AircrafDESIGN by S

Preliminary design and sizing of a large civilian aircraft

(based on the mission profile of Boeing 787-8 Dream Liner)

!

By Sergejs Svircenkovs DEN6305 Aircraft Design

2014/15

Abstract

Design of the aircraft is a very complicated process involving several different areas such as aerodynamics, propulsion, stability, structural analysis etc, put together in order to achieve intended design goal and be sellable and attractive to customers in future.

Needless to say that, the developing aircraft must satisfy all Federal Aviation Regulations (FAR), which is a list of defined performance characteristics and are primary constraints in the preliminary sizing. Based on the FAR 25 (Airworthiness Standards: Transport Category Airlines) regulation, the following work aims to show the preliminary sizing of the recently developed Boeing 787-8 Dream Liner. As that is a preliminary sizing, the analysis required a number of estimation, which were based on the given tables of same category aircraft, and are included in the appendix.

Upon the completed preliminary analysis and sensitivity analysis, collected data and results were summarised in the result section. The discussion section briefly states further related work and latter stages of the design process.

2

ContentsPreliminary design and sizing of a large civilian aircraft 1 ...........................

Abstract 2 .......................................................................................................

Contents 3 .....................................................................................................List of Tables 5 ...............................................................................................

List of Figures 6 .............................................................................................

List of symbols 7 ............................................................................................

1.Preliminary Sizing 8 .................................................................................1.1. Introduction 8 ..............................................................................................

1.1. Report Structure 8 .......................................................................................

1.2. Mission overview 8 .....................................................................................

1.3. Initial Calculations 9 ...................................................................................

1.4. Empty Weight Estimation 10 ......................................................................

1.5. Landing Weight Estimation 10 ...................................................................

1.6. Fuel Weight Fractions 11 ............................................................................2. Sensitivity Analysis 13 ...........................................................................

2.1. Sensitivity to empty weight 13 ...................................................................

2.2. Sensitivity to payload 13 ............................................................................

2.3. Sensitivity to range 13 ................................................................................

2.4. Sensitivity to endurance 13 .........................................................................

2.5. Sensitivity to speed 13 ................................................................................

2.6. Sensitivity to specific fuel consumption 13 ................................................

2.7. Sensitivity to lift to drag ratio 14 ................................................................

3. Estimation of Wing Parameters 15 ......................................................3.1. Take-off Distance Requirements 15 ..........................................................

3.2. Landing Distance Requirements 16 ..........................................................

3.3. Drag Polar and FAR 25 requirements 16 ....................................................

3.4. Stall Speed Sizing 17 .................................................................................

3.5. Wing sweep 18 ...........................................................................................

3.7. Wing width 18 .............................................................................................2

4. Climb Sizing 19 ......................................................................................4.1. Take - off Climb Sizing 19 .........................................................................

4.2. Normal Climb 20 .......................................................................................

4.3. Landing Climb Sizing 20 ............................................................................

4.4. Direct Climb Sizing 21 ...............................................................................

5. Cruise Speed Sizing 22 ..........................................................................6. Discussion 23 ..........................................................................................

6.1. Limitations and Further Work 23 ................................................................

7. REFERENCES 24 ................................................................................8. Appendix 25...........................................................................................

2

Preliminary sizing Boeing 787-8 Dream Liner

List of Tables 1. Table 1.3.1 Atmosphere Dependant Parameters for Climb

2. Table 1.3.2 Atmosphere Dependant Parameters for Level Flight

3. Table 1.3.3 Atmosphere Dependant Parameters for Descent

4. Table 1.3.4 Detailed Climb and Descent Profile

5. Table 1.6.1 Suggested and Estimated Mission Fuel Ratios

6. Table 2.1 summary of parameters used in sensitivity analysis

7. Table 3.1.1 Summary of maximum lift coefficients

8. Table 3.1.2 Take-off parameters

9. Table 3.2.1 Landing Wing Loading

10. Table 3.3.1 Landing Wing Loading

11. Table 3.3.2 Drag Coefficient Constants

12. Table 3.4.1 Take-off Stall Speed / kts sigma = 1

13. Table 3.4.2 Cruise Stall Speed / kts sigma = 0.735 (35,000ft)

14. Table 3.4.3 Landing Stall Speed / kts sigma = 1

15. Table 4.1.1 Initial Take - off Climb Power to Weight Ratios

16. Table 4.1.2 Take - off Climb Power to Weight Ratios

17. Table 4.2.1 Normal Climb Power to Weight Ratios

18. Table 4.3.1 Approach Climb Power to Weight Ratios

19. Table 4.3.2 Balked Landing Climb Power to Weight Ratios

20. Table 5.1 Thrust to Weight Ratios for Cruise

21. Table 8.01 Standar Atmosphere

22. Table 8.02 Preliminary Weight Characteristics

23. Table 8.03 Preliminary Fuel System

24. Table 8.04 Suggested Mission Fuel Fractions

25. Table 8.05 Suggested Coefficient of Lift and Drag

26. Table 8.06 Suggested Cruise Performance Chart

27. Table 8.07 Suggested Loiter Data Performance Chart

28. Table 8.08 Equivalent skin friction coefficient values for different aircraft categories

29. Table 8.09 Drag Correction Coefficients

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List of Figures 1. Figure 1.2.1 Mission Profile

2. Figure 3.1.1 Thrust to Weight Ratio versus Wing Loading for Take-off

3. Figure 3.1.2 Thrust to Weight Ratio versus Wing Loading for Landing

4. Figure 3.2.1 Thrust to Weight Ratio versus Wing Loading

5. Figure 4.1.1 Thrust to Weight Ratio versus Wing Loading for Initial Climb

6. Figure 4.1.2 Thrust to Weight Ratio versus Wing Loading for Climb

7. Figure 4.2.1 Thrust to Weight Ratio versus Wing Loading for Normal Climb

8. Figure 4.3.1 Thrust to Weight Ratio versus Wing Loading for Approach

9. Figure 4.3.2 Thrust to Weight Ratio versus Wing Loading for Balked Landing

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List of symbols WTO - Take-off weight Empty weight - WE Weight of all trapped, unusable fuel - WFTO Manufacturer’s empty weight - WME Weight of the crew - WCREW Fixed equipment weight such as: avionics, air-

conditioning, radars, etc - WFIXED Mission fuel weight - WF Reserve fuel weight - WFres Specific fuel consumption - cj Fuel fractions

- Taxi - w1 - Take-off -w2 - Climb to 1500 ft -w3 - Climb to 10000 ft - w4 - Climb to cruise (35000 ft) - w5 - Descent to loiter (10000 ft) - w10 - Reserve Climb to 20000 ft - w11 - Reserve Descent to 10000 ft - w12 - Descent - w13,14,15 - Landing, Taxi and Shut down - w16

