What if the most economical use of a nuclear powered spacecraft is not direct to escape but just to get above the atmosphere? The economics of nuclear thermal rockets

A guest article by Joseph Friedlander

First let us discuss the dream of nuclear thermal rockets. Powered by a reactor light enough to fly, hot enough and with power enough to energize a reaction fluid (hopefully a light fluid with high exhaust velocity) and efficient enough to carry a large fraction of launch weight as payload to low orbit, high orbit or even escape velocity.

If you recall the Heinlein based movie Destination Moon from 1950,

This direct launch scenario from Earth to Lunar surface, then from Lunar surface to Earth, all in one stage, was solely possible using a nuclear thermal rocket.

However to pull this off requires an exhaust velocity of around 20-30 kilometers per second, which in real life would take a very speculative gas-core reactor to make possible.

The Liberty Ship idea, which Brian has covered before, is one such design. Even an early version can have an exhaust velocity equivalent to the 11 km/sec of Earth escape velocity and make achieving orbit trivial and landing on the Moon (one way) doable.

A gas-core reactor is one in which the reacting Uranium 235 for example is in the form of superhot gas. The prospect of a leak of live fissionables is disquieting at best and terrifying if things become anything less than nominal. So however amazing the numbers look, one can just imagine the protests if any gas-core reactor gets anywhere near launch.

The more buildable solid core DUMBO design can output enough nuclear power per unit of weight (with liquid hydrogen reaction mass) to achieve exhaust velocities of 8-11 km/sec, which is enough for a cheap to orbit shuttle IF the flight economies work out. Of course on paper chemical propulsion need be no more expensive than say $50-100 a kilogram to orbit TODAY and obviously we are about 50-100 times more expensive than that.

Hopefully a completely reusuable Space-X Falcon Heavy might cut that inefficiency penalty to a small multiple of the theoretical price— but there is a minimum price for anything that cannot be bettered but it can always be exceeded.

This article is focusing on an idea for a practical nuclear thermal booster with today’s technology—whose success would make any reusable chemical rocket yet cheaper to use.

Any given rocket if it starts its journey in vacuum 100 km up, is going to be able to bring at lest twice as much to orbit compared to starting at sea level.

So a robust and buildable nuclear booster, massively reusable (a couple times an hour not a week) that uses fresh water as reaction mass (cheapest fluid available) that takes off and lands (and is based) in freshwater and repumps itself full within minutes for another run would be capable of greatly efficient amortization of costs and great economies of use.

It would accelerate for under 90 seconds, hop up to space and eject the multi-staged chemical rocket from an internal bay—the “garage”—the equivalent of an air launch but in space.

I have named this concept a “nuclear hopper” in analogy to the European Space Agency Hopper spacecraft and the similar flown Phoenix prototype.

Note that there the designers say it would cut the cost of a launch in half from $15,000 a kg to $7,500 a kg—a fancy way of saying that they intend to fly a rocket in the garage just as expensive as a ground based rocket but simply double the payload by starting at 130 km instead of the ground.

However, the whole point is to fly a rocket in the launch bay on board the hopper craft of radically cheaper and more reliable construction. Costs should not be cut in half but rather to say 1% of the cost of ground based launches. Literally an amateur rocket could reach orbit from a starting point of 100 km up because so many launch failure modes are left behind on the surface. (Because air friction is a millionth of sea level the minimum size to reach orbit is theoretically something that could fit in a lunch box, not a 30-foot telephone pole and so forth) It requires a Burt Rutan type approach of radically simpler spacecraft. But this is much easier to do once you can launch from a garage at 100 km up. Theoretically you don’t need electronics at all, the chemical booster can be spin stabilized, (launched spun up from a tilt table) timer triggered, and using concepts proposed for minimum satellites in the late 1950s before flyable computers. With today’s $50,000 cubesats as a brain such a supercheap booster should be doable for a few hundred thousand dollars.

