Shaped Charge/Hypervelocity Penetration(Created October 2009~) |
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:
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
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/cm^{3}, and Aluminum a density of 2.70 g/cm^{3}, 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/cm^{3}) |
Actual Penetration |
Calculated Penetration |
Armor Plate (RHA) |
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/cm^{3}) |
Calculated Penetration |
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 Material_{}Yield_{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/cm^{3}, and AD-90 a density of 3.70 g/cm^{3}, 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/cm^{3} and a jet compressive yield of 1,100 MPA:
Target Material |
Target Density |
Target Comp. |
Actual Penetration |
Calculated Penetration |
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.