Spring
2010
SYSTEM
REQUIREMENTS
REVIEW
Chad Carmack
Aaron Martin
Ryan Mayer
Jake Schaefer
Abhi Murty
Shane Mooney
Ben Goldman
Russell Hammer
Donnie Goepper
Phil Mazurek
John Tegah
Chris Simpson
Table of contents
INTRODUCTION ............................................................................................................................................. 1
Mission statement .................................................................................................................................... 1
Outline ...................................................................................................................................................... 2
MARKET AND CUSTOMERS ........................................................................................................................... 3
Projected Business Market ....................................................................................................................... 3
Cabin Model .............................................................................................................................................. 5
Mission Sketch ........................................................................................................................................ 12
Design Mission ........................................................................................................................................ 13
Operating Mission ................................................................................................................................... 14
SYSTEM DESIGN REQUIREMENTS ............................................................................................................... 15
The House of Quality............................................................................................................................... 15
Compliance Matrix .................................................................................................................................. 18
Benchmark Aircrafts and New Technology ............................................................................................. 20
INITIAL SIZING ESTIMATES .......................................................................................................................... 23
Database ................................................................................................................................................. 23
Constraint Diagram ................................................................................................................................. 25
Initial Estimates ....................................................................................................................................... 26
Summary ................................................................................................................................................. 32
Next Steps ............................................................................................................................................... 32
REFERENCES ................................................................................................................................................ 33
APPENDIX A ................................................................................................................................................. 34
INTRODUCTION
The past decade has seen a considerable amount of economic advancement take
place in the international markets, where countries such as China and India have become
industrial leaders. Due to such rapid growth, many fortune 500 companies seek to take
advantage of this situation by expanding their businesses in these countries. Keeping this in
mind, designing a long range aircraft with time saving capabilities is promising.
The team will target multinational corporations as their main clients, for whom time
is money. Providing an aircraft which will save clients time and help increase revenue is a
crucial design objective. The proposed aircraft will also be designed to meet and exceed all
of the environmental N+2 standards set forth by NASA.
Research, use of historical data, and other tools such as computational packages, are
being used to design the aircraft. The team has taken into consideration every customer
requirement and has developed an aircraft catered to meet these requirements. The goal of
the project is to design an aircraft that gives its customer a truly elite ownership
experience.
Mission statement
The main goal of this project is to design a cost effective aircraft with high speed
capabilities, which is able to transport its customers to their desired locations in the least
amount of time possible. The project’s secondary goal is to meet NASA’s N+2 criteria,
reducing the environmental impact of the aircraft. The proposed aircraft will be able to
compete with other aircraft in the ultra long range category.
1
Outline
This report is comprised of five sections. The first section will give the reader a brief
market overview discussing customer needs and benefits. It will also discuss current
market sizes and address competitor’s aircraft. The next section is the concept of
operations section, also referred to as the CONOPS. In this part of the paper, the team will
address crucial components of the project’s goals such as customer satisfaction and its
affect its influence on the aircraft. The CONOPS section will also cover expected flight
ranges and required runway lengths, the aircraft’s payload and passenger capability,
mission sketches, and segment descriptions.
The system design requirements section follows the CONOPS section, and contains
the house of quality in detail. It also explains how the team intends on meeting NASA’s N+2
goals, and introduces new technologies that might be integrated to assist the design in
meeting these goals.
Following system design requirements, initial sizing estimations will be computed.
These estimates contain values such as; lift to drag ratios, Specific Fuel Consumption (SFC),
and empty weight fractions. The final section discusses the projects future design goals.
This includes the future steps which will need to be taken in order to accomplish the
objective of the project.
2
MARKET AND CUSTOMERS
Primary customers
Prior to starting the design process, a market analysis study was conducted to find
the ideal market niche to accommodate. Identifying the primary client was the first step. In
the past 2 years there has been a substantial plummet in the financial market. The only
groups of people that have not changed their outlook as a result of this downfall are the
wealthier side of society, including CEO’s of multinational corporations and celebrities. This
elite class of passenger prefers a luxurious, fast, and private travel experience. Using a
public airport is usually a very inconvenient and time consuming endeavor. Historically
this side of society has a proven financial stability track record and was deemed to be the
primary customer. With this historically stable clientele, the outlook for expected aircraft
sales in this class has remained and is expect to stay stable and maintain steady growth.
Other possible clientele include fractional air services.
Projected Business Market
According to the Research firm Frost & Sullivan, the Middle East and Asia are one of
the few world regions where the long haul business jet market has registered growth. The
air-taxi segment is also expected to be a major driver for this market. According to the
Frost & Sullivan’s data, the Middle East logged 93,000 business jet movements in 2008, this
number was projected to reach 103,000 last year. Growth is expected to continue, reaching
160,000 jets in 2018. Frost & Sullivan projected the compound annual growth rate of
business jet movements in the Middle East will be about 6.21 percent from 2008 to 2018.
Figure 1 depicts markets in various regions of the world.1
3
Figure 1: Business Aircraft Expansion Percentage.
