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\title{Financial Operational Losses in Space Launch}
\author{Tom Robert Boone, IV}
\date{May 2017}

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UNIVERSITY OF OKLAHOMA
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GRADUATE COLLEGE
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FINANCIAL OPERATIONAL LOSSES IN SPACE LAUNCH
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A DISSERTATION
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SUBMITTED TO THE GRADUATE FACULTY
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in partial fulfillment of the requirements for the
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By
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TOM ROBERT BOONE, IV
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Norman, Oklahoma
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2017
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FINANCIAL OPERATIONAL LOSSES IN SPACE LAUNCH
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A DISSERTATION APPROVED FOR THE
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SCHOOL OF AEROSPACE AND MECHANICAL ENGINEERING
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BY
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\  \  \  \  \  \  \  & Dr. David Miller, Chair\\
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\copyright \    Copyright by TOM ROBERT BOONE, IV \   2017

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``For which of you, intending to build a tower, sitteth not down first, and counteth the cost, whether he have sufficient to finish it?''

\hfill Luke 14:28, KJV

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\chapter*{Abstract}

  The high cost of access to space has been a problem since the beginning of the space age.  Most attempts to reduce this cost are centered on improvements to launch vehicle design.  While this approach has been fruitful, less attention has been paid to other causes of high cost.  Two of these are wastage of launch vehicle payload capacity and use of cost-ineffective launch vehicles.  Both of these are associated with the way the launch vehicles are operated, and so are \textit{operational losses.}  This work examines the extent of operational losses in space launch over the period January 1, 2000, to September 29, 2013, and considers strategies for reducing these losses.  The cumulative worldwide wastage for this period was 654 tons, which is 20.4\% of total payload capacity, and represents a financial loss of no less than \$8.72 billion (2014\$).  The cumulative loss due to cost-ineffective launch vehicle selection is less certain, but is no greater than 43.8\% of total launch cost, or \$19.3 billion.  Two possible strategies may combat operational losses: changing launch vehicle selection or rearranging payloads.  Changing launch vehicle selection can in principle eliminate cost-ineffective launch vehicle use, but is prevented in some measure by non-economic considerations.  Rearrangement of payloads cannot eliminate wastage, but can reduce it considerably, to as little as 2\% in some cases.  Combining these two strategies by applying a bin-packing algorithm to the set of launch vehicles and payloads can yield a considerable cost savings, reducing total launch costs to geosynchronous orbit by as much as 53\% if both launch vehicle selection and payload arrangement are unrestricted.  Even in the most restrictive scenario where payloads must be launched in the same calendar year they actually were and launch vehicle choice is restricted to the launch vehicles actually used during that year, cost savings of 19.1\% over the actual launches are possible.
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\chapter{Introduction}
\label{sec:intro}

	The space launch industry is currently at a crossroads.  Over the past decade, it has experienced drastic shifts, and the pace of change is increasing.  In the last decade, the United States retired Atlas II, Titan and the Space Shuttle, and drastically reduced use of the venerable workhorse Delta II in favor of three all-new launch vehicle families: Delta IV, Atlas V, and Falcon 9.  Though progress has been slow, Russia plans to both roll out the all-new Angara launch vehicle family, whose modular configuration and elimination of reliance on toxic storable propellants addresses the two main weaknesses of Proton, and construct an entirely new cosmodrome at Vostochny to replace Baikonur.  China became the third nation to achieve human spaceflight and construct a space station.  Japan has introduced a powerful new launch vehicle, H-IIB, capable of delivering the 18-ton HTV to the International Space Station.
	  
	Equally important breakthroughs are on the horizon.  The NASA COTS and CCDev initiatives have opened the door for commercial human spaceflight, with multiple competitors vying to supply America's next manned space vehicle.  Reusable Falcon 9 core stages promise a five or ten-fold reduction in launch costs with a series of exciting tests that are ongoing.  

	Despite these advances, space launch is still an extremely expensive and exacting business.  Minimum costs for orbital launches are still in the thousands of dollars per kilogram, and often the cost to deliver a payload to space can be higher than is immediately apparent.  As will be shown in this work, the often-quoted cost per payload mass is often not what is actually paid.  Wastage of launch vehicle payload capacity and insurance drive this cost upward.  For example, Ariane 5ECA costs \$15,670 per kilogram of geosynchronous transfer orbit payload capacity, but after a total wastage of 21.87\%, customers actually paid an average of \$20,056 per kilogram delivered to GTO before the cost of insurance, which averages an additional 15-20\%\cite{spaceeconomics}.
	
\section{Overview of Operational Losses}
	
	The intent of this research is to provide answers to three research questions:
	
	\begin{itemize}
	
	  \item How much can launch costs be reduced through operational strategies?
	  
	  \item What usage patterns do these strategies create?
	  
	  \item Which type of operational loss causes the greater amount of financial loss?
	
	\end{itemize}
	
	In order to begin to answer these questions, it is necessary to quantify the operational losses associated with spaceflight.  There are two types: wastage and cost-ineffective launch vehicle selection.  Chapters \ref{sec:wastage} and \ref{sec:usage} examine these in detail, quantifying the extent of both and their effects on the price to deliver a payload to space.  Total wastage over the January 1, 2000 to September 29, 2013 period was 654 tons.  This is 20.4\% of total payload capacity, or a financial loss of \$8.72 billion.  The loss due to cost-ineffective launch vehicle selection alone is less certain owing to some non-technical constraints on launch vehicle selection, but could be as much as \$19.3 billion, or 43.8\% of total cost.
	
	The second goal of this research is to determine how much reduction of these two sources of operational losses is possible.  Implicit in this is some discussion of means, although any discussion of the means will be generic.  The solution to cost-ineffective launch vehicle selection is simply selecting more cost-effective launch vehicles, although there are some complications to this discussed in Chapter \ref{sec:usage}.  It is possible to limit wastage to some degree through launch vehicle selection, although this may not be the most cost-effective method to deal with that particular problem.  Launching multiple payloads on the same launch vehicle is the primary method examined here to reduce wastage.  While multiple payload launches are already a common practice, the majority of launches, 710 out of 913, are still single payloads.  Many of these single payloads have significant wastage, and taking measures to utilize this unused capacity can reduce the cost per payload mass delivered to orbit.    
	
	The costs listed above illustrate the value of reducing operational losses.  Analysis conducted in Chapter \ref{sec:usage} concludes that a reduction in launch costs of up to 43\% is possible with improved launch vehicle selection using the existing mission manifests.  Coupled with an average wastage over the studied period of roughly 20\%, there is potential for significant savings.  Further savings may be possible.  As stated in Chapter \ref{sec:lvtrends}, larger launch vehicles tend to be more cost-effective than smaller launch vehicles, so rearranging payloads such that they can all launch on the largest launch vehicle possible has potential to reduce costs even further.  Chapter \ref{sec:arrangement} contains an analysis of this sort, showing that large reductions in the cost of payload delivery to geosynchronous orbit are possible through a combination of these strategies.  
	  
	It is not, of course, possible to eliminate all operational losses.  Cost is not the only factor considered when selecting launch vehicles or determining payload manifests for missions.  These other considerations prevent realization of all possible gains.  When applicable, chapters in this work discuss the potential obstacles to improvement.  For launch vehicle selection, national security considerations, availability of the desired launch vehicles, and reliability of launch vehicles all play a role.  Reduction of wastage by alteration of payload manifests is made more difficult by the time schedule requirements of payloads, the potential reduction in reliability caused by multiple payload releases, and institutional roadblocks such as those described by Buckley\cite{excesscapacity}.
	
  To summarize, the intent of this work is to quantify the two types of operational losses and determine how much it is possible to reduce them.  In order to do so, it is necessary to gather data about both space payloads and the vehicles that launch them.  Once this is complete, an assessment of the amount of wastage and the cost-effectiveness of launch vehicle choices is possible.  Lastly, strategies for reducing launch costs via changing launch vehicle selection and/or payload arrangement are developed and assessed.
  
\section{Structure of Dissertation}

  This work will take a four step approach to answering the research questions:

  \begin{enumerate}
  
    \item Gather, validate, and find any trends in data to determine the extent of the problem.
 
    \item Determine how much may be saved with changing launch vehicle selection alone.

    \item Determine savings if payloads can be rearranged on the same launch vehicles.

    \item Determine savings if payloads can be arranged in the most cost effective fashion on any launch vehicle.
  
  \end{enumerate}

  Chapter \ref{sec:review} reviews relevant literature.  There are only a few mentions of wastage in the literature.  Of these Koelle approaches the subject most directly, and presents a value for wastage close to that obtained in the analysis in Chapter \ref{sec:wastage}\cite{stc}.  Discussion of launch vehicle selection is also limited, although Chapter 4 of Greenberg contains some information\cite{economicprinciplesspace}.  Aside from the central research questions posed above, however, a considerable amount of background information in diverse topics such as launch insurance, launch vehicle pricing, and payload data is necessary.  Chapter \ref{sec:review} enumerates the sources used to obtain necessary data for the analyses in Chapters \ref{sec:payloadtrends} through \ref{sec:risk}.
  
  Chapter \ref{sec:payloadtrends} describes a payload database with data drawn from multiple sources and then analyzes the data for trends relevant to the problem of operational losses.  The most important of these trends is the split between large payloads and small payloads.  The vast majority of individual payloads are small low Earth orbit payloads, but large geosynchronous orbit payloads drive the demand for launch vehicles, accounting for the majority of launch vehicle usage.  This problem is difficult to solve with launch vehicle design because as shown in Chapter \ref{sec:lvtrends}, small launch vehicle designs are inherently less cost-effective.  Appendix A contains the payload database.
  
  Chapter \ref{sec:lvtrends} investigates trends in launch vehicle cost-effectiveness, including developing several cost models.  An understanding of trends in launch vehicle cost-effectiveness with regard to design is important to both parts of the operational loss problem.  Additionally, much of the existing launch vehicle price data is unreliable or fails to make statements about what the given price includes.  Comparative analysis of cost models, both existing models and newly developed models, provides a check on the reasonableness of the cost data as well as providing insights into the design traits of cost-effective launch vehicles.  Most critical of these are large size and high efficiency.  Production numbers or flight rate seem to have little correlation with prices of existing launch vehicles.  Appendix B contains the price data used in the analyses in this chapter.
  
  Chapter \ref{sec:capability} analyzes launch vehicle capability to launch payloads.  Capability drives the potential market share of a launch vehicle.  Large launch vehicles have much greater capability than small launch vehicles, with the smallest current launch vehicle, Pegasus XL, only having the capability to launch 1.12\% of payload mass.  This greater capability gives large launch vehicles another advantage in the market in addition to their inherently superior cost-effectiveness.  Chapter \ref{sec:capability} also investigates the market share of existing launch vehicles.  Very few launch vehicle families have large individual shares of the market for payloads they are capable of launching, and the few exceptions, such as Soyuz, are the beneficiaries of exceptional situations.
  
  Chapter \ref{sec:wastage} computes wastage for launches in the data set with sufficient data.  Total wastage for the missions with sufficient data is 20.4\%, or 653 tons out of a total capacity to all orbits of 3,208 tons.  To place this value in perspective, it is greater than the mass of the International Space Station, at 416 tons, and nearly half of NASA's estimate of the low Earth orbit payload mass required for a manned Mars mission, at 1,316 tons\cite{dra50}.  In actuality, it is even greater than the value implied by raw mass because 58.9\% of total wastage is to geosynchronous orbit, and launch vehicle payload capacity to low Earth orbit is usually two to four times that to geosynchronous orbit.

  Chapter \ref{sec:usage} investigates usage of launch vehicles.  Surprisingly, while use of the cheapest launch vehicle capable of launching a mission is a plurality of launches, it is not the majority.  Approximately 50\% of missions select a launch vehicle that is ranked in the top four for cost-effectiveness for their particular mission, and 75\% select one that is ranked in the top ten.  Chapter \ref{sec:usage} also analyzes total usage of each launch vehicle type.  Some launchers, such as Dnepr and Delta IV, see usage on missions where they are not the most cost-effective, but missions where they are the most cost-effective choice do not use them.  
  
  Chapter \ref{sec:arrangement} describes the use of bin-packing algorithms to assign payloads to launch vehicles in a manner designed to minimize total launch cost.  Significant reductions in wastage and cost are possible, especially in the most permissive scenario where any payload from the dataset may be assigned to any launch.  This scenario can result in a savings of up to 45\% for geosynchronous payloads.  Progressively more restrictive scenarios, such as those limiting the use of launch vehicles or requiring that payloads launch in the same year that they were launched in reality, decrease savings, but even the most restrictive scenario still nets savings of 19.1\% for geosynchronous payloads.  
  
  Chapter \ref{sec:risk} provides a metric for computing the additional risk imposed by multiple-payload launches.  While launching in this fashion has the potential to greatly reduce launch cost to the payload owner, there is an increased risk imposed by carrying and separating multiple payloads.  This risk should, all other things being equal, express itself in a higher insurance cost for the launch.  Accordingly, Chapter \ref{sec:risk} develops a simple model for the loss chance of a payload based on the reliability of the launch vehicle and the separation events.  Under the assumptions of the analysis, ten equally sized payloads on a single launch would incur an additional insurance cost of roughly 5\% of launch vehicle cost.  This is half of 2013 wastage, and derives from several pessimistic assumptions that increase the risk and thus cost.
  
  Chapter \ref{sec:conclusions} provides a summary of the investigation into operational losses.  Additionally, it contains recommendations for future reduction of these operational losses.  The most important of these recommendations is the development of improved, standardized systems for multiple payload launch, ideally modeled on Earthbound logistics systems such as ISO containers.  Such a system would enable a significant reduction in wastage and thus cost.

\chapter{Literature Review}
\label{sec:review}

	Comparatively little has been written on the subject of launch vehicle capacity wastage.  Passing references to it do exist in the literature, usually in the context of increasing multi-payload capabilities for launch vehicles.  Steven J. Buckley's ``Utilizing Excess Capacity of Current Launch Vehicles to Lift Secondary Payloads'' is an excellent example of this type\cite{excesscapacity}.  This paper is largely concerned with the operational difficulties associated with multiple manifests.  While it is understood that wastage is a loss, there is no attempt to quantify it.  He also provides insight into the human factors that cause wastage.  As he puts it, ``the primary payload and launch managers rightfully see the burden of manifesting secondary payloads on their mission as added risk and complexity''.  
	
	Koelle refers to wastage in passing in ``Specific Transportation Costs to GEO - Past, Present, and Future.''\cite{stc}  He discusses a `payload utilization factor', which is simply the fraction of the launch vehicle's capacity that is composed of useful payload, or \textit{1-W}.  He comments that ``A generic cost reduction of 25 to 35\% is feasible.''  His comments on problems with multiple payload systems reducing payload capacities, however, seem to be overly conservative.  If a launch vehicle can be built with a structural fraction of less than 5\%, as Atlas D was more than 50 years ago\cite{blazingthetrail}, including complex thermomechanical and electronic systems for propulsion and guidance, then it does not seem reasonable to conclude that the necessary adapters for multiple payload deployments would erase most of the potential savings.  Available data on multiple payload systems currently in use bears this out; most variants of the Ariane 5 SYLDA have a mass of approximately 500kg, slightly less than 5\% of the maximum GTO payload capacity of that vehicle\cite{arianeug}.  
	
	Koelle's comments on the real world difficulties of scheduling payloads together are well taken, and an effect that is difficult to quantify.  His paper is also interesting in that it contains results of payload analyses similar to that performed in Chapter~\ref{sec:payloadtrends}, giving the average mass of payloads to orbits.  His work, however, rates geosynchronous payloads on their final mass after performing the circularization and plane change burns, and so is not directly comparable to results obtained in Chapter \ref{sec:payloadtrends}.	
	
	Like wastage, the literature does not extensively discuss launch vehicle selection.  However, Greenberg examines the subject to some degree in Chapter 4 of \textit{Economic Principles Applied to Space Industry Decisions}\cite{economicprinciplesspace}.  His analysis of a hypothetical choice between `Proton' and `Atlas' (given the date of his work, probably Proton-K and Atlas II) accounts for more variables than the comparisons of total launch cost executed in Chapter \ref{sec:usage}.  Specifically, his model accounts for differences in the cost of insurance and payment schedules, and produces a `net present value' for each potential launch vehicle choice.
	
	While Greenberg's approach is more accurate in terms of making a correct decision, it requires information that is not readily available for contemporary launch vehicles.  Knowledge of the prospective payment schedules and the cost of launch insurance is not widely available.  As discussed in Chapter \ref{sec:lvtrends} a considerable amount of the current launch vehicle price data is unreliable.  Additionally, while insurance cost is often given as a fraction of launch vehicle cost, the cost of the payload must have some influence on it, as the payload is typically at least two to four times more valuable than the launch vehicle itself\cite{bigdumbbooster}, and so will constitute the majority of the insured value.
	
	While little has been written on the overarching problem of wastage and launch vehicle selection, several of the subordinate topics in this work have been examined in detail.  Some attempts have been made in the past to quantify the space launch market.  The Federal Aviation Administration prepares Launch Reports and Year In Review reports\cite{faa2000q1,faa2004q1,faa2006q1,faa2011q3q4,faa2013yir} that list payloads launched into space and plot data such as the number of launches, their affiliation, their masses, and other information.  Other than this work, they are the only source that attempts to quantify payload masses, although they do so by loose categories rather than listing the mass of each payload.  These data are also only presented for each quarter or year, rather than for a longer period.  They also track the number of commercial versus government launches.    
	
	Robert L. Sackheim's ``Overview of United States Space Propulsion Technology and Associated Space Transportation Systems''\cite{aiaasurvey} provides a general overview of launch vehicle technology.  His arguments for development of improved propulsion systems are well taken, especially given the analysis presented in Chapter \ref{sec:lvtrends} tying improved propulsion system performance to cost-effectiveness.
	
	Cost models for launch vehicle development and production are important to understand the consequences of launch vehicle usage and design choices.  A number of models of varied complexity are extant, of which a review may be found in Trivailo et al\cite{costestimation}.  These include the NASA and Air Force Cost Model (NAFCOM), Koelle's TRANSCOST, and others.  It is worth considering, however, that cost and price are not the same thing, and what matters to the owners of the payload is the price.  Chapter \ref{sec:lvtrends} discusses trends in launch vehicle price.  Nonetheless, knowing the cost and possible trends in cost is valuable in that no matter what price the end user pays, someone must absorb the costs in the end.  Typically, that someone is a government entity if the costs are not passed on to the end user.
	
  When discussing any new approach to an engineering problem, an assessment of the risk is necessary.  The cost of insurance can provide a measure of risk.  This is a subject that crosses diciplines between engineering and business.  Greenberg and Herzfeld discuss launch insurance briefly in \textit{Space Economics}\cite{spaceeconomics}.  While they do not examine the details of launch insurance pricing closely, they do state that it is approximately 15-20\% for most payloads at the time of their writing.  This estimate parallels that obtained in the analyses in Chapter \ref{sec:risk}. Gould and Linden discuss launch insurance in ``Estimating Satellite Insurance Liabilities'' from a more business-oriented perspective.  They liken spacecraft insurance to human life insurance: there is a relatively high chance of infant mortality (launch failure, deployment failure, or payload failure during the first six months of operation) followed by a period of lower risk, which then slowly ramps up due to aging.
	
	Gathering reference data for the various studies performed in this work required special effort, and so merits additional discussion aside from the brief overview given in Chapter \ref{sec:payloadtrends}.  The payload database described in Chapter \ref{sec:payloadtrends} draws data from multiple sources.  Most important of these, as detailed in that chapter, is the Satellite Catalog, or SATCAT\cite{satcat}.  However, it does not contain all of the data required for payload trending, such as payload mass data, and occasionally the data it does contain is incomplete.  This will be marked with the legend `NEA' (No Elements Available) within the SATCAT data files.  This not only necessitates obtaining mass data from other sources, but obtaining the orbital elements as well.
	
	Another problem that arises with SATCAT is due to spacecraft whose orbits have decayed.  In some places, instead of orbital elements for the satellite when it was in service, SATCAT contains orbital elements for its deorbit trajectory.  This is of course quite different from whatever orbit the payload occupied in its useful career.  In this case, other sources provided data for the payload's intended orbit.  
	
	For older (pre 2004) payloads, AIAA's \textit{International Reference Guide to Space Launch Systems}\cite{irgsls} contains useful data on payloads.  It also contains data for launch vehicle prices.  Unfortunately, it is somewhat dated, and the majority of the data set postdates its publication.  
	  
	Space enthusiasts and hobbyists maintain several websites that contain useful spacecraft data.  Unfortunately, the provenance of some of it is suspect, and there is no commitment to archive data.  Encyclopedia Astronautica\cite{astronautix} is a well-respected, longstanding resource of this type, to the point that \textit{International Reference Guide to Space Launch Systems} actually uses it as a source.  It was the first source consulted when searching for payload masses and the launch vehicle used.  EOPortal\cite{eoportal} has a wealth of data on Earth science spacecraft, and has more frequent updates than Encyclopedia Astronautica, making it more useful for later missions in the data set.  
	
	Two additional United States government agencies maintain registries of space objects.  NASA's National Space Science Data Center\cite{nssdc} contains much of the same data as SATCAT, in addition to brief descriptions of the payloads' missions and technical characteristics.  The US Registry of Objects Launched into Outer Space\cite{usro} is maintained by the US Department of State in accordance with the 1976 UN Convention on Registration of Objects Launched into Outer Space.  This contains much of the same information as SATCAT and the NSSDC database, but occasionally one of them will have data that the other two lack. 
	 
	The Union of Concerned Scientists maintains a database of spacecraft\cite{ucs}.  This does not contain orbital elements but it has a few pieces of information that the other sources listed here lack, such as who constructed the payload.  It also has some payload masses, including some for national security satellites that are not available elsewhere.
	
	A single database compiles data from the above sources, along with notes that indicate potential inaccuracies, conflicts, or assumptions.  Appendix A contains a table of the most critical data from the database, including payload masses and launch vehicle payload capacities.  
	
	Launch vehicle pricing poses a similar problem.  Many of the extant sources are conflicting and few of them make clear statements about what the price they present includes.  For instance, the 2006 FAA Q1 Launch Report gives the price of Delta IV Heavy as \$155M, which is \$182M in 2014 dollars\cite{faa2006q1}. The Congressional Budget Office indicates the current price may be as much as \$411M (2014\$), more than twice as much\cite{cbo}.  Some of this is an effect of different measures of cost.  The Congressional Budget Office's 2006 study differentiates between the actual cost of the launch vehicle hardware and `launch services' or the overhead associated with actually carrying out the launch.  The hardware-only price given for Delta IV Heavy in that report is \$235M in 2014 dollars, which is much more in line with the FAA's earlier estimate.  Unfortunately, few of the other sources of launch vehicle data make this distinction. 
	
	The analyses herein use the lowest price given by a reputable source, adjusted for inflation to 2014 dollars.  The intent of this practice is to avoid subjective evaluation of cost claims for launch vehicles.  Such an evaluation would be based on little more than the evaluator's judgment.  It is more valuable in this case to have an even basis for comparison, even if it may not be accurate.  This also has the result of providing a `best case' scenario.  The financial losses incurred by wastage and cost-ineffective launch vehicle selection may be much greater than the values obtained in this work.
	
	The preferred sources for price data are the launch vehicle providers.  Of these, only SpaceX provides an upfront cost for their launch services.  \$56.5M was the Falcon 9 launch price in 2014 and in the analyses in this work, although in 2015 SpaceX raised this to \$61.5M\cite{spacexcosts}.  ULA released a price for Atlas V 401 of \$164M in 2013\cite{ulacosts}, but this includes government overhead, and as discussed in Chapter \ref{sec:lvtrends}, this is a considerable expense, and one that is difficult to estimate.  Cost data for the remainder of the launch vehicles must be obtained from other sources.
	
	Many of the same sources used for payload data also contain launch vehicle data.  Encyclopedia Astronautica contains a considerable amount of cost data for launch vehicles, although it has limited data on newer launch vehicles such as Falcon 9 and H-IIB.  \textit{International Reference Guide to Space Launch Systems} is similar in this respect, as it contains much of the same data.  
	
	FAA Launch Reports and Year In Review reports also contain cost data for launch vehicles.  These provided the bulk of the launch vehicle cost data.  Chapter 11 of \textit{Satellite Communications Systems: Systems, Techniques, and Technology} by Maral and Bousquet provides some launch vehicle data\cite{satellitecommunications}.  It is similar in approach to \textit{International Reference Guide to Space Launch Systems} but contains data that are more recent.  Some individual papers contain launch vehicle price data, such as much of Koelle's work.  ``Specific Transportation Costs to GEO – Past, Present, and Future'' contains a table listing the cost of several launch vehicles.\cite{stc}  Since Koelle also cites an older edition of \textit{International Reference Guide to Space Launch Systems}, these data may be sourced from there.
	
	Appendix B contains the compiled launch vehicle data.  Some launch vehicle configurations do not have price data extant.  For most of these, the price of some configuration in the same family is known.  For instance, there is cost data for Delta IV Medium+ (4,2), but not for Delta IV Medium.   If the price is unknown, the price of the nearest configuration in size is used.  There is no price data available for H-IIB, and a price of \$180M was assigned based on Ariane 5, which is a launch vehicle of similar size and configuration.
  
\chapter{Payload Trends}
\label{sec:payloadtrends}

  In order to perform any analysis on the employment of launch vehicles to carry payloads, some knowledge about the characteristics of these payloads is necessary.  It is critical to know their mass and final orbit, as these two considerations determine the payload capacity of the launch vehicle for the mission in question.  It is also important to know how these values trend over time.  Changes in the average mass of payloads or the number of payloads going to each orbit are critical knowledge for future developers and users of launch vehicles.  

	It is difficult to look forward at payload trends.  While some information is available, such as NASA budget estimates\cite{nasafy15estimates}, and in FAA Launch Reports, it is incomplete.  Very little of it goes more than a few years into the future, and given the nature of budgeting in both commercial and governmental organizations there must also be a great deal of uncertainty.  
	
	Fortunately, a good deal of information is available on past missions, raising the possibility of estimating future trends by projecting past trends into the future.  The US Department of Defense tracks every object deliberately launched into space.  This responsibility originally belonged to NORAD, the North American Aerospace Defense Command, and passed through several agencies before falling to US Strategic Command, where it currently resides.  This Satellite Catalog, or SATCAT, lists the payload name, COSPAR and NORAD numbers, nationality, orbital elements, launch date, decay date (if applicable) and other information for all of these space objects.  The most important part of this additional information consists of flags indicating the nature of the object.  Objects marked `R/B' (rocket body) or `DEB' (debris) are not payloads and will not be counted as such.  
	
	Unfortunately, SATCAT alone is not sufficient for payload trend analysis of the type required because it does not contain mass data.  Additional research is required to determine the mass of each payload.  This data is available from several sources, including the payload registries discussed in Chapter~\ref{sec:review}, government reports, and press releases.  Official sources, such as press releases from either the launching agency or the agency that owns the payload, are preferred.  If official sources are unavailable, a number of secondary sources for payload mass data exist, such as AIAA's \textit{International Reference Guide to Space Launch Systems}\cite{irgsls} and other secondary sources.
	
	The data set under investigation consists of 1,405 payloads launched between January 1, 2000, and September 29, 2013, beginning with object 2000-001A, a DSCS 3 geosynchronous communications satellite belonging to the US Department of Defense, launched on January 21, 2000, and ending with object 2013-056A, SES' Astra 2E geosynchronous communications satellite, launched on September 29, 2013. 
	
	Most analyses in this work excluded payloads or missions with certain characteristics.  105 of the payloads have no mass data available, and were therefore excluded.  This includes a number of United States, Russian, and Chinese national security payloads.  The 85 manned missions were also excluded, since the safety requirements for manned missions are much more stringent than those for unmanned missions, which imposes additional costs.  It is also difficult to make a level comparison between crew or passengers and cargo.  That is, it can be difficult to determine the additional mission mass requirement for each passenger or crewmember for comparison purposes.  For a system like Soyuz, this may be relatively easy to determine by dividing the mass of the capsule by the number of humans carried, but for a system like the Space Shuttle, it is less obvious.  Finally, interplanetary and lunar craft were excluded, since it is difficult to find a basis for comparison between them and they constitute a small portion of all spacecraft, with only 29 in the data set.  This leaves 1,186 payloads.
	
	An important part of the analysis is assigning payloads to orbits.  Throughout this work, LEO is defined as an orbit with perigee and apogee less than 2000km altitude, MEO is defined as having perigee and apogee greater than 2000km but less than GEO, and HEO is defined as having an apogee above 2000km and a perigee below it.  Some payloads have orbits that do not correspond to these groupings, resulting in their exclusion from the analysis.  There are five of these not already excluded for missing payload mass or payload capacity data, leaving a grand total of 1,181 payloads being considered in payload trending.
	
	Figure~\ref{fig:payloadbyorbit} displays the number of payloads deployed to each orbit by year.  2013 is omitted since it is not complete.  A number of trends are apparent.  The first is the great increase since the middle of the last decade in LEO payloads, caused by the rise of the microsatellite.  The second is the relatively slow, steady increase in the number of geosynchronous payloads.
	    
\begin{figure}%[htbp]
  \begin{center}
    \includegraphics[width=140mm]{payloadsbyorbit.png}
    \caption{Payloads By Orbit, 2000-2013}
    \label{fig:payloadbyorbit}
  \end{center}
\end{figure}  

	Figure~\ref{fig:payloadmassbyorbit} contains the total payload mass delivered to each orbit by year.  Total LEO payload mass is highly variable, with a large decline in 2003.  This coincides with the \textit{Columbia} disaster, even though there are no Space Shuttle payloads included in this data.  GEO payload mass has the same slow, steady rise shown in Figure~\ref{fig:payloadbyorbit}.    
	
\begin{figure}%[htbp]
  \begin{center}
    \includegraphics[width=140mm]{payloadmassbyorbitnoshuttle.png}
    \caption{Payload Mass By Orbit, 2000-2013}
    \label{fig:payloadmassbyorbit}
  \end{center}
\end{figure} 

	Figures~\ref{fig:frequencyofpayloadmass} and \ref{fig:massofpayloads} contains a histogram and cumulative histogram of payload masses, respectively.  This figure shows a conundrum that space launch presents: 51\% of the payload mass, and therefore demand for launch vehicles, is for payloads in the 4000-8000kg range, but the majority of individual payloads are small payloads with a plurality massing less than 1000kg.  This trend has significant consequences for launch vehicle development and operations, as outlined in subsequent chapters.  
	
\begin{figure}%[htbp]
  \begin{center}
    \includegraphics[width=140mm]{frequencyofpayloadmass.jpg}
    \caption{Number of Payloads of Mass, 2000-2013}
    \label{fig:frequencyofpayloadmass}
  \end{center}
\end{figure} 

\begin{figure}%[htbp]
  \begin{center}
    \includegraphics[width=140mm]{massofpayloads.jpg}
    \caption{Total Mass of Payloads in kg by Individual Mass, 2000-2013}
    \label{fig:massofpayloads}
  \end{center}
\end{figure}  

	Given the great difference in energy requirements between orbits, it is important to know how these masses break down between orbits.  The most important question from an operational perspective is determining which orbit this large majority of small individual payloads are being sent to.
	
\begin{figure}%[htbp]
  \begin{center}
    \includegraphics[width=140mm]{leopayloadmass.png}
    \caption{Number of LEO Payloads of Mass, 2000-2013}
    \label{fig:leopayloadmass}
  \end{center}
\end{figure}  

	The majority of individual spacecraft are in LEO.  LEO missions are extremely diverse, ranging from small student-built CubeSats to the NRO's twenty-ton \textit{Lacrosse} radar surveillance satellite.  It is clear that both the majority of LEO payloads are small (\textless 1000kg) and the majority of small payloads are in LEO.  451 out of the 521 payloads massing less than 1000kg are in LEO.  Notwithstanding their numbers, however, these payloads only constitute 9.47\% of the total LEO payload mass.  Figure~\ref{fig:leopayloadmass} contains a histogram of LEO payload masses.  
	
\begin{figure}%[htbp]
  \begin{center}
    \includegraphics[width=140mm]{geopayloadmass.png}
    \caption{Number of GEO Payloads of Mass, 2000-2013}
    \label{fig:geopayloadmass}
  \end{center}
\end{figure}  

	Figure~\ref{fig:geopayloadmass} is a histogram of geosynchronous payloads.  Geosynchronous orbit is generally the province of communications satellites.  The fixed longitude of payloads there relative to the Earth's surface renders them uniquely suited to this task, and geosynchronous orbit's greater distance from the Earth renders surveillance assets placed there less effective.  It also provides no added benefit to many types of space science.  Accordingly, the masses of payloads to this orbit are close to normally distributed.
	