Endurance - E Range - R Cruise speed - Vcruise Lift-drag ratio - L/D Fuel mass flow rate - f Climb speed - Vclimb Stall speed - Vs

- Clean configuration - (Vs)CLEAN - Climb configuration - (Vs)CLIMB - Descent configuration - (Vs)D - Landing configuration - (Vs)L

Take-off field length - SFL Landing field length - SL Climb rate - RC Centre of gravity (CG) Lift coefficient - CL

- Clean configuration - (CL)CLEAN - Climb configuration - (CL)CLIMB - Descent configuration - (CL)DESCENT - Landing configuration - (CL)LANDING Bank angle - ß˚´ Wing area - SWING Climb gradient - CGR Climb gradient parameter - CGRP Time to

- Climb to 1500 ft - tCLIMB1500 - Climb to 10000 ft - tCLIMB10000 - Climb to cruise (35000 ft) - tCLIMBCRUISE - Descent to loiter (10000 ft) - tCLIMBLOITER - Reserve Climb to 20000 ft - tCLIMBRES - Reserve Descent to 10000 ft - tDESCENTRES - Descent - tDESCENT

Oswald’s efficiency - e Drag coefficient - CD

- Clean configuration - (CD)CLEAN - Climb configuration - (CD)CLIMB - Descent configuration - (CD)DECSENT - Landing configuration - (CD)LANDING

Atmospheric Parameters - Temperature - T - Pressure - P - Density - ρ

Angle of attack - α Engine thrust - T Wing loading - W/S - Take-off - (W/S)TO - Climb - (W/S)CLIMB - Cruise - (W/S)CRUISE - Descent - (W/S)DESCENT - Landing - (W/S)L Load Factor - N

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1.Preliminary Sizing

!

1.1. Introduction In general to arrive at the aircraft preliminary

parameters two approaches could be used. Firstly, the bottom up methodology is based on some

initially known information of the proposed aircraft which may concern power plant, available materials, or other specific part of an airplane, which will be used in its final appearance. In such way the subsequent design process is directly related to this predefined part and is hugely dependant on it. However it is not always the case, when specific engine or a wing geometry is initially supplied, instead it is far more common to observe when some existing part is shaped or adjust to a required set of parameters, which could be established by a reverse design process.[2][3]

In contrast, the top down method implies that initially there is a given set of requirements, which the aircraft must meet, wherein all the other aircraft parts are left to be chosen based on the estimated aircraft design target, mission specification, an aircraft layout, etc. Although the method does not restrict an aircraft designer in a conceptual point of view, its drawback is an uprising tendency for relatively wide spread in the required component parameters, making the selection of a particular wing shape and/or power plant type and/or its arrangement an open question. [2][4]

Consequently, along the design process both methods are usually implemented at the same time. In real life, among the aircraft intrinsic characteristics, the aspects of its development and manufacturing costs turn to be of the same importance. For an aircraft manufacturer the former type of the cost features much higher degree of uncertainty, as it is unknown how much of the budget will it take. More importantly, it should be noted, that during the preliminary estimations of the aircraft’s design, one could expect an advances in both materials and technology, which may completely reshape calculated design envelope or even the whole aircraft concept.[6]

For that reason, a clear margin should be drawn, to minimise unexpected aspects in all design areas. Therefore it common to observe, that the new aircraft in a category is very similar to a previous one.

1.1. Report Structure To proceed with the first stages of the aircraft design,

it is important to establish initial constraint envelope for the proposed aircraft, based on the typical mission profile, Flight Aviation Regulation (FAR), available material, capacity etc. Ideally, after all requirements are meet, the design should offer an advantage in some of the parameters, comparing to alternative aircraft designs in order to be attractive for potential buyers.

In the following work only the mission layout and FAR regulations were two major constraints in the numerically evaluations. The analysis stages included weight sizing, sensitivity analysis, landing and take-off estimations and some of the manoeuvring margin estimations.

To avoid ambiguity, all values which were required for calculations were given along the analysis, however should the reader be interested in original sources, the additional information about the tables and charts used was provided in the appendix section.

Apart from that an overview table of all collected results was added in the beginning of the discussion section. The discussion on the other hand, featured limitations of the represented methods and and suggested their applicability with respect to the further related work.

1.2. Mission overview The mission layout used for the following analysis

comprised several typical flight phases, represented by the stage list and figure 1.0 below. The mission profile of commercial flight offered some room for an emergency and subsequent diversion to an alternate aerodrome.

1) Engine start up 2) Taxi 3) Take off and initial climb out to 35 ft 4) Climb to 1500 ft. 5) Climb to 10000 ft. 6) Climb to 35000 ft. 7) Cruise at 35000 ft. and mach number 0.85 8) Descent to 10000 ft. 9) 30 min loiter at 10000 ft. 10) Ascent back to 20000 ft. 11) 200 nm to alternate aerodrome 12) Descent to 10000 ft. 13) Descent to 1500 ft. 14) Descent to 50 ft. 15) Landing phase 16) Taxi and engine shut down

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Figure 1.2.1

! Take-off and landing aerodromes were suggested

both to be at the sea level (S.L.) and required take-off and landing distances were required to be 9,255 ft. and 4,986 ft. respectively. Cruise range during stage 7 is 8345 nm. An aircraft configuration should involve two turbofan engines, 40% composite structure, certification FAR25, 224 passengers, 2 pilots, 6 cabin attendants. It was also suggested to add additional 20 lbs per passenger to account for a baggage.[1]

An additional alternate flight including stages 10 and 12 was considered to be a reserve fuel.

1.3. Initial Calculations As the mission profile includes operations at various

altitudes, appropriate corrections were made to the aircraft velocities, lift to drag ratios, mach number and specific fuel consumption ( s.f.c. ). Following set of tables for climb, cruise and descent parameters was achieved, based on the standard atmosphere parameters and tables 8.02, 8.04 and 8.05 in the Appendix section. Note that the speed values are average for that category. Further analysis will determine more accurate speeds.

Mach number values other than a given cruise mach number were calculated using the following formula:

! 1.3.01 [3] !

Here values for the sound speed at a corresponding height were taken from the standard atmosphere table.

On the other hand, values for different speeds were estimated based on the aircrafts of the same category.[2]

It is important to pay attention to s.f.c. and L/D ratio values. Obtained from the table 8.08 their variations interpret strong dependence on both altitude and configuration.[1][2]

Referring to the performance and procedures of similar category aircrafts it was estimated that the vertical ascend and descent speeds from S.L. to 20,000 ft is 1,800 feet per minute and that from 20,000 to 35,000 is 1,000 fpm, which means that for a represented flight velocities, total distance covered during the ascent and descent stages excluding stages 10 and 12 is about 340 nm. Total distance for the reserve climb and descent is 59.2 nm. A more detailed overview of the vertical profile is given in the table 1.3.

