Effects of Mach cruise number on conventional civil jet aircraft sizing

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BACHELOR THESIS IN

AERONAUTICAL ENGINEERING

15 CREDITS, BASIC LEVEL 300

School of Innovation, Design and Engineering

Effects of Mach cruise

number on conventional

civil jet aircraft sizing

Author: Niklas Bergman Report code: MDH.IDT.FLYG.0216.2009.GN300.15HP.Ae

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ABSTRACT

This thesis work was executed at Swift Engineering Incorporated located in San Clemente, California during spring in 2009. Placement supervisor from Swift was Mark Page and advisor and examiner from the Division of future products at Mälardalen University, Sweden was Gustaf Enebog.

The objective with this thesis work was to examine the effects of fitness ratio, lift over drag, lift coefficient at cruise, winglet span, wing sweep angle, wing aspect ratio, wing area and weights with respect to Mach number for a conventional business jet capable of 18 passengers. The cruise speed study range from Mach 0.88 to 0.99.

The Excel based conceptual design tool Jetsizer 2008c was used to make four models with similar configuration and mission but with different cruise Mach numbers.

A new Jetsizer module was then created to handle a modification process where the models are optimized for their speed and configuration. The result in this report gives guidelines for the needed values when creating an initial CFD model for this type of airplane.

Date: 31 July 2009

Carried out at: Swift Engineering Inc. Advisor at MDH: Gustaf Enebog

Advisor at Swift Engineering Inc: Mark Page Examinator: Gustaf Enebog

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iii

NOMENCLATURE

Abbreviation Declaration

AR Wing Aspect Ratio

c Chord of wing

CD Drag coefficient

CD,i Induced drag coefficient

CL CRZ Lift coefficient at cruise speed

CFD Comptional fluid dynamics

ICA Initial cruise altitude

ISA International Standard Atmosphere

L/D Lift over Drag

M Mach number

MCRZ Mach number at cruise

MLW Maximum Landing Weight

MTOW Maximum TakeOff Weight

ROC Rate Of Climb

SL Sea Level

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Chapter 1 INTRODUCTION

1.1 Background

Swift was consulted by a customer to design and build a civil jet aircraft based on a special developed wing structure. The requirements where similar to the daily operating civil jets but with a preferably higher cruise speed near Mach one. In order to design this airplane an initial study was needed to investigate the relations of aircraft geometry and the aerodynamic effects on an airplane with cruise speed near Mach one.

This study was needed to be able to generate a conventional baseline which allows Swift to develop the initial CFD geometry for this project.

1.2 Objective

The purpose of this study is to demonstrate the effects of Mach number ranging from 0.88 to 0.99 for a conventional business jet in respect to

• fitness ratio • lift over drag

• lift coefficient at cruise • winglet span

• wing sweep angle • wing aspect ratio

By creating a number of aircraft models with the same configuration but optimized for different speeds a study can be made to compare the geometry variation due to the Mach number. This result will give guidelines for the geometry when making CFD models for a certain cruise speed.

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1.3 Problem formulation

First a mission has to be defined in order to be able to define a design and to have a meaningful study.

A tool has to be chosen to use in the aircraft sizing stage in order to generate different models that can be compared in a Mach cruisestudy. It is recommended to use Jetsizer 2008c for this study but it is maybe necessary to implement some new modules to estimate the transonic wave drag since Jetsizer does not take that in count.

Another tool has to be created to handle the input values in the optimization process and to display the results from each iterated step.

1.4 Limitations

This survey is only aimed at generating guidelines for a future conceptual study. For this reason there are some limitations.

• Engine inlet effects have not been taken account of.

• Limited to the size and configuration of a conventional civil jet aircraft capable of caring 18 passengers.

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3

Chapter 2 METHOD

When design an aircraft from scratch you usually start with determine the mission profile. In the early phase of this project there was no specific mission. The only given specification was that it should be a civil jet aircraft with competitive performance of modern aircrafts in the same category.

The first step was to do a basic investigation of already constructed and functional civil jet aircrafts and take their mission and performance as guidelines for this project.

In order to calibrate and to see how well Jetsizer correlate its calculations a model of the Gulfstream G650 was entered in Jetsizer with a set mission.

2.1 Mission

The mission for the models was determined by looking at other aircrafts. A summary of airplane performance was found in Aviation week & space technology1. It was decided to use the Gulfstream G650 as a calibration baseline. The G650 has a very high cruise speed together with a very long range as shown in table 1 below. The results made it to be an interesting baseline for the initial study in Jetsizer.

Table 1: Mission for Gulfstream G650

1

Aviation week & space technology, Aerospace source book, January 26, 2009

Maximum Range 7000 nm (Mach 0.85)

Normal Cruise Mach 0.85 / 488 ktas

High Speed Cruise Mach 0.90 / 516 ktas

Takeoff Distance (SL, ISA, MTOW) 6000 ft Landing Distance (SL, ISA, MLW) 3000 ft

Initial Cruise Altitude 41000 ft

Maximum Takeoff Weight 99600 lb

Basic Operating Weight 54000 lb

Maximum Fuel Weight 44200 lb

Passengers 11 - 18

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The final mission and requirements for the Mach study was determined from the G650. An increase of the Mach number will affect some of the mission variables there for are only a few clarified. Table 2 shows the mission for the models in the mach study.

Table 2: Mission for the increased mach study model

2.2 Sizing tool

Jetsizer2008c was used as the sizing tool for this research. It is user friendly and it is possible to remodel the program for suiting the study since the source code is open. It is capable of the most important calculations in the conceptual design stage of general configured passenger jets. Since Jetsizer is based on Excel, it is very easy for the user to work through another Excel documents and by a macro import and export data for analysis.

Sizing tool modification

The wing area in Jetsizer is calculated in a conventional manner including the whole wing span through the fuselage. This gives an incorrect geometry when entering a specified wing area that does not involve the middle section through the fuselage. When sizing an airplane it makes a good assumption to let the configured wing for a conventional design pass all the way through the fuselage to obtain elliptical lift distribution. When calculating the drag, this section through the fuselage gives a drag rise that Jetsizer does not neglect. This drag rise was left in the calculations to be canceled by other drag distributing sources that Jetsizer does not recognize e.g. interference between wing and fuselage.