As the economy recovers from the current downturn, orders for business aircraft
are expected to increase, which should sustain sales for new business jets over the next 10
years. The sharp contraction of the U.S. economy and ensuing worldwide recession during
2008-2009 is expected to cause a significant reduction in the near term demand for
business jets. Many original equipment manufacturers (OEMs) have and will likely
continue to receive order cancelations in early 2009 . Order intake is forecast to fall as low
as 375 units in 2009, and is expected to improve by the end of the year, reaching 2008
levels of approximately 1,400 units per year by 2013. 2
4
Figure 2: Purchase Plan Analysis.
Figure 2 depicts a pie chart which breaks down intended purchases by aircraft type.
The chart clearly shows that the bulk of jets to be purchased are of the large cabin class.
The following pages discuss the technical details of our design, which is believed to offer
the best possible solution for the customers. 2
Cabin Model
The aircraft was conceived as a 16-passenger business class jet. Accordingly, the
initial sizing of the aircraft was directly dependent on an efficient and attractive layout
capable of comfortably seating 16 passengers.
Design began by choosing the general
shape of the cabin, and a cylindrically-shaped cabin was found to be of the greatest benefit
due to its association with reduced manufacturing costs. Additionally, this design would
simplify the pressurization of the cabin.
Once the shape of the cabin was determined, the next step was to scale the aircraft.
The two major dimensions requiring attention in the sizing of the cabin were its length and
5
interior diameter. The aircraft that is most similar (currently in certification testing) is the
Gulftsream G650. Therefore, when determining the cabin’s diameter (and length), figures
were checked against Gulfstream’s to ensure an additional level of realism. Numerous
layouts were considered before settling on one which offers the client a wide variety of
seating arraignments and ample personal space.
The cabin currently accommodates
seating for up to 16 passengers and a resting area for 2 crew members. The cabin is
furnished with 2 sofas, 6 individual seats, and conference seating for 4. It is also equipped
with a large galley and two lavatories, one at the front of the cabin and one positioned aft of
the main cabin where the tail meets the fuselage. The main entrance and exit is positioned
between the forward lavatory and the nose of the aircraft.
Even with all of the
aforementioned amenities, the cabin still boasts a personal volume of 81.5 cubic feet. Note
that this volume is calculated for a full cabin of 16 passengers, which means that any flights
carrying fewer than 16 passengers (which is expected to be quite often) will allow for even
more personal space. The graph in Figure 3 shows a correlation between trip duration and
cabin space. This graph was provided from Torenbeek, synthesis of subsonic aircraft
design. From this graph, it is possible to see that with a volume of 81.5 cubic feet per
passenger, our aircraft will allow 16 passengers to fly in “plush” comfort for up to a four
hour trip. As the number of passengers decreases, each passenger will have more room and
the amount of time for the “plush” category will be increased. The trend lines for this plot
are linear, so it is also possible to continue them out to a max flight time of 12 hours. Even
with a full cabin of 16 passengers, the aircraft boasts comfortable accommodations for a
full length flight.3
6
Figure 3: Comfort vs. Duration.
However, this number is low in comparison to the G650, due to two main factors:
the G650’s greater cabin length and elliptical cabin shape. This style of cross section has a
flatter lower section to make better use of internal volume. Still, the team’s design is both
attractive and efficient, and therefore its general shape will not be changed at this point. By
affording accurate sizing and spacing to the cabin layout, an estimate of its initial length
was found to be an even 50 feet. The cabin’s inner diameter was chosen after careful
consideration of current similarly scaled business jets and the client’s needs.
The length of the nose and tail are usually sized according to a fineness ratio,
calculated to be the ratio of the length of the section divided by the cabin diameter. Sizing
7
began by investigating the range of fineness ratios currently in use and it was found that
the nose of current aircraft usually have a fineness ratio between 1.5 and 2, while the tail of
current aircraft usually have a fineness ratio of between 2.5 and 3. At this point in the
design, no consideration for the aerodynamic impact from fineness ratio has been made;
aside from staying within current ranges. It is however recognized that, particularly for a
transonic aircraft, the fineness ratio of the aircraft plays a critical role in drag production.
The nose and tail were designed with fineness ratios of 1.6 and 2.7, respectively, based
upon visual cues from current high performance business jets. However, these lengths are
by no means finalized and changes are anticipated further into the design process. Because
the fineness ratio is a comparison of section length to cabin diameter, the resolution of
these ratios also means that the first estimates for the lengths of the nose and tail. These
estimates are 1.6*(8.83 feet) = 14.17 feet for the nose and 2.7*(8.83 feet) = 23.9 feet for the
tail. This provided the first practical approximation of the aircraft’s total length at 88 feet.
The aircraft’s total fineness ratio was found by dividing the aircrafts total length by
the cabin diameter. Currently the aircraft boasts a fineness ratio of 9.96. Comparing this to
the G650’s ratio of 11.08, this aircraft’s fineness ratio is certainly well within realistic
range. This is based on the fact that this aircraft is designed to compete with the G650 at its
own transonic flight regime. Also, while the fineness ratio is not the ultimate choice when it
comes to performance, it is a very important characteristic to consider and likely one
whose impact will have to be weighed against other necessary performance characteristics
in the future. Comparing the nose and tail to the main cabin visually, the chosen fineness
ratio set the aircraft’s lines in terms of length ratios, visually depicted in Figure 4 below.
8
Figure 4: Effect of Overall Fineness Ratio on Aircraft Length.