So let’s concentrate on the hopper design. For me the definitive approach to the problem of a robust and buildable solid core thermal rocket reactor is Zuppero et al’s 1998 paper on a Lunar South Pole Space Water Extraction and Trucking System.

There, Zuppero et al postulate easily sublimed lunar volatiles that can be captured near the lunar poles and then trucked to lunar orbit 20 tons at a time (throwing away 92.6 tons propellant water per flight, part of which (75.7 tons) gets them liftoff to orbit, part of which (16.9 tons) retros them and enables landing back on the Moon. The dry ship weighs 10.4 tons including a 292 thermal megawatt reactor deliberately engineered for many many cycles for robustness, durability and low maintenance—keys, as it happens—to economical reuse.

The Zuppero et al paper says,

The nuclear reactor mass of 1818 kg (4000 lbs) is considered 50% more than minimum. The reactor must deliver 292 megawatts to the steam at a mixed mean outlet temperature of 1100 K with propellant flow of 155 kg/s. A rocket nozzle area ratio of 200:1 will deliver a specific impulse of 198 seconds.

Gives for a wet weight of 123 tons

A dry weight of 47.3 tons (16.9 tons retro water, 20 tons payload, 10.4 tons ship)

And specific impulse of 198 seconds (1941.7167m/sec) exhaust velocity

A delta V of 1855 meters a second—compare to SpaceShip One’s (from an atmospheric start) 1400-1700 m/s

http://en.wikipedia.org/wiki/Delta-v_budget

A dry weight of 47.3 tons (16.9 tons retro water, 20 tons payload, 10.4 tons ship)

And specific impulse of 198 seconds (1941.7167m/sec) exhaust velocity

A delta V of 1855 meters a second

On Earth using an additional 12 tons of retro water for extra speed (A dry weight of 35.3 tons (4.9 tons retro water, 20 tons payload, 10.4 tons ship) since in this scenario we are braking by atmosphere on Earth and just retroing right at water landing–

And specific impulse of 198 seconds (1941.7167m/sec) exhaust velocity

A delta V of 2423 meters a second

So the takeaway from all this is that 1700 m/sec delta V or over will allow easy achievement of 100 km and greater altitudes for launch of a chemical booster carried in a ‘garage’ on board the nuclear booster. Better than 100 km in fact–.possibly up to 300 km.

The form factor I visualize is something like the Chrysler SERV design

Proof of this from historical missiles—the V-2 and the Scud (R-11)

gives 1,341 m/sec –this might not be referring to true delta V but to net velocity achieved after gravity and drag losses. (One reason why you burn fuel as rapidly as possible is indeed to limit gravity losses)

The comparable Scud had maximum altitude 78 km. Time of flight 5.4 minutes. Max velocity at burnout 1430 m/s.

We have just now described a ’hopper’ architecture for a nuclear steam rocket. What is the difference between a nuclear steam rocket and a conventional steam rocket–such as the rocket used by Evel Knievel in his attempt to jump the Snake River Canyon near Twin Falls, Idaho on September 8, 1974.

A conventional steam rocket uses preheated water on the ground for launch with a simple pressure valve. Alas, the exhaust velocity is a mere 300 m/s or so.

What is different here? A nuclear reactor is heating the water literally on the fly—so we are not storing superpressured steam or supercritical water but low-pressure water in light tanks and heating it live. Exhaust velocity is around 6 times greater.

Notice that we are separating between the functions of high mass flow and high exhaust velocity in the nuclear hopper design. We are proposing a very buildable system with no hope of reaching orbit but an immediately realizable hope of reaching space—100+ km up. In fact, this nuclear hopper is a means of substituting for a 100 km launch tower (carbon fiber) above the perceptible atmosphere.

This is the kind of thing they would see from the windows of the hopper–

Wikipedia caption– The first photos taken from space were taken on October 24, 1946 on the sub-orbital U.S.-launched V-2 rocket (flight #13) at White sands Missile Range. Photos were taken every second and a half. The highest altitude (65 miles, 105 km) was 5 times higher than any picture taken before.