	The remaining two Earth orbit categories see much less usage.  Medium Earth orbit payloads are suitable for a few specialized tasks.  The most important of these is navigation.  The GPS and GLONASS constellations both have orbits of this sort.  Due to this similarity, they exhibit trends in their masses similar to those of geosynchronous payloads.  Like MEO spacecraft, highly elliptical orbit spacecraft see limited specialized use.  The most important of this is provision of communications services to high latitudes, where geosynchronous spacecraft are unable to perform this mission.  `Molniya' is another term for this orbit, derived from a series of Soviet communications satellites that used it.
	
  It is also important to consider the number of payloads per launch.  Many launch vehicles launch multiple payloads at once.  The COSPAR number assigned to each payload (shown in Appendix A) indicates which payloads launched together, with each launch having a different number and components that reach space having a letter suffix.  Figure~\ref{fig:payloadsperlaunch} presents the average number of payloads per launch for each year.  This quantity increased relatively steadily throughout the entire period.

\begin{figure}%[htbp]
  \begin{center}
    \includegraphics[width=140mm]{payloadsperlaunch.png}
    \caption{Payloads Per Launch, 2000-2013}
    \label{fig:payloadsperlaunch}
  \end{center}
\end{figure}  

  Finally, it can be instructive to examine the average mass of each payload.  For missions with similar individual requirements, a reduction in mass over time might occur due to improvements in technology.  The increase in the number of micro- and nano-satellites over time may also factor in to such a trend.        

\begin{figure}%[htbp]
  \begin{center}
    \includegraphics[width=140mm]{massperpayload.png}
    \caption{Average Mass Per Payload, All Orbits, 2000-2013}
    \label{fig:massperpayload}
  \end{center}
\end{figure}  

  Examining these trends leads to a few conclusions of importance.  The first is that LEO missions are highly variable, while GEO missions are much less so.  This owes to the homogeneity of GEO missions.  Virtually all GEO payloads are communications satellites.  While there are varying degrees of capability, their missions are very similar.

  As stated in the previous discussion, however, LEO missions are highly variable.  This results in their masses being highly variable, and having no real trends, other than the preponderance of small payloads.  This behavior is again due to the increased presence of microsatellites and the improvement in electronics and other spacecraft systems, which makes reduction in mass and therefore expense possible. 
  
  For most years, the payload mass delivered to LEO and GEO are roughly similar, but this does not provide a clear picture of total launch vehicle requirements because GEO is a much more difficult orbit to reach, which reduces launch vehicle payload capacity.  For example, a Falcon 9 v1.1 can place 13,150 kg into LEO, but only 4,850 kg into a GTO\cite{spacexcosts}, making GEO payloads 2.71 times more expensive per mass for this launch vehicle.  This ratio varies somewhat depending on launch vehicle design, but usually lies between two and three, as shown in Table \ref{tbl:leogeo}.

% Table generated by Excel2LaTeX from sheet 'LEOGEO'
\begin{table}%[htbp]
  \centering
  \caption{Ratio of LEO Payload to GTO Payload for Selected Launch Vehicles}
    \begin{tabular}{lrrrr}
    \hline \hline     
    \multicolumn{1}{l}{LV} & \multicolumn{1}{l}{Config} & P (LEO) & P (GTO) & Ratio \\
    \hline
    \multicolumn{1}{l}{Long March} & \multicolumn{1}{l}{2C} & 4400  & 1400  & 3.14 \\
    \multicolumn{1}{l}{} & \multicolumn{1}{l}{2E} & 9500  & 3500  & 2.71 \\
    \multicolumn{1}{l}{} & \multicolumn{1}{l}{3A} & 6000  & 2600  & 2.31 \\
    \multicolumn{1}{l}{} & \multicolumn{1}{l}{3B} & 11200 & 5100  & 2.20 \\
    \multicolumn{1}{l}{} & \multicolumn{1}{l}{3C} & 9100  & 3800  & 2.39 \\
    \multicolumn{1}{l}{Ariane 5} & \multicolumn{1}{l}{G} & 16000 & 6700  & 2.39 \\
    \multicolumn{1}{l}{} & \multicolumn{1}{l}{ECA, ES} & 21000 & 10500 & 2.00 \\
    \multicolumn{1}{l}{Proton-K} & \multicolumn{1}{l}{Block DM} & 19760 & 4930  & 4.01 \\
    \multicolumn{1}{l}{Proton-M} & \multicolumn{1}{l}{Briz-M} & 21000 & 5500  & 3.82 \\
    \multicolumn{1}{l}{Atlas V} & \multicolumn{1}{l}{401} & 9797  & 4950  & 1.98 \\
    \multicolumn{1}{l}{} & \multicolumn{1}{l}{411} & 12150 & 5950  & 2.04 \\
    \multicolumn{1}{l}{} & \multicolumn{1}{l}{421} & 14067 & 6830  & 2.06 \\
    \multicolumn{1}{l}{} & \multicolumn{1}{l}{431} & 15718 & 7640  & 2.06 \\
    \multicolumn{1}{l}{} & \multicolumn{1}{l}{501} & 10300 & 3970  & 2.59 \\
    \multicolumn{1}{l}{} & \multicolumn{1}{l}{511} & 12590 & 5270  & 2.39 \\
    \multicolumn{1}{l}{} & \multicolumn{1}{l}{521} & 15080 & 6285  & 2.40 \\
    \multicolumn{1}{l}{} & \multicolumn{1}{l}{531} & 17250 & 7200  & 2.40 \\
    \multicolumn{1}{l}{} & \multicolumn{1}{l}{541} & 18955 & 7980  & 2.38 \\
    \multicolumn{1}{l}{} & \multicolumn{1}{l}{551} & 20520 & 8670  & 2.37 \\
    \multicolumn{1}{l}{Delta IV} & \multicolumn{1}{l}{Medium} & 9420  & 4440  & 2.12 \\
    \multicolumn{1}{l}{} & \multicolumn{1}{l}{Medium+ (4,2)} & 13140 & 6390  & 2.06 \\
    \multicolumn{1}{l}{} & \multicolumn{1}{l}{Medium+ (5,2)} & 11470 & 5490  & 2.09 \\
    \multicolumn{1}{l}{} & \multicolumn{1}{l}{Medium+ (5,4)} & 14140 & 7300  & 1.94 \\
    \multicolumn{1}{l}{} & \multicolumn{1}{l}{Heavy} & 28790 & 14220 & 2.02 \\
    \multicolumn{1}{l}{Falcon 9} & \multicolumn{1}{l}{-} & 13150 & 4850  & 2.71 \\
    \hline \hline
    \end{tabular}%
  \label{tbl:leogeo}%
\end{table}% 
  
  This behavior results in significant consequences for the development and employment of launch vehicles.  The most important of these consequences is wastage, as discussed and quantified in Chapter~\ref{sec:wastage}.  Chapter~\ref{sec:arrangement} discusses strategies to alleviate wastage, but also demonstrates that given current payloads and launch vehicles, there is no way to completely eliminate wastage.  However, it is possible to reduce wastage considerably.

% \begin{table}[htbp]
%   \centering
%   \caption{LEO Payload Mass for Selected Payload Owners}
%   \resizebox{\columnwidth}{!}{
%     \begin{tabular}{lllllllllllllllll}
%     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%     %%                                                                  %%
%     %%  This is a LaTeX2e table fragment exported from Gnumeric.        %%
%     %%                                                                  %%
%     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%     \hline \hline
%     \multicolumn{17}{l}{Categorized Total Payload Mass to LEO (All Launches other than Manned)}\\
% 	    &	&2000	&2001	&2002	&2003	&2004	&2005	&2006	&2007	&2008	&2009	&2010	&2011	&2012	&2013	&Total\\
% 	  \hline
%     Government - Civilian	&	&	&	&	&	&	&	&	&	&	&	&	&	&	&	&\\
% 	    &NASA	&0	&1060	&4247	&1633	&7443	&360	&2935.5	&0	&4307	&674	&8000	&0	&8000	&11000	&49660\\
% 	    &Roscosmos	&55865	&46455	&21750	&22050	&31763	&29600	&22350	&29800	&29800	&37050	&37250	&29800	&29800	&22350	&4E+05\\
% 	    &JAXA	&0	&0	&0	&0	&0	&2310	&4955	&0	&0	&17750	&0	&16000	&16000	&16000	&73015\\
% 	    &ISRO	&0	&1108	&0	&0	&0	&1602	&0	&1230	&768	&1340	&0	&0	&0	&0	&6048\\
% 	    &ESA	&0	&0	&0	&0	&0	&6535	&630	&0	&19357	&1230	&669	&19357	&19357	&19357	&86492\\
% 	    &CNSA	&0	&0	&0	&0	&4200	&0	&5700	&0	&0	&0	&0	&8000	&0	&0	&17900\\
% 	    &NOAA	&1476	&0	&1475	&0	&0	&1420	&0	&0	&0	&1420	&0	&0	&0	&0	&5791\\
% 	    &Total	&57341	&48623	&27472	&23683	&43406	&41827	&36571	&31030	&54232	&59464	&45919	&73157	&73157	&68707	&7E+05\\
%     Government - Military	&	&	&	&	&	&	&	&	&	&	&	&	&	&	&	&\\
% 	    &DOD	&15005	&5093	&0	&6074	&0	&562	&1524	&1839	&395	&5844	&5161	&5000	&5000	&0	&51497\\
% 	    &NRO	&0	&16650	&0	&0	&0	&39500	&0	&1346	&0	&0	&0	&0	&0	&0	&57496\\
% 	    &Russian MoD	&9900	&3825	&15675	&11280	&14320	&7870	&16600	&10725	&13975	&15450	&7725	&0	&0	&0	&1E+05\\
% 	    &Chinese MoD	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0\\
% 	    &French MoD	&0	&0	&0	&0	&4680	&0	&0	&0	&0	&4200	&0	&0	&0	&0	&8880\\
% 	    &Total	&24905	&25568	&15675	&17354	&19000	&47932	&18124	&13910	&14370	&25494	&12886	&5000	&5000	&0	&2E+05\\
%     Private	&	&	&	&	&	&	&	&	&	&	&	&	&	&	&	&\\
% 	    &PanAmSat	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0\\
% 	    &Intelsat	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0\\
% 	    &Eumetsat	&0	&0	&7911	&0	&0	&0	&4093	&0	&0	&0	&0	&0	&0	&0	&12004\\
% 	    &Globalstar	&1800	&0	&0	&0	&0	&0	&0	&3600	&0	&0	&4200	&8400	&0	&4200	&22200\\
% 	    &Orbcomm	&0	&0	&0	&0	&0	&0	&0	&0	&270	&0	&0	&0	&142	&0	&412\\
% 	    &Echostar	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0\\
% 	    &Iridium	&0	&0	&4830	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&4830\\
% 	    &DirecTV	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0\\
% 	    &Sirius XM	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0\\
% 	    &SES	&0	&0	&5250	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&5250\\
% 	    &RSCC	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0\\
% 	    &Eutelsat	&0	&0	&4050	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&4050\\
% 	    &Total	&1800	&0	&22041	&0	&0	&0	&4093	&3600	&270	&0	&4200	&8400	&142	&4200	&48746\\
% 	    \hline \hline
%       \end{tabular}
%       }
%   \label{tbl:leopayloadbyowner}
% \end{table}% 
%
% \begin{table}[htbp]
%   \centering
%   \caption{GEO Payload Mass for Selected Payload Owners}
%   \resizebox{\columnwidth}{!}{
%     \begin{tabular}{lllllllllllllllll}
%       %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%       %%                                                                  %%
%       %%  This is a LaTeX2e table fragment exported from Gnumeric.        %%
%       %%                                                                  %%
%       %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%       \hline \hline
%       \multicolumn{17}{l}{Categorized Total Payload Mass to GEO (All Launches other than Manned)}\\
% 	      &	&2000	&2001	&2002	&2003	&2004	&2005	&2006	&2007	&2008	&2009	&2010	&2011	&2012	&2013	&Total\\
% 	    \hline
%       Government - Civilian	&	&	&	&	&	&	&	&	&	&	&	&	&	&	&	&\\
% 	      &NASA	&3180	&0	&6382	&0	&0	&0	&0	&0	&107	&0	&3000	&0	&0	&0	&12669\\
% 	      &Roscosmos	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&6100	&6100\\
% 	      &JAXA	&0	&0	&0	&0	&0	&0	&3000	&0	&2700	&0	&0	&0	&0	&0	&5700\\
% 	      &ISRO	&0	&0	&1000	&7533	&1950	&0	&0	&3035	&0	&0	&0	&0	&0	&0	&13518\\
% 	      &ESA	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0\\
% 	      &CNSA	&0	&0	&0	&2200	&0	&0	&0	&2200	&3000	&0	&2200	&0	&0	&0	&9600\\
% 	      &NOAA	&2217	&0	&0	&0	&0	&0	&3199	&0	&0	&0	&3240	&0	&0	&0	&8656\\
% 	      &Total	&5397	&0	&7382	&9733	&1950	&0	&6199	&5235	&5807	&0	&8440	&0	&0	&6100	&56243\\
%       Government - Military	&	&	&	&	&	&	&	&	&	&	&	&	&	&	&	&\\
% 	      &DOD	&8212	&10650	&4550	&11668	&2380	&0	&1000	&8260	&0	&0	&6168	&0	&0	&0	&52888\\
% 	      &NRO	&0	&0	&0	&5200	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&5200\\
% 	      &Russian MoD	&2400	&2000	&0	&2155	&2000	&0	&0	&1900	&2154	&2300	&2500	&0	&0	&0	&17409\\
% 	      &Chinese MoD	&2300	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&2300\\
% 	      &French MoD	&0	&0	&0	&0	&0	&3725	&3750	&0	&0	&0	&0	&0	&0	&0	&7475\\
% 	      &Total	&12912	&12650	&4550	&19023	&4380	&3725	&4750	&10160	&2154	&2300	&8668	&0	&0	&0	&85272\\
%       Private	&	&	&	&	&	&	&	&	&	&	&	&	&	&	&	&\\
% 	      &PanAmSat	&7327	&0	&0	&6529	&0	&2087	&4640	&0	&0	&0	&0	&0	&0	&0	&20583\\
% 	      &Intelsat	&4167	&9450	&18852	&9013	&5575	&2033	&0	&4750	&8790	&8147	&7453	&6200	&22094	&0	&1E+05\\
% 	      &Eumetsat	&0	&0	&2010	&0	&0	&2034	&0	&0	&0	&0	&0	&0	&2010	&0	&6054\\
% 	      &Globalstar	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0\\
% 	      &Orbcomm	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0\\
% 	      &Echostar	&0	&0	&5350	&0	&0	&0	&4333	&0	&5511	&0	&11900	&0	&6100	&0	&33194\\
% 	      &Iridium	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0\\
% 	      &DirecTV	&0	&4245	&8490	&0	&5483	&15907	&8180	&5893	&5920	&5900	&0	&0	&0	&0	&60018\\
% 	      &Sirius XM	&7600	&9334	&0	&0	&0	&4703	&6100	&0	&0	&5976	&5984	&0	&0	&0	&39697\\
% 	      &SES	&16186	&3728	&10762	&4100	&12877	&5000	&6413	&9097	&7844	&12020	&8060	&8437	&18187	&6000	&1E+05\\
% 	      &RSCC	&5200	&0	&2600	&2600	&5084	&5200	&0	&0	&2579	&4812	&0	&0	&0	&0	&28075\\
% 	      &Eutelsat	&5690	&6199	&9775	&1525	&4250	&4981	&8975	&2200	&8340	&16402	&11520	&10000	&10200	&11470	&1E+05\\
% 	      &Total	&46170	&32956	&57839	&23767	&33269	&41945	&38641	&21940	&38984	&53257	&44917	&24637	&58591	&17470	&5E+05\\
% 	      \hline \hline
% 	      \end{tabular}
%       }
%   \label{tbl:geopayloadbyowner}
% \end{table}% 
%
\chapter{Launch Vehicle Trends}
\label{sec:lvtrends}

	Understanding trends in launch vehicle usage, development, and pricing is a critical component of the operational loss problem.  It is clear that selecting an overly large or cost-ineffective launch vehicle can greatly increase launch costs for the user.  As shown in Appendix B, cost-effectiveness can vary by as much as a factor of ten between different launch vehicles.  Losses of a similar order of magnitude are possible with excessive wastage; Appendix A contains several launches with wastage in excess of 80\%, effectively increasing the cost of access to space by a factor of at least five.
	
  Table~\ref{tbl:launchvehiclesused} contains usage data by year for launch vehicle families.  As elsewhere in this work, a `family' uses the same core stage, e.g. the EELT (Extra-Extended Long Tank Thor) for Delta II or the CCB (Common Core Booster) for Atlas V.  A `family' may include multiple generations of the same basic launch vehicle as well, even though they are not strictly speaking identical and may have served concurrently.  For instance, Proton-K launches continued after the introduction of Proton-M, a modernized and much more capable version of the same basic launch vehicle.  Figure~\ref{fig:lvs} contains representatives of selected launch vehicle families drawn to scale.
  
\begin{figure}%[htbp]
  \begin{center}
    \includegraphics[width=140mm]{lvcomparison.png}
    \caption[Selected Launch Vehicles Drawn to Scale]{Selected Launch Vehicles Drawn to Scale (Adapted from Refs. \cite{astronautix}, \cite{avug}, \cite{f9ug})}
    \label{fig:lvs}
  \end{center}
\end{figure}  
  

  There is some confusion of terms regarding `cost' and `price' in the launch vehicle world.  `Launch cost' is often used to describe the money that must be paid to the launch vehicle provider to buy the launch vehicle, integrate the payload, and launch it into a desired orbit.  This is really a price, which is subject in some degree to market forces and other influences\cite{economicprinciplesspace}. 
  
	As noted in Chapter \ref{sec:review}, there are several models for estimating the costs of space missions and their components.  These include TRANSCOST by Koelle\cite{transcost}, the NAFCOM cost model developed by the US Air Force and NASA, and other forms of cost estimation\cite{costestimation}.  While these are valuable for estimating the cost of launch vehicle development and construction, it does not necessarily follow that trends in prices will mirror trends in cost.  While there must be some relation, other considerations such as profit and subsidies can divorce cost from price to some degree.  
	
	The most common metric used to evaluate launch vehicles is price per maximum payload capacity.  Determining pricing can be somewhat difficult.  As of this writing, only SpaceX publicly provides price data for its launch vehicles.  For other launch vehicle providers, the price data used herein are from secondary sources, which include FAA Launch Reports and AIAA's \textit{International Reference Guide to Space Launch Systems}.  Some sources, in particular the FAA reports, give a price range for launch vehicles, e.g. `\$15-20M'.  If this is the case, the lowest price in the range is used.  If multiple sources disagree on what a launch vehicle's price is, the lowest price from a reputable source is used.  These prices were converted to 2014 USD using Federal CPI data.   
	
	Determining payload capacity is much simpler.  Most launch vehicle providers publish a users' guide for their launch vehicle, and these typically provide payload capacities to a wide variety of orbits\cite{avug,divug,diiug,f9ug,vegaug,dneprug,pegasusug,soyuzug,hiiug,protonug,antaresug}.  Some users' guides are not available, such as those for the Titan launch vehicle family.  In this case, secondary sources can provide maximum payload capacities, although few of these are as detailed as the users' guides. 
	  
	One important detail that appears in the users' guides is the actual definition of `payload capacity.'  Some manufacturers, such as ULA, specify a `payload systems weight' that is the sum of the actual payload weight and that of fairings and payload adapters, while other providers count these items as part of the launch vehicle.  In this work, the latter approach is used, as the amount of useful payload delivered is what is valuable.
	
  Since payload capacity varies greatly depending on the payload's final intended orbit and exactly how the payload gets there, providers usually give data for some typical mission, such as a 28.5-degree 185 km low Earth orbit from Cape Canaveral or a GTO.  This work follows this approach.  LEO cost effectiveness is rated by the highest maximum payload capacity to LEO.  This is a minimum altitude circular orbit at an inclination corresponding to the launch site's latitude, e.g. 28.5 degrees for Cape Canaveral.  GTO payload capacity will be rated by the launch vehicle's capacity to a 200 km perigee geosynchronous transfer orbit.  As discussed in further detail in Chapter~\ref{sec:wastage}, this is the most common mission profile for geosynchronous missions.
  
  Price and maximum payload capacity data for 101 launch vehicle configurations were obtained from the above sources.  These are all launch vehicles available between 2000 and 2013.  Some launch vehicles with very few flights, such as Epsilon, Naro-1, Unha 1, and others are not included.  Appendix B contains the launch vehicle data used in this work.

	Understanding how a launch vehicle's characteristics relate to its cost-effectiveness is critical to proper selection and development of launch vehicles.  Evaluation of cost models also serves as a check on the cost data, which are uncertain.  Several possible characteristics will be considered in order to determine if there is a correlation between any of them and the launch vehicle's price per maximum payload capacity.  These include the maximum payload capacity itself, a `performance number' detailed below, flight rate, and total production.
	
	The function of sizing in cost and therefore price has been understood for some time.  It is analogous to the same behavior in conventional aircraft design.  Most previous models used empty mass and then related payload mass to it by setting a structural fraction\cite{costestimation}.  These models will directly use maximum payload capacity to low Earth and geosynchronous orbits.  They make use of logarithmic regression, since this is the trend observed both in cost models\cite{costestimation} and real price data.
	
  It would be desirable to know how the performance of the launch vehicle relates to its price.  That is, determine whether it is desirable to build the smallest empty weight launch vehicle possible by using advanced technologies, or if it is more cost-effective to select a simpler design, with lower performance, and consequently higher empty weight.
  
  The rocket equation dictates two ways to improve launch vehicle performance: increase the specific impulse $I_{sp}$ of the propulsion system, or reduce the structural fraction $\epsilon$ by either reducing the weight of the rocket structure or using an engine with greater thrust to weight ratio. Both approaches are used in any successful space vehicle design, and taken together they provide a measure of the vehicle's efficiency. A metric for this can be created by eliminating the constant g from the rocket equation as well as the payload fraction, resulting in $I_{sp} \ln\frac{1}{\epsilon}$, referred to in the remainder of this work as the `performance number.'  Vacuum specific impulse is used in all cases to ensure an equal comparison, although most first stage engines are not optimized for operation in vacuum.
  
  Many space vehicles have different specific impulse values for each stage. For comparison purposes, a weighted specific impulse value was obtained using the weight fraction of each stage multiplied by the specific impulse of the stage. For instance, a Saturn V has a weighted $I_{sp}$ of 328.66 s ((304s * 5040245lbs + 421s * 1346280lbs) / 6698700lbs).  This provides a general overall estimate of the efficiency of the vehicle's propulsion systems. 
  
	Studying the effects of flight rate is also important, as many cost models \cite{costestimation} are very concerned with flight rate and the effects of the learning curve.  An increase in the number of flights has historically been postulated as a primary method to drastically reduce launch costs.  Flight rates are computed by family, again defined as using the same core stage.  Finally, the total number of each launch vehicle produced is a variable that requires study.  This is the truest measure of the learning curve, although it is less of a measure for fixed costs that may have a cost associated with time as opposed to launches, such as launch facilities and engineering support.
	
	With these data in hand, multiple regression analyses were performed on the data set.  The baseline case consists of a linear regression in two variables, the natural logarithm of the maximum payload capacity and the `performance number,' on all 101 configurations in the data set.  This was done for both LEO and GEO payloads.  Subsequent analyses investigated the effects of flight rate and total production number on launch vehicle prices.  Surprisingly, there appears to be little or no correlation.
	

\begin{table}%[htbp]
  \centering
  \caption{Summary of Cost Estimation Models}
  \label{tbl:costmodels}
  \resizebox{\columnwidth}{!}{
  \begin{tabular}{lccccccccc}
  \hline \hline
  & \multicolumn{4}{l}{Coefficients} & \multicolumn{4}{l}{P-values} & $R^2$ \\
  Model & $a$ & $b$ & $c$ & $d$ & $a$ & $b$ & $c$ & $d$ & Adjusted \\
  \hline
  $C = a \ln P + b n_p + c$, LEO & -3636 & -23.03 & 61690 & - & $4.847 \times 10^{-7}$ & $8.158 \times 10^{-5}$ & $9.919 \times 10^{-15}$ & - & 0.4275\\
  $C = a \ln P + b n_p + c$, GTO & -16230 & -21.68 & 177800 & - & $4.055 \times 10^{-9}$ & 0.1897 & $2.495 \times 10^{-14}$ & - & 0.5070 \\
  $C = a \ln P + b n_p + c r_f + d$, LEO & -3832 & -23.14 & 224.1 & 62730 & $6.670 \times 10^{-7}$ & $7.994 \times 10^{-5}$ & 0.4231 & $1.406 \times 10^{-14}$ & 0.4248\\
  %$C = a \ln P + b n_p + c r_f + d$, GTO \\
  $C = a \ln P + b n_p + c n + d$, LEO & -3658 & -22.89 & -1.140 & 62020 & $4.91 \times 10^{-7}$ & $9.72 \times 10^{-5}$ & 0.5313 & $1.221 \times 10^{-14}$ & 0.4229\\
  %$C = a \ln P + b n_p + c n + d$, GTO \\
  $C = a \ln P + b n_p + c$, US LEO & -4678 & -29.43 & 78310 & - & $1.651 \times 10^{-9}$ & $4.984 \times 10^{-7}$ & $6.422 \times 10^{-16}$ & - & 0.7204 \\
  $C = a \ln P + b n_p + c$, US GTO & -18130 & -48.41 & 217600 & - & $2.283 \times 10^{-8}$ & 0.02103 & $3.518 \times 10^{-14}$ & - & 0.7177 \\
  \hline \hline
  \end{tabular}
  }
\end{table}

\todo[inline]{Note: Analysis ToolPak disabled on work computer.  Call tech support.  In meantime, two missing analyses are commented out.}

	The final analysis is for US launch vehicles only.  This is intended to determine if the trends observed in the two previous analyses are different for a single country of origin than they are for the world as a whole.  The United States was selected for this analysis due to its greater diversity of launch vehicles and their configurations, which provides more data points.  The results of this analysis are presented in Table~\ref{tbl:costmodels} and Figure~\ref{fig:nplnpusonly}.      
	
\begin{figure}%[ht!]
  \begin{center}
    \includegraphics[width=140mm]{nplnpusonly.png}
    \caption{Payload Mass Versus Cost Per Unit Payload Mass Capacity to Low Earth Orbit, US Only}
    \label{fig:nplnpusonly}
  \end{center}
\end{figure}  

	The logarithmic relationship between sizing (either in the form of payload capacity or empty mass) and cost per payload capacity has been known and remarked on for many years. The relationship between efficiency and cost per payload capacity has been less clear.  In the past, various design organizations proposed very large, low performance vehicles (so-called `big dumb boosters')\cite{bigdumbbooster,seadragonp1}. Fierce debate accompanied these proposals.  Analysis of the data shows, however, that among the designs actually built, cost decreases with increasing performance number.  Therefore, the most cost-effective launch vehicle is not a `big dumb booster,' but a `big smart booster.'
	
	One of the prevailing arguments against large boosters of both the `smart' and `dumb' types has been that the development cost begins to suffer a reverse economy of scale, i.e. if a large booster is constructed, the development cost associated with such a difficult engineering challenge grows out of proportion to the payload, destroying the economy of scale.  Furthermore, it is often argued in parallel that the loss of the learning curve benefit associated with high production quantities is a disadvantage.  Both of these arguments are in principle valid, but the price data here in general do not reflect their effects.
	
  Surprisingly, flight rate seems to have little or no effect on current launch vehicle price, which seems to fly in the face of the accepted wisdom.  In actuality, it might not, because of the distinction between cost and price.  Using cost models to determine prices implicitly assumes that the user ultimately pays development costs, which is the exception rather than the rule for most real-world launch vehicles.  Governments have historically financed launch vehicle development for national security or national space program purposes to some greater or lesser extent, whereas private space development of this size has typically proven to be a poor investment.  For instance, SpaceX spent nearly \$90M developing Falcon 1, which ended up having two paying launches at \$7M apiece.  While this was not a total loss, as SpaceX later used the same engine on Falcon 9, it represents a loss of at least \$76M less whatever value SpaceX derived from having an engine design in place when beginning Falcon 9 development.

  This gives rise to an interesting comparison.  The USAF invested approximately \$500M in 1998 dollars in EELV development for each of the winning designs in that program, or \$726.1M in 2014 dollars\cite{spacelaunchhearing}.  NASA's investment in Falcon 9 and Dragon development was approximately \$396M\cite{spacexsaa}\cite{spacexcostvideo}, with SpaceX contributing an additional \$450M of private funding.  It is interesting to note that presumably the cost to develop Falcon 9 was on par with the cost to develop the EELVs, even if the unit cost of the final product is considerably cheaper.

