RE: High Velocity AP round hit-zones (Full Version)

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Yoozername -> RE: High Velocity AP round hit-zones (7/27/2013 5:13:49 AM)

There is a story abut a Nashorn 88mm L71 TD firing at 4Km and KO a T34. According to the data above, if the range is known, then it would be be a 40% chance or so.

Supposedly, the Nashorn was warned of the threat by a infantry officer. I have also read of US armored AFV being warned by ground troops (weapons platoon officer) of enemy threats and ranges. In one case, 1040 meters. Now, that is very indicative of a instrument that measures distance in tens of meters. Some US weapons units had BC scopes similar to EM34.

But, your wargaming may vary.



Mobius -> RE: High Velocity AP round hit-zones (7/28/2013 3:13:08 PM)

Speaking of accuracy the post WWII DDR firing table for the 122mm D-25 contains dispersion tables for the BR-471 and BR-471B rounds. The 122mm gun appears very accurate. At least when firing 1950-1960 ammo.

The redactions don't help in determining what rounds either table is for.
But either would produce a German style accuracy table superior to the 88/L71.

[image]local://upfiles/21308/A1605F6CE6754C30ABA67D2808B392A2.jpg[/image]



Yoozername -> RE: High Velocity AP round hit-zones (7/28/2013 5:07:33 PM)

Not sure if the numbers represent the same thing. Mittlere Streuung may not be the same as the 50% values seen in the German tables. It is possibly 'average deviation'. A sum of all the distances divided by the number of number of shots. I am convinced that the Germans are using statistics as I have shown in this thread.

My understanding of how the Germans got their WWII numbers is that they would separate each shot into it's vertical and horizontal component and then use statistics to find the 50% zone. It isn't really a rectangle or square they were using. Considering the number of shots needed for each range, and the effect this would have on the gun itself, I would guess that they really used curve fitting to get intermediate data. Possibly just testing at 100m, 500m, 1000m, etc. The 'double-dispersion' is, of course, just calculated.

Edit:
quote:

mittlere Streuung
(average deviation)
Die mittlere Streuung wird bestimmt durch die Summe der Absolutbeträge
der Abweichungen der Stichprobenwerte vom Mittelwert, dividiert durch
den Stichprobenumfang n:


Translate.... mean scatter (Average deviation) The mean dispersion is determined by the sum of the absolute values ​​of the deviations of the sample values ​​from the mean, divided by the sample size.


I would like to see the methodology for any of these shoots. Number of rounds fired, measurements and data manipulation. If the average deviation is reported, then I would certainly like to know a bit more. Using the 50% number, one can calculate the whole dispersion.

122 info: Table 3 seems to be for the HE and a type of AP while table 4 is for another type of AP.



Mobius -> RE: High Velocity AP round hit-zones (7/28/2013 5:59:02 PM)

quote:

ORIGINAL: Yoozername
My understanding of how the Germans got their WWII numbers is that they would separate each shot into it's vertical and horizontal component and then use statistics to find the 50% zone. It isn't really a rectangle or square they were using.

I think so too. They aren't comparing an area as much as considering the horizontal and vertical dispersions as two independent relationships and then finding their product.
(Since that is what I do and get almost identical results.)
A 1969 study of statistical hit probability at Cornell Laboratory described the pretty big mathematical equations needed to arrive at a hit percent as an area using the std. dev. of a number of impeding factors, including dispersion and it required an exponential function. I don’t think something like that was used.



Mobius -> RE: High Velocity AP round hit-zones (7/28/2013 6:13:56 PM)

quote:

ORIGINAL: Yoozername
Edit:
quote:

mittlere Streuung
(average deviation)
Die mittlere Streuung wird bestimmt durch die Summe der Absolutbeträge
der Abweichungen der Stichprobenwerte vom Mittelwert, dividiert durch
den Stichprobenumfang n:

Translate.... mean scatter (Average deviation) The mean dispersion is determined by the sum of the absolute values ​​of the deviations of the sample values ​​from the mean, divided by the sample size.


Wouldn't they be the same as saying 50% are higher and 50% are lower?

quote:

ORIGINAL: Yoozername
122 info: Table 3 seems to be for the HE and a type of AP while table 4 is for another type of AP.
Then probably Table 3 is for the APBC and HE rounds as they both had ballistic caps of similar shapes. Table 4 is the older AP ogive nosed round. Though I would have thought it the other way round.

[:D]I would of guessed the reason some of the words were blacked out is because it said 'this is what our Soviet overlords say the values are' and the other is 'this is what we say they are'.



