Author Topic: Aircraft gun article  (Read 7849 times)

Offline gripen

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Aircraft gun article
« Reply #30 on: March 24, 2006, 04:18:36 PM »
Tony,
It does not matter how the guns are located or harmonized; if we assume that all other parameters are constant except the ROF and the guns are used as burst type weapons (short aimed bursts), then the higher ROF will give more hits and also higher probability of the hits regardless the source(s) of the uncertainty (harmonization, dispersion, aiming error and/or what ever).

gripen

Offline Knegel

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« Reply #31 on: March 24, 2006, 04:37:54 PM »
Hi,

Hohun,

Nf = number of rounds fired
Nh = number of hits
Ph = hit probability

Ph = Nf / Nh

I dont know where you got this formula from, but NF / NH is = hitquote, not hitprobability.

A probability never is exact!!

It depends on many factors, like Pilot skill, dispersion, middle bullet velocity, distance to target, size of target, speed of the gun in relation to the target, attacking angle etc etc.

Many of this factors influence each other, even the weather(turbulences) is a factor.

The rate of fire increase the hitprobability as more the dispersion increase (longer range, turbulences, nervouse pilot, unstable plane at slowspeed etc) and as faster the target move while shooting with big deflection.

Compare the extreme to see the influence of the rof to the hitprobability.

Take the M4 37mm with 2,5 rps(900m/s Muzzvel) and a MG151/15 with 12rps (i often saw 15 rps, also around 900m/s).

You realy think the hitprobability of the slow firing gun while a turnfight was same high like with the MG151/15??

If yes, i wonder why you think the militair did introduce MG´s at all??

Of course a muzzle loader rifle( 1 shot) have the same hitprobability like a MG42,  if the target is a elephant in 5m distance, but what if there is a kangaroo running/jumping around like mad in 100m distance??



Tony,

"If the guns are mounted in the nose, or are otherwise harmonised to group tightly at a particular distance, then it doesn't matter what the rate of fire is, if you're off-target all of your shots will miss."

Most WWII aimpoints was around the target most of the time, the pilot shot, failed in most cases and adjusted the aim by watching the tracers. Since a plane dont always react always nice to this adjustings the aim often was only for some milli sec on the target, specialy if the attacked one started to evade.  Probably thats the reason why many planes only got some hits and 'smal' damages.
As higher the rof, as higher the hitprobability while this short moments on target is.

I also think wingmounted guns suffer more by a smaler rof, but even nosemounted guns can show a big pilot/plane related dispersion.

Greetings, Knegel

Offline HoHun

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Aircraft gun article
« Reply #32 on: March 24, 2006, 06:31:12 PM »
Hi Knegel,

>I dont know where you got this formula from, but NF / NH is = hitquote, not hitprobability.

It is the expectancy value of the hit probability and equivalent to the hit probability for sufficiently large values of Nf.

>The rate of fire increase the hitprobability as more the dispersion increase (longer range, turbulences, nervouse pilot, unstable plane at slowspeed etc) and as faster the target move while shooting with big deflection.

The rate of fire increases the number of rounds fired and the number of hits, but not the hit probability.

The only increase you get is the probability of scoring AT LEAST n hits, which is something completely different than the hit probability.

And is quite obvious that the kangaroo vs. elephant question depends on the lethality of the round you are using. Assume you've got two almost identical guns, just that one has five times the rate of fire and the other has five times the lethality per round:

Pkill1 = Pkill0
Pkill2 = 5 * Pkill0
ROF1 = 5 * ROF0
ROF2 = ROF0
Ph = const

Ptrophy1 = Pkill1 * ROF1 * Ph
Ptrophy2 = Pkill2 * ROF2 * Ph

Ptrophy1/Ptrophy2 = Pkill0/(5*Pkill0) * 5*ROF0/ROF0 * Ph/Ph = 1/5 * 5 * 1 = 1

=>

Ptrophy1 = Ptrophy2

In short, both guns have the same probability of turning your target into a trophy. There is no benefit to be gained by distributing the same combined lethality into more rounds unless you start with an overkilling round. (For the US gun question, a single 20 mm round can hardly be considered overkilling even against a fighter, so this is no concern.)

