Armor Penetration Model
Gillingham Shear/Plug Equation

(Created April 2024)

Source: IDA Paper P-5032: Method of Estimating the Principal Characteristics of an Infantry Fighting Vehicle from Basic Performance Requirements (1.37~ MB PDF)

IDA Paper P-5032, in Appendix D: Derivation of Scaling Law for the Minimum Metallic Armor Thickness to Defeat Armor-Piercing Ammunition features a simple shear plugging equation developed using data found in Manufacturing Engineering and Technology by S. Kalpakjian and S. Schmid. It apparently works decently enough in the velocity range of 500 to 1500 m/sec.

The equation is:

Where:

T = Thickness of Material Perforated (millimeters)
D = Diameter of Projectile (millimeters)
M = Mass of Projectile (grams)
V = Striking Velocity (m/sec)
Y = Ultimate Tensile Strength of Target (megapascals)

UTS Values for Armor, as used in P-5032, are:

Rolled Homogeneous Armor (MIL-DTL-12560J): 1170 MPa.
High Hardness Armor (MIL-DTL-46100E): 1640 MPa.
Ti6AlV Armor (MIL-DTL-46077G): 970 MPa.
7039 Al Armor (MIL-DTL-46063G): 393 MPa. (from actual spec)

The authors of P-5032 suggest that it's possible to adjust T for obliquity by a simple LOS adjustment via the following formulas:

30 deg pen = T / [1 / cosine(0.523599 radians)] (30 degrees = 0.523599 radians)
60 deg pen = T / [1 / cosine(1.0472 radians)] (60 degrees = 1.0472 radians)

But these are only simple approximations and break down rather quickly.

DTIC AD301343 – Final Report on An Analytical Study of Data on Armor Penetration by Tank-Fired, Kinetic Energy Projectiles (31 May 1958) [Physical Page 35] gives us the performance of the shot at different obliquities; with the data below:

76mm M79 APC

15 lb (6.8 kg)

2,600 ft/sec (790 m/s) muzzle velocity

3” (76.2 mm) of 363 BHN @ 0 deg

1336 ft/sec (407.21 m/s)

RHA UTS = 1170

3” (76.2 mm) of 363 BHN @ 10 deg

1424 ft/sec (434.04 m/s)

RHA UTS = 1320

3” (76.2 mm) of 363 BHN @ 20 deg

1901 ft/sec (579.42 m/s)

RHA UTS = 2350

3” (76.2 mm) of 363 BHN @ 30 deg

1927 ft/sec (587.35 m/s)

RHA UTS = 2400

3” (76.2 mm) of 379 BHN @ 40 deg

2012 ft/sec (613.26 m/s)

RHA UTS = 2650

3” (76.2 mm) of 379 BHN @ 50 deg

2369 ft/sec (722.07 m/s)

RHA UTS = 3650

3” (76.2 mm) of 295 BHN @ 60 deg

2838 ft/sec (865.02 m/s)

RHA UTS = 5250

Curve Expert and Modified Power Law gives the following equations:

ATS = UTS * 1.02568702209668^A
(Using only 363 BHN Datapoints)

ATS = UTS * 1.02514853986326^A
(Using all Datapoints)

Where

ATS = Adjusted Tensile Strength
UTS = Ultimate Tensile Strenth
A = Angle in Degrees.

Pre-Built Calculator for Gillingham-Patel Shear Plug Model




Projectile Mass (grams)
Projectile Striking Velocity (m/sec)
Projectile Diameter (mm)

Ultimate Tensile Yield of Target (MPa)

Penetration (mm) (0 deg) (P-5032 Equation)
Penetration (mm) (30 deg) (Scaled Estimate)
Penetration (mm) (60 deg) (Scaled Estimate)