MA SS AV"HjS F.T-r 41: TF
Modeling the Characteristics of Propulsior- ARCHIVES Systems Providing Less Than 10 N Thrust
by Thomas Michael Chiasson
B.S. Astronautics, United States Air Force Academy (2010)
Submitted to the Department of Aeronautics and Astronautics in partial fulfillment of the requirements for the degree of
Master of Science in Aeronautics and Astronautics at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2012
@ Massachusetts Institute of Technology 2012. All rights reserved.
A
Author ...... Department of Aeronautics and Astronautics May 24, 2012 \F7 Certified by...... -Paulo C. Lozano H.N. Slater Associate Professor of Aeronautics and Astronautics Thesis Supervisor / / I Accepted by ...... ( Eytan H. Modiano Professor of Aeronautics and Astronautics Chair, Graduate Program Committee
2 4 Acknowledgments
I would first like to thank my advisor, Prof. Paulo Lozano, for his patient guidance and advice during my two years at MIT. I couldn't have chosen a better lab or advisor.
I would also like to thank Jaime Ramirez and Jim Sisco at Aurora Flight Sciences for including me on the project that led to this research and giving much needed assistance on a program that turned out to be much bigger than I expected.
Special thanks goes to Tom Coles for his genius on every software program I could ever want to use. If you were an app, I'd put you on my home screen.
As always, I am grateful to the U. S. Air Force and the U. S. taxpayer for providing for my education. I hope I prove to be a good investment.
At the end of 20 years of education, it seems appropriate to thank the teachers who have inspired and believed in me over the years: Mrs. Kilgore, Ms. Diaz, Ms.
Aragon, Coach Scott, Eric Hamp, Mr. Thomas, Lt Col Adelgren, Dr. Vergez, Zhou
Laoshi, Kevin Gibbons, Maj Hague, Dr. Brown, Col Lawrence, and Col Anthony, to name just a few. I hope that someday I can do for someone else what each of you have done for me.
Thanks to my GC brothers who convinced me to come here in the first place:
Tony, Joel, Daniel, Bruce, and countless others. Thanks to my family in Boston who made sure I stayed: Mark, John, Nayoon, Chance, Adelina, Chi, Sofia, Megan, and everyone at the Justice House of Prayer.
Thanks to my family, without whom I would never have achieved anything, and especially to my parents, Mike and Louisa. You believed in me before I believed in myself. I hope I can make you as proud of me as I am of you.
Finally, but most importantly, thanks to Abba Father, Jesus, and Holy Spirit. You never cease to surprise and amaze me, and I know that it's always just the beginning of eternity.
5 6 Contents
1 Introduction 15
2 Fundamentals of Space Propulsion 19
3 Predicting Relationships from Historical Data 23
3.1 Cold Gas Thrusters ...... 26
3.2 Monopropellant Thrusters ...... 30
3.3 Bipropellant Thrusters ...... 36 3.4 Resistojets ...... 38 3.5 Arejets ...... 4 3
3.6 Ion Engines ...... 4 9
3.7 Hall Effect Thrusters ...... 5 1
3.8 Pulsed-Plasma Thrusters ...... 54
3.9 Vacuum Arc Thrusters ...... 56
3.10 Field-Emission Electric Propulsion ...... 56
3.11 Colloid Thrusters ...... 5 9
3.12 Electrospray Thrusters ...... 6 1
4 Modeling Propellant Storage and Management 63
5 Validation 67 5.1 Aerojet Cubesat Propulsion Module ...... 67
5.2 BepiColombo Ion Engines ...... 69
7 5.3 University of Minnesota Shackleton Crater Reconnaisance Mission Bipro-
pellant System ...... 70 5.4 Clyde Space PPT Module ...... 70
6 Applications 73
7 Conclusion 79
A Thruster Data 83
B Source Code 105
8 List of Figures
3-1 Historical data for xenon Hall thrusters...... 24 3-2 Historical data for hydrazine monopropellant thrusters...... 25 3-3 Historical data for cold gas thrusters. Most of the data is gathered from using nitrogen gas, and the outlier is from using helium..... 27 3-4 Historical data for cold gas thrusters...... 28 3-5 Historical data for cold gas thrusters...... 28 3-6 Historical data for cold gas thrusters...... 29 3-7 Historical data for cold gas thrusters, looking at just the low thrust regim e...... 29 3-8 Historical data for hydrazine monopropellant thrusters...... 31 3-9 Historical data for hydrazine monopropellant thrusters...... 32 3-10 Historical data for hydrazine monopropellant thrusters...... 32 3-11 Historical data for hydrazine monopropellant thrusters...... 33 3-12 Historical data for hydrogen peroxide monopropellant thrusters. . . . 33
3-13 Historical data for hydrogen peroxide monopropellant t hrusters. . .. 34
3-14 Historical data for hydrogen peroxide monopropellant t hrusters. . . . 34
3-15 Historical data for hydrogen peroxide monopropellant t hrusters. . . . 35 3-16 Historical data for bipropellant thrusters...... 37 3-17 Historical data for bipropellant thrusters...... 37 3-18 Historical data for hydrazine resistojets...... 39 3-19 Historical data for hydrazine resistojets...... 39 3-20 Historical data for hydrazine resistojets...... 40 3-21 Historical data for hydrazine resistojets...... 40
9 3-22 Historical data for water resistojets...... 41 3-23 Historical data for water resistojets...... 41 3-24 Historical data for water resistojets...... 42 3-25 Historical data for water resistojets...... 42 3-26 Historical data for arcjets using various propellants...... 44
3-27 Historical data for arcjets using various propellants, zooming in on the
low thrust regime...... 4 5
3-28 Historical data for ammonia arcjets...... 4 5 3-29 Historical data for ammonia arcjets...... 4 6
3-30 Historical data for hydrogen arcjets...... 4 6
3-31 Historical data for hydrogen arcjets...... 4 7
3-32 Historical data for hydrazine arcjets...... 4 7
3-33 Historical data for hydrazine arcjets...... 4 8 3-34 Historical data for hydrazine arcjets...... 4 8
3-35 Historical data for hydrazine arcjets...... 4 9 3-36 Historical data for xenon ion engines...... 50 3-37 Historical data for xenon ion engines ...... 50 3-38 Historical data for xenon ion engines ...... 5 1
3-39 Historical data for xenon Hall thrust,ers ...... 52 3-40 Historical data for xenon Hall thrust ers ...... 53 3-41 Historical data for xenon Hall thrust ers ...... 53 3-42 Historical data for PPTs...... 54 3-43 Historical data for PPTs...... 55 3-44 Historical data for PPTs...... 55 3-45 Historical data for FEEPs...... 57 3-46 Historical data for FEEPs...... 58 3-47 Historical data for FEEPs...... 58 3-48 Historical data for colloid thrusters...... 59 3-49 Historical data for colloid thrusters...... 60 3-50 Historical data for colloid thrusters...... 60
10 6-1 Results from application of a preliminary version of the program for
the System F6 project...... 73 6-2 Using the program to compare propulsion options for a 100 kg space-
craft. Electrosprays are not compared. Mass fractions over 90% are
not shown...... 74
6-3 Using the program to compare propulsion options for a 100 kg space-
craft, including electrosprays. Mass fractions over 90% are not shown. 75
6-4 Using the program to compare propulsion options for a 10 kg space-
craft. Electrosprays are not compared. Mass fractions over 90% are
not shown...... 76 6-5 Using the program to compare propulsion options for a 10,000 kg space-
craft. Electrosprays are not compared. Mass fractions over 99% are
not shown...... 77
11 12 List of Tables
3.1 Thrusters included in the database...... 24 3.2 Specifications of VACCO MiPS butane thruster unit with integrated propellant tank for cubesats.[38] ...... 30 3.3 Specifications of Alameda Applied Sciences Corporation pVAT for Illi- nois Observing NanoSatellite (ION)...... 56 3.4 Specifications of MIT Space Propulsion Lab's electrospray arrays. . . 62
4.1 Choosing a tank material...... 64
5.1 Comparison of results from program with actual propulsion systems. . 68
A. 1 Cold gas thrusters ...... 83 A.2 Cold gas thrusters with liquid propellant (mass includes integrated tank) 85
A.3 Hydrazine monopropellant thrusters ...... 86
A.4 Hydrogen peroxide monopropellant thrusters ...... 88
A.5 Bipropellant thrusters ...... 88
A.6 Water resistojets ...... 89
A.7 Hydrazine resistojets ...... 90
A.8 Ammonia arejets ...... 90
A.9 Hydrogen arcjets ...... 91
A.10 Hydrazine arcjets ...... 91 A.11 Ion engines ...... 92 A.12 Hall Thrusters ...... 94
A.13 Pulsed plasma thrusters ...... 98
13 A.14 Vacuum arc thrusters ...... 101 A.15 Field emission electric propulsion ...... 102 A.16 Colloid thrusters ...... 103
14 Chapter 1
Introduction
In spacecraft design, scaling equations are often used to estimate the mass of a system for preliminary design purposes. Although well developed scaling equations have long been used for space lift or orbit insertion propulsion systems, few if any can be applied to the low thrust regime. [35} Thrusters providing less than 10 N of thrust are currently the focus of the majority of research and development on space propulsion.[115] [361
These systems range from integrated tank, thruster, and power processing units for cubesats, to interplanetary travel, to extremely fine precision control. They are even more diverse in the means that they provide propulsion; the database that has been ac- cumulated in the course of this research includes models (specific historical thrusters) categorized into eleven distinct types of propulsion, electrical and chemical, using a variety of propellants, with several other propulsion concepts for which not enough data could be gathered to form equations.
However, the systems level designers are usually not interested in how the thruster works, they care about what it will provide to their spacecraft in terms of thrust and total velocity change and what it will cost in terms of mass, power, volume, risk, or money. These numbers require an initial design phase in which the type of propulsion is chosen and some initial calculations are done to estimate how large the thruster, propellant storage, and (if necessary) electrical power system will be.
In scenarios when designers want to compare several different spacecraft options, of which propulsion is only one term in a larger equation, this process can be tedious.
15 Perhaps the designer wants to run some simulations of several different options for
the space system in which the number of satellites and their masses are varying, drastically changing the propulsion requirements, or perhaps some initial calculations
need to be run to compare the merits of one propulsion system against another to
make an initial design decision. The variety of propulsion options often makes these
situations like comparing apples and oranges. The fact that there is ongoing research
into improving and miniaturizing virtually every type of propulsion only makes these
decisions even more difficult, stressing the need for the most current data.[70][71]
This project was initially started to answer the seemingly simple question of how
spacing in a satellite cluster would cause the collision avoidance requirements to
change the mass fraction of their propulsion systems. A program that quickly and
reliably estimated the mass fraction of propulsion systems featuring monopropellant, cold gas, and Hall thrusters based off required acceleration, total change in velocity
(AV), and initial satellite mass was created as part of a parametric model that
would run several thousand scenarios. The program was then used to help simulate
scattering and regathering the cluster. Surprisingly, the results indicated that such
operations would be feasible even for satellites under 10 kg using dual high thrust
and low thrust monopropellant propulsion systems. Furthermore, since the program
was created from the ground up using historical data, there was already information
gathered on actual thrusters on the market that could conceivably be a part of such a system.
Since then, the program has been expanded to include eighteen different propul-
sion and propellant options built off of data gathered from over 300 thruster models
ranging from 10 N to to 10 IN of maximum thrust. It can be run iteratively within a
larger program, or it can be used stand alone: any situation where a designer requires
a quick estimate of required power or mass of a propulsion system (including thruster, propellant, propellant management, and power system) given the initial mass of the spacecraft and the required AV and maximum acceleration. Data has also been gath- ered on specific impulse, efficiency, minimum impulse bit, and feed pressure, although only specific impulse and feed pressure go into the mass calculations and efficiency
16 and minimum impulse bit could not be found for a few thrusters. This thesis will describe how the program was created, including the database of thruster specifications, equations that were developed from the database, equations used to model the other parts of a propulsion system, a few necessary assumptions, validation, and some interesting applications.
17 18 Chapter 2
Fundamentals of Space Propulsion
Before an examination of the program itself it would be useful to review some funda- mentals of space propulsion. Space propulsion at the most basic level is the applica- tion of Newton's third law by expelling mass at a rate n and velocity c to propel a spacecraft in the opposite direction. In propulsion, the resulting force is called thrust (T).
T =m -c (2.1)
While thrust relates to how quickly a spacecraft can change velocity, in orbital mechanics it is often useful to describe maneuvers in terms of total velocity change
(AV) required to move the spacecraft from one orbit to another. These two variables, thrust and AV, tend to dictate propulsion choice from a design standpoint. Large spacecraft, short schedules, or rapid maneuvering will require higher thrust from a propulsion system, whereas drag cancellation, non-elliptical orbits, and long mission times and/or distances will require larger AV.[66]
AV is by definition dependent on the mass of propellant (mp)expelled from the propulsion system. This relationship is described in the rocket equation, where ms/c is the initial mass of the spacecraft including propellant and g is the acceleration of
19 9.81 m/s 2 due to gravity.
myro, = ms/c(1 - e~ V "IP9) (2.2)
As can be seen from this equation, specific impulse (I,,) is also a determining
factor of a spacecraft's propellant mass fraction. Ip describes the amount of thrust derived from a propulsion system compared to the mass flow rate of its exhaust (rh).
T ISP = T rh - g (2.3)
Although the concepts are different, the relationship between AV and I,, is analo-
gous to that between distance and miles per gallon. Missions requiring high AV must
use propulsion systems with high I,p in order to keep the propellant mass fraction
from being prohibitively large. Unfortunately, propulsion systems with high I, tend to have low thrust to power ratios.
For the purposes of this thesis, power refers to the electric power input of a
propulsion system. All propulsion systems require some minimal amount of power
to operate valves and possibly heaters or pumps, but some propulsion systems use
electric power to create thrust, as opposed to depending on chemical reactions. The
thrust of these electric propulsion systems is directly dependent on the input power.
Increasing the power in turn requires a power system, including a power source
such as batteries and/or solar panels and a power processing unit. All spacecraft
require a power system regardless of propulsion, but electric propulsion systems can
have power requirements high enough to significantly increase the mass of a space-
craft's power system. In practice, this means that electric propulsion systems provide limited thrust.
This brings up a fundamental distinction between electric and chemical propul-
sion. Chemical propulsion provides unmatched thrust, whereas no electric propulsion system has ever been designed that can lift the weight of its own required power sys- tem off the surface of the planet. However, electric propulsion far surpasses chemical propulsion in terms of I,p, resulting in less propellant and making them the natural
20 choice for high AV missions, such as interplanetary travel.
Another important factor in propulsion system design is the propellant manage- ment system. Depending on the propellant used (which also depends on the type of propulsion), multiple tanks may be required. The pressurization of propellant tanks is also important, and an optimal low mass balance must be found between large thin-walled tanks and small thick-walled tanks. For some types of propulsion sys- tems, thrust or I, may be dependent on the feed pressure of the propellant into the thruster.
21 22 Chapter 3
Predicting Relationships from Historical Data
The foundation of the modeling process is a spreadsheet containing specifications of all the models of thrusters providing 10 N or less of thrust that could be found. Data has been collected on 385 specific thruster models. Best fit equations were then found to represent the relationships between different system characteristics. For example, Figure 3-1 shows the relationship of thrust to efficiency for Hall thrusters. Each point represents data gathered from a real world Hall thruster, while the curve is a best fit of the historical data, which is used to predict system characteristics in the modeling process.
This approach is time intensive due to the difficulty of finding published speci- fications for many thrusters; however, it ensures that the modeling process is using hard data gathered from real world systems to compare thruster options. Of course, it does not guarantee that every thruster designed will also fit this historical data.
In some case, the data was so chaotic that it was difficult or impossible to find a re- lationship between certain system specifications, and a flat average was used instead of an equation. Figure 3-2 gives an example of data that was just barely organized enough to find an equation for. In this case, it was decided that although some of the data points were drastically different from the best fit curve, using the equation of the curve would still be preferable to taking a flat average. So although the historical
23 Table 3.1: Thrusters included in the database. Thruster Number of Models Cold Gas (gas) 32 Cold Gas (liq) 3 Monopropellant (H4N2) 32 Monopropellant (H202) 7 Bipropellant (liq) 9 Resistojet (H20) 9 Resistojet (H4N2) 7 Arcjet (NH3) 7 Arcjet (H2) 5 Arcjet (H4N2) 11 Arcjet (other) 4 Ion Engine (Xe) 37 Hall Thruster (Xe) 81 PPT 63 VAT (Cr) 4 PEEP 18 Colloid 13 Unused 43 Total 385
80
70
60
50
5-40
30
20
10
0 0 0.5 1 1.5 2 2.5 3 3.5 Thrust (N)
Figure 3-1: Historical data for xenon Hall thrusters.
24 1.4 i
1.2
1
-0.8
20.6
0.4
0.2
0 0 2 4 6 8 10 12 Thrust (N)
Figure 3-2: Historical data for hydrazine monopropellant thrusters.
data provides the best starting point for generating a quick initial estimate of the characteristics of an undesigned system, it should be kept in mind that once such a system is actually designed, its characteristics could be very different, for better or for worse.
Special care was taken to ensure that the equations were most accurate for lower levels of thrust, where slight differences in mass have a more serious impact on the system as a whole. Sometimes the thrusters were divided into two different regimes and separate equations were developed for both. However, the low thrust end of thruster technology is currently a focus of much research, meaning that low thrust data is few and far between, has often been gathered from experimental models, and is subject to change in the near future.[36] However, the data gathered is still more useful that what can be predicted by extrapolating from larger thrusters. Low thrust technology often uses innovative designs employing different technology and throws out assumptions that are essential to traditional methods of thruster design, which have been developed for the high thrust regime.[115]
25 It is important to stress that although this method uses real world data, it will not necessarily output the specifications of an actual real world thruster. The results from this method are representative of all of the thrusters researched and will probably not be an exact match of any of them specifically. These results are better thought of as the specifications of a theoretical thruster that could be built given what has been built in the past. Some of the thrusters in the database have not yet been flown or are engineering models of thrusters still in development, but they still provide useful data points on what can be achieved. In light of this, special care was taken not to propagate relationships beyond the limits of the data that has been gathered. If a thruster providing less than 1 N of thrust has never been built, this program will not try to conjure up what such a thruster might look like. But if thrusters providing 1 and 2 N have been built, this program will predict the characteristics of a thruster that provides 1.5 N. On the other hand, if the required thrust is higher than that of any existing model, then the program will divide the thrust until it is in range of existing models and design a system that includes multiple thrusters but unified propellant and power systems. If the user wants to know what the options are in terms of thrusters that have already been built, the database itself is still a very useful starting point. Past users have been able to validate results of this program by finding thrusters in the database that are on the market and provide even better performance than what the program estimates. In conclusion, while the relationships developed from this database of historical data are not perfect, they are the most logical starting point for providing a solid backbone of historical data to the model. As will be discussed, each propulsion type provided its own unique set of challenges.
