First Round Accuracy of German Tungsten Core Ammo

[rexford]

FIRST ROUND ACCURACY OF GERMAN TUNGSTEN CORE AMMO

This article looks at the basic ballistic characteristics of the German tungsten core APCR (Armor Piercing Composite Rigid) rounds, estimates first round hit probability against a 2m high by 2.5m wide target and compares APCR to APC and APCBC results.

APCR is a full caliber projectile which encloses a small, high density tungsten core penetrator in a light weight carrier.

The following table presents the hit percentages against a 2m high by 2.5m wide target when the aim is at the center of a stationary object with a known range, where misses are due to twice the firing trial random scatter: (source is German set of ballistic tables for tungsten core and other projectiles):

HIT PERCENTAGE AT A KNOWN RANGE

TUNGSTEN CORE AMMUNITION

DOUBLED DISPERSION

RANGE...50L60...75L48...88L56...88L71

100m..........100......100........100.......100

300m..........100......100........100.......100

500m............98........99........100.......100

700m............84........88..........95.........98

900m........................69..........87.........93

1100m......................52..........74.........85

1300m......................37..........63.........76

1500m......................25..........52.........66

1700m......................19.......................58

1900m......................14.......................50

Notes:

All rounds are later type tungsten core ammo , no arrowhead types

Misses due to doubled random scatter

Calculated by Germans from vertical and lateral scatter data

German ballistic tables provide data for 100m range increments

The 75L48 scatter beyond 700m is markedly inferior (wider spread) to both 88mm rounds., which is similar to the comparison of APCBC results.

The German APC and APCBC hit percentage at a known range against a stationary 2m by 2.5m target is presented for comparison purposes:

HIT PERCENTAGE AT A KNOWN RANGE

APC AND APCBC AMMUNITION

DOUBLED DISPERSION

RANGE...50L60...75L48...88L56...88L71

100m..........100......100........100.......100

300m..........100......100........100.......100

500m..........100......100........100.......100

700m..........100........92..........99.........97

900m.......... 98........75..........96.........90

1100m..........92........58..........90.........81

1300m..........81........44..........82.........71

1500m..........68........33..........74.........61

1700m......................24..........64.........53

1900m......................18..........56.........46

Notes:

50L60 firing APC, others fire APCBC

Misses due to doubled random scatter

Calculated by Germans from vertical and lateral scatter data

While the random scatter of the tungsten core ammo is greater and the hit percentages at constant aim are lower for 50L60, 75L48 and 88L56 rounds, the scatter pattern for 88L71 Pzgr 40/43 is smaller than the APCBC dispersion. (resulting in a higher hit rate).

Combining the scatter data with a 25% average range estimate error (bell shaped error curve) results in the following first round hit probabilities for German tungsten core ammo against a stationary 2m x 2.5m target:

FIRST ROUND HIT PROBABILITY BY TUNGSTEN CORE AMMO

25% AVERAGE RANGE ESTIMATE ERROR

RANGE...50L60...75L48...88L56...88L71

500m.......... 86........86.........88.........97

800m...........43........39.........48.........65

1100m.........18........16.........26.........38

1400m.......................8.........15.........22

Note:

Muzzle velocities are 1130 m/s for 50L60 and 88L71, and 930 m/s for 75L48 and 88L56

The following table presents the computed hit probabilities for the APC and APCBC ammo fired by the same guns against a stationary 2m x 2.5m target with 25% average range error:

FIRST ROUND HIT PROBABILITY BY APC AND APCBC CORE AMMO

25% AVERAGE RANGE ESTIMATE ERROR

RANGE...50L60...75L48...88L56...88L71

500m.......... 81........73.........81.........93

800m...........35........33.........39.........57

1100m.........17........15.........20.........32

1400m.........10..........7.........12.........18

Note: 50mm gun firing APC, others firing APCBC.

