Primary variables for high-energy compounds. Detonation Velocity ($D$) regulates shock arrival coordinates, and Gurney Constant ($\sqrt{2E}$) controls casing shard kinetic energy.
| Name |
Density (g/cc) |
Gurney const (m/s) |
Det. Speed (m/s) |
TNT Equiv. |
| HMX |
1.90 |
2800 |
9100 |
1.32 |
| PETN |
1.77 |
2680 |
8400 |
1.25 |
| Comp A-3 |
1.65 |
2630 |
8200 |
1.18 |
| Comp B |
1.71 |
2700 |
7900 |
1.15 |
| TNT |
1.65 |
2370 |
6900 |
1.00 |
| Ammonite |
1.00 |
2119 |
4400 |
0.65 |
| Lead Azide |
4.00 |
1600 |
5000 |
0.38 |
Physical properties of casing walls, flyers, and target armors. Mott constant ($\mu$) determines fragment sharding count, and density regulates charge-to-mass ($M/C$) ratios.
| Name |
Density (g/cc) |
Sound Speed (m/s) |
Mott const (in^1/2) |
Yield Str. (MPa) |
| 4340 Steel |
7.85 |
5940 |
0.035 |
860 |
| 1018 Mild |
7.87 |
5900 |
0.060 |
370 |
| HF-1 Frag |
7.85 |
5920 |
0.025 |
950 |
| Copper |
8.96 |
5010 |
0.080 |
220 |
| Aluminum |
2.70 |
6420 |
0.100 |
270 |
| Concrete |
2.40 |
3700 |
0.180 |
30 |
| Lead |
11.34 |
2160 |
0.150 |
15 |
Gurney Shard Velocity
Cylindrical Geometry:
V = √(2E) · [ M/C + 1/2 ]-1/2
Spherical Geometry:
V = √(2E) · [ M/C + 3/5 ]-1/2
Flat Sandwich / Plate:
V = √(2E) · [ M/C + 1/3 ]-1/2
Fermat Detonation Pathfinder
First-arrival Huygens sweep contour times computed via minimum path integral around inert wave shapers:
Td = ∫ [ 1 / D(s) ] ds
Where medium speed varies based on explosive zone:
D(s) = Dbooster in booster core
D(s) = Dmain in main charge
Shaped Charge Jet (Birkhoff Theory)
Hydrodynamic steady-state penetrative depth through layered target plates:
P = L · √( ρjet / ρtarget )
Linear stretching length over time due to velocity gradient from cone collapse:
L(t) = L0 + (Vtip - Vtail) · t
Mott Fragmentation Sharding
Distribution density of fragment masses after casing expansion collapse:
N(m) = (N0 / (2·μ2)) · e-(m/μ)1/2
Air drag velocity decay curve over travel range ($x$):
v(x) = v0 · e-kx where k = 1/2 · Cd · ρair · A / m