3.1 Cold Gas Thrusters
Cold gas thrusters are the simplest type of thruster. Pressurized gas is simply released through a nozzle to create thrust. Specific impulse (I.,) is largely a function of
26 propellant choice, and any kind of gas can be used. Lighter gases deliver higher I,, at the cost of lower density, resulting in heavier tanks. Nitrogen gas is usually chosen for its lack of reactivity and balance of relatively low molecular mass and relatively high density, although helium has also been used, as can be seen in Figure 3-3.
160
140 *
120
100
C80
60*
40
20
0 0 2 4 6 8 10 Thrust (N)
Figure 3-3: Historical data for cold gas thrusters. Most of the data is gathered from using nitrogen gas, and the outlier is from using helium.
Because of the low I, provided by inert gas, propellant mass is usually pro- hibitively large, making cold gas thrusters uncompetitive compared to other options as a primary propulsion system. Usually cold gas thrusters are chosen for their sim- plicity and low cost, and little thought is given to optimizing the mass of a small valve attached to a comparatively large propellant tank. The chaotic nature of the data reflects the crude nature of this propulsion option. However, the simplicity, flight heritage, and comparative safety of cold gas thrusters have made them an attractive option for small, cheap university satellites that often face safety restrictions due to being secondary missions on larger rockets.[70] Special attention has been paid towards propellants that can be stored as a liquid and expand
27 0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05 * ** 0 I 0 2 4 6 8 10 Thrust (N)
Figure 3-4: Historical data for cold gas thrusters.
40
35
30
25
20 a: 15
10
5
0 0 2 4 6 8 10 Thrust (N)
Figure 3-5: Historical data for cold gas thrusters.
28 18
16
14
S12
e 10 1.1 8
wo 6 LL. 4
2 T+ 0 0 2 4 6 8 10 Thrust (N)
Figure 3-6: Historical data for cold gas thrusters.
0.8 -
0.7 -
0.6 -
2 0.5 -
0.4 y =0.0881n(x) +0.7413 0.3R2= 0.3686
0.2
0.1
0 0 0.02 0.04 0.06 0.08 0.1 0.12 Thrust (N)
Figure 3-7: Historical data for cold gas thrusters, looking at just the low thrust regime.
29 into a gas during emission. Liquefied gas thruster packages with integrated propellant tanks and nozzles have recently been developed specifically for cubesats.[71] Most of the characteristics of cold gas thrusters were predicted by simply averaging the data that was gathered, since no relationships could be found except for I,,, which
is a constant dependent on propellant choice. For feed pressure, which is the driving
factor of tank mass (a dominating part of propellant heavy cold gas systems), an
equation was developed specifically for the low thrust regime. Even this equation is
a poor fit of the data, but it is more accurate than a flat average across the entire range of thrust.
The program offers three propellant options for cold gas thrusters: nitrogen, he-
lium, or butane (stored as a liquid). The characteristics for nitrogen and helium
thrusters are identical except for the I,. The characteristics for butane thrusters are
gathered from VACCO's MiPS thruster shown in Table 3.1. (Only three models of
liquefied gas thrusters could be found, the data on this model was the most complete, and it is currently on the market for use on cubesats.) All characteristics except for
feed pressure for low thrust helium and nitrogen thrusters are constant.
Propellant Butane Max Thrust (mN) 55 Mass (g) 456 I,, (s) 65 Min Impulse Bit (mNs) 0.25 Max Propellant Storage (g) 53
Table 3.2: Specifications of VACCO MiPS butane thruster unit with integrated pro- pellant tank for cubesats.[38]
3.2 Monopropellant Thrusters
Monopropellant thrusters use the chemical decomposition of a single propellant, his-
torically either hydrazine or hydrogen peroxide, to create thrust. The propellant
flows through a heated catalytic bed in the combustion chamber to initiate the re-
action. Hydrazine delivers a higher specific impulse, but because it is toxic and
30 1.4
1.2
1
-0.8
20.6
0.4
0.2
0 0 2 4 6 8 10 12 Thrust (N)
Figure 3-8: Historical data for hydrazine monopropellant thrusters.
unstable, hydrogen peroxide is sometimes chosen instead. As with other chemical thrusters, I., is largely a constant dependent on propellant choice, although some models have decreased feed pressure at the expense of I., in order to optimize for lighter tanks. Although monopropellant thrusters are certainly a chemical and not an electric propulsion system, higher thrust does correlate to higher electrical power requirements of the heated catalytic bed.[116]
Monopropellant thrusters are a natural choice for secondary thrusters or station keeping on large systems. [5][35][90][30] Only one propellant tank is required, specific impulse is substantially higher than that of cold gas thrusters, and electrical power re- quirements are minimal. Recent research has focused on miniaturizing this propulsion option down to the micro- and nanosat range; however, utilization of monopropellant thrusters in this regime is dependent on the miniaturizing of the associated valves.
If developed, monopropellant thrusters could provide an attractive option for a dual propulsion system on small satellites by attaching high and low thrust thrusters to a single propellant tank.
31 240
220 '
- 200
0 y = 206.21x 048 2 180 A R = 0.5934
160 4
140 0 2 4 6 8 10 12 Thrust (N)
Figure 3-9: Historical data for hydrazine monopropellant thrusters.
4
3.5
3
$ 2.5 2 2. y = 0.0026eoc lmm R2 =0.7599 t.2 v 1.5
0.5
0 140 160 180 200 220 240 Isp (s)
Figure 3-10: Historical data for hydrazine monopropellant thrusters.
32 40-
35 -
30 -
25 -
0 20 20 y = 28.684x0-7943 R2 = 0.8878
10
5
0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Mass (kg)
Figure 3-11: Historical data for hydrazine monopropellant thrusters.
0.07 .
0.06
0.05 7 y = 0.0077e'.4 x 2 0.04 -R =0.5954
20.03
0.02
0.01> *
0 0.2 0.4 0.6 0.8 1 1.2 Thrust (N)
Figure 3-12: Historical data for hydrogen peroxide monopropellant thrusters.
33 160 -
150 y = 136.76x 0"" 9 R2 = 0.6005 140
- 130
120
110
100 0 0.2 0.4 0.6 0.8 1 1.2 Thrust (N)
Figure 3-13: Historical data for hydrogen peroxide monopropellant thrusters.
0.7 -r-
0.6 -
- 0.5
0.4 0 01 y = 0.1034e .- 0.8267 0.3 -R2=
0.2
0.1
0 80 100 120 140 160 Isp (s)
Figure 3-14: Historical data for hydrogen peroxide monopropellant thrusters.
34 2.5
2 y =0.4715el-3&" 0.9848 1.5
CLI
0.5 .- tr
0 0 0.2 0.4 0.6 0.8 1 1.2 Thrust (N)
Figure 3-15: Historical data for hydrogen peroxide monopropellant thrusters.
Two separate sets of equations were developed for thrusters using hydrazine and hydrogen peroxide. Although trends could be identified, the data is still relatively scattered. This suggests that either other factors are at work in the design of mono- propellant thrusters, or that they have not been optimized as much as they could be, perhaps because I., is still low enough that propellant tank mass dominates the sys- tem. Theoretically, monopropellant thrusters could be miniaturized and integrated with propellant storage as cold gas thrusters have been, although not to the same extent, since the heat gradient caused by propellant decomposition becomes harder to manage as mass and volume decrease. Issues with propellant storage and safety would still prohibit their use on many small satellites, which tend to be launched as a secondary payload on a rocket whose main customer would not welcome the risk of a volatile propulsion system stored next to their larger and more expensive spacecraft.[70] Despite these barriers, Aerojet has been developing a 1U hydrazine thruster module for cubesats in accordance with most range safety requirements. [91]
35 3.3 Bipropellant Thrusters
Bipropellant thrusters, the powerhouses of space propulsion, use the chemical reaction
of two propellants to create thrust. These thrusters are unmatched in terms of thrust
to weight ratio and boast the highest I, of any type of purely chemical propulsion.
However, they are also the most complicated chemical propulsion option, requiring
two propellant tanks and the associated equipment required for pressurization and fuel delivery.
While often the only viable option for space lift and orbit insertion, the complex-
ity of bipropellant thrusters does not lend itself to miniaturization and low thrust
applications. Thrusters that do provide less than 10 N are usually used as secondary
propulsion, and as the chaotic nature of the data suggests, have not been optimized for
mass. [27] [23][5] While there has been initial investigation into miniaturizing bipropel-
lant thrusters using microelectricmechanical systems (MEMS) technology, propellant
storage is still a barrier to implementation. [71] [561
On the other end of the spectrum, electric propulsion often outperforms bipropel-
lant thrusters on large satellites if the AV requirement is high. While bipropellant thrusters have the highest I, out of any chemical propulsion option, it is still far sur- passed by most electric propulsion options. A high AV requirement often demands
a high I,, to keep the propellant and tank masses from becoming prohibitively large.
These factors restrict bipropellant thrusters to high thrust operations, most of which are over 10 N and outside the scope of this research.
Although data from all available models was averaged to predict thruster charac- teristics, the program assumes monomethylhydrazine as fuel and nitrogen tetroxide as oxidizer in its propellant storage calculations. Power requirements were only found for one thruster and feed pressures were only found for two.
36 0.8
0.7
0.6
0.5
0.3
0.2
0.1
0 0 2 4 6 8 10 12 14 Thrust (N)
Figure 3-16: Historical data for bipropellant thrusters.
325 320 315 310 305 300 e 295 290 285 280 275 270 0 2 4 6 8 10 12 14 Thrust (N)
Figure 3-17: Historical data for bipropellant thrusters.
37 3.4 Resistojets
Resistojets improve the performance of cold gas thrusters by heating the propellant using electric resistors. This method raises the I, of the thruster, decreasing the tank and propellant masses, but adds the complexity and mass associated with the electrical power requirements.
The first widely used resistojets were actually modified monopropellant thrusters, and as a hybrid of chemical and electrical thrusters were called electrothermally aug- mented hydrazine thrusters (EHTs). The development of EHTs arose from the conver- gence of stringent mass limits and surplus power supply on communication satellites that were already using monopropellant hydrazine thrusters. [35] [90] [30] However, re- sistojets can use inert gas as well. Often propellants that can be stored as a liquid and easily vaporized are chosen, such as water or ammonia.
The heat augmentation process raises I. up to a point and then levels out, mean- ing that the specific impulse of resistojets is largely a function of propellant choice.
There is a relatively strong correlation between thrust and power, although low power resistojets can have abnormally high thrust to power ratios due to the mechanical thrust provided by propellant pressure.
Resistojets are often chosen instead of cold gas thrusters in cases where spare electrical power is already available. This similarity of application with cold gas thrusters, combined with the greater variety of propellants used, makes the data difficult to analyze.
Resistojets are also amiable to miniaturization for the same reasons as cold gas thrusters, although limits are reached due to the difficulty of transferring heat to the propellant within a smaller chamber. The increase in specific impulse and using liquid propellant can keep mass low, however, this must be balanced against the higher power requirements. On the high thrust end of the spectrum, resistojets are limited by the material properties of the heating element, a barrier which is overcome by arcjets.
Two sets of equations for resistojets have been developed, one for hydrazine and
38 1000
900 800
700
-600 d 500
400 2 + 770.3x + 52.949 300 y = 373.54x R = 0.7676 200 200
100
0 0 0.2 0.4 0.6 0.8 1 Thrust (N)
Figure 3-18: Historical data for hydrazine resistojets.
1
0.9
0.8
0.7
0.6
10.5 20.4
0.3
0.2
0.1
0 0 200 400 600 800 1000 Power (W)
Figure 3-19: Historical data for hydrazine resistojets.
39 320
300
280 y = 186.93x0.0s VI R2 = 0.9485 .260
240
220
200 0 200 400 600 800 1000 Power (W)
Figure 3-20: Historical data for hydrazine resistojets.
2.8
2.6
2.4
. 2.2
2
= 0.8191n(x) + 2.8825 1.8 y a. 0.7511 z R= 1.6
1.4
1.2
1 0 0.2 0.4 0.6 0.8 1 Thrust (N)
Figure 3-21: Historical data for hydrazine resistojets.
40 1600
1400
1200
= 0.9263 1000 R2 i 800
600
400
200
0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Thrust (N)
Figure 3-22: Historical data for water resistojets.
3.5
3
2.5
no2
1.5
1
0.5
0 0 200 400 600 800 1000 Power (W)
Figure 3-23: Historical data for water resistojets.
41 240
220
200
180 n. 160
140
120
100 0 200 400 600 800 1000 Power (W)
Figure 3-24: Historical data for water resistojets.
2.5
2.0 y = 4.1265x + 0.1122 R2 =0.4415 ~1.5
~-1.0
0.5
0.0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Thrust (N)
Figure 3-25: Historical data for water resistojets.
42 one for water. The sparse data for water resistojets raises the question as to whether they could be further optimized for small satellites, since they don't carry the risks that monopropellants do. Resistojets also enjoy an abundance of other propellant options that could open up further possibilities. A team at the University of Arkansas recently developed a 1U resistojet propulsion module for cubesats that uses R-134a refrigerant. [69]
3.5 Arcjets
Arcjets are very similar to resistojets but use an electric arc to heat propellant instead of resistors. This allows for higher input power thresholds and correspondingly higher thrust and specific impulse, although efficiency is compromised. As with resistojets, ammonia is a common propellant choice. Despite the storage problems associated with light gases, some research has focused on creating high power hydrogen arcjets with the expectation that large manned space systems would have an excess on board due to boil off from cryogenically stored hydrogen.[7]
As with resistojets, the first arcjets used hydrazine to take the place of hydrazine monopropellant thrusters. In a monopropellant hydrazine thruster, hydrazine is de- composed into ammonia and nitrogen in an extremely exothermic reaction, while some fraction of ammonia is further decomposed into nitrogen and hydrogen in an endothermic reaction. Good design minimizes this fraction in order to keep the ex- haust gases as hot as possible. However, the addition of heat in resistojets and arcjets, while more than compensating for the heat lost in the decomposition of ammonia, can actually raise the fraction decomposed to the point that there is no real difference be- tween using hydrazine and hydrogen nitrogen mixture as propellant.[66] In hydrazine arcjets, for example, the heat added through electrical means totally decomposes the ammonia and drowns out much of the benefit that the first chemical decomposition of hydrazine might still have to offer. The question designers are faced with is why to use hydrazine at all given its toxicity and instability. I,, is still dependent on propellant choice, especially at high power levels, but it is the molecular mass of the
43 80
70
60 y = 0.7834x- 2 50 R = 0.6326
v40
30
20
10
0 0 20 40 60 80 100 120 Power (kW)
Figure 3-26: Historical data for arcjets using various propellants.
propellant (or its products after decomposition) that are decisive rather than any chemical reaction.
Arcjets straddle the middle ground between purely chemical bipropellant thrusters and high powered Hall thrusters or ion engines in terms of I and required power, striking a balance between tank mass and power system mass. As with resistojets, the modeling process is complicated by the variety of the propellants used, but the high dependency performance characteristics have on electrical power makes the data much more organized. Three sets of equations have been developed for ammonia, hydrogen, and hydrazine propellants. Unfortunately, no mass data could be found for ammonia or hydrogen arcjets and feed pressures could only be found for hydrazine arcjets. The mass data for all of the arcjets, regardless of propellant, was propagated out to the maximum power recorded to estimate thruster mass, as shown in Figures
3-26 and 3-27. It is uncertain how accurate this equation is in the high thrust, high power regime. It is likely an overestimation of thruster mass, which typically increases slightly less than linearly with relation to power.
44 2
1.8
1.6
1.4
1.2 vsI
0.8 y = 0.001xO-9677 0.6 0.R= 0.6326 0.4
0.2
0 0 500 1000 1500 2000 2500 3000 Power (W)
Figure 3-27: Historical data for arcjets using various propellants, zooming in on the low thrust regime.
30
25 y =5.8358x2 +1.1817x + 0.2925 20 R2 = 0.9998 20
15
10
0
0 0.5 1 1.5 2 2.5 Thrust (N)
Figure 3-28: Historical data for ammonia arejets.
45 900
800
700
~600
500
400
300 0 5 10 15 20 25 30 Power (kW)
Figure 3-29: Historical data for ammonia arcjets.
120
100
80 y = 18.886x'.0172 R2 = 0.9592 -60
40
20
0 0 1 2 3 4 5 Thrust (N)
Figure 3-30: Historical data for hydrogen arcjets.
46 1600
1500
1400
1300
1200
.C1100 0 -10 1000 y =1270.6x 9 R2 = 0.9844 900
800
700
600 0 1 2 3 4 5 Thrust (N)
Figure 3-31: Historical data for hydrogen arcjets.
2.5
2
0.5
0 '- 0.05 0.1 0.15T 0.2 0.25 0.3 Thrust (N)
Figure 3-32: Historical data for hydrazine arcjets.
47 1.7
1.6
1.5
1.4
11.3
1.2
1.1
1
0.9
0.8 1 1.2 1.4 1.6 1.8 2 2.2 Power (kW)
Figure 3-33: Historical data for hydrazine arcjets.
650
600
550
_500* -
450
400
350 0 0.5 1 1.5 2 2.5 Power (kW)
Figure 3-34: Historical data for hydrazine arcjets.
48 1.85
1.8
1.75
S1.7
1.65 .6
1.55
1.5
1.45 0.05 0.1 0.15 0.2 0.25 0.3 Thrust (N)
Figure 3-35: Historical data for hydrazine arcjets.
3.6 Ion Engines
Ion engines accelerate ionized gas using an electric field created by a potential dif- ference between two grids in order to create thrust. The gas is usually ionized using electron bombardment or radio frequency-induced gas discharge in a chamber before being accelerated through biased grids. Electric propulsion in general favors propellants with high molecular mass and low ionization potential. Early ion engines used mercury or cesium, which were largely abandoned due to their toxicity and tendency to contaminate the spacecraft.[88] Most ion engines today use xenon, an inert gas which is much easier to handle. The equations have been developed using data only from xenon ion engines. In comparison with the thrusters discussed so far, ion engines offer a much higher specific impulse but limited thrust to power ratio. The high specific impulse translates to propellant mass savings, but high power requirements in turn drive up the mass of the required power system. Most models are clustered around the low power end of the spectrum, but recent research has focused on high power models for use in
49 45
40
2 35 y = 64.664x + 18.216x + 0.0462 30 R2 = 0.9848
25
20 C.15
10
5
0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Thrust (N)
Figure 3-36: Historical data for xenon ion engines.