Table 1.3.1 Atmosphere Dependant Parameters for Climb

Altitude / ft Speed /kts Mach number Specific fuel

consumption / lb/hr/lbf L/D

35 - 1,500 170 0.26 0.705 16.58

1,500 - 10,000 255 0.40 0.626 21.52

10,000 - 20,000 320 0.51 0.605 21.19

20,000 - 35,000 475 0.80 0.557 21.37

Table 1.3.2 Atmosphere Dependant Parameters for Level Flight

Altitude / ft Speed /kts Mach number

Specific fuel consumption /

lb/hr/lbf

Lift to drag ratio

S.L. 120 (take-off) 0.18 0.699 14.15

10,000 230 (loiter) 0.36 0.630 19.48

20,000 340 (alternate) 0.55 0.579 18.84

35,000 490 (cruise) 0.85 0.527 20.83

Table 1.3.3 Atmosphere Dependant Parameters for Descent

Altitude / ft Speed /kts Mach number

Specific fuel consumption /

lb/hr/lbf

Lift to drag ratio

35,000 - 20,000 480 0.81 0.527 18.84

20,000 - 10,000 320 0.51 0.579 19.48

10,000 - 1,500 290 0.45 0.577 7.92

1,500 - S.L. 190 0.29 0.633 6.96

M = Vγ RT

Table 1.3.4 Detailed Climb and Descent Profile

Altitude / ft Delta in height / ft

Vertical climb/descent

rate / fpm

Horizontal distance /

nm

Weight Fraction

for Climb

Weight Fraction

for Descent

S.L. - 1,500 1,500

1,800

2.4 0.999 0.999

1,500 - 10,000 8,500 20.0 0.998 0.995

10,000 - 20,000 10,000 29.6 0.997 0.997

20,000 - 35,000 15,000 1,000 118.0 0.994 0.993

Total trip and reserve climb/descent distance / nm 399.2

0.988 0.984

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Corresponding horizontal distances were substituted into the transformed range equation:

1.3.02 [1]

!

This gave a perspective of the mission fuel fractions. Surprisingly, the fraction for the descent indicates a higher amount of burned fuel. This is caused by the relatively low lift to drag ratio at approach phases. Comparing total fractions to the table 8.04 one could spot a notable overall fuel savings, which are explained by the fact, that the table was based on the older aircrafts.

To finish initial estimations it was suggested to calculate combined fuel fraction for both taxi and take-off. In order to do this, it was found that on average time spent on the taxi and ground operations is about 20 minutes, hence using an endurance equation:

1.3.03 [1]

!

1.3.04

!

It could be calculated that the corresponding fuel fraction is 0.984, which is slightly more than 0.985 given in the table 8.04, again which could be explained by increased air traffic intensity since the release date of the table.

1.4. Empty Weight Estimation It could be argued that among the other input

parameters the empty weight of the aircraft is one of the most important, as it portrays aircraft size and capacity and performance. The initial empty weight value was suggested to be around 280,000 lbs. It was also assumed that this value represents weight of an aircraft, which is made entirely out of aluminium. To account for 40% composite structure it was suggested to convert this fraction off aluminium into carbon fibre composite material as it is a suitable candidate. Hence the simple relationship could be derived based on the fractional amount of material and density ratio between aluminium and composite:

1.4.01

!

Taking the aluminium and composite densities as 2810 and 1820 kgm-3 respectively, the new weight figure is then 239,200 lb.

1.5. Landing Weight Estimation As the aircraft landing weight strongly depends on

the specific mission and fuel burn, before the actual landing weight calculation, it was suggested to state the limiting values for the mission fuel fraction and rough estimations for trip fuel. These were obtained using table 8.04 and next equation:

1.5.01 [1] !

Substituting maximum take-off and landing weights from the table, leads to:

1.5.02

!

Now if we use equation: 1.5.03 [1]

!

It could be derived that the maximum fuel, which can be taken aboard is about 125,000 lbs provided that the aircraft is fully loaded. Alternatively, with an empty weight value of 239,200 lbs, using a more detailed equation:

1.5.04 [1] !

Where, payload and crew weights are given from initial requirements. Referring to the table 8.03 unusable/trapped fuel weight could estimated that, leading to:

1.5.05 !

Consequently, in order to meet payload requirements and not exceed suggested maximum weight of 502,500 lbs, mission fuel weight should be less than 221,020 lbs.

Now comparing it to the suggested value of the specific fuel consumption in litres per 100 km of flight and passenger, additional limits could be established on the fuel required to achieve total range of 8545 nm ( including reserve ). Converting suggested value of 2.67 litres/100km per passenger into lbs/nm:

1.5.06 [4]

!

winitial

w final

= e−

Rcj

V LD

⎛⎝⎜

⎞⎠⎟

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

E = 1cj

LD

⎛⎝⎜

⎞⎠⎟ ln

w8w9

⎛⎝⎜

⎞⎠⎟

wfinal

winitial

= e−

EcjLD

⎛⎝⎜

⎞⎠⎟

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

WE( )NEW = WE( )OLD 0.6 + 0.4 *ρcomposite

ρalumin ium

⎛⎝⎜

⎞⎠⎟

WTOM ff =WL

M ff =380,000502,500

= 0.756

WFused = 1−M ff( )WTO

WTO =WME +WFEQ +Wtfo

WE

! "### $###+Wcrew +WFused +WFres +WPL

WF =WTO − 239,200WE

!"# $# + 224 *(175 + 20)Passangers

! "## $## + 8*175Crew!"$ = 221,020lbs

P = 2.67 litres100kmpassenger

= 19.64 lbsnm

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Hence for the full required range the weight of the fuel should be at least:

1.5.07 !

Should the new value be found, it must satisfy those two boundary limits. [5]

1.6. Fuel Weight Fractions In the previous section there were already given

some examples of fuel weight fractions, which were based on the altitude profile table. However for the further analysis it is essential to obtain all remaining fractions, as it will allow to estimate take-off weight and will be used in the further analysis. The equation which will be used for that purpose, is transformed equation 1.5.04 and has the view:

1.12

!

Where reserved fuel fraction and unusable fuel fraction are:

1.13 [1]

!

1.14 [1]

!

On other hand mission fuel fraction may be written in a following format:

1.14 [1]

!

Where i represents particular stage. For example number 4 corresponds to the climb from S.L. to 1,500 ft, whereas number 16 is a landing weight. The following table shows two sets of fuel fractions for each stage.[1]

In terms of the analysis it was thought to use calculated fractions whenever possible, although for the landing & taxi stage fuel fraction suggested value was used.

To estimate first cruise fuel fraction at 35,000 ft marked with red in the table, equation 1.02 was used.

An example of calculation: 1.6.01

!

The reason for subtraction in the range term is explained by the horizontal distances travelled during both climb and descent stages. Similarly, an example of fuel fraction for diversion at 20,000 ft to looks like:

1.6.02

!

