Spring
2010
SYSTEM
DESIGN
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
EXECUTIVE SUMMARY
Team Two is designing a business jet aircraft that is both environmentally responsible
and meets the needs of a selected target customer. These two major drivers for the design of the
aircraft were examined in the previous System Requirement Review document which yielded the
main requirements of a long range, high cruise speed, and low environmental noise and
emissions aircraft.
Many possible designs and advanced technologies were analyzed in order to develop an
aircraft that best meets these requirements. The initial aircraft designs considered included a
hybrid wing aircraft, several conventional aircraft with different engine placements and tail
configurations, and canard aircraft with aft mounted wings and various engine and vertical tail
placements. These aircraft were evaluated and compared until the two best were ultimately
selected. One of these remaining aircraft was a conventional aircraft similar to a G550 except
using an advanced engine and some composite materials. The second was a canard aircraft with
an aft mounted swept back wing using the same advanced engines and composite materials.
In order to meet the NASA N+2 environmental goals, drastic changes will have to be
made in comparison to modern business jet aircraft. To do this, advanced technologies were
evaluated for their potential use in 2020. Two new engine types that are currently in research
phases were examined: an unducted turbofan and a geared turbofan. Using one of these two
engines, and the addition of light weight materials, may provide enough benefit to meet the
goals.
Current calculations show that the conventional aircraft with the advanced technologies
will weigh about 71,000 lbs and the second design using canards and an aft wing, also with the
same advanced technologies will weigh 73,000 lbs. Both aircraft have been determined to have
adequate static stability. Further analysis will be done to determine more precisely which of the
two aircraft designs and which of the engines will best provide an environmentally responsible
aircraft to the customer.
Table of contents
MISSION STATEMENT ............................................................................................................................. 1
DESIGN AND OPERATING MISSION ..................................................................................................... 1
AIRCRAFT CONCEPT SELECTION ......................................................................................................... 2
ADVANCED TECHNOLOGIES ............................................................................................................... 13
SIZING CODE............................................................................................................................................ 16
ENGINE SELECTION ............................................................................................................................... 30
SUMMARY ................................................................................................................................................ 39
NEXT STEPS ............................................................................................................................................. 39
REFERENCES ........................................................................................................................................... 41
APPENDIX A ............................................................................................................................................. 42
APPENDIX B ............................................................................................................................................. 46
APPENDIX C ............................................................................................................................................. 50
MISSION STATEMENT
It is the mission of Team 2 to be the primary systems integrator of a cost effective, long
range, environmentally friendly business aircraft that is able to serve as a high speed
transportation solution for its customers. The design will have a reduced impact on the
environment by meeting NASA’s N+2 criteria while still remaining competitive in the ultra-long
range business jet market.
DESIGN AND OPERATING MISSION
The design mission was developed and optimized with the city pair of Los Angeles
and Hong Kong in mind accounting for a 60 knot head wind. The design mission consists of
eight mission legs between nine points as illustrated in the following figure.
Figure 1: Design Mission Flight Plan.
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
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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.
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 Van Nuys. 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.
AIRCRAFT CONCEPT SELECTION
Following the system requirements phase of design, concept generation and selection was
required to further the design process. After great thought and consideration, the team was able
to generate eight initial designs, as shown in Figure 2, for further analysis. Rather than
subjectively choosing one of the eight concept designs, the team implemented Pugh’s method as
a means to add objectivity to the decision making process. The first step was to establish a set of
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criteria against which all of the proposed aircraft would be evaluated. The house of quality that
was constructed during the design requirements phase helped in the establishment of evaluation
criteria. This provided criteria that were centered on the needs of the customer and not the
desires of the designers. Ultimately, ten different criteria, as listed in Table 1, were used in the
first iteration of Pugh’s method.
Figure 2: Eight Proposed Aircraft Designs
The next step of Pugh’s method was the creation of a matrix relating the established
criteria to each of the proposed designs. The matrix’s purpose was to help clarify how each
aircraft concept rated under each criterion relative to a benchmark aircraft. Based on the selected
benchmark aircraft, all other concepts were evaluated on whether or not they were better, worse,
or equivalent to the benchmark aircraft for a given criterion. These relationships were illustrated
in the matrix using the symbols ‘+’, ‘-’, and ‘s’ respectively. Each decision was made with
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cursory calculations whenever possible, relying on the team’s best collective engineering
judgment when not possible.
After evaluating each aircraft in the matrix against every specified criterion, the total
number of positive, negative, and equivalent marks were separately compiled in order to
maintain evaluation details. For instance, if positives and negatives were allowed to cancel each
other out, it would be unclear whether or not an aircraft received a score of zero due to average
qualities or because all of its positive aspects were offset by negative ones. Evaluating the
positives and negatives allowed the team to clearly define the favorable and unfavorable aspects
of each individual aircraft. The matrix comparing the eight initial designs to the ten criteria is
shown in Table 1.
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Table 1: Concept Selection, Pugh's Method 1st Iteration
After studying the different ratings given to each aircraft, the team decided to repeat
Pugh’s method using the top four aircraft designs determined by the first iteration. This was done
because the first iteration of Pugh’s method did not define a single best design for the given
mission, but rather judged each aircraft qualitatively against the chosen benchmark. The
benchmark aircraft clearly cannot receive a positive or negative rating for any criterion, since it
is equivalent to itself. Thus, two iterations of the method were completed, each with a different
benchmark aircraft.
Examining the outcomes of the first Pugh’s method iteration, it was decided that the
canard equipped aircraft could offer a potential advantage in cruise drag over conventional tube
and wing designs. The overall weight of each design was compared by counting the number of
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control surfaces used and observing the general structural complexity of the configuration. No
material considerations were incorporated into these decisions as they could apply to any of the
designs. An increased number of surfaces, or additional structural requirements such as those
found on a blended wing body, were deemed less favorable for overall weight than a
conventional aircraft configuration of the same size.
In order to meet the project’s goal of having a reduced environmental impact, it was
desired that the airframe be able to utilize a variety of high speed engine technologies, including
unducted fans. To this end, aircraft with rear pylon mounted engines similar to the baseline
model were assigned equivalences to the baseline, whereas designs that would place the engines
in locations interfering with the cabin from vibration, noise, and safety perspectives were
assigned negative ratings. Specifically relating cabin noise relative to the baseline design, a
negative rating was assigned to engine locations in line with the center of the main cabin area.
Further in regard to addressing environmental impact, the environmental noise of each
proposed design was considered. As every design was evaluated with the possibility of using a
variety of engine types, the aircraft structure was the primary consideration for this criterion.
Designs providing noise shielding due to wing placement, vertical stabilizer placement, or
having shielding due to a blended wing configuration were all given positive ratings relative to
the baseline.
The placement of each design’s landing gear was also considered. Designs
requiring excessively long and robust landing gear were given a negative rating, whereas the
blended wing body design with a structural framework capable of mounting the landing gear in a
variety of locations was assigned a positive rating relative to the baseline.