50
45
40 y 61.162x+0.6/61 35 R2= 0,9152
30
25
20
15
10
5
0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Thrust(N)
Figure 3-37: Historical data for xenon ion engines.
50 12000
10000
8000
-C 6000 FAy = -4.3967x2 + 357.29x + 2661.7 R2 =0.8464 4000
2000 *
0 0 10 20 30 40 50 Power (kW)
Figure 3-38: Historical data for xenon ion engines. interplanetary travel. [25] [39] As with many of the electric propulsion options to be discussed, the significantly reduced propellant mass brought on by higher I.,, and the complexity of the thruster makes the thruster itself a more significant contributor to the mass of the system as a whole than in chemical systems. This means that ion engines have been the focus of quite a bit of optimization, especially in the low thrust regime, and that the data lends itself to tight, orderly relationships.
3.7 Hall Effect Thrusters
Hall thrusters accelerate ionized gas using a combination of electric and magnetic fields in order to create thrust. Propellant is fed into a ring shaped chamber with magnets arranged to create a radial magnetic field and an anode and cathode arranged to created an axial electric field pointing out of the open end of the thruster. Ions are accelerated out of the thruster towards the cathode by the axial electric field.
51 80
70 y 0.8441x3 - 0.0386x2 + 18.768x + 0.1972 2 60 R = 0.9694
.. 50
S40
30
20
10
0 0 0.5 1 1.5 2 2.5 3 3.5 Thrust (N)
Figure 3-39: Historical data for xenon Hall thrusters.
The electrons, instead of accelerating in the opposite direction towards the anode, are trapped in a Hall current by the perpendicular electric and magnetic fields and exert a force on the magnets which propels the thruster. Some of the electrons make it to the anode and are in turn propelled out of the cathode to neutralize the exhaust plume.
Xenon is usually chosen as a propellant for its high molecular mass, low ionization potential, and because it is inert and easy to handle. The possibility of using bismuth has been explored in high power hall thrusters for it's even higher molecular mass, lower ionization potential, and lower cost, often resulting in higher I,.[92] However, not enough data on bismuth hall thrusters exists to identify any relationships and the equations were developed using data from only xenon Hall thrusters.
Research on Hall thrusters has been continuing for decades and is now concen- trated on the high and low power ends of the spectrum. The consistent, ordered data reflects the high level of effort directed towards the optimization of Hall thrusters, and the sudden decrease in performance in the low power regime is indicative of the
52 90
80
70
60
150
40
30
20
10
0 0 10 20 30 40 50 60 70 80 Power (W)
Figure 3-40: Historical data for xenon Hall thrusters.
4500
4000
3500
3000
2500 C. 22000
1500
1000
500
0 0 10 20 30 40 50 60 70 80 Power (kW)
Figure 3-41: Historical data for xenon Hall thrusters.
53 the challenges of miniaturizing this propulsion option. In general, hall thrusters offer higher thrust but lower I,, than ion engines.
3.8 Pulsed-Plasma Thrusters
Pulsed-plasma thrusters (PPTs) also use a combination of electric and magnetic fields to accelerate propellant. Arc discharges are pulsed through the propellant, which is accelerated by the force created from the current of the discharge and its associated magnetic field.
PPTs are low thrust, low efficiency, and low Ip compared to ion engines. Their advantage is their simplicity and low power requirements. Most models use solid
Teflon as propellant, which is ablated and vaporized by the discharge. This makes propellant storage on PPTs extremely simple and reliable. The low minimum impulse bit resulting from the pulsed firing of PPTs also makes them a good choice for attitude control.
300
250 0 y = 56.634xo 6e R2= 0.867 200
150
100 0
50
0 0.00 1.00 2.00 3.00 4.00 5.00 6.00 Thrust (mN)
Figure 3-42: Historical data for PPTs.
54 9
8
7
6
15 y = 4.9919xO.2-57 R2 = 0.2343 3
2
1
0 0.00 1.00 2.00 3.00 4.00 5.00 6.00 Thrust(mN)
Figure 3-43: Historical data for PPTs.
3000
2500 y = 917.28xo.29 1 R2 = 0.4414 2000
-1500 IA
1000
500
0 0.00 1.00 2.00 3.00 4.00 5.00 6.00 Thrust (mN)
Figure 3-44: Historical data for PPTs.
55 Although trends can be observed in the characteristics of PPTs, the data is still very chaotic and suggests that further optimization is possible. In addition, thrust to power ratio was found for many high I, models without any accompanying max thrust or max power data, implying that these relationships are not representative of PPTs' full potential.
3.9 Vacuum Arc Thrusters
Vacuum Arc Thrusters (VATs) are very similar to PPTs except that the discharge ablates propellant off of the cathode itself, which replaces the Teflon block and retains the advantage of solid propellant storage. Performance is very similar to that of PPTs but with higher Ip, although some models utilize permanent magnets to substantially increase thrust. Very few VATs have been built, but they have been tested and scheduled to fly on microsatellite missions.
Propellant Chromium Max Thrust (mN) 1 Mass (g) 100 IS, (s) 2000 Min Impulse Bit (pNs) 0.25
Table 3.3: Specifications of Alameda Applied Sciences Corporation pVAT for Illinois Observing NanoSatellite (ION).
Since data on only four VATs could be gathered, two of which were augmented with magnets and had very different characteristics, only one was chosen to represent
this propulsion option. The pVAT, built by Alameda Applied Sciences Corporation, was chosen by the University of Illinois for deployment on their satellite, ION.
3.10 Field-Emission Electric Propulsion
A form of electrostatic propulsion like ion engines, field-emission electric propulsion (FEEP) extracts and propels ions from liquid metal propellant (usually cesium or
56 120 y = 72.257x'o5 R2 = 0.9161 100
80
~60 0 CL 40
20
0 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 Thrust (mN)
Figure 3-45: Historical data for FEEPs.
indium) using a potential difference. The potential difference causes Taylor cones on the surface of the propellant, which in turn allows the emission of ions from the tips.
FEEPs offer the highest I, and the smallest minimum impulse bit out of any propulsion option, but thrust is limited to the micronewton and low millinewton regime. Most applications of FEEPs take advantage of their low minimum impulse bit to provide high accuracy pointing or control, but their high I,, makes them favorable for any high AV, low thrust mission.
One difficulty with FEEPs is propellant management, since the indium or cesium must be melted before emission. On the other hand, solid propellant lends itself to simple storage, and since the thruster is emitting ions, the propellant can be fed by capillary forces and requires no pressurization.
Except for I,,, the data for FEEPs is relatively consistent, though sparse.
57 6
5 y = 0.2141xo0I R2 = 0.6261 4
3
2
1
0 0 20 40 60 80 100 Power (W)
Figure 3-46: Historical data for FEEPs.
14000
12000
10000 .
8000 --
6000
4000 e
2000
0 0 20 40 60 80 100 Power (W)
Figure 3-47: Historical data for FEEPs.
58 3.11 Colloid Thrusters
Colloid thrusters are very similar to FEEPs except that they extract and accelerate charged droplets instead of ions and use different propellant. Colloid thrusters were one of the earliest forms of electric propulsion to be investigated, but the lack of suitable propellants inhibited their development until the invention of liquid salts at room temperature. Today's colloid thrusters offer a higher thrust to power ratio than FEEPs, ion engines, and Hall thrusters but a lower specific impulse. A major advantage of colloid thrusters is the ease of propellant management. Liquid salts are easily manufactured with the right equipment, require little pressurization, and are safe to handle and store.
Figure 3-48: Historical data for colloid thrusters.
Unfortunately, no relationships can be discerned from the data on colloid thrusters and flat averages must be taken in order to predict most characteristics. This is prob- ably because most of the data is from old research before liquid salts were invented, and is hardly indicative of the potential of colloid thrusters. Although a variety
59 0 1 2 3 4 56 7 Power (W)
Figure 3-49: Historical data for colloid thrusters.
1600
1400
1200
1000
C800
600
400
200
0 0 2 4 6 8 10 12 Power (W)
Figure 3-50: Historical data for colloid thrusters.
60 of propellants have been used, the program assumes the liquid salt EMI-BF4 in its propellant storage calculations.
3.12 Electrospray Thrusters
Electrospray thrusters are conceptually identical to FEEPs except that they use liquid salt as propellant, and identical to colloid thrusters except that they emit ions instead of droplets. In fact, it may be possible to develop a single thruster using the same propellant that can act as both a colloid thruster and an electrospray.
Although electrosprays offer a lot of promise, they have not yet been flown in space.
Current research has achieved thrust and specific impulse levels similar to standard ion engines. Propellant management is identical to liquid salt colloid thrusters ex- cept that the propellant can be passively fed into the thruster using just capillary forces. Miniaturization of electrosprays using MEMS technology could enable them to replace ion engines in many applications due to their low mass and easy propellant management.
Another unique characteristic of MEMS electrosprays is their scalability. Electro- sprays consist of hundreds of microscopic needles from which liquid salt is propelled using a voltage difference. Scaling the thruster is simply a matter of creating more needles. For low thrusts, this can be achieved by increasing the density of the needles, and the mass of the thruster remains constant. At some point the a density limit is reached and larger area is required, at which point mass will increase with thrust.
Efficiency and specific impulse remain constant throughout.[55]
Because of both their scalability and lack of historical data, this research models electrospray thrusters using constant scaling equations instead of equations derived from historical specifications. Even if there was extensive flight data on electrosprays, it would be more logical to use that data to find constants for the known scaling equations than to work entirely off of historical specifications, as has been done for the other propulsion types. The constants used in this research were measured from
MIT Space Propulsion Laboratory's MEMS electrosprays, which are due to be tested
61 in orbit by 2014.
Propellant EMI-BF4 Specific Mass (kg/N) 6.32 I,, (s) 3500 Efficiency (%) 80
Table 3.4: Specifications of MIT Space Propulsion Lab's electrospray arrays.
62 Chapter 4
Modeling Propellant Storage and Management
The database and the resulting equations provide the tools needed to quickly and repeatedly estimate the mass of a given thruster from the required thrust. However, as shown by the focus on developing high I, electric propulsion systems, the mass of the propellant and the storage and management requirements that come with it is often a driving force in propulsion design and a deciding factor when choosing a propulsion system. Fortunately, the physics of how much propellant is needed and how big its tank needs to be are relatively simple.
The equations developed in the previous chapter can provide I,,. From there, the mass of the propellant (mp,p) is found from the required AV and the initial mass of the spacecraft (ms/c) (provided by the user) using the rocket equation, where g is the acceleration of 9.81 m/s 2 due to gravity.
M,,.4 = ms/c(l - 6e 3P9"v1) (4.1)
The mass of the propellant tank (mtank) is then calculated by assuming spherical tanks with a factor of safety (FoS) of two and some given material properties. The material properties are read from within the database and can tuned specifically to each thruster type. Titanium alloy is preferable, but aluminum alloy was used in
63 Titanium Aluminum 6Al-4V 2014-T6 Yield Strength - Uyield (MPa) 924 414 Density - Ptank (kg/m) 4430 2790 Propellants Nitrogen Hydrazine Helium Hydrogen Peroxide Water Hydrogen Ammonia EMI-BF4 Xenon
Table 4.1: Choosing a tank material.
light of the chemical properties of certain reactive propellants.
Under these assumptions, the mass of a propellant tank can be calculated using the equations for thin walled pressure vessels and the volume of a sphere. All that's left is to find the volume (V,,.p) and maximum pressure (Pma) within the tank.
mtank = 41r[(rtank - ttank)3 - rtank]ptank (4.2)
2 ttank = FoS ma rtank (4.3) 207yield
rtank = L (4.4) 3
rtank and ttank represent the radius and wall thickness of the tank, respectively.
All tank masses calculated by this method are multiplied by two to account for other factors such as acceleration and dynamic loads, stress concentrations, and weld efficiencies. [35]
For thrusters that use pressurized gas (nitrogen, helium, hydrogen, and xenon), the propellant is assumed to be an ideal gas, the minimum pressure (Pmin) is set to the feed pressure estimated from the database, and a leftover mass of propellant (mleftoverprop) is accounted for that will fill the propellant tank at the required minimum pressure.
The mass of the leftover propellant is added to the mass of the tank, and the following
64 equations along with equations 4.2, 4.3, and 4.4 are optimized for minimum tank mass.
mltoverprop = minitialpro, - myo, (4.5)
Vr= mi R (4.6)
_maminitialproRT (4.7)
minitialpro represents the mass of all of the propellant initially stored in the tank and m, represents just the mass of the propellant that's expelled in order to achieve
the required AV. R, T, and M are, respectively, the universal gas constant (8.3145
J/mol/K), temperature of propellant (set to 293.15 K), and molar mass of each the
propellant (varies by propellant).
For thrusters using pressurized liquid propellant (water, ammonia, hydrazine, and
hydrogen peroxide), the propellant tank is assumed to be at constant feed pressure
and mass is estimated using equations 4.2, 4.3, and 4.4 by calculating the volume
from the density of the liquid (pprp).
V,-, = m'"" (4.8) Pprop
A titanium nitrogen pressurant tank is then modeled using a process similar to
that for pressurized gas thrusters except that the mass of the gas (mpres,) is constant, final volume is the combined volume of the pressurant (Vank) and propellant tanks
(Vop), and minimum pressure is the pressure of the propellant (which has already
been set to the feed pressure for the thruster). As with the pressurized gas tank
method, the mass of the pressurant is added to the mass of the pressurant tank and
the equations are optimized with 4.2, 4.3, and 4.4 for minimum pressurant tank mass.
mp.ess - PPro(V±op+ Vank)M (4.9) mesRT (.0
Pmax = m,ek (4.10)
For bipropellant thrusters, two liquid propellant tanks are calculated, one for the
65 fuel and one for the oxidizer, and a single pressurant tank with enough nitrogen to fill all three tanks at the feed pressure is calculated. Colloid thrusters are pressurized, but only slightly. Many models use pumps instead of pressurization, and recent models have used a compressible tank attached to a spring. This program calculates the mass of colloid thruster tanks the same as other liquid propellants (equations 4.2, 4.3, 4.4, 4.8) but neglects the pressurant tank. For thrusters that do not use solid or unpressurized liquid propellants (PPTs, VATs, FEEPs, and electrosprays) the propellant system mass was estimated to be 5% of propellant mass. Finally, 10% is added onto the combined mass of the thruster and tanks of all propulsion types to account for feed lines and support structures. The mass of the power system is also estimated using an assumed power density of 15 kg/kW. This mass includes power source and processing, and is representative of solar panels.[35]
66 Chapter 5
Validation
Several difficulties are encountered when validating the results of the program. The first is that complete mass breakouts of propulsion systems can be difficult to find.
The second is that when such data is found, it's often from systems that violate assumptions used in the program. For example, many propulsion systems use multiple thrusters even when a single thruster with the necessary thrust has been designed, either for redundancy or for attitude control. Some spacecraft end their missions without using all their propellant, and the achieved AV actually corresponds to a much smaller tank. Usually the tanks themselves are not spherical or made out of a single material, which are assumed in the tank estimation process. All of these are indicative of the fact that there are many factors in propulsion system design that this program does not take into account, such as cost, reliability, volume, and schedule.
Quite simply, the program predicts what is possible, but not necessarily what is.
That said, comparing the results with what data can be gathered from real world systems yields some interesting results. The four systems in Table 5.1 are those for which the most complete specifications could be found.
5.1 Aerojet Cubesat Propulsion Module
The first system is a 1U hydrazine propulsion module being developed by Aerojet for cubesats. This is an example of a system for which the technology exists and
67 Aerojet Cubesat U of Minnesota Propulsion Module BepiColombo Shackleton Crater Cyde Space Hydrazine MMH/MON-1 Propulsion Type Monopropellant Xe Ion EnRine Bioronellant Teflon PPT
Thrust (N) P 2.81 1 0.1451 41 100.E-051 dV (m/s) 4501 57601 102111 3.53 Mass: S/C (kg) 2 4100 445 Propulsion (kg) Propellant (kg) Thruster (kg) Tanks (kg) Isp (s) Power (W) Max Pressure (MPa) Tank Volume (m3)
Table 5.1: Comparison of results from program with actual propulsion systems. feasible thrusters are recorded in the database, but which has never been integrated before into such a tight package. Aerojet uses MR-140A thrusters, for which no mass data could be found and are therefore not included in the database. The inputs in yellow are the capabilities Aerojet advertises for this system on a hypothetical cubesat. Although Aerojet is still working to make sure that the system meets range safety requirements, the program confirms that the design is feasible.[91]
There are a few key differences between the system designed by Aerojet and the one that the program predicts. First of all, Aerojet's system is volume limited and designed to fit entirely within a 10 cm cube, which changes the shape of the tank from an optimal sphere. Second, Aerojet's system cannot provide its max thrust of
2.8 N at end of life, whereas the program designs a system so that the max thrust can still be achieved until all the propellant needed to achieve the required AV has been expelled. This accounts for the vast difference in maximum tank pressures, since both are designed with blow down propellant feed systems. The first difference should result in Aerojet's system being heavier, and the second should result in it being lighter than what the program predicts. Another difference is that Aerojet's system actually includes four thrusters in its mass figures, but the thrust value is for an individual thruster. The calculated numbers have been adjusted so that the mass of the predicted thruster is multiplied by four to account for this.
68 This comparison is especially exciting because the program has predicted a system that is on the edge of what is feasible, and it just so happens that a very similar system is in the process of being built and tested. It validates the program's ability to predict systems in the low thrust regime, where much of the data is from experimental systems and the margin for error is especially tight.
5.2 BepiColombo Ion Engines
The second system is the electric propulsion system on BepiColombo, a European
Space Agency mission to Mercury that will be launched in 2013 and will take 6 years and 5760 m/s AV to complete the journey from Earth. This is an example of a fairly straightforward electric propulsion system within the range of what has been accomplished before. It uses T6 ion engines, which are well documented in the database.[271[111]
The data for BepiColombo was assembled from two sources which were not in complete agreement. It is possible that the numbers were from different periods of the design phase, or that they actually referred to different things. Mass of the propulsion system, for example, could be taken to mean simply the mass set aside for propulsion or the mass of the propulsion module designed to ferry the spacecraft from Earth to Mercury, including guidance and control. BepiColombo actually consists of two spacecraft on a single propulsion module which will separate upon reaching Mercury, and it is unclear whether some of the numbers refer to combined propulsion on all three systems or just the propulsion module.
Regardless, this case scenario provides another interesting comparison. The I, for BepiColombo's engines is higher than that predicted by the program. This is to be expected since the program estimates Ip from its historical correlation with thrust and power, but in reality I,, is somewhat independent in the design process. The mission designers no doubt picked a higher I,, to design for because of the large AV.