P*Rtotal = 19.64 *8,545 = 167,823.8lbs

WTO = WE +WPL +WCrew

1− 1−M ff( ) 1+MFres( )−Mtfo

=WTO

Mres =WFres

WFused

Mtfo =Wtfo

WTO

M ff =w1w16

wi+1

wii=1

15

∏

Table 1.6.1 Suggested and Estimated Mission Fuel Ratios

Stage nameCalculated

Weight Fraction

Suggested Weight Fractions

1 Engine Start up

0.984

0.990

2 Taxi 0.990

3 Take off and initial climb out to 35 ft 0.995

4 Climb to 1,500 ft 0.999 0.980

5 Climb to 10,000 ft 0.998 0.980

6 Climb to 35,000 ft 0.991 0.980

7 Cruise at 35,000 0.662 -

8 Descent to 10,000 ft 0.990 0.990

9 30 min loiter 0.984 -

10 Ascent to 20,000 ft 0.997 0.980

11 200 nm flight to alternate 0.987 -

12 Descent to 10,000 ft 0.997 0.990

13 Descent to 1,500 ft 0.995 0.990

14 Descent to S.L. 0.999 0.990

15 Landing, Taxi and Shutdown - 0.992

16 Trip Fuel Fraction 0.618 Reserve fuel fraction* 0.982

w7w6

= e−

Rcj

V LD

⎛⎝⎜

⎞⎠⎟

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

= exp −8345 − 340( )*0.527

490*20.83⎛⎝⎜

⎞⎠⎟= 0.662

w11w10

= e−

Rcj

V LD

⎛⎝⎜

⎞⎠⎟

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

= exp −200 − 59.2( )*0.579340*18.84

⎛⎝⎜

⎞⎠⎟= 0.987

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Based on the requirements, loiter activity is 30 minutes. So the weight fraction is then:

1.6.03

!

Since all the weight fractions are now estimated it is possible to find mission fuel fraction and hence verify whether it satisfies limiting values, imposed earlier.

1.6.04

!

Fortunately, the mission fuel fraction did not exceeded the limit. Next equation could be used to determine how relationship between take-off weight and the total fuel burned.

1.6.05 [1] !

Considering a reserve fuel weight, one should look for the product of fuel fraction representing the accent from 10,000 ft to 20,000 ft, 200 nm flight to alternate and descent back to 10,000ft. Hence it could be shown that the fuel fraction illustrating how much fuel should be burned during the reserve stage is:

1.6.06

!

1.6.07 !

Combining it with previous equation and comparing it to expression 1.6.05 it could written that:

1.6.08

!

On the other hand, the value for unusable fuel to take-off weight ratio was evaluated to be 0.00139 based on the table 8.03.

Finally, returning back to the equation 1.5.04 and substituting the values for empty and payload weights it could be shown that:

1.6.09 !

Which means that for the mission profile selected, take-off weight is below maximum preliminary weight. Using equation 1.6.06 and 1.6.07 trip and reserve fuel

weights are 190,132 lbs and 8,708 lbs, which again is acceptable as it is in the range derived earlier.

With respect to the following section the next set of equations should be satisfied:

1.6.10 [1]

!

Here the values A and B were suggested to be 0.0833 and 1.0383 respectively. However it is important to verify wether these are appropriate. Moreover, should there be a mismatch caused by selected values, it will indicate reliability of further resutls. Hence it could be written that:

1.6.11

!

Which implies that for values selected the expression shows an average accuracy.

w9w8

= exp −E *cjLD

⎛⎝⎜

⎞⎠⎟

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟= exp − 0.5*0.630

19.48⎛⎝⎜

⎞⎠⎟ = 0.984

M ff = 0.984 *0.999*0.998*0.991*0.662*0.990*0.984 *0.997*0.987*0.997*0.9950.999 = 0.607

WFused = 1−M ff( )WTO = 0.393WTO

WFres = 1−MFRES*( )WTO

WFres = 0.018WTO

Mres =WFres

WFused

=1−MFRES

*( )WTO

1−M ff( )WTO

= 0.0180.393

= 0.0458

WTO = 239,200 + 45,0800.5876

C!"#

= 483,800lbs

log10 WTO( ) = B log10 WE( )+ Alog10 WTO( ) = B log10 CWTO − D( )+ AC = 1− (1−M ff ) 1+Mres( )−Mtfo

D =Wpayload +Wcrew

⎧

⎨

⎪⎪⎪

⎩

⎪⎪⎪

log10 483,800( ) ∼ 0.0833+1.0383log10 239,200( ) 5.685 ≈ 5.67

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Sensitivity Analysis Boeing 787-8 Dream Liner

2. Sensitivity Analysis

! The purpose of the sensitivity analysis is to

determine, how the take-off weight is correlated with regards to the variations in other parameters such as: payload, empty weight, range, endurance etc. These estimations will explore the parameters, which have the highest influence on the take-off weight characteristics.

To begin, the expression 1.6.10 is a good starting point. By differentiating it with respect to some variable y (to be selected arbitrary) gives:

2.01 [1]

!

Should y be replaced with some other parameter it is possible to arrive at the following relationships for the take-off mass sensitivity.

However before that, it was suggested to summarise all relevant parameters, which will be used further in the sensitivity calculations.

2.1. Sensitivity to empty weight Could be calculated as:

2.1.01 [1]

!

Hence for every 1 lbs increase in empty weight, the take-off weight will be increase by about 2.1 lbs.

2.2. Sensitivity to payload Could be calculated as:

2.2.01 [1]

!

2.3. Sensitivity to range 2.3.01 [1]

!

For cruise at 35,000 ft: 2.3.01

!

2.4. Sensitivity to endurance Could be calculated as:

2.4.01 [1] !

2.4.02 !

2.5. Sensitivity to speed Could be calculated as:

2.5.01 [1] !

2.5.02

!

2.6. Sensitivity to specific fuel consumption

Could be calculated as: 2.6.01 [1]

!

2.6.02

!

