report section 1 - engineering.purdue.edu
TRANSCRIPT
Project Bellerophon 1
1.0 Foreword
This report represents the culmination of an intensive spacecraft design course, A&AE 450,
undertaken by seniors during a single semester. The students perform a feasibility study for a
specified mission goal subject to certain constraints.
The entire class works as a single team to achieve this goal. They elect a Project Manager and an
Assistant Project Manager and organize into specialized groups to study (in this case)
aerothermodynamics, avionics, dynamics and control, propulsion, structures and materials, and
trajectory optimization.
The class formally meets five hours a week to provide status reports and to listen to guest
lecturers from academia and industry. They also meet informally for many hours of study.
At the end of the semester the students deliver a formal presentation of their results. Besides this
report, the class provides appendices, which provide detailed analyses of their methods and
trades studies. The trade studies in this particular report are significant and substantial.
The quality of the work in this report is consistent with the high standards of the aerospace
industry. The students who participated in this study have demonstrated that they have mastered
the fundamentals of astronautics, have learned to work efficiently as a team, and have discovered
innovative ways to achieve the goals of this project.
This project was particularly challenging because it sought to find the most economical method
to launch very small payloads (200 grams to 5 kilograms) into low-Earth orbit. Myriad
combinations of the launch architecture, propellants, and materials were considered along with
the effects of uncertainties in key parameters. While cost was very difficult to assess (in large
part because of the proprietary nature of the subject), the students managed to give meaningful
and reasoned estimates of the driving factors.
Project Bellerophon 2
Probably the most significant contribution of this work is the process the students developed to
analyze the enormous design space they consider here. While there may be debate about the cost
assessment, their method is sound and can easily be modified to accommodate additional
scenarios and different weights in the cost modifiers.
I believe this design team rose to the occasion to produce an important feasibility study. The
leadership of the Project Manager and the Assistant Project Manager as well as the outstanding
cooperation of the team members were key elements in the success of their project. They have
every right to feel proud of Project Bellerophon and I am proud of them.
Professor James M. Longuski
Purdue University
March 28, 2008
Project Bellerophon 3
Author: Alan Schwing
2.0 Introduction
2.1 Abstract Space access is limited to large corporations and governments with hundreds of millions of
dollars to spend on launch programs. Current launch vehicles are designed for these customers
who want to deliver hundreds or even thousands of kilograms into Low Earth Orbit (LEO). This
price tag is prohibitive for a small company or university with a small payload destined for
space. Project Bellerophon is an investigation into the minimum absolute cost of sending a small
payload into orbit.
Requirements for the project include preliminary development for three launch vehicles, one for
each of three payload masses: 200 g, 1 kg, and 5 kg. These vehicles must be able to achieve an
orbit with a perigee altitude of 300 km. Additionally, the chance of success must be greater than
90.00%, and greater than 99.86% assuming the launch vehicle suffers no catastrophic failures.
We investigate a wide range of launch vehicle architecture and launch methods, including launch
from a balloon, an aircraft, a rail-gun, and the ground. The study also incorporates several
propellant and material options. To understand these difficult trades, we develop a process that
involves a complex system of codes that perform first-order design for all of the possible
combinations. From this list of viable configurations, we select the launch vehicle for each
payload with the smallest cost.
In our analysis, we found that the optimal vehicle architecture remained the same for all three
payloads considered. All three vehicles have three propulsive stages and are launched from a
balloon at an altitude of 30 kilometers. A hybrid rocket engine powers the first stage and solid
motors power the second and third stages. All tanks and structural members are made from
aluminum; the nose cone is titanium. Our vehicles’ avionics are stored on the second stage and
the third stage is spin-stabilized.
Real vehicles inherently have variation in production and propellant performance. Our designs
have each undergone a Monte Carlo analysis that incorporates standard deviations on values for
inert mass, propellant mass, propellant mass flow rate, drag, thrust misalignment, and gyro drift.
Project Bellerophon 4
Author: Alan Schwing
In order to ensure that we meet the design requirement of 99.86% reliability, we ran 10,000
simulations for each of the three launch vehicles. Our results show that each vehicle has a
success rate of at least 99.99% assuming no catastrophic failures.
We define catastrophic failure as a failure in any subsystem that eliminates the possibility of
mission success. Catastrophic failure rates are predicted by looking at historical launch vehicle
performance. Most launch vehicles have high failure rates for their initial 15-20 launches. This
is part of the iterative process involved in development. For this reason, we project the following
success rates for our initial launches:
Number of Launches Failure Rate Success Rate Less than 12 40.00 % 60.00 % Less than 24 20.00 % 80.00 % 24 or greater 06.16 % 93.84 %
We determine total vehicle cost by examining each component’s individual cost. This method
incorporates historical correlations for prices and our best estimates of labor requirements for
assembly and launch. Cost and many other important parameters are included in the following
table:
Payload Mass Vehicle GLOW [kg] ∆V [m/s]
Nominal Controlled
Perigee [km] Total Cost
200.00 [g] 2,583.83 10,730 486.00 $ 3,625,196001.00 [kg] 1,745.22 9,500 366.96 $ 3,178,447005.00 [kg] 6,294.80 11,313 513.00 $ 4,672,258
We came into this project wondering if space access is attainable for a single university or small
company with a reasonably size research grant. Our results indicate that low-cost vehicles can
be designed for small payloads, but are only affordable to multiple universities or companies in
collaboration.