The probability that BepiColombo plans to keep some propellant in reserve after it reaches Mercury can account for the higher propellant and propulsion masses. Data
69 on the tanks was not found, so it is unsure what effect they have on the results.
5.3 University of Minnesota Shackleton Crater Re- connaisance Mission Bipropellant System
The third system is a design of a reconnaissance mission to Shackleton Crater on the south pole of the moon by students at the University of Minnesota. This is an example of a chemical propulsion system that is within the range of many systems that have been built in the past.[23] Although the spacecraft uses the 420 N EADS Astrium S400-12 as its main thruster to provide the 1021 m/s of AV, it also uses 4 N EADS Astrium S4 as guiding thrusters. The mass budget for one 4 N thruster was added to the mass budget for tanks and propellant for comparison. This assumes that the 4 N thruster provides the same I,, as the 420 N, although it as actually quite lower.[5] As can be expected, the mass of propellant is predicted to be higher than the what is budgeted for the Shackleton mission, along with the tank masses and total mass of propulsion. The difference between the actual and predicted total propulsion mass is almost en- tirely accounted for by the discrepancy between propellant and tank masses. The pressure of the tank reveals that the propellant storage system is different than the one the program designs, perhaps using pumps. In addition, it is known that the actual design uses composite tanks. Still, the programs results are remarkably similar to the actual design. This shows the validity of the model within a well known regime for chemical systems just as the BepiColombo example does for electric systems.
5.4 Clyde Space PPT Module
The PPT propulsion module build by Clyde Space is a bit of a different case. First of all, it should be noted that the only data found for this system was for mass, power, and I,.[57] The inputs were chosen to predict the same propellant mass at the lowest
70 mass and power.
Glancing at the database (see Table A.13), it is obvious why the program predicts higher power and mass requirements than Clyde Space's module. No thruster that requires that little power is recorded. Furthermore, Clyde Space doesn't provide any thrust data on this model, so it can't be used to extend the equations for PPTs into this regime. The program is already using the lowest thrust recorded in the database, and this system is simply outside the range of what has been recorded.
This example illustrates a limitation of the program: it can only predict within the regime of what has been recorded. Clyde Space's PPT propulsion module pro- vides an I.,, that surpasses most other PPTs at a highly optimized mass and power requirement. Although the program returns reasonable characteristics, it should al- ways be kept in mind that it is possible to design a system with characteristics much worse, and sometimes much better, than predicted.
71 72 Chapter 6
Applications
As previously described, one of the most useful applications of this program is within larger simulations where mass and propellant fractions of hypothetical spacecraft must be generated for a range of scenarios. The program was initially written as part of a parametric model for DARPA's System F6 project that analyzed collision avoidance in satellite clusters. An example of the results generated by the program as it was then can be seen in Figure 6-1.
104. - 0 10 10 10 10 Average Propulsion System Mass Fraction
Figure 6-1: Results from application of a preliminary version of the program for the System F6 project.
73 These results were generated for a range of mission profiles in which the mass of the satellite and the required acceleration were varying. At that point, the program included equations for cold gas, monopropellant, and Hall thrusters, and did not differentiate according to propellant.
When the mass of the satellite was brought into the nanosatellite range (1-10 kg), the program showed that monopropellant thrusters were the most feasible option.
Thrusters that met the requirements were found in the database that were being sold by Micro Aerospace Solutions.[94] Later it was found that Aerojet was in the process of designing an integrated system that would fly on satellites down to 2 kg in mass.[91]
Lowest Mass Propulsion Option for 100 kg Satellite 10, X X + + X + Monopropellant (H4N2) + + + + + x x x X X x x x x X + Monopropellant (H202) + + + + + x X x x x x x x x X Blpropellant (NTO/MMH) 0 + + + + + X x x x x x x X x x x. x Arcjet(NH3) + + + + + + x x x x x x< x x x xIon\Engine(Xe) + + + + + + + X * VAT (Cr) + + + + + + + x FEEP
+ + + + + + + X x x x + + + + + + + x ' x x X 0 1 0 [ 1
- + + + + x xa aE 0 C 0
+ + + + - + + X X O E O 102++ + + + + + x a a a a O a a + +- + + + + x x a a a a a a - + +. + + + + + x Y 1 0 01 0 4- + + +- + + xx C D 0 C O 0 +K+ + +- + +- + + x x K~ a a1 a[ *
1 + + + +- -+ + + x * * * * * * -*
+ + + + - + * * * * - *
+ + + + + ++~ 4- ±-[ - -- * * - --
10 10 102 103 01 (m/s)
Figure 6-2: Using the program to compare propulsion options for a 100 kg spacecraft. Electrosprays are not compared. Mass fractions over 90% are not shown.
Much more extensive applications are possible with the most recent version of the program. For demonstration purposes, the program was iterated for a wide range
74 of thrust, mass, and AV combinations. The first example in Figure 6-2 compares propulsion options on a 100 kg spacecraft.
It should be noted that some propulsion options cannot provide thrust as low as shown in these plots. If the thrust was lower than the range in the database for that type of propulsion, the program reset the thrust to the lowest recorded and calculated mass accordingly. So even though monopropellant thrusters cannot provide thrust less than 1 mN, at low AV they can still result in a smaller system than those that do. These plots assume that having more than the required thrust is acceptable, and contain no information with regard to minimum impulse bit.
Lowest Mass Propulsion Option for 100 kg Satellite 10 x x x x M x x x X X x X x X x +A onopropellant (H4N2)
+ + + + + x x x x x x x x - x x X- + Monopropellant (H2O2) + + + + + - x - x X X Bipropellant (NTO/MMH) + + + + + + x x X X X X x X X X x Arcjet(NH3) 100 + + + + + + x X x X x x x x X x FEEP + + + + + + + X x x X x X X X X x x Electrospray(EMI-BF4) +- A- A- A- A- + +- x x x x + + + A- + + + xX A- + A- A- + + +- x- x x x x x-
10 +- + + A- + + +A- x x x
+ + A-+ + + x X
10 - . ------. + 1 . . 10-2 1 10 C10 -+4 A+ + +- A-+ - + A + + A- 4- 4. . ..- 3 A- IT + A-A+ - - A A- A -A- A 4
10.. , ......
10, 10 l01010p OW (m/s)
Figure 6-3: Using the program to compare propulsion options for a 100 kg spacecraft, including electrosprays. Mass fractions over 90% are not shown.
Figure 6-3 includes electrospray thrusters in the comparison. As can be expected, they dominate a sizable portion of mission scenarios, replacing ion engines and VATs.
In order to better observe the capabilities of other electric propulsion options, elec-
75 trosprays were excluded from the other plots. Two other interesting cases are the high and low mass ends of the spectrum.
Lowest Mass Propulsion Option for 10 kg Satellite 10 x x xx x Cold Gas (N2) 4- + +- + + + + + x x x x x x x x x x + + + +-+ + + + + + x x x x X x x x + Monopropellant (H4N2) + ± +- + +- + + + + +- x x x x + Monopropellant (H202) + + + + + + + + + + + x . x - Bipropellant (NTO/MMH) 10P + + + + + + + + + + + x x x x x x x I on Engine (Xe) + + +- + + + + + + + +X X x- x VAT(Cr) + + + + + + + + + ± + 4- x- FEEP +4 ++- + +4- 4 +- + +4+- + 4- 4 -4-x x x x4
+ + 4- + + + +- +- + + 4- 4- +- 4x4 x x 10 -+ + + + +- + +. + + ± + + 4 X + + + + + + + + + + + + +. x x x x + + + + +- + + + + 4- + + x x xx
+- + + + + + + X X - 4 4 -4-7o 4- + +-+ + + + + + + + + + x C 4 0 r *
+ + + + + + + +*******---- 1010~ +f+ + + + + + ++4 + + + + 4- + + * * * + + + + + + + + + 4+ 4- + + * * * -- 4- + + + + + + + + + ------
1 4- + t ,+,,t * 4- 4 4-,+ 4- 4- " , - , * 10 7 4- 4 + 4- 4- 04- 4 4-4+ 4 4 - + 4 +4- 4+ + 4-* 4- + 4- 4- 4- + 4- 4- 4- 4- 4-.
10 * 10 1- ice 103 4- 4-i 4 --
0/ (m/s)
Figure 6-4: Using the program to compare propulsion options for a 10 kg spacecraft. Electrosprays are not compared. Mass fractions over 90% are not shown.
76 Lowest Mass Propulsion Option for 10000 kg Satellite 10 x x x 1Bipropellant (NTO/MMH) A ~> N A N N ArcJet (NH3) 0 0 ArcJet (H4N2) $ U N N 71 Ion Engine (Xe) e o o o C1 C Hall Thruster (Xe) . -VAT (Cr) 0 o e o NU~ N . -FEEP 10 0 o o o a UN. o o o o 10~ D - Dro z 1o N - U F N NFl . CO e - 2102 - I- -
N F * - 10~ +*--
104
10~~ 10 10 10 10 10 10 e/ (m/s)
Figure 6-5: Using the program to compare propulsion options for a 10,000 kg space- craft. Electrosprays are not compared. Mass fractions over 99% are not shown.
77 78 Chapter 7
Conclusion
This research has resulted in a useful tool for spacecraft design and simulation. Al- though it has limitations that are important to understand, it also carries the unique capability of providing quick preliminary design estimates that would otherwise be much more time consuming. In addition, the database itself can be useful if searching for a particular thruster model. The validity of the program lies in its use of histori- cal data. Assumptions are made, but a lot of these are constants that can easily be adjusted. There are several improvements that could be made to the program that are still unexplored. The first is the calculation of power system mass. Instead of using a single constant for power density, different constants could be used for different types of propulsion to represent the diverse power conditioning requirements for each type of propulsion. Scaling equations instead of constants could be used as well, reflecting the difficulty of scaling power systems into the low mass regime. If the data on power processing units and power system design is readily available, this would be very easy to add into the program. A second possibility for improvement would be in the propellant storage calcu- lations. Particularly, storage mass for unpressurized propellant is assumed to be a constant 5% of propellant mass. This may not be accurate across a wide range of propellant mass. Perhaps some estimation of surface area of the propellant can be used, but this would have to take into account the highly integrated nature of un-
79 pressurized propellant storage at low AV in FEEPs, PPTs, VATs, and electrosprays.
In all practicality, some of these systems may never be designed for high AV because of their low thrust, and their propellant calculations may only be relevant within a certain regime anyways.
Also, the calculations for pressurized propellants do not account for cryogenic storage, composite tanks, or fuel pumping. The reason for this was that the program was focused on systems providing less than 10 N of thrust, and the calculations require more precision as mass decreases. Systems in this regime are less likely to be optimized with these features. However, for high AV, these features open up the possibility to further optimization.
Two specific sets of equations that could use some more attention are those for ion engines and for PPTs. The ion engine equations estimate I. from thrust, and this may be more accurately correlated to AV. The data for PPTs is extensive but chaotic. Perhaps more complete data can be found, or perhaps older, less optimized models can be excluded from the database. There are some PPT models that are competitive with the single VAT model used, but since they are averaged in with other models the equations portray VATs in a much better light.
Some thrusters, such as PPTs, FEEPs, and VATs, are commonly integrated with their propellant and power systems. Although the program calculates thrusters, pro- pellant storage, and power separately, exceptions could be made for these thrusters if the necessary data was gathered.
Most other possibilities would require a significant addition to the database, which would be very time consuming. For example, propellant storage calculations could follow the same method as thruster calculations if a database of tank specifications was created. Information on the the cost, reliability, or flight status of thrusters could be added and filters could be implemented to only return data on, for example, commercially available flight qualified thrusters. Ultimately, this direction leads away from simulation and prediction and towards choosing an actual thruster model for the designer. It is worth noting, however, that data on efficiency and minimum impulse bit have already been gathered for many thrusters in the database and could easily
80 be incorporated into any modifications.
The real strength in the program, as said, lies in how quickly it can compare so many different options. As a spacecraft moves from its preliminary design phase, more extensive and specific calculations are required. For assistance in comparing propulsion options or estimating mass fractions, however, this research fills a much needed role.
81 82 Appendix A
Thruster Data
Table A.1: Cold gas thrusters
Tmax ISP Ibt Pnax Pin Thruster (N) m (g) (s) (mNs) (W) (MPa) ref.
ALMASat CGMPS 0.00075 0.75 1.5 0.14 [pog]
AMPAC SV-14 0.04000 75.00 3.5 0.25 [8o][63]
AMPAC-ISP 0.00100 300.00 70 0.10 ["u7 VP-03-001
Bradford Engineering 0.00200 175.00 60 4.5 0.25 [121 PMT
DASA CGT1 0.02000 120.00 67 0.70 [117][82][110
EG&G 0.10000 75 5.0 [52]
ESMO-CGS 0.20000 140 10.0
Marotta 0.05000 70.00 1.0 0.69 [117]
Marotta Gold Gas 2.36000 70.00 65 44 1.0 15.44 [71][62] Micro-Thruster
Marotta MCGT 0.44500 50.00 73 44 1.0 3.45 [61][115
Marquardt 4.50000 5.40 8.84 [70]
Continued on next page
83 Table A.1 - continued from previous page
Tmax Isp Ibit Pmax Pin Thruster (N) m (g) (s) (mNs) (W) (MPa) ref.
Moog 58-102 1.11000 15.00 30.0 0.63 117][82]
Moog 58-103 5.55000 15.00 30.0 0.63 [117][382]
Moog 58-112 1.11000 15.00 30.0 0.49 [1171[82]
Moog 58-113 3.33000 15.00 30.0 0.63 [117]
Moog 58-115 2.89000 13.00 30.0 1.46 [in73[o]
Moog 58-118 3.60000 23.00 65 30.0 1.59 [71][281
Moog 58-125 0.00450 7.34 65 0.1 2.4 0.03 [117[70][61]
Moog 58E142 0.12000 16.00 57 35.0 2.07 [71[28][29)
Moog 58E143(-6) 0.04000 40.00 60 10.0 0.25 [711][28
Moog 58E151 0.12000 70.00 65 10.5 2.76 [71[(28]129]
Moog 58X125A 0.00440 9.00 65 10.0 0.34 [71][281
Moog B 0.00500 5.50 73 [61]
RDMT-0.8 0.80000 100.00 70 [6]
RDMT-5 5.00000 350.00 70 [6]
Sterer 1.00000 174.00 68 6.0 0.35 [82)
VACCO 8.89600 376.00 20.0 1.72 [37] Gas Cold Thruster
84 Table A.2: Cold gas thrusters with liquid propellant (mass includes integrated tank)
Tmax IN t Pmax Thruster Propellant (mN) m (g) I, (s) (mNs) (W) ref.
CNAPS liq SF6 5 35 100 [22]
VACCO MiPS liq Butane 55 456 65 0.25 [71][38][36]
VACCO Piezo liq Butane 25 30 70 1 [71]
85 Table A.3: Hydrazine monopropellant thrusters
Tmax Isp Ibut Pmax Pin Thruster (N) m (g) (s) (mNs) (W) (MPa) ref.
AMPAC 1.00000 330 232 11.00 [45][811 MONARC 1 AMPAC 5.00000 370 230 90.00 [41[81] MONARC 5
DASA CHT 0.5 0.50000 195 222 7.50 2.20 [116][11o[5[1
DASA CHT 1 1.10000 290 220 10.00 15.90 2.20 [11o][5][61]
DASA CHT 10 10.00000 240 225 7.40 2.20 [5][116][110][1]
DASA CHT 2.0 2.00000 210 221 200.00 6.00 [5]
DASA CHT 5 6.00000 220 222 100.00 8.37 2.20 [s][116)[11o
DOK-10 10.00000 600 229 [6]
DOT-5 5.00000 900 230 [6]
HmNT 0.12900 40 150 0.05 8.25 [71]
Marquardt KMHS 1.42000 330 226 10.00 [61][70][16) 10
Marquardt KMHS 4.45000 380 230 2.97 [70][61][16] 17
MEMS /Yuan 0.00144 162 71] and Li pAerospace M005 0.00500 10 150 0.17 0.50 0.35 [94) pAerospace M010 0.05000 12 160 6.00 0.50 0.35 [941 pLAerospace M050 0.50000 15 170 30.00 1.00 0.35 [94] pAerospace M100 1.00000 30 200 30.00 2.00 0.35 [94]
Primex 0.10000 220 10.00 [52]
Continued on next page
86 Table A.3 - continued from previous page
Tmax Isp bit Pmax Pin Thruster (N) m (g) (s) (mNs) (W) (MPa) ref.
Primex MR-111C 5.30000 330 228 80.00 13.64 2.76 [116][70][61][45)[61
Primex MR-111E 2.20000 330 219 20.00 13.64 2.55 [70][61][6]
Rafael LT-1N SP 1.10000 250 210 32.00 9.00 2.20 [8i]
Rafael LT-5N SP 6.00000 230 200 120.00 9.60 2.20 [u16[1]
Redmond MR-103 1.13000 330 215 13.30 14.57 2.83 [701[6][61][103][45][36) Redmond 2.04000 1270 217 30.00 29.14 2.76 [6] MRM-103
SEP CHT 2 3.50000 460 216 11.20 2.20 [116]
TRW MRE-0.1 1.00000 500 216 17.80 15.00 2.41 [70][17[110]
TRW MRE-1 5.00000 500 218 2.76 [70][61][17]
87 Table A.4: Hydrogen peroxide monopropellant thrusters
Ist Pmax Pin Thruster Tmax (N) m (g) I., (s) (mNs) (W) (MPa) ref.
ARC Seibersdorf 0.800 153 [71]
Fotec 0.900 60.0 153 1.5 0.60 [po6]
Kuan et al. 0.221 5.8 125 [71] piAerospace M005HP 0.005 10.0 100 0.12 0.5 0.35 [94] pAerospace M010HP 0.100 11.0 110 0.90 0.5 0.35 [94] ptAerospace M050HP 0.500 15.0 120 4.00 1.0 0.35 [8][94) pAerospace M100HP 1.000 20.0 120 8.50 2.0 0.35 [94]
Table A.5: Bipropellant thrusters
Tmax m IV Pmax Mixture Pin Thruster Propellant (N) (g) (s) (W) Ratio (MPa) ref.
EADS S4 MON/MMH 4.00 290 285 [110][5[116][70
AMPAC LTT NTO/MMH 9.25 275 [81]
EADS S10 MON/MMH 12.50 350 287 1.64 2.3 [116][70o[110][5
Fotec RP-1/H202 3.00 100 320 3 1.2 [16
LEROS 10 N202/MMH 9.50 460 285 [45]
Marquardt NTO/H4N2 4.45 430 280 1.65 [116[70 R-2/R-2B
Marquardt R-52 MMH/NTO 10.00 295 [70]
Marquardt R-53 12.90 410 295 1.65 [16]
Rocketdyne NTO/MMH 4.50 730 300 1.6 [116] RS-45
88 Table A.6: Water resistojets
Tmax m ISP Pmax Pin
Thruster (mN) (kg) (s) (W) 7) (%) (MPa) ref.
