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Cost and benefit analysis of space debris mitigation measures
Acta Astronautica 55 (2004) 311 – 324 www.elsevier.com/locate/actaastro
Cost and bene t analysis of space debris mitigation measures Carsten Wiedemanna;∗ , Michael Oswalda , J)org Bendischb , Holger Sdunnusc , Peter V)orsmanna a Institute
of Aerospace Systems, ILR, Technische Universitat Braunschweig, Hermann-Blenk-Str.23, 38108 Braunschweig, Germany b Aerodata AG, Braunschweig, Germany c eta max space GmbH, Braunschweig, Germany
Abstract The increasing number of orbital debris objects is a risk for satellites. To reduce the risks for future space missions several mitigation strategies have been developed during the last years. In this paper the long-term cost development of space debris mitigation measures is analyzed. Di6erent mitigation scenarios are de ned and compared. Cost models are derived for mitigation measures and for the loss of amortization in the case of hypervelocity impacts on operating satellites. Long-term simulations of the space debris environment based on a conservative orbital tra8c model have been made for a 50 years time interval beginning in 2001. The simulations consider di6erent mitigation scenarios. The output data have been combined with the cost models. The mitigation scenarios were compared, and a cost-bene t analysis has been performed. The result of the investigation is, that the most e6ective mitigation measures are passivation (suppression of fragmentation events) and slag prevention. c 2003 International Astronautical Federation. Published by Elsevier Ltd. All rights reserved.
1. Introduction The economic e8ciency of mitigation measures, which is the main design driver for many missions, has not been investigated yet. A current study has the goal of estimating the mission costs for di6erent mitigation scenarios. A business as usual (BAU) scenario (without mitigation) is compared to scenarios considering di6erent types of mitigation measures. The objective is to estimate the break-even point when the investment in mitigation causes an e6ective reduction of the mission cost. Mitigation strategies like the reduction of the orbital lifetime or re-orbiting of non-operational ∗ Corresponding author. Tel.: +49-531-391-9970; fax: +49537-391-9966. E-mail address: [email protected] (C. Wiedemann).
payloads into graveyard orbits are methods to control the space debris environment. These methods initially cause an increase of costs. In order to estimate the cost associated to debris-related damages or mitigation measures, it is necessary to know the tendencies and bandwidths of the development of the future debris population. In particular, the number of objects with time and the expected damages, as well as the e6ectiveness of debris measures to control the debris environment are of concern. Mission costs can be increased by orbital debris hazards concerning for example the total loss of operational spacecraft due to a collision, and damage on operational spacecraft due to debris impact. Debris mitigation in terms of minimization and control of the debris environment can have an impact on cost items like for example the mission and spacecraft design. Cost occurs for spacecraft
c 2003 International Astronautical Federation. Published by Elsevier Ltd. All rights reserved. 0094-5765/$ - see front matter doi:10.1016/j.actaastro.2004.05.011
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passivation and minimization of mission related objects (MRO), and design costs, operational costs and extra fuel (lifetime/mass penalty, respectively) for deor re-orbit at end-of-life (EOL). The bene ts due to debris mitigation, compared to a BAU scenario, are for example the reduced damage on spacecraft and preserving the possibility of future missions in currently used orbital regions. Furthermore a collision cascading can be prevented in the far future. The simulations are made for a time interval of 50 years beginning in 2001. This paper presents the results of cost estimations for satellite missions and the impact of debris mitigation measures on the costs. Selected results of a cost and bene t analysis are presented. 2. Satellite mission cost An important part of this work was the development of cost models. These cost models were mainly developed for satellites, because most mitigation measures a6ect the satellite design. Also cost models for upper stage modi cations and orbital maneuvers were developed. The rst task of the cost models is to give a rough order of magnitude (ROM) cost estimation for a typical satellite. The cost model shall be able to consider the inFuence of mitigation measures on a satellite mission. Furthermore the cost model must permit an estimation of the cost due to hypervelocity particle impacts on satellites. 2.1. Literature review There are several types of cost models described in the literature. Parametric cost models have been selected here. Published parametric equations provide the desired transparency of the cost model. A design modi cation requires a cost model modi cation. Consequently in this work variants of existing cost models have been derived. An important question is the application of cost models. The cost models needed here require a low number of input parameters. The input parameters should be easy to estimate. Several parametric cost models are given in the literature. There are cost models for complete satellites and satellites subsystems. Some simple satellite cost models are based on cost per dry mass [1,2]. These models are based on relatively new data. There are also some older
satellite cost models. Satellite cost models have been developed for research satellite buses (without payload) and complete applications satellites [3]. The literature also gives summaries of multivariable satellite cost models [4–6]. Detailed cost models, which are broken down to satellite subsystems, are given for communications satellites [7], for electric propulsion modules [8], and for all types of satellites [9]. The latter is preferred here. 2.2. Cost model modi5cations Mitigation measures require modi cations of subsystems. These modi cations cause an increasing complexity of a certain subsystem. As a result the subsystem hardware cost is increasing. The subsystem level of the selected cost model has the advantage that it allows an estimation of the impact of the increasing complexity on the overall satellite cost. Complexity is de ned here as degree of di8culty. The modi cation of subsystem cost models for the development of cost models for mitigation measures is shown for two examples. In the following sections a survey is given that describes the satellite mission cost, satellite hardware cost, the space debris environment, the cost of satellite damage due to impacts and the cost of mitigation measures. 2.3. Satellite subsystems The subsystem cost model uses subsystem masses as input parameter. A model for satellite subsystems is required that covers the wide range of di6erent satellite types and masses on orbit and gives rough estimates for the subsystem masses [10]. This subsystem breakdown is needed to consider the inFuence of design changes on the subsystem cost. The de nition of a standard satellite is made by a rough sizing of a spacecraft, based on mass models of its subsystems. A satellite consists of a payload and several support subsystems, which are summarized in Table 1. 2 msub = c1 mcBOL
(1)
Subsystem masses can be expressed as a function of the beginning of life (BOL) mass [7]. Applying a regression analysis to collected subsystem data by using a simple power function Eq. (1) is giving the coe8cients presented in Table 1. The exponents shown
C. Wiedemann et al. / Acta Astronautica 55 (2004) 311 – 324 Table 1 Coe8cients of the satellite subsystem mass model Subsystem
c1
c2
Harness Payload Thermal Power Propulsion Structures & mechan. ADCS (TT&C)/DH AKM
2.1741E−02 1.4550E−01 2.4927E−02 2.1999E−01 2.0699E−01 3.0666E−01 4.2679E−01 4.1595E−01 2.4929E+00
1.1943E+00 1.0624E+00 1.0065E+00 9.6938E−01 9.3678E−01 9.1662E−01 7.0875E−01 7.0047E−01 8.4812E−01
The apogee kick-motor (AKM) is not included in the BOL mass.