Resulting from the interior sizing is an aircraft cross-section with two rows of
outboard seating, and a center aisle from the fore end of the cabin until the conference
area. Primary dimensions for the interior cross sectional area are shown in Figure 5, and a
dimensioned top-view of the main cabin is provided in Figure 6, with a detailed drawing
showing seating dimensions in Figure 7.
Figure 5: Interior Main Cabin Cross Section.
9
Figure 6: Top View of Interior Cabin Dimensions.
Figure 7: Detail of Cabin Amenity Dimensions.
While the specifications of the aforementioned cabin layout can provide passengers
with a plush flight experience for a set duration, a cabin re-design is currently underway to
further heighten passenger comfort.
The incorporation of an industry-competitive
quantity of windows placed in a manner to provide ample passenger view while retaining
cabin flexibility is currently being incorporated in the cabin layout. A “designing from the
cup holders”, comfort first, interior design mentality is shaping the next generation of cabin
interior. The incorporation of minor amenities such as the very cup holders, individual
ventilation outputs, the infringement of chair reclining on other passengers, aisle widths
and personal privacy concerns are also under current refinement.
In addition to the chair and sofa design, passenger comfort was addressed in
regards to lavatory size and placement.
The rear lavatory’s location aft of the rear
bulkhead provides a visual separation from the passengers in the main cabin, but maintains
a close proximity to the conference area and galley. Emergency exit placement was chosen
10
from both safety, as well as spatially contributing perspectives. The emergency exit was
placed approximately mid-length in the cabin, and on the opposite outboard wall of the
main cabin door. This location provided both an easily accessible location for exit from the
conference and mid-cabin seating areas, and further ensured a wide aisle width through
the conference seating, providing a spatial break from the non-conference seating.
Location of the emergency exit and other key features of the aircraft interior are visible in
Figure 8 below.
Figure 8: Aircraft Interior Key Features
Focusing not only on passenger comfort, crew comfort on extended flights is
currently under design refinement. While the two crew seats can be fully reclined, a crew
rest area containing two stacked bunks is under development, though its isolation from the
main cabin without infringement upon aisle width requires further assessment.
The
expanded crew rest will provide a bunk for an additional pilot and a current crew member
during extended flights. Cabin adjustment with the incorporation of the crew rest area will
necessitate a re-arrangement of interior cabin space, incorporating the currently unused
space along the right outboard wall at the rear of the main cabin. A rendered image of the
current cabin layout is provided in Figure 9 below for visual reference.
11
Figure 9: Rendered Image of Current Cabin Mockup
CONCEPT OF OPERTATIONS
Mission Sketch
It is understood that with businesses time is money so the need to move people
quickly and efficiently to and from meetings is of utmost importance. In today’s economy,
businesses are not necessarily tied down to one country but instead are spread across
several locations around the world.
This
makes
personal
meetings
substantially more difficult. Flying
conventional commercial flights to
and from meetings, while seemingly
cheaper than taking a business jet,
actually incurs larger costs due to
the major losses in time. It is this
dilemma of unnecessary and costly
Figure 10: Representative City Pairs 4
12
wasted time that this project looks to address. A key component of this aircraft is to
provide a long range business jet that enables truly global transportation. With a still-air
range of 6350 nautical miles, this aircraft is capable of making non-stop international
flights; eliminating the costly layovers associated with commercial flights and shorter
ranged business jets. As seen in the following table, the range of 6350 nautical miles puts
several desirable destinations well within reach.
Table 1: Distances between City Pairs.
Los Angeles
to
Seoul
5209 nm
Dallas
to
Moscow
5035 nm
Los Angeles
to
Beijing
5432 nm
New York
to
Dubai
5949 nm
Chicago
to
Tokyo
5452 nm
Los Angeles
to
Hong Kong
6309 nm
Design Mission
The design mission was developed and optimized with the city pair of Los Angeles
and Hong Kong in mind. The design mission consists of eight mission legs between nine
points as illustrated in the following figure.
Figure 11: Design Mission Flight Plan.
13
The first leg of the mission, from points 0 to 1, is taxi and takeoff to an altitude of 50
feet. From points 1 to 2 is the climb portion of the mission where the aircraft climbs at best
rate to an altitude of 42,000 feet. From there the aircraft enters the cruise leg of the
mission, between points 2 and 3, and begins cruising at a Mach number of 0.85 for 6350
nautical miles. Cruise is then followed directly by a no range credit descent to land where
the aircraft will attempt a landing, from points 4 to 5, climb to an altitude of 5000 feet at
best rate climb, points 5 to 6, and commence cruise to an alternate airport 200 nautical
miles away. Once at the alternate airport, the aircraft will enter a holding pattern for 45
minutes, from points 7 to 8, and then begin a no range credit descent to land. Finally, the
aircraft lands at the alternate airport and completes the last mission leg at point 9 when it
comes to a stop.
Operating Mission
While the design mission is the optimal, most efficient use of this aircraft, several
other operating missions can be made by this aircraft as well. One such operating mission
would be flying from New York to Los Angeles. The distance between the two cities, which
is 2146 nautical miles, falls well within the maximum still-air range of 6350 miles. To
compensate for the largely unused range, the aircraft can then be flown at its maximum
Mach number of 0.9 at a maximum capacity of 16 passengers. This range tradeoff allows for
tremendous flexibility in speed and capacity for shorter ranged flights.