Mark IV 50.0 1.500 180 100 0.50 [18
Marquardt 44.0 220 200 0.25 1521
MightySat II 75.0 1.240 152 100 1.00 [53][52][59]
Morren @ NASA Lewis 360.0 180 904 2.20 [521
Othman, Makled 118.0 0.400 140 700 75 [77
Rocketdyne Technion coupled 122.0 138 505 0.20 [52
Rocketdyne Technion decoupled 240.0 144 708 0.20 [52]
SSTL Micro Resistojet 3.3 0.013 3 [71][8]
SSTL UoSAT-12 45.0 1.240 152 100 34 [1181
89 Table A.7: Hydrazine resistojets
Tmax Iep Ibit Pmax Pin Thruster (mN) m (g) (s) (mNs) (W) (MPa) ref.
DCA PACT 500 360.0 306 20.00 515 2.20 [118][119]
Redmond 177 300 350 [52][31)
Redmond MR-501B 369 889.0 300 2.20 487 2.41 [52][82][119][118][45[6][36]
Redmond MR-502A 800 870.0 299 88.96 899 2.65 (52][82][118][45[6[36]
Sol Rad-10 10 [85][65]
TRW HiPEHT 490 295 550 [82][118]
TRW 245 226.8 223 4.45 12 1.55 [72]
Table A.8: Ammonia arcjets
Tmax Pmax Thruster (N) m (g) I, (s) (kW) rM(%) ref.
ESEX Arcjet 2.000 800 26.000 11o][8216][36]
IRS 600 2.000 [36]
IRS VELARC 0.028 520 0.375 18.5 [1]
IRS VELARC 0.035 350 0.240 25.0 p1
LeRC Mini LPATS 0.051 360 0.250 36.0 [1]
PSU Microwave 0.300 550 1.100 [52)
U of Stuttgart 0.115 480 480 0.750 [52][120][47]
90 Table A.9: Hydrogen arcjets
Thruster Tmax (N) I,, (s) Pmax (kW) 77(%) ref.
HIPARC 3.000 1500 100.000 22 [r
HIPARC-R 4.000 1400 100.000 28 [7][87]
IRS ESA BMDO 1.364 1300 10.000 40 [36]
IRS VELARC 0.023 865 0.365 26 [
IRS VELARC 0.014 820 0.310 18 1
Table A.10: Hydrazine arcjets
Tmax Pmax Pin Thruster (mN) m (kg) I, (s) (kW) (MPa) ref.
BPD/Centrospazio 130 440 1.000 [96]
DCA HAJ1 100 530 0.250 1.80 [a8][1uo]
GE Arcjet 210 1.00 502 1.600 po]
ISAS SEGAMI-I 176 600 1.500 p96
OSAKA-IHHI 150 475 1.200 IN]
Redmond MR-507 220 1.50 465 1.400 [118]
Redmond MR-508 230 1.34 502 1.808 1.51 [118][6][?][45]
Redmond MR-509 254 1.48 502 1.808 1.76 [82][6][45]
Redmond MR-510 258 1.58 600 2.000 1.79 [45][6][82][36][1o2]
Redmond MR-512 254 1.03 502 1.788 1.76 [6]
U of Stuttgart 230 1.30 520 1.200 p96
91 Table A.11: Ion engines
Tmax m Isp Pmax Thruster (mN) (kg) (s) (kW) r (%) ref.
13cm XIPS 17.80 6.50 2507 0.500 68.0 [70][21] [96][36[45][108][6][611
25cm XIPS Hughes 165.00 3500 4.500 65.0 [97[96] [45
25cm XIPS INTELSAT 63.00 9.70 2800 1.300 [21][97][82][36][75][108][511
ARTEMIS 15.00 1.60 3000 0.600 [96]
CIT 3 cm 0.50 3703 0.024 37.7 [18]
DERA T5 25.00 1.70 3110 0.644 60.0 [82][36][118][108][61]
DERA T6 150.00 6.20 3470 3.900 65.0 [36][118][61]
ETS-6 Kaufman 23.30 3.70 2910 0.600 [20][96]
ETS-8 Kaufman 23.20 2665 0.611 49.7 [2o][1m8]
EURECA 10.00 1.50 3300 0.440 [96]
GRC 8 cm 3.60 1760 0.100 31.0 [18][36]
HiPEP 670.00 46.50 9620 39.300 80.0 [24][25][36)
HiPER DS3G 450.00 10000 25.000 [39]
JPL 31.00 2.50 3200 0.900 66.0 [61][70)
Keldysh Res Center 6.00 3650 0.162 66.0 [61]
Keldysh Res Center 19.00 3500 0.494 65.0 [61] p 10 ECR 8.10 2910 0.340 36.0 [76][73][108] pNRIT-2.5 0.60 0.21 2861 0.034 25.5 [1][71]
MiXI 1.50 0.20 2850 0.050 40.0 [71]
NAL 14 cm 25.00 3500 0.600 [96,
NASA 30cm 178.00 7.00 3610 4.880 67.0 [79]
NASA LeRC 72.00 7.00 2130 1.500 [96]
Continued on next page
92 Table A.11 - continued from previous page
Tmax m I., Pmax Thruster (mN) (kg) (s) (kW) 7 (%) ref.
NASA Lewis 11.00 2650 0.308 47.0 [61]
NEXIS 470.00 28.70 8500 25.000 78.0 [108][26][24][67][36]
NEXT 238.00 4070 6.860 59.0 [95][36]
NSTAR 92.70 8.20 2500 2.325 61.8 [6][98][61][51][821[361[45][1081
RIT-10 15.00 1.00 3058 0.459 36.0 [5][61][36111][108][82][118]
RIT-10 EVO 41.00 1.80 3300 1.050 67.0 [5][61][36][70]
RIT-15PL 50.00 3600 1.350 67.0 (611
RIT-22 250.00 7.00 6400 5.000 [5][36]
RIT-25 25.00 1.75 3060 0.800 67.0 161][a8]
RJT-XT 210.00 4448 6.850 75.5 [5][61]
RMT 12.00 2.00 3600 0.480 55.0 [13][101][61][36]
RUS 5 cm 1.60 2900 0.072 31.6 [18]
SCATHA P78-2 0.14 350 0.045 [6][97][99]
93 Table A. 12: Hall Thrusters
Tma m 'bit Pmax Thruster (mN) (kg) I., (s) (mNs) (kW) 77(%) ref.
BHT-1500 102.0 1820 1.700 54.6 [10]
BHT-200 17.0 1.1 1390 2 0.300 32.5 [112][36][71][18]
BHT-20k 1080.0 2750 20.000 70.0 [10][67]
BHT-600-X2B 17.0 0.9 1600 0.600 45.0 [61]
BHT-8000 512.0 20.0 1900 8.000 60.0 [10[15][36]
BHT-HD-1000 55.5 3.5 1700 1.000 56.0 [61]
BHT-HD-600 36.0 2.2 1700 0.600 50.0 [61][36)
D-100 2500 4.500 60.0 [19]
D-100-II 65.0 4250 15.000 65.0 [6][461
D-20 17.0 2000 0.300 40.0 [19]
D-35 82.0 4.4 1263 1.230 40.0 [61]
D-38 35.0 2000 0.750 45.0 [19][104][61]
D-50 48.0 1700 [6]
D-55 1600 1.400 50.0 [191[82)
DS-HET 300.0 12.0 3000 5.000 50.0 [poi]
Fakel SPT-25 6.4 948 0.154 19.0 [18[61][112]
Fakel SPT-35 10.0 1200 0.196 30.0 p
HIVHAC 0.4 2500 8.000 62.0 [6][441
HTX 9.3 1350 0.200 31.0 [112
IT-100 18.0 3100 0.500 50.0 [46]
IT-50 5.0 2900 0.140 55.0 [46]
Jacobson, Jankovsky 1.0 3250 25.000 60.0 [87]
Continued on next page
94 Table A.12 - continued from previous page
Tmax m bit Pmax
Thruster (mN) (kg) I., (s) (mNs) (kW) t; (%) ref.
Keldysh K-15 16.0 1718 0.400 36.0 [61]
Keldysh KM-32 10.4 1410 0.156 45.0 [61]
Keldysh KM-37 18.4 1635 0.294 49.0 [61]
Keldysh X-40 35.0 1750 0.525 56.0 [61]
KeRC 5.7 895 0.109 22.9 [18]
KM-20 8.8 1850 0.210 39.0 [1121
MHT-9 16.6 1676 0.481 29.0 [112]
MIT 50W 1.8 865 0.126 6.0 [71](112
Moskow SPT-30 13.0 0.4 1170 0.260 30.0 [61][112]
NASA Glenn 1.0 0.500 [40]
NASA Glenn 2.5 1.000 [40]
NASA Glenn 2.5 1.500 [40
NASA Glenn 3.0 2.000 [40]
NASA Glenn 4.3 2.000 [40]
NASA Glenn 5.5 4.500 40]
NASA Glenn 6.5 5.000 40]
NASA Glenn 7.0 5.000 [40]
NASA Glenn 8.0 5.500 [40]
NASA Glenn 12.0 8.000 [40]
NASA Glenn 12.0 10.000 [40]
NASA Glenn 12.0 11.000 [40]
NASA Glenn 20.0 15.500 [40]
Continued on next page
95 Table A.12 - continued from previous page
Tm. m Iuit Pmax Thruster (mN) (kg) I, (s) (mNs) (kW) r (%) ref.
NASA Glenn 18.0 16.500 [40]
NASA-137Mv2 342.0 3000 7.872 59.6 [33]
NASA-300M 1130.0 2640 20.000 67.0 [67][41]
NASA-457M 2900.0 80.0 2900 75.000 56.0 [67][6[87][41]
NASA-457Mv2 1280.0 2520 25.200 63.0 [41]
P5 246.0 2326 5.000 [6]
PP Annul 3.5 1086 0.098 19.0 [18]
PP Cylind 3.7 1136 0.103 20.0 [18]
PPPL CHT 2.6 12.0 0.300 23.5 [71]
PPPL CHT 3.0 6.0 1325 0.185 23.5 [71]
PPS 1350-G 90.0 4.5 1650 1.500 45.0 [19][61][o][93]
PPS-20k ML 1050.0 25.0 2500 22.400 60.0 [121][46][67]
PPSX000 340.0 2480 6.000 [82][36]
Princeton 54.4 1550 0.870 46.0 [61]
Redmond BPT-2000 0.1 5.2 1765 2.200 48.0 [6]
Redmond BPT-4000 0.3 7.5 1950 4.500 58.0 [6]
SPT-100 100.0 3.5 1600 1.400 50.0 [36][45][108
SPT-140 300.0 1750 5.000 55.0 [108]
SPT-160 400.0 2500 4.500 60.0 [19]
SPT-200 498.0 2250 11.000 63.0 [40
SPT-290 1500.0 23.0 3300 30.000 70.0 [40][67][15]
SPT-30 13.0 1.0 973 0.258 25.0 [71]
Continued on next page
96 Table A.12 - continued from previous page
Tmax m INt Pmax Thruster (mN) (kg) I, (s) (mNs) (kW) 7 (%) ref.
SPT-50 20.0 0.9 1100 0.350 35.0 [19][61][108][4]
SPT-60 30.0 1300 0.510 38.0 [61]
SPT-70 40.0 2.0 1500 0.700 45.0 [108][82](45]
Stanford 1.6 575 0.040 12.5 1112]
Stanford 11.0 544 0.277 10.6 [18]
T-100 82.4 1573 1.400 47.0 [61][821
T-140 300.0 2000 4.500 [g9][74][45]
T-220 1000.0 1950 20.000 62.0 [40][19]36
T-220HT 1180.0 22.000 [74s36]
T-27 9.5 1430 0.201 33.0 [112][61]
T-40 20.0 1300 0.400 60.0 [19][74]
TAL TM-50 1114.0 2400 25.000 66.0 [40]
Thales HEMP 152.0 6.0 3500 3.000 58.0 [50[49][36]
Thales HT-100 12.5 1650 0.400 29.0 [112]100]
U of Hifa 39.0 1656 0.663 49.0 [61]
97 Table A.13: Pulsed plasma thrusters
Tmax m Isp Ibit Pmax Thruster (mN) (kg) (s) (pNs) (W) 'q (%) ref.
37 min parabolic 2.800 280 2.30 [68]
Academy Sinica 445 133.00 4.00 [68] Geom-Varying advPPT 4.200 515 133.0 8.00 [61]
AFRL 0.030 2.00 20.0 [71]
APPT 5.200 1700 650.00 250.0 17.00 [68][61
ARCS 0.025 2.00 4.0 [71]
ASU 1616 490.00 10.50 [68]
Busek jPPT 827 80.00 10.0 [11]
China Lab 990 448.00 [83]
CSSAR 40J 1188 605.00 9.00 [68]
CU UI PPT-11 1400 100.0 15.00 [36]
CU UI PPT-8 360 533.00 4.00 [68]
Dawgstar 0.112 1.720 483 56.10 10.2 1.80 [114][91]ts[71][113]
ETS-IV (Japanese) 0.029 6.600 300 2.2 1.92 [9][68]
Fairchild, NASA 808 6640.00 10.00 [68]
FalconSat-3 1.700 827 8.40 [113][11][68
FOTEC pLPPT 0.010 500 10.00 2.0 [106]
lIT7 U Singapore 1600 30.00 6.00 [68] self-ignited
IL PPT-3 Lab 600 450.00 [83]
IRS ADD-Simplex 1.370 2620 1200.00 68.0 14.00 [1][68]
Continued on next page
98 Table A.13 - continued from previous page
Tmax m 1,p INt Pmax Thruster (mN) (kg) (s) (pNs) (W) rq (%) ref.
Jiaotong nozzled 765 82.00 8.00 [68]
KIT, U Tokyo 1675 25.00 8.00 [68] liq prop Lab Combustao 68 1.12 38.00 [68] Propulsao
LES 6 0.026 1.400 300 26.00 2.5 2.90 [9][83][68][61][102]
[14] [9][83][68] LES 8/9 (MIT) 0.600 6.700 1000 297.00 25.5 7.00 [61][82][102][45]
Mars Space pPPT 585 29.00 4.48 [68]
MDT-2A (Chinese) 0.064 280 [9]
MILIPULT 0.014 0.40 [71]
Millipound 4.450 1210 2230.00 150.0 18.00 [68][61[
MIPD-3 1.130 1130 2250.00 13.00 [83][68]
MIT Lab 600 454.00 183]
NASA 450J 3000 8259.00 27.00 [68]
NASA HEPPT 2770 1300.00 23.00 [68]
NOVA 0.378 6.350 543 378.00 5.31 [14]s"][102][45]
NOVA (TIP-Il) 0.375 7.100 850 378.00 30.0 7.80 [9][68][61]
OS-1 1.400 4.950 1400 70.0 14.00 [61]
Osaka IT 445 200.00 13.50 [68]
PPT 1.000 1500 100.0 7.40 [18]
PPT 0.090 0.500 20.0 [61]
PPT 2.000 800 100.0 8.00 [61]
Continued on next page
99 Table A.13 - continued from previous page
Tm. M I,,p it Pma Thruster (mN) (kg) (s) (iNs) (W) 77(%) ref.
PPT 0.140 500 12.5 3.00 [61]
PPT-4 0.450 1250 15.0 18.00 [61]
PPT-5 0.750 1750 50.0 13.00 [61]
Primex 4.500 1500 120.0 [5211821
PRIMEX EO-1 1.400 4.950 1136 100.00 130.8 5.50 [14u[113][114][83][68]
Princeton 400 650.00 6.00 [r,8 UM AZPPT
PRS-101 1.420 4.740 1350 100.0 [6[45]
RRC Kurchatov 3000 41.21 13.00 [68] 9-APPT array RRC Kurchatov 3000 1600.00 22.00 [68] High Energy RLRC Kurchatov 4200 3883.00 37.00 [68] Very High Energy
Shairf U of T 720 660.00 10.00 [68]
SMS 0.133 4.100 400 22.0 3.00 [9][68][61][1021
STSAT-2 800 1.34 [68]
Teflon PPT 2.900 745 100.0 10.40 [18]
TMIT-5 945 17.00 3.30 [68]
TMIT-6A 1057 35.00 5.00 [68]
TMU Co-III 3-12mm 400 49.00 10.20 [68]
TMU PPT-B20 960 22.00 3.10 [68]
Tokai U Laser 2025 4.00 5.50 [68] Assisted Continued on next page
100 Table A.13 - continued from previous page
Tmax m Isp Ibit Pmax Thruster (mN) (kg) (s) (pNs) (W) 7 (%) ref.
U Tokyo External B 423 469.00 3.00 [8s][68]
UCV XPPT-8 1210 320.00 9.00 [68]
UI PPT 3,4,5 2200 150.00 19.50 [68]
Zond 2 2.000 5.000 410 50.0 8.04 [9][68][61]
Table A.14: Vacuum arc thrusters
Tmax Ibit Pmax Thruster (mN) m (kg) I-, (s) (pNs) (W) (%) ref.
AASC VAT (ION) 1.000 100 2000 0.25 100 [36][32][71][89]
AASC MVAT 0.125 150 2000 100 10.00 [36][8][84][107]
Lun 56.000 500 160 10 0.05 [w]o
MPNL CT 10.000 140 3500 0.10 2 14.00 [43][42]
101 Table A.15: Field emission electric propulsion
Tmax m I.,p Ibi Pmax 'r Thruster Propellant (mN) (kg) (s) (nNs) (W) (%) ref.
Alta FEEP-100 Cs 0.120 10000 7.2 82 [61]
Alta FEEP-150 Cs 0.300 1.41 9000 20.0 90 [3[781
Alta FEEP-1000 Cs 1.200 5.00 10000 72.0 82 [61]
ARCS GOCE MTA In 0.650 12000 80.0 [71]
ARCS InFEEP-100 In 0.100 12000 10.0 61][711
ARCS In 1.000 12000 80.0 [36][71] InFEEP-1000
ARCS inFEEP-25 In 0.025 7.10 10000 161136]
Centrospazio Cs 0.800 3.50 8000 60.0 [70
Centrospazio Cs 0.100 0.45 8000 9.0 [70]
Centrospazio FEEP Cs 1.000 6000 60.0 (521
Centrospazio Cs 0.040 0.60 9000 2.7 65 [61][71] FEEP-5
Centrospazio Cs 1.400 1.20 9000 93.0 [61][71]
FEEP-50 [86]
FEEP In 0.100 2.50 10000 10 6.7 34
FOTEC mN-FEEP In or Ga 0.300 0.30 4000 5 7.0 50 [106]
FOTEC In 0.015 0.08 5000 5 0.5 50 [106] Single FEEP
InFEEP In 0.120 12000 95 [4]
In-FEEP In 0.100 2.50 8000 5 13.0 95 [105]
Slit Emitter FEEP Cs 1.200 2.20 9000 1 [4]
102 Table A.16: Colloid thrusters
Tma m Pmax Pin Thruster (pN) (kg) Ip (s) (W) r (%) (kPa) ref.