in the third column are sorted in a way that indicates whether a subsystem mass changes more or less rapidly with scale. 2.4. Satellite cost The life cycle cost (LCC) of a satellite includes development cost (non-recurring cost), production cost (recurring cost), launch cost, and orbital operations cost. Mitigation measures can have di6erent inFuences on these cost elements. Cost is related to project phases. The development cost includes expenses for research and development during the phases 0, A, B, and C. Production and operations cost refer to phases D and E. Development and production cost are di8cult to separate. Development cost includes the production of a prototype and is very di8cult to estimate, because it depends on inFuencing factors which cannot be described mathematically [3]. Development is de ned as new design with proven technology. Definitions like technological readiness levels (TRL) or heritage factors can be used for a grading between development and production cost. Development cost covers expenses for research, development, test, and evaluation (RDT&E). This includes production of a prototype (ground test unit) but not the production and testing of Fight units. Production cost comprises the production and test of Fight units. The development cost can vary between high risk technology development, classical development, purchase with signi cant modi cation, purchase with interface adaptation, and pure purchase [11]. Production cost is less sensitive to program characteristics and is much easier to
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Table 2 Development and production cost models for satellite subsystems and payloads Subsystem
Cost model
Payload (Scienti c Instrument) Payload (Communications) Propulsion (Liquid) ADCS (TT&C)/DH Power Thermal Structures & Mechanisms AKM (Solid) AKM (Liquid)
APDTICM [16] SMAD [9] TRANSCOST 7.0 [15] SMAD [9] SMAD [9] SMAD [9] SMAD [9] SMAD [9] TRANSCOST 7.0 [15] TRANSCOST 7.0 [15]
estimate than development cost [12]. Operations cost includes variable and xed cost and is very di8cult to determine. It depends on ground station cost, number of satellites in orbit and orbital lifetime [7]. Mostly there is a substantial amount of existing ground station hardware that can be used by several satellite systems [13]. There are essential cost parameters like BOL mass and payload requirements [7]. Especially mass is a good cost driver, because all required performance characteristics a6ect satellite mass. Thus mass is the most frequently used independent variable in such models [12–14]. The selected cost model should have a su8cient complexity and a high acceptance in the satellite industry. Several cost models have been investigated. Most software cost model tools are either very complicated or not transparent enough. The investigation of the structure, on which they are based, is mostly not possible. 2.5. Satellite hardware cost Mainly elements of a cost model on a subsystem level taken from “Space Mission Analysis and Design” (SMAD) have been selected here [9]. Some elements from TRANSCOST 7.0 were used to estimate the cost of propulsion systems [15]. For scienti c payloads an instrument model was selected [16]. The cost models are summarized in Table 2. The models are suitable to determine the development and theoretical rst unit (TFU) production cost of satellites. All elements use
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parametric methods, which means a projection of the experience of the past into the future. The parametric estimation has the advantage, that it is based on historical data and includes inFuences like scheduling delays, mistakes, redesigns, etc. Thus the cost estimation considers these factors too. The breakdown of a satellite in subsystems allows the formulation of parametric expressions for satellite performance, mass, and cost [17]. The disadvantage of this procedure is, that there is no standard subsystem description [12]. 2.6. Operations cost Due to the lack of a suitable operations cost model, a more simple approach is chosen here. It is assumed that a satellite has constant annual operations cost, which depends on the complexity of the spacecraft. This concept is realized by relating the annual operations cost to the satellite hardware cost. To calibrate this relation, estimates from Vandenkerckhove [7] have been used here. It was found, that the relation of annual operations cost to hardware cost is about 3%. 2.7. Launch cost The average launch cost is estimated by using data of several rockets from Isakowitz et al. [18]. The speci c launch cost is based on the price of a launcher related to its payload capability. The speci c launch price is about 14,000 FY02$/kg for low earth orbits (LEO) and 31,000 FY02$/kg for geo-synchronous transfer orbit (GTO) injection including launch insurance. This cost has to be multiplied by a factor of 1.2, because the actual launched mass is typically 83% of the payload capability. 2.8. Proto:ight cost The satellite cost model uses a protoFight unit as typical reference satellite for a certain BOL mass. A protoFight unit is a prototype (ground test unit), which is refurbished to be used in operational Fight. To calculate average cost it is considered that typically a reduced share of the development cost occurs. This is reasonable, because during the development of supporting subsystems existing components and technologies are used in reality. The development expense
is graded by using the TRL [19–21]. Development cost includes production and test expenses for ground test units. Normally this cost has to be amortized by a series production. Because of the low production rates, often no separate Fight unit is produced. The protoFight cost is a mixture of development and production costs. In a protoFight unit the ground test unit is upgraded to a Fight unit. This requires additional test e6ort, which is about 30% of the production effort. Due to the very small series production rates in the satellite industry, this protoFight approach seems to be a suitable approximation for the estimation of the average cost of satellite hardware. 3. Cost of mitigation measures For the cost estimation of mitigation measures all subsystem cost models are combined. This combination is used to determine the average cost for a certain mitigation measure. The goal of this approach is to derive simpli ed cost models. These cost models are used to estimate the correct order of magnitude of a certain mitigation measure. The particular model must be able to show the correct tendency of cost evolution depending on the satellite mass. The BOL mass has been selected here as suitable parameter to consider scaling e6ects. This allows to determine the speci c impact of cost on satellites. The generation of cost models is illustrated using a satellite with a BOL mass of 1000 kg as example. Di6erent mitigation measures are de ned. Each mitigation measure is represented by one cost model. Most of these cost models are based on the concept of considering the complexity increase due to a mitigation measure. At rst the cost of a complete satellite is estimated. In a next step the complexity of certain subsystems is increased. The subsystem cost is multiplied by this complexity factor. Both cost calculations are compared. The di6erence between the modi ed satellite and the original design is presented and described in a model. The concept is based on subsystem mass models, which are combined with subsystem cost models. The most important cost driving factor is the system mass. Consequently, the BOL mass is used as a reference value for a complete satellite. The resulting cost model gives average values for the impact of a modi cation
C. Wiedemann et al. / Acta Astronautica 55 (2004) 311 – 324
on the overall satellite design. The models provide a reasonable estimation for the correct order of magnitude of the cost. The advantage of this approach is that scaling e6ects are considered. The speci c cost decreases with increasing unit mass. The subsystems, which are modi ed by a mitigation measure, are addressed directly using a complexity factor. The value of the complexity is estimated. The di6erent complexity factors are combined with the subsystem cost models. Normally the mass is the most important cost driver. But a small modi cation of a subsystem has no signi cant impact on the subsystem mass. So the mass increase is negligible and thus no suitable criterion for cost estimation. Consequently it is better to determine the cost increase by a complexity factor. 3.1. Cost model equations Several cost model equations have been developed. One group of equations describe complete mitigation measures as function of a cost driving factor. To this group belong models for MRO prevention, passivation, slag prevention, and GEO re-orbit maneuvers. A second group of equations was created to describe more expensive orbital maneuvers. There are models for the increasing subsystems complexity, the enlargement or addition of propulsion systems, and additional launch cost due to the increasing propulsion system mass. Some of these models use the velocity increment Tv as cost driving factor. A last group contains models for operations cost, launch cost, and cost of complete satellites. From these sets of equations two, passivation and slag prevention for satellites, are presented as examples here. All equations concerning costs of satellite modi cations are based on a reference protoFight satellite with a high degree of completion for the satellite bus. For most mitigation cost models the BOL mass is used as cost driving factor. It was found that in all cases the dependency of the BOL mass can be expressed by a simple power function. The exponents are always smaller than “one”. This is showing the scaling effect. Cost is not increasing directly proportional with the hardware mass. For small spacecraft the speci c costs of a modi cation are higher. The scaling e6ect is caused by the application of the cost and mass models, which include scaling e6ects by themselves.
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Table 3 Assessment factors with a nearly logarithmic scale for the estimation of “orders of magnitude” 0.99 0.90 0.50 0.10 0.01
Very high High Medium Low Very low
The mitigation measure cost models are derived from a subsystem level, which allows to consider a certain inFuence on a selected subsystem. Thus the correct order of magnitude of a subsystem modi cation can be considered. The mitigation measure costs have been calculated and presented graphically. So it is possible to show the cost evolution with the system mass. The cost models have been derived by applying a regressional analysis to the graphical presentation. For the following mitigation measures the complexity factors are derived by estimating the overall impact on the subsystem cost by using Table 3. Then it is considered if this modi cation has a high or low degree of di8culty by multiplying the value of Table 3 with the factor “2” or “1/2”. 3.2. Example: MRO prevention The complexity factor for MRO prevention describes the increasing cost due to a modi cation of the structure subsystem. The complexity factor is applied to the structure and mechanisms subsystem. The impact on the subsystem cost is small. The degree of di8culty is high. A redesign requires the integration of movable parts, which are more complicated than detachable elements. The complexity factor is given in Eq. (2). fMRO = 1:0 + 0:1 ∗ 2:0 = 1:20:
(2)
It is assumed that the expense has a comparable order of magnitude for upper stages. Thus this cost model is also used for that case, by replacing the BOL mass by the stage dry (NET) mass. The cost of subsystem is multiplied with the complexity factor of Eq. (2). The cost increase of the subsystems has also an inFuence on the cost for integration, assembly and test (IA&T) and on the
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3.3. Application of mitigation cost models
80 70 60
Cost of MRO Prevention
50
Cost 40 30 20
Program Level
IA&T
Structure
Thermal
Power
TT&C/DH
ADCS
Propulsion
0
Scientific Payload
10
Fig. 1. Cost breakdown of a typical scienti c satellite with a BOL mass of 1000 kg including additional cost due to MRO prevention (cost in FY02$M).
MRO Prevention Cost 1E+07
Cost[$]
y = 6,7618E+03x 7,9383E-01 R2 = 9,9999E-01
The cost models for these two examples are additional hardware costs. As input parameter the system mass in terms of BOL mass has been selected. This simpli ed choice is reasonable, because most cost driving modi cations a6ect the satellite bus. They are independent of the complexity of the payload. Furthermore the BOL mass is known or can roughly be estimated for most satellite hardware in the phases A/B. The output value is directly the cost in FY02$. The presented models have the advantage that they have a transparent structure. As shown for these two examples, they are expressed as simple power functions. They can be applied to all kinds of spacecraft, either applications or scienti c satellites. Because the system mass is used as scale basis, the models can be applied to a wide range of satellite masses. The equations guarantee a high reliability of cost estimation. This is possible, because the equations are based on very complex subsystem mass and cost models. Based on this, a suitable average cost values can be provided. 4. Mitigation scenarios
1E+06
1E+05 100
1000
10000
BOL Mass[kg]
Fig. 2. Graphical presentation of cost of MRO prevention as function of BOL mass (cost in FY02$).
program level (management). The cost comparison is shown in Fig. 1. MRO prevention causes a small cost increase. The additional cost of MRO prevention as a function of satellite BOL mass is given in Fig. 2. Using the graph from Fig. 2 the cost model for MRO prevention can be derived as function of BOL (resp. NET) mass. The cost model is given in Eq. (3) with FY02$ as cost unit. 0:79383 CostMRO = 6761:8mBOL=(NET) :
(3)
The approach of cost estimation is combined with results of numerical simulations of the future space debris environment to evaluate the cost and bene t of mitigation. The analysis is performed by an upgraded version of the long-term debris environment model LUCA, which has been developed at the Institute of Aerospace Systems. LUCA considers the generation and reduction of space objects. The software tool computes object sources, sinks, and velocity increments for di6erent types of mitigation maneuvers. The tool considers object sources like launches of payloads, release of MRO, explosions and collisions. An important sink is the re-entry of objects due to natural decay and active de-orbiting. The input and output parameters are for example object masses (e.g. of satellites and upper stages) and velocity increments for transfer maneuvers (e.g. re-orbiting and de-orbiting) [22]. These output parameters are related to di6erent types of costs like for example cost of a satellite mission or cost of a transfer maneuver. The next step is the estimation of increase of cost due to debris hazard and mitigation.
