2008-2009 AIAA Foundation Team Aircraft Design Competition -Proposal-
_____________________________________________
University of Southern California
Kristina Larson Member # 306306 Stability Flight Dynamics Weight & Inertia
Vanessa Wright
Sina Golshany
Member # 305720 Mission Optimization Aerodynamics Performance
Member # 281677 Lead Designer Prolusion Structure
Taylor Chen Member # Numerical Analysis Environmental Impact Cost
Michael Asfaw
Charles Peot
Devin Lewis
Chris Lovdahl
Member # Acoustics System Integration Configuration
Member # Management Structure Landing Gear
Member # Aesthetics Ergonomics Interior Architecture
Member #296606 Aerodynamics Performance Configuration
Dr. Ron Blackwelder
Dr. Oussama Safadi
Project Advisor
Faculty Advisor
Member # 1460
Member # 283128
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Table of Contents Page #
Nomenclature 2 Executive Summery 7 Overview of Approach and Methods 9 1. Preliminary Sizing & Initial Studies 1.1 Statistical and Mission Based Weight Estimation 13 1.2 Sensitivity Analyses 16 1.3 Performance Sizing via Constraint Plots 17 1.4 Development of the Aerodynamic Measure of Merit 19 1.5 Conceptual Studies 21 1.6 Initial Fuselage Geometry 24 1.7 Wing Planform Design 30 1.8 Airfoil Selection 35 1.9 Center of Gravity 37 2. Detailed Design & Analyses: Aerodynamics, Trim and Powerplant integration 2.1 Wing Geometric Twist & Airfoil Optimization 38 2.2 Sizing of High Lift Devices 39 2.3 Initial Drag Analysis 42 2.4 Determination of Wing Longitudinal Location 43 2.5 Horizontal Tail Surface Area Estimation 46 2.6 Vertical Tail Surface Area Estimation 47 2.7 Engine Selection 49 2.8 Engine Fuselage Integration 52 2.9 Landing Gear Design 60 3. Design Verification: Detailed Aerodynamics, Weight & Performance Analysis 3.1 Optimization of Initial Cruise Altitude 63 3.2 Force Laminar Flow Systems and Winglets 65 3.3 Detailed Drag Verification 69 3.4 Detailed Weight Estimation 70 3.5 System Architecture & Integration 72 3.6 Locating Center of Gravity Based on Detailed Weight 73 3.7 Detailed Performance Validation 75 4. Stability & Control Analyses: Trim, Static and Dynamic Stability 4.1 Sizing of the Elevator 79 4.2 Trim Satisfaction 81 4.3 Longitudinal & Lateral-Directional Static Stability 83 4.4 Longitudinal Dynamic Stability 84 4.5 Sizing of the Ailerons 86 4.6 Lateral-Directional Dynamic Stability 86 5. Acoustics, Structural & Cost Analysis 5.1 Detailed Acoustics Analysis 88 5.2 Load Determination & Structural Design 91 5.3 Structural Material 95 5.4 Structural Analysis & Integrity Verification 97 5.5 Cost Analysis 99 2
Nomenclature a, b, c, d,A,B a ARW AC
Regression coefficient for drag calculation Speed of sound Wing aspect ratio Inlet area
A∞ a g
Stream tube cross-section at infinity
BDPClean
Induced drag coefficient,
Average deceleration in ground run
CD 0Clean,M
1 eAR Airplanes clean zero-lift drag coefficient
C Lmax
Maximum lift coefficient for clean stall configuration
S ( Clean )
CLopt ,MaxR
Lift coefficient correspond to the optimum range performance
Cl f
Section-lift-coefficient-due-to-flap deflection derivative
C L
wf
Cl
, C L
h
Contribution of wing-fuselage and horizontal tail to lift curve slope The average airfoil lift curve slope of that part of the wing covered by the aileron
a
Cla
Airplane rolling-moment-coefficient due to ailerons deflection
Cm ,
Airplane pitching-moment-coefficient-due-to-AOA derivative
Cl
Airplane rolling-moment-coefficient-due-to-yaw rate-derivative
Cn
Airplane yawing-moment-coefficient-due-to-side-slip-derivative
C N max , CNmax ( )
Maximum positive and negative normal fore coefficient
C y
Vertical tail contribution to the airplane side force-coefficient-due-to-sideslip
v
derivative ce
ch
WFusedi
Ratio of elevator chord to horizontal tail chord Fuel weight used in the i’th segment
clf , clf L
Change of sections airfoil coefficient due to flaps deflection
ΔC LWδfTO , CLWfL
Change in wing lift coefficient due to flap deflection
T clmax
Temperature increment for atmospheric properties calculation
TO
e
f
TO
cl
Ratio of airfoils section maximum lift coefficient to change in airfoils maximum lift coefficient at constant AOA due to deflection of flaps Elevator deflection angle Flap surface deflection
3
∂WTO ∂WTO
∂WPL
Sensitivity of takeoff weight to payload weight
∂WE
Sensitivity of takeoff weight to crew weight
∂WTO ∂WTO
∂R
Sensitivity of takeoff weight to range
∂E
Sensitivity of takeoff weight to lift to endurance
n V VC
Slope of gust line for design cruise speed
n V VD
Slope of gust line for design dive speed
d h d
Downwash gradient at the horizontal tail
e Clean
Clean Oswald’s coefficient
i
Flap inboard station, in term of wing half span
f
O
Flap outboard station, in term of wing half span
f
a , a
Aileron inboard and outboard station, in terms of wing half span
FWStructure , . . .
Weight fractions
i
O
T actual
Thrust inclination angle Bank angle achieved for the required roll time by FAR-25
Maximum bank angle to maximum side-slip ratio during Dutch roll
D
hTO
I xx B , I yyB , I zz B ′, K L′ K TO
Take-off altitude Moment of inertia along the body axis
M ff
Flap effectiveness for take-off and landing Trim penalty incurred by use of flaps Fuel Fraction
M CrMax
Maximum cruise Mach number
M 0WB
Wing-body moment at zero attack angle
K trim
M WB NP free
Steady-state wing-body moment Wing-ground rolling friction coefficient Free stick neutral point location in terms of wing aerodynamic chord
nlimit (+), nlimit (-)
Positive and negative load factor limits
g
nult Level t
Design ultimate load factor Level for the roll performance
LevelTR
Level for roll-mode time constant 4
Level S
Level for spiral stability
Level D Level D , 25
Level for Dutch rolls damping Level for Dutch rolls damping based of FAR-25 requirements
Level nD
Level for Dutch rolls frequency
Level nD D
Level for Dutch rolls X damping ration
LevelP Level SP Level n ,SP w
Level for Phugoid stability Level for short period damping Level for short period frequency
w
Wing taper ratio Wing sweep angle
n
Longitudinal phugoid mode un-damped natural frequency
n ,S . P
Short period un-dapped natural frequency
n F
Dutch roll undamped natural frequency Engine setting Landing gears lateral tip over angle Fuel density Take-off ground run distance Wing surface area Wet surface area
P ,long
D
S TOG SW S wet
SW f
SW
Ratio of flap area to wing area
SM free
Average static margin Free stick static margin
TUnInsavail
Available engine uninstalled thrust
SM
t c
w
Thickness to chord ratio of the wing
TClong (1) ,…
Longitudinal time constant(s)
T1
Time to halve the amplitude in phugoid mode
2P
T2P
Time to double the amplitude in phugoid mode
TS
Spiral role mode time constant
Tset TR T2S
Steady-state thrust Roll mode time constant Time to double the amplitude in spiral mode
U1 VSclean
Steady state speed Clean stall speed
VS ( - )
Stall speed for maximum negative normal force coefficient 5
VAeas
Design optimum maneuver speed (Equivalent airspeed)
VBeas
(Equivalent airspeed) Design speed for maximum gust intensity Minimum design equivalent speed (Equivalent airspeed)
VCeas (min) VLOF VA
Wtfo
WPL WE WTO W S TOmax W T TOmax X apexW
x ac , xacwf , xach X CG , YCG , Z CG
Lift-off velocity Optimum maneuvering speed Trapped fuel weight Payload weight Empty weight Take-off weight Maximum take-off wing loading Maximum take-off power loading X coordinate of the wing apex (i.e. distance b/w wing quarter chord station and the nose reference point) X coordinate of aerodynamic center in terms of mean aerodynamic chord
xcg
Location of center of gravity X coordinate of center of gravity in terms of mean aerodynamic chord
SP P ,long
Short period mode damping ratio Longitudinal phugoid mode damping ratio
D
Dutch roll mode damping ratio
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Executive Summary:
T
he next generation of short to medium range commercial transport aircraft is considered to be the focal point of present-day research in the aerospace industry. The expected
increase in oil price, the possible introduction of a carbon tax, and stricter environmental constraints have made the development of more efficient and environmentally compatible jetliners a necessity for the aerospace industry.
In addition, many short and medium range jetliners currently in
operation are approaching retirement. This has created a substantial demand for viable successors to some of the most produced aircrafts in the history of commercial aviation. The demand for these replacements has initiated significant development in the fields of aircraft propulsion, systems, and structure to ameliorate the shortcomings of conventional configurations in the areas of fuel economy, aircraft acoustics, and passenger ergonomics. A request for proposal (RFP) issued by the American Institute of Aeronautics and Astronautics (AIAA) calls for the design of a 150 passenger environmentally-compatible aircraft with a transcontinental maximum range of 2800 nautical miles. The RFP requires that this aircraft be capable of taking off from a 7000 ft. runway in a temperature of 86o F with 150 passengers each weighing 225 lbs. Cruise speed is required to be at least 0.78 Mach with an objective speed of 0.8 Mach. Furthermore, the RFP demands that the community noise levels be in agreement with ICAO Chapter 4 level minus 20 dB cumulative, and also requires an improvement of at least eight percent in direct operating cost compared to the present day models. This proposal presents the design of Tranquillus. It is unique in that considerable attention was devoted to optimize aircraft noise levels and environmental impacts. Furthermore, these are achieved while reducing weight and direct operational cost, in addition to improving the performance and handling qualities of the aircraft.
This design process investigated various
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possibilities in the design of an advanced commercial transport which utilizes modern technologies and would be viable for entry into service by 2018. In order to approach the design process, a design structure matrix (DSM) and other methods of management were used. As a result, feedback cycles were minimized and alternative designs were explored in greater detail. This served to enhance the team dynamic and improved the efficiency of the development process. General techniques for multidisciplinary optimization in conjunction with modern empirical and finite element acoustics codes were utilized to perform trade studies and to verify the satisfaction of the requirements set forth by the RFP. Furthermore, highly detailed threedimensional CAD models were used to define the geometry of the aircraft allowing for threedimensional CFD analyses with the highest degree of precision possible. Many of the aerodynamic issues, such as asymmetric flows and separated regions due to geometric irregularity, were discovered as a result of these analyses in the early stages of the design of Tranquillus. Accordingly, design modifications were implemented to rectify these issues.
Additionally, this project
incorporates the development and use of numerous spreadsheets and MATLAB codes to complete certain operations that were not possible through the use of commercial software packages.
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Overview of Approach and Methods:
T
he general design philosophy of Tranquillus has been substantially influenced by methodology presented by Jan Roskam 1 and Edward Heinemann 2. It should be noted that
these methods are often quite extensive and cover technical aspects of the analysis in great detail. The majority of calculations performed and referenced within the proposal use published graphs and tables in order to determine the constants and parameters, often consisting of multiple, timeconsuming permutations. While the theoretical background of these methods is discussed in various parts of this proposal, in the interests of brevity, many of the mathematical models and statistical data used in the design are not presented in their entirety. Therefore, in order to allow for the full engineering evaluation of this project, the basis for all calculations is presented in two separate volumes provided with this proposal and are referenced as needed.
Design Structure Matrix (DSM), a modern method of development management, has been applied to determine the optimum design process by combining feedback cycles and determining possible parallel analysis. This method, described by Eppinger et al. 3, is used to organize interrelated tasks in the design process in a way that minimizes the number of feedback cycles. In order to apply this method, the design process is broken down into 32 major tasks in an initial order as shown in Figure 1-a. Utilizing a DSM-based code, parallel processes were identified, and the entire process was re-ordered based on the level of dependency of each process on the outputs of other processes. As a result of this analysis, the design approach presented by Roskam has been slightly modified to allow for additional parallel processes and consequently, improved development speed.
Roskam J., Airplane Design ,part I trough VIII , DAR Corporation, 2003 Heinemann, E., Raussa, R. and Van Every, K., Aircraft Design, The Nautical and Aviation Publication Co., 1985. 3 Eppinger, Steven D. and Ulrich, Karl T., Product Design and Development, Second Edition, Irwin McGraw-Hill, Boston, 2000 1 2
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Figure 1-a. Initial Design Structure Matrix using PSM32 Code, accounting for the 32 most critical tasks in the development of Tranquillus
Fiure 2. Reduced process flowchart.
Figure 1-a. The DSM used for optimization of the design process prior to parallel process separation. This figure presents the 32 most critical tasks for the development of Tranquillus arranged in the initial order in a square matrix. Both rows and columns represent the same task, and the number in the intersection of a particular row and column denotes the interdependency of the two tasks. For example the number 2 located at the intersection of row 15 and column 16 indicates a strong, one way dependency of the optimization of the engine characteristics on the environmental trade studies performed using the GasTurb software. Figure 1-b. The optimized DSM, marking the bands of parallel tasks in the order of interdependency to other design processes. This method allowed for the reduction in the time of development for each concept studied as a part of this project, therefore allowing the final design concept to be developed in considerable detail. Figure 2. The reduced process flowchart marks the significant index numbers in relation to the Design Structure Matrix used to optimize the design process.
Figure 1-b. Optimized DSM based on the interdependency of the critical tasks in the order of low to high dependency.
A variety of configurations have been studied, including the concept of a lifting fuselage and blended-wing-body. These alternative concepts have been developed in great detail in order to make possible a precise comparison and to ensure the validity of the design assumptions. Different modules of ANSYS Multiphysics package have been used for computational fluid dynamics, finite element analysis, and acoustics analysis to confirm the calculation results achieved using standard methods of analysis. In particular, two primary analytical tools were used in order to perform the trade studies or detailed analysis of each of the configurations. As a flexible configuration validation tool, a spreadsheet with interconnected modules was developed in order to make a rapid sizing of each concept possible. This software was also used for numerous initial trade studies due to its flexibility in rapid sizing of different configuration concepts. Secondly, to perform a detailed analysis of each configuration and advanced trade studies, Advanced Aircraft Analysis (AAA) was used after the final design configuration was selected.
GasTurb software was another useful
analytical tool which was used in order to perform environmental trade studies, in addition to optimizing and evaluating different engine concepts. This software was further used to study the effects of mission variables on NOx emission levels and fuel consumption in order to minimize the environmental impact of the selected power plant, which was accomplished by optimizing the flight condition and engine characteristics. Additionally, NASA ANOPP code was used to perform community noise evaluations. The compiled code used the outputs from the aerodynamics module of AAA to compute the airframe noise, the outputs concerning engine parameters from GasTurb, and noise attenuation results from the ANSYS finite element acoustics module.
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1
Perliminary Sizing & Initial Studies
Tranquillus was designed to replace the aging fleet of Boeing 737 and Airbus A320 aircraft. Its entry into service is scheduled for 2018. As a replacement for two of the most successful commercial airliners ever produced, it presents vast economic potential for aircraft manufacturers. Both of these aircraft have served in airlines all over the world with exceptional economic success. They have received multiple upgrades to accommodate a variety of range and payload requirements and include modern avionics and power plant options. However, the skyrocketing price of fuel over the past five years and the potential market for the next generation of the short and medium range aircraft has initiated significant research and development to improve the fuel efficiency of engines and aircrafts 4. Table 1 presents the performance figures for the current operating Boeing 737 and Airbus A320 aircrafts, as well as the requirements set by the RFP. Table 1. Performance of major competitors’ and RFP requirements
Aircraft Takeoff Weight [lb.] Empty Weight [lb.] Number of Passengers Maximum Range [n.m.] Fuel burn (max range, max payload)[lb.] Cruise Mach Number Optimum Cruise Alt. Sequence [ft.] Takeoff field length (ISA+27 F) [ft.] Landing Field Length [ft.] Unit Cost [US Million $] Number Manufactured (April 2009)
Boeing 737-700 154000 1 84100 149 (Dense) 2200 278801 0.785 31-35-39000 8280 4550 58.5-69.5 2 6012
Airbus A320-200 170000 93000 148 (2-class) 2600 37854 0.780 31-34-38000 6900 5085 73.2-80.6 3 3859
RFP No Requirement No Requirement 150 (2-class) 2800 No Requirement 0.78-0.80 >35000 7000 ft No Requirement Competitive N/A
1 Source: Boeing Specification Sheet, Airplane Performance Vol., P.95 Oct. ’05. This figure is assuming winglets installed, full payload onboard and assuming 15 percent fuel remaining at landing with no auxiliary tanks. 2 Source: Boeing Aircraft, web site, retrieved on May 5th 2009 3 Source: Airbus Aircraft, Range of 2008 List Prices, dated May 1st 2008) 4 Airlines devote 40% of the retail price of an air ticket to pay for fuel in 2008, versus 15% in 2000. Source: "To Save Fuel, Airlines Find No Speck Too Small." New York Times, June 11, 2008.
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Comparing the Boeing 737-700 and Airbus A320-200 with the requirements of the RFP, it is evident that both aircraft possess similarities to the requirements presented by the RFP. Computing the average unit cost per unit empty weight for each aircraft, the Boeing 737-700 is 8.6% more expensive than the Airbus A320, but its fuel burn per passenger for an identical payload weight performing the same mission is 14.8% lower.
The better market performance of the Boeing 737
when compared to the Airbus A320 highlights the fact that the fuel economy of the aircraft is a decisive factor in the eventual financial success of the product. Considering the fact that the environmental impact of the aircraft is often characterized as a function of the fuel burn, as argued by Schwartz et al. 1, significant improvements could be achieved regarding the operational cost and environmental impact of the aircraft by reducing the fuel burn via mission optimization and use of modern propulsion concepts.
