Sizing and Balance Module Development for Aircraft Conceptual Design

Gustav Peterson

Vehicle Design

Master thesis Department of Mechanical Engineering

LIU-IEI-TEK-A--07/00217--SE

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Presentationsdatum 2007-10-05 Publiceringsdatum (elektronisk version) 2007-10-09

Institution och avdelning Institutionen för ekonomisk och industriell utveckling IEI

URL för elektronisk version

Publikationens titel Sizing and Balance Module Development for Aircraft Conceptual Design Författare Gustav Peterson

Sammanfattning På Saab Aerosystems finns ett conceptstudieprogram kallat DIBA där man tittar på flygplans design i dess tidigaste skeden. Detta program har utökats med moduler för sizing och balancering av en flygfarkost. Generering av ett sizing diagram kopplat till givna indata har tagits fram. Tyngdpunktsplacering och neutralpunktsestimeringsrutiner har också utvecklats för att utvärdera balancering vid t.ex. lastförflytting.

Nyckelord Sizing, Balance, Aircraft, Concept, Design, FAR, Matlab

Språk Svenska X Annat (ange nedan) Engelska Antal sidor 81

Typ av publikation Licentiatavhandling X Examensarbete C-uppsats D-uppsats Rapport Annat (ange nedan)

ISBN (licentiatavhandling) ISRN LIU-IEI-TEK-A--07/00217--SE

Serietitel (licentiatavhandling) - Serienummer/ISSN (licentiatavhandling)

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1 EXPLANATIONS 5

1.1 ABSTRACT 5 1.2 UNITS & CONVERSION TABLES 6 1.3 AXIS DEFINITIONS 6 1.4 DEFINITIONS 7

2 INTRODUCTION 11

2.1 BACKGROUND 11 2.2 PURPOSE 12 2.3 DEMARCATIONS 13

3 PRESENTATION 14

3.1 SIZING MODULE 14 3.1.1 THE CIVIL REQUIREMENTS 15 3.1.2 THE FAR PERFORMANCE REQUIREMENT 16 3.1.3 MILITARY 21 3.1.4 NEUTRAL POINT ESTIMATION FUNCTION 24 3.1.5 TRIM FUNCTION 24

4 ANALYSIS 26

4.1 SIZING MODULE 26 4.1.1 THE CIVIL SIZING TOOL 26 4.1.2 THE DRAG METHOD INVESTIGATION IN THE MILITARY SIZING TOOL 35 4.1.3 THE MILITARY SIZING TOOL 42 4.2 BALANCE AND STABILITY 47 4.3 LANDING GEAR PROGRAM – PLGEAR 48 4.4 CENTER OF GRAVITY EXCURSION PROGRAM 54 4.5 NEUTRAL POINT ESTIMATION PROGRAM 59 4.6 TRIMFUNCTIONS 62

5 CONCLUSION 66

6 FUTURE WORK 67

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7 APPENDIX 68

7.1 FUNCTION DESCRIPTION 68 7.1.1 DIBA AIRCRAFT ANALYSIS FILES 68 7.1.2 SIZING FUNCTIONS 70 7.1.3 BALANCE AND STABILITY PROGRAMS 74 7.2 AIRCRAFT GEOMETRY DESCRIPTION 75 7.2.1 SAAB AIRPLANES 75 7.2.2 OTHER AIRPLANES 77

8 REFERENCE 78

BOOKS 78 THESIS AND PAPERS 78 HOMEPAGES 79

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1 Explanations

1.1 Abstract This thesis work was done in order to improve the capabilities in a preliminary aircraft analysis program, DIBA, at Saab Aerosystems. The areas that this was done are in the sizing and balance. One sizing tool was developed in order to make a performance analysis with the DIBA generated geometry and customer and/or regulation based criteria. A balance diagram, a neutral point estimation function, a landing gear plot and a trim program was created in order to extend the weight and balance analysis. Results show that various aircraft both military and civil can be analyzed with good comparison to other analysis and reality. For example EXCEL implemented analysis and graphs over real aircrafts shown in the report.

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1.2 Units & Conversion tables 1 knot = 0.51444 m/s 1 knot = 1.852 km/h 1km/h = 0.2777 m/s 1 m/s = 3.6 km/h 1 kg/m2 = 0.20482 lb/sq. feet

1.3 Axis definitions

x

yz

(LongitudinalAxis)

(Vertical Axis)(Lateral Axis)

m n

l

Fig 1, Ref 3 X The Longitudinal axis rolling occurs about this axis Y The Lateral axis pitching occurs about this axis Z The Vertical axis yawing occurs about this axis

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1.4 Definitions A AEO All Engine Operable Aircraft categories In the regulations, different rules apply for different categories Far23

Aerobatic Designed to withstand high g-loads for advanced flying. Only flight test restricted.

Utility Limited aerobatic maneuvers. Max 90 degrees of bank. Normal Normal maneuvers. Max 60 degrees of bank.

Commuter Propeller driven with normal category restrictions. Far25 Transport Normal maneuvers. The first three categories have a weight limit of 5650 kg and passenger limit of 9, the forth of 8600 kg and 19 passengers and the fifth have no weight or seating limit. Altitude The height above ground measured in either feet or meters. AMC See MAC. Angle of attack The angle between an airfoils chord line and the relative airflow. Aspect ratio A measure of the wings slenderness. AR = b2/S, where b = span,

S = Wing reference area. B Balance The different weights are distributed throughout the aircraft in

order to balance it and get the desired c.g position and range. Bank A place were you can take out cash money. Here related to how

much the aircraft is tilted in the roll axis. Measured in degrees. BFL Balanced field length. See presentation. BWB Blended wing body. C CD0 Zero-lift drag coefficient is the drag on the aircraft independent of

lift. Center of gravity The weight of a solid concentrated in one point. CGR See Climb gradient Climb rate Relates to how fast the aircraft moves in the vertical plan.

Measured in ftp, feet per second

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Climb gradient CGR, Relates to the angle the aircraft climbs and is measured in %. Climb gradient times the airspeed in kts is Climb rate. Configuration The aircraft in a mode to perform a certain task, landing

configuration for example, flaps fully out and landing gear extended. To change from one configuration to another one makes a transition.

Control authority The amount of change which a control surface is able to make on an aircraft’s trim condition. Also that sufficiently large moments are generated when controls are used.

D Design point The point on the sizing diagram that represents the aircraft in a

certain configuration. DIBA Digital Interactive Basic Aircraftanalysis, preliminary aircraft

design program at Saab. Dihedral The angle of the wing rotated around the roll axis. Downwash A downward component of flow velocity caused by wingtip

vortices. Drag The force that resists the movement of a solid through fluid. Dynamic pressure The pressure that increases with the square of the speed times the

density. Defined as q = density*V2/2. E Elevator A control surface mounted on the horizontal stabilizer used to

control pitch. F Flaps Device used on aircraft to increase the lift at slow sweeps in

landing and takeoff configuration for example. FORTRAN Programming language used in the drag calculations in DIBA. G g-load A measure of acceleration on the aircraft related to the gravity.

One g is level flight and a 60 degree bank turn gives 2 g’s. Ground roll When the aircraft lifts the nose wheel in the air in the takeoff

phase. H Height The elevation the aircraft is located either above ground or above

sea level. See also altitude.

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I ISA ISA temperature is 15 degrees Celsius at sea level. K Knots The speed the aircraft travels. 1 knot (kt) is one nautical mile in

one hour. L Leading edge The farthest forward point of an airfoil or wing. Lift The mechanical force generated by a solid with a certain shape as

they move through a fluid. (Wikipedia) The component of the aerodynamic force which is perpendicular to the freestream velocity vector. (Ref 3)

M MAC Mean Aerodynamic chord. See Ref 2 and Ref 3. Mach The speed of the aircraft related to the speed of sound. Mach

number varies with altitude. N Nautical mile Almost identical to one minute latitude. The origin is in boat travel

related to actual knots counted. See 1.2 Unit & Conversion tables Neutral point The location of an aircraft’s center of gravity which causes it to

have neutral static stability. O OEI One Engine Inoperable P Payload The weight of the items loaded in the aircraft. Can be cargo or people for

example. S SEP Specific Excess Power. The thrust subtracted by the drag divided by the

weight. Sizing Refers to the dimensioning of the aircrafts major components to one

another. For example engine and wing size compared to weight. Span Distance from one wingtip of a wing to the other. SSC Second Segment Climb Stability The tendency to return to equilibrium. Stall When the lift becomes lower at higher angle of attack one has reached

stall.

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Stall speed The speed at which the aircraft can no longer generate enough lift to remain in the air. Lower with higher angle of attack. See stall def.

T Takeoff Refers to procedure when the aircraft leaves the ground and becomes

airborne. Thrust is a reaction force described quantitatively by Newton's Second and Third

Laws. When a system expels or accelerates mass in one direction the accelerated mass will cause a proportional but opposite force on that system.

T-O Takeoff Transition Change from one configuration to another. Trim A condition in which the sum of the moments on an aircraft is zero. longitudinal When the pitching moment about the center of gravity is zero. Turn rate The speed in degrees per second the aircraft can turn. U Upwash An upward component of flow velocity caused by wingtip vortices. W Wing loading The aircraft loaded weight divided by the wing area. Y Yaw Rotation about an aircraft’s vertical axis

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2 Introduction

2.1 Background The creation of anything has different phases, and so does the creation of an aircraft. In the earliest aviation years the pioneers had a vision before the first ever airborne machine were built. This vision remains in the mind of the aircraft designer, although not always as groundbreaking, to create an aircraft that can handle new tasks or existing tasks better than before. In the process of creating an aircraft the design phase is the most important. In this thesis work the earlier phases of aircraft design are described, namely the requirements, the specifications and the concept phase. In the concept phase, there is a need to evaluate many different approaches to the problem and hence the need of a tool where this evaluation can take place. A figure below describes the whole design process in general:

Mission Requirements

Wind Tunnel Testing Computational

Flow Simulations

CAD / CAM

ComputationalFlow Simulations

Performance& Cost Goals Conceptual Design

Preliminary Design

Detailed Design & Manufacturing

Flight Testing

Production

Fig 2 Ref 3: Introduction to Aeronautics: A Design Perspective.