Although the accuracy of tungsten core ammo beyond close range is often downplayed due to the greater velocity loss with range compared to APCBC ammunition, the 75mm and 88mm guns are more accurate firing tungsten core due to the higher velocities and flatter trajectory.

The basis for the computed hit percentages against a stationary 2m by 2.5m target is a statistical analysis using the vertical and lateral scatter patterns obtained from firing tests. The 50% zone for the scatter follows (50% of scatter with a constant aim within the stated distance):

50% ZONES FOR VERTICAL AND LATERAL SCATTER

VERTICAL/LATERAL ZONE LENGTH FOR CONSTANT AIM

SINGLE VALUES OF DISPERSION

50L60 TUNGSTEN CORE

100m....0.05m/0.05m

300m....0.17m/0.16m

500m....0.30m/0.28m

800m....0.51m/0.49m

Note:

At 800m range, 50% of the rounds fired at a constant aim will be within a box that is 0.51m high and 0.49m wide, which corresponds to a vertical distance of 0.26m above or below the mean impact point and a lateral distance of 0.25m right or left.

50L60 APC

100m....0.03m/0.03m

300m....0.09m/0.09m

500m....0.15m/0.15m

800m....0.26m/0.24m

1000m..0.33m/0.30m

1300m..0.47m/0.41m

1500m..0.58m/0.50m

75L48 TUNGSTEN CORE

100m....0.1m/0.0m

300m....0.2m/0.1m

500m....0.3m/0.3m

800m....0.5m/0.4m

1000m..0.7m/0.6m

1300m..1.0m/0.8m

1500m..1.2m/1.0m

2000m..1.8m/1.5m

Note:

When only one decimal point is provided the figure has been rounded up or down. The actual figure may be up to 0.049m above or below the listed number.

75L48 APCBC

100m....0.1m/0.0m

300m....0.2m/0.2m

500m....0.3m/0.2m

800m....0.4m/0.4m

1000m..0.6m/0.5m

1300m..0.8m/0.7m

1500m..1.0m/0.9m

2000m..1.6m/1.3m

2500m..2.4m/1.8m

3000m..3.3m/2.3m

88L56 TUNGSTEN CORE

100m....0.1m/0.1m

300m....0.2m/0.1m

500m....0.2m/0.1m

800m....0.4m/0.2m

1000m..0.5m/0.3m

1300m..0.7m/0.4m

1500m..0.8m/0.5m

88L56 APCBC

100m....0.1m/0.1m

300m....0.2m/0.1m

500m....0.2m/0.2m

800m....0.3m/0.2m

1000m..0.4m/0.2m

1300m..0.5m/0.3m

1500m..0.6m/0.3m

2000m..0.9m/0.5m

2500m..1.2m/0.7m

3000m..1.7m/1.0m

Note:

The remarkable aspect of the Tiger 88mm firing APCBC is that 50% of the constant aim rounds at 1000m will be within 0.1m or 10cm (4 inches) right or left of the mean impact point, and equal to or less than 0.2m or 20cm (8 inches) above or below the average impact, after rounding to the nearest tenth of a meter. The Tiger rounds had unusual repeatability.

88L71 TUNGSTEN CORE

100m....0.0m/0.0m

300m....0.1m/0.1m

500m....0.2m/0.2m

800m....0.3m/0.3m

1000m..0.4m/0.3m

1300m..0.5m/0.4m

1500m..0.6m/0.5m

2000m..0.8m/0.7m

3000m..1.2m/1.0m

88L71 APCBC

100m....0.1m/0.0m

300m....0.1m/0.1m

500m....0.2m/0.2m

800m....0.4m/0.3m

1000m..0.5m/0.3m

1300m..0.6m/0.4m

1500m..0.7m/0.5m

2000m..0.9m/0.7m

2500m..1.1m/0.9m

3000m..1.4m/1.0m

3500m..1.6m/1.2m

4000m..1.8m/1.4m

Since the above data is for the 50% zone and is based on a bell shaped normal distribution curve, the following multipliers would be used to convert to other coverages:

50% zone includes half of the random scatter and equals the listed distance

68.26% zone equals 1.48 times the 50% zone lengths (68.26% is one standard deviation)

75% zone covers 1.71 times the 50% zone lengths

80% zone covers 1.90 times the 50% zone dimensions and includes 80% of shots

85% zone includes 2.14 times the 50% zone lengths

90% zone covers a distance 2.44 times as large as the 50% zone

95% zone covers 2.91times the 50% zone size

For double dispersion, the listed 50% zone dimensions would be doubled.