1.1 Statistical and Mission Based Weight Estimation Statistical methods presented by Roskam 2 based on the extrapolated regression coefficients are used to obtain an initial estimate based on the typical mission provided by the RFP. An iterative process is used to solve for the takeoff weight and empty weight by goal seeking to converge on a combination of takeoff weight and empty weight that satisfies the coupled Equations 1 and 2. log 10 W TO A B W E CWTO D
log 10 W E
(1) (2)
Constants A and B may be extrapolated from available weight data for aircraft with similar range and performance by fitting an exponential curve, and the values for these constants are computed as: A=0.0833 B=1.0383
1 Emily Schwartz, and Ilan M. Kroo, Aircraft Design: Trading Cost and Climate Impact, presented at the 47th AIAA Aerospace Science meeting, Jan. 5-9 2009 by Stanford University 2 Roskam J., Airplane Design Part I; 1999 Section 2.7.1, P. 69
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Coefficients C and D are obtained using Equations 3 and 4:
C 1 1 M ff 1 M Fres M tfo D W PL WCrew
(3) (4)
where the overall fuel fraction (Mff ) for the mission is computed from a linear product of the fuel fractions of each segment as described by Equations 5: n
M ff M ff i
(5)
i 1
and the corresponding fuel fraction for each segment is defined as: Wi WFusedi (6) M ff i Wi Fuel fractions of each individual segment are estimated using the relations presented in the Data Unit Vol I 1, based on the mission profile characteristics for each segment. Knowing the overall fuel fraction, the fuel burn during the mission is computed using Equation 7: WFused (1 M ff )WTO
(7)
and the total fuel required for the mission is obtained from Equation 8:
(8)
WF 1 M Fres WFused
Correspondingly, the airplane weight at the beginning of each mission segment is computed from Equation 9: Wbegin i Wbegin i 1 WFused i WFrefuel i 1 WPL expi 1
(9)
where the fuel weight at the beginning of each segment is computed from Equation 10:
WFbegini 1 WFusedi WFrefueli
2
(10)
Making numerous assumptions in order to compute the fuel fractions for each individual mission segment, the first estimation of takeoff weight, empty weight, and fuel burn for the aircraft is
1
“Tranquillus Project Technical Data Unit”, Vol. I” PP. 5-6
14
obtained. A visual representation of the mission profile is shown in Figure 3 below while Tables 2 and 3 provide a summary of the results of this analysis.
Figure 3. Typical Mission Profile used for the initial weight estimation
Mission Segment
M ff
Wbegin (lb )
W FUsed (lb )
WFbegin (lb )
1-Taxi Out (9 min.) 2-Takeoff past the 35’ obstacle 3-Climb to 1500’, accelerate to 250 kts. 4-Climb to 10000’, at 250 kts. 5-Accelerate to Climb Speed & Climb to LRC 6- Cruise at LRC for 1200 n.mi. 7- Climb to improve efficiency 8- Cruise at LRC for 1200 n.mi. 9- Descend to 1500 ft. 10- Approach, Land, Taxi (5 min.) 11- Missed Approach 12- Climb to LRC 13- Cruise at LRC for hold (200 n.mi.) 14- Descent 15- Re-approach 16- Loiter (30 min. 1500 ft.)
0.9900 0.9950 0.9997 0.9989 0.9966 0.9423 0.9997 0.9426 0.9900 0.9920 0.9985 0.9986 0.9905 0.9900 0.9900 0.9911
139479 138084 137393 137357 137206 136740 128854 128811 121422 120208 119246 119066 118898 117772 116594 115428
1395 690 36.1 151 467 7886 41 7389 1214 962 180 168 1126 1106 1166 1031
26336 24941 24251 24214 24063 23597 15711 15668 8279 7065 6103 5923 5755 4348 3451 2285
Table 2. Results of weights for the mission segments presented in Figure 3
The reserve segment of the mission, and in particular the requirements regarding a 30 minute hold at 1500 ft. altitude are in agreement with the requirements set by FAR regulations sections 121.645 part c, which is
Table 3. Summary of the initial weight
WE WTO
74905 lb 139479 lb
M ff
0.8202
WFused
25081 lb 15
determined to be more critical than parts a and b of the aforementioned regulation which demands reserve fuel for only 10% of the total cruise time for the maximum range of the aircraft.
1.2 Sensitivity Analyses The sensitivity analysis assesses the effects of different design specifications on the final product performance by means of evaluating proper partial derivatives of performance characteristic equations. The results of these studies affect the initial configuration of the aircraft by eliminating improper configurations in terms of range and endurance, as well as determining the parameters which drive the design. The theoretical background and the derivatives are presented in Data Unit Volume I 1 . All of these derivatives are defined as the summation of continued product of a sequence of fuel fractions. As an example, the sensitivity of the take-off weight to payload weight at the kth segment is calculated from: (11)
WTO BWTO WPL C.WTO (1 B) D B(1 M Fres )WF
where the coefficients B, C, and D have been previously defined in equations (1), (3), and (4). The result of the analysis of general and mission related sensitivity partials are presented in tables 4 and 5. Mission Segment
WTO
c j
lb hr
WTO
R
lb n.mi.
WTO
L
WTO
D
lb E hr
5 – Climb to LRC
4654.6
------------------
-107.4
10184.5
6 – Cruise at 37000’
64265.8
21.9
-1511.0
------------------
8 – Cruise at 38000’
63913.9
21.7
-1494.5
------------------
12 – Climb to LRC
1933.4
------------------
-39.0
8911.4
13 – Loiter at 37000’
13006.5
31.8
-262.6
------------------
Table 4. Mission related sensitivity partials matrix for the longest mission segments Note that the mission index matches the mission segments previously defined in Table 2. For the assumptions made for each segment refer to Data Unit Volume I 1.
1
Table 5. General sensitivity partials
WTO WPL
10.74
WTO WE
1.49
“Tranquillus Project Technical Data Unit”, Vol. I” PP. 7-10
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The partial derivative of takeoff weight due to change in specific fuel consumption, WTO c j suggests that the thrust specific fuel consumption is the most significant factor in the
performance of the aircraft in all mission segments except for both climbs to Long Range Cruise (LRC) altitude. The second most influential parameter was determined to be the lift to drag ratio, which heavily influences the fuel burn during both LRC segments. The partial derivative of takeoff weight due to change in lift-to-drag ratio WTO L D suggests that a high lift-to-drag ratio can cause significant reduction in the aircraft takeoff weight, resulting in a reduction of almost 1500 lbs per unit in lift-todrag ratio. Given the relatively large projected market for a single aisle commercial jetliner, options such as customized airfoil design, advanced wing tips and high aspect ratio composite wings with variable camber are available to the designer as financially feasible solutions to improve the lift-todrag ratio.
1.3 Performance Sizing via Constraint Plots In order to ensure that all of the RFP requirements were simultaneous satisfied of, performance equations were solved and plotted as a function of the thrust loading and wing loading of the aircraft. Since there are no requirements set by FAR25 on the maximum stall speed of the aircraft, the aircraft was sized based on a clean stall speed of 130 kts and a takeoff stall speed of 114 kts, similar to the Boeing 737 and Airbus A320. Equations 12 to 14 were used in order to obtain the limiting wing loading for stall:
W W W TO S TO WS S S
(12)
1 W 2 Vs C LmaxS S S 2
(13)
where:
17
VS
2Wcurrent Tset sin current T SW C Lmax
(14)
The assumptions made can be found in Data Unit Volume I 1 . Based on the recommendations of FAR-25, the thrust-to-weight ratio for the takeoff distance was computed from Equation 15:
T W TO
W S TO 0.0296 STOCLmax FTO
(15)
The required thrust-to-weight ratio is plotted on the matching plot with three different lift coefficients, all close to the statistical data obtained from single aisle jetliners of a similar size. In order to achieve the required maximum cruise speed specified by the RFP, the drag polar of the aircraft was first determined by means of extrapolating statistical data from similar aircrafts, and applying regression coefficients as suggested by Roskam 2 and Loftin 3, which is also reflected in volume I of this project’s technical data unit 4. Based on the estimated drag coefficient, Equation 16 was used to determine the optimum wing loading and thrust-to-weight ratio to satisfy the cruise speed requirement. 2
CD0 ,Clean W BDPclean W T Cr q W W TO WTO q FCr S TO FCr S TO Using Equation 17, the constraint curve for landing distance is plotted:
W W 0.5 h, L ( ISA) C Lmax L S L F1 TO WL S L
(16)
(17)
where factor F1 for FAR-25 certified aircraft is assumed to be 9.365.
1
“Tranquillus Project Technical Data Unit”, Vol. I” P.18 Table 17 Roskam J., Airplane Design Part I; Section 3.4.1, P. 118-127 , DAR Corporation, 1997 3 Loftin, Jr., L.K, Subsonic aircraft: Evaluation and the Matching of Size to Performance, NASA Reference Publication 1060. 1980 4 “Tranquillus Technical Data Unit, Vol. I” PP. 20-23, 2
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The thrust-to-weight ratio to satisfy the climb requirements presented by FAR-25 sections 119 and 121 for one-engine-operational and fully operational conditions was computed and plotted versus wing loading. The final constraint plot is shown in Figure 4.
Figure 4. Final constraint plot, showing initial and final design points
The initial design point (105, 0.28) was selected based on the initial sizing of the high lift devices, including an efficient leading edge device producing a maximum lift coefficient of 2.0. From this analysis and using the result of the preliminary mission-based weight analysis, a wing area of 1380 square feet was selected for further studies. It was determined that a thrust of 44600 lbs would be sufficient to meet all the performance requirements set by the RFP and FAR-25 based on the initial weight estimation.
1.4 Development of the Aerodynamic Measure of Merit In order to compare different configurations, it is necessary to develop multiple measures of merit that quantify different performance and acoustic parameters as a function of simple geometric properties of each configuration. To be concise, only the derivation for the aerodynamic measure of
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merit is provided below. In order to obtain an expression for the lift-to-drag measure of merit as a function of geometric parameters, it is necessary to define induced and parasite drag as follows: L2 eb2 q D p qSWet C f Di
(18) (19)
It is possible to express the product of induced and parasite drag by combining Equations 18 and 19.
Di D p
L2 SWet C f
eb 2
(20)
Assuming that the induced and parasite drag are each 50% of the total drag, it is possible to write the following:
D Di D p Di D p
(21)
1 2 D (22) 4 Equations 20 and 22 are equal according to Equation 21. Therefore, the squared lift-to-drag ratio Di2
can be written as:
L2 b 2e D 2 4SWet C f which yields the lift-to-drag measure of merit as:
(23)
L b e (24) D Merit SWet 4C f For the purpose of a configuration tradeoff, it is assumed that the Oswald Efficiency and skin friction coefficient are 0.9 and 0.0044, respectively. This simplifies Equation 24 to: L b 13 D Merit SWet
(25)
This geometric global measure of merit has been used to compare different configurations and select configurations with the highest potential lift-to-drag ratio. It should be noted that in most cases this measure of merit is not a critical factor in choosing the configuration due to strict acoustic requirements set by the RFP. 20
1.5 Conceptual Studies The initial design phase of Tranquillus saw the exploration of numerous design concepts before the current configuration was selected. The investigated concepts included lifting fuselage, blended-wing-body, strut-braced high aspect ratio wings, over the wing (OTW) engine mount design, V-tail configuration, and fuselage-mounted engines combined with an H-tail.
As one of the
selection criteria, these concepts were explored through geometric measurements of the wetted area from sized study models and the application of the previously mentioned lift-to-drag merit. One of the initial configurations explored in the design process was the concept of a blended-wing-body (BWB). Given its long history of usage in the aviation industry, this concept was given particular attention in order to determine its possible success as a short-haul 150 passenger aircraft. The final study model can be seen in Figure 5. The BWB possesses remarkable aerodynamic efficiencies due to the reduction of induced drag and additional lift generated by the fuselage which leads to an increase in the
Figure 5. BWB study model, using Northrop-Grumman airfoils K1, K2, and K3 for wing & fuselage cross-sections.
cruise lift-to-drag ratio. This reduction in the induced drag is caused by the aircraft’s capability to fly at a lower lift coefficient requirement due to the larger area of lifting surfaces. Using the lift-to-drag measure of merit, as derived in the previous section, it was confirmed that this design concept would possess an L/D of approximately 24. It was determined that currently operational short-haul aircrafts possess an L/D of approximately 16 using the lift-to-drag measure of merit. The BWB concept’s takeoff weight reduction can be calculated using Table 5 and the average value of the partial derivative of takeoff weight with respect to L/D for the cruise phase. This design will also experience a takeoff weight reduction of almost 7,000 lbs due largely to the reduced fuel burn during 21
cruise. Also, as established by the joint MIT-Cambridge silent aircraft project 1, the BWB concept possesses considerable potential for reducing the aircraft noise during landing and take-off, primarily as a result of noise shielding effects. Despite this significant increase in fuel efficiency, the BWB design was not selected for further development. This choice was influenced mainly by the possible increase in development costs due in part to increased certification costs for such a novel configuration, for which no prior rigorous certification procedure exists. Further planform studies revealed that for small payload volumes (passenger and cargo), the BWB concept would be increasingly unsuitable for the specific payload provided by the RFP, primarily due to the resulting increase in structural weight, wetted surface area, and subsequent increase in parasite drag and fuel burn.
Results of polling performed by Boeing indicate that the general public exhibits an
unfavorable reaction towards flying in a BWB, reducing potential public demand for this concept. The concept of a lifting fuselage was also studied during the initial stages of development. As a compromise between a BWB and a conventional configuration, this concept was perceived to be capable of improved lift-to-drag performance, without a significant increase in weight. This design was conceptualized with a fuselage mounted mixedflow turbofan, and the engine was installed to take advantage of the noise shielding provided by the conventional empennage for the engines. Figure 6 Figure 6. Study model and structural arrangement shows a rendition of this aircraft. After detailed
drawing for the lifting fuselage concept, featuring a K1 transonic airfoil for the fuselage and aft mounted mixed-flow high BPR turbofans.
analysis was performed, it was determined that while this concept produces noticeable additional lift, it also creates a considerable amount of induced drag as a result of counter rotating vortices formed
1
James I. Hileman et al., “Development of Approach Procedures for Silent Aircraft�, 54th AIAA Aerospace Science meeting, Jan. 8-11th, 2007, Reno,Nevada
22
in the wake of the aircraft. This determination was confirmed following a transonic CFD simulation for the fuselage. Results of this analysis are displayed in Figure 7 and 8.
Figure 7. Velocity Contour for the lifting fuselage.
Figure 8. Turbulent kinetic energy contour for lifting fuselage.
Figure 7 and 8. The lifting fuselage is modeled using 3d Fluent elements in ANSYS CFD. This transient analysis simulated the air flow at a speed of 0.6 Mach and an altitude of 35,000 ft, corresponding to 210 m/sec. and a Reynolds Number of 20 million (Ď =0.325 kg/m3, ν=0.00005 m2/s, and P=21,330 Pa). Shear Stress Transport model is used to simulate the turbulence for this Reynolds Number. The intense vortex aft of the tail cone is identified by the sudden drop in the velocity magnitudes and the sudden increase in the turbulent kinetic energy levels.
Having a lift-to-drag ratio measure of merit of 15, this design was not selected for further development due to aerodynamic inefficiencies, multiple structural issues, and safety considerations for engine integration. Aft fuselage-mounted engines combined with an H-tail were also explored during the preliminary configuration process. Ray tracing using Rhinoceros 4.0 indicated that the horizontal and vertical surfaces of the H-tail are capable of lowering far-field noise by reflecting the propagating acoustic waves created by the engine nozzle and the hot turbulent jet exiting the engine. A preliminary rendition of this configuration is presented
in
Figure
9.
The
general
configuration of the aircraft presented a remarkable potential for further development considering the promising quality of aft mounted engine noise suppression and clean wing,
Figure 9. Initial high aspect ratio wing and tail configuration for Tranquillus.
23
in addition to the simplicity of development and certification of the aircraft. Different propulsion options such as unducted fans, 3 spool turbofans, and a variety of geared turbofans including mixed and unmixed flow turbofans are studied as a potential power plant for the aircraft. Multiple optimizations using GasTurb were performed to obtain the characteristics of the optimum power plant. The sizing process presented in section 1.3 using the constraint plots was repeated to ensure the simultaneous satisfaction of the performance requirements set by the RFP for all the variations of this design throughout the design process.
1.6 Initial Fuselage Geometry 1.6.1 Initial Interior Arrangement In order to determine the approximate dimensions of the fuselage, an estimation of the required fuselage volume was made using the statistical data and recommendations presented by Roskam 1 regarding the required floor area for each passenger and the required volume of bag racks, galley units, and lavatories. This was also confirmed by computing the required cabin length for a single aisle aircraft using the statistical method presented by Torenbeek
2
.
A variety of
passenger cabin configurations were studied, and a 3+3 single aisle configuration was selected for the design of the aircraft cross section. As an alternative to the conventional triplet seats, the concept of the staggered seating first explored by Thompson Solutions was considered for the interior design. Figure
1 2
Figure 10. Thompson Solution速 inclined seat concept. Note the sidewise headrest and divider.
Roskam J., Airplane Design Part III; Section 3.3.2.2, P. 58-66 , DAR Corporation, 1990 Torenbeek E., Synthesis of Subsonice Aircraft Design, Kluwer Boston Inc. , Hingham, Maine, 1982, Figure 3-13
24
10 presents a rendition of this type of seat studied as a part of the interior design tradeoffs.
Despite the
extreme comfort and privacy provided to each passenger due to the sidewise head rest, it is perceived that this type of seat may have an increased price compared to the conventional seats with no particular
Figure 11. Conventional ergonomic seats.
benefit to the interior arrangement of a narrow body jetliner. Ultimately, conventional seats shown in Figure 11 were chosen for the interior arrangement of the aircraft.
1.6.2 Development of the cross-section: Multiple geometries for the construction of the main cross section were explored, including elliptical, circular, multi-arc, and double bubble cross-sections. Cross-sections were designed by applying the recommendations provided by Roskam 1 for minimum clearances required for the interior geometry of the cabin. Ratio of the cross-section perimeter to the enclosed area was selected as a measure of merit for each cross-section to represent the ratio of the wetted area of the cabin to the interior volume. Among the developed concepts for the main cross-section of the cabin, the elliptical and multi-arc cross-sections presented the lowest ratio of perimeter to enclosed area, but they were not chosen for further development due to the expected non-uniform load distribution caused by the varying curvature of the pressure vessel. Recommendations made by the American Society of Human Factors and Ergonomics were used for the interior arrangement and furniture of the cabin. In particular, recommendations regarding the width of the cabin seats that are situated in between two other seats are followed in designing the seats 2. As a result, the width of the middle seats in the cabin is selected to be one and half inch wider and the mid armrests (shared 1
Roskam J., Airplane Design Part III; Section 3.3.1.1, P. 52 , DAR Corporation, 1990 Kroemer, Karl E.H. "Extra-Ordinary" Ergonomics: How to Accommodate Small and Big Persons, The Disabled and Elderly, Expectant Mothers, and Children, Section 5.1. American Society of Human Factors and Ergonomics, 2005
2
25
by two passengers) are 0.5 inches wider than in a usual A320 or B737 cabin. Due to the use of stabilized composite sandwiches for the fuselage structure, it is expected that the thickness of the fuselage outer ramparts will be reduced by one inch compared with the conventional aluminum constructions. This implies that the eye level width of cabin could be increased by as much as two inches with no implications on the fuselage wetted surface area. The final cross-section designed for the economy cabin of the aircraft is shown in Figure 12.