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The phases following the conceptual design, tests and refines the chosen design and relies heavily on that a good concept was chosen. If not, time and money may be spent to refine something less than optimal. This is of course not desired and to prevent this from happening, sufficient amount of effort in the early stages of the design is required. With the growing technology development the possibilities increase tremendously and the choice between the methods are a challenge in itself. The ability to do more in the concept phase, that was originally parts of preliminary and detailed design, with for example CAD tools are changing the design process and the graph above is more and more a simplification of the actual process.

2.2 Purpose The purpose of this thesis work was to improve and extend the concept development tool at SAAB Aerosystems called DIBA with the following items: Sizing module Aircraft balancing tool Propeller and jet implementation Landing gear plot tool Neutral point estimation function Trim function The implementation of these functions will be tested on several different aircrafts to verify and evaluate there functionality and reliability.

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2.3 Demarcations To limit the area of this work the various functions capabilities are restricted as follows.

• When one is to size an aircraft there are many ways to go about this, but in this report, thrust to weight ratio is plotted against the wing loading for different restrictions.

• The aircraft weight is plotted against the center of gravity. • A simple propeller model was used to describe the characteristic of the engine at

different speeds and altitudes, so also for the jet engine. • The landing gear plot is limited to a three view plot and a three dimensional was

not made. • Only a simple first estimation of the neutral point is made in this program and

does not use new advanced panel code calculations for example. • The trim function is also a simple formula to give a value for the control sizing. • Further limitations are related to the sizing module that in the civil case describes

the FAR 23 and the FAR 25 restrictions and for the military case are limited to a few fictive aircraft performance specifications.

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3 Presentation In this chapter the main areas of DIBA are presented, in which new modules has been created and the capabilities of existing ones extended.

3.1 Sizing module Fifty years ago the main design drivers were performance, especially for military customers. Today however the cost is the main drive and lesser performance is usually accepted for a reduction in cost. When an aircraft is to be defined and designed some type of sizing is made. The term sizing is referred to the fact that during this phase, some parameters are descried upon, for example the wing area related to the weight and the thrust related to the weight. Both these parameters are of vast importance for the success of the design. To create an overall picture of the airplane requirements, a so called sizing diagram is drawn. In this diagram different requirements are plotted and the aircraft is plotted at the design point. The graph below shows a general sizing diagram. All the requirements will be described later in more detail. The airplane sizing graph plotted below is for the Lockheed Starfighter F104. The first aircraft designed for sustained flight above Mach 2.

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Fig 3.1 Sizing diagram As seen above the various requirements are plotted in a graph where the thrust to weight ratio are on the y-axis and the wing loading on the x-axis. The red dot roughly in the center is the design point and shows how much thrust the engine produces related to the aircrafts weight and also the wing area related to the weight. The requirements and therefore the sizing criteria differ between the civil and the military case. These requirements will now be described separately, starting with the civil case.

3.1.1 The Civil requirements The civil requirements are more regulation based than the military. It exist two major documents of requirements for the civil aviation field, namely FAR and JAR, where the FAR is the American document and the JAR the European one. They are very similar but differ here and there. Both this regulations have to be met by the aircraft manufacturer in order to have its aircraft airworthy on both the U.S and the European market. These documents are very massive and this report limits the description to two parts of the FAR document, namely the FAR 23 and the FAR 25. The abbreviation FAR stands for Federal Aviation Regulation and the part 25 stands for airworthiness standards transport category. FAR 23 describe lighter aircrafts, below 5700kg. Normal, Utility, Aerobatic and commuter are all categories under FAR 23 regulation. The commuter classed aircrafts can weigh as much as 8600 kg and still be under the FAR 23 regulation. Even the FAR 23 and FAR 25 are very large documents, see Ref 21, and only the performance part of these two documents is used in this sizing module.

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3.1.2 The FAR performance requirement This part of the FAR document is divided into several parts, different regulations for Takeoff and landing for example. A description of each regulation that was implemented in the sizing tool will now be described. The requirements will be divided into two parts, the Takeoff and landing part and the in flight part. To predict the performance in the Takeoff and landing phases are more difficult due to the pilot influence and the more complex aerodynamics low velocity flying conditions. Here are the requirement starting with the takeoff and landing ones.

3.1.2.1 Balanced Field Length This requirement is when the aircraft is in takeoff configuration and is considered to be one of the most critical. The Balanced Field Length, BFL, is defined as when the horizontal distance the aircraft travels on takeoff until it reaches a height hto* is equal to the distance the aircraft travels from stand still to V1, critical decision speed, and then decelerated to a full stop. The Critical decision speed must therefore be less than VR, the rotation speed. *hto is 50 ft for FAR 23 and 35 ft for FAR 25. In the FAR 23 there exists no specific regulation regarding engine failure during takeoff. There exists however more strict rules for light aircraft like the NRPM 68-37 where the BFL requirement does apply. The expression to calculate the Balanced Field Length is explained and derived in Ref 1 Torenbeek chapter 5.4.5. Below is the BFL formula:

{ } )895(2

1)/(

1)/(

1)//(12 2

210

22 −

Δ+⎟⎟⎠

⎞⎜⎜⎝

⎛+⋅

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

++⋅

=− σγ

toto

stopstop

SVgh

gagagagV

BFL (3.1)

This formula is then transformed using a given BFL and additional simplifications mentioned in Ref 1 to get the following formula:

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⎭⎬⎫

⎩⎨⎧

−+−

Δ+Δ−≤

− toto

toL

to hWT

SBFLgCS

W7.2)'/(

)3.21)(/(159.11

22 μ

γσρ (3.2)

This is an expression for the wing loading for a given BFL with varying thrust to weight ratio. If one transform this formula it is possible to derive T/W as a function of varying W/S. And that expression was implemented in the sizing tool. A graph will later be presented with all the requirements drawn for a dependence analysis under the title analysis.

3.1.2.2 Second Segment Climb The flight configuration Second Segment Climb, SSC, is a climbing requirement. With the aircraft in a takeoff configuration and the landing gear fully retracted the following climbing requirements exist: Flapps: Takeoff configuration Climb: 0-400 ft

Climb rate FAR 23 FAR 25

Nr engines % % 2 2.0 2.4 3 2.3 2.7 4 2.6 3.0

Table 3.1 Rate of climb

The FAA decided that aircrafts carrying more than two engines, usually heavier, had a longer accelerated stop distance and should therefore be required to have better climbing performance. It is assumed that the critical engine has failed and the aircraft have to climb without its power so it is in the so called one engine inoperable OEI configuration. The climb rate are usually called climb gradients CGR and these values were implemented in a formula used to plot the sizing diagram. The formula was taken from ref 5 Roskam chap 3.4.6.2.

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3.1.2.3 Missed approach This is also a climb requirement, but with the aircraft in a landing configuration. This is due to the fact that the pilot for some reason had to abort the landing and climb to go around or elsewhere. The flaps are therefore in landing configuration and the climbing performance less than that of the Second segment climb requirement. The critical engine is still assumed to have failed, OEI mode. The aircraft is further assumed to be 400 ft above the ground or more. The aircraft is flown at V=1.5Vs . Here is the table for the missed approach CGR values:

Climb rate FAR 23 FAR 25

Nr engines % % 2 2.1 2.1 3 2.4 2.4 4 2.7 2.7

Table 3.2 Rate of climb Ref 21 FARS

3.1.2.4 Time to climb What this requirement describes is how fast the aircraft can reach the decided cruising altitude. This is not a regulation requirement and is more a customer or manufacturer choice of how per formant the aircraft is accepted to be. The formula for this curve on the sizing graph is taken from Ref 5 Roskam. A linear between rate of climb, RoC, and altitude is assumed for simplicity. The rate of climb is highest at sea level and decreased in a manner described in this formula: RoC = RoC0 (1 – h/habs) The habs is aircraft specific and the following values can be assumed, Ref 5.

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Airplane type habs [(ft) 10-3] Piston 12-18

Piston supercharge 15-25 Jet commercial 40-50

Jet military 40-55 Jet fighter 55-75 Jet trainer 35-45

Turbo propeller com 30-45 Turbo propeller mil 30-50 Supersonic Cruise 55-80

Table 3.3 absolute height The flight path is assumed to be shallow, under 15 degrees. To determine a requiring thrust to weight ratio using the RoC one can use the following formula: RoC0 = (habs/tcl)ln(1 – h/ habs)-1

3.1.2.5 Ceiling AEO A requirement similar to the time to climb is the Ceiling AEO. The values and tables in this section are taken from Ref 5. The definition of Airplane Ceilings is the minimum rate the airplane must be able to climb at service ceiling level.

Ceiling type Min req. climb rate (ftm)

Absolute 0 Service piston com 100

Service jet com 500 Service military 100

Combat subsonic 500 Combat supersonic 1000

Cruise subsonic 300 Cruise supersonic 1000

Table 3.4 Climb rate The table above was used to create the service ceiling climb for the civil case sizing, with the two cases AEO and the OEI.

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3.1.2.6 Cruise The Cruise requirement comes from the fact that one wants to use as little power from the engines during cruise as possible, in order to save fuel. The curve that is created uses the cruise Mach number at different heights and therefore different dynamic pressures. The thrust to weight ratio varies with the wing loading, the wing size, because for example a bigger wing creates more drag and therefore the aircraft needs more thrust to be able to cruise. First the lift coefficient is calculated using varying wing loading. Then drag is calculated and assumed to be equal to the thrust. The T/W for cruise is then the ratio between the thrust required divided by the thrust available divided by the weight.