14
SYSTEM DESIGN REQUIREMENTS
The House of Quality
A house of quality was constructed as the primary tool of Quality Function
Deployment (QFD) for this project. The house of quality is shown in Figure 12. The house
was built in the traditional order, starting with an analysis of customer needs. Eleven
customer needs were identified, and organized into 4 groups. The importance of each need
was then ranked on a scale of one to ten. Since no customers were available, these tasks
were completed using the design team’s beliefs of how customers would perceive the
product. The customer attributes of a relatively fast aircraft, having a long range, were
considered the most important. After the importance of the attributes was assessed,
competing products were compared in terms of these needs. Two competing products
were selected from the ultra-long range jet market. These aircraft were the Gulfstream
G650, and the Bombardier Global Express XRS. For both competing aircraft, the same two
areas contained the greatest room for improvement. These were the nitrous oxide
emissions of the aircraft (desired to be lower), and the ability of the aircraft to fly out of
small airports. Note that certain benchmark values in Figure 12 are highlighted to indicate
that there was not enough information available to make a firm conclusion. After these
benchmarks were determined, the engineering characteristics for the design were
determined. These engineering characteristics were measurable specifications that would
control the design’s ability to meet customer needs. Threshold values were also identified
as these requirements were drafted. Twelve engineering requirements were listed, created
a matrix of 132 cells.
15
Each of the cells was evaluated in terms of the strength of the relationship between
a customer attribute and its corresponding engineering characteristic. There was a strong
relationship between the aircraft’s need to be “fast” (one of the most important customer
attributes) and the aircraft’s cruise mach, which had a threshold value set at 0.8. This value
was established based on the idea that the aircraft could not be considered fast by any
customer if it cruised at a speed noticeably slower than most modern jet transports. The
other customer attribute judged to be particularly important, a long flight range, was most
strongly affected by the fuel consumption of the aircraft and its design range. A threshold
value of 6000 nautical miles was set for the design range at this phase, as a result of
studying historical ultra-long range jet specifications and market segmentation. After all of
the relationships between the customer attributes and the engineering requirements were
determined, the importance of each engineering characteristic was calculated from the
strength of its relationships with the customer needs. There were three engineering
characteristics which came out to be in the highest range of importance. These
characteristics were cruise mach, takeoff distance, and fuel consumption.
After the house of quality’s matrix was complete, the interactions between the
various engineering characteristics were assessed. Multiple strong relationships were
observed with both fuel consumption and passenger capacity. It was determined that fuel
consumption had a strongly positive relationship with both nitrous oxide emissions and
range. It was also determined that passenger capacity had a strongly negative relationship
with takeoff distance, range, and variable cost. While the positive relationships associated
with fuel consumption are worth noting as opportunities to easily improve the design; the
16
negative relationships associated with the aircraft’s capacity are particularly important
because they are indicative of potential future tradeoffs.
Figure 12: House of Quality.
17
Compliance Matrix
The compliance matrix is a key component of the design process. The compliance
matrix helps keep track of goals and aids in determining the current status of the design. A
compliance matrix lists the important engineering parameters and assigns target and
threshold values for each of those parameters, along with an estimate of each value in the
current design.
The engineering characteristics in the compliance matrix are the same as those in
the house of quality that address the needs of the customer. The target values are the
values of the engineering parameters that are thought to best fit the customer needs.
These target values are the ultimate goals of the aircraft design. The threshold values are
the values of each of the parameters that were determined to be the minimum
requirements of the final product. Some threshold values are determined by laws and
regulations, while others are determined by the design team in order to establish a baseline
for the design.
The target and threshold values of each of the engineering parameters in the
compliance matrix were chosen for different reasons. Both the threshold and target values
of the still air range were chosen based on distances between major destinations and
specifications of similar existing aircraft. A still air range of 6350 nautical miles provides a
route between many of the world’s most popular business travel destinations.
The cruise altitude is an important parameter because if the aircraft can climb above
the traffic, it can fly more quickly to the destination. For this reason, the target value of
cruise altitude is 45000 ft, and the threshold is 40000 ft.
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The target value for the LTO NOx emissions is 75% below the levels in CAEP 6. This
is a number that is taken directly from the N+2 goal set by NASA. The threshold value is
60% below the levels in CAEP 6, which corresponds to the NASA’s N+1 goal. Similarly, the
cumulative certification noise level target corresponds to the N+2 goal of 42 dB below the
stage 4 level, and the threshold value corresponds to the stage 4 level.5
The N+2 goal set by NASA also includes a 40% reduction in fuel burn. The target
value for fuel burn was determined by deducting 40% from the fuel burn of a similar
aircraft, the Gulfstream G650. Similarly, the threshold value was determined by the 33%
reduction for the N+1 goal. The fuel burn of the G650 was determined by dividing the
maximum fuel capacity by the maximum range due to the lack of published data regarding
the fuel burn for the G650. Inverting these numbers gives the specific range.5
The sill height is an important parameter because the passengers need to be able to
enter and exit the aircraft without necessarily requiring special services from the airport.