Figure 12. Final cross-section designed for Tranquillus. Dimensions in this drawing are in inches.
Bag racks were designed to provide 2.7 cubic feet of onboard bag racks per passenger, while the main cargo bay was designed to provide room for 1250 cubic feet of bulk cargo to be stored. This implies that the cargo capacity is almost 10% more than what is asked by the RFP, which allows for future modifications of the aircraft to increase the passenger count. Two 40�×36� cargo doors provide access to front and aft cargo holdings. The cargo handling system consists of ball rollers in front of the main loading doors and powered bi-directional rollers in longitudinal direction with a longitudinal spacing of one foot. The movement of the cargo is controlled trough an electronic 26
system installed on cargo bay ceiling near each loading door. Tie down hard points and cargo net attachment points are provided to allow for safe storage of cargo. Figure 12 presents the final cargo bay layout for Tranquillus.
1.6.3 Refined Interior Arrangement: Reviewing the results of the weight optimization outlined by Leibeck et al 1 for the fuselage, a fineness ratio of 9.6 was selected for the fuselage and by applying the results obtained in section 1.6.1, the interior arrangement of the fuselage was determined. Initial longitudinal profile for the aircraft was designed with a length of 130 ft, which was reduced to 126 feet after 4 consecutive design iterations. Based on the statistical data provided by Roskam 2, two lavatories for the economy cabin and one lavatory for the first class cabin were designed. Two main galley units were designed to accommodate 15 galley carts and the relevant food preparation equipments such as microwave ovens, coffee makers, and refrigerators. In order to provide sufficient exit routes to meet emergency protocols regarding safe evacuation, guidelines provided by Roskam 3 was pursued to determine the number and type of the doors for the aircraft. As a result, by sizing the doors for a goal capacity of 185 passengers 4, a pair of A-type main doors with the dimensions of 42” by 72” in the front and a pair of 32” by 72” B-type doors in the aft compartment was selected. Two on wing emergency exits with the dimensions of 20” by 36” inches were also added to ensure the safe emergency egress of the passengers in less than 90 seconds, as it is required by the FAA to certify the aircraft. Figures 14 and 15 present the interior arrangement for dual class and single class configurations for Tranquillus.
Liebeck, R, H., Page, M. A., Rawdon, Blaine K., Scott, Paul W., and Wright Robert A., "Concepts for Advanced Subsonic Transports," NASA CR-4628, McDonnell Douglas Corporation, Long Beach, CA, Sep. 1994. 2 Roskam J., Airplane Design Part III; Section 3.3.4, P. 73 , DAR Corporation, 1990 3 Roskam J., Airplane Design Part III; Section 3.3.1.2, P. 70 , DAR Corporation, 1990 4 This decision is made in order to allow a future 25 percent increase in capacity of the present design, without a need to re-design the door systems. 1
27
Figure 13. Cargo layout showing the main cargo handling systems Figure 14. Dual class configuration for 150 passenger, 12 first class seats with 36� pitch, and 138 economy seats. Figure 15. Single class configuration for 162 passengers, tourist class with 30� pitch. 4 flight attendants are sufficient for both designs.
Figure 13. Cargo layout showing the main cargo handling systems
Figure 14. Dual Class Interior Configuration
Figure 15. Single Class Interior Configuration
Considering the goal for maximum cruise speed of Tranquillus (0.82 Mach), a length to diameter ratio of 1.5 was selected to design the nose compartment. Reviewing the statistical data obtained from 3 view drawings of aircrafts with similar mission, a tail length to diameter ratio of three was selected for the design of the aft compartment.
1.6.4 Cockpit Design: The cockpit is designed to accommodate two 6’-2” pilots.
Therefore, using the standard
dimensioned views of 6’-2” pilots released by Boeing in Wichita 1, the cockpit for the aircraft is designed. The critical eye vectors were projected on the cockpit surfaces to determine the optimum geometry of the transparencies for the cockpit. The scaled 3-view drawing of the cockpit showing the location of the pilots and critical eye vectors can be seen in Figure 16. It should also be noted that
the
high
droop
configuration was selected to provide better local flow around the nose, since it was discovered that the angle of attack of the aircraft will be slightly higher than aircrafts of similar mission due to the reduced size of the leading edge high lift devices to reduce the airframe noise 2.
Figure 16. Cockpit Layout
1
Roskam J., Airplane Design Part III; Figure 2.8, P. 16 , DAR Corporation, 1987 First Edition Leifur T. Leifsson, William H. Mason, Joseph A. Schetz, Raphael T. Haftka, Bernard Grossman, “Multidisciplinary Design Optimization of Low-Airframe-Noise Transport Aircraft, 44th AIAA Aerospace Sciences Meeting and Exhibit, 2006
2
29
Much effort has been devoted to pilot visibility in order to comply with the suggested cockpit layout by Roskam 1 for commercial aircraft as
well
as
FAR-25
visibility
requirements. Visibility pattern for the cockpit and FAR25 visibility Figure 17. Cockpit visibility pattern (black) and FAR-25 visibility
requirements are presented in Figure 17.requirement (red)
1.7 Wing Planform Design The selection of wing planform was mainly a tradeoff between the structural weight, and the fuel burn during the cruise block for the aircraft.
Using the first class estimation of weight, and
assuming a specific fuel consumption of 0.4 lb/lb.hr., a parametric study was performed to observe the effects of wing aspect ratio and wing sweepback angle on the maximum takeoff gross weight and the empty weight of the aircraft. This trade study revealed that for a properly sized wing, at a sweepback angle of approximately 30 degrees the maximum takeoff gross weight (MTOGW) and the operational empty weight (OEW)
for
minimized.
the
aircraft
are
The result of this
parametric study is presented in Figure 18. To confirm that the reduction in MTOGW was due only to the reduction in block fuel weight, another parametric study was
1
Figure 18. MTOGW plotted versus OEW for different aspect ratios and sweep back angles. Computation was done for a mission range of 2800 n.mi. using the detailed weight analysis. A macro was used to size the aircraft for performance requirements at each data point by goal seeking for wing area and sea-level installed thrust.
Roskam J., Airplane Design Part III; Figure 2.17, P. 27 , DAR Corporation, 1987 First Edition
30
performed, varying the aspect ratio and sweepback angle and computing the fuel burn using the Bereguet range Equation for 2800 n.mi. cruise.
Figure 19
shows the result of this analysis, performed
using
JetSizer
interconnected spreadsheet. Although the result of the trade studies shown in figure 10 suggests that an aspect ratio of ~10 is the global optimum in the stand point of the maximum
Figure 19. MTOGW plotted versus block fuel burn for different aspect ratios and sweepback angles. Computation was done for a mission range of 2800 n.mi. using the detailed weight analysis. A macro was used to size the aircraft for performance requirements at each data point by goal seeking the wing area and sea-level installed thrust.
takeoff gross weight for Tranquillus, the fuel burn trade study indicated a rapidly decrease at aspect ratios higher than 10. As these analyses were not conclusive about the optimum or limiting aspect ratio of the aircraft, another parametric study was performed to select the proper aspect ratio. In this analysis, for different wing reference areas and aspect ratios, wing span was plotted versus mean aerodynamic chord. Flutter bounds were also computed for each aspect ratio, using the derivations presented by Haris 1 and Leiback 2 et al for both composite and aluminum-lithium wing structures. These derivations used semi-empirical methods to identify the boundaries at which the structural oscillation of the wing would match the natural frequency of the wing structure. It was concluded that if modern materials such as composites and lithium-aluminum alloys were selected as the primary structural material for the wings, the flutter was most likely not going to be the limiting
1
Harris G. “Flutter Criteria for Preliminary Design�, LTV aerospace corporation, Voughts Aeronautics and Missile Division, Engineering report 2-53450/3R-467 under Bureau of Naval Weapons Contract NOW 61-1072C,September 1963. 2 Liebeck, R, H., Page, M. A., Rawdon, Blaine K., Scott, Paul W., and Wright Robert A., "Concepts for Advanced Subsonic Transports," NASA CR-4628, McDonnell Douglas Corporation, Long Beach, CA, Sep. 1994.
31
factor in selecting the aspect ratio for the wing planform; rather, the span of the wing limited by the present hangers defines the geometry of the wing. The result of this analysis is shown in Figure 20. Increasing the initial wing area selected for the aircraft by 5 percent, the initial value, aspect ratio of the wing was selected as 9.9, which is marginally higher than the aspect ratio of Boeing 737-700 (9.4), limited by the same hanger size. It was observed from the results that composite wings can be used
Figure 20. Wing span versus aerodynamic mean chord of the wing, for different aspect ratios and wing reference areas. This analysis is performed assuming a sweepback angle of 30 degrees.
at an aspect ratio almost 12 percent higher than the selected aspect ratio for Tranquillus with no risk of flutter; however they can not pass within the present day hanger doors. To remedy this problem a folding wing concept was studied. Reviewing the patent documents released by Boeing regarding the folding wing system designed for the Boeing 777 aircraft 1, it was revealed that use of a selfmonitoring latch pin lock systems would be associated with an increase in structural weight of approximately 3000 2 pounds for Tranquillus. Referring to the trade study shown in Figure 11 it can be observed that the fuel burn reduction associated with increasing the aspect ratio to an unrealistic value of 14 (corresponding to a span of 139 ft.) is approximately 1000 pounds. It is clear that an addition of ~ 3000 pounds of folding mechanism is not a feasible improvement for aircraft in size of Tranquillus.
1
Renzelmann, Michael E. on behalf of Boeing Commercial Aircraft. “Self-monitoring latch pin lock for folding wing aircraft�. U.S. Patent office number 5201479, Issued April 13th 1993. 2 This figure is normalized with the empty weight of the 777 to compensate for the larger structural loads experienced by 777.
32
Considering the selected values for the wing planform, a trade study was performed to determine the corresponding thickness to chord ratio of the wing airfoil in order to satisfy the cruise speed requirements. Methods presented by Roskam 1 were used in order to compute the corresponding critical Mach number for a transonic airfoil at different values of thickness to chord ratio or sweepback angle. Figure 21 presents the result of this analysis together with the boundaries set by the RFP on minimum cruise Mach number and the suggested goal for the cruise Mach number.
Figure 21. Wing Critical Mach number plotted vs. wing weight for different quarter chord sweep back angles and thickness to chord ratios.
Based on this parametric study, it was decided that a thickness to chord ratio of 12 percent should be able to satisfy the requirement for the cruise speed of the aircraft. This criterion for thickness to chord ratio was used to narrow down the list of airfoils for detailed studies using CFD simulations later during the project. Choosing a thickness to chord ratio of 12%, a parametric study was performed to observe the effects of variation of altitude on the wing lift curve slope, to verify the optimality of the selected aspect ratio for takeoff.
1
Roskam J., Airplane Design Part VI; Section 2.1.1, P. 3-7 , DAR Corporation, 1990
33
Advanced Aircraft Analysis software was used to perform this trade study for which the results are presented in Figure 22. From this result, it can be seen that the aspect ratio of the wing is situated at a near optimum value for which the lift curve slope does not significantly increase as the aspect ratio increases.
Figure 22. wing lift curve slope vs. aspect ratio for sea level and the initial cruise altitude.
Trade studies were also performed to observe the effects of the taper ratio of the wing on the lift curve slope, which indicated that the taper ratio of the wing have a purely monotonic behavior, with negligible effects on the curve slope of the wing. Therefore by reviewing the statistical data of aircraft of the same class, a taper ratio of 0.25 was selected. Figure 23 presents the initial wing planform selected for Tranquillus based on the results of the optimization performed.
Figure 23. Initial wing planform selected for Tranquillus. Table to the right presents the geometric characteristics of the planform
34
1.8 Airfoil Selection The selection of the airfoil for Tranquillus was primarily driven by the transonic aerodynamic properties of the airfoil as well as the high lift qualities that play a significant role during takeoff. More than 30 transonic airfoils were analyzed using DesignFoil in order to observe both the transonic and high lift performance of these airfoils. A hierarchical elimination was employed to narrow down the list of the airfoils, in order to make an extensive CFD simulation possible. These airfoils were selected on the basis of their superior maximum lift to drag ratio, and the percentage of the laminar flow maintained on the upper surface. Final airfoils that were selected for further transonic CFD analysis include: RAE-2812, RAE 5212, and SC20712. Results of the CFD analysis on the selected airfoils are shown in Figures 24 trough 26.
Figure 24-a. RAE 5212
Figure 25-a. RAE 2822
Figure 24-b. RAE 5212
Figure 25-b. RAE 2822
Figure 26-a. SC 20712
Figure 26-b. SC 20712
Figures 24-a, 25-a, and 26-a. ANSYS CFD simulation of the three final airfoils selected for further development. Transient CFD analysis was converged for 35000 ft, 0.815 mach with Re=7.16Ă—106, using free hexagonal elements and the Shear Stress Transport turbulence model. Results were post processed using ANSYS CFX software. Figures 24-b, 25-b, and 26-b. Freestream velocity plotted versus the chord length for each airfoil. These results were obtained by plotting the data points along an Spline, defined on the edge of the momentum thickness formed on the top surface of each airfoil. Sonic speed is marked by the broken blue line in each graph
35
From these CFD analyses, it was observed that all three airfoils have a relatively smooth shock on the upper surface, but the RAE 5212 has the lowest amount of sonic flow in cruise condition. Reviewing the drag polars obtained using ANSYS for each airfoil, it was concluded that RAE-5212 posses the highest lift to drag ratio and lift curve slope among the selected airfoils, and therefore this airfoil was selected for further development. The lift and drag versus angle of attack curves for RAE 5212, RAE 2822, and SC 20712 airfoils can be seen in Figure 27.
Figure 27. Comparison of the aerodynamic characteristics of final airfoils. These results are obtained using DesignFoil for a Reynolds number of 9 million, and flow speed of 0.7 Mach.
This analysis revealed that all airfoils reach the optimum L/D at an attack angle of approximately 4 degrees, which considering a wing incidence angle of three degrees corresponds to a flight attack angle of one degree. This is indicative of the fact that the transonic airfoils with high cross-section L/D have a tendency to fly at slightly higher angles of attack than the airfoil with moderate lift to drag ratio, which often maintain steady flight at an attack angle of about 0.3 degrees.
36
This fact was considered while designing the fuselage in order to select a relatively high nose droop and a slightly elliptical tail cone cross section to improve the local flow at relatively high angles of attack in cruise condition.
1.9 Center of Gravity Based on the configuration and placement of major components, using information presented in the Data Unit Volume I 1, and also suggested values for each component C.G. 2, the center of gravity of the aircraft was estimated. As required by the RFP, the change in the location of the center of gravity, due to fuel consumption over different segments of flight was studied. These studies are used later on in order to determine the longitudinal location of the wing installation and study the possibility of maintaining the trim in all flight conditions. A selection of the results of these analyses for major flight conditions are presented in Table 8 below. Table 6. Empty weight components center of gravity (below) ↓ Table 7. Empty CG locations (right) →
Mission segment
W (lb)
Fuselage Group 14628 Wing Group 15509 Empennage Group 3077 Landing Gear Group 5754 Nacelle Group 2549.6 Power Plant Group 10556 Fixed Equipment Group 19246
X CG ( ft ) 63.6 65.5 119.8 41.7 113.3 117.5 51.65
YCG ( ft ) 0 0 0 0 0 0 0
Z CG ( ft ) 1.20 -3.5 10.5 -6.2 15.3 15.3 -3.0
Wstructure
41519 lb
WE X CGstructure
71323 lb 11.75 ft
X CGE
73.3 ft
YCGstructure
0 ft
YCG E
0 ft
Z CGStructure
-0.2 ft
Z CGE
1.43 ft
Table 8. CG location for selected mission segments based on initial weight estimation (2800 n.mi.)
1 2
Mission segment
W FBegin (lb )
X CG ( ft )
1-Warm-up and Taxi 5-Accelerate to Climb Speed & Climb to LRC 6- Cruise prior to climb at LRC for 1200 n.mi. 8- Cruise after 1000 ft. climb 9- Descent to 1500 ft. 10-Land 16-Loiter
26335.7 24063.1 23596.6 15667.8 8279 7065 2285
69.50 68.92 68.94 68.43 68.06 68.00 65.37
Z CG ( ft ) 3.13 3.17 3.24 3.73 3.51 3.47 3.62
“Tranquillus Project Technical Data Unit, Vol. I” PP. 14-15
Advanced Aircraft Analysis documentation, component center of gravity, DAR. Corporation
37
2
Detailed Design & Analyses Aerodynamics, Trim and Power plant Integration
Because of the important contribution of fuselage-wing aerodynamics and geometry to stability and flying qualities of the aircraft, many iterative design processes are performed in order to achieve the optimum aerodynamic and geometric configuration of wing, empennage, and other aerodynamic surfaces. Due to the crucial effect of the power plant on the economy, noise, and performance of the aircraft, particular attention is paid to the selection and optimization of the powerplant. As part of the detailed design and analysis phase of the project, AAA was used as the primary computer aided engineering software package to perform the trade studies.
In particular, the weight,
aerodynamics, propulsion, and stability modules of this software were used in order to achieve the optimum configuration for the aircraft.
2.1 Wing Airfoil and Geometric Twist Optimization As previously mentioned in section 1.6, RAE 5212 airfoil was chosen for further modification in order to improve the aerodynamic efficiency of the wing. This was done by modifying the pressure distribution via changing the location and the magnitude of the camber of the airfoil to reduce the regions with sonic speeds. Due to the compressible nature of flow, it was realized that panel codes such as Xfoil or DesignFoil can not be used to perform the analysis due to theoretical limitations. Instead ANSYS CFD module was used to analyze the flow properties and the characteristics of the root and tip airfoils by mean of a transient compressible analysis, for which the results were later post processed using ANSYS CFX to obtain velocity distributions and lift and drag characteristics. Figures 29 and 30 present the finalized root and tip airfoils and Figure 28 presents the obtained lift and drag characteristics corresponding to each airfoil.
38
Figure 28. Lift and drag characteristics of the tip and root airfoils. Analysis are performed using ANSYS CFD and results are post processed using ANSYS CFX to obtain lift and drag characteristics.
