flight vehicle design aircraft design

8/7/2019 FLIGHT VEHICLE DESIGN AIRCRAFT DESIGN

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FLIGHT VEHICLE DESIGN

AIRCRAFT DESIGN

Introduction:-Aircraft design is both art and science and is a separate discipline of aeronautical

engineering different from analytical discipline such as aerodynamic structural, control

and propulsion. It is an intellectual engineering process of creating on paper flyingmachine.

To meet certain specifications

Certain finite innovative, new design and technologyAircraft design is by its nature an iterative process. This means that estimates and

assumptions have sometimes to be made with inadequate data such guess estimates

must be check when more accurate data on the aircraft is available.Requirements are set by prior design trade studies. Concepts are developed to meet

requirements. Design analysis frequently points towards new concepts and technologies

which can initiate a whole new design effort. All of these activities are equally important

in producing a good aircraft concept.The start of the design process requires the recognition of a need. This normally comes

from a project brief or a request for proposals (RFP)

Purpose and scope of aircraft design:-An airplane is designed to meet the functional and safety requirements. The actual

process of design is a task involving

Selection of airplane type and data Determination of the geometric parameters

Selection of power plant

Structural design and analysis of various components

Determination of airplane flight and operational characteristics

Preliminary design:-It briefly describes the overall process by which an aircraft is designed. The preliminary

phase starts with the project brief and ends when the designers have found and definedfeasible base line design layout .it provides a root map from the initial project brief to the

validated base line aircraft layout. This includes sections that deal with Defining and understanding the problem

Collecting useful information

Setting the aircraft requirements

Producing initial aircraft configuration

Finally the initial aircraft layout can be refined using constrained analysis and trade off

studies. At the end of the preliminary design phase, a document is produced which

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contains a summary of the technical and geometric details known about the base line

design. This forms the initial draft of the document that will be subsequently revised to

contain a thorough description of the aircraft. This is known as the aircraft typespecification.

The preliminary design task include:- Layout of the main component

Arrangement of airplane equipment and control system

Selection of power plant

Aerodynamic and stability calculations

Preliminary structural design of components

Weight estimation and centre of gravity travel

Preliminary wind tunnel and structural design

Drafting the preliminary 3-D view drawing

Project Design:-It takes the aircraft configuration define toward the end of the preliminary design phaseand involves conducting analysis to improve the technical confidence in the design.

Wind tunnel test and CFD analysis are used to refine the aerodynamic shape of

aircraft

Finite element analysis is used to understand the structural integrity, stability and

control analysis and simulations will be used to appreciate the flying characteristics.

Mass and balance estimations will be performed in increasingly fine detail.

Operational factors (cost, maintenance, marketing and manufacturing process)will be

investigated to determine what effects these may have on the final design layout .all

these investigations will be done so that we will be able to take a decision to proceedto manufacture.

Detailed Design:-The third phase of the design process ie., detailed design starts when a decision to

built the aircraft has been taken. In this phase all the details of the aircraft are

translated into the drawings, manufacture instructions and supply requests (sub

contractor agreement and purchase orders) progressively throughout this phase, theseinstructions are released to the manufacturer.

Tasks of Design Phase:-

Preliminary Design:- Freeze the configuration

Develop lofting

Design major items

Develop actual cost estimate

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Project Design:-

Development of wind tunnel models and detailed model study

Stress analysis of individual components indicates or includes the static,

dynamic, fatigue and aero elasticity Aerodynamic analysis by wind tunnels and CFD

Detailed Design:- Design the actual pieces to be built

Design the tooling and fabrication process

Test major items landing gear etc.,

Finalize the weight and performance estimates

Flight test analysis

Design Procedure for Aircraft:-Aircraft design is to know what type of aircraft is to be design, size and purpose.Hence designer must familiarize with specifications and command on existingaircraft.

Specification for General Aircraft:-These specifications made by the customer based on the requirements or based on

the market selling and its potential to establish superiority.

1. Larger, more comfortable seat with more luggage

2. Premium in Flight service3. Separation from tourist class passengers in airport launches during

boarding and un-boarding of the aircraft4. Faster flight checking and post flight language retrieval5. Advance technologies to reduce operating cost

6. Operate from regional airports

7. Alternative rolls for the aircrafts

Design Specifications (General):-Designer prior to design establishes these specifications based on customer

requirements Economy, Time, Size and Purpose.

