Knowing the amount of water consumed by most nuclear powerplants, its hard to believe they could fit in enough water to operate the tanks powerplant (assuming it uses a turbine to generate electricity to power teh tank)
If they had somehow managed to get this working for less than half a billion dollars a tank, it would solve most of the logisitcal problems that currently limit armored warfare.
Nuclear powerplants consume water because they have access to large volumes of cheap water. A mobile plant would use a steam condenser and recover the steam, with water/air heat exchangers to reject the heat in the same way a diesel engine water cooling system works. You'll need a bit more airflow for cooling, but if you can run a gas turbine in a tank, a steam turbine shouldn't be a big problem.
There was in fact another, different Army concept for nuclear power on land but used in “trains” – tanks. At one time the Army had a concept for cutting the diesel fuel use that resulted from tanks driving from rear areas all the way up to the front lines – a nuclear mobile power station that would drive along with the tanks. Each tank – of very conventional design – was to have included an electric drive motor on its transmission and a sturdy pole on the top rear of the tank. Cables would have strung together a dozen or more tanks with the nuclear unit in the middle; the whole line would then have moved along from the rear up to relatively near the combat zone (but out of danger) where the cables would have been taken down and the tanks dispatched on their own. The power unit would then return to ferry more tanks. Obviously, this concept was fraught with problems. For example, the extremely heavy tracked power unit would not have been able to go through terrain that tanks might well have been forced to cross – and even some bridges would have been too light for it. Not surprisingly, ferrying tanks simply under their own power was found to be much better and this non-solution was never applied.
There was in fact another, different Army concept for nuclear power on land but used in “trains” – tanks. At one time the Army had a concept for cutting the diesel fuel use that resulted from tanks driving from rear areas all the way up to the front lines – a nuclear mobile power station that would drive along with the tanks. Each tank – of very conventional design – was to have included an electric drive motor on its transmission and a sturdy pole on the top rear of the tank. Cables would have strung together a dozen or more tanks with the nuclear unit in the middle; the whole line would then have moved along from the rear up to relatively near the combat zone (but out of danger) where the cables would have been taken down and the tanks dispatched on their own. The power unit would then return to ferry more tanks. Obviously, this concept was fraught with problems. For example, the extremely heavy tracked power unit would not have been able to go through terrain that tanks might well have been forced to cross – and even some bridges would have been too light for it. Not surprisingly, ferrying tanks simply under their own power was found to be much better and this non-solution was never applied.
Soviets built mobile nuclear powerplant called TES-Z (or object 27) on T-10 tank gear. However gear was longer compared to T-10 and had wider chains. It was manufactured in Kirovsk factory with help of "Laboratory V" or better to said Russian nuclear scientific center in Obninsk. Overal weignt was about 90 tons and output power 1,5 MW. One prototype was manufactured and from 1960 rarely used.
Utterly impractical for the same reason that nuclear powered aircraft never made it off the ground - the good idea fairy loses out to the cold hard b**** of physics every time.
Nuclear power systems have a number of non-linear scale factors, which collectively mean that even for very low power outputs you have a considerable volume/weight, and there's a hard minimum in size/weight. For instance, you need a certain minimum mass of fuel to sustain a critical reaction, and a reactor close to the minimum is very inefficient in fuel use. Likewise a certain thickness of shielding is required pretty much regardless of reactor power.
The submarine NR-1 is probably the closest thing to a real world mobile nuclear plant in the desired power range. The pressure hull of the boat is a cylinder roughly 12x100 ft, and it appears from publicly available drawings that the reactor/engine room took up some 2/3 of that. There's probably some inefficient use of space and systems that would only be required for a submarine in there, but probably not that much. Hence a reasonable ballpark is a cylinder of roughly 12x50 ft. Perhaps with careful engineering this could fit in a volume the size of a 53 ft semi trailer, but doubtful it going to get any smaller.
Even at that, there's 2 significant issues - low power and shielding.