3.1.2.7 Landing

sdecel

sland

sroll

Transition or Roundout

Clear Obstacle

strans

sLand Over Obstacle

Touchdown

Approach

Fig 3.2 Landing phase, Ref 3 Landing is in a sense takeoff in reverse. Instead of increasing speed until transition and climb one descends to transition and decelerates to stop.

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The landing requirement in FAR 23 and 25 that was implemented in the sizing tool came from Ref 1, Torenbeek. It is there stated that the approach speed should at least be 30% more than the stall speed. That is: VA=1.3 VSL The stall speed is that in the landing configuration. The landing distance is related to the square of the stall speed. This in turn can be used to determine the wing loading of the aircraft. Since no thrust is accounted for during this phase this requirement is only W/S dependent.

3.1.3 Military When sizing a military aircraft one looks at what specifications and requirements that should be met, what performance is desired. These performance requirements are then plotted to illustrate which of the requirements are the driving ones. That is which are the most requiring and therefore sizing. The requirements that will be described here are the following: Takeoff ground roll Takeoff 50 ft clearance Specific excess power SEP Time to accelerate Landing ground roll Instant turn rate

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3.1.3.1 Takeoff ground roll

saccel

sTO

srot

Transition

Climb Over Obstacle

strans

sTO & Climb Fig 3.3 Takeoff phase, Ref 3 A certain distance is desired by the customer when the aircraft should be able to leave the ground. This distance is defined in the Takeoff ground roll, when the main wheels are in the air. To reduce this distance one can increase the lift, either with a larger wing or advanced lifting devices, or a greater thrust to weight ratio. The formula from this requirement is taken from Ref 2.

3.1.3.2 Takeoff 50 ft clearance This is basically the same as the previous one but with the criteria that the aircraft should reach a height above ground of 50 ft, and is therefore more demanding than the Takeoff ground roll.

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3.1.3.3 Specific Excess Power SEP or Specific Excess Power is a measurement of how maneuverable or agile the aircraft is at different speeds and altitudes. It can either be measured in speed or climb rate. This is a powerful tool to compare aircraft performance. Usually the SEP is plotted in a height vs. speed diagram for different levels. Ref 3.

⎥⎦⎤

⎢⎣⎡ −

=W

DTVSEP )( where V is velocity, T thrust, D drag and W is weight.

Many times SEP is denoted Ps.

3.1.3.4 Time to accelerate This is a requirement that states how fast the aircraft can be accelerated at different speed ranges at different altitudes. Ref 3.

3.1.3.5 Landing ground roll States how long distance the aircraft needs to come to a stop after it reaches the ground. Ref 3.

3.1.3.6 Instant turn rate Describes how steep turns can be made at different speeds and altitudes. This and the other requirement functions that were implemented in the sizing tool will be described in the analysis section. Ref 2.

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3.1.4 Neutral Point estimation function The definition of the neutral point is the point where the moments acting on the aircraft are zero. An aircrafts neutral point is vital to estimate early on in the design due to the demand to be able to stabilize and control the aircraft in various conditions. For a naturally stable aircraft the neutral point is located behind the center of gravity. Many disciplines in aircraft design are closely coupled and in this case the neutral point and the c.g position are coupled to determine the static margin. The c.g travel is related to the trim ability of the tail which also is related to the neutral point. For example, when an aircraft is cruising it is desirable to locate the neutral point at the center of gravity with a minimum of trim drag. This can be done if careful consideration is taken to determining the neutral point for different configurations of the aircraft related to the tail sizing. In this report a description of a function that makes a rough neutral point estimation will be presented. Ref 3.

3.1.5 Trim function The aircraft is said to be in trim when the sum of all moments acting upon it are zero. This can be done in various ways. If the angle of attack is changed within the operational range the tail or canard should be able to trim away the stick forces and still keep a certain amount of control authority. The aerodynamic characteristics can only be calculated very approximately. For example the complex flow over the tail in the case of one engine inoperative. Also nonlinear behavior and compressibility can be of much more importance in flying qualities than on performance values. To valuate the data given in calculations the pilot has the final saying, therefore it can be of interest to introduce a simulator early in the design process. Another parameter that is important for the tail sizing and therefore the trim capability is the downwash gradient. And it is, according to DATCOM dependent on the following parameters: Aspect ratio, wing sweep, taper ratio, wing span, distance between the horizontal tail and the wing both in x and z direction and the lift coefficients for the wing at zero speed and at flying mach.

SqLCL ⋅

= This is the lift coefficient for the whole aircraft. And in equilibrium the lift

equals the weight. The lift is affected by both Reynolds number and compressibility effects.

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With increasing angle of attack there is a drag improvement, lower drag, with higher Reynolds numbers. The compressibility is not corrected for in the programs created for trim analysis. With the volume coefficient one can evaluate the capability of the horizontal tail to stabilize the aircraft. With a greater volume coefficient there is a higher control authority, but the price is a bigger tail surface or a longer lever arm and therefore a longer aircraft and thereby a weight penalty. Ref 2, 3.

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4 Analysis How these new modules and functions were created is described in this section. Starting with the sizing tool.

4.1 Sizing module This is where the sizing tool will be analyzed and described more thorough than in the presentation. First the Civil part will be analyzed, followed by the military.

4.1.1 The Civil sizing tool The Civil sizing tool is designed to be a sub function to analyze an aircraft in the preliminary design MATLAB program called DIBA. All the requirements previously described were implemented in a MATLAB function called plsize that plots the different curves and the design point of the aircraft. One sub function for each requirement was used to calculate the data needed for the complete sizing diagram. In the beginning of plsize an initiating value function called indata_civil_size was used.

Fig 4.1 program structure

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In this function the aircraft geometry defined in DIBA was used along with drag estimation calculations and the specific requirement parameters. The drag calculation was an EXCEL based one. To give a better understanding of the process the program uses, an example aircraft will now be presented and analyzed:

4.1.1.1 Saab 200 sizing example

Fig 4.2 Saab 2000 The aircraft above is the Saab 2000. A distinction from the real aircraft and the computer model is a tremendous task but can be accomplished. Even if very few indata parameters are used in the geometric description a reasonable analysis can be made. One can see the overall shape similarities, low wing with dihedral, conventional tail with dihedral wing mounted engine pylons long slender fuselage and so on. This model is used to calculate the drag by simple EXCEL formulas.

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A three plane view is also generated in DIBA to present the layout:

Fig 4.3 Saab 2000 three view layout The Geometric description of the Saab 2000 was of level 1, that means the wing was represented in one piece and the fuselage only have one main cross section value. A short description of all the MATLAB sub functions that were created by the author during this thesis work will now follow: All the functions below uses the DIBA geometry extracted from the indata_civil_size file and will be represented in a sizing graph presented later. And the functions starting with TW generates varying Thrust to Weight ratios with the given wing loading spectrum. TW_climb = Represents the Time to climb requirement.

Uses the Ref 5 formulas for climb performance. The varying wing loading demands different speeds which in turn require different thrust to weight ratios.

TW_BFL = Represents the Balanced field length requirement.

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Uses the empirical Roskam formula stated in Ref 5. TW_2seg = Represents the Second Segment Climb requirement. Formulas from Ref 5.

The number of engines and the weight of the aircraft generate the correct climb gradient, CGR, complying with the FAR regulation.

TW_miss = Represents the Missed approach requirement.

Different CGR values for different number of engines as for the SSC function. Ref 5.

TW_ceiling= Represents the Ceiling AEO requirement. Formulas from Ref 5. TW_cruise = Represents the Cruising requirement. Empirically generated formulas. mS_land = Represent the Landing distance criteria. Formulas from Ref 5. Table 4.1 requirement list The design point is in this case represented by the maximum Takeoff weight MTOW and the reference wing area for the wing loading and the reference thrust for the thrust to weight ratio. MTOW = 22700 kg (maximum Takeoff weight) FREF = 42591 N (reference thrust) SW = 54.5 m2 (wing area) Now all the function will be plotted and the indata for each graph presented. The Design point is the same with the values above giving it: T/W = 0.38 [-] W/S = 416 [N/m2]

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4.1.1.2 The Time to climb criteria plotted

Graph indata: Climb t_clb=10

h_clb=6000 h_abs=9450+2000

Fig 4.4 Time to climb The graph indata explained: t_clb is the time to climb in minutes, here 10 minutes. h_clb the cruise altitude and in this example 6000 meters h_als the absolute ceiling assumed to be 2000 feet over the service ceiling As can be seen in the graph it can be concluded that the thrust to weight ratio to climb to 6000 meters in 10 minutes are under 0.2 and well under the design point and should therefore be possible. There was however an optimistic L/D estimation in this function but even with that considered this requirement seems to be on the safe side. The Saab 2000 have a world record in climb performance, climbing from ground to 20 000 ft in 8 minutes. In Ref 9, a time to climb to 20000 ft in 11 minutes is mentioned. Both this data seems to comply with the sizing result.

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4.1.1.3 Balanced Field Length Graph indata:

BFL1: BFL1=1300 BFLalt1=0 BFL_ISA1=0 W_Wo1=1

BFL2: BFL2=1500

BFLalt2=500 BFL_ISA1=15 W_Wo1=1

Fig 4.5 BFL

• BFL1 is the balanced field length in meters at sea level and ISA temperature. • BFL2 is the balanced field length in meters at sea 500ft above sea level and 15

degrees Celsius over ISA temperature. This seems to be a more demanding requirement than the previous one and it is but maybe not as sever as it looks. As seen in the graph data a weight fraction of 1 is used and this is very high. Looking in the Saab 2000 specification sheet, Ref 9, one can extrapolate the landing distance with the weight above, MTOW and will get a value of about 5000 ft. This corresponds to about 1520 meters. The sizing seems reasonable in this aspect considering that the thrust available fraction calculation for the turboprop model is rather crude. With an increase in wing loading, or a smaller wing it is more difficult to Takeoff with an increasing thrust demand as a result.