Project Bellerophon 5
Author: Alan Schwing
2.2 How to Use This Report Our report is divided into two major sections: A Main Body and an Appendix. The Main Body
consists of a project overview and high-level specifications for the team’s vehicles. All analysis
and many of the details are contained in the Appendix. Codes used for the project are provided
online via the course website.
For a better understanding of a topic presented in the Main Body, please refer to the section in
the Appendix covering that material. A complete table of contents is included at the beginning
of this report to help locate sections of interest.
We choose to write the report in active voice and also in the present tense. Some sections,
though, require past tense as much of our work involves a process or sequence of steps. We
hope this document guides you through our analysis and clearly conveys our work.
Project Bellerophon 6
Author: Alan Schwing
2.3 Acknowledgements The design team for Project Bellerophon would like to thank the following individuals for
sharing their time, their experience, and their advice. Without their contributions and support,
the team would not have been able to create the document you now hold.
AAE 450 Instructional Team
James M. Longuski, Professor - Instructor
Kevin Kloster, Graduate Student - Teaching Assistant
John Tsohas, Graduate Student - Project Advisor
We would like to also recognize those individuals who came in to give guest lectures to the
design team. These lectures provided valuable insight into difficult problems and gave us
important information at the onset of design.
Guest Lectures
David Filmore, Professor - Link Budget Analysis
Stephen Heister, Professor - Propulsion Design Issues
Rober Manning, Graduate Student - Thermal Control Issues
John Sullivan, Professor - Manufacturing Issues
John Tsohas, Graduate Student - Launch Method Analysis
Project Bellerophon 7
Author: Alan Schwing
Also important to the project were those individuals in industry and academia that responded to
the team’s inquiries and shared their insight into the design process. The information that they
provided was invaluable.
Industry and Academic Contacts Steven Collicott, Professor - Purdue University
James Doyle, Professor - Purdue University
David Filmore, Professor - Purdue University
Stephen Heister, Professor - Purdue University
Ivana Hrbud, Professor - Purdue University
Scott Meyer, Senior Engineer - In Space, Purdue University
Paul Morissette, Project Manager - Gilchrist Metal Fabricating
Mike Murphy - Spincraft
Charlene Smoot, Logistics Management Specialist - Defense Energy Support Center
Mark Sutton - General Electric
Walter Tam, Sales and Production - ATK Space Systems, Inc.
Jerry White, Capt./Owner - Oregon Offshore Towing
Bob Williams, Sales Contact - Scaled Composites
Marc Williams, Professor - Purdue University
Project Bellerophon 8
Author: Alan Schwing
3.0 Project Overview
3.1 Design Goals The major limitation on access to space is cost.
For launch vehicles, a valuable cost metric is dollars per kilogram or dollars per pound. United
States launch systems have historical values for cost between 2,000 and 20,000 dollars per pound
for vehicles delivering payload of 1,000 to 70,000 pounds into a variety of orbits. The absolute
cost for these systems (cost for the vehicle itself and all associated overhead) range from $13M
to $360M.1
In general, the cost per unit mass reduces as vehicle size increases. This can be thought of as a
distribution of nearly-fixed costs over an ever-increasing payload. These nearly-fixed costs are
those that do not scale substantially with vehicle size. Examples include manufacturing and
assembly overhead, cost for avionics systems, and launch costs.
While it is possible to obtain very reasonable rates on a cost per mass basis, the absolute cost for
such systems is still far beyond the reach of most organizations. A common practice for some
groups is to ‘piggy-back’ on larger payloads by paying a premium to have their smaller payload
launched with the larger one. This keeps total cost down, but ties the launch to the whims of
another’s, thereby removing control over launch specifics.
Our team’s goal is to perform a feasibility study to develop three cost-effective launch vehicles
that have a minimum absolute, per-unit cost. These vehicles should be able to deliver very small
payloads (200 g, 1 kg, and 5 kg) into Low Earth Orbit (LEO). With small payloads and small
absolute costs, this analysis may allow groups requiring space access to launch on their own
schedules with their own equipment.
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Author: Alan Schwing
References: 1 Ventura, Mark, “The Lowest Cost Rocket Propulsion System.” AIAA Paper 2006-4782, Joint Propulsion
Conference and Exhibit, 42nd, Sacramento, Ca, July, 9-12, 2006.
Project Bellerophon 10
Author: Alan Schwing
3.2 Design Requirements The goal of this analysis is to minimize the absolute, per-unit production cost of three separate
launch vehicles. These vehicles are capable of carrying their respective payload into Low Earth
Orbit (LEO) with the following requirements:
1) The probability of insertion into an orbit with a perigee of at least 300 km is at
least 99.86% - assuming no catastrophic failure. Catastrophic failures are
categorized as a failure in any subsystem that eliminates the possibility of mission
success.
2) Allowing for catastrophic failures, the probability of assuming the required orbit
with a perigee of at least 300 km is 90.00%.
Along with these mission requirements, two considerations exist:
1) The team will consider launching from the ground, a balloon, an aircraft, a rail
gun, or a conventional gun.
2) Analysis to insure the probability of success should include analysis of many error
sources. Examples include: wind, atmospheric density, mass flow rate, thrust
alignment, gross weight, burn time, and drag.
