1 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Design for Value Lecture 24 10 May 2004 Karen Willcox Olivier de Weck Acknowledgments: Jacob Markish and Ryan Peoples Multidisciplinary System Design Optimization (MSDO) 2 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Today’s Topics An MDO value framework Lifecycle cost models Value metrics & valuation techniques Value-based MDO Aircraft example Spacecraft Example 3 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Optimal Design Traditionally, design has focused on performance e.g. for aircraft design optimal = minimum weight Increasingly, cost becomes important 85% of total lifecycle cost is locked in by the end of preliminary design. But minimum weight z minimum cost z maximum value What is an appropriate value metric? 4 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Design Example We need to design a particular portion of the wing Traditional approach: balance the aero & structural requirements, minimize weight We should consider cost: what about an option that is very cheap to manufacture but performance is worse? aerodynamics? How do we trade performance and cost? How much performance are we willing to give up for $100 saved? What is the impact of the low-cost design on price and demand of this aircraft? What is the impact of this design decision on the other aircraft I build? What about market uncertainty? structural dynamics? manufacturing cost? aircraft demand? aircraft price? tooling? environmental impact? 5 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Cost Module “Value” metric Performance Module Aerodynamics Structures Weights Mission Stability & Control Revenue Module Value Optimization Framework Manufacturing Tooling Design Operation Market factors Fleet parameters Competition “Optimal” design 6 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Challenges Cost and revenue are difficult to model – often models are based on empirical data – how to predict for new designs Uncertainty of market Long program length Time value of money Valuing flexibility Performance/financial groups even more uncoupled than engineering disciplines 7 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Cost Model Need to model the lifecycle cost of the system. Life cycle : Design - Manufacture - Operation - Disposal Lifecycle cost : Total cost of program over life cycle 85% of Total LCC is locked in by the end of preliminary design. Cost Module “Value” metric Performance Module Revenue Module 8 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Lifecycle Cost 0 20 40 60 80 100 65% Conceptual design Preliminary design, system integration Detailed design Manufacturing and acquisition Operation and support Disposal Time Impact on LCC (%) 85% 95% (From Roskam, Figure 2.3) 9 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Non-Recurring Cost Cost incurred one time only: Engineering - airframe design/analysis - configuration control - systems engineering Tooling - design of tools and fixtures - fabrication of tools and fixtures Other - development support - flight testing Engineering Tooling Other 10 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Development Cost Model Cashflow profiles based on beta curve: Typical development time ~6 years Learning effects captured – span, cost 11 )1()(   ED tKttc 0 0.01 0.02 0.04 0.05 0.06 1 2 3 4 5 6 7 8 9 1011121314151617181920212223242526272829303132333435363738394041424344454647484950515253 normalized time Support Tool Fab Tool Design ME Engineering normalized cost (from Markish) 11 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Recurring Cost Cost incurred per unit: Labor - fabrication - assembly - integration Material to manufacture -raw material - purchased outside production - purchased equipment Production support -QA - production tooling support - engineering support Labor Material Support 12 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Learning Curve As more units are made, the recurring cost per unit decreases. This is the learning curve effect. e.g. Fabrication is done more quickly, less material is wasted. n x xYY 0 Y x = number of hours to produce unit x n = log b/log 2 b = learning curve factor (~80-100%) 13 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Learning Curve 0.55 0 0.2 0.4 0.6 0.8 1 1020304050 Unit number C o s t of uni t b=0.9 Typical LC slopes: Fab 90%, Assembly 75%, Material 98% Every time production doubles, cost is reduced by a factor of 0.9 14 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics CASH AIRPLANE RELATED OPERATING COSTS: Crew Fuel Maintenance Landing Ground Handling GPE Depreciation GPE Maintenance Control & Communications Airplane