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4.1.1.4 Second Segment climb, Missed approach, Ceiling AEO, Ceiling OEI

All this requirements uses formulas from Ref 5 Roskam. Graph indata: SSC CLmax = 2.7 (lift coef) CGR = 0.024 (2 eng) Missed approach CLmax_land=2.8 Missappalt=0 (sea level) W_WoMissapp=0.9 (weight ratio) Missapp_ISA=0 (ISA temp) Ceiling AEO RoC=500 (climb rate in [ft/min]) W_WoCeilAEO=0.9 Ceiling OEI RoC=500 (climb rate in [ft/min]) W_WoCeilOEI=0.9

Fig 4.6 SSC, Missed approach, Ceiling In the OEI mode there should be a windmill increase term in the drag but this is not taken into account. That means these criteria could be further restricting. The least demanding is the SSC because the flaps are not fully extended as in Missed approach. The Ceiling OEI requirement due to the difficulty to climb with one engine inoperable is the most requiring.

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4.1.1.5 Cruise, Landing

Graph indata: Cruise W_WoCruise=0.9 (weight ratio) Cruisealt=6000 Throttle=40 (pwr set in %) CruiseMach=0.59 Landing W_WoLand=0.9 CLmax_land=2.8 Landing_field=1250 Landingalt=1000

Fig 4.7 Cruise, Landing The landing graph is the vertical line and is not dependent on thrust. Landing is assumed to take place on an airfield at 1000 meters altitude and have a landing distance of 1250 meters. This could according to the calculation be done with a somewhat smaller wing but to have some margin is always preferred. The cruise criterion shows that a bigger wing costs power to cruise with.

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Now we will display a graph with all the requirement curves represented.

Fig 4.8 Sizing diagram The graph above shows that the design drivers for this aircraft are the BFL requirements and perhaps the landing requirement.

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4.1.2 The Drag method investigation in the Military sizing tool Two different drag estimation calculation methods were investigated in the military sizing tool. These methods were a DIBA generated method that used a FORTRAN code from Northrop and an EXCEL method with functions taken from Ref 8. It was concluded that the difference between the two methods were very small at low mach numbers. This is why only one drag method, the simpler EXCEL one, was used in the civil sizing tool described above. The method implemented in EXCEL is a plate form drag method. The drag methods investigation will now be presented. The preliminary design tool DIBA has functions to calculate drag. These were first not implemented in the sizing tool. Instead a simpler plate method from Ref 8 was used. To make the sizing tool use more DIBA functions a change was made so it could use both methods. The zero drag from the plate method was compared with the zero drag from DIBA calculated drag. To accomplish this some new test functions were created and modified drag functions implemented in them. DIBA uses the geometry implementation to calculate the wetted area and other parameters such as the aspect ratio in order to calculate the drag curve. To investigate the different drag methods a few aircraft were studied and here the Starfighter F104 will be presented.

Fig 4.9, F104 Starfighter

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The DIBA drag calculation for the F104 starfighter was compared to data given in Ref 2. Here is the CD0 graph, both from the reference and the calculated one.

Fig 4.10 Zero drag real aircraft, Ref 2

Fig 4.11 Zero drag estimated

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The calculated one above is for the slim version described in the drag investigation section. This configuration gave the most realistic drag value. Here is the drag for the “fat” F104:

Fig 4.12 Zero drag estimated As can be seen above the drag value is a lot higher than that of the Ref 2 value. This is due to the nonrealistic drag buildup on the intake that here only generates drag. According to Ref 2, Raymer Aircraft design the zero-lift drag CD0 varies between 0.017 and 0.051. As can be seen on the first graph, the calculated value is somewhat higher, about 7%. This is quite good considering that wave drag estimation is difficult. Here is a graph over the CD0 for the starfighter F104 aircraft over a certain mach range at the same altitude for both methods as a comparison. The values are taken from the slim version that seemed to resemble the Reference zero-lift drag value the best.

Graph info: red DIBA blue fat EXCEL Mach range 0.3-0.8 Altitude Sea level

Fig 4.13 Zero drag estimated

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As one can see there is a difference in the methods when calculating the CD0 values. The difference however is considered small enough that both methods can be applicable. This is due to in part due to the fact that at these subsonic speeds the greatest drag values are generated from the induced drag that is visualized later in the total drag. The error for the CD0 of the different models is about 20 % in the beginning of the range down to under 1 %. The rougher EXCEL method is a bit further from the reference value. Jas 39 Gripen showed a similar CD0 comparison but with somewhat smaller values. In the sizing tool the total drag is used instead of the CD0 in the calculations. To illustrate the methods here a graph over the same mach range and airplane air is here presented.

Fig 4.14 Zero drag estimated The thin line is the DIBA calculated drag and the thick wavy line is the curve from EXCEL. The error is a lot less due to the mentioned fact that at low mach numbers most of the drag comes from the induced drag term. The error percentage is greatest at about M0.45 where it reaches 6.5%.

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To illustrate the differences in the methods the sizing graph over the Starfighter is drawn here with the graphs overlapping. There are only in two different requirements that the drag is involved, namely specific excess power and time to accelerate, but due to the fact that the SEP have five different indata values it does a affect the graph quite a bit, as seen below:

Fig 4.15 Sizing diagram A difference is noticeable between the methods where the DIBA is the most restrictive. The red horizontal lines show the biggest separation and the second acceleration requirement, the thick blue horizontal line differ the most. And the difference is greatest at the lowest wing loading value. Taken at 350 kg/m2 the red lines difference is 0.3936/0.3691 = 1.06637…gives 6.6% and for the thick blue ones, 0.5206/0.5005 = 1.04015… gives 4.0%. To track why the biggest difference is here is easily done when one looks at the indata for the sizing diagram:

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Ground roll: H=0, M=0.2, To_SLS=1, mstto=0, CLto=0.75, gd_roll=1700 Takeoff 50 ft: dist50=1700 Time to acc1: time1=35, Mo1=0.3, Mf1=0.8, alt1=0 Time to acc2: time2=25, Mo2=0.8, Mf2=0.9, alt2=10000 SEP1: SEP1alt=0, SEPM=0.9, SEP1v=0, nz1=4.0 SEP2: SEP2alt=3000, SEPM=0.8, SEP1v=0, nz1=4.5 SEP3: SEP3alt=0, SEPM=0. 7, SEP1v=70, nz1=1.0 SEP4: SEP4alt=6000, SEPM=0. 8, SEP1v=60, nz1=1.0 SEP5: SEP5alt=5000, SEPM=0.9, SEP1v=80, nz1=1.0 mS Land: CLmax_land=0.9, CLmax_lowM=1.4, land_dist=950 Inst turn: alt=0, M=0.40, inst_turn_rate=21 Design point: m0Sref=(OEW+0.6*WEIGHTFUEL(1)*2)/SW(1), M0=(OEW+0.6*WEIGHTFUEL(1)*2) n_eng=1, ToWo=n_eng*To/(M0*g) Table 4.2 Indata On deciphering these values the speed is highest on the second time to accelerate and the first SEP requirement. The difference in the methods is greater with high mach numbers for the thicker geometric presentation of the F104. This also seems to be the case in the sizing diagram. So far during this investigation, the F104 has been calculated with the intake area included. In reality some of the air that flows here does not contribute to the total drag because it is sucked into the engines. Below a picture of a Starfighter without the intake area is displayed:

Fig 4.16 F104 Starfighter slim

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The following sizing diagram corresponds to this geometry.

Fig 4.17 Sizing diagram Here the greatest difference between the methods is within 2.5%. This is not considered to be the correct method. The reality is probably somewhere in between the two geometrical descriptions. It has been shown that at low mach numbers the drag calculation methods differ within accepted values. This concludes the drag investigation.

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4.1.3 The Military Sizing tool This tool was designed with the basic sub structures as the Civil Sizing tool and the main difference is the requirement criteria sub functions. They will be described and a few implementation examples will also be presented. The following requirements as mentioned in the presentation section have the corresponding MATLAB function: Takeoff ground roll TWto_gd_roll Takeoff 50 ft clearance cTWto_dist50 Specific excess power SEP TW_SEP Time to accelerate cTW_acc Landing ground roll mS_land Instant turn rate mS_turn Table 4.3 requirement list A graph over the starfighter sizing diagram is presented below:

Fig 4.18 Sizing diagram

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It can be difficult to know which graph is which but the thick graph closest to the design point is the Takeoff 50 ft curve. This and also the instant turn rate are the design drivers in this sizing analysis. When looking at the F104 star fighter this can seem reasonable because of its small wings it is difficult to turn rapidly and Takeoff quickly. The indata for all the requirements functions are the same as in the drag investigation. A description of the functions as such will now follow.

4.1.3.1 Takeoff ground roll TWto_gd_roll This function uses a sub function that with a given estimated Takeoff field length calculates a TOP, a takeoff parameter with a curve fit, according to Ref 2 Raymer. The curve was created based on statistical values from existing aircrafts. The TOP value is then used to calculate a range of T/W with a given W/S range, with the following formula applied for jets only. In case of a propeller aircraft, exchange T to hp, horsepower.

( ) ( ) ( )WTCTOPSWTOLσ=

4.1.3.2 Takeoff 50 ft clearance cTWto_dist50 Uses the same structure as for ground roll but another curve fit to generate the TOP for this requirement. Because the aircraft needs to takeoff and reach 50 ft this requirement is more demanding and therefore generates a greater distance for the same design value.