Busek 189.0 2.50 390 6.00 [61][34][451
Busek ST-7 35.8 240 103.4 [71][36][45
Electro Optical System 8.0 7.33 700 0.03 78 [61]
GRC 200.0 2.50 390 0.50 70 [18]
Hruby et al. 190.0 400 10.00 [2]
MAI 1000.0 30.00 [2]
Stanford 500.0 0.50 200 6.00 [45][48]
Stanford EMERALD 315.0 0.25 600 6.00 [48]
TRW 1.0 1450 0.01 69 [61]
TRW/ Edwards AFB 159.0 1382 1.40 77 [61]
TRW/ Edwards AFB 129.0 1405 1.15 77 [61]
TRW/ Edwards AFB 335.0 4.95 1029 2.41 70 [61]
Velasquez 450.0 300 [2
103 104 Appendix B
Source Code
i function [propellant-mass-fraction, propulsion-mass-f raction, ...
inert-mass, propellant.mass, . ..
max-power ]=thruster-mas s (deltaV, total-init ial-mas s, max-accelerat ion,
thruster-type)
2
3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
4 %
s % Filename: thruster-mass.m
6 % Filetype: Function
7 % Project: F6
8 % Author: Thomas Chiasson
9 % Mod Date: 19/8/2011
10 % ii % PURPOSE: Estimates the mass of a propulsion system.
12 %
13 % USAGE: This is the main program called for propulsion system
14 % estimation. It can be used stand-alone or called within is % another program. The equations formed from the database are
16 % hardcoded and propellant and tank constants are read from
17 % the database, 'thrustertradespace.xlx'. All other constants
18 % and equations are in this program, with programs for tank
19 % optimization called from within this code.
105 20
21 % INPUT:
22 % 'deltaV' (m/s) Change in velocity that the thruster
23 %- should provide over its entire lifetime.
24 'total-initialamass' (kg) The total initial mass of the satellite,
25 (10-10,0 00) including propulsion and propellant.
26 'max-acceleration' (m/s^2) Maximum acceleration expected from the
27 (10^-6-10^-3) thruster.
28 'thruster-type' Row number of desired thruster in
29 'thrustertradespace.xlx.'
30
31 % OUTPUT:
32 % 'propellantamass-fraction' fraction of total initial mass that is
33 % propellant
34 % 'propulsionmass-fraction' fraction of total initial mass that is
35 % propellant or inert propulsion mass
36 % 'inertamass' (kg) Mass of thruster, tank(s), power system,
37 % lines, supports
38 % 'propellant-mass' (kg) Mass of propellant from rocket equation.
39 % 'max-power' (W) Estimated maximum required power.
40
41 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
42
43 %clc
44 global g R FS;
45
46 g = 9.81; %m/s2
47 R = 8.3145; %J/(mol K)
48 FS = 2;
49 specificpower = .015; %kg/W
5o tank-factor = 2.5;
si ullage-volume = 5; % %
52
53 % Import the file
54 [numbers, strings] = xlsread('thrustertradespace.xlsx', 'Input Calcs');
55 if ~isempty(numbers)
106 56 thrusterData.data = numbers;
57 end
58 if ~isempty(strings)
59 thrusterData.textdata = strings;
6o end
61
62 % Create new variables in the base workspace from those fields.
63 vars = fieldnames(thrusterData);
6 for i 1:length(vars)
65 assignin('base', vars{i}, thrusterData.(vars{i}));
66 end
67
68 % extract values from file
69 tank-density=thrusterData.data(thruster-type, 14);
7o tank-yield-strength=thrusterData.data(thruster-type, 13);
71
72 %Calculate thrust
73 max-thrust = total-initial-mass *max-acceleration;
74 thrusters=1;
75
76 if max-thrust>10 || max-thrust<.000009999999999
77 fprintf('\nERROR: Thrust out of range for this model. Please .
input 10 < total-initialamass < 10,0000 and 10e^-6 < ...
max-acceleration < 10e^-3\n')
78 end
79
8o if max-thrust>thrusterData.data (thruster-type, 6)
81 fprintf('\nWARNING: The required thrust is higher than that of
any thruster in the database. Multiple thrusters will be ...
simulated.\n')
82 while max-thrust/thrusters>thrusterData.data(thruster-type, 6);
83 thrusters=thrusters+1;
84 end
85 max-thrust=max-thrust/thrusters;
86 end
87
107 s if max-thrust 89 fprintf('\nWARNING: The required thrust is lower than that of ... any thruster in the database. Thrust is being raised to that ... of the lowest thrust model in the database: %i N\n', thrusterData. data (thruster.type, 4) ) 90 max-thrust = thrusterData.data(thruster-type,4); 91 end 92 93 9 %Calculate specs and masses (see thrustertradespace.xls for equations) 95 switch thruster..type 96 97 case 1 %Nitrogen Cold gas thruster 98 exhaust-velocity = thrusterData. data (thruster-type, 7) *g; 99 max-power = 11.607*max-thrust^0.2294; 100 thruster.mass = thrusterData. data (thruster-type, 10); 101 102 %Calculate propellant mass 103 propellant-mass=total.initial.mass.*(1-exp(-deltaV./exhaust-velocity)); 104 105 %Calculate tank mass 106 if max-thrust<=.12 107 propellant._pres sure=88030*log (max..thrust) +741342; ios else 1o9 propellant.pres sure=3165825; 110 end mll propellant-temperature=thrusterDat a. data (thruster.type, 16); 112 propellant-molar.mass=thrusterData.data (thruster-type,15); 113 initial.propellant-mass = ... fminsearch(@ (initial.propellant..mass) ... cold-tank.nass (initial-propellant-mass, propellant..mass, propellant..temperature, propellant-molar..mas s, ... propellant.pres sure, tank..yield.strength, ... tank-density) ,propellant..mass); 114 tank..mass=tank..factor*cold.tank..mass (initial.propellant.mass, propellant-mass, propellant.temperature, ... 108 propellant.molar-mass, propellant-pressure, tank-yield-strength, tank-density); 115 116 if initial-propellant..mass < propellant-mass 117 fprintf('\nERROR: tank optimization incorrect\n') 118 thruster-type 119 deltaV 120 total.initial.mass 121 max-acceleration 122 end 123 124 %syms mO real; 125 %s impIify(estimate-tank-mass (mO, propellant-mass, propellant _temperature, propellant-molar-mass, ... propellant-pressure, tank-yield-strength, tank-density)) 126 %ezplot(cold.tank.mass (mO, propellant.mass, ... propellant.temperature, propellant..molar-mass, propellant-pressure, tank-yield-strength, ... tank-density), [propellant-mass, propellant-mass*1.3] ) 127 128 case 2 %Helium Cold gas thruster 129 exhaust.velocity = thrusterData. data (thruster-type, 7) *g; 130 max-power = 11.607*max-thrust^0.2294; 131 thrustermass = thrusterData.data (thruster.type, 10); 132 133 %Calculate propellant mass 134 propellant-mass=total.initial-mass .*(1-exp(-deltaV./exhaust-velocity)); 135 136 %Calculate tank mass 137 if max-thrust<=.12 138 prope llantpressure=88030*log (max-thrust) +741342; 139 else 140 propellant.pre s sure=3165825; 141 end 142 propellant-temperature=thrusterData. data (thruster-type, 16); 143 propellant-molar-mas s=thrusterData.data (thruster.type,15) ; 109 144 initial..propellant-mass = ... fminsearch (@ (initial-propellant-mass) ... cold..tank-mass (initial.propellant-mass, propellant.mass, ... propellant.temperature, propellant-molar..mass, ... propellant-pressure, tank.yield-strength, ..- tank.density) ,propellant-mass) ; 145 tank-mass=tank.factor*cold-tank.mass (initial-propellant.mass, propellant-mass, propellant-temperature, ... propellant.molar-mass, propellant-pressure, ... tank-yield-strength, tank-density); 146 147 if initial.propellant..mass < propellant..mass 148 fprintf('\nERROR: tank optimization incorrect\n') 149 thruster...type iso deltaV 151 total-initial..mass 152 max.acceleration 153 end 154 155 %syms mO real; 156 %simplify(estimate-tank-mass (mO, propellant-mass, propellant-temperature, propellant-molar..mass, ... propellant.pres sure, tank-yield-strength, tank-density)) 157 %ezpiot(cold-tank_mass(mO, propellant-mass, ... propellant-temperature, propellantmolar-mas s, ... propellant-pressure, tank-yield-strength, ... tank-density), [propellant-mass*.7,propellant-mass*1.3]) 158 159 case 3 %Butane Cold gas thruster 160 exhaust.velocity = thrusterData. data (thruster-type, 7) *g; 161 max-power = thrusterData.data(thruster-type, 9); 162 thruster-mass = thrusterData.data(thruster-type, 10); 163 164 %Calculate propellant mass 165 propellant..mass=total-initial-mass.*(1-exp(-deltaV./exhaust-velocity)); 166 if propellant.mass/thrusters > .053 110 167 fprintf('\nWARNING: This thruster is integrated with its propellant tank and the required deltaV is higher ... than what can be provided. Multiple thrusters will ... be simulated.') 168 while propellant-mass/thrusters > .053 169 thrusters=thrusters+1; 170 end 171 end 172 173 %tank mass included in thruster mass 174 tank-mass=O; 175 176 case 4 %Hydrazine Monopropellant thruster en exhaust-velocity = 206.21*max-thrust^0.048*g; 178 thrustermass = 0.161*max-thrust^0.5778; 179 max-power = 28.684*thrusternass^0.7943; 180 181 %Calculate propellant mass 182 propellant.mass=total-initial-mass.*(1-exp(-deltaV./exhaust-velocity)); 183 184 %Calculate propellant tank mass 185 propellant-pressure=2558.7*exp(0.0311*exhaust-velocity/g); 186 propellant-tank-volume=(1+ullagevolume/100) *propellant-mass/... 187 thrusterData.data(thruster-type,12); i8 tank-radius=(propellant-tank-volume./ (4/3*pi)) .(1/3); 189 tank-thickness=propellant-pressure. *tank-radius*FS/tank-yield-strength/2; 190 propellant-tankamass=tank-factor*4/3*pi* ( (tank-radius+... 191 tank-thickness) .^3-tank-radius.^3) .*tankdensity; 192 193 %Calculate pressurant tank mass 194 pressurant-temperature=thrusterData.data(1, 16); 195 pressurant-molar-mass=thrusterData.data(1,15); % use N2 gas ... as pressurant i9 pressurant-tank-density=thrusterData.data(1,14); 197 pressurant-tank-yield-strength=thrusterData.data(1,13); % ... use Ti alloy as tank material 111 198 199 %syms VO real 200 %pretty (simplify (mono.tank-mass (mO, pres surant..temperature, pressurant..molar.mass, propellant-pres sure, ... propellant-tank-volume, pressurant-tank-yield-strength, ... pressurant-tank-density))) 201 %ezplot(mono.tank..mass (VO, pre s surant _temperature, pressairant_molar-mass, propellant-pressure, ... propellant-tank-volume, pressurant-tank-yield.strength, ... pressurant.tank-density), [0, propellant..tank.volume*.2]) 202 203 pressurant.tank.volume = fminsearch (@ (pressurant_tank-volume) ... mono..tank.mass (pressurant-tank-volume, . . . pressurant.temperature, pressurant-molar-mass, ... propellant-pressure, propellant.tank.volume, ... pre s surant-t ank-yield-s trength, pressurant.tank-density) , O); 204 pressurant-tank-mass = ... t ank-factor*mono-t ankimass (pressurant-tankvolume, ... pressurant-temperature, pressurantmolar-mass, ... propellant.pressure, propellant-tank..volume, ... pressurant..tank-yield-strength, pressurant-tank-density); 205 206 %initial-pressurant.volume = fminsearch(@ (initialpressurant-volume) ... mono.tank-mass2 (initial-pressurant..volume, pressurant-temperature, pressurant-molar..mass, propellan t.pres sure, propellant-tank-volume, ... tank-yield-strength, ... tank-density) ,propellant-tank-volume*.1) 207 %tank-mass = mono.tank-mass2(initialpressurantvolume, pressurant-temperature, pressurant-molar-mass, ... propellant_pres sure, propellant...tank-volume, ... tank-yieldstrength, tank-density) 208 209 if pressurant.tank-volume < 0 112 210 fprintf('\nERROR: tank optimization incorrect\n') 211 thruster-type 212 deltaV 213 total-initial-mass 214 max-acceleration 215 end 216 217 %propellant-mass 218 %propeIlant-tank-volume 219 %propellant-tankanass 220 %pressuranttank-volume 221 %pressurant-tank-mass 222 223 tank-mass=propellant-tank-ass+pressuranttbank-mass; 224 225 case 5 %Hydrogen peroxide Monopropellant thruster 226 exhaust-velocity = 136.76*max-thrust^0.0649*g; 22T thruster-nass = 0.0077*exp(1.4637*max-thrust); 228 max-power = 0.4715*exp(1.3858*max-thrust); 229 230 %Calculate propellant mass 231 propellant-mass=total-initialamass.*(1-exp(-deltaV./exhaust-velocity)); 232 233 %Calculate propellant tank mass 234 propellant-pressure=103421*exp(0.011*exhaust-velocity/g); 235 propeilant-tank-volume= (1+ullage-volume/100) *propellant-mass/... 236 thrusterData.data(thruster-type,12); 237 tank-radius=(propellant-tank-volume./ (4/3*pi)) (1/3); 238 tank-thickness=propellant-pressure. *tank-radius*FS/tank-yieldstrength/2; 239 propellant-tank-mass=tank-factor*4/3*pi*( (tank-radius+... 240 tankathickness) .^3-tank-radius.^3) .*tank-density; 241 242 %Calculate pressurant tank mass 243 pressurant-temperature=thrusterData.data(1, 16); 244 pressurant-molar.aass=thrusterData.data(1,15); % use N2 gas ... as pressurant 113 245 pressurant-tank-density=thrusterData. data (1, 14) ; 3 246 pressurant-tank-yield-strength=thrusterData.data(1,1 ); % ... use Ti alloy as tank material 247 248 %syms VO real 249 %pretty (simplify (mono-tank-mass (mO, pressurant-temperature, pressurant-molar-mass, propellant.pres sure, ... propellant-tank-volume, pressurantt ank-yield-strength, ... pressurant.tank-density))) 250 %ezplot(mono-tank-mass (VO, pres suranttemperature, . pressurant-molar-mass, propellant-pressure,. .. propellant-tank-volume, pressurant-tank-yield-strength, ... pressurant-tank-density), [0, propellant-tank-volume*.2]) 251 252 pressurant-tank-volume fminsearch(@(pressurant-tank-volume) mono-tank-mass (pressurant..tank-volume, ... pressurant-temperature, pressurant-nolar-mas s, ... propellant-pressure, propellant.tank-volume, ... pressurant-tank.yield-strength, pressurant..tank-density) , O); 253 pressurant.tank-mass = ... tank-factor*mono-tank..mass (pressurant-tank-volume, ... pressurant-temperature, pressurant-molar-mass, ... propellant-pressure, propellant-tank-volume, . pressurant-tank-yield.strength, pressurant-tank..density); 254 255 %initial-pressurant-volume = fmlnsearch(@ (initial-pressurant-volume) ... mono..tank-mass2 (initial-pressurant.volume, pressurant-temperature, pres surant.molar.mas s, propellant.pressure, propellant.tank-volume, ... tank-yield-strength, ... tank-density) , propellant..tank-volume*. l) 256 %tank-mass = mono.tank-mass2 (initialpressurant-volume, pressurant-temperature, pressurant.molar-mass, ... propellant-pressure, propellant.tank-volume, . 114 tank-yield-strength, tank-density) 257 258 if pressurant-tank-volume < 0 259 fprintf('\nERROR: tank optimization incorrect\n') 260 thruster-type 261 deltaV 262 total..initial-mass 263 max-acceleration 264 end 265 266 %propellant-mass 267 %propellant-tank-volume 268 %propellant..tank-mass 269 %pressurant-tank-volume 270 %pressurant-tank-mass 271 272 tank-mass=propellant.tank.mass+pressurant..tank-mass; 273 274 case 6 %Nitrogen tetroxide monomethylhydrazine bipropellant thruster 275 exhaust.velocity = thrusterData.data(thruster-type,7) *g; 276 max...power = thrusterData.data (thruster-type, 9) ; 277 thruster-mass = thrusterData.data (thruster..type, 10); 278 279 %Calculate propellant masses 280 oxidizer-fuel-ratio = 1.65; 281 propellant-mass=total-initial-mass.*(1-exp(-deltaV./exhaust.velocity)); 282 fuel-mass=propellant.mass/ (1+oxidizer..fuel..ratio); 283 oxidizer-mass=propellant-mass-fuel.mass; 284 propellantpres sure=thrusterData. data (thruster..type, 11); 285 286 %Calculate fuel tank mass 287 fuel.density = 878; %kg/m3 (MMH) 288 fuel.tank-volume=(+ullage.volume/100) *fuel-mass/fuel-density; 289 fuel.tank-radius=(fuel.tank.volume. /(4/3*pi) ) .^ (1/3) ; 29W fuel-tank-thickness=propellant-pressure. *fuel-tank.radius*FS/... 291 tank.yield..strength/2; 115 292 fuel-tankmass=tank-ffactor*4/3*pi*( (fuel-tank-radius+... 293 fuel..tank-thickness) .^3-fuel-tank-radius. ^3) .*tank-density; 294 295 %Calculate oxidizer tank mass 29 oxidizer-density = 1440; %kg/m3 (NTO) 297 oxidizer.tank-volume=(1+ullage..volume/100) *oxidizer.mass/oxidizer-density; 298 oxidizer..tank-radius=(oxidizer-tank-volume. / (4/3*pi)) .^ (1/3) ; 2 oxidizer-tank-thickness=propellant-pressure. *oxidizer-tank-radius... 300 *FS/tank-yield..strength/2; 301 oxidizer.tank-mass=tank-f actor*tank-factor*4/3*pi* ((.*. 302 oxidizer-tank-radius+oxidizer-tank-thickness) .^3-. 303 oxidizer-tank.radius. ^3) .