Hit Probability, Rate of Fire Muzzle Velocity

The statement :

"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 EQUAL!"

Is an excerpt from a Shaw's analysis about gun effectiveness.

This is why my personal feeling on the subject is to actually try to understand what is the basis of such statement. IMHO if Shaw is telling us that the effectiveness is not simply proportional to the ROF, but is more than proportional, then I believe a good reason is hidden somewhere and an effort to discover it is well worth. If unable to get a direct explanation by ourself, then maybe a document from some airforce or from another reliable source could help a lot. This is why I renew my call for such contributions.

Turning to MV, all things pointed out by Shortround6 are "dead right". The quantitative finding "The US figured that an increase in velocity of 50% would increase the hit rate by 3 times" is an example of what we are looking for, provided an explanation is provided. So my question for Shortround6 is: Could you be so kind to give us references for it?

Before closing this post, just another point: do we all agree that a well concentrated burst is better than a "sparse one" or opinion on this point diverge?

Again, thanks for any contribution

Dealing with the effect of the MV on HP, I'd the opportunity to read a 2008 thread where Rob Philips wrote about an invention by a Czeck named Janececk. Here are the important things:

"…….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……. 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……."

A reference to a document related to the invention is made. Is there someone having such document and willing to share it here?

Again
Thanks in advance

I have been reading with great interest all the information presented here. However, something seems missing-forgive me if it's there and I missed it;
When comparing the armament of the ME-262 and say a F4U-1, I have not seen a discussion of available ammunition. The 2 installations are about the same weight, but i think the F4U may have an advantage; the F4U carries about 30-40 seconds of ammunition, while the ME-262 carries enough to fire only about 6-10 seconds. The F4U pilot can hold his trigger finger down a little longer, giving him a much larger hit "window". Just a thought.
I would choose the armament set up best suited to the assignment; attacking fighters, F4U. Attacking bombers, ME-262. That is what each was designed to do.
Thanks

ME-262 90 and 120 round so 380 RPM/ ~ 14 and 19 seconds. But with their fuel at the most they had 3-4 passes at a bomber column so it was enough.

F4U never fought bomber columns so its moot.

I am certainly no expert on Aircraft guns, but a couple experts have had this kind of discussion already.
Emmanuel Gustin's Home Page
CANNON, MACHINE GUNS AND AMMUNITION

I believe the most important aspect of aerial hit probability was mentioned once but not emphasized:
Gun harmonization.

Keep in mind that machine guns are not known for grouping ability or "accuracy" as riflemen might describe it.
A rifle may shoot a 2 inch group at 100 yards. A typical machine gun in the same caliber would do well to shoot a 8 inch or 1 foot group at the same distance. Basically they don't shoot groups; they shoot patterns. It would be nice if the pattern from each gun actually lined up on the target aircraft. Unless they are located at the same place, the patterns will only line up at a single distance.

When you harmonize all the guns on a fighter, it matters where they are mounted. All centerline or cowl mounted is the best. The angular dispersion is very low. Next best is a setup like the P-47 or Hawker Hurricane where all the guns are grouped in each wing. Each group has all of the guns firing pretty much parallel. The worst is an arrangement like on the Spitfire Mk.I where the guns are separated along the leading edge. There will only be ONE distance where the guns are concentrated.

Regarding a couple topics already mentioned, the 30 mm MK108 was quite a deadly weapon against bombers as well as fighters. The German statistics showed that it took an average of only THREE hits to kill a heavy bomber and only ONE hit to kill a fighter. If you look for photographs of survivors of a MK108 hit, you generally find holes that are about three feet in diameter. There aren't many places you can mangle a three foot sphere of aircraft structure on a fighter without it being fatal.

Regarding jams, Just about all the belt fed guns had serious jams. The P-51B/C models were known for them which is why they changed the wing structure for the P-51D. The German 20 mm Gondola weapons were also known for jams as described in the book "Messerschmitt, Aircraft Designer" published by Schiffer.

Yet another subject not covered here is the amount of firing rate that is lost on a synchronized installation. The Browning designs apparently were quite poor in this kind of installation. This is covered fairly well in a discussion of cowl armament on the Ki-43 at the site. I don't know if the discussion is accurate, but it is worth reading anyway.

Nakajima Ki-43

Hope this adds to the discussion.
- Ivan.

Dear All,
Hit Probability (HP) is undoubtely related to the many other factors you have added along this thread, but, since my first post here on this subject, no theoretical evidence about the "more than proportional" quantitative link between HP and Muzzle velocity (MV) and Rate of Fire (ROF) appeared, in spite of some statements contained into WWII Luftwaffe, Russian or USAAF reports or written by historical gurus. Moreover, the quantitative statements don't state always the same things. Factors like distance, gun number layout, fire dispersion and harmonization can influence the quantitative result but the answer to the question why the only "constant" refrain" is: "more than proportional", is still missing. Are those reports/statements wrong? Frankly speaking I don't think so, even if I'm still unable to see what we are missing here.
Again, imagine just one gun. If we put it in the same position on the same aircraft, firing against the same flying target and we change the MV only or the ROF only why the HP changes should be more than proportionally related to MV or ROF changes?
Again, thanks for your present and future contributions.