The confusion in this thread is due to not telling apart the basic random event ("Fire one bullet") and its basic probability space with the complex compound event ("Fire n bullets") and then failing to properly define the event to be analysed ("Plane is shot down"/"Plane is hit by at least one bullet").

What's the desired event? "Plane is shot down"? Nothing to gain from rate of fire if it comes at the cost of lethality of the individual rounds. Nothing to gain from an increase in dispersion either.

"Plane is hit by at least one bullet"? The probability for this event does in deed increase with the rate of fire, and it might be influenced both up or down by dispersion.

Now back to air combat: I have not seen any historical evidence to suggest that any air force ever actively pursued a "better three damaged than one shot down" policy. Most tactical guidelines provided by successful fighter pilots do indeed stress "Get in close and don't waste your ammunition for uncertain shots". I have yet to see a real-world pilot to advise "Your best option is to spray them from long range". Wing gun trajectory divergence, which is not the same as dispersion, is seldom commented on, but all the comments I have found are negative. Dispersion is especially mentioned in the German "Schießfibel": "Verlaß dich also nicht auf die Waffenstreuung - sie hilft dir nicht, wenn du schlecht gezielt hast! Du siehst hier klar, wie g e n a u Du den Vorhalt kennen und halten muß, wenn nicht der ganze Segen daneben gehen soll." ('Thus, don't rely on weapon dispersion - it won't help you if your aim was poor! You can clearly see here how a c c u r a t e you have to know and hold the lead if you don't want the entire 'blessing' to miss.")

I don't know where the "shotgun" romanticism comes from, but apparently the mistake of thinking that weapon dispersion will make it easier to get kills was common in WW2, too, as the Schießfibel directly addresses and rejects it.

Regards,

Henning (HoHun)

Offline gripen

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Aircraft gun article
« Reply #33 on: March 25, 2006, 12:06:41 AM »
Quote
Originally posted by HoHun
Dispersion is especially mentioned in the German "Schießfibel": "Verlaß dich also nicht auf die Waffenstreuung - sie hilft dir nicht, wenn du schlecht gezielt hast! Du siehst hier klar, wie g e n a u Du den Vorhalt kennen und halten muß, wenn nicht der ganze Segen daneben gehen soll." ('Thus, don't rely on weapon dispersion - it won't help you if your aim was poor! You can clearly see here how a c c u r a t e you have to know and hold the lead if you don't want the entire 'blessing' to miss.")


Actually that part of the "Schießfibel" means that if you aim good enough, the some amount of dispersion will help you. The only case when some dispersion does not help you is the purely theoretical case of shooting without any kind of error.

Naturally that means that there is a connection between amount of error (which is practically allways systematical) and optimal amount of dispersion; the more error, the higher the optimal dispersion. The good point in dispersion (if compared to harmonization or other solutions to same problem) is that it's absolute amount increases with range just like the error in the aerial shooting (neglible at short range).

Quote
Originally posted by HoHun

I don't know where the "shotgun" romanticism comes from...


The shotgun analogy comes from the simple facts that these weapons are burst type and there is allways some error in the aerial shooting. As Galland noted: Flying targets are normally shot with shotgun.

Besides, the analogy with shotgun fits particularly well to the comparison between the FN M2 and the american M2 (the FN version having 50% higher ROF). Calculating probability of the hit for a single projectile does not account the time effect which is the main advantage of the higher ROF.

In fact the only things I see here as "romanticism" are assumtions based on extremely accurate shooting and avoiding burst nature of these weapons.

gripen

Offline Knegel

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« Reply #34 on: March 25, 2006, 01:44:15 AM »
Hi,

the lethality dont have to do anything with hitprobability!!

It have to do with kill probability!

If your bullet with 5 times as high lethality simply dont hit, cause the much smaler hitprobability, its worthless, at least less worth than the smaler gun.
Specialy if the smaler gun is enough to strike the kangaroo down.


"I have not seen any historical evidence to suggest that any air force ever actively pursued a "better three damaged than one shot down" policy.