The Germans used the above 50% zone figures to compute the hit percentages against a 2m high by 2.5m wide target assuming constant aim at a known range. As an example of use we'll look at the case for an 800m shot by 50mm L60 APCR using doubled dispersion.

The doubled dispersion 50% zone for APCR at 800m is 1.02m high and 0.98m wide. Dividing the vertical target height of 2m by 1.02m equals 1.96 times the doubled 50% zone height. Dividing 2.5m by the 0.98m 50% zone width results in 2.55.

The above calculations result in vertical and lateral hit probabilities of 81.4% and 91.5%, which are multiplied together to obtain an overall hit percentage of 74% after rounding. The German ballistic table for 50L50 APCR presents a 74% hit chance against a 2m x 2.5m target at 800m with doubled dispersion and constant aim. It appears that the Germans used dispersion data with two decimal places when they calculated the hit probability against a 2m by 2.5m target even though they usually only show one decimal place in the tables.

The German ballistic tables which were used as a reference for this article contain trajectory information for APC, APCBC, APCR, HEAT and HE rounds, use 100m range increments and provide data for flight time, gun elevation, descent angle, 50% zones for vertical and lateral scatter and ground impact of round, velocity at range, maximum trajectory height and battlesight aim range against a 2m high target.

VELOCITY VS RANGE DATA FOR GERMAN APCR

RANGE..50L60..75L48..88L56..88L71

0m.....1130.....930......930......1130

100m...1074.....910......916......1116

500m....862.....832......863......1061

800m....717.....775......824......1020

1000m...........739......798........994

1500m...........651......736........928

RETAIN..........70%.......79%.......82%

Weight.1.07.....4.1...... 7.3.......7.3

Note:

Velocity in m/s

Weight refers to total projectile kg

RETAIN refers to percentage of muzzle velocity available at 1500m

VELOCITY VS RANGE DATA FOR GERMAN APC AND APCBC

RANGE..50L60...75L48....88L56......88L71

0m......835.....750......780.......1000

100m....809.....738......770........990

500m....707.....691......734........952

800m....636.....659......707........924

1000m...591.....637......690........906

1500m.. 491.....585......647........860

2000m...........536......607........815

3000m...........451......532........729

4000m....................................648

RETAIN..58%.....78%.......83%.......86%

Weight.2.06.....6.8......10.0......10.16

Note:

50mm round is APC, others are APCBC

RETAIN refers to percentage of muzzle velocity available at 1500m

The difference in velocity loss percentage at 1500m between APCR and APCBC rounds is less than -5% for 88mm ammo and is about -10% for 75mm APCR. The 75mm and 88mm APCR rounds also possess a higher velocity at 1500m than APCBC, which results in a flatter more accurate trajectory for APCR and contributes to a higher hit percentage.

MAXIMUM TRAJECTORY HEIGHT

APCR VS APC/APCBC AMMO

RANGE..50L60.....75L48....88L56...88L71

500m...0.3/0.5..0.4/0.6..0.4/0.5..0.3/0.3

800m...1.0/1.5..1.1/1.5..1.0/1.4..0.7/0.9

1000m..............1.8/2.5..1.7/2.3..1.1/1.4

1500m..............4.5/6.3..4.0/5.5..2.7/3.2

Notes:

Max trajectory heights in meters

Slash separates APCR/AP trajectory data

Applying a curve of best fit approach to the German base data for 0m to 1000m shots, the vertical and lateral 50% zones for 88L56 APCBC were estimated to two decimal places:

50% DISPERSION ZONES FOR 88L56 APCBC

VERTICAL AND LATERAL DISTANCES

RANGE…VERTICAL..LATERAL

100m………0.10m………0.09m

200m………0.13m………0.11m

300m………0.16m………0.12m

400m………0.19m………0.14m

500m………0.21m………0.15m

600m………0.24m………0.17m

700m………0.27m………0.18m

800m………0.30m………0.19m

900m………0.34m………0.21m

1000m...0.37m………0.22m

On constant aim shots at 1000m, half of the 88mm rounds would vary from the mean impact point by less than 7.3 inches vertically and 4.4 inches laterally during the firing tests (single dispersion).

It is worth noting that the muzzle velocities for German 75L48 and 88L56 APCR are lower than the corresponding velocities for the tungsten core rounds used by the Americans (76mm at 1037 m/s and 90mm HVAP at 1021 m/s) and Russians (76.2mm at 965 m/s and 85mm HVAP at 1050 m/s).

Even though the early arrowhead tungsten core rounds (APCR) had a relatively poor ballistic shape and sometimes became stuck in the barrel of German guns, the later war APCR appears to have possessed good ballistic characteristics and was more accurate than the 75mm and 88mm APCBC rounds.

[ August 21, 2004, 07:55 AM: Message edited by: rexford ]

[Mr. Tittles]

Since the above data is for the 50% zone and is based on a bell shaped normal distribution curve, the following multipliers would be used to convert to other coverages:

50% zone includes half of the random scatter and equals the listed distance

68.26% zone equals 1.48 times the 50% zone lengths (68.26% is one standard deviation)

75% zone covers 1.71 times the 50% zone lengths

80% zone covers 1.90 times the 50% zone dimensions and includes 80% of shots

85% zone includes 2.14 times the 50% zone lengths

90% zone covers a distance 2.44 times as large as the 50% zone

95% zone covers 2.91times the 50% zone size

For double dispersion, the listed 50% zone dimensions would be doubled.

Did the German data state it was a bell shaped curve or are you assuming that?

The 50% zone is an area. Should the first deviation be 1.48 times the 50% area?

[ August 21, 2004, 10:04 AM: Message edited by: Mr. Tittles ]

[Mr. Tittles]

Wasn't the early 50mmL60 APCR higher velocity than the later model (called Pzgr40/1 I believe)?

Should be on Guns and ARmor site.

Also, the 50mmL42 Pnzrg40 was made in some large numbers.

[ August 21, 2004, 01:13 PM: Message edited by: Mr. Tittles ]

[Mr. Tittles]

The US 76mm HVAP round was said to be extremely accurate also. I just wonder if they had sights that were marked for this ammo?

Perhaps HVAP/APCR got a bad rap early in the war and it stuck?

[Mr. Tittles]

I really have my doubts about how this data is being analyzed.

First off..This Double Dispersion is said to be doubling both the height and width. So for a single dispersion of 1m by 1m (1 sq. m) you get a double dispersion of 2mx2m=4sqm? Its quadrupling the area? It really seems a major error fudge considering it does not take into accout range estimation errors..

Take the 75mmL48 (single dispersion). If it fires 10 rounds at 800m, then 5 will generally land in a area the size of my computer monitor screen. But I am not certain just where rexford thinks the other five would actually land. Given double dispersion initial fudge, it may miss a 5 sq m target. (Note: A German 88mmL56 could put 5 out of 10 on a sheet of 11.5 x8 inch paper)

Germans used to zero their tank guns at 1000m. If you have ever zeroed a weapon, then you know what a shot group is and how important it is to be able to move a shot group (After achieving it).

If you fire 10 rounds and 5 are nearly kissing each other, but the other 5 are distributed squares away; then you don't have a shot group. You don't have repeatability and you don't have a basis for zeroing. A rule of thumb is that the shot group should be smaller than the target area size!