Business jet passengers demand a higher comfort than a regular commercial airliner offers. There for a comfort factor was added to simulate the assumed weight increased for cabin equipment. The comfort factor works as a multiplier to the passenger weight.

Jetsizer 2008c lacks the ability to handle cruise speed near Mach one. A module was implemented to handle compressibility interference between components. This module is based on two papers from NACA, “Examples of the Applications of the Transonic and

Maximum Range @ ICA & Mcrz 7000 nm Takeoff Distance (SL, ISA, MTOW) 11000 ft Landing Distance (SL, ISA, MLW) 5000 ft

Initial Cruise Altitude 41000 ft

Passengers 18

Mission revenue cargo 2630

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5 2.3 Baseline model

The first model that was made in Jetsizer was based on data from the Gulfstream G650. The unpublished geometry was measured from a 3-view picture and entered in Jetsizer. The model was not supposed to be identical with the G650 but similar enough to see how well Jetsizer correlates with the published performance.

Table 3: Geometry of Gulfstream G650 that was used in the baseline model. Wing AR 7.73 Area 1283 ft2 Axial position 366 ft Dihedral 3 deg Span 99.58 ft Sweep @ c/4 33 deg Horizontal stabilizer AR 4.84 Dihedral 0 deg Sweep @ c/4 33 deg Taper ratio 0.47 Vertical stabilizer AR 1.07 Sweep @ c/4 30 Taper ratio 0.95 Fuselage Total length 1043.3 in Cabin length 643 in Cabin width 102 in Cabin height 77 in

The generated results were at first not satisfying but after some modifications in Jetsizer and to the model it correlated with the G650. The modifications were; inserting the comfort factor in Jetsizer, changing structural materials to correlate the empty weight and modifying wing area to meet the performance.

The baseline model was later used in the mach study as the model with the lowest cruise speed, Mach 0.88.

The complete baseline model is found in appendix A.

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2.4 Mach study models

Four different models were entered in Jetsizer with a conventional civil jet configuration and with individually determined mach cruise numbers ranging from 0.88 to 0.99. The purpose was to have four optimized models for each cruise speed with similar configuration. In that way it is possible to see the effects of geometric related to the cruise speed.

The mission used for the models is determined in chapter 2.2.

To keep the models comparable regarding to cabin size the middle fuselage section diameter was kept constant as well as the cabin floor area. The upper and lower lobe diameter was set to 102 inches and with a separation vertically of 3 inches. The cabin floor length was set to 767 inches. These measurements are based on the G650 and defined by the first baseline model.

Figure 2: Fuselage cross section of the models.

The four models were all generated from the baseline model and then converged with a defined cruise Mach number. Each model works as a baseline for the individual Mach number. The models were optimized by using the geometry modification tool. By taking the best values from the iterating process a new model for each study was generated. Data from the final optimized models can be found in Appendix B to E.

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7

2.5 Geometry modification tool

To investigate the relations between the geometry and Mach number a tool was needed to handle the input data and the communication with the sizing tool and to display the calculated results. This tool was made in excel with a macro to control the calculations and the communication with Jetsizer. The specific models are designed in Jetsizer after a defined cruise Mach number which allows the modification tool to only look at one model and Mach number at a time. By combining the results from several studies it is possible to make a trend of the Mach number effects.

The application works directly under Jetsizer were the user is allowed to select a range of values for a specified study. For each step Jetsizer is told to modify and converge to the model for the best result. The results are given back to the application and are shown in a table.

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The application is limited to handle only six different studies for each model (AR, wing sweep, winglet span, fuselage length, bypass ratio and SLST) which was decided to be enough for this study. Figure 4 shows the interface were the user is allowed to enter a number or a series of numbers in the cells to the right of AR, Sweep, Winglet span, Fuselage length, Bypass ratio or SLST.

In the top left corner the user is allowed to enter the Jetsizer file name that wants to be used. The only criterion is that both the active Jetsizer file and this tool have to be saved in the same map. The archive is directly connected to which archived model in Jetsizer the user wants to use.

By pressing one of the buttons to the left for each study respectively the program will start the calculation on the active cell and continue as long as there is a number written on that same row. The results will be shown in respectively column below where it is easy to see the trend or copy the values to make a plot.

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9

Chapter 3 RESULTS

The project resulted firstly in a tool that can be used with Jetsizer to optimize different geometries. Although it is limited to only a few different modification options it can easily be extended for other studies of interest by copying the code and entering new addresses in the links to Jetsizer.

3.1 Mach cruise study

The results from the optimization tool is gathered and summarized in some plots. These shows the trend lines for the increasing Mach number and the modifications needed to the models. 0 20 000 40 000 60 000 80 000 100 000 120 000 0,86 0,88 0,9 0,92 0,94 0,96 0,98 1 lb s Mach number

Weights

TOGW OEW FB

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The total weight is increasing a lot due to higher speed as shown in figure 5. This is an effect of the acting transonic wave drag when traveling in high speeds. The rise of the operating empty weight is an effect of the increasing wing area that is needed for high speeds.

It can be seen in figure 6 that the aspect ratio is descending when the Mach number goes up. By lowering the AR the fuel volume in the wings increases and the weight of the wing structure decreases. ROC decrease and TOFL gets longer. This is an effect of CD,i that is inversely proportional to the aspect ratio (equation 3.1) which then affects the total drag (equation 3.2). With a higher Aspect Ratio the induced coefficient of drag will decrease.

࡯_ࡰ,࢏= ࡯ࡸ૛ ࣊ࢋ࡭ࡾ ࡯_ࡰ= ࢉ_ࢊ+ ࡯_ࡰ,࢏ 800 850 900 950 1 000 1 050 1 100 1 150 1 200 1 250 0 1 2 3 4 5 6 7 8 9 0,86 0,88 0,9 0,92 0,94 0,96 0,98 1 W in g A re a , ft 2 A R Mach number

Wing Aspect Ratio & Area

AR

Sw

Figure 6. Trend line of AR and Sw versus Mach number.