Me neighter,t hats why i wrote:"Better bring 3 emenys damaged downward, than 1 exploded"

But actually while a escort and while trying to help a wingi it count as more important to bring the enemy off target than to destroy him. Thats why the pilots didnt expected many kills while escort missions. Thats the reason for the germans and brits to keep the smal MG´s that long.  They was good enough to "ring the bell" and did provide a big amoload(not unimportant while a escort).

Of course it was/is the wish of all countrys to have a gun which provide higherst firepower and highest hitprobability, but in WWII no nation had the perfect gun, so they had to decide between most firepower and hitprobability. Often the decission was based on the order.

And of course the pilots got told "Get in close and don't waste your ammunition for uncertain shots", but as we know this was more a wish than reality. While a turnfight there are not many certain shots.

"What's the desired event? "Plane is shot down"? Nothing to gain from rate of fire if it comes at the cost of lethality of the individual rounds. Nothing to gain from an increase in dispersion either."

If a .50cal is good enough to bring a target down with some lonly hits, cause missing selfsealing tanks or cause the bullet was strong enough to get through the plating( according to all i did read, this was the case vs Japanese planes and smal fighters), there is nothing to gain from lethality at the cost of rate of fire.

Only if you consider the big dispersion even while good aiming, and so the high quote of not hitting bullets, you can see in what way the hitprobability get increased by the rof.
Its simply more likely that a bullet hit, if more rounds fly toward the target.

I dont say that dispersion help aiming!!! Its the other way around, the dispersion(gun/pilot/plane/turbolences related) minimize the hitprobability. Specialy with the very smal archived hitprobability due to this dispersion in general, the rof increase the hitprobability much.

Its like shooting with rifle to a bird and a shotgun. The hitquote of the rifle may be similar and the destructive power is much more big, but the hitprobability of the shotgun is much more big on a moving target.  

Only if we consider a absolut exact aiming, the rof dont count, but thats unrealistic in WWII, specialy on ranges above 100m and specialy while attacking a turning enemy.

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

As higher the rof, as longer the practical effective range was(the theoretical range of a .50cal got assumed by the USAF with 900yard).

Specialy in the PTO it was wise to carry 6 x M2 .50cal with enough amo to shoot  30sec(F4U)  than  4 x  hispano M2 with enough amo to shoot 12sec(also F4U).
The hitprobability while shooting in general was more big, the hitprobability per amoload was much bigger.

I think you mix up hitquote with hitprobability.
The hitquote is a backward calculation, based on results, describing a special moment of history. Although the hitquote is = the hitprobability for this exact circumstance, its only a smal part of the whole picture.
The hitprobability, so the hitquote of the same armament will increase with a better gunsight, better pilot, good weather(no turbolences), bigger target, poor enemy pilot skill etc. and the other way around.
The hitquote depends on the hitprobability, but the hitprobability dont depends on the hitquote.

To say the rof dont influence the hitprobability, cause if the pilot aim well he hit anyway, and if he dont aim well he fail anyway, is the same like to say a better gunsight dont improve the hitprobability, cause a good pilot always go very close and always know the needed lead.

Greetings, Knegel
« Last Edit: March 25, 2006, 01:57:45 AM by Knegel »

Offline Tony Williams

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Aircraft gun article
« Reply #35 on: March 25, 2006, 01:44:47 AM »
Quote
Originally posted by gripen
Tony,
It does not matter how the guns are located or harmonized; if we assume that all other parameters are constant except the ROF and the guns are used as burst type weapons (short aimed bursts), then the higher ROF will give more hits and also higher probability of the hits regardless the source(s) of the uncertainty (harmonization, dispersion, aiming error and/or what ever).

I agree with you that a higher RoF (other things being equal) will give more hits - once you're on target.  But the probability of getting into the 'hit zone' has more to do with the shot pattern of the guns - their dispersion - than their RoF.

I would basically summarise the situations like this:

1. Accurate shooting and concentrated fire = many hits (increased RoF will further increase the hits, and allow a shorter burst of fire to be effective)

2. Accurate shooting and dispersed fire = few hits (increased RoF will increase the number of hits)

3. Less accurate shooting and concentrated fire = no hits (increased RoF will have no effect, except wasting more ammo)

4. Less accurate shooting and dispersed fire = few hits (increased RoF will increase the number of hits)

In the first case, increased RoF is not so important because you'll probably shoot the target down anyway, so it's mainly important in the case of dispersed fire.