Related Operating Costs CAROC is only 60% - ownership costs are significant! CAROC 60% 40% Capital Costs CAPITAL COSTS: Financing Insurance Depreciation 15 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Value Metric Need to provide a quantitative metric that incorporates cost, performance and revenue information. In optimization, need to be especially carefully about what metric we choose... Cost Module “Value” metric Performance Module Revenue Module 16 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics What is Value? Objective function could be different for each stakeholder e.g. manufacturer vs. airline vs. flying public Program related parameters vs. technical parameters cost, price, production quantity, timing Traditionally program-related design uncoupled from technical design Customer Value Shareholder Value Product Quality Schedule Cost Economic Value Added Demand Revenue EBIT System Design Price From Markish, Fig. 1, pg 20 Customer value derived from quality, timeliness, price. Shareholder value derived from cost and revenue, which is directly related to customer satisfaction. 17 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Value Metrics performance weight speed Traditional Metrics cost revenue profit quietness emissions commonality ... Augmented Metrics The definition of value will vary depending on your system and your role as a stakeholder, but we must define a quantifiable metric. 18 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Valuation Techniques Investor questions: How much will I need to invest? How much will I get back? When will I get my money back? How much is this going to cost me? How are you handling risk & uncertainty? Investment Criteria Net present value Payback Discounted payback Internal rate of return Return on investment 19 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Net Present Value (NPV) Measure of present value of various cash flows in different periods in the future Cash flow in any given period discounted by the value of a dollar today at that point in the future – “Time is money” – A dollar tomorrow is worth less today since if properly invested, a dollar today would be worth more tomorrow Rate at which future cash flows are discounted is determined by the “discount rate” or “hurdle rate” – Discount rate is equal to the amount of interest the investor could earn in a single time period (usually a year) if s/he were to invest in a “safer” investment 20 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Discounted Cash Flow (DCF) Forecast the cash flows, C 0 , C 1 , ..., C T of the project over its economic life – Treat investments as negative cash flow Determine the appropriate opportunity cost of capital (i.e. determine the discount rate r) Use opportunity cost of capital to discount the future cash flow of the project Sum the discounted cash flows to get the net present value (NPV)  NPV C 0  C 1 1r  C 2 1r 2 !  C T 1r T 21 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics DCF example Period Discount Factor Cash Flow Present Value 0 1 -150,000 -150,000 1 0.935 -100,000 -93,500 2 0.873 +300000 +261,000 Discount rate = 7% NPV = $18,400 22 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Risk-Adjusted Discount Rate DCF analysis assumes a fixed schedule of cash flows What about uncertainty? Common approach: use a risk-adjusted discount rate The discount rate is often used to reflect the risk associated with a project: the riskier the project, use a higher discount rate Typical discount rates for commercial aircraft programs: 12-20% Issues with this approach? 23 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Net Present Value (NPV) 0 (1 ) T t t t C NPV r  | -1500 -1000 -500 0 500 1000 1500 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 Cashflow DCF (r=12%) Program Time, t [yrs] Cashflow, P t [$ ] 24 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Payback Period How long it takes before entire initial investment is recovered through revenue Insensitive to time value of money, i.e. no discounting Gives equal weight to cash flows before cut-off date & no weight to cash flows after cut-off date Cannot distinguish between projects with different NPV Difficult to decide on appropriate cut-off date 25 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Discounted payback Payback criterion modified to account for the time value of money – Cash flows before cut-off date are discounted Overcomes objection that equal weight is given to all flows before cut-off date Cash flows after cut-off date still not given any weight 26 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Internal rate of return (IRR) Investment criterion is “rate of return must be greater than the opportunity cost of capital” Internal rate of return is equal to the discount rate for which the NPV is equal to zero IRR solution is not unique – Multiple rates of return for same project IRR doesn’t always correlate with NPV – NPV does not always decrease as discount rate increases  NPV C 0  C 1 1IRR  C 2 1IRR 2 !  