I would really like to see raw data and am leary of some quantum leaps taking place here.

[ August 21, 2004, 11:12 PM: Message edited by: Mr. Tittles ]

[Mr. Tittles]

Die Munitionsfertigung für die 8,8-cm-KwK 36 sah wie folgt aus (in 1.000 Schuß):

Bezeichnung ___________1942___1943____1944

8,8-cm-Sprenggranate ___14,1__1.392,2__459,4

8,8-cm-Panzergranate39__21,2___324,8___394,4

8,8-cm-Panzergranate40___0,8_____8,9 ------

The 88mmL56 PnzGr40 was only produced in very small quantities. Total of less than 10,000.

[Mr. Tittles]

Bezeichnung _________1942__1943__1944__1945

5-cm-Sprenggranate 38 753,8 1.138,7 684,8 11,3

5-cm-Panzergranate 39 644,5 1.186,6 410,1 28,7

5-cm-Panzergranate 40 184,6 135,9 - -

This data shows that the 50mmL60 APCR was produced in 1942 in substantial numbers. It generally fell off in 43 as regular AP nearly doubles.

The 50mmL42 APCR was also produced in sizable numbers. In both 1941 and 1942, 50mmL42 APCR accounts for about 1 out of 4 antitank rounds produced for this weapon (note: 50mmL42 and 50mmL60 fired different cartridges). These were probably arrowhead types. The data that rexford has for the 50mmL60 above appears to be the later model 50mmL60 improved APCR.

http://gva.freeweb.hu/weapons/german_guns3.html

The fact is that 75mm and 88mm APCR was produced in very small numbers. Especially when you consider that 75mmL48 were very common (being used in Panzer IV, StugIII and Hetzer as well as other vehicles), it represents a very special round indeed.

[ August 22, 2004, 09:13 AM: Message edited by: Mr. Tittles ]

[Mr. Tittles]

The raw data I would like to see is exactly where all the test shots landed. I would like to know not only where 50% would be contained in a rectangle, but where the other 50% actually land.

I am not attacking rexford but I have my doubts about the methodology used here. It may be the Germans methods are screwy.

Basically, the 'scatter' is eliptical in nature. generally, the height difference is greater than the width difference. Since the target size is more forgiving in the width (2.5m vs. 2m), the critical data is the height variation.

If I understand what rexford claims, he is saying that 50% of the rounds could land with a box of 1 sq meter but the other 50% could be in a box of up to 8.5 sq meters or so? This is for single dispersion mind you. The target is only 5 sq. meters.

This would make adjusting fire almost meaningless. An example would be a 75mmL48 firing at 1500m. It would be such a loose group that keeping rounds on target would be luck. Walking rounds in from an unknown range begs any method to be worthwhile.

The shot group must be tighter. I suspect some dimensional mistake.

[ August 22, 2004, 01:12 PM: Message edited by: Mr. Tittles ]

[Andreas]

Hi Lorrin

Can you drop me an email please?

Cheers

Andreas

[Mr. Tittles]

The German ballistic tables which were used as a reference for this article contain trajectory information for APC, APCBC, APCR, HEAT and HE rounds, use 100m range increments and provide data for flight time, gun elevation, descent angle, 50% zones for vertical and lateral scatter and ground impact of round, velocity at range, maximum trajectory height and battlesight aim range against a 2m high target.

I would like to see the 75mmL48 HE and HEAT vertical scatter if you would post it. It would be interesting to compare with the AP.

[Mr. Tittles]

(1000's of rounds)

Bezeichnung _______________1942__1943__1944__1945

7,5-cm-Granate 38 HL - - - ---572,2 --1.157,1 - -

7,5-cm-Panzergranate 39 - - - 262,5--1.924,0--1.906,5-82,0

7,5-cm-Panzergranate 40 - - -7,0 ----36,4 - -

7,5-cm-Panzergranate 40 W - -4,4---70,3 - -

I would assume 7,5-cm-Panzergranate 40 W is an improved APCR round. This data is for 75mmL48 and 75mmL43 guns. Interestingly, they stopped making HEAT and APCR after 1943.