	These practices can `hide' the development cost and some of the other fixed costs of most launch vehicles from the market.  As a result, the `flight rate' effects that were expected are virtually nonexistent.  The sole possible exception to this is the learning curve, whose effects by themselves can in many cases be equal to or smaller than the residuals from the current models.  For instance, at a 90\% learning curve, the cost difference between the 100th and 1000th unit constructed is approximately 31\%, with the 100th unit costing 49\% of the original cost and the 1000th unit costing 34\% of the original cost.  The average residual from the baseline (np-lnP) model is 30\% for all launch vehicles and 27\% for US launch vehicles.  Comparatively few launch vehicles have such high production numbers; the only launch vehicle with more than 1000 units produced is Soyuz, of which 1,727 had been built as of the end of the data set.  The legacy Delta family (from the earliest Thor derivatives to Delta III) ranks second, with 701 units produced, and no other family has a production quantity higher than 500.  
	
	Another problem with using flight rate or total production as a variable is that the learning curve is not necessarily constant across designs or across development organizations.  Some designs will have inherent advantages over others.  As an example, compare Falcon 9 with Atlas V 401.  Falcon 9 uses nine identical first stage engines and a second stage engine that is substantially identical with the exception of the nozzle.  Atlas V 401 uses one first stage engine and a different second stage engine.  Therefore, Falcon 9, all other things being equal, will be ten times farther down the learning curve than its competition on one of the key components of the launch vehicle.  Of course, other compromises must be made to do this, but this results in even more cost changes, rendering the possibility of determining cost from flight rate or total production even more difficult.
	
  From a more strictly engineering perspective, the results obtained here contradict the assertions made by Koelle and others\cite{costestimation} that advanced materials and other innovative techniques actually increase cost.  For US launch vehicles, the relationship between increasing performance number and decreasing price is quite strong.  It is difficult to say how much of the cost associated with the use of advanced technology is paid on the development side and how much is paid on the production side, but whatever additional costs are being incurred on the production side are more than being repaid.
  
\begin{landscape}
%\begin{table}%[htbp]
\begin{longtable}{lrrrrrrrrrrrrrrrr}
  %\centering
  \caption{Launch Vehicles Used, 2000-2013}\\
  \label{tbl:launchvehiclesused}\\
   \hline \hline
   &       & 2000  & 2001  & 2002  & 2003  & 2004  & 2005  & 2006  & 2007  & 2008  & 2009  & 2010  & 2011  & 2012  & 2013  & Total \\
   \hline
  \endfirsthead
  %\resizebox{\columnwidth}{!}{
    %\begin{tabular}{lrrrrrrrrrrrrrrrr}
          &       & 2000  & 2001  & 2002  & 2003  & 2004  & 2005  & 2006  & 2007  & 2008  & 2009  & 2010  

& 2011  & 2012  & 2013  & Total \\
    \hline
    \endhead
    \hline
    \endfoot
    \hline
    \endlastfoot
    \multicolumn{1}{l}{Ariane 4} & \multicolumn{1}{l}{} & 7     & 6     & 7     & 1     & 0     & 0     & 

0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 21 \\
    \multicolumn{1}{l}{Ariane 5} & \multicolumn{1}{l}{} & 4     & 2     & 3     & 3     & 0     & 2     & 

5     & 4     & 6     & 5     & 5     & 3     & 3     & 4     & 49 \\
    \multicolumn{1}{l}{Atlas} & \multicolumn{1}{l}{} & 8     & 2     & 4     & 2     & 4     & 0     & 0 

    & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 20 \\
    \multicolumn{1}{l}{Atlas V} & \multicolumn{1}{l}{} & 0     & 0     & 0     & 2     & 1     & 1     & 1 

    & 2     & 1     & 3     & 3     & 1     & 1     & 1     & 17 \\
    \multicolumn{1}{l}{Delta II} & \multicolumn{1}{l}{} & 1     & 1     & 1     & 2     & 3     & 1     & 2 

    & 1     & 3     & 2     & 1     & 1     & 0     & 0     & 19 \\
    \multicolumn{1}{l}{Delta IV} & \multicolumn{1}{l}{} & 0     & 0     & 0     & 2     & 0     & 0     & 

1     & 1     & 0     & 0     & 0     & 0     & 0     & 0     & 4 \\
    \multicolumn{1}{l}{Proton} & \multicolumn{1}{l}{} & 8     & 5     & 4     & 3     & 5     & 4     & 3  

   & 4     & 8     & 8     & 8     & 5     & 0     & 1     & 66 \\
    \multicolumn{1}{l}{Soyuz} & \multicolumn{1}{l}{} & 8     & 7     & 4     & 5     & 3     & 6     & 5   

  & 9     & 5     & 7     & 6     & 5     & 4     & 1     & 75 \\
    \multicolumn{1}{l}{PSLV} & \multicolumn{1}{l}{} & 0     & 1     & 1     & 1     & 0     & 1     & 0    

 & 2     & 1     & 0     & 0     & 1     & 0     & 0     & 8 \\
    \multicolumn{1}{l}{GSLV} & \multicolumn{1}{l}{} & 0     & 1     & 0     & 1     & 1     & 0     & 0    

 & 1     & 0     & 0     & 0     & 0     & 0     & 0     & 4 \\
    \multicolumn{1}{l}{Long March 2} & \multicolumn{1}{l}{} & 0     & 0     & 0     & 0     & 1     & 1    

 & 1     & 1     & 0     & 0     & 0     & 0     & 0     & 0     & 4 \\
    \multicolumn{1}{l}{Long March 3} & \multicolumn{1}{l}{} & 3     & 0     & 0     & 2     & 1     & 1    

 & 2     & 4     & 3     & 1     & 1     & 6     & 0     & 0     & 24 \\
    \multicolumn{1}{l}{Long March 4} & \multicolumn{1}{l}{} & 0     & 0     & 1     & 1     & 1     & 0    

 & 2     & 1     & 2     & 0     & 1     & 2     & 0     & 0     & 11 \\
    \multicolumn{1}{l}{Zenit} & \multicolumn{1}{l}{} & 4     & 3     & 1     & 2     & 4     & 3     & 4   

  & 0     & 5     & 1     & 0     & 1     & 0     & 0     & 28 \\
    Titan &       & 3     & 3     & 2     & 3     & 1     & 2     & 0     & 0     & 0     & 0     & 0     

& 0     & 0     & 0     & 14 \\
    Kosmos &       & 3     & 1     & 4     & 3     & 2     & 2     & 1     & 3     & 3     & 0     & 1     

& 0     & 0     & 0     & 23 \\
    Molniya &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0    

 & 0     & 0     & 0     & 0 \\
    Dnepr &       & 1     & 0     & 1     & 0     & 1     & 1     & 1     & 3     & 2     & 1     & 3     

& 0     & 0     & 0     & 14 \\
    H-II  &       & 0     & 0     & 2     & 1     & 0     & 0     & 2     & 1     & 1     & 2     & 1     

& 1     & 2     & 1     & 14 \\
    Rokot &       & 1     & 0     & 2     & 2     & 0     & 1     & 1     & 0     & 1     & 2     & 2     

& 1     & 0     & 1     & 14 \\
    Minotaur 1 &       & 2     & 0     & 0     & 0     & 0     & 2     & 2     & 1     & 0     & 1     & 0 

    & 1     & 0     & 0     & 9 \\
    Pegasus &       & 1     & 0     & 1     & 4     & 0     & 0     & 0     & 1     & 2     & 0     & 0    

 & 0     & 0     & 1     & 10 \\
    Falcon 1 &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 1     & 0   

  & 0     & 0     & 0     & 1 \\
    Falcon 9 &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 2   

  & 0     & 2     & 1     & 5 \\
    Antares &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0    

 & 0     & 0     & 2     & 2 \\
    Start-1 &       & 1     & 1     & 0     & 0     & 0     & 0     & 1     & 0     & 0     & 0     & 0    

 & 0     & 0     & 0     & 3 \\
    Tsyklon &       & 0     & 3     & 0     & 0     & 1     & 0     & 1     & 0     & 0     & 0     & 0    

 & 0     & 0     & 0     & 5 \\
    Vega  &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 1     & 1     & 2 \\
    Total &       & 55    & 36    & 38    & 40    & 29    & 28    & 35    & 39    & 43    & 34    & 34    

& 28    & 13    & 14    & 466 \\
   \hline \hline
    %\end{tabular}%
    %}
%\end{table}%
\end{longtable}
\end{landscape}


\chapter{Capability of Launch Vehicles}
\label{sec:capability}

	A launch vehicle is only useful for launching payloads that are less massive than its maximum payload capacity to the desired orbit.  That is, it must have capability to carry the payload to the desired trajectory.  Since sizing is a critical design decision for any aerospace vehicle, determining the relative capability and therefore usefulness of a launch vehicle requires evaluation of launch vehicle designs according to the payload trends observed in Chapter~\ref{sec:payloadtrends}.
	
	Payload capacity can vary widely within the orbital categories defined in Chapter~\ref{sec:payloadtrends}.  This is especially true for low Earth orbits, given the wide variety of desired altitudes and inclinations.  A considerable number of these are in polar or sun-synchronous (98.1 degree inclination) orbits which impose a significant extra delta-V requirement and corresponding loss of payload capacity.  Other orbit types are more consistent since they are typically tied to a single type of usage, but even geosynchronous transfer orbit capacity can change depending on mission profile\cite{avug,divug}.
	
	This analysis requires the same restrictions as the payload trending in Chapter~\ref{sec:payloadtrends}, with a few additions.  201 additional payloads were excluded as there was no payload capacity data for their launch vehicles.  The primary cause for this is missing data for capacities to certain sorts of orbits.  For many launch vehicles where the users' guides are unavailable, payload capacity is only given to a few orbits, and if a payload is not in one of these, it is not possible to determine the launch vehicle's payload capacity for its mission.  Some users' guides are also missing data for certain orbits, such as the Arianespace Soyuz users' guide\cite{soyuzug}, which is missing data for certain low Earth orbits.  This leaves a total of 985 payloads.
	
	Table~\ref{tbl:suitability} contains the percentage of individual payloads that each launch vehicle family could launch by year.  `Family' is again defined as using the same core stage or stages.  As might be expected, Delta IV, which with Delta IV Heavy has the largest launcher in existence as of this writing, can launch any payload in the data set.  The smallest launchers, Pegasus and Falcon 1, can launch approximately 33\% of individual payloads.  The remainder of launch vehicle families fall somewhere in between, depending on the maximum payload capacity of their largest configuration.
	
		Table~\ref{tbl:suitabilitypercentage} lists the capability of each launcher as a percentage of the total payload mass.  The picture here is completely different.  Falcon 1 and Pegasus' 33\% of individual \textit{payloads} translate into less than 2\% of total payload \textit{mass}.  	Combined with the results of the analysis presented in Chapter~\ref{sec:lvtrends}, it is clear that small launch vehicles labor under a considerable disadvantage.  Not only are they inherently more expensive per unit of payload mass capacity due to their small size, they are incapable of launching much of the revenue-generating payload mass required to repay their development costs.
		
		Given the utilization data, it is also possible to make statements about each launch vehicle's real market share, i.e. fraction of individual payloads or payload mass that it launched versus the total number of payloads or payload mass that it was capable of launching.  Tables~\ref{tbl:massmarketshare}, \ref{tbl:payloadmarketshare}, and \ref{tbl:fractionmarketshare} present the market share of each launch vehicle family in terms of percentage of payload mass that it was capable of launch, percentage of individual payloads that it was capable of launching, and fraction of individual payloads that it was capable of launching.  As elsewhere in this work, this is done only for the 525 LEO and GTO launches with complete data.
		
		As can be seen, in terms of market share, Soyuz is far ahead of any of its competitors, with a payload mass market share of 45.48\% of the payloads that it is capable of launching, or 17.2\% of all payload mass.  Single digit percentage market shares are far more typical.
  
	This is an important consideration for launch vehicle development, especially privately funded development.  Many launch vehicle design studies estimate the overall size of their market or their production numbers, which amounts to the same thing\cite{costestimation}.  But it is clear that even a highly successful launch vehicle like Soyuz, which is both very cost-effective and very reliable, can only capture less than half of its possible market.  Furthermore, even in Soyuz's case, a considerable percentage of its unmanned launches are Russian government launches in the form of Progress ISS logistics craft and military payloads.  Progress alone accounted for 56 of the 83 unmanned Soyuz launches in the data set.  Strictly speaking, it does not have to compete for either of these, as Progress is specifically designed to be launched on Soyuz and Russia, like most nations, will not launch national security payloads on another country's launch vehicles.
	
	As touched on in Chapter~\ref{sec:lvtrends}, for a government developing a launch vehicle, this consideration may not be a problem.  A government can estimate its own future need for launch vehicles based on its own requirements and determine whether the development costs, which it usually pays up front, are justified.  Privately funded launch vehicle development cannot do this.  It must estimate what the market will offer.  Unfortunately, these data indicate that in the majority of cases the answer will be `very little.'
		
\begin{landscape}
%\tiny
\begin{table}%[htbp]
  \centering
  \caption{Percentage of the Number of Payloads Launchable, 2000-2013}
  \resizebox{\columnwidth}{!}{
  \label{tbl:suitability}
    \begin{tabular}{lrHHrrrrrrrrrrrrrrr}
    \hline \hline
          &       & LEO (kg) & GTO (kg) & 2000  & 2001  & 2002  & 2003  & 2004  & 2005  & 2006  & 2007  & 2008  & 2009  & 2010  & 2011  & 2012  & 2013  & 2000-2013 \\
  \hline
    \multicolumn{2}{l}{Ariane 4} & 7600  & 4300  & 87.23\% & 81.25\% & 80.00\% & 88.24\% & 89.09\% & 

76.36\% & 77.46\% & 84.52\% & 75.31\% & 82.42\% & 81.82\% & 77.22\% & 77.97\% & 87.50\% & 81.91\% \\
    \multicolumn{2}{l}{Ariane 5} & 16000 & 10500 & 93.62\% & 89.06\% & 93.33\% & 98.53\% & 100.00\% & 

96.36\% & 95.77\% & 96.43\% & 93.83\% & 94.51\% & 96.59\% & 94.94\% & 98.31\% & 98.44\% & 95.53\% \\
    \multicolumn{2}{l}{Atlas} & 6580  & 3630  & 74.47\% & 67.19\% & 73.33\% & 79.41\% & 72.73\% & 61.82\% 

& 63.38\% & 76.19\% & 64.20\% & 68.13\% & 73.86\% & 69.62\% & 69.49\% & 81.25\% & 71.21\% \\
    \multicolumn{2}{l}{Atlas V} & 20520 & 8900  & 94.68\% & 90.63\% & 93.33\% & 98.53\% & 100.00\% & 

98.18\% & 95.77\% & 96.43\% & 95.06\% & 94.51\% & 96.59\% & 96.20\% & 100.00\% & 100.00\% & 96.21\% \\
    \multicolumn{2}{l}{Delta II} & 13443 & 4787  & 91.49\% & 89.06\% & 92.00\% & 95.59\% & 94.55\% & 

81.82\% & 85.92\% & 92.86\% & 79.01\% & 83.52\% & 82.95\% & 79.75\% & 81.36\% & 87.50\% & 86.87\% \\
    \multicolumn{2}{l}{Delta IV} & 28790 & 14220 & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 

100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 

100.00\% \\
    \multicolumn{2}{l}{Proton} & 19760 & 6920  & 93.62\% & 90.63\% & 93.33\% & 98.53\% & 100.00\% & 

96.36\% & 94.37\% & 96.43\% & 95.06\% & 94.51\% & 96.59\% & 96.20\% & 100.00\% & 100.00\% & 95.91\% \\
    \multicolumn{2}{l}{Soyuz} & 7450  & 3250  & 78.72\% & 73.44\% & 76.00\% & 83.82\% & 81.82\% & 69.09\% 

& 70.42\% & 82.14\% & 69.14\% & 75.82\% & 80.68\% & 75.95\% & 72.88\% & 82.81\% & 76.75\% \\
    \multicolumn{2}{l}{PSLV} & 3700  & 0     & 44.68\% & 42.19\% & 48.00\% & 54.41\% & 54.55\% & 45.45\% & 

45.07\% & 63.10\% & 48.15\% & 56.04\% & 56.82\% & 55.70\% & 49.15\% & 68.75\% & 52.43\% \\
    \multicolumn{2}{l}{GSLV} & 0     & 2500  & 17.02\% & 12.50\% & 6.67\% & 16.18\% & 10.91\% & 7.27\% & 

9.86\% & 10.71\% & 7.41\% & 6.59\% & 6.82\% & 6.33\% & 5.08\% & 4.69\% & 9.24\% \\
    \multicolumn{2}{l}{Long March 2} & 9200  & 0     & 52.13\% & 54.69\% & 61.33\% & 60.29\% & 65.45\% & 

56.36\% & 56.34\% & 70.24\% & 56.79\% & 64.84\% & 67.05\% & 64.56\% & 62.71\% & 76.56\% & 62.06\% \\
    \multicolumn{2}{l}{Long March 3} & 12000 & 5500  & 92.55\% & 89.06\% & 93.33\% & 98.53\% & 96.36\% & 

85.45\% & 91.55\% & 94.05\% & 87.65\% & 85.71\% & 90.91\% & 91.14\% & 84.75\% & 90.63\% & 90.86\% \\
    \multicolumn{2}{l}{Long March 4} & 4200  & 1500  & 46.81\% & 45.31\% & 57.33\% & 61.76\% & 58.18\% & 

45.45\% & 53.52\% & 63.10\% & 51.85\% & 58.24\% & 59.09\% & 59.49\% & 55.93\% & 73.44\% & 56.42\% \\
    \multicolumn{2}{l}{Zenit} & 13740 & 5250  & 92.55\% & 89.06\% & 93.33\% & 98.53\% & 94.55\% & 85.45\% 

& 90.14\% & 94.05\% & 86.42\% & 84.62\% & 85.23\% & 88.61\% & 84.75\% & 89.06\% & 89.69\% \\
    \multicolumn{2}{l}{STS} & 25000 & 0     & 60.64\% & 65.63\% & 68.00\% & 61.76\% & 65.45\% & 61.82\% & 

60.56\% & 73.81\% & 62.96\% & 71.43\% & 70.45\% & 70.89\% & 66.10\% & 79.69\% & 67.22\% \\
    \multicolumn{2}{l}{Titan IV} & 21680 & 5760  & 94.68\% & 90.63\% & 93.33\% & 98.53\% & 98.18\% & 

89.09\% & 91.55\% & 94.05\% & 91.36\% & 90.11\% & 92.05\% & 94.94\% & 88.14\% & 93.75\% & 92.90\% \\
    \multicolumn{2}{l}{Kosmos} & 775   & 0     & 38.30\% & 31.25\% & 36.00\% & 33.82\% & 36.36\% & 34.55\% 

& 28.17\% & 45.24\% & 44.44\% & 42.86\% & 45.45\% & 48.10\% & 40.68\% & 60.94\% & 40.76\% \\
    \multicolumn{2}{l}{Dnepr} & 3200  & 0     & 43.62\% & 42.19\% & 48.00\% & 54.41\% & 54.55\% & 45.45\% 

& 45.07\% & 63.10\% & 48.15\% & 56.04\% & 56.82\% & 55.70\% & 49.15\% & 65.63\% & 52.14\% \\
    \multicolumn{2}{l}{H-II} & 16500 & 8000  & 93.62\% & 89.06\% & 93.33\% & 98.53\% & 100.00\% & 96.36\% 

& 94.37\% & 96.43\% & 93.83\% & 94.51\% & 96.59\% & 94.94\% & 98.31\% & 98.44\% & 95.43\% \\
    \multicolumn{2}{l}{Rokot} & 2150  & 0     & 42.55\% & 37.50\% & 44.00\% & 52.94\% & 41.82\% & 41.82\% 

& 40.85\% & 57.14\% & 46.91\% & 52.75\% & 54.55\% & 55.70\% & 47.46\% & 64.06\% & 48.93\% \\
    \multicolumn{2}{l}{Minotaur 1} & 1350  & 0     & 40.43\% & 35.94\% & 40.00\% & 44.12\% & 40.00\% & 

36.36\% & 39.44\% & 52.38\% & 44.44\% & 49.45\% & 53.41\% & 51.90\% & 45.76\% & 62.50\% & 45.82\% \\
    \multicolumn{2}{l}{Minotaur V} & 1600  & 0     & 42.55\% & 35.94\% & 41.33\% & 48.53\% & 40.00\% & 

40.00\% & 40.85\% & 54.76\% & 44.44\% & 50.55\% & 53.41\% & 54.43\% & 45.76\% & 64.06\% & 47.28\% \\
    \multicolumn{2}{l}{Pegasus} & 376   & 0     & 25.53\% & 28.13\% & 22.67\% & 33.82\% & 34.55\% & 

29.09\% & 23.94\% & 29.76\% & 34.57\% & 40.66\% & 36.36\% & 31.65\% & 30.51\% & 48.44\% & 32.10\% \\
    \multicolumn{2}{l}{Falcon 1} & 409   & 0     & 26.60\% & 28.13\% & 22.67\% & 33.82\% & 34.55\% & 

29.09\% & 23.94\% & 29.76\% & 35.80\% & 41.76\% & 36.36\% & 31.65\% & 35.59\% & 50.00\% & 32.78\% \\
    \multicolumn{2}{l}{Falcon 9} & 13150 & 4850  & 91.49\% & 89.06\% & 93.33\% & 95.59\% & 94.55\% & 

81.82\% & 85.92\% & 92.86\% & 80.25\% & 83.52\% & 84.09\% & 81.01\% & 81.36\% & 87.50\% & 87.26\% \\
    \multicolumn{2}{l}{Antares} & 6000  & 0     & 44.68\% & 43.75\% & 54.67\% & 54.41\% & 56.36\% & 

45.45\% & 47.89\% & 63.10\% & 49.38\% & 57.14\% & 60.23\% & 56.96\% & 55.93\% & 70.31\% & 54.38\% \\
\hline \hline
    \end{tabular}%
    }
\end{table}%
%\normalsize
\end{landscape}
    
\begin{landscape}	
\begin{table}%[htbp]
  \centering
  \caption{Percentage of Total Payload Mass Launchable, 2000-2013}
  \label{tbl:suitabilitypercentage}%
  \resizebox{\columnwidth}{!}{
    \begin{tabular}{lrHHrrrrrrrrrrrrrrH}
    \hline \hline
          &       & LEO (kg) & GTO (kg) & 2000  & 2001  & 2002  & 2003  & 2004  & 2005  & 2006  & 2007  & 2008  & 2009  & 2010  & 2011  & 2012  & 2013  & 2000-2013 \\
    \hline
    \multicolumn{2}{l}{Ariane 4} & 7600  & 4300  & 45.41\% & 38.43\% & 39.89\% & 62.15\% & 77.17\% & 

43.79\% & 43.86\% & 47.16\% & 33.78\% & 39.44\% & 44.00\% & 32.64\% & 45.99\% & 49.98\% & 43.77\% \\
    \multicolumn{2}{l}{Ariane 5} & 16000 & 10500 & 58.66\% & 46.17\% & 57.39\% & 84.01\% & 100.00\% & 

77.99\% & 70.76\% & 68.42\% & 60.60\% & 62.06\% & 71.69\% & 65.22\% & 89.40\% & 86.27\% & 67.79\% \\
    \multicolumn{2}{l}{Atlas} & 6580  & 3630  & 25.73\% & 20.30\% & 29.61\% & 37.94\% & 38.21\% & 20.36\% 

& 20.44\% & 27.87\% & 15.10\% & 16.26\% & 25.38\% & 17.53\% & 27.57\% & 31.42\% & 23.88\% \\
    \multicolumn{2}{l}{Atlas V} & 20520 & 8900  & 64.55\% & 51.67\% & 57.39\% & 84.01\% & 100.00\% & 

87.90\% & 70.76\% & 68.42\% & 67.12\% & 62.06\% & 71.69\% & 72.49\% & 100.00\% & 100.00\% & 71.78\% \\
    \multicolumn{2}{l}{Delta II} & 13443 & 4787  & 52.96\% & 46.17\% & 55.69\% & 77.21\% & 87.45\% & 

50.68\% & 54.61\% & 61.04\% & 38.49\% & 40.92\% & 45.73\% & 37.37\% & 51.07\% & 49.98\% & 51.17\% \\
    \multicolumn{2}{l}{Delta IV} & 28790 & 14220 & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 

100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 

100.00\% \\
    \multicolumn{2}{l}{Proton} & 19760 & 6920  & 58.66\% & 51.67\% & 57.39\% & 84.01\% & 100.00\% & 

77.99\% & 67.49\% & 68.42\% & 67.12\% & 62.06\% & 71.69\% & 72.49\% & 100.00\% & 100.00\% & 70.34\% \\
    \multicolumn{2}{l}{Soyuz} & 7450  & 3250  & 36.86\% & 32.21\% & 35.95\% & 54.56\% & 64.91\% & 36.67\% 

& 36.33\% & 43.62\% & 27.31\% & 32.12\% & 42.46\% & 31.21\% & 40.21\% & 42.50\% & 37.82\% \\
    \multicolumn{2}{l}{PSLV} & 3700  & 0     & 5.55\% & 5.29\% & 8.41\% & 14.55\% & 19.95\% & 7.34\% & 

8.68\% & 15.21\% & 4.71\% & 7.01\% & 8.26\% & 7.07\% & 6.53\% & 14.10\% & 8.56\% \\
    \multicolumn{2}{l}{GSLV} & 0     & 2500  & 9.56\% & 4.93\% & 2.34\% & 11.80\% & 9.12\% & 4.03\% & 

3.64\% & 8.55\% & 2.79\% & 4.09\% & 5.28\% & 2.82\% & 2.94\% & 3.18\% & 5.17\% \\
    \multicolumn{2}{l}{Long March 2} & 9200  & 0     & 19.72\% & 23.35\% & 29.06\% & 33.43\% & 49.75\% & 

28.53\% & 29.11\% & 33.76\% & 20.68\% & 24.18\% & 30.36\% & 25.64\% & 32.22\% & 37.44\% & 28.07\% \\
    \multicolumn{2}{l}{Long March 3} & 12000 & 5500  & 54.44\% & 46.17\% & 57.39\% & 84.01\% & 91.50\% & 

55.63\% & 62.73\% & 63.26\% & 50.36\% & 44.15\% & 60.01\% & 54.60\% & 56.65\% & 57.33\% & 57.41\% \\
    \multicolumn{2}{l}{Long March 4} & 4200  & 1500  & 6.32\% & 6.22\% & 14.13\% & 18.62\% & 24.06\% & 

7.34\% & 12.86\% & 15.21\% & 5.29\% & 8.67\% & 11.35\% & 8.41\% & 13.78\% & 18.65\% & 11.01\% \\
    \multicolumn{2}{l}{Zenit} & 13740 & 5250  & 54.44\% & 46.17\% & 57.39\% & 84.01\% & 87.45\% & 55.63\% & 65.34\% & 60.09\% & 67.09\% & 58.67\% & 66.43\% & 51.59\% & 62.51\% & 63.39\% \\
    \multicolumn{2}{l}{Titan IV}      & 21680 & 5760  & 64.55\% & 51.67\% & 57.39\% & 84.01\% & 95.61\% & 72.73\% & 62.73\% 

& 63.26\% & 60.63\% & 54.38\% & 62.15\% & 69.96\% & 76.02\% & 82.40\% & 65.48\% \\
    \multicolumn{2}{l}{Kosmos}        & 775   & 0     & 2.22\% & 1.04\% & 2.70\% & 1.53\% & 1.74\% & 1.65\% & 1.34\% & 3.92\% 

& 2.75\% & 1.08\% & 2.93\% & 4.04\% & 2.49\% & 5.33\% & 2.40\% \\
    \multicolumn{2}{l}{Dnepr}        & 3200  & 0     & 4.51\% & 5.29\% & 8.41\% & 14.55\% & 19.95\% & 7.34\% & 8.68\% & 

15.21\% & 4.71\% & 7.01\% & 8.26\% & 7.07\% & 6.53\% & 9.14\% & 8.25\% \\
    \multicolumn{2}{l}{H-II}  &        16500 & 8000  & 58.66\% & 46.17\% & 57.39\% & 84.01\% & 100.00\% & 77.99\% & 67.49\% & 

68.42\% & 60.60\% & 62.06\% & 71.69\% & 65.22\% & 89.40\% & 86.27\% & 67.55\% \\
    \multicolumn{2}{l}{Rokot} &       2150  & 0     & 3.58\% & 2.68\% & 5.40\% & 12.59\% & 4.88\% & 4.37\% & 5.15\% & 9.47\% 

& 3.97\% & 4.52\% & 6.25\% & 7.07\% & 5.16\% & 7.22\% & 5.52\% \\
    \multicolumn{2}{l}{Minotaur 1}       & 1350  & 0     & 2.74\% & 2.01\% & 3.62\% & 5.91\% & 3.33\% & 2.06\% & 4.60\% & 

6.79\% & 2.75\% & 2.94\% & 5.59\% & 5.24\% & 4.07\% & 6.23\% & 3.95\% \\
    \multicolumn{2}{l}{Minotaur V}        & 1600  & 0     & 3.58\% & 2.01\% & 4.13\% & 8.84\% & 3.33\% & 3.54\% & 5.15\% & 

8.01\% & 2.75\% & 3.38\% & 5.59\% & 6.33\% & 4.07\% & 7.22\% & 4.59\% \\
    \multicolumn{2}{l}{Pegasus}      & 376   & 0     & 0.41\% & 0.72\% & 0.56\% & 1.53\% & 1.18\% & 0.82\% & 0.54\% & 

0.96\% & 0.98\% & 0.75\% & 0.78\% & 0.70\% & 0.92\% & 1.71\% & 0.82\% \\
    \multicolumn{2}{l}{Falcon 1}        & 409   & 0     & 0.52\% & 0.72\% & 0.56\% & 1.53\% & 1.18\% & 0.82\% & 0.54\% & 

0.96\% & 1.11\% & 0.87\% & 0.78\% & 0.70\% & 1.58\% & 2.00\% & 0.90\% \\
    \multicolumn{2}{l}{Falcon 9}        & 13150 & 4850  & 52.96\% & 46.17\% & 57.39\% & 77.21\% & 87.45\% & 50.68\% & 54.61\% 

& 61.04\% & 40.10\% & 40.92\% & 47.59\% & 39.18\% & 51.07\% & 49.98\% & 51.74\% \\
    \multicolumn{2}{l}{Antares}        & 6000  & 0     & 5.55\% & 6.94\% & 16.42\% & 14.55\% & 23.05\% & 7.34\% & 11.91\% & 

15.21\% & 6.16\% & 8.32\% & 13.29\% & 8.95\% & 15.90\% & 16.94\% & 11.17\% \\
   \hline \hline
    \end{tabular}%
  }
  
