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Analysis of Chinese Cryogenic Launch Vehicles and YF-100 Engine

Thesis

Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the

Graduate School of The Ohio State University

By

Kayleigh Elizabeth Gordon, B.S.

Graduate Program in Aeronautical and Astronautical Engineering

The Ohio State University

2018

Thesis Committee:

John M. Horack, Advisor

Caroline Wagner

Elizabeth K. Newton

Copyright by

Kayleigh Elizabeth Gordon

2018

Abstract

This research synthesizes the technical capabilities of the currently developing fleet of Chinese liquid launch vehicles, specifically the , 6, and 7 families. This thesis articulates the types of missions each rocket has performed, and where each may be applied for future missions. Other topics included are the technical strengths and limitations of each launch vehicle, such as weights and achievable . Additionally, the types of are considered when determining which rocket family would be best for launching Chang’e lunar orbiters, the Tiangong space stations, and human missions, etc.

To better understand the way these launch vehicles operate and how they were designed, an in- depth analysis of the YF-100 engine is carried out. This engine is used on the first stage and boosters of the Long March 5, , and vehicles so the analysis of this engine is the foundation for gaining insight into how the Chinese design and develop their space capabilities.

This research differs from other work in that it gathers publicly available data and compares that data with engineering analysis to determine if ’s advertised capabilities are realistic.

Furthermore, this research puts the technical capabilities of the Chinese launch vehicles into perspective both domestically and internationally. This thesis provides background on the which includes a broad understanding of who is involved in space activities, what those activities entail, where these vehicles are launched from, when the Chinese made significant

i developments in their capabilities, and why the Chinese are interested in participating in this industry. These three launch vehicles are also put into perspective within the international vehicle industry. A price comparison of light, medium, and heavy lift launch vehicles are gathered to determine where the Chinese would need to price their new launch vehicles to be competitive if they were to sell them to international customers. This thesis combines an understanding of the technical capabilities of the Long March 5, Long March 6, and Long March

7 launch vehicles within the context of the Chinese space program and international launch vehicle industry to give a comprehensive understanding of China’s involvement in space activities.

ii Acknowledgements

There are many people that I would like to thank for their help and support throughout my time in graduate school. Its completion is thanks in large part to the special people who challenged, supported, and stuck with me along the way. I am tremendously fortunate to have committee members John Horack, Elizabeth Newton, and Caroline Wagner who have brought a depth of knowledge that few could match. I thank them for supporting this research and giving such thoughtful feedback, always aimed at moving me forward. I have learned a great deal both academically and professionally from these advisors, and I appreciate their guidance, time, and support.

I would also like to thank my mentors at OSTP for teaching me the importance of understanding both the technical content and policy context to develop the full picture which inspired the scope of my research.

I would also like to thank my friends and family for their encouragement and support throughout my time in graduate school.

iii Vita

2012 ……………………………………….... Centerville High School

2015 ……………………………………….... Flight Control Intern, Naval Air Systems Command (NAVAIR)

2016 ……………………………………….... B.S. Aeronautical and Astronautical Engineering, The Ohio State University

2016 ……………………………………….... Flight Control Intern, Naval Air Systems Command (NAVAIR)

2016 to 2017 ………………………………… Graduate Teaching Associate, Department of Mechanical and Engineering, The Ohio State University

2017 to present ……………………………… Graduate Research Associate, Department of Mechanical and Aerospace Engineering, The Ohio State University

2017 to present ……………………………… Graduate Research Associate, Battelle Center for Science, Engineering, and Public Policy, The Ohio State University

2017 ……………………………………….... Policy Intern, White House Office of Science and Technology Policy

Publications

Gordon, K. et al. (2017). Technical Capabilities of Chinese Launch Vehicles. Paper presented at International Astronautical Congress. Adelaide, Australia: IAC 2017 Technical Programme.

Fields of Study

Major Field: Aeronautical and Astronautical Engineering

Minor Field: Public Policy and Management

iv Table of Contents

Abstract ...... i

Acknowledgements ...... iii

Vita ...... iv

List of Tables ...... vii

List of Figures ...... ix

Chapter 1: Chinese Space Program Overview ...... 1

1.1 Key Agents within the Chinese Space Program ...... 2

1.2 New Family of Liquid Cryogenic Launch Vehicles ...... 9

1.3 Launch Center Locations and Purposes ...... 13

1.4 History and Future Timeline of Long March Launch Vehicle Family ...... 16

1.5 Motivation for Analyzing the Chinese Space Program ...... 21

Chapter 2: Technical Capabilities of Chinese Cryogenic Launch Vehicles ...... 24

2.1 Long March 5 ...... 24

2.2 Long March 6 ...... 30

2.3 Long March 7 ...... 35

2.4 Summary of New Family of Chinese Liquid Cryogenic Launch Vehicles ...... 41

Chapter 3: YF-100 Engine Analysis ...... 43

3.1 Background on the YF-100 Engine ...... 43

3.2 General Characteristics of the YF-100 ...... 46

3.3 Design Estimates ...... 59

3.4 Conclusions of the YF-100 Engine Analysis ...... 71

v Chapter 4: Comparison to International Competitors ...... 73

4.1 International Light Lift Launch Vehicles ...... 74

4.2 International Medium Lift Launch Vehicles...... 75

4.3 International Heavy Lift Launch Vehicles...... 77

Chapter 5: Summary ...... 79

Chapter 6: Areas for Future Investigation ...... 81

References ...... 83

Appendix A: Technical Parameter Calculations MATLAB Code ...... 90

Appendix B: Change in Velocity and Specific Calculations MATLAB Code ...... 103

Appendix C: YF-100 Design Calculations MATLAB Code ...... 109

Appendix D: Price Comparison Plots MATLAB Code ...... 113

vi List of Tables

Table 1. Technical parameters of the Long March 5 strap-on boosters ...... 25

Table 2. Technical parameters of the Long March 5 first stage ...... 26

Table 3. Technical parameters of the Long March 5 second stage...... 27

Table 4. Dimensions of the Long March 5 optional YZ-2 upper stage ...... 28

Table 5. Dimensions of the Long March 5 ...... 28

Table 6. Summary of masses for each stage of the Long March 5 ...... 30

Table 7. Technical parameters of the Long March 6 first stage ...... 31

Table 8. Technical parameters of the Long March 6 second stage...... 32

Table 9. Technical parameters of the Long March 6 third stage ...... 33

Table 10. Dimensions of the Long March 6 payload fairing ...... 33

Table 11. Summary of masses for each stage of the Long March 6 ...... 34

Table 12. Technical parameters of the Long March 7 strap-on boosters ...... 35

Table 13. Technical parameters of the Long March 7 first stage ...... 37

Table 14. Technical parameters of the Long March 7 second stage ...... 38

Table 15. Technical parameters of the Long March 7 optional upper stage ...... 39

Table 16. Dimensions of the Long March 7 payload fairing ...... 39

Table 17. Summary of masses for each stage of the Long March 7 ...... 41

vii Table 18. Published data for YF-100 engine ...... 46

Table 19. Mass flow rate and ...... 49

Table 20. Effective exhaust velocity values and change in velocity values...... 51

Table 21. coefficients, throat area, and exit diameter values ...... 59

Table 22. chamber parameters ...... 62

Table 23. Converging nozzle parameters ...... 63

Table 24. Diverging nozzle parameters ...... 65

Table 25. Injector parameters ...... 65

Table 26. mass parameters ...... 68

Table 27. Propellant tank parameters ...... 70

Table 28. Price comparison for light lift launch vehicles ...... 74

Table 29. Price comparison for medium lift launch vehicles ...... 76

Table 30. Price comparison for heavy lift launch vehicles ...... 78

viii

List of Figures

Figure 1. Network analysis of key agents within the Chinese space program ...... 9

Figure 2. Long March 5 at Wenchang Space Launch Center...... 11

Figure 3. Long March 6 at Taiyuan Launch Center ...... 12

Figure 4. Long March 7 at Wenchang Space Launch Center...... 13

Figure 5. Map of four Chinese launch sites ...... 14

Figure 6. Timeline of Major Developments ...... 17

Figure 7. Launches per year for Long March Series of Launch Vehicles ...... 18

Figure 8. Schematic of the YF-100 ...... 45

Figure 9. Change in velocity versus specific impulse for the YF-100 engine...... 52

Figure 10. Adiabatic flame temperature versus chamber pressure ...... 53

Figure 11. molecular weight versus chamber pressure ...... 54

Figure 12. Specific heat ratio versus chamber pressure ...... 55

Figure 13. Thrust coefficient CF versus nozzle area ratio for k=1.20...... 57

Figure 14. Price per Kilogram for Small Lift Launch Vehicles ...... 75

Figure 15. Price per Kilogram for Medium Lift Launch Vehicles ...... 76

Figure 16. Price per Kilogram for Heavy Lift Launch Vehicles ...... 78

ix CHAPTER 1:

Chinese Space Program Overview

As the fifth nation to obtain independent launch capability, and only the third country to send humans to space independently after the () and the (US), China has achieved many successful missions in their short time of . These include the

Chang’e lunar orbiter and placing the Tiangong-2 space lab into , later servicing it automatically with the -1 resupply craft (“China Great Wall Industry Corporation

(CGWIC)”, 2017). China also has significant plans for the next five years to send a probe to the far side of the and conduct in-situ roving detection and relay communications at the second

Earth-moon point (L2) (“China Academy of ”, 2003). In order to bring their large goals to fruition, a new series of liquid is needed. The Long March 5 (LM-5),

Long March 6 (LM-6), and Long March 7 (LM-7) launch vehicles comprise China’s primary family that is being developed to meet the needs of the ever-advancing and ambitious Chinese space program.

The heritage launch vehicle series, Chang Zheng 2 (CZ-2) through Long March 4 (LM-4), originally derived from Chinese two-stage intercontinental ballistic (“China Great Wall

Industry Corporation (CGWIC)”, 2017). But due to the diverging market between missiles and commercial space launch vehicles, the subsequent models have been completely redesigned. The

LM-5 rocket is the first iteration of the brand-new design and is China’s first ever purely space launch vehicle design (“China Great Wall Industry Corporation (CGWIC)”, 2017). The LM-6 and

1 LM-7 designs are derivative of LM-5 liquid rocket boosters and are used as small-to-mid size launch vehicles (“China Great Wall Industry Corporation (CGWIC)”, 2017).

1.1 Key Agents within the Chinese Space Program

Over the past several decades there has been significant restructuring efforts within the Chinese government to make their reflect a more western defense style. Formerly, China had organizations such as the Ministry of Aerospace Industry within the Commission of Science,

Technology, and Industry for National Defense (COSTIND). However, in their effort to emulate the western defense industries they separated many entities to clarify their role in the contracting process.

Currently in China the chief administrative authority, the State Council, has twenty-five cabinet level departments. The department of primary interest here is the Ministry of Industry and

Information Technology (MIIT). MIIT was established to (The State Council of the People’s

Republic of China, 2014):

• Determine China’s industrial planning, policies and standards

• Monitor the daily operation of industrial branches

• Promote the development of major technological equipment and innovation concerning the

communication sector

• Guide the construction of information systems

• Safeguard China’s information security

2 MIIT consists of semi-government, government, and commercial entities. MIIT has three main subordinate units – State Administration for Science, Technology, and Industry for National

Defense (SASTIND), China Northern Industries, and China Southern Industries (The State

Council of the People’s Republic of China, 2014). Collectively, these three branches, combined with the People’s Liberation Army, previously made up COSTIND. SASTIND is now a civilian unit that is similar in to Defense Advanced Research Projects Agency (DARPA) here in the

United States (The State Council of the People’s Republic of China, 2014). The previous Ministry of Aerospace Industry was divided into the two main space agencies, China National Space

Administration (CNSA) and China Aerospace Science and Technology Corporation (CASC), which now exist within SASTIND (“China Satcom Taken Over Amid Telecom Reshuffle”, 2009).

CNSA is a purely government organization and has four subordinate units. The departments within

CNSA are the Department of Foreign Affairs, the Department of Science, Technology and Quality

Control, the Department of System Engineering, and the Department of General Planning

(“Institutional Functions”). CNSA is similar in nature to the National and Space

Administration (NASA). CNSA is responsible for “signing governmental agreements in the space area on behalf of organizations, inter-governmental scientific and technical exchanges; and also, being in charge of the enforcement of national space policies and managing the national space science, technology and industry” (“Institutional Functions”).

The other branch of SASTIND, CASC, is a semi-government entity. It is state owned, but it is not actively managed by the state (China Aerospace Science and Technology Corporation). In addition to space and defense work, CASC is also responsible for producing many high-end civilian

3 products and providing commercial launch services to the international market state (China

Aerospace Science and Technology Corporation). CASC has three categories of subordinate units

- research, development and production complexes, directly subordinate government units, and specialized companies state (China Aerospace Science and Technology Corporation). The research, development, and production complexes include the following semi-government organizations, government entities, and academies:

• China Academy of Launch Vehicle Technology

• China Academy of Space Technology

Academy of Spaceflight Technology

• Academy of Aerospace Solid Propulsion Technology

• Academy of Aerospace Liquid Propulsion Technology

Academy of Aerospace Technology

• China Academy of Aerospace Electronics Technology

The directly subordinate units are all government organizations and the companies were created by the state but operate as contractors to the other organizations. The directly subordinate entities include:

• China Standards Institute

• China Astronautics Publishing House

• Space Archives

• Aerospace Communication Center

• China Space News

• Chinese Society of Astronautics 4 • Aerospace Talent Development and Exchange Center

• Aerospace Printing Office

There are twelve specialized companies that are considered subordinate entities to CASC. These twelve specialized companies are commercial entities that act as contractors to CASC. However,

China’s idea of a commercial company varies slightly to that of western commercial companies since many of the commercial companies are majority owned by the state. So, while these commercial companies act as commercial contractors, they are also owned by the state. They are:

• China Satellite Communications Corporation

• China Great Wall Industry Corporation

• China Aerospace Engineering Consultation Center

• China Center for Resources Satellite Data and Application

• Aerospace Science and Technology Co. Ltd.

• Aerospace Capital Holding Co. Ltd.

• China Aerospace Times Electronics Corporation

• China Aerospace International Holdings, Ltd.

Aerospace Software Technology Co. Ltd.

• Shenzhen Academy of Aerospace Technology

• Aerospace Long-March International Trade Co. Ltd.

• China Siwei Surveying and Mapping Technology Co. Ltd.

The subordinate unit of CASC that is of primary interest is the China Academy of Launch Vehicle

Technology (CALT) since they design and produce the Long March rocket families (Pike, 2016). 5 A few other organizations of interest include China Academy of Space Technology (CAST),

Shanghai Academy of Spaceflight Technology (SAST), Academy of Aerospace Liquid Propulsion

Technology (AALPT), and China Space News (China Academy of Space Technology (CAST),

2003; Shanghai Academy of Spaceflight Technology (SAST), 2002).

In addition to these primarily civilian organizations, there are military entities that are key to the

Chinese space program. The primary office of interest is the China Manned Space Engineering

Office. This office is one of 9 bureaus within the People’s Liberation Army’s Equipment

Development Department. Within the China Manned Space Engineering Office there are five departments including:

• Science and Technology Planning Bureau

• Engineering Construction Bureau

• General Technology Bureau

• International Cooperation Bureau

• News Bureau

Even though China has recently restructured their space program to better reflect a more western style of organization, there are still military influences and involvement throughout all of the

Chinese space organizations. For example, CNSA claims to be responsible for (“Institutional

Functions”)

• Studying and formulating policies and regulations of the space industry

• Organizing and implementing the major space projects and programs

6 • Managing the international space exchanges and cooperation, and participating in the

related international organizations and their activities on behalf of the Chinese government

Yet, the China Manned Space Engineering Office, which falls under military leadership, also claims to be responsible for “planning, overall technology, engineering development, supporting construction, outlay, international cooperation, news releasing” (China Manned Space

Engineering Office). These two agencies, while being labeled as separate entities with clearly civilian and military leadership respectively, have very similar roles and likely work closely together to develop these policies and oversee technology developments.

Furthermore, the People’s Liberation Army (PLA) is a direct military subordinate to the Central

Military Commission which is run by the Communist Party of China. is the President of the People’s Republic of China, the General Secretary of the Communist Party of China, and

Chairman of the Central Military Commission. Since he holds these top leadership offices of the party, state, and military he is seen as the core leader and is one common connection between the civilian and military agents within the Chinese space program. Recently, China agreed to eliminate a term limit for Xi Jinping. This will allow him to align these three positions for a long term. A full visual representation of these agents can be seen below in Figure 1.

In order for China to accomplish its goal of working cooperatively with foreign countries, it could consider how other countries view the widespread involvement of the PLA in China’s civil space activities. China has said that “international exchanges and cooperation should be strengthened on the basis of equality and mutual benefit, peaceful utilization and inclusive development” (China

Daily, 2016). With respect to cooperative missions between China and the United States, there are

7 limited ways in which the two countries are to work together due to the which prohibits bilateral collaboration between the National Aeronautics and Space

Administration or the White House Office of Science and Technology Policy with Chinese organizations for any joint scientific activities. However, if China were to mitigate the PLA’s involvement in space activities to help ensure the “peaceful utilization” of space, the United States might be more enticed to work jointly with the Chinese. One way in which China could help mitigate military involvement could be to transition the China Manned Space Engineering Office to a civilian government leadership rather than its current military leadership. The China Manned

Space Engineering Office is critical to the Chinese space program and with its current leadership the United States is cautious to avoid helping China develop space technologies that could so easily be modified for military purposes. While this one transition may not completely eliminate military involvement or influence throughout the Chinese space program, it might be enough of a step forward to promote peaceful cooperative space science research and projects between China and the United States.

8

Figure 1. Network analysis of key agents within the Chinese space program

1.2 New Family of Liquid Cryogenic Launch Vehicles

Beginning in 2002, the LM-5, LM-6, and LM-7 launch vehicle designs were originally envisioned to be a series of completely customizable rockets assembled from a collection of three sizes of modules that could be used as different stages or boosters on any given launch vehicle. After fifteen years of development, the new series of Chinese liquid rockets has been produced. To date (March 9 2018), the success rate has been four out of five launches. The LM-5 had one mission success out of two launches thus far. Both the LM-6 and LM-7 currently have 100% mission success rates, albeit with one and two launches respectively.

1.2.1 Long March 5

The LM-5 was designed to be a heavy-lift launch vehicle, which is classified as being capable of lifting up to 50,000 kilograms (McConnaughey, 2010). The LM-5 has the ability to launch 14 metric tons (14,000 kilograms) to a geostationary transfer orbit, or 25 metric tons (25,000 kilograms) to (LEO). The LM-5 utilizes the YF-100 engine, which was developed by the Xi’an Aerospace Propulsion Institute at the Academy of Aerospace Liquid Propulsion

Technology (AALPT). Two YF-100 engines power each of the four strap-on boosters. Each is capable of generating 1200 kilonewtons of thrust at sea-level. The LM-5 also uses the

YF-77 and YF-75 engines that were developed by the same institute (“Chang Zheng 5 (Long

March 5)”, 2016; Clark, 2016; Kyle, 2017). Two YF-77 engines produce a total of 1020 kilonewtons at sea level for the first stage and two YF-75 engines produce a total of 156 kilonewtons in vacuum for the second stage. The optional upper stage, YZ-2, was developed by the CALT and was modified from the LM-3B upper stage. The China National Space

Administration (CNSA) directed engine testing for all of the LM-5, LM-6, and LM-7 vehicles.

10

Figure 2. Long March 5 at Wenchang Space Launch Center. For reference, the LM-5 has a

height of approximately 56.97 meters and a core diameter of 5 meters. The LM-5 strap on

boosters have a height of 26.28 meters and a diameter of 3.25 meters.

1.2.2 Long March 6

Unlike the LM-5, the LM-6 does not include any strap-on boosters. The LM-6 has two core stages and a third kick stage. Together these three stages provide light-lift capabilities which is classified as payloads less than 2,000 kilograms. The first stage of the LM-6 uses the YF-100 engine seen in the LM-5 boosters, but the LM-6 needed some new cryogenic engines to meet the designs for the second and third stages. For the second stage, the LM-6 uses an YF-115 engine, which was designed by the same institute as the engines found in the LM-5, the Xi’an Aerospace Propulsion

Institute at the Academy of Aerospace Liquid Propulsion Technology (“Chang Zheng (Long

March 6)”, 2016). CALT developed the upper kick stage of the LM-6, which is powered by four

11 parallel liquid engines. The third stage, -1 (YZ-1A), was modified from the YZ-1 to fit into the smaller upper module on the LM-6. Shanghai General Factory of Aerospace Equipment

Manufacturing, which is a subsidiary of SAST, manufactures the LM-6 Technology (“Chang

Zheng (Long March 6)”, 2016).