4.1.3.3 Specific Excess power SEP TW_SEP Here the given SEP value generates a T/W range with the indata matrix of W/S values. The total drag is calculated for the Mach number used in each specific SEP calculation. The greater the drag and the SEP desired, the greater the T/W must be. When calculating this, the following formula was used. ( ) ( ) ( )gmSSrefDtotMaSEPWT ⋅⋅+= // SEP is the desired excess power measured in m/s M the mach number Dtot the total drag turm Sref the wing reference area mS the wing loading matrix g the gravitational constant

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4.1.3.4 Time to accelerate cTW_acc In this sub function the time it takes to accelerate the aircraft at a certain altitude from one Mach number to another is calculated. This is done in a loop sequence that calculates the differences of the thrust and drag at each point during the acceleration. The sum of all the steps is then added to give the total acceleration time. This only works if the thrust available is greater than the drag value. The thrust available is calculated with a simple curve fit equation.

4.1.3.5 Landing ground roll mS_land This is a vertical criteria meaning that it does not vary with thrust. Given a certain landing distance this function generates the maximum wing loading required.

4.1.3.6 Instant turn rate mS_turn Given the desired turn rate at a certain mach number. This function calculates at what maximum wing loading level this can be accomplished. If the requirements were to change to the following values the sizing graph will change accordingly. A graph over this change is presented after the indata. The indata is here deliberately changed so that no margin is possible to investigate the max performance of the aircraft, at the design point that is with no payload and 60 % fuel. Ground roll: H=0, M=0.2, To_SLS=1, mstto=0, CLto=1.55, gd_roll=550 Takeoff 50 ft: dist50=750 Time to acc1: time1=35, Mo1=0.3, Mf1=0.8, alt1=1000 Time to acc2: time2=18, Mo2=0.8, Mf2=0.9, alt2=10000 SEP1: SEP1alt=0, SEPM=0.9, SEP1v=0, nz1=6.5 SEP2: SEP2alt=3500, SEPM=0.8, SEP1v=0, nz1=4.5 SEP3: SEP3alt=0, SEPM=0. 7, SEP1v=130, nz1=1.0 SEP4: SEP4alt=8000, SEPM=0. 8, SEP1v=60, nz1=1.0 SEP5: SEP5alt=5000, SEPM=0.9, SEP1v=100, nz1=1.0 mS Land: CLmax_land=1.6, CLmax_lowM=1.4, land_dist=550 Inst turn: alt=0, M=0.40, inst_turn_rate=21 Table 4.4 Indata

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Fig 4.19 Sizing diagram

4.1.3.7 Ground Roll According to this sizing analysis, the ground roll distance of 550 m. This is at the design point with 60 % fuel and carrying no payload. In Ref 10 the F104 has a T/W of 0.54 at maximum Takeoff weight. The calculated value of 0.61 seems reasonable considering the fact that the loading is less. M0 = 8795 kg ( aircraft weight ) ( DIBA ) T-O speed = 190 kts ( takeoff speed ) ( Ref 34 ) CLmax_to 1.55 ( Takeoff lift coefficient ) To get a reasonable value of the CLmax for the F104, Ref 34s takeoff speed and the weight taken from the DIBA calculation was used. This resulted in a CLmax of 1.55 at sea level. It needs to be able to be greater for maximum takeoff mass or at airports higher up or at higher than ISA temperature.

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In Ref 34 the maximum time to accelerate was 10 seconds. Assuming a linear acceleration up to the T-O speed gives a distance of the following:

2

2atS = and atV =

V = 190 kts = 97.74…m/s t = 10 seconds gives an average acceletion a of 9.8 m/s2. This in turn gives a distance S = 445 meters. This is shorter than the one calculated in the ground roll but the acceleration is in reality not linear. A DIBA function is available to calculate the ground roll using the MTOW and the CLmax. Using this function with CLmax = 1.55 as above and the MTOW = 10600 kg giave a ground roll distance of Sgr = 754 meters. This value is more reasonable than that from the sizing calculation.

4.1.3.8 Takeoff 50 ft This gives a distance of 750 meters, 200 meters more than the ground roll. The 200 meters extra seems reasonable and would take about 2 seconds at the speed above. And a climb angle of little over 4 degrees. It is reasonable in comparison to the calculated ground roll distance but is in reality to short.

4.1.3.9 SEP Here a summary of the SEP values will be given. The two first criteria shows that the aircraft is capable of a load factor of 6.5 at zero altitude at Mach 0.9 and at 3500 meters and Mach 0.8 a load factor of 4.5 with no excess power. The following three requirements show that the greatest SEP can be achieved at sea level and at normal loading. SEP decreases with increased altitude and or load factor. The third SEP requirement at sea level gave a SEP velocity of 130 m/s at n=1 (normal load factor). Compared to the value of a F104 in Ref 7 it was capable a little over 400 ft/s which corresponds to at least 122 m/s. This seems to be correct. The forth give a SEP of 60 m/s and in Ref 7 of 100 m/s. The model seems to be too restrictive when calculating the loss of SEP during an increase in altitude.

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4.1.3.10 mS Land This criterion gives a landing distance of 550 meters. This is very short and is likely not possible. When looking at the landing specifications in Ref 34 one sees that the values 5000 ft for 50 ft and 2500 ft for the landing ground roll is mentioned, but this is landing with a parachute. If no chute is applied the ground roll is increased to 4500 ft, which corresponds to 1372 meters. A estimate landing distance value is calculated from a formula in ref 2. Sland = 80*(W/S)*(1/ CLmax) at sea level Calculating the landing distance in this way gives a landing distance of about 5000 ft that is more reasonable than the one from the sizing.

4.2 Balance and Stability For stability and handling of the aircraft it is essential to know the c.g of the aircraft. A certain c.g travel range is desired by the costumer to allow for easy loading arrangements and increased usage. This and control requirements sizes the horizontal stabilizer. To be able to do this sizing, the moment arm to the c.g has to be known. Complex six-degree-of-freedom analysis is made for sizing tail and c.g location at large aircraft companies. In preliminary design much simpler formulas can be used. Four different balancing and stability sub programs were designed in order to increase the capabilities of DIBA. These different functions to illustrate the balancing and stability of the aircraft will be analyzed: A Center of gravity excursion program, a Landing gear plot program, a Neutral point estimation program and a trim-ability program. Let us start with the Landing gear program.

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4.3 Landing gear program – plgear To analyze this program several different aircraft geometries was implemented to do a robustness check. The first aircraft that was subject to this analysis was the JAS 39 Gripen. A complete placement description was the initial indata and was then changed to less and less given indata to a more generic formation of the landing gear. During this test it was found that it was necessary to put indexes on some variables to improve the robustness. For example, the center of gravity c.g, defined as CG in DIBA sometimes represented an array of different positions at different loadings. And to clarify witch CG value one should use in the landing gear plot program the index CG(1) was implemented. There are a few parameters one are to think about when creating a suitable landing gear for an aircraft: Rotation criterion – both for the nose wheel and the main wheels The Over turn angle – the angle defined by the geometry placement of the gear and the two main parameters that dictates the Overturn angle are how high the aircraft sits above ground and how far apart the main gear are on span wise direction, the track gauge. If the aircraft sits too high related to its track gauge the aircraft can tip over easily. The common design criterion is an Overturn angle of 63 degrees or less for enough taxi stability. All this criteria were implemented in the plgear program and related to the available geometry description. There are of course more factors to think about when designing a landing gear like the loading on each wheel, the size of the wheels and their bay in the aircraft, the strength of the landing gear struts in case of a hard landing and so on. The two criteria mentioned above are essential for the placement of the landing gear and important in preliminary design and the others criteria comes later and are outside the scope of this report. In the preliminary aircraft calculation program DIBA it is possible to make a three plane view of the aircraft. This was shown in the analysis of the sizing tool where the Saab 2000 was displayed. Since the landing gear program was created using the Jas 39 Gripen airplane this will be shown as the first example.

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Fig 4.20 the picture was taken from the Czech air show 2006, Ref 39. A three plane view of the Jas 39 Gripen is displayed below:

Fig 4.21 Three plane view of Gripen, Left Ref 41.

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As can be seen there are no landing gear displayed in the picture above to the right. The program that was created first took the geometry as such and drew a gear like this: Indata for landing gear: Nosegear: x 3.523 m from nose Main gear: x 8.77 m from nose y 1.22 m from roll axis (the values are ground contact distances)

Fig 4.22 Three plane view with landing gear The landing gear program assumes that the aircraft are drawn with the ground at zero and everything above positive. It is further assumed that the gear is drawn sitting on the ground, with the shock absorbers pressed with the weight of the aircraft. From the main landing gear two blue lines are drawn. The first one is drawn from the contact point to the center of gravity of the aircraft. Since the c.g of Jas 39 Gripen was unknown to the author of this report some estimation had to be made, both in x-dir and z-dir. One criteria for the landing gear is that the angle between the contact point to the c.g is greater than the tip over angle, which is the second blue line drawn in the figure. The criterion for this line is 15 degrees. As seen above the line just barely clears the back of the nozzle of the aircraft which theoretically opens for a 15 degree angle at touchdown. This would require a pilot view angle of at least 15 degrees as well and seems reasonable looking at the side view over the aircraft. The height of the gear is related to the other criterion, namely the over turn angle, taken from Ref 2, Raymer. It is related to the height of the aircrafts c.g and the track width. If the c.g is high up in the air before the aircraft has left the ground, a sufficient track width must be incorporated so that it is a bit trickier to tip it over.

