At the risk of committing the cardinal sin of applying real world logic to Star Trek I'm here to present some math, specifically regarding explosions. The thread has speculated about the potential offensive capability of the Halley's cargo pod, ranging from using it as a minelayer to using it as an enormous photon torpedo. I won't be covering the photon torpedo case as that has already been covered by
@Tank man here and also because I believe that antimatter is expensive enough that filling the pod with it would be too costly to be practical especially when their are plenty of nuclear fuels that will do. I will be examining four possible scenarios, one assuming the pod is filled with a nuclear explosive with a similar yield to volume ratio as that which can be achieved with modern technology, using the
W71 warhead as a template, one assuming it is filled with liquid deuterium, one assuming it is filled with lithium-6 deuteride, a common fusion fuel in modern thermonuclear weapons, and one assuming it is filled with pure plutonium-239. I'd like to mention two caveats, first is that I will not be using Tank man's figures for the cargo pod but rather my own measurements solely of the cylindrical portion of the cargo pod neglecting the rounded ends, with a diameter of 35.5 meters and a length of 123 meters. This is because I'm assuming you can't actually fill the cargo pod with an amount of material the same volume as the cargo pod as well, the walls have to have thickness after all and there are probably other things that take up space inside too so I'm assuming that the amount of space the rounded ends could store and the amount of space lost to overhead inside the cargo pod roughly cancel each other out. This decision has nothing to do with the fact that calculating the volume of the rounded ends would take some mildly complicated math and I don't want to put in the effort for such a small factor. Secondly I'm assuming 100% burnup of all nuclear fuels except the W71 equivalent, in real life nuclear bombs become more efficient as you scale them up as the probability of a neutron hitting another atom and triggering another reaction instead of escaping the bomb goes up, at the scale of the cargo pod only the very edges should have any escaping neutrons and unburnt fuel and can be neglected. I have used Wolfram alpha for the calculations, the internet for the density of the nuclear fuels and the
Nuclear Weapons Archive for the energy density of the nuclear fuels as measured in kilotons per kilogram.
With all that out of the way lets get on with the numbers. I will be displaying the cargo pod's weight, its yield in joules and tons of TNT, how it compares in percent to the Chicxulub impactor which killed the dinosaurs and is estimated to have been 120 teratons of TNT, as well as a series of radii representing at what distance the energy/area of the explosion would reach one kiloton per square meter, one terajoule per square meter, one tonne of TNT per square meter, and one gigajoule per square meter. We don't know precisely how much punishment Star Trek shields can take but presumably between some of these distances it can't handle it anymore and the ship is destroyed.
W71 Equivalent
- 49272 times the volume of the W71
- Mass of 63561 tonnes
- 1.031*10^21 joules
- 246.36 gigatons
- 0.205% of the Chicxulub impactor
- Kiloton/meter^2 radius = 4.427 km
- Terajoule/meter^2 radius = 9.056 km
- Tonne of TNT/meter^2 = 140 km
- Gigajoule/meter^2 radius = 286.4 km
Pure Deuterium
- Density of 162.4 kg/meter^3
- 82.2 kilotons/kg
- Mass of 19771 tonnes
- 6.7999*10^21 joules
- 1.6252 teratons
- 1.355% of the Chicxulub impactor
- Kiloton/meter^2 radius = 11.372 km
- Terajoule/meter^2 radius = 23.262 km
- Tonne of TNT/meter^2 = 359.6 km
- Gigajoule/meter^2 radius = 735.6 km
Lithium-6 Deuteride
- Density of 820 kg/meter^3
- 64 kilotons/kg
- Mass of 99831 tonnes
- 2.673*10^22 joules
- 6.389 teratons
- 5.324% of the Chicxulub impactor
- Kiloton/meter^2 radius = 22.548 km
- Terajoule/meter^2 radius = 46.122 km
- Tonne of TNT/meter^2 = 713 km
- Gigajoule/meter^2 radius = 1458.5 km
Pure Plutonium-239
- Density of 19860 kg/meter^3
- 18.29 kilotons/kg
- Mass of 2417859 tonnes
- 1.85*10^23 joules
- 44.2226 teratons
- 36.852% of the Chicxulub impactor
- Kiloton/meter^2 radius = 59.322 km
- Terajoule/meter^2 radius = 121.34 km
- Tonne of TNT/meter^2 = 1876 km
- Gigajoule/meter^2 radius = 3837 km
These cargo pod nukes could simply serve as stationary mines, however if one were to wish to turn them into giant torpedoes one would merely need to remove a portion of the fuel to make room for a propulsion system, the new explosive yield would be reduced by however much percent was removed and the new radii can be derived by taking the old radii and multiplying the by the square root of (new amount of fuel)/(original amount of fuel).
Note how the option with the most yield is the plutonium based one, this is because despite its inferior yield to weight ratio it is much denser than its alternatives allowing one to pack much more into the cargo pod. While 2417859 tonnes is a large amount of plutonium it is not unattainably so, humanity had mined 2818415 tonnes of uranium by 2014 and the 99.3% of uranium made of the isotope uranium-238 can easily be converted into plutonium-239 by neutron irradiation with a fission or fusion reactor. One would have to find a method by which to prevent the plutonium from reaching criticality and exploding before the desired time but a honeycomb of forcefields partitioning it into millions of subcritical masses should suffice. I did not do the calculations for uranium but given its density and kilotons per kilogram are similar to plutonium the results would be similar as well.
Given that the
Federation-Kzin War update mentions the need to put in an absolute minimum detonation distance for photon torpedoes of two kilometers it seems reasonable to assume that battles take place within an order of magnitude or two of this distance, implying that cargo pod nukes would have a useful lethal radius and would be combat effective, especially for the plutonium based nuke whose tonne of TNT/meter^2 radius of 1876 km exceeds the Moon's radius of 1737.4 km and whose gigajoule/meter^2 radius of 3837 km exceeds that of Mars's 3390 km. Cargo pod sized nuclear mines could reasonably interdict spaces the size of astronomical bodies.
Anyway that's it for now, need to go to sleep soon. Hope you guys appreciate my irrational attempt to apply logic and math to something as silly as Star Trek, the pinnacle of soft sci-fi which if it were any softer would be liquid.