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Window placement and an unobstructed cabin view were also evaluated for each design,
and aircraft with aft-mounted wings provide a clear window view, which was deemed superior to
the baseline configuration. Difficulties associated with placing an abundant number of windows
in a blended wing body configuration resulted in a negative rating for the design relative to the
baseline. Though a subjective and hotly debated criterion, each design’s attractiveness and
visual appeal was also considered. By majority vote, negative values were assigned to the high
wing design, as well as aircraft with less sleek lines. The team agreed that canard designs with
aft wing sweep and more futuristic configurations were more visually appealing than the baseline
configuration. In addition, it was decided that the forward wing sweep included in design one
made it less visually appealing.
Each of the eight designs were investigated in relation to two remaining criteria, the first
of which was the complexity of cabin pressurization. Every design with the exception of the
blended wing body contained a relatively easy to pressurize cylindrical fuselage and these
designs, therefore, received equivalency ratings.
The blended wing body was assigned a
negative value relative to the baseline due to its non-cylindrical shape. Finally, static margin and
stability were considered for each design. It was decided that canard aircraft, with the exception
of the tri-surface aircraft, would provide a smaller static margin and contain potential center of
gravity challenges, which earned these designs a negative value relative to the baseline. The
limited historical data available suggests center of gravity difficulties and a small static margin
on existing blended wing body designs, thereby also providing it a negative value relative to the
base design. The tri-surface aircraft was given a positive value in relation to static margin, as
data available for the minimalistic number of tri-surface aircraft suggested an ability to design
for a larger static margin.
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After evaluating each of the eight designs relative to the initial ten criteria, design
numbers two, four, six, and seven were chosen as the best designs and were used in the next
iteration of the method. Out of these four designs, number six was chosen as the new benchmark.
Design six was chosen because it was very dissimilar to the remaining aircraft. It was important
to choose a new baseline model so that the outcomes from the second iteration would not be
identical to the first, and would allow the previous baseline, design four, to be rated.
It was noted during the first iteration of Pugh’s method that there were no criteria related
to development cost. In order to improve the value of the second iteration, development cost was
added to the matrix for the four remaining designs, as shown in Table 2. Each design was then
reevaluated for every criterion based on the new benchmark aircraft. Ratings were assigned in a
manner similar to the first iteration, with the same considerations taken into account.
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Table 2: Concept Selection, Pugh's Method 2nd Iteration
Using the results of the second Pugh’s method iteration, two design choices were selected
as best meeting the evaluation criteria and requiring further analysis. Designs four and seven had
the fewest number of negative ratings, with design seven having the most positive ratings during
the second iteration. Since the goal was only to narrow the field of designs down to two options
for additional analysis, further iteration was avoided and designs four and seven were selected.
Designs four and seven, selected by the Pugh’s method process, are henceforth referred to as
concepts one and two, respectively, and are shown in Figure 3.
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Figure 3: Concept One, Formerly Design Four (left) and Concept Two, Formerly Design
Seven (right)
Concept one, the first iteration’s baseline design, presented a number of advantages that
caused it to be worthy of further investigation.
Concept one is configured similarly to a
conventional business jet, thus providing a pre-optimized platform for technological
improvement and analysis.
Through the evolution of aircraft design, this conventional
configuration has been refined to the extent that a reinvention of the wheel may not be required
to meet the desired end goals. In other words, the application of new technologies and additional
improvements to current aircraft configurations may be able to meet the required design goals
with minimal developmental costs and a conservative amount of risk. Concept one requires no
additional control surfaces, and the aft fuselage engine mounting allows for a wide variety of
engine choices. In addition, this mounting location would facilitate an unducted fan by keeping
internal cabin noise and vibration to a minimum. Concept one’s T-tail configuration, which can
be seen in Figure 4, can provide a necessary amount of horizontal stabilizer and elevator surface
area while still being able to facilitate an aft mounted unducted fan.
Additional benefits of concept one include a low wing design that allows for minimal
spar interference with the main cabin, shorter and lower weight landing gear struts, ease of
maintenance, and can serve as an emergency exit platform. Concept one’s circular fuselage also
facilitates cabin pressurization and eliminates the need for any special structural reinforcements.
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A circular cross section also allows for a large interior cabin volume and adequate storage area
with no increased development costs. Concept one also provides adequate measures of stability,
and incorporates the wide static margin common to current business jets. A large number of
windows can be incorporated into this concept, and its appearance is both attractive and familiar
to the end user.
Figure 4: Concept One Three View
Concept two also presented a number of advantages warranting further analysis. Sharing
some conventional aircraft characteristics, but capitalizing on many innovative configuration
changes, concept two promises potential improvements effectual of a more pioneering design
toward the system’s overall goals. Similar to concept one, concept two may incorporate several
new technologies to meet the desired mission goals, but also requires higher development costs
and is associated with a higher amount of risk. As in concept one, concept two features an aft
fuselage engine placement that enables a wide variety of engine choices while reducing internal
11
cabin noise. Though requiring additional structural weight, concept two’s design specifically
addresses environmental noise through the placement of wings below the entirety of the engines.
Lateral engine noise is also shielded using twin outboard-located vertical stabilizers. Again as in
concept one, concept two shares the same advantages of a low wing configuration with a circular
fuselage. The same material technology factors that can be utilized on concept one are equally
applicable to concept two.
Unique to concept two is the potential cruise drag reduction
associated with a lifting canard, which can benefit the environment through reduced fuel
consumption.
Concept two’s development costs promise to be higher than concept one, but are again
variable based upon the degree of improvement desired and number of new technologies
incorporated. The use of a lifting canard requires a more aggressive design process with regard to
stability, and may potentially contain a smaller static margin. Window placement in concept two
is similar to concept one, however the cabin view through the windows in concept two provides
a clear view of the ground from nearly the entire cabin. Concept two’s swept wings, lifting
canards, and twin vertical stabilizers provide it with a futuristic yet familiar set of lines that are
visually stimulating to end users, as shown by the conceptual sketches in Figure 5.
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Figure 5: Concept Two Three View
ADVANCED TECHNOLOGIES
The two advanced technologies that were investigated were an unducted propfan for a
propulsion system and use of composite materials for the structure of the aircraft. 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 to achieve a noise
reduction down to 42 dB below stage 4 certification, 75% reduction in NOx emissions, 40%
reduction in fuel consumption, and a performance field length reduction of 50%.1 The first three
design goals will hopefully be met by using an innovative propulsion system. An unducted
propfan is an advanced engine design that would incorporate two counter rotating fans that
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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.2 The 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. Robert Nuttal, RollsRoyce’s vice president of future programs strategic marketing, says that “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.”2 The
unducted propfan technology is the most promising to meet NASA’s N+2 goals within the
specified time frame. 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. Guy Norris states “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.”2 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”.2 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.