In essence we can use a spacecraft light (in construction, not mass) as a Lunar Module upper stage to get to Earth orbit.

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(By launching at 100 km, what are the advantages? We get rid of gravity loss, drag loss, we increase engine thrust perhaps a fifth or so over sea level (not fighting the atmosphere) we can have solar panels already deployed, all jettisonable aeroshields removed, all disposable shrouds removed, and in general make things lots lighter and cheaper and more reliable. We don’t have to face significant Max Q and things can be enormously lighter.)

During a normal Space Shuttle launch, for example, max Q occurred at an altitude of approximately 11 km (35,000 ft). The three Space Shuttle Main Engines are throttled back to about 70% of their rated thrust as the dynamic pressure approaches max Q;[2] combined with the nozzle design of the solid rocket boosters, which reduces the thrust at max Q by 1/3 after 50 sec of burn, the total stresses on the vehicle are kept to a safe level.

During a typical Apollo mission, max Q occurred between 13 and 14 km of altitude (43,000–46,000 ft).

The point of max Q is a key milestone during a rocket launch, as it is the point at which the airframe undergoes maximum mechanical stress.

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Suppose we could make such a radically cheaper hopper to routinely launch rockets into the ionosphere (mesosphere) –what would be the economics of running a hopper?

This entire sequence could theoretically be done twice per hour—actual flight time is only a few minutes, comparable to a V-2 whose actual burn time was 60 -70 seconds or so. More details at.

Flight time up and down have been under 10 minutes (or even 5) so theoretically such a hopper could fly and tank up water twice an hour (one rocket released per hour then flying itself back for maximum flight readiness or two rockets released per hour for maximum economy. Obviously this would allow mass production of thousands of supercheap vacuum optimized rockets and drive costs down that way.) John Walker has already written of this– www.fourmilab.ch/documents/rocketaday.html

A link on the gap between Spaceship One (or V-2, or Scud) class delta Vs and actually achieving orbit

Suppose the hopper reactor could put out 6 times the Zuppero et al design for equivalent weight, the mode of operation for such a nuclear hopper(ideally) would be between two separate freshwater lakes on Earth.

The nuclear steam hopper would pump in pure water (distilling might be necessary but a distill barge might be part of the floating lake base) light up, fly in an arc to its apogee, release its chemical booster, retro before landing at most a few hundred miles away, pump in new water, and fly back to the initial base. Better yet, have bases at each lake and make every flight pay. You are just going for height, the vacuum launched rocket in the garage on board does the entire boost to orbit.

Depending on the exact flight profile vertical recovery to the same launch site is eminently possible.

If $4 billion dollars for a prototype and 8000 back and forth flights in a year, (8000 launches and 8000 recoveries) the cost per released rocket would be half a million dollars. Add as much for a 20 ton rocket of very light construction, 1 ton payload, 1 ton structure (probably in multiple stages) with 3500 m/sec exhaust velocity would orbit payload for $1000 kg.

The Zuppero et al design assumed 1.5 times thrust to weight ratio starting on the Lunar surface. To keep that ratio constant on Earth we need to upgrade the nuclear core to 6 times the power (and 6 times the flowthrough, propellant flow of 930 kg/s

exhausting the water in less than 2 minutes) all this for equivalent reactor weight.

This is theoretically quite doable but practically uncertain to be achievable. If it were–.

1752 megawatts in the nuclear core for 1.8 gigawatts output.

Supposing we scale it up 10 times, that is around 18 gigawatts, propellant flow of 9300 kg/s and a larger but equally cheap rocket (200 tons release weight, 10 tons up) for the same $4 billion the cost drops to $100 kg. Note that this variant can probably fly the cheapo equivalent of a Falcon 9. (Single stage, no disposable parts)

We can imagine one more scale up of factor 10 to 180 gigawatts (remember a Saturn V main stage was 190 gigawatts for a few minutes). 93000 kg/s propellant flow. This outmasses the Saturn V, around 12000 tons, almost all water.

