Hi Karnak,
thanks for the correction, i dont had a other source.
HoHun,
"All my nice formulae can be used quite nicely to estimate relative effectiveness of the guns because the unknown factor hit probability is eliminated as soon as we calculate an effectiveness ratio"
Whats about this?
ROF(MG) = 13rps
ROF(Ca) = 10rps
Tf = 2sec
Ph = 2%
Nh(2*MG) = 2 x 13r/sec * 2sec + 2% = 1,04
Nh(2*Ca) = 2 x 10r/sec * 2sec + 2% = 0,8
With other words: in this example the 2 x MG´s got at least a hit, while the cannons tend to fail.
If we now compare the armaments:
Nh(2*MG) = 6 x 13r/sec * 2sec + 2% = 3,04
Nh(2*Ca) = 4 x 10r/sec * 2sec + 2% = 1,6
With other words a average pilot have a double high hitprobability with the .50cal´s armament, while attacking a strait flying big target!
The interesting point is: While attacking a smal or unprotected target, the 3 hits of the .50cal provide a high probability to hit a vital or overkill area, the 1-2 hits of the 20mm also may bring the plane down or not.
If the estimation is right that it need around 4 x 20mm hits to bring down a fighter, the 4 x 20mm armarment need a 5 sec burst.
In this time the 6 x .50cal armament already did hit 8 times, what also provide a good probability to hit a vital or overkill area(fuel tank, pilot, engine, radiator).
All damage power estimations need to depents to the target, same like on the bullet/gun.
The hitprobability get influenced by even more.
If we assume a hitprobability of 30%(maybe a ace on close distance).
4 x HispanoII provide 40 hits = Absolutly overkill(vs fighters) = not needed
6 x .50cal provide 78 hits = Deadly = same result like with the 20mm´s.
In the case of an unprotected plane without selfsealing tanks ALL used guns in WWII was relative easy able to bring down the plane with one bullet.
Therefor the big advantage of the 20mm´s regarding structural damages get minimized, in relation to a tough good protected plane with selfsealing tanks.
As result the hitprobability and killprobability are not linear with all targets and also not with the distance.
The importance of the hitprobability increase even more, if we consider that while a escort flight or while helping a wingi its more important to be able to 'ring the bell', than to knock the door off.
And we always need to keep in mind that MG armned planes tend to carry more amo(longer time to shoot), what enhance the hitprobability(armament + amo) even more.
"If we want to see if the USA made a good decision when they decided to use the 12.7 mm machine gun, we need to compare the armament they had to the armament they could have had if they had made a different decision."
They made the different decission and what i compare are the different armaments they did use for the same plane. As Karmak did point out, my source regarding the F4U-1C amoload was wrong, so the time to shoot increase to around 22 sec, what is still good below that of the .50cal´s.
"Come on, the Spitfire simply carried 2 x 20 mm because of performance concerns. The so-called "ground attackers" Hurricane and Typhoon were indeed purpose-built fighters relegated to ground attack duties because of insufficient performance. In the Far East where no Spitfires were available at first, they occasionally pulled one pair of Hispanos from the Hurricane in a similar manner"
Yes, but why they pulled two hispannos and used MG´s instead, if the Hispano did provide a higher kill probability? They could have used a higher amoload for the remaining hispanos.
Actually i think you be in a trap of pseudo logic. Math dont help much if we have to many unknown values. In our case math is only good to style a statistic. Show me a statistic and i show you how to style it to my need!!
In this case math get reduced to a same unexact speach like english and german, so why not staying in out speack, where we dont need to learn new therms?
If i talk to someone who dont know my laguage, but i know his language, i tend to use the language we both know. You seems to be aware of my missing knowledge regarding the currently common therms at school, nevertheless even dont try to think in 'normal' therms, you simply expect that i learn this new language, just while a discussion.
Or do you forgot the language of the 'normal' people?
Only cause someone dont know your language, it dont mean he dont know what he talk about!!
Anyway, probabilitys in a complex system cant get calculated exact without many datas based on former made experiences.
You try to calculate a killprobability, without to consider the hitprobability, without to consider the real used amoloads, without to consider the damagepower probability (we dont have a static damagepower, it depents much to the structural toughness, size and protection of vital areas of the target).
You do what many people do who did study, you take a statistic and count it as static fact, without to take the possibility into account that every statistic is more a approach than a fact. Every little mistake in such a statistic lead to bad mistakes while calculating with such values.
Thats why i avoid to use math in such cases, as long as i dont have exact datas for every single situation.
Statistics are only good as base for a good estimation, but to be able to use it you need to know the exact circumstances where the values comes from.
Tony Williams statistic is a very good work, but do you realy seems to think a Hispano II round always had damagepower of 201, while the .50cal always had a damagepower of 46.
You dont seems to consider that a .50cal was able to generate a overkill shot in the same way like a 20mm.
How likely this is depents to the "overkill area/target area relation". As more overkill area a plane have, as higher the probability to hit this area.
If there would be a plane with 100% overkill area for a MG, no cannons would be needed at all, cause every hit would lead to a failsure.
I assume that fighters had a much higher "overkill area/target area relation" than a Bomber. This relation is much different if we compare planes with and without selfsealing tanks.
(overkill area = area on a plane where one hit is able to cause damages to bring down the plane)
As higher the "overkill area/ target area relation" as more important get the hitprobability over the damagepower.
Of course the gun and the target determine which area is a overkill area.
Probably the overkill area will be more big for a 20mm than for a .50cal.
Additionanlly we need to consider 'vital areas', where some hit cause damages to bring the plane down.
For a 20mm probably on a fighter the whole plane is a vital area, while some bombers can absorb even a 20mm on big areas without to suffer much.
Thats the reason why 30mm´s was better vs Bombers, the gun alone did increase the vital area much.
"Well, the Germans had a lot more combat experience and went to cannon against all types of targets as quickly as possible. The British also had two years of a headstart in combat experience and got rid of their machine guns as quickly as possible, too."
Not all was happy with the MGFF and its poor rof and MuzzVel, even more wasnt happy with the single cannon in the nose, compared to the 2 x MGFF.
Maybe if the MG131 would have been available in 1937, the 109E would have carried four of this guns instead of cannons?
Maybe the Me109E would have been better able to protect the bombers with 4 x MG131 instead of the 2 x MGFF? We dont know this.
German fighters switched from smal MG´s to big MG´s in the nose, not to a 'only cannon setup' (only some planes, supposed to fight bombers, had only cannons).
Germany had to fight tough bombers with selfsealing tanks from the beginning of war!!
Afaik, the brits dont was unhappy with their 8 x .30cal vs Fighters, they was unhappy with this armament vs Bombers mainly.
Though later , with more plating the .30cal got to be a real problem. Thats probably why they did introduce the .50cal in 1944 to the Spits.
The brits had mainly the .30cal and Hitpano II, so of course they did switch to the 20mm, cause the .30 cal wasnt strong enough to penetrate the common amor in the needed way. The USA had the .30cal, .50cal and their 20mm.
They switched to the .50cal and the results in war show that they got pretty good results, even at times when the enemy still was strong in numbers and high in pilot skill(pacific mainly).
As i wrote before: Iam sure that they would have switched to 20mm´s if they would have had B17´s(or Wellingtons, Mosquitos, Lancasters, Ju88´s, IL-2´s) as oponent.
If you read how suprising fast US fighters, also with only 4 x .50cal, was able to destroy Japanese fighters and bombers, i realy dont see the need to carry 20mm´s for the price of around 30% time to shoot.
Greetings, Knegel