Figure 3. Long March 6 shortly after launching from Taiyuan Satellite Launch Center. The LM-6

is approximately 29.237 meters tall with a diameter of 3.35 meters.

1.2.3 Long March 7

Similar to the Long March 5, the Long March 7 is composed of multiple stages and boosters. Both the boosters and the first stage utilize the YF-100 engine, each producing 1200 kilonewtons at sea level to combine for a total take-off thrust of 7200 kilonewtons. The second stage uses four YF-

115 engines, which provide 720 kilonewtons of total sea level thrust. The LM-7 has an optional upper stage that uses two YF-75 engines that can each produce 78 kilonewtons in vacuum. The

12 China Aerospace Science and Technology Corporation (CASC) managed the project, while CALT headed the design and CALT’s subsidiary Capital Aerospace Machinery Company manufactured the LM-7 (“Chang Zheng 7 (Long March 7)”, 2017). The LM-7 is considered a medium-lift launch vehicle since it’s payload capabilities fall between the 2,000 kilograms and 20,000 kilograms classification of medium lift launch vehicles (McConnaughey, 2010).

Figure 4. Long March 7 at Wenchang Space Launch Center. The LM-7 core is 53. 075 meters in

length and 3.35 meters in diameter. The strap on boosters for the LM-7 are 29.903 meters in

length and have a diameter of 2.25 meters.

1.3 Launch Center Locations and Purposes

The Chinese have four launch sites that they use for various orbital functions, payloads, and launch vehicles.

13

Figure 5. Map of four Chinese launch sites including Jiuauan Launch Site (red), Launch

Site (blue), Taiyuan Launch Site (yellow), and Wenchang Launch Site (purple).

1.3.1 Launch Site

The Jiuquan Launch Site is China’s oldest launch facility and it is located in the northwest portion of China about 150 kilometers south of the Sino-Mongolian border. This site is primarily used for high inclination payloads such as Earth observations and military that have Low Earth

Orbits (LEO). Some of the previous missions that have launched from this site include Shenzhou

6, , and the “Micius” quantum satellite. For reference, the Shenzhou spacecraft are China’s crew transportation vehicles for their manned and the

14 Shenzhou spacecraft have an orbit of 300 to 400 kilometers at an inclination of 42.5 degrees. Since the Jiuquan Launch Site already has a latitude of nearly 40 degrees north, this site helps minimize the change in inclination needed to launch the Shenzhou to the desired orbit (“Jiuquan Satellite

Launch Centre”, 2016).

1.3.2 Xichang Launch Site

The Xichang Launch Site is located in the southern portion of China in the Sichuan province. The center is headquartered in Xichang City which is 65 kilometers from the launch site. This launch site is primarily used for the launch of broadcast, communications, and meterological satellites into geostationary orbits. This launch site is a convenient location for communication satellites due to its relatively low latitude of 28.2 degrees north (“Xichang Satellite Launch Center”).

1.3.3 Taiyuan Launch Site

The Taiyuan Launch Site was first opened in the late 1960s for ICBM tests. It adapted to a space launch center in the late 1980s with the main purpose of supporting sun-synchronous launches. The Taiyuan Launch Site remains a military installation to this day, otherwise known as the 25th Test and Training Base (“Taiyuan Satellite Launch Centre”, 2016). The one and only LM-

6 launch took place from the Taiyuan Launch Site (see Figure 5).

1.3.4 Wenchang Launch Site

Wenchang Launch Site is China’s newest which had its inaugural launch on June 25,

2016. The Wenchang Launch Site is located in China’s southernmost province, on Island

(“Wenchang Space Launch Centre”, 2016). This location provides a low latitude and proximity to

15 the equator, as well as southeast flight path over the South Pacific, which mitigates the possibility of rocket debris falling over populated areas. Wenchang Launch Site has been used for both of the previous LM-5 launches (November 2016, July 2017) and both of the previous LM-7 launches

(June 2016, April 2017). This is the launch site for LM-5 launches since the LM-5 has a core diameter of 5 meters which is too large to be transported to the other launch sites by rail.

1.4 History and Future Timeline of Long March Launch Vehicle Family

While the Chinese space program appears to have made significant over the past fifteen years, the beginnings of the program reach all the way back to 1956 when the first Chinese rocket and missile research institute was created (Meyers, & Landsberg, 2017). Figure 6 below shows the major milestones and developments for the Chinese, American, and Russian space programs for comparison. On the left side of the figure, the Chinese developments are shown in green. On the right side, the American developments are shown in blue, the Russian developments are shown in red, and collaborative projects between the United States and Russia are shown in purple.

16

Figure 6. Timeline of major developments for the Chinese, American, and Russian space programs

This timeline shows that the American and Russian programs’ developments were concentrated more towards the beginning of the timeline whereas the Chinese program has had significant progress during the more recent years. Furthermore, China has accomplished many of the same

17 type of missions as both the United States and Russia have. However, China has yet to work collaboratively with a foreign country on manned missions like the US and Russia have.

This concentrated progress corresponds with the number of Long March launch vehicles that the

Chinese have launched. In Figure 7, an increase in number of launches beginning in the early

2000’s can be observed (“List of Long March Launches”, 2018).

Figure 7. Launches per year for Long March series of launch vehicles (“List of Long March Launches”, 2018)

In June of 2002 the Commission for Science, Technology, and Industry for National Defense

(COSTIND) approved the development of new cryogenic engines. As a part of this program four new engines were designed for use on the LM-5, LM-6, and LM-7 launch vehicles. This marked perhaps the single- important transition in China launch-vehicle technology, namely the move away from hypergolic engines to cryogenic engines with larger thrust and payload capabilities, which are also expected to be more affordable to produce. 18

After governmental approval for the LM-5 development project in June 2004, the contract for the

LM-5 was awarded to the Chinese Academy of Launch Vehicle Technology (CALT) with

Shanghai Academy of Spaceflight Technology (SAST) sharing some development tasks (“Change

Zheng 5 (Long March 5)”, 2016; Clark, 2016; Kyle, 2017). The heavy-lift LM-5 has been launched twice now with a 50% mission success rate. The first launch, on November 3rd 2016 from

Wenchang Space Launch Center, delivered Shijian-17 satellite to a and using the optional YZ-2 upper stage the Shijian-17 was placed into a . The second mission, launched on July 2nd 2017 from Wenchang Space Launch Center, was intended to deliver the Shijian-18 communication satellite into orbit, but the LM-5 vehicle failed during flight. This failure was due to a exhaust issue on one of the two YF-77 liquid rocket engines that power the first stage. The turbopump exhaust structure failed under complex thermal conditions (Jones, 2018). Due to the LM-5 failure that occurred in July 2017, the Chinese have delayed the next for these cryogenic launch vehicles. The redesigned YF-77 engines have been tested to ensure the necessary measures to prevent future failure have been taken (Jones,

2018). The next planned launch is set to occur during the fourth quarter of 2018, likely in

November. This will be a LM-5 launch of the Shijian-20 to replace the

Shijian-S18 satellite that was lost during the LM-5 failure. In 2019, the LM-5 will launch the

Chang’e 5 lunar probe and the New Generation Manned Spacecraft Test Ship (Pietrobon, 2018).

The LM-6 preceded the LM-5 and was the first all-new Chinese launch vehicle to be introduced in nearly two decades (“Chang Zheng 6 (Long March 6)”, 2016). The development of the LM-6

19 was originally awarded to CALT, but in 2008 it was reassigned to SAST. The LM-6 has had one flight on September 19th 2015 which launched from Taiyuan Satellite Launch Center.

The LM-7 program was first revealed in the mid-2000s. Development of the LM-7 began in 2010 and launched for the first time in June 2016 (“Chang Zheng 7 (Long March 7)”, 2017). Its inaugural flight, on June 25th 2016, was a demonstration of a scaled Next Generation Crew Capsule plus microsatellites and ballast. On April 20th 2017 the LM-7 delivered the Tianzhou-1 unmanned to the Tiangong-2 space laboratory. The LM-7 is set to deliver the Tianzhou 2 spacecraft in 2019. During the following year, August of 2020, the Chinese are planning on launching their Global Orbiter and Small Rover on the LM-5 (Pietrobon,

2018).

The transitions seen in Figure 6 and Figure 7 combined with the approval to design the new cryogenic family of Long March launch vehicles support the idea that the Chinese space program had a shift in priority in the early 2000’s. Prior to the new millennium, the Chinese efforts in space were primarily based on research. The new Long March cryogenic family were the first set of launch vehicles designed entirely for space exploration purposes and not modified from ballistic missiles. The rapid development over the past 15 years or so is largely due to the use of Russian engines and designs as references. The YF-100 engine, for example, is used as the powerhouse engine on the boosters and first stages in the new family of Long March rockets and it is considered a Chinese copy of the Russian RD-120 engine (“Chinese YF-100 (Russian RD-

120) to Power CZ-5”). The Chinese have relied on Russian designs to help them progress so

20 quickly. Although the Chinese have redesigned the technology to fit their purposes, most of the

Chinese capability is dependent upon non-native engineering of these technologies.

1.5 Motivation for Analyzing the Chinese Space Program

Since China is the fifth nation to obtain independent launch capability and the second most active country in space activities it is imperative to have an understanding of what they are capable of and what they plan to accomplish with those capabilities (Howell, 2016). In China’s 2016 White

Paper on Space Activities, it was stated that their vision for future developments in space are

To build China into a space power in all respects, with the capabilities to make innovations

independently, to make scientific discovery and research at the cutting edge, to promote

strong and sustained economic and social development, to effectively and reliably

guarantee national security, to exercise sound and efficient governance, and to carry out

mutually beneficial international exchanges and cooperation; to have an advanced and open

space science and technology industry, stable and reliable space infrastructure, pioneering

and innovative professionals, and a rich and profound space spirit; to provide strong

support for the realization of the of the renewal of the Chinese nation, and

make positive contributions to human civilization and progress (, 2016).

This statement gives some insight into why China is interested in participating in space activities.

However, one purpose for this analysis of the Chinese space program is to better understand if any of these reasons are more important to China than others. For example, they said in the white paper that they envisage an open space science and technology industry but are their efforts to guarantee national security taking priority.

21 China has accomplished many successful missions in their short time of space exploration and they have lofty goals for the next few years. China is actively working to develop ground- and space-based anti-satellite weapons while simultaneously working on expanding their own commercial presence (China Daily, 2016). These normally would be two separate concerns, but

China has a pervasive military involvement in all aspects of their which makes it even more complicated to fully understand the Chinese space program. Due to domestic regulations, Americans are barred from participating in the Chinese commercial space industry and marketplace. Although some concerns such as technology transfer are legitimate issues,

American leadership in space faces major threats and challenges if China’s growing presence in space continues to be ignored.

The purpose of the following analysis is to better understand China’s technical capabilities of their new liquid cryogenic launch vehicles so that it can be determined if China’s future planned missions are achievable. Using this analysis of the LM-5, LM-6, LM-7, and YF-100 engine, a complete characterization of their capabilities can be used to see where they stand on an international scale. A comparative commercial market analysis (Chapter 4) will put the technical capabilities into perspective with other major spacefaring nations. This thesis is not an all-inclusive analysis of the Chinese space program, but rather the first step into better understanding China’s capabilities and goals for their program. This analysis is a building block for future work that will fill in the gaps and give a more complete understanding of China’s space program. With more detailed information and analysis of the Chinese space program, the United States and other spacefaring countries will be able to better understand the motives behind China’s space program and will be able to preserve leadership and development in space exploration. Having a better

22 understanding of the Chinese space program will also allow countries to negotiate fair agreements with China that will enable innovation and competition while mitigating technology transfer and other prevalent issues.

23 CHAPTER 2:

Technical Capabilities of Chinese Cryogenic Launch Vehicles

This chapter outlines the technical parameters for the LM-5, LM-6, and LM-7 launch vehicles.

The length, diameter, thrust, propellant, oxidizer, chamber pressure, combustion temperature, nozzle , burn time, specific impulse, and specific heat ratio of the boosters and core stages are laid out below in the following sections as appropriate for each launch vehicle. This chapter discusses and compares the calculated specific impulses that are derived from basic published data with the published anticipated specific impulse values. The gross, empty, and propellant masses for each stage are also included. Finally, the achievable orbits and mission applications for each of the Long March launch vehicles are reviewed.

2.1 Long March 5

When configured for geostationary orbit missions, the LM-5 consists of three stages and four strap-on boosters.

2.1.1 Strap-On Boosters

The Long March 5 utilizes four strap-on boosters in addition to the first stage. The 3.35-meter diameter boosters hold two YF-100 engines each, described in the table below (Table 1). Each of the boosters can provide 2400 kilonewtons of thrust at sea level, which combine to provide 9600 kilonewtons of thrust in total at lift-off (“Chang Zheng 5 (Long March 5)”, 2016; Kyle, 2017).

24 The boosters burn for 180 seconds before being jettisoned (“Chang Zheng 5 (Long March 5)”,

2016; Kyle, 2017). Specific impulse is 300 seconds at sea level and 335 seconds in vacuum according to published information for the YF-100 engine. It will be shown in Chapter 3 that the specific impulse is actually expected to be 290 seconds at sea level or 328 seconds in vacuum conditions. These values are calculated using the published data for thrust, propellant mass, and burn time.

Table 1. Technical parameters of the Long March 5 strap-on boosters and the YF-100 engines

(“-Pacific Space-Rocket Liquid-Propellant Engines”, 2017; Braeunig, 2005; “Chang Zheng

5 (Long March 5)”, 2016)

Strap on Boosters (8 YF-100 Engines) Length 26.28 m Diameter 3.35 m Thrust at Sea Level 1200 kN per engine Thrust in Vacuum 1360 kN per engine Propellant Kerosene (RP) Oxidizer Liquid (LOX) Chamber Pressure 18 MPa Combustion Temperature 3670 K Nozzle Expansion Ratio 35:1 Burn Time 180 seconds Isp 290 – 328 seconds Cp/Cv ~1.213

2.1.2 First Stage

The first stage of the LM-5 is a 5-meter diameter vehicle that houses two YF-77 engines, described in the table below (Table 2). These engines use a and liquid bipropellant.

When combusted through a cycle, each engine can produce 510 kilonewtons of thrust at sea level or up to 700 kilonewtons in vacuum (“Chang Zheng 5 (Long March 5)”, 2016; Kyle,

25 2017). Together the first stage and the boosters provide the LM-5 with approximately 10570 kilonewtons of lift-off thrust. After the boosters separate from the main vehicle the first stage continues to burn for an additional 300 seconds for a total burn time of approximately 480 seconds

(“Chang Zheng 5 (Long March 5)”, 2016; Kyle, 2017). The published specific impulse is 333 seconds at sea level and 438 seconds in vacuum, but the calculated specific impulse for the YF-77 engine is between 315 and 434 seconds based on the thrust, mass, and burn time values.

Table 2. Technical parameters of the Long March 5 first stage and the YF-77 engines (“Asia-

Pacific Space-Rocket Liquid-Propellant Engines”, 2017; Braeunig, 2005; “Chang Zheng 5 (Long

March 5)”, 2016)

First Stage (2 YF-77 Engines) Length 31.02 m Diameter 5 m Thrust at Sea Level 510 kN per engine Thrust in Vacuum 700 kN per engine Propellant (LH2) Oxidizer Liquid Oxygen (LOX) Chamber Pressure 10.2 MPa Combustion Temperature 3450 K Nozzle Expansion Ratio 49:1 Burn Time 480 seconds Isp 315 – 434 seconds Cp/Cv ~1.2015

2.1.3 Second Stage

Once the first stage separates, the second stage ignites. This stage consists of two YF-75 engines, described in the table below (Table 3). This stage ignites and burns for 615 seconds. The second stage is housed in a 5-meter diameter vehicle and can produce up to 78 kilonewtons from each engine in a vacuum for a total of 156 kilonewtons thrust (“Chang Zheng 5 (Long March 5)”, 2016;

26 Kyle, 2017). The engines use a closed-circuit expander cycle to combust liquid hydrogen and liquid oxygen. The published data suggests that the specific impulse of the LM-5 second stage is

438 seconds, but the calculated specific impulse is 427 seconds in vacuum.

Table 3. Technical parameters of the Long March 5 second stage and the YF-75 engines (“Asia-

Pacific Space-Rocket Liquid-Propellant Engines”, 2017; Braeunig, 2005; “Chang Zheng 5 (Long

March 5)”, 2016)

Second Stage (2 YF-75 Engines) Length 12 m Diameter 5 m Thrust in Vacuum 78 kN per engine Propellant Liquid Hydrogen (LH2) Oxidizer Liquid Oxygen (LOX) Chamber Pressure 4.068 MPa Combustion Temperature 3550 K Nozzle Expansion Ratio 80:1 Burn Time 615 seconds Isp 427 seconds Cp/Cv ~1.198

2.1.4 Optional Upper Stage

On the LM-5 there is an optional upper stage, YZ-2. The upper stage is housed in a 5.2-meter diameter vehicle and is used as an individual propulsion system to perform orbital maneuvers such as altitude and orbital plane changes. The optional upper stage is used to place spacecraft and satellites directly into the required orbits. The optional upper stage reduces the need for spacecraft and satellites to use their own propulsions systems to place them into their precise orbits. The upper stage can burn for 1105 seconds. Published data suggests that the specific impulse for the

YZ-2 optional upper stage is approximately 316 seconds but could not be verified since the propellant mass is unknown (“Chang Zheng 5 (Long March 5)”, 2016; Kyle, 2017). 27

Table 4. Dimensions of the Long March 5 optional YZ-2 upper stage

Upper Stage – Optional (YZ-2) Length N/A Diameter 3.8 m Burn Time 1105 seconds Isp 316 seconds

2.1.5 Payload Fairing

The 5.2-meter diameter upper stage can attach to the payload fairing with the same diameter. The three stages and four boosters combine to a total length of 59.97 meters and a gross mass of 869 metric tons which includes fuel and payload masses (“Chang Zheng 5 (Long March 5)”, 2016).

Table 5. Dimensions of the Long March 5 payload fairing

Payload Fairing Length 12.5 m Diameter 5.2 m

2.1.6 Mission Capabilities

2.1.6.1 Maximum Payloads and Achievable Orbits

With the aid of all three stages and the four boosters the LM-5 can deliver a payload with a mass of up to 14 metric tons into a geostationary transfer orbit (“Chang Zheng 5 (Long March 5)”, 2016;

Clark, 2016; Kyle, 2017). The LM-5 can also deliver a payload with a mass up to 25 metric tons to low earth orbit.

28 2.1.6.2 Mission Applications

The heavy-lift LM-5 has been launched twice now with a 50% mission success rate. The first launch, on November 3rd 2016 from Wenchang Space Launch Center, delivered Shijian-17 satellite to a geosynchronous orbit and using the optional YZ-2 upper stage the Shijian-17 was placed into a geostationary orbit. This satellite has a mass of about 4 metric tons (“Chang Zheng 5 (Long

March 5)”, 2016; Pietrobon, 2017; “Wenchang Space Launch Centre”, 2016).

The second mission, launched on July 2nd 2017 from Wenchang Space Launch Center, was intended to deliver the Shijian-18 communication satellite into orbit, but the LM-5 vehicle failed during flight. The failure occurred shortly after the four boosters were released on time. However, the first stage continued to burn and did not jettison until more than a minute after the predicted time. The second stage ignited and continued to lift the LM-5 towards orbit, but the stream was cut short just before the Chinese authorities confirmed the failure. The investigation of the launch failure is ongoing at this time (March 2018), but the LM-5 is set to deliver the Shijian-20 communications satellite to a geostationary orbit during the fourth quarter of 2018 (Clark 2017;

Pietrobon, 2017; “Wenchang Space Launch Centre”, 2016). The next LM-5 mission was set to launch the Chang’e 5 lunar probe on November 30th 2017 but has been delayed to 2019 due to the mission failure during the second mission. The LM-5 is currently set to launch the New Generation

Manned Spacecraft Test Ship in 2019 additionally. The heavy-lift capability provided by the LM-

5 will likely be used for future Chang’e lunar missions and to deliver future experiment modules to the (Clark 2017; Lei, 2016; Pietrobon, 2017).

