43. In addition to that you have one more great advantage - that is you can have longer and more frequent bursts without damage to the gun with the 20 than you can have from the .50 cal. That is important for the strafing airplane, because they are burning up their barrels and ruining their guns on one flight. Sometimes it is long before that one flight is over. They will come down with screaming barrels and get trigger happy, and then all the barrels are gone in one flight. It should not happen in a 20mm. Of course, you have disadvantages. You have a heavier installation, one-half as much ammunition for the same weight. Our standard ammunition in the Navy is 400 rounds in one gun. The Fleet has set up 30 seconds of fire as a minimum requirement for the .50 cal gun. We can't do that with the 20, so we give them 200 rounds. The 20 is lethal enough to get far more results out of that 200 rounds than the .50 ever will out of 400 rounds."

From: "USN Report of Joint Fighter Conference NAS Patuxent River". (October 1944)

PeterVerney
10th September 2008, 17:13
Fascinating stuff. Actually our pilots were taught deflection shooting on the Mosquito which had a fixed ring gun sight!.
The radius could be varied by setting the span of the target aircraft and so the range would be correct when the targets span filled the ring. With me so far; then pilots were taught to "lead off" by say "half a rad", or "one and a half rads", according to their judgement of angle off and closing speed.
If you have shot birds or game with a shotgun you will know what I mean. In fact we had a supply of shotguns, clay pigeons and ammo so that the pilots could practice. In addition we did many sorties of "cine", where aircraft flew in pairs and took turns to be fighter and target. High quarter attacks were the norm and cine taken when the pilot judged he was right. Then the films were assesed, frame by frame to judge how good the pilot was and he was criticised as required. I used to help our gunnery officer by doing some of this tedious work, in retrurn for a go on the clay pigeon shoots.
When we got the Meteor, with a gyro gunsight, of course things were much easier to assess, but as in all instances accurate flying was essential.
I must visit the NA again, I had no idea of all those references that's a goldmine. What I put down here is dredged from some recess of my antique brain.

Rob Philips
10th September 2008, 18:09
Thanks, Peter. Your brain is probably well filled rather than antique. Furthermore, that term also means "value increases with age".

The statement that clay pigeon shooting was one form of preparation for aerial combat, is very clarifying.

Regards,

Rob

Harri Pihl
10th September 2008, 23:54
To be precise, the M2 was a moderately high-velocity gun (the muzzle velocity was little more than the 20mm Hispano's) and they rejected an extremely high-velocity one (the T17 - the MG 151 copy - was chambered for the US 15.2x115 round, far more powerful than the MG 151's 15x96).

The point is that USAF did not go towards lower velocity weapons like the Germans; possible replacements of the M2 had about same or higher muzzle velocity.

I suspect that there were two reasons why the US stayed with the .50: it was the only reliable aircraft gun they had, and it proved adequate as long as they fitted at least six of them. That is not exactly a ringing endorsement.

My impression is that good combat results were the main reason why USAF (and NAVY) continued with the M2 despite obvious benefits of the possible replacements. Note that at spring 1944 the P-51B, with only four M2s, proved to be extremely succesfull despite the problems with gun feed etc. some pilots prefered it over the P-51D.


The following extract from a 1944 US evaluation may be of interest:"As it is now, we have the 50-cal. gun which has reached its peak. The only improvements will be minor. The only good increase is to increase the number of guns. So it seems to be just about the right time to look for a better weapon. There are two possibilities here - the one we have and the one we might get shortly. The one we have is a 20-mm gun. I think very highly of it. In fact, it is one we have here, and it is one in hand. It won't do what the 60 will do, but we haven't got the 60, and we won't have it for a year. So, we are gradually working into all of our aircraft the 20-mm gun. To give you some idea of the 50 versus the 20 and dispel a lot of ideas that have bothered us, I would like to give you a comparison. When somebody goes from four 50's to two 20's, to the layman that means a decrease in fire power. Actually, quite the reverse is true. In the horsepower of the gun, one 20 is equal to three .50-calibers. In the actual rate of fire delivered at the target, one 20 equals three 50's; in kinetic energy at 500 yards, one 20 equals two and one half 50's.[N.B. This takes no account of the effect of the HE content of the 20mm shells]