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On the other hand, there is current engine technology from Pratt & Whitney in the form
of a geared turbofan that shows promise. More importantly, the technology is slated for
production before the 2020 production date for N+2. A geared turbofan engine utilizes a gearbox
between the fan and main power shaft to decouple the fan from the engine’s compressor. The
technology allows for a very large fan to rotate at slower speeds while moving large amounts of
air with little noise. The gearbox also allows for the compressor and turbine to spin at faster
speeds to further increase efficiency. Pratt and Whitney claims that the PurePower 1000 series
offers proven efficiency with no life limited parts, a 20 dB reduction in noise over current
engines, a reduction in NOx emissions by 50% over the CAEP/6 margins, and a 15% reduction
in fuel burn over current engines.3 The PurePower 1000 series offer a thrust range between
13,000 lbf- 24,000 lbf depending on engine selection. The thrust range is ideal for our aircraft
and allows the team to continue using the rubber engine assumption in sizing.
The other possible advanced technology 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. Up to 50% of the structure of some
aircraft has been constructed out of composite materials. There has been a lot of research on the
use of composite materials within the past few decades. The technology has been proven to be
reliable and beneficial in the aerospace industry and is currently being fielded in many designs
that are currently in production. The technology is likely to keep improving and deliver even
more advantages in aircraft design by the 2020 production date. Research and past applications
suggest a reduction of approximately 20% in structural weight. This value is used directly as a
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technology factor in the sizing process and is applied to the structural weight components of the
fuselage, wings, horizontal and vertical tails, canards, pylons, and nacelles.
SIZING CODE
Constraint Diagrams
Two separate constraint diagrams, one for each design concept, were used in this portion
of the design process. The constraint diagram associated with the conventional configuration
changed very little since the System Requirements Review; the only significant changes were
updating plane geometry inputs such as aspect ratio and adjusting landing and takeoff distances
through design iterations. A second constraint diagram was developed for the canard pusher
configuration. All the necessary plane sizing inputs were changed, but many values remained the
same. For example, values for CLmax at landing and takeoff are the same for both concepts
because we have assumed that these values are limited primarily by the flaps included on the
plane; both configurations currently use single slotted flaps. Future analysis will consider adding
Fowler flaps to determine if they are beneficial. Our design group currently does not definitively
know how adding a canard will change many of the values associated with the canard pusher
configuration. Because of that, many values have been assumed to be the same as the
conventional configuration until further differentiation can be achieved. Table 3 lists some inputs
for both configurations.
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Table 3: Aircraft Input Values
W0/S
TSL/W0
(CL)maxT/O
(CL)maxLanding
CD0
e
AR
Conventional
76
.33
1.5
2.0
.018
.8
8
Canard-Pusher
84
.33
1.5
2.0
.018
.8
10.5
Some values, such as CD0 and SFC, are calculated many times in the sizing code at
different flight velocities and thrust settings.
Because of that, theses values vary widely
depending on the location of interest in the flight mission. The corresponding values reported in
the above table are representative of the appropriate flight condition.
It is also clear from this table that both configurations have identical input values for
some significant variables. This is based on an early design-phase assumption necessitated by a
lack of knowledge that both configurations will have similar constraining variables.
It is
anticipated that many more differences will exist between the two models as progress is made in
how to mathematically and systematically represent the differences between the two
configurations. Also the engine type will be differentiated between the geared turbofan and the
unducted turbofan jet engines. Both have varying benefits with regards to fuel efficiency, noise,
and emissions. Future additions to the sizing code will attempt to quantify these variations of the
two engines to see which is most beneficial overall to both aircraft concepts.
Figure 6 below shows the current constraint diagram for the conventional configuration.
This model is limited by second segment climb and landing ground roll. Figure 7 shows the
current constraint diagram for the canard pusher configuration, which is limited primarily by
landing ground roll, takeoff ground roll, and second segment climb. The first two columns of
Table 3 above summarize the initial starting points used in the code for the thrust to weight ratio
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and wing loading. The wing loading for both configurations has changed since the system
requirements review, in which the wing loading was estimated at 100 lb/ft2. Both values have
dropped based upon research of exiting planes and because of iteration results in the design
process.
Constraint Diagram of Conventional
0.5
0.45
0.4
0.35
TSL/W0
0.3
top of climb (1g steady, level flight, M
= 0.85 @ h=42K, service ceiling)
subsonic 2.5g manuever, 250kts @ h
=10K
takeoff ground roll 4700 ft @ h = 5K,
+15° hot day
landing ground roll 3500 ft @ h = 5K,
+15° hot day
second segment climb gradient
above h = 5K, +15° hot day
0.25
0.2
0.15
0.1
0.05
0
40
60
80
100
120
140
W0/S [lb/ft2]
Figure 6: Constraint Diagram for Conventional Configuration
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Constraint Diagram of Canard Pusher
0.5
0.45
0.4
0.35
TSL/W0
0.3
top of climb (1g steady, level flight, M
= 0.85 @ h=42K, service ceiling)
subsonic 2.5g manuever, 250kts @ h
=10K
takeoff ground roll 4700 ft @ h = 5K,
+15° hot day
landing ground roll 2950 ft @ h = 5K,
+15° hot day
second segment climb gradient
above h = 5K, +15° hot day
0.25
0.2
0.15
0.1
0.05
0
40
60
80
100
120
140
W0/S [lb/ft2]
Figure 7: Constraint Diagram for Canard Pusher Configuration
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Sizing Methods
A detailed Matlab script has been developed in order to size both configurations. This
code is used to estimate the size of the aircraft required to complete our design mission, which is
provided in Figure 1.
The code takes in approximately one hundred inputs for each
configuration, utilizes a drag calculation at each step of the mission, predicts the empty weight
with a component build up method, and incorporates an early but detailed engine model. While
the code is functioning and provides reasonable estimates, it is under constant revision in an
attempt to improve estimations, to make assumptions more accurate, and to further differentiate
between the two configurations. The general process of the sizing code is shown below in
Figure 8, which displays the solution process graphically in a flow chart.
Figure 8: Flow Chart for Sizing Code
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After every significant change, the sizing code is calibrated twice, once for each
configuration. The conventional model is calibrated against the Gulfstream G550 and the canard
pusher model is calibrated against the Beechcraft Starship. Both of the chosen calibration
models were used because their configurations closely match the design configurations our group
has chosen. Calibration is carried out by running our sizing code with all inputs describing the
corresponding calibration aircraft. The code’s predictions of empty weight, fuel weight, and
gross weight are then compared to published data for each calibration aircraft, and the
appropriate calibration factors are calculated. The calibration factors for the G550 are used in
sizing our conventional model and the calibration factors for the Starship are used in sizing our
canard pusher model. The final calibration factors are listed below in Table 4.
Table 4: Final Calibration Factor Values
Canard
Conventional
Empty Weight
0.77
0.77
Fuel Weight
1.33
1.28
Gross weight
1.05
1.01
The calibration factors shown above are larger than desired. This is most likely caused
by two significant sources of error.
The first issue in the current sizing code is that the
component-build-up equations used best describe cargo and transport planes from the 1970’s.