C T 1IRR T 0 27 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Return on Investment (ROI) Return of an action divided by the cost of that action Need to decide whether to use actual or discounted cashflows revenue cost cost ROI  28 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Decision Tree Analysis (DTA) NPV analysis with different future scenarios Weighted by probability of event occurring 29 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Real Options Valuation Approach ?In reality: ?Cashflows are uncertain ?Ability to make decisions as future unfolds ?View an aircraft program as a series of investment decisions ?Spending money on development today gives the option to build and sell aircraft at a later date ?Better valuation metric: expected NPV from dynamic programming algorithm (Markish, 2002) 30 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Dynamic Programming: Problem Formulation The firm: – Portfolio of designs – Sequential development phases – Decision making The market: – Sale price is steady – Quantity demanded is unpredictable – Units built = units demanded Problem objective: – Which aircraft to design? – Which aircraft to produce? – When? 31 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Dynamic Programming: Problem Elements 1. State variables s t 2. Control variables u t 3. Randomness 4. Profit function 5. Dynamics Solution: Solve iteratively. >@ ? ? ? ˉ ? -    )( 1 1 ),(max)( 11 tttttt u tt sFE r ussF t S 32 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Dynamic Programming: Operating Modes How to model decision making? 33 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Example: BWB Blended-Wing-Body (BWB): – Proposed new jet transport concept 250-seat, long range Part of a larger family sharing common centerbody bays, wings, ... 34 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Example: BWB Simulation Run -4,000,000 -3,000,000 -2,000,000 -1,000,000 0 1,000,000 2,000,000 3,000,000 0 2 4 6 8 1012141618202224262830 time (years) cash flow ($K) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 2 4 6 8 1012141618202224262830 time (years) operating mode 0 20 40 60 80 100 120 qua ntity demande d per year mode demand 35 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Example: BWB Importance of Flexibility -10 -5 0 5 10 15 20 25 3 5 7 11 18 28 44 69 108 171 270 initial annual demand forecast program value ($B) dynamic programming deterministic NPV At baseline of 28 aircraft, DP value is $2.26B versus deterministic value of $325M 36 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Traditional Design Optimization ? Objective function: usually minimum weight ? Design vector: attributes of design, e.g. planform geometry ? Performance model: contains several engineering disciplines Performance Model Optimizer Design vector x Objective function J(x) 37 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Coupled MDO Framework Performance Model Cost Revenue Optimizer Valuation Market VD Price, Demand Cost Design vector x Objective function J(x) ?Objective function: value metric, e.g. NPV ?Simulation model: performance and financial ?Stochastic element 38 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Value-Based Optimization Results ?Boeing BWB case study ?475 passengers, 7800 nmi range ?Baseline: optimized for minimum GTOW ?Outcomes ?Comparison of min GTOW and max E[NPV] designs ?Traditional NPV vs. stochastic E[NPV] ?Effect of range requirement on program value ?Effect of speed requirement on program value 39 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Different Objectives, Different Designs ?New objective results in tradeoff: ?Lower structural weight, lower cost ?Higher fuel burn, lower price ?Net result 2.3% improvement in value ?Overall design very similar ?Constrained to satisfy design requirements ?Unable to move dramatically in design space Minimum-GTOW planform Maximum-value planform 40 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Deterministic vs. Stochastic Valuation Discount rates: 12% and 20% – Computational expense reduced, but NPV results are negative – E[NPV] for 12% design = 0.58% decrease – E[NPV] for 20% design = 3.7% decrease High-r d drives design to reduced development costs Traditional NPV not appropriate – As valuation metric – As optimization objective