No. of Engines

Wing type

Material used Landing gear type

In general for passenger Aircraft Engines two or more

Cantilever wing

Metal or composite

Retractable landing gear

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Performance requirements:- Range

Take off distance

Stalling velocity Endurance

Maximum velocity

Rate of climb

Maximum and Minimum turn rates

Maximum load factor

Service ceiling

Cost

Reliability and Maintainability

Maximum size

Stations Specifications:-

Station:-Accommodate Pilot, Co-pilot and forward portion it should be isolated from

passenger compartment by bulk heads with doors.

Passengers Cockpit:-Located 1st Cockpit next to cockpit passenger compartment provides comfortable

and required to number of parts

It contains Windows for each seat position.

Mail and Baggage:-Located at nose, under cockpit and cabin floor should be accessible from left or

part size.

Preliminary weight estimation:-

Introduction:-No aeroplane can get off the ground unless it produce a lift greater than its weight

and no airplane design process can get off the ground without the first estimation of the

gross take off weight. In preliminary design of an airplane we cannot go any further untilwe have a first estimate of the take off gross weight however the weight estimated in this

stage is crude and can be refined further.

Preliminary design take off weight of the aircraft as it begins the machine forwhich it was design. Weight is the main consideration as far as the structural aspect of

design or as a matter any airplane design of any configuration .Engineer always strives

hard to reduce the structural weight without compromising on the strength factor because

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less weight means less take off time. Thus helping in fuel economy and also for given

amount of fuel more payload or passengers can be accommodated.

The weight of aircraft is determined in two stages.The first estimation of weight is only approximate one and the value obtained

gives a rough idea of the weight but it is enough to design whether the design is heading

in right direction or not.Design take off gross weight can be broken down into

1. structural weight(Ws)

2. payload weight (Wp)3. power plant weight (Wpp)

4. fuel weight Wc)

5. fixed equivalent weight (Wfe)

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Passenger aircraft weight fraction:- Based on the study of existing passenger aircraft, weight fraction is approximated

for first estimation .We can some what rely with this data for initial estimation with theuse of this fraction we can approximately design our aircraft gross weight.

The weights below are listed in percentage of gross weight1. Wing (13%-17%)

2. Tail (1.5%-2.5%)

3. Fuselage (8%-13%)4. Main landing gear(5%-8%)

5. Tail wheel:-

1. For tricycle (4%-7%)

2. Main landing gear (1.5%-2.5%)

3. Nose (15%-25%)6. Power plant (1%-2%)

7. Engine accessories (0.1%-0.4%)8. Power plant control (2%-4%)

9. Propeller (0.3%-0.9%)

10. Starting system (0.3%-0.6%)11. Lubricating system (1.5%-2.5%)

12. Fuel system (0.5%-1.2%)

13. Instruments

Surface control (1%-2%)14. Furnishing (4%-10%)

15. Weight per passenger (90lb-215lb)16. Communication equipment (2%-3%)17. Possible useful load (food, water) (3.5lb-9lb)

18. De-icer installation (0.06%)

19. Residual fuel, oil (30lb per engine)

For economy of operation, the useful load must be about 25% - 40% of airplane

gross weight with this above detail, it is possible to make1. Wing and tail surface area

2. Design layout

3. Location of passenger, cargo and fuselage equipment

4. Position of nacelle, fuel, oil tank and engine5. Shape and position of wing tail surface

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Performance calculations:-Performance requirements are set forth in specifications should meet or approached

.

Preliminary calculations:-

1. Maximum lift coefficient2. Lift to drag ratio

3. Wing loading

4. Thrust to weight ratio5. characters Take of distance

6. Service ceiling

7. Maximum endurance and range8. Landing speed etc.,

As design progresses, more accurate data can be obtained from wind tunnel data, the

performancedepend on external load as well. In two ways we can obtain accurate data:-

1. Theoretical calculations and it should be ensured that the result of calculationsare correct and no error as taken place.

2. Wind tunnel test by scale model. This is more satisfactory than calculation. Butmost wind tunnel tests are carried on power of condition. Hence it is necessary to

carry out corrections for power effect. From wind tunnel test, we can get lift, drag,

propulsive property flow visualization and aerodynamic moments. This enabledesigner to calculate all flight spped, rate of climb, ceiling, landing and take off

distance etc.,

Mock up:-The construction of mock up which is essentially a full scale reproduction of

certain section of proposed design and is started immediately after preliminary designphase. Mock up model is a flexible quantity which can be modified as design progressesnormally this is made by plywood or sheet metal.