Even then, however, you have to be good enough to get your cone of fire to coincide with the position of the target; if you're very inaccurate then you're going to miss regardless of shot dispersion or RoF.

Tony Williams: Military gun and ammunition website and discussion forum

Offline Knegel

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« Reply #36 on: March 25, 2006, 02:31:39 AM »
Hi,

if we believe the 2% hitquote estimation of the Luftwaffe while attacking strait flying 4Mots, the dispersion must have been a very big aspect, therfor i would say number 1. and 3. dont weight that much while aircombat.

With dispersion i dont mean only the gunsetting and gun related dispersion.
I guess the biggest dispersion is caused by the try of the pilot to keep the target in the gunsight.  The planes wasnt fixed, the pilot had to adjust the aiming point all the time, while this he moved often for a very short period over the target.  

So i would say:

As shorter the range or as bigger the target = as higher the hitprobability of a single round = as less important the rof is, regarding the hitprobability of the armament.

As longer the range or as smaler the target = as smaler the hitprobability of a single round = as more important the rof is, regarding the hitprobability of the armament.

Since on smal targets around 50m count as safe kill distance, but already 250m turn to be luck, the rof will be a not to smal factor at a range of around 150m.

Greetings,

Offline HoHun

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« Reply #37 on: March 25, 2006, 04:42:47 AM »
Hi Knegel,

>the lethality dont have to do anything with hitprobability!!

>It have to do with kill probability!

We agree.

>If your bullet with 5 times as high lethality simply dont hit, cause the much smaler hitprobability, its worthless, at least less worth than the smaler gun.

The hit probability Ph is the same. It has nothing to do with rate of fire.

>Specialy if the smaler gun is enough to strike the kangaroo down.

To be exact: If the lethality of the greater gun is so high that it achieves a Pk of 100% and still has some lethality reserve against the kangaroo. That is the overkill phenomenon I wrote about, and it certainly does not apply to the 20 mm cannon.

>Me neighter,t hats why i wrote:"Better bring 3 emenys damaged downward, than 1 exploded"

Well, I misunderstood that as normal WW2 air force use was "kill" to describe a target that was probably shot down, "probable" a target that might have been shot down, and "damaged" a target that was not shot down. Anyway, then your point is overkill again, and the 20 mm cannon does not overkill.

>Often the decission was based on the order.

How about some clear historical evidence?

>>"What's the desired event? "Plane is shot down"? Nothing to gain from rate of fire if it comes at the cost of lethality of the individual rounds. Nothing to gain from an increase in dispersion either."

>If a .50cal is good enough to bring a target down with some lonly hits, cause missing selfsealing tanks or cause the bullet was strong enough to get through the plating( according to all i did read, this was the case vs Japanese planes and smal fighters), there is nothing to gain from lethality at the cost of rate of fire.

Not anything that could happen will happen. You could bring down a Zero with a single 12.7 mm hit, but even the Zero is not all unprotected fuel tank. Even the chance for hitting the fuel tank, never mind doing lethal damage to hit, might be as low as 15% even if you manage to hit the Zero. A 20 mm mine shell can do serious damage on 90% of the airframe, so it will end up with a higher Pk in the end, making cannon superior aginst Zeros as well. (Interesting side note: The un-armoured, un-protected, machine-gun-armed Curtiss CW-21 light-weight fighter fought some battles against cannon-armed Zeros in the Pacific, suffering much heavier losses than they could afflict to the Zeros.)

Anway, it's all rolled up in this formula:

Pdestruction = Pkill * Nf * Ph

>Only if you consider the big dispersion even while good aiming, and so the high quote of not hitting bullets, you can see in what way the hitprobability get increased by the rof.

Hit probability does not increase through rate of fire. Basic stochastics.

>Its simply more likely that a bullet hit, if more rounds fly toward the target.

That's the completely different event "at least one bullet hits the target". This is not connected to the probability of destruction.