29 2.1.7 Summary of Launch Vehicle Parameters

2.1.7.1 Masses of Stage Structures and

Table 6. Summary of the gross, empty, and propellant masses for each stage of the Long March 5

plus the payload and payload fairing (“Chang Zheng 5 (Long March 5)”, 2016)

Masses LM-5, gross 869 metric tons First Stage, gross 175.8 metric tons empty 17.8 metric tons propellants 158 metric tons Boosters, gross 165 metric tons empty 13 metric tons propellants 152 metric tons Second Stage, gross 26 metric tons empty 3.1 metric tons propellants 22.9 metric tons Upper Stage, gross 1.8 metric tons Payload Fairing, gross 63.4 metric tons Payload, gross Up to 14 metric tons to GTO gross Up to 25 metric tons to LEO

2.2 Long March 6

2.2.1 First Stage

The first stage has only one YF-100 engine within the 3.35-meter diameter frame. This stage can provide up to 1200 kilonewtons of thrust at sea level or up to 1360 kilonewtons in vacuum through combusting kerosene and liquid oxygen for about three minutes (“Chang Zheng 6 (Long March

6)”, 2016). Published information about the first stage of the LM-6 states that the specific impulse at sea level is about 300 seconds and about 335 seconds in vacuum. However, the calculated values for the specific impulse were found to be 290 seconds at sea level and 328 seconds in vacuum.

Details of these calculated values can be found in Chapter 3. These values are only slightly smaller

30 than the published values and are consistent with the data found for the YF-100 in the various launch vehicles.

Table 7. Technical parameters of the Long March 6 first stage and the YF-100 engine (“Asia-

Pacific Space-Rocket Liquid-Propellant Engines”, 2017; Braeunig, 2005; “Chang Zheng 6 (Long

March 6)”, 2016; Krebs)

First Stage (1 YF-100 Engine) Length N/A Diameter 3.35 m Thrust at Sea Level 1200 kN per engine Thrust in Vacuum 1360 kN per engine Propellant Kerosene (RP) Oxidizer Liquid Oxygen (LOX) Chamber Pressure 18 MPa Combustion Temperature 3670 K Nozzle Expansion Ratio 35:1 Burn Time 180 seconds Isp 290 – 328 seconds Cp/Cv ~1.213

2.2.2 Second Stage

Once the first stage burnouts and separates the 2.25-meter diameter second stage, which uses one

YF-115 engine, ignites a kerosene and liquid oxygen bi-propellant for about 290 seconds to produce 180 kilonewtons of thrust in vacuum (“Chang Zheng 6 (Long March 6)”, 2016). The YF-

115 engine is described below in Table 8. Public data recommends that the specific impulse of the

LM-6 second stage is about 335 seconds in vacuum and using the calculation methods laid out in

Chapter 3, the specific impulse is closer to 355 seconds.

31 Table 8. Technical parameters of the Long March 6 second stage and the YF-115 engines (“Asia-

Pacific Space-Rocket Liquid-Propellant Engines”, 2017; Braeunig, 2005; “Chang Zheng 6 (Long

March 6)”, 2016; Krebs)

Second Stage (1 YF-115 Engine) Length 8 m Diameter 2.25 m Thrust at Sea Level 180 kN per engine Propellant Kerosene (RP) Oxidizer Liquid Oxygen (LOX) Chamber Pressure 12 kPa Combustion Temperature 3625 K Nozzle Expansion Ratio 11.66:1 Burn Time 290 seconds Isp 355 seconds Cp/Cv ~1.215

2.2.3 Third Stage

The third stage YZ-1A, has four YF-85 liquid engines, detailed in Table 9, that burn and kerosene. The four engines fit within the 2.25-meter diameter vehicle. Each engine has a swinging nozzle (four degrees of freedom) and restart capability so that it can function as the launch vehicle’s reaction control system. The YZ-1A engine is capable of producing 4 kilonewtons each in vacuum (“Chang Zheng 6 (Long March 6)”, 2016). The original YZ-1 design utilized a tetroxide and unsymmetrical dimethyl propellant which was capable of producing a specific impulse of 315 seconds. But the LM-6 uses the smaller diameter YZ-1A which was adapted from the YZ-1. The YZ-1A is supposed to provide a specific impulse of 285 seconds according to public data (“Chang Zheng 6 (Long March 6)”, 2016). Currently there are many unknown parameters for the YZ-1A engine, such as the chamber pressure, combustion temperature, and nozzle expansion ratio. Additionally, the burn time and gross, empty, or propellant masses are not available to verify the published specific impulse value. 32

Table 9. Technical parameters of the Long March 6 third stage and the YZ-1A engines (“Chang

Zheng 6 (Long March 6)”, 2016)

Third Stage (4 YZ-1A Engines) Length N/A Diameter 2.25 m Thrust at Sea Level 4 kN per engine Propellant Kerosene (RP) Oxidizer Hydrogen Peroxide (H2O2)

2.2.4 Payload Fairing

The payload fairing has a diameter of 2.6 meters. The three stages plus the payload fairing combine to a total length of 29.237 meters and a lift off gross mass of 103.2 metric tons (“Chang Zheng 6

(Long March 6)”, 2016).

Table 10. Dimensions of the Long March 6 payload fairing

Payload Fairing Length ~5-7 m Diameter 2.6 m

2.2.5 Mission Capabilities

2.2.5.1 Maximum Payloads and Achievable Orbits

The LM-6 can support a payload up to 1000 kilograms and is able to deliver the payload to a 700- kilometer sun synchronous orbit (“Chang Zheng 6 (Long March 6)”, 2016; Krebs).

33 2.2.5.2 Mission Applications

The LM-6 has had one flight on September 19th 2015 which launched from Taiyuan Satellite

Launch Center. During this flight the LM-6 carried a multi-payload of twenty micro- and nano- satellites to orbit. Due to the nature of small-load orbital launchers, the LM-6 has limited mission capabilities. Currently, the LM-6 is slotted for a first stage landing test with an unidentified payload in 2020 and could be used for future launches of small and micro-satellites that are under 1000 kilograms in mass (“Chang Zheng 6 (Long March 6)”, 2016; Pietrobon, 2017).

2.2.6 Summary of Launch Vehicle Parameters

2.2.6.1 Masses of Stage Structures and Propellants

Table 11. Summary of the gross, empty, and propellant masses for each stage of the Long March

6 plus the payload and payload fairing (“Chang Zheng 6 (Long March 6)”, 2016)

Masses LM-6, gross 103 metric tons empty 9 metric tons First Stage, gross 83.53 metric tons empty ~7.53 metric tons propellants 76 metric tons Second Stage, gross ~16.49 metric tons empty ~1.49 metric tons propellants 15 metric tons Third Stage, gross N/A empty N/A propellants N/A Payload Fairing, gross N/A Payload, gross Up to 1000 kg to 700 km sun synchronous

34 2.3 Long March 7

2.3.1 Strap-On Boosters

To augment the core first stage, four 2.25-meter diameter boosters are strapped-on. The boosters each house one YF-100 engine. Each of the YF-100 engines produce 1200 kilonewtons at sea level which combines with the first stage to produce a total lift off thrust of approximately 7200 kilonewtons (“Chang Zheng 7 (Long March 7)”, 2017). The calculated specific impulse values are

245 seconds at sea level or 277 seconds in vacuum compared to the published values of 300 seconds at sea level or 335 seconds in vacuum. The calculated values are substantially lower than the anticipated values, but they are consistent with the other iterations of the YF-100 in the other

Long March launch vehicles.

Table 12. Technical parameters of the Long March 7 strap-on boosters and the YF-100 engines

(“Asia-Pacific Space-Rocket Liquid-Propellant Engines”, 2017; Braeunig, 2005; “Chang Zheng

7 (Long March 7)”, 2017)

Strap on Boosters (4 YF-100 Engines) Length ~26.28 m Diameter 2.25 m Thrust at Sea Level 1200 kN per engine Thrust in Vacuum 1360 kN per engine Propellant Kerosene (RP) Oxidizer Liquid Oxygen (LOX) Chamber Pressure 18 MPa Combustion Temperature 3670 K Nozzle Expansion Ratio 35:1 Burn Time 155 seconds Isp 245 – 277 seconds Cp/Cv ~1.213

35 2.3.2 First Stage

The first stage core is a 3.35-meter diameter vehicle and supports two YF-100 engines. The first stage of the LM-7 has the same configuration as the boosters used for the LM-5. The propellants and sizes are the same between the two vehicles, but the difference lies in the mass of propellant used (“Chang Zheng 5 (Long March 5)”, 2016; “Chang Zheng 7 (Long March 7)”, 2017). The

LM-7 can hold up to 174 metric tons of propellants in the first stage as compared to the 135 metric tons of propellant held in the LM-5 boosters. Since the LM-7 has the same configuration and engines as used by the LM-5 boosters, the LM-7 has the same features such as an efficient oxygen rich pump-fed staged cycle engine, a heat exchanger in the oxidizer tank, and a single turbine that drives the pumps for both the single stage oxygen pump and the dual stage kerosene pump (“Chang

Zheng 5 (Long March 5)”, 2016). The first stage of the LM-7 has a specific impulse between 253 and 287 seconds based on the public data for the gross and fuel masses as well as the burn time and for sea level and vacuum conditions. This compares to the published specific impulse values of 300 seconds for sea level and 335 seconds for vacuum. While the calculated values are lower than the published values, the calculated values are consistent with the calculated specific impulse values for the other placements of the YF-100 engine throughout the Long March rocket family.

36 Table 13. Technical parameters of the Long March 7 first stage and the YF-100 engines (“Asia-

Pacific Space-Rocket Liquid-Propellant Engines”, 2017; Braeunig, 2005; “Chang Zheng 7 (Long

March 7)”, 2017)

First Stage (2 YF-100 Engines) Length 26.28 m Diameter 3.35 m Thrust at Sea Level 1200 kN per engine Thrust in Vacuum 1360 kN per engine Propellant Kerosene (RP) Oxidizer Liquid Oxygen (LOX) Chamber Pressure 18 MPa Combustion Temperature 3670 K Nozzle Expansion Ratio 35:1 Burn Time 155 seconds Isp 253 – 287 seconds Cp/Cv ~1.213

2.3.3 Second Stage

The second stage of the LM-7 holds four YF-115 engines, which are described below (Table 14).

These staged combustion engines operate on kerosene and liquid oxygen and each engine provides

180 kilonewtons. The second stage contains approximately 65 metric tons of propellants, which burns for about 296 seconds. The second stage of the LM-7 has a specific impulse of about 335 seconds according to (“Chang Zheng 7 (Long March 7)”, 2017). The calculated specific impulse is 334 seconds which validates the published value of 335 seconds.

37 Table 14. Technical parameters of the Long March 7 second stage and the YF-115 engines

(“Asia-Pacific Space-Rocket Liquid-Propellant Engines”, 2017; Braeunig, 2005; “Chang Zheng

7 (Long March 7)”, 2017)

Second Stage (4 YF-115 Engines) Length 8 m Diameter 3.35 m Thrust at Sea Level 180 kN per engine Propellant Kerosene (RP) Oxidizer Liquid Oxygen (LOX) Chamber Pressure 12 MPa Combustion Temperature 3625 K Nozzle Expansion Ratio 11.66:1 Burn Time ~296 seconds Isp 334 seconds Cp/Cv ~1.215

2.3.4 Optional Upper Stage

The LM-7 has an optional upper stage that uses two YF-75 engines within the 3-meter diameter vehicle. Each engine in the upper stage can produce 78 kilonewtons of thrust in vacuum through combusting liquid hydrogen and liquid oxygen (“Chang Zheng 7 (Long March 7)”, 2017). The

YF-75 engines burn for 615 seconds and have a calculated specific impulse of 427 seconds. This compares closely to the published specific impulse value of 438 seconds for the optional upper stage of the LM-7.

38 Table 15. Technical parameters of the Long March 7 optional upper stage and the YF-75 engines

(“Asia-Pacific Space-Rocket Liquid-Propellant Engines”, 2017; Braeunig, 2005; “Chang Zheng

7 (Long March 7)”, 2017)

Upper Stage – Optional (2 YF-75 Engines) Length 12.38 m Diameter 3 m Thrust in Vacuum 78 kN per engine Propellant Liquid Hydrogen (LH2) Oxidizer Liquid Oxygen (LOX) Chamber Pressure 4.068 MPa Combustion Temperature 3550 K Nozzle Expansion Ratio 80 Burn Time 615 seconds Isp 427 seconds Cp/Cv ~1.198

2.3.5 Payload Fairing

The three stages and 3.35-meter diameter payload fairing used for the LM-7 combine to a total length of 53.1 meters and a gross mass of 594 metric tons (“Chang Zheng 7 (Long March 7)”,

2017).

Table 16. Dimensions of the Long March 7 payload fairing

Payload Fairing Length ~5-10 m Diameter 3.35

2.3.6 Mission Capabilities

2.3.6.1 Maximum Payloads and Achievable Orbits

Without the optional upper stage, the LM-7 can deliver a payload with a gross mass of 13.5 metric tons to a 200-kilometer by 400-kilometer by 42 degrees orbit. Alternatively, the LM-7 can deliver

39 a 5.5 metric ton payload to a 700-kilometer sun synchronous orbit (“Chang Zheng 7 (Long March

7)”, 2017).

2.3.6.2 Mission Applications

The LM-7 design has flown twice. Its inaugural flight, on June 25th 2016, was a demonstration of a scaled Next Generation Crew Capsule plus microsatellites and ballast. For this launch the LM-7 utilized the optional upper stage to deliver the 12-metric ton payload to a low earth orbit. The 2.6 metric ton Next Generation Crew Capsule reentered and was recovered the following day. The inaugural flight of the LM-7 was also the inaugural launch from the Wenchang Space Launch

Center (“Wenchang Space Launch Centre”, 2016). Since the first flight, the LM-7 has had one other successful mission that also launched from the Wenchang Space Launch Center. On April

20th 2017 the LM-7 delivered the Tianzhou-1 unmanned cargo spacecraft to the Tiangong-2 space laboratory. In the future, the LM-7 may be used to deliver the Tianzhou-2 in late 2019 and for the new generation manned spaceflight first flight in 2020. As a medium-lift capability launch vehicle, the LM-7 will initially function as a cargo vehicle to deliver the Tianzhou spacecraft to the

Tiangong space laboratory, but it is expected to replace most members of the CZ-2, CZ-3, and CZ-

4 families of launch vehicles by 2021. Once the vehicle has been sufficiently tested it will be adopted for the launch of the Next Generation Crew Capsule (“Chang Zheng 7 (Long March 7)”,

2017).

40 2.3.7 Summary of Launch Vehicle Parameters

2.3.7.1 Masses of Stage Structures and Propellants

Table 17. Summary of the gross, empty, and propellant masses for each stage of the Long March

7 plus the payload and payload fairing (“Chang Zheng 7 (Long March 7)”, 2017)

Masses LM-7, gross 594 metric tons First Stage, gross ~186.5 metric tons empty 12.5 metric tons propellants ~174 metric tons Boosters, gross 81.5 metric tons empty 6 metric tons propellants 77.5 metric tons Second Stage, gross ~70.5 metric tons empty ~5.5 metric tons propellants ~65 metric tons Upper Stage, gross 26.4 metric tons empty 3.5 metric tons propellants 22.9 metric tons Payload Fairing, gross N/A Payload, gross Up to 13.5 metric tons to 200 x 400 km x 42 deg gross Up to 5.5 metric tons to 700 km sun synchronous

2.4 Summary of New Family of Chinese Liquid Cryogenic Launch Vehicles

Currently China has many planned launches set to take place over the next few years, but most of those launches will be CZ-2, Chang Zheng 3 (CZ-3), and LM-4 vehicles

(Pietrobon, 2018). This is likely due to time, manufacturing, and reliability reasons.

However, beginning in 2019 there will be a need for the LM-5, LM-6, and LM-7 for placing the Tiangong core module into orbit, sending Mars Global Remote Sensing Orbiter and

Small Rover to Mars, and getting the Chang’e 6 sampler to the moon and back. The LM-

41 5, LM-6, and LM-7 have many missions to come over the next decade. Looking farther into the future of China’s space launch vehicles, one might expect to see the debut of the

Long March 9 (LM-9) as early as 2028 with the goal of an inaugural launch by 2030. The

LM-9 will be a super heavy lift launch vehicle comparable to the USA’s Space Launch

System or SpaceX’s Heavy. The LM-9 is expected to be able to carry 50 metric tons to a lunar transfer orbit.

42 CHAPTER 3:

YF-100 Engine Analysis

Chapter 3 focuses on the powerhouse engine that is the main driver for the LM-5, LM-6, and LM-

7. The first portion of this chapter discusses the origin and design of the YF-100 engine. Following that, the engine is characterized by the mass flow rate, specific impulse, effective exhaust velocity, change in velocity, characteristic velocity, thrust coefficient, throat area, and exit diameter values for each placement of the YF-100 engine throughout the LM-5, LM-6, and LM-7 launch vehicles.

The third major section of this chapter consists of design estimates to characterize the sizing of all of the YF-100 engine systems. Chapter 3 is concluded with a summary of the characteristics of the

YF-100 engine.

3.1 Background on the YF-100 Engine

The YF-100 engine began development in 2000 with the intention of powering the CZ-5, CZ-6, and CZ-7 rockets which are commonly called the LM-5, LM-6, and LM-7 rockets respectively.

The YF-100 engine was developed by the Xi’an Aerospace Propulsion Institute at the Academy of Aerospace Liquid Propulsion Technology (AALPT) in Xi’an, Province. The China

National Space Administration (CNSA) directed the engine testing for all of the LM-5, LM-6, and

LM-7 vehicles and the engine was certified by the State Administration for Science, Technology and Industry for National Defense (SASTIND) in 2012. The YF-100 was first used in 2015 for the inaugural flight of the LM-6 launch vehicle.

43 The YF-100 engine is the powerhouse liquid rocket engine that is used in the first stage and boosters of the new series of cryogenic liquid Long March rockets. It is a Chinese copy of the

Russian RD-120 engine (“Chinese YF-100 (Russian RD-120) to Power CZ-5”). The YF-100 engine is found in the LM-5 strap on boosters and each booster houses two YF-100 engines. One

YF-100 engine also powers the first stage of the LM-6. Two YF-100 engines power the first stage of the LM-7 and each of the LM-7 strap on boosters houses one YF-100 engine.

Published information suggests that the YF-100 engine is capable of producing 1200 kilonewtons of thrust at sea-level or 1360 kilonewtons of thrust in vacuum. The engine design includes a pump- fed staged cycle where there is a single stage oxygen pump for the oxidizer and a dual stage kerosene pump for the fuel. The same turbine drives these two pumps, which is a common characteristic of Soviet engine designs. The oxygen rich staged combustion is used to minimize propellant waste which means that it is a more complex system, but also more efficient (“Chang

Zheng 5 (Long March 5)”, 2016). Additionally, there is a heat exchanger in the oxidizer tank to heat the oxygen gas for the liquid oxygen pressurization. High-pressure kerosene from the fuel tank can also be used as a hydraulic fluid for the control actuators in the booster engines. A schematic of the YF-100 engine can be seen below in Figure 6.

44

Figure 8. Schematic detailing the oxygen rich utilized in the YF-100

rocket engine.

Depending on the vehicle placement of the engine, the YF-100 engine burns for either 155 seconds or 180 seconds (“Chang Zheng 5 (Long March 5)”, 2016; Kyle, 2017). A video of a test fire of the

YF-100 engine that took place on November 11, 2010 in the Shaanxi Province supports that the

45 burn time of the YF-100 engine is up to 180 seconds (SciNewsRo, 2017). The published data for gross mass, total fuel mass, and burn time are summarized below in Table 18. This published information was used to calculate subsequent characteristics of the YF-100 to verify published performance.

Table 18. Given published data for YF-100 engine including gross mass, total fuel mass, and

burn time (“Chang Zheng 5 (Long March 5)”, 2016; “Chang Zheng 6 (Long March 6)”, 2016;

“Chang Zheng 7 (Long March 7)”, 2017; Kyle, 2017)

Gross Mass Total Fuel Mass Engine Placement Burn Time (s) (metric tons) (metric tons) LM-5 Booster 82.50 76.00 180 (two engines) LM-6 First Stage 83.53 76.00 ~180 (one engine) LM-7 Booster 81.50 77.50 155 (one engine) LM-7 First Stage 93.25 87.00 180 (two engines)

3.2 General Characteristics of the YF-100 Engine

3.2.1 Mass Flow Rate and Specific Impulse

3.2.1.1 Mass Flow Rate of Total Fuel Mass

Using the assumed propellant mass and burn time for each placement of the YF-100 engine, the mass flow rate of fuel was calculated using equation 1.