The BIG problem with the slow 30mm has getting the 3 hits. When the ME262 was flying at 500 MPH and maneuvering to get a shot the rounds came off like rainbows (that is a quote from a German pilot somewhere). The Germans did not have the chrome and nickel to make the high pressure high velocity 30mm version in numbers.
Also quoted from Rall is the FW-190 had the 2x13mm and 2x20mm near centerline so they could shoot from any distance and have a concentration of firepower.

Bruno HP is affected greatly by dispersion. You can look it up but major influences are angle of attack (from target), wind, round flight characteristics (they do not all fly the same), barrel wear and length, muzzle velocity, sighting mechanism, (lead predictor or open sight), G force on plane (gun) at firing and many more. Hence both tracer fire and lead predicting guns sights help the pilot quite a bit from the reports I have seen.
One report I saw said the last German gunsight (Revi?) gave a 30% higher hit probability and was gyro stabilized to give lead.

zjtins said:

The BIG problem with the slow 30mm has getting the 3 hits. When the ME262 was flying at 500 MPH and maneuvering to get a shot the rounds came off like rainbows (that is a quote from a German pilot somewhere). The Germans did not have the chrome and nickel to make the high pressure high velocity 30mm version in numbers.
Also quoted from Rall is the FW-190 had the 2x13mm and 2x20mm near centerline so they could shoot from any distance and have a concentration of firepower.

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Would really like to see the quotes.

The Germans have had produced two automatic cannons preceding the MK-108, that were of 'high pressure, high velocity' kind - the MK-101 and MK-103. Mostly used against tanks. True that Germany was not awash with crome and nickel, seems that metals were not crucial for autocannons.

The MK-108 was maybe of slow muzzle velocity, but the RoF was comparable with Hispano cannon. The quartet of cannons in the Me-262 makes up a lot for the low MV, and that cannon was being installed in almost all German fighters as the war was drawing to the end. The MK-108 was vastly better than MG-FF or similar Japanese cannon, yet those cannons, in wing installations (= far away from ideal position) have brought down a lot of Allied planes, fighters included.

Dear zjtins,
I totally agree about the paramount importance of dispersion. This is one of the major reasons why firing at close distance is fundamental. But, that said, are you suggesting that MV and ROF have an influence on the amount of dispersion?

ROF a little depends on gun mounting. If it s not ridge or a harmonic builds, that could affect dispersion.

MV yes, cross wind, G force (not a straight shot but pulling G as you shoot), delta MV (round to round MV is different depending upon quality control), are a few factors that tie into MV and dispersion.

The Gunther Rall comments were from the history channel program and can be found on Youtube.

Actually the Mk-108 brought down relatively few aircraft. I will try to find some data on that. I remember seeing some old post WWII info and analysis of what guns brought down what aircraft and the MK-108 was near the bottom.

Remember the post about the Germans believing it took 3x30mm rounds to bring down a B-17 and it took 26x20MM rounds to do the same. Problem was fast aircraft and slow RoF made it difficult to get three rounds on target PLUS the MV of the 108 was so low the shot was like a rainbow... difficult to lead and get a hit.

ROF not really, MV yes, slower equals more time for other factors to influence the flight, wind speed (gusting too), deflection angle, round quality to name a few.

@zjtins: Thus you suggest: the higher ROF the Higher the dispersion and the higher the MV the lower the dispersion. Did I get it right?

ROF has no real affect. MV does, lower MV = higher dispersion

zjtins said:

Actually the Mk-108 brought down relatively few aircraft. I will try to find some data on that. I remember seeing some old post WWII info and analysis of what guns brought down what aircraft and the MK-108 was near the bottom.

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I'd love to see your evidence for this, given that the MK 108 was the standard weapon against heavy bombers, and the Allies lost around 14,000 heavy bombers and another 4,400 light and medium bombers over the course of the war against Germany and Italy.

I wonder how even the Germans could know exactly which weapon was responsible for a aircraft coming down.
They'd know if it was flak or fighers usually. But several fighters had mixed armament, and i'm sure the pilots attacking would use them all.
So unless it was like the Me262, with all Mk-108s, how would they know which weapon brought a aircraft down ?

The ME-190 and FW-190 both had field kits (those R-x numbers) with 2xMk108 in wings available. Problem is getting numbers. There were so many configuration that the German rationalized the ME-109 build to ME109 K standard but those were relatively few, late, not much fuel and mostly poorly trained pilots. Somewhere in the late 1944 time frame I believe.

I'd love to see your evidence for this, given that the MK 108 was the standard weapon against heavy bombers, and the Allies lost around 14,000 heavy bombers and another 4,400 light and medium bombers over the course of the war against Germany and Italy.

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Since you have loss data show it.


Jabberwokcy,not sure what planet your are one

from:8th Air Force Combat Losses in World War II ETO Against the AXIS Powers
Other losses occurred too. Collisions, training accidents and so on. The table below summarizes all losses in the ETO during the war:

Aircraft Type Number Lost
B-17 4,754
B-24 2,112
P-47 1,043
P-38 451
P-51 2,201
Total 10,561

zjtins said:

Jabberwokcy,not sure what planet your are one

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Don't let this discussion turn sour.