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4.1. Initial debris population The most recent MASTER population (reference epoch May 2001) has been used as initial population. It reFects a well proven data set, which has been validated against radar and optical observations, continuous (US SPACECOM catalogue) and sporadic (dedicated) campaigns. The detailed properties of this population are described in the related ESA report (delivered with the MASTER2001 CD ROM). 4.2. Tra=c model For the purpose of this work, the ILR tra8c model has been used, which is based on a series of analysis over the most recent years. Following this analysis, a tra8c growth rate (which is not the net increase rate of the population) of 3% per year related to the basic population has been selected for the next 5 decades. A major nding of previous studies was that any more detailed tra8c de nition is not reasonable, since too many estimates and assumption (technical, nancial and political) would be necessary. The assumptions, however, are not reliable, even for some years ahead. The above tra8c rate corresponds with the observed development of the population over the last decade. Thus, it is a feasible and applicable, as well as an conservative assumption. 4.3. Scenario parameters Two starting points for the implementation of mitigation measures have been selected here, to study the inFuence of time on the cost. The implementation starts either 2001 or 2020. For the scenarios MIT1, MIT3, and MIT5 two versions concerning the beginning of mitigation have been simulated. The implementation of all mitigation measures for the scenarios MIT1-01, MIT2, MIT4, and MIT5-01 begins in 2001. The implementation of all mitigation measures for the scenarios MIT1-20 and MIT3-20 begins in 2020. For MIT3-01 and MIT5-20 a mixture has been chosen, where especially the slag prevention begins in 2001. The parameters for the di6erent scenarios are summarized in Table 4. Impacts: Every satellite which is penetrated by an object greater than 1 mm has a failure probability of 10%. This causes cost of 10% lost amortization. The
317
number of impacts is controlled by the tra8c model and the mitigation measures. The increasing tra8c during the next 50 years causes more debris particles and thus most impact cost. Thus the cumulative impact cost is di6erent for each mitigation scenario. MRO prevention and passivation: Cost for MRO prevention and passivation is related to satellites and upper stages. The tra8c model for satellite launches is identical in all mitigation scenarios. The cost for MRO prevention and passivation is also the same in all mitigation scenarios. Slag prevention: Cost for slag prevention is related to satellites and upper stages, which are injected into GTO or GEO. The tra8c model for satellite launches is identical in the mitigation scenarios MIT2 to MIT5. The cost for slag prevention is also the same in these mitigation scenarios. GEO re-orbit: Cost for GEO re-orbiting (or GEO disposal) is related to satellites, which are transferred into a graveyard orbit at EOL. This parameter indicates, from which point in time onwards the spent GEO payloads are re-orbited to the graveyard orbit (300 km above GEO). The tra8c model for GEO re-orbit maneuvers is identical in the mitigation scenarios MIT4 and MIT5. The cost for GEO re-orbiting is also the same in these mitigation scenarios. In order to use realistic assumption (malfunctions, non conform operators), this method is applied to 50% of the payloads launched after the given point in time. De-Orbit: Cost for de-orbiting (reduction of the orbital lifetime of LEO objects to 25 years) is related to satellites and upper stages. The tra8c model for de-orbiting maneuvers is di6erent in the mitigation scenarios MIT4 and MIT5. Purpose of this parameter variation is to show the impact of de-orbiting strategies with high or low expense on the overall mitigation cost. This parameter indicates, from which point in time onwards the orbital lifetime of LEO objects is limited to 25 years according to the Inter-Agency Space Debris Coordination Committee (IADC) approach. For this purpose, the operational lifetime of a payload has been set to 7 years. In order to come to reasonable results, the fuel needed for the reduction of the orbital lifetime has been limited to 10% in MIT4 and 20% in MIT5 of the initial mass, assuming fuel exhaust velocity of 1:5 km=s (MIT4) and 3 km=s (MIT5). This assumption represents the upper limit of fuel burden to be considered, resulting
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Table 4 Parameters of the mitigation scenarios MIT
1-01
1-20
2
3-1
3-20
4
5-01
5-20
MRO prevention Passivation Slag prevention GEO re-orbit De-Orbit LEO disposal
2001 2001 — — — —
2020 2020 — — — —
2001 2001 2001 — — —
2020 2020 2001 — — —
2020 2020 2020 — — —
2001 2001 2001 2001 2001 —
2001 2001 2001 2001 2001 2001
2001 2001 2001 2020 2020 2020
in the maximum e6ectiveness to be achieved. LUCA monitors and reports the actual fuel needs for each payload under consideration. LEO disposal: Cost for LEO disposal is related to satellites above 1400 km in MIT5. According to a NASA proposal as of 1997, the disposal of spent LEO payloads to higher altitudes (2500–2700 km) may be an option for future operations. This may be applicable for payloads operating above 1400 km, where a lifetime reduction to 25 years is to costly in terms of fuel. For LEO disposal, the fuel considerations as given above for the lifetime reduction apply. Fig. 3. Cumulative cost over time for mitigation scenario MIT1-01 (cost in FY02$).
5. Results The parameters for the di6erent scenarios are summarized in Table 4. The purpose of the simulations is to compare the cost of mitigation with cost of debris impacts on satellite hardware. The e6ectiveness of the mitigation measures controls the number of debris objects in space. To verify the inFuence of a certain mitigation measure on the overall debris population, di6erent scenarios were de ned. Comparing MIT1-01 with MIT1-20 the beginning of the implementation of MRO prevention and passivation is varied, to show the inFuence of a late implementation on the overall debris population. A comparison of MIT1-01 with MIT2 presents the inFuence of slag prevention on cost. A comparison of MIT2 with MIT3-1 shows, if an early implementation of slag prevention combined with a late start of MRO prevention and passivation is reasonable. A comparison of MIT3-1 with MIT3-20 presents the inFuence of a late implementation of slag prevention. A comparison of MIT2 with MIT4 shows, if an additional GEO
re-orbiting and a de-orbiting (lifetime reduction) of LEO objects saves cost. A comparison of MIT4 with MIT5-01 points out, if the cost for more extensive de-orbit maneuvers is justi ed and if the implementation of LEO disposal is reasonable. A comparison of MIT5-01 with MIT5-20 shows, if a late implementation of GEO re-orbit, de-orbit, and LEO disposal is reasonable. The costs of impacts and mitigation measures is graphically presented as function of time. The simulations are started in 2001 resp. 2020 and consider 50 years up to the year 2051. The cost unit is FY01$M. 5.1. MIT1-01 In the mitigation scenario MIT1-01 the cost of debris impacts represents the highest share. The results are presented in Figs. 3 and 4. The expenses for MRO prevention and passivation are low. The cost development of MIT1-01 is similar to the BAU scenario. There is a small cost increase
C. Wiedemann et al. / Acta Astronautica 55 (2004) 311 – 324
319
9E+10 Impacts (BAU)
8E+10
MIT1-01 Cumulative Cost[$]
7E+10 6E+10 5E+10 4E+10 3E+10 2E+10 1E+10 2051
2046
2041
2036
2031
2026
2021
2016
2011
2006
2001
0E+00
Year
5.3. MIT2 In the mitigation scenario MIT2 the sum of mitigation measures represent the highest cost share. The expenses for slag prevention are high. The cost development of MIT2 is very di6erent from the BAU scenario. There is a signi cant cost increase after the implementation of the mitigation measures in the year 2001. The break-even point is reached in 2031. After this point there is a signi cant cost saving due to the reduced numbers of generated slag particles in this scenario. There is a reduced slope in the cost
7E+10 6E+10 5E+10 4E+10 3E+10 2E+10 1E+10 2051
2046
2041
2036
2031
2026
2021
2016
0E+00 2011
In the mitigation scenario MIT1-20 the cost of debris impacts represents the highest share. The expenses for MRO prevention and passivation are low. The cost development of MIT1-20 is similar to the BAU scenario. There is a small cost increase after the implementation of the mitigation measures in the year 2020. The break-even point is not reached till 2051. There is still a signi cant slope in the cost development increase for the future. The results are presented in Figs. 5 and 6.
Impacts (BAU) MIT1-20
8E+10
2006
5.2. MIT1-20
9E+10
2001
after the implementation of the mitigation measures in the year 2001. The break-even point is reached in 2025. After this point there is a small cost saving due to the reduced numbers of generated fragments in this scenario. There is still a signi cant slope in the cost development increase for the future.
Fig. 5. Cumulative cost over time for mitigation scenario MIT1-20 (cost in FY02$).
Cumulative Cost[$]
Fig. 4. Comparison of the cumulative cost over time of MIT1-01 with BAU scenario (cost in FY02$).
Year
Fig. 6. Comparison of the cumulative cost over time of MIT1-20 with BAU scenario (cost in FY02$).
development increase for the future. The results are presented in Figs. 7 and 8. 5.4. MIT3-1 In the mitigation scenario MIT3-1 the cost of debris impacts represents the highest share. The cost development of MIT3-1 is similar to the BAU scenario with only small cost savings after reaching the break-even point in 2048. There is still a signi cant slope in the cost development increase for the future. The results are presented in Figs. 9 and 10. 5.5. MIT3-20 In the mitigation scenario MIT3-20 the cost of debris impacts represents the highest share. There is a
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C. Wiedemann et al. / Acta Astronautica 55 (2004) 311 – 324 9E+10 Impacts (BAU) MIT3-1
8E+10 Cumulative Cost [$]
7E+10 6E+10 5E+10 4E+10 3E+10 2E+10 1E+10 2051
2046
2041
2036
2031
2026
2021
2016
2011
2006
2001
0E+00
Year
Fig. 7. Cumulative cost over time for mitigation scenario MIT2 (cost in FY02$).
