Shaped Charge/Hypervelocity Penetration

Shaped Charge/Hypervelocity
Penetration
by Ryan Crierie

At very high impact velocities (above 1,400 m/sec) projectiles actually take on many of the properties of a shaped charge jet upon impact on a target; particularly saboted long-rod projectiles fired from tank guns. In those circumstances, a modified shaped charge equation can be actually quite useful.

Traditional Shaped Charge Penetration Equation

Penetration = Length_Jet (Density_Jet / Density_Target)^0.5

Where:

EXAMPLE: Our shaped charge has a jet length of 80mm, it has a steel liner, and the target is aluminum.

Since Steel has a density of 7.86 g/cm³, and Aluminum a density of 2.70 g/cm³, the formula writes itself out as:

80 (7.86 / 2.70)^0.5 = 136.5

Thus, the penetration of our hypothetical shaped charge would be 136.5 millimeters.

The above formula only works for very specialized and narrow applications, because it does not take into account material properties other than density which can retard shape charge penetration.

For example, the Charge, Demolition, Shaped, 150mm has data easily obtainable for it's penetration into various materials from empirical testing along with having a known liner material (steel), allowing us to check the “traditional” formula, as shown below.

Target Material	Target Density (g/cm³)	Actual Penetration	Calculated Penetration (178mm jet)
Armor Plate (RHA) (Baseline to find jet length)	7.86	178mm	178mm
Mild Steel	7.86	250mm	178mm
Granite	2.75	380mm	301mm
Reinforced Concrete	2.4	760mm	322mm
Sandstone	2.3	910mm	329mm
NOTES: Results are rounded off to the nearest whole number.

Additionally, when materials used in modern anti-HEAT armor, such as Chobham are “tested” via the traditional calculations, they fare poorly:

Target Material	Target Density (g/cm³)	Calculated Penetration (178mm jet)
Alumina AD-90	3.7	259mm
Titanium Diboride	4.5	235mm
RHA (for Comparison)	7.86	178mm
NOTES: Results are rounded off to the nearest whole number.

Clearly, the traditional equation doesn't work very well for modern anti-armor shape charge warheads.

A slight modification of the traditional equation, yields surprisingly accurate results.

Penetration = Length_Jet (Density_Jet / Density_Target)^0.5 times (Yield_Jet / Yield_Target)^0.5

Where:

Penetration = Penetration of Shaped Charge in millimeters.
Length_Jet = Length of Shaped Charge Jet
Density_Jet = Density of Shaped Charge Jet (Liner Material)
Density_Target = Density of Target Material
Yield_Jet = Compressive Yield of Shaped Charge Liner MaterialYield_Target = Compressive Yield of Target Material

EXAMPLE: Our Shaped charge has a jet length of 80mm and the charge's liner is good, high quality steel , and we are attacking an AD-90 target.

Since Steel has a density of 7.86 g/cm³, and AD-90 a density of 3.70 g/cm³, so the left-hand side writes itself out as:

(7.86 / 3.70)^0.5 = 1.46

Our Steel has a compressive yield of 463 MPA, and AD-90 a compressive yield of 2600 MPA, the right-hand side writes itself out as:

(463 / 2600)^0.5 = 0.42

Computing each side individually gives us the simplified equation:

80 (1.46 x 0.42) = 49.2

Thus, the penetration of our hypothetical shaped charge would be 49.2 millimeters against an AD-90 target.

With this modified formula; you can now get more accurate results using our previous example of the Charge, Demolition, Shaped, 150mm, shown below; using a jet density of 7.86 g/cm³ and a jet compressive yield of 1,100 MPA:

Target Material	Target Density (g/cm³)	Target Comp. Yield (MPA)	Actual Penetration	Calculated Penetration (178mm jet)	Penetration Differential
Armor Plate (RHA) (Baseline to find jet length)	7.86	1,100	178mm	116mm	-35%
Mild Steel	7.86	463	250mm	274mm	+10%
Granite	2.75	844	380mm	344mm	-9%
Reinforced Concrete	2.4	200	760mm	755mm	-1%
Sandstone	2.3	100	910mm	1,091mm	+20%

While the results are not exactly spot on, due to the fact that this is essentially a very simplistic formula trying to model a highly complex system of interactions, the results are good enough to make some rough comparisons of the resistive properties of various materials to shaped charges.