*tank-density; 304 305 %Calculate pressurant tank mass 306 pressurant.temperature=thrusterData. data (1, 16); 307 pressurant-molar.mass=thrusterData.data (1, 15) ; % use N\12 gas as pressurant 3So pressurant-tank-density=thrusterData.data(1,14); 309 pressurant..tank.yield.st rength=thrusterData.data (1, 13) ; % ... use Ti alloy as tank materiai 310 311 %syms VO real 312 %pretty (simplify (mono-t ank-mas s (mO, pressurant-temperature, pressurant-molar-mass, propellant-pressure, ... propellant-tank-volume, pressurant-tank-yield-strength, ... pressurant-tank-density))) 313 %ezplot(mono-tank-mass(VO, pre s surant-temperature, pressurant-molarmass, propellant-pressure, ... fuel-tank-volume+oxidizer-tank-voiume, ... pressurant-tank-yieLd-strength, ... pressurant-tank-density), [0, (fuel-tank-volume+oxidizer-tank-voiume)*.2]) 314 315 pressurant-tank-volume = fminsearch(@(pressurant-tank-volume) ... mono..tank-mass (pressurant..tank-volume, ... pressurant-temperature, pressurant..molar.mass, ... 116 propellant-pressure, . .. fuel-tankvolume+oxidizer-tank-volume, ... pressurant-tank-yield-strength, pressurant..tank.density) , O); 316 pressurant-tank...mass = ... t ank-f actor*mono..t ankmas s (pressurant..t ankvolume, ... pressurant-temperature, pressurant-molar-mass, ... propellant-pressure, ... fuel-tank-volume+oxidizer-tank-volume, ... pressurant-tank..yield.strength, pressurant..tank.density); 317 318 %initial pressurant-volume = fminsearch(@ (initial-pressurantvolume) ... mono-tank-mass2 (initial-pressurant.volume, pressurant-temperature, pressurant-molar-mas s, propellant-pres sure, propellant-tank-volume, ... tank-yield-strength, ... tank-density) ,propellant-tank-volume*.1) 319 %tank-mass = mono-tank-mass2 (initial-pressurant-volume, pressurant-temperature, pressurant..molar-mass, propellant-pressure, propellant-tank-volume, tank-yield-strength, tank-density) 320 321 if pressurant.tank-volume < 0 322 fprintf('\nERROR: tank optimization incorrect\n') 323 thruster-type 324 deltaV 325 total-initial..mass 326 max.acceleration 327 end 328 329 %propellant.mass 330 %fuel.mass 331 %fueltank-volume 332 %f ue l..t ank..na s s 333 %oxidizer-mas s 334 %oxidizer-tank.voIume 117 335 %oxidizer-tank-mass 336 %pressurant-tank-volume 337 %pressurant-tank-mass 338 339 tank-mass=fue1-tank-mass+oxidizer.tank.mass+pressurant-tank-mass; 340 341 case 7 %Water Resistojet 342 exhaust-velocity = thrusterData. data (thruster-type, 7) *g; 343 max-power = 5156.5*max..thrust^1.2627; 344 thruster.mass = 0.0149*max-power^0.7736; 345 346 %Calculate propellant mass 347 propellant-mass=total.initial.mass.*(l-exp(-deltaV./exhaust-velocity)); 348 349 %Calculate propellant tank mass 350 propellant-pressure=4E6*max.thrust + 112214; 351 prope llant-_tank-volume= (1+ullage-volume/100) *propellant.mass/... 352 thrusterData.data(thruster-type,12); 353 tank-radius= (propellant-t ank-volume. / (4/3*pi)) (1/3); 354 tank...thickness=propellant.pressure. *tank-radius*FS/tank..yield-strength/2; 355 propellant-tank.mass=tank-factor*4/3*pi* ( (tank..radius+. .. 356 tank-thickness) .^3-tank-radius.^3) .*tank.density; 357 358 %Calculate pressurant tank mass 359 pressurant-temperature=thrusterData. data (1, 16); 360 pressurant..molar-mas s=thrusterData.data (1, 15) ; % use N2 gas ... as pressurant 361 pressurant-tank-density=thrusterData. data (1, 14); 362 pres surant-tank..yie ld.strength=thrusterData.data (1, 13) ; % use Ti alloy as tank material 363 364 %syms VO real 365 %pretty (simplify (mono-tank.mass (mO, pressurant.temperature, pressurant-molar-imass, propellant...pres sure, ... propellant.tank-volume, pressurant-tank-yield.strength, ... pressurant-tank-density))) 118 366 %ezplot (mono-tank-mass (VO, pres surant.temperature, pressurantmolarmass, propellantpres sure, . .. propellant-tank-volume, pressurant-tank-yield-strength, ... pressurant-tank-density), [0, propellant-tank...volume*.2]) 367 368 pressurant..tank-volume = fminsearch(@(pressurant-tank-volume) ... mono-tank.mass (pre ssurant.tank-volume, ... pressurant.temperature, pressurant-molar-mass, ... propellant-pres sure, propellant.tank-volume, ... pressurant..tank-yield-strength, pressurant..tank-density),0); 369 pressurant-tank..mass = ... t ank.factor*mono.t ank..mas s (pres surant..t ank.volume, ... pressurant-temperature, pressurant-molar-mass, ... propellantpres sure, propellant.tank-volume, ... pressurant..tank..yield.strength, pressurant-tank-density); 370 371 %init ial .pressurant-volume = fminsearch (@ (initial-pressurant-volume) ... mono-tank-mass2 (initial-pres surant-volume, ... pressurant-temperature, pressurant.molar.mass, propellant_pres sure, propellant-tank-volume, ... tank-yieldcstrength, ... tank-density) , propellant-tank-volume *.1) 372 %tank-mass = mono-tank-mass2 (initial.pressurant-volume, pre ssurant.temperature, pressurantmolar-mass, propellantpres sure, propellant-tank-volume, ... tank-yield-strength, tank-density) 373 374 if pressurant.tank-volume < 0 375 fprintf( '\nERROR: tank optimization incorrect\n') 376 thruster..type 377 deltaV 378 total.initial-mass 379 max-acceleration 380 end 119 381 382 %propellant-mass 383 %propellant-tank-volume 3M4 %propellant..tank-mass 385 %pressurant.tank-volume 386 %pressurant.tank-mass 387 388 tank-mass=propellant-tank..mass+pressurant-tank-mass; 389 390 case 8 %Hydrazine Resistojet 391 max-power = 373.54*max..thrust^2 + 770.3*max..thrust + 52.949; 392 exhaust-velocity = 186.93*max-power^0.075*g; 393 thruster..mass = 0.1119*max-power^0.2762; 394 395 %Calculate propellant mass 396 propellant-mass=total-initial..mass.*(1-exp(-deltaV./exhaust.velocity)); 397 398 %Calculate propellant tank mass 399 propellant..pressure=818 966*log (max..thrust) + 3E6; 400 prope llant..t ank-volume= (1+ullage..volume/100) *propellant..mass/. . . 401 thrusterData.data(thruster-type,12); 402 tank-radius= (propellant.tank-volume. / (4/3*pi)) .^ (1/3); 403 tank..thickne s s=prope llant.pres sure. *tank-radius*FS/tank..yield-strength/2; 404 propellant..tank.mass=tank-f actor*4/3*pi* ( (tank-radius+. .. 405 tank..thickness) .^3-tank-radius.^3) .*tank-density; 406 407 %Calculate pressurant tank mass 408 pressurant..temperature=thrusterDat a. data (1, 16); 409 pressurant-molar.mass=thrusterData.data (1, 15) ; % use N2 gas ... as pressurant 410 pres surant-t ank-dens ity=thrusterData. data (1, 14); 411 pres surant-tank-yie1d-strength=thrusterData.data (1, 13); % use Ti alloy as tank material 412 413 %syms VO real 414 %pretty (simplify (mono.tank.mass (mO, pressurant.temperature, 120 pressurant.molar.mass, propellant-pressure, . .. prope llant-tank-volume, pressurant-t ank-yieldst rength, ... pressurant-tankdensity))) 415 %ezplot(mono-tank-mass(VO, pre s surant-temperature, pressurant-molar-mass, propellant..pressure, ... prope llant-t ank-volume, pressurant.. ank-yield-strength, ... pressurant.tank...density), [O,propellant-tank-volume*.2]) 416 417 pressurant.tank-volume = fminsearch(@ (pressurant-tank-volume) ... mono-tank.mass (pre ssurant-tank-volume, ... pressurant..temperature, pressurant-molar.mass, ... propellant.pressure, propellant..tank-volume, ... pressurant..tank.yield-strength, pressurant..tank.density) , 0); 418 pressurant..tank-mass = ... tank-factor*mono-t ank-.mass (pressurant.tank.volume, ... pressurant-temperature, pressurant.molar-mass, ... propellant-pres sure, propellant-tank-volume, ... pressurant-tank.yield-strength, pressurant-tank-density); 419 420 %initial.pressurant-volume = fminsearch(@ (initial-pressurant-volume) ... mono-tankrmass2 (init ialipres surant-volume, ... pressurant.temperature, pressurant-nolar-mass, ... propellant-pressure, propellant-tank-volume, tank-yield-strength, ... tank-density) ,propellanttank-volume*.1) 421 %tank-mass = mono-tank-mass2 (initial-pressurant..volume, pressurant.temperature, pressurant..molar-mass, propellant-pres sure, propellant.tank-volume, ... tank-yield-strength, tank-density) 422 423 if pressurant-tank..volume < 0 424 fprintf('\nERROR: tank optimization incorrect\n') 425 thruster.type 426 deltaV 121 427 total-initial-mass 428 max.acceleration 429 end 430 431 %propellant-mass 432 %propellant-tank-volume 433 %propellant-tankrnass 434 %pressurant-tank-volume 435 %pressurant-tank-mass 436 437 t ank-mass=propellant-tank-mas s +pres surant-tankmas s; 438 439 case 9 %Ammonia arcjet 440 max-power = 5835.8*max-thrust^2 + 1181.7*max-thrust + 292.45; 441 exhaust-velocity = (89.808*log(max-power) - 97.058)*g; 442 thruster-mass = 0.001*max-power^0.9677; 443 4 %Calculate propellant mass 445 propellant-mass=total-initial-mass .* (1-exp(-deltaV./exhaust-velocity)); 446 447 %Calculate propellant tank mass 448 propellant-pressure=thrusterData.data (thruster-type,11); 449 propellant-tank-volume= (1+ullage-volume/100) *propellant-mass/... 450 thrusterData.data(thruster-type,12); 451 tank-radius=(propellant-tank-volume./ (4/3*pi)) .^ (1/3); 452 tank-thickness=propellant-pressure. *tank-radius*FS/tank-yieldstrength/2; 453 propellant-tank-mass=tank-f actor*4/3*pi* ( (tank-radius+... 454 tank-thickness) .^3-tank-radius. ^3) .*tank-density; 455 456 %Calculate pressurant tank mass 457 pressurant-temperature=thrusterData.data(1, 16); 458 pressurant-mo laramass=thrusterData.data(1,15); % use N2 gas ... as pressurant 459 pressurant-tank-density=thrusterData.data (1,14); 460 pressurant-tank-yield-strength=thrusterData.data(1,13); use Ti alloy as tank material 122 461 462 %syms VO real 463 %pretty (simplify (mono.tankmass (mO, pressurant..temperature, pressurant..molar-mass, propellant-pressure, ... propellant..tank-volume, pressurant-tank-yield-strength, pressurant-tank-density))) 464 %ezplot(monotankmass(VO, pressurant..temperature, pressurant-molar..mass, propellant.pressure, ... propellant-tank-volume, pressurant-tank-yield-strength, pressurant-tank.density), [0, propellant-tank-volume*. 21) 465 466 pressurant.tank.volume fminsearch(@ (pressurant-tank-volume) ... mono.tank-mass (pre ssurant-t ank-volume, . .. pressurant...temperature, pressurantmolar.mass, ... propellant.pressure, propellant-tank-volume, . pressurant.tank-yield-strength, pressurant.tank.density) , O); 467 pressurant-tank-mass = ... t ank..factor*mono-tank.mas s (pres surant-tank-volume, ... pressurant-temperature, pressurant-molar-mass, ... propellant-pressure, propellant-tank-volume, ... pressurant-tank-yield-strength, pressurant-tank-density); 468 469 %initial.pressurant-volume = fminsearch (@ (init ial...pres surant _volume) ... mono-tank..nass2(initial-pressurant-volume, ... pressurant-temperature, pressurantmolar-mass, propellant-pressure, propellant-tank-volume, tank-yield-strength, ... tank-density) ,propellant..tank-volume*.l) 470 %tank-mass = mono.tank-mass2 (initial.pressurant-volume, ... pressurant-temperature, pressurant..molarrmass, ... propellant -pressure, propellant.tank-volume, tank.yield-strength, tank-density) 471 472 if pressurant-tank-volume < 0 123 473 fprintf('\nERROR: tank optimization incorrect\n') 474 thruster-type 475 deltaV 476 total-initial-mass 477 max-acceleration 478 end 479 480 %propellant-mass 481 %propellant-tank..volume 482 %propellant-tank-mass 483 %pressurant..tank-volume 484 %pressurant-tank-mass 485 486 tank-mass=propellant-tank-mass+pressurant.tank-mas s; 487 488 case 10 %Hydrogen arcjet 489 max.power = 18886*max-thrust^1.0172; 490 exhaust-velocity = (1270.6*max-thrust^0.1019) *g; 491 thruster-mass = 0.001*max-power^0.9677; 492 493 %Calculate propellant mass 494 propellant-mass=total-initial-mass.*(1-exp(-deltaV./exhaust-velcity)); 495 496 %Calculate propellant tank mass 497 propellant-pres sure=thrusterData. data (thruster-type, 11); 498 propellant-temperature=thrusterData.data(t'hruster.type, 16); 499 propellant.molar.mass=thrusterData.data(thruster-type,15); soo initial-propellant.mass = ... fminsearch(@ (initial-propellant-mass) ... cold-tank-mass (initial.propellant-mass, propellant..mass, ... propellant-temperature, propellant-molar-mass, ... propellant-pressure, tank.yield.strength, ... tank.density) ,propellant.mass) ; 501 t ank.mass=t ank.f actor*c old.tank-mas s (initial-propellant.mass, propellant.mass, propellant.temperature, ... propellant-molar..mass, propellant-pressure,. .. 124 tank-yield-strength, tank-density); 502 503 if initial-propellant.mass < propellant-mass 504 fprintf('\nERROR: tank optimization incorrect\n') 505 thruster-type 506 deltaV 507 total-initial-mass 508 max-acceleration 509 end 510 511 %syms mO real; 512 %simplify(estimate-tank-mass (mO, propellant-mass, propellant _temperature, propellant..molar-mass, propellant-pressure, tank-yieldstrength, tank-density)) 513 %ezplot(cold.tank-mass(mO, propellant-mass, ... propellant-temperature, propellant-molar-mas s, ... propellant.pressure, tank-yield.strength, ... tank-density), [propellantmass,propellant-mass*l.3] ) 514 515 %propellant-mass 516 %tank-mass 517 518 case 11 %Hydrazine arcjet 519 max-power = 1428.1*log(max-thrust) + 3762.3; 520 exhaust-velocity = thrusterData. data (thruster-type, 7) *g; 521 thruster-mass = thrusterData.data (thruster-type, 10); 522 523 %Calculate propellant mass 524 propellant-mass=totalinitial..mass.*(-exp(-deltaV./exhaust-velocity)); 525 526 %Calculate propellant tank mass 527 propellant..pressure=thrusterData.data (thruster-type, 11); 528 propellant.tank.volume= (1+ullage.volume/100) *propellant.mass/ ... 529 thrusterData.data(thruster-type,12); 530 tank-radius= (propel1ant-tank-volume. / (4 /3*pi)) (1/3); 531 tank-thickness=propellant.pressure. *tank-radius*FS/tank..yield.strength/2; 125 532 propellant.tank-mass=tank-f actor*4/3*pi* ( (tank-radius+... 533 tank..thickness) .^3-tank-radius.^3) .*tank-density; 534 535 %Calculate pressurant tank mass 536 pres surant.temperature=thrusterData. data (1, 16); 537 pressurant-molar-maass=thrusterData.data (1, 15) ; % use N2 gas as pressurant 538 pres surant-t ank-dens ity=thrusterData. data (1, 14); 539 pres surant-tank-yield-strength=thrusterData.data (1, 13) ; % ... use Ti alloy as tank material 540 541 %syms VO real 542 %pretty (simplify (mono-tank..mass (mO, pressurant-temperature, pressurant-molar.mass, propeIlant-pressure, ... propellant.tank-volume, pressurant-tank-yielidstrength, pressurant-tank-density))) 543 %ezplot(mono-tank-mass (VO, pres surant _temperature, pressurant.molar-mass, propellantpres sure, . . prope llant.t ank-volume, pressurant-t ank-yield-st rength, ... pressurant-tank-density), [O,propellant.tank-volume*.2]) 544 545 pres s urant-tank-volume = fminsearch (@ (pres surant-tank-volume) ... mono..tank-mass (pressurant-tank-volume, . .. pressurant-temperature, pressurant-molar-mass, ... propellant-pres sure, propellant..tank-volume, ... pressurant -tank-yield-strength, pressurant..tank-density) , 0); 546 pressurant..tank..mass = ... t ank-factor*mono-t ank.mass (pressurant-t ank-volume, ... pressurant..temperature, pressurant..molar.mass, ... propellant-pressure, propellant..tank..volume, ... pressurant..tank-yield-strength, pressurant-tank-density); 547 548 %initial-pressurant-volume = fminsearch(@ (initial-pressurant-volume) ... mono-tank-mass2 (initial-pressurant-volume, 126 pressurant-temperature, pressurant-molar-mass, ... propellantpres sure, propellant.tank-volume, ... tank-yield-strength, ... tank.density) propellant-tank-volume*.1) 549 %tank-mass = mono.tank.nass2(initial-pressurant-volume, pressurant-temperature, pressurant..molar..mass, ... propellant-pres sure, propellant..t ank-volume, ... tank-yield-strength, tank-density) 550 551 if pres surant.tank.volume < 0 552 fprintf('\nERROR: tank optimization incorrect\n') 553 thruster.type 554 deltaV 555 total..initial-mass 556 max-acceleration 557 end 558 559 %propellant.mass 560 %propellant-tank-volume 561 %propellant-tank-mass 562 %pressurant-tank-volume 563 %pressurant-tank-mass M64 565 tank...mass=propel lant.tank-mass+pressurant-t ank.mas s; 566 567 case 12 %Xenon Ion Engine 5" max..power=64724*max.thrust^2 + 18165*max-thrust + 54.78; 569 exhaustvelocity = (-4E-6*max-power^2 + 0.357*max-power + 2665) *g; 570 thruster-mass=61.162*max.thrust + 0.6761; 571 572 %Calculate propellant mass 573 propellant.mass=total-initialmass.