This means that the door to the aircraft needs to be reasonably close to the ground to make
it easier to incorporate stairs into the aircraft. The target and threshold values were
chosen as 4 feet and 5 feet, respectively.
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Table 2: Requirement Compliance Matrix
Performance Characteristic
Target
Threshold
Current
Headwind Range
6300 nmi
6000 nmi
6300 nmi
Takeoff Distance Field Length
6000 ft
7000 ft
6000 ft
Maximum Passengers
17
8
16
Cruise Mach
.85
.8
.85
Cruise Altitude
45000 ft
40000 ft
45000 ft
Cabin Noise
60 dB
70 dB
65 dB
LTO NOx Emissions
Cumulative Certification Noise Level
Specific Range
CAEP 6 -75% CAEP 6 -60% CAEP 6 -70%
232 dB
274 dB
274 dB
0.263 nmi/lb 0.208 nmi/lb 0.161 nmi/lb
Loading Door Sill Height
4 ft
5 ft
4 ft
Variable Costs
$4100/hr
$4300/hr
$4100/hr
Benchmark Aircrafts and New Technology
One of the major goals of the project is to reduce fuel consumption. Green
technology will be used to reduce emissions, but the most effective method to reduce
carbon dioxide and NOx output is by reducing overall fuel consumption. An aircraft had to
be selected for a fuel consumption benchmark. The Gulfstream G650 currently performs a
similar design mission with a fuel consumption rate of 0.158 nm/lbs. This figure was
calculated by dividing the maximum range by the maximum fuel weight. The design
mission was to reduce current fuel burn by as much as 40%. A reduction of 40% in fuel
consumption based upon the G650 would be a fuel burn of .265 nm/lbs. A modern aircraft
20
that has a similar fuel consumption is the Gulfstream G150 with a current fuel consumption
of .287 nm/lbs. The G150 is considerably smaller than the current aircraft proposed in the
design; therefore such a large reduction in fuel burn will require extensive use of advanced
technology and engineering. 6
The reduction in fuel consumption is just one of the many goals proposed by NASA’s
subsonic fixed wing program. NASA has set four fundamental goals referred to as N+2 for a
subsonic fixed wing business aircraft set for production in the 2020 timeframe. The four
goals are 42 dB below stage 4 certification, 75% reduction in NOx emissions, 40%
reduction in fuel consumption, and a performance field length reduction of 50%. The first
three design goals will be met by using an innovative propulsion system. Due to the long
range and high capacity of the current design mission, the reduction in field length will
most likely not be met. 5
The team currently proposes to use advanced technologies that are currently under
research to achieve NASA’s N+2 goals. The first design component will be the use of
composite materials. Aircraft such as the Boeing 787 have achieved a significant empty
weight reduction by utilizing composite materials in the majority of the airframe. A
reduction in aircraft weight will allow for reduced fuel consumption and a reduction in take
off length. Another advanced technology that is being explored is the use of an unducted
propfan for a propulsion system. An unducted propfan is an advanced engine design that
would incorporate two counter rotating fans that would be directly connected to the
engine’s turbines. General Electric explored the unducted propfan concept in the 1980s
and 1990s and even flew a design named the GE36 on a Boeing 727 test aircraft. The
21
project had problems with noise levels and vibration due to the wave drag created by the
high speed fans. The noise levels and plummeting fuel costs of the 1990s caused the
cancellation of the project. Currently, Rolls-Royce, General Electric, and NASA are working
together to achieve a noise reduction level in the unducted propfan concept. “The outcome
of this work is that we are now confident that open-rotor-powered aircraft will be quieter
than any equivalent aircraft flying today and that it will comfortably meet Stage 4 noise
legislation,” says Robert Nuttal, Rolls-Royce’s vice president of future programs strategic
marketing (Norris 54). The unducted propfan technology is currently the only possible
solution to meet NASA’s N+2 goals within the specified time frame.7
In fact, NASA’s environmentally responsible aviation program (ERA) is devoting
much of its research in the subsonic fixed wing project to the unducted propfan technology.
“ERA is focused on the goals of NASA’s N+2, a notional aircraft with technology primed for
development in the 2020 time frame as part of the agency’s subosonic fixed-wing
program,” Guy Norris. Nuttal was quoted in Aviation Week’s December 14, 2009 issue as
saying, “So far the GE-NASA experience seems to echo that of Rolls-Royce. We are able to
confirm that the fuel burn will be 25-30% better than today’s products. And, because of the
engine cycle of the open rotor; the nitrous oxide will be 20% lower than another engine
with an equivalent combustor technology. We are now preparing for the next tranche with
the next build of the rig taking place in Q2 2010”. Because of the current development
being made on the concept and NASA’s faith in the technology, the team feels it is an
appropriate decision to anticipate using unducted propfans as a propulsion system for the
design project. 7
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INITIAL SIZING ESTIMATES
Database
A database of aircraft was developed to be used in sizing the aircraft to meet the
requirements for achieving the design mission. Other aircraft with similar weights, ranges,
number of passengers, and purposes were included. The aircraft in the database are shown
in Table 3 below, as well as some of the important specifications associated with each
aircraft. All of these aircraft are business jets that carry between 8 and 18 passengers.