Figure 29. Root airfoil, modified RAE-5212 with one percent reduction in camber
Figure 30. Tip airfoil, modified RAE-5212 with 3 percent increase in camber and maximum camber point shifted aft by 10 percent
As it can be seen from Figure 28, root airfoil produces the minimum amount of drag at an attack angle between three and six degrees. This modification is done mindful of the fact that the root incident angle of the wing will most likely to be around three degrees. Same is true for the tip airfoil, where the airfoil is optimized to maintain lowest drag levels at an attack angle around zero degrees, which correspond to a conventional wing with a geometric twist of negative three degrees at cruise. Also from this figure it can be observed that the tip airfoil does not progress to its highest lift coefficient at the same angle that the wing root is approaching stall. These characteristics make it possible to maintain considerable roll control at relatively high attack angles and low speed, considering the fact that the effectiveness of the ailerons is directly related to the near stall behavior of the outer wing cross section. 39
In conjunction with the optimization of the wing airfoil, studies were performed using AAA to determine a desirable value for the geometric twist of the wing, considering the previously selected wing planform. By obtaining the span-wise lift distribution of each combination of airfoils and geometric twist, the value of the geometric twist for the wing was selected to be -3 degrees. Figure 31 presents an example of different
span-wise
lift
distribution resulted from the
variation
in
the
geometric twist of the wing.
Figure 31. Section lift coefficient vs. spanwise station for different geometric twists using the final root and tip airfoils.
2.2 Sizing of High Lift Devices
The flap and slat sizing has been performed based on the assumptions made for the maximum lift coefficient in section 1.3. The method presented by Roskam and Torenbeek for sizing the flap is based on solving the Equation 28 for the outboard station of the flap using numerical methods, in consideration of the expected values for the maximum lift coefficient and also airfoil geometric and aerodynamic properties: Swf Sw
C Lwf C lmax c l
3 c l f cos 4 c 4
1.0 0.08 cos 2 c 4 w
w
(26)
The outboard station of the flap is solved using the following relation for the flapped wing area ratio:
Swf Sw
Of
i f
1 w
2 1 w o f i f .
(27)
The ratio of the increment in the maximum sectional lift coefficient due to flaps to the increment in the sectional lift coefficient is found from Figure 7.4 in Airplane Design Part II by Roskam as a function of flap chord ratio and the flap type: 40
clmax cl
cf f , Type cw
(28)
Reviewing the results presented in ESDU-90023 1 , it is established that a double slotted flap generates less noise in comparison to a single slot flap of the same size operated at the same lift coefficient. In order to reduce the airframe noise, the flap type is chosen to be double-slotted. Considering the maximum diameter of the fuselage in the wing region to be 13 ft., it was assumed that the wing fairing will occupy approximately 2 ft. of the wing span, moving the inboard station of the flap surface to 14 percent of the half-span of the wing. The assumptions for this analysis and results of the numerical calculations are presented in tables 9 and 10. Figure 32 shows the final flap arrangement based on the results obtained from AAA. C Lmax TO
2.2
f
25 deg.
c l
0.9668 6.4253 rad .1
C Lmax L
1.78
c l
f
35 deg.
F1 F 2 L
0.50
F1 F 2 TO clfTO
0.75
clf L
0.6724
C LWfTO
0.3618
C LWfL
0.3618
SW f
0.652
L
C Lmax,Clean
1.425
Cf
25%
i
Figure 32. Final Flap Arrangement
TO
c lmax
Cw
f
14%
K trim
1.050
t c w ARw
12 %
SW
1380
W
0.25
9.95
Table 9. Assumed aerodynamic characteristics for flap sizing
f
O
f
1.4383
SW
74.0%
Table 10. Results of the analyses and intermediate parameters for flap sizing
To verify the choice which was made for the flap chord to wing chord ratio, the effect of this parameter on wings’ maximum lift coefficient was studied by mean of plotting values of C L max 1
Engineering Science Data Unit”, Series 2 Volumes on Aircraft Noise, Section 8, item 90023; ESDU Int. Ltd., 2008
41
versus flap deflection angle for different values of
Cf
C w . As it can be seen from the graph
presented in Figure 33, in order to achieve CL,max=2.2 with flap deflection of 35º as it was assumed for landing condition, the extended
Cf
C w should be around 0.20.
Fig. 33. L,max vs. flap deflection for different chord ratios
Fig. 34. velocity contour, U= 120kts. 25˚ deflection
Fig. 33) The effect of the flap chord to wing chord ratio on the maximum expected lift coefficient achieved. Fig. 34) In order to avoid supersonic flow velocities on the upper flap surfaces and significant noise penalty, an ANSYS CFD analysis was performed to determine the proper size of the openings between the primary and secondary surfaces. This figure shows the air speed profile around the wing with the flap deflected at 25º, in takeoff configuration (Alt =0 ft, V= 120 kts.). K-ε model is used to simulate the turbulence. Fig. 35) This figure shows the enlarged view of the air velocity vector plot on top of the deflected flap mechanism. It is evident that the increased flow velocities on top of the primary and secondary flap surfaces, creates a flow with the speed of the free stream velocity outside the wake of the wing, therefore improving the effectiveness of the flaps tremendously
Fig. 35.Velocity contour, U= 120kts. 25˚ deflection
Fig. 36) Flow streamlines are shown for the deflected flap. It is evident that flow circulation dose not take place on top of the primary flap surfaces due to the optimized flow velocities trough small orifice on top of the deflected surface.
Fig. 36.streamlines, U= 120kts. 25˚ deflection
42
2.3 Initial Drag Analyses Based on the method outlined by Roskam 1 presented in Data Unit Volume I 2, initial drag curves are plotted in order to demonstrate the effects of various aerodynamic configurations in different flight segments on lift and drag (see fig. 37). This calculation of drag characteristics was refined after determining exact geometry and lift properties of the aircraft through performing detailed aerodynamics analyses. Also, studies were performed in order to validate the choice of the airfoil
and
aerodynamic
configuration by mean of plotting lift coefficient versus ratios of different powers of C L and C D
Fig. 37) Lift Coefficient vs. Drag Coefficient
simultaneously for cruise condition. These graphs can be seen in Figure 38.
Note: The optimum L0.5/D also roughly matches the optimum CL-Cd of the airfoil at the setting angle of the wing. The small deviation is due to the assumption of a finite wing for this analysis.
Fig. 38. Lift Coefficient vs. Drag Coefficient, obtained using the initial estimations of lift and drag
1 2
Roskam J., Airplane Design Part II; Section 3.4.1 PP 118-127; 1997 “TranquillusProject Technical Data Unit, Vol. I� Pages.20 and 21
43
2.4 Determination of Wing Longitudinal Location One of the goals of this design was to keep the static margin (S.M.) of the aircraft in between 1015%. Studies were performed using the aerodynamic module and detailed static margin feature of
AAA to determine the proper longitudinal location of the wing. After the first cycle of iterations, using the stability and control module of the same software, the required empennage surface areas were determined and implemented to optimize the longitudinal location of the wing. Thanks to the capabilities of AAA, each of the calculations has been done in sufficient theoretical detail presented in provided Data Units. 2.4.1) Lift curve slopes of wing and horizontal tail: The lift curve slopes of the wing, horizontal and vertical tail were calculated based on the relations presented in Data Unit Volume I 1. It has been assumed that the horizontal tail will use a symmetric NACA 0009 (with t c = 9%) as a cross-section airfoil. Therefore, C l α was estimated based on the method provided in Data Unit Volume I 2, and the airfoil data presented by Abbot and von Doenhoff 3. The same process was repeated in order to determine the C Lα for the combination of the wing and fuselage. A selection of the results is presented in Table 11 below: Table 11. Components of the lift curve slope for different flight segments
Mission Segment Index: 2 5 6 8 9 10 16 -1 4.8786 5.6843 5.2563 6.2061 4.9613 4.8664 4.9038 C L (rad ) wf
C Lα C Lα
h
(rad -1 ) (rad -1 )
0.4434 0.4265 0.4377 0.4066 0.4431 0.4434 0.4423 5.5737 6.7754 5.9352 6.8308 5.6563 5.5626 5.5958
1
“Tranquillus Technical Data Unit, Vol. I” PP. 30-32, Methods represented here is obtained from “Synthesis of subsonic aircraft design” by E. Torenbeek. 2 “Tranquillus Project Technical Data Unit, Vol. I” P. 36 Equation 7 3 I.H. Abbott and A.E. von Doenhoff, Theory of Wing Sections, Dover Publications Inc., New York, 1959.
44
2.4.2) Location of aerodynamic center: Based on the relations presented in Data Unit Volume I 1, the location of the Aerodynamic Center (A.C.) of each aerodynamic component was determined. Using the quarter chord method presented by Roskam 2, initial sizes for the empennage were estimated, and it was assumed that they are installed at the end of fuselage. 2.4.3) The airplane pitching-moment-coefficient-due-to-AOA derivative: Using the method presented in Data Unit Volume II 3, the airplane’s pitching-moment-coefficientdue-to-AOA derivative ( C m ) was calculated. The result of this analysis is presented in Table 12. α
Table 12. Components of the lift curve slope for different flight segments
Mission Segment Index: 2 5 6 8 9 10 16 -1 -0.7425 -0.9201 -0.7250 -0.7370 -1.3156 -1.3336 -1.3748 ( ) Cm , rad 2.5.4) The downwash gradient at the horizontal tail ( h ) and final wing apex: Using the method presented in Data Unit Volume I 4, the downwash gradient at the horizontal tail was determined (see Table 13). This estimation was refined during the process of design based on change in aerodynamics and geometry of the wing and empennage later on. Table 13. Downwash gradient at the horizontal tail
Mission Segment Index: dεh dα
2 5 6 8 9 10 16 0.2894 0.3183 0.3758 0.3450 0.3147 0.2916 0.2969
Using the class I weight and C.G. information, the wing’s apex and vertical location was changed by a minimal degree range in order to obtain the proper value of the Static Margin 5. Repeating the process for all of the seventeen flight conditions, the best value of final estimations for S.M. are presented in Table 15. It should be noted that the sweep back angle of the wing was reduced to 28 degrees (from 30 deg.) in order to reduce the static margin to approximately 10 percent.
1
“Tranquillus Project Technical Data Unit, Vol. I” PP. 33-35 Roskam J., Airplane Design Part II; Section 11.1 PP 259-263; 1997 3 “Tranquillus Project Technical Data Unit, Vol. II” P. 23 4 “Tranquillus Project Technical Data Unit, Vol. I” PP. 40-41, Equations 32 to 35 5 Range of changes has been limited to mid body region: 64 to 70 feet from the nose reference point. 2
45
A review of the assumptions used in this section is presented in tables 15. Table 14. Assumptions for S.M. SW 1380 ft 2 Methods and relations applied for detailed calculations of Static Margin 9.90 ARW 1 could be found in Data Unit Volume II . 0.25 w 28.0 deg. w Table 15. Static Margin for seven selected flight conditions 49.2 X apex W
x cg
2 5 6 8 9 10 16 0.4260 0.3837 0.3845 0.3381 0.3181 0.3181 0.1717
0.5592 0.5387 0.4906 0.5219 0.5419 0.5538 0.5579 xac 15.5 10.6 18.4 22.4 23.6 21.18 SM % 13.3 2.4.4) Wing dihedral angle: Since performing a comfortable cruise while maintaining safety and controllability in low speeds is the major goal of this design, static stability
xacwf ∂X CG ∂S h
0.2888 0.002 ft
-1
CLh
2.3266 rad.-1
X ach
112.58 ft.
d h d
0.3188 PO
SM
15.4 %
characteristics, play an important role in developing the design parameters. The airplane dihedral effect coefficient or rolling-moment-coefficient-due-to-sideslip-derivative ( C l β ) is heavily affected by the wing dihedral angle. This coefficient affects both spiral and Dutch roll modes of the aircraft, which should be considered in order to comply with guidelines provided in civil design codes 2. The negative value for C l β should be maintained in all of the flight conditions in order to meet design codes. On the other hand, if C l β takes too large of a negative value it can result in lowering the damping ratio of the Dutch roll mode and lead to low flight handling qualities while performing Dutch roll maneuvers. Considering C l β being equal to -0.15, using AAA’s stability derivatives module, an iteration was performed in order to calculate the corresponding value of the dihedral angle. This value was determined to be approximately 3 degrees. Phillips 3 presents an analytical
1
“Tranquillus Project Technical Data Unit, Vol. II” PP. 28-29 FAR-25 (CFR) Title 14, Parts 1-59 Jan. 1st 1990, US Government Printing Office. Also, MIL-F-87830 Military Specification Flying Qualities of Piloted Airplanes; Nov. 5th, 1980: Air Force Flight Dynamics Laboratory, WP AFB, Dayton, Ohio Also : Codes of Federal Aviation Regulation, 3 W.F. Philips, “Analytical Solution for Wing Dihedral Effects” Journal of aircraft, Vol. 39 №3. 2002 2
46
method for estimating the dihedral angle, which was utilized to verify the selected dihedral angle for Tranquillus, with favorable results. 2.5 Horizontal Tail Surface Area Estimation The main goal of this analysis was to rapidly size the horizontal tail surface area, in order to satisfy the minimum S.M. of 15 percent 1 as Roskam suggests 2 for initial sizing of commercial aircrafts. Results were considered against the required surface area for the initiation of take-off rotation later on, in order to validate the properties of the designed elevator for longitudinal trim. As it was considered in the initial configuration studies, an H-tail was selected for the empennage configuration due to it’s potential for shielding ground from the engine related noise. Given that the surface area and the span of the horizontal tail play a major role in the efficiency of the noise hampering phenomena by the empennage, a parametric study was performed to investigate the effects
of
variation
of
these
parameters on the weight and drag of the horizontal tail.
Relations
presented by Roskam 3 and Raymer 4 were used to estimate the weight and drag of the horizontal tail for different horizontal tail area and span. Figure 39 presents the results of this parametric study.
Fig. 39. Trimmed Horizontal Tail Drag vs. Horizontal Tail Weight for various horizontal tail area and span.
1
The difference between this assumption and the assumption made in section 2.5 is because of application of different weight factors to the contribution of the horizontal tail to the static margin. 2 Roskam J., Airplane Design Part II; Section 11.1 PP 259-263; 1997 3 Roskam J., Airplane Design Part V; Section 5.22, PP 73-74; 1999 4 Raymer, Daniel P. , Aircraft Design – A Conceptual Approach; P-402 AIAA Education Series, Veston, VA 1992.
47
From the results it is clear that maintaining the area of the horizontal tail constant, drag rapidly increases as the span becomes shorter than 30 ft. It is also observed that for the typical values of the horizontal tail area for this class of airplanes, weigh is slightly decreased as the span is reduced. Based on the relations presented in Data Unit Vol. I 1, the required area for the horizontal tail was estimated. This process has been repeated for all of the flight conditions and different values of S.M. in order to determine the largest area required for the horizontal tail surface to maintain the trim. The results of this analysis can be found in Table 16. Later analysis regarding the effectiveness of the horizontal tail to initiate the takeoff rotation indicated a need for increased horizontal tail surface area. As a result, the area of the horizontal tail was increased by almost 20 percent. Subsequent analysis regarding the effects of the horizontal tail geometry in shielding the engine noise in takeoff resulted in another
Table 16. Horizontal tail
X CG , mid
67.4 ft.
xCG , mid
0.3070
with a lower span provides better noise shielding qualities due to the
xac ,TO
0.5592
increase in the horizontal tail root chord. Results and the description of
Sh
the geometric optimization of the horizontal tail for far field noise
xac h Airfoil
436 ft.2 106.16
change in the geometry of the horizontal tail: it was discovered that a tail
reduction are presented in section 4.1 of this document. The final results
i
h
NACA 0009 +5º to -15º
and assumptions for sizing the horizontal tail can be seen in Table 15.
2.6 Vertical Tail Surface Area Estimation In order to ensure the directional stability characteristics of the design, the method presented in Data Unit Volume I 2 was applied to determine the required surface area for the vertical tail. It is assumed that the yawing-moment-coefficient-due-to-side-slip derivative ( C n β ) should be greater
1 2
“Tranquillus Project Technical Data Unit, Vol. I” PP. 24-25 Equations 28-32 “Tranquillus Project Technical Data Unit, Vol. I” PP. 42-44
48
than 0.3
1
per radians to create a
desirable Dutch role mode and provide lateral directional stability for the aircraft. Based on the previously determined
parameters
for
the
geometry of wing and fuselage, a parametric study was performed by changing the vertical tail surface area and the moment arm lv to observe the
Fig. 40. Vertical tail weight vs.
Cn for various horizontal tail
area and span.
effect of these parameters on vertical tail weight and C n β . Figure 40 presents the result of this parametric study.
Considering the length of the fuselage and the selected geometry for the
horizontal tail, the vertical tail was sized for a tail moment arm of 52 feet. As a result, to satisfy the
C n β requirement, the vertical tail area was initially determined to be 262 square feet. Table 17 presents the contributions of fuselage, wing, and the vertical tail to C n β during the cruise as well as the assumptions made to perform the vertical tail sizing. It should be noted that the effects of the winglets and pylons on the parameter C n β was later added to ensure the stability of the Dutch role modes for the aircraft.
The initial geometry of the vertical tail was 2
modified based on aesthetic considerations that can tremendously affect the market for such an aircraft. The final vertical tail is a tapered and
Table 17.
Cn Contributions
C n CyV
0.3175 rad 1 -0.8682 rad
X acv
120.4 ft
C n
-0.0633 rad
SV
1
f
1
2 262 ft
Airfoil NACA 0009
1
Suggested by: Roskam J., Airplane Design Part II; Section 11.2 P 265; 1997 J. Roskam, Roskam’s Airplane War Stories, DAR Corp. 2002 P. 82: Cessna 172’s sales have been increased by almost 30% as a result of similar changes effecting the look of the design. Such an improvement in sale can be crucial for the profitability of Tranquillus, given that the market for a transition trainer for commercial purposes is not well understood as of now.
2
49
swept back surface with a similar surface area. Parameter l v , or vertical tail arm, was increased as a result of this improvement, which increases the effect of the tail on directional stability of the aircraft. Based on the result acquired by performing analyses mentioned in sections 2.4 and 2.5, the basic configuration CAD drawing of the aircraft was updated (see Figures 36).
Fig. 41. Initial configuration drawing, prior to landing gear and power plant integration
2.7 Engine Selection Based on the sensitivity analysis performed earlier during the project (section1.2), it was concluded that the type of the engine and its method of integration will play a major role in improving the fuel efficiency and the acoustic characteristics of the aircraft and its environmental impact. Based on the recommendation of the RFP, different variations of three main types of engines including unducted rotors, geared turbofans, and advanced 3 spool turbofans were studied 50
in order to make a decision regarding the type of power plant to be used in the final design. Given the “under development” status of most of the concepts studied as a part of this design project, many assumptions were made in order to make the analysis of each power plant possible. Available drawings and cutaway views published for advertisement purposes were analyzed and used to obtain basic parameters regarding the turbomechanical configuration of each engine such as number of stages and approximate dimensions. GasTurb 1 was the software of choice for propulsion analysis and was used to determine the main performance characteristics of each engine and compare the different choices for the powerplant.