It facilitate designer to

1. Installation2. Accommodation

3. Accessibility problem

4. Arrangements of controls and cables5. Ducts

6. Seating space and accessibility control

Second weight estimation:-The second weight estimation will be made by detail consideration of each

component or group of component.

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1. Wing group :-Components to be considered as wing panels, ailerons, flaps, struts, wires,

fairings, attaching both etc.,

Important factors:-

Wing area, aspect ratio, lift to drag ratio, thickness by chord, taper ratio, load

considering ratio.

1. Effect of aerodynamic load pressure and shear load2. Effect of dead load structure (spars, ribs etc.), unstructured (fuel etc.)

Determination:-1. Material that resist bending of wing

2. Shear material

3. Ribs and other members

Bending considerations:-1. Spars resist bending load

2. Cantilever beam no end loads and stress by bending3. Total lift in normal flight gross weight

Shear considerations:-1. Ribs receives shear loads from skin through stiffness and redistribute among

stringers

2. Stiffened panel resist shear by reducing effective length3. Direct pressure ribs are used to withstand these stresses

Tail group :Tail surface weight is greatly influenced by wing and its position, aero

dynamic, static, stability requirements are also significant along with dynamic balance.

Fuselage group:-Fuselage weight is based on gross weight and is given in terms of weight /

square feet , for this purpose fuselage is considered in three parts.

1. Front nose combination of 10% of total length2. Centre cylinder portion

3. After 25% cone

Components to be considered:-1. Skin

2. Bulk Head3. Stringer

4. Frames

5. Longerons6. Flooring and its support

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7. Windows and their frames

8. Nose wheel provision

9. Nose installation10. Pilot enclosure

11. Tail combination and its struts

12. Cabin ceiling and pressure installation

Load consideration:-1. Circumferential stress2. Longitudinal load

3. Pressurization load

4. Other external attachment (Wing, landing gear) and localized strength

consideration

Landing gear:-Landing gear weight is considered in 2 parts:

1. Primary part Chassis directly carry primary stress (gross weight and landingload)

2. Secondary part Wheel tires, tubes and retracting mechanism

Nacelle group:-Weight of nacelle depends on size of engine in turn weight of engine and it

varies with position on wing, landing gear hoisted by nacelle or not, nacelle is a part of

wing or not.

The weight of power plant will depend on thrust requirements and can betaken from power plant manual of engine that has previously been selected.

Fuel System:-Weight depend on fuel capacity in turn range. Tank weight depends on

integral or separate tank. Integral tank eliminate separate tank weight but some structure

weight must be there to ceiling and leak proof. Integral tanks are less in weight than

separate tanks.

Instruments:-Weight depends on number of instruments involved and this weight includes

tubing, wiring and supports . Instruments are divided in to 3 groups.

1. Auto pilot (Navigation)

2. Flight instruments

3. Engine instrumentsAdding of individual weight calculation for this group gives the complete

weight of instrument.

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Surface controls:-Weight consists of aileron, rudder, elevator, flap and tab controls. Weight of

the tabs entirely depends on loads. These weights are normally assumed as a function ofwing span.

Furnishing:-These weights are highly variable and depend normally upon customers need either

actual or imagine. Furnishing group estimate by sketching internal arrangements and

individual weight will be considered.

Communication equipments:-Weight depends upon amount and type of equipment in turn depend on Civil

Aviation Authority or service requirement and purpose.

Electrical Equipments:-Instead of 12 Volts or 20 Volts DC, 110 Volts AC is used. The total weight

for large aircraft may be appreciably reduced because of a great saving in transmissionwire weight.

Deicer installation :-Weight of De-icer equipment is equal approximating 0.06% of design gross

weight.

Possible useful load:-This group consists of food stores and water. These weight are fixed for given

aircraft and can be used for empty or gross weight calculation and balance consideration.