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This criterion was not implemented in the first gear plotting function. The second modified function could take it into account and in addition generate a gear if one was not given as indata. This is now shown:

Indata: Same as above Output: Tip over angle plot ( green )

Fig 4.23 Three plane view with landing gear The tip over angle is plotted here and is in this case 61.1 degrees, barely under the 63 degree maximum recommended criteria. Now the main wheels were moved to do a robustness check of the function.

Indata: y-dir placement 0.2m 84.7o

0.8m 69.9o 1.1m 61.5o 1.8m 51.7o

Fig 4.24 Landing main gear movement

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The main gear was placed according to the table above with the corresponding tip over angle. An increase in error was detected with a decrease in tip over angle. This can be accepted when the error is of greater importance at larger angles, around 60 degrees and more. To tell the designer that the gears have been placed too tight an error message was generated.

Fig 4.25 Landing gear requirement check The narrow gear placement is here shown with the normal placement. As can be see the main gear is plotted straight and is the geometric generated model. Here deliberately made to create an error message.

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A picture below shows two different self generated landing gear placements and their indata.

Fig 4.26 Landing gear straight A straight gear is assumed for simplicity. The main gear is at placed 25 % and 35 % from half span. Both this is within acceptable values 61.6 o respectively 53.7 o. The tip back angle here is the same as before but the angle from the c.g is different. Here it is stated that the gear is placed 15 degrees back from the c.g. On the real drawing the angle becomes whatever the geometry dictates. The real c.g is unknown and therefore the angles as well. The nose wheel is here assumed to be 25 % of the aircrafts length, counting from the nose. The height is dictated by the ground placement.

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4.4 Center of gravity excursion program To know the c.g of gravity of an aircraft is of outmost importance. It determines the stability related to the neutral point. Early in the design process it is vital to estimate the c.g in order to keep the aircraft in balance throughout the development. The design tool DIBA can generate a weight report, after an aircraft analysis has been executed. This Center of gravity excursion program was created with the F104 starfighter first. Therefore this will be the example described. The program is called CGED, Center of Gravity Excursion Diagram. The weight report for the starfighter looks like this: Aircraft F104 WEIGHT REPORT MAXIMUM TAKE OFF WEIGHT 10737.4 DESIGN WEIGHT 8487.4 OPERATIONAL EMPTY WEIGHT 7087.4 TOTAL STRUCTURE WEIGHT 3269.7 XCG (EMPTY AIRCRAFT) 9.600 XCG (MAX.FUEL, MAX.PAYLOAD) 9.615 XCG (MAX.FUEL, NO PAYLOAD) 9.570 XCG (MAX.PAYLOAD, NO FUEL) 9.659 WEIGHT BREAK-DOWN STRUCTURE Wings Weight of MAIN 626.0 xcg 10.227 Fuselage Weight of Main 1916.4 xcg 7.594 Surface Weight of VTAIL right 128.8 xcg 15.250 Weight of Horisontal tail 214.1 xcg 15.976 Landing gear Weight of NOSE 76.9 xcg 3.000 Weight of MAIN 153.8 xcg 8.000 Weight of MAIN 153.8 xcg 8.000 Other Weight of Engine installation 280.0 xcg 7.000 Weight of Hydraulic 209.7 xcg 9.000 Weight of Surface control 314.6 xcg 8.000 Weight of Furnishing 100.0 xcg 4.050 Weight of APU 0.0 xcg 15.021 Weight of Aircond 176.7 xcg 5.600 Weight of Oxygen 16.0 xcg 4.050 Weight of Avionic 270.0 xcg 2.650

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Weight of Electrical 567.6 xcg 10.288 Weight of Miscellaneous 84.9 xcg 7.594 Weight of Radar & sensorer 223.0 xcg 1.900 Weight of Extra motorinst. 0.0 xcg 0.000 Weight of Gun 120.0 xcg 4.000 Weight of Vapenschakt 100.0 xcg 10.000 Weight of Engines 1055.0 xcg 13.000 Max Fuel weight 3000.0 xcg 9.500 Payload 650.0 Table 4.4 Weight distribution The slim geometry representation was used in the file above. The weights of each components and its corresponding moment arm weight estimated or taken from data tables and should not be seen as actual aircraft data. It is to illustrate the c.g excursion for different loadings. The aircraft weights here are estimated by DIBA sub functions and the placement of the parts is estimated by a drawing over the F104 aircraft. At the beginning of the weight report the different weights and moments arms of the aircraft are listed. This data was used and transferred to the center of gravity excursion program. Some estimation had to be made for other data needed in the program. A list of these estimations and explanation follow below. Clmaxto = 1.55 Taken from the sizing analysis T = 0.85*FREF A 15 % reduction in thrust due to installation [N] Cl_fix = 0.1 Extra lift due to ground effect [-] ZE = 1.5 Thrust center in z-dir [m] Tailplane_trim_anlge = 30 Tail incidence in degrees Elevator_def = 25 Elevator deflection in degrees Cm = -0.25 Moment due to flap deflection Iy = 0.19*LF(1) radius of gyration Z_cg = 1.19 c.g of the aircraft in z-dir [m] Xdelta = 75 Control load cp due as percentage of MAC [-] Flap_area = 67 Area relative the wing area in percent [-] angrot = 0.2 angle rotation speed, weight related [1/s2] K = 1 Efficiency factor for the tail lift [-] Kf = 0.6 flap deflection plain correction term [-] Cldelta = 4.25 lift increment term [-] CLdelta = 1.45 calculated lift for whole tail Table 4.5 Indata The values and formulas were taken from Ref 2, Raymer. FREF is assumed to be after burner thrust at 70kN.

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Fig 4.27 Landing gear tip over plot The Starfighter is 11.4m long and the green point is the estimated c.g location at 9.6meters. In the picture above the tip over angles drawn are 10 and 15 degrees and in this model it is impossible to land or rotate at 15 degrees. That can be related to the inexact model of the exhaust and in the estimate of the center of gravity or that the real aircraft actually cannot rotate at 15 degrees.

Fig 4.28 c.g location The diagram above shows the weight distribution of the aircraft and the forward and aft c.g limitations. On generating the aft limit it was estimated that for control ability the aircraft c.g could move to 55 % of MAC. A deeper analysis of this will be made in the explanation of the neutral program plac.

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The forward c.g limit is rotation capability limit. For the aircraft to be able to takeoff, it has to rotate and the moments acting to accomplish this must be greater than the counteracting ones. If the c.g is too far in front, takeoff is impossible. The placement of the gear is related to the most aft c.g because on landing, the aircraft must be able to rotate forward in this case. These are the moments acting on the aircraft at takeoff, all related to the main wheels: Forward rotation: Center of gravity Engine thrust Rearward rotation: Lift of wing Lift of horizontal surface Drag The lift of the horizontal surface is negative in the case of a conventional tail and positive in the case of a canard configuration. The drag can be a forward rotating moment in the case that center of gravity is above the center of pressure. To illustrate what happens when one changes loading and/or c.g position of the aircraft, weight redistribution was made and a series of diagram that show this was created. One of this will be shown now and the rest for trim analysis program ctrim.

Fig 4.29 c.g location If the center of gravity were to change to 9.2 m, the c.g excursion would change accordingly as above. One can se that this would make it impossible for the light front loaded aircraft to rotate.

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If the horizontal tail could not be placed as far aft as it is now another rotaion problem would occur. Now the moment arm to the horizontal tail is X_delta=16.06 m from the nose to the estimated pressure center. When an arm of 14.06 m is available the following diagram will represent this case:

Fig 4.30 c.g location

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A 2 meter decrease resulted in a 40 cm aft movement of the rotation criterion.or the gripen aircraft the following c.g excursion diagram was generated:

Fig 4.31 c.g location The geometry is the same as the one in the plgear program.

4.5 Neutral Point estimation program The neutral point is related to the c.g in the following equation for the static stability.

αα

αα

ddCddC

ddCddC

dCdC

c

xx

L

m

N

m

N

mcgn

//

//

_ −=−=−=−

Where the condition for static stability is αddCm / <0, therefore the center of gravity most be forward of the neutral point for static stability. A first estimation of horizontal sizing is the stick-fixed static margin condition should at least have some minimum value.

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This condition is depicted in the figure below The neutral point estimation program plac takes the geometry files from DIBA and calculates the aerodynamic center of the wing and the horizontal tail or canard. It then calculates a difference in location and scales them area wise to create a neutral point aft of the wing in the tail case and in front in the canard case. To illustrate these cases, two examples will be shown; one canard (JAS39 Gripen) and one tail (F104 Starfighter).

Neutral point: Red dot Aerodynamic center: Blue dot Gravity center: Green dot

Fig 4.32 neutral point location on gripen As one can see, the neutral point is moved forward on the Gripen, in front of the aerodynamic center and the aircraft becomes instable at subsonic speeds. This is because the neutral point is in front of the gravity center and this was made in order to make it more agile at supersonic speeds.

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Fig 4.33 neutral point location on F104 On the starfighter the c.g is well in front of the neutral point. The c.g plotted in the graph is estimated and the real c.g may be more aft making the aircraft less stabile. This is especially important at high speeds were the aerodynamic center and therefore the neutral point is moved aft at high speeds. The program uses a level 2 description of the wing. And if this was not made during the geometric generation, there is a way in DIBA to create that level. Using the commando wing1to2 on the level one wing, only tip and root chord, is divided in 5 sections.