In addition to performance and environmental analysis
performed using GasTurb, basic risk and feasibility considerations were also influential in choosing the type of the engine for Tranquillus. Measures of merit and selection strategies developed by Bonnacorsi et al. 2 was used to narrow down the selection domain by integrating multiple performance characteristics and empirical market preferences into the selection strategy. In the following sections, a brief description of each of the concepts and the result of the performed analysis is presented. 2.7.1) Unducted Rotor Concept: The unducted rotor (or propfan) concept is basically a modified turbofan engine, with the fan blades placed outside of the engine nacelle on the same axis as the compressor blades. Propfans are known to posses extremely high bypass ratio, offering the speed and performance of a turbofan, with the fuel economy of a turboprop engine. This concept has also been subjected to substantial experimental studies. NASA PTA project is a remarkable example of these studies, and the official reports of the project 3 indicate considerable potential for implementation of this concept into modern day commercial aircraft. Snecma and Rolls Royse have both invested in unducted rotors
1
Developed by Joachim Kurzke, U.S. Distributor: Concept NREC, MA A. Bonaccorsi, P. Giuri, and F. Pierotti, Discontinuities, Convergence and Survival of Inefficient Trajectories in Aeroengine Selection. Economics and Management Laboratory, Santa Anna School of Advanced Studies, Pisa, Italy, Sep. 2001 3 Garber, Edwin J., Overview of NASA PTA Propfan Flight test Program, NASA Technical Note № 2-25536, 1988 2
51
with an estimated reduction in SFC of 20 percent, and the Airbus NSR 1 project has shown willingness to utilize these engines in their design 2. Despite the enormous advantages in the standpoint of fuel economy, propfans are know to generate incredibly high noise levels due to the sonic speed induced in the flow field around the external fans. Reducing the far near field noise of an open rotor has been the subject of many research efforts, most notably the extensive research performed by NASA1 and by Holste et Al. 3 from the Institute for Advancement in Flight, Germany. After much investigation, Holste concludes that the possible reduction in the source noise as a result of blade optimization and improved turbo machinery does not exceed 10 dB due to the extremely high flow speeds generated by the fan. It is notable that Airbus NSR project has been dealing with substantial issues in fields of acoustics of open-rotor engines.
Using a Rolls-Royce RB3011 propfan, it is believed that the engine without any
suppression effects from the fuselage and empennage will hardly satisfy the ICAO chapter-4 noise requirements, and suppression using the empennage structure will only provide 7-10 dB improvement in the cumulative noise levels2, far from ICAO Ch.4 -20dB required by the RFP. Other than noise, the open rotor concepts are believed to face major reliability challenges, because they mount the blades on a hot rotating structure around the engine’s exhaust end, exposing it to possible heat fatigue2. Also, other issues such as the containment of lost blades present a serious configuration challenge, which could only be addressed by application of armor plating on the aft fuselage. Garber mentions the installation of 700 lbs of 3/8 in. stainless steel armor plating as a method of blade containment on the fuselage of the Gulfstream II prototype used by NASA to test
New Short Range Project intending to replace the A320 series by 2018 Robert Wall, Michael A. Taverna, and Guy Noris, “Push or Pull: Airbus & Boeing Vision Split on Open-Rotor Applications”, Aviation Weekly, May 4th 2009 3 F. Holste, W. Neise, “Noise Source Identification in a Propfan Modeled by Means of Acoustic Near Field Meassurements”, Journal of Sound and Vibration №203(4), 1997 1 2
52
the initial open-rotor concepts 1. A protective armored system for a commercial transport plane is expected to weight substantially more. All the aforementioned issues have caused Rolls-Royce and Snecma to push back the entry to service date of their open rotor engines to 2020 2, in order to allow more time to improving the engine characteristics, reliability, and safety. Given the significant financial risks associated with the application of an open rotor concept and availability of safer options for the power plant, this concept was not chosen for the development of Tranquillus. 2.7.2) Advanced direct drive and geared turbofans: It can be argued that given the challenges faced by the open rotor concept, modified turbofan concepts present a considerable potential for utilization in the next generation of short to medium range aircraft. Two main commercial engines under development are considered to power Tranquillus: Pratt & Whitney 1000G geared turbofan and CFM Leap-X direct drive turbofan which both are capable of satisfying the requirements for maximum sea level thrust for the aircraft. Due to propitiatory nature of the information related to the performance of these two engines, only scarce information regarding the performance of these
engines
Considering
a
is
currently
available.
conventional
turbofan
configuration and mindful of the claims made by P&W and CFM, a parametric study was performed to observe the effects of the changes in BPR on the MTOGW and the block fuel burn for the aircraft flying a 2800
Fig. 42. MTOGW vs. Block Fuel Burn for different AR and BPR (M=0.8, ICA=38000 ft.)
n.mi. cruise mission. Result of this investigation is presented in Figure 42. From this parametric
1
Garber, Edwin J., Overview of NASA PTA Propfan Flight test Program, P-365. NASA Technical Note № 2-25536, 1988 2 Douglass Barie, and Guy Noris, “Sound and Vision”, Aviation Weekly, Oct. 13, 2008
53
study, it was concluded that in case of using a direct drive turbofan and an aspect ratio of 10 for the wing, a by-pass ratio of eight is the optimum configuration for a conventional turbofan engine 1. This result confirms the unofficial reports regarding the bypass ratio of the under development CFM Leap-X engine which is believed to have a BPR of approximately eight 2. Assuming a three spool engine configuration with a sea level installed thrust of 22000 lbs, a GasTurb model of the engine was constructed by defining the approximate geometry of the leap-X engine and applying the efficiencies computed by the software to obtain a bypass ratio of eight. Figures 43 and 44 present the cross-section of the constructed GasTurb model for the high BPR direct drive turbofan in the mixed and unmixed flow configurations.
Fig. 43. General arrangement cross-section of the mixed flow Fig. 44. General arrangement cross-section of the un-mixed high BPR direct drive turbofan concept investigated flow high BPR direct drive turbofan concept investigated Fig. 43 and 44. Cross-section of both mixed-flow and unmixed-flow high bypass ratio turbofans were modeled using Gasturb, based on the basic parameters obtained trough analyzing pictures and cut-away views of the CFM Leap-X engine. Diameter of the engine was measured to be approximately 70 inches.
Parametric studies were performed to identify the thrust and specific fuel consumption characteristics of these two configurations in form of an engine map. During this analysis, it was assumed that no bleed air is taken from the engine. Instead an increased power extraction of 75 KW takes place by the accessories and gearbox installed on the engine. In order to also asses the The non-monotonic behavior is attributed to the increased weight of the direct drive turbofan engines and the nacelle associated with them, as projected by the JetSizer propulsion module. 2 Robert Wall, Michael A. Taverna, and Guy Noris, “Push or Pull: Airbus & Boeing Vision Split on Open-Rotor Applications�, Aviation Weekly, May 4th 2009 1
54
environmental effects of these configurations, the NOx Severity Index was chosen as the environmental measure of merit.
This parameter, presented by Committee of Aeronautical
Technologies 1 is defined as: 0.4
T3 826 K 6.29100 war 194 K 53.2
P3 S NOx e 2965kPa
(29)
where P3 and T3 are pressure and temperature inside the burner of the engine and war denotes the liquid water to air ratio of the air entering the combustion chamber. NOx Severity index was chosen mainly due to the emphasis placed on the role of nitrogen oxides in the destruction of the ozone layer by Schwartz et al. 2 In her extensive study of the effects of different emitted gasses from aero engines, Schwartz et al. concludes that the Nitrogen Oxides are the most significant contributors to the destruction of Ozone layer. Results of the NOx severity analysis were combined with the result of the engine performance analysis to visualize the trend between engine performance and environmental impacts. Figures 45 and 46 present the results of the analysis for both mixed and unmixed flow direct drive concepts considered for Tranquillus. Fig. 45. Installed engine map for direct drive, unmixed flow high BPR turbofan. NOx Severity index is plotted as a color contour indicating the areas of high emission levels with bright colors. At cruise condition (M=0.8/38000 ft) SFC is equal to 0.44 lbm./lbf.hr, and installed thrust is equal to 4500 lbs NOx severity parameter for cruise at 38000 ft. and 0.8 Mach is equal to 0.55 1
Committee of Aeronautical Technologies, Aeronautics and Space Engineering Board, Commission on Engineering and Technical Systems, National Research Council of Aeronautical Technology for the Twenty-First Century National Academy Press, Washington, D.C. 1992 2 Emily Schwartz, and Ilan M. Kroo, Aircraft Design: Trading Cost and Climate Impact, presented at the 47th AIAA aerospace Science meeting, Jan. 5-9 2009, Stanford University
55
Fig. 46. Installed engine map for direct drive, mixed-flow high BPR turbofan. NOx Severity index is plotted as a color contour indicating the areas of high emission levels with bright colors At cruise condition (M=0.8/38000 ft) SFC is equal to 0.40 lbm./lbf.hr, and installed thrust is equal to 4400 lbs NOx severity parameter for cruise at 38000 ft. and 0.8 Mach is equal to 0.55.
Similar to the advanced direct drive turbofans, Pratt & Whitney’s geared turbofan was modeled using GasTurb based on the released cutaway views of P&W-1000g 1. Parameters regarding the performance of the gearbox, efficiency of high and low pressure compressors and turbines were varied to obtain an engine with a thrust at sea level of 22000 lbs. This engine was also studied in two configuration of mixed and unmixed duct flow, for which the general arrangements are shown in Figures 47 and 48.
Fig. 47. General arrangement cross-section of the mixed flow geared turbofan concept investigated
Fig. 48. General arrangement cross-section of the un-mixed flow geared turbofan concept investigated
Fig. 47 and 48. Cross-section of both mixed-flow and unmixed-flow geared turbofans were modeled using Gasturb, based on the basic parameters obtained trough analyzing the cut-away view of the P&W -1000g. Diameter of the engine was measured to be approximately 75 inches. 1
Pratt & Whitney Technical Brochure titled Pure Power PW-1000g. Dec. 2008
56
Analysis of these concepts indicated that the by-pass ratio of the engines with a gear ratio of 4 is approximately 10. It should be noted that the trade study performed prior to the engine selection processes presented in Figure 42 does not apply to a geared turbofan concept, and therefore the BPR of 10 obtained for the geared turbofan can not be regarded as non optimum. Result of this analysis can be seen in Figures 49 and 50.
Fig. 49. Installed engine map for, unmixed-flow geared turbofan. NOx Severity index is plotted as a color contour indicating the areas of high emission levels with bright colors. At cruise condition (M=0.8/38000 ft) SFC is equal to 0.45 lbm./lbf.hr, and installed thrust is equal to 4400 lbs NOx severity parameter for cruise at 38000 ft. and 0.8 Mach is equal to 0.55.
Fig. 50. Installed engine map for, mixed-flow geared turbofan. NOx Severity index is plotted as a color contour indicating the areas of high emission levels with bright colors At cruise condition (M=0.8/38000 ft) SFC is equal to 0.41 lbm./lbf.hr, and installed thrust is equal to 4400 lbs NOx severity parameter for cruise at 38000 ft. and 0.8 Mach is equal to 0.55.
From the result of these analyses it was concluded that the NOx severity parameter attains very similar values during cruise in both geared and direct drive turbofan engines. It was also concluded 57
that the type of the by-pass flow (mixed and unmixed) have a significant effect on the fuel consumption of both engines, with a more significant impact on the fuel consumption of the geared turbofan concepts. Since both geared and advanced direct drive concepts attain approximately same fuel consumption and thrust characteristics during the cruise, noise and feasibility considerations became critical in selection of the engine. Mindful of the fact that the Pratt& Whitney geared turbofan has already started the testing process and is selected as the engine for the Mitsubishi Regional Jet and Bombardier C-series, it can be argued that the Pratt & Whitney geared turbofan concept faces less technical challenges and delays in development, and therefore it presents a smaller financial risk for the aircraft. Also given the lower rotation speed of the main fan due to the implementation of the Epilicyclic gear system, it is expected that the geared turbofan can have lower fan noise levels which is critical to satisfaction of the Noise requirements set by the RFP. All these factors led the design team to select the Pratt & Whitney-1000g geared turbofan in a mixed flow configuration as the choice of the power plant.
2.8 Engine-Fuselage Integration As it was considered in the initial configuration studies, the H-tail empennage was selected to shield the ground from the noise of the jet engine. Referring to ESDU 89041 1 it was concluded that the mixing noise level of a circular subsonic jet should reach maximum at a certain distance after exiting the engine nozzle. In order to obtain the maximum shielding effects from the empennage, it was necessary to place the engines at this particular distance from the empennage center line, so the region of maximum noise mixing is shielded from the ground. As suggested by Hunter et Al. 2, the rate of change in turbulent kinetic 1
Engineering Science Data Unit”, Series 2 Volumes on Aircraft Noise, Section 6, item 89041 “Estimation of subsonic farfield jet-mixing noise from single-stream circular nozzles”; ESDU Int. Ltd., 2008 2 Craige A. Hunter, James Bridges, Abbas Khavaran, “Assessment of Current Jet Noise Prediction Capabilities”, 29th AIAA Aeroacoustics Conference, 5-7th May 2008, Vancouver, BC, Canada
58
energy dissipation was selected as the measure to determine the point of maximum jetmixing noise in the flow. Using the obtained results regarding the mass flow rate, core and by-pass temperature and pressures, a 3 dimensional CFD analysis was performed using ANSYS to determine the location of the maximum turbulent kinetic energy in the flow exiting the engine. Contours of kinetic energy dissipation and flow velocity for the jet are shown in Figures 52, and 52 below.
Fig. 51. Flow velocity contours for P&W Geared Fig. 52. A close-up of the turbulent kinetic energy Turbofan during takeoff (ISA Condition) obtained using dissipation contours for P&W Geared Turbofan in ANSYS CFD Takeoff setting (ISA Condition) Fig. 52. Velocity contours on the centerline of the P&W 1000g engine in the mixed flow configuration while takeoff. The computed nozzle mass flow rate, temperature and pressure using GasTurb were applied to a hexagonal free mesh to investigate the characteristics of the induced jet behind the engine. K-Îľ turbulence model was used to simulate the turbulence. Fig. 51. A close-up view of the Turbulent kinetic energy dissipation contours on the centerline of the P&W 1000g engine in the mixed flow configuration. It should be noted that the two high intensity regions are formed on the boundaries of the jet as a result of the loss of kinetic turbulent energy to the surrounding air. The highest rate of change in the energy dissipation levels are measured at a distance of 1.9 times the diameter of the engine outlet (~9.2 ft) visualized with the red contours. (Refer to Figure 54 for further clarification)
From these results it can be seen that the rate of change in turbulent kinetic energy of the flow exiting the engine nacelle reaches a maximum at around 1.9 times the nacelle exit diameter (approximately 9.2ft. away from the nacelle exit). This rule was implemented to determine the location for the installation of the engines on the fuselage with respect to the empennage. A clearance cone of 7 degrees was used to determine the separation of engines 59
from the horizontal tail and from the fuselage. The inlet for the engine was designed by applying the method presented by Seddon et. al 1 in order to achieve a full pressure recovery at the fan station of the engine. Trade studies were performed to observe the effects of duct length and inlet cross-section area on inlet pressure recovery, and to determine the shortest length and smallest cross-section area for the inlet of the utilized engine. This trade study and the cross-section of the intake and the mixed flow nacelle designed for Tranquillus is shown in Figures 53 and 54 below. Figure 55 presents the engine installation with respect to the location of the maximum rate of turbulent kinetic energy dissipation of the jet exiting the engine.
Fig. 53. Intake Geometry using a fully mixed flow nacelle
Fig. 54. Intake geometric trade study, showing the design point
Fig. 55. Engine installation in relation to the geometry of the empennage and the counters of turbulent kinetic energy dissipation. It can be seen that the horizontal tail shields the ground from the regions of the flow with the highest turbulent kinetic energy dissipation in the jet exiting the engine. 1
J. Seddon E. L. Goldsmith, “Intake Aerodynamics�, AIAA Education Series, Reston, VA, 2007
60
2.9 Landing Gear Design In order to integrate the landing gear system for Tranquillus, a tricycle landing gear was selected. This decision was mainly influenced by the low weight and cost of a tricycle landing gear due to the simplicity of the associated shock absorption system and its good handling performance on the ground. Based on the first class estimations of the aircraft’s weight, and considering the properties of tires presented by Roskam 1, it was concluded that 4 main tires could satisfy the load consideration for hard landings. Using the procedure outlined by Currey 2 for sizing the landing gear for commercial aircraft, the strut travel for the aircraft was computed for a maximum sink rate of 10 feet per second for an approach speed of 135 kts as required by the RFP. Considering a 10 percent margin of safety, the stroke of the shock absorption system was determined to be 18 inches. Static loads for each landing gear are calculated by solving the static equilibrium equation for nose and main landing gear in order to transfer 90 percent of the static load to the main landing gear and 10 percent to the nose landing gear. This load distribution is necessary in order to create good onground handling qualities for the nose landing gear. Based on this load distribution, and also taking into account the safety factor of 1.25, a number of tire sizes were studied in order to select the best combination of tire weight and maximum rated speed. The main landing gear tire is determined to be a Goodrich type VII with dimensions of 16”×44” and the nose tire with the dimensions 12” × 34”.
Considering the most aft location of CG, the landing gear geometry was determined to be in
compliance with requirements for tricycle layouts presented by Roskam 3. As it can be seen in the following general arrangement drawing, a tail clearance of 11˚ (uncompressed), and a longitudinal tip-over angle of 15˚is achieved with loaded landing gears. The lateral tip-over (Ψ) is found to be 57.0˚ and 53.0˚ respectively for takeoff and landing condition using the method presented in Data 1
Roskam J., Airplane Design Part IV ; Section 2.4.5 P 33; 2004 Currey, Norman S. Aircraft Landing Gear Design: Principles and Practices. AIAA. Washington DC. 1988 3 Roskam J., Airplane Design Part IV ; Section 2.8.2 P 76; 2004 2
61
Unit vol. II1. The aircraft also meets the requirement of 10˚ roll at 9˚ rotation with extended landing gear. Nose and main landing gear are located 668.5 inches apart and the main landing gear struts are located 120 inches away from the fuselage centerline. The main landing gear retracts approximately vertically into a compartment immediately after the front cargo bay into the wing root box. Nose landing gear is hydraulically steered and is retracted forward in to a bay under the nose compartment. The landing gear mechanism is hydraulically powered and locked. Figures 56 and 57 present the retraction geometry and the structural integration of the nose landing gear, respectively.
Fig. 56. Nose Landing gear retraction geometry
Fig. 57. Nose Landing gear structural integration. Landing gear bay is highlighted in red
Both nose and main landing gears are stored in a bay that is fully enclosed with hydraulically actuated doors. It is speculated that the addition of the main landing gear doors will reduce the profile drag of the aircraft and the airframe noise compared to the Boeing 737 family, which does not employ a door for the main landing gear bay. Details regarding the integration of the main landing gear could be found in the following general arrangement drawing.