This will likely cause some degree of error, in that a business jet in 2020 will have many
significant differences. Additionally, the engine model in use attempts to scale a 50,000 lbs
thrust engine down to approximately 15,000 lbs of thrust. This process, described later in the
report, will also likely cause some degree of error. As the code is continually refined and made
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more and more accurate, it is hoped that the calibration factors will decrease in magnitude and
become continually closer to one.
It is also important to note that both calibrations yield the same value for the fuel weight.
This is because the Starship, which is used to calibrate the canard pusher configuration, uses a
turboprop engine while our code predicts the engine performance of a turbofan or unducted fan.
Because the turboprop engine is so fundamentally different from what the codes analyzes, the
G550 calibration is carried out first, and it is assumed that the fuel weight calibration factor for
the Starship will be the same as the G550. So after the Starship is calibrated, its fuel weight
calibration factor is replaced with the fuel weight calibration factor of the G550.
The inputs for each of our two configurations are provided in Appendix A and Appendix
B. The variables have been sufficiently commented such that the variables and their values
should be self explanatory. A final weights table for all components of our two planes has been
provided below as Table 5.
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Table 5: Final Weight Values
Canard (lbs)
Conventional (lbs)
Canard (lbs)
Conventional (lbs)
Wing
5,367
6,232
Flight Instruments
260
254
Canard/Horizontal Tail
728
753
Hydraulics
179
171
Vertical Tail
879
662
Electrical System
943
1,125
Fuselage
7,445
7,392
Avionics
471
394
Main Gear
922
986
Installed Avionics
359
359
Nose Gear
107
162
Air Conditioning
171
466
Nacelle
1,628
1,656
Anti-Ice
147
145
Engine Controls
90
98
Crew
800
800
Engine Starter
130
130
Payload
1,760
1,760
Fuel System
352
360
Fuel Weight
27,300
28,383
Flight Controls
683
766
Empty Weight
39,742
41,257
Installed APU
440
275
Takeoff Gross Weight
72,944
71,365
Stability and Control
It is important for any business jet to be statically stable. Even at the early design stage,
our sizing code predicts the static stability of each configuration very simply by calculating the
static margin. The static margin measures the distance between the aerodynamic center and the
center of gravity of the airplane and normalizes this distance relative to the chord of the wing. In
order to be statically stable, the static margin must be positive. The sizing code calculates the
static margin according to the equation listed below.
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𝑆𝑀 =
𝑋𝐴𝐶 − 𝑋𝐶𝐺
𝐶𝑚𝑎𝑐
This calculation is carried out as one of the final steps in the code because the final sizes
and locations of each component must be known to accurately find the center of gravity. If the
location of any component cannot be calculated, it is given directly as an input.
The
aerodynamic center for the conventional model is assumed to be at the quarter chord. The
aerodynamic center for the canard pusher is slightly more complicated since it is not explicitly
known how much the canard will affect its location. The effect of the canard on the aerodynamic
center will also depend greatly on whether or not the canard is a lifting canard. For now, we
have assumed that our canard pusher configuration includes a lifting canard, and that this will
cause the aerodynamic center to shift from the quarter chord point of the main wing to the
leading edge of the main wing. With these assumptions, the static margin and center of gravity
have been calculated for each configuration. These values are listed below in Table 6. It is
important to note that the center gravity is listed as a percentage of the fuselage length while the
static margin is listed as a percentage of the chord of the wing. As expected, the center of
gravity for the canard pusher model is much further aft. Because of this, it also makes sense that
the static margin is smaller for the canard pusher model.
Table 6: Static Margin and Center of Gravity
Center of Gravity (% Fuselage Length)
Static Margin (% Cmac)
Conventional
51%
37%
Canard
74%
29%
24
Additionally, the code also calculates the general sizes of the wing and tail surfaces.
These calculations are based primarily on the aspect ratio, the wing loading, and the tail volume
coefficients. The tail volume coefficients are provided in Daniel Raymer’s textbook and are
based primarily on historical data. It was assumed that the canard can be sized using the
horizontal tail volume coefficients from Raymer’s textbook.4 The current sizes for the wing,
horizontal tail, vertical tail, and canard surfaces are listed below as Table 7.
Table 7: Wing Sizes
Wing
Vertical Tail Horizontal tail
Canard
AR
10.5
2.4
-
9
b
96.1
28.1
-
40.7
c
10.5
10.5
-
4.5
S
876.5
329.5
-
183.6
AR
8.0
1.0
2.0
-
b
87.2
13.7
23.8
-
c
12.0
12.3
8.9
-
S
950.7
186.6
284.2
-
Canard
Conventional
Drag Component Buildup
The drag for the aircraft may initially be estimated by considering component
contributions. Essentially, the aircraft may be broken down into a handful of major sections with
each section’s drag estimated through a combination of theoretical and empirical equations.
Each component’s drag may also be modeled as a sum of different types of drag.
25
There are four major types of drag being considered in our analysis. The first is parasite
drag, Dp. Parasite drag is comprised of skin friction drag, pressure drag and interference drag.
This drag is a result of surface interactions with a viscous fluid, in this case, air. The coefficient
of parasite drag is defined as:
# 𝑐𝑜𝑚𝑝
𝐶𝐷𝑝 =
∑
𝑖=1
𝐾𝑖 𝑄𝑖 𝐶𝑓𝑖 𝑆𝑤𝑒𝑡𝑖
+ 𝑘𝐶𝐿2
𝑆𝑟𝑒𝑓
However, the second term will be used in a different manner described later. Sref is the
reference area, in this case the wing planform area.
K is the form factor, a function of
component shape that takes into account pressure drag. Q is interference factor. Depending on
the placement of the component, Q may range from 1 to 1.5. In this case of this aircraft, Q will
be usually be 1. Swet is the wetted surface of the component, described as being the surface area
of the object which would be wetted by dropping the aircraft into a bucket of water.
The second major type of drag is induced drag, Di. Induced drag is a product of finitespan airfoils, whereby wingtip vortices flow from the lower to upper surface of the wing,
lowering the airfoil’s effective angle of attack. The presence of wingtip vortices leads to a
component of the lift acting as drag since drag is defined as the force produced parallel to the
free stream. The induced drag coefficient is defined according to the equation below.
𝐶𝐷𝑖 =
𝐶𝐿2
𝜋𝐴𝑅µ
Here, µ is the span efficiency factor, defined to be 1 when the wing produces an elliptic lift
distribution. Wing shape is very important in determining the lift distribution and many aircraft
employ near-elliptic lift distributions.
Current general aviation aircraft generally have an
efficiency factor ranging between 0.75 and 0.85. The aircraft’s induced drag coefficient is
currently being estimated using an efficiency factor of 0.80.
26
The third type of drag is wave drag, Dw, also known as compressibility drag. Wave drag
results from the formation of shock waves produced around the aircraft at sonic or near-sonic
speeds. The energy of the shock waves radiating off the aircraft is perceived as drag. While the
aircraft will not ever fly at Mach 1, localized airflow will most certainly reach sonic speed. As
of yet, no method for predicting or estimating wave drag has been found or included for this
application, thus it is currently assumed that the aircraft experiences 20 counts of wave drag.