>Its like shooting with rifle to a bird and a shotgun. The hitquote of the rifle may be similar and the destructive power is much more big, but the hitprobability of the shotgun is much more big on a moving target.

Actually, it's not. The trick about the shotgun is that it shoot a vast number of small projectiles, most of which miss. Basic stochastics.

What you are considering is the event "at least one of the shotgun pellets hits", which does indeed have a higher probability, but makes the example different from the MG vs. cannon example.

The probability for each shotgun pellet to hit is just the same as the probabilty for each rifle bullet to hit. It's just that the shotgun fires hundreds of projectiles in a fraction of second, but most of them miss just the same as hundreds of rifle projectiles would miss.

The shotgun analogy typically is completely misunderstood by simulator pilots.

>As higher the rof, as longer the practical effective range was(the theoretical range of a .50cal got assumed by the USAF with 900yard).

Best keep that out of the discussion since "effective range" is another can of worms. Just to illustrate this: What is the effective range of one 12.7 mm machine gun? And if rate of fire increases effective range, what is the effective range of eight 12.7 mm guns? And of course lethality enters the picture, too, since "effective" implies the capability not just to hit but to damage upon hitting. (If I remember correctly, when I asked Tony, he mentioned that there was no scientific definition of the term "effective range" anyway.)

>I think you mix up hitquote with hitprobability.

Read this first: http://de.wikipedia.org/wiki/Erwartungswert

(First paragraph could be enough.)

I regret that there seems to be no similar concise explanation in the English Wikipedia, it would be quite useful for our discussion here.

Regards,

Henning (HoHun)

Offline HoHun

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« Reply #38 on: March 25, 2006, 04:51:35 AM »
Hi Knegel,

>Since on smal targets around 50m count as safe kill distance, but already 250m turn to be luck, the rof will be a not to smal factor at a range of around 150m.

This is the formula in which ROF is a factor:

Pdestruction = Pkill * ROF * Tf * Ph

Note that it is just one factor.

Using the approximation that Pkill is approximately proportional to the total energy of the projectiles, you get the following comparison:

2x Hispano II - 193 rpg - 195 kg - 125% firepower - firepower per weight: 244%
6x ,50 Browning M2 - 313 rpg - 381 kg - 100% firepower - firepower per weight: 100%

Which is exactly what I posted above. By the way, since you mentioned ammunition loads: If you examine the weight of the ammunition load required for equal total energy, you'll find that cannon are superior to machine guns and thus would have been a better choice for the USAAF even by your criterium.

Regards,

Henning (HoHun)

Offline gripen

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« Reply #39 on: March 25, 2006, 08:05:43 AM »
Quote
Originally posted by Tony Williams


I would basically summarise the situations like this:

1. Accurate shooting and concentrated fire = many hits (increased RoF will further increase the hits, and allow a shorter burst of fire to be effective)


Shorter bursts will result smaller dispersion due to wandering of the aim ie higher probability of the hit with given amount of rounds even in the case of the relatively accurate shooting. This can be seen from the gun camera films; even in the close range shooting most projectiles seem to miss due to wandering.

Note that the time is the key to understand the advantages of the increased ROF;  there is basicly allways lack of time to aim and shoot. A good example of this is head on attack on bombers as the Germans did against American bombers, another example is shooting a maneuvering fighter.

Shortly the advantages of the increased ROF here are that shorter burst are needed for same amount of hits (same killing probability with better hit probability) or similar bursts will result more hits (better killing probability with same hitting probability).

Quote
Originally posted by Tony Williams

2. Accurate shooting and dispersed fire = few hits (increased RoF will increase the number of hits)


That is true only in the more or less theoretical case of shooting without any error.

In reality the sitution is pretty much same as in the first case because the dispersion (from the gun or mounting) is practically allways much smaller than the dispersion caused by even very small aiming errors (or other errors; wandering, harmonization etc.).

Notable thing here is that there is no reason to believe that the other errors (aiming or what ever) are some how evenly distributed ie the error is practically allways systematical. And that is the reason why some guns have some amount of purpose built dispersion.

Quote
Originally posted by Tony Williams

3. Less accurate shooting and concentrated fire = no hits (increased RoF will have no effect, except wasting more ammo)


Generally I understand less accurate shooting as more error in shooting.