(3.1) (3.2)

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11

In figure 7 it is shown the result of wing sweep angle when converging to the lowest CD possible. With a grater sweep the total coefficient of drag is reduced and there for ROC is increased. Greater sweep gives a heavier wing structure and a lower fuel capacity which is there for compensated with a larger wing area.

41 42 43 44 45 46 47 48 49 50 0,86 0,88 0,9 0,92 0,94 0,96 0,98 1 S w e e p a n g le Mach number

Wing Sweep

Swe…

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The reason for the dropping Lift over Drag curve in figure 8 is generally because the drag gets significantly higher when it closes to Mach one. Also the increase of weight due to higher speed affects the lift directly. The CLcrz curve is mainly effected by the Weight devided by the wing area which both increases with the higher speeds.

Winglet height study

The winglet span (or height) is proportional to the vortex drag and is also affecting the weight of the wing structure and fuel quantity.

When extending the winglets the vortex drag decreases and the weight of the wing increases this result in a loss of total fuel because of the change of the wing structure and a lower CD. When adding a winglet in Jetsizer it affects the CD and when extending the winglet you will get an even lower CD.

In the winglet height study it was discovered that Jetsizer uses a simplified formula for the winglet calculations. This results in an endless decrease of CD when the winglet height goes towards infinity. This result rejected the winglet span study.

0,000 0,050 0,100 0,150 0,200 0,250 0,300 0,350 0,400 0,450 0,500 13,50 14,00 14,50 15,00 15,50 16,00 16,50 17,00 0,86 0,88 0,9 0,92 0,94 0,96 0,98 1 C Lc rz L/ D Mach number

L/D & CLcrz

L/D CLcrz

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13

Figure 9 shows the Fuselage length trend line, same as fuselage length to thickness ratio in this study because the thickness does not vary between the models. This curve is only affected by the transonic wave drag in this study.

1 000 1 050 1 100 1 150 1 200 1 250 1 300 1 350 0,86 0,88 0,9 0,92 0,94 0,96 0,98 1 Le n g th , in ch Mach number

Fuselage length

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Chapter 4 DISCUSSION

First of all, this study is only meant to give guidelines for the initial input values of a future conceptual study on this type of aircraft. The characteristics of the results are known from fundamental aeronautical equations but the numerical values related to the speed and geometry is individual for each aircraft. The result of the plots shows expected shapes in the higher Mach region and by comparing other airplanes in the same category it shows similar results.

For M=0.88 and M= 0.92 the results show no or only a slight change in the performance which should need a more accurate investigation. This could be an effect of converge the models to the lowest CD. Probably should the M=0.88 study be rejected because that case is not optimized in perspective of the compressibility interference module. Instead it is made directly from the baseline of G650.

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15

Chapter 5 FUTURE WORK

• Improve the modification tool with more input variables and include it in Jetsizer. • Improve the winglet formula in Jetsizer.

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Chapter 6 ACKNOWLEDGEMENTS

I want to thank my supervisor Mark Page at Swift Engineering for arranging this thesis work and made it possible for me to join them at Swift for 10 weeks. I have to thank Mark for all his help and for his imaginativeness that usually solves even the toughest problems.

Thanks to all the guys at Swift; Ed Smetak, for helping me arrange a living during the stay and driving me to work every day and letting me experience the life in California. Any Luo, for supervising me in this project and helping me with everything associated with computers and aerodynamics. John Winkler, for your experienced help with aeronautical topics and for showing me around in the mountainous Californian run track.

Thanks to Chris Thompson for letting a complete stranger from Sweden to occupy one of your wonderful bedrooms in the magnificent beach house.

Special thank to my supervisor Gustaf Enebog at MDH, Sweden, for helping me with the formal elements of this thesis work and for the contacts who gave me this opportunity.

I finally want to thank the international unit at MDH for financing my time abroad.

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17

Chapter 7 REFERENCES

1. Dr. Jan Roskam. Airplane Design Part I,”Preliminary Sizing of Airplanes”, DARcorporation 2005, ISBN-13: 978-1-884885-42-6

2. Dr. Jan Roskam. Airplane Design Part II, ”Preliminary Configuration Design and Integration of the Propulsion System” ,DARcorporation 2005, ISBN: 1-884885-43-8

3. Dr. Jan Roskam. Airplane Design Part III, ”Layout Design of Cockpit, Fuselage, Wing and Empennage: Cutaways and Inboard Profiles”, DARcorporation 2005, ISBN: 1-884885-56-x

4. Dr. Jan Roskam. Airplane Design Part VI, ”Preliminary Calculations of Aerodynamic, Thrust and Power Characteristics”, DARcorporation 2005, ISBN-13: 978-1-884885-

52-5

5. Dr. Jan Roskam. Airplane Design Part VII, ”Determination of Stability, Control and

Performance Characteristics: FAR and Military Requirements”, DARcorporation 2005, ISBN-13: 978-1-884885-54-9

6. Aviation week & space technology, Aerospace source book, January 26, 2009

7. Robert L. Nelson Clement J. Welsh. “Examples of the Applications of the Transonic and Supersonic Area Rules to the Prediction of Wave Drag”, NACA RM L56D11, Langley Aeronautical Laboratory, Langley Field, Va., 20 March 1957.

8. Whitcomb, Richard T. “A Study of the Zero-Lift Drag-Rise Characteristics of Wing-Body Combinations Near the Speed of Sound”, NACA RM L52H08, Langley Aeronautical Laboratory, Langley Field, Va., 3 September 1952.

9. John D. Anderson, Jr. Fundamentals of Aerodynamics, Mc Graw Hill 2007, ISBN: 007-125408-0

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A. APPENDIX

Baseline model cruise speed Mach 0.88.

Fuselage & Materials

Ncrew = 2 n.d.