*(1-exp(-deltaV./exhaust-velocity)); 574 575 %Calculate tank mass 576 propellant-pressure=thrusterData. data (thruster-type,11); 127 577 propellant-temperature=thrusterData.data (thruster.type, 16); 578 propellant-molar.mass=thrusterData.data (thruster-type, 15); 579 initial-propellant..mass = ... fminsearch(@ (initial-propellant..mass) ... cold-tank-mass (initial-propellant.mass, propellant-mass, . propellant.temperature, propellant_molar.mass, ... propellant-pressure, tank-yield-strength, ... tank-density) ,propellant.mass); s8o t ank..mas s=t ank-f actor*cold-tank.mas s (init ial.propellant..mas s, propellant-mass, propellant-temperature, ... propellant..molar-mass, propellant.pressure, ... tank-yield-strength, tank-density); 581 582 if initial-propellant..mass < propellant.mass 583 fprintf('\nERROR: tank optimization incorrect\n') 584 thruster-type 585 deltaV 586 total-initialmass 587 max-acceleration 58s end 589 590 %syms mO real; 591 %simplify(estimate.tank..mass (mO, propellant-mass, propellant-temperature, propellant-molar-mass, ... propellant..pressure, tank-yied.strength, tank.density)) 592 %ezplot(cold-tank..mass(mO, propellant-mass, ... propellant.temperature, propellant-molar-mas s, propellant-pressure, tank-yield.strength, ... tank-density), [propellant-mass, propellant-mass*1.l]) 593 594 %propellant.mass 595 %tank...mass 596 597 case 13 %Hall thruster 3 598 max.power=837.41*max-thrust^ - 3.0262*max.thrust^2 + ... 599 18713*max..thrust + 222.35; 128 600 exhaust-velocity = (518.65*max..power^0.1702) *g; 601 thruster..nass=0.0107*max.power^0.7786; 602 60s %Calculate propellant mass 604 propellant..mass=total-initial-mass.*(l-exp(-deltaV./exhaust-velocity)); 605 606 %Calculate tank mass 607 propellant-pressure=thrusterData.data (thruster.type,11); 608 propellant..temperature=thrusterData.data (thruster-type, 16); 609 propellant-molar.mass=thrusterData.data (thruster.type, 15); 610 initial-propellant-mass = ... fminsearch(@ (initial-propellant-mass) ... cold.tank.mass (initial.propellant.mass, propellant..mass, ... propellant-temperature, propellant..molar.mas s, ... propellant-pressure, tank...yield.strength, tank.density) ,propellant-mass) ; 611 t ank-ma ass=t ank.f actor*cold.t ank-ma s s (init ial-propellant..mas s, propellant..mass, propellant-temperature, ... propellant..molar-mass, propellant-pressure, tank-yield-strength, tank-density); 612 613 if initial-propellant.mass < propellant.mass 614 fprintf('\nERROR: tank optimization incorrect\n') 615 thruster.type 616 deltaV 6i7 total..initial-mass 618 max-acceleration 619 end 620 621 %syms mO real; 622 %simplify(estimate-t ank-mass (mO, propellant-mass, propellant-temperature, propellant.molar.mass, propellant-pressure, tank-yield.strength, tank.density)) 623 %ezplot(cold-tank-mass(mO, propellant-mass, ... propellant.temperature, propellant-molar-mas s, ... propellant-pres sure, tank-yield-strength, ... 129 tank-density), [propellant-mass,propellant-mass*1.1]) 624 625 %propellant-mass 626 %tank-mass 627 628 case 14 %teflon pulsed plasma thruster 629 exhaust-velocity = 4784.7*max-thrust^0.2391*g; 630 max-power = 6506.7*max-thrust^0.6868; 631 thruster-mass = 29.394*max-thrust^0.2567; 632 633 %Calculate propellant mass 634 propellant-mass=total-initialamass.*(1-exp(-deltaV./exhaust-velocity)); 635 636 %Unpressurized solid propellant 637 tank-nass=.05*propellantamass; 638 639 case 15 %Chromium vaccum arc thruster 64o exhaust-velocity = thrusterData.data(thruster-type,7) *g; 64u max-power = thrusterData.data(thruster-type, 9); 642 thruster-nass = thrusterData.data (thruster-type, 10); 643 61 %Calculate propellant mass 645 propellant-mass=total-initialinass .*(1-exp(-deltaV./exhaust-velocity)); 646 647 %Unpressurized solid propellant 648 tank-mass=. 05*propellantamass; 649 650 case 16 %field emission electric propulsion 651 max-power = 99014*max-thrust^1.0456; 652 thruster-mass = 0.2141*max-power^0.6287; 653 exhaust-velocity = thrusterData.data(thruster-type,7) *g; 654 655 %Calculate propellant mass 656 propellantmnass=total-initial-mass.*(1-exp(-deltaV./exhaust-velocity)); 657 658 %Unpressurized solid propellant 130 659 tankrnass=. 05*propellantamass; 660 661 case 17 %colloid thruster 662 exhaust-velocity = thrusterData.data(thruster-type,7) *g; 663 max-power = 47501*max-thrust^1.1542; 64 thruster-rnass = thrusterData.data(thruster-type, 10); 665 666 %Calculate propellant mass 667 propellant.mass=total-initial-nass.*(1-exp(-deltaV./exhaust-velocity)); 668 669 %Calculate tank mass 670 propellant-pressure=thrusterData.data(thruster-type,11); 671 propellant-tank-volume= (1+ullage-volume/100) *propellantxnass/. .. 672 thrusterData.data(thruster-type,12); 673 tank-radius=(propellant-tank-volume./ (4/3*pi)) (1/3); 674 tank-thickness=propellant-pressure. *tank-radius*FS/tank-yield-strength/2; 675 tank-nass=tank-factor*4/3*pi*( (tank-radius+tank-thickness) .^3... 676 -tank-radius. ^3) .*tank-density; 677 678 case 18 % Electrospray -- equations are used instead of ... historical data 679 exhaust-velocity = thrusterData.data(thruster-type,7) *g; 680 efficiency = thrusterData.data(thruster-type,8)/100; 681 682 propellant-nass=total-initial-mass.*(1-exp(-deltaV./exhaust-velocity)); 683 684 specific-mass=6.32;%kg/N (representative of a Ni ILIS array with 300 micrometer spacing) 685 thrusteranass=specific-nass*max-thrust; 686 687 % unpressurized liquid propellant 688 tankamass=.05*propellantamass; 689 690 max-power=max-thrust*exhaust-velocity/2/efficiency; 691 692 otherwise 131 693 fprintf('\nERROR: The thruster type you have requested is unavailable. Please see thrustertradespace.xls') 694 end 695 696 697 %if thrusterData.data (thruster-type, 2)==O 698 %Calculate power system mass 699 power-mass = max-power*specific-power*thrusters; 700 %else 701 % power-mass=O; 702 %end 703 704 %Calculate inert mass, add %10 for feed lines and supports 705 margin = .1*(thruster-mass*thrusters+tank.mass); 706 inert.mass=thruster-mass *thrusters+tank..mass+power-mass+margin; 707 708 propulsion-mass...fraction ... = (inert..mass+propellant-mass) /total-initial.mass; 709 propellant-mass.fraction =propellant..mass/total-initial-nass; 710 711 %thruster-mass 712 %thrusters 713 %propellant-mass 714 %tank.mass 715 %power-mass 716 %margin 717 %inert-mass 718 %propulsion-mass-fraction 719 %max.power 132 i function tankamass = mono-tank-ass(pressurant-tank-volume, ... pressurant-temperature, pressurantamolaramass, final-pressure, ... propellant-tank-volume, tank-yield-strength, tank.density) 2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 3 4 % Filename: mono-tankamass.m 5 % Filetype: Function 6 % Project: F6 7 % Author: Thomas Chiasson 8 % Mod Date: 19/8/2011 9 10 % PURPOSE: Calculates the mass of a pressurant tank. 11 12 % USAGE: This program calculates the mass of a pressurant tank 13 (including pressurant) for a blowdown system of a liquid 14 propellant. It is called iteratively in an optimization is routine in thrustermass.m while estimating the mass of 16 propulsion systems using pressurized liquid propellant. 17 % INPUT: 'pressurant-tank-volume (m3) Volume of pressurant tank 'pressurant-temperature' (K) Temperature of pressurant (assumed constant) 'pressurant-molar-mass' (kg/mol) Molar mass of pressurant 'final-pressure' (Pa) Minimum required pressure for ... thruster 'propellant-tank-volume' (m3) Volume of propellant 'tank-yield-strength' (Pa) Stress at which tank material yields 'tank-density' (kg/m3) Density of tank material % OUTPUT: % 'tank-mass' (kg) Mass of pressurant tank % (including pressurant) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% global R FS; 133 34 35 pres surant..ma s s=final.pres sure* (pressurant.t ank-volume+ ... 36 propellant...tank-volume) *pressurant.molar.mass/ (R*pressurant..temperature); 37 initial-pressure=pressurant.mass*R*pressurant-temperature/ ... 38 pres surant-t ank-volume*pres surant..molarma s s); 39 tank-radius=(pressurant-tank-volume. / (4/3*pi)) (1/3); 40 tank-thickness=initial.pressure.*tankradius*FS/tank-yield..strength/2; 41 tank.mass=4/3*pi* ( (tank...radius+tank-thickness) .^3-tank..radius. ^3) .*. 42 tank.density+pressurant..mass; 43 44 %init ial.pres sure 134 i function tankamass = cold-tankamass(initial-propellantamass, ... propellant-mass, propellant-temperature, propellantamolarmass, propellant-pressure, tank-yield-strength, tank-density) 2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 3 % 4 % Filename: cold-tankmass.m 5 % Filetype: Function 6 % Project: F6 7 % Author: Thomas Chiasson 8 % Mod Date: 19/8/2011 9 % 10 % PURPOSE: Calculates the mass of a spherical cold gas propellant tank. 11 % USAGE: This program calculates the mass of a gas propellant % tank. It is called iteratively in an optimization % routine in thrusteramass.m while estimating the mass of % propulsion systems using pressurized gas propellant. % % INPUT: % 'initial-propellant-mass ' (kg) Mass of propellant before thruster use % 'propellant-mass' (kg) Mass of propellant used over thruster lifetime % 'propellant-temperature' (K) Temperature of propellant assumed constant % 'propellant-molaramass' (kg/mol) Molar mass of propellant % 'propellant-pressure' (Pa) Minimum required pressure for thruster % 'tank-yield-strength' (Pa) Stress at which tank material yields % 'tank.density' (kg/m3) Density of tank material 29 30 % OUTPUT: 31 % 'tank-mass' (kg) Mass of tank, including leftover 32 % propellant 33 34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 135 35 global R FS; 36 37 leftover-propellant.mass=initial..propellant..mass-propellant-mass; 38 tank..volume=lef tover.propellant..mas s*R*propellant.temperature/ (... 39 propellant-pressure*propellant..molar-mass); 40 max.pressure=initial-propellant-mass*R*propellant-temperature/ (... 41 t ank-volume *propellant-molar.mass) ; 42 tank-r adius=(tankvolume./ (4/3*pi)) . ^ (1/3); 43 tank-thickness=max-pressure. *tank-radius*FS/tank-yield-strength/2; 44 tank..mass=4/3*pi* ( (tank-radius+tank.thickness) .^3-tank.radius.^3) .* 45 tank..density+leftover..propellant-mass; 136 2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 3 % 4 % USAGE: This is the script used to generate the graphs in Chapter 5 % 6. I recommend toying with marker-type on line 39 for 6 % visibility purposes. 7 % 8 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 9 10 clear all 11 clf 12 clc 13 14 deltaV-space = logspace(0,5,26); 15 max-thrust-space = logspace(-5,1,31); 16 total-initialamass = 100; 17 18 margins = .2; 19 marker-size = 60; 20 mass-fractionlimit = .9; 21 22 last-thruster=17; 23 last-deltaV=length (deltaV-space); 24 last-max-thrust=length (max-thrust-space); 25 26 figure(1) 27 hold on; 28 set(gca,'FontSize',14); 29 set(gca, 'XScale' ,'Ilog') ; 3o set(gca, 'XLim', [deltaV-space(1)*(1-margins) ,deltaV-space (last-deltaV) *(1+margins)]); 31 set(gca,'YScale','log'); 32 set(gca, 'YLim', [max-thrust-space (1) * (1-margins) ,max-thrust-space(... 33 lastmax-thrust) * (1+margins)]); 34 xlabel(' \DeltaV (m/s) ') ; 35 ylabel('Max Thrust (N)'); 36 title(['Lowest Mass Propulsion Option for 137 'num2str (total-initialamass),. 37 'kg Satellite']); 38 39 marker-type={'bo','gp','r+','ys','g.','kx','g+','r*','g*', 'bs','yp','Iydl, 40 'k+', 'bp','b.','go','rd', 'mh'}; 41 marker-label={'Cold Gas (N2)','Cold Gas (He)','Cold Gas (Butane)',... 42 'Monopropellant (H4N2)','Monopropellant (H202)',... 43 'Bipropellant (NTO/MMH)','Resistojet (H20)','Resistojet (H4N2)',... 44 'Arcjet (NH3)','Arcjet (H2)','Arcjet (H4N2)','Ion Engine (Xe)',... 45 'Hall Thruster (Xe)','PPT (teflon)','VAT (Cr)','FEEP',... 46 'Colloid (EMI-BF4)','Electrospray(EMI-BF4)'}; 47 48 for n = 1:last-thruster 49 hgg (n) =hggroup; 5o end 51 52 deltaV-point=1 53 54 while deltaV-point <= last-deltaV 55 56 max-thrust -point=last -naxJthrust 57 58 while max-thrust-point > 0 59 60 thruster=l; 61 62 while thruster <= last-thruster 63 64 [propellantamass-fraction, propulsionxmass-fraction (thruster), inert-mass, propellant-mass, ... max-power]=thruster-mass(deltaV-space(deltaV-point), ... total-initial-mass, ... max-thrust-space (max-thrust-point) /total-initial-mass, .. thruster); 65 138 66 if propellant-mass-fraction<=0 || . 67 propulsion..mass-fract ion (thruster)<=O | . inert-mass<=O I|I .. . 68 max.power<=O || imag (propellant-mass-f ract ion+... 69 max-power+inert-mas s+propuls ion-mas s-f ract ion (thruster) ) ~=0 70 fprintf('\nERROR: thruster characteristics incorrect\n') 71 thruster 72 deltaV-space (deltaV-point) 73 max-thrust-space (max-thrust-point) 74 pause 75 end 76 77 thruster = thruster+1; 78 end 79 so [ lowest-mass.fract ion (deltaV-point, max-thrust.point) , 81 best..thruster (deltaV-point,max-thrust-point) min (... 82 propulsion-mass.fraction (1: last-thruster)) 83 84 if max-thrust..point < last-max.thrust && ..- lowest-mass.fraction (deltaV.point, max.thrust..point) > ... lowest.mass-fraction (deltaV..point, max-thrust..point+1) 85 lowest..mass..f raction (deltaV-point,max-thrust-point ) = lowest.mass-fraction (deltaV-point,max.thrust-point+l); 86 best-thruster (deltaV-point , max.thrust.point) = ... best-thruster (deltaV..point, max-thrust-point+1) 87 end 88 89 if lowest -mass..fraction (deltaV-point, max-thrust.point) < mass-fraction-limit 90 scatter (deltaV.space (deltaV-point), max-thrust.space (... 91 max-thrust-point), marker-size, 'filled', marker-type{. .. 92 best-thruster (deltaV-point, max-thrust-point)}, 93 'displayname',marker-label{best-thruster(delta-point,... 139 94 max.thrust.point) }, 'parent', hgg (best.thruster (... 95 deltaV.point, maxthrust.point) ) ) ; 96 set (get (get (hgg (best..thruster (deltaV-point, max.thrust-point)),... 97 'Annotation'),'LegendInformation'),'IconDisplayStyle','on'); 98 end 99 100 max...thrust-point = max..thrust-point-1 101 end 102 103 deltaV-point = deltaV-point+1 104 end 105 106 %for n = l:last.thruster 107 % set(get(get(hgg(n),'Annotation'),'LegendInformation'),'IconDisplayStyle','on'); 108 %end 109 110 leg=legend(hgg,marker-label, 'location', 'northeastoutside', 'FontSize',10); 140 i function [imp, min-bit, thrust]=getThrust(thruster-type, range, level) 2 3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 4 % s % Filename: thrust.m 6 % Filetype: Function 7 % Project: F6 8 % Author: Thomas Chiasson 9 % Mod Date: 18/8/2011 10 % 11 % PURPOSE: Returns thrust information on given thruster types. 12 13 % USAGE: This is a very useful program if you want to call 14 % thrusteramass.m iteratively from within a larger program 15 % when you don't have any information on the propulsion 16 % types. It will find the thrust range of a propulsion 17 % type from the database and create a user defined 18 % logarithmic scale so that the user gets a complete picture 19 % of a thruster's capabilities. 20 21 INPUT: 22 'thruster-type' Row number of desired thruster in 23 'thrustertradespace.xlx.' 24 'range' Number of logarithmic steps to divide thrust range 25 'level' The desired step of thrust out of 'range' 26 27 OUTPUT: 28 'imp' 1 for chemicai thrusters, 0 for electric 29 'thrust' (N) the thurst at 'level' out of the entire thrust range 30 'min-bit' (Ns) average min impulse for 'thrust' 31 32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 33 3 % Import the file 35 [numbers, strings] = xlsread('thrustertradespace.xlsx', 'Input Calcs'); 36 if ~isempty(numbers) 141 37 thrusterData.data = numbers; 38 end 39 if ~isempty(strings) 40 thrusterData.textdata = strings; 41 end 42 43 % Create new variables in the base workspace from those fields. 4 vars = fieldnames(thrusterData); 45 for i = 1:length(vars) 46 assignin('base', vars{i}, thrusterData.(vars{i})); 47 end 48 49 % extract values 5o imp=thrusterData.data(thruster-type,2); % will be 1 for chemical thrusters, 0 for electric si min-thrust=thrusterData.data(thruster-type,4); 52 max-thrust=thrusterData.data(thruster-type, 6); 5 % create thrust range 55 thrusts = logspace(log10(min-thrust) ,loglO (max-thrust) ,range); 56 57 thrust=thrusts(level); 58 59 switch thruster-type 60 case 3 61 min.bit= 0.0097*thrust^0.8823; 62 otherwise 63 min-bit=thrusterData.data (thruster-type, 3); 6 end 142 Bibliography [1] Common Arcjet Advantages and Mission Examples. 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