Expansion-cooled, Curved-nozzle stealth rocket

Here, we will look at a design for engines that can accelerate a spacecraft without producing detectable emissions. It is best fitted to a stealth spaceship described in 'The Hydrogen Steamer: Stealth Spaceship Concept'.

Stealth designs in space rely mainly on low temperatures to remain undetected. However, low temperatures are the antithesis of efficient propulsion: exhaust velocity suffers, and improbable propellant to dry mass ratios are required to achieve any sort of useful deltaV.

Some propulsion designs allow for undetectable propulsion, but they suffer from low specific power, creating situations where the spaceship has to accelerate for months to break an orbit. 

Here is a design which might alleviate this issue.

Expansion-cooled Nuclear Thermal Rocket

Most rocket nozzles are a balance between weight, wall temperature and expansion ratio. Lightweight nozzles are better for high power-to-weight ratio, higher wall temperatures allows for higher exhaust velocity and less regenerative cooling requirements, while lower expansion ratios allow for shorter, lighter nozzles.

For a stealth spaceship, a different set of characteristics are required. 

The Children of a Dead Earth game has an accurate physical model of these rocket engines. While it makes some sacrifices in detail, it does render an accurate picture of how exhaust gasses are cooled as they expand. 

Here is a design created in the game's Module Designer:

Details from the editor

Maximal expansion of the gasses was selected, with a low initial temperature. Performance suffers, and the nozzle weighs a lot, but the exhaust is released at the extremely low temperature of 22K. 

Coincidentally, this is just over the vaporization temperature of hydrogen, which the hydrogen steamer concept boils off to keep cool. This means it is no more or less detectable than the main hull of the stealth ship.

If we use the 2*10^-18 watt per square meter figure from this lecture on the sensitivities of the Spitzer telescope, and assuming the hydrogen plume has an emissivity of 0.01 at 22K temperature and vacuum pressure, the detection range is about 8154km. 

However, the instruments are assumed to look at the same spot in the sky for 10000 seconds to obtain a signal-to-noise ratio of 10. Also, the telescope's field of view is only 5.2x5.2 arcminutes. Considering that the sky's area is 148,510,800 square arc minutes, a much lower 'dwell time' per section has to be accepted. With 100 seconds of observation, detection range is only about 800km!

This can be compensated for by using multiple telescopes and increasing sensitivity, but there is a lower limit determined by how quickly the stealth spaceship crosses the field of view. 

Curved Nozzle

A solution to up-the-nozzle emissions

A regular straight-nozzled rocket engine is very visible as the temperature at the nozzle's throat can reach thousands of degrees. This 'hot spot' can be seen by looking up the nozzle. This means that even if the expansion of exhaust gasses creates a very cold stream, and the nozzle walls themselves are cooled and insulated, the rocket will remain visible to sensors looking directly up the nozzle.

A curved nozzle attachment can remedy this issue, and prevent direct 'up-the-nozzle' observation of the high temperature gasses at the nozzle throat. All that can be seen by an external observer is the cool gasses and cold nozzle walls.  

Care will have to be taken to prevent gases from colliding with the curved walls at compressing, which raises their temperature again. We would need a wall that curves very smoothly, which makes for a very large nozzle.

Performance

With 4.48km/s exhaust velocity, the 'ECCN' rocket engine designed in the game editor vastly outperforms traditional stealth options, such as cold gas thrusters (400-700m/s). 

While the pulsed solar-thermal thruster has higher exhaust velocity (9km/s) and a mass driver has potentially unlimited exhaust velocity (10-100km/s+), both suffer from various downsides. The pulsed thruster is limited to the amount of sunlight that can be captured by the spaceship for propulsion, leading to very low thrust. A mass driver must rely on an on-board power generation system which has to be cooled and creates a system with very low specific power.

In comparison, the ECCN here generates a respectable 110kN of thrust and has a specific power of 46MW/ton! This is over twenty times better than solar power, and nearly five times better than most nuclear reactors. 

The best part is that the ECCN has no overhead requirements (power consumption, solar panels, radiators ect.). These rockets can be mounted in multiples. Two ECCN rockets will produce 220kN, three will produce 330kN, and adding more will not compromise stealth. 

The ECCN design can also be scaled up and down. A gigawatt engine with a sufficiently long nozzle is conceivable. An ECCN with an even more extreme expansion ratio can create even colder gasses.

Note that this is just one possible design that can illustrate the concept. It is possible to use even larger expansion ratios, so that the gases start at an even high temperature and end up with an even lower temperature. For example, hydrogen propellant can start at 3000K and end at 14K. This allows for both an increase in exhaust velocity to 9km/s and a decrease in detection range by a factor 6!