Typ 3 class Nattendants = 2 n.d. Natt =1 Diameter (avg), Dfus = 8,6 ft Dfus =6,1

Total Length, Lfus = 87 ft Lfus =59 # Coach Seats Abreast = 2 n.d. -

Number of Aisles = 1 n.d. - Fineness Ratio (L/Dia)fus = 10,0 n.d.

LH2:TankWt/FuelWt |

InsulatnWt/Area = 0,0 0,0

n.d. | lbs/ft2

Wing Materials = COMP "AL", "ALLI", "COMP" Fuselage Materials = COMP "AL", "ALLI", "COMP" Empennage Materials = COMP "AL", "ALLI", "COMP" Fuel Type = Kerosene "Kerosene", "LH2"

Propulsion SLST per engine = 14 600 lbs 2 Engines Neng = 2 n.d. Eng Location = F "W"ing, "F"uselage Engine Cert Date & EIS = 1980 year

Bypass Ratio (BPR) = 4,4 n.d. **TFAN** SexposedPylon = 86,0 sq-ft per pylon

Fuel Price = 1,1 $/USg al

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19

Mean Aero Chord, MAC = 12,2 8,0 9,9

Croot = 17,4 10,5 12,9 Ctip = 4,4 4,9 6,1 CSOB = 16,2 _- _- bH/bw = - 0,309 - Wing Sw = 950 sq-ft

(t/c)avg = 0,101 n.d. Drag Div AOK

Λχ/4 = 35,00 deg Drag Div AOK

ARw = 8,00 n.d. AOK - no flutter

Ult. Load Factor Nult = 3,5 g's TRw = 0,25 n.d.

Winglet Height, hwglt = 6,0 ft AOK - no flutter

SplanformWinglet = 35,3 sq-ft total both panels Airfoil Type = SCDTE "CONV", "SC", "SCDTE" Φλαπ Σπαν ηΟ/Β φλαπ = 0,75

fraction of semispan

FlapType = D "N"one,"S"ingle,"D"ouble Leading Edge Slat = No "Yes". "No"

Empennage Horizontal Vertical

Tail Volume Ratio, VH = 0,707

0,04

1 n.d. Aspect Ratio, ARH = 3,50 1,15 n.d. Tail Sweep, LH = 44,0 44,0 deg Taper Ratio, TRH = 0,47 0,47 n.d.

Tail Length, LH = 39,5 32,9 ft

Elevator / Rudder Types = Simple SHR See comments SASoff SM% / Tail Pos'n = 9 T See comments

D

Performance Actual Limit

Crz SFC = 0,633743 - lb/hr/lb TOGW = 84 326 - lbs MLW = 73 652 - lbs OEW = 38 195 - lbs Fuel Burn = 35 566 - lbs TOFL = 10 368 11 000 ft @TOGW LFL = 4 989 5 000 ft @ MLW Buffet Limited CL@ICA = 0,43 0,67 n.d.

ROC@ICA = 301 300 fpm Wingspan = 87 120 ft VLdg@MLW = 136 150 @1.3Vsmin L/Dcrz = 16,77 - n.d. DOC/pax-nmi = 0,19 $/pax-nmi Performance Summary TOGW/Sw = 88,8 psf TOGW/PaxNmi = 0,67 lbs/Pax-nmi

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Thrust/TOGW = 0,35 n.d.

FB/PaxNmi= 0,282 lbs/Pax-nmi Floor Space per Pax = #N/A sq-ft

Cargo Bay Volume per Pax = 6,71 cu-ft under-floor cargo OEW/TOGW = 45,3% n.d.

FB/TOGW = 42,2% n.d. PAY/TOGW = 7,7% n.d.

Cruise Conditions

Max Allowable CL@ICA = 0,67

n.d. Buffet Limited CLcrz =CLbuffet/1.3

qCrz = 202,9 psf VtrueCrz = 851,789 fps

Mission Requirements

Mixed-Class Pax Count = 18

n.d.

(Pax) Customer Reqm't Still Air Range = 7 000 nmi. Customer Reqm't Mcrz = 0,88 n.d. Design Variable Mission Revenue Cargo = 2 630 lbs Customer Reqm't

Max Payload @ MLW = 35 000 lbs Customer Reqm't %Mission Fuel @ MLW = 0,1 % Customer Reqm't User Selected ICA = 41 000 ft Design Variable Min ROC @ICA = 300 fpm Customer Reqm't Max TOFL @ MTOGW = 11 000 ft Customer Reqm't Max LFL @ MLW = 5 000 ft Customer Reqm't Max VLdg @MLW = 135 KEAS Customer Reqm't TOFL & LFL Altitude = 0 ft Customer Reqm't TOFL & LFL Temp = 59 °F Customer Reqm't Max Wingspan = 99,85 ft Customer Reqm't Number of Planes Built = 500 n.d. Customer Reqm't

Wing & Tails Wing Horiz. Vertical Winglet

Tail Volume Ratio, V = NA 0,71 0,041 NA n.d. Axial Tail Pos'n (Xc/4-Xblkhd) = NA 180 100 NA in.

Aspect Ratio, AR = 8,00 3,50 1,15 2,04 n.d. Sweep Angle, Lc/4 = 35,00 44,00 44,00 40 deg Planform Break Pos'n Ybreak/(b/2) = 0,2 0,00 0,00 NA n.d. Break Taper Ratio Cbreak/Croot = NA 1,00 1,00 NA n.d. Tip Taper Ratio, Ctip/Croot = 0,25 0,47 0,47 0,35 n.d.

Glove Extension at SOB, DC/CSOB = 0 NA NA NA 0,5

Yehudi Extension at SOB, DC/CSOB = 0,15 NA NA NA n.d. Flap Chord Fraction Cflap/Cw = 0,18 0,25 0,25 NA n.d. Area, total trapezoidal, S = 950 207 104 35 sq-ft

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Airfoil t/c @ Tip = 0,085 NA NA NA n.d.