Arrangements:-Considering arrangements it should be noted that external dimension depends

on or external dimension must be at least be as large as the inside dimension.Three things considered for arrangements

1. Weights

2. Location

3. Relationship with other items of equipments, personnel or structure

For some safety consideration and equipment Civil Aviation Authority also

made their restriction and should be followed while designing arrangement. Somepreliminary consideration are given below:

1. Balance consideration :-Location of C.G with respect to centre of lift is very important for Aero

dynamic and stability consideration. So calculating the position of C.G is a with respect

of arrangement will play major roll in balance.

Major weight items may broken down into 2 main groups.

1. Empty weight :

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Wing, tail, fuselage, power plant, landing gear

Furnishing, instruments, surface controls, electrical equipments, communicationequipments

2. Useful load:

Fuel, Oil

Passenger, Crew and Cargo

In general passenger load and its position are variable and fuel, Oil load arediminishes over a flight mission and these should be considering while balance

consideration

2. Comfort consideration:-Comfort of passenger depends on length of non-stop flight ,means we need

more comfort for long rage flight than shorter oneMajor items include:

1. Noise level :

Chief noise sources: Power-plant, propeller, ventilation fans

Noise reduction: Avoid to enter inside cabin by shielding,

Eliminating the openings. Absorb the noise asenters rapidly by absorption materials. Prevent

noise source.

2. Propeller location and clearance:

Maximum propeller noise levels lies in the plane

of propeller rotation and drops on either directionfrom plane of rotation.

3. Vibration:

Source: Propeller and engine these are fixed quantity.

Aerodynamic sources such as tail buffeting.

Fuselage large plate area resonance with some

fluctuating energy, there is always a possibility thatfew panels in the aircraft may go into resonance at

some speed and some engine rpm.

Prevention: Aerodynamic noise can be prevented by amount

will reduce the power plant vibration transmitted to

other parts, vibration damping material placed inwing attachments and other parts. Resonance can

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be avoided by coating the high damp co-efficient

material inside the panel surface. But this may lead

some additional weight. Hence divide the panelsinto unequal odd shaped panels by stiffener, which

will not go into resonance at some higher harmonic

of panel frequency.

4. Vision:

Vision is a major important for Military Aircraft.

For passenger aircraft passenger visibility is

secondary, high wing monoplane leads good

passenger visibility, but increased landing gearheight and associated weight, over shadowing

problem results seldom used.

5. Heating and Ventilation:

It provides uncontaminated air. Sources ofuncontaminated air must be located at a place where

fumes from engine should not be entered into flow.

Heat source by engine exhaust, electrical heating.

Electrical heating over loads generator, hencemostly exhaust heating utilized with some

additional weight.

Two possible locations Nose of fuselage the duct must run through the

area where large number of controls and nose

landing arrangement are present and heat source islocated engine result need of additional and

complicated ducting .Wing leading edge simpler

and easier ducting only the disadvantage is, if notmade carefully then severs aerodynamic problems.

3. Operating consideration:Easier provision for loading and unloading. Forairplane with tri-cycle landing gear, it is possible for

enough passengers to congregate near a rear door to

put the C.G. behind rear wheel and hence airplaneto drop by tail this must be prevented. Space for

beggaging should near doors ease of loading and

unloading result avoiding delays. Internalarrangement should such that supply fi foot and

service will be with minimum effort. Maintenance

is an important factor in operation; all-importantitems should be inspectable, removable and

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replaceable easily. Safety features includes fire

extinguishers, emergency exist, safety locks on all

doors, warming signals for flabs, labs, landing gearposition, would be placed in proper locations.

4. Manufacturing considerations:

Manufacturing should be economical-avoidcomplexity in arrangements. Limitation of shop

floor, tools, machines should be considered.

5. Fixed equipments: All the items of equipments must be considered forproviding space, general location.

Software required:- a) Microsoft Excel:

Microsoft Excel:

1. Introduction:-Microsoft Excel is a spread sheet application written and distributed by Microsoft.

It features calculations, graphics, charts, tools, pivot tables and Macro programminglanguage called VBA. It has been the mostly widely used spread sheet application

available. It has many useful capabilities for Engineering calculations. In particular it can

be used to solve equations and optimization problems.When the program is invoked, it opens what is called the work-book. A work-

book contains several pages called worksheets . These worksheets may be used to store

related data and information. Each work sheet is divided into cells that referenced bytheir location, the column row number. All the information, data and its manipulations

must be organized in terms of cells. Cells may contain raw data , formulas and references

to other cells.

