16.885
Aircraft Systems
Engineering
Cost Analysis
Karen Willcox
MIT
Aerospace Computational Design Laboratory
AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Outline
•
•
•
•
•
•
Lifecycle cost
Operating cost
Development cost
Manufacturing cost
Revenue
Valuation techniques
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Lifecycle Cost
Lifecycle :
Design - Manufacture - Operation - Disposal
Lifecycle cost :
Total cost of program over lifecycle
85% of Total LCC is locked in by the end of
preliminary design.
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Impact on LCC (%)
60
40
20
0
65%
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Disposal
Operation
and support
Manufacturing
and acquisition
80
Detailed design
100
Preliminary design,
system integration
Conceptual
design
Lifecycle Cost
95%
85%
Time
(From Roskam, Figure 2.3)
AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Operating Cost
¾ Airplane Related Operating Cost
(AROC)
¾ Passenger Related Operating Cost
(PROC)
¾ Cargo Related Operating Cost
(CROC)
¾ Systems Related Operating Cost
(SROC)
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SROC
10%
CROC
2%
PROC
18%
AROC
70%
AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Airplane Related Operating
Costs
CAPITAL COSTS:
Financing
Insurance
Depreciation
Capital
Costs
CAROC
40%
60%
CASH AIRPLANE RELATED
OPERATING COSTS:
Crew
Fuel
Maintenance
Landing
Ground Handling
GPE Depreciation
GPE Maintenance
Control & Communications
CAROC is only 60% - ownership costs are significant!
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
CAROC Breakdown per Trip
Control
& Comm
Ground
Handling
Other
3%
9%
7%
Landing
Crew
40%
6%
Fuel is roughly 20% of
60% of 70% of Total
Operating Cost
i.e. 8%
Maintenance
15%
Fuel
20%
typical data for a large commercial jet
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
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Tooling
Other
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
Non-Recurring Cost
AEROSPACE COMPUTATIONAL DESIGN LABORATORY
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Material
Support
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
Recurring Cost
AEROSPACE COMPUTATIONAL DESIGN LABORATORY
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.
Yx
Y0 x
n
Yx = number of hours to produce unit x
n = log b/log 2
b = learning curve factor (~80-100%)
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Learning Curve
1
Cost of unit
0.8
0.6
0.4
b=0.9
0.55
0.2
Every time
production
doubles, cost
is reduced
by a factor
of 0.9
0
0
10
20
30
40
50
Unit number
Typical LC slopes: Fab 90%, Assembly 75%, Material 98%
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Number of planes
Elements of a Cost Model
Engineering Data
& Performance
Build Schedule
120
80
40
0
2000
2010
2020
Recurring
Cost
2030
Year
Component Breakdown
Plane
Wing
COST
MODEL
Fuselage
Winglet Skin Ribs
NRC/lb
RC/lb
Weight
Subparts/lb
Learning Curve
NRC Distribution
2
NRC ($B)
Cost of unit
1
0.8
0.4
0
Non-Recurring
Cost
0
10
20
30
Unit number
40
1
50
0
2003
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2007
2011
Year
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2015
AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Typical Cost Modeling
1. Take empirical data from past programs.
2. Perform regression to get variation with
selected parameters, e.g. cost vs. weight.
3. Apply “judgment factors” for your case.
e.g. configuration factors, complexity
factors, composite factors.
There is widespread belief that aircraft
manufacturers do not know what it actually
costs to turn out their current products.
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Cost Modeling
• Aircraft is broken down into modules
– Inner wing, outer wing, …
– Modules are classified by type
•
Wing, Empennage, Fuselage, …
• Cost per pound specified for each module type
– Calibrated from existing cost models
– Modified by other factors
•
•
Learning effects
Commonality effects
• Assembly & Integration: a separate “module”
• 2 cost categories: development & manufacturing
Production run: a collection of modules
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Cost Modeling
Plane
Landing
Gear
Centerbody Wing
Winglet
Inner
Wing
Outer
Wing
Identifier
Weight
Material &
Equipment
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Payloads Final
Assembly
At this level, the
degree of detail can
range from e.g. “wing”
to “rivet”.
