Author Topic: Aircraft gun article  (Read 7857 times)

Offline HoHun

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Aircraft gun article
« Reply #60 on: March 27, 2006, 08:04:05 AM »
Hi Knegel,

>As the calculations with a possible bullet hitprobability show, the hitprobability of 6 x 50.cal is twice as high as the 4 x Hispano II.

This is not the hit probability but the number of hits.

What you choose to ingore is Pk. Pk ist approximately proportional to the total energy of the round, and greatly favours cannon shells over bullets.

Instead of properly continuing the calculation to its logical conclusion, you break off here and assert the superiority of 12.7 mm guns with some handwaving arguments that don't hold water.

Here is the full calculation:

Pdestruction (6 MG) = Pk (MG) * Nh(6 MG) = 3.4% * 6 * 13 rps * 2 s * 2%

Pdestruction (4 Ca) = Pk(Ca) * Nh (4 Ca) = 16.7% * 4 * 10 rps * 2 s * 2%

=>

Pdestruction (6 MG) = 10.6%

Pdestruction (4 Ca) = 26.7%

This means that a 4-cannon-battery has a firepower of 250% of that of a 6-machine-gun-battery.

>How i shal know that he speak about the hitprobability of every single round, while i clearly wrote about the hitprobability of the gun(armament)?

Because I pointed that out in my first reply to you here in this thread:

"I know what you mean, but hit probability is really just the ratio of hits to total shots fired and has nothing to do with rate of fire."

I read what you wrote, and replied. Browse back and read it again. It's worth it as you still still haven't got over your misunderstanding.

Regards,

Henning (HoHun)

Offline Knegel

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Aircraft gun article
« Reply #61 on: March 27, 2006, 08:51:00 AM »
Hi,

"The energy comparison shows us that each cannon hit is almost five times as powerful as a 12.7 mm hit, so cannon still do more damage."

If the .50cal hit unprotected not selfsealing fueltank, at the end it cause the same result like the 20mm, same count for the pilot.
Since the pilot and the fueltank cover a pretty big part of a plane, the question is how much different is the effect?

"You don't merely lack the language, you lack the basic concepts described by the terms that don't even exist in everyday language. A teacher might be inclined to explain the concepts you are lacking more thoroughly in plain language here, but I am no teacher, and I don't consider your "know-it-all, don't-need-math" attitude a good basis for teaching anyway."

This is what you wrote before:"........you don't have the vocabulary to talk about the different aspects of random experiments so that you don't understand my explanations."

Strangewise i dont say i know all, its rather you who dont read exact what i wrote, and without to waste a though that my therms could offer a correct describtion with for you not common words, you go on and refer to absolut not relevant things.
After you took notice that i talk about the gun hitprobability, you dont say, 'ah ok, now i understand', you dont come down from your high horse. You immediately switch and claim 'hitprobability is nothing, killprobability is all'.

"The energy comparison shows us that each cannon hit is almost five times as powerful as a 12.7 mm hit, so cannon still do more damage."

How you know that the cannon do more damage, if there is a not to smal possibility that the .50cal hit a fueltank or the pilot?  In this case there dont will be a real different of the result.

"A good method of estimating the Pk of a round is to examine the total energy it carries because this energy will be converted into destructive power as soon as it strikes the target:"

I dont think this is a good method of estimating the Pk, cause you dont take the target into account.

As i wrote before, i think the killprobability change with the target, not only with the damagepower.
A not protected target, without selfsealing tanks offer a much higher killprobability for a .50cal than a on a plane with selfsealing tanks and good amor.
While i guess the cannon round provide a much more constant killprobability, cause it mainly aim for the structure of the plane and it isnt a big different if a 20mm hit a selfsealing tank or a not selfsealing tank, same count for the amor.

On a unprotected target specialy smal MG´s have a much higher kill probability than on a same sized, protected target.

If i hit the head of the pilot, it dont matter if i do this with a .30cal, .50cal or 20mm. The killprobability is pretty the same in this rare but without plating possible example. With plating to cover the pilot, the killprobability in this case will will be much higher for the cannons.

Btw. Somewhere i did read the Luftwaffe did estimate around 4 x Mk108 hits are needed to take down a B17 and around 20 x MG151/20mm to get the bombwer down.

catrige power MK108 = 58  * 3 = 174
catrige power MG151/20 = 12 * 20 = 240

I also did read that on smal fighters 1 * MK108 was enough, while around 4 * MG151/20 rounds did the job.
1 * 58 = 58
4 * 12 = 48

What a suprise, on smal(less tough) targets the effectiveness of the smaler gun increase in relation to the big gun.