Yoozername -> RE: High Velocity AP round hit-zones (7/28/2013 6:48:41 PM)

quote:

ORIGINAL: Mobius



Wouldn't they be the same as saying 50% are higher and 50% are lower?


Yes but how much higher and how much lower?

With a dispersion, and given a 50% range, it is trivial to find the 95% and 99% total range and distance. With the average, how do you figure the spread??? I would prefer, in both cases, to actually see the raw data.



Yoozername -> RE: High Velocity AP round hit-zones (7/28/2013 7:24:05 PM)

This data is nothing new and I think I have seen Mobius post it around the internet...

WO 291/751 AORG Memo No.427, 24th Nov 1944, "Comparative Dispersion of Tank Guns"
Probability of a hit when firing for effect on a target 2' high by 5' wide (M.P.I. assumed on centre of target) at
.................................................. 500yds; 800yds; 1000yds; 1500yds:
Churchill IV 6pdr APCBC 150rnds......74% 73% 62% 42%
Churchill IV 6pdr APDS 90rnds..........74% 50% 37% 20%
Sherman 17pdr APC 100rnds............88% 66% 52% 32%
Sherman 17pdr APDS 40rnds...........42% 21% 14% 7%
Comet 77mm APC 40rnds.................98% 86% 76% 53%
Sherman 75mm M3 APC M61 150rnds..100% 96% 90% 73%
Sherman 76mm APC M62 40rnds..........100% 100% 96% 92%

What strikes me, besides the superiority of the US guns, is that they report the number of rounds fired. At first I thought that was the total for the test...i.e. if they fired 40 rounds, then it would be 10 rounds at each range...but the percentage numbers tell a different story!, it would seem that to get the percentages, they actually fired 40 rounds (or more) at each range! In testing, it is my experience that at least a sample of a few dozen tells a story. So, if I am reading this correctly, it's good data.

Note that the target is very small in height. 0.61m. I would almost have to assume that it is a test with a known range and zeroed weapons. Assuming a dispersion, one could claim that a sherman 76mm is showing a 0.61 m height 2 sigma score at 1000 meters.



Mobius -> RE: High Velocity AP round hit-zones (7/28/2013 8:03:40 PM)

quote:

ORIGINAL: Yoozername
At first I thought that was the total for the test...i.e. if they fired 40 rounds, then it would be 10 rounds at each range...but the percentage numbers tell a different story!, it would seem that to get the percentages, they actually fired 40 rounds (or more) at each range!
I wouldn't bet on it. 96% of 40=38.4 and 92% of 40 is 36.8.
If they had 38 hits it should be 95%.

quote:

ORIGINAL: Yoozername
Note that the target is very small in height. 0.61m. I would almost have to assume that it is a test with a known range and zeroed weapons. Assuming a dispersion, one could claim that a sherman 76mm is showing a 0.61 m height 2 sigma score at 1000 meters.
Using the numbers to try to determine a 50% zone at 1000 yds I get a vertical dispersion of 0.22y. Exceeding that of the 90mm said to be more accurate gun.



Yoozername -> RE: High Velocity AP round hit-zones (7/28/2013 9:50:02 PM)

Well, what would you bet? Are you saying that 10 rnds. were fired? Your math approach wouldn't work on that either.

Maybe some rounding errors? You must have looked at that data before. Did you ever notice the ammunition info? Perhaps they gave partial credit to edge-hits.

As far as a 50% zone, How did you get 0.22y?



Mobius -> RE: High Velocity AP round hit-zones (7/28/2013 11:23:31 PM)

quote:

ORIGINAL: Yoozername
far as a 50% zone, How did you get 0.22y?

Trial runs.

It's easier to work forward then back.
Target height is 2/3 yd.
Target height above aim point 1/3yd or 0.3333yds.
50% dispersion height = 0.22yd.
Divide this by 2 for 50% zone above aim point. =(.11yd)
Divide this by .67448 to convert to std dev above aim point. =(.1631yd)
Ratio of target to std dev .3333yd/.1631yd (yds cancel out so pure number)=2.0438
What is the area under the curve % of 2.0438 ? = 95.89%

For a more square target you would have to multiply the vertical % by horizontal % but in this case the width % is 100% so it just becomes a case of finding the vertical number.