That adds up to four 20's equaling twelve 50 calibers, judging by those standards. Of course you have other advantages of the 20. You have the much greater penetration of armor. The 20 will go through 3/4 inch of armor at 500 yards, while the .50 cal, will go through only .43. In addition to that you have one more great advantage - that is you can have longer and more frequent bursts without damage to the gun with the 20 than you can have from the .50 cal. That is important for the strafing airplane, because they are burning up their barrels and ruining their guns on one flight. Sometimes it is long before that one flight is over. They will come down with screaming barrels and get trigger happy, and then all the barrels are gone in one flight. It should not happen in a 20mm. Of course, you have disadvantages. You have a heavier installation, one-half as much ammunition for the same weight. Our standard ammunition in the Navy is 400 rounds in one gun. The Fleet has set up 30 seconds of fire as a minimum requirement for the .50 cal gun. We can't do that with the 20, so we give them 200 rounds. The 20 is lethal enough to get far more results out of that 200 rounds than the .50 ever will out of 400 rounds."

From: "USN Report of Joint Fighter Conference NAS Patuxent River". (October 1944)


From hindsight we know that the 50-cal gun had not reached it's peak 1944; M3 entered service next year and offered about 50% increase in fire power. Infact there was allready a 1100rpm version of the original M2, twice the rate of the original MG53-2, in production three years before US entered war as you probably know. The design had some potential left, USAF was just slow to utilize it.

However, as noted above, I agree that the cannons had great advantages over the M2 but it's not the point of this discussion.

Harri Pihl
11th September 2008, 00:12
Does any of the forum visitors have any of the documents mentioned by Harri available, as that would be the fast way to obtain the information?


I have some pages which looked interesting photographed, not entire docs. I'll PM some samples sooner or later. As an example I can list some Radial sighting errors in dead astern attack. Source first, gun sight type, radial error in Mills:

WWII (RAF gun camera, flying bombs), fixed, 4.4-5.5
Squadron training exercise, fixed, 5.7
A&AEE trial with average pilots, gyro, 9.12
Fighter Command Trial with experienced pilots, fixed, 2.2
A&AEE trial with experienced pilot, gyro, 1.6

As you can see, there is quite a variation depending on pilot.

Juha
11th September 2008, 02:42
Rob
There at least has been Des Jägers Schiessfibel somewhere in net: It’s an official LW guide for aerial gunnery from 1944.

And in Fighting in the Air. The official combat technique instructions for British fighter pilots, 1916-1945. ISBN 0 85368 3921 there are:
some 90 pages long Notes on Air Gunnery and Air Fighting by WinCo E. M. Donaldson from 1943
some 20 pages long Bag the Hun! (estimation of range & angle off) from 1943.

Juha

Rob Philips
11th September 2008, 11:33
Thanks, Juha, first class. What I'm after is more likely in research notes than in pilot's instructions, but we'll know that once these works have been studied. Shall try to get them.

Regards,

Rob

Rob Philips
11th September 2008, 12:55
Have found in the web "Horrido! - Des Jägers Schiessfibel", ed. June 1944, German doc D. (Luft) 5001, approved by A. Galland.

The title translates as "The hunters shooting manual". "Horrido!" is a German hunters expression when greeting the other, or when calling all present to attention. This 36 page brochure is written in a P/O. Percy style used by the RAF, designed to explain complicated matters in the easiest possible way to many, using cartoons to make certain points stick. The matter has even been translated into a deck of cards, with which the basics are explained in an easy way, and with which you can gain money too! Call the General der Jagdflieger (Galland) to get the cards...

Hit probability is explained almost entirely as a function of pilot skills, so there is little answer here to the question I raised. However, the following remarks are noteworthy:

1. Page 7, shooting distance. It is explained that at a range of 600 meters perhaps one hit is scored. This changes to 4 hits at 300m, 9 at 200m, and 36 at 100m. This increase is not proportional but exponential, leading to only one conclusion: "Also ran!", meaning "go close!".
Obviously pattern density has been considered to come to this statement.