∂WTO

∂y=BW 2

TO∂C∂y

− BWTO∂D∂y

C(1− B)WTO − D

Table 2.1 summary of parameters used in sensitivity analysis

A 0.083 WTO 484,800 lbs

B 1.0383 WE 239,200 lbs

C 0.599 Mff 0.618

D 45,080 lbs F 2,806,289 lbf

R 8,345 nm L/D 20.83

VCruise 35,000 ft 490 cj 0.527

MFres 0.0458

∂WTO

∂WE

= BWTO

WE

= 2.104

∂WTO

∂WPl

= − BWTO

C 1− B( )WTO − D= 8.956

∂WTO

∂R= −

BW 2TO 1+MFres( )M ff

C(1− B)WTO − DF

! "#### $####*

cj

VcruiseLD

⎛⎝⎜

⎞⎠⎟

∂WTO

∂Range⎛⎝⎜

⎞⎠⎟V=490kts

= 144.9lbs / nm

∂WTO

∂E= F *

cjLD

⎛⎝⎜

⎞⎠⎟

∂WTO

∂E= 71,000.0lbs / h

∂WTO

∂Vcruise= −F *

Rcj

Vcruise2 L

D⎛⎝⎜

⎞⎠⎟

∂WTO

∂Vcruise= −2,467.7lbs / kts

∂WTO

∂cj= F * R

VcruiseLD

⎛⎝⎜

⎞⎠⎟

∂WTO

∂cj= 2,294,422lbf ⋅hr

Sensitivity Analysis Boeing 787-8 Dream Liner

2.7. Sensitivity to lift to drag ratio Could be calculated as:

2.7.01 [1]

!

2.7.02 !

By completing such exercise, it could be seen that among the other parameters only lift to drag ratio and speed magnifications may result in the decrease of the total weight. In contrast any adjustments to the specific fuel consumption will lead to the significant changes in take-off weight. [2]

∂WTO

∂ LD

⎛⎝⎜

⎞⎠⎟= −F *

Rcj

VcruiseLD

⎛⎝⎜

⎞⎠⎟2

∂WTO

∂ LD

⎛⎝⎜

⎞⎠⎟= −58,048.99lbs

Estimation of Wing Parameters Boeing 787-8 Dream Liner

3. Estimation of Wing Parameters

! Since the initial weight estimations were made, it is

possible to determine preliminary wing parameters and take-off characteristics. To begin it is essential to pay attention to FAR and mission requirement for take-off.

3.1. Take-off Distance Requirements

The figure 3.1.1 shows how the take-off distances are classified.

Figure 3.1.1

! For example, the total take-off distance includes

both ground run and initial climbing to 50 ft. Taking into account correlation represented on Figure 8.06 given in the Appendix the take-off distance could be correlated to the wing loading and power ratio in a following way:

3.1.01 [1]

!

Apart from that, referring to the table 3.1.1 gives a clue on what could be the maximum lift coefficients depending on a particular configuration.

Based on the mission requirements and atmosphere characteristics at sea level:

3.1.02 [1]

!

Hence, the take-off equation: 3.1.03

!

3.1.04

!

By making wing loading an arbitrary number from 40 to 120, one can arrive at the following model.

The following graph represents obtained T/W ratios

!

STOFL = 37.5

WS

⎛⎝⎜

⎞⎠⎟ TO

σ ρ

σ T

CLmax( )TO

TW

⎛⎝⎜

⎞⎠⎟ TO

= 37.5TOP25

Table 3.1.1 Summary of maximum lift coefficients

Take-off Configuration 1.6 - 2.2

Clean configuration 1.2 - 1.8

Landing configuration 1.8 - 2.8

σ ρ =ρρsea

= 1

σ = TseaTact

*σ ρ = 1

9225 ≤ 37.5

WS

⎛⎝⎜

⎞⎠⎟ TO

CLmax( )TO

TW

⎛⎝⎜

⎞⎠⎟ TO

TW

⎛⎝⎜

⎞⎠⎟ TO

≥ 0.004052

WS

⎛⎝⎜

⎞⎠⎟ TO

CLmax( )TO

Table 3.1.2 Take-off parameters

1.6 1.8 2.0 2.2

40 0.1013 0.0900 0.0810 0.0737

60 0.1520 0.1351 0.1216 0.1105

80 0.2026 0.1801 0.1621 0.1473

100 0.2533 0.2251 0.2026 0.1842

120 0.3039 0.2701 0.2431 0.2210

! WS

⎛⎝⎜

⎞⎠⎟ TO

! CLmax( )TO

Figure 3.1.2

(T/W

) tak

e-of

f

0

0.1

0.2

0.3

0.4

(W/S) take-off / lbs/ft^20 30 60 90 120

Cl = 1.6Cl = 1.8Cl = 2.0Cl = 2.2

Met Not met


3.2. Landing Distance Requirements

Figure 3.1.1 illustrates how the landing distances are defined. Relationship between two distances and speeds:

3.2.01 [1]

!

3.2.02 [1] !

The correlation between landing field length and approach speed may be written as:

3.2.03 [1]

!

Wing loading could be related to the stall speed in this way:

3.2.04 [1]

!

Combination of two equations together with the landing airport length requirements gives the next equation:

3.2.05 [1]

! !

Hence, it could be derived that: 3.3.06

!

By substituting several values for lift coefficient it is possible to achieve following table.

! Note that the wing loadings calculated for landing

were transformed into take-off wing loading via trip fuel ratio given in the table 1.4.

On the power to weight ratio versus wing loading diagram these values could be represented as vertical lines. Note that in order to met landing requirements the wing loading should be not more than 97.11 lbd/ft2.

3.3. Drag Polar and FAR 25 requirements

The drag estimations are based on the next two relationships:

3.3.01 [1]

!

Where: 3.3.02 [2]

! !

Furthermore the relationship between these two values was achieved after statistical analysis and may be written as:

3.3.03 [1]

!

From the table 8.07 it found that for transport category aircrafts value for c.f.e is 0.0030, consequently based on the tables 4.2 and 4.3 the values for a, b, c, d constants are -2.5229, 1, 0.0199 and 0.7531. Using, the values obtained it can be estimated that:

3.3.04

!

SFL =10.6

SL

VA = 1.3VSL

SFL = 0.3VA2

VSL2 =

0.701165 WL

⎛⎝⎜

⎞⎠⎟ L

σ ρρS .L . CLmax( )L

SFL0.507

=0.701165 W

L⎛⎝⎜

⎞⎠⎟ L

σ ρρS .L . CLmax( )L

≤ 49860.507

WL

⎛⎝⎜

⎞⎠⎟ L

≤ 33.34 CLmax( )L

Table 3.2.1 Landing Wing Loading

1.8 60.01 97.11

2.2 73.35 118.69

2.4 80.02 129.48

2.6 86.68 140.27

2.8 93.35 151.06

! CLmax( )L

� WS

⎛⎝⎜

⎞⎠⎟ L

� WS

⎛⎝⎜

⎞⎠⎟ TO

Figure 3.2.1

(T/W

) tak

e-of

f

0

0.05

0.1

0.15

0.2

(W/S) take-off / lbs/ft^20 40 80 120 160

Cl = 1.8, W/S ≤ 97.11Cl = 2.2, W/S ≤ 118.69Cl = 2.4, W/S ≤ 129.48Cl = 2.6, W/S ≤ 140.27Cl = 2.8, W/S ≤ 151.06

CD = CD0+ CL

2

πAe+∆CD0

CD0= Cfe

SwetS

= fS

log10 f( ) = a + b log10 Swet( )log10 Swet( ) = c + d log10 WTO( )

f = 10 a+b c+d log10 WTO( )( )( )

Met Not met


On the other hand values for wing surface area can be obtained referring to the arbitrary wing loading values as shown:

3.3.05

! !