Table 3: Aircraft Database
Tsl/W0
Range
(nmi)
W0/S
7.688874
0.338132
6750
80.03518
Long
range
cruise
M
0.8
0.542169
6.850399
0.323293
7000
77.630553
0.85
98000
0.507653
8.645793
0.30102
6150
95.890411
0.85
92500
0.562162
8.645793
0.318919
5280
90.508806
0.85
Gulfstream G500
85100
0.564042
7.688874
0.361575
5800
74.846086
0.8
Aircraft
W0
(lb)
We/Wo
AR
Gulfstream G550
91000
0.530769
Gulfstream G650
99600
Bombardier Global
Express XRS
Bombardier Global 5000
Citation X
36,100
0.59903
7.772296
0.374737
3070
68.500949
0.82
Bombardier Challenger
300
Bombardier Challenger
850
Bombardier Learjet
38,850
0.585586
7.80592
0.351403
3100
74.425287
0.75
51,000
0.505882
8.247044
0.361569
3120
86.867655
0.74
23,500
0.624723
7.236531
0.391489
2405
88.846881
0.74
Bombardier Learjet 85
33,500
0.629851
9.438487
0.364179
2700
83.541147
0.78
Cessna Citation
Sovereign
Gulfstream G150
30,300
0.576238
7.77497
0.380858
2800
58.732312
0.76
26,100
0.563218
7.723767
0.338697
2950
65.25
0.75
Hawker 4000
39,500
0.577215
7.180909
0.34957
2855
74.387947
0.78
Hawker 750
27,000
0.6
7.045751
0.345185
2170
72.192513
0.76
Hawker 850XP
28,000
0.583214
7.748314
0.332857
2600
73.490814
0.76
Hawker 900XP
28,000
0.586429
7.748314
0.339286
2904
73.490814
0.76
There is a large range in weight within the aircraft in the database, from a low of
23,500 lbs to a high of 99,600 lbs. It was initially desired to only include heavier planes
23
similar to the size of the plane our group is designing. However, there are a limited number
of planes that exist with size and performance characteristics similar to ours. This places
several limitations on our sizing methods, which caused us to include more dissimilar
planes into the database. Because of this, there are clearly two different classes within our
database. The first group focused on the larger aircraft with longer ranges which more
closely match the design mission. The second group includes mostly smaller business jets.
Figure 13 shows the division of these two groups and graphically illustrates the difference in
size between them. The large group, called “Class 1,” has aircraft with gross weights greater
than 80,000 lbs while the smaller group, called “Class 2,” has aircraft with gross weights
less than 52,000 lbs. Also Figure 13 shows the variation even within each group for We/Wo
as a function of Wo. This will potentially cause uncertainty in the initial sizing estimates as
the trends have large R2 values.
Figure 13: Aircraft Database Groups.
24
Constraint Diagram
A constraint diagram was used to find initial estimates for the wing loading and
thrust to weight ratio of our aircraft. These numbers were found by plotting various flight
conditions and maneuvers to graphically asses the plane’s performance. The constraint
diagram associated with our initial design is shown below in Figure 14. The aircraft must
operate in the upper left part of the diagram, above the second segment climb, and left of
the landing ground roll. This means that the wing loading is limited primarily by landing
ground roll and the thrust to weight ratio is limited primarily by second segment climb. It
is important to note that the landing ground roll appears as a vertical line because there is
no reverse thrust included in the calculations. Reverse thrust was not included because the
engine we plan to use, an unducted fan, is not capable of producing reverse thrust. If the
wing loading of our design is lowered enough, top of climb could become a limiting factor.
Also if the takeoff ground roll is reduced much below 4700 ft, it will become a constraining
factor. A subsonic 2.5g maneuver at 250 knots is not a design-limiting constraint at this
time.
25
Figure 14: Constraint Diagram.
The constraint diagram shows that the aircraft must have a wing loading of less than
101 lbs/ft2 due to the landing ground roll of 3500 feet or less and the landing CL max of 2
which corresponds to the slotted flaps that our plane is using. The aircraft must also have a
TSL/W0 of greater than .33 because of the second segment climb. If the wing loading goes
below 65, then the TSL/W0 must increase in order to meet the top of climb requirements.
Initial Estimates
Initial sizing estimates were based primarily on trends calculated from our database
as well as some historical estimates. First, an estimated aspect ratio of 8.0 was chosen
based on the similarly sized “Class 1” aircraft in our database. From this estimate, the
corresponding cruise lift to drag ratio can be calculated through a combination of equations
presented by Raymer, Nicolai, and Carte.8 Using the equation listed as equation 1, a cruise
26
lift to drag ratio for our plane can be found to be 15.56. The specific fuel consumption was
also estimated based on existing business jets; our calculations assumed that SFC cruise is 0.5
and SFCloiter is 0.6.
L
 0.85*(1.4* AR  7.1)
D Cruise
Eq. 1
With these values, the weight of the aircraft can be estimated. Two methods were
used, the first of which was to simply create a curve fit from similar aircraft relating the
gross weight (W0) to the empty weight fraction (We/W0). The curve fit through Group 1
aircraft produced equation 2.
