10. Cost and Risk Analysis
Jaret B. Matthews
10.1.1 Introduction
The major goal for this project is to design a cost effective human mission to Mars. We are also simultaneously charged with the task of ensuring that the crew has a 95% chance of surviving with an 80% chance of completing the mission as planned. This is all to be accomplished while also guaranteeing significant science returns. To evaluate our performance with respect to the above aspirations, we conducted a cost and risk analysis largely based on historical data. One limitation to this approach is the fact that an actual human mission to Mars has yet to be attempted. Therefore, the analysis is conducted using a composite of historical precedents and rough estimations.
10.1.2Cost Analysis
The cost analysis is conducted using two cost models developed by NASA. The first of which is the Advanced Missions Cost Model (AMCM). The AMCM is a derivative of the NASA Air Force Cost Model (NAFCOM), which is in turn based on historical development and production costs of various types of aerospace vehicles. The AMCM does a quick rough-order-of-magnitude estimation of the development and production costs of spacecraft based on the fowling criteria1:
Quantity
The quantity is the total number of units to be produced. This includes prototypes, test articles, operational units, and spares.
Dry weight
The dry weight is the total empty weight of the system in pounds, not including fuel, payload, crew, or passengers.
Mission type
The mission type classifies the type of system by the operating environment and the type of mission to be performed. Select one that best describes the system you wish to estimate.
IOC Year
The IOC is the year of Initial Operating Capability. For space systems, this is the year in which the spacecraft or vehicle is first launched.
Block Number
The block number represents the level of design inheritance in the system. If the system is a new design, then the block number is 1. If the estimate represents a modification to an existing design, then a block number of 2 or more may be used. For example, block 5 means that this is the 5th in a series of major modifications to an existing system.
Difficulty
The difficulty factor represents the level of programmatic and technical difficulty anticipated for the new system. This difficulty should be assessed relative to other similar systems that have been developed in the past. For example, if the new system is significantly more complex than previous similar systems, then a difficulty of high or very high should be selected.
Using the AMCM we were able to obtain the results in Table 10.1.1. Because the Hab and ERA act as both habitats and entry vehicles, we ran the AMCM for both cases. Entry vehicles are nearly twice the cost of habitats therefore, we assumed that a reentry vehicle better represents the likely cost of the vehicles. The additional assumptions necessary to run the code are also summarized in Table 10.1.1.
Table 10.1.1 ADCM Assumptions and Results for 1 MissionVehicle / Mass(kg) / Quantity / Mission / IOC Year / Block # / Difficulty / FY2000 millions
Hab / 73530 / 1 / Manned-Reentry / 2014 / 1 / Average / 10947
Hab / 73530 / 1 / Manned-Habitat / 2014 / 1 / Average / 5959
ERA / 85650 / 1 / Manned-Reentry / 2011 / 1 / Average / 11759
ERA / 85650 / 1 / Manned-Habitat / 2011 / 1 / Average / 6401
Table 10.1.2 are the results of the AMCM if a total of three Habs and 3 ERAs are desired. Such a cost estimate will allow us to make a more relevant comparison to the estimated cost of the NASA Design Reference Mission and Dr. Zubrin’s Mars Direct, both of which plan for three missions to Mars in their architectures.
Table 10.1.2 ADCM Assumptions and Results for 3 MissionsVehicle / Mass(kg) / Quantity / Mission / IOC Year / Block # / Difficulty / FY2000 millions
Hab / 73530 / 3 / Manned-Reentry / 2014 / 1 / Average / 21028
Hab / 73530 / 3 / Manned Habitat / 2014 / 1 / Average / 11447
ERA / 85650 / 3 / Manned-Reentry / 2011 / 1 / Average / 22587
ERA / 85650 / 3 / Manned-Habitat / 2011 / 1 / Average / 12296
The cost of developing and producing the first ELV is estimated in Section 4.1 to be $3 billion FY2000. The production cost of subsequent vehicles is estimated to be on the order of $500M FY2000.1 The NTR development is estimated to cost $2.5 billion FY2000 in Section 4.2. The production cost of the NTR stage is also estimated to cost on the order of $500M FY2000.1 The results of the total development and production cost of the first mission and for a total of three missions are summarized in Table 10.1.3.