\end{table}%
\end{landscape}	

\begin{landscape}
% Table generated by Excel2LaTeX from sheet 'Plots'
\begin{table}%[htbp]
  \centering
  \caption{Market Share as a Percentage of Possible Payload Mass}
    \resizebox{\columnwidth}{!}{
    
    \begin{tabular}{rrHHrrrrrrrrrrrrrrr}
    \hline \hline
          &       & LEO (kg) & GTO (kg) & 2000  & 2001  & 2002  & 2003  & 2004  & 2005  & 2006  & 2007  & 2008  & 2009  & 2010  & 2011  & 2012  & 2013  & Total \\
    \hline
    \multicolumn{2}{l}{Ariane 4} & 7600  & 4300  & 16.94\% & 21.39\% & 27.78\% & 4.94\% & 0.00\% 

& 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 5.93\% \\
    \multicolumn{2}{l}{Ariane 5} & 21000 & 10500 & 8.79\% & 4.84\% & 12.50\% & 11.74\% & 7.86\% & 

15.95\% & 23.05\% & 27.20\% & 30.76\% & 20.12\% & 24.41\% & 24.33\% & 30.75\% & 29.27\% & 19.93\% 

\\
    \multicolumn{2}{l}{Atlas I} & 6580  & 3630  & 24.98\% & 18.00\% & 17.27\% & 12.51\% & 22.33\% 

& 10.86\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 8.62\% \\
    \multicolumn{2}{l}{Atlas V} & 20520 & 8900  & 0.00\% & 0.00\% & 0.00\% & 6.06\% & 3.06\% & 

3.27\% & 2.43\% & 5.57\% & 3.31\% & 5.15\% & 7.43\% & 2.46\% & 2.22\% & 9.18\% & 3.45\% \\
    \multicolumn{2}{l}{Delta 7} & 13443 & 4787  & 1.74\% & 1.42\% & 3.97\% & 4.39\% & 6.20\% & 

1.32\% & 1.76\% & 4.17\% & 7.36\% & 6.47\% & 1.44\% & 3.20\% & 0.00\% & 0.00\% & 3.19\% \\
    \multicolumn{2}{l}{Delta IV} & 28790 & 14220 & 0.00\% & 0.00\% & 1.91\% & 3.10\% & 0.00\% & 

0.00\% & 2.44\% & 1.38\% & 0.00\% & 1.56\% & 1.70\% & 0.00\% & 0.00\% & 0.00\% & 0.80\% \\
    \multicolumn{2}{l}{Proton} & 19760 & 6920  & 25.18\% & 8.78\% & 18.38\% & 9.00\% & 18.63\% & 

14.41\% & 11.20\% & 10.34\% & 15.82\% & 19.83\% & 26.88\% & 13.54\% & 20.87\% & 14.25\% & 16.76\% 

\\
    \multicolumn{2}{l}{Soyuz} & 7450  & 3250  & 37.66\% & 52.05\% & 28.11\% & 35.79\% & 40.45\% & 

56.77\% & 51.73\% & 48.26\% & 53.17\% & 51.47\% & 40.21\% & 53.23\% & 43.43\% & 54.72\% & 45.58\% 

\\
    \multicolumn{2}{l}{PSLV} & 3700  & 0     & 0.00\% & 9.27\% & 4.37\% & 6.12\% & 0.00\% & 

10.81\% & 0.00\% & 4.66\% & 7.86\% & 5.16\% & 3.83\% & 17.28\% & 15.73\% & 10.09\% & 6.21\% \\
    \multicolumn{2}{l}{GSLV} & 0     & 2500  & 0.00\% & 10.24\% & 0.00\% & 10.14\% & 15.77\% & 

0.00\% & 0.00\% & 10.75\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 4.04\% \\
    \multicolumn{2}{l}{Long March 2} & 9200  & 0     & 0.00\% & 0.00\% & 0.00\% & 5.88\% & 7.73\% 

& 9.59\% & 4.12\% & 3.91\% & 2.35\% & 0.00\% & 3.19\% & 11.16\% & 6.33\% & 2.37\% & 3.92\% \\
    \multicolumn{2}{l}{Long March 3} & 12000 & 5500  & 4.01\% & 0.00\% & 0.00\% & 3.51\% & 1.10\% 

& 3.99\% & 5.55\% & 9.65\% & 5.82\% & 4.84\% & 1.37\% & 18.61\% & 4.98\% & 5.91\% & 4.95\% \\
    \multicolumn{2}{l}{Long March 4} & 4200  & 1500  & 6.08\% & 0.00\% & 7.98\% & 5.63\% & 

12.31\% & 0.00\% & 16.07\% & 11.78\% & 17.85\% & 3.39\% & 22.82\% & 15.84\% & 8.58\% & 0.00\% & 

9.66\% \\
    \multicolumn{2}{l}{Zenit} & 13740 & 5250  & 11.86\% & 8.73\% & 2.93\% & 7.73\% & 15.01\% & 

14.29\% & 12.61\% & 2.18\% & 18.68\% & 8.31\% & 0.00\% & 6.82\% & 13.71\% & 1.24\% & 9.05\% \\
    \multicolumn{2}{l}{Titan}        & 21680 & 5760  & 7.75\% & 15.34\% & 3.63\% & 9.11\% & 1.82\% & 22.74\% & 

0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 4.23\% \\
    \multicolumn{2}{l}{Kosmos}       & 775   & 0     & 33.49\% & 26.07\% & 29.29\% & 73.06\% & 53.77\% & 55.64\% & 

22.99\% & 26.02\% & 21.67\% & 0.00\% & 10.88\% & 0.00\% & 0.00\% & 0.00\% & 19.81\% \\
    \multicolumn{2}{l}{Dnepr}       & 3200  & 0     & 0.76\% & 0.00\% & 0.59\% & 0.00\% & 0.81\% & 4.25\% & 6.26\% 

& 8.25\% & 10.54\% & 1.57\% & 10.76\% & 0.00\% & 0.00\% & 0.00\% & 3.30\% \\
    \multicolumn{2}{l}{H-II}       & 16500 & 8000  & 0.00\% & 0.00\% & 5.08\% & 1.60\% & 0.00\% & 2.03\% & 8.02\% 

& 1.25\% & 1.50\% & 8.72\% & 2.10\% & 8.68\% & 9.18\% & 11.57\% & 4.40\% \\
    \multicolumn{2}{l}{Rokot}       & 2150  & 0     & 9.51\% & 0.00\% & 13.24\% & 5.01\% & 0.00\% & 7.94\% & 6.19\% 

& 0.00\% & 7.63\% & 10.15\% & 9.75\% & 6.29\% & 4.93\% & 13.95\% & 6.97\% \\
    \multicolumn{2}{l}{Minotaur 1}       & 1350  & 0     & 2.98\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 13.53\% & 

6.90\% & 3.14\% & 0.00\% & 3.45\% & 0.00\% & 3.10\% & 0.00\% & 0.00\% & 2.19\% \\
    \multicolumn{2}{l}{Minotaur V}       & 1600  & 0     & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 

0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% \\
    \multicolumn{2}{l}{Pegasus}       & 376   & 0     & 26.91\% & 0.00\% & 28.08\% & 47.70\% & 0.00\% & 21.86\% & 

0.00\% & 8.86\% & 17.27\% & 0.00\% & 0.00\% & 0.00\% & 20.83\% & 7.65\% & 12.67\% \\
    \multicolumn{2}{l}{Falcon 1}       & 409   & 0     & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 

0.00\% & 0.00\% & 0.00\% & 6.41\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.58\% \\
    \multicolumn{2}{l}{Falcon 9}       & 13150 & 4850  & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 

0.00\% & 0.00\% & 0.00\% & 0.00\% & 6.51\% & 0.00\% & 7.50\% & 6.54\% & 1.17\% \\
    \multicolumn{2}{l}{Antares}       & 6000  & 0     & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 

0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 28.53\% & 1.80\% \\
    \hline \hline
    \end{tabular}%
  }
  \label{tbl:massmarketshare}%
\end{table}%
\end{landscape}
\begin{landscape}
% Table generated by Excel2LaTeX from sheet 'Plots'
\begin{table}%[htbp]
  \centering
  \caption{Market Share as a Percentage of Possible Individual Payloads}
    \resizebox{\columnwidth}{!}{
    
    \begin{tabular}{rrHHrrrrrrrrrrrrrrr}
    \hline \hline
          &       & LEO (kg) & GTO (kg) & 2000  & 2001  & 2002  & 2003  & 2004  & 2005  & 2006  & 2007  & 2008  & 2009  & 2010  & 2011  & 2012  & 2013  & Total \\
    \hline
    \multicolumn{2}{l}{Ariane 4} & 7600  & 4300  & 10.34\% & 13.73\% & 16.39\% & 1.67\% & 0.00\% 

& 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 3.09\% \\
    \multicolumn{2}{l}{Ariane 5} & 21000 & 10500 & 9.57\% & 5.26\% & 7.04\% & 8.96\% & 14.29\% & 

14.55\% & 14.49\% & 14.63\% & 14.29\% & 11.24\% & 14.12\% & 10.00\% & 16.25\% & 9.86\% & 11.81\% 

\\
    \multicolumn{2}{l}{Atlas I} & 6580  & 3630  & 11.11\% & 7.14\% & 9.09\% & 3.70\% & 9.76\% & 

2.86\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 3.03\% \\
    \multicolumn{2}{l}{Atlas V} & 20520 & 8900  & 0.00\% & 0.00\% & 0.00\% & 2.99\% & 1.79\% & 

1.82\% & 1.45\% & 9.76\% & 1.30\% & 3.37\% & 3.53\% & 1.25\% & 12.50\% & 5.63\% & 3.39\% \\
    \multicolumn{2}{l}{Delta 7} & 13443 & 4787  & 7.69\% & 5.36\% & 8.57\% & 7.69\% & 5.66\% & 

2.17\% & 8.06\% & 3.85\% & 6.25\% & 7.59\% & 1.39\% & 10.61\% & 0.00\% & 0.00\% & 5.51\% \\
    \multicolumn{2}{l}{Delta IV} & 28790 & 14220 & 0.00\% & 0.00\% & 1.41\% & 2.99\% & 0.00\% & 

0.00\% & 2.90\% & 1.22\% & 0.00\% & 1.12\% & 1.18\% & 0.00\% & 0.00\% & 0.00\% & 0.77\% \\
    \multicolumn{2}{l}{Proton} & 19760 & 6920  & 12.90\% & 8.77\% & 9.86\% & 7.46\% & 12.50\% & 

11.11\% & 7.35\% & 4.88\% & 10.39\% & 12.36\% & 18.82\% & 10.00\% & 12.50\% & 5.63\% & 10.49\% \\
    \multicolumn{2}{l}{Soyuz} & 7450  & 3250  & 10.53\% & 17.39\% & 7.02\% & 8.77\% & 10.87\% & 

20.51\% & 15.69\% & 21.74\% & 10.71\% & 18.06\% & 8.57\% & 36.51\% & 18.97\% & 26.32\% & 16.52\% 

\\
    \multicolumn{2}{l}{PSLV} & 3700  & 0     & 0.00\% & 11.54\% & 2.78\% & 2.70\% & 0.00\% & 

8.00\% & 0.00\% & 9.43\% & 25.64\% & 11.32\% & 10.20\% & 17.39\% & 7.32\% & 16.67\% & 9.30\% \\
    \multicolumn{2}{l}{GSLV} & 0     & 2500  & 0.00\% & 12.50\% & 0.00\% & 9.09\% & 16.67\% & 

0.00\% & 0.00\% & 11.11\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 3.96\% \\
    \multicolumn{2}{l}{Long March 2} & 9200  & 0     & 0.00\% & 0.00\% & 0.00\% & 2.44\% & 

10.81\% & 6.25\% & 2.50\% & 3.39\% & 6.52\% & 0.00\% & 5.17\% & 1.89\% & 10.20\% & 7.55\% & 

3.95\% \\
    \multicolumn{2}{l}{Long March 3} & 12000 & 5500  & 4.35\% & 0.00\% & 0.00\% & 2.99\% & 1.85\% 

& 2.08\% & 4.55\% & 5.06\% & 4.23\% & 2.47\% & 1.25\% & 8.00\% & 2.94\% & 1.56\% & 3.09\% \\
    \multicolumn{2}{l}{Long March 4} & 4200  & 1500  & 2.17\% & 0.00\% & 7.14\% & 4.76\% & 6.06\% 

& 0.00\% & 7.69\% & 3.77\% & 7.14\% & 3.64\% & 11.76\% & 20.00\% & 6.52\% & 0.00\% & 6.14\% \\
    \multicolumn{2}{l}{Zenit} & 13740 & 5250  & 4.35\% & 12.50\% & 1.41\% & 2.99\% & 7.55\% & 

6.25\% & 6.15\% & 1.27\% & 8.57\% & 5.00\% & 0.00\% & 5.48\% & 4.41\% & 1.61\% & 4.59\% \\
    \multicolumn{2}{l}{Titan}       & 21680 & 5760  & 3.19\% & 5.26\% & 2.82\% & 5.97\% & 1.82\% & 4.00\% & 0.00\% 

& 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 1.51\% \\
    \multicolumn{2}{l}{Kosmos}       & 775   & 0     & 19.44\% & 5.00\% & 22.22\% & 39.13\% & 15.00\% & 63.16\% & 

5.00\% & 7.89\% & 22.22\% & 0.00\% & 2.56\% & 0.00\% & 0.00\% & 0.00\% & 11.83\% \\
    \multicolumn{2}{l}{Dnepr}       & 3200  & 0     & 11.90\% & 0.00\% & 16.67\% & 0.00\% & 25.81\% & 8.00\% & 

3.13\% & 30.19\% & 15.38\% & 11.32\% & 8.16\% & 0.00\% & 0.00\% & 0.00\% & 9.71\% \\
    \multicolumn{2}{l}{H-II}       & 16500 & 8000  & 0.00\% & 0.00\% & 8.45\% & 2.99\% & 0.00\% & 1.85\% & 5.88\% 

& 2.44\% & 1.32\% & 10.11\% & 4.71\% & 1.27\% & 5.06\% & 1.43\% & 3.41\% \\
    \multicolumn{2}{l}{Rokot}       & 2150  & 0     & 4.88\% & 0.00\% & 11.76\% & 25.00\% & 0.00\% & 4.35\% & 

3.45\% & 0.00\% & 10.53\% & 10.00\% & 8.51\% & 2.17\% & 5.13\% & 13.33\% & 7.46\% \\
    \multicolumn{2}{l}{Minotaur 1}       & 1350  & 0     & 28.95\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 10.00\% & 

28.57\% & 2.27\% & 0.00\% & 10.87\% & 0.00\% & 2.38\% & 0.00\% & 0.00\% & 5.76\% \\
    \multicolumn{2}{l}{Minotaur V}       & 1600  & 0     & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 

0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% \\
    \multicolumn{2}{l}{Pegasus}       & 376   & 0     & 8.33\% & 0.00\% & 5.88\% & 17.39\% & 0.00\% & 6.25\% & 

0.00\% & 4.00\% & 7.14\% & 0.00\% & 0.00\% & 0.00\% & 3.57\% & 2.86\% & 3.80\% \\
    \multicolumn{2}{l}{Falcon 1}       & 409   & 0     & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 

0.00\% & 0.00\% & 0.00\% & 2.70\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.29\% \\
    \multicolumn{2}{l}{Falcon 9}       & 13150 & 4850  & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 

0.00\% & 0.00\% & 0.00\% & 0.00\% & 13.70\% & 0.00\% & 4.69\% & 13.11\% & 2.26\% \\
    \multicolumn{2}{l}{Antares}       & 6000  & 0     & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 

0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 0.00\% & 12.24\% & 1.04\% \\
    \hline \hline
    \end{tabular}%
  }  
  \label{tbl:payloadmarketshare}%
\end{table}%
\end{landscape}
\begin{landscape}
% Table generated by Excel2LaTeX from sheet 'Plots'
\begin{table}%[htbp]
  \centering
  \caption{Market Share as a Fraction of Possible Individual Payloads}
    \resizebox{\columnwidth}{!}{
   
    \begin{tabular}{rrHHrrrrrrrrrrrrrrr}
    \hline \hline
          &       & LEO (kg) & GTO (kg) & 2000  & 2001  & 2002  & 2003  & 2004  & 2005  & 2006  & 

2007  & 2008  & 2009  & 2010  & 2011  & 2012  & 2013  & Total \\
    \hline
    \multicolumn{2}{l}{Ariane 4} & 7600  & 4300  & 9/87  & 7/51  & 10/61 & 1/60  & 0/50  & 0/43  

& 0/56  & 0/71  & 0/61  & 0/78  & 0/71  & 0/64  & 0/61  & 0/60  & 27/874 \\
    \multicolumn{2}{l}{Ariane 5} & 21000 & 10500 & 9/94  & 3/57  & 5/71  & 6/67  & 8/56  & 8/55  

& 10/69 & 12/82 & 11/77 & 10/89 & 12/85 & 8/80  & 13/80 & 7/71  & 122/1033 \\
    \multicolumn{2}{l}{Atlas I} & 6580  & 3630  & 8/72  & 3/42  & 5/55  & 2/54  & 4/41  & 1/35  & 

0/46  & 0/64  & 0/52  & 0/65  & 0/64  & 0/58  & 0/56  & 0/56  & 23/760 \\
    \multicolumn{2}{l}{Atlas V} & 20520 & 8900  & 0/94  & 0/57  & 0/71  & 2/67  & 1/56  & 1/55  & 

1/69  & 8/82  & 1/77  & 3/89  & 3/85  & 1/80  & 10/80 & 4/71  & 35/1033 \\
    \multicolumn{2}{l}{Delta 7} & 13443 & 4787  & 7/91  & 3/56  & 6/70  & 5/65  & 3/53  & 1/46  & 

5/62  & 3/78  & 4/64  & 6/79  & 1/72  & 7/66  & 0/63  & 0/61  & 51/926 \\
    \multicolumn{2}{l}{Delta IV} & 28790 & 14220 & 0/94  & 0/57  & 1/71  & 2/67  & 0/56  & 0/55  

& 2/69  & 1/82  & 0/77  & 1/89  & 1/85  & 0/80  & 0/80  & 0/71  & 8/1033 \\
    \multicolumn{2}{l}{Proton} & 19760 & 6920  & 12/93 & 5/57  & 7/71  & 5/67  & 7/56  & 6/54  & 

5/68  & 4/82  & 8/77  & 11/89 & 16/85 & 8/80  & 10/80 & 4/71  & 108/1030 \\
    \multicolumn{2}{l}{Soyuz} & 7450  & 3250  & 8/76  & 8/46  & 4/57  & 5/57  & 5/46  & 8/39  & 

8/51  & 15/69 & 6/56  & 13/72 & 6/70  & 23/63 & 11/58 & 15/57 & 135/817 \\
    \multicolumn{2}{l}{PSLV} & 3700  & 0     & 0/43  & 3/26  & 1/36  & 1/37  & 0/31  & 2/25  & 

0/32  & 5/53  & 10/39 & 6/53  & 5/49  & 8/46  & 3/41  & 8/48  & 52/559 \\
    \multicolumn{2}{l}{GSLV} & 0     & 2500  & 0/17  & 1/8   & 0/5   & 1/11  & 1/6   & 0/4   & 

0/8   & 1/9   & 0/6   & 0/7   & 0/6   & 0/6   & 0/5   & 0/3   & 4/101 \\
    \multicolumn{2}{l}{Long March 2} & 9200  & 0     & 0/50  & 0/34  & 0/45  & 1/41  & 4/37  & 

2/32  & 1/40  & 2/59  & 3/46  & 0/61  & 3/58  & 1/53  & 5/49  & 4/53  & 26/658 \\
    \multicolumn{2}{l}{Long March 3} & 12000 & 5500  & 4/92  & 0/56  & 0/71  & 2/67  & 1/54  & 

1/48  & 3/66  & 4/79  & 3/71  & 2/81  & 1/80  & 6/75  & 2/68  & 1/64  & 30/972 \\
    \multicolumn{2}{l}{Long March 4} & 4200  & 1500  & 1/46  & 0/28  & 3/42  & 2/42  & 2/33  & 

0/25  & 3/39  & 2/53  & 3/42  & 2/55  & 6/51  & 10/50 & 3/46  & 0/51  & 37/603 \\
    \multicolumn{2}{l}{Zenit} & 13740 & 5250  & 4/92  & 7/56  & 1/71  & 2/67  & 4/53  & 3/48  & 

4/65  & 1/79  & 6/70  & 4/80  & 0/74  & 4/73  & 3/68  & 1/62  & 44/958 \\
    \multicolumn{2}{l}{Titan}       & 21680 & 5760  & 3/94  & 3/57  & 2/71  & 4/67  & 1/55  & 2/50  & 0/66  & 0/79  

& 0/74  & 0/85  & 0/81  & 0/78  & 0/70  & 0/66  & 15/993 \\
    \multicolumn{2}{l}{Kosmos}      & 775   & 0     & 7/36  & 1/20  & 6/27  & 9/23  & 3/20  & 12/19 & 1/20  & 3/38 

 & 8/36  & 0/38  & 1/39  & 0/38  & 0/34  & 0/43  & 51/431 \\
    \multicolumn{2}{l}{Dnepr}       & 3200  & 0     & 5/42  & 0/26  & 6/36  & 0/37  & 8/31  & 2/25  & 1/32  & 16/53 

& 6/39  & 6/53  & 4/49  & 0/46  & 0/41  & 0/46  & 54/556 \\
    \multicolumn{2}{l}{H-II}       & 16500 & 8000  & 0/93  & 0/56  & 6/71  & 2/67  & 0/56  & 1/54  & 4/68  & 2/82  

& 1/76  & 9/89  & 4/85  & 1/79  & 4/79  & 1/70  & 35/1025 \\
    \multicolumn{2}{l}{Rokot}       & 2150  & 0     & 2/41  & 0/23  & 4/34  & 9/36  & 0/24  & 1/23  & 1/29  & 0/48  

& 4/38  & 5/50  & 4/47  & 1/46  & 2/39  & 6/45  & 39/523 \\
    \multicolumn{2}{l}{Minotaur 1}       & 1350  & 0     & 11/38 & 0/23  & 0/30  & 0/30  & 0/22  & 2/20  & 8/28  & 

1/44  & 0/36  & 5/46  & 0/46  & 1/42  & 0/37  & 0/44  & 28/486 \\
    \multicolumn{2}{l}{Minotaur V}       & 1600  & 0     & 0/41  & 0/23  & 0/32  & 0/33  & 0/23  & 0/22  & 0/29  & 

0/46  & 0/36  & 0/47  & 0/46  & 0/44  & 0/37  & 0/45  & 0/504 \\
    \multicolumn{2}{l}{Pegasus}       & 376   & 0     & 2/24  & 0/18  & 1/17  & 4/23  & 0/19  & 1/16  & 0/17  & 

1/25  & 2/28  & 0/36  & 0/31  & 0/25  & 1/28  & 1/35  & 13/342 \\
    \multicolumn{2}{l}{Falcon 1}      & 409   & 0     & 0/25  & 0/18  & 0/17  & 0/23  & 0/19  & 0/16  & 0/17  & 

0/25  & 0/29  & 1/37  & 0/31  & 0/25  & 0/31  & 0/36  & 1/349 \\
    \multicolumn{2}{l}{Falcon 9}       & 13150 & 4850  & 0/91  & 0/56  & 0/71  & 0/65  & 0/53  & 0/46  & 0/62  & 

0/78  & 0/65  & 0/79  & 10/73 & 0/67  & 3/64  & 8/61  & 21/931 \\
    \multicolumn{2}{l}{Antares}       & 6000  & 0     & 0/43  & 0/27  & 0/40  & 0/37  & 0/32  & 0/26  & 0/34  & 

0/53  & 0/40  & 0/54  & 0/52  & 0/47  & 0/45  & 6/49  & 6/579 \\
    \hline
    \end{tabular}%
  }
  \label{tbl:fractionmarketshare}%
\end{table}%
\end{landscape}

\chapter{Wastage of Launch Vehicle Capacity}
\label{sec:wastage}

	The confluence of several trends in the space launch industry results in wastage of launch vehicle capacity.  As noted in Chapter~\ref{sec:lvtrends}, larger launch vehicles tend to benefit from an economy of scale in several ways.  Since cost per maximum payload capacity is an often-used performance metric when evaluating launch vehicles, this encourages the design and construction of larger launch vehicles.  In addition to this, the market itself encourages the development of larger launch vehicles.  As stated in Chapter~\ref{sec:capability}, small launch vehicles are incapable of launching many of the payloads that are in demand.  This prevents their use, even if the cost-effectiveness penalty associated with losing the economy of scale benefits of larger boosters is not a factor.  
  
  This bias towards heavier launch vehicles, coupled with the significant numbers of small payloads, results in wastage of launch vehicle capacity.  This wastage is here defined as payload mass subtracted from the launch vehicle's maximum capacity to the desired orbit.  It specifically does not include fairings or payload adapters, which count against the launch vehicle.  Some care is required, since some manufacturers count some or all such items as payload mass, as discussed in Chapter~\ref{sec:lvtrends}\cite{avug}.
  
  While this definition of wastage may appear simple, several complications expose themselves in the process of determining wastage.  The first is the role that the payload's own propulsion system plays in determining the mission payload capacity.  For low Earth orbit missions this is seldom problematic as the launch vehicle will generally place the payload directly into an orbit close to the one desired, and any onboard orbital maneuvering systems only perform small adjustments.  In contrast, most geosynchronous missions place the payload into a geosynchronous transfer orbit, or GTO, which is a transfer orbit from the Earth's surface to the geosynchronous orbital radius, and then rely on the payload itself to perform circularization and plane change if necessary.  However, this is not the only mission profile that is possible.  Many upper stages, such as Centaur, Briz-M, and others, have the capability to place a payload directly into geosynchronous orbit at a drastically reduced payload capacity. 
  
  Typically, mission planners assign the payload to provide approximately 1500-2300 m/s of delta V, as shown in the various ULA users' guides\cite{avug,diiug,divug} and Chapter 11 of Maral and Bosquet\cite{satellitecommunications}. This is dependent on the latitude of the launch site, although some variation is possible; for example, the ULA users' guides have data for a 1500 m/s GTO launched from Canaveral as distinct from the 1800 m/s normally required for plane change and circularization from that launch site.  Often, sources do not provide the exact trajectory used by the payload or details about the payload's onboard orbital maneuvering systems.  Since the industry standard for geosynchronous payloads is to use a geosynchronous transfer orbit, the listed capacity for that trajectory will be assumed unless there is specific evidence otherwise.  This does introduce a potential for error into calculations of geosynchronous orbit wastage.
  
  Some missions have negative wastage.  There are multiple possible reasons for this.  The first is that the listed maximum payload capacity may have some additional margin.  For example, ULA specifies in their users' guides that their payload capacities are computed to 2.33 standard deviations, or 99\% confidence.  They note in the Atlas V Users' Guide that ``It is practical for Centaur to burn all its propellants when the SC [spacecraft] has a liquid propulsion system capable of correcting for variations in LV performance.''\cite{avug}  The payload may also have an onboard propulsion system.  Both of these scenarios imply a complete use of launch vehicle capacity, and so any analysis of wastage in this work assigns these missions zero wastage.
  
	Figure~\ref{fig:wastage} shows the worldwide wastage percentage for LEO and GEO missions.  As can be seen, wastage in general has declined over the period studied, but is still generally above 10\%.  The outlier for LEO wastage in 2007, at nearly 35\%, was due to several US and Japanese national security missions that had high wastage.  On March 9, 2007, OE-ASTRO, a DARPA payload, launched on an Atlas V 401 with a LEO payload capacity of 9000kg, despite only massing 1839kg.  This resulted in wastage of 7161kg, or 79.6\% of payload capacity.
	
\begin{figure}%[ht!]
  \begin{center}
    \includegraphics[width=140mm]{wastage.png}
    \caption{Wastage to LEO and GTO, 2000-2013}
    \label{fig:wastage}
  \end{center}
\end{figure}  

Figure~\ref{fig:wastagehistogram} is a histogram of wastage for all 589 launches in the data set with complete payload and payload capacity data.  While the overall wastage percentage for the data set is 20.35\%, it is most common for launches to have low wastage, with 167 launches having negligible wastage and 329 of 589 being below the average.  

\begin{figure}%[ht!]
  \begin{center}
    \includegraphics[width=140mm]{wastagehistogram.png}
    \caption{Number of Launches with Given Wastage Percentage, 2000-2013}
    \label{fig:wastagehistogram}
  \end{center}
\end{figure}  

  The preceding data gives some idea of overall wastage trends by year.  Further analysis is necessary to determine whether any other factors affect wastage.  These possible factors include the launch vehicle used, its payload capacity to the desired orbit, and the owner of the payload.  Tables \ref{tbl:leowastagebylv} and \ref{tbl:geowastagebylv} contain wastage data categorized by launch vehicle family for low Earth and geosynchronous orbits respectively.  
  
  Given that wastage is a function of launch vehicle choice and payload arrangement, both of which the customer controls to some degree, measuring wastage by payload owner can provide some measure of merit for the user's attempts to reduce wastage.  Tables \ref{tbl:orgwastageleo} and \ref{tbl:orgwastagegto} contain wastage data categorized by the payload owner to LEO and GTO.
  