� (��) ∗ (1000 ��⁄��) (1) �̇ (��⁄�) = � (�)

46 Where �̇ is the mass flow rate of the total fuel in kilograms per second (kg/s), � is the total fuel mass in metric tons (MT), and � is the burn time in seconds (s). The calculated mass flow rate of the total fuel is the sum of the propellant mass flow rate and the oxidizer mass flow rate for the

YF-100 engine. For the various engine placements, the mass flow rate of the total fuel ranges between 422.2 kg/s and 500.0 kg/s. The full list of calculated mass flow rates can be found below in Table 19. Published data estimates the total mass flow rate to be 409.7 kg/s where the fuel mass flow rate is 296.39 kg/s and the oxidizer mass flow rate is 113.31. These values were found from a static test fire not an actual launch of one of the LM-5, LM-6, or LM-7 launch vehicles. Since the burn time has been verified from videos of test fires and launches, the discrepancy between the calculated values and the published data is likely due to a change in fuel mass between the static test fire and the actual integration of the YF-100 engine into the Long March family of cryogenic rockets.

3.2.1.2 Specific Impulse at Sea Level and in Vacuum

The specific impulse of the YF-100 engine was calculated using the assumed thrust values at sea level and in vacuum, and the calculated total fuel mass flow rates described in section 3.2.1.1. The specific impulses were calculated for sea level and vacuum using equations 2 and 3 respectively.

� (��) ∗ (1000 �⁄��) (2) � (�) = �̇ (��⁄�) ∗ � (�⁄� )

� (��) ∗ (1000 �⁄��) (3) � (�) = �̇ (��⁄�) ∗ � (�⁄� )

Where � and � are the specific impulse at sea level and in vacuum in seconds, � and � are the corresponding assumed thrust values in kilonewtons, �̇ is the total fuel mass flow rate in

47 kilograms per second, and � is the gravity constant which is equal to 9.81 meters per second. The calculated values for specific impulse at sea level range from 244.6 seconds to 289.7 seconds and the calculated values for specific impulse in vacuum range from 277.2 seconds to 328.3. These calculated values were found assuming that thrust is constant and there is no throttling. The mean specific impulse is 269.3 seconds at sea level and 305.2 seconds in vacuum. These values are lower than expected when compared to the suggested values of 300 seconds at sea level and 335 seconds in vacuum. The mass flow rates and the specific impulses for the LM-5 and LM-6 are within a reasonable range from the anticipated values. The mass flow rates for the LM-7 are significantly higher than the anticipated value which causes the associated specific impulse values to be considerably too low. The differences in specific impulse values between the calculated values and the anticipated values is possibly due to the actual engines throttling throughout flight or the discrepancies could be a result of the engines not burning all of the available fuel.

3.2.1.3 Summary of Mass Flow Rate and Specific Impulse Values

The calculated and anticipated values for the total mass flow rate, the specific impulse at sea level, and the specific impulse in vacuum are summarized below in Table 19.

48 Table 19. Calculated and anticipated values for total mass flow rate, specific impulse at sea

level, and specific impulse in vacuum (“Chinese YF-100 (Russian RD-120) to Power CZ-5”)

Mass Flow Rate of Specific Impulse at Specific Impulse in Engine Placement Propellant and Sea Level (I ) (s) Vacuum (I ) (s) Oxidizer (�̇ ) (kg/s) sp sp LM-5 Booster 422.2 289.7 328.3 LM-6 First Stage 422.2 289.7 328.3 LM-7 Booster 500.0 244.6 277.2 LM-7 First Stage 483.3 253.1 286.8 Anticipated Values 409.7 300.0 335.0

3.2.2 Effective Exhaust Velocity and Change in Velocity

3.2.2.1 Effective Exhaust Velocity at Sea Level and Vacuum

Similar to the specific impulse calculations, the effective exhaust velocity was found by using the assumed values of thrust and specific impulse at sea level and vacuum. The effective exhaust velocity at sea level was calculated using equation 4 and the effective exhaust velocity in vacuum was found using equation 5.

� (��) ∗ (1000 �⁄��) (4) � (�⁄�) = �̇ (��⁄�)

� (��) ∗ (1000 �⁄��) (5) � (�⁄�) = �̇ (��⁄�)

Where � and � are the sea level and vacuum effective exhaust velocities in meters per second,

� and � are the assumed values for sea level and vacuum thrusts in kilonewtons, and �̇ is the total mass flow rate of the fuel. The effective exhaust velocity at sea level ranges from 2400.0 meters per second to 2842.1 meters per second and the effective exhaust velocity ranges from

2720.0 meters per second to 3221.1 meters per second in vacuum conditions. 49

3.2.2.2 Change in Velocity at Sea Level and Vacuum

The change in velocity was estimated using the assumed values for gross mass, fuel mass, and the calculated value of effective exhaust velocity. Equations 6 and 7 below were used to calculate the change in velocity at sea level and in vacuum conditions for each YF-100 placement.

� (��) (6) Δ� (�⁄�) = � (�⁄�) ∗ log � (��)

� (��) (7) Δ� (�⁄�) = � (�⁄�) ∗ log � (��)

Where Δ� and Δ� are the sea level and vacuum change in velocities in meters per second, � and � are the sea level and vacuum effective exhaust velocities in meters per second, � is the assumed value for the initial gross mass in metric tons, and � is the difference between initial gross mass and total fuel mass in metric tons. The gross and fuel masses for the LM-5 booster and the LM-7 first stage are estimated since there are two engines in each placement. The change in velocity ranges from 6710.2 meters per second to 7234.3 meters per second at sea level or from

7604.8 meters per second to 8198.9 meters per second in vacuum. These changes in velocity correspond to a minimum acceleration of about 3.80g and a maximum acceleration of 5.39g. While the calculated change in velocity values do appear to be high, they are within a reasonable g-force range if any of the cryogenic Long March family rockets were to be human rated.

50 3.2.2.3 Summary of Effective Exhaust Velocity and Change in Velocity Values

Table 20 below summarized the effective exhaust velocities and change in velocity values calculated in sea level and vacuum conditions.

Table 20. Calculated effective exhaust velocity values and change in velocity values at sea

level and vacuum

Effective Effective Change in Change in Engine Exhaust Exhaust Velocity at Sea Velocity in Placement Velocity at Sea Velocity in Level Vacuum Level (m/s) Vacuum (m/s) (∆�) (m/s) (∆�) (m/s) LM-5 Booster 2842.1 3221.1 7221.8 8184.7 LM-6 2842.1 3221.1 6839.1 7750.9 First Stage LM-7 Booster 2400.0 2720.0 7234.3 8198.9 LM-7 2482.8 2813.8 6710.2 7604.8 First Stage

3.2.3 Change in Velocity versus Specific Impulse Comparison

The previously calculated values for specific impulses and change in velocities for the LM-5 booster, LM-6 first stage, LM-7 booster and first stage are plotted against each other below in

Figure 7. The four lines represent the linear relationship between both change in velocity and specific impulse with the thrusts. The lines show the range between sea level thrust and vacuum with the former being represented by the lower left data point of the lines and the later by the upper right data points of the lines. Furthermore, Figure 7 shows a crosshatched box labeled ‘Expected

Delta V and Isp Range’. Based on the anticipated values of specific impulse, mean structure mass, and mean burn time, the corresponding range of change in velocity was calculated. Together with the anticipated specific impulse range, the calculated change in velocity range compose the

51 crosshatched box shown in Figure 7. Since the mean propellant mass and mean burn time were used for the calculations, the expected change in velocity could fall anywhere within the box rather than along a linear relationship like the other four engine placements.

Delta V vs. Specific Impulse for YF-100 Engine (Independent of Full System) 9000

8500

8000 Expected Delta V and Isp Range

7500 Delta V (m/s)

7000 LM 5 Booster LM 6 First Stage LM 7 Booster LM 7 First Stage 6500 240 250 260 270 280 290 300 310 320 330 340 350 Specific Impulse (s)

Figure 9. Change in velocity versus specific impulse for the YF-100 engine.

3.2.4 Characteristic Velocity

Based on the published value for the YF-100 engine’s chamber pressure of 18 megapascals and mixture ratio of 2.38, the chamber temperature can be estimated using the adiabatic flame temperature versus chamber pressure chart for liquid oxygen and kerosene engines Figure 8 below.

The estimated chamber temperature is 3670 Kelvin.

52

Figure 10. Adiabatic flame temperature as a function of chamber pressure and mixture ratio for

liquid oxygen and kerosene rocket engines (Braeunig, 2005).

Based on similar combustion charts the gas molecular weight and specific heat ratio as functions of chamber pressure and mixture ratio were estimated to be 22.2 grams per mole and 1.213 respectively. The gas molecular weight gives a specific gas constant of 374.505 joules per kilogram per kelvin. The gas molecular weight and specific heat ratio charts are shown in Figures

9 and 10 below.

53

Figure 11. Gas molecular weight as a function of chamber pressure and mixture ratio for

liquid oxygen and kerosene rocket engines (Braeunig, 2005).

54

Figure 12. Specific heat ratio as a function of chamber pressure and mixture ratio for liquid

oxygen and kerosene rocket engines (Braeunig, 2005).

Using the estimated values from the combustion charts for chamber temperature, specific gas constant, and specific heat ratio, the characteristic velocity was calculated using equation 8.

� (8) � ∗ � �� ∗ � ∗ � (�) �∗(�/�) = 2 � � + 1

Where �∗ is the characteristic velocity in meters per second, � is the specific heat ratio, � is the specific gas constant, and �is the combustion chamber temperature in kelvin. Based upon these

55 estimated values, the characteristic velocity was calculated to be 1800.7 meters per second. This calculated value of the characteristic velocity was verified by taking the ratio of the sea level effective exhaust velocities over the corresponding thrust coefficients.

3.2.5 Thrust Coefficient, Throat Area, Exit Diameter

3.2.5.1 Thrust Coefficient at Sea Level and Vacuum

The thrust coefficient was calculated using effective exhaust velocities and the characteristic velocity previously calculated. The thrust coefficient was computed using equation 9.

� (�/�) (9) � = �∗ (�/�)

∗ Where � is the thrust coefficient, � is the effective exhaust velocity at sea level or vacuum and � is the characteristic velocity. For the various engine placements, the thrust coefficient ranges between 1.333 and 1.578 at sea level or between 1.511 and 1.789 in vacuum.

For the anticipated nozzle ratio of 48, the optimum thrust coefficient is approximately 1.8 which is slightly above all of the calculated thrust coefficient values. As seen below in Figure 11, the estimated thrust coefficients for the LM-5 at sea level, LM-6 at sea level, and the LM-7 at both sea level and in vacuum fall within the incipient flow separation region. The chart in Figure 11 was used to compare thrust coefficients since the specific heat ratio used for the thrust coefficients was

1.213 which can be estimated with the specific heat ratio of 1.2 used in the chart. The calculated thrust coefficients for the LM-5 and LM-6 in vacuum fall within the expected range of favorable thrust coefficients.

56

Figure 13. Thrust coefficient CF versus nozzle area ratio for k=1.20 (Sutton & Biblarz, 2010).

3.2.5.2 Throat Area, Exit Area, and Exit Diameter

The throat area of the YF-100 engine was estimated by using the total mass flow rate, chamber pressure, specific heat ratio, specific gas constant, and combustion chamber temperature to calculate equation 10.

� (10) �̇ � ∗ � �� ∗ � ∗ � (�) �∗ (�) = ∗ 2 ∗ � (��) ∗ � 2 � + 1

57 Where �∗ is the throat area in squared meters, �̇ is the total mass flow rate in kilograms per second,

� is the combustion chamber pressure in pascals, � is the specific heat ratio, � is the specific gas constant in joules per kilogram per kelvin, and � is the combustion chamber temperature in kelvin.

The calculated throat area values range between 0.0188 and 0.0250 square meters. Since the throat area is not variable, the true throat area likely falls somewhere within that range.

From the calculated throat areas, the assumed nozzle ratio of 48 was used to find the corresponding exit areas and exit diameters. The estimated exit diameters range between 1.0707 and 1.2363 meters. All of these estimated exit diameters are viable since they would all fit within the casings for each engine placement. The published data on the YF-100 suggests that the exit diameter is

1.338 meters which is slightly larger than the estimated values found.

3.2.5.3 Summary of Thrust Coefficient, Throat Area, and Exit Diameter Values

Table 21 below summarizes the estimated values for the thrust coefficient at sea level and vacuum conditions as well as the estimated throat areas and exit diameters for each engine placement.

58 Table 21. Summary of estimated thrust coefficients at sea level and in vacuum, throat area, and

exit diameter values

Thrust Thrust Engine Throat Area Exit Diameter Coefficient at Coefficient in Placement (m2) (m) Sea Level Vacuum LM-5 Booster 1.578 1.789 0.0211 1.1361 LM-6 1.578 1.789 0.0211 1.1361 First Stage LM-7 Booster 1.333 1.511 0.0250 1.2363 LM-7 1.3787 1.563 0.0242 1.2156 First Stage Anticipated 1.8 0.0293 1.338 Values

3.3 Design Estimates

The following calculations were based on the assumption that the true specific impulse at sea level is 300 seconds and that the corresponding change in velocity is 7.4506 kilometers per second. This change in velocity is the maximum velocity achievable and does not account for any losses due to steering, drag, gravity, etc. Additionally, the sea level thrust of 1200 kilonewtons, a mixture ratio of 2.38, a chamber temperature of 3670 Kelvin, a specific heat ratio of 1.213, a molecular weight of 22.2, a chamber pressure of 18 megapascals, and a thrust coefficient of 1.8 were used in the design estimate calculations carried out in section 3.3.

Initially, the theoretical mass flow rate was calculated by equation 1 where the above-mentioned sea level thrust, specific impulse and gravity constant were used. Next, the characteristic velocity was found through equation 8 which was then used to find the throat area and diameter using equations 11 and 12.

59 �� ∗ � (11) �̇ � ∗ � � �∗ (�) = � (��)

(12) �∗ (�) �∗ (�) = 2 ∗ �

Where �∗ is the throat area, �̇ is the mass flow rate of the propellant, �∗ is the characteristic velocity, and � is the chamber pressure. The throat area and diameter for these conditions were found to equal 0.0370 meters squared and 0.2172 meters respectively. This throat area is slightly larger than the values found in section 3.2.5.3 but is still within a reasonable range.

3.3.1 Combustion Chamber

3.3.1.1 Combustion Chamber Geometry

Assuming that the ratio of characteristic length to chamber length is directly proportional to the ratio of chamber area to throat area and that the ratio of chamber area over throat area is equal to

2.89, the length of the combustion chamber was calculated to be 0.3460 meters. Using the chamber to throat areas ratio, the chamber area was found to be 0.1070 meters squared and the chamber diameter was 0.3692 meters. Combining the calculated chamber area with the chamber length, the chamber volume was calculated to equal 0.0370 meters cubed.

3.3.1.2 Combustion Chamber Wall Thickness

The assumption was made that the combustion chamber is composed of a Columbium material which has a of 8550 kilograms per meter cubed. Additionally, a factor of safety of 1.5 was used to calculate the combustion wall thickness as seen in equation 13 below.

60 � � (��) ∗ (�) ∗ �� (13) � (�) = 2 310 ∗ 10

Where � is the chamber wall thickness, � is the chamber pressure, � is the diameter of the combustion chamber, and �� is the factor of safety. For these given conditions, the combustion chamber wall thickness was found to be 0.0162 meters.

3.3.1.3 Combustion Chamber Mass

The total mass of the combustion chamber was calculated using equation 14 where � is the total combustion chamber mass, � is the length of the chamber, � is the density of the Columbium material used for the chamber, � is the chamber wall thickness, and � is the radius of the combustion chamber. The total mass of the combustion chamber found by equation 14 equaled

57.5635 kg.

�� (14) � (��) = � ∗ � (�) ∗ � ∗ � (�) + � (�) − � (�) �

3.3.1.4 Combustion Chamber Parameters

The combustion chamber parameters are summarized below in Table 22.

61 Table 22. Combustion chamber parameters

Parameter Calculated Value Chamber Length 0.3460 meters Chamber Area 0.1070 meters squared Chamber Diameter 0.3692 meters Chamber Volume 0.0370 meters cubed Chamber Material Density 8550 kilograms per meter cubed Factor of Safety 1.5 Chamber Wall Thickness 0.0162 meters Combustion Chamber Mass 57.5635 kg

3.3.2 Converging Nozzle

3.3.2.1 Converging Nozzle Mass

The mass of the convergent nozzle was found using equation 15. Equation 15 uses the density of chamber material (�), the wall thickness of the combustion chamber (�), the radii of the chamber

(�) and throat (�), and the taper angle of the combustion chamber (�) which was assumed to be

45 degrees for these estimations.

�� (15) � ∗ � ∗ � (�) ∗ � (�) − � (�) � � (��) = tan �

Equation 15 produced an estimated convergent nozzle mass equal to 14.5647 kilograms.

3.3.2.2 Converging Nozzle Parameters

Key parameters of the converging nozzle are listed below in Table 23.

62 Table 23. Converging nozzle parameters

Parameter Calculated Value Taper Angle of Combustion Chamber 45 degrees Convergent Nozzle Mass 14.5647 kg

3.3.3 Diverging Nozzle

3.3.3.1 Diverging Nozzle Wall Thickness

The diverging nozzle wall thickness was estimated to be one fourth of the thickness of the combustion chamber wall. Therefore, the wall thickness of the diverging nozzle equals 0.0040 meters.

3.3.3.2 Diverging Nozzle Exit Diameter

Using the published value of the expansion ratio , which is equal to 48, the diverging nozzle ∗

∗ exit area (�) was calculated using the previously calculated throat diameter (� ). Equation 16 below produces an exit diameter equal to 1.5045 meters. Each engine placement of the YF-100 is able to accommodate this exit diameter. In the cases of the LM-5 boosters and the LM-7 first stage where there are two engines, the casing diameter is 3.35 meters and in the cases of the LM-6 first stage and the LM-7 boosters the casing diameters are 3.35 meters and 2.25 meters respectively.

(16) � (�) � (�) = �∗ (�) ∗ �∗ (�)

63 3.3.3.3 Diverging Nozzle Mass

Similar to equation 15, equation 17 below was used to calculate the mass of the diverging nozzle.

Equation 17 uses the density of the diverging nozzle material (�), the wall thickness of the diverging nozzle (�), the exit radius (�), the throat radius (�), and the taper angle of the divergent nozzle (�). For these calculations, the same Columbium material with a density of

8550 kilograms per meter cubed and a taper angle of 15 degrees were assumed. The diverging nozzle mass equals 227.8568 kilograms.

�� (17) � ∗ � ∗ � (�) ∗ � (�) − � (�) � � (��) = tan �

3.3.3.4 Diverging Nozzle Length

The taper angle (�), exit radius (�), and throat radius (�) were also used to find the length of diverging nozzle (�) in equation 18. The diverging nozzle length is 2.7383 meters.

� − � (18) � (�) = tan �

3.3.3.5 Diverging Nozzle Parameters

A summary of the diverging nozzle parameters is shown below in Table 24.

64 Table 24. Diverging nozzle parameters

Parameter Calculated Value Diverging Nozzle Wall Thickness 0.0040 meters Diverging Nozzle Exit Diameter 1.5045 meters Diverging Nozzle Material Density 8550 kilograms per meter cubed Diverging Nozzle Mass 227.8568 kilograms Diverging Nozzle Taper Angle 15 degrees Diverging Nozzle Length 2.7383 meters

3.3.4 Injectors

3.3.4.1 Injector Mass

Based on heritage data, the injector mass was estimated to be 25 percent of the weight of the total engine mass. The injector mass was estimated to be 187.4906 kilograms.

3.3.4.2 Ablative Cooling Material Mass

Similarly, the ablative cooling material mass was estimated to equal 35 percent of the total engine weight, which equals 262.4869 kilograms.

3.3.4.3 Injector Parameters

The injector mass and ablative cooling material mass are summarized in Table 25.

Table 25. Injector parameters

Parameter Calculated Value Injector Mass 187.4906 kilograms Ablative Cooling Material Mass 262.4869 kilograms

65 3.3.5 Feed System Pressure Levels

The total tank pressure for the kerosene and liquid oxygen tanks were found by summing the combustion chamber pressure, the injector pressure drop, the feed line pressure drop, and the dynamic pressure drop. The injector pressure drop was estimated to be 20 percent of the combustion chamber pressure and the feed line pressure drop was approximately 50000 pascals.