MAC Incidence Angle = 2 -3,00 NA NA deg

Axial Wing pos'n, Xc/4trap@C/L = 454,1984 NA NA NA in. Front Spar Pos'n, XFS/C

= 0,1 NA NA NA n.d.

Rear Spar pos'n at SOB, XRS/C = 0,75 NA NA NA n.d. Rear Spar pos'n, Break->Tip, XRS/C = 0,7 NA NA NA n.d.

Fuselage

Total Fuselage Length, Lfus = 1040 in. Nose Fineness Ratio, Lnose/Dia = 1,9 n.d. Tailcone Fineness Ratio, Ltail/Dia = 3,5 n.d. Tailcone Height Ratio, Htip/Hfus = 0,2 n.d. Tailcone Width Ratio, Wtip/Wfus = 0,05 n.d. Nose Droop Ratio, DZ/Hfus = 0,16 n.d. Tailcone Rise Ratio, DZ/Hfus = 0,2 n.d. Cockpit Bulkhead pos'n, DX/Lnose = 0,65 in. Aft Blkhd pos'n, DX/Ltailcone = 0,6 in. Cabin FloorSpace (blkhd to blkhd) = #N/A sq-ft Usable Floor Space per Passenger = #N/A sq-ft/pax

Nacelles

Number of Nacelles = 2 1-4

Fan diameter, Dfan = 48,84282 in.

Length Ratio, L/Dfan = 3 n.d.

Dia.Ratio, Dnac/Dfan = 1,25 n.d.

Inboard Outboard Lateral pos'n Y = 0,00 80,00 in. (Xnozzle-XLEwing) = 0,00 -20,00 n.d. Z rel to WingLE or floor = 0,00 35,00 n.d.

Nose Gear

Z pos'n of Trunnion = -30 in. X station of nosegear = 98,0 in. Tire Pressure = 900 psi Number of Tires = 2 1,2

Limits

MinWng/GW @ aft c.g. = 0,04 n.d. 1g Pitch Angle = 10,0 deg No Gear Load Pitch Angle

= 12,0 deg

1g Roll Clearance Angle = 8,0 deg

Main Gear

Static Ground Line pos'n

= -90,0 in.

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Y pos'n of Trunnion = 75,0 in. Strut Aft-sweep,

Extended = 3,0 deg Strut Aft-sweep,

Retracted = 6,0 deg Oleo Stroke-Out from 1g

= 10,0 in.

Oleo Stroke-In from 1g

= 1,0 in. X maingear = 642,0 in. Tire Pressure = 200 psi Number of Tires per

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23 B. APPENDIX

Optimized model for cruise speed Mach 0.88

Fuselage & Materials Ncrew = 2 n.d. Typ 3 class Nattendants = 2 n.d. Natt =1 Diameter (avg), Dfus = 8,6 ft

Dfus =6,1 Total Length, Lfus = 87 ft Lfus =59 # Coach Seats Abreast = 2 n.d. -

LH2:TankWt/FuelWt |

n.d. | lbs/ft2

Wing Materials = COMP "AL", "ALLI", "COMP" Fuselage Materials = COMP "AL", "ALLI", "COMP" Empennage Materials = COMP "AL", "ALLI", "COMP"

Fuel Type = Kerosene "Kerosene", "LH2" Propulsion SLST per engine = 15 200 lbs 2 Engines Neng = 2 n.d. Eng Location = F "W"ing, "F"uselage Engine Cert Date & EIS = 1980 year

Bypass Ratio (BPR) = 5 n.d. **TFAN** SexposedPylon = 86,0 sq-ft per pylon

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Geometry (Trap) Wing Horiz Vert

Planform Area, S = 930,0 183,7 105,5

Span, b = 86,3 25,4 11,0

Croot = 17,3 9,9 13,0

Ctip = 4,3 4,6 6,1

CSOB = 16,0 _- _-

bH/bw = - 0,294 - Mission Requirements

n.d. (Pax)

Customer Reqm't Still Air Range = 7 000 nmi.

Customer Reqm't Mcrz = 0,88 n.d.

Design Variable Mission Revenue Cargo = 2 630 lbs

Customer Reqm't Max Payload @ MLW = 35 000 lbs Customer Reqm't %Mission Fuel @ MLW = 0,1 % Customer Reqm't User Selected ICA = 41 000 ft

Design Variable Min ROC @ICA = 300 fpm

Customer Reqm't Max TOFL @ MTOGW = 11 000 ft

Customer Reqm't Max LFL @ MLW = 5 000 ft Customer Reqm't Max VLdg @MLW = 135 KEAS Customer Reqm't TOFL & LFL Altitude = 0 ft

Customer Reqm't TOFL & LFL Temp = 59 °F

Customer Reqm't Max Wingspan = 99,85 ft Customer

Reqm't

Number of Planes Built = 500 n.d. Customer Reqm't

Wing

Sw = 930 sq-ft

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25

Leading Edge Slat = No "Yes". "No"

0,04

D

ROC@ICA = 302 300 fpm Wingspan = 86 120 ft VLdg@MLW = 136 150 @1.3Vsmin L/Dcrz = 16,72 - n.d. DOC/pax-nmi = 0,19 $/pax-nmi Performance Summary TOGW/Sw = 89,4 psf TOGW/PaxNmi = 0,66 lbs/Pax-nmi Thrust/TOGW = 0,37 n.d. FB/PaxNmi= 0,274 lbs/Pax-nmi Floor Space per Pax = #N/A sq-ft

Cruise Conditions

Aspect Ratio, AR = 8,00 3,50 1,15 2,06 n.d. Sweep Angle, Lc/4 = 42,00 44,00 44,00 40 deg

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Planform Break Pos'n

Ybreak/(b/2) = 0,2 0,00 0,00 NA n.d. Break Taper Ratio Cbreak/Croot

= NA 1,00 1,00 NA n.d.

Tip Taper Ratio,

Ctip/Croot = 0,25 0,47 0,47 0,35 n.d. Glove Extension at SOB,

DC/CSOB = 0 NA NA NA 0,5

Yehudi Extension at SOB,

DC/CSOB = 0,15 NA NA NA n.d.