The problem isnt to calculate something, its to know what we need to consider while the calculation.


Greetings,  Knegel

Offline Knegel

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« Reply #62 on: March 27, 2006, 08:56:49 AM »
Quote
Originally posted by straffo
Look like Hohun is reasoning in term of probability and Knegel in expected value (espérance).

But some post make me wonder what you really mean ,for example this :
 

%2 is the hit probability !

Mathematically this as no sense ,as you need to throw a percentile dice 156 or 80 times to obtain a real result.
ok , the laws of large numbers apply here and I guess you are thinking of a normal law distribution but ... well it's not a valid statement :)


Hi,

yes, 2% is the hitprobability of the bullet, thats what the Luftwaffe did estimate when a average pilot  attack 4mot bomber.


Greetings, Knegel

Offline Knegel

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« Reply #63 on: March 27, 2006, 09:59:59 AM »
Hi,

"this is not the hit probability but the number of hits."

Rather the expected number of hits, but i would say it isnt wrong to call this the hitprobability of the gun or armament.

Or is Tony Williams also wrong if he once write "CARTRIDGE POWER" and next time "Gun Power"?

The word Power is not limitted to the smalest unit, same like i dont think hitprobability is limited to the smalest unit.
Gunpower is also 'only' catrige power * ROF!!

Therfor we can define "catrige hitprobability" and "gun hitprobability", i dont see any mistake in this!

""I know what you mean, but hit probability is really just the ratio of hits to total shots fired and has nothing to do with rate of fire.""

If you keep in mind that i was thinking of the the gun hitprobability, this sentence is misleading like mad!!  Why you dont write: "In school the hitprobability is related to only one bullet/Pellet, not to a gun or shotgun shell."??

But actually on different shotgun pages they use the therm 'probability of hit' when they talk about a shotgun shell.

Anyway, this misunderstanding is solved now, now we can go on with the damage power thingi! :D

Greetings, Knegel

Offline BlauK

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« Reply #64 on: March 27, 2006, 10:44:59 AM »
HoHun.. and all

You and your friend are equally good and accurate throwers.
You have a baseball in your hand and your friend has a handful of small stones.
You both are trying to hit a bird sitting in a tree not too far away with what you have in your hand.

Which one of you (people, not projectiles) have a higher probability to hit the bird (=hit probability) until it flies away?

Is it not true that the number of projectiles would increse the hit probability... not talking about what will happen to the bird if/when it is hit.


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Offline HoHun

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« Reply #65 on: March 27, 2006, 11:19:43 AM »
Hi Knegel,

>Why you dont write: "In school the hitprobability is related to only one bullet/Pellet, not to a gun or shotgun shell."??

Because it's the same in real life. Non scholam, vitam discimus.

>But actually on different shotgun pages they use the therm 'probability of hit' when they talk about a shotgun shell.

Sure, everything you read on the internet is correct.

Regards,

Henning (HoHun)

Offline HoHun

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« Reply #66 on: March 27, 2006, 11:20:25 AM »
Hi Knegel,

>While i guess the cannon round provide a much more constant killprobability, cause it mainly aim for the structure of the plane and it isnt a big different if a 20mm hit a selfsealing tank or a not selfsealing tank, same count for the amor.

You have established a hit probibility for the entire aircraft, then you draw conclusions for the critical areas of the aircraft, thus breaking the logical chain in your argument. You are again neglecting the higher destructiveness of cannon shells which mean that they can easily cause destruction by attacking non-critical areas.

> Somewhere i did read the Luftwaffe did estimate ...

The Luftwaffe estimated that it was the chemical energy in the cannon shells that brought down aircraft. That is not entirely accurate since it neglects the kinetic energy, which admittedly in the case of cannon shells doesn't make that much of a difference.

>What a suprise, on smal(less tough) targets the effectiveness of the smaler gun increase in relation to the big gun.

The reports with the numbers of hits required define different desctruction probabilities, so you are most likely comparing apples and oranges. From what reports are your numbers?

Regards,

Henning (HoHun)

Offline Karnak

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« Reply #67 on: March 27, 2006, 11:20:49 AM »
BlauK,

But that isn't what we are talking about.  the .50 installations are not a shotgun.  They produce a bullet stream just as the Hispano installation does, simply with about half again as many projectiles.  If the stream misses, it misses and how many projectiles are in the stream are irrelevant.  If it hits, it hits and likewise the number of projectiles in it is irrelevent.

When you realize that you realize that the number of times the .50 cal installation will score hits while the 20mm installation does not is vanishingly small and talking about the hit probability of a given round does not accurately describe the practical reality.