The fuel and oxidizer dynamic pressure drop were estimated to be 40500 pascals and 57100 pascals respectively. These estimated values combined with the published value for the combustion chamber pressure gives estimated total tank pressures for the fuel and propellant tanks equal to

21.6905 megapascals and 21.7071 megapascals respectively.

3.3.6 Propellant Masses

In order to calculate the propellant mass, the propellant ratio was first found using equation 19 where � is the propellant ratio, ∆� is the change in velocity in meters per second, � is the specific impulse at sea level, and g is gravity. The propellant ratio was found to be 0.9205. Since the upper limit of the total mass was known from published data to be equal to 83.53 metric tons, the propellant mass was found by multiplying the propellant ratio by the upper limit of the total mass. This method produced a propellant mass of 76.887 metric tons. This value is in line with data found for each engine placement. In fact, this calculated value is approximately the average of the four propellant masses found.

∆ (19) ()∗ � = 1 − �

66 The propellant mass divided by the mass flow rate of the propellant found using equation 1 was calculated to estimate the burn time. The burn time (�) is estimated to be 188.5652 seconds. This burn time is slightly above what is expected since the published data suggests that the burn time is either 155 seconds or 180 seconds depending upon the engine placement. The resulting total impulse (�) is 2.2628x108 Newton-seconds. The total impulse was found by using equation 20 below.

� (� ∙ �) = � (��) ∗ � (�) (20)

3.3.6.1 Fuel Mass

The published mixture ratio of 2.38 was used to estimate the mass flow rate of the fuel and the mass of the fuel using equations 21 and 22 respectively. The mass of the kerosene fuel used in the

YF-100 engine is estimated to be 54.139 metric tons. However, the fuel mass may vary slightly for each mission since the mixture ratio is adjustable in either direction by 10 percent.

�� (21) �� � ∗ �̇ � �̇ = � 1 + �

�� (22) � (��) = �̇ ∗ � (�) �

3.3.6.2 Oxidizer Mass

Similar to the fuel mass flow rate and fuel mass calculations, the oxidizer mass flow rate and oxidizer mass were calculated with respect to the mixture ratio as seen in equations 23 and 24. The mass of the oxidizer was found to be 22.748 metric tons.

67 �� (23) �� �̇ � �̇ = � 1 + �

�� (24) � (��) = �̇ ∗ � (�) �

3.3.6.3 Propellant Mass Parameters

The key parameters used to calculate the design estimates for the propellant masses are listed in

Table 26 below.

Table 26. Propellant mass parameters

Parameter Calculated Value Propellant Ratio 0.9205 Upper Limit of Total Mass 83.53 metric tons Propellant Mass 76.887 metric tons Burn time 188.5652 seconds. Total Impulse 2.262x108 Newton-seconds Fuel Mass 54.139 metric tons Oxidizer Mass 22.748 metric tons

3.3.7 Propellant Tanks

The calculations of the propellant tanks assume that each engine has its own set of tanks regardless of how many engines are placed within one casing.

3.3.7.1 Mass of Structures

The difference between the upper total mass limit and the propellant mass is the mass of the structure. Under these conditions the structural mass is 6.6431 metric tons.

68 3.3.7.2 Fuel Tank Volume

The fuel tank volume was estimated using equation 25 where � is the volume of the fuel tank,

� is the mass of the fuel, and � is the density of the fuel. The density of kerosene is known to be 810 kilograms per meter cubed. The volume based upon the necessary amount of fuel and the density of the fuel was multiplied by a factor of 1.1 to ensure that there is a small amount of extra fuel that burns off before launch. The calculated volume for the fuel tank is 73.5225 meters cubed. � ( ) (25) � � = 1.1 ∗ �

3.3.7.3 Fuel Tank Mass

The length to height ratio of the fuel tanks in centimeters was estimated from literature to be

3 (“ Tank Design”). The pressure (�), volume (�) of the fuel tank, circumferential stress (�), density of the tank material (�), the fraction of the tank filled by propellant (�), and the density of the fuel (�) were used in equation 26 to find the mass of the fuel tank (� ). In this calculation, the circumferential stress was estimated to be equal to 1034 megapascals and the fraction of the tank filled by the propellant was estimated to be 80 percent.

These two values were approximated from literature (“Rocket Propellant Tank Design”). The tanks were assumed to be made of an aluminum material which has a density of 2700 kilogram per meter cubed. The estimated value of the fuel tank is 4.283 metric tons.

� � (��) �� (26) ( ) 3 ∗ � �� ∗ 1 + ∗ ∗ � � 2�(��) � � (��) = 3 � �� 1 + ∗ � ∗ � 2 � �

69 3.3.7.4 Oxidizer Tank Volume

The oxidizer tank volume was found using the same method as the fuel tank. Using the liquid oxygen density of 1142 kilograms per meter cubed, the estimated oxidizer tank volume is 21.9110 meters cubed. This calculation was done using equation 27. � ( ) (27) � � = 1.1 ∗ �

3.3.7.5 Oxidizer Tank Mass

The oxidizer tank mass was estimated by the same method as the fuel tank mass (equation 28).

The estimated oxidizer tank mass is 3.037 metric tons.

� � (��) �� (28) ( ) 3 ∗ � �� ∗ 1 + ∗ ∗ � � 2�(��) � � (��) = 3 � �� 1 + ∗ � ∗ � 2 � �

3.3.7.6 Tank Parameters

The propellant tank parameters are summarized below in Table 27.

Table 27. Propellant tank parameters

Parameter Calculated Value Structural Mass 6.6431 metric tons Fuel Tank Volume 73.5225 meters cubed Fuel Tank Mass 4.283 metric tons Oxidizer Tank Volume 21.9110 meters cubed Oxidizer Tank Mass 3.37 metric tons

70 3.3.8 Total Mass of Engine and Propellant Tanks

The total mass of the combustion chamber, converging and diverging nozzles, injectors, propellant, structures, and tanks is 108.155 metric tons. This estimated total mass of the engine and propellant tanks is slightly higher than the range of published values for the wetted gross mass of each engine placement stage. The published values for the wetted gross mass of each stage that houses the YF-100 engine ranges between 81.5 metric tons and 93.25 metric tons. The design estimates suggest that the actual mass of the YF-100 engine is about 108.155 metric tons, however these estimates used several assumptions about the construction of the engine that may vary to allow the engine to have a smaller mass that is closer to the published values. For example, the mass of the diverging nozzle was estimated assuming a taper angle of 15 degrees. If this parameter alone changed by 5 degrees that would make an overall change in mass of the entire engine of approximately 250 kilograms. This is just one of several assumptions that were made throughout this estimation that could account for the differences found in the overall mass of the engine as compared to the stage gross masses.

3.4 Conclusions of the YF-100 Engine Analysis

This chapter characterized the YF-100 engine through a variety of parameter calculations. Based on the values that were found for the change in velocity and the specific impulse, it can be concluded that there are some discrepancies between the use of the YF-100 on the LM-5, LM-6, and LM-7. On the LM-7, the YF-100 engine is able to produce similar changes in velocity over the respective burn time, but it is much less efficient than when it is used on the LM-5 or LM-6.

This is seen by the significantly lower specific impulse on the LM-7 (as seen in Figure 7). A similar trend was seen in the thrust coefficient calculations where the LM-5 and LM-6 were relatively 71 similar to the anticipated value, but the LM-7 was considerably off. This in turn meant that there were dissimilarities between the calculated values of the exit diameter. Although, all exit diameter values that were found were valid and would fit within the corresponding shell diameter.

The second portion of this chapter focused on design estimates to fully characterize the shape and size of the engine. These estimates produced an exit diameter prediction of about 1.5 meters which larger than the anticipated exit diameter, but still within a reasonable size to fit within the core or booster shells as appropriate.

72 CHAPTER 4:

Comparison to International Competitors

In order for China to participate commercially, they must sell their products. In China’s 2016

White Paper on Space Activities, it was stated that “China encourages and supports Chinese enterprises to participate in international commercial activities in the space field” (China Daily,

2016). In the past, China has provided launch services to Turkey, and when launching their own satellites has taken on small satellites for Ecuador, , , and Luxembourg (China

Daily, 2016). Currently China has not sold a LM-5, LM-6, or LM-7 internationally. Since it is

China’s intent to support commercial launch services, if they wish to be commercially competitive in an international market, China must be able to price their launch vehicles competitively, as well as provide technical transparency, integration, and open failure analyses.

The discussion in this chapter is not intended to act as a full economic analysis of the industry since the international launch vehicle industry is not necessarily a fully developed market with consistent demand. This chapter is meant to give perspective on how the new family of Chinese cryogenic launch vehicles compare to international competitors. These comparisons are based on listed selling prices for each launch vehicle and do not account for government subsidies, fixed costs, marginal costs, or development costsfor which each selling organization or agency is not responsible. The following sections also compare payload capacities and historical reliability to give a perspective of where China would need to price their LM-5, LM-6, and LM-7 launch vehicles. Again, these estimated prices would need to be the selling price and the various agents

73 within the Chinese space program would need to account for any built-in costs appropriately to make these selling prices possible.

4.1 International Light Lift Launch Vehicles

The published prices of several international light lift launch vehicles are listed below in Table 28.

These prices should be comparable to that of the LM-6. Two of the most similar launch vehicles are USA’s -C, which can deliver 1050 kg to a sun synchronous orbit, and Russia’s , which can deliver 1200 kg to a sun synchronous orbit (Central Intelligence Agency; Messier,

2016). Based on the average price per kilogram from this sample of light lift launch vehicles, the

LM-6 should be priced at approximately 26.85 million US dollars per launch to remain comparable and competitive to similar international launch vehicles. Table 28 also highlights the reliability of these light lift launch vehicles. The right-most column shows the number of successful missions compared to the number of total launches for each launch vehicle. Figure 12 illustrates where the

LM-5 should be priced relative to similar Russian and American launch vehicles.

Table 28. Price comparison for light lift launch vehicles internationally (US dollars) (Central

Intelligence Agency; Forecast International, 2015; Messier, 2016)

Country Vehicle Payload Capability Price Reliability 1000 kg to 700 km China LM-6 $26.85M 2:2 SSO Russia 100 kg to LEO $1-1.5M 1:5 USA Minotaur 1 580 kg to LEO $40M 11:11 USA Minotaur IV 1735 kg to LEO $46M 6:6 USA Minotaur-C 1050 kg to SSO $40-50M 7:10 Russia Start-1 350 kg to SSO $8-9M 6:6 Russia Rokot 1200 kg to SSO $6M 27:30

74

Price per Kilogram for Light Lift Launch Vehicles 55

50

US (LEO) 45 US (SSO)

40 US (LEO)

35

30

25 Competitive Price for Long March 6

20

(US Dollars) 15 Price in Millions 10 Russia (SSO) 5 Russia (SSO) Russia (LEO) 0 0 200 400 600 800 1000 1200 1400 1600 1800 Payload Capacity (kilograms)

Figure 14. Price per Kilogram for Small Lift Launch Vehicles Internationally

4.2 International Medium Lift Launch Vehicles

Based on the types of missions that LM-7 is designed to carry out, the most similar international competitors are USA’s Falcon 9 for low earth orbit missions or ’s (ESA)

Vega for sun synchronous missions (Table 29). Based on the prices of the Falcon 9 and , 48.3 million and approximately 26 million US dollars, respectively, the LM-7 needs to be priced at about 65.3 million US dollars for a sun synchronous mission or 93.2 million US dollars for a low earth orbit mission (De Selding, 2012; De Selding, 2016). Figure 13 illustrates where the LM-7 should be priced relative to similar medium lift launch vehicles from USA, Russia, India, ESA and

Italy.

75 Table 29. Price comparison for medium lift launch vehicles internationally (US dollars) (De

Selding, 2012; De Selding, 2016; “Discover the Value of Launching on ULA’s V”; Bagla,

2017; Vick, 2005; Weitering, 2016)

Country Vehicle Payload Capability Price Reliability 13500 kg to 200km x 400km x $65.3M for SSO; China LM-7 42deg or 5500 kg to 700 km 2:2 $93.2M for LEO SSO Falcon 9 (reusable USA 15960 kg to LEO $48.3M 50:52 configuration) USA 18810 kg to LEO $153M 75:76 Russia -2 8200 kg to LEO $30-50M 69:76 USA 6500 kg to LEO $190M 6:7 GSLV Mk. III 10000 kg to LEO, 4000 to India $46-62M 2:2 (LVM3) GTO ESA/Italy Vega 2300 kg to LEO, 1330 to SSO $26-38M 11:11

Price per Kilogram for Medium Lift Launch Vehicles 200 US (LEO) 180

160 US (LEO) 140

120

100 Competitive Price for Long March 7 (LEO)

80 India (GTO)

(US Dollars) 60 Competitive Price for Long March 7 (SSO) US (LEO)

Price in Millions India (LEO) 40 ESA (SSO) Russia (LEO) ESA (LEO) 20

0 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 Payload Capacity (kilograms)

Figure 15. Price per Kilogram for Medium Lift Launch Vehicles Internationally

76

4.3 International Heavy Lift Launch Vehicles

The primary international comparable launch vehicles for the LM-5 are ESA’s 5, USA’s

Delta IV Heavy, and Russia’s -M. The prices for these three international competitors range from 100 million to 435 million US dollars (Table 30) (De Selding, 2014; Strikland, 2011;

Nowakowski, 2014). Previously, for China’s LM-5 to be competitive in an international market, it must be priced at or less than 250.36 million US dollars per launch for a low earth orbit mission.

However, since the recent introduction of the into the field of competition, the LM-

5 must now drive its price down to 202.4 million US dollars per launch to be competitive internationally. As seen in Figure 14, the slope of the price curve is actually negative which is opposite of what would be expected for a price versus payload capacity graph. This just shows how disruptive to the industry the introduction of the Falcon Heavy has been. The Falcon Heavy is priced similarly to the Russian Proton-M and the European , but it is capable of carrying significantly more payload to a low earth orbit comparatively. If the international market for commercial launch vehicles continues in this direction, then the Chinese will need to bring down the price of their heavy lift LM-5 launch vehicle to remain competitive. Just from this one new launch vehicle, the price would need to change from the initial estimate of 250.36 million US dollars to 202.4 million US dollars per launch. With the development of other similar new launch vehicles such as ’s or ’s Vulcan, the price for heavy lift launch vehicles will need to be adjusted. Figure 14 below illustrates where the LM-7 should be priced relative to similar heavy lift launch vehicles from USA, Russia, and ESA.

77 Table 30. Price comparison for heavy lift launch vehicles internationally (US dollars) (De

Selding, 2014; SpaceX; Strikland, 2011; Nowakowski, 2014)

Payload Country Vehicle Cost Reliability Capability 25000 kg to LEO, 14000 kg to $202.4M for China LM-5 1:2 GTO LEO ESA Ariane 5 21000 kg to LEO $100M 93:98 Delta IV USA 28790 kg to LEO $435M 8:9 Heavy Russia Proton-M 23000 kg to LEO $115M 92:102 $90M 63800 kg to LEO (28.5°), Falcon (reusable) USA 1:1 Heavy 26700 kg to GTO (27°), 16800 $150M kg to Mars, 3500 kg to Pluto (expendable)

Price per Kilogram for Heavy Lift Launch Vehicles 500

450 US (LEO)

400

350

300

250 Competitive Price for Long March 5 (LEO) 200 US (LEO) - Expendable

(US Dollars) 150

Price in Millions Russia (LEO) 100 ESA (LEO) US (LEO) - Reusable

50

0 20000 25000 30000 35000 40000 45000 50000 55000 60000 65000 70000 Payload Capacity (kilograms)

Figure 16. Price per Kilogram for Heavy Lift Launch Vehicles Internationally

78 CHAPTER 5:

Summary

The Chinese space program is outlined in chapter 1. This chapter outlined who is involved in the

Chinese space program and how some key agents are involved in the overall program. Chapter 1 also gave a brief introduction into the new family of liquid cryogenic launch vehicles. The location and primary purpose of each of the four Chinese launch sites were described. The first chapter concluded with a timeline of the Chinese space program and an explanation of the motivation for this analysis of the program.

Chapter 2 explored the physical and technical parameters of the LM-5, LM-6, and LM-7 launch vehicles. The physical parameters such as gross, empty, and propellant masses were combined with basic technical parameters such as thrust and burn time to calculate the specific impulse of each stage and booster. These calculated values were compared to the published values to determine if the LM-5, LM-6, and LM-7 are actually capable of their anticipated missions. The calculated specific impulse values were all relatively similar to the published values with the exception of the booster and first stage of the LM-7. The specific impulse values were further investigated in chapter 3.

In chapter 3, the YF-100 engine was characterized through various calculations. Based on the values that were found for the change in velocity and the specific impulse, it can be concluded that there are some discrepancies between the use of the YF-100 on the LM-5 boosters and on the LM-

79 6 first stage as compared to the use of the YF-100 on the LM-7 boosters and first stage. On the

LM-7, the YF-100 engine is able to produce similar changes in velocity over the respective burn time, but it is much less efficient than when it is used on the LM-5 or LM-6. This is seen by the significantly lower specific impulse on the LM-7. Since the LM-7 will primarily be used to deliver the Tianzhou cargo spacecraft to the Tiangong space laboratory, this use of the LM-7 does not need to be as effective with its use of fuel as it might need to be when delivering manned spacecraft or very small payloads as is the case with the LM-5 and LM-6 respectively. Furthermore, all of the calculations carried out in chapters 2 and 3 were done assuming constant thrust and no losses to the change in velocity from steering, drag, gravity, etc. So, while the initial conclusions suggest that there are incongruities mainly with the YF-100 engine on the LM-7 there are likely further differences that would be seen by considering these varying aspects.

While China has previously focused on and has set goals for their future missions domestically, an international comparison was carried out to give perspective on how the Chinese space program stands up to other major spacefaring countries. Chapter 4 analyzed the price per kilogram for light, medium, and heavy lift launch vehicles to determine where China would need to price the LM-5,

LM-6, and LM-7 launch vehicles if they wanted to compete commercially on an international scale. It was determined that the LM-5 would need to be priced at 202.4 million US dollars per launch, the LM-6 would need to be priced at 26.85 million US dollars per launch, and the LM-7 would need to be priced at 65.3 million US dollars for a sun synchronous mission or 93.2 million

US dollars for a low earth orbit mission to remain competitive in an international commercial market. This analysis is a beginning step in fully understanding the motive and direction of the

Chinese space program.

80 CHAPTER 6:

Areas for Future Work

To better and more fully understand the motive and direction of the Chinese space program further investigations could be carried out. A key aspect of the Chinese space program that was not investigated in this analysis is that of how China cooperates with foreign space programs. For future work, a risk analysis of partnering with the Chinese on space projects could be carried out.

This would take into consideration the associated technical, financial, economic, societal, and political consequences of a potential cooperative space-based project between China and another spacefaring country. Using previous cooperative projects that China has participated in as examples, a general threat framework that depicts the different types of risks and their relative significance could be used to identify recommendations for risk mitigating practices. A risk analysis of how China works cooperatively with foreign space agencies can give insight into how the Chinese space program functions and what their motives and directions are.

Another area of future work is to look at key policies at play that affect the way China operates in space. This would include any policies that China has set forth, any international policies, treaties, and laws, as well as policies set in the United States that might affect international cooperation on space-based projects between the two countries.

The analyses carried out in this thesis focus primarily on the technical capabilities of the Long

March family of liquid rockets, but it is necessary to consider the economic and policy aspects of the Chinese space program more fully to get a clear full picture of what China is accomplishing. 81 Considering these areas of future work, will give a better understanding of the full picture of the

Chinese space program, including their motive and direction.