Fig. 10. Comparison of the cumulative cost over time of MIT3-1 with BAU scenario (cost in FY02$).
9E+10 Impacts (BAU)
8E+10
MIT2 Cumulative Cost [$]
7E+10 6E+10 5E+10 4E+10 3E+10 2E+10 1E+10 2051
2046
2041
2036
2031
2026
2021
2016
2011
2006
2001
0E+00
Year
Fig. 8. Comparison of the cumulative cost over time of MIT2 with BAU scenario (cost in FY02$).
Fig. 11. Cumulative cost over time for mitigation scenario MIT3-20 (cost in FY02$).
cost increase after the implementation of the mitigation measures in the year 2020. The break-even point is not reached till 2051. The results are presented in Figs. 11 and 12. 5.6. MIT4
Fig. 9. Cumulative cost over time for mitigation scenario MIT3-1 (cost in FY02$).
In the mitigation scenario MIT4 the sum of mitigation measures represents the highest cost share. The results are presented in Figs. 13 and 14. The expenses for slag prevention are high. The cost development of MIT4 is very di6erent from the BAU scenario. There is a signi cant cost increase after the implementation of the mitigation measures in the year 2001. The break-even point is reached in 2041. After this point there is a signi cant cost saving due to the reduced numbers of generated slag particles in this
C. Wiedemann et al. / Acta Astronautica 55 (2004) 311 – 324
321
9E+10 Impacts (BAU)
8E+10
MIT3-20 Cumulative Cost [$]
7E+10 6E+10 5E+10 4E+10 3E+10 2E+10 1E+10 2051
2046
2041
2036
2031
2026
2021
2016
2011
2006
2001
0E+00
Year
Fig. 12. Comparison of the cumulative cost over time of MIT3-20 with BAU scenario (cost in FY02$).
Fig. 15. Cumulative cost over time for mitigation scenario MIT5-01 (cost in FY02$).
9E+10 Impacts (BAU)
8E+10
MIT5-01
Cumulative Cost [$]
7E+10 6E+10 5E+10 4E+10 3E+10 2E+10 1E+10
2051
2046
2041
2036
2031
2026
2021
2016
2011
2006
2001
0E+00
Year
Fig. 13. Cumulative cost over time for mitigation scenario MIT4 (cost in FY02$).
scenario. There is a reduced slope in the cost development increase for the future.
9E+10 Impacts (BAU) MIT4
8E+10 Cumulative Cost [$]
7E+10
Fig. 16. Comparison of the cumulative cost over time of MIT5-01 with BAU scenario (cost in FY02$).
6E+10
5.7. MIT5-01
5E+10 4E+10 3E+10 2E+10 1E+10 2051
2046
2041
2036
2031
2026
2021
2016
2011
2006
2001
0E+00
Year
Fig. 14. Comparison of the cumulative cost over time of MIT4 with BAU scenario (cost in FY02$).
In the mitigation scenario MIT5-01 the sum of mitigation measures represents the highest cost share. The expenses for slag prevention and de-orbiting are high. The cost development of MIT5-01 is very different from the BAU scenario. There is a signi cant cost increase after the implementation of the mitigation measures in the year 2001. The break-even point is not reached till 2051. The results are presented in Figs. 15 and 16.
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C. Wiedemann et al. / Acta Astronautica 55 (2004) 311 – 324 9E+10 MIT1-01
8E+10
MIT1-20
Cumulative Cost [$]
7E+10
MIT2 MIT3-1
6E+10
MIT3-20 5E+10
MIT4 MIT5-01 MIT5-20
4E+10 3E+10
BAU
2E+10 1E+10 2051
2046
2041
2036
2031
2026
2021
2016
2011
2006
2001
0E+00
Year
Fig. 17. Cumulative cost over time for mitigation scenario MIT5-20 (cost in FY02$). 9E+10 Impacts (BAU) MIT5-20
8E+10 Cumulative Cost [$]
7E+10 6E+10 5E+10 4E+10 3E+10 2E+10 1E+10
2051
2046
2041
2036
2031
2026
2021
2016
2011
2006
2001
0E+00
Year
Fig. 18. Comparison of the cumulative cost over time of MIT5-20 with BAU scenario (cost in FY02$).
5.8. MIT5-20 In the mitigation scenario MIT5-20 the sum of mitigation measures represents the highest cost share. The expenses for slag prevention and de-orbiting are high. The break-even point is reached in 2042. There is still a signi cant slope in the cost development increase for the future. The results are presented in Figs. 17 and 18. 5.9. Comparison of results The cumulative cost are compared in the year 2051, where the simulation stops. The results are presented in Fig. 19. This comparison is a snap-shot it is used to derive qualitative information about the cost e6ectiveness of the di6erent mitigation scenarios.
Fig. 19. Comparison of the cumulative cost over time of MIT1, MIT2, MIT3, MIT4, and MIT5 with the BAU scenario (cost in FY02$).
Information about the continuing of the cost development are neglected. In the year 2051 the scenarios MIT3-20, MIT5-01, and MIT1-20 are the most expensive. A cost saving occurs for the scenarios MIT2, MIT4, MIT1-01, MIT5-20, and MIT3-1. The following reasons can be given for the di6erent behavior. An important contribution to the space debris environment are fragments from explosions and slag particles. If passivation and slag prevention is implemented very late, there are more debris objects, causing more damages. In MIT3-20 all e6ective mitigation measures are implemented late. So the scenario has high costs due to satellite damages. MIT5-01 includes beside the above mentioned e6ective mitigation measures several more, sometimes very costly but less e6ective measures. Thus MIT5-01 is altogether too expensive. MIT1-20 does not include slag prevention. The cost of this scenario is comparable to the BAU scenario. MIT3-1 begins too late with passivation. The cost of this scenario is comparable to the BAU scenario. MIT5-20 considers the e6ective mitigation strategies from the beginning. There is a cost saving due to the fact that the less e6ective but partly very costly mitigation measure are implemented very late. MIT1-01 saves cost by preventing explosions due to passivation. MIT4 combines all e6ective mitigation measures with some cheap, less e6ective measures. MIT2 includes only the most effective mitigation measures and is thus the scenario with the best cost savings. Another criteria for the e6ectiveness of the scenarios is the slope of cost. MIT3-20, MIT1-20, MIT3-1,
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MIT5-20, and MIT1-01 show a high slope of cost in 2051. In MIT3-20 all e6ective mitigation scenarios are implemented very late. In MIT1-20 and MIT3-1 passivation is implemented late. MIT5-20 shows a strong cost increase due to the late implementation of less e6ective and partly costly mitigation measures. MIT1-01 has no slag prevention. MIT5-01, MIT4, and MIT2 include all e6ective mitigation measures from the beginning. In these cases the slope of cost increase is reduced.
MASTER MRO NaK RDT&E S/S SMAD SRM TFU TRL
323
Meteoroid and Space Debris Terrestrial Environment Model Mission Related Object sodium-potassium alloy Research, Development, Test, and Evaluation Subsystem Space Mission Analysis and Design Solid Rocket Motor Theoretical First Unit Technology Readiness Level
5.10. Conclusion Long-term simulations of the space debris environment based on a conservative tra8c model have been performed. The output data have been combined with cost models for mitigation measures and satellite damages (due to impacts). Two points in time (2001 and 2020) have been considered for the implementation of mitigation measures. One result of the investigations is that the most e6ective mitigation measures are passivation (suppression of fragmentation events) and slag prevention. A second result is that a late implementation of mitigation measures, especially passivation and slag prevention, is less e6ective.
Acronyms (TT&C)/DH Telemetry, Tracking, and Command/ Data Handling ADCS Attitude Determination and Control Subsystem AKM Apogee Kick-Motor APDTICM Advanced Projects Design Team Instrument Cost Model BAU Business As Usual BOL Beginning Of Life EOL End Of Life FY02$ Fiscal Year 2002 Dollar GEO Geo-stationary Orbit GTO Geo-stationary Transfer Orbit IA&T Integration, Assembly, and Test ILR Institut f)ur Luft- und Raumfahrtsysteme LCC Life Cycle Cost LEO Low Earth Orbit
Acknowledgements The results presented in this paper were achieved during the research project “Space Debris End-to-End Service” (50JR0132) of the German Federal Ministry of Education and Research. All responsibilities for the contents of this publication resides with the authors. References [1] C.C. Gumbert, M.D. Violet, D.E. Hastings, W.M. Hollister, R.R. Lovell, Cost per billable minute metric for comparing satellite systems, Journal of Spacecraft and Rockets 34 (6) (1997) 837–846. [2] T. Kashitani, Development and application of an analysis methodology for satellite broadband network architectures, AIAA paper 2002-2019. [3] D.E. Koelle, Statistisch-Analytische Kostenmodelle f)ur die Entwicklung und Fertigung von Raumfahrtger)at, Teil I: Statistische Fertigungskostenpreis- und EntwicklungskostenModelle, Raumfahrtforschung 15 (5) (1971) 181–197 (in German). [4] S.L. Rosing, W.J. Bursnall, Analysis and comparison of spacecraft resources forecasting techniques for unmanned missions, Journal of Spacecraft and Rockets 5 (5) (1968) 522–530. [5] G. Dondi, Cost estimation of satellite projects, Large Space Programs Management, Proceedings of the European Colloquium, 1971, pp. 127–157. [6] A. Franzke, K. Niebisch, Cost estimating and price analysis in satellite projects, ESRO Project Management and Project Control, 1973, pp. 259–287. [7] J.A. Vandenkerckhove, Economics of telecommunications space segments, Acta Astronautica 12 (11) (1984) 745–770. [8] B.A. Palaszewski, Electric propulsion cost estimation, AIAA paper 85-2044. [9] H. Apgar, D. Bearden, R. Wong, Cost modeling, in: J.R. Wertz, W.J. Larson (Eds.), Space Mission Analysis and Design, 3rd Edition, Microcosm/Kluer, Dordrecht, 1999, pp. 783–820.