  Chapter~\ref{sec:arrangement} examines the relationship between the maximum payload capacities of launch vehicles and the minimum possible wastage if operators arrange payloads in a way intended to reduce wastage as much as possible.  The result obtained there is that the minimum wastage associated with launching a group of payloads on a given launch vehicle decreases with increasing maximum payload capacity.  Data for real world wastage versus launch vehicle payload capacity are presented in Figures~\ref{fig:leowastagevcap} and \ref{fig:geowastagevcap}.
	
\begin{figure}%[ht!]
  \begin{center}
    \includegraphics[width=140mm]{leowastagevcap.png}
    \caption{Overall Wastage Percentage versus Maximum Payload Capacity to LEO}
    \label{fig:leowastagevcap}
  \end{center}
\end{figure}  

\begin{figure}%[ht!]
  \begin{center}
    \includegraphics[width=140mm]{geowastagevcap.png}
    \caption{Overall Wastage Percentage versus Maximum Payload Capacity to GTO}
    \label{fig:geowastagevcap}
  \end{center}
\end{figure}  
	
	There appears to be little or no relationship between current real world wastage and payload capacity.  This indicates that there is currently no concerted effort to reduce wastage, and that only individual users or launch vehicle enterprises are attempting to do so.  While their efforts have the effect of reducing overall wastage over time and increasing the number of payloads per launch, this deviation from the wastage from ideally packed payloads, as explored in Chapter~\ref{sec:arrangement}, indicates that much more improvement is possible.
\begin{landscape}
\begin{table}%[htbp]
  \centering
  \caption{Wastage Percentage to Low Earth Orbit by Launch Vehicle and Year, 2000-2013}
    \resizebox{\columnwidth}{!}{
      \begin{tabular}{lllllllllllllllll}
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        %%                                                                  %%
        %%  This is a LaTeX2e table fragment exported from Gnumeric.        %%
        %%                                                                  %%
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        \hline \hline
        \multicolumn{17}{l}{Wastage Percentage (LEO)}\\
	      &	&2000	&2001	&2002	&2003	&2004	&2005	&2006	&2007	&2008	&2009	&2010	&2011	&2012	&2013	& 2000-2013\\
	      \hline
        Ariane 4	&	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-\\
        Ariane 5	&	&-	&-	&12.43\%	&-	&51.75\%	&-	&-	&-	&0.00\%	&32.26\%	&-	&0.00\%	&0.00\%	&0.00\%	&8.65\%\\
        Atlas	&	&0.83\%	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&0.83\%\\
        Atlas V	&	&-	&-	&-	&-	&-	&-	&-	&82.55\%	&-	&82.86\%	&37.04\%	&15.34\%	&36.71\%	&-	&49.35\%\\
        Delta II	&	&14.02\%	&57.26\%	&0.84\%	&23.60\%	&34.86\%	&28.36\%	&24.27\%	&14.22\%	&32.74\%	&29.39\%	&10.29\%	&27.52\%	&-	&-	&26.76\%\\
        Delta IV	&	&-	&-	&-	&-	&-	&-	&84.19\%	&-	&-	&-	&-	&-	&-	&-	&84.19\%\\
        Proton	&	&0.00\%	&-	&0.00\%	&-	&-	&-	&-	&-	&-	&13.03\%	&-	&-	&-	&-	&0.77\%\\
        Soyuz	&	&15.16\%	&2.59\%	&3.51\%	&1.74\%	&1.44\%	&1.58\%	&8.02\%	&16.06\%	&0.00\%	&0.00\%	&0.00\%	&6.32\%	&8.95\%	&0.00\%	&5.39\%\\
        PSLV	&	&-	&7.43\%	&-	&0.00\%	&-	&0.00\%	&-	&67.76\%	&37.74\%	&71.17\%	&25.64\%	&25.90\%	&-	&40.95\%	&44.08\%\\
        GSLV	&	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-\\
        Long March 2	&	&-	&-	&-	&14.29\%	&43.35\%	&14.29\%	&0.00\%	&83.64\%	&-	&-	&-	&3.13\%	&-	&-	&18.91\%\\
        Long March 3	&	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-\\
        Long March 4	&	&46.43\%	&-	&52.86\%	&42.86\%	&25.00\%	&-	&3.57\%	&25.86\%	&50.00\%	&61.07\%	&15.19\%	&36.98\%	&3.04\%	&0.00\%	&27.25\%\\
        Zenit	&	&18.89\%	&45.94\%	&-	&-	&36.00\%	&-	&-	&-	&-	&-	&-	&-	&-	&-	&26.57\%\\
        STS	&	&0.00\%	&0.00\%	&0.00\%	&0.00\%	&-	&0.00\%	&0.00\%	&0.00\%	&0.00\%	&0.00\%	&0.00\%	&0.00\%	&-	&-	&0.00\%\\
        Titan	&	&33.03\%	&23.20\%	&32.25\%	&72.66\%	&-	&20.43\%	&-	&-	&-	&-	&-	&-	&-	&-	&26.22\%\\
        Kosmos	&	&19.54\%	&0.00\%	&30.06\%	&17.10\%	&0.00\%	&14.19\%	&0.65\%	&0.43\%	&23.87\%	&-	&0.00\%	&-	&-	&-	&14.86\%\\
        Molniya	&	&-	&-	&0.00\%	&0.00\%	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&0.00\%\\
        Dnepr	&	&95.94\%	&-	&95.81\%	&-	&70.06\%	&47.50\%	&48.68\%	&38.74\%	&23.45\%	&64.92\%	&26.88\%	&-	&-	&-	&57.23\%\\
        H-II	&	&-	&-	&23.67\%	&82.52\%	&-	&-	&52.22\%	&60.95\%	&-	&13.92\%	&-	&0.00\%	&8.44\%	&0.00\%	&22.80\%\\
        Rokot	&	&6.14\%	&-	&33.43\%	&51.85\%	&-	&47.76\%	&41.96\%	&-	&12.20\%	&27.59\%	&39.42\%	&12.50\%	&0.00\%	&44.91\%	&31.22\%\\
        Minotaur 1	&	&54.68\%	&-	&-	&-	&-	&24.77\%	&25.68\%	&0.00\%	&-	&37.85\%	&-	&0.00\%	&-	&-	&26.16\%\\
        Minotaur V	&	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-\\
        Pegasus	&	&0.00\%	&-	&0.00\%	&11.11\%	&-	&0.00\%	&-	&21.20\%	&0.00\%	&-	&-	&-	&0.00\%	&0.00\%	&5.34\%\\
        Falcon 1	&	&-	&-	&-	&-	&-	&-	&-	&-	&-	&44.62\%	&-	&-	&-	&-	&44.62\%\\
        Falcon 9	&	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&61.68\%	&-	&61.04\%	&61.72\%	&61.44\%\\
        Antares	&	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&16.07\%	&16.07\%\\
        \hline \hline
      \end{tabular}
      \label{tbl:leowastagebylv}
  }
\end{table}
\end{landscape}
\begin{landscape}
\begin{table}%[htbp]
  \centering
  \caption{Wastage Percentage to Geosynchronous Orbit by Launch Vehicle and Year, 2000-2013}
    \resizebox{\columnwidth}{!}{
      \begin{tabular}{lllllllllllllllll}
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        %%                                                                  %%
        %%  This is a LaTeX2e table fragment exported from Gnumeric.        %%
        %%                                                                  %%
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        \hline \hline
        \multicolumn{17}{l}{Wastage Percentage (GEO)}\\
	      &	&2000	&2001	&2002	&2003	&2004	&2005	&2006	&2007	&2008	&2009	&2010	&2011	&2012	&2013	& 2000-2013\\
	      \hline
        Ariane 4	&	&7.72\%	&4.54\%	&8.87\%	&0.95\%	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&6.91\%\\
        Ariane 5	&	&22.80\%	&35.51\%	&30.74\%	&24.44\%	&12.50\%	&29.45\%	&21.66\%	&19.04\%	&20.81\%	&28.52\%	&26.08\%	&14.58\%	&20.23\%	&14.92\%	&22.51\%\\
        Atlas	&	&18.91\%	&14.38\%	&24.03\%	&12.09\%	&20.97\%	&-	&-	&-	&-	&-	&-	&-	&-	&-	&19.44\%\\
        Atlas V	&	&-	&-	&-	&30.80\%	&35.14\%	&22.61\%	&27.19\%	&14.66\%	&4.21\%	&30.97\%	&25.01\%	&0.00\%	&-	&13.45\%	&21.83\%\\
        Delta II	&	&-	&-	&-	&-	&-	&-	&45.02\%	&-	&-	&-	&-	&-	&-	&-	&45.02\%\\
        Delta IV	&	&-	&-	&40.19\%	&49.13\%	&-	&-	&39.64\%	&66.37\%	&-	&15.43\%	&15.28\%	&0.00\%	&-	&-	&25.94\%\\
        Proton	&	&31.06\%	&31.65\%	&17.78\%	&24.39\%	&33.51\%	&34.28\%	&37.11\%	&29.08\%	&37.91\%	&20.79\%	&21.45\%	&28.81\%	&9.65\%	&5.01\%	&25.11\%\\
        Soyuz	&	&-	&-	&-	&69.35\%	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&69.35\%\\
        PSLV	&	&-	&-	&0.00\%	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&0.00\%\\
        GSLV	&	&-	&38.80\%	&-	&27.00\%	&22.00\%	&-	&-	&14.80\%	&-	&-	&-	&-	&-	&-	&25.65\%\\
        Long March 2	&	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-\\
        Long March 3	&	&22.12\%	&-	&-	&16.67\%	&48.89\%	&8.24\%	&3.90\%	&8.44\%	&24.41\%	&19.10\%	&10.39\%	&5.07\%	&10.80\%	&0.00\%	&11.71\%\\
        Long March 4	&	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-\\
        Zenit	&	&16.50\%	&11.10\%	&7.62\%	&5.58\%	&7.40\%	&3.43\%	&14.45\%	&-	&14.84\%	&33.68\%	&-	&26.64\%	&0.00\%	&-	&13.63\%\\
        STS	&	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-\\
        Titan	&	&58.68\%	&52.24\%	&49.44\%	&46.11\%	&58.68\%	&-	&-	&-	&-	&-	&-	&-	&-	&-	&51.09\%\\
        Kosmos	&	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-\\
        Molniya	&	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-\\
        Dnepr	&	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-\\
        H-II	&	&-	&-	&-	&-	&-	&37.14\%	&19.23\%	&-	&46.00\%	&-	&2.44\%	&-	&-	&-	&25.66\%\\
        Rokot	&	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-\\
        Minotaur 1	&	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-\\
        Minotaur V	&	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-\\
        Pegasus	&	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-\\
        Falcon 1	&	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-\\
        Falcon 9	&	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-\\
        Antares	&	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-\\
        \hline \hline
        \end{tabular}
        \label{tbl:geowastagebylv}
  }
\end{table}
\end{landscape}
\begin{landscape}
\begin{table}
  \centering
  \caption{Low Earth Orbit Wastage Percentage by Organization and Year, 2000-2013}
  \resizebox{\columnwidth}{!}{
  \begin{tabular}{lllllllllllllll}
    \hline \hline
    \\
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %%                                                                  %%
    %%  This is a LaTeX2e table fragment exported from Gnumeric.        %%
    %%                                                                  %%
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

		  &2000	&2001	&2002	&2003	&2004	&2005	&2006	&2007	&2008	&2009	&2010	&2011	&2012	&2013\\
    \multicolumn{15}{l}{\textit{Government - Civilian}}\\
    \hline
	  NASA	&-	&65.52\%	&18.86\%	&35.45\%	&34.86\%	&0.00\%	&38.50\%	&-	&27.06\%	&59.18\%	&61.68\%	&-	&61.04\%	&47.18\%\\
	  Roscosmos	&12.12\%	&6.00\%	&1.47\%	&0.23\%	&11.07\%	&0.00\%	&0.00\%	&0.00\%	&0.00\%	&0.00\%	&0.00\%	&0.00\%	&0.00\%	&0.00\%\\
	  JAXA	&-	&-	&-	&-	&-	&47.50\%	&15.79\%	&-	&-	&13.92\%	&-	&0.00\%	&0.00\%	&0.00\%\\
	  ISRO	&-	&7.43\%	&-	&-	&-	&0.00\%	&-	&-	&37.74\%	&71.17\%	&-	&-	&-	&-\\
	  ESA	&-	&-	&-	&-	&-	&9.24\%	&85.52\%	&-	&0.00\%	&16.81\%	&0.00\%	&0.00\%	&0.00\%	&0.00\%\\
    CNSA	&-	&-	&-	&-	&25.00\%	&-	&1.89\%	&-	&-	&-	&-	&4.76\%	&-	&-\\
    NOAA	&32.20\%	&-	&32.25\%	&-	&-	&28.36\%	&-	&-	&-	&10.07\%	&-	&-	&-	&-\\
	  \\
    \multicolumn{15}{l}{\textit{Government - Military}}\\
    \hline
	  DOD	&33.43\%	&-	&-	&45.39\%	&-	&24.77\%	&80.62\%	&79.57\%	&0.00\%	&65.80\%	&37.04\%	&36.71\%	&36.71\%	&-\\
	  NRO	&-	&23.20\%	&-	&-	&-	&20.43\%	&-	&85.45\%	&-	&-	&-	&-	&-	&-\\
	  Russian MoD	&18.85\%	&39.74\%	&6.19\%	&3.87\%	&11.79\%	&0.00\%	&0.00\%	&0.00\%	&0.00\%	&5.66\%	&0.00\%	&-	&-	&-\\
	  French MoD	&-	&-	&-	&-	&51.75\%	&-	&-	&-	&-	&32.26\%	&-	&-	&-	&-\\
	  \\
    \multicolumn{15}{l}{\textit{Private}}\\
    \hline
	  Eumetsat	&-	&-	&20.89\%	&-	&-	&-	&6.98\%	&-	&-	&-	&-	&-	&-	&-\\
	  Globalstar	&23.44\%	&-	&-	&-	&-	&-	&-	&62.89\%	&-	&-	&-	&-	&-	&-\\
	  Orbcomm	&-	&-	&-	&-	&-	&-	&-	&-	&65.16\%	&-	&-	&-	&-	&-\\
	  Iridium	&-	&-	&0.00\%	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-\\
	  Sirius XM	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-\\
	  SES	&-	&-	&0.00\%	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-\\
	  Eutelsat	&-	&-	&0.00\%	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-\\
	  \hline \hline
	  \end{tabular}
  }
  \label{tbl:orgwastageleo}
\end{table}   
\end{landscape}
\begin{landscape}
\begin{table}
  \centering
  \caption{Geosynchronous Transfer Orbit Wastage Percentage by Organization and Year, 2000-2013}
  \resizebox{\columnwidth}{!}{
  \begin{tabular}{lllllllllllllll}
  \hline \hline
  \\  	
  \multicolumn{15}{l}{\textit{Government - Civilian}}	\\
  \hline
  &2000	&2001	&2002	&2003	&2004	&2005	&2006	&2007	&2008	&2009	&2010	&2011	&2012	&2013\\
	  NASA	&0.00\%	&-	&0.00\%	&-	&-	&-	&-	&-	&-	&-	&36.84\%	&-	&-	&-	\%\\
	  Roscosmos	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&0.00\%	\\
	  JAXA	&-	&-	&-	&-	&-	&-	&40.00\%	&-	&46.00\%	&-	&-	&-	&-	&-	\\
	  ISRO	&-	&-	&0.00\%	&29.30\%	&22.00\%	&-	&-	&26.95\%	&-	&-	&-	&-	&-	&-	\\
	  %ESA	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	\\
	  CNSA	&-	&-	&-	&18.52\%	&-	&-	&-	&15.38\%	&21.05\%	&-	&42.11\%	&-	&-	&-	\\
	  NOAA	&27.05\%	&-	&-	&-	&-	&-	&39.64\%	&-	&-	&-	&49.30\%	&-	&-	&-	\\
	  \\

  \multicolumn{15}{l}{\textit{Government - Military}}	\\
  \hline
  &2000	&2001	&2002	&2003	&2004	&2005	&2006	&2007	&2008	&2009	&2010	&2011	&2012	&2013\\
	  DOD	&46.77\%	&42.09\%	&49.44\%	&44.22\%	&58.68\%	&-	&45.02\%	&40.25\%	&-	&-	&17.48\%	&-	&-	&-	\\
	  NRO	&-	&-	&-	&42.22\%	&-	&-	&-	&-	&-	&0.00\%	&-	&-	&-	&-	\\
	  Russian MoD	&44.83\%	&0.00\%	&-	&0.00\%	&0.00\%	&-	&-	&41.54\%	&0.00\%	&0.00\%	&23.08\%	&-	&-	&-	\\
	  Chinese MoD	&11.54\%	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	\\
	  %French MoD	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	\\
	  \\

  \multicolumn{15}{l}{\textit{Private}}	\\
  \hline
  &2000	&2001	&2002	&2003	&2004	&2005	&2006	&2007	&2008	&2009	&2010	&2011	&2012	&2013\\
	  PanAmSat	&18.00\%	&-	&-	&9.77\%	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	\\
	  Intelsat	&0.00\%	&1.36\%	&0.35\%	&19.56\%	&19.44\%	&15.32\%	&-	&-	&23.57\%	&28.85\%	&36.62\%	&14.72\%	&13.85\%	&-	\\
	  %Eumetsat	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	\\
	  %Globalstar	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	\\
	  %Orbcomm	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	\\
	  Echostar	&-	&-	&40.49\%	&-	&-	&-	&20.50\%	&-	&0.00\%	&-	&14.02\%	&-	&22.76\%	&-	\\
	  %Iridium	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	&-	\\
	  DirecTV	&-	&0.00\%	&17.17\%	&-	&0.00\%	&26.37\%	&0.00\%	&14.84\%	&0.00\%	&14.74\%	&-	&-	&-	&-	\\
	  Sirius XM	&12.64\%	&11.10\%	&-	&-	&-	&10.42\%	&0.00\%	&-	&-	&13.64\%	&13.53\%	&-	&-	&-	\\
	  SES	&21.08\%	&14.30\%	&2.04\%	&5.75\%	&37.66\%	&27.75\%	&27.19\%	&24.24\%	&22.77\%	&27.73\%	&39.72\%	&17.20\%	&8.78\%	&13.29\%	\\
	  RSCC	&43.78\%	&-	&40.23\%	&40.23\%	&48.12\%	&-	&-	&-	&62.73\%	&30.46\%	&-	&-	&-	&-	\\
	  Eutelsat	&36.46\%	&26.78\%	&29.01\%	&31.74\%	&38.58\%	&28.02\%	&29.55\%	&15.38\%	&20.57\%	&9.34\%	&22.04\%	&8.06\%	&0.00\%	&11.56\%	\\
	  \\
	  \hline \hline
	\end{tabular}
	}
  \label{tbl:orgwastagegto}
\end{table} 
\end{landscape}
	
		
\chapter{Optimal Usage of Launch Vehicles}
\label{sec:usage}

  The wastage problem constitutes a considerable loss, both in direct financial terms and in terms of lost opportunities to launch useful space payloads.  Yet there is little work dedicated to reducing it, or even computing the losses from it.  While a detailed hardware or operational solution to wastage is beyond the scope of this work, examination of some means of combatting wastage is necessary to determine how much improvement is actually possible.  
  
  One obvious approach to the problem is to select different launch vehicles.  One way of looking at wastage is that the payload's owner selected a larger launch vehicle to deploy it than was necessary.  If a smaller launch vehicle launches the payload, then costs may be reduced.  This is not a given, however.  Since cost-effectiveness varies widely among different launch vehicle configurations, even an increase in wastage may actually reduce the cost per payload mass if there is a correspondingly greater improvement in launch vehicle price per payload mass. 
  
  This analysis may seem trivial at first glance, as it stands to reason that an organization making such an important decision would carefully research all the available alternatives and select the launch vehicle that best suited their needs.  Given the looming financial considerations, one would expect most organizations to select the least expensive launch vehicle that has sufficient payload capacity for their mission.  Since launch vehicle cost-effectiveness varies, it follows that there are situations where using a launch vehicle with higher wastage for the desired mission could actually be cheaper.
  
  Other considerations can come into play when selecting a launch vehicle.  Reliability is a consideration.  Launch insurance is a significant cost, often costing as much as 15\% or more of a single launch, and it is tied directly to launch vehicle reliability\cite{spaceeconomics,insurance}.  This does not include the potential negative business repercussions of not having the payload on station when expected.  Chapter~\ref{sec:risk} further investigates the effect of reliability on launch costs, but its role bears some brief mention here.  
  
  More important, however, are non-financial concerns.  Many national security payloads are limited to launch on their own nation's launch vehicles, which prevents them from using the lowest cost launch vehicle that is suitable.  For example, the least expensive launch vehicle capable of launching the US Air Force's X-37 OTV is Soyuz, which costs at most half as much as the Atlas V 501 commonly used to deliver it.  It is highly unlikely, however, that the US Air Force would entrust one of its most secret spacecraft to its occasional adversaries.  There may be contractual constraints as well, such as the Air Force's `block buy' of Atlas V/Delta IV cores from ULA\cite{ulacosts}.

% Note:  This is not an absolute.  Israel, Germany, and the UK have all launched national security missions on other nations' launch vehicles, since the UK and Germany have none of their own and Israel's Shavit is only suitable for a limited number of missions.  Germany even used Russian LVs, despite the rivalry between the two nations.

% Note:  While on this subject, it is interesting that Israel is so diversified with their national security payloads, using their own, Indian, and Russian vehicles.  This may be the only case in the world of a power purposely making contingency plans against the loss of space launch capability.

  The lowest-cost scenario would be if customers selected the lowest cost launch vehicle available that is suitable for their mission.  Table~\ref{tbl:optimallaunchvehicle} contains yearly usage data for this case for LEO and GEO payloads combined.   

  There are some limitations to this comparison.  Most important of these is that only the maximum listed launch vehicle payload capacities are used for this comparison.  Payloads placed directly into geosynchronous orbits and payloads placed into low Earth orbits quite different from the orbit given for maximum payload capacity have the potential to skew the results.  Since both of these factors create a tendency to overestimate wastage and potential cost savings, the results here represent a best-case scenario for possible savings.
  
  The other limitation is that it is very difficult, given the complexities of laws such as the International Traffic in Arms Regulations (ITAR) and the difficulty of ascertaining what other circumstances constrain particular launch vehicle selections, to determine what the cheapest launch vehicle permissible to use was.  Once again, this causes these results to present an idealized case.   
  
  It is possible to obtain some idea of the effect of these restrictions by performing the analysis again, but requiring that each payload use a launch vehicle sourced in its country of origin.  This analysis excludes payloads owned by countries that do not have domestic launch vehicles, with the exception that it combines the European Union members into one country.  If the previous analysis was optimistic, this will prove too pessimistic, as many payloads source launchers internationally to reduce cost.  Some nations even use foreign launchers for their national security payloads: Germany uses Russian launchers for its reconnaissance satellites, and Israel uses Indian and Russian launchers in addition to their domestic Shavit launch vehicle.  Table \ref{tbl:optimallaunchvehiclenatlim} contains the results of this analysis.
  
  Usage patterns change considerably in these cases from actual utilization patterns as shown in Chapter \ref{sec:lvtrends}.  Proton and Soyuz were the most common launchers for the actual launches.  The lowest cost option for the greatest number of launches was Dnepr, a launch vehicle conversion of SS-18 `Satan' ICBMs.  Long March 3 ranked second, followed by Soyuz.  Proton falls far behind, despite its relatively low overall cost.  These changes in usage reduce the total cost for all LEO and GEO launches with complete data from \$44.2B (2014\$) to \$24.9B, a 44\% savings, while reducing wastage from 20\% to 18\%.  While wastage is reduced, the benefit mostly comes from selection of more cost-effective launch vehicles.  
  
  The usage patterns for the nationality-restricted case much more closely resemble actual usage, with many more types of launch vehicles used.  Some launch vehicles, such as Ariane 4, that are in overall terms not very cost-effective are the least expensive launch vehicle available to their respective nations for their own payloads.  In some cases this is because nations only have one launcher, e.g. the European Union and Ariane 5 prior to the development of Vega.  
  
	How does real-world usage compare to this `optimal' scenario? Table~\ref{tbl:optimalusage} shows how often each launch vehicle was the optimal choice if it was used, and contains data for how often the optimal choice was selected for each year and over the entire 2000-2013 period.  Figure~\ref{fig:mincostlvselectionrate} graphically represents the rate at which launches used the minimum cost launch vehicle capable of accomplishing their mission.
	
	\begin{figure}[htbp]
  \begin{center}
    \includegraphics[width=140mm]{cheapestselected.png}
    \caption{Minimum Cost Launch Vehicle Selection Rate, 2000-2013}
    \label{fig:mincostlvselectionrate}
  \end{center}
\end{figure} 

	18.45\% of the time the lowest cost launch vehicle is selected for a given payload or set of payloads. While there are multiple possible reasons, such as those mentioned above, that the most cost-effective launch vehicle might not be selected for a particular mission, it is highly unlikely that they apply to nearly 82\% of all space launches.
	
	Table~\ref{tbl:optimalusage} can be inverted conceptually. That is, rather than asking ``if a particular launch vehicle was used, was it the `optimal' choice?'' asking ``if the launch vehicle was `optimal', was it used?''  Table~\ref{tbl:usageifoptimal} contains the results of this analysis.
	
	Some interesting trends may be observed from Tables~\ref{tbl:optimalusage} and \ref{tbl:usageifoptimal}. The first is that there are some launch vehicles that are used commensurate with their cost effectiveness, but they are not used on the launches where they are optimal. For instance, Delta IV is the lowest cost option for some launches, but is literally never used over the 2000-2013 period when it is the cheapest option.  Dnepr is probably the most underutilized launch vehicle in existence, never being used more than a quarter of the time that it is the cheapest option in any year, yet it is not the cheapest option for many of the payloads that actually do use it.
	
	The second trend of interest is that over time launch vehicle selection is improving.  In 2002, selection of the most cost-effective launch vehicle reached a minimum, with users only selecting the most cost-effective launch vehicle 9.52\% of the time.  Post 2004, there is a steep rise in this percentage.
	
  The previous analyses show that usage of the minimum cost launch vehicle is relatively rare.  It is also known, however, that there are limitations on launch vehicle selection that are difficult to evaluate quantitatively.  Given such restrictions, a rational selector of a launch vehicle for a given mission would select the least expensive launch vehicle that did not violate any of them.  This leads to the question of how highly ranked the actual choices are.  Figure~\ref{fig:rankings} is a histogram of the cost-effectiveness ranking of the launch vehicle actually chosen for both the minimum cost scenario and the minimum cost scenario where payloads must use their own nation's launch vehicles.

\begin{figure}%[ht!]
  \begin{center}
    \includegraphics[width=140mm]{mincostranks.jpg}
    \caption{Minimum Cost Ranking for Launches}
    \label{fig:rankings}
  \end{center}
\end{figure}    

	While relatively few customers select the most cost-effective launch vehicle for their application, a majority of them select one that is in the top four for their particular mission.  Nearly 75\% select one that is in the top ten.  The tail of the distribution is rather long, however, with the `worst' decision being 51st out of 74. This was launch 2000-065, with a single payload, 2000-065A, a geosynchronous payload launched on Atlas IIA at 59.36\% wastage.   Since it was a US Department of Defense payload, it is probably a case where the requirement to use certain launch vehicles, no matter how poor of a financial decision it was, was a factor. 
	
	 For the scenario where payloads must use a launcher from their own country, the results show a much greater number of first-ranked choices.  Nearly 50\% of launches of payloads owned by nations with their own launch vehicles selected the cheapest launch vehicle from their own nation that was capable of launching the payload.  Coupled with the lower rate of selecting the lowest cost launch vehicle worldwide, this is a strong indication that launch vehicle nationality is a strong noneconomic consideration for launch vehicle decisions.
	
% 	It is important to know going into the future what the benefits of launch vehicle development in the last decade are.  Some of the most cost-effective launch vehicles available now were not available around the turn of the century.  Since 2000-2002 was also an upswing in the number and mass of payloads, it would be instructive to see how the `optimal' case would change if all current launch vehicles were available at that time.  The data for this case are in Table~\ref{tbl:optimalusagenorestriction}. 
% 	 
% \begin{table}%[htbp]
%   \centering
%   \caption{Lowest Cost Launch Vehicle (No Restrictions), 2000-2013}
%   
%   \resizebox{\columnwidth}{!}{
%     \begin{tabular}{lrrrrrrrrrrrrrrrr}
%     \hline \hline
%           &       & 2000  & 2001  & 2002  & 2003  & 2004  & 2005  & 2006  & 2007  & 2008  & 2009  & 2010  
%
% & 2011  & 2012  & 2013  & Total \\
%     \hline
%     \multicolumn{2}{l}{Ariane 4} & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 
%
% 0     & 0     & 0     & 0     & 0     & 0 \\
%     \multicolumn{2}{l}{Ariane 5} & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 1     & 0     & 
%
% 0     & 1     & 0     & 1     & 1     & 4 \\
%     \multicolumn{2}{l}{Atlas} & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 
%
% 0     & 0     & 0     & 0     & 0     & 0 \\
%     \multicolumn{2}{l}{Atlas V} & 0     & 0     & 0     & 0     & 0     & 1     & 3     & 3     & 4     & 
%
% 3     & 2     & 2     & 1     & 2     & 21 \\
%     \multicolumn{2}{l}{Delta II} & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 
%
% 0     & 0     & 0     & 0     & 0     & 0 \\
%     \multicolumn{2}{l}{Delta IV} & 4     & 0     & 0     & 3     & 2     & 3     & 3     & 2     & 7     & 
%
% 6     & 8     & 5     & 0     & 1     & 44 \\
%     \multicolumn{2}{l}{Proton} & 1     & 1     & 0     & 0     & 0     & 2     & 0     & 0     & 1     & 1 
%
%     & 0     & 2     & 2     & 2     & 12 \\
%     \multicolumn{2}{l}{Soyuz} & 7     & 8     & 6     & 4     & 3     & 6     & 5     & 6     & 5     & 7  
%
%    & 7     & 6     & 5     & 1     & 76 \\
%     \multicolumn{2}{l}{PSLV} & 1     & 0     & 2     & 1     & 0     & 0     & 1     & 0     & 2     & 0   
%
%   & 0     & 0     & 0     & 2     & 9 \\
%     \multicolumn{2}{l}{GSLV} & 0     & 0     & 0     & 1     & 0     & 0     & 0     & 1     & 0     & 0   
%
%   & 0     & 0     & 0     & 0     & 2 \\
%     \multicolumn{2}{l}{Long March 2} & 1     & 0     & 1     & 1     & 1     & 0     & 0     & 0     & 0   
%
%   & 0     & 2     & 0     & 2     & 1     & 9 \\
%     \multicolumn{2}{l}{Long March 3} & 22    & 10    & 6     & 8     & 6     & 4     & 6     & 4     & 7   
%
%   & 3     & 5     & 5     & 0     & 0     & 86 \\
%     \multicolumn{2}{l}{Long March 4} & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0   
%
%   & 0     & 0     & 0     & 0     & 0     & 0 \\
%     \multicolumn{2}{l}{Zenit} & 1     & 0     & 3     & 0     & 0     & 0     & 0     & 0     & 0     & 0  
%
%    & 0     & 0     & 0     & 0     & 4 \\
%     Titan &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     
%
% & 0     & 0     & 0     & 0 \\
%     Kosmos &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     
%
% & 0     & 0     & 0     & 0 \\
%     Molniya &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0    
%
%  & 0     & 0     & 0     & 0 \\
%     Dnepr &       & 7     & 7     & 7     & 8     & 7     & 5     & 10    & 14    & 9     & 7     & 7     
%
% & 5     & 1     & 1     & 95 \\
%     H-II  &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     
%
% & 0     & 0     & 0     & 0 \\
%     Rokot &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     
%
% & 0     & 0     & 0     & 0 \\
%     Minotaur 1 &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0 
%
%     & 0     & 0     & 0     & 0 \\
%     Pegasus &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0    
%
%  & 0     & 0     & 0     & 0 \\
%     Falcon 1 &       & 6     & 1     & 2     & 5     & 2     & 1     & 2     & 4     & 2     & 2     & 1   
%
%   & 0     & 0     & 2     & 30 \\
%     Falcon 9 &       & 5     & 9     & 9     & 7     & 7     & 3     & 4     & 3     & 4     & 4     & 1   
%
%   & 2     & 0     & 1     & 59 \\
%     Antares &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0    
%
%  & 0     & 0     & 0     & 0 \\
%     Start-1 &       & 0     & 0     & 2     & 2     & 1     & 3     & 1     & 1     & 2     & 1     & 0    
%
%  & 1     & 1     & 0     & 15 \\
%     Tsyklon &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0    
%
%  & 0     & 0     & 0     & 0 \\
%     Total &       & 55    & 36    & 38    & 40    & 29    & 28    & 35    & 39    & 43    & 34    & 34    
%
% & 28    & 13    & 14    & 466 \\
%     \hline \hline
%     \end{tabular}%
%     }
%   \label{tbl:optimalusagenorestriction}%
% \end{table}%
%
%   The availability of Falcon 9 would have made a great difference during this time, as would have the availability of the EELV families.  Overall, it would have increased the `optimal' case savings from 22\% to 40\%.  This sounds surprising, until one considers that Falcon 9 can launch many of the geosynchronous payloads that the Titan IV family could, while costing almost \textit{eight times} less.  Even if dreams of reusability and other radical cost-cutting measures fall short, the future still holds great promise for lower cost access to space.
%
%\todo[inline]{Fix these data, they are incorrect.}
\begin{figure}%[ht!]
  \begin{center}
    \includegraphics[width=140mm]{wastagebyorg.png}
    \caption{Average Cost Per Payload Mass Delivered to Orbit, 2000-2013}
    \label{fig:costdelivered}
  \end{center}
\end{figure} 

  Figure \ref{fig:costdelivered} plots the average cost per kilogram of payload mass delivered to orbit for the actual and `ideal' cases.  Actual GEO costs have declined significantly, while LEO costs were relatively flat over the studied interval.  Interestingly, costs for the `ideal' cases are also relatively flat over the entire interval, despite the introduction of several new launch vehicle families.  This is a possible indication of the relative importance of operational losses: it is possible to achieve nearly the same costs in 2013 as it was in 2000, despite the availability of superior launch vehicles.
  