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89

Appendix A MATLAB: Technical Parameter Calculations

90 %Kayleigh Gordon %Master's Thesis Technical Parameter Calculations 2 %LM 5, LM 6, LM 7 clear; clc;

%% LM 5 gross_mass=869; %metric ton g=9.81; %m/s2

%Boosters (8 engines) length_booster=26.28; %m diameter_booster=3.35; %m sea_level_thrust_booster=1200; %kN per engine vacuum_thrust_booster=1360; %kN per engine gross_mass_booster=147; %metric ton per booster empty_mass_booster=12; %metric ton per booster propellant_mass_booster=135; %metric ton per booster burn_time_booster=180; %s isp_booster=(180+335)/2; %s burnout_velocity_booster=(2.9+3.29)/2; %km/s

%First Stage (2 engines) length_first=31.02; %m diameter_first=5; %m sea_level_thrust_first=510; %kN each vacuum_thrust_first=700; %kN each gross_mass_first=175.8; %metric ton empty_mass_first=17.8; %metric ton propellant_mass_first=158; %metric ton burn_time_first=480; %s isp_first=(310+510)/2; %s burnout_velocity_first=(3.04+4.2)/2; %km/s

%Second Stage (2 engines) length_second=12; %m diameter_second=5; %m vacuum_thrust_second=78; %kN each gross_mass_second=26; %metric ton empty_mass_second=3.1; %metric ton propellant_mass_second=22.9; %metric ton burn_time_second=780; %s isp_second=442; %s burnout_velocity_second=4.33; %km/s

%Upper Stage diameter_upper=5.2; %m gross_mass_upper=1.8; %metric ton burn_time_upper=1105; %s isp_upper=316; %s burnout_velocity_upper=3.10; %km/s

%Payload Fairing 91 length_payload=12.5; %m diameter_payload=5.2; %m gross_mass_payload_fairing=63.4; %metric ton gross_mass_payload_gto=14; %metric ton gross_mass_payload_leo=25; %metric ton

%Mass Flow Rates mdot_booster=propellant_mass_booster*1000/burn_time_booster; %kg/sec mdot_first=propellant_mass_first*1000/burn_time_first; %kg/sec mdot_second=propellant_mass_second*1000/burn_time_second; %kg/sec %mdot_upper=propellant_mass_upper/1000/burn_time_upper; %kg/sec

%Specific Impulse Verification Isp_sea_level_booster_lm5=sea_level_thrust_booster*1000/(mdot_booster*g); Isp_vacuum_booster_lm5=vacuum_thrust_booster*1000/(mdot_booster*g); Isp_sea_level_first=2*sea_level_thrust_first*1000/(mdot_first*g); Isp_vacuum_first=2*vacuum_thrust_first*1000/(mdot_first*g); Isp_vacuum_second=2*vacuum_thrust_second*1000/(mdot_second*g);

%Effective Exhaust Velocity c_sea_level_booster=sea_level_thrust_booster*1000/mdot_booster; %m/s per booster engine %c_sea_level_per_booster=2*sea_level_thrust_booster*1000/mdot_booster; %m/s per booster c_vacuum_booster=vacuum_thrust_booster*1000/mdot_booster; %m/s per booster engine c_sea_level_first=2*sea_level_thrust_first*1000/mdot_first; %m/s for the first stage at sea level c_vacuum_first=2*vacuum_thrust_first*1000/mdot_first; %m/s for the first stage in vacuum c_vacuum_second=2*vacuum_thrust_second*1000/mdot_second; %m/s for the second stage

%Delta V mi_booster=gross_mass_booster*1000; mf_booster=(gross_mass_booster-propellant_mass_booster)*1000; deltav_sea_level_booster_lm5=c_sea_level_booster*log(mi_booster/mf_booster); %Delta V booster at sea level (m/s) mi_booster=gross_mass_booster*1000; mf_booster=(gross_mass_booster-propellant_mass_booster)*1000; deltav_vacuum_booster_lm5=c_vacuum_booster*log(mi_booster/mf_booster); %Delta V booster in vacuum (m/s)

%Propellant Mass Ratios mf_booster=gross_mass-(4*propellant_mass_booster); xi_booster=(gross_mass-mf_booster)/gross_mass; mi_first=mf_booster-empty_mass_booster; mf_first=mi_first-propellant_mass_first; xi_first=(mi_first-mf_first)/mi_first; mi_second=mf_first-empty_mass_first; mf_second=mi_second-propellant_mass_second; 92 xi_second=(mi_second-mf_second)/mi_second; xi_overall=(gross_mass-mf_second)/gross_mass;

%Exit Area, c*, throat area for Boosters (YF-100 Engine) nozzle_ratio_100=35; %According to Wikipedia!!!!!!!!! k_100=1.213; %From braeunig chart!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level chamber_pressure_100=18e6; %According to Wikipedia!!!!!!! pressure_ratio_100=(2/(k_100+1))^(k_100/(k_100+1)); %throat/chamber chamber_temperature_100=3670; %From braeunig chart!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level R_100=8314/22.2; %Gas Molecular Weigh from braeunig chart!!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level cstar_100=sqrt(((2*k_100)/(k_100+1))*(R_100*chamber_temperature_100)); %m/s throat_area_100=((mdot_booster/2/chamber_pressure_100/k_100)*sqrt(k_100*R_100 *chamber_temperature_100))/sqrt((2/(k_100+1))^((k_100+1)/(k_100-1))); %m^2 exit_area_100=throat_area_100*nozzle_ratio_100; exit_diameter_100=2*sqrt(exit_area_100/pi);

%Exit Area, c*, throat area for First Stage (YF-77 Engine) nozzle_ratio_77=49; %According to Wikipedia!!!!!!!!! k_77=1.2015; %From braeunig chart!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level chamber_pressure_77=102e5; %According to Wikipedia!!!!!!! pressure_ratio_77=(2/(k_77+1))^(k_77/(k_77+1)); %throat/chamber chamber_temperature_77=3450; %From braeunig chart!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level R_77=8314/12.7; %Gas Molecular Weigh from braeunig chart!!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level cstar_77=sqrt(((2*k_77)/(k_77+1))*(R_77*chamber_temperature_77)); %m/s throat_area_77=((mdot_first/2/chamber_pressure_77/k_77)*sqrt(k_77*R_77*chambe r_temperature_77))/sqrt((2/(k_77+1))^((k_77+1)/(k_77-1))); %m^2 exit_area_77=throat_area_77*nozzle_ratio_77; exit_diameter_77=2*sqrt(exit_area_77/pi);

%Exit Area, c*, throat area for Second Stage (YF-75 Engine) nozzle_ratio_75=80; %According to Wikipedia!!!!!!!!! k_75=1.198; %From braeunig chart!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level chamber_pressure_75=4.068*(10^6); %According to Wikipedia!!!!!!! pressure_ratio_75=(2/(k_75+1))^(k_75/(k_75+1)); %throat/chamber chamber_temperature_75=3550; %From braeunig chart!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level R_75=8314/13.5; %Gas Molecular Weigh from braeunig chart!!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level cstar_75=sqrt(((2*k_75)/(k_75+1))*(R_75*chamber_temperature_75)); %m/s throat_area_75=((mdot_second/2/chamber_pressure_75/k_75)*sqrt(k_75*R_75*chamb er_temperature_75))/sqrt((2/(k_75+1))^((k_75+1)/(k_75-1))); %m^2 exit_area_75=throat_area_75*nozzle_ratio_75; exit_diameter_75=2*sqrt(exit_area_75/pi);

%Print Calculated Values: fprintf('Long March 5:\n\n'); fprintf('Boosters:\n\nSea Level Isp: %.2f seconds\nVacuum Isp: %.2f seconds\nc*: %2.f meters/second\nSea Level V2: %.5f meters/second\nVacuum V2: 93 %.5f meters/second\nExpansion Ratio: %i:1\nThroat Area: %.4f meters squared\nNozzle Area: %.4f meters squared\nExit Diameter: %.5f meters\nInternal Chamber Pressure: %i MPa\n\n',Isp_sea_level_booster_lm5,Isp_vacuum_booster_lm5,cstar_100,c_sea_lev el_booster,c_vacuum_booster,nozzle_ratio_100,throat_area_100,exit_area_100,ex it_diameter_100,chamber_pressure_100/(10^6)); fprintf('First Stage:\n\nSea Level Isp: %.2f seconds\nVacuum Isp: %.2f seconds\nc*: %2.f meters/second\nSea Level V2: %.5f meters/second\nVacuum V2: %.5f meters/second\nExpansion Ratio: %i:1\nThroat Area: %.4f meters squared\nNozzle Area: %.4f meters squared\nExit Diameter: %.5f meters\nInternal Chamber Pressure: %.1f MPa\n\n',Isp_sea_level_first,Isp_vacuum_first,cstar_77,c_sea_level_first,c_va cuum_first,nozzle_ratio_77,throat_area_77,exit_area_77,exit_diameter_77,chamb er_pressure_77/(10^6)); fprintf('Second Stage:\n\nVacuum Isp: %.2f seconds\nc*: %2.f meters/second\nVacuum V2: %.5f meters/second\nExpansion Ratio: %i:1\nThroat Area: %.4f meters squared\nNozzle Area: %.4f meters squared\nExit Diameter: %.5f meters\nInternal Chamber Pressure: %.3f MPa\n\n',Isp_vacuum_second,cstar_75,c_vacuum_second,nozzle_ratio_75,throat_ar ea_75,exit_area_75,exit_diameter_75,chamber_pressure_75/(10^6));

%% LM 6 gross_mass=103; %metric ton g=9.81; %m/s2

%First Stage (1 engine) % length_booster=26.28; %m diameter_first=3.35; %m sea_level_thrust_first=1200; %kN per engine vacuum_thrust_first=1360; %kN per engine gross_mass_first=83.53; %metric ton per booster empty_mass_first=7.53; %metric ton per booster propellant_mass_first=76; %metric ton per booster burn_time_first=155; %s isp_first=(300+335)/2; %s % burnout_velocity_booster=(2.9+3.29)/2; %km/s

%Second Stage (1 engine) length_second=8; %m diameter_second=2.25; %m sea_level_thrust_second=180; %kN each %vacuum_thrust_second=700; %kN each gross_mass_second=16.49; %metric ton empty_mass_second=1.49; %metric ton propellant_mass_second=15; %metric ton burn_time_second=290; %s isp_second=335; %s % burnout_velocity_second=(3.04+4.2)/2; %km/s

%Third Stage (2 engines) % length_third=12; %m diameter_third=2.25; %m sea_level_thrust_third=4; %kN each 94 % % gross_mass_third=26; %metric ton % % empty_mass_third=3.1; %metric ton % % propellant_mass_third=22.9; %metric ton burn_time_third=780; %s isp_third=285; %s % burnout_velocity_third=4.33; %km/s

%Payload Fairing length_payload=6; %m diameter_payload=2.6; %m % gross_mass_payload_fairing=63.4; %metric ton gross_mass_payload_sso=1; %metric ton

%Mass Flow Rates mdot_first=propellant_mass_first*1000/burn_time_first; %kg/sec mdot_second=propellant_mass_second*1000/burn_time_second; %kg/sec % mdot_third=propellant_mass_third*1000/burn_time_third; %kg/sec

%Specific Impulse Verification Isp_sea_level_first_lm6=sea_level_thrust_first*1000/(mdot_first*g); Isp_vacuum_first_lm6=vacuum_thrust_first*1000/(mdot_first*g); Isp_sea_level_second_lm6=sea_level_thrust_second*1000/(mdot_second*g); %Isp_sea_level_third=4*sea_level_thrust_third*1000/(mdot_third*g);

%Effective Exhaust Velocity c_sea_level_first=sea_level_thrust_first*1000/mdot_first; %m/s for the first stage c_vacuum_first=vacuum_thrust_first*1000/mdot_first; %m/s for the first stage c_sea_level_second=sea_level_thrust_second*1000/mdot_second; %m/s for the second stage at sea level %c_sea_level_third=4*sea_level_thrust_third*1000/mdot_third; %m/s for the third stage

%Delta V mi_first=gross_mass_first*1000; mf_first=(gross_mass_first-propellant_mass_first)*1000; deltav_sea_level_first_lm6=c_sea_level_first*log(mi_first/mf_first); %Delta V first at sea level (m/s) mi_first=gross_mass_first*1000; mf_first=(gross_mass_first-propellant_mass_first)*1000; deltav_vacuum_first_lm6=c_vacuum_first*log(mi_first/mf_first); %Delta V first in vacuum (m/s)

% %Propellant Mass Ratios % mf_first=gross_mass-propellant_mass_first; % xi_first=(gross_mass-mf_first)/gross_mass; % % mi_second=mf_first-empty_mass_first; % mf_second=mi_second-propellant_mass_second; % xi_first=(mi_second-mf_second)/mi_second;

% mi_third=mf_second-empty_mass_second; % mf_third=mi_third-propellant_mass_third; 95 % xi_third=(mi_third-mf_third)/mi_third; % % xi_overall=(gross_mass-mf_third)/gross_mass;

%Exit Area, c*, throat area for Boosters (YF-100 Engine) nozzle_ratio_100=35; %According to Wikipedia!!!!!!!!! k_100=1.213; %From braeunig chart!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level chamber_pressure_100=18e6; %According to Wikipedia!!!!!!! pressure_ratio_100=(2/(k_100+1))^(k_100/(k_100+1)); %throat/chamber chamber_temperature_100=3670; %From braeunig chart!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level R_100=8314/22.2; %Gas Molecular Weigh from braeunig chart!!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level cstar_100=sqrt(((2*k_100)/(k_100+1))*(R_100*chamber_temperature_100)); %m/s throat_area_100=((mdot_first/chamber_pressure_100/k_100)*sqrt(k_100*R_100*cha mber_temperature_100))/sqrt((2/(k_100+1))^((k_100+1)/(k_100-1))); %m^2 exit_area_100=throat_area_100*nozzle_ratio_100; exit_diameter_100=2*sqrt(exit_area_100/pi);

% M1=1; % Tt=(pressure_ratio_100*chamber_pressure_100)*cstar_100/R_100; % T2=Tt*(cstar_100/c_sea_level_first)^(k_100-1); % M2=c_sea_level_first/sqrt(k_100*R_100*T2); % nozzle_ratio_100=(M1/M2)*(((1+(((k_100- 1)/2)*M2^2))/((k_100+1)/2))^((k_100+1)/(k_100-1))) % throat_area_100=((mdot_first/2/chamber_pressure_100/k_100)*sqrt(k_100*R_100*c hamber_temperature_100))/sqrt((2/(k_100+1))^((k_100+1)/(k_100-1))); %m^2 % exit_area_100=throat_area_100*nozzle_ratio_100; % exit_diameter_100=sqrt(exit_area_100/pi)

%Exit Area, c*, throat area for First Stage (YF-115 Engine) M1=1; k_115=1.215; %From braeunig chart!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level R_115=8314/22.1; %Gas Molecular Weigh from braeunig chart!!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level chamber_pressure_115=12e6; %According to Wikipedia!!!!!!! pressure_ratio_115=(2/(k_115+1))^(k_115/(k_115+1)); %throat/chamber chamber_temperature_115=3625; %From braeunig chart!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level cstar_115=sqrt(((2*k_115)/(k_115+1))*(R_115*chamber_temperature_115)); %m/s Tt=(pressure_ratio_115*chamber_pressure_115)*cstar_115/R_115; T2=Tt*(cstar_115/c_sea_level_second)^(k_115-1); M2=c_sea_level_second/sqrt(k_115*R_115*T2); nozzle_ratio_115=(M1/M2)*(((1+(((k_115- 1)/2)*M2^2))/((k_115+1)/2))^((k_115+1)/(k_115-1))); throat_area_115=((mdot_second/2/chamber_pressure_115/k_115)*sqrt(k_115*R_115* chamber_temperature_115))/sqrt((2/(k_115+1))^((k_115+1)/(k_115-1))); %m^2 exit_area_115=throat_area_115*nozzle_ratio_115; exit_diameter_115=2*sqrt(exit_area_115/pi);

% %Exit Area, c*, throat area for Third Stage (4 YF-85 Engines) % M1=1; 96 % k_1A=1.215; %From braeunig chart!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level % R_115=8314/22.1; %Gas Molecular Weigh from braeunig chart!!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level % chamber_pressure_115=12e6; %According to Wikipedia!!!!!!! % pressure_ratio_115=(2/(k_115+1))^(k_115/(k_115+1)); %throat/chamber % chamber_temperature_115=3625; %From braeunig chart!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level % cstar_115=sqrt(((2*k_115)/(k_115+1))*(R_115*chamber_temperature_115)); %m/s % Tt=(pressure_ratio_115*chamber_pressure_115)*cstar_115/R_115; % T2=Tt*(cstar_115/c_sea_level_second)^(k_115-1); % M2=c_sea_level_second/sqrt(k_115*R_115*T2); % nozzle_ratio=(M1/M2)*(((1+(((k_115- 1)/2)*M2^2))/((k_115+1)/2))^((k_115+1)/(k_115-1))); % throat_area_115=((mdot_first/2/chamber_pressure_115/k_115)*sqrt(k_115*R_115*c hamber_temperature_115))/sqrt((2/(k_115+1))^((k_115+1)/(k_115-1))); %m^2 % exit_area_77=throat_area_77*nozzle_ratio_77; % exit_diameter_77=sqrt(exit_area_77/pi);

%Print Calculated Values: fprintf('\n\nLong March 6:\n\n'); fprintf('First Stage:\n\nSea Level Isp: %.2f seconds\nVacuum Isp: %.2f seconds\nc*: %.2f meters/second\nSea Level V2: %.3f meters/second\nVacuum V2: %.3f meters/second\nExpansion Ratio: %.3f:1\nThroat Area: %.4f meters squared\nNozzle Area: %.4f meters squared\nExit Diameter: %.5f meters\nInternal Chamber Pressure: %i MPa\n\n',Isp_sea_level_first,Isp_vacuum_first,cstar_100,c_sea_level_first,c_v acuum_first,nozzle_ratio_100,throat_area_100,exit_area_100,exit_diameter_100, chamber_pressure_100/(10^6)); fprintf('Second Stage:\n\nSea Level Isp: %.2f seconds\nc*: %.2f meters/second\nSea Level V2: %.3f meters/second\nExpansion Ratio: %.3f:1\nThroat Area: %.4f meters squared\nNozzle Area: %.4f meters squared\nExit Diameter: %.5f meters\nInternal Chamber Pressure: %.1f MPa\n\n',Isp_sea_level_second,cstar_115,c_sea_level_second,nozzle_ratio_115,t hroat_area_115,exit_area_115,exit_diameter_115,chamber_pressure_115/(10^6)); % fprintf('Second Stage:\n\nVacuum Isp: %.2f seconds\nc*: %2.f meters/second\nVacuum V2: %.5f meters/second\nExpansion Ratio: %i:1\nThroat Area: %.4f meters squared\nNozzle Area: %.4f meters squared\nExit Diameter: %.5f meters\nInternal Chamber Pressure: %.3f MPa\n\n',Isp_vacuum_second,cstar_75,c_vacuum_second,nozzle_ratio_75,throat_ar ea_75,exit_area_75,exit_diameter_75,chamber_pressure_75/(10^6));

%% LM 7 gross_mass=594; %metric ton g=9.81; %m/s2

%Boosters (4 engines) length_booster=26.28; %m diameter_booster=2.25; %m sea_level_thrust_booster=1200; %kN per engine vacuum_thrust_booster=1360; %kN per engine gross_mass_booster=81.5; %metric ton per booster empty_mass_booster=6; %metric ton per booster propellant_mass_booster=77.5; %metric ton per booster 97 burn_time_booster=155; %s isp_booster=(300+335)/2; %s % burnout_velocity_booster=(2.9+3.29)/2; %km/s

%First Stage (2 engines) length_first=26.28; %m diameter_first=3.35; %m sea_level_thrust_first=1200; %kN each vacuum_thrust_first=1360; %kN each gross_mass_first=186.5; %metric ton empty_mass_first=12.5; %metric ton propellant_mass_first=174; %metric ton burn_time_first=180; %s isp_first=(300+335)/2; %s % burnout_velocity_first=(3.04+4.2)/2; %km/s

%Second Stage (2 engines) length_second=8; %m diameter_second=3.35; %m sea_level_thrust_second=180; %kN each gross_mass_second=70.5; %metric ton empty_mass_second=5.5; %metric ton propellant_mass_second=65; %metric ton burn_time_second=296; %s isp_second=335; %s % burnout_velocity_second=4.33; %km/s

%Upper Stage length_upper=12.38; %m diameter_upper=3; %m vacuum_thrust_upper=162; %kN each gross_mass_upper=21; %metric ton empty_mass_upper=2.8; %metric ton propellant_mass_upper=18.2; %metric ton burn_time_upper=615; %s isp_upper=438; %s % burnout_velocity_upper=4.33; %km/s

%Payload Fairing length_payload=7.5; %m diameter_payload=3.35; %m % gross_mass_payload_fairing=63.4; %metric ton gross_mass_payload_200_400=13.5; %metric ton gross_mass_payload_sso=5.5; %metric ton