In practice this case is similar with the first case, the probabilities of the killing and hitting are just lower due to larger error,  the advantages of the ROF being the same.

Quote
Originally posted by Tony Williams

4. Less accurate shooting and dispersed fire = few hits (increased RoF will increase the number of hits)


Agreed, this is a typical shotgun case; the dispersion and the ROF help you.

gripen

Offline Knegel

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« Reply #40 on: March 25, 2006, 09:44:11 AM »
Hi,

if you agree that a shotgun provide a higher hitprobability, while shooting to a smal fast moving target, than a normal rifle, you also must agree that a MG, which shoot 12 rps have a higher hitprobability than a rifle.
And of course also 6 x 13rps(78 rps) provide a higher hitprobability, while shooting to this smal target, than 4 x 10rps(40 rps).

If you combine this hitprobability advantage with the much bigger amoload and the fact that the .50cal brought suprising easy kills vs almost all japanese planes, the .50 cal turn out to be the better weapon.

If the rof is not important, why they did introduce AAA guns with 4 x 20mm instead of using the realy deadly but slow firing 37mm only??

While a flyby of a plane, which did last maybe 30sec, the 3,7-cm-Flak 43 could shoot max 30 rounds, while the 2-cm-Flakvierling 38 was able to shoot max 600 rounds, and you realy think the hitprobability was the same???

I dont think that the kill probability of a 20mm vs a unprotected plane, without selfsealing tanks was that much better than that of .50cal. At least the lot of snapshot kill storys while shooting down japanese planes make me believe it couldnt get much better.

Hitprobability, not expection is what we talking about, right?
http://de.wikipedia.org/wiki/Wahrscheinlichkeit

Are you kidding regarding the CW21??  Many Zeros with combat experienced pilots vs some splitted Dutch planes??  
The question is: How it was possible to get a Zero down with this obvious disadvantage?
http://www.warbirdforum.com/cw215.htm

Later the Zeros and other japanese planes got shot down in a high sequence almost only by 4-6 x .50cal, until 1943 mainly carried by F4F´s and P40´s.
Specialy while shooting to the nimble japanese fighters, often from horrible positions(cause the japanese planes simply had a advanced turn climb performence) the increased hitprobability was a good advantage.

Greetings, Knegel

Offline HoHun

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« Reply #41 on: March 25, 2006, 10:52:56 AM »
Hi Knegel,

>if you agree that a shotgun provide a higher hitprobability ...

The point is, I don't.

What the shotgun does it to provide a greatly increased number of rounds at the same hit probability as a rifle:

Pigeon-killing example:

Shotgun: Pkill = 2% per pellet, Nf = 250 pellets, Ph = 20%
Rifle: Pkill = 100% per bullet, Nf = 1 bullet, Ph = 20%

Shotgun: Pdestruction = Pkill * Nf * Ph = 2% * 250 pellets * 20% = 100%
Rifle: Pdestruction = Pkill * Nf * Ph = 100% * 1 bullet * 20% = 20%

So in this example, everything is different between shotgun and rifle except for the hit probability.

Of course, the shotgun example is a bad choice for comparing it to WW2 aerial guns since the firing of the individual pellets is not a series in independend random events. Still, if one insists on comparing them, one should be aware that a shotgun fire a large number of projectiles, most of which miss even if you manage to hit the pigeon.

>Hitprobability, not expection is what we talking about, right?

The link explains why it's perfectly fine to use Ph = Nf / Nh. If you don't follow, try to re-read the first paragraph in the Wikipedia article I gave you, and click the link "Gesetz der großen Zahlen", too.

>Are you kidding regarding the CW21??  Many Zeros with combat experienced pilots vs some splitted Dutch planes??  

It should be pretty obvious that I am not kidding. The CW21 example shows the result of applying 20 mm fire to unprotected airframes. Study history with an open mind, it might have a lesson for you.

Regards,

Henning (HoHun)

Offline Knegel

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« Reply #42 on: March 25, 2006, 02:07:45 PM »
Hi,

if the hitprobability while shooting with a shotgun to a smal fast moving target is the same like with a rifle, can you please explain why a hunter use a shotgun??