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4.6 Trimfunctions The definition of trim is when the sum of all moments acting on the aircraft is equal to zero. For the pilot this means when there is no stick force when flying. To be able to trim the aircraft one most be able to generate enough control authority at all flight configurations after the trimmed state has been set. There are several configurations to consider and these will now be described. One critical configuration is the landing phase where the aircraft is flying at near stall speed and low speed means less force on the control areas. To calculate the maximum lift coefficient at landing the following formula are used.

aLflappnoLL CCC ααΔ⋅+≅ )_(maxmax

from Ref 3 The angle at takeoff and landing is limited by the shape of the tail. It usually lays around 15 degrees. Another important configuration is that the aircraft must be able to trim for cruise. Not only must it be trimable but the deflections of the control surfaces most be kept to a minimum in order to reduce trim drag at this phase where the most fuel is consumed. To be able to do this one must look at the trim-ability. A program was created called ctrim that is capable of making a trim-ability analysis. The program has four sources of indata:

• The DIBA generated geometry • Weights from the CGED program • Estimated values written in the ctrim program • Calculated indata also in the ctrim program

In the DIBA generated geometry some aerodynamic parameters had to be calculated and this was done in small sub functions executed in ctrim. These sub functions are explained in the appendix, where all functions are summarized and explained. The program ctrim uses data from the weight report in the form that the c.g excursion program did. Therefore one must run the CGED program first in order to generate the

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variables need in ctrim. The variables are the weights with the corresponding moment arms of the aircraft at different configurations. A few other variables had to be estimated in order to execute the trim evaluation. These are them: %***** INDATA ******************************************************* g=9.81; % gravity constant v_app=190*0.51444; % approach speed v_crusise=MC*300; % cruise speed i_wing=0; % wing incisense flappdeff=45; % flapp deflection alfa0=0%-2; % AoA at zero lift flapparea=75; % Perscentige of wing arae that is flapped most_thickness=24; % MAC % where wing is thickest Cl_alfa=0.105; % wing profile lift coeffcient ETA_h=1; % efficiency due to stabilazer placement Cm=-0.25; % moment of wing around aerodynamic center K=0.0429; % contant depenent on length of fuselage in % front of the aerorynamic center alfag=1; % angle of attack %******************************************************************** Table 4.6 Indata In ctrim the indata were used to calculate further indata needed for the trim analysis. These indata are the following:

Upwash Downwash

Fig 4.34 upwash and downwash display, Ref 3

• Downwash gradient Is the affect the main wing has on the tail on the lift. Has can be seen on the picture above, incase of a canard one obtains an upwash instead. They depend on the placement of the tail/canard relative the wing, the aspect raito of the wing and the span of the tail or canard. The formulas to calculate the downwash and upwash were taken from Ref 3.

)/4.57(1 eARcc

Cl

lL

a

⋅+=

πα

α

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• CL h_tail

This is the lift coefficient for the tail. This is calculated using the estimated value for the airfoil for the wing using the formula above.

• CL w_tail

The lift coefficient for the wing is calculated the same way as for the tail, but with its aspect ratio.

Dynamic pressure Calculated for two different speeds, the approach speed and the cruise speed. Now that all indata is obtained the trim analysis can begin. It is done by comparing the actual c.g positions to the calculated c.g position using a certain formula. And if these values differ the incidence of the tail is changed and the calculations are done again. This loop continues until a certain level of equality is obtained. The trim points are then printed in the CGED generated diagram. For the F104 starfighter in approach configuration the following diagram was created:

Fig 4.35 c.g location with trim points It generated the following i_htail values: -0.8 degrees -0.7 degrees

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This is rather small values and show that the aircraft need little tail deflection to be trimmed. A lot of values have been estimated but if a better knowledge of the wing is known a more accurate analysis can be made.

Fig 4.36 c.g location with trim points If the F104 were to be front loaded and have a OEW c.g at 8 meters the aircraft would need more force generated by the tail and the calculated trim positins in the graph turned out tho be the following: -2.1000 -3.5000 -3.8000 degrees The reverse is also true, if the aircraft are loaded in the back it will have to use positive inclination of the tail. The instability characteristics that then will occur are not taken into considerations in this analysis.

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5 Conclusion The work that has been done deals with the early phases of aircraft development. Therefore it is not of use to spend too much time on detail in one part rather to look at the aircraft as one part and research many different approaches. Adaptable modules and functions have been created to be able to size and balance an aircraft in the conceptual phase. They are illustrative and easy to understand. For the sizing, there are a lot of assumptions that needs to be made in early designs in order to make a preliminary estimation of the aircraft. So the level of accuracy is never very high. What one can do is to see which requirements are driving and see if they can be met or not. Accurate performance analysis is more in the field of detailed design when a concept has been chosen. Not necessary full scale testing, but more rigorous simulations with stronger software and more accurate variables as indata will then be used. In the military sizing, some other measures of merit can be considered. If the behavior is unpredictable at high angles of attack, the combat effectiveness will be affected and turn rate alone cannot describe this. These criteria were not taken into account in this study. To know the weight and balance are of outmost importance and the simple graph generated in the program above can be of great help to keep track of the c.g position. The neutral point is only estimated roughly in this program. It gives a picture of what to expect when one changes the lever arm or the size of the horizontal surface. A lot of indata is needed in order to calculate the parameters needed to trim the aircraft. Many of them have to be estimated very roughly with assumptions or empirical formulas. This means that one cannot expect a very high degree of accuracy. The tests show reasonable values for deflection within normal configuration usage.

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6 Future work Looking at the sizing tool it would be of interest to have a more graphical interface. A user friendly faster link so changes can be made and the result recalculated and plotted again with the push of a button. It would be useful to develop an optimizing system between variables. This could for example mean that a certain mission is flown with in a loop with different wing layouts and the most favorable is stored in a file. The sizing requirement time to climb could use better methods to choose which absolute height to use for each aircraft type. If one tries to implement a lifting tail/canard or a tandem wing system one runes into trouble due to geometry definition in the programs. Also with a Blended wing body configuration. With some effort, a generic code could adapt and calculate the neutral point for example. The c.g plot program could be made with a better and easier loading change capability. One could also implement other criteria in the center of gravity excursion program related to control authority and stability. The trim function works on a controlling tail/canard configuration but if the aircraft is tailless or have lifting horizontal surfaces the capabilities needs to be further extended. For the time to accelerate requirements a better description of the engine is desirable in order to better estimate the thrust to drag difference. It was stated that a turboprop model should be implemented in this thesis work. This has not been done due to lack of time. Only a simple formula was used so that the thrust available could be calculated in the sizing of the Saab 2000. An in depth model of a turboprop engine that could be scaled in size and thrust would be of great use to compare it with a jet alternative for example. The fuel consumption calculated in the mission in DIBA is about 20% more than in the Saab 2000 specification, Ref 9 and Ref 40 if the generic turboprop engine was used. This could improve if a newer model was used. The landing gear program needs the aircraft to be defined a certain way. Namely the fuselage above ground at a height above ground dictated by the compressed landing gear due to the weight of the aircraft. If one defines the fuselage at ground the program needs to be updated to take this into account. Effects of the fuselage on the neutral point have not yet been taken into account. And for a double delta wing the calculation for the mean aerodynamic chord needs to be improved.

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7 Appendix

7.1 Function description Gripen will be the example describing the files used in the aircraft analysis.

7.1.1 DIBA aircraft analysis files cbd_gripen were aircraft is evaluated has the following structure

Fig A.1 Aircraft evaluation structure

1. Geometry 2. Cruise speed

Cruise altitude Range

3. cswet chdrag cclmax 5. Weight loop

7. Mission calc

4. Engine file

6. Weight calc

9. Weight report

8. Center of gravity

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Now a description of each box will follow:

1. The geometry description consists of general, fuselage, wing, surfaces, landing gear, fuel, engine inlet and system description. Example given in Ref 10.

2. A cruise speed and altitude and a range is given, used in the mission calculation.

3. The wetted area and drag polar, calculated from the geometry, for the aircraft is used in the mission.

4. Engine data for different height and speeds are implemented in the mission.

5. The weight loop estimates the emtpty weight from the given geometry and mission set and loops it until a given break criteria is reached.

6. In this loop a weight function is used that estimates the weights for all components of the aircraft.

7. The mission consists of different phases that consume fuel. Usually a taxi, takeoff, climb, cruise, loiter, descend and landing phase are implemented.

8. The center of gravity is estimated for each component and then the whole aircrafts c.g is calculated.

9. A weight report is calculated and given in the form of Table 4.4 in chapter 4.4.

plmission_tot plots the mission used in the weight estimation loop. A graph is

shown as an example of outcome result.

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Fig A.2 mission plot As one can see the cruise speed is mach 0.7 and the cruise altitude 10 km. At a little over 2 hours, about 3 tons of fuel is estimated to be consumed during the mission. On the above left picture one can see that the rate of climb is a lot steeper then than the descend phase. This is not a fuel optimized mission. DIBA geometry

7.1.2 Sizing functions plsize Described in chapter 4.1.1 with all its sub functions. To

show an example of a program code, the code of this program is presented.

indata_Mil_size_gripen Geometry description and drag calculations made used in

the plsize program. Also consists of a requirement description further described in chapter 4.