1
“Tranquillus Project Technical Data Unit, Vol. II” P. 80, Equations 1-6
62
C 4
C 4
C 4
t c avg .
t c avg .
t c avg .
iroot
iroot
iroot
itip
itip
itip
V
V
V
3
Design Verification and Optimization: Detailed Aerodynamics, Weight, and Performance Analyses The purpose of detailed analyses of aerodynamic, weight, and performance is to increase the
precision of estimations made in the previous chapter and verify the satisfaction of the requirements by the RFP. The analyses presented in this section were also used to determine the flight envelope, and flight capabilities of the aircraft in terms of acoustics and flight mechanics, while acquiring a more detailed view of the changes that may be necessary in order to increase the quality of the final product while reducing the operating and acquirement cost. Given the length and complexity of the analytical methods utilized, these methods are not presented in this proposal.
3.1 Optimization of the Initial Cruise Altitude In order to ensure the optimum operation of the aircraft, multiple parametric studies were performed in order to optimize the provided mission profile guidelines by the RFP. Given that the aircraft is expected to perform transport missions in a variety of ranges specified by the RFP, these parametric studies were repeated to accommodate different weights. As it was previously established through sensitivity analysis of the typical mission profile in section 1.2, cruise (index numbers 6&8) and hold segment (index number 16) are the most influential segments in terms of fuel economy of the mission and consequently the direct operating cost of the aircraft. In order to model the direct operating cost of the aircraft as a function of the mission variables such as average block speed and initial cruise altitude as well as the optimum aircraft geometry and weight to satisfy the requirements set by the RFP, the financial model provided by Roskam 1for estimation of the RDTE, acquisition, and operating cost was programmed into the JetSizer optimization spreadsheet. Considering that previously mentioned results for the engine optimization, the direct operating cost (DOC) and the corresponding aircraft unit cost was computed for a range of Mach numbers and initial cruise 1
Roskam J., Airplane Design Part VIII ; Section 5.2.4; 1990, DAR Corp, Wichita, Kansas
64
altitudes. This analysis was performed using the weighted average range of the typical mission provided by the RFP (850 n.mi) for a manufacturing run of the 500 and 1500. Selecting a cruise speed of 0.8 Mach as the cruise speed defined by the RFP, the direct operating cost was computed for different initial cruise altitudes. Results of these parametric studies are presented in Figures 58 trough 60.
Fig. 58. DOC vs. Unit Cost, different ICA & Mach number (production run: 500 aircraft over 20 years)
Fig. 59. DOC vs. Unit Cost, different ICA & Mach number (production run: 1500 aircraft over 20 years)
Fig. 58. & 59. DOC vs. Aircraft Unit Cost for different cruise Mach numbers and altitudes for the maximum range of the aircraft (2800 n.mi.) Cost figures were estimated for optimum wing area and the corresponding takeoff weight for each initial cruise altitude and cruise Mach number. The increase in the aircraft unit cost as a result of the increased Mach number is due to the increased structural weight of the aircraft as cruise Mach number is increased. Fig. 60. Direct Operating Cost (DOC) vs. Initial Cruise Altitude (ICA). The computation is performed assuming the weighted average of the mission ranges provided by the RFP (850 n.mi.). Fig. 60. DOC vs. ICA for a M=0.8 and Range of 850 n.mi.
Reviewing the result of this analysis, it can be seen that at an altitude of 37800 feet, the direct operating cost attains a global minimum independent of the range and cruise Mach number of the
mission performed by the aircraft. Further studies indicated that the fuel burn of the aircraft and the NOx intensity index are reduced as the initial cruise altitude increase. This translate to lower NOx and CO2 emission levels both as a result of the reduced fuel burn and the increased efficiency of the 65
engine burners in higher altitudes as observed during the engine analysis.
Mindful of the
aforementioned environmental and economic considerations, the initial cruise altitude of 37800 was selected, which is nearly 3000 feet higher than the regular ICA attained by present day commercial transports (35000 ft.). This is mainly attributed to the high BPR of the engines as well as the lighter empty weight of Tranquillus compared to the similar designs.
3.2 Forced Laminar Flow System and Winglets In order to improve the aerodynamic efficiency of the wing, studies were performed to determine the potential benefits of using advanced concepts to reduce the drag generated by the wing. Forced laminar flow systems and addition of the winglets were both studied in detailed, using both emperical and numerical methods. To study the posible gains from using forced laminar flow techniques, the method presented by Roskam 1 was used to assess the effects of extended laminar flow on the parasite drag generated by wing. It was discovered that reducing the percentage of the wing chord exposed to turbulent flow from 80 percent to 40 percent improves the cruise lift-to-drag ratio from 16.6 to 17.6 (6 percent), maintaining the same wing geometry. Using the result of the initial sensitivity analysis presented in section 1.2, it was concluded that this improvement in lift-to-drag ratio during the cruise coresponds to a fuel burn reduction of approximately 900 lbs for the average mission range set by the RFP (850 n.mi). Given this significant weight reduction, two main techniques of forced laminar flow control were selected for further investigation.
Due to its small weight and relative simplicity, the
Dielectric Barrier Discharg (DBD) flow control system was investigated initially. This system induce a negative charge in the local flow passing over the wing, and by inducing a 1
Roskam J., Airplane Design Part VI ; Section 1.1-4.13 P 44-116; 1990
66
posative charge on the surface of the wing cause the airflow to remain laminar due to electric pull between air molecules and wing surface. Reviewing the results presented by Jayaraman et al. 1it was concluded that the DBD concept will not be feasable due to the high Reynold number of the wing during the cruise (12 million) which is expected to require enormous electric power to maintain a laminar flow. Following this conclussion, efforts were focoused on the design and implementation of a system based on the boundary layer suction concept explored by Pfenning 2 and Neumann 3, in order to assess the weight and feasibility of such systems for a narrow body commercial jetliner. This concept, utilizes a weak suction to keep the flow attached to the upper surface of the wing, therefore delaying the flow transition to turbulence and consequently reducing the parasite turbulent drag. Based on the suggestions made by Pfennig, holes with a diameter of 30 μm and a density of 1000 holes per square inch were selected to create the porosity required to apply suction on the wing surface. These holes could be manufactured via spark erosion or other more specialized methods using high energy electron beams on a titanium shell of 3/8 in. thickness 4. A MATLAB code was developed to perform momentum integration based on a vector of boundary layer thickness obtained using Xfoil to determine the flow rate required to remove the boundary layer at 0.15 percent of the wing mean aerodynamic chord. Using this code, it was estimated that a flow rate of 5.1 lbs. per second is required to be removed from the wing upper surface to remove the boundary layer air. Given that the core efficiency of high BPR engines such as Pratt & Whitney 1000G is very susceptible to bleed air extraction, a decision was made to base the suction system entirely on electrical power. Using system architecture similar to Balaji Jayaraman, Yongshen Lian, and Wei Shyy, “Low-Reynolds Number Laminar Flow Control Using Dielectric Barrier Discharge Actuators” 37th AIAA Fluid Dynamics Conference & Exhibit 25-28 June 2007, Miami, FL. 2 Jurgen Pfening “Suction Device For Boundary Layer Control in an Aircraft”, US Patent Number 6216982-B1, Issued: April 2001 to Boeing Commercial Aircraft Representative 3 Pradip G. Parikh et al., “Aircraft Boundary Layer Control System with Discharge Transpiration Panel”, US Patent Number 5772156, Issued: June 30th 1998 to Boeing Commercial Aircraft Representative. 4 Suggested by B. Rawdon, Aircraft Design Professor at University of Southern California, Los Angeles, 1
67
the suction system designed by Gazdinski for road high performance vehicles 1 , the supporting system was designed for the suction system based on a high capacity radial pump. A 3d model of the suction manifold was prepared to estimate the weight of this system as well as to observe any possible interference with the structural integrity of the wing. Figures 61 and 62 present the structural integration required to remove the boundary layer near the front shear web of the wing as well as the system architecture of the forced laminar flow system.
Fig. 61. Integration of vacuum manifold with the front shear web located at 15 percent of the wing chord ↑ Fig. 62. Forced Laminar Flow system architecture→
Analyzing the weight of the titanium suction manifold and assuming the associated system will weight at least 300 pounds, it was concluded that the gross weight of the forced laminar flow system will exceed 500 lbs. Given the computed value of the sensitivity partial of the takeoff weight with respect to empty weight, it was estimated that for one pound increase in the empty weight of the aircraft, the takeoff gross weight will increase by 1.49 pounds 2. Applying this result to the perceived increase in the empty weight of the aircraft as a result of implementation of the forced laminar flow system, it was determined that the 500 pound increase in the empty weight of the aircraft, will cause approximately 1000 pounds increase in the takeoff gross weight, which is greater than the benefits achieved by not using such a system. Also, it was observed that in order to integrate such a system, 1
Robert E. Gazdzinski, “Vehicular Boundary Layer Control Systems and methods”, US Patent Number 6068328, Issued: May 30th 2000 to the inventor. 2 Section 1.2 of this document
68
the structural connectivity of the wing box will be jeopardize, requiring more fasteners and structural reinforcement which will in all likelihood increase the structural weight of the wing. Ultimately, considering the increase in price of the aircraft and the reduced integrity of the structure of the wing box, the forced laminar flow system was not integrated in to the final design. As a more common method to improve the aerodynamic efficiency of the wing, i.e. winglets was considered for further studies. In order to observe the effects of the variation of the geometry of the winglet and it’s interaction with the wing, an AVL model of the aircraft was created using an automated Excel-based ASCI Fig. 63. AVL model used for winglet optimization and further
compiler which can be seen in Figure 63. detailed aerodynamic analysis.
A parametric study was performed by varying the area and taper ratio of the winglet to observe the caused effects on the wing Oswald efficiency factor. Based on the suggestion made by M. Page 1, the weight of the winglets was modeled as linearly proportional to their area considering a weight of seven pounds per square feet. Figures 64 present the results of this parametric study. From
this
analysis
it
was
concluded that a taper ratio of 0.6 for the winglet will cause the most drastic improve in the aerodynamic efficiency of the 1
Fig. 64. Wing Oswald efficiency for different winglet area and taper ratio obtained using AVL for cruise condition.
Professor of Aircraft Design at University of Southern California
69
wing for the smallest area. A winglet area of 47 square feet and a taper ratio of 0.4 was selected for the final winglet design.
3.3 Detailed Drag Verification Using the method and relations presented by Covert 1 , Roskam 2 , and Torenbeek
3
a detailed drag
analysis was performed using AAA based on the optimized mission profile for the aircraft. Due to the changes in the aerodynamic properties of the wing, and other surfaces in different altitudes ( C l α and correspondingly C Lα ), the calculations were repeated for all 16 flight conditions presented in section 1.1. Drag estimations were later verified for significant mission segments later on during the verification of the dynamic behavior of the aircraft using the AVL panel code. Figure 65 presents the parasite drag breakdown for takeoff, cruise and landing. Pylons 1%
Pylons 6%
Horizontal Tail 1%
Trim 1%
Pylons 1%
Fuselage 7%
Nacelle 12%
Nacelle 1%
Landing Gear 54%
Flap 22%
Wing: 36%
Fuselage 7% Nacelle 1%
Landing Gear 44%
Fuselage 31% Flap 35%
Horizontal Tail Vertical tail 6% 8%
a) Takeoff, total drag: 511 counts
Vertical Tail 2%
Wing 9%
Vertical Tail 3%
Wing 11%
Horizontal Tail 1%
b) Cruise, total drag: 310 counts
c) Landing, total drag: 634 counts
Fig. 65. Parasite Drag Breakdown for: (a) takeoff , (b)cruise, (c) landing
Drag polars for the aircraft were constructed using the results of the second class drag estimation. Figure 66 presents the obtained drag polar for takeoff, cruise, and landing configurations for Tranquillus. Covert E.; “Thrust and Drag: It’s prediction and verification” Section V, 2.2.2 P 140, 1985 Roskam J., Airplane Design Part VI ; Section 1.1-4.13 P 44-116; 1990 3 Torenbeek, E. , Synthesis of subsonic aircraft design, Appendix G, P 550, 1981 1
2
70
Fig. 66. Drag polars for cruise, takeoff, and landing, computed using the detailed drag analysis module in AAA software.
3.4 Detailed Weight Estimations Based on the methods presented in Data Unit Volume I 1, the detailed weight of the aircraft was determined based on the geometry, and design requirements. In order to account for significant utilization of light weight composites in Tranquillus, the weight fractions for Boeing 787 were compared with older aircraft of similar size to obtain the percentage of weight savings achieved as a result of using modern structural material. This result was used to correct the weight figures computed by applying methods for conventional systems and airframes and systems. The applied weight reductions are presented in Table 18. Two different methods were utilized to estimate the weight of the components and the results were averaged with the initial first class
Table 18. Weight Correction
Empennage Wing Fuselage Nacelle Landing Gear Fixed Equipment
-15 % -20 % -17 % -10 % -3% -7%
weight estimates to increase the accuracy of the estimations. Table 19 presents the result of each method together with the average results. Table 20 and Figure 67 presents a summary of the detailed takeoff weight breakdown. 1
“Tranquillus Project Technical Data Unit, Vol. I� PP. 48-49
71
Table 19. Weight Estimations
Components
GD Method (lbs.)
Torenbeek Method (lbs.)
Statistical Results (lbs.)
Averaged Values (lbs.)
Wing Horizontal Tail Vertical Tail Fuselage Nacelles Nose Landing Gear Main Landing Gear Engines Fuel System Propulsion System Flight Control System Hydraulic System Instrumentation Electrical System Air Conditioning Oxygen System APU Furnishing Cargo Handling Operational Items Other Items
10013 1036 1862 12200 ------598 3251 ------------142 3468 ------1699 1914 5367 243 ------6173 -------------------
15162 2074 2315 19509 ------845 4596 7999 887 238 2332 407 2098 4752 1696 217 1628 8169 1500 4580 679
15334 1691 1352 14463 2521 883 4806 9206 1021 210 2038 261 1334 2342 2481 162 1044 5038 961 2935 435
13561 1607 1848 15446 2550 779 4238 8655 960 197 2620 336 1715 3011 3191 208 1342 6479 1236 3774 559 Table 20. Detailed takeoff weight
Fuel 15%
Fixed Equipment 19%
Payload & Crew 27% Structure 31%
Power Plant 8%
Fig. 67. Structural weight Breakdown
W fix
24471 lb.
W Structure WPP WPL WCrew M ff
40026 9813 33750 1350 0.8202
Mtfo
0.5%
W FUsed
19250 lb.
W F , max
24350 lb.
Wtfo
679
WE WTO
74310 lb. 135706 lb.
lb. lb. lb. lb.
lb.
72
3.5 System Architecture & Integration The aircraft system architecture was based on mainly electrical components in order to reduce the weight and improve reliability of the systems by providing multiple parallel backups. Given the low mass flow rate trough the core of the selected geared turbofan, decision was made to use no-bleed architecture for the A/C units. The selected air-conditioning packs will use electric compressors and heaters to regulate the pressure and the temperature of the ram air taken from outside. Based on the thermodynamic analysis performed on the air-condition system, the electric power use of the aircraft is expected to increase by 23 KW compared to a 110 KW conventional system architecture for the aircraft of the same size 1. As a result of using non-bleed power plant integration, the efficiency of engine’s high pressure compressor and turbine by 5 percent cumulative, causing a 1.5 percent reduction in the specific fuel consumption 2. A Hamilton- Sundstrand Auxiliary Power Unit was also implemented to provide the power required during ground operations and in case of an emergency. Figure 68 presents the APU integration in the fuselage aft compartment.
Fig. 68. APU Integration, APU is 62� long
Due to use of composite wing structures, FAA regulations require that empty spaces inside the wing fuel tanks to be filled with inert gasses to reduce the risk of expulsion in case of a lightening strike or static electricity discharge between the wing structural components. An On Board Inert Gas Generation System is suggested to pump highly diluted nitrogen mixtures in to the wing tanks. This system is expected to weight about 110 pounds 3.
1
Roskam J., Airplane Design Part IV ; Section 7.1 P 322; 1990 Results are obtained from the Previously presented GasTurb model of the geared turbofan. 3 The weight figures cited for F-22 Raptor were scaled to account for the maximum fuel volume. 2
73
3.6 CG Location Based on the Detailed Weight Based on the decisions made about internal configuration, and according to the data discovered by performing detailed weight analysis, location of the center of gravity was found for the aircraft. The defined locations of the empty weight components are shown in Table 21, and are also located in the updated side profile for the aircraft in Figure 69 on the following fold out. Table 21. Detailed CG location, Indexes refer to the markers of the drawing on the next page
Component 1-Wing 2-Horizontal tail 3-Vertical tail 4-Fuselage 5-Nacelles 6-Nose Landing Gear 7-Main Landing Gear 8-Engine 9-Fuel System 10-Propulsion System 11-Flight Control System 12-Hydraulic & Pneumatic System 13- Avionics, Electronics & Instrum.
14-Electrical System 15-Air Conditioning/ Anti Icing
16-Oxygen System 17-Auxilary Power Unit 18-Furnishings 19- Cargo Handling Equipment 20-Operational Items 21-Other
Weight (lb.)
X CG ( ft .)
Z CG ( ft.)
13561 1607 1848 15446 2550 779 4236 8655 960 197 2620 336 1715 3011 3191 208 1342 6479 1236 3774 559
68.47 115.62 121.41 60.63 100.71 15.95 71.60 103.59 90.00 103.00 86.00 105.00 20.10 95.00 70.00 55.70 120.00 80.00 50.00 50.00 100.00
-3.12 6.85 15.86 0.32 15.10 -4.90 -1.66 15.10 -0.80 15.44 4.17 2.53 -1.53 0.82 1.23 1.23 4.23 4.79 -2.00 2.00 3.00
Table 22. Moment of Inrtia
133353 slug-ft2
L xx (lb. ft .) 928521.7 185801.3 224365.7 936491 256810.5 12425.05 303297.6 896571.5 86400 20291 225320 35280 34471.5 286045 223370 11585.6 161040 518320 61800 188700 55900
L zz (lb. ft .) 42310.3 11008 29309.3 4942.72 38505 3817.1 7031.76 130691 768 3041.68 10925.4 850.08 2623.95 2469.02 3924.93 255.84 5676.66 31034.4 2472 7548 1677
Table 23. Empty Weight CG
X CG
75.76 ft.
I yy B
2
1645879 slug-ft
YCG
0 ft
I zz B
1512225 slug-ft2
Z CG
3.51 ft.