These requirements and constraints were presented by design proposal at the start of the semester
to the design team. New considerations were added later in the design process and are discussed
in the following section.
Project Bellerophon 11
Author: Alan Schwing
3.3 Interpretation of Requirements Our analysis is a feasibility study aimed at providing meaningful information and direction for
further development of low cost launch vehicles. This limitation on scope is a powerful tool that
sweeps away many of the obstacles involved in detailed design. For our purposes, we curtail the
analysis in the following ways:
1) Our work investigates physics not politics. Launches in the U.S.A are governed by
the standards imposed by the FAA. These standards require more expensive
components and more rigorous testing than for which we account. Additional
constraints appear when launch sites near populated areas or trajectories over land are
considered.
The team is interested in how the physics affect launch vehicle design and ultimately
risk and cost. To this aim, FAA regulations and conventional safely guidelines were
stretched and, in some cases, ignored. However, we did include analysis regarding
how design might change if certain requirements were followed. For vehicles as
small as ours, we might be able to secure exemptions, so this might not be as reckless
as it may appear.
2) Cost was the major parameter for design. As stated previously, per-unit cost was
the important driver. Development costs were not explicitly examined, but they did
not play a key role in many design decisions. Historically, costs for launch vehicle
design and development are substantial when compared to the per-unit cost of the
launch vehicle. We believe that by implementing techniques and technologies
currently used today we can minimize the per-unit cost, and in turn minimize the
developmental costs associated with our design.
Project Bellerophon 12
Author: Alan Schwing
3) In order to show that the design meets the mission requirement of a 99.86%
success rate, the team relies upon a simplified Monte Carlo analysis. Standard
deviations exist for many of the physical parameters in our design space. Using these
deviations and simulating thousands of launches, we measure the robustness of the
system.
4) It is not possible to construct the vehicle and test for catastrophic failure, so
historical data provides insight into expected performance based on the design.
Studies exist that provide details into failure rates for components in past launch
vehicles.1,2 By applying these values to the vehicles designed in this analysis,
catastrophic failure rates based on tested vehicles can be approximated.
5) Several design decisions depend on the demand for the launch vehicle. For this
reason, we assume that there is a demand for twelve launches per year. We also
assume that this demand continues for a minimum of three years.
All design requirements and goals posed to the team deal with cost, risk, and reliability. These
three factors are very elusive and are based on judgment as much as data. What we provide is
the most detailed and most balanced study that our resources allow. This presentation of our
results is hopefully transparent enough that more experienced hands may take what we have
done and build off of it.
References: 1 Chang, I-Shih., Tomei, Edmardo Joe., “Solid Rocket Failures in World Space Launches.” AIAA Paper 2005-3793, Joint Propulsion Conference and Exhibit, 41st, Tuscon, Az, July, 10-13, 2005. 2 Futron Corporation, Bethesda, MD. “Design Reliability Comparison for SpaceX Falcon Vehicles.” November 2004.
Project Bellerophon 13
Author: Alan Schwing
3.4 Design Process The requirements encourage a wide range of design options, so a majority of the effort expended
on the project revolves around determination of the most cost effective launch architecture. Our
conclusions depend on our method and the decisions that we made throughout the evolution of
our three launch vehicles. A different method may reveal a different conclusion.
This section summarizes the team’s work and presents it in chronological order to walk the
reader through our process. We present our discoveries and decisions in an order that we feel
better captures our reasoning. Being a high-level overview, many details for avenues not
pursued are not shown and can be found in the Appendix.
Project Bellerophon 14
Author: Alan Schwing
3.4.1 Preliminary Analysis There is no universally agreed upon launch configuration for delivering a payload into orbit.
With very few exceptions, current launch vehicles are launched from a platform at sea level (on
land or at sea). Many studies can be found by a quick search through the AIAA archives
detailing proposals for launches from balloons, aircraft, or by using more exotic methods.
Our analysis considered a total of five launch methods: launch from sea level, launch from a
balloon, launch from and aircraft, launch by a rail-gun, and launch by a conventional gun. The
payloads that we considered are much smaller than those conventionally launched, so it was
possible that an unconventional launch method might prove advantageous. Since payload mass
is pivotal to design of the vehicle, our work did not assume that one configuration was ideal
across all three payloads.
In order to provide a uniform ∆V assist from earth, we selected Cape Canaveral, Florida as the
launch location for the vehicle. Additionally, all launches were assumed to be Easternly. The
launch vehicles under consideration were all multi-stage with either two or three stages. We
found that a single-stage vehicle simply was to heavy and therefore expensive. A vehicle with
more than three stages was too complex to be cost effective and reliable for such small payloads.
Preliminary analysis of the design methods concluded that the rail-gun and conventional gun
launch methods had several problems for our application. We found that these methods were
unproven for the scales necessary for an orbital launch. Using a rail-gun or conventional gun,
then, would require considerable and costly research and development. Additionally, the g-loads
created by a gun launch imparted additional requirements onto vehicle hardware, driving the per-
launch cost up. Analysis showed that launch from the ground, a balloon, or an aircraft was still
attractive for orbital launches.
We noticed that a large number of propellant / oxidizer pairs are used in modern launch vehicles.