Table 10.1.3 Development and Production Costs1 Mission / 3 Missions
Component / FY2000$Billion / FY2000$Billion
Hab / 11 / 21
ERA / 12 / 23
2ELVs / 4 / 6
2NTRs / 3 / 5
Total / 30 / 55
The second cost model used was the Mission Operations Cost Model (MOCM). The MOCM estimates the cost involved in ”maintaining and upgrading ground systems; mission control; tracking; telemetry; command functions; mission planning; data reduction and analysis; crew training and related activities.”1 The MOCM uses the initial investment cost (Table 10.1.3) and the type of mission (“Manned”) to determine a rough-order-of-magnitude estimation of the mission’s yearly operational costs. The MOCM analysis is based on spacecraft flown between 1962 and 1990. The results of this analysis are summarized in Table 10.1.4.
Table 10.1.4 Mission Operations Cost# of / Initial Investment / Total Program / Operations Cost
Missions / FY2000$Billions / Duration (Years) / FY2000$Billions
1 / 30 / 4 / 3.8
3 / 55 / 10 / 15.5
This brings the total cost of launching one human mission to Mars to ~$34 billion FY2000 and the cost of a 10-year, 3-mission Mars program to ~ $70 billion FY2000. While large, this price tag bodes fairly well when compared to the $50 -$60 billion NASA now estimates for its Design Reference Mission and to Dr. Zubrin’s $30-40 billion dollar Mars Direct Plan. While this analysis is merely a rough cut estimation of what it might cost to send humans to Mars, it is important to note that, if spread out over the course of the next 15-20 years as proposed, the quoted cost could be covered by the existing NASA budget.
10.1.3Risk Analysis
Risk is difficult, if not impossible, to quantify on the level of mission design. To fully evaluate the risks involved in sending humans to Mars it would be necessary to know a great deal about all of the hardware and software involved. Because we are completing a high-level mission design, a simple estimate of the risks will have to suffice.
The number of risks involved in a mission to Mars are nearly infinite, however we make an attempt in this section to identify the major risks involved. Wherever possible, we attempt to use probabilities of failure that have historical precedent. In the few instances where data is lacking or sparse, we attempt to make reasonable estimations as to the levels of risk involved.
To evaluate the risks we employed the Probabilistic Risk Assessment (PRA) method. PRA is a comprehensive risk assessment that quantitatively expresses the risk of failure.2 An example of PRA is shown in Figure 10.1.1. In a PRA, risks are evaluated as event sequences with their associated probability of occurrence. In the figure, the scenario of solar panel damage is examined. There exists an 80% probability that the cells will continue to function normally and a 20% chance that the cell will stop producing power. If the cells stop producing power, then the PRA moves to the backup system, the fuel cells. Again, there is an associated probability that the fuel cells will fail. This process is repeated for all known failure scenarios and a comprehensive failure rate is reached by multiplying the probability of each event to give an overall failure rate for each possible outcome. The probability of the entire system’s success is found by adding the successful outcomes (those that produce power). Similarly, the comprehensive failure rate is the sum of the probabilities of those outcomes that are considered failure (those that do not produce power).
Figure 10.1.1 Example of Probabilistic Risk Analysis.
Crew Survivability
The overall risk to crew survivability was interpreted to mean the probability that the crew would succumb to a fatal accident at some point within the time of launch and landing on Earth. To assess this risk, we divided the mission up into three large segments: launch and landing, transit, and time on the surface.
Launch and Landing. In the 40 years that humans have been flying into space there have been more than 200 crewed flights (Russian and US). Unfortunately, three of these missions resulted in the loss of human life (Soyuz I, Soyuz 11, and STS51L).3 All of the above failures occurred on launch or landing, representing a 2% chance that the crew will not survive the launch or landing phase of the mission. However, in our mission architecture, the crew is subjected to a total of two launches and two landings. Therefore, the 2% risk is added for each launch and landing, giving a composite risk for launch and landing at 8%.
Transit. For the transit section of space missions, experience is limited. In the 200 plus missions into space, only nine have left the confines of low Earth orbit. While, to date, no crew have been lost in either Earth orbit or transiting out to the Moon, it would be unreasonable not to assume some level of risk to crew safety. Apollo 13 is the one instance that the crew was in serious danger, however because their disabled craft was allowed to coast back to Earth on a pseudo free-return, the crew was not lost.4
Because we have incorporated a free-return into the mission, a water shield for solar proton events, as well as several layers of redundancy on all life critical components and systems, we will assume that the risk on transit is comparable to, but somewhat smaller than, launch or landing. For each of the two transits we will assume a 1% risk to crew survivability.
Surface. The final section of the mission examined is the time the crew spends on Mars. Here again, experience is limited. There have been only six instances when humans have spent time on the surface of another planetary body. All six instances were completed without loss of human life, yet it would be unreasonable to assume that this period of the mission is without risk.