[Mr. Tittles]

These are numbers collected by British Army Operational Research Sections during WWII (summarized in WO 291/180) Ranges are in yards, report indicates that the target is assumed to be a approximately the size of a Tiger Ie. Hit probability also assumes no crew error in line or range estimation.

Versus a Hull-Up static Target

6 pdr @ 500yrds…..100 percent chance of a First Round Hit (FRH: first round hit)

6 pdr @ 1000yrds…100 percent FRH

6 pdr @ 1500yrds…96 percent FRH

6 pdr @ 2000yrds…87 percent FRH

17 pdr @ 500yrds……100 percent FRH

17 pdr @ 1000yrds….100 percent FRH

17 pdr @ 1500yrds….100 percent FRH

17 pdr @ 2000yrds….98 percent FRH

17 pdr @ 2500yrds….93 percent FRH

Probability of a hit on first round, hull down static Tiger Ie sized target, assumed no error in line or range by crew.

Versus a Hull-down static Target

6 pdr @ 500yrds…..85 percent FRH

6 pdr @ 1000yrds…43 percent FRH

6 pdr @ 1500yrds…22 percent FRH

6 pdr @ 2000yrds…14 percent FRH

Versus a Hull-down static Target

17 pdr @ 500yrds…..88 percent FRH

17 pdr @ 1000yrds…51 percent FRH

17 pdr @ 1500yrds…29 percent FRH

17 pdr @ 2000yrds…18 percent FRH

17 pdr @ 2500yrds…12 percent FRH

[Mr. Tittles]

The above data was cut and paste from an old post by Jeff Duquette.

Note that a Tiger I is not 2mx2,5m. And niether is a Sherman tank (2.9mx2.67m?).

My point is that the German data is for a relatively small target. Antitank fire is sort of a step function in that close don't count when its a miss.

I think the casual reader show note that the German numbers that rexford posted above are calculated numbers based on data about where 50% of the rounds land (we all followed his example about the 50mmL60 APCR at 800m right?). They are using a statistical method to try to fudge in human errors and other factors.

The British data is based on actual firing under pristine conditions. Range is known and everything else is minimized. It is showing the precision of the weapon itself. Notice just how precise it is against a large target such as a TigerI.

[ August 23, 2004, 11:31 AM: Message edited by: Mr. Tittles ]

[rexford]

Originally posted by Mr. Tittles:

Wasn't the early 50mmL60 APCR higher velocity than the later model (called Pzgr40/1 I believe)?

Should be on Guns and ARmor site.

Also, the 50mmL42 Pnzrg40 was made in some large numbers.

Yes, early 50mm APCR was higher velocity but a much worse ballistic shape so it lost velocity a heck of alot faster.

[rexford]

Originally posted by Mr. Tittles:

The US 76mm HVAP round was said to be extremely accurate also. I just wonder if they had sights that were marked for this ammo?

Perhaps HVAP/APCR got a bad rap early in the war and it stuck?

Tungsten core rounds with a ballistic shape similar to U.S. 76mm HVAP or later war German APCR (75mm and up) would lose velocity much slower than arrowhead and would be more accurate than APCBC shots, with greater accuracy advantages at short and medium ranges.

The data sheets that went with the ballistic tables indicate that the 50% zones were part of a bell shaped normal distribution curve, and the multipliers which went with it are what would occur with that sort of curve.

During the German firing trials the 1500m results for 75L48 APCBC resulted in 50% of the shots falling within a 0.6m x 0.5m box. So the box was not really a square, the vertical scatter is usually larger than the lateral.

Measured from box center, 50% of the rounds are contained within plus or minus 0.3m from center (about 1 foot), and high or low within 0.25m (10 inches or so).