Mobius -> RE: High Velocity AP round hit-zones (7/29/2013 1:32:09 AM)

Let's see if the Germans were doing their calculations in a similar fashion.
Target size 2.50 x 2.0m.
1.25m width from aim point, 1.0m above aim point.
88mm/L71 50% zone @ 2000m
lat=0.7, vert=0.9

converting 50% zone dispersion to terms of std dev:
lat: 0.7m/2/.67448 = 0.5189m
vert:0.9m/2/.67448 = 0.6672m

target / std devs ratio:
lat: 1.25m/0.5189m = 2.409 std dev = 98.396%
vert: 1.0m/0.6672m = 1.4988 std dev = 86.06%
98.306% x 86.06% = 84.67% ~ 85% as listed at 2000m in the 88mm/L71 firing table.



Yoozername -> RE: High Velocity AP round hit-zones (7/29/2013 1:35:40 AM)

I thought the 'y' was for vertical and you were saying 0.22 meters in the y axis.

The EZ way to do this is to realize that 95%ish is 2 sigma. So, 0.61 meters can just be divided by 3 to get the 50% of 0.203 meters or so. Which is very close to your 0.22*yds.(roughly 8 inches).



Yoozername -> RE: High Velocity AP round hit-zones (7/29/2013 2:32:12 AM)


quote:

ORIGINAL: Mobius

Let's see if the Germans were doing their calculations in a similar fashion.
Target size 2.50 x 2.0m.
1.25m width from aim point, 1.0m above aim point.
88mm/L71 50% zone @ 2000m
lat=0.7, vert=0.9

converting 50% zone dispersion to terms of std dev:
lat: 0.7m/2/.67448 = 0.5189m
vert:0.9m/2/.67448 = 0.6672m

target / std devs ratio:
lat: 1.25m/0.5189m = 2.409 std dev = 98.396%
vert: 1.0m/0.6672m = 1.4988 std dev = 86.06%
98.306% x 86.06% = 84.67% ~ 85% as listed at 2000m in the 88mm/L71 firing table.


I am absolutely sure this is correct. I had disregarded the lat calcs since they don't usually play in till longer range. But 2000 meters seems to show that the 88mmL71 wasn't the super-gun most believe. But since it was shooting at tall shermans and t34/85 and Stalins, it was more than accurate enough under most battlefield ranges.

I do wonder if the actual mounting plays in. That is, if it's mounted on a carriafe or a turret.



Mobius -> RE: High Velocity AP round hit-zones (7/29/2013 3:30:59 AM)

quote:

ORIGINAL: Yoozername
I do wonder if the actual mounting plays in. That is, if it's mounted on a carriafe or a turret.
I am able to run that. For the 88mm/71 at a firing height of 7 ft there is a 4.5% better chance of hitting a T-34 sized target than at 4.5ft at 1000m. At 1500m this advantage drops to only 1.5%.
[Edit]That is with a range estimation error of 18%.

I have to say, you getting onto this subject steered me into finding an error in Lorrin Bird’s hit percent program. I thought I had it right in my program but trying to match my results with the dispersion graphics you started the thread with made me review the program formula. As you have his book, page 95 step 5. Lorrin says the standard deviation at target range is .44. It is not. The 88mm/L56 50% zone is .3 at this range. Divided by 0.67448 it is .44, but he missed dividing by 2. So it should be .22. Other than that it is OK.



Yoozername -> RE: High Velocity AP round hit-zones (7/29/2013 2:33:13 PM)

Any chance of a patch?

In regards to the US tank weapons, I was reading a post war investigation and it was clearly stated that US tankers had rangefinders at platoon leader level and higher. Models M7 and M9A1. These are very similar to the German EM34. Almost all the tankers said that they did not use them. Training was inadequate and it was long and bulky and they felt it was vulnerable to damage while being used atop the tanks.

Given the accuracy of the weapons themselves, if combined with a rangefinder, US tankers could have had an advantage. But most actions in the ETO were short ranged and movement was considered more important. Using one of these coincidence rangefinders needed the AFV to be at a dead stop and the TC to be a still target himself. I think the US tankers believed to much in the TD theory of war. Basically, they did not want to tangle with German armor and certainly not at long range.

US tankers certainly liked to use HE at long range. Even the Germans commented on how lavishly the enemy tanks were supplied with HE. But HE can be 'walked-in' given it's pronounced end-effect. Supposedly HE and WP did not have tracer and this was something the tankers requested post war. They also liked the lower velocity 75mm HE since it could be controlled better as far as ricochet effect.



Yoozername -> RE: High Velocity AP round hit-zones (7/29/2013 3:09:47 PM)

M7 mounted on a tripod. If used by a TC, it would be laid across the cupola.

