I'm having trouble with a set of equations meant to describe the velocity of an Explosively Formed penetrator, called the Gurney equations. Specifically, the kinetic energy delivered by the explosive charge, and the kinetic energy contained in the EFP, do not add up.
Here is the set-up:
M is the metal plate, or the 'flyer'. C is the explosive charge. N is the tamper or backplate. In our scenario, M is the projectile, C is the beryllium filler and N is the nuclear warhead of mass about 10 times greater than explosive charge. It allows us to consider the metal plate as infinitely tamped.
Here is the equation:
Vm: Velocity of the metal plate E: yield energy converted into thermal energy within the filler. (2E)^0.5 is the specific velocity of our device. M: mass of metal plate C: mass of filler
Let's use a 1 kiloton yield warhead, massing 100kg. It is configured like a pulse propulsion unit for an Orion driver, delivering about 85% of its energy into heating a beryllium filler. This is 3.56 TJ.
The beryllium masses 10kg.
The metal plate is 10kg.
Using the equation, we get an EFP flying out at 2311km/s.
10kg at 2311km/s contains 26TJ of kinetic energy. This is higher than the energy delivered by the warhead.
Units do not match up in the equation. Right side is unitless. Left numerator is velocity. Denominator is sqrt(energy), which is a factor of sqrt(mass) away from matching up. I think it is probably meant to be sqrt(2E/C), but the C got omitted somewhere and now people just look at a table for the value of sqrt(2E). Taking the limit as C>>M, the value of V should be a bounded constant.
Wiki says sqrt(2E) is the Gurney constant and has dimensions of velocity.
Okay, but inputting total energy applied to the Be will need mass divided somewhere for units to be correct.
Further research into conventional explosives (which probably put me on a list somewhere) shows that the Gurney constant is an energy density. However, there is not simple relationship between energy density and detonation velocity because the explosive gasses have different molecular weights. So, for most hydrocarbons at 2-3000K temperatures, detonation velocity is a third of the gurney constant. It cannot be scaled up accurately to nuclear levels of energy or with any propellant.
Okay, so I would be suspicious of seeing a <200mm thick piece of Be absorb that and tries to push something much faster than 200mm/200ns = 1000km/s (dissassembles itself more efficiently as this ratio is approached). Not itself necessarily a limitation.
Echoing leerooooooy , the piece of Be will not act like an explosive. It is going to be heated more uniformly by the blast. I think all this really changes is that less energy is forced to go into the Be. This may require a different model.