Flap Chord Fraction Cflap/Cw = 0,18 0,25 0,25 NA n.d. Area, total trapezoidal, S = 930 184 106 35 sq-ft

Span, b = 86 25 11 6 ft

Wing Dihedral Angle, G = 3 0,00 NA 75 deg Vertical Offset, DZ = -40 150,00 30,00 NA in. Airfoil t/c @ SOB = 0,150 NA NA NA n.d.

Airfoil t/c @ Break = 0,128 0,07 0,07 NA n.d. Airfoil t/c @ Tip = 0,105 NA NA NA n.d. MAC Incidence Angle = 2 -3,00 NA NA deg Axial Wing pos'n, Xc/4trap@C/L

= 403,3681 NA NA NA in.

Front Spar Pos'n,

XFS/C = 0,1 NA NA NA n.d.

Rear Spar pos'n at SOB,

XRS/C = 0,75 NA NA NA n.d.

Rear Spar pos'n, Break->Tip,

Fuselage

Total Fuselage Length,

Lfus = 1040 in.

Nose Fineness Ratio,

Lnose/Dia = 1,9 n.d. Tailcone Fineness Ratio,

Ltail/Dia = 3,5 n.d. Tailcone Height Ratio,

Htip/Hfus = 0,2 n.d. Tailcone Width Ratio,

Wtip/Wfus = 0,05 n.d. Nose Droop Ratio,

DZ/Hfus = 0,16 n.d. Tailcone Rise Ratio,

DZ/Hfus = 0,2 n.d. Cockpit Bulkhead pos'n,

DX/Lnose = 0,65 in. Aft Blkhd pos'n,

DX/Ltailcone = 0,6 in. Cabin FloorSpace (blkhd to

blkhd) = #N/A sq-ft Usable Floor Space per

Passenger = #N/A sq-ft/pax

Nacelles

(31)

27

Z rel to WingLE or floor = 0,00 35,00 n.d.

Nose Gear

Z pos'n of Trunnion

= -30 in. X station of

nosegear = 98,0 in. Tire Pressure = 900 psi Number of Tires = 2 1,2

Limits

MinWng/GW @ aft

c.g. = 0,04 n.d. 1g Pitch Angle = 10,0 deg No Gear Load Pitch

Angle = 12,0 deg 1g Roll Clearance

Angle = 8,0 deg

Main Gear

Static Ground Line

pos'n = -90,0 in. Z pos'n of Trunnion = -46,0 in. Y pos'n of Trunnion = 75,0 in. Strut Aft-sweep, Extended = 3,0 deg Strut Aft-sweep, Retracted = 6,0 deg Oleo Stroke-Out from 1g = 10,0 in. Oleo Stroke-In from 1g = 1,0 in. X maingear = 638,8 in. Tire Pressure = 200 psi Number of Tires per

(32)

C. APPENDIX

Ncrew = 2 n.d.

Typ 3 class Nattendants = 2 n.d. Natt =1 Diameter (avg), Dfus = 8,6 ft

LH2:TankWt/FuelWt |

n.d. | lbs/ft2

(33)

29

Planform Area, S = 940,0 116,4 97,7

Span, b = 86,7 20,2 10,6

Croot = 17,3 7,8 12,5

Ctip = 4,3 3,7 5,9

CSOB = 16,1 _- _-

n.d. (Pax)

Customer Reqm't

Mcrz = 0,92 n.d. Design Variable Mission Revenue Cargo = 2 630 lbs

Customer Reqm't Max Payload @ MLW = 35 000 lbs Customer Reqm't %Mission Fuel @ MLW = 0,1 % Customer Reqm't

User Selected ICA = 41 000 ft Design Variable Min ROC @ICA = 300 fpm

Customer Reqm't Max Wingspan = 105 ft Customer

Reqm't

Wing

Sw = 940 sq-ft

SplanformWinglet = 35,1 sq-ft total both panels Airfoil Type = SCDTE "CONV", "SC", "SCDTE" Φλαπ Σπαν ηΟ/Β φλαπ = 0,75 fraction of semispan

(34)

0,04

D

Cruise Conditions

(35)

31

Tip Taper Ratio, Ctip/Croot = 0,25 0,47 0,47 0,35 n.d. Glove Extension at SOB, DC/CSOB

= 0 NA NA NA 0,5

Flap Chord Fraction Cflap/Cw = 0,18 0,25 0,25 NA n.d. Area, total trapezoidal, S = 940 116 98 35 sq-ft

Span, b = 87 20 11 6 ft

Wing Dihedral Angle, G = 3 0,00 NA 75 deg

Vertical Offset, DZ = -40 140,00 35,00 NA in. Airfoil t/c @ SOB = 0,150 NA NA NA n.d.

Airfoil t/c @ Break = 0,130 0,07 0,07 NA n.d. Airfoil t/c @ Tip = 0,100 NA NA NA n.d.

Axial Wing pos'n, Xc/4trap@C/L = 451,9088 NA NA NA in. Front Spar Pos'n,

Fuselage

Lfus = 1108 in.

Nose Fineness Ratio, Lnose/Dia

= 2,9 n.d.

Tailcone Fineness Ratio,

Ltail/Dia = 3,5 n.d. Tailcone Height Ratio, Htip/Hfus

= 0,2 n.d.

Tailcone Width Ratio,

DZ/Hfus = 0,16 n.d.

Tailcone Rise Ratio,

DZ/Hfus = 0,2 n.d.

Cockpit Bulkhead pos'n, DX/Lnose

= 0,65 in.

Aft Blkhd pos'n,

DX/Ltailcone = 0,6 in. Cabin FloorSpace (blkhd to blkhd)

= #N/A sq-ft Usable Floor Space per Passenger

= #N/A sq-ft/pax

Nacelles

Dia.Ratio, Dnac/Dfan = 1,25 n.d. Inboard Outboard Lateral pos'n Y = 0,00 80,00 in. (Xnozzle-XLEwing) = 0,00 40,00 n.d. Z rel to WingLE or floor = 0,00 33,00 n.d.