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[10] C. Wiedemann, H. Krag, J. Bendisch, H. Sdunnus, Analyzing costs of space debris mitigation methods, COSPAR paper PEDAS1-B1.4-0053-02, 2002. [11] D. Hayn, ATV/CTV Kostenanalyse, Endbericht, IABG, B-TRT-0014, 16 May 1995 (in German). [12] J.A. Dryden, J.P. Large, A critique of spacecraft cost models, Rand, R-2196-1-AF, September 1977. [13] W.L. Pritchard, Economics of satellite communications systems, Acta Astronautica 8 (11–12) (1981) 1321–1341. [14] Z. Yilin, Synthetic estimation of development cost of satellite, Acta Astronautica 32 (9) (1994) 645–648. [15] D.E. Koelle, Handbook of Cost Engineering for Space Transportation Systems with TRANSCOST 7.0, StatisticalAnalytical Model for Cost Estimation and Economical Optimization of Launch Vehicles, TCS TransCostSystems, Ottobsunn, November 2000. [16] K. Roust, K. War eld, The JPL advanced projects design team’s spacecraft instrument cost model: an objective, multivariate approach, First Annual Joint ISPA/SCEA International Conference, June 1998.
[17] J.D. Kiesling, B.R. Elbert, W.B. Garner, W.L. Morgan, A technique for modeling communications satellites, COMSAT Technical Review 2 (1) (1972) 73–103. [18] S.J. Isakowitz, J.P. Hopkins, J.B. Hopkins, International Reference Guide to Space Launch Systems, 3rd Edition, AIAA, Virginia, 1999. [19] J.C. Mankins, Technology Readiness Levels, A White Paper, April 6, 1995, NASA http://www.hq.nasa.gov/o8ce/ codeq/trl/. [20] M.R. Kirby, D.N. Marvis, M.C. Largent, A process for tracking and assessing emerging technology development programs for resource allocation, AIAA paper 2001-5280. [21] T.-L. Lee, L.D. Thomas, Cost growth models for NASA’s programs: a summary, Computing Science and Statistics 33 (2001) 431–440. [22] J. Bendisch, P. Wegener, Analysis of debris mitigation scenarios in terms of cost and bene t, Proceedings of the Third European Conference on Space Debris, European Space Operations Centre (ESOC), Darmstadt, Germany, 19–21 March 2001, ESA SP-473, 2001, pp. 717–722.
Cost and bene t analysis of space debris mitigation measures Carsten Wiedemanna;∗ , Michael Oswalda , J)org Bendischb , Holger Sdunnusc , Peter V)orsmanna a Institute
of Aerospace Systems, ILR, Technische Universitat Braunschweig, Hermann-Blenk-Str.23, 38108 Braunschweig, Germany b Aerodata AG, Braunschweig, Germany c eta max space GmbH, Braunschweig, Germany
Abstract The increasing number of orbital debris objects is a risk for satellites. To reduce the risks for future space missions several mitigation strategies have been developed during the last years. In this paper the long-term cost development of space debris mitigation measures is analyzed. Di6erent mitigation scenarios are de ned and compared. Cost models are derived for mitigation measures and for the loss of amortization in the case of hypervelocity impacts on operating satellites. Long-term simulations of the space debris environment based on a conservative orbital tra8c model have been made for a 50 years time interval beginning in 2001. The simulations consider di6erent mitigation scenarios. The output data have been combined with the cost models. The mitigation scenarios were compared, and a cost-bene t analysis has been performed. The result of the investigation is, that the most e6ective mitigation measures are passivation (suppression of fragmentation events) and slag prevention. c 2003 International Astronautical Federation. Published by Elsevier Ltd. All rights reserved.
1. Introduction The economic e8ciency of mitigation measures, which is the main design driver for many missions, has not been investigated yet. A current study has the goal of estimating the mission costs for di6erent mitigation scenarios. A business as usual (BAU) scenario (without mitigation) is compared to scenarios considering di6erent types of mitigation measures. The objective is to estimate the break-even point when the investment in mitigation causes an e6ective reduction of the mission cost. Mitigation strategies like the reduction of the orbital lifetime or re-orbiting of non-operational ∗ Corresponding author. Tel.: +49-531-391-9970; fax: +49537-391-9966. E-mail address: [email protected] (C. Wiedemann).
payloads into graveyard orbits are methods to control the space debris environment. These methods initially cause an increase of costs. In order to estimate the cost associated to debris-related damages or mitigation measures, it is necessary to know the tendencies and bandwidths of the development of the future debris population. In particular, the number of objects with time and the expected damages, as well as the e6ectiveness of debris measures to control the debris environment are of concern. Mission costs can be increased by orbital debris hazards concerning for example the total loss of operational spacecraft due to a collision, and damage on operational spacecraft due to debris impact. Debris mitigation in terms of minimization and control of the debris environment can have an impact on cost items like for example the mission and spacecraft design. Cost occurs for spacecraft
c 2003 International Astronautical Federation. Published by Elsevier Ltd. All rights reserved. 0094-5765/$ - see front matter doi:10.1016/j.actaastro.2004.05.011
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passivation and minimization of mission related objects (MRO), and design costs, operational costs and extra fuel (lifetime/mass penalty, respectively) for deor re-orbit at end-of-life (EOL). The bene ts due to debris mitigation, compared to a BAU scenario, are for example the reduced damage on spacecraft and preserving the possibility of future missions in currently used orbital regions. Furthermore a collision cascading can be prevented in the far future. The simulations are made for a time interval of 50 years beginning in 2001. This paper presents the results of cost estimations for satellite missions and the impact of debris mitigation measures on the costs. Selected results of a cost and bene t analysis are presented. 2. Satellite mission cost An important part of this work was the development of cost models. These cost models were mainly developed for satellites, because most mitigation measures a6ect the satellite design. Also cost models for upper stage modi cations and orbital maneuvers were developed. The rst task of the cost models is to give a rough order of magnitude (ROM) cost estimation for a typical satellite. The cost model shall be able to consider the inFuence of mitigation measures on a satellite mission. Furthermore the cost model must permit an estimation of the cost due to hypervelocity particle impacts on satellites. 2.1. Literature review There are several types of cost models described in the literature. Parametric cost models have been selected here. Published parametric equations provide the desired transparency of the cost model. A design modi cation requires a cost model modi cation. Consequently in this work variants of existing cost models have been derived. An important question is the application of cost models. The cost models needed here require a low number of input parameters. The input parameters should be easy to estimate. Several parametric cost models are given in the literature. There are cost models for complete satellites and satellites subsystems. Some simple satellite cost models are based on cost per dry mass [1,2]. These models are based on relatively new data. There are also some older
satellite cost models. Satellite cost models have been developed for research satellite buses (without payload) and complete applications satellites [3]. The literature also gives summaries of multivariable satellite cost models [4–6]. Detailed cost models, which are broken down to satellite subsystems, are given for communications satellites [7], for electric propulsion modules [8], and for all types of satellites [9]. The latter is preferred here. 2.2. Cost model modi5cations Mitigation measures require modi cations of subsystems. These modi cations cause an increasing complexity of a certain subsystem. As a result the subsystem hardware cost is increasing. The subsystem level of the selected cost model has the advantage that it allows an estimation of the impact of the increasing complexity on the overall satellite cost. Complexity is de ned here as degree of di8culty. The modi cation of subsystem cost models for the development of cost models for mitigation measures is shown for two examples. In the following sections a survey is given that describes the satellite mission cost, satellite hardware cost, the space debris environment, the cost of satellite damage due to impacts and the cost of mitigation measures. 2.3. Satellite subsystems The subsystem cost model uses subsystem masses as input parameter. A model for satellite subsystems is required that covers the wide range of di6erent satellite types and masses on orbit and gives rough estimates for the subsystem masses [10]. This subsystem breakdown is needed to consider the inFuence of design changes on the subsystem cost. The de nition of a standard satellite is made by a rough sizing of a spacecraft, based on mass models of its subsystems. A satellite consists of a payload and several support subsystems, which are summarized in Table 1. 2 msub = c1 mcBOL
(1)
Subsystem masses can be expressed as a function of the beginning of life (BOL) mass [7]. Applying a regression analysis to collected subsystem data by using a simple power function Eq. (1) is giving the coe8cients presented in Table 1. The exponents shown
C. Wiedemann et al. / Acta Astronautica 55 (2004) 311 – 324 Table 1 Coe8cients of the satellite subsystem mass model Subsystem
c1
c2
Harness Payload Thermal Power Propulsion Structures & mechan. ADCS (TT&C)/DH AKM
2.1741E−02 1.4550E−01 2.4927E−02 2.1999E−01 2.0699E−01 3.0666E−01 4.2679E−01 4.1595E−01 2.4929E+00
1.1943E+00 1.0624E+00 1.0065E+00 9.6938E−01 9.3678E−01 9.1662E−01 7.0875E−01 7.0047E−01 8.4812E−01
The apogee kick-motor (AKM) is not included in the BOL mass.