Now if returning back to the equation 3.3.03 for a range of wing loadings one could arrive at the following table.

Note that three columns on the right represent correction terms for zero drag coefficients, depending on a configuration. Now if we recall values for Oswald’s efficiency from table 8.10 and assuming that the aspect ratio is about 10, which is true for that type of category, resulting drag coefficients depending on the parameters stated a priori could be written as:

3.3.06 [1]

!

From data represented in the table 3.3 it could be seen, that the maximum wing loading established by the stalling speed, landing and take-off requirements leads to the surface area of 4,982 ft2.

So the drag coefficient as a function of lift coefficient could be represented as set of equation for several flight configurations as follows:

3.3.07

!

3.4. Stall Speed Sizing For that type of sizing it is common to have some

initial stall speed requirements, otherwise it is difficult to establish additional limits on wing loading value. For this reason it was suggested to use following equation to arrive at stall speeds given in table

3.4.01 [1]

!

Here it should be noted that value of stall speed strongly depends on the aircraft configuration and wing loading. Hence for a range of wing loading and maximum lift coefficients it is possible to derive following three tables for take-off, cruise and landing configurations.

WTO

S= 100⇒ S = 4,838 ft 2 CD0

Table 3.3.1 Landing Wing Loading

Wing Surface /ft2

Zero Drag Coefficient correction term

Clean Take-off Landing Landing gear

60 8,063.3 0.00744

0 0.010 -0.020 0.055 - 0.075 0.015 - 0.025

80 6,047.5 0.00992

100 4,838.0 0.01240

120 4,031.7 0.01488

140 3,455.7 0.01736

160 3,023.8 0.01984

180 2,687.8 0.02232

! WS

⎛⎝⎜

⎞⎠⎟ L

!CD0

CD( )TAKE-OFF, GEAR DOWN = A1 + B1CL2

CD( )TAKE-OFF, GEAR UP = A2 + B2CL2

CD( )CLEAN = A3 + B3CL2

CD( )LANDING, GEAR UP = A4 + B4CL2

CD( )LANDING GEAR DOWN = A5 + B5CL2

⎧

⎨

⎪⎪⎪⎪

⎩

⎪⎪⎪⎪

CD( )TAKE-OFF, GEAR DOWN = 0.047 + 0.0411CL2

CD( )TAKE-OFF, GEAR UP = 0.027 + 0.0411CL2

CD( )CLEAN = 0.012 + 0.0386CL2

CD( )LANDING, GEAR UP = 0.077 + 0.0439CL2

CD( )LANDING GEAR DOWN = 0.097 + 0.0439CL2

⎧

⎨

⎪⎪⎪⎪

⎩

⎪⎪⎪⎪

Table 3.3.2 Drag Coefficient Constants

Config. Const.Wing Loading

1/∆πAe

60 80 100 120 140 160 180

Take-off Gear

Down

A1 0.0424 0.0449 0.0474 0.0499 0.0524 0.0548 0.0573 —

B1 No Effect 0.0411

Take-off Up

A2 0.0224 0.0249 0.0274 0.0299 0.0324 0.0348 0.0373 —

B2 No Effect 0.0411

CleanA3 0.0074 0.0099 0.0124 0.0149 0.0174 0.0198 0.0223 —

B3 No Effect 0.0386

Landing Gear Up

A4 0.0774 0.0799 0.0824 0.0849 0.0874 0.0898 0.0923 —

B4 No Effect 0.0439

Landing Gear

Down

A5 0.0974 0.0999 0.1024 0.1049 0.1074 0.1098 0.1123 —

B5 No Effect 0.0439

VStall =

WS

⎛⎝⎜

⎞⎠⎟ Pa

ρS .LσCLmax

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

12

Table 3.4.1 Take-off Stall Speed / kts sigma = 1

1.6 1.8 2.0 2.2

60 86 80 74 70

80 99 92 86 81

100 111 103 96 91

120 122 113 105 99

140 131 122 114 107

160 140 130 122 115

! WS

⎛⎝⎜

⎞⎠⎟ TO

! CLmax( )TO


From the table it could be seen that the take-off speed lies some where between 80 and 100 kts, however it is preferred to chose higher wing loadings and and lift coefficient as they are more realistic with relatively high take-off weight.

From the cruise data it could be argued that it is more reasonable to maintain moderate wing loading, but select low lift coefficient, to allow considerable few savings.

Finally, for the landing stage significant reductions in corresponding stall speed could be achieved if the lift coefficient would be maximised.

The reason why it was suggested to stick to one value of wing loading throughout all three stages, as in other case changes in wing loading would result in induced fatigue stress of the wings during the flight. Such stress is dangerous as it produces structural cracks on the micro level, which are often hidden from visual inspection. [2][4]

3.5. Wing sweep Earlier during the analysis of the drag polar, it was

assumed that the aspect ratio is about 10. Such value was chosen based on the aircraft’s category.

In this chapter the focus was placed primarily on the selection of a wing profile, flaps configuration and as the result determination of required sweep angle, in order to promote transition free flight at mach number of 0.85.

As the starting point it was suggested to use one of the NACA supercritical profiles such as SC(2)-0612. Its critical mach number is about 0.78. Maximum lift

coefficient is about 1.5 and zero drag coefficient is around 0.009. The information regrind critical mach number give a limit for minimum sweep angle in terms of the following equation:

3.5.01 [5] !

Rearranging for sweep angle gives: 3.5.02 [5]

!

Substituting appropriate value for critical mach number and cruise mach number gives:

3.5.03 [6] !

Hence to provide 5% margin for cruise mach number, the sweep angle is therefore:

3.5.04 [5]

!

With respect to the flap configuration, as the variation of lift coefficient was estimated to lie between 1.2 and 2.8, this requires a minimum of 40 - 50 % increase in the lift coefficient. However as it was derived above the transonic flight condition requires a sweep angle to be about 32 degrees. Hence it could be written that:

3.5.05[1] !

Substituting required number of 2.8 for lift coefficient will require a wing, which is capable of producing 3.3 as the maximum lift coefficient. The way it could be achieve is to use Fowler type of flaps, as they are able to increase the lift coefficient up to 60 - 70%.

3.7. Wing width As it was discovered earlier, higher wing loadings

allow to use lower wing surface areas, however it is only true when the wing’s maximum lift coefficient is sufficient to allow such wing loading with respect to the landing and take-off requirements.

For the wing width estimations it was proposed to stick to the wing loading value of 120 lbf/ft2 and use 10 for the Aspect ratio, gives surface area of 4031 ft2 and around 200 ft as the wing span. Assuming the wing has a trapezium planform it could be derived that:

3.7.01

! ; !