%Mass Flow Rates mdot_booster=propellant_mass_booster*1000/burn_time_booster; %kg/sec mdot_first=propellant_mass_first*1000/burn_time_first; %kg/sec mdot_second=propellant_mass_second*1000/burn_time_second; %kg/sec mdot_upper=propellant_mass_upper*1000/burn_time_upper; %kg/sec

%Specific Impulse Verification Isp_sea_level_booster=sea_level_thrust_booster*1000/(mdot_booster*g); Isp_vacuum_booster=vacuum_thrust_booster*1000/(mdot_booster*g); Isp_sea_level_first=sea_level_thrust_first*1000/(mdot_first*g); %per engine 98 Isp_vacuum_first=vacuum_thrust_first*1000/(mdot_first*g); %per engine Isp_sea_level_second=4*sea_level_thrust_second*1000/(mdot_second*g); Isp_vacuum_upper=2*vacuum_thrust_upper*1000/(mdot_upper*g);

%Effective Exhaust Velocity c_sea_level_booster=sea_level_thrust_booster*1000/mdot_booster; %m/s per booster c_vacuum_booster=vacuum_thrust_booster*1000/mdot_booster; %m/s per booster c_sea_level_first=sea_level_thrust_first*1000/mdot_first; %m/s for the first stage at sea level c_vacuum_first=vacuum_thrust_first*1000/mdot_first; %m/s for the first stage in vacuum c_sea_level_second=4*sea_level_thrust_second*1000/mdot_second; %m/s for the second stage c_vacuum_upper=2*vacuum_thrust_upper*1000/mdot_upper; %m/s for the second stage

%Propellant Mass Ratios mf_booster=gross_mass-(4*propellant_mass_booster); xi_booster=(gross_mass-mf_booster)/gross_mass; mi_first=mf_booster-empty_mass_booster; mf_first=mi_first-propellant_mass_first; xi_first=(mi_first-mf_first)/mi_first; mi_second=mf_first-empty_mass_first; mf_second=mi_second-propellant_mass_second; xi_second=(mi_second-mf_second)/mi_second; mi_upper=mf_second-empty_mass_second; mf_upper=mi_upper-propellant_mass_upper; xi_upper=(mi_upper-mf_upper)/mi_upper; xi_overall=(gross_mass-mf_upper)/gross_mass;

%Delta V mi_booster=gross_mass_booster*1000; mf_booster=(gross_mass_booster-propellant_mass_booster)*1000; deltav_sea_level_booster=c_sea_level_booster*log(mi_booster/mf_booster); %Delta V booster at sea level (m/s) mi_booster=gross_mass_booster*1000; mf_booster=(gross_mass_booster-propellant_mass_booster)*1000; deltav_vacuum_booster=c_vacuum_booster*log(mi_booster/mf_booster); %Delta V booster in vacuum (m/s) mi_first=gross_mass_first*1000; mf_first=(gross_mass_first-propellant_mass_first)*1000; deltav_sea_level_first=c_sea_level_first*log(mi_first/mf_first); %Delta V first at sea level (m/s) mi_first=gross_mass_first*1000; mf_first=(gross_mass_first-propellant_mass_first)*1000;

99 deltav_vacuum_first=c_vacuum_first*log(mi_first/mf_first); %Delta V first in vacuum (m/s)

%Exit Area, c*, throat area for Boosters (YF-100 Engine) nozzle_ratio_100=35; %According to Wikipedia!!!!!!!!! k_100=1.213; %From braeunig chart!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level chamber_pressure_100=18e6; %According to Wikipedia!!!!!!! pressure_ratio_100=(2/(k_100+1))^(k_100/(k_100+1)); %throat/chamber chamber_temperature_100=3670; %From braeunig chart!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level R_100=8314/22.2; %Gas Molecular Weigh from braeunig chart!!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level cstar_100=sqrt(((2*k_100)/(k_100+1))*(R_100*chamber_temperature_100)); %m/s throat_area_100=((mdot_booster/2/chamber_pressure_100/k_100)*sqrt(k_100*R_100 *chamber_temperature_100))/sqrt((2/(k_100+1))^((k_100+1)/(k_100-1))); %m^2 exit_area_100=throat_area_100*nozzle_ratio_100; exit_diameter_100=2*sqrt(exit_area_100/pi);

%Exit Area, c*, throat area for First Stage (YF-100 Engine) nozzle_ratio_100=35; %According to Wikipedia!!!!!!!!! k_100=1.213; %From braeunig chart!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level chamber_pressure_100=18e6; %According to Wikipedia!!!!!!! pressure_ratio_100=(2/(k_100+1))^(k_100/(k_100+1)); %throat/chamber chamber_temperature_100=3670; %From braeunig chart!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level R_100=8314/22.2; %Gas Molecular Weigh from braeunig chart!!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level cstar_100=sqrt(((2*k_100)/(k_100+1))*(R_100*chamber_temperature_100)); %m/s throat_area_100=((mdot_first/2/chamber_pressure_100/k_100)*sqrt(k_100*R_100*c hamber_temperature_100))/sqrt((2/(k_100+1))^((k_100+1)/(k_100-1))); %m^2 exit_area_100=throat_area_100*nozzle_ratio_100; exit_diameter_100=2*sqrt(exit_area_100/pi);

%Exit Area, c*, throat area for Second Stage (YF-115 Engine) M1=1; k_115=1.215; %From braeunig chart!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level R_115=8314/22.1; %Gas Molecular Weigh from braeunig chart!!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level chamber_pressure_115=12e6; %According to Wikipedia!!!!!!! pressure_ratio_115=(2/(k_115+1))^(k_115/(k_115+1)); %throat/chamber chamber_temperature_115=3625; %From braeunig chart!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level cstar_115=sqrt(((2*k_115)/(k_115+1))*(R_115*chamber_temperature_115)); %m/s Tt=(pressure_ratio_115*chamber_pressure_115)*cstar_115/R_115; T2=Tt*(cstar_115/c_sea_level_second)^(k_115-1); M2=c_sea_level_second/sqrt(k_115*R_115*T2); nozzle_ratio_115=(M1/M2)*(((1+(((k_115- 1)/2)*M2^2))/((k_115+1)/2))^((k_115+1)/(k_115-1))); throat_area_115=((mdot_second/2/chamber_pressure_115/k_115)*sqrt(k_115*R_115* chamber_temperature_115))/sqrt((2/(k_115+1))^((k_115+1)/(k_115-1))); %m^2 exit_area_115=throat_area_115*nozzle_ratio_115; exit_diameter_115=2*sqrt(exit_area_115/pi);

100 %Exit Area, c*, throat area for Upper Stage (YF-75 Engine) nozzle_ratio_75=80; %According to Wikipedia!!!!!!!!! k_75=1.198; %From braeunig chart!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level chamber_pressure_75=4.068*(10^6); %According to Wikipedia!!!!!!! pressure_ratio_75=(2/(k_75+1))^(k_75/(k_75+1)); %throat/chamber chamber_temperature_75=3550; %From braeunig chart!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level R_75=8314/13.5; %Gas Molecular Weigh from braeunig chart!!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level cstar_75=sqrt(((2*k_75)/(k_75+1))*(R_75*chamber_temperature_75)); %m/s throat_area_75=((mdot_second/2/chamber_pressure_75/k_75)*sqrt(k_75*R_75*chamb er_temperature_75))/sqrt((2/(k_75+1))^((k_75+1)/(k_75-1))); %m^2 exit_area_75=throat_area_75*nozzle_ratio_75; exit_diameter_75=2*sqrt(exit_area_75/pi);

%Print Calculated Values: fprintf('\nLong March 7:\n\n'); fprintf('Boosters:\n\nSea Level Isp: %.2f seconds\nVacuum Isp: %.2f seconds\nc*: %2.f meters/second\nSea Level V2: %.5f meters/second\nVacuum V2: %.5f meters/second\nExpansion Ratio: %i:1\nThroat Area: %.4f meters squared\nNozzle Area: %.4f meters squared\nExit Diameter: %.5f meters\nInternal Chamber Pressure: %i MPa\n\n',Isp_sea_level_booster,Isp_vacuum_booster,cstar_100,c_sea_level_boost er,c_vacuum_booster,nozzle_ratio_100,throat_area_100,exit_area_100,exit_diame ter_100,chamber_pressure_100/(10^6)); fprintf('First Stage:\n\nSea Level Isp: %.2f seconds\nVacuum Isp: %.2f seconds\nc*: %2.f meters/second\nSea Level V2: %.5f meters/second\nVacuum V2: %.5f meters/second\nExpansion Ratio: %i:1\nThroat Area: %.4f meters squared\nNozzle Area: %.4f meters squared\nExit Diameter: %.5f meters\nInternal Chamber Pressure: %.1f MPa\n\n',Isp_sea_level_first,Isp_vacuum_first,cstar_100,c_sea_level_first,c_v acuum_first,nozzle_ratio_100,throat_area_100,exit_area_100,exit_diameter_100, chamber_pressure_100/(10^6)); fprintf('Second Stage:\n\nSea Level Isp: %.2f seconds\nc*: %2.f meters/second\nSea Level V2: %.5f meters/second\nExpansion Ratio: %i:1\nThroat Area: %.4f meters squared\nNozzle Area: %.4f meters squared\nExit Diameter: %.5f meters\nInternal Chamber Pressure: %.3f MPa\n\n',Isp_sea_level_second,cstar_115,c_sea_level_second,nozzle_ratio_115,t hroat_area_115,exit_area_115,exit_diameter_115,chamber_pressure_115/(10^6)); fprintf('Upper Stage:\n\nVacuum Isp: %.2f seconds\nc*: %2.f meters/second\nVacuum V2: %.5f meters/second\nExpansion Ratio: %i:1\nThroat Area: %.4f meters squared\nNozzle Area: %.4f meters squared\nExit Diameter: %.5f meters\nInternal Chamber Pressure: %.3f MPa\n\n',Isp_vacuum_upper,cstar_75,c_vacuum_upper,nozzle_ratio_75,throat_area _75,exit_area_75,exit_diameter_75,chamber_pressure_75/(10^6));

% Isp Plots figure; hold on; isp_booster_lm5=[Isp_sea_level_booster_lm5,Isp_vacuum_booster_lm5]; dv_booster_lm5=[deltav_sea_level_booster_lm5,deltav_vacuum_booster_lm5]; isp_first_lm6=[Isp_sea_level_first_lm6,Isp_vacuum_first_lm6]; 101 dv_first_lm6=[deltav_sea_level_first_lm6,deltav_vacuum_first_lm6]; isp_booster=[Isp_sea_level_booster,Isp_vacuum_booster]; isp_first=[Isp_sea_level_first,Isp_vacuum_first]; dv_booster=[deltav_sea_level_booster,deltav_vacuum_booster]; dv_first=[deltav_sea_level_first,deltav_vacuum_first]; plot(isp_booster_lm5,dv_booster_lm5,'-c',isp_first_lm6,dv_first_lm6,'- r',isp_booster,dv_booster,'-b',isp_first,dv_first,'-k'); legend('LM 5 Booster: t=180s, m_p=135 MT','LM 6 First Stage: t=155s, m_p=76 MT','LM 7 Booster: t=155s, m_p=77.5 MT','LM 7 First Stage: t=180s, m_p=174 MT'); xlabel('Specific Impulse (s)'); ylabel('Delta V (m/s)'); title('Delta V vs. Specific Impulse for YF-100 Engine (Independent of Full System)'); plot(Isp_sea_level_booster,deltav_sea_level_booster,'xb') plot(Isp_vacuum_booster,deltav_vacuum_booster,'xb') plot(Isp_sea_level_first,deltav_sea_level_first,'xk') plot(Isp_vacuum_first,deltav_vacuum_first,'xk') plot(Isp_sea_level_first_lm6,deltav_sea_level_first_lm6,'xr') plot(Isp_vacuum_first_lm6,deltav_vacuum_first_lm6,'xr') plot(Isp_sea_level_booster_lm5,deltav_sea_level_booster_lm5,'xc') plot(Isp_vacuum_booster_lm5,deltav_vacuum_booster_lm5,'xc')

102

Appendix B MATLAB: Change in Velocity and Specific Impulse Calculations

103 %Kayleigh Gordon %MS Thesis %4/17/18 %Delta V vs. Specific Impulse Plots for YF-100 Engine g=9.81;

%% Characteristic Velocity chamber_temperature_100=3670; %From braeunig chart!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level R_100=8314/22.2; %Gas Molecular Weight from braeunig chart!!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level k_100=1.213; %From braeunig chart!!! For a chamber pressure of 18MPa and mixture ratio of 2.38 at sea level cstar=sqrt(k_100*R_100*chamber_temperature_100)/(k_100*sqrt((2/(k_100+1))^((k _100+1)/(k_100-1)))); chamber_pressure_100=18e6; nozzle_ratio_100=48; %% LM 5

%Boosters (8 engines) sea_level_thrust_booster=1200; %kN per engine vacuum_thrust_booster=1360; %kN per engine gross_mass_booster=165/2; %metric ton per engine propellant_mass_booster=152/2; %metric ton per engine burn_time_booster=180; %s

%Mass Flow Rates mdot_booster=propellant_mass_booster*1000/burn_time_booster; %kg/sec

%Specific Impulse Verification Isp_sea_level_booster_lm5=sea_level_thrust_booster*1000/(mdot_booster*g); Isp_vacuum_booster_lm5=vacuum_thrust_booster*1000/(mdot_booster*g);

%Effective Exhaust Velocity c_sea_level_booster=sea_level_thrust_booster*1000/mdot_booster; %m/s per booster engine c_vacuum_booster=vacuum_thrust_booster*1000/mdot_booster; %m/s per booster engine

%Thrust Coefficient cf_sea_level_booster=c_sea_level_booster/cstar; cf_vacuum_booster=c_vacuum_booster/cstar;

%Throat Area and Exit Diameter throat_area_100=((mdot_booster/2/chamber_pressure_100/k_100)*sqrt(k_100*R_100 *chamber_temperature_100))/sqrt((2/(k_100+1))^((k_100+1)/(k_100-1))); %m^2 exit_area_100=throat_area_100*nozzle_ratio_100; exit_diameter_100=2*sqrt(exit_area_100/pi);

%Delta V mi_booster=gross_mass_booster*1000; mf_booster1=(gross_mass_booster-propellant_mass_booster)*1000; 104 deltav_sea_level_booster_lm5=c_sea_level_booster*log(mi_booster/mf_booster1); %Delta V booster at sea level (m/s) mi_booster=gross_mass_booster*1000; mf_booster2=(gross_mass_booster-propellant_mass_booster)*1000; deltav_vacuum_booster_lm5=c_vacuum_booster*log(mi_booster/mf_booster2); %Delta V booster in vacuum (m/s)

%% LM 6

%First Stage (1 engine) sea_level_thrust_first=1200; %kN per engine vacuum_thrust_first=1360; %kN per engine gross_mass_first=83.53; %metric ton per booster propellant_mass_first=76; %metric ton per booster burn_time_first=180; %s

%Mass Flow Rates mdot_first=propellant_mass_first*1000/burn_time_first; %kg/sec

%Specific Impulse Verification Isp_sea_level_first_lm6=sea_level_thrust_first*1000/(mdot_first*g); Isp_vacuum_first_lm6=vacuum_thrust_first*1000/(mdot_first*g);

%Effective Exhaust Velocity c_sea_level_first=sea_level_thrust_first*1000/mdot_first; %m/s for the first stage c_vacuum_first=vacuum_thrust_first*1000/mdot_first; %m/s for the first stage

%Thrust Coefficient cf_sea_level_first=c_sea_level_first/cstar; cf_vacuum_first=c_vacuum_first/cstar;

%Throat Area and Exit Diameter throat_area_100=((mdot_first/2/chamber_pressure_100/k_100)*sqrt(k_100*R_100*c hamber_temperature_100))/sqrt((2/(k_100+1))^((k_100+1)/(k_100-1))); %m^2 exit_area_100=throat_area_100*nozzle_ratio_100; exit_diameter_100=2*sqrt(exit_area_100/pi);

%Delta V mi_first=gross_mass_first*1000; mf_first3=(gross_mass_first-propellant_mass_first)*1000; deltav_sea_level_first_lm6=c_sea_level_first*log(mi_first/mf_first3); %Delta V first at sea level (m/s) mi_first=gross_mass_first*1000; mf_first4=(gross_mass_first-propellant_mass_first)*1000; deltav_vacuum_first_lm6=c_vacuum_first*log(mi_first/mf_first4); %Delta V first in vacuum (m/s)

%% LM 7

%Boosters (4 engines) 105 sea_level_thrust_booster=1200; %kN per engine vacuum_thrust_booster=1360; %kN per engine gross_mass_booster=81.5; %metric ton per booster propellant_mass_booster=77.5; %metric ton per booster burn_time_booster=155; %s

%First Stage (2 engines) sea_level_thrust_first=1200; %kN each vacuum_thrust_first=1360; %kN each gross_mass_first=186.5/2; %metric ton propellant_mass_first=174/2; %metric ton burn_time_first=180; %s

%Mass Flow Rates mdot_booster=propellant_mass_booster*1000/burn_time_booster; %kg/sec mdot_first=propellant_mass_first*1000/burn_time_first; %kg/sec

%Specific Impulse Verification Isp_sea_level_booster=sea_level_thrust_booster*1000/(mdot_booster*g); Isp_vacuum_booster=vacuum_thrust_booster*1000/(mdot_booster*g); Isp_sea_level_first=sea_level_thrust_first*1000/(mdot_first*g); %per engine Isp_vacuum_first=vacuum_thrust_first*1000/(mdot_first*g); %per engine

%Effective Exhaust Velocity c_sea_level_booster=sea_level_thrust_booster*1000/mdot_booster; %m/s per booster c_vacuum_booster=vacuum_thrust_booster*1000/mdot_booster; %m/s per booster c_sea_level_first=sea_level_thrust_first*1000/mdot_first; %m/s for the first stage at sea level c_vacuum_first=vacuum_thrust_first*1000/mdot_first; %m/s for the first stage in vacuum

%Thrust Coefficient cf_sea_level_booster=c_sea_level_booster/cstar; cf_vaccum_booster=c_vacuum_booster/cstar; cf_sea_level_first=c_sea_level_first/cstar; cf_vacuum_first=c_vacuum_first/cstar;

%Throat Area and Exit Diameter throat_area_100=((mdot_first/2/chamber_pressure_100/k_100)*sqrt(k_100*R_100*c hamber_temperature_100))/sqrt((2/(k_100+1))^((k_100+1)/(k_100-1))); %m^2 exit_area_100=throat_area_100*nozzle_ratio_100; exit_diameter_100=2*sqrt(exit_area_100/pi);

%Delta V mi_booster=gross_mass_booster*1000; mf_booster5=(gross_mass_booster-propellant_mass_booster)*1000; deltav_sea_level_booster=c_sea_level_booster*log(mi_booster/mf_booster5); %Delta V booster at sea level (m/s) mi_booster=gross_mass_booster*1000; 106 mf_booster6=(gross_mass_booster-propellant_mass_booster)*1000; deltav_vacuum_booster=c_vacuum_booster*log(mi_booster/mf_booster6); %Delta V booster in vacuum (m/s) mi_first=gross_mass_first*1000; mf_first7=(gross_mass_first-propellant_mass_first)*1000; deltav_sea_level_first=c_sea_level_first*log(mi_first/mf_first7); %Delta V first at sea level (m/s) mi_first=gross_mass_first*1000; mf_first8=(gross_mass_first-propellant_mass_first)*1000; deltav_vacuum_first=c_vacuum_first*log(mi_first/mf_first8); %Delta V first in vacuum (m/s)

%% Delta V Estimate isplow=300; %s isphigh=335; %s sea_level_thrust=1200; %kN per engine vacuum_thrust=1360; mdotlow=(sea_level_thrust*1000)/(isplow*g); mdothigh=(vacuum_thrust*1000)/(isphigh*g); c_sea_level=sea_level_thrust*1000/mdotlow; %m/s per booster c_vacuum=vacuum_thrust*1000/mdothigh; burntime=mean([155 180]); propellant_mass=mean([mdotlow mdothigh])*burntime; % propellant_mass2=0.4038*1000*burntime mf=mean([mf_booster1, mf_booster2, mf_booster5, mf_booster6, mf_first3, mf_first4, mf_first7, mf_first8]); deltav_sea_level=c_sea_level*log((mf+propellant_mass)/mf); deltav_vacuum=c_vacuum*log((mf+propellant_mass)/mf);