in the third column are sorted in a way that indicates whether a subsystem mass changes more or less rapidly with scale. 2.4. Satellite cost The life cycle cost (LCC) of a satellite includes development cost (non-recurring cost), production cost (recurring cost), launch cost, and orbital operations cost. Mitigation measures can have di6erent inFuences on these cost elements. Cost is related to project phases. The development cost includes expenses for research and development during the phases 0, A, B, and C. Production and operations cost refer to phases D and E. Development and production cost are di8cult to separate. Development cost includes the production of a prototype and is very di8cult to estimate, because it depends on inFuencing factors which cannot be described mathematically [3]. Development is de ned as new design with proven technology. Definitions like technological readiness levels (TRL) or heritage factors can be used for a grading between development and production cost. Development cost covers expenses for research, development, test, and evaluation (RDT&E). This includes production of a prototype (ground test unit) but not the production and testing of Fight units. Production cost comprises the production and test of Fight units. The development cost can vary between high risk technology development, classical development, purchase with signi cant modi cation, purchase with interface adaptation, and pure purchase [11]. Production cost is less sensitive to program characteristics and is much easier to
313
Table 2 Development and production cost models for satellite subsystems and payloads Subsystem
Cost model
Payload (Scienti c Instrument) Payload (Communications) Propulsion (Liquid) ADCS (TT&C)/DH Power Thermal Structures & Mechanisms AKM (Solid) AKM (Liquid)
APDTICM [16] SMAD [9] TRANSCOST 7.0 [15] SMAD [9] SMAD [9] SMAD [9] SMAD [9] SMAD [9] TRANSCOST 7.0 [15] TRANSCOST 7.0 [15]
estimate than development cost [12]. Operations cost includes variable and xed cost and is very di8cult to determine. It depends on ground station cost, number of satellites in orbit and orbital lifetime [7]. Mostly there is a substantial amount of existing ground station hardware that can be used by several satellite systems [13]. There are essential cost parameters like BOL mass and payload requirements [7]. Especially mass is a good cost driver, because all required performance characteristics a6ect satellite mass. Thus mass is the most frequently used independent variable in such models [12–14]. The selected cost model should have a su8cient complexity and a high acceptance in the satellite industry. Several cost models have been investigated. Most software cost model tools are either very complicated or not transparent enough. The investigation of the structure, on which they are based, is mostly not possible. 2.5. Satellite hardware cost Mainly elements of a cost model on a subsystem level taken from “Space Mission Analysis and Design” (SMAD) have been selected here [9]. Some elements from TRANSCOST 7.0 were used to estimate the cost of propulsion systems [15]. For scienti c payloads an instrument model was selected [16]. The cost models are summarized in Table 2. The models are suitable to determine the development and theoretical rst unit (TFU) production cost of satellites. All elements use
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parametric methods, which means a projection of the experience of the past into the future. The parametric estimation has the advantage, that it is based on historical data and includes inFuences like scheduling delays, mistakes, redesigns, etc. Thus the cost estimation considers these factors too. The breakdown of a satellite in subsystems allows the formulation of parametric expressions for satellite performance, mass, and cost [17]. The disadvantage of this procedure is, that there is no standard subsystem description [12]. 2.6. Operations cost Due to the lack of a suitable operations cost model, a more simple approach is chosen here. It is assumed that a satellite has constant annual operations cost, which depends on the complexity of the spacecraft. This concept is realized by relating the annual operations cost to the satellite hardware cost. To calibrate this relation, estimates from Vandenkerckhove [7] have been used here. It was found, that the relation of annual operations cost to hardware cost is about 3%. 2.7. Launch cost The average launch cost is estimated by using data of several rockets from Isakowitz et al. [18]. The speci c launch cost is based on the price of a launcher related to its payload capability. The speci c launch price is about 14,000 FY02$/kg for low earth orbits (LEO) and 31,000 FY02$/kg for geo-synchronous transfer orbit (GTO) injection including launch insurance. This cost has to be multiplied by a factor of 1.2, because the actual launched mass is typically 83% of the payload capability. 2.8. Proto:ight cost The satellite cost model uses a protoFight unit as typical reference satellite for a certain BOL mass. A protoFight unit is a prototype (ground test unit), which is refurbished to be used in operational Fight. To calculate average cost it is considered that typically a reduced share of the development cost occurs. This is reasonable, because during the development of supporting subsystems existing components and technologies are used in reality. The development expense
is graded by using the TRL [19–21]. Development cost includes production and test expenses for ground test units. Normally this cost has to be amortized by a series production. Because of the low production rates, often no separate Fight unit is produced. The protoFight cost is a mixture of development and production costs. In a protoFight unit the ground test unit is upgraded to a Fight unit. This requires additional test e6ort, which is about 30% of the production effort. Due to the very small series production rates in the satellite industry, this protoFight approach seems to be a suitable approximation for the estimation of the average cost of satellite hardware. 3. Cost of mitigation measures For the cost estimation of mitigation measures all subsystem cost models are combined. This combination is used to determine the average cost for a certain mitigation measure. The goal of this approach is to derive simpli ed cost models. These cost models are used to estimate the correct order of magnitude of a certain mitigation measure. The particular model must be able to show the correct tendency of cost evolution depending on the satellite mass. The BOL mass has been selected here as suitable parameter to consider scaling e6ects. This allows to determine the speci c impact of cost on satellites. The generation of cost models is illustrated using a satellite with a BOL mass of 1000 kg as example. Di6erent mitigation measures are de ned. Each mitigation measure is represented by one cost model. Most of these cost models are based on the concept of considering the complexity increase due to a mitigation measure. At rst the cost of a complete satellite is estimated. In a next step the complexity of certain subsystems is increased. The subsystem cost is multiplied by this complexity factor. Both cost calculations are compared. The di6erence between the modi ed satellite and the original design is presented and described in a model. The concept is based on subsystem mass models, which are combined with subsystem cost models. The most important cost driving factor is the system mass. Consequently, the BOL mass is used as a reference value for a complete satellite. The resulting cost model gives average values for the impact of a modi cation
C. Wiedemann et al. / Acta Astronautica 55 (2004) 311 – 324
on the overall satellite design. The models provide a reasonable estimation for the correct order of magnitude of the cost. The advantage of this approach is that scaling e6ects are considered. The speci c cost decreases with increasing unit mass. The subsystems, which are modi ed by a mitigation measure, are addressed directly using a complexity factor. The value of the complexity is estimated. The di6erent complexity factors are combined with the subsystem cost models. Normally the mass is the most important cost driver. But a small modi cation of a subsystem has no signi cant impact on the subsystem mass. So the mass increase is negligible and thus no suitable criterion for cost estimation. Consequently it is better to determine the cost increase by a complexity factor. 3.1. Cost model equations Several cost model equations have been developed. One group of equations describe complete mitigation measures as function of a cost driving factor. To this group belong models for MRO prevention, passivation, slag prevention, and GEO re-orbit maneuvers. A second group of equations was created to describe more expensive orbital maneuvers. There are models for the increasing subsystems complexity, the enlargement or addition of propulsion systems, and additional launch cost due to the increasing propulsion system mass. Some of these models use the velocity increment Tv as cost driving factor. A last group contains models for operations cost, launch cost, and cost of complete satellites. From these sets of equations two, passivation and slag prevention for satellites, are presented as examples here. All equations concerning costs of satellite modi cations are based on a reference protoFight satellite with a high degree of completion for the satellite bus. For most mitigation cost models the BOL mass is used as cost driving factor. It was found that in all cases the dependency of the BOL mass can be expressed by a simple power function. The exponents are always smaller than “one”. This is showing the scaling effect. Cost is not increasing directly proportional with the hardware mass. For small spacecraft the speci c costs of a modi cation are higher. The scaling e6ect is caused by the application of the cost and mass models, which include scaling e6ects by themselves.