relative to max-E[NPV] design -10 -8 -6 -4 -2 0 2 1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930 Program Year Relative Cash Flow r_d = 12% r_d = 20% 41 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Range Specification Comparison of min-GTOW and max-E[NPV] design solutions E[NPV] for varying ranges relative to max-E[NPV] design Design decisions based on understanding of E[NPV] impact 0 0.2 0.4 0.6 0.8 1 1.2 5000 5500 6000 6500 7000 7500 8000 8500 9000 9500 10000 Range (nmi) Relative E[NPV] max E[NPV] min GTOW 42 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Speed Specification Comparison of E[NPV] and other metrics for varying speeds 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 0.78 0.8 0.82 0.84 0.86 0.88 0.9 0.92 Cruise Mach number R e lat iv e met r ic v a lue E[NPV] M*L/D M*P/D M*P*R/GTOW 43 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Lecture Summary Designing for value is crucial: for a program to be successful, we cannot focus exclusively on performance The definition of value is flexible, and will vary depending on the application and on your interest as a stakeholder Financial metrics can be used to quantifying value, but use caution in your choice of value objective function Cost and revenue are difficult to model – often use empirical data It is important that uncertainty and risk are handled appropriately There is much work to be done on this issue 44 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics References Brealey, R. & Myers, S., Principles of Corporate Finance, 7 th Edition, McGraw-Hill, NY 2003 Markish, J., “Valuation Techniques for Commercial Aircraft Program Design”, Masters Thesis, MIT Dept. of Aeronautics & Astronautics, June 2002. Markish, J. and Willcox, K., “Value-Based Multidisciplinary Techniques for Commercial Aircraft System Design”, AIAA Journal, Vol. 41, No. 10, October 2003, pp. 2004-12. 3HRSOHV5DQG:LOOFR[.9DOXH%DVHG0XOWLGLVFLSOLQDU\2SWLPL]DWLRQ IRU&RPPHUFLDO$LUFUDIW'HVLJQ$,$$ 3HRSOHV5DQG:LOOFR[.$9DOXH%DVHG0'2$SSURDFKWR$VVHVV %XVLQHVV5LVNIRU&RPPHUFLDO$LUFUDIW'HVLJQ$,$$ Roskam, J., Airplane Design Part VIII, 1990. Raymer, D., Aircraft Design: A Conceptual Approach, 3 rd edition, 1999. Schaufele, R., The Elements of Aircraft Preliminary Design, 2000. 45 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics System Cost Modeling This section will: - present a process for obtaining system cost estimates, particularly for space systems - provide cost-estimating relationships - describe how to assess uncertainty in cost estimates - provide a specific example: optical systems cost dWo, 5-6-2002 46 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Cost Breakdown Structure (CBS) Organizational Table that collects costs, covers: - research, development, test and evaluation (RDT&E) - production, including learning curve effects - launch and deployment - operations - end-of-life (EOL) disposal Space Mission Architecture Program Level Costs Space Segment Launch Segment Ground Segment Operations and Support Management Systems Eng Integration Payload Spacecraft Software “Systems” Launch Vhc Launch Ops S/C-L/V integration Facilities Equipment Software etc Personnel Training Maintenance Spares RDT&E Production Operations 47 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Cost Estimating Methods Basic techniques to develop Cost Models: (1) Detailed bottom-up estimating - identify and specify lower level elements - estimated cost of system is 6 of these - time consuming, not appropriate early, accurate (2) Analogous Estimating - look at similar item/system as a baseline - adjust to account for different size and complexity - can be applied at different levels (3) Parametric Estimating - uses Cost Estimation Relationships (CER’s) - needed to find theoretical first unit (TFU) cost 48 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Parametric Cost Models Are most appropriate for trade studies: Advantages: less time consuming than traditional bottom-up estimates more effective in performing cost trades more consistent estimates traceable to specific class of (space) systems Major Limitations: applicable only to parametric range of historical data lacking new technology factors, adjust CER to account for new technology composed of different mix of “things” in element to be costed usually not accurate enough for a proposal bid 49 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Process for developing CER’s Subsystem A Subsystem B Subsystem N …. Cost/parametric data Constant Year Costs Regression Analysis Preferred Form (Cost Model Assumption) Subsystem A Subsystem B Subsystem N …. $ Weight - kg $ b AW Computer Software Step 1 Develop Database