The crew spends 590 days on the surface of Mars, a great deal longer than the cumulative time spent on the Moon during Apollo. However, time on the surface is relatively benign when compared to the conditions during launch and landing, therefore a conservative estimate would be to assume that the crew is equally likely to die on the surface as they are on any given launch.
The results of the estimation of risk to crew survivability are summarized in Table 10.1.5
Table 10.1.5 Risk to Crew SurvivabilityContributor / # of Events / %Risk/Event / % Risk
Launches / 2 / 2 / 4
Landings / 2 / 2 / 4
Transit / 2 / 1 / 2
Surface / 1 / 2 / 2
Total / - / - / 12
Therefore, there exists an 88% chance that the crew would survive the mission to Mars. While this is below the goal of 95% in the mission directive, it represents a conservative and realistic approximation of the risks involved.
Mission Success
Assessing the risk of not completing the mission as described in Section 1.1 or of not having the opportunity to do a significant amount science is similar to the approach of assessing crew survivability. There are however other sources of risk to consider, therefore in addition to looking at the risk of losing the mission on launch and landing, during transit, or on the surface, we will also examine programmatic risks.
Launch and Landing. Again, for the launch and landing sections of the mission we will exploit historical precedent for appraisal of the risk. Of the 200- plus crewed missions into space, six have been unable to complete their mission.3 This represents a 3% chance of failure on each launch or landing critical to the mission.
Transit. The risk of losing the mission on transit is assumed to be similar but somewhat higher than the risk of losing the crew. Of the nine transits to the Moon and back, only one (Apollo 13) was unable to complete the desired mission. While the crew was saved, the mission was lost.4 Lacking extensive precedent for this stage of the mission, a reasonable 2% risk to mission success was assigned for each transit period.
Surface. Here again, the necessary experience database is limited to Apollo. The risk of losing the mission while on the surface is assumed to be no better and no worse than the risk to crew survivability. This assumption is made because the only foreseeable scenarios that would completely impede the gathering of scientific data would involve a risk to crew safety. Therefore, again the risk of loosing the mission while on the surface is assumed to be 2%.
Programmatic. Programmatic risks are unique to the mission success assessment because they would not be a factor if the crew were already on its way to Mars. Programmatic risks include slips in schedule and loss of funding. Because our mission hinges on a very specific trajectory, we are at risk of losing the mission in the event of a slip in the schedule. If, for example, the development of the NTR does not go as planned, it could delay the launch of the ERA in 2011 and therefore slip the Hab launch in 2014. The inclusion of international partners (using the Russian designed Energia launch vehicle), as the experience of the International Space Station shows, may also cause a delay of schedule.
Another threat to mission success is the dependence on government funding. While the government is the only entity with the resources to fund such an undertaking, it also makes our mission susceptible to loss of funding. With up to three Presidents between now and 2011, a mission to Mars is at the mercy of various administrations.
While schedule and funding are most likely the largest threats to mission success, we will assume that there exists both a solid political mandate and sound project management. This being the case, we will not include a value for programmatic risks in the overall risk assessment, but only mention that this is likely to be a contributing factor.
The results of the mission success risk analysis are summarized in table 10.1.6.
Table 10.1.6 Risk to Mission SuccessContributor / # of Events / %Risk/Event / % Risk
Launches / 3 / 3 / 9
Landings / 3 / 3 / 9
Transit / 2 / 1 / 2
Surface / 1 / 2 / 2
Programmatic / ? / ? / ?
Total / - / - / 22
Therefore, neglecting programmatic risks, there is a 78% that the crew will be able to complete its mission. While several probabilities were assumed for this risk analysis, it provides a rough order-of-magnitude estimate of the risks that a mission to Mars is likely to encounter.
10.1.4Acknowledgements
I would like to thank Professor Longuski and all of the Professors that volunteered as guest lecturers to our class. I would also like to thank Alec Spencer for organizing the appendix, as well as the rest of the AAE450 class for, despite being a very large group, being very easy to work with.
References
- NASA Johnson Space Center Cost Estimating Group, April 2001.
- Greenfield, Michael A. “ Risk Management Tools”, Presentation at NASA Langley Research Center, May, 2000. April 2001.
- Wright, K.M., de Montlivault, J.L. “Manned Spaceflight Certification”, Space Safety and Rescue, 1991, American Astronautical Society, San Diego, CA.
- NASA Kennedy Space Center History of Apollo, April 2001.
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