…
Area RC per
pound
Labor
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Propulsion Systems
Subparts
per pound
Support
NRC per
pound
Tooling
NRC time
distribution
Engineering
Other
AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Development Cost Data
non-dimensional labor hours
Baseline QA
Baseline Dev. Labs
Baseline Tool Fab.
Baseline
QA QA
Baseline
Baseline
Dev.Dev.
Labs
Baseline
Labs
Baseline
ToolTool
Fab.
Baseline
Fab
Baseline
ToolTool
Design
Baseline
Design
Baseline
M.E.M.E.
Baseline
Baseline Tool Design
.
Baseline
Engr.
Baseline
Engr.
Baseline M.E.
Baseline Engr.
non-dimensional time
Boeing data for large commercial jet
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Development Cost Model
• Cashflow profiles based on beta curve:
c(t ) Kt D 1 (1 t ) E 1
• Typical development time ~6 years
• Learning effects captured – span, cost
0.06
Support
0.05
normalized cost
Tool Fab
0.04
Tool Design
ME
0.02
(from Markish)
Engineering
0.01
0
normalized time
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Development Cost Model
Payloads
8%
Wing
20%
Systems
17%
Empennage
9%
Installed Engines
8%
Landing Gear
1%
Fuselage
37%
Representative non-recurring cost breakdown by parts for
large commercial jet (from Markish).
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Development Cost Data
For your reference: $/lb assembled from public domain
weight and total cost estimates plus representative NRC
breakdown by aircraft part (see Markish).
Engineering
ME
Tool
Design
Tool Fab
Support
Totals
40.0%
10.0%
10.5%
34.8%
4.7%
100.0%
Wing
$7,093
$1,773
$1,862
$6,171
$833
$17,731
Empennage
$20,862
$5,216
$5,476
$18,150
$2,451
$52,156
Fuselage
$12,837
$3,209
$3,370
$11,169
$1,508
$32,093
$999
$250
$262
$869
$117
$2,499
Installed Engines
$3,477
$869
$913
$3,025
$408
$8,691
Systems
$13,723
$3,431
$3,602
$11,939
$1,612
$34,307
Payloads
$4,305
$1,076
$1,130
$3,746
$506
$10,763
Landing Gear
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Manufacturing Cost Model
•
•
Aircraft built Æ modules required
Modules database
– Records quantities, marginal costs
– Apply learning curve effect by module, not by aircraft
Labor
Materials
Support
85%
95%
95%
time
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Manufacturing Cost Model
Final Assembly
6%
Wing
27%
Payloads
11%
Systems
6%
Installed Engines
9%
Empennage
10%
Landing Gear
3%
Fuselage
28%
Representative recurring cost breakdown by parts for large
commercial jet (from Markish).
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Manufacturing Cost Data
For your reference: $/lb values assembled from public
domain weight and total cost estimates plus representative
RC breakdown by aircraft part (see Markish).
Labor
Materials
Other
Total
$609
$204
$88
$900
$1,614
$484
$233
$2,331
Fuselage
$679
$190
$98
$967
Landing Gear
$107
$98
$16
$221
Installed Engines
$248
$91
$36
$374
Systems
$315
$91
$46
$452
Payloads
$405
$100
$59
$564
Final Assembly
$58
$4
$3
$65
Wing
Empennage
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
NASA Cost Models
Online cost models available at
http://www.jsc.nasa.gov/bu2/airframe.html
e.g. Airframe Cost Model
- simple model for estimating the development and
production costs of aircraft airframes
- based on military jet data
- correlation with empty weight, max. speed, number of flight test vehicles, and production quantity
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Revenue Model
Revenue model must predict market price
and demand quantity.