315
Table 3 Assessment factors with a nearly logarithmic scale for the estimation of “orders of magnitude” 0.99 0.90 0.50 0.10 0.01
Very high High Medium Low Very low
The mitigation measure cost models are derived from a subsystem level, which allows to consider a certain inFuence on a selected subsystem. Thus the correct order of magnitude of a subsystem modi cation can be considered. The mitigation measure costs have been calculated and presented graphically. So it is possible to show the cost evolution with the system mass. The cost models have been derived by applying a regressional analysis to the graphical presentation. For the following mitigation measures the complexity factors are derived by estimating the overall impact on the subsystem cost by using Table 3. Then it is considered if this modi cation has a high or low degree of di8culty by multiplying the value of Table 3 with the factor “2” or “1/2”. 3.2. Example: MRO prevention The complexity factor for MRO prevention describes the increasing cost due to a modi cation of the structure subsystem. The complexity factor is applied to the structure and mechanisms subsystem. The impact on the subsystem cost is small. The degree of di8culty is high. A redesign requires the integration of movable parts, which are more complicated than detachable elements. The complexity factor is given in Eq. (2). fMRO = 1:0 + 0:1 ∗ 2:0 = 1:20:
(2)
It is assumed that the expense has a comparable order of magnitude for upper stages. Thus this cost model is also used for that case, by replacing the BOL mass by the stage dry (NET) mass. The cost of subsystem is multiplied with the complexity factor of Eq. (2). The cost increase of the subsystems has also an inFuence on the cost for integration, assembly and test (IA&T) and on the
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3.3. Application of mitigation cost models
80 70 60
Cost of MRO Prevention
50
Cost 40 30 20
Program Level
IA&T
Structure
Thermal
Power
TT&C/DH
ADCS
Propulsion
0
Scientific Payload
10
Fig. 1. Cost breakdown of a typical scienti c satellite with a BOL mass of 1000 kg including additional cost due to MRO prevention (cost in FY02$M).
MRO Prevention Cost 1E+07
Cost[$]
y = 6,7618E+03x 7,9383E-01 R2 = 9,9999E-01
The cost models for these two examples are additional hardware costs. As input parameter the system mass in terms of BOL mass has been selected. This simpli ed choice is reasonable, because most cost driving modi cations a6ect the satellite bus. They are independent of the complexity of the payload. Furthermore the BOL mass is known or can roughly be estimated for most satellite hardware in the phases A/B. The output value is directly the cost in FY02$. The presented models have the advantage that they have a transparent structure. As shown for these two examples, they are expressed as simple power functions. They can be applied to all kinds of spacecraft, either applications or scienti c satellites. Because the system mass is used as scale basis, the models can be applied to a wide range of satellite masses. The equations guarantee a high reliability of cost estimation. This is possible, because the equations are based on very complex subsystem mass and cost models. Based on this, a suitable average cost values can be provided. 4. Mitigation scenarios
1E+06
1E+05 100
1000
10000
BOL Mass[kg]
Fig. 2. Graphical presentation of cost of MRO prevention as function of BOL mass (cost in FY02$).
program level (management). The cost comparison is shown in Fig. 1. MRO prevention causes a small cost increase. The additional cost of MRO prevention as a function of satellite BOL mass is given in Fig. 2. Using the graph from Fig. 2 the cost model for MRO prevention can be derived as function of BOL (resp. NET) mass. The cost model is given in Eq. (3) with FY02$ as cost unit. 0:79383 CostMRO = 6761:8mBOL=(NET) :
(3)
The approach of cost estimation is combined with results of numerical simulations of the future space debris environment to evaluate the cost and bene t of mitigation. The analysis is performed by an upgraded version of the long-term debris environment model LUCA, which has been developed at the Institute of Aerospace Systems. LUCA considers the generation and reduction of space objects. The software tool computes object sources, sinks, and velocity increments for di6erent types of mitigation maneuvers. The tool considers object sources like launches of payloads, release of MRO, explosions and collisions. An important sink is the re-entry of objects due to natural decay and active de-orbiting. The input and output parameters are for example object masses (e.g. of satellites and upper stages) and velocity increments for transfer maneuvers (e.g. re-orbiting and de-orbiting) [22]. These output parameters are related to di6erent types of costs like for example cost of a satellite mission or cost of a transfer maneuver. The next step is the estimation of increase of cost due to debris hazard and mitigation.
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4.1. Initial debris population The most recent MASTER population (reference epoch May 2001) has been used as initial population. It reFects a well proven data set, which has been validated against radar and optical observations, continuous (US SPACECOM catalogue) and sporadic (dedicated) campaigns. The detailed properties of this population are described in the related ESA report (delivered with the MASTER2001 CD ROM). 4.2. Tra=c model For the purpose of this work, the ILR tra8c model has been used, which is based on a series of analysis over the most recent years. Following this analysis, a tra8c growth rate (which is not the net increase rate of the population) of 3% per year related to the basic population has been selected for the next 5 decades. A major nding of previous studies was that any more detailed tra8c de nition is not reasonable, since too many estimates and assumption (technical, nancial and political) would be necessary. The assumptions, however, are not reliable, even for some years ahead. The above tra8c rate corresponds with the observed development of the population over the last decade. Thus, it is a feasible and applicable, as well as an conservative assumption. 4.3. Scenario parameters Two starting points for the implementation of mitigation measures have been selected here, to study the inFuence of time on the cost. The implementation starts either 2001 or 2020. For the scenarios MIT1, MIT3, and MIT5 two versions concerning the beginning of mitigation have been simulated. The implementation of all mitigation measures for the scenarios MIT1-01, MIT2, MIT4, and MIT5-01 begins in 2001. The implementation of all mitigation measures for the scenarios MIT1-20 and MIT3-20 begins in 2020. For MIT3-01 and MIT5-20 a mixture has been chosen, where especially the slag prevention begins in 2001. The parameters for the di6erent scenarios are summarized in Table 4. Impacts: Every satellite which is penetrated by an object greater than 1 mm has a failure probability of 10%. This causes cost of 10% lost amortization. The
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number of impacts is controlled by the tra8c model and the mitigation measures. The increasing tra8c during the next 50 years causes more debris particles and thus most impact cost. Thus the cumulative impact cost is di6erent for each mitigation scenario. MRO prevention and passivation: Cost for MRO prevention and passivation is related to satellites and upper stages. The tra8c model for satellite launches is identical in all mitigation scenarios. The cost for MRO prevention and passivation is also the same in all mitigation scenarios. Slag prevention: Cost for slag prevention is related to satellites and upper stages, which are injected into GTO or GEO. The tra8c model for satellite launches is identical in the mitigation scenarios MIT2 to MIT5. The cost for slag prevention is also the same in these mitigation scenarios. GEO re-orbit: Cost for GEO re-orbiting (or GEO disposal) is related to satellites, which are transferred into a graveyard orbit at EOL. This parameter indicates, from which point in time onwards the spent GEO payloads are re-orbited to the graveyard orbit (300 km above GEO). The tra8c model for GEO re-orbit maneuvers is identical in the mitigation scenarios MIT4 and MIT5. The cost for GEO re-orbiting is also the same in these mitigation scenarios. In order to use realistic assumption (malfunctions, non conform operators), this method is applied to 50% of the payloads launched after the given point in time. De-Orbit: Cost for de-orbiting (reduction of the orbital lifetime of LEO objects to 25 years) is related to satellites and upper stages. The tra8c model for de-orbiting maneuvers is di6erent in the mitigation scenarios MIT4 and MIT5. Purpose of this parameter variation is to show the impact of de-orbiting strategies with high or low expense on the overall mitigation cost. This parameter indicates, from which point in time onwards the orbital lifetime of LEO objects is limited to 25 years according to the Inter-Agency Space Debris Coordination Committee (IADC) approach. For this purpose, the operational lifetime of a payload has been set to 7 years. In order to come to reasonable results, the fuel needed for the reduction of the orbital lifetime has been limited to 10% in MIT4 and 20% in MIT5 of the initial mass, assuming fuel exhaust velocity of 1:5 km=s (MIT4) and 3 km=s (MIT5). This assumption represents the upper limit of fuel burden to be considered, resulting
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Table 4 Parameters of the mitigation scenarios MIT
1-01
1-20
2
3-1
3-20
4
5-01
5-20
MRO prevention Passivation Slag prevention GEO re-orbit De-Orbit LEO disposal
2001 2001 — — — —
2020 2020 — — — —
2001 2001 2001 — — —
2020 2020 2001 — — —
2020 2020 2020 — — —
2001 2001 2001 2001 2001 —
2001 2001 2001 2001 2001 2001
2001 2001 2001 2020 2020 2020
in the maximum e6ectiveness to be achieved. LUCA monitors and reports the actual fuel needs for each payload under consideration. LEO disposal: Cost for LEO disposal is related to satellites above 1400 km in MIT5. According to a NASA proposal as of 1997, the disposal of spent LEO payloads to higher altitudes (2500–2700 km) may be an option for future operations. This may be applicable for payloads operating above 1400 km, where a lifetime reduction to 25 years is to costly in terms of fuel. For LEO disposal, the fuel considerations as given above for the lifetime reduction apply. Fig. 3. Cumulative cost over time for mitigation scenario MIT1-01 (cost in FY02$).