Propellant selection varied with a number of parameters based on the application for the engine
in question. In order to understand the design space a little better, our technique grouped
propellants into four categories: cryogenic, storable, solid, and hybrid. Within these four
categories, research encouraged the group to select one propellant combination that is
Project Bellerophon 15
Author: Alan Schwing
representative of that group and had the most promise for our application.
For our purpose, a cryogenic propellant is one that requires storage at temperatures near or below
70 K. A storable propellant is a liquid that can be stored at room temperature. A solid
propellant can be stored at room temperature as a solid. Hybrid propellants can be stored at
room temperatures and are composed of one part solid and one part liquid.
In our analysis, the cryogenic propellant combination considered was a liquid oxygen and liquid
hydrogen, the storable was hydrogen peroxide and RP-1. The solid propellant combination was
ammonium perchlorate (AP), aluminum (Al), and hydroxy-terminated polybutadiene (HTPB)
and the hybrid was hydrogen peroxide (H2O2) and HTPB. We collected information on
important characteristics for these propellants to aid a detailed trade study later. In order to
select a propellant for each stage, how these propellants affect overall design had to be
understood.
The materials we identified as possibilities for this analysis were aluminum, composites, steel,
and titanium. Each tank, skirt, and structural element had the possibility to be made of one or
more of these materials - these materials had applications for all portions of the launch vehicle.
Preliminary analysis performed on these materials removed composites from the list of viable
options. Industry contacts informed the team that the lead time (and therefore labor costs)
required for production of a component made from a composite material would be prohibitive
when compared to that of the same component made from aluminum or steel.
From this preliminary analysis, the major components in the design trade were known. These
components were a subset of those proposed in the design goals and requirements. The design
space was not needlessly constrained, and all options that we deemed feasible by this first
investigation were carried to the next stage in design
Project Bellerophon 16
Author: Alan Schwing and Danielle Yaple
3.4.2 Model Analysis Our work on the preliminary analysis helped identify the major components that would have to
be traded between, but there were still a large number of viable configurations for the three
launch vehicles. There were 39,168 possibilities for launch vehicles, accounting for two and
three-stage launch vehicles with a choice of four propellants and three materials for each stage!
Designing over 39,000 vehicles in order to make an absolute decision on cost was impossible.
Instead, we chose to use a simplified model analysis technique. This technique required multiple
stages with a system of codes that the team refined between iterations.
Our scope for this system of codes was quite large. We designed codes to vary a number of
parameters for each possible configuration. After specifying a specific combination of
propellants and materials for the vehicle and a required total ΔV, the code would vary the ΔV
allotted per stage and also each stage’s inert mass fraction, creating a host of possible
configurations.
A propulsion code would size each of these test vehicles and determine the required propellant
mass in each stage. Many of these designs did not budget enough inert mass, so a structural code
was written to weed out those cases. These two codes left only test vehicle cases that delivered
the required energy and were realistic to construct. All of these cases were possible solutions for
the material, propellant, and ΔV combination selected. In order to find the optimum the case the
lowest gross liftoff mass (GLOM) and cost were recorded for each case and compared. The
team repeated this process for all possible configurations with a few possible ΔV values (9000,
12000, 15000 and 18000 m/s) that encompassed our feasible range of ΔV.
At this point in the analysis, the propulsion, structure, and cost codes were based on historical
data. Important values for material thickness, number of structural members, engine mass,
propellant performance characteristics, and required hours for manufacture and launch support
were all derived from studies of previously successful designs.
Cost was the most important factor when considering possible configurations, so in order to rank
the designs, the team created a simple cost model. This first model included costs for the
materials used in the vehicle, the cost of propellant, handling modifiers for toxic or cryogenic
Project Bellerophon 17
Author: Alan Schwing and Danielle Yaple
propellants, and also modifiers for a balloon or aircraft launch that incorporated rental fees
associated with these launches. We believed that other costs would be similar across all models
so they were not incorporated at this time.
This iteration of this design process involved a great deal of effort by the team. There was
minimal automation and due to the sheer number of configurations and limits to computational
time, an exhaustive analysis was not possible. Also, because our models were still based on
historical data, it would have been hasty to trust these results completely. We examined a subset
of the total number of cases with a test matrix that included design variations that touched on
each of the variables. That helped highlight some of the high level decisions to be made.
Our test matrix involved only a couple of thousand cases at our selected ΔV values, but revealed
some valuable trends. Configurations with a solid propellant in the upper stage were most
attractive across the board in terms of cost and GLOM. Also, two-stage vehicles were routinely
out-performed by their three-stage counterparts. It was clear that we wanted to make the top
stage the lightest possible. Seeing the difference in GLOMs between a titanium and steel top
stage showed how important it was to limit the mass placed in that stage. These trends helped
trim the design matrix for subsequent model analysis.
This analysis however did not help with determining our launch method. The costing models
were still missing a lot of key costs that would affect the different launch types. Also we had yet
to determine the difference in ΔV from a ground launch and an air launch. This first analysis
helped us to see what areas we needed to investigate further to make our model analysis more
accurate and complete.
With our testing iteration done and the process understood, we prepared for a more extensive
study on the launch vehicles. Before we could finalize our design, we needed to make sure that
we examined the possible configurations with a much more detailed model. Each group on our
team worked to make their codes include important physics and provide a holistic view of the
launch vehicle.