We
 aW0c  67.69W00.422
W0
Eq. 2
This equation was then used inside of a sizing loop to converge upon a final weight
estimate. The full MATLAB code used in this process can be found in Appendix A. This
curve-fit method yielded a gross weight of 92,000 lbs. While this method provided a
reasonable gross weight estimate, there were some reasons to be skeptical. Figure 15 shows
that there is a large variation in the data and that the trend line may not be a good estimate
as there are only 5 data points with a large variance. Because of the lack of similarly sized
planes and the large variation in data, a second sizing method was also used.
27
Figure 15: Curve Fit of Similar Aircraft.
In order to improve our weight estimate, a least squares regression was used. This
method was appealing because it included much more than just the empty weight fraction
in its calculation. The second method used equation 3 below.
We
c5
 bW0c1 AR c 2 (TSL / W0 )c 3 (W / S )c 4 M cruise
Rangec 6
W0
Eq. 3
The challenge in using this method is that each additional unknown exponent
requires an additional aircraft in the database in order to solve the equation. Our own
database only contains five aircraft in the similarly sized “Class 1” genre. Because of this,
the entire database of aircraft was used. Solving for the unknown constants in equation 3
provided the complete equation shown in equation 4 below.
We
0.934
 3.08 W00.154 AR 0.016 (TSL / W0 )0.394 (W / S )0.089 M cruise
Range0.032
W0
Eq. 4
28
This method again uses a loop to converge on a final gross weight, and also includes
other design variables where the first method did not. This method gave a gross weight of
108,000 lbs which is 18,000 lbs greater than the previous estimate and 8,000 lbs greater
than even the largest business jet in the database, the G650. These estimates are, however,
still based on a database of aircraft with a large variation amongst them. This could result
in a large error when attempting to make trends amongst the data. One clue that the
approximations may not be perfect can be found in examining the signs of the exponents.
For example, one might intuitively conclude that as the aspect ratio increases, so does the
empty weight fraction. This should produce a positive exponent for the aspect ratio
variable, but the solution from our database produces a negative exponent. Likewise, as
the wing loading increases, the size of the wing decreases, and therefore the empty weight
fraction should also decrease. This should produce a negative exponent for the wing
loading variable, but the solution from our database produces a positive exponent. As the
design moves forward, the challenge will be to improve upon the database and find planes
that better relate to the one we are designing. A better, more representative database
should resolve the inaccuracies present in the sizing methods.
Both weight estimation methods will continue to be developed until they either
converge upon the same solution, or until one becomes clearly better than the other. The
method of the least squares regression is more desirable, however, since it includes many
more design variables in its calculation and therefore characterizes many traits
simultaneously. Table 4 below summarizes the current weight prediction values produced
by the two sizing methods.
29
Table 4: Estimated Weights
Curve Fit Weights
(lbs)
LSR Weights
(lbs)
Wo
92,100
108,200
We
50,100
59,300
Wf
39,500
46,300
While the sizing code was used primarily to find an initial estimate for the gross
weight of the aircraft, it could be adjusted slightly to predict the performance of the plane
under various loading conditions. This was desirable in assessing how the plane would
perform for typical operating missions that differ greatly from the design mission. In
particular, it was important to know how the range would be affected by flying at faster or
slower Mach numbers. This information would be useful in determining whether or not
our plane could carry a certain amount of people over a particular distance at a desired
speed. Using a fixed initial gross weight, Figure 16 was generated, which predicts the
performance of the plane under various conditions.
30
Range vs. Mach for Various Loadings
08 Passengers
12 Passengers
16 Passengers
7200
7000
Range (nmi)
6800
6600
6400
6200
6000
5800
5600
0.7
0.72
0.74
0.76
0.78
0.8
0.82
Mach Number
0.84
0.86
0.88
0.9
Figure 16: Range vs. Mach Number.
This plot shows that the plane can travel at Mach 0.9 for any range less than 5500
nmi for any number of passengers. A longer distance, or a strong headwind, could require
a slower cruise speed. This plot also shows the tradeoff between range and cruise Mach
number. While business jet owners often want to fly as fast possible, doing so will reduce
the range of the plane. For short missions, this is not an issue. But for longer missions,
such as the design mission, the pilot must be very aware of this tradeoff.
31
CONCLUSION
Summary
The initial phase of the project consisted of indentifying customer needs and target
markets. After this was completed, customer needs were translated into system
requirements using Quality Function Deployment methods. Various mission sketches and
design missions were then computed and analyzed using target performance values, such
as range. In addition, with the use of advanced technologies such as unducted propfans
and composites, NASA’s N+2 goals should be attainable within the given time frame.
Aircraft weight was determined through the application of iterative sizing methods using
both a least squares regression and generic curve fits of historical aircraft data.
Next Steps
This System Requirements Review completes the initial step in the design process,
and will serve as a stepping stone for the remainder of the project. The next step is to go
into further detail. More accurate L/D equations will need to acquired. Technology factors
will also need to be included in the sizing code. Aircraft configurations will need to be taken
into consideration, such as the propulsion system, wing design and placement, control
surfaces, cabin layout and amenities as well as landing gear. Lastly, attitude dynamics of the
aircraft will need to be researched.
32
REFERENCES
1
"Avionics Magazine :: Outlook: High Hopes for General Aviation." Breaking News and Analysis on
Aviation Today. Web. 11 Feb. 2010. <http://www.avtoday.com/av/categories/bga/Outlook-HighHopes-for-General-Aviation_12515.html>.
