Shaped Charge/HypervelocityPenetrationby 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.

Penetration = LengthJet (DensityJet / DensityTarget)0.5

Where:

Penetration = Penetration of Shaped Charge in millimeters.
LengthJet = Length of Shaped Charge Jet
DensityJet = Density of Shaped Charge Jet (Liner Material)
DensityTarget = Density of Target Material

 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 = LengthJet (DensityJet / DensityTarget)0.5 times (YieldJet / YieldTarget)0.5

Where:

Penetration = Penetration of Shaped Charge in millimeters.
LengthJet = Length of Shaped Charge Jet
DensityJet = Density of Shaped Charge Jet (Liner Material)
DensityTarget = Density of Target Material
YieldJet = Compressive Yield of Shaped Charge Liner Material
YieldTarget = 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.