While likely incorrect, the inclusion of a constant value of wave drag serves as a place holder for
future development and as a rough estimate for the early design stage analysis. This omission
will be corrected in the future.
The last type of drag being considered is miscellaneous drag, Dmisc, which is a factor
taking into account leakage, protuberance, and imperfections in manufacturing. This drag
accounts for issues such as gaps in control surfaces, external lighting, antennae, rivets and other
surface blemishes. Based off of sample drag prediction information, conservative estimates put
the aircraft’s miscellaneous drag coefficient at 5% of the aircraft’s parasite drag coefficient. This
approximation is used exactly in the current drag prediction.
To vary slightly from the described list of drag coefficients, it is convenient to redefine
two aspects of the total drag into a new term called ‘drag due to lift’. This term is comprised of
the parasite drag term dependent on CL, kCL2, and the induced drag term,
terms are combined to produce the term
𝐶𝐿2
𝜋𝐴𝑅𝑒
𝐶𝐿2
. Together these
𝜋𝐴𝑅µ
, the drag due to lift, where e is Oswald’s efficiency
factor. As stated previously, e is estimated to be 0.8. For the purpose of this report it is
reasonable to determine CL at cruise based off of the assumption that lift equals weight during
cruise. Accordingly, Wcruise = CLqS. Sample calculations are provided in APPENDIX C.
27
Now that the types of drag have been discussed, it is time to consider the contributions
from the aircraft components themselves. The major components being considered on the
aircraft are the fuselage, main wing, vertical and horizontal tails, canards, nacelles and pylons.
The fuselage is currently being modeled as a cylinder with a nose and tail section added on. The
fineness ratio of the aircraft, λf, was determined via a combination of current similar aircraft’s
fineness ratios and mission design criteria such as ceiling height and volume per passenger.
The wetted area of the fuselage is a function of the fineness ratio, and can be calculated
according to the following equation.
2⁄
3
𝑆𝑤𝑒𝑡𝑓
2
= 𝜋𝐷𝑓 𝑙𝑓 (1 − )
𝜆𝑓
(1 +
1
𝜆𝑓 2
)
Here, Df and lf are the diameter and length of the fuselage, respectively. The wetted area is
necessary to calculate the parasite drag, as skin friction only affects the wetted area of the
aircraft. The wetted area for the nacelles uses a simple model of a cylinder. For this the wetted
area is computed with the following equation.
𝑆𝑤𝑒𝑡𝑁 = 𝜋𝐷𝑁 𝑙𝑁
Similarly to the fuselage D is the diameter and l is the length. Since the wings, horizontal tail,
vertical tail, and pylons all all similar shapes, it is possible to use the same equation. For these
surfaces, the wetted area was calculated with the following equation.
𝑆𝑤𝑒𝑡 = 𝑆𝑤 2𝑐
Sw is the plan form area, c is the curvature of the surface, and multiplied by 2 to take the top and
bottom surface into account.
28
For the component drag build up, the form factor for the shape of each component was
needed. The form factor is shape dependent and varied for each component according to the
equations listed below.
𝐾𝑓 = 1 +
60
λ𝑓3
𝐾𝑁 = 1 +
+
λ𝑓
400
0.35
𝑙
( 𝑁⁄𝐷 )
𝑁
𝑡
𝑡
𝐾𝑤 = 1 + 𝑍 ( ) + 100( )4
𝑐
𝑐
In these equations, the subscript f is for the fuselage, N is for the nacelle, and W is for the wings.
The equation for the wings was also used for the pylons, vertical tail, and horizontal tail. Here,
λf is again the fineness ratio, Z is the sweep correction factor, and t/c is the thickness to cord
ratio. To find this form factor, the sweep correction factor is needed. This factor was found using
the following equation.
𝑍=
(2 − 𝑀2 ) cos Λ𝑐/4
√1 − 𝑀2 (cos Λ𝑐/4 )2
With the form factor and wetted area known, the last required piece is the interference
factor. The interference factor is determined by where different components are located relative
to each other. For this aircraft the nacelles have an interference factor with the fuselage. This
factor is based on the distance from the fuselage to the nacelle. If the distance is greater than the
diameter of the nacelles, the interference factor, Q, equals one. If the nacelle is resting directly on
the fuselage then the interference factor, Q, is 1.5. The wing and the fuselage also interfere with
each other. The position of the wing, being a low wing with fillets, results in an interference
factor that is also 1. For the pylons and tail, it is similar to a midwing set up, which will result in
29
an interference factor also of 1. With these four factors all known, it is possible to use the
following equation to sum up the different components and their drags to form a total parasite
drag.
# 𝑐𝑜𝑚𝑝
𝐶𝐷𝑝 =
∑
𝑖=1
𝐾𝑖 𝑄𝑖 𝐶𝑓𝑖 𝑆𝑤𝑒𝑡𝑖
𝑆𝑟𝑒𝑓
The total drag coefficient, CD is very simply defined to be a sum of the four types of drag
discussed previously.
𝐶𝐷 = 𝐶𝐷𝑝 + 𝐶𝐷𝑖 + 𝐶𝐷𝑚𝑖𝑠𝑐 + 𝐶𝐷𝑤
𝑐𝑜𝑚𝑝
𝐶𝐷 = ∑#𝑖=1
𝐾𝑖 𝑄𝑖 𝐶𝑓𝑖 𝑆𝑤𝑒𝑡𝑖
𝑆𝑟𝑒𝑓
𝐶2
𝐿
+ 𝜋𝐴𝑅𝑒
+ 𝐶𝐷𝑚𝑖𝑠𝑐 + 𝐶𝐷𝑤
ENGINE SELECTION
Two separate and distinct engine concepts are being explored by the team: an unducted
propfan and a geared turbofan. Both concepts offer significant savings in both emissions and fuel
consumption, and incorporate the most modern designs in the aircraft propulsions industry. The
details of each particular engine model were discussed previously in the Advanced Technologies
section of this report, but a table of the estimated performance improvements is provided below
as Table 8.
30
Table 8: Engine Model Projection and Comparison
Predicted Engine Performance by 2020
% Fuel Reduction Noise Reduction (dB) % Emission Reduction
Unducted fan
25-30
Meets Stage 4
20
Geared TurboFan
15
20
50
An in depth analysis process is currently being used to model the engine as part of the
sizing code. The main purpose of the engine model is to predict how much fuel will be required
to complete the design mission, and more specifically the fuel weight. This process starts with
the engine data provided in Raymer’s textbook for a “High Bypass Turbofan.”4 Unfortunately,
Raymer is not more specific than that as to what model the engine actually is. The engine data
plots are scanned directly into a MATLAB script which converts the data to tabular form and
interpolates where necessary. This engine is much larger than required, and must be scaled
down from 50,000 lbs of thrust to approximately 15,000 lbs of thrust in order to be useful. The
scaling process is performed simply by calculating a scale factor, which equals the desired
amount of thrust at any given time divided by 50,000 lbs, and multiplying the thrust data by this
value.