So the central (b) and edge lengths are about 29.5 and 10.8 ft.

Table 3.4.2 Cruise Stall Speed / kts sigma = 0.735 (35,000ft)

1.2 1.4 1.6 1.8

60 100 93 87 82

80 115 107 100 94

100 129 120 112 105

120 141 131 122 115

140 153 141 132 125

160 163 151 141 133

! WS

⎛⎝⎜

⎞⎠⎟ TO

!CLmax( )

TO

Table 3.4.3 Landing Stall Speed / kts sigma = 1

1.8 2.2 2.5 2.8

60 70 63 60 56

80 81 73 69 65

100 91 82 77 73

120 99 90 84 80

140 107 97 91 86

160 115 104 97 92

! WS

⎛⎝⎜

⎞⎠⎟ TO

! CLmax( )TO

M∞ cos Λ( ) ≤ Mcrit

Λ ≤ cos−1 Mcrit

M∞

⎛⎝⎜

⎞⎠⎟

Λ ≤ 28.1!

Λ = cos−1 0.751.05*0.85

⎛⎝⎜

⎞⎠⎟ ≈ 32

!

CL( )max Λ( ) = CL( )max Λ=0( ) cos Λ( )

b = 14h tan Λ( )+ h

ARa = 2h

AR− b

Climb Sizing Boeing 787-8 Dream Liner

4. Climb Sizing

! In order to do sizing for climb it is essential to refer

to FAR 25.111, 25.121, 25.119 and 25.121 regulations to establish values for climb gradient (CGR) requirements, which will be used in the next equation:

4.01 [1]

!

Note that in this case term N showing the number of engines is equal to two.

In practise there are two stages for take - off climb. One which occurs as soon as the aircraft lifts off and the other, when the aircraft establishes positive rate of climb and retracts landing gears. However, it should be kept in mind that as well as initial take - off climb the second one is also transient. Should be there given an air traffic control clearance to proceed for intended flight level, the aircraft configuration is altered to the clean one and the subsequent vertical distances are covered in this particular configuration.

4.1. Take - off Climb Sizing It was suggested to first perform take - off climbing

at take - off flaps settings and gear down, since that is the first type of the climbing an aircraft performs after its rotation. For that type of climb the CGR value should be just above zero, also the speed should be between 1.2 of stall speed and lift off speed, hence parameter B is about 1.1.

On the other hand as sophisticated expression of drag coefficient was derived earlier, the expression 4.01 could be transformed into:

4.1.01 [1]

! !

For the range of take - off maximum coefficients of lift, one could arrive at the following table.

On the power to weight ratio versus lift loading diagram, results obtained could be represented as the series of horizontal lines.

! Following the same method the values for similar

terms could be found for climb rate after the landing gears are retracted, typically this occurs shortly after take-off as the speed reaches 1.2 of stall speed rather quickly. Hence the table of values obtained and corresponding take - off trust to weight ratio versus wing loading graph both are represented below. Now the value for CGR is 0.012 and B is 1.2.

!

TW

= NN −1

1/ LD

⎛⎝⎜

⎞⎠⎟ +CGR

⎡⎣⎢

⎤⎦⎥

CGR = 1Vdhdt

TW

⎛⎝⎜

⎞⎠⎟ TO, GEAR DOWN

≥ 2 1/CLmax( )

TO

β 2 CD( )TO, GEAR DOWN

⎛

⎝⎜⎜

⎞

⎠⎟⎟+ CGR ≈ 0( )

⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

Table 4.1.1 Initial Take - off Climb Power to Weight Ratios

1.6 1.8 2.0 2.2

1.3223 1.4876 1.6529 1.8182

0.1189 0.1380 0.1593 0.1829

0.1798 0.1855 0.1927 0.2012

! CLmax( )TO

! TW

⎛⎝⎜

⎞⎠⎟ TO, GEAR DOWN

! CLmax( )TO

β 2

!CD

Figure 4.1.1

(T/W

) tak

e-of

f

0.16

0.173

0.185

0.198

0.21

(W/S) take-off / lbs/ft^20 35 70 105 140

Cl = 2.2, W/T ≥ 0.2012Cl = 2.0, W/T ≥ 0.1927Cl = 1.8, W/T ≥ 0.1855Cl = 1.6, W/T ≥ 0.1798

Table 4.1.2 Take - off Climb Power to Weight Ratios

1.6 1.8 2.0 2.2

1.1111 1.2500 1.3889 1.5278

0.0777 0.0912 0.1063 0.1229

0.1398 0.1458 0.1529 0.1608

!CLmax( )

TO

� TW

⎛⎝⎜

⎞⎠⎟ TO, GEAR UP

! CLmax( )TO

β 2

!CD

Figure 4.1.2

(T/W

) tak

e-of

f

0.12

0.133

0.145

0.158

0.17

(W/S) take-off / lbs/ft^20 35 70 105 140

Cl = 2.2, W/T ≥ 0.1608 Cl = 2.0, W/T ≥ 0.1529Cl = 1.8, W/T ≥ 0.1458Cl = 1.6, W/T ≥ 0.1398


4.2. Normal Climb After climb out and returning to clean configuration,

the aircraft climb is said to be normal. On the other hand estimations of power to weight ratio could be still performed in a similar manner. It was however suggested to recall modified 4.1.01 equation appropriate for such purpose:

4.2.01

! ! !

Where B was selected to be 1.25 and v is 0.9 a continuous power correction. Hence the subsequent table and graph representing achieved power to weight ratios.

!

4.3. Landing Climb Sizing With respect to the following passage, the climb is

used for any vertical movement, the magnitude of which depends on the context.

As far as the landing climb sizing is concerned there are two main stages of climb at the landing flaps setting with landing gears deployed and a balked landing configuration. The last second is only different from the full landing configuration (i.e. gears and flaps) as now there is a full take - off thrust. With respect to the above, these stages typically occur before and during final approaches of the aircraft, when both gliding slope and localiser contact are established. However, if there are bad weather conditions or a heavy gusts and/or cross

winds the go - around procedure may be executed, if an aircraft misses intended landing path.[7][8]

Consequently, after the go - around is initiated, the aircraft continues to fly and climb in its previous configuration for a brief moment, and similarly to usual take - off procedure, landings gears are raised and flaps are changes to take - off setting, only after stable positive climb is reached.

From the calculation point of view there should be made some adjustments to aircraft approach lift coefficient and decreased aircraft weight.

Firstly, as there is some difference between approach and landing lift coefficient, this could be represented as:

4.3.01 [1] !

Hence dividing it by B, to account for aircraft speed it gives:

4.3.02 [1]

!

On the other hand drag coefficient for approach stage could be thought as the average between landing and take - off gear-less configuration. Hence for the drag coefficient correction term it could be written that:

4.3.03 [1]

!