2. Page 14 shows drawings, that suggest that the pattern size was small for the Me.109, the main German fighter aircraft. There are no explanations or technical details given, but I assume that this is the results of the limited number of guns, their grouping close together, and the firing rate of the average model of Me.109. From this it follows that aiming has to be good; letting the attacked aircraft fly into the pattern is bound to fail. Trusting barrel wear and poor harmonisation to produce a wider, and more effective, pattern, is a bad idea. The pattern will be wider, but pattern density shall be reduced, leading to less effectiveness. For the same reason the following two advises are given:

A. Harmonisation should be as prescribed, and be checked on a regular basis. Tracer ammo can be used to check in flight, as opposed to on the firing range at base.

B. Harmonisation experiments are discouraged. Harmonizing the guns to longer ranges is called counterproductive. Reasons are not clearly stated; reference is made to results of the research work done by the specialists.

The ins and outs of the use of tracer ammo are mentioned too. Tony Williams mentioned that Allied pilots had objections against the use of tracer, as it would give away to the enemy that shots were being fired. In this German document the matter is seen in a different light:

A. Most aerial combat firing was done, not with too much, but with too little deflection. From that we can deduce that chances are much smaller that the attack is reported by tracer to the target pilot. In any case, the German document does not report this.

B. At longer ranges, tracer appears to represent curved projectile trajectories, that can be confusing. These curves do not result from projectile flight, but from the aircraft flying curves whilst firing bursts. Each projectile flies in a basically straight line, but the sum of these lines produced by firing in a curve is seen as a curve. It is advised to use the additional info given by tracer only on short ranges - both eyes open.


Therefore, hit probability is explained in this work mainly as a function of pilot skills, with reference to the armament characteristics of Germany's main fighter aircraft. Nevertheless, it offers some useful points when looking for ways that would increase hit probability, ways that would not be dependent on pilots skills.

"Fighting in the Air. The official combat technique instructions for British fighter pilots, 1916-1945" cannot be downloaded from the web. Shall order it.

Rob

Rob Philips
11th September 2008, 13:28
Have made an application in Excel, that calculates and graphically shows pattern density and size, as a function of
- number of guns
- their firing rates
- the distances between the guns
- the harmonisation type
- the harmonisation distance
- the distance to target
Leading to pattern densities and sizes per second of firing.

This is to be expanded with more harmonisation strategies, and all other parameters that are not related to pilot skill. This should enable to play with parameters, and see what comes up best under selected conditions. The ambition is to include ammo effectiveness parameters after that. Results, if any, shall be shared here. Right now I'm struggling with a silly "division by zero" error...

It strikes me that "harmonisation" (-zation?) is a subject that can do with some more thoughts. It is usually understood as meaning trajectories from multiple guns converging at a set point in space. We have already learnt that harmonisation to two or more points has been done. To this I shall add harmonisation to infinity, and negative harmonisation, meaning diverging trajectories. Furthermore, it seems that harmonisation is usually considered in a single surface, parallel to the trajectories of guns that are basically located in one plane (meaning surface here, not aircraft). It seems that this x-distance notion of harmonisation leaves out an y-spread notion that is important too. This already gives one preliminary conclusion: more guns enable better harmonisation in the y-axis than fewer guns can do. Shall explain with drawings later.

Rob

Stewart
6th October 2008, 22:39
You have posted an interesting article. There are how ever some glairing mistakes.

Sycronisation was the act of fixing the weapon to fire in between the spinning propellor blades with out hitting them. The term that you need is "Harmonisation" or Zeroing. This is probably the single largest factor in dertemining the effectiveness of any planes weapons system.

Many pilots tried many systems for this and three general trends emerged based on the type of fit in the plane.

1. Widely spaced wing guns, like in the early model Spitfires were the worst possable solution to the problem. This lead to pointing all of the guns at either one point in space ahead of the fighter at some range that coincided with the phylosiphy in force. This varied between 200-250 Yards, with some very few exceptions as close as 150 or as far as 400 Yards. This was not very successfull because at other ranges, even perfectly aimed shots would, because of the range they were "Hamonised" at be absolutely guaranteed to miss at other ranges!

This lead to the idea of pointing each of the four pairs of guns at a slightly different range, so that at least some of the bullets would hit if the piper covered the target. This was also a failure because it did not consentrate the fire enough, to cause significant damage durring the very short time that the target was passing threw the leathal point of aim.