This would rise from the freshwater lake and return there in the style of the Sea Dragon Note on that page the proof of concept tests of Sea Bee and Sea Horse—actual water launched rockets that worked.

Encyclopedia Astronautica

Sea-Launched

Category of launch vehicles.

http://www.astronautix.com/fam/seanched.htm

There is a limit to how cheaply a chemical rocket could be made so we do not imagine the cost going much below $100 a kg but other effects are possible—for example synergistic uses of tethers for space launch operation (given the large mass of the ship in this case, around 1000 tons dry). As in all tether operations, much depends on the break strength of the tether. Suppose we can lift 1000 tons of characteristic velocity 2.7-km/sec tether and spin up a rocket weighing 1000 tons—then the rocket only need add 5 km per second velocity to achieve a minimum orbit and becomes far more economical. With an exhaust velocity of 3500 m/s, a wet weight of 1000 tons and a dry weight of 200 tons delta V is 5633 m/sec. A payload of up to 100 tons plus 100 tons empty stage in orbit should be possible. If the 180 gigawatt (Saturn V class) 12000 ton vehicle costs $4 billion and $500,000 per flight amortized and the chemical booster can be made for $5 million a flight ($50/kg dry weight) then the cost per kg orbited would be $55.

Zuppero et al calculate that within a few minutes residual reactor power dropped to less than 1% of full power. But with this scenario from lake to lake the reactor is never more than a few minutes from abundant coolant.

Fuel Burnup–A thermal reactor operating at a power level of one megawatt consumes 1.23 grams of U-235 per day

The original Zuppero et al ship lunar ship burned for 20 minutes 292 megawatts totaling 240 hours per year. Assuming 3 trips per day for a year that was given as burning less than 5 kg U-235 (which costs somewhere above $50000 a kilogram)

This Friedlander hopper version burns 6 times hotter for 1/6 the time—1.8 gigawatts for at most 200 seconds. (Possibly quite a bit less depending on how much altitude is sufficient)

For a 1.8 gigawatt ship (120 ton class liftoff weight) cycling twice an hour for a year that is 16000 * 200 seconds or 3200000 (3.2 million seconds, about 10% of a year active use or 180 megawatts average power during a year) 180 * 365 is 65700 megawatt days * 1.23 grams or 80.811 kilograms of U-235 per year (at $100000 a kilogram, over $8 million worth that must be replaced)

For a 18 gigawatt ship (1200 ton class liftoff weight) cycling twice an hour for a year that is 16000 * 200 seconds or 3200000 (3.2 million seconds, about 10% of a year active use or 1800 megawatts average power during a year) 1800 * 365 is 657000megawatt days * 1.23 grams or 808.11 kilograms of U-235 per year (at $100000 a kilogram, over $80 million worth that must be replaced)

For a 180 gigawatt ship (12000 ton class liftoff weight)—Super Saturn V class cycling twice an hour for a year that is 16000 * 200 seconds or 3200000 (3.2 million seconds, about 10% of a year active use or 18000 megawatts average power during a year) 18000 * 365 is 6570000 megawatt days * 1.23 grams or 8081.1 kilograms of U-235 per year (at $100000 a kilogram, over $800 million worth that must be replaced)

These statistics just emphasize the amazing amount of power in nuclear reactions—here we are carrying 2000 tons at a shot to the edge of space 16000 times a year—that is 32 million tons brought to 100 km—and it all is done by 8 tons of U-235 boiling away within minutes (each flight) 8700 tons or so of water. That is over 139 million tons of water turned to steam a year at very high velocity.