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cAmax Calculates the maximum cross sectional area of the aircraft

at a given mach number. Matlab code function []=plsize(caseid) % % []=plsize(caseid) % % Plots a sizing diagram for the given airplane. % Without AB put 1, with AB put 2 in caseid. indata_Mil_size_gripen; TWgdr=cTWto_gd_roll(H,M_gr,To_SLS,mstto,CLto,gd_roll,m0_S,Sref,caseid); % TWd50=cTWto_dist50(H,M_gr,To_SLS,mstto,CLto,dist50,m0_S,Sref,caseid); mS=(m0_S-(1-fuelfraction/100)*fuel/Sref+m_st/Sref); for i=1:10 f(i)=(m0_S(i)*Sref-(1-fuelfraction/100)*fuel+m_st)/(m0_S(i)*Sref); TW_acc1(i)=cTW_acc(time1, mS(i), Mo1, Mf1, alt1, dry_ab, M_tab, CDS_tab, Swet, Sref, l_mean, AR, sweep_LE, m_st); TW_acc2(i)=cTW_acc(time2, mS(i), Mo2, Mf2, alt2, dry_ab, M_tab, CDS_tab, Swet, Sref, l_mean, AR, sweep_LE, m_st); end TW_acc1=TW_acc1.*f; TW_acc2=TW_acc2.*f; % if dry_ab==1 x1=1/cT_maxDry(SEP1alt,SEP1M,1); x2=1/cT_maxDry(SEP2alt,SEP2M,1); x3=1/cT_maxDry(SEP3alt,SEP3M,1); x4=1/cT_maxDry(SEP4alt,SEP4M,1);

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x5=1/cT_maxDry(SEP5alt,SEP5M,1); else x1=1/cT_maxAB(SEP1alt,SEP1M,1); x2=1/cT_maxAB(SEP2alt,SEP2M,1); x3=1/cT_maxAB(SEP3alt,SEP3M,1); x4=1/cT_maxAB(SEP4alt,SEP4M,1); x5=1/cT_maxAB(SEP5alt,SEP5M,1); end for i=1:10 f(i)=(m0_S(i)*Sref-(1-fuelfraction/100)*fuel+m_st)/(m0_S(i)*Sref) TW_SEP1(i)=TW_SEP(SEP1v, mS(i), SEP1M, SEP1alt, nz1, M_tab, CDS_tab, Swet, Sref, l_mean, AR, sweep_LE, m_st); TW_SEP2(i)=TW_SEP(SEP2v, mS(i), SEP2M, SEP2alt, nz2, M_tab, CDS_tab, Swet, Sref, l_mean, AR, sweep_LE, m_st); TW_SEP3(i)=TW_SEP(SEP3v, mS(i), SEP3M, SEP3alt, nz3, M_tab, CDS_tab, Swet, Sref, l_mean, AR, sweep_LE, m_st); TW_SEP4(i)=TW_SEP(SEP4v, mS(i), SEP4M, SEP4alt, nz4, M_tab, CDS_tab, Swet, Sref, l_mean, AR, sweep_LE, m_st); TW_SEP5(i)=TW_SEP(SEP5v, mS(i), SEP5M, SEP5alt, nz5, M_tab, CDS_tab, Swet, Sref, l_mean, AR, sweep_LE, m_st); end TW_SEP1=TW_SEP1.*x1.*f; TW_SEP2=TW_SEP2.*x2.*f; TW_SEP3=TW_SEP3.*x3.*f; TW_SEP4=TW_SEP4.*x4.*f; TW_SEP5=TW_SEP5.*x5.*f; %landing mS_Land=mS_land(land_dist, CLmax_land); m0_S_Land(1)=(mS_Land*Sref-mstto)/0.85/Sref; m0_S_Land(2)=m0_S_Land(1); TW_Land=[0 1.2]; %instant turn rate mS_turn=CLmax(inst_turn_rate_M,CLmax_lowM)*q(inst_turn_rate_alt,inst_turn_rate_M)/g/((inst_turn_rate/57.3*inst_turn_rate_M*a(inst_turn_rate_alt)/g)^2+1)^0.5; m0_S_turn(1)=(mS_turn*Sref-m_st)/(fuelfraction/100*Sref); m0_S_turn(2)=m0_S_turn(1); TW_turn=[0 1.2]; % Plot routine figure(51) hold on grid on

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title('Gripen') xlabel('Wingloading [W/S]') ylabel('Thrust to Weight ratio [T/W]') plot(m0_S,TWgdr,'LineWidth',1) plot(m0_S,TWd50,'LineWidth',2) plot(m0_S,TW_acc1,'x-') plot(m0_S,TW_acc2,'LineWidth',2) plot(m0_S,TW_SEP1,'r') plot(m0_S,TW_SEP2,'g') plot(m0_S,TW_SEP3,'b') plot(m0_S,TW_SEP4,'k') plot(m0_S,TW_SEP5,'c') plot(m0_S_Land,TW_Land,'b') plot(m0_S_turn,TW_turn,'*-r') plot(m0Sref,ToWo,'rx') plot(m0Sref,ToWo,'ro') legend('Ground roll','Take off 50 ft','Time to acc1','Time to acc2','SEP 1','SEP 2','SEP 3','SEP 4','SEP 5','mS Land', 'Inst turn', 'Design', 'point','Location','NorthEastOutside')

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7.1.3 Balance and stability programs Landing gear plot program plgear_mod plots the landing gear and is described in chapter 4.3. Center of gravity program CGED Plots the c.g at different loadings and is further described in chapter 4.4.

This function uses the following functions: camc calculates the MAC of the aircraft cxacs calculates the aerodynamic center of the aircraft surfaces with the DIBA

geometry as indata. The horizontal tail/canard is the one normally used and is assumed to have index 2.

lesweeps calculates the leading edge sweep of the surfaces. Also mostly used for the

horizontal surface tail/canard. Further the forward c.g limit is calculated and drawn as the left blue line in the diagram 4.28 in chapter 4.4. Neutral point estimation function plac Uses the DIBA generated geometry and the cxacs function described

above. Trim program ctrim Is the program that estimates the trim-ability of the aircraft and uses the

following functions. cyamc Calculates how far out on the wing MAC is located. Formula from Ref 2. camcs Calculates the MAC for the aircraft surfaces. Formula from Ref 2. cams Gives a value of the aircraft MAC for the wing. Formula from Ref 2. lesweep Generates the leading edge sweep of the wing. Formula from Ref 2. lesweeps Generates the leading edge sweep of the surfaces. Formula from Ref 2. Further this function uses the geometry from the CGED program.

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7.2 Aircraft geometry description

7.2.1 Saab airplanes Saab J35 - Draken

Fig A.3 Draken Första flygning 1955 Max startvikt 17 600 kg Saab 105 – SK60

Fig A.4 Saab 105 Första flygning 1963 Max startvikt 3700 kg

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Saab J37 - Viggen

Fig A.5 Viggen Första flygning 1967 Max startvikt 20 000 kg Saab JAS39 – Gripen

Fig A.6 Gripen Första flygning 1988 Max startvikt 14 000 kg

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Saab 2000

Fig A.7 Saab 2000 Första flygning 1992 Max startvikt 23 000 k

7.2.2 Other airplanes L39 Albatross

Fig A.8 L39 Albatross Första flygning 1968 Max startvikt 4700 kg

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8 Reference Books 1. Synthesis of subsonic Airplane Design - Egbert Torenbeek 1982 2. Aircraft Design: A Conceptual Approach - Daniel P.Raymer 3. Introduction to Aeronautics: A Design Perspective - Steven A. Brandt, Randall J. stiles, John J. Bertin Ray Whitford 4. Användarhandling för MATLAB 6 - Eva Pärt-Enander Anders Sjöberg 5. Airplane Design: Part 1: Preliminary sizing of airplanes - Dr Jan Roskam 6. FLYGPLAN KORT 1998 – Lennart Berns HKV, Försvarsmakten och FMV i

samverkan 7. Aircraft performance and design, John D. Andersson Jr. 8. Introduction to flight 3rd ed. – John D. Anderson, JR. (p.145 flat plate

resistance) Thesis and Papers 9. SAAB 2000: The High Speed Turboprop Airliner SAAB-SCANIA AB Aircraft

divition 10. DIBA; Manual and System Description 11. Geometrical properties of craked and straight tapered wing planforms. 76003

ESDU

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Homepages 12. http://www.aoe.vt.edu/~mason/Mason_f/ConfigAeroAppC.pdf 13. http://www.antiquark.com/randimg2/large/x15-rocket-plane.jpg 14. http://www.bartleby.com/61/ 15. http://wright.nasa.gov/wilbur.htm 16. http://www-scf.usc.edu/~tchklovs/Proposal_files/image117.jpg 17. http://www-scf.usc.edu/~tchklovs/Proposal.htm 18. http://www.airwar.ru/other/draw2/l39-3.html 19. http://www.fschwerelos.de/Klemm_35/klemm_35.html 20. http://www.nasa.gov/centers/dryden/news/NewsReleases/1997/97-20_pf.html 21. http://www.flightsimaviation.com/data/FARS/ 22. http://www.hq.nasa.gov/pao/History/SP-468/contents.htm 23. http://www.aerodyn.org/Drag/tables.html 24. http://exploration.grc.nasa.gov/education/rocket/shaped.html 25. http://www.accessmylibrary.com/coms2/summary_0286-9343723_ITM 26. http://adsabs.harvard.edu/abs/1976NASSP.405...49B 27. http://selair.selkirk.bc.ca/aerodynamics1/controls/Page2.html 28. http://sv.wikipedia.org/wiki/Viggen 29. http://en.wikipedia.org/wiki/Aero_L-39_Albatros 30. http://www.lissys.demon.co.uk/pug/c08.html#s13 31. http://en.wikipedia.org/wiki/Vno 32. http://www.skyways.se/upload/saab2000-450x200.jpg

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33. http://www.aerospace-technology.com/projects/saab_2000/specs.html 34. http://www.airplanedriver.net/study/f104.htm 35. http://www.aerospaceweb.org/question/planes/q0143.shtml 36. http://www.aeronautics.ws/blunder8.html 37. http://agert.homelinux.org/~fredrik/flyg/plotfoil/pdf/ 38. http://www.volvo.com/volvoaero/se/sv-

se/products/aircraft+engines/RM12/technical+data.htm 39. http://www.richard-

seaman.com/Aircraft/AirShows/Ciaf2006/Highlights/index.html 40. http://www.saabaircraft.com/download/files/Saab2000FAR.pdf 41. http://www.ksak.se/klubbar/EskilstunaMFK/emfk_new/fd/gripen_info_2.htm 42. http://www.principalmetals.com/utilities/mil-a-sp.htm