Our design in other areas of the project has also matured and some changes were made to the
Project Bellerophon 18
Author: Alan Schwing and Danielle Yaple
overall design. Most important was our decision to move the majority of the avionics into the
second stage. Analysis showed that having high-mass items like the battery and self-destruct
mechanism in the final stage quickly overshadowed the mass of the payload and washed out any
difference between the three satellites. Also, we found that placing these items in the second
stage lowered GLOM and total cost. We had also decided on using purely pressure-fed systems
in order to avoid the high cost of turbo-pump machinery.
The propulsion codes were revised to no longer rely solely on historical data. Instead, optimum
expansion ratios and mixture rations were selected by using NASA’s thermochemistry code and
engine performance parameters were recalculated for each stage for each possible case. In other
words, the important characteristics for the propulsion system were specified and made-to-order
on a case-by-case basis. Calculations for pressurant were also included.
Another update included changes in the structures codes to dynamically designed each stage’s
inert components as well. Based on the g-loading predicted by the trajectory requirements, the
number and size of each structural member was modified. Tanks for the pressurant, thrust vector
control propellant, and main propellant were each designed with fidelity indicative of our final
design. Intertank regions and payload fairing were also sized for each vehicle as well.
In order to manage all of the 39,000 cases we developed a naming scheme incorporating the
payload, launch type, propellants, and tanks. Each case was assigned an 8 character (3 stages) or
6 character (2 stages) code. The first 2 characters represented the payload and launch type. S for
the small, 200g payload, M for the medium, 1 kg payload and L for the large 5kg. The launch
type was represented by either G for ground, B for balloon, and A for aircraft. The following
characters were for each stage, 2 characters per stage. The first character represented the
propellant type, C for Cryogenic, S for Storable, D for Solid and H for Hybrid. The second
character is for the tank material, S for Steel, A for Aluminum, C for Composite and T for
Titanium. One example is MG-CA-SC-DT this is a 1kg ground launch case with a cryogenic and
aluminum first stage, storable and composite second stage, and a solid with titanium third stage.
One limitation that plagued our analysis was the limited computational resources available and
the requirement for manual input for each configuration. Each possible configuration took
Project Bellerophon 19
Author: Alan Schwing and Danielle Yaple
upwards of 5 minutes, so for thousands of cases, this translated into days on a typical
workstation. For the second analysis, a more capable automation routine was written and
streamlined so that it could be run remotely on the department’s servers. We still required
almost three days to run all possible configurations, but it was possible to evaluate each and
every option to totally exhaust the design space. With the more refined propulsion and structures
codes, we felt ready to limit the number of models under consideration to only a mere handful.
The following tables list the 5 winning cases for each payload.
Table 3.4.2.1 Winning Cases – 200g
Model Name Cost GLOM (kg)SB-CA-DA-DS 4134770.44 6348SB-CA-DA-DA 4135005.02 6348SB-CA-DA-DT 4174441.05 6348SG-CT-DT-DASA-CT-DT-DA
4294144.034294144.03
65286528
Table 3.4.2.2 Winning Cases – 1kg
Model Name Cost GLOM (kg) MB-SA-DS-DA 4085248.85 11497 MB-SA-DA-DA 4086343.04 11497 MG-SA-DA-DA 4104172.25 9292 MA-SA-DA-DA 4104172.25 9292 MB-SA-DA-DT 4125954.08 11497
Table 3.4.2.3 Winning Cases – 5 kg
Model Name Cost GLOWLG-SA-DS-DA 4103413.74 11572 LA-SA-DA-DA 4104510.54 11572 LG-SA-DA-DS 4110887.84 13573 LB-SA-DA-DA 4224938.33 12678 LB-CA-DA-DA 4247196.12 10177
We used this data to set up trends and find errors in our analysis. We also came to the conclusion
that we couldn’t always pick the model with the lowest cost. If the cost between two designs
were close and we went with the smaller GLOM. Since there are a lot of uncertainties in our cost
models we knew it would be a safer to relate the GLOM because it was associated with physics,
Project Bellerophon 20
Author: Alan Schwing and Danielle Yaple
rather than cost and we had more confidence on the physics calculation that than the calculation
of cost. Engine costs for example are based off historical data and then the inflation rate of the
years since the data. This is probably not the most accurate prediction of cost because technology
is constantly changing and making production of complex systems more efficient and thus more
affordable. Another reason the physics is more reliable is due to the fact that our costs are based
on estimates from companies providing space rated components which may or may not meet our
exact specifications, our requirements are a lot more relaxed than more space missions so the
costs for different components could vary greatly.
From this surface analysis we were able to gain a better insight into what ranges of inert mass
fractions and ∆V breakups would be feasible. This data relationship was hard to make any
correlations about a ground verses an air launch because we were using a ∆V of 12,000 m/s,
given from trajectory, for all of the cases. A comparison between a ground and air launch can not
be reasonable without having different ∆V requirements for the launch type.
The next step was to fix the analysis for hybrid and storable propulsion. We gained more
information about the costs associated with having variable and directional thrusts which
depended on the propulsion system. LITVC and gimbaling varies the thrust, but the system
depends on the propellant and thus costs are not equal across all possible models. We also
developed a more in-depth launch type cost modifier before the next model run was completed.
