Report Section 1 - engineering.purdue.edu

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.


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


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.



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.



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.



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



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



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.



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.



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.



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.



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.



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.



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



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


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



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



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



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,



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.



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.


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.



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



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



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%.



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



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,



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.



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



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



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.

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