As engines shrink in size and performance, however, their fuel consumption and
efficiency generally worsen. Because of this, the specific fuel consumption was scaled inversely
proportional to the established scale factor.
With the data provided and the scaling operations performed, the fuel consumption can
then be predicted as a function of Mach number, altitude, and throttle setting.
Different
calculations are used for each segment of the flight mission: taxi, takeoff, climb, cruise, descent,
loiter, and land. The appropriate equations provided by Professor Crossley in lecture were used
31
exactly for each mission segment. Some sections are simple and straight forward, such as taxi,
takeoff, and landing, while the others require some looping to find optimum climb rates or lift to
drag ratios. The climb calculations predict the fuel consumed at a velocity of 250 knots up to
10,000 ft followed by the fuel consumed at best rate of climb up to the initial cruise altitude of
41,000 ft. The calculations are broken down into 500 vertical foot increments in which it is
assumed that atmospheric properties are constant. The cruise section is broken into twenty
equal-portion increments, and it is assumed that cruise altitude will remain constant at 41,000 ft.
The aircraft is now also assumed to be flying at its maximum lift to drag ratio. This same
performance assumption is used for loiter calculations. Descent is given a zero-range credit,
which has not changed since the System Requirements Review.
Each engine is analyzed using the above process with the technology factors from Table
8 included. When research states that a particular engine will decrease fuel consumption by X%,
that factor is used directly when applied to the specific fuel consumption value in calculations.
For example, the unducted fan reportedly reduces fuel consumption by 30%, so all SFC values
taken from the engine model in Raymer’s textbook are scaled and then multiplied by 0.70.
While noise emission is not currently predicted, this same method will be used when the
calculations become possible.
32
SUMMARY OF AIRCRAFT CONCEPTS
The major goals of this design are to provide an environmentally conscious, ultra-long
range corporate aircraft, which meets NASA’s N+2 goals, is fast enough to be marketable, and
can operate out of general aviation airports. Over the course of the design process, these broad
goals have given way to a detailed set of requirements. These requirements are shown in the left
column of the requirements compliance matrix in Figure 9. In addition to specifying the name of
the criteria being measured, this matrix also specifies the target value of each criterion, the
minimum threshold value necessary to satisfy each requirement, and the current value based on
the present state of the design. It is important to note that several of the current values shown are
estimates, and may not be constrained by the current level of system detail. These estimated
values are denoted by a trailing asterisk in the matrix.
The range, cruise mach, and initial cruise altitude requirements were derived from the
design mission. While the locations of the design mission have not changed, the still-air range of
the mission has been adjusted since the System Requirements Review (SRR). Originally, the
aircraft’s design mission range was specified as the great circle distance between Los Angeles
(LAX) and Hong Kong (HKG). This range ignored the fact that strong headwinds would likely
be unavoidable when traveling west to Hong Kong over the Pacific. As a conservative figure, a
headwind of 60 knots was assumed for the duration of the flight. This resulted in an equivalent
still-air range of 7100 nautical miles. A threshold value of 6960 nautical miles was then
determined from a less conservative, but still realistic, headwind of 50 knots. The cruise mach
and initial cruise altitude remain on target since the SRR, and are incorporated into the aircraft’s
current sizing and weight estimates. The target and threshold values of these requirements are
both based on producing an aircraft that is fast enough to be marketable. The cruise mach is
33
representative of most modern jet aircraft; and the initial cruise altitude is high enough to allow
for flight above most of the cruise altitudes used by part 121 carriers.
The maximum passenger capacity and the volume per passenger per hour requirements
were obtained from the aircraft’s cabin layout and design mission. The maximum number of
passengers has remained on target since the SRR, and is factored into the cabin’s seating
configuration. The threshold value of 8 listed in Figure 9 signifies the number of passengers
carried on the aircraft’s design mission. The volume per passenger per hour requirement was a
new system requirement added to provide a measure of passenger comfort. The current threshold
value of 2.28 ft3/(pax·hr) represents the minimum level necessary to ensure the design mission is
not arduous to passengers.5 The current and target value of volume per passenger hour is 13.3
ft3/(pax·hr). This value was calculated from a CATIA model of the aircraft’s cabin, and is
considered to be comfortable over the course of the design mission, which is approximately 13
hours.5
The balanced takeoff field length at maximum takeoff weight (MTOW) is also a new
requirement, which replaced the previous and more ambiguous requirement of “takeoff distance”
featured in the SRR. Balanced takeoff field length is the minimum length of runway required
such that a twin engine aircraft can operate safely with one engine inoperative during any stage
of takeoff. It was chosen as the metric for the design’s takeoff performance, since it specifies the
minimum amount of runway necessary to comply with safety regulations. The target value of
6000 ft was selected since it is close to the length of runways found at many general aviation and
regional airports. The threshold of 7000 ft was chosen since it was approximated as the
maximum required field length at which the aircraft could still be marketed as having reasonable
airport access. Since the current level of design detail was not sufficient to calculate balanced
34
field length, the ground roll values for each concept were included in the matrix. These ground
roll values were calculated using the constraint diagrams for each concept. While the current
ground roll values are promising in comparison to existing aircraft, this requirement will
continue to be of great concern until field length can be approximated.
The cabin noise, cumulative noise, emissions, sill height, and variable cost requirements
remain unchanged since the SRR, and are currently only estimates unconstrained by the present
level of design detail. Reasonable cabin noise values were estimated from existing aircraft data.
However, it is not yet possible to calculate cabin noise, or the difference in cabin noise that is
expected to exist between the two concepts. Cumulative noise limits were also estimated from
existing aircraft data, while emissions levels were placed relative to the NASA N+2 goals.
Cumulative noise limits cannot yet be calculated, but emissions levels will be able to be refined
once more detail on the power plants is obtained. Sill height was estimated based on the need to
facilitate aircraft loading, and also by studying the sill heights of existing business jets. This is
expected to be governed by takeoff rotation considerations in the future. Variable costs were
estimated from existing aircraft cost data, and the cost of operating a current aircraft with a
similar design mission was used as the threshold. Clearly, the variable cost cannot be calculated
at this point in the design.
Lastly, the cruise specific range requirement represents the desired fuel efficiency of the
design. The threshold value of 0.26 nm/lb was based on existing aircraft performance.6 Current
values were calculated for each concept, using the fuel weight determined from the sizing code
and the range of the design mission. This method was a crude approximation, but a more
accurate answer will be achievable once more power plant details are determined. The target
35
value was set to the range necessary to fly the design mission with reserves, assuming current
fuel weight.
Figure 9: Requirements Compliance Matrix.
Scaled models of each concept have been developed in CATIA. Three view drawings
with a few general sizing dimensions and a three dimensional screen shot from CATIA have
been provided for the Canard Pusher Configuration as Figure 10 and Figure 11. Similar plots
follow for the Conventional Configuration in Figure 12 and Figure 13.