This coding system was slightly limited due to the fact that the GLOM values are not optimized
between the structures and propulsion codes. From the ideal rocket equation, the propulsion’s
code calculated an inert mass required and then it passed that mass into structure’s code to see if
the case was feasible. Yet, the minimal mass that structures calculated was not recorded.
We did not have the computational power that would be needed to run thousands of cases each to
an optimized configuration. Thus we used the model analysis to optimize and pick the best cases
from the trends and data given here. Trends like having titanium saves mass in the GLOM but it
is only cost effective to have titanium in an upper stage because it is smaller and not as much
material is required.
Project Bellerophon 21
Author: Alan Schwing and Danielle Yaple
The model analysis eventually morphed into an optimization task with trajectory. In this phase
additional codes which just added more details in cost and mass like hoops in the tanks and cost
quotes from a few additional companies. This analysis resulted in limiting the cases to the
models we selected.
Project Bellerophon 22
Author: Amanda Briden
3.4.3 Final Design In what we have labeled our final design phase, automated design codes were used to speed up
an iterative design process. Subsystems involved in this process were Propulsion, Structures,
Trajectory, and D&C. First, mass fidelity was manually updated in an inert mass budget
constructed by Propulsion and Structures. Then, Propulsion ran the MAT code to re-size the
launch vehicles. These vehicles were passed to Trajectory who found the sub-optimal trajectory
that satisfied the perigee requirement of 300 km. D&C took these launch vehicles and controlled
them to follow the sub-optimal ascent path. If the launch vehicle could be controlled to an orbit
greater than 300 km, it was deemed the final design. In order to prove a launch vehicle success
rate of 99.86%, including non-catastrophic failures, D&C ran a Monte Carlo analysis on the final
designs for at least 10,000 cases. This entire process required a nontrivial amount of time and
people power.
The front end of the final design phase involved an iterative process between Propulsion and
Structures. Figure 3.4.3.1 shows a flowchart detailing the communication that occurred between
Propulsion and Structures. For a given ∆V, Propulsion ran the MAT code to produce inert mass
fractions, propellant masses, and fuel tank volumes. Propulsion then passed this information to
Structures. A refined structures code found the actual inert mass fractions for each stage. If the
refined inert mass fractions were larger than those proposed by Propulsion, the inert mass input
to Propulsion was increased. For the new percent ∆V breakdown per stage, Propulsion found
new inert mass fractions, propellant mass, and tank volumes. The revised values were given to
Structures who re-ran the refined code to calculate inert mass fractions.
Project Bellerophon 23
Author: Amanda Briden
Fig. 3.4.3.1: Final Design Phase – Propulsion and Structures Iteration.
(Amanda Briden)
This iterative process continued until the inert mass fractions calculated by Structures were less
than or equal to those calculated by Propulsion. After having satisfied this condition, we referred
to the ∆V as ∆Vnominal, percent ∆V imparted by each stage as percent ∆Vnominal, and the sized
launch vehicle as the nominal launch vehicle. Nominal cases were found for each payload.
The team understood that a Monte Carlo performed on only a nominally sized vehicle would
cause the vehicle to frequently fail to meet the required perigee. To remedy this, for each
payload, Propulsion and Structures re-sized the nominal launch vehicles for ∆Vs ranging from
105 – 150% ∆Vnominal in increments of 5%. Next, the re-sized vehicles were given to Trajectory.
The iteration between Propulsion and Structures took a day.
Once Propulsion and Structures provided sized launch vehicles, Trajectory had to figure out
which vehicles made it into orbit using a sub-optimal trajectory. Trajectory needed to answer the
Project Bellerophon 24
Author: Amanda Briden
question, “what is the path of least resistance into orbit?” A launch vehicle’s orientation at every
instant in time is defined by its steering law. Trajectory ran an automated optimization code to
find this steering law. In this optimization scheme, the orientation of the launch vehicle (defined
as an angle) at the end of each stage’s burn was varied until a combination of three angles was
found that met the following criterion; the launch vehicle entered an orbit with a perigee of
300km and eccentricity less than 0.5. The code met this criterion in two steps. First, a search
was completed of all angle combinations until a set was found that minimized the orbit perigee.
Second, a refined search around the angle combination that produced the orbit with a perigee
closest to 300km was completed. Of these, the orbit with the smallest eccentricity was kept. We
called this the sub-optimal trajectory and predicted orbit. Then, Trajectory gave the smallest re-
sized launch vehicle, for each payload, to D&C. The launch vehicles that met the criterion are
shown below in Table 3.4.3.1. For each launch vehicle in Table 3.4.3.1, the final design
subsystems provided D&C with an ephemeris file including the predicted inertial position and
velocity vectors for the entire ascent, the final steering law, and performance characteristics.
Getting all of this information to D&C took two days.
Table 3.4.3.1 Final Re-Sized Vehicles for D&C
Payload Size % ∆Vnominal200g 1451kg 1155 kg 125
D&C was the last subsystem involved in the final design phase. Their responsibilities entailed
determining if the launch vehicle could follow the ascent path laid out by Trajectory. The
automated D&C simulation incorporated a six degrees of freedom (6DOF) model and thrust
vector control (TVC). D&C began its involvement by fitting a spline curve to the steering law
provided by Trajectory. This spline curve made the steering law first derivative continuous. In
order for the controller to follow the steering law, it had to have a continuous first derivative.