I xz B
2
I xxB
235951 slug-ft
74
3.7 Detailed Performance Validation Using GasTurb, the installed thrust for the engine was computed assuming a 75 KW power extraction for the accessory gear box on each engine. Result of the engine performance estimations for Pratt & Whitney geared turbofan is presented in Figure 50 in this document. These results were used to verify the satisfaction of the performance requirements for the aircraft set by the RFP and the Federal Aviation Regulations title 25.
3.7.1 Takeoff Performance: The required takeoff field length is determined through applying relations presented in the Data Unit Volume II 1, and considering the ground effect on generated lift and drag 2. It is assumed that the aircraft uses the previously sized flaps and slats during takeoff, and therefore the maximum lift coefficient ( C L
max
2 .2 ) is attainable. Takeoff trajectory was computed for the normal takeoff using
ANOPP and can be seen in Figure 70. Assumptions regarding takeoff performance computations, and
also
the
result
of
this
analysis
are
presented
in
tables
24
and
25.
Fig. 70. Takeoff Trajectory Table 24. Takeoff Condition
C LmaxTO
2.20
V STO
118 kts
C DO ,TO
0.0511
VLOF
142 kts
L
15.1
S TO
6880 ft
S TO ,G
4310 ft
D TO ΠTO
1 2
Table 25. Takeoff Performance
0.95
“Tranquillus Project Technical Data Unit, Vol. II” Pages 4 and 5 “ Engineering Science Data Unit”, Series 2 Volumes on Aerodynamics, Vol. 2-c, item71007; ESDU Int. Ltd., 1987
76
From the result of this analysis it can be seen that the takeoff field length is slightly shorter than the required TOFL by the RFP (7000 ft) 3.7.2 Climb Performance: Using the obtained data regarding the performance of the engine at different altitudes from GasTurb as well as the aerodynamic characteristics of the aircraft, the rate of climb was determined for a variety of altitudes. It is evident that the speed corresponding to the maximum rate of climb varies for different altitudes, and it increases as the altitude increases. Figure 71 presents the result of this analysis.
Fig. 71. Rate of Climb vs. Mach number for different altitudes.
As it can be seen from this Figure, the maximum rate of climb achieved at 43,000 ft. is greater than 300 feet per second, which demonstrate that the aircraft satisfy the requirement for the maximum operating altitude specified by the RFP (43,000 ft.). 3.7.3 Thrust-Speed Relations & Validation of Maximum Cruise Speed: In order to verify the RFP requirements regards to cruise speed performance, the required thrust for maintaining a level flight was computed for the aircraft using Equation 30: 77
Treq
C D 0Clean ,M S wVCr2 max 2 cos( T )
2WCr2 BDPclean S wVCr2 cos( T ) max
(30)
This relation was plotted versus the installed thrust data obtained for the selected engine using GasTurb to verify the satisfaction of the cruise speed requirements. Figure 72 presents a graph of installed thrust vs. required thrust for the cruise altitude of 37800 ft. It can be seen from this figure that the maximum cruise speed is equal to 488 knots in an altitude of 37800 ft., which corresponds to 0.82 Mach, therefore satisfying the
Figure 72. Available and required thrust versus velocity (cruise)
goal set by the RFP (0.8 Mach). The velocity corresponding to maximum range was also determined from this analysis to be 450 kts (0.76 Mach at 37800 ft altitude). The maximum excess thrust is estimated to be achieved at a speed of 385 kts. (0.65 Mach at 37,800 ft. altitude), which yields the maximum maneuverability and endurance within the flight envelope of the aircraft.
3.7.4 Range/payload and Fuel Burn Performance: In order to asses the economic advantages of Tranquillus over the present day technology, detailed analysis of the block fuel burn was performed for the aircraft. Analysis was repeated for a three different block ranges of 500, 850 and 2800 nautical miles for 150 passengers with the relevant full baggage capacity. A step climb of 1600 ft. was assumed to take place in the middle of the cruise phase to reduce the fuel burn as suggested by Schwartz et. al 1. Figure 73 presents the result of this analysis. From this figure it is evident that for a block range of 2800 nautical miles, an initial cruise 1
Emily Schwartz, and Ilan M. Kroo, Aircraft Design: Trading Cost and Climate Impact, presented at the 47th AIAA aerospace Science meeting, Jan. 5-9 2009, Stanford University
78
altitude of 37800 ft. will cause a drastic reduction in fuel burn. This result also agrees with the result of the mission optimization performed in section 3.1 for the direct operating cost of the aircraft. For shorter ranges, such as the weighted average block range specified by the RFP (850 n.mi.), a lower altitude of 36800 ft. is perceived to cause the most significant reduction in the block fuel burn. From this analysis, it was also confirmed that the fuel
Figure 73. Block fuel burn vs. Initial Cruise Altitude for different ranges
burn for a 500 mile mission with 150 passengers onboard is approximately 5400 lbs, which corresponds to a fuel burn per passenger of 36 lbs/seat. This figure is almost 6 percent lower than the goal set by the RFP (38 lbs/seat), which confirms that the power plant technology level selected for Tranquillus is capable of satisfying the customers need, without aggressive use of more fuel efficient yet challenging engines such as open rotor concepts. A Payload-Range chart was also constructed for Tranquillus and is presented in Figure 74. Assumptions made for this analysis are presented in Table 26. Table 26. Assumptions
C L AR
0.432
Tavail ď Ą U1 C Lopt , MaxR
9960 lb
ICA FCA
0.6 deg. 475 kts. 0.4157
C D0
37800 ft. 39400 ft. 0.0310
Cj
0.408 lb./hr./lb. Figure 74. Payload-Range chart for maximum fuel capacity of 21000 lb.
79
3.7.5 Landing Distance: The landing distance for the aircraft was computed assuming a maximum landing weight (MLW) of 12995 lbs. MLW is defined by the RFP as the maximum zero-fuel weigh (107735 lbs), plus fuel reserve for the longest range and highest payload for the aircraft (5260 lbs). It was assumed that the aircraft is equipped with thrust reversers to reduce the landing field length in case of ice on the runway, therefore expanding the potential market for the aircraft to those airlines operating mainly from small suburb runways. The ground effects are taken into account for this analysis for which the result is presented in detail in data unit volume II 1 . Table 27 presents a summary of the assumptions and results for the landing performance calculations. Landing trajectory for the aircraft was also determined by running the landing simulation module in ANOPP. Figure 75 presents the result of the simulation for landing trajectory of the aircraft.
Table 27. Landing performance
VSL
0.200 0.01 106 kts.
VA S air
135 kts. 3704 ft.
S LG
2100ft.
SL
5804 ft.
FL
4
Figure 75. Landing Trajectory for MLW of 107700lbs.
Stability & Control Analyses: Trim, Static & Dynamic Stability
4.1 Sizing of the Elevator
The following criteria are considered in order to size the suitable elevator: -
Satisfying the trim requirements in the most critical condition of flight
-
The ability to initiate takeoff rotation
Several steps were taken in order to determine the size of the elevator surface. 1
“Tranquillus Project Technical Data Unit, Vol. II” Pages 11 -12
80
4.1.1) The required pitching moment for initiating the takeoff rotation, Mt is calculated from Equation 31: M t = M 0WB + M CG - MWB
(31)
Relevant moment coefficients were calculated using relations presented in Data Unit Volume I 1.
4.1.2) The required tail lift coefficient in order to maintain the state of equilibrium, for the most forward location of CG in the cruise condition is found by equation 32: Mt - C LT = 1 ρV 2 S (X MG - X CG ) 2
(32)
CLT = - 0.1447
In order to determine the elevator chord,
the
derivative C L e
different values of
ce
plotted
the
versus
for
c h has been
elevator
deflection angle, using relations presented in Data Unit Volume II 2. The generated graph can be seen in Figure 76.
Fig. 76. Elevator lift coefficient ( C Le ) vs. elevator deflection ( δe ) for different c e c
As it can be seen from this graph, as the deflection angle increases, the slope of the lift coefficient curve decreases. This can be (justified) by the creation of slow and turbulent flow regions on the elevator surfaces in angles more than ±12º.
1 2
“Tranquillus Project Technical Data Unit, Vol. I” PP. 96-100 “Tranquillus Project Technical Data Unit, Vol. II” P-49 (Particularly equations 1-5)
81
Based on the calculations performed for the lift coefficient of the horizontal tail at maximum incidence angle (with no elevator effect), it is possible to determine the maximum increase necessary in the tail lift coefficient to maintain the trim: C LT
m
C LH C Le → -0.1447 -0.0147 C Le → C Le -0.130
(33)
Referring to the graph presented in Figure 86, it can be seen that an elevator surface with ce
ch
≈ 0.23 can produce such a lift coefficient while having a deflection of 20º.
4.1.3) The horizontal tail and the elevator design were analyzed in order to determine whether or not they are capable of initiating the takeoff rotation. The method suggested by Roskam
1
was
applied, which could be found in Data Unit Volume II 2. Ground effects were considered in order to achieve a higher accuracy in the calculations. The required horizontal tail surface area at maximum incidence angle (-15º) for initiating the takeoff rotation was determined to be 417 square feet, This value is smaller than the designed horizontal tail area for satisfying the trim requirements (436 ft2) and therefore verifies the capability of the aircraft in terms of initiating the takeoff rotation.
4.2 Trim Satisfaction Satisfaction of the state of equilibrium for this configuration was studied using two methods: 1- Calculating the required elevator deflection for maintaining trim 2- Plotting trim diagrams for different flight conditions
4.2.1 Deflection of Control Surfaces: Since the aircraft was configured with all moving horizontal tails, methods presented in Data Unit Volume II 3 were used to compute the required horizontal tail incidence angle and elevator deflection to maintain trim for all segments of the mission. Since the center of gravity is located in 1
J. Roskam, Airplane Flight Dynamics and Automatic Flight Controls Part 1, Section 4.9 PP 288-292 DAR Corp. 2003 “Tranquillus Project Technical Data Unit, Vol. II” PP.76-77 3 “Tranquillus Project Technical Data Unit, Vol. II” PP.68-70 2
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different locations, ranging from most forward to most aft-ward station, these calculations demonstrate the fulfillment of trim requirements if all the horizontal tail inclinations and elevator deflections are within the possible range (-15º<ih<5º & -20º<δe<20º) Segment e trim (deg.)
2 -9.2º
5 0.0
6 -1.0
8 -4.5
9 -10.6
10 -6.34
16 -20
ih trim (deg.)
-10.0º
-5.2º
-1.2
-2.2
-5.0
-5.0
-13
Table 28. Required elevator deflection for maintaining trim in different flight conditions
As it can be seen from this table, the required angles are in between the range of elevator deflection selected in section 4.1.1 and trim could be achieved during all flight conditions.
4.2.2 Trim Diagram: A trim diagram 1 is a graphical solution for determination of trim possibility, based on the equations presented in Data Unit Volume II 2. The trim diagram is comprised of a lift coefficient vs. angle of attack graph and a lift coefficient vs. pitching moment coefficient graph. The "trim triangle" is defined as the triangular area bound between the forward and (aft) center of gravity lines and by the maximum airplane angle of attack line. This method is useful in demonstrating the following: 1) Whether or not an airplane can be trimmed at any center of gravity location with reasonable surface deflections in different flight conditions. 2) Whether or not tail stall is a limiting factor in trim. 3) The elevator deflection and lift coefficient at different angles of attack and center of gravity locations. This method offers a more detailed view of effective elements in trim of the aircraft. Trim diagrams are constructed for all of the flight conditions, and status of the aircraft is studied in comparison to boundaries of trim triangle.
1 2
Trim diagram sometimes being called trim triangle. “Tranquillus Project Technical Data Unit, Vol. II” PP.70-72
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All the diagrams have been studied in order to determine whether the aircraft could maintain the state of equilibrium in all flight conditions by using the elevator. No elevator tab was considered in these analyses, although, due to small elevator deflections, a proper light-weight elevator tab was considered in further development of the project. An example of generated trim diagrams can be found in Figure 77 1.
Fig. 77. Trim diagram, cruise condition
4.3 Longitudinal & lateral-directional static stability The static longitudinal stability of the aircraft was studied by two means: 1) Location of the aircraft’s neutral point (NP) compared to the location of CG 2) Calculating important longitudinal stability derivatives C mα , C mα Based on MIL-F-8785 B 2, every aircraft with a neutral point located behind the most aft center of gravity has static longitudinal stability in all flight conditions.
1
All of the trim diagrams could be found in data unit II PP. 71-75 Military Specification MIL-F-8785 B Flying Qualities of Piloted Airplanes; 1969: Air Force Flight Dynamics Laboratory, WP AFB, Dayton, Ohio
2
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The location of the aircraft’s neutral point was determined using the method presented in Data Unit Volume II 1. A selection of the results are presented in Table 29. As it can be seen from this table, the location of the free stick neutral
Table 29. free stick neutral point
point, NPfree in terms of wing
x cg
chord, is always behind the
x ac NP free
2 5 6 8 0.4826 0.4522 0.4403 0.4147
9 0.3747
10 0.3739
16 0.3692
0.5592 0.6001 0.5953 0.5984 0.5864 0.5100 0.4776 0.4797
0.6104 0.4225
0.6165 0.3860
0.6165 0.3859
location of the center of gravity in all segments of the flight. In order for the aircraft to be statically stable, the pitching moment coefficient due to the angle of attack ( C mα ), and pitching moment coefficient due to angle of attack rate derivatives ( C mα ) both should be negative. These derivatives are calculated based on the methods provided in Data Unit Volume II 2 3 and results are represented in tables 30. Table 30. C mα
and C m
α
for different flight segments
Segment: 2 5 6 8 9 10 16 1 C mα rad -0.2341 -0.5793 -0.5753 -0.9747 -1.0255 -1.0305 -1.3748 C m rad 1 -3.8391 -4.8517 -4.3779 -4.4914 -6.1652 -6.3958 -4.0376 α
Notice that these derivatives are negative in all of the flight conditions and therefore the initial static longitudinal stability requirement is satisfied. 4.3.1) Static lateral-directional stability: In order to verify the lateral and directional static stability of the aircraft, yawing-moment coefficientdue-to-sideslip derivative ( C n β ) should be positive, and rolling-moment-coefficient-due-to-sideslip derivative ( C l β ) should be negative. These derivatives were calculated based on the method presented in Data Unit Volume II 4 1, and results are presented in Table 31. 1 2 3 4
“Tranquillus Project Technical Data Unit, Vol. II” PP. 28-29 “Tranquillus Project Technical Data Unit, Vol. II” Page 23 “Tranquillus Project Technical Data Unit, Vol. II” Page 25 “Tranquillus Project Technical Data Unit, Vol. II” Pages 35 and 36
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Table 31.
C l and C n β
β
for different flight segments
Flight Segment : 2 5 6 8 9 10 16 1 -0.1594 -0.1929 -0.1748 -0.1727 -0.1773 -0.1674 -0.1524 Clβ rad
rad 1
Cnβ
0.3615
0.4165
0.3866
0.2938
0.3851
0.3828
0.3865
As it can be seen from the data table, the mentioned requirements for static lateral-directional stability are satisfied in all flight conditions defined by the mission profile.
4.4 Longitudinal dynamic stability Longitudinal dynamic stability derivatives were evaluated along x, y and z axis, in order to determine the transfer functions and characteristic equations. The methods applied were obtained from USAF Stability and Control DATCOM 2, and are presented in Data Unit Volume II 3. Natural frequencies and damping ratios for short period oscillations, and phugoid mode, were calculated based on the methods presented by Roskam 4. Values of short period and long period natural frequencies and damping ratios could be seen in Table 32. Flight segment: rad ω n ,S . P s
2 0.8171
5 1.0578
6 1.0134
8 1.7251
9 0.9825
10 0.9339
16 0.8752
ζ SP
0.514 0.2748
0.426 0.0646
0.458 0.1023
0.391 0.0607
0.474 0.2173
0.490 0.2018
0.455 0.1410
ζ P ,long
0.052
0.086
0.028
0.115
0.024
0.028
0.212
TC long ( 1 ) (s)
---------
--------
--------
--------
--------
--------
--------
TC long ( 2 ) (s)
---------
--------
--------
--------
--------
--------
--------
TC long ( 3 ) (s)
---------
--------
--------
--------
--------
--------
--------
TC long ( 4 ) (s)
---------
--------
--------
--------
--------
--------
--------
rad ωnP ,long
s
Table 32. Dynamic longitudinal stability characteristics in different flight conditions
1
“Tranquillus Project Technical Data Unit, Vol. II” PP. 32-35 Hoak. D.E.,”USAF Stability and Control DATCOM, Write Paterson AFB, OH 3 “Tranquillus Project Technical Data Unit, Vol. II” PP. 83-86 4 J. Roskam, Airplane Flight Dynamics and Automatic Flight Controls Part I, Section 5.2.4 & 5.2.5 PP 329-337 DAR Corp. 2003 2
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Since FAR/VLA requirements do not set specific limits on the undamped natural frequency, military requirements (MIL F-8785C) were adopted for the purpose of verifying the longitudinal flight qualities, and dynamic stability characteristics. Results of these analyses were plotted using defined boundaries for flight qualities in order to demonstrate the levels achieved for all flight conditions. Table 33 demonstrates the achieved longitudinal flying qualities by Tranquillus. Table 33. Dynamic lateral-directional stability characteristics in different flight conditions
Flight segment: T2 P sec .
2 -----
5 16.05
6 -----
T1
23.22
-----
55.03 94.48 36.54 18.52 23.22
I I
I I
2P
sec .
Level P Levelď ¸ SP
I I
8 ----I I
9 ----I I
10 ----II I
16 ----I I
4.5 Sizing of the ailerons Due to the acceptability and availability of FAR-25 standards for commercial aircrafts, guidelines suggested by this code are used in order to estimate the size of the required ailerons for the aircraft. To estimate the size of the aileron for this aircraft, a theoretical approach presented in the Technical Data Unit Volume I (pages 83 to 88) has been used. In order to be concise, this method is not presented in this proposal. The goal of achieving â&#x20AC;&#x153;level Iâ&#x20AC;? rolling qualities in the takeoff flight condition was followed using the rolling time constants (TR) suggested by FAR-25. Assuming the aileron to have a Ca/Cw equal to 20 percent starting at 75 percent of the half-span (following the flap), the outboard station of the aileron is calculated to be located at 89 percent of the half span. This aileron geometry was validated later during the analysis of the lateral directional flying qualities through fulfilling the rolling requirements defined in FAR-25.