Nose Gear

(36)

X station of nosegear = 100,0 in. Tire Pressure = 900 psi Number of Tires = 2 1,2

Limits

MinWng/GW @ aft c.g.

= 0,04 n.d.

1g Pitch Angle = 10,0 deg No Gear Load Pitch

Angle = 8,0 deg

Main Gear

Static Ground Line

pos'n = -90,0 in. Z pos'n of Trunnion = -42,0 in. Y pos'n of Trunnion = 75,0 in.

Strut Aft-sweep,

Retracted = 6,0 deg Oleo Stroke-Out from

1g = 8,0 in. Oleo Stroke-In from

1g = 1,0 in. X maingear = 683,0 in. Tire Pressure = 200 psi Number of Tires per

(37)

33 D. APPENDIX

Ncrew = 2 n.d.

LH2:TankWt/FuelWt |

n.d. | lbs/ft2

Bypass Ratio (BPR) = 4,5 n.d. **TFAN** SexposedPylon = 86,0 sq-ft per pylon

(38)

Planform Area, S = 1025,0 107,3 96,6

Span, b = 84,7 19,4 10,5

Croot = 19,4 7,5 12,5

Ctip = 4,8 3,5 5,9

CSOB = 17,9 _- _-

n.d. (Pax)

Customer Reqm't

Reqm't

Wing

Sw = 1 025 sq-ft

SplanformWinglet = 39,2 sq-ft total both panels Airfoil Type = SCDTE "CONV", "SC", "SCDTE"

(39)

35

0,04

D

Cruise Conditions

Aspect Ratio, AR = 7,00 3,50 1,15 1,84 n.d. Sweep Angle, Lc/4 = 45,00 55,00 55,00 40 deg Planform Break Pos'n Ybreak/(b/2)

(40)

Break Taper Ratio Cbreak/Croot = NA 1,00 1,00 NA n.d. Tip Taper Ratio, Ctip/Croot = 0,25 0,47 0,47 0,35 n.d. Glove Extension at SOB, DC/CSOB

= 0 NA NA NA 0,5

Flap Chord Fraction Cflap/Cw = 0,18 0,25 0,25 NA n.d. Area, total trapezoidal, S = 1 025 107 97 39 sq-ft

Span, b = 85 19 11 6 ft

Fuselage

Lfus = 1283 in.

= 5,5 n.d.

= 0,2 n.d.

DZ/Hfus = 0,16 n.d.

DZ/Hfus = 0,2 n.d.

= 0,65 in.

Aft Blkhd pos'n,

= #N/A sq-ft/pax

Nacelles

Dia.Ratio, Dnac/Dfan = 1,25 n.d. Inboard Outboard

(41)

37

Z pos'n of Trunnion = -30 in. X station of nosegear = 100,0 in. Tire Pressure = 900 psi Number of Tires = 2 1,2

Limits

= 0,04 n.d.

Angle = 8,0 deg

Main Gear

Static Ground Line

Strut Aft-sweep,

(42)

E. APPENDIX

Ncrew = 2 n.d.

LH2:TankWt/FuelWt |

n.d. | lbs/ft2

(43)

39

Planform Area, S = 1210,0 124,5 138,4

Span, b = 85,2 19,3 12,6

Croot = 22,7 8,8 14,9

Ctip = 5,7 4,1 7,0

CSOB = 21,0 _- _-

n.d. (Pax)

Customer Reqm't

Reqm't

Wing

Sw = 1 210 sq-ft

SplanformWinglet = 46,0 sq-ft total both panels Airfoil Type = SCDTE "CONV", "SC", "SCDTE" Φλαπ Σπαν ηΟ/Β φλαπ = 0,75 fraction of semispan

(44)

0,05

D

Cruise Conditions

(45)

41

Tip Taper Ratio, Ctip/Croot = 0,25 0,47 0,47 0,35 n.d. Glove Extension at SOB, DC/CSOB

= 0 NA NA NA 0,5

Flap Chord Fraction Cflap/Cw = 0,18 0,25 0,25 NA n.d. Area, total trapezoidal, S = 1 210 125 138 46 sq-ft

Span, b = 85 19 13 6 ft

Fuselage

Lfus = 1316 in.

= 6 n.d.

= 0,2 n.d.

DZ/Hfus = 0,16 n.d.

DZ/Hfus = 0,2 n.d.

= 0,65 in.

Aft Blkhd pos'n,

= #N/A sq-ft/pax

Nacelles

Dia.Ratio, Dnac/Dfan = 1,25 n.d. Inboard Outboard Lateral pos'n Y = 0,00 80,00 in. (Xnozzle-XLEwing) = 0,00 0,00 n.d. Z rel to WingLE or floor = 0,00 33,00 n.d.

Nose Gear

(46)

X station of nosegear = 100,0 in. Tire Pressure = 900 psi Number of Tires = 2 1,2

Limits

= 0,04 n.d.

Angle = 8,0 deg

Main Gear

Static Ground Line

Strut Aft-sweep,

(47)

43 F. APPENDIX

Program codes for the modification tool excel macro.

Dim JetsizerFile As String

Sub Iterate_AR() '

' Iterate_AR Macro '

'

Dim MTOGW As Double, OEW As Double, FB As Double, LD As Double, CLCZ As Double

Dim SLST As Double, tcroot As Single, tcbreak As Single, tctip As Single Dim Archive As Integer

Dim VarVal As Variant

Dim i As Integer, j As Integer, index As String Dim Flutter As String

Application.ScreenUpdating = False JetsizerFile = Cells(2, 3)

ParentWin = ThisWorkbook.Name

Windows(ParentWin).Activate 'Change to WKname

i = Selection.Row 'Always assume user selects first variable step on execution j = Selection.Column

Archive = Cells(3, 3) 'list baseline archive index to load index = "C11"

Do While Cells(i, j) <> Empty

VarVal = Cells(i, j)

Windows(JetsizerFile).Activate

'Load baseline from archive Sheets("Archive").Select

(48)