36
Figure 10: Three View Drawing - Canard Pusher Configuration
Figure 11: Isometric CATIA Screen Shot - Canard Pusher Configuration
37
Figure 12: Three View Drawing - Conventional Configuration
Figure 13: Isometric CATIA Screen Shot - Conventional Configuration
38
SUMMARY
The second phase of this project consisted of developing many designs using various
technologies and configurations and then to narrow those designs down to the two best choices
for further analysis. The two choices that best met the developed requirements are a conventional
aircraft and an aircraft with canards and an aft swept back wing. Using these two configurations,
advanced technologies will be implemented such as composites and more efficient engines like
the unducted turbofan or the geared turbofan. Current calculations show that the aircraft, sized to
meet the demands of the target customer and designed to achieve the environmental goals, are in
the low 70,000 lb range. Further analysis will be done to evaluate these two designs to determine
which is best and which meets those requirements best.
NEXT STEPS
Now that Team 2 has finished the System Design, there are many more steps that need to
be taken before the conceptual design of the aircraft can be completed. For the wing, tail, and
canard, airfoils need to be selected to better predict the drag polar and general performance of
each piece. In propulsion, the engine selection between the geared turbofan and unducted fan
needs to be decided. In structures, a lot of work needs to be done especially in loading of
different parts and in integrating the landing gear. The longitudinal stability of each aircraft
needs to be finalized and the lateral stability needs to be analyzed for cross-wind landing and one
engine out conditions. Using all of this updated data, the best performance data needs to be
calculated including all airplane weights and sizes. The internal and external noise of each
aircraft needs to be assessed. Finally the estimated cost of each aircraft need to be found. Using
39
all of this and our component sizing code, carpet plots need to be used to graphically optimize
each of our designs. Once all of the calculations and optimizations have been completed a final
aircraft selection will be made.
40
REFERENCES
1
“Subsonic Fixed Wing Project”. NASA. 08 February 2010.
http://www.aeronautics.nasa.gov/fap/sfw_project.html
2
Norris, Guy. “Rotor Revival”. Aviation Week & Space Technology. 14 December 2009. pages
54-57.
3
"PurePower PW1000G." Home. Web. 30 Mar. 2010.
<http://www.pw.utc.com/Products/Commercial/PurePower+PW1000G>.
4
Raymer, Daniel P. Aircraft Design A Conceptual Approach (Aiaa Education Series). New
York: AIAA American Institute of Aeronautics & Ast, 2006. Print.
5
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.
6
Jane's All The World's Aircraft. Web. 11 Feb. 2010.
<http://jawa.janes.com/public/jawa/index.shtml>.
41
APPENDIX A
Conventional Configuration Input Variables
42
%% Input section
% aircraft contant ratios
Wo_S = 76; %lbs/ft^2 from initial contrait diagram
Cfactor = GetCfactors('G650');
%Tech Factors
engine.tech_fact = .7; %Technology factor - SFC (~30%) (~40%=projected)
% wing variables
wing.AR = 8;
wing.taper = .3;
wing.sweep = deg2rad(35); %rad
wing.t_c = .08;
wing.Scs = 25; %control surface area on wing (ft^2)
%vertical tail variables
tail_vt.Cvt = .09;
tail_vt.Lvt = 40; %feet
tail_vt.taper = .8;
tail_vt.sweep = deg2rad(25); %rad
tail_vt.t_c = .08;
tail_vt.Ttail = 1; %1 for t-tail, 0 otherwise
tail_vt.AR = 1;
tail_vt.Scs = 40; %control surface area on vertical tail (ft^2)
% canard variables
canard.Lc = 40; %feet
canard.taper = .5;
canard.Cc = 1;
canard.AR = 2;
canard.sweep = deg2rad(40); %rad
canard.t_c = .08;
canard.Kuht = 1; %all moving = 1.143, otherwise 1
canard.Fw = 9; %fuselage width at canard location (ft)
canard.Scs = 50; %control surface area on canard (ft^2)
%pylon/Nacelles
nacelle.L = 20;
nacelle.D = 5;
pylon.c = 1;
pylon.t_c = .3;
pylon.S = 10;
%fuselage
fuselage.L = 90; %length of fuselage (ft)
fuselage.D = 9; %diameter of fuselage (ft)
fuselage.SDepth = 7; %fuselage structural depth (diam at wing box) (ft)
fuselage.Lc = 40; %wing mac to canard mac (ft)
%landing gear
gear.location = 1; %1 = wing, 1.12 for fuselage mounted
43
gear.Nl = 2.5; %ultimate landing
gear.length_main= 5; %ft
gear.length_nose = 5; %ft
gear.main_wheels = 4; %number of
gear.main_struts = 2; %number of
gear.nose_wheels = 2; %number of
load factor (1.5*Ngear)
main gear wheels
main gear shock struts
nose gear wheels
% mission variables
mission.num_pax = 16;
mission.weight_pax = 220;
mission.num_crew = 4;
mission.weight_crew = 200;
mission.range = 7000; %nmi
mission.q = 200; %dynamic pressure at cruise
mission.Nz = 2.5*1.5; %ultimate load factor (1.5*load factor)
mission.Mcruise = .85;
mission.cruise_alt = 42000;
%engine variables
engine.Kng = 1.017; %1.017 for pylon mounted nacelle, 1.0 otherwise
engine.nacelle_length = 20; %ft
engine.nacelle_width = 5; %ft
engine.weight = 3000; %lbs
engine.number = 2; %total number of engines
engine.d2c = 110; %ft - total distance from engines to cockpit (sum for both
engines)
engine.Kr = 1; %1.133 if reciprocating engine, 1.0 otherwise
engine.Ktp = 1.0; %0.793 if turboprop, 1.0 otherwise
engine.SFC_cruise = .5; %1/hr
engine.SFC_loiter = .4; %1/hr
%controls variables
controls.num_fnx = 5; %number of functions performed by controlls (usually 47)
controls.num_mech = 1; %number of mechanical functions (usually 0-2)
controls.Iy = 1001000; %yawing moment of inertia (lb ft^2)
% aerodynamic
aero.V_stall = 210; %ft/s - stall for the main wing
%weight
weight.Wo_guess = 100000;
weight.APU_u = 125; %lbs - uninstalled weight
weight.avionics_u = 250; %lbs - uninstalled avionics weight