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4.6 Lateral-directional dynamic stability Longitudinal dynamic stability derivatives were evaluated along the x, y and z axes, in order to determine the transfer functions and characteristic equations. Applied methods are obtained from USAF Stability and Control DATCOM 1, and presented in Data Unit Volume II 2. The Dutch mode roll’s undamped natural frequency, damping ratio and the spiral mode time constant are calculated and are presented in Table 34. Table 34. Dynamic lateral-directional stability characteristics in different flight conditions
Flight Segment: 2 5 6 8 9 10 16 1.1734 2.2137 1.8093 2.5118 1.8876 1.3147 2.3451 rad ωnD s 0.177 0.023 0.070 0.118 0.167 0.267 0.289 ζD 375.30 74.88 155.23 -157.39 505.38 19.36 -25.230 TS (s) 0.071 0.068 0.051 0.042 0.043 0.059 0.034 TR (s) In order to have enough damping during a Dutch roll, FAR-25 suggests that D should be greater than zero and does not specify any level for Dutch roll flying qualities. In order to determine the lateral-directional flying qualities of the aircraft, military standards (MIL-F8785C) were adopted. The requirements for rolling performance are obtained from FAR-25 in order to determine the rolling performances of the aircraft in different flight conditions. These requirements are presented in Data Unit Volume II 3. There are no specific requirements for spiral stability in any airplane. However, the military requirements place limits on the allowable divergence of the spiral mode, and are presented in Data Unit Volume II page 109. The results of the analysis for the Dutch-roll mode were illustrated through locating the status of the aircraft on a lateraldirectional stability diagram for all of the flight conditions.
Achieved flying qualities by the
proposed design are presented in tables 36 and 37. 1
Hoak. D.E.,”USAF Stability and Control DATCOM, Write Paterson AFB, OH “Tranquillus Project Technical Data Unit, Vol. II” Pages 103-110 3 “Tranquillus Project Technical Data Unit, Vol. II” Pages 104-109 2
88
Table 36. Dutch roll and short period flying qualities and characteristics in different flight phases
Flight Segment: D T2 (s)
2
5
6
8
9
10
16
0.7523
1.7922
1.3163
1.0825
0.5786
0.9575
1.3002
------
------
107.68
109.09
350.31
19.532
13.4200
T1 (s)
260.4
107.67
------
------
------
-------
-------
Level S
1
1
1
1
1
1
1
Level D Level D , 25
1 Met
2 Met
1 Met
1 Met
1 Met
1 Met
1 Met
Level n D
1
1
1
1
1
1
1
Level n D D
1
1
1
1
1
1
1
S
2S
Table 37. Rolling flying qualities for different flight phases. Note that there is no criteria set by the FAR-25 for the majority of the flight phases, therefore military standards (MIL-F-8785 C) are utilized. (N/R) = No requirements exist
Flight Segment: LevelTR Levelt
actual (deg)
5
2 1 1
5 1 1
6 1 1
8 1 1
9 1 1
10 1 1
16 1 1
28.8 63.8 56.6 60.2 43.6 36.4 24.8
Acoustics, Structural and Cost Analysis
5.1 Detailed Acoustics Analysis 5.1.1 Noise Requirements and Modeling: The ICAO Chapter 4 noise requirement defines three main noise measurement positions for the processes of noise certification of the aircraft. Flyover noise of the aircraft is measured on the ground at a point 6500 meters away from the start of the takeoff roll, while the approach noise is measured on the extended centerline of the runway 2000 meters away from the edge of the landing field. The lateral noise for the aircraft is measured on a line parallel to the axis of the runway 450
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meters away from the centerline, at the location with the maximum noise level. Figures 78 through 80 illustrate these noise measurement reference points as specified by ICAO Chapter 4.
Figure 78. Lateral Noise Reference positions
Figure 79. Flyover Noise Reference Point (D)
Figure 80. Approach Noise, Reference Point (B)
ICAO Chapter 4 also cites the maximum value of the acceptable noise for each of the described reference measurement positions, and allows a cumulative deviation of 3 dB from the reference noise levels, while limiting the deviations at each point to 2 dB 1. Table 38 presents the maximum noise levels required by ICAO chapter 4. The RFP requires a total reduction of 20 EPNdB compared to the ICAO-4 values. Three different modules of the
Table 38. Noise Level Requirements
Position: ICAO-Ch. 4 (EPNdB) Lateral Noise 94 Flyover Noise 89 Approach Noise 98
ANOPP 2 software were used to predict the noise levels of the aircraft corresponding to each of the measurement positions for flyover, approach, and lateral noise. Each module consisted of an executable file, including sub-modules such as atmospheric absorption, geometry, and noise level. The engine noise was modeled by modifying the Circular Single-Stream jet noise module (SGLJET) using the results of the engine performance analysis using GasTurb. Inputs were provided via onscreen plain text data entry and the outputs from ANOPP were produced in the form of plain ASCI disabled .txt files, which were transferred to a spreadsheet for post-processing.
Annex 16 to the conventions on International Civil Aviation, Volume I, Aircraft noise, P. II.3.3 dated 20/11/2008, International Civil Aviation Organization 2 Aircraft Noise Prediction Program, developed by NASA Langley Aeroacoustics research center 1
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5.1.2 Noise Suppression: In order to improve the noise attenuation of the vertical tail, ray tracing analysis was performed using Rhinoceros 3D software. A simplified three dimensional model of the aircraft was constructed using the ANSYS acoustics module to assess the noise suppression achieved by the relative positioning of the empennage with respect to the engine. Figures 81 and 82 present the simplified geometric model of Tranquillus and the analysis domain used for the acoustics suppression analysis. The model domain is 6500 meters long and 120 meters high. The acoustic triangular mesh was refined near the surfaces of the aircraft to improve the accuracy of the analysis.
Figure 81. Simplified Aircraft geometry for acoustic suppression analysis
Figure 82. Domain for acoustic suppression analysis. Element count: 520000
Using GasTurb, the pressure, temperature, and flow rate through the nozzle of the aircraft were determined. These loads were then applied to the analysis key points defined at the location of the engine nozzles. To achieve the maximum attenuation possible from the empennage, it was decided that both horizontal and vertical tails should be manufactured out of materials with the highest acoustic impedance. Although carbon-fiber composites often have a density 10-20 percent lower than aluminum lithium alloys, the sonic velocity in composites is at least twice the sonic velocity in
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aluminum-lithium alloys 1, which make them preferable for the purpose of acoustic attenuation due to their extremely high acoustic impedance. Therefore, it was determined that the horizontal and vertical tails should be manufactured using carbon fiber composites. Modal Acoustic FEA was performed after applying the relevant acoustic impedances and source loads to determine the acoustic pressure distribution within the acoustic model with and without airframe noise suppression for a band range of 50 to 10000 Hz. The difference between the noise levels with and without the presence of suppression is attributed to the airframe shielding. As seen below, Figures 83 and 84 present a longitudinal cross-section of the model for acoustic pressure distribution.
Figure 83. Cross-section of the acoustic model showing the distribution of the acoustic pressure 8 ft. above the aircraft reference line
Figure 84. Close up view of the acoustic pressure distribution near the empennage of the aircraft. Pnoz=146000 Pa, Tnoz=830 K, Wnet,eng=384 kg./sec
Equation 34 was used to compute the suppression factor using the result of acoustic pressure distribution. Table 39 presents the values of the suppression factors for the aircraft obtained from this analysis, used for parametric studies and the final noise evaluation.
Fsup 10
2 ln P1 / Pref
(34)
Table 39. Noise Reduction due to shielding at ICAO reference points
Position: Δ EPNdB Fsup Lateral Noise 3.1 dB 2.04 Flyover Noise 4.2 2.63 Approach Noise 4.0 2.51
1
E Koray Akdon “Piezoelectric and acoustic material for transducer applications”, Springer 2008 P.180
92
5.1.3 Parametric Studies and Noise Optimization: Due to the relatively small suppression of the lateral noise for the design, an analysis was conducted to identify the location of the maximum lateral noise for the aircraft. Perceived noise levels were plotted versus the distance traveled on the runway on a line parallel to the axis of the runway, 450 meters away from the centerline.
Figure 85 presents the
results of this analysis. As can be seen from this figure, the maximum lateral noise of 92 dB is expected to be observed at 5800 ft down the runway. Using these results, a parametric study
Figure 85. Lateral EPNdB vs distance on Runway
was performed to optimize the takeoff flap deflection and thrust setting in order to minimize the noise at 5800 ft down the runway as well as at the flyover point 6500 m. down the runway. Figures 86 and 87 present the results of these optimizations for takeoff configuration.
Figure 86. Lateral noise for different combinations of thrust setting and flap deflection measured at 5800 ft. downs the runway
Figure 87. Flyover noise for different combinations of thrust setting and flap deflection measured at 6500 m. downs the runway
From these analyses it was observed that a thrust setting of 95 percent combined with a flap setting of 25 percent would yield the largest reduction in cumulative aircraft noise for takeoff. It should be noted that maintaining 95 percent thrust levels at low altitudes immediately after takeoff reduces the
93
flyover noise of the aircraft tremendously, while simultaneously having no notable effects on the lateral noise characteristics of the aircraft.
5.1.4 Final Noise Evaluation: A final noise evaluation was performed using ANOPP to confirm that the RFP’s requirement with regards to aircraft noise was satisfied. Table 39 presents the results of the final noise calculations in the optimum configurations, as well as the difference of noise levels with the requirements set by ICAO Chapter 4 for twoengine commercial airliners. As it can be seen from these figures, Tranquillus achieves 23 dBs 1 reduction in noise compared to
Table 40. Final Noise Evaluation
Position: EPNdB Lateral Noise 92 Flyover Noise 78 Approach Noise 88 Total
ICAO Ch. 4 requirements presented in Table 40.
ICAO-4 Offset -2 dB -11 dB -10 dB -23 dB
This noise performance surpasses the
requirements set by the RFP in terms of noise reduction and highlights one of the most important features of Tranquillus.
5.2 Load Determination The velocity-load diagram for the aircraft was constructed using the methods outlined by Roskam 2 to determine the aircraft maneuvering limit loads at various speeds. Additionally, gust conditions suggested by FAR-25
3
code were applied to determine limitations dictated by
atmospheric turbulences. Methods, assumptions, and detailed results are presented in Data Unit Volume I 4. Given that the gust loads are most critical at low altitudes around 1000 feet, the velocityload diagram was constructed for this altitude. Figure 88 presents this graph, and Table 41 presents a summary of the critical speeds and loads obtained from this analysis. Pratt & Whitney Claims that each of the two P&W-1000 engines are 20 dB more quiet than present day turbofan technology, which is ICAO Ch.4 Compatible for the most part. 2 Roskam J., Airplane Design Part V ; Section 4.2 P 31-45; 1999 3 Code of Federal Regulation, FAR-23 & FAR-25 (CFR), Jan. 1st 1990, US Government Printing Office. 4 “Tranquillus Technical Data Unit, Vol. I” PP. 45-48 1
94
Table 41. V-n graph Parameters
Figure 88. Equivalent Airspeed vs. Load Factor for 1000 ft Altitude Gust lines per FAR-25 are also shown for 25 & 50 ft/sec. gust velocities
nlimit
2.50 g
n limit ( )
-1.00 g
C N max ( )
-0.301
VS
130 keas
VS ( )
310 keas
V Aeas
225 keas
VBeas
277 keas
VCeas (min)
343 keas
V Deas (max)
606 keas
n V VC
0.0058 keas 1
n V VD
0.0029 keas 1
5.3 Structural Material Given the results of the initial sensitivity analysis in section 1.2, it was determined that the low empty weight can play a decisive role in the financial successes of the aircraft by reducing the fuel burn and consequently, direct operating cost. As shown in section 3.4, carbon-fiber composites reduced the structural weight by approximately 18 percent which, based on the initial sensitivity analysis (section 1.2), corresponds to a reduction of 3600 lbs in gross takeoff weight for the maximum range of the aircraft. Cost adjustment factors presented by Hess et al. 1 regarding the use of advanced material for the airframe were used in conjunction with methods presented by Roskam 2 and Raymer 3 to model the material cost and quality control cost as two main measures of merit for selection of the structural material. In these trade studies, both material cost and quality control cost were computed as a
R. W. Hess, and H. P. Romanoff, “Aircraft Airframe Cost Estimating Relationships” RAND Corp. R 3235-AF, Dec. 1987, Santa Monica, CA 2 Roskam J., Airplane Design Part VIII ; Section 4.2 P 50-54; 1999 3 Raymer, Daniel P. , Aircraft Design – A Conceptual Approach; P-508 AIAA Education Series, Veston, VA 1992 1
95
function of the number of planes built with 65% of their airframe composed of a modern structural material (i.e. Carbon-Fiber composites or Al-Li Alloys) with the rest built using conventional aluminum alloys (Al-2024, al-7075). Figures 89 and 90 present the results of this analysis.
Figure 89. Material Cost vs. Number Manufactured
Figure 90. Quality Control Cost vs. Number Manufactured
It can be seen from this analysis that for a manufacturing run of 1500, cost of quality control is increased by 40 million dollars as a result of using composite materials while the material cost is reduced by more than two orders of magnitude, almost 4 billion dollars compared to conventional aluminum alloys. This is attributed to the higher buy-to-fly ratio associated with the composite materials 1. Buy-to-fly ratio is the ratio of the weight of the purchased raw material to the weight of the finished structure, which also reflects the amount of wasted material during the manufacturing process. Issues such as damage detection and repair as well as treatment of lightning strikes were studied to ensure the viability of the carbon fiber composites as the main structural material for Tranquillus.
1
Raman Raj et al.â&#x20AC;? â&#x20AC;&#x153;The Effects of Advanced Materials on Airframe Operating and Support Costs,â&#x20AC;? The RAND Corp, Santa Monica, CA, 2003
96
It should also be noted that the methods explored by Beachcraft & Boeing for manufacturing relatively complex single piece structures could be employed to manufacture the main structural components such as fuselage, wing, and empennage. The material usage for the aircraft is shown in Figure 89 on the following foldout.
5.4 Structural Analyses & Integrity Verification Based on the structural layout of fuselage, wing, empennage, and undercarriage, a three dimensional model of the detailed structural arrangement was prepared. Having a tolerance of ±0.05 inches for the main structural components as suggested by Young-Niu 1, this model was used to perform finite element analysis using ANSYS in order to validate the fulfillment of failure criteria in important structural members such as the wing boxes. Guidelines set by ESDU 84042 2 were used in order to simplify the major structural assemblies for finite element analysis. As an example, the finite element analysis of the upper and lower wing skins based on the critical loading data is shown in Figure 92. Although it is an incredibly versatile and powerful tool in handling the complex coupled analysis,
ANSYS lacks the simple interface required to apply and distribute very complex sets of loading manually.
Therefore, to assist in the application of the determined loads resulting from the
Advanced Aircraft Analysis load module, a MATLAB code was written to effectively distribute the shear forces and moments. This code receives the number of loaded nodes and the perimeter of the ribs as input from the user and returns the values for shear forces and moments along the x, y, and z axes for each loaded node.
Results show that the wing skin undergoes a tip deflection of
approximately 1 inch during takeoff, whit maximum fuel.
1 2
Chun-Yung Niu, Airframe Structural Design: Practical Design Information and Data on Aircraft Structures, “ Engineering Science Data Unit”, Series 3 Volumes on Aerostructure, items 84042 IHS Co., 2003
97
Figure 95. Material Distribution
Figure 94. Wing/fuselage intersections
Figure 93. General Structural Arrangement
Figure 91. Shear force distribution on wing, as a function of panel number. Each panel have a length of 31 inches, starting at the intersection of wing main structure & fuselage.
Figure 92. Vertical displacement of the wing structure at takeoff with maximum fuel, computed using ANSY FEA. Maximum displacement of 0.0251 meters is observed.
Carbon Laminate Composite Mechanical Properties: Ex=10.28 msi , Ey=5.01 msi , Gxy=5.01 msi , v=0.403
98
5.5 Cost Analysis Given the emphasis placed on the competitiveness of the flyaway and operating cost for the aircraft, special attention was paid to the financial drivers in various stages of the design. Multiple independent methods presented by Roskam, 1 Raymer, 2 and Nicolai, 3 in addition to the methods developed by the RAND 4 corporation were used to estimate the cost to increase the accuracy of the projections and to estimate the uncertainty associated with each cost. Each analysis was repeated for two production runs of 500 and 1500 as requested by the proposal. Figure 96 presents the results of the analysis for the flyaway cost as a function of the number manufactured using four different independent methods.
Figure 96. Flyaway Cost vs. Number of Manufactured Aircraft using 4 independent methods. For a 500 aircraft manufacturing run, Tranquillus is projected to have a flyaway cost of 67±8 million Dollars, while for a 1500 manufacturing run, Tranquillus will cost 47±15 million Dollars.
1
Roskam J., Airplane Design Part VIII ; Section 4.2 P 50-54; 1999 Raymer, Daniel P. , Aircraft Design – A Conceptual Approach; P-508 AIAA Education Series, Veston, VA 1992 3 Nicolai L.M., Fundamentals of Aircraft Design, METS, Inc., San Jose, CA 1984 4 R. W. Hess, and H. P. Romanoff, “Aircraft Airframe Cost Estimating Relationships” RAND Corp. R 3235-AF, Dec. 1987, Santa Monica, CA 2
99
As can be seen, the flyaway cost of Tranquillus is significantly less than the cost figures previously presented for Boeing 737 and Airbus A320 (Table. 1). This is mainly due to the weight reductions gained as a result of the application of lightweight composite structures. Analyses were also performed to determine the Life Cycle Cost (LCC) for the airplane program for two different manufacturing runs of 500 and 1500 aircraft1. Figures 97 and 98 present the results of these analyses.
Figure 97. LCC, 500 Aircraft Manufacturing run Total LCC=373.417x109 US $, 2018
Figure 98. LCC, 1500 Aircraft manufacturing run Total LCC=975.467x109 US $, 2018
Direct Operating Cost (DOC) for the aircraft was also estimated1 to verify the requirement of a 10 percent reduction compared to present day comparable aircraft (A320-200 and Boeing 737-700) for the weighted average block range of 850 n.m as specified by the RFP. Results of this analysis are presented in Table 42 confirming that the desired reduction in DOC has indeed been achieved. Table 42. Direct Operating Cost elements for Tranquillus compared to the closest competitors
Airbus A320-200 Boeing 737-700 Tranquillus Average Improvement
Annual Utilization (n.mi.) Crew ($/n.mi) Fuel & Oil ($/n.mi) Insurance ($/n.mi) Maintenance ($/n.mi) Depreciation ($/n.mi) Landing & Navigation Fees Total DOC2 1 2
1,865,256 0.96 4.53 0.15 2.96 4.93 0.40 15.03
1,891,081 0.95 3.85 0.15 2.84 4.68 0.36 13.85
1,957,656 0.92 3.24 0.15 2.66 4.32 0.32 12.51
4.0 % 4.0 % 25 % 0 % 8.2 % 11.5% 15.8% 13.4 %
Previously introduced methods by Roskam and Raymer were averaged to obtain this results Including the Financing Cost with a rate of 7 percent.
100