Range("A69").Select

Do While ActiveCell.Value <> Archive ActiveCell.Offset(59, 0).Select Loop

Application.Run JetsizerFile & "!RestoreFile"

'Load in new Variable Value Sheets("Configuration").Select Range(index).Value = VarVal

'Iterate on tc

Do While Cells(81, 2) <> "FAIL" And Cells(23, 3) < 0.151 Cells(23, 3) = Cells(23, 3) + 0.001 Cells(24, 3) = Cells(23, 3) * 0.85 Cells(25, 3) = Cells(23, 3) * 0.7 Loop Cells(23, 3) = Cells(23, 3) - 0.001 Cells(24, 3) = Cells(23, 3) * 0.85 Cells(25, 3) = Cells(23, 3) * 0.7

'Run for Convergence

Application.Run "Convergebuttons" Application.Run "reduceslst"

'Get Weights and Parameters

MTOGW = Sheets("Mission").Range("I29") OEW = Sheets("Mission").Range("I31") FB = Sheets("Mission").Range("I32") LD = Sheets("Mission").Range("I39") CLCZ = Sheets("Aero").Range("I19") SLST = Sheets("Mission").Range("D19") tcroot = Sheets("Configuration").Range("C23") tcbreak = Sheets("Configuration").Range("C24") tctip = Sheets("Configuration").Range("C25")

If Sheets("Mission").Range("K8") = "FLUTTER" Then Flutter = "Flutter"

End If

Windows(ParentWin).Activate 'Change to WKname Cells(i + 1, j) = MTOGW

Cells(i + 2, j) = OEW Cells(i + 3, j) = FB Cells(i + 4, j) = LD Cells(i + 5, j) = CLCZ

(49)

45 If Flutter = "Flutter" Then

Cells(i - 1, j) = Flutter End If Flutter = Empty j = j + 1 Loop

'Load from archive

Windows(JetsizerFile).Activate Sheets("Archive").Select Range("A69").Select

End Sub

Sub ConvergeButtons()

Application.Run JetsizerFile & "!ConvergeCLandTOGW" loopnum = 0

maxloop = 20 indexch = 33

Do While loopnum < maxloop And indexch <= 38

Application.Run JetsizerFile & "!ConvergeCLandTOGW"

indexch = 33

Do While Cells(indexch, 14) = "OK" indexch = indexch + 1

Loop

Select Case indexch Case 33

Application.Run JetsizerFile & "!SLSTforTOFL" Case 34

Application.Run JetsizerFile & "!SizeSwForLFL" Case 35

(50)

Application.Run JetsizerFile & "!SizeSwForCLICA" Case 36

Application.Run JetsizerFile & "!SizeSLSTforROC" Case 38

Application.Run JetsizerFile & "!SizeSwForVldg" End Select loopnum = loopnum + 1 Loop End Sub Sub reduceSLST() Windows(JetsizerFile).Activate Sheets("Mission").Range("D19").Select SLSTtemp = ActiveCell.Value indexch = 39 Do While indexch > 38 SLSTnew = SLSTtemp - 1000 Sheets("Mission").Range("D19").Select ActiveCell.Value = SLSTnew indexch = 33

Do While Cells(indexch, 14) = "OK" indexch = indexch + 1 Loop Application.Run "ConvergeButtons" SLSTtemp = SLSTnew Loop End Sub

(51)

47

Dim i As Integer, j As Integer, index As String Dim Flutter As String, MDD As String

Archive = Cells(3, 3) 'list baseline archive index to load index = "C12"

'Load baseline from archive Sheets("Archive").Select Range("A69").Select

'Iterate on tc

Do While Cells(81, 2) <> "FAIL" And Cells(23, 3) < 0.151 Cells(23, 3) = Cells(23, 3) + 0.001

Cells(24, 3) = Cells(23, 3) * 0.85 Cells(25, 3) = Cells(23, 3) * 0.7 Loop

(52)

Cells(23, 3) = Cells(23, 3) - 0.001 Cells(24, 3) = Cells(23, 3) * 0.85 Cells(25, 3) = Cells(23, 3) * 0.7

If Sheets("Mission").Range("K8") = "FLUTTER" Then Flutter = "Flutter"

End If

If Sheets("Mission").Range("K7") = "FAIL" Then MDD = "MDD" End If

Windows(ParentWin).Activate 'Change to WKname Cells(i + 1, j) = MTOGW Cells(i + 2, j) = OEW Cells(i + 3, j) = FB Cells(i + 4, j) = LD Cells(i + 5, j) = CLCZ Cells(i + 6, j) = SLST Cells(i + 7, j) = tcroot Cells(i + 8, j) = tcbreak Cells(i + 9, j) = tctip

If Flutter = "Flutter" Then Cells(i - 1, j) = Flutter End If

If MDD = "MDD" Then Cells(i - 1, j) = MDD End If

(53)

49 Loop

'Load from archive

End Sub

Sub Iteration_Winglet_Span() '

' Iteration_Winglet_Span Macro '

Dim i As Integer, j As Integer, index As String

Archive = Cells(3, 3) 'list baseline archive index to load index = "F20"

(54)

'Iterate on tc

Windows(ParentWin).Activate 'Change to WKname Cells(i + 1, j) = MTOGW

Cells(i + 2, j) = OEW Cells(i + 3, j) = FB

(55)

51 Cells(i + 8, j) = tcbreak Cells(i + 9, j) = tctip j = j + 1 Loop

'Load from archive

End Sub

Sub Iteration_Fuselage_length() '

' Iteration_Fuselage_length Macro '

(56)

index = "C34"

'Iterate on tc

(57)

53 Cells(i + 4, j) = LD Cells(i + 5, j) = CLCZ Cells(i + 6, j) = SLST Cells(i + 7, j) = tcroot Cells(i + 8, j) = tcbreak Cells(i + 9, j) = tctip j = j + 1 Loop

'Load from archive

End Sub

Sub Iteration_Bypass_Ratio() '

' Iteration_Bypass_Ratio Macro '