Estimating Muzzle Velocity via Gun Caliber

(Created September 2016)

Sometimes all you have is the barest pieces of data on a gun, particularly for German “Paper” guns in World War II, where they're described as “7.5cm KWK 42 L/100” and that's it. No detailed data.

NOTE: The U.S. measured “calibre” as the length from the muzzle to the rear of the barrel (bore), while the Germans measured it from the muzzle to the rear of the breech. Thus, the US 90mm M3 gun would have a calibre of L50 under the US system and L52.5 under the German system.

There is a way to estimate muzzle velocity from gun caliber, however.

A graph found in the November 1944 issue (#17) of Nachrichtenblatt der Panzertruppen (available on NARA RG 242 T78 Roll 623) and reproduced (with Imperial Measurements) in Armoured Firepower: The Development of Tank Armament 1939-45 by Peter Gudgin has a very strong fit to actual muzzle velocity/calibers, as shown in the images below.

Original German Image in #17 of Nachrichtenblatt der Panzertruppen (Nov 1944)

Translated version with Imperial units found in Armoured Firepower: The Development of Tank Armament 1939-45 by Peter Gudgin (Bigger version)

Actual Round/Gun Combinations (Blue Circles) scatter plotted against graph line from Nachrichtenblatt der Panzertruppen.

What makes the NdP data so important is that it covers the Caliber ranges all the way down to L/0 and up to L/100, which is very hard to find data on, as guns in those ranges are experimental and aren't mentioned outside engineering or research reports.

Thus, with the velocity curve “filled” in by the NdP data, I evaluated other types of rounds and found that it also fit APCR (HVAP) rounds pretty well. I then plotted other types, resulting in the data below:

Data Used:

Caliber (L/x)

APBC/HE Curve (Baseline)

APCR Curve (Estimated)

APDS Curve (Estimated)

APDFS (Rifled) Curve (Estimated)

APDFS (Smoothbore) Curve (Estimated)

Curve % Adjustment
vs Baseline (L/50)

0

0

0

0

0

0

0.00%

5

105

129

154

180

210

13.14%

10

203

250

298

349

406

25.41%

15

294

363

433

506

589

36.80%

20

380

468

559

654

761

47.56%

25

460

567

677

792

922

57.57%

30

536

661

788

922

1,073

67.08%

35

607

749

893

1045

1,216

75.97%

40

675

832

992

1,161

1,351

84.48%

45

738

911

1,086

1,271

1,479

92.37%

50

799

985

1,175

1,375

1,600

100.00%

55

856

1,055

1,259

1,473

1,714

107.13%

60

910

1,122

1,338

1,566

1,822

113.89%

65

960

1,184

1,412

1,653

1,923

120.15%

70

1,007

1,242

1,482

1,734

2,018

126.03%

75

1,051

1,296

1,546

1,809

2,105

131.54%

80

1,091

1,345

1,605

1,878

2,185

136.55%

85

1,127

1,389

1,657

1,939

2,257

141.05%

90

1,158

1,428

1,703

1,993

2,319

144.93%

95

1,184

1,460

1,742

2,038

2,372

148.19%

100

1,205

1,486

1,772

2,074

2,413

150.81%

NOTES:

1.) Charts are based off using L50 entry as baseline and calculated using the percentage differences in the German AP/HE Curve to that L50 Baseline.

2.) When introducing APDS/APDFS Sabot Rounds, subtract about 100~ m/sec from the velocity to account for the newness of the type (APDS in WW2, APDFS rounds in the late 1950s/early 1960s)

3.) US Heavy Naval Guns generally have HE shells 60 to 100 m/sec faster than the AP shell for that gun. Use the APBC/HE curve as given for AP shells, and add 60-100 for HE shells.

USING THE DATA ABOVE

Let's say you have the 20 pounder gun, which is L/64, and you'd like to estimate the performance of a hypothetical “cut down” L/45 version for use in lightweight (compared to the Centurion) tanks circa 1946.

Example 1 (Directly from Chart):

This method is useful for completely hypothetical weapons that never actually existed.

Looking at the chart, you see that for a L/45 gun, performance would be about:

APCBC/HE: 740~ m/sec
APCR: 900~ m/sec
APDS: 986 to 1,000 m/sec (remember to subtract about 100 m/sec to take into account the fact that APDS shot was still in its infancy in 1946).

And if the tank somehow survives to the 1970s in active duty (a high probability in poorer countries), then you'd see 1,250~ m/sec APDFS rounds about then.

Example 2 (Adjustment of Actual Data):

For cases where you have actual shot data (20 pdr APDS was about 1,430 m/sec and caliber was L/64); you can adjust using the percentages:

L45 (92.37%)
L65 (120.15%)

0.9237 / 1.2015 = 0.7688

Adjusting the 1,430 m/sec shot (1,430 * 0.7688 = 1099.384) results in an APDS muzzle velocity of 1,100 m/sec.

Likewise, adjusting the L45 APDS Curve with the L45 APDFS (Rifled) Curve (1,271 / 1,086 = 1.1703) and then applying that to the above APDS muzzle velocity (1,100 m/sec * 1.1703 = 1,287.33 m/sec) gives you a readout of 1,287 m/sec for the rifled fin stabilized sabot round of the 1970s.