The other type of wing mounted gun system was to cluster all of the guns in each wing into a small group and then point the entire group at the Harmonisation range. This was done in the Hurricane and all most all American Fighters. This was universaly aknowledged to be the far supirior solution for wing mounter guns. But this suffered from the same faults as the Spit's fit above, but to a lessor but still unsatisfactory degree.

The Russians, American P-38/39 and to a very much larger degree the Germans TENDED to mount all the guns in or very close to the nose, which tended to put ALL the bullets/shells into the same stream regardless of range. This was found to be many times more effective than any type of wing mounted guns, with planes like the P-38s, later Me-109s and the D model 190 found to be particularly devistating in this regard.

The second factor of grate import was the single gun's dispersion and this had two causes;
1. The basic design of the weapon, recoild opperated guns have more dispersion than gas opperated guns.
2. The strength of the mounting system in wing guns. Some planes had very flimsy structures like the Spitfire which caused very large dispersions beyond what is normal for the gun. IE, 100-110Cm at 100 yards, Vs 50-60Cm at 600 yards in other planes with stronger wings like the P-47 and -51.

3. This was much less of a problem for planes with the guns mounted in clusters or attached to very solid parts of the basic structure like wing roots or engine mounts.

Then there is rate of fire. Because of the inhearant difficulty in pointing the figher plane at any target, even those stationary on the ground or flying in formation WO maneuvering, the rate of fire must be as high as possable. Given a projectile of certain minimum energy dencity required to provide a minimum level of damage to the average un-armored target plane, it matters very little wether it is .30 or .50 caliber. Having said that, balistics comes into play, where the typicle ~.30 caliber slug has that much energy at 300-400 Meters and the typicle .50 caliber will do more damage at 2000M. Cannon shells will meet that minimum level of damage at any range at which they will still reliably detonate. So regardless of caliber, IF the range is short enough, the more bullets the better.

To find out the effective relationship between any two weapons systems, simply square the ratio between their rates of fire. IE, a plane that fires twice as many bullets as another will be four times as effective, ALL OTHER THINGS BEING EQUIL!

That brings up the issue of armor plating protecting vital parts of the plane. This rases the damage level high enough that ~.30 caliber weapons are no longer effective. Armor also greatly reduces the effect of cannon shells which explode on or just after perforating the air craft's skin and fail to damage vital items protected by even the thinest armor. Again having said all that, there was no armor fitted to any plane which could provide protection from .50 caliber fire at common combat ranges!

Lastly, In some of your formula, you mentioned that energy was the product of velocity and weight, or mass of the projectile. This is not strictly true. Energy is the product of 1/2 of the mass and the velocity squared! This is vitaly import because velocity has two extreamly important effects on weapon effectiveness!

1. First is the stated effect on the energy available to damage the target plane.

2. Vastly more important is velocity's effect on the shooter's ability to hit the target!
The higher the MV the easier it is to hit a moving target!

Studies AND extencive testing back in the ~70s by the USAF concluded that the combination of MV and BC was so important that they spent dozzens of millions of dollars developing EACH of half a dozzen different gun weapon systems! 25MM Caseless, 25MM telescoped cased, 25MM liquide propellant, 20MM super velocity ammo for the standar Vulcan gun, which lead to the long barreled gun in the F/A-22 and both of the Mauser BK-27 and ADEN-25 guns when that data was shaired with our friends!

There are other factors, which have been found to be of marginal importance to modern gunnery, but they are not really realivant to WW-II because they are so far over shadowed by other factors.

Hope this helps. Sincerely, Stewart.

Stewart
7th October 2008, 03:37
The reason that small increses in MV/BC are so much more effective is not because of the differances between target and projectile velocities as you surmise, but because you required less lead on a target apearantly moving accross the line of fire.

The USAF made many studdies and determined that the third power of the differance between any two MVs would show the differance in probability to hit. In WW-II the Germans determined that the square of the differances in MV was equal to the differance in hit probability. The Ruskis came to much the same conclusions, but then determined that weight of shell Vs the heavy American Bombers was more inportant as they were very easy to hit. later guns had much higher MV/BCs!

Stewart
7th October 2008, 04:06
The example is the Hispano Suiza 20mm cannon, widely used in fighter aircraft in WW2. The cartridge is 110mm long, rimless. A HE (High Explosive) projectile weighs 130 grams, and carries 6 grams of TNT. A solid non-explosive projectile weighs 150 grams. Both are fired at a muzzle velocity of 850 m/s.( Should be 840M/S!) TNT has a detonation speed of 7.000 m/s.