%  The increase in LEO payload costs in 2002 and 2003 corresponds to the great reduction in payload mass that occurred at that time.  Interestingly, this corresponds with a downturn in the selection of the most cost-effective launch vehicle to that orbit.  
  
  The analyses conducted in this chapter show that while the majority of launch vehicle users select one of the best choices available to them for their mission, it is nonetheless possible to realize a savings in launch costs by improving the selection of launch vehicles.  It is uncertain what savings is actually possible, since launch vehicle selection requires consideration of variables that are difficult to quantify.  
\begin{landscape} 
\small
%\begin{table}%[htbp]
\begin{longtable}{lrrrrrrrrrrrrrrrr}
  %\centering
  \caption{Lowest Cost Launch Vehicle, 2000-2013}\\
  \label{tbl:optimallaunchvehicle}\\
  %\resizebox{\columnwidth}{!}{
  %  \begin{tabular}{lrrrrrrrrrrrrrrrr}
    \hline \hline
          &       & 2000  & 2001  & 2002  & 2003  & 2004  & 2005  & 2006  & 2007  & 2008  & 2009  & 2010  & 2011  & 2012  & 2013  & Total \\
    \hline
    \endfirsthead
     &       & 2000  & 2001  & 2002  & 2003  & 2004  & 2005  & 2006  & 2007  & 2008  & 2009  & 2010  & 2011  & 2012  & 2013  & Total \\
    \hline
    \endhead
    \hline
    \endfoot
    \hline
    \endlastfoot
    \multicolumn{2}{l}{Ariane 4} & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 

0     & 0     & 0     & 0     & 0     & 0 \\
    \multicolumn{2}{l}{Ariane 5} & 0     & 0     & 0     & 0     & 0     & 0     & 1     & 1     & 1     & 

0     & 1     & 0     & 1     & 1     & 6 \\
    \multicolumn{2}{l}{Atlas} & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 

0     & 0     & 0     & 0     & 0     & 0 \\
    \multicolumn{2}{l}{Atlas V} & 0     & 0     & 0     & 0     & 0     & 1     & 3     & 3     & 4     & 

3     & 2     & 2     & 1     & 2     & 21 \\
    \multicolumn{2}{l}{Delta II} & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 

0     & 0     & 0     & 0     & 0     & 0 \\
    \multicolumn{2}{l}{Delta IV} & 0     & 0     & 0     & 3     & 2     & 3     & 2     & 1     & 6     & 

6     & 8     & 2     & 0     & 1     & 34 \\
    \multicolumn{2}{l}{Proton} & 5     & 1     & 0     & 0     & 0     & 2     & 0     & 0     & 1     & 1 

    & 0     & 2     & 2     & 2     & 16 \\
    \multicolumn{2}{l}{Soyuz} & 7     & 8     & 6     & 4     & 3     & 6     & 5     & 6     & 5     & 7  

   & 7     & 6     & 5     & 1     & 76 \\
    \multicolumn{2}{l}{PSLV} & 1     & 0     & 2     & 1     & 0     & 0     & 1     & 0     & 2     & 0   

  & 0     & 0     & 0     & 2     & 9 \\
    \multicolumn{2}{l}{GSLV} & 0     & 0     & 0     & 1     & 0     & 0     & 0     & 1     & 1     & 1   

  & 0     & 0     & 0     & 0     & 4 \\
    \multicolumn{2}{l}{Long March 2} & 1     & 0     & 2     & 1     & 1     & 0     & 0     & 0     & 0   

  & 0     & 2     & 0     & 2     & 1     & 10 \\
    \multicolumn{2}{l}{Long March 3} & 27    & 19    & 15    & 15    & 13    & 7     & 10    & 8     & 10  

  & 6     & 5     & 8     & 0     & 0     & 143 \\
    \multicolumn{2}{l}{Long March 4} & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0   

  & 0     & 0     & 0   & 0     & 0     & 0 \\
    \multicolumn{2}{l}{Zenit} & 1     & 0     & 2     & 0     & 0     & 0     & 0     & 0     & 0     & 0  

   & 0     & 0     & 0     & 0     & 3 \\
    Titan &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     

& 0     & 0     & 0     & 0 \\
    Kosmos &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     

& 0     & 0     & 0     & 0 \\
    Molniya &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0    

 & 0     & 0     & 0     & 0 \\
    Dnepr &       & 7     & 7     & 7     & 8     & 7     & 5     & 10    & 14    & 8     & 7     & 7     

& 5     & 1     & 1     & 94 \\
    H-II  &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     

& 0     & 0     & 0     & 0 \\
    Rokot &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     

& 0     & 0     & 0     & 0 \\
    Minotaur 1 &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0 

    & 0     & 0     & 0     & 0 \\
    Minotaur V &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0 

    & 0     & 0     & 0     & 0 \\
    Pegasus &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0    

 & 0     & 0     & 0     & 0 \\
    Falcon 1 &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 2     & 1   

  & 0     & 0     & 2     & 5 \\
    Falcon 9 &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 1   

  & 2     & 0     & 1     & 4 \\
    Antares &       & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0     & 0    

 & 0     & 0     & 0     & 0 \\
    Start-1 &       & 6     & 1     & 4     & 7     & 3     & 4     & 3     & 5     & 5     & 1     & 0    

 & 1     & 1     & 0     & 41 \\
    Total &       & 55    & 36    & 38    & 40    & 29    & 28    & 35    & 39    & 43    & 34    & 34    

& 28    & 13    & 14    & 466 \\
    \hline \hline
    %\end{tabular}%
    %}
%\end{table}%
\end{longtable}
\end{landscape}
  
\begin{landscape}
\begin{table}
  \centering
  \caption{Lowest Cost Launch Vehicle, Nationality of Choice Restricted, 2000-2013}
  
  \resizebox{\columnwidth}{!}{
    \begin{tabular}{lrrrrrrrrrrrrrrrr}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      %%                                                                  %%
      %%  This is a LaTeX2e table fragment exported from Gnumeric.        %%
      %%                                                                  %%
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \hline \hline
	    & &2000	&2001	&2002	&2003	&2004	&2005	&2006	&2007	&2008	&2009	&2010	&2011	&2012	&2013	&Total\\
	    \hline
	    
      \multicolumn{2}{l}{Ariane 4}	&8	&7	&13	&3	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&31\\
      \multicolumn{2}{l}{Ariane 5}	&2	&0	&0	&0	&8	&4	&5	&9	&10	&13	&11	&9	&11	&6	&88\\
      \multicolumn{2}{l}{Atlas}	&9	&3	&3	&2	&1	&0	&0	&0	&0	&0	&0	&0	&0	&0	&18\\
      \multicolumn{2}{l}{Atlas V}	&0	&0	&0	&0	&0	&2	&0	&1	&0	&0	&0	&0	&1	&0	&4\\
      \multicolumn{2}{l}{Delta II}	&5	&1	&5	&2	&3	&1	&3	&4	&2	&3	&0	&0	&0	&0	&29\\
      \multicolumn{2}{l}{Delta IV}	&0	&0	&0	&4	&1	&4	&5	&3	&6	&5	&6	&2	&1	&0	&37\\
      \multicolumn{2}{l}{Proton}	&5	&3	&1	&3	&2	&0	&0	&1	&2	&2	&1	&1	&3	&0	&24\\
      \multicolumn{2}{l}{Soyuz}	&7	&7	&5	&4	&3	&6	&6	&6	&6	&7	&6	&5	&4	&3	&75\\
      \multicolumn{2}{l}{PSLV}	&0	&1	&1	&1	&0	&1	&0	&0	&1	&2	&1	&2	&0	&1	&11\\
      \multicolumn{2}{l}{GSLV}	&0	&1	&0	&1	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&2\\
      \multicolumn{2}{l}{Long March 2}	&2	&0	&1	&1	&5	&2	&3	&2	&3	&1	&4	&5	&3	&1	&33\\
      \multicolumn{2}{l}{Long March 3}	&3	&0	&0	&2	&1	&1	&2	&2	&1	&1	&6	&6	&2	&1	&28\\
      \multicolumn{2}{l}{Long March 4}	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0\\
      \multicolumn{2}{l}{Zenit}	&1	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&1\\
      \multicolumn{2}{l}{Titan}	&3	&5	&3	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&11\\
      \multicolumn{2}{l}{Kosmos}	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0\\
      \multicolumn{2}{l}{Dnepr}	&3	&5	&3	&3	&4	&2	&1	&1	&1	&2	&2	&1	&2	&3	&33\\
      \multicolumn{2}{l}{H-II}	&2	&0	&3	&1	&2	&1	&3	&1	&1	&1	&1	&0	&3	&1	&20\\
      \multicolumn{2}{l}{Rokot}	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0\\
      \multicolumn{2}{l}{Minotaur 1}	&5	&1	&1	&3	&1	&3	&1	&2	&1	&0	&1	&1	&0	&0	&20\\
      \multicolumn{2}{l}{Minotaur V}	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0\\
      \multicolumn{2}{l}{Pegasus}	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0\\
      \multicolumn{2}{l}{Falcon 1}	&0	&0	&0	&0	&0	&0	&0	&0	&0	&1	&0	&0	&1	&1	&3\\
      \multicolumn{2}{l}{Falcon 9}	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&5	&5	&3	&6	&19\\
      \multicolumn{2}{l}{Antares}	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0	&0\\
      \multicolumn{2}{l}{Start-1}	&1	&0	&1	&2	&1	&0	&1	&0	&0	&0	&0	&0	&0	&0	&6\\
      \hline \hline
    \end{tabular}
    }
  \label{tbl:optimallaunchvehiclenatlim}
\end{table}
\end{landscape} 
  
\begin{landscape}	
%\begin{table}%[htbp]
%  \centering
\small
\begin{longtable}{lrccccccccccccccc}
  \caption{Launches Where LV Used was Lowest Cost, 2000-2013}\\
    \label{tbl:optimalusage}\\
%  \resizebox{\columnwidth}{!}{
%    \begin{tabular}{lrccccccccccccccc}
    \hline \hline
          &       & 2000  & 2001  & 2002  & 2003  & 2004  & 2005  & 2006  & 2007  & 2008  & 2009  & 2010  

& 2011  & 2012  & 2013  & Total \\
    \endfirsthead
     &       & 2000  & 2001  & 2002  & 2003  & 2004  & 2005  & 2006  & 2007  & 2008  & 2009  & 2010  & 2011  & 2012  & 2013  & Total \\
    \hline
    \endhead
    \hline
    \endfoot
    \hline
    \endlastfoot
    \multicolumn{2}{l}{Ariane 4} & 0/7   & 0/6   & 0/7   & 0/1   & -     & -     & -     & -     & -     & 

-     & -     & -     & -     & -     & 0/21 \\
    \multicolumn{2}{l}{Ariane 5} & 0/4   & 0/2   & 0/3   & 0/3   & -     & 0/2   & 1/5   & 1/4   & 1/6   & 

0/5   & 1/5   & 0/3   & 1/3   & 1/4   & 6/49 \\
    \multicolumn{2}{l}{Atlas} & 0/8   & 0/2   & 0/4   & 0/2   & 0/4   & -     & -     & -     & -     & 

-     & -     & -     & -     & -     & 0/20 \\
    \multicolumn{2}{l}{Atlas V} & -     & -     & -     & 0/2   & 0/1   & 0/1   & 0/1   & 0/2   & 0/1   & 

0/3   & 0/3   & 0/1   & 0/1   & 0/1   & 0/17 \\
    \multicolumn{2}{l}{Delta II} & 0/1   & 0/1   & 0/1   & 0/2   & 0/3   & 0/1   & 0/2   & 0/1   & 0/3   & 

0/2   & 0/1   & 0/1   & -     & -     & 0/19 \\
    \multicolumn{2}{l}{Delta IV} & -     & -     & -     & 0/2   & -     & -     & 0/1   & 0/1   & -     & 

-     & -     & -     & -     & -     & 0/4 \\
    \multicolumn{2}{l}{Proton} & 0/8   & 0/5   & 0/4   & 0/3   & 0/5   & 0/4   & 0/3   & 0/4   & 0/8   & 

0/8   & 0/8   & 0/5   & -     & 0/1   & 0/66 \\
    \multicolumn{2}{l}{Soyuz} & 7/8   & 5/7   & 3/4   & 4/5   & 3/3   & 6/6   & 5/5   & 6/9   & 5/5   & 

7/7   & 6/6   & 5/5   & 4/4   & 1/1   & 67/75 \\
    \multicolumn{2}{l}{PSLV} & -     & 0/1   & 1/1   & 0/1   & -     & 0/1   & -     & 0/2   & 0/1   & -   

  & -     & 0/1   & -     & -     & 1/8 \\
    \multicolumn{2}{l}{GSLV} & -     & 0/1   & -     & 1/1   & 0/1   & -     & -     & 0/1   & -     & -   

  & -     & -     & -     & -     & 1/4 \\
    \multicolumn{2}{l}{Long March 2} & -     & -     & -     & -     & 0/1   & 0/1   & 0/1   & 0/1   & -   

  & -     & -     & -     & -     & -     & 0/4 \\
    \multicolumn{2}{l}{Long March 3} & 0/3   & -     & -     & 0/2   & 0/1   & 1/1   & 1/2   & 2/4   & 2/3 

  & 1/1   & 1/1   & 6/6   & -     & -     & 14/24 \\
    \multicolumn{2}{l}{Long March 4} & -     & -     & 0/1   & 0/1   & 0/1   & -     & 0/2   & 0/1   & 0/2 

  & -     & 0/1   & 0/2   & -     & -     & 0/11 \\
    \multicolumn{2}{l}{Zenit} & 0/4   & 0/3   & 0/1   & 0/2   & 0/4   & 0/3   & 0/4   & -     & 0/5   & 

0/1   & -     & 0/1   & -     & -     & 0/28 \\
    Titan &       & 0/3   & 0/3   & 0/2   & 0/3   & 0/1   & 0/2   & -     & -     & -     & -     & -     

& -     & -     & -     & 0/14 \\
    Kosmos &       & 0/3   & 0/1   & 0/4   & 0/3   & 0/2   & 0/2   & 0/1   & 0/3   & 0/3   & -     & 0/1   

& -     & -     & -     & 0/23 \\
    Molniya &       & -     & -     & -     & -     & -     & -     & -     & -     & -     & -     & -    

 & -     & -     & -     & 0/0 \\
    Dnepr &       & 0/1   & -     & 0/1   & -     & 0/1   & 0/1   & 1/1   & 2/3   & 1/2   & 0/1   & 2/3   

& -     & -     & -     & 6/14 \\
    H-II  &       & -     & -     & 0/2   & 0/1   & -     & -     & 0/2   & 0/1   & 0/1   & 0/2   & 0/1   

& 0/1   & 0/2   & 0/1   & 0/14 \\
    Rokot &       & 0/1   & -     & 0/2   & 0/2   & -     & 0/1   & 0/1   & -     & 0/1   & 0/2   & 0/2   

& 0/1   & -     & 0/1   & 0/14 \\
    Minotaur 1 &       & 0/2   & -     & -     & -     & -     & 0/2   & 0/2   & 0/1   & -     & 0/1   & - 

    & 0/1   & -     & -     & 0/9 \\
    Minotaur V &       & -     & -     & -     & -     & -     & -     & -     & -     & -     & -     & - 

    & -     & -     & -     & 0/0 \\
    Pegasus &       & 0/1   & -     & 0/1   & 0/4   & -     & -     & -     & 0/1   & 0/2   & -     & -    

 & -     & -     & 0/1   & 0/10 \\
    Falcon 1 &       & -     & -     & -     & -     & -     & -     & -     & -     & -     & 1/1   & -   

  & -     & -     & -     & 1/1 \\
    Falcon 9 &       & -     & -     & -     & -     & -     & -     & -     & -     & -     & -     & 0/2 

  & -     & 0/2   & 0/1   & 0/5 \\
    Antares &       & -     & -     & -     & -     & -     & -     & -     & -     & -     & -     & -    

 & -     & -     & 0/2   & 0/2 \\
    Start-1 &       & 1/1   & 1/1   & -     & -     & -     & -     & 1/1   & -     & -     & -     & -    

 & -     & -     & -     & 3/3 \\
    Tsyklon &       & -     & 0/3   & -     & -     & 0/1   & -     & 0/1   & -     & -     & -     & -    

 & -     & -     & -     & 0/5 \\
    Vega  &       & -     & -     & -     & -     & -     & -     & -     & -     & -     & -     & -     

& -     & 0/1   & 0/1   & 0/2 \\
    Total &       & 8/55  & 6/37  & 4/38  & 5/40  & 3/29  & 7/29  & 9/37  & 11/41 & 9/43  & 9/35  & 10/34 & 11/31 & 5/13  & 2/14  & 99/466 \\
    \hline \hline
%    \end{tabular}%
%    }
%\end{table}%
\end{longtable}
\end{landscape}

\begin{landscape}
%\begin{table}%[htbp]
\small
\begin{longtable}{lrrrrrrrrrrrrrrrr}
%  \centering
  \caption{Launches Where Lowest Cost LV was Used, 2000-2013}\\
  \label{tbl:usageifoptimal}\\
%  \resizebox{\columnwidth}{!}{
%    \begin{tabular}{lrrrrrrrrrrrrrrrr}
    \hline \hline
          &       & 2000  & 2001  & 2002  & 2003  & 2004  & 2005  & 2006  & 2007  & 2008  & 2009  & 2010  

& 2011  & 2012  & 2013  & Total \\
    \hline
    \endfirsthead
     &       & 2000  & 2001  & 2002  & 2003  & 2004  & 2005  & 2006  & 2007  & 2008  & 2009  & 2010  & 2011  & 2012  & 2013  & Total \\
    \hline
    \endhead
    \hline
    \endfoot
    \hline
    \endlastfoot
    \multicolumn{2}{l}{Ariane 4} & -     & -     & -     & -     & -     & -     & -     & -     & -     & 

-     & -     & -     & -     & -     & 0/0 \\
    \multicolumn{2}{l}{Ariane 5} & -     & -     & -     & -     & -     & -     & 1/1   & 1/1   & 1/1   & 

-     & 1/1   & -     & 1/1   & 1/1   & 6/6 \\
    \multicolumn{2}{l}{Atlas} & -     & -     & -     & -     & -     & -     & -     & -     & -     & 

-     & -     & -     & -     & -     & 0/0 \\
    \multicolumn{2}{l}{Atlas V} & -     & -     & -     & -     & -     & 0/1   & 0/3   & 0/3   & 0/4   & 

0/3   & 0/2   & 0/2   & 0/1   & 0/2   & 0/21 \\
    \multicolumn{2}{l}{Delta II} & -     & -     & -     & -     & -     & -     & -     & -     & -     & 

-     & -     & -     & -     & -     & 0/0 \\
    \multicolumn{2}{l}{Delta IV} & -     & -     & -     & 0/3   & 0/2   & 0/3   & 0/2   & 0/1   & 0/6   & 

0/6   & 0/8   & 0/2   & -     & 0/1   & 0/34 \\
    \multicolumn{2}{l}{Proton} & 0/5   & 0/1   & -     & -     & -     & 0/2   & -     & -     & 0/1   & 

0/1   & -     & 0/2   & 0/2   & 0/2   & 0/16 \\
    \multicolumn{2}{l}{Soyuz} & 7/7   & 5/8   & 3/6   & 4/4   & 3/3   & 6/6   & 5/5   & 6/6   & 5/5   & 

7/7   & 6/7   & 5/6   & 4/5   & 1/1   & 67/76 \\
    \multicolumn{2}{l}{PSLV} & 0/1   & -     & 1/2   & 0/1   & -     & -     & 0/1   & -     & 0/2   & -   

  & -     & -     & -     & 0/2   & 1/9 \\
    \multicolumn{2}{l}{GSLV} & -     & -     & -     & 1/1   & -     & -     & -     & 0/1   & 0/1   & 0/1 

  & -     & -     & -     & -     & 1/4 \\
    \multicolumn{2}{l}{Long March 2} & 0/1   & -     & 0/2   & 0/1   & 0/1   & -     & -     & -     & -   

  & -     & 0/2   & -     & 0/2   & 0/1   & 0/10 \\
    \multicolumn{2}{l}{Long March 3} & 0/27  & 0/19  & 0/15  & 0/15  & 0/13  & 1/7   & 1/10  & 2/8   & 

2/10  & 1/6   & 1/5   & 6/8   & -     & -     & 14/143 \\
    \multicolumn{2}{l}{Long March 4} & -     & -     & -     & -     & -     & -     & -     & -     & -   

  & -     & -     & -     & -     & -     & 0/0 \\
    \multicolumn{2}{l}{Zenit} & 0/1   & -     & 0/2   & -     & -     & -     & -     & -     & -     & -  

   & -     & -     & -     & -     & 0/3 \\
    Titan &       & -     & -     & -     & -     & -     & -     & -     & -     & -     & -     & -     

& -     & -     & -     & 0/0 \\
    Kosmos &       & -     & -     & -     & -     & -     & -     & -     & -     & -     & -     & -     

& -     & -     & -     & 0/0 \\
    Molniya &       & -     & -     & -     & -     & -     & -     & -     & -     & -     & -     & -    

 & -     & -     & -     & 0/0 \\
    Dnepr &       & 0/7   & 0/7   & 0/7   & 0/8   & 0/7   & 0/5   & 1/10  & 2/14  & 1/8   & 0/7   & 2/7   

& 0/5   & 0/1   & 0/1   & 6/94 \\
    H-II  &       & -     & -     & -     & -     & -     & -     & -     & -     & -     & -     & -     

& -     & -     & -     & 0/0 \\
    Rokot &       & -     & -     & -     & -     & -     & -     & -     & -     & -     & -     & -     

& -     & -     & -     & 0/0 \\
    Minotaur 1 &       & -     & -     & -     & -     & -     & -     & -     & -     & -     & -     & - 

    & -     & -     & -     & 0/0 \\
    Minotaur V &       & -     & -     & -     & -     & -     & -     & -     & -     & -     & -     & - 

    & -     & -     & -     & 0/0 \\
    Pegasus &       & -     & -     & -     & -     & -     & -     & -     & -     & -     & -     & -    

 & -     & -     & -     & 0/0 \\
    Falcon 1 &       & -     & -     & -     & -     & -     & -     & -     & -     & -     & 1/2   & 0/1 

  & -     & -     & 0/2   & 1/5 \\
    Falcon 9 &       & -     & -     & -     & -     & -     & -     & -     & -     & -     & -     & 0/1 

  & 0/2   & -     & 0/1   & 0/4 \\
    Antares &       & -     & -     & -     & -     & -     & -     & -     & -     & -     & -     & -    

 & -     & -     & -     & 0/0 \\
    Start-1 &       & 1/6   & 1/1   & 0/4   & 0/7   & 0/3   & 0/4   & 1/3   & 0/5   & 0/5   & 0/1   & -    & 0/1   & 0/1   & -     & 3/41 \\
    Tsyklon &       & -     & -     & -     & -     & -     & -     & -     & -     & -     & -     & - 

    & -     & -     & -     & 0/0 \\
    Vega &       & -     & -     & -     & -     & -     & -     & -     & -     & -     & -     & - 

    & -     & -     & -     & 0/0 \\
    \hline \hline
%    \end{tabular}%
%    }
%\end{table}%
\end{longtable}
\end{landscape}
	
\chapter{Optimal Arrangement of Payloads}
\label{sec:arrangement}

	The existence of launches with high percentages of wastage indicates that the least expensive launch vehicle capable of delivering a payload to the desired trajectory is not necessarily the one with the lowest wastage.  The analysis in Chapter~\ref{sec:usage} confirms this, where it was shown that selecting the minimum cost launch vehicle capable of performing the mission for all real missions in the studied period results in little change in wastage despite a significant financial savings.
	
	At the same time, wastage constitutes exactly what it says: a `waste' of capacity.  Nor is it required to arrange future payloads in a similar fashion to those launched in the past.  If it is possible to control the arrangement of the payloads, how much reduction in wastage is possible?  As discussed in Chapter \ref{sec:payloadtrends}, the number of payloads per launch has been rising slowly since 2000.  This appears to indicate that actors in the market are already attempting to use improved payload arrangement strategies.
	
	Finding an optimal arrangement of payloads and launch vehicles, in the simplest case, is an example of a bin packing problem.  A case involving a single type of launch vehicle is a classical bin packing problem, which has been studied extensively, and has several algorithms dedicated to solving it\cite{binpacking}.  In the case that multiple types of launch vehicles are available, the problem becomes a variable bin-packing problem with fixed costs, as described in Crainic et al\cite{variablebinpacking}.  As examined in that work, an approximate algorithm is available to solve this problem, albeit with less accuracy than for the classical bin-packing problem.
	
  While there are algorithms that provide exact solutions to the classical bin packing problem\cite{binpacking,binpacking2}, a best fit descending, or BFD, algorithm was chosen instead for the sake of simplicity. This algorithm will provide a solution that uses no more than 11/9 the optimal number of bins, and in the majority of cases will return the optimal number of bins. Korf cites a problem of 90 elements, with elements ranging in size from zero to one million, and bin capacities of one million, where BFD returns the optimal solution 94.832\% of the time\cite{binpacking}.
  
  The BFD algorithm requires that the elements (in this case, payloads) first be sorted in descending order. Then the algorithm assigns each payload to the fullest launch vehicle in which it can fit. If there are no launch vehicles with enough capacity remaining, another one is added. In the case where the payload is too large for the launch vehicle in question, it is not assigned, and is added to a `NMC' (not mission capable) list.
  
  The physical nature of the problem, however, introduces a few additional complications. The most important of these is that launch vehicle capacity depends on the payload's trajectory. For example, Pegasus XL can place 450 kg into a 200km altitude, 28.5 degree orbit, but only 120 kg into a 1400km 28.5 degree orbit\cite{pegasusug}. This means that the launch vehicles cannot be treated as simple bins; there must be a mechanism to account for the payload's orbit.
  
  Another complication follows from this. Two payloads in wildly different orbits cannot be launched together unless one or both of them is provided with a propulsion system. This introduces additional variables into the problem. Payloads are occasionally delivered to very different orbits by the same launch vehicle. For example, launch 2002-042, a H-IIA 2024, placed two USERS satellites into LEO and the Kodama satellite into GTO on September 10, 2002. However, this behavior is not common and in some cases imposes significant additional delta V requirements.
  
  The variability of launch vehicle payload capacity and the need to roughly match payload orbits primarily affects payloads in low and medium Earth orbits. Since geosynchronous orbits are characterized by a specific orbital radius, they have very similar delta V requirements, making them much more amenable to the bin packing approach. While the delta V requirements may not be completely homogeneous owing to differences in the trajectory and/or amount of delta V provided by the payload, they will be assumed to have similar delta V requirements.
  
  For these reasons, this portion of the work will only consider geosynchronous payloads.  The algorithm is applied for this data set to all 63 launch vehicle configurations used during that period with geosynchronous transfer orbit capacity.
  
  Launch times are an additional constraint.  Some payloads must launch at certain times, such as payloads intended to function as part of a constellation.  Others may be less time critical, such as many microsatellites or scientific payloads.  It is difficult to determine the time schedule requirements for individual payloads.  Therefore, two individual analyses examine the studied interval as a whole and sum the total results for individual years.  For the most part, the results obtained are very similar. 
   
	The optimal arrangements to launch as many of the 358 payloads as possible were determined for each of the 97 launch vehicle configurations using the BFD algorithm.  Table~\ref{tbl:assignmentx} contains an example of the results for an individual launch vehicle.  This is an excerpt from the optimal payload arrangement for the Falcon 9 v1.1 launch vehicle.

\begin{table}%[htbp]
  \begin{center}
    \caption{Payload Assignments for Falcon 9}
  \label{tbl:assignmentx}
    \begin{tabular}{l l l}
    \hline \hline
    Manifest 104: & & \\
    \hline
        & 2003-020A: & 3440 kg\\
        & 2011-034A: & 1410 kg\\
    Manifest 105: & & \\
    \hline
        & 2008-034B: & 3400 kg\\
        & 2013-034A: & 1425 kg\\
    Manifest 106: & & \\
    \hline
        & 2012-051B: & 3400 kg\\
        & 2000-081A: & 1414 kg\\
    Manifest 107: & & \\
    \hline
        & 2012-043B: & 3325 kg\\
        & 2003-043A: & 1525 kg\\
    Manifest 108: & & \\
    \hline
        & 2000-054A: & 3320 kg\\
        & 2001-015A: & 1530 kg\\
    ...........................\\
    NMC list: & & \\
    \hline
        & 2006-043A: & 8180 kg\\
        & 2009-035A: & 6910 kg\\
        & 2008-018A: & 6740 kg\\
        & 2011-059A: & 6740 kg\\
    ...........................\\
% Statistics:
% Falcon 9
% GEO Capacity: 4850 kg
% Launches: 187
% Total Mass: 819012 kg
% Total Cost: \$1.06e+10
% Actual Cost: \$2.33e+10
% Cost Per Delivered Payload: \$12900.30/kg
% Wastage: 9.70\%
% NMC Mass: 500161
% Capability: 270/358
% Mass Capability: 62.09\%

    \hline \hline
    \end{tabular}
  \end{center}
\end{table}

	Table~\ref{tbl:assignmentx} identifies payloads by their COSPAR identification numbers.  Mass is also listed here for reference.  As stated earlier, the NMC list is composed of payloads too heavy for the given launch vehicle to launch.
	
