Daily Archives: November 10, 2022

Low-Pressure NTR for Dissociated Hydrogen Speed

Nuclear Thermal Rockets (NTR’s) once seemed like a fantastic idea to the Sci-Fi greats who were involved in the early days of the post-War Space Age.

Prometheus with Alpha and Beta ready to fly

In the UK Arthur C Clarke wrote of a two-stage hybrid nuclear rocket “Prometheus” for Moon missions in his “Prelude to Space” (written in 1947, but published in 1951). To get the required performance Clarke fudged a little for the air-breathing nuclear Ramjet Beta component, hoping a high temperature system could be created to provide the required thrust. To get the required performance for the Moon return-mission, the Alpha component depended on methane heated to a high enough temperature to mostly dissociate into carbon and hydrogen and increase the exhaust velocity with a high atomic hydrogen fraction.

In the USA Robert Heinlein wrote many tales with Nuclear Thermal Rockets – his 1947 “Space Cadet” featured monatomic hydrogen sub-orbital rockets. By 1950 the first hard performance data of high temperature reactors was available and the first nuclear thermal rocket designs were appearing in the journals. His most detailed discussion was in “The Rolling Stones” (1952) about a family on the Moon buying a second hand NTR spaceship to take to Mars, then the Asteroids and Saturn. The characters mention tanking up on monatomic hydrogen for the long range destinations. Back in the infancy of cryogenics, monatomic hydrogen seemed potentially stable over long periods of time. Using just H, rather than H2, increases the exhaust velocity of an NTR by 50% or so.

Low Pressure Nuclear Thermal Rocket schematic

Atomic hydrogen doesn’t like being by itself and quickly recombines into molecular hydrogen all by itself. However once molecular hydrogen gas is hot enough, it starts breaking apart and this fact can improve exhaust velocity. That’s the basic physics idea behind the Low-Pressure Nuclear Thermal Rocket (LPNTR) which feeds the gas into a really hot reactor, but at a low enough pressure to minimise the recombination of the hot atomic hydrogen. The improvement is significant – the Specific Impulse jumps from NERVA’s 850-925 seconds to 1210-1350 seconds.

Titan Base from "The Invisible Enemy"
Titan Base in the year 5050 CE

However making hydrogen is a non-trivial exercise – about 120 MJ/kg when making it from steam. Chemically free hydrogen is rare anywhere but the Sun and the Gas Giants. And one other place. Titan, which has an atmosphere that’s 0.1% hydrogen. While that doesn’t sound like much, it’s readily extracted and liquefied for a lot less energy than cracking it out of water ice. The total mass of H2 is about 675 billion tonnes. The delta-vee to launch to the Earth-Moon system from the surface of Titan is about 4.8 km/s – round it to 5 km/s to account for gravity losses. In energy terms roughly 12.5 MJ/kg. Using the high-thrust mode of the LPNTR, the mass-ratio is ~1.54, meaning the rocket can be mostly payload. For the long cruise back home, the reactor’s fission-product decay heat coupled by heat exchanger to a thermophotovoltaic system can run a cryo-cooler to keep the hydrogen chilled.

In terms of energy expenditure, sourcing hydrogen from Titan makes more sense than anywhere else in the Solar System. Hohmann Transfer Orbit launch windows open more frequently for Saturn-Earth, every 12.4 months, versus 26 months for Mars-Earth, thus more frequent delivery opportunities. The Transfer time is 6 years, but this can be scheduled for. Faster elliptical (~3 years), parabolic (~2 years) and hyperbolic orbits are possible for higher hydrogen expense, but for a well established automated delivery schedule the Hohmann transfer is sufficient.