Kinetic energy (Joules) = 0,5 x projectile weight (kg) x the square of the muzzle velocity (m/s)

The muzzle energy of the non-explosive round is calculated as follows:
0,5 x 0,150 x 850 x 850 = 54.188 Joules, or 54 kiloJoulesShould be = 52.92Kj.

The muzzle energy of an exploding round is calculated as follows:
0,5 x 0,124 x 7.000 x 7.000 = 3.038 kJ Should be = 840X840X130/2000 = 45.864Kj. Then the explosive content should be found by multipliing the energy yeald per gram, times the number of grams. The yeald of Grade one TNT is 4,185J/Gram or 25.11Kj for a total of 70.974 Kj or on the surface appierance 34.1% increase in energy effectivness! But this is false. The solid AP projectiles will drill right threw the target plane and unless it hits some very strong massive part will waist most of their energy on the air on the far side of the target.

This is important now, but not back in WW-II because the planes of that time had numerious single point failures which would down the plane and were vulnerable to plain bullets. Then the effect of bursting munitions is widely over stated as it relates to WW-II planes!

To this should be added the kinetic energy of the round directly prior to explosion:
0,5 x 0,130 x 850 x 850 = 47 kJ
Total = 3.085 kJ

Meaning that the explosive round has 3.085/54 = 57 times the energy of the non-explosive round.Massive failure of the math proccesses!

Stewart
7th October 2008, 04:24
However, with automatic guns, such as aircraft cannons, a round fired earlier, ie. in case of higher cyclic rate during a given time frame will reach the target earlier, than in a case of a higher velocity round fired at a slower cyclic rate. For practical applications, careful aiming and application of proper lead is less attractive than just let the target 'walked into' a sufficiently dense line of firepower applied - ie. point and shoot. Its a fail-proof method. No, it is not! actively "Dragging" the bullet stream accross the target is much better than waiting for the target to fly threw. The neccessary ingreadient is that the shorter the ToF, the more likely you are to be able to score hits!

There is a reason for using shotguns for hunting small game and birds with a high number of slow pellets instead of .223 bolt action rifles with 1200-1300 m/sec. This argument is faseeshious on it's face! There are numerious reasons why it is not true!

Stewart
7th October 2008, 04:47
Infact I agree with you that the USAF might have done better by adopting a cannon like the Hispano or the MG 151. However, it's not the point discused here. I dispute this idea! That the USAF shot down many more Axis planes than any of, or possably all of the other Allied powers is not open to dispute! Given that the allies planes all had about the same performance Vs their Axis opponents, yet scored so much better, both in absolute numbers and as a ratio of the number of missions representing opportunity.
That the Germans chose to use guns not well suited to shooting fighter planes, but which were much better at bombers is a politicle desision.

George Hopp
7th October 2008, 04:49
2. Increase the rate at which projectiles are fired by increasing the number of guns or speeding up their rate of fire (N.B. The Luftwaffe preferred to fit 2x low-velocity 30mm MK 108 rather than 1x high-velocity 30mm MK 103 for the same weight, because the MK 108 combo put shells into the air at three times the rate). However, that requires a bigger ammo capacity and more weight again.

The Germans at Tarnewitz compared the two weapons in a report dated 7.9.43. They concluded several things:

1. For the weapon + mounting + accessories + ammunition for 20 sec. firing, the MK 103 weighed 259kg (taking a volume of .29m cubed space) and the MK 108, 214kg (volume, .10m cubed space).

2. They noted that that between 400m and 1000m,
with an attack from directly behind the MK 108 would score more hits.
with an attack at 15 degrees deflection, both cannon would score the same number of hits.
with an attack at 60 degrees deflection, the MK 103 would score more hits.
But, if two MK 108s were installed, weighing 428kg and taking up .20m cubed space, vs. the MK 103's 259kg and .29 m cubed space, the twin MK 108 armament would be more powerful than that of the single MK 103 under all circumstances.

3. While the MK 103 had a greater vo: 900m/s vs the MK 108's 525 m/s; it also had a far lower firing rate: 380/min vs. the MK 108's 680/min.

All the above data is from the report.