	How much improvement is possible?  Table~\ref{tbl:comparison} compares wastage and cost per payload mass delivered in actual geosynchronous service for selected launch vehicles with what is theoretically possible if the launch vehicle were to launch all geosynchronous payloads that it was capable of launching and they were packed optimally.  As can be seen, many launch vehicles have much higher wastage than the minimum theoretically possible with all payloads from the data set.  Note, however, that the entire data set may not be representative of what any individual launch vehicle is used for, and so it would be possible to have a lower wastage in actual service than this theoretical limit by the simple virtue of not launching payloads that are not a good fit for the given launch vehicle.  Given the relative homogeneity of the GEO market, both in mass and in function, and the cost benefit obtained from larger launch vehicle production runs via the learning curve, this approach would be strategically unwise from a business perspective in most cases.
\begin{table}%[ht!]
  \begin{center}
    \caption{Comparison of Real and All Payloads Optimally Packed Geosynchronous Wastage for Selected Launch Vehicles}
    \small
    \resizebox{\columnwidth}{!}{
  \label{tbl:comparison}
    \begin{tabular}{lll|lll}
    \hline \hline
    & \multicolumn{2}{l}{Wastage} & & \multicolumn{2}{l}{Wastage} \\
    LV & Actual & `Optimal' & LV & Actual & `Optimal' \\
    \hline 
    Ariane 40 & - & 23.31\% &
    Ariane 42L & 18.93\% & 15.95\%\\
    Ariane 42P & - & 13.88\% &
    \textit{Ariane 44L} & 4.74\% & 9.30\%\\
    \textit{Ariane 44LP} & 0.33\% & 16.94\% &
    \textit{Ariane 44P} & 4.43\% & 15.87\%\\
    Ariane 5ECA & 11.37\% & 2.60\% &
    Ariane 5G & 14.22\% & 7.39\%\\
    \textit{Atlas IIA} & 16.63\% & 17.04\% &
    \textit{Atlas IIAS} & 15.33\% & 18.14\%\\
    \textit{Atlas IIIA} & 9.62\% & 17.08\% &
    Atlas IIIB & 30.46\% & 15.93\%\\
    Atlas V 401 & 25.88\% & 10.31\% &
    Atlas V 411 & 29.82\% & 9.34\%\\
    \textit{Atlas V 421} & 6.34\% & 6.86\% &
    Atlas V 431 & 21.40\% & 3.05\%\\
    Atlas V 501 & - & 18.52\% &
    Atlas V 511 & - & 7.51\%\\
    Atlas V 521 & 35.33\% & 8.28\% &
    Atlas V 531 & 18.15\% & 3.66\%\\
    Atlas V 541 & - & 1.62\% &
    \textit{Atlas V} 551 & 0.92\% & 1.83\%\\
    Delta 7326-10 & - & 11.28\% &
    Delta 7326-9.5 & - & 14.70\%\\
    Delta 7425-10 & - & 14.09\% &
    Delta 7425-9.5 & - & 16.95\%\\
    Delta 7426-10 & - & 10.42\% &
    Delta 7426-9.5 & - & 12.71\%\\
    Delta 7925-10 & - & 20.05\% &
    Delta 7925-10L & - & 19.69\%\\
    Delta 7925-9.5 & 15.00\% & 21.92\% &
    Delta 7925H & - & 16.10\%\\
    Delta 7925H-10 & - & 18.87\% &
    Delta 7925H-10L & - & 18.41\%\\
    Delta 7926-10 & - & 15.90\% &
    Delta 7926-10L & - & 15.74\%\\
    Delta 7926-9.5 & - & 19.28\% &
    Delta 7926H & - & 22.76\%\\
    Delta 7926H-10 & - & 24.65\% &
    Delta 7926H-10L & - & 23.95\%\\
    Delta IV Heavy & 10.50\% & 1.30\% &
    Delta IV Medium & 60.02\% & 12.56\%\\
    Delta IV Medium+ (4,2) & 30.58\% & 8.90\% &
    Delta IV Medium+ (5,2) & - & 8.49\%\\
    Delta IV Medium+ (5,4) & - & 3.44\% &
    Falcon 9 & - & 9.69\%\\
    GSLV & 33.75\% & 23.31\% &
    \textit{H-IIA 202} & 2.43\% & 15.54\%\\
    H-IIA 2024 & 28.66\% & 9.39\% &
    H-IIB & - & 1.87\%\\
    Long March 2C & - & 13.07\% &
    Long March 2E & - & 16.71\%\\
    Long March 3A & 17.93\% & 13.88\% &
    \textit{Long March 3B} & 2.38\% & 8.61\%\\
    \textit{Long March 3C} & 17.48\% & 18.85\% &
    \textit{M-V} & 0\% & 12.56\%\\
    \textit{Proton-K/DM-2} & 3.53\% & 10.42\% &
    Proton-K/DM-2M & 16.92\% & 10.42\%\\
    Proton-M/Briz-M & 28.61\% & 8.12\% &
    PSLV & - & 12.21\%\\
    Soyuz FG & 67.89\% & 19.28\% &
    Soyuz U & - & 19.28\%\\
    Titan 2G & - & 11.62\% &
    Titan 402B & 60.35\% & 8.23\%\\
    Titan 401B & 75.89\% & 8.23\% &
    \textit{Zenit 3SL} & 6.77\% & 8.46\%\\
    Zenit 3SLB & 34.24\% & 18.44\%\\
    \hline
    \multicolumn{3}{l}{`-' indicates no actual geosynchronous usage.} & \multicolumn{3}{l}{\textit{Italics} indicate real wastage lower than optimal.}\\
    \hline \hline
    
    \end{tabular}
    }
  \end{center}
\end{table}

	Most of this excess wastage is due to the difficulty of launching multiple payloads at once.  The available adapters and other factors besides the raw mass of the payload limit the number and size of secondary payloads.  These effects may be seen to the greatest effect in the case of Ariane 5ECA, which despite having a very low theoretically ideal wastage and a robust multi-payload capability still has in excess of 20\% wastage in actual service.
	
	As has been alluded to elsewhere in this work, historically there has been some debate about the sizing of launch vehicles.  How does sizing affect costs in this `ideally packed' scenario?  Is there a relationship between payload capacity and cost per payload mass delivered?  Figure~\ref{fig:pvpcreal} plots the maximum payload capacity of the launch vehicle against the cost per payload mass actually delivered to orbit if the payloads were ideally packed.  
	
\begin{figure}%[htbp]
  \begin{center}
    \includegraphics[width=140mm]{pvpcreal.png}
    \caption{Cost Per Payload Mass Delivered versus Payload Capacity for Real Launch Vehicles with BFD Algorithm Applied to All Geosynchronous Payloads}
    \label{fig:pvpcreal}
  \end{center}
\end{figure} 


	It is clear that there is a trend in this ideal case between maximum payload capacity and cost per unit payload mass delivered to orbit.  However, it is somewhat obscured by variations in launch vehicle prices from other causes.  A simple comparison demonstrates this: a Falcon 9 v1.1 has a maximum payload capacity of 4,850 kg to GTO, and costs \$11,649 per kg of maximum payload capacity, while an Atlas V 401 has a maximum GTO payload capacity of 4,950 kg, yet costs \$16,841 per kg of maximum payload capacity.  In order to determine the effect of maximum payload capacity on cost per payload delivered to GTO, these variations must be removed, which requires only comparing launch vehicles with an identical cost per maximum payload capacity.  Figure~\ref{fig:pvpctheoretical} shows the result of the analysis in Figure~\ref{fig:pvpcreal} if the cost per unit payload capacity for all launchers is set to 1.

\begin{figure}%[htbp]
  \begin{center}
    \includegraphics[width=140mm]{pvpctheoretical.png}
    \caption{Cost Per Payload Mass Delivered versus Payload Capacity With Launch Vehicle Cost Per Unit Payload Mass Capacity Equalized}
    \label{fig:pvpctheoretical}
  \end{center}
\end{figure}

	Figure~\ref{fig:pvpctheoretical} shows that launch vehicles with payload capacities of 8,000 kg or more have a great advantage in price to geosynchronous orbit if optimally packed.  This advantage tends to flatten out after this point, although it still slowly decreases.  This makes intuitive sense: the larger individual launch capacity yields more potential configurations of the payloads, which provides more opportunities to reduce wastage.
	
	It is interesting to compare this relationship between wastage and payload capacity to that shown for real launch vehicle usage in Figures~\ref{fig:leowastagevcap} and \ref{fig:geowastagevcap} in Chapter \ref{sec:wastage}.  The results in these tables indicate that in current service there is no correlation between wastage and payload capacity.  This indicates that currently there is no concerted effort to schedule payloads on any sort of scale.  While individual operators may improve their practices over time, resulting in the decreasing trend seen in wastage and the increase in number of payloads per launch, the market is nowhere near a minimum wastage scenario.
	
	It is clear that the use of larger launch vehicles reduces wastage in the ideally packed scenario with one type of launch vehicle.  It is less certain, however, that this trend holds true if multiple types of launch vehicles are available, and if so, what the cost savings are.  While the previous analysis provides a means for comparing individual launch vehicles, in order to determine the maximum possible savings, it is necessary to vary both the launch vehicle type and the arrangement of payloads.
	
\begin{figure}%[htbp]
  \begin{center}
    \includegraphics[width=120mm]{a-bfd.png}
    \caption{Flowchart of A-BFD Algorithm as Applied to Space Payload Scheduling}
    \label{fig:abfd}
  \end{center}
\end{figure}
	
	Crainic et al provide a possible solution with their A-BFD algorithm, dedicated to solving this variable bin-packing problem with fixed costs.  Figure~\ref{fig:abfd} presents a flowchart of this algorithm.  While subject to the same physical limitations on the problem as the BFD algorithm, A-BFD allows variation of the launch vehicle, both in number and type.  This algorithm is very similar to BFD as used in the previous analysis, with two additional steps.  The various bin types must be sorted in increasing order of the ratio $\frac{c}{V}$, where c is cost and V is volume.  For this problem, this corresponds to the cost per maximum payload capacity.  When a bin must be added, the bin with the best cost effectiveness capable of holding the object being evaluated is added if the object cannot fit in one of the existing bins.  Bins of identical c/V must then be sorted in ascending order of capacity.
	
	Given the fact that larger launch vehicles are generally more cost-effective than smaller launch vehicles, it may seem that this approach will cause excessive wastage, especially in the last few manifests assigned.  Crainic addresses this issue by introducing a postprocessing step where the algorithm may swap each loaded bin with a new bin from the set of unused bins if the second bin is less expensive and has enough capacity to hold the contents of the first bin.  For instance, if a very small payload is assigned to a very large capacity launcher by itself owing to this launchver's superior cost-effectiveness in the algorithm's first pass, the postprocessing step evaluates this situation and selects the cheapest launch vehicle capable of launching this payload, even if its cost-effectiveness is poor.
	
	Table~\ref{tbl:abfdmincost} presents launch vehicle usage for the A-BFD algorithm in the same case as the individual launch vehicle analyses.  As would be expected, the results emphasize the most cost-effective launch vehicles, such as Falcon 9 and Long March 3B.  The heaviest geosynchronous payload in the data set masses more than eight tons, far beyond the current capacity of either of these vehicles.  This drives use of larger, more powerful, but less cost-effective launchers such as Atlas V 551.  The end result is a total launch cost savings of 53\% over the missions as actually launched, with a reduction in wastage from 21.8\% to 9.66\%.
	
\begin{table}%[htbp]
  \begin{center}
    \caption{Launch Vehicle Usage for Worldwide Minimum Cost Scenario}
  \label{tbl:abfdmincost}
    \begin{tabular}{ll}
    \hline \hline
    Launch Vehicle & Number\\
    \hline
      Atlas V 421 & 22 \\
      Atlas V 551 & 2 \\
      Delta IV Medium+ (4,2) & 46 \\
      Falcon 9 & 187 \\      
      Long March 3B & 18 \\
      \textbf{Total} & 275\\
      
    \hline \hline
    \end{tabular}
  \end{center}
\end{table}
	
	The results obtained using the variable bin-packing algorithm suggest that the `optimal' solution for any given set of launch vehicles and payloads will maximize use of the least expensive launch vehicles, subject ot limitations in payload capacity.  However, this presents an obvious real world problem: availability.  Even if one launch vehicle is far superior in terms of cost-effectiveness than any other there is some limit as to how many could be produced.  It is highly unlikely that all launch vehicle providers were producing at maximum capacity over this entire period, so some variance might not be of consequence, but the above solutions that only use one or two types of launch vehicles present a problem.
	
	Table~\ref{tbl:abfdmincostlvlimited} presents launch vehicle usage if only the launch vehicles used in any given year are available for that year.  This scenario limits the use of the most popular launchers in Table~\ref{tbl:abfdmincost}, especially Falcon 9, which was not actually used for any geosynchronous missions during the studied interval, and so offers lesser savings of 27.3\% while reducing wastage to 4.73\%.   
	
	\begin{table}%[htbp]
  \begin{center}
    \caption{Launch Vehicle Usage for Worldwide Minimum Cost Scenario with Limited Launch Vehicle Availability}
    \resizebox{\columnwidth}{!}{
    \label{tbl:abfdmincostlvlimited}
    \begin{tabular}{lll|lll}
    \hline \hline
    & \multicolumn{2}{l}{Usage} & & \multicolumn{2}{l}{Usage}\\
    Launch Vehicle & Minimum Cost & Actual & Launch Vehicle & Minimum Cost & Actual\\
    \hline
    Ariane 42L & 0 & 4 &
    Ariane 44L & 0 & 11\\
    Ariane 44LP & 0 & 4 &
    Ariane 44P & 1 & 3\\
    Ariane 5ECA & 38 & 38 &
    Ariane 5G & 10 & 10\\
    Atlas IIA & 0 & 7 &
    Atlas IIAS & 0 & 7\\
    Atlas IIIA & 2 & 2 &
    Atlas IIIB & 4 & 4\\
    Atlas V 401 & 4 & 4 &
    Atlas V 411 & 2 & 2\\
    Atlas V 421 & 2 & 2 &
    Atlas V 431 & 2 & 2\\
    Atlas V 521 & 2 & 2 &
    Atlas V 531 & 1 & 1\\
    Atlas V 551 & 1 & 1 &
    Delta 7925-9.5 & 0 & 1\\
    Delta 7925H-10 & 0 & 0 &
    Delta IV Heavy & 1 & 1\\
    Delta IV Medium & 1 & 1 &
    Delta IV Medium+ (4-2) & 5 & 5\\
    GSLV & 0 & 4 &
    H-IIA 202 & 1 & 1\\
    H-IIA 2024 & 2 & 2 &
    Long March 3A & 12 & 12\\
    Long March 3B & 13 & 13 &
    Long March 3C & 4 & 4\\
    Proton-K/DM-2 & 6 & 6 &
    Proton-K/DM-2M & 17 & 17\\
    Proton-M/Briz-M & 59 & 59 &
    PSLV & 0 & 1\\
    Soyuz FG & 0 & 1 &
    Titan 401B & 0 & 4\\
    Titan 402B & 0 & 3 &
    Zenit 3SL & 27 & 27\\
    Zenit 3SLB & 6 & 6 &
    \textbf{Total} & 223 & 272\\

    \hline \hline
    \end{tabular}
    }
  \end{center}
\end{table}    
	
	Some missions are time-critical, such as space station resupply.  While these constraints do not apply to all missions, it is necessary to investigate the effects of schedule constraints on the potential for scheduling to reduce costs.  This may be done by running the algorithm on a single year's payloads at a time and then summing all years in the dataset, which has the end result of constraining all payloads to be launched in the calendar year they were actually launched in.  Tables \ref{tbl:abfdmincostyearlimited} and \ref{tbl:abfdmincostyearlvlimited} contain results for this case.  For the case with unrestricted launch vehicle selection, this reduces the total cost savings to 43.7\%.  If launch vehicle selection is constrained, cost savings are reduced to 19.1\%.
	
\begin{table}%[htbp]
  \begin{center}
    \caption{Launch Vehicle Usage for Worldwide Minimum Cost Scenario with Time Constraints}
  \label{tbl:abfdmincostyearlimited}
    \begin{tabular}{ll}
    \hline \hline
    Launch Vehicle & Number\\
    \hline
    Atlas V 421 & 18 \\
    Atlas V 551 & 2 \\
    Delta IV Medium+ (4,2) & 50\\
    Falcon 9 & 187\\
    Long March 3A & 6\\
    Long March 3B & 18\\
    GSLV & 2\\
    PSLV & 1\\
    \textbf{Total} & 284\\
    \hline \hline
    \end{tabular}
  \end{center}
\end{table}

\begin{landscape}
%\begin{table}[htbp]
%  \begin{center}
\small
\begin{longtable}{lllllllllllllll}
    \caption{Launch Vehicle Usage for Worldwide Minimum Cost Scenario with Limited Launch Vehicle Availability and Time Constraints}\\
    \label{tbl:abfdmincostyearlvlimited}\\
%    \resizebox{\columnwidth}{!}{
%    \begin{tabular}{lllllllllllllll}
      \hline \hline
      & \multicolumn{14}{l}{Usage By Year (Scenario/Actual)}\\
      LV & 2000 & 2001 & 2002 & 2003 & 2004 & 2005 & 2006 & 2007 & 2008 & 2009 & 2010 & 2011 & 2012 & 2013\\
      \hline
      \endfirsthead
      LV & 2000 & 2001 & 2002 & 2003 & 2004 & 2005 & 2006 & 2007 & 2008 & 2009 & 2010 & 2011 & 2012 & 2013\\     
    \hline
    \endhead
    \hline
    \endfoot
    \hline
    \endlastfoot
      Ariane 42L & 3/3 & 0/0 & 1/1 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Ariane 42P & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Ariane 44L & 1/1 & 3/3 & 6/6 & \textbf{0/1} & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Ariane 44LP & 3/3 & 1/1 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Ariane 44P & 1/1 & 2/2 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Ariane 5ECA & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & \textbf{0/2} & 5/5 & 4/4 & 5/5 & 5/5 & \textbf{4/5} & 3/3 & 6/6 & 3/3\\
      Ariane 5G & 4/4 & 2/2 & 1/1 & 3/3 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Atlas IIA & \textbf{2/4} & 1/1 & 2/2 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Atlas IIAS & 2/2 & 1/1 & 1/1 & 0/0 & 3/3 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Atlas IIIA & 1/1 & 0/0 & 0/0 & 0/0 & 1/1 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Atlas IIIB & 0/0 & 0/0 & 2/2 & 2/2 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Atlas V 401 & 0/0 & 0/0 & 0/0 & 1/1 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 &  \textbf{0/1} & 0/0 & 0/0 & 2/2\\
      Atlas V 411 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 1/1 & 0/0 & 0/0 & 1/1 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Atlas V 421 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 1/1 & 1/1 & 0/0 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Atlas V 431 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/1 & 0/0 & 0/0 & 0/0 & 1/1 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Atlas V 521 & 0/0 & 0/0 & 0/0 & 1/1 & 1/1 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Atlas V 531 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 &  1/ 1 & 0/0 & 0/0 & 0/0\\
      Atlas V 541 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Atlas V 551 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 &  0/ 0 & 0/0 & 0/0 & 1/1\\
      Delta 7925-9.5 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 1/1 & 0/0 & 0/0 & 0/0 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Delta IV Heavy & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 1/1 & 0/0 & 0/0 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Delta IV Medium & 0/0 & 0/0 & 0/0 & 1/1 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Delta IV Medium+ (4,2) & 0/0 & 0/0 & 1/1 & 1/1 & 0/0 & 0/0 & 1/1 & 0/0 & 0/0 & 1/1 &  1/ 1 & 0/0 & 0/0 & 0/0\\
      GSLV & 0/0 & \textbf{0/1} & 0/0 & \textbf{0/1} & 1/1 & 0/0 & 0/0 & \textbf{0/1} & 0/0 & 0/0 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      H-IIA 202 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 &  \textbf{0/1} & 0/0 & 0/0 & 0/0\\
      H-IIA 2024 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 1/1 & 0/0 & \textbf{0/1} & 0/0 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Long March 3A & 4/4 & 0/0 & 0/0 & 2/2 & 1/1 & 0/0 & 1/1 & \textbf{0/2} & \textbf{0/1} & 0/0 &  0/ 0 & 0/0 & 1/1 & 0/0\\
      Long March 3B & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & \textbf{0/1} & 1/1 & 2/2 & 1/1 & 1/1 &  0/ 0 & 5/5 & 1/1 & 1/1\\
      Long March 3C & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 1/1 & 1/1 &  1/ 1 & 1/1 & 0/0 & 0/0\\
      Proton-K/DM-2 & 1/1 & 2/2 & 0/0 & 1/1 & 1/1 & 0/0 & 0/0 & 0/0 & 0/0 & 0/1 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Proton-K/DM-2M & 7/7 & 2/2 & 4/4 & 2/2 & 1/1 & 0/0 & 0/0 & 0/0 & \textbf{0/1} & 0/0 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Proton-M/Briz-M & 0/0 & 1/1 & 0/0 & 0/0 & 4/4 & \textbf{0/4} & 3/3 & 4/4 & 7/7 & 7/7 & 10/10 & 6/6 & 9/9 & 4/4\\
      PSLV & 0/0 & 0/0 & 1/1 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Soyuz FG & 0/0 & 0/0 & 0/0 & \textbf{0/1} & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Titan 401B & 0/0 & \textbf{0/1} & 1/1 & \textbf{0/2} & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Titan 402B & \textbf{0/1} & \textbf{0/1} & 0/0 & 0/0 & 1/1 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 &  0/ 0 & 0/0 & 0/0 & 0/0\\
      Zenit 3SL & 2/2 & 2/2 & 1/1 & 2/2 & 3/3 & \textbf{0/3} & 4/4 & 0/0 & \textbf{3/5} & \textbf{0/1} &  0/ 0 & 1/1 & 3/3 & 0/0\\
      Zenit 3SLB & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & 0/0 & \textbf{0/1} & \textbf{0/3} &  0/ 0 & \textbf{1/2} & 0/0 & 0/0\\
      %\textbf{Total} & 30/33 & 18/20 & 21/21 & 16/21 & 17/17 & & & & & & & & &\\
      \hline \hline
%      \end{tabular}
%      }
%  \end{center}
%\end{table}
\end{longtable}
\end{landscape}
%
% 	It is important to ask what the practical use of this is.  In the real world, there are many actors in the launch vehicle market, and while some users are much larger than others (such as the Department of Defense or Roscosmos) none of them has a majority of the market on their own.  What are the potential benefits for a single user?  Table X presents the results of the above analyses applied to single customers.  
% 	\todo[inline]{Apply these analyses to Roscosmos et al}
	
	Several conclusions may be drawn from the results presented in this chapter.  The first is that aside from their larger potential market share, large launch vehicles have another potential advantage over smaller ones.  The current \textit{raisons d'etre} for small launch vehicles are flexibility and launching small payloads, which as discussed in Chapter \ref{sec:payloadtrends} are actually the majority of payloads to LEO. If payloads can be loaded without prejudice on large launch vehicles, however, their wastage is actually lower than that of small launch vehicles, increasing their already formidable cost advantage.
	
  These results set a boundary for what a large launch vehicle is with regard to the capability to reduce wastage. Most of the potential reduction in wastage and thus cost is obtained at a GTO payload capacity of approximately 8000 kg. Beyond that, only small improvement from increasing size occurs. Since the development of ever-larger launch vehicles begins to increase the life-cycle cost per payload mass of the launch vehicle, it is clear that there is a point of diminishing returns. This figure is based on the assumption that payload masses remain relatively static over time. Historical data, as discussed in Chapter \ref{sec:payloadtrends}, indicates that average payloads are decreasing somewhat in mass over time. Thus, over time this optimum will have a tendency to decrease, barring some other change in the market that causes payload masses to increase.
  
  Both the cost and price models show this point of diminishing returns to be near 8000 kg as well. Thus, given current market conditions, this represents an optimal payload capacity from a cost perspective. Only a single payload of the 337 in the data set masses more than 8000 kg, and the remainder can be launched at a wastage of 2.07\%. Given that some sort of payload adapters would be required to attach the payloads to the launch vehicle, this probably represents a practical lower limit on wastage.  As stated in Chapter~\ref{sec:review}, the SYLDA dual payload adapter for Ariane 5 masses slightly less than 5\% of total GTO payload capacity.
  
  In scenarios where multiple types of launch vehicle are available, several interesting trends are apparent.  The first is that competition in these scenarios is very cutthroat.  If launch vehicle selection and manifesting is completely free, the number of launch vehicle types used decreases from 37 to only 5.  Limiting the launch vehicle availability to what was actually used still reduces the launch vehicle types used to 26.  Investigation of Table~\ref{tbl:abfdmincostlvlimited} shows that usage is very much a binary decision: either a launch vehicle is cost effective enough to be used, in which case all of those available are used, or it is not, in which case none are used.  The sole exception in that scenario is the single Ariane 44P launch.  Adding the time constraint increases the number of types used.  Only one launcher, Ariane 42P, is completely eliminated, although all launchers with poor cost-effectiveness suffer a reduction in numbers.
  
	  A significant savings in terms of launch cost is possible for most launch vehicles if multiple manifesting of payloads is increased in a systematic way.  Assuming that each launch vehicle's individual market is similar to the geosynchronous market as a whole, many popular launch vehicles could reduce wastage and thus launch cost by up to 15\% by arranging multiple manifests in a way designed to reduce wastage.  This practice would also in theory promote additional savings because it enables the use of heavier launch vehicles that usually have lower costs per unit payload capacity.  While there is a point of diminishing returns at approximately 8000 kg GTO capacity, below this, the higher the launch vehicle's capacity, the better.  Reducing the use of cost inefficient small launch vehicles will result in additional savings.  
    
    If payloads' manifests could be arranged in the most cost-optimal way on the varied types of existing launch vehicles with no regard to time schedules or the number that can be produced, launch cost savings of up to 52\% over existing costs are possible.  Placing constraints such as time schedules or availability restrictions reduces this, but even in the most restrictive case, where launcher selection is restricted to the quantities actually produced and the payload must launch on a manifest in the same year that it actually launched in, a savings of up to 19\% is possible over existing usage.
    
    These results also give insights into which launch vehicle types have better cost-effectiveness for missions in the current market.  Especially in the cases where availability is not restricted, entire classes of launch vehicles are not used owing to their inferior cost-effectiveness.  In fact, if launcher selection were completely free over the studied interval, the lowest cost scenario only uses five distinct booster types.  Even if launchers are restricted to the quantities actually used, eleven launch vehicle configurations are completely eliminated from use.  It also seems that launcher utilization in this `ideal' scenario is a binary proposition: either the complete quantity of available boosters is used or none are used.
    
    Both wastage and low launch vehicle cost-effectiveness increase launch costs.  These analyses show that launch vehicle cost-effectiveness is the primary driver behind high launch costs.  If launch vehicle choice is unrestricted, wastage actually increases as costs are dramatically reduced.  This is similar to the results in Chapter \ref{sec:usage}, where costs were reduced through changing launch vehicle selection for the as-launched manifests without significantly reducing wastage.  However, if launch vehicle choice is restricted and scheduling constraints are imposed, reduction of wastage becomes more and more important.  The most restrictive of the scenarios considered in this work actually retains a very cost-ineffective Titan IV launch while reducing usage of the much more cost-effective Ariane 5.
  
\chapter{Risk of Multiple Payload Launches}
\label{sec:risk}

  The results obtained in previous chapters suggest that significant savings are possible from rearrangement of payloads on launch vehicles.  However, before proposing this as a future course of action to reduce launch costs, it is necessary to investigate any potential disadvantages this rearrangement may have.  Most important of the potential disadvantages is the potential for increased risk of loss of some or all of the payloads in a launch.  Buckley notes the effects of this risk\cite{excesscapacity}, commenting that concern over this risk is a known barrier to combining payloads.  Addressing this concern is critical to evaluation of the potential benefits of combining payloads.

  Multiple payloads add complexity and failure points to individual launch events, reducing the chance that the entire launch and deployment of the onboard payloads will be successful.  The additional risk to each payload from launching multiple payloads at once is dependent on the specific design of the payload adapters used to carry multiple payloads. Some adapters are configured such that a failure to separate one payload only causes the loss of that payload, while others, such as CubeSat launch tubes, may cause multiple payloads to be lost with a single separation failure\cite{cubesat}.

  This chapter will attempt to quantify the cost associated with this increased risk by estimating the cost to insure said risk.  This approach is necessarily approximate, as any number of factors might affect real-life insurance costs.  Different insurance policies also cover different types of losses; for instance, many launch insurance contracts also provide insurance on the payload itself for some specified period after reaching orbit, with one year being common\cite{insurance}.  However, at a minimum insurance has to charge enough to cover the occasional losses from launches and payload deployments, plus its own business costs and some amount of profit, and so that yields a floor on the minimum price of insurance over the long term.

  It is important to note that this analysis is not intended to make definitive statements about actual insurance costs.  First, some payloads, such as most United States government payloads, do not have insurance.  This means that the `insurer,' i.e. themselves, does not pass profit or overhead on to the end user.  Second, past loss rates do not always drive future insurance costs.  Insurers occasionally use other methods to determine their risk exposure, especially for newer, relatively untested launch vehicles\cite{insurance}, where the past launch data may be misleading.  For example, failure on the first flight does not necessarily imply that a design really has 0\% reliability.  Notwithstanding these considerations, in the long run, the cost of the losses must be paid by someone, and estimating the insurance costs based on past loss rates can provide an idea of how much the additional risk adds to the final cost.
  
  The cost of insurance is ideally a function of three variables: the value of the payload, the reliability of the launch vehicle and its subordinate systems, and the rate of profit of the insurance company. The rate of profit is not an engineering consideration.  Strictly speaking, the value of the payload is not either, but cost analysis can provide some estimation of its value.  Assuming relative homogeneity in payload value per mass, payload value should increase in proportion to the reduction in wastage. That is, reduction of wastage from 20\% of maximum payload capacity to 10\%, the value of the payload should increase by 12.5\% (0.9/0.8-1).
  
  The risk of a certain kind of loss comes from the risk of each potential cause.  Separation events are a well-known cause of launch failures\cite{insurance}. Depending on the design of the payload adapters, a payload separation failure may only cause the loss of the payload separating, or cause the loss of all payloads still attached to the upper stage. It is even conceivable that in the future the payload may not be lost at all; a launch vehicle with payload recovery capability such as the Space Shuttle could return payloads that failed to deploy, and the loss would be reduced to the payload's launch cost. The analysis done below will assume the worst-case scenario of all remaining payloads attached to the upper stage being total losses once a separation failure occurs.
  
  A simple analysis of the worst-case scenario provides a way to quantify the cost effect of increased risk. A single payload, and thus a single separation event, is the baseline case. The chance of failure is $1-R$, where $R$ is the reliability of the separation system. For multiple payloads in this scenario, a failure of the first payload separation is a complete loss, so the chance of losing any of the subsequent payloads is at minimum $1 - R$. It will be assumed that all separations have the same reliability $R$.
  