5. Results The parameters for the di6erent scenarios are summarized in Table 4. The purpose of the simulations is to compare the cost of mitigation with cost of debris impacts on satellite hardware. The e6ectiveness of the mitigation measures controls the number of debris objects in space. To verify the inFuence of a certain mitigation measure on the overall debris population, di6erent scenarios were de ned. Comparing MIT1-01 with MIT1-20 the beginning of the implementation of MRO prevention and passivation is varied, to show the inFuence of a late implementation on the overall debris population. A comparison of MIT1-01 with MIT2 presents the inFuence of slag prevention on cost. A comparison of MIT2 with MIT3-1 shows, if an early implementation of slag prevention combined with a late start of MRO prevention and passivation is reasonable. A comparison of MIT3-1 with MIT3-20 presents the inFuence of a late implementation of slag prevention. A comparison of MIT2 with MIT4 shows, if an additional GEO
re-orbiting and a de-orbiting (lifetime reduction) of LEO objects saves cost. A comparison of MIT4 with MIT5-01 points out, if the cost for more extensive de-orbit maneuvers is justi ed and if the implementation of LEO disposal is reasonable. A comparison of MIT5-01 with MIT5-20 shows, if a late implementation of GEO re-orbit, de-orbit, and LEO disposal is reasonable. The costs of impacts and mitigation measures is graphically presented as function of time. The simulations are started in 2001 resp. 2020 and consider 50 years up to the year 2051. The cost unit is FY01$M. 5.1. MIT1-01 In the mitigation scenario MIT1-01 the cost of debris impacts represents the highest share. The results are presented in Figs. 3 and 4. The expenses for MRO prevention and passivation are low. The cost development of MIT1-01 is similar to the BAU scenario. There is a small cost increase
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9E+10 Impacts (BAU)
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5.3. MIT2 In the mitigation scenario MIT2 the sum of mitigation measures represent the highest cost share. The expenses for slag prevention are high. The cost development of MIT2 is very di6erent from the BAU scenario. There is a signi cant cost increase after the implementation of the mitigation measures in the year 2001. The break-even point is reached in 2031. After this point there is a signi cant cost saving due to the reduced numbers of generated slag particles in this scenario. There is a reduced slope in the cost
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In the mitigation scenario MIT1-20 the cost of debris impacts represents the highest share. The expenses for MRO prevention and passivation are low. The cost development of MIT1-20 is similar to the BAU scenario. There is a small cost increase after the implementation of the mitigation measures in the year 2020. The break-even point is not reached till 2051. There is still a signi cant slope in the cost development increase for the future. The results are presented in Figs. 5 and 6.
Impacts (BAU) MIT1-20
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5.2. MIT1-20
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after the implementation of the mitigation measures in the year 2001. The break-even point is reached in 2025. After this point there is a small cost saving due to the reduced numbers of generated fragments in this scenario. There is still a signi cant slope in the cost development increase for the future.
Fig. 5. Cumulative cost over time for mitigation scenario MIT1-20 (cost in FY02$).
Cumulative Cost[$]
Fig. 4. Comparison of the cumulative cost over time of MIT1-01 with BAU scenario (cost in FY02$).
Year
Fig. 6. Comparison of the cumulative cost over time of MIT1-20 with BAU scenario (cost in FY02$).
development increase for the future. The results are presented in Figs. 7 and 8. 5.4. MIT3-1 In the mitigation scenario MIT3-1 the cost of debris impacts represents the highest share. The cost development of MIT3-1 is similar to the BAU scenario with only small cost savings after reaching the break-even point in 2048. There is still a signi cant slope in the cost development increase for the future. The results are presented in Figs. 9 and 10. 5.5. MIT3-20 In the mitigation scenario MIT3-20 the cost of debris impacts represents the highest share. There is a
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C. Wiedemann et al. / Acta Astronautica 55 (2004) 311 – 324 9E+10 Impacts (BAU) MIT3-1
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Fig. 7. Cumulative cost over time for mitigation scenario MIT2 (cost in FY02$).
Fig. 10. Comparison of the cumulative cost over time of MIT3-1 with BAU scenario (cost in FY02$).
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MIT2 Cumulative Cost [$]
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Fig. 8. Comparison of the cumulative cost over time of MIT2 with BAU scenario (cost in FY02$).
Fig. 11. Cumulative cost over time for mitigation scenario MIT3-20 (cost in FY02$).
cost increase after the implementation of the mitigation measures in the year 2020. The break-even point is not reached till 2051. The results are presented in Figs. 11 and 12. 5.6. MIT4
Fig. 9. Cumulative cost over time for mitigation scenario MIT3-1 (cost in FY02$).
In the mitigation scenario MIT4 the sum of mitigation measures represents the highest cost share. The results are presented in Figs. 13 and 14. The expenses for slag prevention are high. The cost development of MIT4 is very di6erent from the BAU scenario. There is a signi cant cost increase after the implementation of the mitigation measures in the year 2001. The break-even point is reached in 2041. After this point there is a signi cant cost saving due to the reduced numbers of generated slag particles in this
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Fig. 12. Comparison of the cumulative cost over time of MIT3-20 with BAU scenario (cost in FY02$).
Fig. 15. Cumulative cost over time for mitigation scenario MIT5-01 (cost in FY02$).
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Fig. 13. Cumulative cost over time for mitigation scenario MIT4 (cost in FY02$).
scenario. There is a reduced slope in the cost development increase for the future.
9E+10 Impacts (BAU) MIT4
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7E+10
Fig. 16. Comparison of the cumulative cost over time of MIT5-01 with BAU scenario (cost in FY02$).
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5.7. MIT5-01
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Fig. 14. Comparison of the cumulative cost over time of MIT4 with BAU scenario (cost in FY02$).
In the mitigation scenario MIT5-01 the sum of mitigation measures represents the highest cost share. The expenses for slag prevention and de-orbiting are high. The cost development of MIT5-01 is very different from the BAU scenario. There is a signi cant cost increase after the implementation of the mitigation measures in the year 2001. The break-even point is not reached till 2051. The results are presented in Figs. 15 and 16.
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C. Wiedemann et al. / Acta Astronautica 55 (2004) 311 – 324 9E+10 MIT1-01
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Cumulative Cost [$]
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Fig. 17. Cumulative cost over time for mitigation scenario MIT5-20 (cost in FY02$). 9E+10 Impacts (BAU) MIT5-20
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Fig. 18. Comparison of the cumulative cost over time of MIT5-20 with BAU scenario (cost in FY02$).
5.8. MIT5-20 In the mitigation scenario MIT5-20 the sum of mitigation measures represents the highest cost share. The expenses for slag prevention and de-orbiting are high. The break-even point is reached in 2042. There is still a signi cant slope in the cost development increase for the future. The results are presented in Figs. 17 and 18. 5.9. Comparison of results The cumulative cost are compared in the year 2051, where the simulation stops. The results are presented in Fig. 19. This comparison is a snap-shot it is used to derive qualitative information about the cost e6ectiveness of the di6erent mitigation scenarios.
Fig. 19. Comparison of the cumulative cost over time of MIT1, MIT2, MIT3, MIT4, and MIT5 with the BAU scenario (cost in FY02$).
Information about the continuing of the cost development are neglected. In the year 2051 the scenarios MIT3-20, MIT5-01, and MIT1-20 are the most expensive. A cost saving occurs for the scenarios MIT2, MIT4, MIT1-01, MIT5-20, and MIT3-1. The following reasons can be given for the di6erent behavior. An important contribution to the space debris environment are fragments from explosions and slag particles. If passivation and slag prevention is implemented very late, there are more debris objects, causing more damages. In MIT3-20 all e6ective mitigation measures are implemented late. So the scenario has high costs due to satellite damages. MIT5-01 includes beside the above mentioned e6ective mitigation measures several more, sometimes very costly but less e6ective measures. Thus MIT5-01 is altogether too expensive. MIT1-20 does not include slag prevention. The cost of this scenario is comparable to the BAU scenario. MIT3-1 begins too late with passivation. The cost of this scenario is comparable to the BAU scenario. MIT5-20 considers the e6ective mitigation strategies from the beginning. There is a cost saving due to the fact that the less e6ective but partly very costly mitigation measure are implemented very late. MIT1-01 saves cost by preventing explosions due to passivation. MIT4 combines all e6ective mitigation measures with some cheap, less e6ective measures. MIT2 includes only the most effective mitigation measures and is thus the scenario with the best cost savings. Another criteria for the e6ectiveness of the scenarios is the slope of cost. MIT3-20, MIT1-20, MIT3-1,
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MIT5-20, and MIT1-01 show a high slope of cost in 2051. In MIT3-20 all e6ective mitigation scenarios are implemented very late. In MIT1-20 and MIT3-1 passivation is implemented late. MIT5-20 shows a strong cost increase due to the late implementation of less e6ective and partly costly mitigation measures. MIT1-01 has no slag prevention. MIT5-01, MIT4, and MIT2 include all e6ective mitigation measures from the beginning. In these cases the slope of cost increase is reduced.
MASTER MRO NaK RDT&E S/S SMAD SRM TFU TRL
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Meteoroid and Space Debris Terrestrial Environment Model Mission Related Object sodium-potassium alloy Research, Development, Test, and Evaluation Subsystem Space Mission Analysis and Design Solid Rocket Motor Theoretical First Unit Technology Readiness Level
5.10. Conclusion Long-term simulations of the space debris environment based on a conservative tra8c model have been performed. The output data have been combined with cost models for mitigation measures and satellite damages (due to impacts). Two points in time (2001 and 2020) have been considered for the implementation of mitigation measures. One result of the investigations is that the most e6ective mitigation measures are passivation (suppression of fragmentation events) and slag prevention. A second result is that a late implementation of mitigation measures, especially passivation and slag prevention, is less e6ective.
Acronyms (TT&C)/DH Telemetry, Tracking, and Command/ Data Handling ADCS Attitude Determination and Control Subsystem AKM Apogee Kick-Motor APDTICM Advanced Projects Design Team Instrument Cost Model BAU Business As Usual BOL Beginning Of Life EOL End Of Life FY02$ Fiscal Year 2002 Dollar GEO Geo-stationary Orbit GTO Geo-stationary Transfer Orbit IA&T Integration, Assembly, and Test ILR Institut f)ur Luft- und Raumfahrtsysteme LCC Life Cycle Cost LEO Low Earth Orbit
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