%miscallaneous
misc.Rkva = 50; %system electrical rating (kV) - usually 40 to 60 for
transports
misc.La = 250; %electrical routing distance, generators to avionics to
cockpit (ft)
misc.Ngen = 2; %number of generators (usually equal to number of engines)
misc.Vp = 4000; %volume of pressurized section (ft^2)
44
%Locations (note, all in feet relative to nose, plane length ~ 90 ft)
loc.apu = 82;
loc.avionics = 5;
loc.fuel = 42.5;
loc.wing = 42.5;
loc.canard = 90;
loc.tail_vt = 86;
loc.fuselage = 45;
loc.main_gear = 50;
loc.nose_gear = 10;
loc.nacelle = 72;
loc.engine_controls = 5;
loc.engine_starter = 5;
loc.fuel_system = 42.5;
loc.flight_controls = 5;
loc.instruments = 5;
loc.hydraulics = 50;
loc.electrical = 45;
loc.furnishings = 35;
loc.airconditioning = 6;
loc.antiice = 35;
loc.crew = 10;
loc.payload = 35;
loc.engines = 72;
loc.AC = 50;
45
APPENDIX B
Canard Pusher Configuration Input Variables
46
%% Input section
% aircraft contant ratios
Wo_S = 84; %lbs/ft^2 from initial contrait diagram
Cfactor = GetCfactors('Starship');
%Tech Factors
engine.tech_fact = .7; %Technology factor - SFC (~30%) (~40%=projected)
% wing variables
wing.AR = 10.53;
wing.taper = .2;
wing.sweep = deg2rad(30); %rad
wing.t_c = .1;
wing.Scs = 10; %control surface area on wing (ft^2)
%vertical tail variables
tail_vt.Cvt = .09;
tail_vt.Lvt = 23; %feet wing mac to tail mac
tail_vt.taper = .8;
tail_vt.sweep = deg2rad(30); %rad
tail_vt.t_c = .08;
tail_vt.Ttail = 0; %1 for t-tail, 0 otherwise
tail_vt.AR = 2.4;
tail_vt.Scs = 20; %control surface area on vertical tail (ft^2)
% canard variables
canard.Lc = 50; %feet
canard.taper = 1;
canard.Cc = 1; %volume coefficient
canard.AR = 9;
canard.sweep = deg2rad(35); %rad
canard.t_c = .08;
canard.Kuht = 1.143; %all moving = 1.143, otherwise 1
canard.Fw = 9; %fuselage width at canard location (ft)
canard.Scs = 35; %control surface area on canard (ft^2)
%pylon/Nacelles
nacelle.L = 15;
nacelle.D = 5;
pylon.c = 1;
pylon.t_c = .3;
pylon.S = 10;
%fuselage
fuselage.L = 90; %length of fuselage (ft)
fuselage.D = 9; %diameter of fuselage (ft)
fuselage.SDepth = 7; %fuselage structural depth (diam at wing box) (ft)
fuselage.Lc = 50; %wing mac to canard mac (ft)
%landing gear
gear.location = 1; %1 = wing, 1.12 for fuselage mounted
47
gear.Nl = 2.5; %ultimate landing
gear.length_main= 4; %ft
gear.length_nose = 4; %ft
gear.main_wheels = 4; %number of
gear.main_struts = 2; %number of
gear.nose_wheels = 1; %number of
load factor (1.5*Ngear)
main gear wheels
main gear shock struts
nose gear wheels
% mission variables
mission.num_pax = 18;
mission.weight_pax = 220;
mission.num_crew = 4;
mission.weight_crew = 200;
mission.range = 7000; %nmi
mission.q = 200; %dynamic pressure at cruise
mission.Nz = 1.5*2.5; %ultimate load factor (1.5*load factor)
mission.Mcruise = .85;
mission.cruise_alt = 42000;
%engine variables
engine.Kng = 1; %1.017 for pylon mounted nacelle, 1.0 otherwise
engine.nacelle_length = 20; %ft
engine.nacelle_width = 5; %ft
engine.weight = 3000; %lbs
engine.number = 2; %total number of engines
engine.d2c = 100; %ft - total distance from engines to cockpit (sum for both
engines)
engine.Kr = 1; %1.133 if reciprocating engine, 1.0 otherwise
engine.Ktp = 1; %0.793 if turboprop, 1.0 otherwise
engine.SFC_cruise = .5; %1/hr
engine.SFC_loiter = .4; %1/hr
%controls variables
controls.num_fnx = 5; %number of functions performed by controlls (usually 47)
controls.num_mech = 1; %number of mechanical functions (usually 0-2)
controls.Iy = 1000100; %yawing moment of inertia (lb ft^2)
% aerodynamic
aero.V_stall = 220; %ft/s - stall for the main wing
%weight
weight.Wo_guess = 75000;
weight.APU_u = 200; %lbs - uninstalled weight
weight.avionics_u = 300; %lbs - uninstalled avionics weight
%miscallaneous
misc.Rkva = 50; %system electrical rating (kV) - usually 40 to 60 for
transports
misc.La = 150; %electrical routing distance, generators to avionics to
cockpit (ft)
misc.Ngen = 2; %number of generators (usually equal to number of engines)
misc.Vp = 737; %volume of pressurized section (ft^2)
48
%Locations (note, all in feet relative to nose, plane length ~ 90 ft)
loc.apu = 10;
loc.avionics = 5;
loc.fuel = 78;
loc.wing = 78;
loc.canard = 10;
loc.tail_vt = 83;
loc.fuselage = 45;
loc.main_gear = 80;
loc.nose_gear = 10;
loc.nacelle = 85;
loc.engine_controls = 5;
loc.engine_starter = 5;
loc.fuel_system = 78;
loc.flight_controls = 5;
loc.instruments = 5;
loc.hydraulics = 40;
loc.electrical = 45;
loc.furnishings = 35;
loc.airconditioning = 6;
loc.antiice = 70;
loc.crew = 10;
loc.payload = 35;
loc.engines = 85;
loc.AC = 70;
49
APPENDIX C
Drag Sample Calculations
50
At a cruise height of 42,000 feet, at a cruise speed of 0.85 Mach, q is found to be
q = 0.5*(0.000532 slugs/ft3)*(0.85*968.076 ft/sec)2
q = 180.11 psf
As well, S for the aircraft is currently estimated at 1035 ft2. Thus,
𝑊
90,000 𝑙𝑏
𝐶𝐿𝑐𝑟𝑢𝑖𝑠𝑒 = 𝑞𝑆 ≈ 180.11 𝑝𝑠𝑓∗1035 𝑓𝑡 2 = 0.483
The drag due to lift will vary slightly based on whether the canard or standard aircraft
setup is considered, since the canard aircraft boasts an AR =10 while the standard aircraft
currently has an AR=8. Thus, for the standard aircraft,
CD = 0.01924 + 0.01159 + 0.0010+ 0.0020
= 0.03384
For the canard,
CD = 0.01924 + 0.009274 + 0.0010 + 0.0020
= 0.03151
Once CD is found the total drag force, DTotal, may be found very easily by the equation
DTotal = CD q S
Thus, the current total drag for the standard aircraft is found to be
DTotal = 0.03384*(180.11 psf)*1035 ft2
DTotal = 6308 lbf ≈ 6310 lbf
The current total drag for the canard aircraft is
DTotal = 0.03151*(180.11 psf)*1035 ft2
DTotal = 5837 lbf ≈ 5840 lbf
Note that it is reasonable to approximate the drag to the ten’s place based on the amount of
approximation present in the calculations.
51