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Rocket Laboratory: Cold Gas Thruster
Performance
Every thruster system developed for spaceflight must go through a rigorous testing process.
Regardless of whether the thruster is designed for space access (launch vehicles) or space
maneuvers (spacecraft), the testing process is critical in determining the performance and the
risks of thruster systems. In this lab, a cold gas thruster operating with a molecular nitrogen (N2)
propellant will be tested. Because of their inherently low specific impulse (a measure of
propulsive efficiency), cold gas thrusters are typically only used on spacecraft for minor attitude
control maneuvers. Although the specific impulse can be low for a typical cold gas system, they
are relatively simple, inexpensive, and have a good flight heritage which makes them desirable
for certain missions. The procedures documented in this lab are essentially the same used by
real world rocket scientists to determine performance parameters for thermodynamic rockets
from the Space Shuttle Solid Rocket Boosters (SRBs) to Digital Micro-thrusters (see below).
Space Shuttle Atlantis launch and TRW micro-fabricated thrusters for small satellite attitude control.
NOTES
Last Major Revision by
Dr. Andrew Ketsdever on 26 APR 2005
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Mission Objectives
Be able to calculate theoretical (predicted) performance values
Understand the cold gas thruster test set up and associated equipment
Compare theoretical versus measured results for the thruster system
Resources/Requirements
For this laboratory mission, you must have;
Read Chapter 14 of Understanding Space
Completed the mission planning described below
Mission Planning
BE ABLE TO CALCULATE THEORETICAL PERFORMANCE VALUES
1.
In this experiment, a nitrogen (N2, =1.40) gas bottle with a volume of 4.3 Liters is pressurized
to 400 PSI (2.721x106 Pa). The gas bottle serves as the propellant tank for this experiment. Once
a valve is opened, the nitrogen will flow through a propellant feed line into a chamber and through a
nozzle. A typical flight unit using cold gas thrusters for 3-axis attitude control is shown
schematically in Figure 1. The nozzle throat diameter is 3/32” (0.238 cm) and the exit diameter is
0.165” (0.419 cm). The nitrogen gas is stored in the propellant tank at room temperature of 298 K.
Assume that there are no losses from the tank to the rocket chamber.
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Last Major Revision by
Dr. Andrew Ketsdever on 26 APR 2005
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Propellant Tank
Rocket Chamber
Nozzle
Figure 1: Schematic of a cold gas thruster system for satellite attitude control. (Note: this is not
the same set up you will see in the lab
The theoretical characteristic exhaust velocity, C* (”C-Star”), is used by propulsion test engineers
as a back-up method to determine whether a thrust stand is working properly. The value of C*
represents the fastest velocity that a particular gas can achieve if every conceivable thrust
parameter is optimized. C* is calculated using the thermodynamic properties of the propellant
gas. Normal thruster systems will have a measured C* between 80-95% of the theoretical C* to
identify problems with the test stand setup. If the ratio of measured C* to theoretical C* is greater
than unity then our measured value exceeded the fastest velocity theoretically possible – clearly
impossible to achieve.
1. The C*of nitrogen at room temperature is: (Ref. Equations 14-23 and 14-24 on pages 547-548
of Understanding Space)
C* 
Pc At ao

 434.4m / sec NOTE: You will compare this to the measured C* from the experiment.
m

2. Using the equation for C * and a thrust chamber pressure Pc=400 PSI (2.721x106 Pa)
 , through the nozzle. The nozzle throat area
calculate the theoretical maximum mass flow rate, m
-6
2
is 4.449x10 m .
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Last Major Revision by
Dr. Andrew Ketsdever on 26 APR 2005
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3. For an atmospheric pressure at USAFA of 11 PSI (7.483x104 Pa) , an exit velocity (Vexit) of 630
m/sec, and an exit pressure (Pexit) of 18 PSI (1.224x105 Pa) calculate theoretical force (Fthrust)
produced by this thruster. (Ref. Equation 14-20 on page 545 of Understanding Space).
 Vexit  Aexit ( Pexit  Patm ) 
Fthrust  m
4. Calculate the theoretical specific impulse, Isp, for the thruster (Ref. Equation 14-7 on page 537
of Understanding Space).
I sp 
Fthrust

m g o
5. What is the V produced for a burn time of 5 seconds? Assume that the entire system mass is
10 kg (Minitial) (Ref. Equation 14-11 on page 539 of Understanding Space).
M