2. Basics of a spread sheet:-

A. Spread sheet details:Spread sheets are made up of

Columns

Rows

Cells Inter section of rows and columns in each cell there may be thefollowing types of data:

Text or labels

Number data or constants

Formulas (mathematical equations that do all the work)

Each cell is assigned a name according to its column letter and row number.

Labels in Excel (Text data) :

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Labels are text entries. They do not have a value associated with them. We typically use

labels to identify what we are taking about.

Constants in Excel (Numeric data) :-Constants are entries that have a specific fixed value.

B. Formulas in Excel:Formulas are entries have an equation that calculates the value to display. We do

not type in the number we are looked for. We type in the equation. This equationwill be updated upon the change or entry of any data ie., referred in the equation.

Formulas must begin with equation sign (=). We can add, subtract, multiply and

divide using these formulas.

C. Solver :Solver is the tool available in Excel to solve a non-linear equation, a system of

linear / non-linear equations and optimization problems. We shall use solver to

find roots of the non-linear equations like x Sin x =O. Solver is invoked throughthe Tools menu. If it is not visible under tools, it is not installed yet. To install

it, use the Add-in command under tools menu. We need to prepare a work sheetthat defines a problem. The work sheet can be prepared in many different ways,

and Fig1 shows one such way. We define cell C3 as x, the solution variable. To

name a cell, use the Inter/Name/Define command and click the Add button todefine names for cells. Defining meaningful names for cells is useful because they

can be referred to by their names rather than their cell numbers.

A B C D

1 Roots of 2x /3 Sin x = 0

23 Variable x 1

4 Equation 2x / 3 Sin x - 0.17480432

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Figure-1 Excel worksheet

Experiments:-

Part-1 Aircraft design and weight estimation nomenclatureWeight components of airplane explained as follows:-

1) Crew Weight (Wc):

The crew comprises the people necessary to operate the airplane in flight eg.,

pilot, Co-pilot, Airhostess etc.,

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2) Payload weight (Wp):

The payload is what the airplane is mentioned to transport passengers, baggage,freight etc., (Military use the payload includes bombs, rockets and other disposable

ordnance).

3) Fuel weight (Wf):

That is the weight of the fuel in the fuel tanks. Since fuel is consumed during the

course of flight W, is a variable, decreasing with time during the light.

4) Empty weight (We):This is weight of everything else-the structure engines (with all accessory

equipment) electronic equipment landing gear, fixed equipment and anything else that isnot crew, payload or fuel.

5) Gross weight (Wo):

The sum of these weights is the total weight of the airplane Wo, Gross weight ortotal weight Wo varieis through the flight because fuel is being consumed. The design

take off gross weight Wo is the weight of the airplane at the instant it begins its mission.It includes the weight of the fuel.

Wo = Wc + Wp +Wf + Wc

Wo = Wc + Wp + (Wf/Wo) Wo +(We/Wo) WoWo = (Wc + Wp) / (1 Wf / Wo We/Wo)

Estimation of empty weight fraction (We / Wo):

The empty weight fraction (We / Wo) can be estimated from data based on

a) Historical data and tables

b) Refined sizing data and tables

Estimation of fuel fraction (Wf / Wo):

The aircrafts fuel supply is available for performing the mission. The other fuelincludes reserve fuel, trapped fuel (which is the fuel which cannot be pumped out of the

tanks).

Fuel fraction (Wf / Wo) is approximately independently of aircraft weight Fuel

fraction will be estimated based on the mission to be flown.

Mission profiles:

Typical mission profiles for various types of aircraft are shown in Fig.1: Thesimple cruise mission is used for many transport and general aviation designs, including

home built. Following are the briefly explained the terms that are used in mission

profiles.

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Warm Up and Take-Off:-

Warm Up is the engine start up for the airplane kept idling for some time to warmup. Take off is the point where aircraft is made lift off from ground. It is the motion after

warm up ie., moving of airplane after starting and till it lifts off from the ground.

Climb:-It is between take-off (TO) and cruise (stead level flight with constant speed)

Increase in height until airplane achieves steady level flight.

Cruise:-It is the steady level flight to cover the mission distance. The mission distance is

called Range.

Loiter:-Represent the airplane spending in air for some fixed number of minutes near

airport before getting the clearance from airport signal or simple spending some time tocollect data of some mission (Terrain data)

Dash:-It is the mission that must be flown at just a few hundred numbers of feet of the

ground for low level strike.