File Step 2 Apply Regression Analysis Step 3 Obtain CER’s and Error Statistics Key statistics: R 2 , U Standard Error: RMSV 50 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Adjustment to constant-year dollars It is critical that cost estimated be based on a constant-year dollar bases. Reason: INFLATION YYN CRC  ? E.g. All costs are adjusted to FY92 (“Fiscal Year 1992”) Past Years Future Years Use actual inflation numbers Use forecasted inflation numbers e.g. 3.1% yearly inflation in U.S. See Table 20-1 on handout 92 93 94 1.040 1.037 1.034 1.115 FY FY FY R    Convert Oct-1991 cost to Oct-1994 costs 1 N RATE Ri  $ 1M in FY 1980 corresponds to $ 2.948M in FY 2005 (projected) 51 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Case: Modular Optics Cost Modeling Investigate economical viability of modular optics given performance constraints Focus on monolithic Cassegrain telescopes versus Golay-3 design Use real data and experience from ARGOS Gk Lk B Dk lk b dk sub-telescope plane (input pupil) combiner plane (exit pupil) foca l p la ne (image pupil) object k-th aperture beam combiner relay optics 52 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Literature Search Kahan, Targrove, “Cost modeling of large spaceborne optical systems”, SPIE, Kona, 1998 Humphries, Reddish, Walshaw,”Cost scaling laws and their origin: design strategy for an optical array telescope”, IAU, 1984 Meinel, “Cost-scaling laws applicable to very large optical telescopes”, SPIE, 1979 Meinel’s law: 2.58 0.37 [M$] (1980)SD ? 53 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Cost Modeling Approach Monolithic System Modular Golay System (A) Sub-telescope Total Cost: 6 total = C A + C B +C C (B) Relay optics and combiner (C) Detector Does not include development cost none 54 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Cost Estimation Relationships AA CLD D ? Next Step: Need to determine coefficients based on available commercial pricing data (A) Optical Telescope Assy: (B) Relay & Combining Optics: (C) Detector: CCD: Modular array telescope: TFU 1log 100% / / log 2 B AA CLDN BS D ao ?? ?? ao ??  cc pix CLn D ? (includes learning curve) Use ARGOS cost database 55 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Small Amateur Telescopes (I) 0 10 20 30 40 50 60 70 80 0 2000 4000 6000 8000 10000 12000 14000 Telescope Comparison Diameter Size[cm] Price [US$] DHQ f/5 DHQ f/4.5 D Truss f/5 Obsession f/4.5 Celestron G-f/10 56 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Small Amateur Telescopes (II) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.5 1 1.5 2 2.5 3 x 10 4 Telescope Diameter D [m] Telesco pe Purch ase Cost C [20 01 $] Telescope Cost CER (Aperture): C=28917*D 2.76 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 x 10 Power Coefficient D Cumul ative Weighte d Fitting Erro r Telescope CER fitting 8 Minimum yields best CER fit exponent D=2.76 57 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Professional Telescope OTA cost 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.5 1 1.5 2 2.5 3 3.5 4 x 10 5 Aperture Diameter D [m] OTA Cost [2001 $] Ritchey-Chretien Classical Cassegrain Company: Optical Guidance Systems (http:www.opticalguidancesystems.com) CERs for Ritchey-Chretien Classical Cassegrain Remarkable Result: virtually identical power law across completely different product lines. 2.80 376000 RC CD ? 2.75 322840 CC CD ? 58 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Relay and Combining Optics Cost of relay optics depends on: number and type of actuators: ODL, FSM, active translation stages, active pyramid mirrors sensing elements (CCD, quad cells etc) aperture magnification m a Quality requirements (RMS WFE) As interim solution use ARGOS cost database: Passive Optics: Collimators, Combiner, etc Active Optics: FSM, Fold Mirrors etc... m a = 10 $ 32,874.- $ 18,859.- About: $ 50,000.- 59 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics CCD Cost Models 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 0 0.5 1 1.5 2 2.5 3 x 10 4 Polynomial Fit of Compiled Data Square Root of Numbers of Pixels Pr i c e [ U S$ ] Least Squares Polynomial Fit Compiled Data 1.23 0.68 CCD pix Cn ? It appears that CCD cost also depends on factors other than raw pixel count. Need to investigate. AP-9 (KAF-6303E) 60 ? Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Break-Even Analysis 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.5 1 1.5 2 2.5 3 3.5 4 x 10 5 Equivalent Aperture D [m] Optical Syst ems Cost [2001 $] Break Even Cost Analysis Monolithic Golay-3 ARGOS Preliminary Analysis suggest crossover around 0.7 m Assumptions: N=3 n pix = 2048 Relay optics and combiner costs fixed