V  I sp g o ln  initial  
M

 final 
NOTES
Last Major Revision by
Dr. Andrew Ketsdever on 26 APR 2005
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Mission Execution
UNDERSTAND THE COLD GAS THRUSTER TEST SET UP AND
ASSOCIATED EQUIPMENT
1.
The purpose of this lab is to show the utility and the limitations of the theory given in the
course text Understanding Space by comparing the theoretical predictions you made in
Mission Planning with actual measurements made in this lab. The Mission Planning
calculations were intended to walk you through the process of predicting the performance of
a simple blow-down cold-gas rocket system. In this lab, we will test the system and see how
well the theory predicts the results, empirically.
The test setup, shown in Figure 2, consists of a 4.3 liter tank, pressurized to about 400 PSI.
The flow from the tank, to the thruster is controlled by a DC-powered solenoid with a ¼”
(0.635 cm) poppett-orifice. The feed lines are ¼” (0.635 cm) inner diameter, Teflon-lined,
braided stainless-steel flexhose. The cold-gas nozzle is simply a machined aluminum
cylinder. The thruster is mounted to a thrust stand via a “sled” mounted on bearings. When
the solenoid is opened, the high-pressure nitrogen gas passes through the nozzle. The force
or thrust created is measured by a strain gauge based load cell mounted on the thrust stand.
Pressure sensors are attached to both the tank and to an X-fitting just before the thruster
nozzle. The data acquisition system is shown in Figure 3.
Nozzle
Thrust Chamber
Pressure Transducer
Thrust Stand
Propellant Tank
Solenoid Valve
Figure 2: Experimental set up for the cold gas thruster laboratory.
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Dr. Andrew Ketsdever on 26 APR 2005
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Figure 3: Data acquisition system for load cell (force measurement) and pressure transducers.
2.
You will need two data files that will be provided to you by your instructor. One has the data
that will allow you to calculate the experimental (measured) mass flow. The other has a plot of the
measured thrust versus time (sample number) and a plot of pressure versus time (sample number) data.
Find the values of C*, thrust and Isp at 1.5 seconds after the valve is opened. In the data (see figure
below), the valve was opened at Sample 217 (this is true for all sections of ASTRO 310). A time of “1.5
seconds after the valve is opened” corresponds to 150 samples past sample 217, since the data was taken
at 100 Hz (100 Samples/sec). The figure below is a graph of the thrust data with labels showing when the
valve was opened and closed in the experiment.
Cold Gas Lab Thrust Data
Valve Open
20
Valve Closed
Thrust (N)
15
10
Thrust Newtons
5
Burn Time
0
-5
0
500
1000
1500
Samples (time)
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Dr. Andrew Ketsdever on 26 APR 2005
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COMPARE THEORETICAL VERSUS MEASURED RESULTS FOR THE
THRUSTER SYSTEM
Again, the goal of this lab is compare the empirical results to the theoretical results. The first
 , C * , Fthrust,
step is to analyze the data from the experiment to obtained measured values of m
and Isp. The next step is to compare the experimental results with what you predicted in the
Mission Planning. The final step is to comment on the similarities and differences between the
theoretical and experimental values.
3.
After the Lab, you will need to do the following:
Using the experimentally determined mass of the propellant tank before and after the
 . Fill these values into Table 2
thruster firing, determine the experimental mass flow, m
below.
Table 1: Experimental mass flow calculation
Calculated M
(kg)
Minitial (kg)
Mfinal (kg)
Burn time (sec)
[Given]
[Given]
[Given]
6.9174
6.8267
5.44
Calculated
Mass Flow
(kg/sec)
4.
Looking at your data, go to a burn time = 1.5 seconds (1.5 seconds after the solenoid valve is
opened) and record the following:
1. What was the thrust?
2. What was the Chamber Pressure?
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Dr. Andrew Ketsdever on 26 APR 2005
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3. What was the average mass flow rate for the experiment (calculated from Table 2)?
4. What was the measured Isp?
5. What was the measured value of C*?
6. From the plot of thrust versus time provided, estimate the total impulse of the cold gas thruster
firing.
7. Compare these results (thrust, Isp, and C*) to the ones you calculated in Mission Planning in
Table 3. Compute the ratios of measured value to theoretical value for C*, thrust, and Isp.
Table 2: Comparison of Measured Data to Theoretical Prediction.
C* (m/sec)
Thrust (N)
Isp (sec)
MEASURED
(burn time = 1.5 sec)
THEORETICAL
434.4 m/sec
RATIO
(Measured/Theoretical)
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Explain why you think the values for the ratios (measured to theoretical values) you
obtained in Table 3 are not unity. Why is the ratio for thrust low compared to the C* or Isp
ratios?
What is the value of the thrust just after the valve is opened? Does this agree more
favorably (compared to the thrust 1.5 seconds after the valve was opened) with the theoretical
thrust you calculated ?
How would you increase the Isp of this system?
Based upon your MEASURED results, what might the cold gas thruster system be useful for
on FalconSat IV (Minitial = 50 kg) if the thruster system is limited to a total mass of 10 kg ?
NOTES
Last Major Revision by
Dr. Andrew Ketsdever on 26 APR 2005