[image]https://fbcdn-sphotos-c-a.akamaihd.net/hphotos-ak-frc3/r90/582804_487235714666077_1177578572_n.jpg[/image]



Mobius -> RE: High Velocity AP round hit-zones (7/31/2013 9:18:41 PM)

Back to the 122mm. I made quick reference table from the DDR D-25T tables which includes the velocities, penetrations and dispersions. Also, it interpolates the same for the A-19 gun. I assume since the round is stable both guns pretty much behave the same at any given velocity.

[image]local://upfiles/21308/81DF824CAF9647BDA82BCC53386AC28F.jpg[/image]



Mobius -> RE: High Velocity AP round hit-zones (8/1/2013 11:58:18 PM)

Now to muddy the waters on Probability to Hit.
I looked more closely at the Cornell Laboratory formulas.

[image]local://upfiles/21308/311F149DD9C04F4A92BB2FD37FB65C69.jpg[/image]
Variables:
Cx=target width/sqrt(pi)
Cy=target height/sqrt(pi)
ux = std dev systematic error
uy = std dev systematic error
dx = std dev x dispersion
dy = std dev y dispersion

When only dispersion is evaluated and ax=0,ay=0 and ux =0,uy=0 this reduces to:

P(hit)=Cx*Cy / sqrt[(Cx^2 + 2*dx^2)*(Cy^2 + 2*dy^2)]

This produces different Phits than the German method.
I'll run through some tests of this and post the results of different methods side by side.




Mobius -> RE: High Velocity AP round hit-zones (8/2/2013 12:28:32 PM)

This is quite a quandary. And not what I expected. Using a 12% ranging error as a test the results are very much the same except for short ranges. (It does look pretty good.)

I also ran a few tests to see if there is a difference in hit percents if the target is circular or elliptical and indeed as one would expect it is slightly less than a rectangular target.


[image]local://upfiles/21308/B37F1B31FB8B48FFAE36ACE6EAF7D7F9.jpg[/image]



Yoozername -> RE: High Velocity AP round hit-zones (8/2/2013 2:40:46 PM)

Looking at the dispersion numbers, in all cases, it jumps out at me how coarse the numbers are. In many cases, it's a tenth of a meter and that must be taken into account. Again, the methodology is what I am interested in.

I shoot and know many people that do. I cringe when I hear them say "I will do a 3 shot grouping". I only do these at very close range, as I was taught in the military, to dial in MY dispersion. That is, repeatability of sighting the weapon and errors from my contribution (breathing, staedying, etc.) A 3 shot grouping at further ranges does not show dispersion data. Even for a weapon put in a vise. You need at least 10 and hopefully 32 or so. Most people have niether the ammo or patience for this sort of shooting.

It's nice to apply math and formala and such but I really think that fundamental issues are here. Check out this data-byte from a Panther book...Is he really saying that ALL the rounds will fall in such a tight group? I suspect a flaw in the data at 1500 meters, but many accounts of the 75mmL70 state that hits were obtained at 2000-3000 meters on average with just 4 rounds (AP and also HE).




Mobius -> RE: High Velocity AP round hit-zones (8/2/2013 3:28:09 PM)

That's a lot of bandwidth and a lot of white space for such a simple image.

That data seems to show that the dispersion is increasing faster with range in the horizontal plane than the vertical.
That's not unheard of as some Russian data from the WOT crowd shows.



Yoozername -> RE: High Velocity AP round hit-zones (8/2/2013 5:04:40 PM)

Actually, there seems to be an anomaly where the horizontal dispersion increases dramatically between 1000m and 1500m. There is no such dramatic increase between 1500m and 2000m. The vertical growth appears to be a linear pattern between 500m, 1000m, 1500m and 2000m.

Perhaps 1.50 should be 1.05?

In any case, the number of rounds fired would be great to know. The data is being reported to the second decimal point or a couple of inches.



[image]local://upfiles/20015/6F0E55EA90054EC88BBC9FC0BA69A9E2.jpg[/image]



Mobius -> RE: High Velocity AP round hit-zones (8/2/2013 5:18:09 PM)

If that is extreme dispersion then it is similar to 90mm M82 dispersion.
Extreme dispersion at 2100yd
90mm M82 2800f/s
@2100yd ex: h=41"/v=70"
75mm/L70
@2187yd ex: h=69"/v=59"



Yoozername -> RE: High Velocity AP round hit-zones (8/2/2013 9:03:03 PM)

I don't see the similarity. The 90mm has typical vertical dispersion greater than the horizontal dispersion. The 75mm seems to have extreme horizontal dispersion in comparison.