I always thought its cause the shotgun provide a better probability to hit a rabbit or bird, no??

I dont know your definiion of probability, according to the link i gave you its this:
Wahrscheinlichkeit ist
(probability is:)
-ein Maß für die Unsicherheit zukünftiger Ereignisse oder zweifelhafter
Aussagen(a measurement for the uncertainness of comming occurrences or problematic testimonys) ,
-ein Maß für die relative Häufigkeit des Auftretens von Ereignissen bei Auswahl aus mehreren Möglichkeiten(a measurement for the relative frequency of occurrence of occurrences by selection out of multiple possibilitys).

So can you please explain why you assume exact the same hitprobability in your formula?? The hitprobability is what we wanna calculate, better to say estimate!!  

Actually i dont understand the corelation of the "Erwartungswert einer diskreten Zufallsvariablen" and "Gesetz der großen Zahlen" to the hitprobability.
The hitprobability of a gun is related to much more important factors than luck.

In our shotgun/rifle example the hitprobability of the shotgun is bigger, cause we dont need to aim that exact, cause the many bullets flying with big dispersion toward the bird(or rabbit).

Actually you already did agree to this:"What you are considering is the event "at least one of the shotgun pellets hits", which does indeed have a higher probability, but makes the example different from the MG vs. cannon example."
There is no different between this  and the high rof vs low rof example.  A shotgun represent a gun with high rof, it dont matter if the bullets get shot at same time or in one hour. Who shot more often simply have a higher probability to hit the target, of course this only is important as long the hitprobability of one bullet is very smal(very smal targets, fast moving targets, very long range, no time to aim etc).
As more the hitprobability of a single gun shot increase as less important is a high rof. Thats why they use rifles while hunting big, still standing animals and thats why they did use rifles with at least two barrel while hunting a tiger(two barrels = a double hitprobability if the 1st bullet fail) and also while hunting partridges and rabbits, cause even the shotgun dont provide nearly a 100% hitprobability.

While estimating the hitprobability it dont matter how many of my bullets hit the target, it only matter how likely it is to hit the target at all. The kill probability determine how likely it is to get enough hits to bring the target down, also here it dont matter how many bullets dont hit, it only matter that at least one bullet hit a critical area.

As long as a probability isnt 100% we cant calculate it exact, as lower the hitprobability get as more the calculation turn into a estimation.

Out of the hitquote while tests we can estimate the hitprobability in a better way.  But we will get much different hitquotes with different testsetups, like different attacking angle, different stable gunplattform(due to turbolences or slow speed), different distances, strait flying or turning target and much more.  Therfor its not possible to estimate a hitprobability without to determine the circumstances exact.

What we know is that the Luftwaffe did estimate the hitquote to around 2% when a average pilot did attack a B17 from the rear.

We also know some storys of Marsaille where he did need only 6 rounds to bring down a plane, how many did hit we dont know, but according to his wingis it looked like almost all did hit. So we have a differeence in hitprobability only due to pilot skill from 2% up to around 90%.

"It should be pretty obvious that I am not kidding. The CW21 example shows the result of applying 20 mm fire to unprotected airframes. Study history with an open mind, it might have a lesson for you."

After i did read the article in what way the CW21´s got shot down and that they was able to destroy some Zeros as well, i dont see any proofe for cannons beeing better vs light armored planes. I think noone told that 20mm´s cant bring down a light armored plane.

Do you think i dont study history with an open mind, while you be sure you do?? I think thats somewhat a contradiction.

Maybe you dont believe me, but the whole time i try to understand your thought´s, but i always come to the same conclusion that you mix up hitprobability with hitquote.

A hitquote can get calculated, a hitprobability is a estimation without a exact value.  A hitquote is exact cause it get calculated out of tested results, a hitprobability is a estimation of how it will be in future under rather less than more exact circumstances.

Greetings, Knegel

Offline HoHun

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Aircraft gun article
« Reply #43 on: March 25, 2006, 04:26:07 PM »
Hi Knegel,

>if the hitprobability while shooting with a shotgun to a smal fast moving target is the same like with a rifle, can you please explain why a hunter use a shotgun??