Given that, the 20mm weapons were clearly superior.
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Offline HoHun

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« Reply #68 on: March 27, 2006, 11:32:37 AM »
Hi BlauK,

>Is it not true that the number of projectiles would increse the hit probability... not talking about what will happen to the bird if/when it is hit.

The difference between the two throwers is that one of them is only allowed to throw one object, while the other is allowed to throw multiple objects. The hit probability is constant.

The question "How likely is it that n out of m thrown objects hit the bird" is a complex random experiment even though the hit probability of each object ist the same.

Applying the same term to both experiments is really means comparing an apple to a grocery store, and since hit probability is a well-defined term, it's plain wrong to tag it on the grocery store situation.

The latter leads to a dead end anyway since we have to consider what will happen to the bird when it is hit.

Regards,

Henning (HoHun)

Offline BlauK

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« Reply #69 on: March 27, 2006, 12:18:28 PM »
Quote
Originally posted by Karnak
If the stream misses, it misses and how many projectiles are in the stream are irrelevant.


So you are assuming a situation where neither the shooter nor the target are not manouvering in any manner?
Why would you want to speculate on such? In such case you are no tspeculating on hits, but on destructive power.


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Offline Karnak

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« Reply #70 on: March 27, 2006, 12:22:12 PM »
Quote
Originally posted by BlauK
So you are assuming a situation where neither the shooter nor the target are not manouvering in any manner?
Why would you want to speculate on such? In such case you are no tspeculating on hits, but on destructive power.

No.  I am saying that in the vast majority of events such manuvering will not produce different results for the Hispano or .50 cals.  In most cases either they would both hit or both miss.  In some rare cases the Hispanos would miss while the .50s hit, but not nearly often enough to remotely redress a gross disparity in firepower between the Hispano and .50.
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Offline BlauK

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« Reply #71 on: March 27, 2006, 12:25:06 PM »
Quote
Originally posted by HoHun
The difference between the two throwers is that one of them is only allowed to throw one object, while the other is allowed to throw multiple objects. The hit probability is constant.


So, are you saying that the probability of winning in lottery (="winprobability") is not affected by the amount of tickets bought? ... "One guy is only allowed to buy 1 ticket while the other can buy 10" ... "the winprobability (of these 2 guys) is constant" ?

I am not really interested in the probability of on esingle ticket.. if I have the option to choose between 1 or 10, which one do you think I should choose to achieve beter chances of a hit = win


Quote
The latter leads to a dead end anyway since we have to consider what will happen to the bird when it is hit.


So you are not actually wanting to talk abot hit probability, but instead about teh probability of killing the.. or destroying an aircraft. That is not hitprobability, that is destruction probability or something like that ;)
« Last Edit: March 27, 2006, 12:29:02 PM by BlauK »


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Offline BlauK

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« Reply #72 on: March 27, 2006, 12:27:41 PM »
Quote
Originally posted by Karnak
No.  I am saying that in the vast majority of events such manuvering will not produce different results for the Hispano or .50 cals.  In most cases either they would both hit or both miss.  In some rare cases the Hispanos would miss while the .50s hit, but not nearly often enough to remotely redress a gross disparity in firepower between the Hispano and .50.


Ok.. so the velocity is so high that the amount of rounds is not relevant anymore? Or the dispersion is equal.. or what ever.. then it would make sence.

I suppose this is only considering one weapon of each type.. and not considering e.g. 6 mgs against 1 cannon?


IMO, again, it would be pretty useless to consider only 1 weapon against 1 weapon if e.g. their weight is dramatically different etc.

NO kind of equations really matter until the question is clearly defined :)
« Last Edit: March 27, 2006, 12:32:40 PM by BlauK »


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Offline HoHun

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« Reply #73 on: March 27, 2006, 12:43:28 PM »
Hi BlauK,

>So you are not actually wanting to talk abot hit probability, but instead about teh probability of killing the.. or destroying an aircraft. That is not hitprobability, that is destruction probability or something like that ;)

What you are talking about is not hit probability, but the probability that out of n shots fired, m hit.

Hit probability the the probability that if one shot is fired, one hits.

Regards,

Henning (HoHun)

Offline BlauK

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« Reply #74 on: March 27, 2006, 12:45:10 PM »
Quote
Originally posted by HoHun

Hit probability the the probability that if one shot is fired, one hits.



Where or by whom is such defined?

You are simply talking about the hit probability of one bullet.. but then, what are the factors affecting the probability?
And what would you try to prove with that kind of probability? Something like the random behaviour of the bullet because of surface defects or such?
« Last Edit: March 27, 2006, 12:50:29 PM by BlauK »


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