Note that I don’t argue that these flight models are particularly plausible, just possible. To make them happen you would need huge lake surface logistics that basically involve moving a sealed barge unit into the open maw of the ‘garage’ within 5 or 10 minutes. Plausible but unheard of today with agonizing months long tweaking by bunny suited technicians.

What might be some more Earthly uses for such a nuclear hopper? Arcane ones, at best. I will concentrate on the largest size hopper—12000 tons liftoff weight– because that’s most fun to write about 🙂

You could hurl ballistically say 2000 tons of insecticide to take out an entire locust swarm over 100 square kilometers in Africa, say, in one 5 minute mission. The swarm would not be able to evade the chemical bomblets in time. But the environmental impact statement is amusing to imagine.

Just to keep the Next Big Future readership happy, there are military uses possible

Let’s extrapolate from known V-2 impact statistics –German General Dornberger compared the 4 ton impact (including warhead) of a V-2 hitting earth at around 1.5 km per second (nearly a mile a second) as equivalent to 50 locomotives hitting the ground at 100 kilometers (60 miles) per hour. So 500 times this would be the equivalent of a 2500 locomotive crash. Ouch.

Impressive.

Wiki says

A scientific reconstruction carried out in 2010 demonstrated that the V-2 creates a crater 20 meters wide and 8 meters deep, throwing up around 3,000 tons of material into the air Blitz Street; Channel 4, 10.5.2010

So theoretically if 500 4-ton bombs were released, most of a square mile gets cratered 8 meters deep and throws up 1.5 million tons of dirt cloud.

Most impressive.

But the thing is the greatest flying infrared beacon imaginable so it would be unbelievably vulnerable- You can imagine it hurling a given payload of bomblets, bb sized iron balls, spears, etc and then being met by every heatseeker missile the enemy had. It would be like an infantryman with a flamethrower—fair game for EVERYONE with a gun. It would not last too long in a military situation barring special circumstances, one thinks.

That is against earth targets. If however you aimed upward at an incoming cluster of nuclear warheads against a point target it might be able to defend 1000 square kilometers of entry footprint for a few seconds of time. That is not terribly impressive considering that the launching hostile power can time their assault and you have to remain ready forever.

A nuclear hopper for cargo is marginally more plausible. It would enable rapid transportation over 300 km (200 miles or so) of 1000-2000 tons at a cost of (say) $1 a kilogram—roughly comparable to airfreight charges. If you had something that needed to go to a mountain lake from sea level, some huge piece of machinery that would fit on a barge that would be a real possibility. But it sounds like a stretch of a scenario.

Suppose you wanted to cross the USA. You would need to hop 13 times New York to LA, and each time would take minimum 5 minutes from ignition to splashdown, 200 miles, and say 10 minutes to refill with water and blast off again. (Keeping this to absolute minimum. So 15 minutes times 13 or 195 minutes, or 3.25 hours. Even though a fraction of the time you are going at almost a mile a second, standing still 2/3 of the time really cuts your average speed down—not to mention the difficulty of going to the bathroom when you are high-g or weightless. Sounds nausea inducing. On the other hand you go to space 13 times and get to float a lot—but then so does your vomit. If we can get the exhaust velocity up to 4 km/sec we can do it in two hops, sounds a lot better. But with 13 hops, say 10000 passengers and $500000 per hop, that’s $6.5 million divided by 10000 or $650. Really, does not sound too competitive other than the going to space and floating part. Presumably you could get a couple charter trips full of extreme sports enthusiasts together per year but I don’t see ordinary people doing it to save 2 hours off coast to coast at double the price.

But for space boost to greatly lower costs of launching—it sounds nearly unbeatable. Rather than something like 1.3 billion to send a 50 ton spacecraft to the Moon, we can imagine doing it for something like $10 million (exclusive of the spacecraft of course). 2000 tons starting at 100 km even at standstill could send that much to the Moon in perhaps 4-5 stages. Doing that a few thousand times a year would enable the beginnings of Lunar colonization. Something to think about.

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