2
"Honeywell Aerospace Business Aviation Outlook Forecasts $200 Billion inGlobal Business Jet Sales
Through 2019." Web. 11 Feb. 2010. <http://www51.honeywell.com/honeywell/news-events/pressreleases-details/10.18.09NBAAForecast.html>.
3
Torenbeek, Egbert. Synthesis of subsonic airplane design an introduction to the preliminary design, of
subsonic general aviation and transport aircraft, with emphasis on layout, aerodynamic design,
propulsion, and performance. Delft: Delft UP, Nijhoff, Sold and distributed in the U.S. and Canada by
Kluwer Boston, 1982. Print.
4
Great Circle Mapper. Web. 11 Feb. 2010. <http://www.gcmap.com>.
5
“Subsonic Fixed Wing Project”. NASA. 08 February 2010.
http://www.aeronautics.nasa.gov/fap/sfw_project.html
6
Jane's All The World's Aircraft. Web. 11 Feb. 2010. <http://jawa.janes.com/public/jawa/index.shtml>.
7
Norris, Guy. “Rotor Revival”. Aviation Week & Space Technology. 14 December 2009. pages 54-57.
8
Raymer, Daniel P. Aircraft Design A Conceptual Approach (Aiaa Education Series). New York: AIAA
American Institute of Aeronautics & Ast, 2006. Print.
33
APPENDIX A
Matlab Sizing Code
34
%% Enter Input Values
num_pass = 8; %number of passengers
num_crew = 4; %number of flight crew
range_design = 6350; %nmi
range_aa = 200; %"aa" = "alternate airport", units = nmi
loiter = 0.5; %hours
AR = 8.0; %aspect ratio
SFC_cruise = 0.5; %1/hour
SFC_loiter = 0.4; %1/hour
M_cruise = .85; %cruise mach
Passenger_weight = 220; %lbs/person
FlightCrew_weight = 200; %lbs/person
Wo_guess =
10000; %lbs
%Some variables from constraint diagram
TW = 0.33;
WS = 100;
%choose weight estimation method (1=curve fit, 2= LSR)
Wo_eqn = 2;
%% Design Mission (find Wf/Wo)
V_cruise = M_cruise*968.1/1.689; %kts
LD_cruise = 0.85*(1.4*AR+7.1); %L/D at cruise
LD_loiter = 1.4*AR+7.1; %L/D during loiter
w1w0 = 0.97; %takeoff
w2w1 = 0.991-.007*M_cruise-.01*M_cruise^2; %climb - Raymer Curve Fit eqn.
w3w2 = exp((-range_design*SFC_cruise)/(V_cruise*LD_cruise)); %cruise Breguet Range eqn.
w4w3 = 0.995; %landing
w5w4 = 0.97; %missed approach (TO)
w6w5 = 0.985; %climb
w7w6 = exp((-range_aa*SFC_cruise)/(V_cruise*LD_cruise)); %divert to alternate
airport - cruise Breguet
w8w7 = exp((-loiter*SFC_loiter)/LD_loiter); %hold at 2nd airport - Endurance
eqn.
w9w8 = 0.995; %landing
Wf_Wo = 1.01*(1-w1w0*w2w1*w3w2*w4w3*w5w4*w6w5*w7w6*w8w7*w9w8); %fuel weight
fraction
%% Loop to find Wo
for n = 1:1:100
if Wo_eqn == 1
%We_Wo = 1.02*Wo_guess^(-0.06); %From Raymer general jet transport
%We_Wo = 1.3783*Wo_guess^(-0.082); %From Raymer - database with all
planes
35
We_Wo = 67.69*Wo_guess^(-0.422); %From Raymer - database with only
the big planes
else
if exist('a','var') == 0
a = GetLSRcoeffs('aircraft_database_updated.xlsx');
end
We_Wo =
exp(a(1))*Wo_guess^a(2)*AR^a(3)*TW^a(4)*WS^a(5)*M_cruise^a(6)*range_design^a(
7);
end
% Other Calcs
Wpayload = Passenger_weight*num_pass;
Wcrew = FlightCrew_weight*num_crew;
We = We_Wo * Wo_guess;
Wf = Wf_Wo * Wo_guess;
Wo_guess = We+Wf+Wpayload+Wcrew;
end
Wo_guess
36
function coeffs = GetLSRcoeffs(filename)
% We_Wo estimate - Least Squares regression
% we/wo = b*wo*AR*(T/W)*(W/S)*Mmax*range
% Columns in order are:
% Aircraft (doesn't read this one in, so Wo is column 1)
% W0, We, We/Wo, AR, T/W, Mmax, Range, W/S, Mcruise
data = xlsread(filename);
WeWo_vect = data(:,3);
Wo_vect = data(:,1);
AR_vect = data(:,4);
TW_vect = data(:,5);
WS_vect = data(:,8);
Mmax_vect = data(:,9); %sometimes use cruise instead of max
Range_vect = data(:,7);
Fbar = log(WeWo_vect);
temp1 = [log(Wo_vect), log(AR_vect), log(TW_vect), log(WS_vect),
log(Mmax_vect), log(Range_vect)];
temp2 = ones(length(Wo_vect),1);
Xbar = [temp2 temp1];
coeffs=Xbar\Fbar;
37