%% Isp Plots figure; hold on; isp_booster_lm5=[Isp_sea_level_booster_lm5,Isp_vacuum_booster_lm5]; dv_booster_lm5=[deltav_sea_level_booster_lm5,deltav_vacuum_booster_lm5]; isp_first_lm6=[Isp_sea_level_first_lm6,Isp_vacuum_first_lm6]; dv_first_lm6=[deltav_sea_level_first_lm6,deltav_vacuum_first_lm6]; isp_booster=[Isp_sea_level_booster,Isp_vacuum_booster]; isp_first=[Isp_sea_level_first,Isp_vacuum_first]; dv_booster=[deltav_sea_level_booster,deltav_vacuum_booster]; dv_first=[deltav_sea_level_first,deltav_vacuum_first]; plot(isp_booster_lm5,dv_booster_lm5,'-c','Linewidth',3); plot(isp_first_lm6,dv_first_lm6,'-r','Linewidth',3); plot(isp_booster,dv_booster,'-b','Linewidth',3); plot(isp_first,dv_first,'-k','Linewidth',3); %leg=legend('LM 5 Booster: t=180s, m_f=67.5 MT','LM 6 First Stage: t=155s, m_f=76.0 MT','LM 7 Booster: t=155s, m_f=77.5 MT','LM 7 First Stage: t=180s, m_f=87.0 MT'); leg=legend('LM 5 Booster','LM 6 First Stage','LM 7 Booster','LM 7 First Stage'); set(leg,'Location','southeast') s=leg.FontSize; 107 leg.FontSize=24; xlbl=xlabel('Specific Impulse (s)'); s=xlbl.FontSize; xlbl.FontSize=28; xlbl.FontWeight='bold'; ylbl=ylabel('Delta V (m/s)'); s=ylbl.FontSize; ylbl.FontSize=28; ylbl.FontWeight='bold'; ttl=title('Delta V vs. Specific Impulse for YF-100 Engine (Independent of Full System)'); s=ttl.FontSize; ttl.FontSize=32; ttl.FontWeight='bold'; plot(Isp_sea_level_booster,deltav_sea_level_booster,'.b','Linewidth',3,'Marke rSize',25) plot(Isp_vacuum_booster,deltav_vacuum_booster,'.b','Linewidth',3,'MarkerSize' ,25) plot(Isp_sea_level_first,deltav_sea_level_first,'.k','Linewidth',3,'MarkerSiz e',25) plot(Isp_vacuum_first,deltav_vacuum_first,'.k','Linewidth',3,'MarkerSize',25) plot(Isp_sea_level_first_lm6,deltav_sea_level_first_lm6,'.r','Linewidth',3,'M arkerSize',25) plot(Isp_vacuum_first_lm6,deltav_vacuum_first_lm6,'.r','Linewidth',3,'MarkerS ize',25) plot(Isp_sea_level_booster_lm5,deltav_sea_level_booster_lm5,'.c','Linewidth', 3,'MarkerSize',25) plot(Isp_vacuum_booster_lm5,deltav_vacuum_booster_lm5,'.c','Linewidth',3,'Mar kerSize',25) axis([240 350 6500 9000]); a=line([300 300],[1000 10000],'LineStyle','--','color',[.5,.5,.5]); b=line([335 335],[1000 10000],'LineStyle','--','color',[.5,.5,.5]); c=[a b]; for i=deltav_sea_level:50:deltav_vacuum line([300 335],[i i],'LineStyle',':','LineWidth',1.5,'color',[.5,.5,.5]); end d=line([240 400],[deltav_sea_level deltav_sea_level],'LineStyle','-- ','color',[.5,.5,.5]); e=line([240 400],[deltav_vacuum deltav_vacuum],'LineStyle','-- ','color',[.5,.5,.5]); t=text(303, (mean([deltav_sea_level deltav_vacuum])+60),'Expected Delta V'); s=t.FontSize; t.FontSize=26; t.FontWeight='bold'; t.FontAngle='italic'; t=text(303, (mean([deltav_sea_level deltav_vacuum])-60),'and Isp Range'); s=t.FontSize; t.FontSize=26; t.FontWeight='bold'; t.FontAngle='italic';

108

Appendix C MATLAB: YF-100 Design Calculations

109 %Kayleigh Gordon %Master's Thesis YF-100 Characteristic Calculations %YF-100 clear clc close all %% Design Notes 1

%Givens g=9.81; %gravity Isp=300; %Sea level published value dV=7.4506e3; %Sea level calculated value amin=dV/167.5/9.81; %Minimum acceleration in g (based on sea level delta v) amax=8.3198e3/167.5/9.81; %Maximum acceleration in g (based on vacuum delta v)

F=1200e3; %Thrust for sea level r=2.38; %2.6+/-1-% is published, but 2.38 falls on Braeunig charts which is within the +/-10% T1=3670; %Chamber temperature k=1.213; %Specific heat ratio M=22.2; p1=18e6; %published combustion chamber pressure

%Initial Calculations mdot=F/Isp/g; %mass flow rate cf=1.8; %based on =10 plot for given nozzle ratio not calculated value cstar=Isp*g/cf; At=mdot*cstar/p1; %Throat Area Dt=sqrt(4*At/pi()); %Throat Diameter

%Length of Combustion Chamber lstar=1; %assumed from notes AcAt=2.89; %Ac/At ratio assumed from notes Lc=lstar/AcAt; %length of comubstion chamber

%Combustion Chamber geometry Ac=At*2.89; %Area of combustion chamber Vc=Ac*Lc; %Volume of combustion chamber Dc=((4/pi())*Ac)^.5; %Diameter of combustion chamber

%Chamber Mass rhocc=8550; %density of Columbium material used for combustion chamber rc=Dc/2; %radius of combustion chamber FS=1.5; %safety factor wc=(p1*rc*FS)/(310*10^6); %chamber wall thickness mcc=pi()*Lc*rhocc*((wc+rc)^2-rc^2);%combustion chamber mass fprintf('The combustion chamber mass is %.3f kg.\n',mcc);

%Convergent Nozzle Section Mass rt=At/2; %throat radius thetacc=45; %taper angle combustion chamber

110 mcnz=(rhocc*pi()*((rc^2)-(rt^2))*wc)/tand(thetacc); %mass of the converging nozzle fprintf('The convergent nozzle section mass is %.3f kg.\n',mcnz);

%Combustion chamber mass including convergent nozzle section mc=mcc+mcnz; fprintf('The mass of the combustion chamber including the convergent nozzle section is %.3f kg.\n',mc);

%Divergent Nozzle Section Mass wnz=.25*wc; %wall thickness of the diverging nozzle rhonz=8550; %density of Columbium material used for divergent nozzle section thetanz=20; %taper angle of divergent nozzle eps=10; %epsilon assumed from research on comparable rockets ( 5) de=Dt*sqrt(48); %exit diameter re=de/2;%re/rt=3 design point - Saturn 5 area ratio ~ 10 so comparable mnz=(rhonz*pi()*((re^2)-(rt^2))*wnz)/tand(thetanz); %divergent nozzle mass fprintf('The divergent nozzle section mass is %.3f kg.\n',mnz); lnz=(re-rt)/tand(thetanz); %divergent nozzle length

%Total Engine Mass mw=(mcc+mnz+mcnz)/.40; %Total engine mass is sum of combustion chamber mass and nozzle masses divided fprintf('The total engine mass is %.3f kg.\n',mw);

%Injector Mass minj=.25*mw; %heritage data fprintf('The injector mass is %.3f kg.\n',minj);

%Ablative material mcool=.35*mw; %heritage data fprintf('The ablative cooling material mass is %.3f kg.\n',mcool);

%Feed system pressure levels dpinj=0.2*p1; %Injector pressure drop dpl=50000; %Feed line pressure drop dpdf=.5*(810*10^2); %Fuel dynamic pressure drop - 10 m/s flowspeed assumed dpdo=.5*1142*10^2; %Oxidixer dynamic pressure drop - 10 m/s flowspeed assumed Pftnk=dpinj+dpl+dpdf+p1; %Fuel tank pressure Potnk=dpinj+dpl+dpdo+p1; %Oxidizer tank pressure

Rp=1-exp(-dV/(Isp*g)); %propellant ratio mt=83.53e3; %upper limit of total mass mp=mt*Rp; %mass of propellant fprintf('The mass of the propellant is %.3f kg.\n',mp); tb=mp/mdot; %burn time

I=F*tb; %Total impulse mdotf=r*mdot/(1+r); %mass flow rate of fuel mdoto=mdot/(1+r); %mass flow rate of oxidizer - assumed from notes ~twice mdotf mf=mdotf*tb; %mass of fuel fprintf('The mass of the fuel is %.3f kg.\n',mf); 111 mo=mdoto*tb; %mass of oxidizer fprintf('The mass of the oxidizer is %.3f kg.\n',mo); ms=mt-mp; %structural mass fprintf('The mass of the structure is %.3f kg.\n',ms);

%mp=72593.856; %mass of the propellant fp=mp/(mp+ms); %propellant fraction fs=1-fp; %structural fraction rhof=810; %fuel density in kg/m3 Vf=1.1*(mf/rhof); %fuel tank volume rhoo=1142; %LOX density Vo=1.1*(mo/rhoo); %oxidizer tank volume

%RP-1 Tank Mass rhocase=2700; %kg/m3 for aluminum (density of tank material) LD=3; %assumed from literature (length to diameter ratio) sigmay=1.034214e+9; %Pa - assumed from literature (circumferential stress) epsilon=0.8; %fill factor of 80% - assumed from literature (tank volume filled by propellant) pc=p1; %(chamber pressure) mtnkrp1=(mf*3*(1+LD)*(pc/(2*sigmay))*rhocase)/((1+(3/2)*LD)*epsilon*rhof); %oxidizer tank mass fprintf('The mass of the RP-1 tank is %.3f kg.\n',mtnkrp1);

%OX Tank Mass rhocase=2700; %kg/m3 for aluminum (density of tank material) LD=3; %assumed from literature (length to diameter ratio) sigmay=1.034214e+9; %Pa - assumed from literature (circumferential stress) epsilon=0.8; %fill factor of 80% - assumed from literature (tank volume filled by propellant) pc=p1; %(chamber pressure) mtnkox=(mf*3*(1+LD)*(pc/(2*sigmay))*rhocase)/((1+(3/2)*LD)*epsilon*rhoo); %oxidizer tank mass fprintf('The mass of the LOX tank is %.3f kg.\n',mtnkox);

%New total mass mw2=mw+minj+mcool+mp+mo+mtnkrp1+mtnkox; fprintf('The total mass of the engine and tanks is %.3f kg.\n',mw2);

112

Appendix D MATLAB: Price Comparison Plots

113 %% Small Lift Launch Vehicles figure; hold on;

x=[1050 350 1200 100 580 1735]; y=[45 8.5 6 1.25 40 46]; p=polyfit(x,y,1); mdl=fitlm(x,y); r_ord_light=mdl.Rsquared.Ordinary; r_adj_light=mdl.Rsquared.Adjusted; x1=linspace(0,1800,200); y1=polyval(p,x1); plot(x1,y1,'-k','LineWidth',5,'MarkerSize',5); lm6=polyval(p,1000); plot([1050,1050],[40,50],'.-b','LineWidth',5,'MarkerSize',40) plot([350,350],[8,9],'.-r','LineWidth',5,'MarkerSize',40) plot(580,40,'+b','LineWidth',5,'MarkerSize',15) plot(100,1,'+r','LineWidth',5,'MarkerSize',15) plot(1000,lm6,'xm','LineWidth',5,'MarkerSize',25) plot([100,100],[1,1.5],'+-r','LineWidth',5,'MarkerSize',15) plot(1735,46,'+b','LineWidth',5,'MarkerSize',15) plot(1200,6,'.r','LineWidth',5,'MarkerSize',40) txt1 = 'US (SSO)'; text(1060,45,txt1,'fontweight','bold','FontName','Times New Roman','FontSize',20,'HorizontalAlignment','left') txt2 = 'US (LEO)'; text(600,40,txt2,'fontweight','bold','FontName','Times New Roman','FontSize',20,'HorizontalAlignment','left') text(1715,46,txt2,'fontweight','bold','FontName','Times New Roman','FontSize',20,'HorizontalAlignment','right') txt3 = 'Russia (SSO)'; text(370,8.5,txt3,'fontweight','bold','FontName','Times New Roman','FontSize',20,'HorizontalAlignment','left') text(1220,6,txt3,'fontweight','bold','FontName','Times New Roman','FontSize',20,'HorizontalAlignment','left') txt4 = 'Russia (LEO)'; text(120,1.25,txt4,'fontweight','bold','FontName','Times New Roman','FontSize',20,'HorizontalAlignment','left') txt5 = 'Competitive Price for Long March 6'; text(1020,25,txt5,'fontweight','bold','FontName','Times New Roman','FontSize',20,'HorizontalAlignment','left') set(gca,'FontName','Times New Roman','fontsize',18) %legend('Location','westoutside','Average Cost in US Dollars per Kilogram of Payload','US Launch Vehicles (SSO)','Russian Launch Vehicles (SSO)','US Launch Vehicles (LEO)','Russian Launch Vehicles (LEO)','Competitive Price for Long March 6'); grid on; 114 xlabel({'Payload Capacity','(kilograms)'},'fontweight','bold','FontName','Times New Roman','FontSize',45); ylabel({'Price in Millions','(US Dollars)'},'fontweight','bold','FontName','Times New Roman','FontSize',45); title('Price per Kilogram for Light Lift Launch Vehicles','fontweight','bold','FontName','Times New Roman','FontSize',50) axis([0 1800 0 55]); set(gca, 'XTickLabel', [0:length(x1):1800]); hold off;

%% Medium Lift Launch Vehicles figure; hold on; x=[15960 18810 8200 6500 10000 4000 2300 1300]; y=[48.3 153 40 190 46 62 26 38]; p=polyfit(x,y,1); mdl=fitlm(x,y); r_ord_medium=mdl.Rsquared.Ordinary; r_adj_medium=mdl.Rsquared.Adjusted; x1=linspace(0,20000,2000); y1=polyval(p,x1); plot(x1,y1,'-k','LineWidth',5,'MarkerSize',5); lm7_leo=polyval(p,13500); lm7_sso=polyval(p,5500); plot(15960,48.3,'+b','LineWidth',5,'MarkerSize',15); plot([8200 8200],[30 50],'+-r','LineWidth',5,'MarkerSize',15); plot(10000,46,'+g','LineWidth',5,'MarkerSize',15); plot(4000,62,'dg','LineWidth',4,'MarkerSize',15); plot(2300, 26,'+c','LineWidth',5,'MarkerSize',15); plot(1330,38,'.c','LineWidth',5,'MarkerSize',40); plot(13500,lm7_leo,'om','LineWidth',5,'MarkerSize',15); plot(5500,lm7_sso,'xm','LineWidth',5,'MarkerSize',25); plot(18810,153,'+b','LineWidth',5,'MarkerSize',15); plot(6500, 190,'+b','LineWidth',5,'MarkerSize',15); txt1 = 'US (LEO)'; text(16160,48.3,txt1,'fontweight','bold','FontName','Times New Roman','FontSize',20,'HorizontalAlignment','left') text(18610,153,txt1,'fontweight','bold','FontName','Times New Roman','FontSize',20,'HorizontalAlignment','right') text(6700,190,txt1,'fontweight','bold','FontName','Times New Roman','FontSize',20,'HorizontalAlignment','left') txt2 = 'Russia (LEO)'; text(8000,40,txt2,'fontweight','bold','FontName','Times New Roman','FontSize',20,'HorizontalAlignment','right') txt3 = 'India (LEO)'; text(10200,46,txt3,'fontweight','bold','FontName','Times New Roman','FontSize',20,'HorizontalAlignment','left')

115 txt4 = 'India (GTO)'; text(3800,67,txt4,'fontweight','bold','FontName','Times New Roman','FontSize',20,'HorizontalAlignment','right') txt5 = 'ESA (LEO)'; text(2500,26,txt5,'fontweight','bold','FontName','Times New Roman','FontSize',20,'HorizontalAlignment','left') txt6 = 'ESA (SSO)'; text(1530,38,txt6,'fontweight','bold','FontName','Times New Roman','FontSize',20,'HorizontalAlignment','left') txt7 = 'Competitive Price for Long March 7 (LEO)'; text(13300,(lm7_leo+5),txt7,'fontweight','bold','FontName','Times New Roman','FontSize',20,'HorizontalAlignment','right') txt8 = 'Competitive Price for Long March 7 (SSO)'; text(5700,(lm7_sso-5),txt8,'fontweight','bold','FontName','Times New Roman','FontSize',20,'HorizontalAlignment','left') set(gca,'FontName','Calibri','fontsize',18) %legend('Location','westoutside','Average Cost in US Dollars per Kilogram of Payload','US Launch Vehicles (LEO)','Russian Launch Vehicles (LEO)','Indian Launch Vehicles (LEO)','Indian Launch Vehicles (GTO)','ESA Launch Vehicle (LEO)','ESA Launch Vehicle (SSO)','Competitive Price for Long March 7 (LEO)','Competitive Price for Long March 7 (SSO)') grid on; xlabel({'Payload Capacity','(kilograms)'},'fontweight','bold','FontName','Times New Roman','FontSize',45); ylabel({'Price in Millions','(US Dollars)'},'fontweight','bold','FontName','Times New Roman','FontSize',45); title('Price per Kilogram for Medium Lift Launch Vehicles','fontweight','bold','FontName','Times New Roman','FontSize',50) axis([0 20000 0 200]); set(gca, 'XTickLabel', [0:length(x1):20000]); hold off;

%% Heavy Lift Launch Vehicles figure; hold on; x=[21000 28790 23000 63800 63800]; y=[100 435 115 90 150]; p=polyfit(x,y,1); mdl=fitlm(x,y); r_ord_heavy=mdl.Rsquared.Ordinary; r_adj_heavy=mdl.Rsquared.Adjusted; x1=linspace(20000,70000,3500); y1=polyval(p,x1); plot(x1,y1,'-k','LineWidth',5,'MarkerSize',5); lm5_leo=polyval(p,25000); lm5_gto=polyval(p,14000); 116 plot(21000,100,'+c','LineWidth',5,'MarkerSize',15); plot(28790,435,'+b','LineWidth',5,'MarkerSize',15); plot(23000,115,'+r','LineWidth',5,'MarkerSize',15); plot(63800,90,'+b','LineWidth',5,'MarkerSize',15); plot(63800,150,'+b','LineWidth',5,'MarkerSize',15); plot(25000,lm5_leo,'xm','LineWidth',5,'MarkerSize',25); txt1 = 'US (LEO)'; text(28300,435,txt1,'fontweight','bold','FontName','Times New Roman','FontSize',20,'HorizontalAlignment','right') txt2 = 'Russia (LEO)'; text(23500,115,txt2,'fontweight','bold','FontName','Times New Roman','FontSize',20,'HorizontalAlignment','left') txt5 = 'ESA (LEO)'; text(23700,85,txt5,'fontweight','bold','FontName','Times New Roman','FontSize',20,'HorizontalAlignment','center') txt4 = 'US (LEO) - Reusable'; text(58500,90,txt4,'fontweight','bold','FontName','Times New Roman','FontSize',20,'HorizontalAlignment','center') txt6 = 'US (LEO) - Expendable'; text(63800,175,txt6,'fontweight','bold','FontName','Times New Roman','FontSize',20,'HorizontalAlignment','center') txt7 = 'Competitive Price for Long March 5 (LEO)'; text(25000,225,txt7,'fontweight','bold','FontName','Times New Roman','FontSize',20,'HorizontalAlignment','left') % % txt8 = 'Competitive Price for Long March 7 (SSO)'; % text(5700,(lm7_sso-5),txt8,'fontweight','bold','FontName','Times New Roman','FontSize',20,'HorizontalAlignment','left')

set(gca,'FontName','Times New Roman','fontsize',18) %legend('Location','westoutside','Average Cost in US Dollars per Kilogram of Payload','ESA Launch Vehicle (LEO)','US Launch Vehicle (LEO)','Russian Launch Vehicle (LEO)','Competitive Price for Long March 5 (LEO)'); grid on; xlabel({'Payload Capacity','(kilograms)'},'fontweight','bold','FontName','Times New Roman','FontSize',45); ylabel({'Price in Millions','(US Dollars)'},'fontweight','bold','FontName','Times New Roman','FontSize',45); title('Price per Kilogram for Heavy Lift Launch Vehicles','fontweight','bold','FontName','Times New Roman','FontSize',50) axis([20000 70000 0 500]); set(gca, 'XTickLabel', [20000:5000:70000]); hold off;

117