Landing:-It is the aircraft landing on the runway till stopping of engine.

Estimation of mission segment weight fractions:-The various mission segments (legs) are numbered starting from zero denoting,

the start of the mission. Mission leg one is usually engine warm up and take-off. The

remaining legs are sequentially numbered. For example in the simple cruise mission thelegs could be numbered as (0) warm-up and take-off, (1) climb (2) Cruise (3) loiter and

(4) landing.

Similarly, the aircraft weight at end of each mission is denoted by Wi, Denoting i th

segment as mission segment weight.

Wo = Beginning airplane weight (Take-off gross weight)

W1 + Weight of the airplane at end of warm-up and take-offW2 = Weight of the airplane at end of climb

W3 = Weight of the airplane at end of cruise

W4 = Weight of the airplane at end of loiterW5 = Weight of the airplane at end of landing

Wx / Wo = W5 / Wo = (W1 / Wo) X( W2 / W1) X (W3 / W2) X( W4 / W3) ..(W5 / W4)

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So in general it can be written as:

Wx / Wo = Wi / Wo = (W1/Wo) X( W2/ W1) X (W3/ W2) X( W4/W3). Wi / Wi 1)

Warm-up/take-off, climb and lending weight fractions:-

The warm-up, take-off and landing weight fractions can be estimated historically

from Table-2.

Table-2 Historical mission segment Weight fractions

(Wi / Wi-1)

Warm up and takeoff 0.970

Climb 0.985

Landing 0.995

Specific fuel consumption (C):-It is the rate of fuel consumption divided by the resulting thrust. Typical values

are depicted in Table-3 and Table-4 for jet and propeller aircrafts respectively. If theaircraft is propeller, then C should be replaced by C = C bhp V / (550p)

Table-3 Specific fuel consumption (C)

Typical jet SFCs Cruise Loiter

Pure turbojet 0.9 0.8

Low-bypass turbofan 0.8 0.7High-bypass turbofan 0.5 0.4

Table-4 Propeller specific fuel consumption (C bhp)

Propeller: C = C bhp V /(550p)

Typical C bhp and p

Cruise Loiter

Piston-prop (fixed pitch) 0.4 / 0.8 0.5 / 0.7

Piston prop (variable pitch) 0.4 / 0.8 0.5 / 0.8

Turboprop 0.5 / 0.8 0.6 / 0.8

Cruise Segment weight fraction:-Weight fraction for cruise segment is found using Breguet range formula:

R = V (L /D)/C In (Wi 1 / Wi) R= range. C= specific fuel consumption

Wi / Wi-1 = exp(- RC/V(L / D)) V= velocity. L/D= left to drag ratio

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Loiter segment weight fraction:-Weight fraction for loiter segment is found using Endurance formula.

E = (L /D)/ C ln (Wi-1/Wi) E= Endurance or loiter time,C= specific fuel consumption

Wi / Wi-1 = exp (- EC/ (L/D)) V = Velocity L/D = lift to drag ratio

The most efficient cruise is velocity for propeller aircraft occurs at velocity

yielding max L/D, where as for the most efficient cruise for a jet aircraft occurs at

slightly at a higher velocity yielding an L/D of 86.6% of the maximum L/D.

Type of aircraft Cruise Loiter

Jet 0.866 (L/D) max L/D max

Propeller L/D max 0.866 (L/D) max

For any mission segment i the mission segment weight fraction is expressed asWi/Wi-1. Wx (Assuming x segments are present for total mission profile) is the aircraft

weight at end of the mission. Wx / Wo ratio can be used to calculate fuel fraction.Wf / Wo = 1- (Wx / Wo)At the end of the mission, the fuel tanks are not completed empty, typically a 6%

allowance is made for reserve and trapped fuel.

Wf / Wo = 1.06 {1 (Wx / Wo) }

Estimate of Gross weight at take-off (Wo) :-We / Wo is function of Wo, Wf / Wo is also a function of Wo. Wo is calculated

from equation (1) through process of iteration. Wo is taken a guess value and, then RHSvalue of equation (1) is calculated which should match the value of assumed, if it doesnt

increment the assumed by some value and iterate it. This process is continued till the

absolute difference of RHS value and assumed value is the least of that the iteration

stepwill be your nearest solution.

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