68.3% of the shots would be within a box about 0.9m x 0.75m (1.5 multiplier after rounding), or 0.45m up or down and 0.38m left or right.

95.5% within a box 1.8m x 1.50m, or 0.9m up/down or 0.75m left/right.

I've looked at ALOT of scatter data for WW II weapons, and the 75L48 APCBC data looks large compared to high quality guns like the 75L70, 88L56 and 88L71 but is similar to the German 76.2L51.5 and other weapons of WW II.

With regard to corrections after a miss, I've stated that the wide double dispersion figures could make good corrections difficult, on occasion, as the range increased.

I don't know if the use of double dispersions would be a good idea for the placement of follow-up shots. Never came to a conclusion on that.

I will get the HEAT and HE data for a variety of guns and ammo and post it here.

[rexford]

Originally posted by Mr. Tittles:

I really have my doubts about how this data is being analyzed.

If you fire 10 rounds and 5 are nearly kissing each other, but the other 5 are distributed squares away; then you don't have a shot group. You don't have repeatability and you don't have a basis for zeroing. A rule of thumb is that the shot group should be smaller than the target area size!

I would really like to see raw data and am leary of some quantum leaps taking place here.

Plot the data on a piece of graph paper.

For a total single dispersion distance of 1.0m (lateral and vertically), the spread of shots is a smooth curve with 50% within 0.5m of the center. And 68% within 0.75m of the center. And 95% within 1.0m.

The shots are bunched up around the center point and the tendency of an individual round to fall further from the center falls off rapidly with distance from the center.

A bell shaped normal distribution curve means it is shaped like a bell, most of the height near the center and very little at the extremes with a rapid fall-off in height from just outside the center to the edges.

Look at a normal distribution curve and you can draw some realistic conclusions from the numbers.

[rexford]

Originally posted by Andreas:

Hi Lorrin

Can you drop me an email please?

Cheers

Andreas

I dropped my internet service and don't have personal e-mail at the library.

Did you have a question or need a copy of something?

[rexford]

Originally posted by Mr. Tittles:

The above data was cut and paste from an old post by Jeff Duquette.

Note that a Tiger I is not 2mx2,5m. And niether is a Sherman tank (2.9mx2.67m?).

My point is that the German data is for a relatively small target. Antitank fire is sort of a step function in that close don't count when its a miss.

I think the casual reader show note that the German numbers that rexford posted above are calculated numbers based on data about where 50% of the rounds land (we all followed his example about the 50mmL60 APCR at 800m right?). They are using a statistical method to try to fudge in human errors and other factors.

The British data is based on actual firing under pristine conditions. Range is known and everything else is minimized. It is showing the precision of the weapon itself. Notice just how precise it is against a large target such as a TigerI.

I doubt that the British data is for actual firing tests, they usually calculated data such as Jeff presented. I will find the original report and see if they were calculated, which is what I would guess they are.

[Mr. Tittles]

My main thought is; Could the curve need to be applied to the area instead of the dimensions? An example would be that 50% of the rounds fall in 1 sq. ft. Then 68.3% would fall in 1.5 sq. ft?

Multiply 1.5 by the dimensions seems to spread out the rounds too much. Especailly when you get to 95% and apply at 1500 meters or so. The rounds are just all over the place.

We are just talking single dispersion here of course. But if you would, please elaborate on how you calculate double dispersion. Thanks.

[rexford]

Originally posted by Mr. Tittles:

I am not attacking rexford but I have my doubts about the methodology used here. It may be the Germans methods are screwy.

Basically, the 'scatter' is eliptical in nature. generally, the height difference is greater than the width difference. Since the target size is more forgiving in the width (2.5m vs. 2m), the critical data is the height variation.

If I understand what rexford claims, he is saying that 50% of the rounds could land with a box of 1 sq meter but the other 50% could be in a box of up to 8.5 sq meters or so? This is for single dispersion mind you. The target is only 5 sq. meters.

I suspect some dimensional mistake.