180
90
160
80
price ($M)
120
100
80
60
40
60
50
40
30
20
10
20
0
1985
A300
A310
A330
A340
747
767
777
MD-11
70
deliveries
767-200ER
767-300ER
777-200
777-300
747-400
MD-11
A300
A330
A340
140
1990
1995
0
1980
2000
1985
1990
1995
2000
year
year
Historical wide body data from Markish. No correlation found
between price and quantity.
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Aircraft Pricing
Cost-Based Pricing
Cost + Profit = Price
Personal aircraft
Business jets?
Military aircraft
Market-Based Pricing
Performance
Operating Cost
Market
Value
Competition
Passenger Appeal
Commercial transport
Source: Schaufele
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Commercial Aircraft Pricing
PRICE
Total AROC
CAROC
• Total Airplane Related
Operating Costs are fairly
constant.
• Aircraft price must balance CAROC.
COST/WEIGHT
TRADE-OFF
(Capital costs)
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Business Jet Empirical Data
Figure A7 in Roskam:
AMP1989 = log-1{0.6570 + 1.4133 log WTO}
AMP1989 is predicted airplane market price in 1989
dollars
Take-off weight: 10,000 lb < WTO < 60,000 lb
BUT Gulfstream GIV and 737 BJ versions do not fit
the linear trend.
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Commercial Jet Empirical
Data
Figure A9 in Roskam:
AMP1989 = log-1{3.3191+ 0.8043 log WTO}
AMP1989 is predicted airplane market price in 1989
dollars
Take-off weight: 60,000 lb < WTO < 1,000,000 lb
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Military Aircraft Empirical
Data
Figure A10 in Roskam:
AMP1989 = log-1{2.3341+ 1.0586 log WTO}
AMP1989 is predicted airplane market price in 1989
dollars
Take-off weight: 2,500 lb < WTO < 1,000,000 lb
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Revenue Model: Price
• Assumption: market price based on
1. Range
2. Payload
3. Cash Airplane-Related Operating Cost (CAROC)
• Regression model:
P
D
k1 (Seats) k 2 (Range) f (CAROC )
• Note that speed does not appear. No significant
statistical relationship between price and speed
was found in available data.
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Revenue Model: Price
Narrow bodies:
0.735(Seats )1.91 0.427(Range) f (CAROC)
Narrow bodies
Estimated price
Estimated
price($M)
($M)
P
80
70
60
50
40
30
y=x
Airbus
Boeing
20
10
0
0
10
20
30
40
50
60
70
80
Actual
price
($M)
Actual
price ($M)
Model from Markish, price data from Aircraft Value News, The Airline Monitor, 2001.
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Revenue Model: Price
Wide bodies:
0.508(Seats)2.76 0.697(Range) f (
CAROC)
Wide bodies
160
Estimated
($M)
Estimatedprice
price ($M)
P
140
120
100
80
60
y=x
Airbus
Boeing
40
20
0
0
20
40
60
80
100
120
140
160
Actual
price ($M)
Actual
price
($M)
Model from Markish, price data from Aircraft Value News, The
Airline Monitor, 2001.
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Revenue Model: Quantity
• Demand forecasts
– 3 sources: Airbus; Boeing; Airline Monitor
– Expected deliveries over 20 years
– Arranged by airplane seat category
• Given a new aircraft design:
4000
Airbus
3500
Airline Monitor
3000
Quantity
Quantity
– Assign to a seat category
– Assume a market share
– Demand forecast Æ
20-year production
potential
Boeing
2500
2000
1500
1000
500
0
100
125
150
175+
200
250
300
350
400
500+
Seat
Category
Seat
Category
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Revenue Model: Dynamics
Expected aircraft deliveries: forecasted
Actual deliveries: unpredictable
Observe historical trends: growth rate, volatility
400
350
300
250
units
narrow
200
y = 94.571e0.0228x
R2 = 0.3724
150
100
50
wide
y = 52.776e0.0167x
R2 = 0.4092
40
37
34
31
28
25
22
19
16
13
10
7
4
0
1
•
•
•
6-mo. period
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Valuation Techniques
The top 5 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
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
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
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Calculating NPV
• Forecast the cash flows 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)
C1
C2
CT
NPV C0 !