Mobius -> RE: High Velocity AP round hit-zones (8/2/2013 9:49:57 PM)

quote:

ORIGINAL: Yoozername

I don't see the similarity. The 90mm has typical vertical dispersion greater than the horizontal dispersion. The 75mm seems to have extreme horizontal dispersion in comparison.

Oh, I thought you were saying the magnitude of the numbers were too unbelievable.

It probably was because there were a limited number of test shots or the gun had some sort of peculiarity in the mounting. Take for example some of the tests of the 75mm M61 done at both Aberdeen and the University of New Mexico. One test of 10 shots had a slightly vertical favor to the dispersion and the other a decidedly horizontal favor.

In fact if the 'rectangle' is the extreme dispersion then it means its possible the 'mean' dispersion can be in say the horizontal but the extreme could be in the vertical or vis versa.

[image]local://upfiles/21308/0033EB82D609499F8549AFF8D9311635.jpg[/image]



Yoozername -> RE: High Velocity AP round hit-zones (8/3/2013 12:14:59 AM)

Yes, 10 rounds would be limited (as far as achieving real dispersion numbers). But it ain't bad needer. It is interesting to compare that data with the 'Brit' shoot at the 5 by 2 foot target (I assume a Panther mantlet model?). Note the 'rectangles' and the mean dispersion relationships. I would say the bottom shoot had some outliers and if both shoots used 32 rounds, the numbers would have converged.



Mobius -> RE: High Velocity AP round hit-zones (8/3/2013 2:46:16 AM)

quote:

ORIGINAL: Yoozername
But it ain't bad needer. It is interesting to compare that data with the 'Brit' shoot at the 5 by 2 foot target (I assume a Panther mantlet model?).

I'll take a stab at reading the runes....
The mean vertical dispersion of 5.1"@1000yds can be converted to SD by dividing it by .67449 = 7.4".
The ratio of 2' turret above (or below) center is: 12"/7.4"=1.62. Convert 1.62 Standard deviations to %=89.5%.

Let's see if the width comes into play.
7.4"/.67449=10.96. 5'/2=30" so 30"/10.96" =2.74 std dev. =99.34%. 99.34x89.5=88.8%.

Virtually the same as the 90% mentioned in WO 291/751 AORG Memo No.427.



Yoozername -> RE: High Velocity AP round hit-zones (8/3/2013 4:31:53 AM)

One criteria that has been buzzing around my brain is "What were the German acceptance tests for receiving new weapons (guns)?".

These Germans certainly tested AP ammo for penetration, they tested armor for resistance...I find it very peculiar if they did not have some accuracy test for guns themselves???



Mobius -> RE: High Velocity AP round hit-zones (8/3/2013 4:44:29 PM)

The Bird/Livingston hit formula does correspond pretty closely with some British gun firing tests. On the other hand the Cornell Lab does have pretty solid theoretical grounding. But it seems a bit low when compared to British firing tests at low ranges. Right now I am leaning to splitting the baby and using an average of both methods.

For an example shown below a theoretical hit probability graph of the 17 pdr with 22.5% ranging error vs. a hull up PZ IV.



[image]local://upfiles/21308/8C7161A32051453DA34FD1DDEE91A736.jpg[/image]



Yoozername -> RE: High Velocity AP round hit-zones (8/4/2013 5:40:52 PM)


quote:

ORIGINAL: Mobius

quote:

ORIGINAL: Yoozername
But it ain't bad needer. It is interesting to compare that data with the 'Brit' shoot at the 5 by 2 foot target (I assume a Panther mantlet model?).

I'll take a stab at reading the runes....
The mean vertical dispersion of 5.1"@1000yds can be converted to SD by dividing it by .67449 = 7.4".
The ratio of 2' turret above (or below) center is: 12"/7.4"=1.62. Convert 1.62 Standard deviations to %=89.5%.

Let's see if the width comes into play.
7.4"/.67449=10.96. 5'/2=30" so 30"/10.96" =2.74 std dev. =99.34%. 99.34x89.5=88.8%.

Virtually the same as the 90% mentioned in WO 291/751 AORG Memo No.427.



US tankers said that they felt the 75mm was as accurate as the 76mm under most battlefield ranges. The 75mm was certainly over-built in that it was rated for thousands of shots. Perhaps this and it's relatively low velocity gave it very repeatable results.



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