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Micropropulsion Technologies 257

11.3.1.1 Principle of Operation
The cold gas thruster is based on gas leaving a pressurized tank into vacuum, which
is accelerated in a converging–diverging nozzle as described in the resistojet section
above. A valve is used to initiate and control this flow. Thrust is produced according
to:

T / _ mmv e / h o Rev e (11:27)

with m ˙ describing the mass flow, v the exit velocity, and h o the nozzle height.
As with the resistojet, the thrust that is produced in such a system can be
calculated with Equation (11.28) as:

T ¼ _ mm v þ ( p e p a )A e (11:28)

where the mass flow is given by:
A t ar 0
_ m m ¼ 1 (11:29)
1 k 1 k 1
2

Compared to the resistojet, it becomes obvious that the lack of additional heating
forces the cold gas thruster to operate at high gas pressure. Another interesting
aspect is that the colder gas leads to an increasing Reynolds number, because of
the lower viscosity at lower temperature. While in principle this leads to higher
thrust values, it will force a more careful production of the exhaust nozzle to
keep the critical value up, which makes the production of small systems more
challenging.
Looking at the cold gas thruster performance and assuming that the gas is at
300 K and purely molecular hydrogen (k ¼ 1.67), the maximum exit velocity will
6
amount to 2500 m/sec and the resulting thrust for a pressure of 2 10 Pa sec and a
2
throat diameter of 1 mm would amount to approximately 1.5 N.
11.3.1.2 System Requirements
The miniaturization of the cold gas thruster poses significant challenges in main-
taining efficiency. As fluidic devices are miniaturized, the surface area to volume
ratio increases, which can result in larger drag forces. The proper design of the exit
nozzle is key to providing maximum thrust. A true 3D-axis symmetric hour-glass
shape nozzle is more efficient than an extruded 2D h-glass nozzle, which is
significantly easier to produce. Other issues involve leakage of gas through the
closed valve, which is a common problem of MEMS devices. While MEMS-based
cold gas thrusters have been developed in the past, reliability was a weak point
and insufficient emphasis was put on complete system design for actual missions.
Either the integrated tank was far too small, or it outsized the MEMS nozzle
so much so that the advantage of using MEMS was minimal. Currently the most

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