2
T
1r 1r 1 r 9/19/2004
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
NPV 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%
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NPV =
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$18,400
AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Discount Rate
• One of the problems with NPV: what discount rate
should we use?
• 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%
• The higher the discount rate, the more it does not
matter what you do in the future...
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
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
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Discounted payback
• Payback criterion modified to account for the time
value of money
– Cash flows before cut-off date are discounted
• Surmounts objection that equal weight is given to all
flows before cut-off date
• Cash flows after cut-off date still not given any weight
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
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
NPV
C1
C2
CT
!
C0 2
T
1 IRR 1 IRR
1 IRR 0
• 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
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Decision Tree Analysis
• NPV analysis with different future scenarios
• Weighted by probability of event occurring
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Dynamic Programming
• A way of including uncertainty and flexibility in the
program valuation
• Key features:
• Certain aspects of the system may be uncertain, e.g. the demand quantity for a given aircraft = UNCERTAINTY
• In reality, the decision-maker (aircraft manufacturer) has
the ability to make decisions in real-time according to
how the uncertainty evolves = FLEXIBILITY
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
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?
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Dynamic Programming:
Problem Elements
1. State variables
2. Control variables
st
ut
3. Randomness
4. Profit function
5. Dynamics
1
½
­
F
t (
st )
max ®S t ( st , ut )
Et >Ft 1 (
st
1 )
@¾
ut
1 r
¿
¯
•
Solution:
•
Solve iteratively.
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Dynamic Programming:
Operating Modes
How to model decision making?
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
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, ...
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Image taken from NASA's web
site: http://www.nasa.gov.
AEROSPACE COMPUTATIONAL DESIGN LABORATORY
operating mode
16
120
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
mode
demand
100
80
60
40
20
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
18
20
22
24
26
28
30
quantity demanded
per year
Example: BWB Simulation
Run
0
time (years)
3,000,000
2,000,000
cash flow ($K)
1,000,000
0
0
2
4
6
8
10
12
14
16
-1,000,000
-2,000,000
-3,000,000
-4,000,000
time (years)
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
Example: BWB Importance
of Flexibility
25
dynamic programming
program value ($B)
20
Net Present Value
15
10
5
0
-5
3
5
7
11
18
28
44
69
108 171 270
-10
initial annual demand forecast
At baseline of 28 aircraft, DP value is $2.26B versus NPV
value of $325M
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY
References
Airbus Global Market Forecast, 2000-2019. Appendix G, Detailed passenger fleet results, p.
74.
Aircraft Value News Aviation Newsletter www.aviationtoday.com/catalog.htm
The Airline Monitor, ESG Aviation Services.
Boeing Current Market Outlook, 2000. Appendix B, p. 42. Jane's All the World's Aircraft. London : Sampson Low, Marston & Co., 2001.
Markish, J. Valuation Techniques for Commercial Aircraft Program Design, S.M. Thesis, MIT, June 2002.
Markish, J. and Willcox, K. “Valuation Techniques for Commercial Aircraft Program Design,” AIAA Paper 2002-5612, presented at 9th Multidisciplinary Analysis and Optimization
Symposium, Atlanta, GA, September 2002.
Markish, J. and Willcox, K., “A Value-Based Approach for Commercial Aircraft Conceptual Design,” in Proceedings of the ICAS2002 Congress, Toronto, September 2002.
NASA Cost Estimating website, http://www.jsc.nasa.gov/bu2/airframe.html
Roskam, J., Airplane Design Part VIII, 1990.
Raymer, D., Aircraft Design: A Conceptual Approach, 3rd edition, 1999.
Schaufele, R., The Elements of Aircraft Preliminary Design, 2000.
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AEROSPACE COMPUTATIONAL DESIGN LABORATORY