I have already explained that above :-)

If a hunter fires his shotgun, the shot spreads out so much that maybe only 10% of them hit the rabbit, which drops dead. Hit probability is 10%, rabbit-kill probability is 100%.

If a hunter fires a rifle, he will miss the rabbit 90% of the time, but that still means he has a 10% hit probability. (And if he hits, the rabbit drops dead.) This translates into a rabbit-kill probability of 10%.

Two weapons with equal hit probability - but the hunter rightly chooses the shotgun.

>Actually i dont understand the corelation of the "Erwartungswert einer diskreten Zufallsvariablen" and "Gesetz der großen Zahlen" to the hitprobability.

As long as we talk about a very large number of rounds fired, we can treat expectancy value and probability as equivalent.

If a guy has fired 110 rounds in one fight, of which 11 hit, that doesn't mean that we can say with any kind of reliability that the hit probability for that weapon under those circumstances is 10%. However, if at the end of the war, we're looking at 1.1 million rounds fired and 110000 hits, we can say with great certainty that the hit probability was 10%.

>There is no different between this  and the high rof vs low rof example.  

The difference is that the rifle overkills a rabbit. The 20 mm cannon does not overkill a fighter.

>While estimating the hitprobability it dont matter how many of my bullets hit the target, it only matter how likely it is to hit the target at all.

>Maybe you dont believe me, but the whole time i try to understand your thought´s, but i always come to the same conclusion that you mix up hitprobability with hitquote.

That's exactly the confusion I pointed out in the beginning: The hit probability describes the likelihood of one shot fired at a target hitting that target. That's a basic random experiment.

You confuse that with the question "If n shots are fired at a target, how likely is it that at least one hit is achieved".

Using the relevant axioms, you can calculate that as:

P (at least one hit with n shots) = 1 - P (no hits with n shots) = 1 - P (no hit with one shot)^n

For example, firing 10 shots with a hit probability of 10%, how likely is it that we score at least one hit?

P (>=1 hit with 10 shots)
= 1 - P (no hit with one shot)^10
= 1 - (1 - P (one hit with one shot))^10
= 1 - (1 - 0,1)^10
= 1 - 0,9^10
= 1 - 0,349
= 65.1%

So we have an exact hit probability of 10%, but the chance of scoring at least one hit with 10 rounds is 65.1%.

These are the two aspects of probabilities that have lead to much confusion in this thread.

I hope I have managed to clear up that confusion now :-)

Regards,

Henning (HoHun)

Offline Knegel

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Aircraft gun article
« Reply #44 on: March 26, 2006, 12:40:44 AM »
Hi,

"If a hunter fires his shotgun, the shot spreads out so much that maybe only 10% of them hit the rabbit, which drops dead. Hit probability is 10%, rabbit-kill probability is 100%."

This show exact that you mix up the hitquote with hitproabbility.

"That's exactly the confusion I pointed out in the beginning: The hit probability describes the likelihood of one shot fired at a target hitting that target. That's a basic random experiment."

We are talking of the hitprobability differents between a gun armament of 6 x .50cal and 4 x Hispano II, not about the hitprobability of a single shot!!


"As long as we talk about a very large number of rounds fired, we can treat expectancy value and probability as equivalent.

If a guy has fired 110 rounds in one fight, of which 11 hit, that doesn't mean that we can say with any kind of reliability that the hit probability for that weapon under those circumstances is 10%. However, if at the end of the war, we're looking at 1.1 million rounds fired and 110000 hits, we can say with great certainty that the hit probability was 10%."

Thats true, but is that of any relevance here?
Do you have a exact hitqote of a 6 x .50cal and 4 x hispano II armament?

I dont know any reliable hitquote of WWII at all, most are only rough estimations. The example of Marsaille and a average luftwaffe pilot show that the hitprobability vary much. If we dont take this big differents into account, the expectancy value only can estimate the need of rounds all over, but it cant give a hint how to change things to a better way.
And for sure this dont help while estimating which of the two armaments show a better hitprobability.

The confusion is that you talk about the hitprobability of a single bullet, while we wanna find out which armament show a better hitprobability.


Greetings, Knegel