No dimensional mistake, perhaps you have not seen the actual 50% zones before and they seem out of line for some guns.

If 50% land within 0.5m left or right of the center, there will be a small probability that one round will land 2.0m right or left. Will almost never occur but could.

[Mr. Tittles]

Thats what I thought it was. You seem to have been saying that the zone lengths were both multiplied by the factor. That would spread out the rounds and make zeroing a nightmare.

[rexford]

Here is a comparison of the 90% zones at 1000m for a few capped AP type rounds:

50L60 APC: 0.81m vertical and 0.73m lateral

88L56 APCBC: 0.98m vert and 0.56m lat

17 pdr APCBC: 1.19m vert and 1.01m lat

75L48 APCBC: 1.37m vert and 1.27m lat

If one doesn't double the dispersion, 90% of the 75L48 APCBC shots at 1000m are no more than 0.685m up or down from the impact center, and no more than 0.635m left or right.

In terms of feet, we're talking a max scatter from impact center (90% of the rounds) of 2.25' vertically and 2.08' laterally.

With regard to the "badness" of the scatter data for 75L48 APCBC, it is similar to the 88mm Flak 18 and 36 firing Pzgr ammo, and is much better than 2 pdr tank killers shooting AP shot.

We've looked at alot of WW II scatter data for 50% and 90% zones, and the 75L48 APCBC figures seem reasonable.

Doubling the dispersion is an attempt to take the basic constant aim scatter pattern, where nerves of steel hold fast to the aim, and mix it up with combat action where nervousness and a possible tendency to shoot before one is hit combines with possible imperfect care of the weapon system to result in not so good an aim as one might do on a proving grounds after a good night's rest and plenty of time to prime up the goods.

[rexford]

Originally posted by Mr. Tittles:

Thats what I thought it was. You seem to have been saying that the zone lengths were both multiplied by the factor. That would spread out the rounds and make zeroing a nightmare.

They are both multiplied by the conversion factor.

If the 50% zone is 1m high and 0.5m wide, the 90% zone is 2.44m high and 1.22m wide (1.22m left and right of center and 0.61m left and right of center).

And the doubled dispersion for the 90% zone would be 4.88m high and 2.44m wide.

[Mr. Tittles]

Plot the data on a piece of graph paper.

For a total single dispersion distance of 1.0m (lateral and vertically), the spread of shots is a smooth curve with 50% within 0.5m of the center. And 68% within 0.75m of the center. And 95% within 1.0m.

You seem to be saying two different things. We are just talking single dispersion here. My origional question still stands; if 50% of the rounds land in 1sq m, where do the rest land?

[ August 23, 2004, 03:18 PM: Message edited by: Mr. Tittles ]

[Mr. Tittles]

The Germans used the above 50% zone figures to compute the hit percentages against a 2m high by 2.5m wide target assuming constant aim at a known range. As an example of use we'll look at the case for an 800m shot by 50mm L60 APCR using doubled dispersion.

The doubled dispersion 50% zone for APCR at 800m is 1.02m high and 0.98m wide. Dividing the vertical target height of 2m by 1.02m equals 1.96 times the doubled 50% zone height. Dividing 2.5m by the 0.98m 50% zone width results in 2.55.

The above calculations result in vertical and lateral hit probabilities of 81.4% and 91.5%, which are multiplied together to obtain an overall hit percentage of 74% after rounding. The German ballistic table for 50L50 APCR presents a 74% hit chance against a 2m x 2.5m target at 800m with doubled dispersion and constant aim. It appears that the Germans used dispersion data with two decimal places when they calculated the hit probability against a 2m by 2.5m target even though they usually only show one decimal place in the tables.

The Germans used the 50% dispersion data to calculate hit percentages. They did not calculate the 100% hit percentage to achieve a 50% chance. They used the 50% data to see the actual hit percentage.

Could you elaborate on how you made the jump from taking 50% data, doubling it and getting to the final hit percentage?