  It follows that the chance of losing the $Nth$ payload to a separation failure in this scenario is:
  
\begin{equation}
L = (1 - R) \prod\limits_{i=1}^N R^{i-1}
\end{equation}

  Each individual payload requires insurance against its own replacement cost and the cost of launching this replacement. Again assuming homogeneity in value per payload mass, and further assuming that wastage on a subsequent flight would be the same, the additional insurance cost for the payloads is:
  
\begin{equation}
C_{IP} = \sum\limits_{i=1}^N [(1-R) \prod\limits_{j=1}^i R^{j-1}] \frac{M_{Pi}}{M_P} (C_{P} + C_{LVe})
\end{equation}

  This charges the risk for the first separation to the payload, rather than the launch vehicle.
	
	There is a possibility that the launch vehicle itself will fail.  While one would not expect delivery of multiple payloads to have an effect on launch vehicle reliability, it has an effect on the cost of insurance because it increases the value of the payload by reducing wastage.  Launch insurance increases the cost of the launch vehicle by a factor of:
	
\begin{equation}
\frac{C_{LVe}}{C_{LV}} = 1+(1+\frac{C_{P}}{C_{LV}})(1-R_{LV})(1+P_{I})
\end{equation}

Adding the cost of insuring the payloads to this increased cost will give the total cost for the launch.

Data collected by Futron Corporation\cite{spacexreliability} suggest that separations have a historical failure rate of approximately .233\%.  Assuming operation at full load (i.e., negligible wastage), Table~\ref{tbl:payloadfailurechance} displays the insurance costs for a given number of payloads as a percentage of launch vehicle cost, assuming 98\% launch vehicle reliability and a $\frac{C_P}{C_{LV}}$ of 3.  The additional insurance beyond that required for the launch vehicle for ten equally sized payloads with zero wastage launched simultaneously under this scheme reaches 5.2\% of launch vehicle cost.  This sets another floor on wastage: if the money saved from reducing wastage is immediately lost due to the cost of assuming increased risk, then nothing is gained.

\begin{table}%[htbp]
  \centering
  \caption{Loss Chance and Insurance Cost}
  \resizebox{\columnwidth}{!}{
    \begin{tabular}{llllllllllll}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %%                                                                  %%
    %%  This is a LaTeX2e table fragment exported from Gnumeric.        %%
    %%                                                                  %%
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \hline \hline
    %\multicolumn{4}{l}{Additional Insurance Cost}	&\multicolumn{8}{l}{Insurance Cost for Payload (Assume 98\% LV reliability and CPCLV of 3)}\\
    & & \multicolumn{10}{l}{Number of Payloads on Launch} \\
    Payload	& \% Loss	&1	&2	&3	&4	&5	&6	&7	&8	&9	&10\\
    \hline
    1	&0.23\%	&0.95\%	&0.48\%	&0.32\%	&0.24\%	&0.19\%	&0.16\%	&0.14\%	&0.12\%	&0.11\%	&0.10\%\\
    2	&0.47\%	&	&0.95\%	&0.64\%	&0.48\%	&0.38\%	&0.32\%	&0.27\%	&0.24\%	&0.21\%	&0.19\%\\
    3	&0.70\%	&	&	&0.95\%	&0.71\%	&0.57\%	&0.48\%	&0.41\%	&0.36\%	&0.32\%	&0.29\%\\
    4	&0.93\%	&	&	&	&0.95\%	&0.76\%	&0.63\%	&0.54\%	&0.48\%	&0.42\%	&0.38\%\\
    5	&1.16\%	&	&	&	&	&0.95\%	&0.79\%	&0.68\%	&0.59\%	&0.53\%	&0.47\%\\
    6	&1.39\%	&	&	&	&	&	&0.95\%	&0.81\%	&0.71\%	&0.63\%	&0.57\%\\
    7	&1.62\%	&	&	&	&	&	&	&0.95\%	&0.83\%	&0.74\%	&0.66\%\\
    8	&1.85\%	&	&	&	&	&	&	&	&0.95\%	&0.84\%	&0.76\%\\
    9	&2.08\%	&	&	&	&	&	&	&	&	&0.95\%	&0.85\%\\
    10	&2.31\%	&	&	&	&	&	&	&	&	&	&0.94\%\\
    \hline
	    \multicolumn{2}{l}{Total}	&0.95\%	&1.43\%	&1.91\%	&2.38\%	&2.85\%	&3.33\%	&3.80\%	&4.27\%	&4.74\%	&5.21\%\\
	    \multicolumn{2}{l}{Increase}	&9.94\%	&14.90\%	&19.85\%	&24.80\%	&29.73\%	&34.66\%	&39.58\%	&44.49\%	&49.40\%	&54.30\%\\
	    \hline \hline
	    \end{tabular}

  \label{tbl:payloadfailurechance}%
  }
\end{table}%
	
	This, however, is a worst-case scenario in several ways.  First, even in the least constrained cases examined in Chapter \ref{sec:arrangement} for the largest launch vehicles, it is seldom necessary to launch ten payloads at once.  In the `ideal' case, the largest number of simultaneous payloads for Ariane 5ECA is seven.  For smaller launch vehicles, the maximum number of simultaneous payloads will be less.
	
	Second, a multi-payload system where failure of any payload dooms all payloads that have not yet separated is pessimistic.  Depending on the size of the subordinate payloads, there are several arrangements that could provide for separation of subsequent payloads even if a payload ahead of them in the queue fails to deploy.  The existing ESPA ring for the EELVs falls into this category, as the payloads are arranged in parallel\cite{divug}. A detailed examination of payload geometries or arrangements and their effect on the rate of payload losses due to separation failure is beyond the scope of this work, but it is clear that even in current practice the assumption that a payload separation failure causes the loss of all subsequent payloads is conservative.
	
	Finally, assuming that all payloads are of equal mass actually causes the insurance cost to increase.  Both in actual service and in the `ideal' case, there is a tendency to pair large payloads with small ones.  Even if forced to adopt a physical configuration where a separation failure of a payload prevents subsequent payloads from deploying, ensuring that the largest and therefore usually most valuable payload deploys first will reduce the cost of insurance, since the first payload has the lowest chance of being lost to separation failure in this scenario.
	
	Surprisingly, for highly reliable launch vehicles launching large numbers of individual payloads concurrently, there may be a higher chance of losing a payload to separation failure than of losing the launch vehicle. This carries a correspondingly higher insurance cost. However, the increased cost, even in the worst case, is far less (at least a factor of two) than average wastage for current launch vehicles. Further, this worst-case scenario is highly unlikely to occur, given that it requires making pessimistic assumptions about virtually all aspects of the launch manifest and payload separation system.
	
	Increasing the number of payloads per launch vehicle is not without risk. The potential for reduced reliability and the requirement to pay launch insurance on an increased amount of payload value can reduce the potential savings. However, even in the most pessimistic scenario, these additional insurance costs will constitute no more than a 5\% additional cost per launch.

\chapter{Conclusions}
\label{sec:conclusions}

  Operational losses constitute a significant expense in the deployment of spacecraft.  Few commentators have remarked on this expense, even though it can be in excess of 20\% from wastage alone.  If the use of cost-ineffective launch vehicles, for whatever cause, is included, the expense can be as much as 53\% of the total launch vehicle expenditure.  Historically, the high cost of launch vehicles and until recently the requirement to expend them to reach space were the primary drivers behind the high cost of access to space.  However, significant reductions in cost to the customer are possible if operational losses can be reduced, and these savings will continue even if launch vehicle technology is improved.
  
  \section{Review of Dissertation}
  
  Investigation of operational losses first requires data on launch vehicle usage and payload characteristics.  Chapter \ref{sec:payloadtrends} analyzed trends in the masses and orbit types of the space payloads in the data set, while Chapter \ref{sec:lvtrends} tabulated launch vehicle prices and historical usage while examining trends in launch vehicle pricing with multiple cost models.  These analyses showed that the majority of individual payloads are small, but the majority of payload mass is contained in large payloads. Further analysis showed that at least among existing launch vehicles, larger size tends to be more cost-effective in terms of price per maximum payload capacity.  This is an inherent conflict that expresses itself in both the wastage and launch vehicle selection problems.  
  
  Chapter \ref{sec:capability} examined the capability of launch vehicles to launch payloads.  The smallest launch vehicles, Pegasus and Falcon 1, are capable of launching approximately 33\% of individual payloads, but this only translates to slightly more than 1\% of payload mass.  In combination with their inherently inferior cost-effectiveness, this makes small launch vehicles less attractive for the user.  This drives the use of larger launch vehicles.  Chapter \ref{sec:capability} also studied the market share of launch vehicles, finding that single-digit shares of the payload mass that a launcher is capable of launching are typical.
  
  Chapter \ref{sec:wastage} computed overall wastage and wastage of certain classes of payloads.  The total wastage for all launches with complete data was 20.38\% of total payload capacity. This results in a financial loss of no less than \$8.72B (2014\$).  Given that the cost computations in this work purposely select optimistic (i.e. low) values for the prices of launch vehicles, the true financial loss could be twice this or more.  It is important to note that wastage decreased sharply over the period 2009-2013, to the point that the wastage to low Earth and geosynchronous orbits for 2013 was less than half the average.
  
  Chapter \ref{sec:usage} investigated launch vehicle usage.  The majority of launches do not use the cheapest launch vehicle capable of carrying out their mission.  To some degree, this is inevitable, given the non-financial considerations highlighted in that chapter.  Nonetheless, the percentage is low enough that making an attempt to improve it will yield significant savings.  A savings of slightly less than 44\% to low Earth and geosynchronous orbits is possible simply by changing launch vehicle selection among those available at the time for the existing payload manifests with no rearrangement at all.
  
	The considerable amount of payload capacity wasted, coupled with the cost-inefficiency of small launch vehicles, represents a large increased cost imposed on the space launch industry.  Analyses conducted in Chapters \ref{sec:usage} and \ref{sec:arrangement} of this work indicate that it is possible to reduce launch costs greatly by improving where possible the selection of launch vehicles and the manifesting of payloads.  
	
  The gains shown in these analyses are not fully possible in reality.  As stated in the relevant chapters, real-world limitations place limits on the potential savings.  Further, most of these real-world limitations, such as national security considerations, are not technical in nature and not amenable to technological or operational solutions.  They are also difficult to quantify.  It may be simple enough to determine the number of national security payloads and exempt them from the analysis performed in Chapters  \ref{sec:usage} and \ref{sec:arrangement}, but determining and quantifying all of the potential reasons to use a launch vehicle that appears to be uneconomical is not possible.
  
  Nonetheless, it is clear that improvement is possible.  The fact that over time the number of payloads per launch has gone up, as shown in Figure~\ref{fig:payloadsperlaunch} while wastage has gone down as shown in Figure~\ref{fig:wastage} is a strong indication of this.  Individual users and launch vehicle producers are already working to increase the utilization of multiple payload launches\cite{excesscapacity}.
  
  Improved selection of launch vehicles offers a greater savings, but is more problematic than improved payload manifesting.  If launch vehicle selection were completely open, a 43.7\% savings over the current situation, even with identical manifests, is possible.  Combining these approaches can result in radical improvement.  As noted in Chapter \ref{sec:arrangement}, a total reduction in launch cost to geosynchronous orbit of nearly 52\% is theoretically possible.  
  
  Merely proposing changes to launch scheduling is not a complete solution.  The current array of payload adapters available for most launch vehicles is incapable of supporting much further increase in multiple payload launch, especially for payloads of larger size.  Smaller satellites are somewhat better provided for in this regard, as the existing adapters are capable of carrying more payloads at once and new developments such as Spaceflight's SHERPA promise to carry considerably more\cite{spaceflightug}.  Larger payloads, however, are still limited to single or double launches, and likely will remain so for the forseeable future.
  
  While some `containerized' satellite deployment systems exist, none operate in the same way that Earthbound containerized shipping systems do.  The ISO container caused a revolution in international shipping and contributed to massive growth in the global economy\cite{containerization}.  No existing satellite transportation and deployment system matches its simplicity, scalability, and modularity.  These traits enabled the ISO container to quickly become the world standard for the emerging intermodal transportation market.
  
  The first requirement for a container is simplicity.  Imposing a heavy additional mass or complexity requirement would eat up the savings the containers are intended to provide.  The average wastage of 20\% sets an upper limit beyond which containers would be of little use.  As discussed in Chapter~\ref{sec:review}, container structural fractions of $\approx 5\%$ or less should be achievable, given that there are entire launch vehicle stages with similar structural fractions.   
  
  The second requirement is scalability.  Some container ships carry thousands of containers of several different sizes.  While the space payload market is not so extensive, it is equally diverse.  The heaviest payloads (e.g. \textit{Lacrosse}) and the lightest payloads (CubeSats) in the data set are four orders of magnitude apart in mass.  Ideally packing payloads in the manner described in Chapter~\ref{sec:arrangement} can, depending on the payload set, result in scenarios where launching many payloads at once might be required.  This is most often seen on the last few manifests with larger launch vehicles, where large numbers of smaller payloads left over from other manifests may be assigned. With current launch vehicles, this requirement could be up to three concurrent payloads for the geosynchronous scenario without launch vehicle selection or time constraints and up to 155 concurrent payloads for the low Earth orbit scenario with the same constraints.  This may seem outlandish, but the Spaceflight SHERPA referenced above is designed to carry as many as 87 payloads concurrently\cite{sherpa87}.
  
  The final requirement is modularity.  Containers of multiple sizes must have some means to fit together.  As briefly discussed in Chapter~\ref{sec:risk} attempts to reduce wastage by changing the arrangement of payloads tend to match a large payload with one or more smaller payloads.  Most current payload adapters are very limited in this regard, only allowing a set number of payloads of given sizes.  Some degree of modularity can be achieved by combining different sorts of adapters, such as the various types of smallsat dispensers designed to attach to ESPA ring interfaces\cite{spaceflightug}, but this is limited.
  
  ISO containers achieve modularity by establishing a universal 8 ft by 8 ft cross-section and allowing for varied container lengths.  This approach is less likely to be successful with spacecraft because of the great variety of sizes of spacecraft.  For ISO containers this is less of a problem because goods are often loosely packed or boxed inside them, and are typically much smaller than the 8 x 8 cross-section.  Given the loads experienced during space launches and the need to deploy the payload once the launch vehicle has reached orbit, this approach cannot be used for a spaceborne container system.
  
  Replication of the traits of the ISO container would provide many of the same benefits that containerization did for global trade.  Containerization enabled ocean-going ships using much the same propulsion and guidance technology as their predecessors to greatly increase their utility and efficiency at moving goods from place to place.  This resulted in rapid growth in the global economy due to increased trade, and the resulting `globalization' still shapes the world today.
  
  This approach stands in stark contrast to current efforts to reduce the cost of access to space that attempt to lower costs by making technological improvements to the launch vehicle.  Until the recent successes of the reusable Falcon 9 program, these efforts, as epitomized by the Space Shuttle, the National Aerospace Plane, and the X-33 program, all failed to deliver the promised drastic reduction in launch costs due to spiraling costs brought on by the significant technical challenges each of these programs posed.  In contrast, reduction of operational losses can, with a minimum of development of new hardware and the associated development costs, provide significant savings in the short term, and continue to provide benefits even if launch vehicle cost can be brought down significantly in the future. 
  
  \section{Future Work} 
  
  There are several possibilities for future work to support these goals.  The first is to examine the non-economic considerations for space operations in more depth.  The results displayed in Figure~\ref{fig:rankings} demonstrate the large effect that non-economic considerations have on launch vehicle selection.  While many of these effects are not amenable to quantification, some additional analysis will prove valuable, such as comparing launch vehicle selection behaviors among payload-owning organizations.
  
  The subjects examined in this work touch on economic and business factors, but examination of such has been simplified, trying to reduce the total cost of launching payloads as much as possible.  In real world space operations, other economic factors can play a role, as alluded to in Chapter~\ref{sec:review} when discussing Greenberg's analysis of a notional launch vehicle selection business decision.  As stated in that chapter, the information he relied on for this analysis is not widely available for most launch vehicles.  However, examination of the effects of payment schedules and other economic factors in conjunction with the effects of operational losses noted in this paper would be useful from a conceptual perspective even if real world data on these factors are not available.
  
  Finally, the amount of work done on launch vehicle cost modeling is limited, and much of it is dated.  Koelle's work relies on an impressive collection of sources from the 1960s and 1970s.  However, the business of developing and constructing launch vehicles has changed significantly since that time, and so this work requires updating.  The rudimentary cost model developed in this work is a first step in this direction, but further work is necessary to confirm the trends observed in Chapter~\ref{sec:lvtrends}.  Not only is this necessary for the uses in this work, it is important in design studies for future launch vehicles. 
  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% BIBLIOGRAPHY %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newpage
\phantomsection
\addcontentsline{toc}{chapter}{Bibliography}
\bibliographystyle{aiaa-ou}
\bibliography{bibliography}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% APPENDICES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\appendix
\chapter{Payload Database}
\todo[inline]{Some of the symbols in the database printout were lost, making which payloads go to which launches unclear.  Fix.}
\include{dissertationappendixa}
\chapter{Launch Vehicle Database}
\small
\begin{landscape}
\begin{longtable}{llllllll}
\hline \hline
    LV    & P (LEO, kg) & P (GTO, kg) & Cost (TY\$) & Cost (2014\$) & C/P (LEO) & C/P (GTO) &\\
    \hline
    \endfirsthead
    LV    & P (LEO, kg) & P (GTO, kg) & Cost (TY\$) & Cost (2014\$) & C/P (LEO) & C/P (GTO) &\\
    \hline
    \endhead
    \hline
    \endfoot
    \hline \hline
    \endlastfoot
  Delta IV Heavy & 28790 & 14220 & 155000000 & 1.81856e+08 & 6316.65 & 12788.8 & 2.02\\

  STS & 24400 & 0 & 491000000 & 491000000 & 20123 & 0 & 0\\

  Titan 402B & 21680 & 5600 & 350000000 & 4.16834e+08 & 19226.7 & 74434.7 & 3.87\\

  Titan 403B & 21680 & 0 & 350000000 & 4.16834e+08 & 19226.7 & 74434.7 & 3.87\\

  Titan 401B & 21680 & 0 & 350000000 & 4.16834e+08 & 19226.7 & 74434.7 & 3.87\\

  Titan 404B & 21680 & 0 & 350000000 & 4.16834e+08 & 19226.7 & 74434.7 & 3.87\\

  Titan Centaur 401B & 21680 & 5600 & 350000000 & 4.16834e+08 & 19226.7 & 74434.7 & 4.87\\

  Ariane 5ES & 21500 & 0 & 140000000 & 1.66734e+08 & 7755.05 & 0 & 0\\

  Proton-M/Briz-M & 21000 & 5500 & 70000000 & 8.33668e+07 & 3969.85 & 15157.6 & 3.82\\

  Atlas V 551 & 20520 & 8670 & 92500000 & 1.08527e+08 & 5288.85 & 12517.6 & 2.37\\

  Proton-K/DM-2M & 19760 & 4930 & 75000000 & 1.06437e+08 & 5386.49 & 21589.7 & 4.01\\

  Proton-K/DM-2 & 19760 & 4930 & 75000000 & 1.06437e+08 & 5386.49 & 21589.7 & 4.01\\

  H-IIB & 19000 & 8000 & 180000000 & 180000000 & 9473.68 & 22500 & 2.38\\

  Atlas V 541 & 18955 & 7980 & 92500000 & 1.08527e+08 & 5725.52 & 13599.9 & 2.38\\

  Atlas V 531 & 17250 & 7200 & 92500000 & 1.08527e+08 & 6291.43 & 15073.2 & 2.4\\

  Zenit 3SL & 15876 & 6066 & 75000000 & 1.06437e+08 & 6704.28 & 17546.5 & 2.62\\

  Atlas V 431 & 15718 & 7640 & 103000000 & 103000000 & 6553 & 13481.7 & 2.06\\

  Atlas V 521 & 15080 & 6285 & 75000000 & 8.7995e+07 & 5835.22 & 14000.8 & 2.4\\

  Delta IV Medium+ (5-4) & 14140 & 7300 & 70000000 & 8.21287e+07 & 5808.25 & 11250.5 & 1.94\\

  Atlas V 421 & 14067 & 6830 & 70000000 & 8.33668e+07 & 5926.41 & 12206 & 2.06\\

  Zenit 2 & 13920 & 0 & 35000000 & 4.96707e+07 & 3568.29 & 0 & 0\\

  Falcon 9 & 13150 & 4850 & 56500000 & 56500000 & 4296.58 & 11649.5 & 2.71\\

  Delta IV Medium+ (4-2) & 13140 & 6390 & 70000000 & 8.21287e+07 & 6250.28 & 12852.7 & 2.06\\

  Atlas V 511 & 12590 & 5270 & 92500000 & 1.08527e+08 & 8620.11 & 20593.4 & 2.39\\

  Atlas V 411 & 12150 & 5950 & 70000000 & 8.33668e+07 & 6861.47 & 14011.2 & 2.04\\

  H-IIA 2024 & 11730 & 5000 & 85000000 & 9.97277e+07 & 8501.94 & 19945.5 & 2.35\\

  Delta IV Medium+ (5-2) & 11470 & 5490 & 70000000 & 8.21287e+07 & 7160.31 & 14959.7 & 2.09\\

  Long March 3B & 11200 & 5100 & 50000000 & 5.95477e+07 & 5316.76 & 11676 & 2.2\\

  Atlas IIIB & 10759 & 4119 & 65000000 & 7.74121e+07 & 7195.1 & 18793.9 & 2.61\\

  Atlas V 501 & 10300 & 3970 & 92500000 & 1.08527e+08 & 10536.6 & 27336.8 & 2.59\\

  Ariane 44L & 10200 & 4790 & 100000000 & 1.41916e+08 & 13913.4 & 29627.6 & 2.13\\

  H-IIA 202 & 9940 & 4100 & 70000000 & 8.33668e+07 & 8387.01 & 20333.4 & 2.42\\

  Atlas V 401 & 9797 & 4950 & 70000000 & 83400000 & 8509.42 & 16841.8 & 1.98\\

  Long March 2E & 9500 & 3500 & 50000000 & 7.09581e+07 & 7469.27 & 20273.7 & 2.71\\

  Ariane 5G & 9500 & 6700 & 125000000 & 1.48869e+08 & 15670.5 & 22219.3 & 1.42\\

  Delta IV Medium & 9420 & 4440 & 70000000 & 8.21287e+07 & 8718.55 & 18497.5 & 2.12\\

  Long March 3C & 9100 & 3800 & 45000000 & 5.3593e+07 & 5889.34 & 14103.4 & 2.39\\

  Ariane 44LP & 9100 & 4030 & 90000000 & 1.27725e+08 & 14035.7 & 31693.4 & 2.26\\

  Atlas IIIA & 8640 & 4037 & 90000000 & 1.27725e+08 & 14782.9 & 31638.5 & 2.14\\

  Atlas IIAS & 8618 & 3719 & 90000000 & 1.27725e+08 & 14820.7 & 34343.8 & 2.32\\

  Ariane 42L & 7900 & 3200 & 80000000 & 1.13533e+08 & 14371.3 & 35479 & 2.47\\

  Ariane 44P & 7600 & 3465 & 80000000 & 1.13533e+08 & 14938.5 & 32765.6 & 2.19\\

  Soyuz U & 7450 & 1660 & 30000000 & 3.57286e+07 & 4795.79 & 21523.3 & 4.49\\

  Soyuz FG & 7450 & 1660 & 30000000 & 3.57286e+07 & 4795.79 & 21523.3 & 4.49\\

  Atlas IIA & 7280 & 3039 & 90000000 & 144000000 & 19748.1 & 47307 & 2.4\\

  Ariane 42P & 6600 & 2600 & 70000000 & 9.93413e+07 & 15051.7 & 38208.2 & 2.54\\

  Delta 7920H-9.5 & 6097 & 0 & 50000000 & 5.95477e+07 & 9766.73 & 0 & 0\\

  Antares 130 & 6050 & 0 & 77500000 & 77500000 & 12809.9 & 0 & 0\\

  Long March 3A & 6000 & 2600 & 45000000 & 5.3593e+07 & 8932.16 & 20612.7 & 2.31\\

  Delta 7920H-10 & 5959 & 0 & 50000000 & 5.95477e+07 & 9992.91 & 0 & 0\\

  Delta 7920H-10L & 5899 & 0 & 50000000 & 5.86634e+07 & 9944.63 & 0 & 0\\

  Antares 131 & 5700 & 0 & 77500000 & 77500000 & 13596.5 & 0 & 0\\

  Delta 7920-9.5 & 5030 & 0 & 50000000 & 7.09581e+07 & 14107 & 0 & 0\\

  GSLV & 5000 & 1900 & 35000000 & 4.16834e+07 & 8336.68 & 21938.6 & 2.63\\

  Ariane 40 & 5000 & 1900 & 65000000 & 9.22455e+07 & 18449.1 & 48550.3 & 2.63\\

  Delta 7920-10 & 4844 & 0 & 50000000 & 7.09581e+07 & 14648.6 & 0 & 0\\

  Delta 7920-10L & 4805 & 0 & 50000000 & 7.09581e+07 & 14767.5 & 0 & 0\\

  Antares 120 & 4800 & 0 & 77500000 & 77500000 & 16145.8 & 0 & 0\\

  Antares 110 & 4800 & 0 & 77500000 & 77500000 & 16145.8 & 0 & 0\\

  Long March 2C & 4400 & 1400 & 20000000 & 2.38191e+07 & 5413.43 & 17013.6 & 3.14\\

  Antares 121 & 4400 & 0 & 77500000 & 77500000 & 17613.6 & 0 & 0\\

  Tsyklon 3 & 4100 & 0 & 20000000 & 2.38191e+07 & 5809.54 & 0 & 0\\

  PSLV & 3700 & 1050 & 15000000 & 1.78643e+07 & 4828.2 & 17013.6 & 3.52\\

  Tsyklon 2 & 3350 & 0 & 20000000 & 2.38191e+07 & 7110.18 & 0 & 0\\

  Dnepr & 3200 & 0 & 11000000 & 1.31005e+07 & 4093.91 & 0 & 0\\

  Delta 7420-9.5 & 3185 & 0 & 45000000 & 6.38623e+07 & 20051 & 0 & 0\\

  Titan 2G & 3175 & 1043 & 34000000 & 70850000 & 22315 & 67929.1 & 3.04\\

  Delta 7420-10 & 3099 & 0 & 45000000 & 6.38623e+07 & 20607.4 & 0 & 0\\

  Delta 7320-9.5 & 2809 & 0 & 45000000 & 6.38623e+07 & 22734.9 & 0 & 0\\

  Long March 4B & 2800 & 0 & 25000000 & 2.97739e+07 & 10633.5 & 0 & 0\\

  Delta 7320-10 & 2703 & 0 & 45000000 & 6.38623e+07 & 23626.4 & 0 & 0\\

  Rokot & 1950 & 0 & 12000000 & 1.42915e+07 & 7328.95 & 0 & 0\\

  M-V & 1900 & 1280 & 57000000 & 6.78844e+07 & 35728.6 & 53034.7 & 1.48\\

  Vega & 1500 & 0 & 21070400 & 2.50939e+07 & 16729.3 & 0 & 0\\

  Kosmos 3 & 1400 & 0 & 12000000 & 1.70299e+07 & 12164.2 & 0 & 0\\

  Kosmos 3M & 1400 & 0 & 12000000 & 1.70299e+07 & 12164.2 & 0 & 0\\

  Taurus XL & 1320 & 0 & 25000000 & 2.97739e+07 & 22556 & 0 & 0\\

  Start-1 & 632 & 0 & 9000000 & 1.07186e+07 & 16959.8 & 0 & 0\\

  Minotaur 1 & 607 & 0 & 14500000 & 1.70124e+07 & 28027 & 0 & 0\\

  Pegasus XL & 443 & 0 & 15000000 & 1.78643e+07 & 40325.8 & 0 & 0\\

  Falcon 1 & 409 & 0 & 6000000 & 7.14573e+06 & 17471.2 & 0 & 0\\

  Ariane 5ECA & 0 & 10500 & 140000000 & 1.64257e+08 & 0 & 15643.6 & 0\\

  Zenit 3SLB & 0 & 3750 & 75000000 & 1.06437e+08 & 0 & 28383.2 & 0\\

  Delta 7326-9.5 & 0 & 934 & 45000000 & 6.38623e+07 & 0 & 68375 & 0\\

  Delta 7326-10 & 0 & 898 & 45000000 & 6.38623e+07 & 0 & 71116.1 & 0\\

  Delta 7425-9.5 & 0 & 1110 & 45000000 & 6.38623e+07 & 0 & 57533.6 & 0\\

  Delta 7425-10 & 0 & 1073 & 45000000 & 6.38623e+07 & 0 & 59517.5 & 0\\

  Delta 7426-9.5 & 0 & 1056 & 45000000 & 6.38623e+07 & 0 & 60475.6 & 0\\

  Delta 7426-10 & 0 & 1029 & 45000000 & 6.38623e+07 & 0 & 62062.5 & 0\\

  Delta 7925-9.5 & 0 & 1819 & 50000000 & 7.09581e+07 & 0 & 39009.4 & 0\\

  Delta 7925-10 & 0 & 1747 & 50000000 & 7.09581e+07 & 0 & 40617.1 & 0\\

  Delta 7925-10L & 0 & 1739 & 50000000 & 7.09581e+07 & 0 & 40617.1 & 0\\

  Delta 7926-9.5 & 0 & 1660 & 50000000 & 7.09581e+07 & 0 & 40804 & 0\\

  Delta 7926-10 & 0 & 1581 & 50000000 & 7.09581e+07 & 0 & 42745.8 & 0\\

  Delta 7926-10L & 0 & 1578 & 50000000 & 7.09581e+07 & 0 & 44881.8 & 0\\

  Delta 7925H & 0 & 2171 & 50000000 & 7.09581e+07 & 0 & 44967.1 & 0\\

  Delta 7925H-10 & 0 & 2123 & 50000000 & 7.09581e+07 & 0 & 32684.5 & 0\\

  Delta 7925H-10L & 0 & 2102 & 50000000 & 7.09581e+07 & 0 & 33423.5 & 0\\

  Delta 7926H & 0 & 1981 & 50000000 & 7.09581e+07 & 0 & 33757.4 & 0\\

  Delta 7926H-10 & 0 & 1934 & 50000000 & 7.09581e+07 & 0 & 35819.3 & 0\\

  Delta 7926H-10L & 0 & 1916 & 50000000 & 7.09581e+07 & 0 & 36689.8 & 0\\

\hline \hline
\end{longtable}
\end{landscape}

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% DEDICATION
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% My parents
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% Luis Eduardo Martinez Villarraga, and
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% Esperanza Pedroza Paipa
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% For
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% Encouraging me to follow my dreams
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\listoftodos

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