Then, D&C ran a simulation for the ascent of the launch vehicle for each case. We wanted the
launch vehicle to over perform and reach an orbit with a periapsis larger than the predicted
trajectory value. If the resulting orbit periapsis from D&C was larger than the predicted
periapsis from Trajectory, we felt confident that including uncertainties in performance
characteristics would not cause the launch vehicle to fail a Monte Carlo run. All of the re-sized
Project Bellerophon 25
Author: Amanda Briden
launch vehicles over performed and we felt these vehicles could be used for the Monte Carlo
analysis. It is important to note that at this point we called the re-sized vehicles the final design
launch vehicles and no longer referred to them as a percent of the ∆Vnominal. It took D&C a day
to see if the launch vehicles could be used for the Monte Carlo.
Before running the Monte Carlo analysis, the uncertainties associated with each performance
characteristic of the launch vehicle were determined by the responsible subsystem. Record of
the percent deviations for each of these performance characteristics was given to D&C.
Performance characteristics including inert mass fractions, coefficient of drag, mass flow rates,
propellant masses, thrust misalignment, and gyro drift all had uncertainties included in the Monte
Carlo. Uncertainties were found from papers or historical data.
D&C did not run the full 10,000 case Monte Carlo simulation right away. First, D&C made sure
that all of requested output was in an organized format. With limited computation time, D&C
also made sure the ascent simulation could run on multiple computers. D&C ran the simulation
for only 100 cases and checked for any failures. After 100 successful cases, D&C ran 1,000.
After 1,000 successful cases, we felt confident enough to run the entire 10,000. Each Monte
Carlo run took three days. All final designs had a success rate of at least 99.99%, exceeding the
required 99.86%.
Project Bellerophon 26
Author: Alan Schwing
3.5 Costing Methods
Our major driver in this analysis is cost. Cost is the metric that helped determine the most
advantageous architecture. Understanding the costs associated with launch vehicles for small
payloads is the purpose of this feasibility study. The final cost models represent the final
iteration of a process that went through many revisions.
As with most parts of this analysis, our goal is to remain as transparent as possible in order to
facilitate future work on similar topics. We understand that more experienced hands might have
access to more refined models, and we believe our system can be easily adapted with additional
information. Our cost models and assumptions are catalogued the Appendix.
We had a great deal of difficulty obtaining precise prices for several important items, namely the
tanks and the engines. For the tanks, our analysis depends on a curve fit derived from several
estimates from ATK Thiokol. Engine cost is calculated from correlations based on historical
engine cost data. Other costs are based on merely a summation of the cost for each component
involved.
Table 3.5.1 provides a summary of the calculated cost for each of our final designs. These costs
are in 2007 US dollars. Complete breakdowns of total vehicle cost are included in the Detailed
Design section.
Table 3.5.1 Total Vehicle Cost for Each Design Payload
Payload Mass Total Cost200.00 [g] $ 3,625,196001.00 [kg] $ 3,178,447005.00 [kg] $ 4,672,258
Project Bellerophon 27
Author: Alan Schwing
3.6 Risk Analysis Our analysis of risk for these launch vehicles is broken into two parts: non-catastrophic risk and
catastrophic risk. Non-catastrophic risk analysis encompasses deviations in flight due to inherent
variations in design and construction of physical vehicles. Catastrophic risk includes the
probability of major subsystem failure that results in failure of mission.
Values for non-catastrophic risk for each of our launch vehicles are presented in Table 3.6.1.
This analysis considers any launch that did not achieve a perigee of 300 km to be a failure.
These results come from Monte Carlo simulations performed by the D&C control model. They
incorporate percent standard deviations on nominal values for: inert mass, propellant mass,
propellant mass flow rate, drag, thrust misalignment, and gyro drift. In order to ensure that we
meet the design requirement of 99.86% reliability, results for 10,000 simulations exist for each
of the three launch vehicles.
Table 3.6.1 Non-Catastrophic Risk Results for Launch Vehicles
Payload Mass Number of Failures
Number of Successes
Total Number of Simulations Success Rate
200.00 [g] 1 a 9,999 10,000 99.99 %001.00 [kg] 1 b 9,999 10,000 99.99 %005.00 [kg] 0 c 10,000 10,000 100.00 % s
a Perigee of 297 km b Perigee of 298 km
All three vehicles achieve the non-catastrophic success rate prescribed in the design
requirements. They achieve this rate with a significant margin, indicating that there might still
be some optimization available in order to minimize cost and reduce success rate to the
requirement. A more detailed presentation of these results is available in the Appendix.
Catastrophic risk analysis is very different than the non-catastrophic analysis. In order to predict
catastrophic failure rate, historical values for launch success provide insight into behavior that
we might expect. Unlike the non-catastrophic rate, we believe that each vehicle has identical
catastrophic failure rates due to similar vehicle architectures.
As vehicles mature and their performance is better understood, their reliability increases. It takes
time to work all of the bugs out of a system. Based on historical performance of the Ariane IV,
Project Bellerophon 28
Author: Alan Schwing
Ariane V, and Pegasus launch vehicle, we believe that our vehicles will take twenty-four
launches before they meet the required success rate of 90.00%. Once we mature, our success
rate should be higher than that minimum set forth in the requirements.
