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Micropropulsion Technologies 251

kinds of thrusters are based on the enthalpy increase of a propellant when it flows
across an electrically heated surface, which causes an increase in pressure. The
thermal energy of the propellant is subsequently transformed, in a Laval nozzle, into
directed kinetic energy and thrust. Typical operational parameters are a moderate I sp
of the order 500 sec (this is too high to be realized in practice) with thrust levels of
approximately 0.1 N at average powers of 100 W. While this technology is mature,
recent efforts have been made to employ microfabrication and to reduce the size of
this thruster technology to a dry mass of greater than 100 g. Therefore, it is
worthwhile to take a closer look at this technology.

11.2.6.1 Principle of Operation
The principle of thrust production for this device is the same as with any chemical
or electrothermal system that relies on expansion of a gas into vacuum to produce
thrust. A gas under high pressure will escape into vacuum as soon as a hole is
punched into the propellant tank. However, the exit velocity is very limited.
Without the use of an additional nozzle, the velocity of the gas could never exceed
the velocity of sound, which is a function of the gas temperature. Increasing the exit
velocity would decrease the amount of fuel that needs to be carried for the missions.
Therefore, a major part of resistojet development has been concentrated on design-
ing nozzles that improve the performance of these thrusters, and has focused on the
use of converging–diverging (CD) nozzles.
The exhaust velocity for a well-designed CD nozzle expanding into vacuum has
been evaluated and can be described by a simple formula:
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

k R
v ¼ 2T 0 (11:24)
k 1 M
with R being the universal gas constant, M the effective molecular weight of the
propellant, k ¼ C P /(C P R)is theeffectiveratio of specific heats (C P ¼ effective heat
capacity of propellant) and T 0 represents the temperature of the medium in the tank.
The thrust that is produced in such a system can be calculated with the
following equation as:

(11:25)
T ¼ _ mmv þ (p e p a )A e
Thus, thrust is a combination of two terms, the momentum thrust (mass flow exit
velocity) and the pressure thrust (pressure difference between nozzle exit pressure
and ambient pressure nozzle exit area).
The mass flow itself is given by:

A t ar
_ m m ¼ 0 1 (11:26)
1 k 1 k 1
2

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