There doesn't seem to be any specs on reactor power available, however I did find a random reddit comment that claims 130 hp. Early US submarines of similar size achieved 9-10 kts submerged on ~600 hp, so 1-200 hp for NR-1's stated 3.5 kts is reasonable. Admittedly this is only propulsion, and some energy went into electrical power as well, but it is seems unlikely to be more than 50 MW or so. Consequently, this plant was almost certainly capable of less than 500 hp of output - some 1/3 of the M-1's existing gas turbine. In reality the situation is even worse as you need additional power to haul around the reactor plant and the structure/road gear/armor associated, which would clearly be quite considerable.
Additionally, NR-1 was only shielded on the forward end of the plant, as there was no need to shield the sides of back of the boat (water is a reasonably effective shield with enough thickness). It should be obvious why this wouldn't work very well in a land based application. Even moderately effective shielding on the other sides of the plant would add considerable weight and not inconsiderable volume.
Another potential example would be the US nuclear aircraft program, which got as far as prototypes for an open circuit nuclear jet engine. The units built (know as HTRE-2 and 3) had a reactor power of ~35 MW and drove a pair of J-47 engines. It is conceptually easy to see how this setup could be used as a gas turbine for shaft power instead of thrust.
However, this setup remains quite large: below is HTRE-3 today (both are part of a static exhibit at EBR-1 in Idaho and open to the public) - note the chain link fence for scale. Some amount of this is test structure, but the reactor is not small - notional installations have it taking up some 20 ft of a 12 ft diameter B-36 fuselage, and that's the reactor proper - engine were external. In addition to needing to house all this in the vehicle, making it into a gas turbine requires the additional of a power turbine section.
Massive air filters would also be needed. Gas turbines in general require large volumes of clear air, but the open cycle nature of the plant makes this even more significant because of neutron activation.
So again we have an impractically large setup, though this one at least makes lots of power to pull itself around.
Operating a vehicle powered this way would be interesting as there would likely be considerable lag time in throttle response. Gas turbine or IC engines have a pretty much instance throttle response - nuclear plants do not. (nor do conventional steam plants) With proper design a PWR can response relatively quickly, but relative in the sense of tens of seconds, not the instant response a driver would want. The aircraft plant would probably slower for various complex reasons. More significantly though, reducing power would likely require a steady taper down vs a sudden stop as core cooling flow is a function of turbine speed. Unlike a combustion plant, you cannot stop heat generation in a reactor - even fully shut down you still have significant decay heat: ~7% of reactor power if it's been run for a while at full power, less for lower power operating history. This would require the turbine to continue running at idle for some time, and once shut down probably requires some form of forced cooling for hours-days to control heating. This would require a source of power, and create a significant IR signature.
Significantly though, there is again a lack of shielding in the original design. In this case it was expected that the cockpit would be shielded and nothing else mattered. Arguably in flight this could be acceptable, though the minor issues of exposure to other aircraft on the field or how you could reload/maintain such an aircraft were never satisfactorily answered. However, in a ground vehicle, especially one that operates with others tanks and vehicles/personnel this is a huge problem.
Neutron activation is also a huge problem - unless a very effective shield is provided, the reactor would activate elements in the soil, air and any airborne debris as it moves, which would be a rather major detriment for pretty much every future use/operation. Significantly, no matter how effective the shield, since it's open cycle a substantial amount of air is exposed to high neutron flux, which results in activation. This particularly concerning for air dust/debris in the air - air alone by and large doesn't result in anything too nasty, but various other elements will.
The actual TV-8 was going to use an 8 cylinder engine anyway, probably a gasoline Hemi. It was basically an M8 AGS of 1952 but it floats.
The only serious proposal for any nuclear tanks were some of the ASTRON vehicles and other Questionmark things like R-32, and they were discarded quickly because it didn't seem like the USAF would get the X-6 or NB-36 flying anytime soon, and all this led to the T95 and his 12 cylinder X-block engine.
Nuclear engines were so out there and crazy even for 1952 that they never got very far beyond someone suggesting them as one of those cool wild ideas and putting a pin in it. Kind of like undersea Rocksite nuclear missile bases for Polaris or big Kevlar blimps for the MX missile.
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