Table 3.6.2 shows our predicted success rate at various times throughout the lifetime of the
vehicle. As the number of launches increases, so does our estimate of reliability for each launch.
We learn from our mistakes and our successes, so it should be noted that the first column in
Table 3.6.2 includes launches that ended in failure.
Table 3.6.2 Catastrophic Failure Rate Based on Number of Attempted Launches
Number of Launches Failure Rate Success Rate Less than 12 40.00 % 60.00 % Less than 24 20.00 % 80.00 % 24 or greater 06.16 % 93.84 %
From both analyses, our vehicles meet the design requirements for risk. With respect to
catastrophic failure, though, time is needed before we can meet the requirement in order to allow
for the system to mature. We believe that our risk analysis is conservative and that it reflects the
best possible estimates for risk at this stage of design.
Project Bellerophon 29
Author: Alan Schwing
3.7 Conclusions
Our feasibility study found that launch vehicles designed for very small payloads can be
manufactured for an order of magnitude less than conventional systems. These vehicles
are as reliable as conventional systems and meet all of the requirements imposed on this
design. That being said, other comments can be made concerning our results.
Important parameters for our three launch vehicles are shown in Table 3.7.1. A clear
discrepancy is the fact that the vehicle carrying the 200 g payload is larger than the
vehicle carrying the 1 kg payload. Note the large difference between the nominal
controlled perigee and the average controlled perigee for the 200 g case. This means that
the 200 g payload vehicle is more sensitive to variations in our design parameters. This
sensitivity necessitates a greater safety margin on the 200 g launch vehicle to ensure that
it meets the requirements. The higher safety margin may prohibit the cost of the 200 g
payload vehicle from being driven below the 1 kg launch vehicle’s cost, even for an
optimized configuration.
Table 3.7.1 Key Characteristics for Project Bellerophon’s Launch Vehicles
Payload Mass Vehicle GLOM [kg] ∆V [m/s]
Nominal Controlled
Perigee [km]
Average Controlled
Perigee [km] a Total Cost
200.00 [g] 2,583.83 10,730 486.00 437.44 $ 3,625,196001.00 [kg] 1,745.22 9,500 366.96 367.73 $ 3,178,447005.00 [kg] 6,294.80 11,313 513.00 516.55 $ 4,672,258
a This average is calculated from a minimum of 10,000 Monte Carlo simulations
The vehicles described in Table 3.7.1 do not represent finalized launch platforms. These
designs are sized in order to meet and exceed the requirements for this study. It is very
time-intensive to design even one of these vehicles. To optimize one of these designs
would be computationally expensive and require several times the amount of effort
necessary for this project. Our team does not have the resources that such an undertaking
would require. We are confident, though, that we have come close to the final designs
and believe that our costs are representative of those for optimized launch vehicles.
On the issue of optimization, our analysis is based on techniques that involve a decoupled
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Author: Alan Schwing
trajectory and D&C design process. Future work must involve more coupled analysis
with controllability considerations kept in mind throughout trajectory optimization. We
have sub-optimal trajectories with discontinuous derivatives. These discontinuities make
those trajectories difficult to control, but we are able to achieve the required perigee by
increasing the propellant mass. Our vehicles, therefore, lack some of the finesse that a
more thorough design could provide.
Due to the lax requirements for the analysis - no required orbit inclination or maximum
perigee - and the very small operating time, our design employs avionics that are not
space rated. It is our opinion that commercial grade components can provide the required
performance. This allows us to select less expensive avionics for our designs. Any
vehicle sized for payloads as small as ours would have to make a similar design decision
to remain affordable. Typical avionics packages can cost as much or more than the total
cost of our vehicles.
The two most expensive items for each vehicle are engines and propellant tanks. Both of
these items are difficult to cost accurately because industry is very tight-lipped about
quoting prices on these components. Information for tank and engine manufacture is
proprietary due to competition in the industry. Our values, therefore, are necessarily
conservative and are derived from cost data that is available. These estimates could
decrease if we had access to more exact pricing information.
One major limitation that we see is that the inert mass of the third stage for our vehicles is
predominantly engine and tank mass. Small decreases in the mass of these components
would reduce the mass of the third stage and in all previous stages. Engine mass for our
designs is based largely on throat and exit diameters. Our throat diameters are already
very small and aggressive in terms of efficiency and manufacturability. In order to
decrease engine mass, we believe that detailed design is necessary to ensure that a
miniature engine can be manufactured to provide the required performance.
Using a small launch vehicle, we pay a high drag penalty when compared to larger
vehicles. Our decision to launch from a balloon above much of the atmosphere saves us
Project Bellerophon 31
Author: Alan Schwing
from paying that penalty. The balloon also gives the launch vehicles an initial altitude,
helping them on their way into orbit. We also see an increase in engine performance
when launching from the balloon, being so close to space. For these reasons, we feel that
a balloon launch is important to realize the low costs present in this analysis.
We came into this project wondering if space access is attainable for a single university
or small company with a reasonably size research grant. Our results indicate that low-
cost vehicles can be designed for small payloads, but are only affordable to multiple
universities or companies in collaboration. The risk and cost assessments show that small
launch vehicles are viable and we can leverage very small payload mass into a vehicle
that is much less expensive than a commercially available one.