Recalling corresponding values from table 8.06, it can be found that:

4.3.04 [1] !

Hence adding this term together with the landing gear correction in to clean drag coefficient leads to:

4.08

!

Where B in this case if 1.5. Also for the approach climb the CGR value is required to be more than 0.021.

On the other hand to account for decreased weight as the result of burned trip fuel, it was suggested to use value of trip fuel fraction from the table 8.01

So modifying expression 3.19 to make it accountable for approach climb gives:

4.09 !

TW

⎛⎝⎜

⎞⎠⎟ CLEAN

≥ 2ν

β 2 CD( )CLEANCLmax( )

CLEAN

⎛

⎝⎜⎜

⎞

⎠⎟⎟+ 0.012

CGR!

⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

TW

⎛⎝⎜

⎞⎠⎟ CLEAN

Table 4.2.1 Normal Climb Power to Weight Ratios

1.2 1.4 1.6 1.8

0.7680 0.8960 1.0240 1.1520

0.0348 0.0430 0.0525 0.0632

0.1145 0.1200 0.1265 0.1338

� CLmax( )CLEAN

� TW

⎛⎝⎜

⎞⎠⎟ CLEAN

� CLmax( )CLEAN

β 2

!CD

Figure 4.2.1

(T/W

) tak

e-of

f

0.1

0.11

0.12

0.13

0.14

(W/S) take-off / lbs/ft^20 35 70 105 140

Cl max = 1.8, W/T ≥ 0.1338 Cl max = 1.6, W/T ≥ 0.1265Cl max = 1.4, W/T ≥ 0.1200Cl max = 1.2, W/T ≥ 0.1145

CLmax( )A= CLmax( )−α

CLmax( )APPROACH

=CLmax( )

A

β 2 =CLmax( )−α

β 2

∆CD0( )APPROACH

=∆CD0( )

TAKE−OFF+ ∆CD0( )

LANDING

2

∆CD0( )APPROACH

= 0.015 + 0.0652

= 0.04

CD( )APPROACH = 0.072 + 0.0386CLmax( )−α

β

⎛

⎝⎜⎜

⎞

⎠⎟⎟

2

TW

⎛⎝⎜

⎞⎠⎟ APPROACH

≥ 2M ff

0.072 + 0.0386CLmax( )−α

β

⎛

⎝⎜

⎞

⎠⎟

2

CLmax( )APPROACH

⎛

⎝

⎜⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟⎟

+ 0.021CGR!

⎡

⎣

⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥


In order to perform calculations it was suggested that the value for alpha and beta are 0.2 CL and 1.5. Hence the following table and graph could be achieved.

! In contrast to previous graphs, in case of approach

phase an increase in maximum lift coefficient positively effects thrust to weight ratio.

Now for the balked landing, several parameters should be adjusted.

Firstly, the speed for that stage was assumed to be 1.3 stall speed.

Secondly, as now the thrust is set to take - off a correction for that should be added into final equation.

Thirdly, it was suggested to use 0.012 for the CGR value.

And finally, the thrust ratio should be corrected for landing weight. Taking into account all of the above it could be shown that:

4.10 [1]

!

Using following expression another pair of figures could be obtained.

!

4.4. Direct Climb Sizing This method is an alternative way of estimating thrust

ratios required to perform various types of climb. The main idea here is to proceed with further calculations from some given climb values, rather than to look for specific CGR value. [7][8]

Related climb rates (RC) were already used in the first chapter, when it was essential to point out that the horizontal distances covered during both descend and ascend stages contribute to the final range. So, it was suggested to stick to the same values, which were 1,800 fpm before 20,000 ft. and 1,000 fpm after 20,000 ft.

By writing rate of climb in a following manner: 4.4.01 [1]

!

Hence rearranging for thrust to weight ratio gives: 4.4.02 [1]

!

By using two values for climb rate as 1800 fpm and 1000 fpm between S.L.-20,000 ft and 20,000 ft-35,000ft respectively, the required take-off ratio is then 0.471

Note, that the velocities which were used to calculate these power ratios in the equation 4.4.02 were derived in the next section. Similar applies to the thrust to weight ratios as those are a function of wing loading.

Table 4.3.1 Approach Climb Power to Weight Ratios

1.8 2.2 2.4 2.8

0.6400 0.7822 0.8533 0.9956

0.0878 0.0956 0.1001 0.1103

0.1955 0.1770 0.1710 0.1628

! CLmax( )CLEAN

! TW

⎛⎝⎜

⎞⎠⎟ APPROACH

! CLmax( )− 0.2 CLmax( )β 2

!CD

Figure 4.3.1

(T/W

) tak

e-of

f

0.1

0.11

0.12

0.13

0.14

(W/S) take-off / lbs/ft^20 35 70 105 140

Cl max = 1.8, W/T ≥ 0.1955 Cl max = 2.2, W/T ≥ 0.1770Cl max = 2.4, W/T ≥ 0.1710Cl max = 2.8, W/T ≥ 0.1628

TW

⎛⎝⎜

⎞⎠⎟ BALKED LANDING

= 2M ff

0.097 + 0.439CLmax

1.32⎛⎝⎜

⎞⎠⎟

2

CLmax

1.32

+ 0.034

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

Table 4.3.2 Balked Landing Climb Power to Weight Ratios

1.8 2.2 2.4 2.8

1.0651 1.3018 1.4201 1.6568

0.5950 0.8409 0.9823 1.3021

0.7300 0.8380 0.8945 1.0109

! CLmax( )LANDING

! TW

⎛⎝⎜

⎞⎠⎟ BALKED LANDING

! CLmax( )LANDING, GEAR DOWN

β 2

!CD

Figure 4.3.2

(T/W

) tak

e-of

f

0

0.4

0.8

1.2

1.6

2

(W/S) take-off / lbs/ft^20 35 70 105 140

Cl max = 2.8, W/T ≥ 1.0109Cl max = 2.4, W/T ≥ 0.8945Cl max = 2.2, W/T ≥ 0.8380Cl max = 1.8, W/T ≥ 0.7300

RC =V TW

−1/ LD

⎡⎣⎢

⎤⎦⎥

TW

⎛⎝⎜

⎞⎠⎟ requried

= RCV

+ CD

CL

Cruise Speed Sizing Boeing 787-8 Dream Liner

5. Cruise Speed Sizing

! In order to estimate cruise speed values it is

suggested to use following set of equations: 5.01

!

Also the thrust to weight ratio could be written as: 5.02 [1]

!

Taking into account the compressibility effects it could be shown that correction for drag coefficient of 0.0005 should be used, also the cruise speed is may related as:

5.03 [1]

!

Hence one could arrive at the following table of thrust to weight ratios

! CD( )CLEAN = 0.012 + 0.0386CL

2

M = 0.85AR = 10e = 0.85

⎧

⎨⎪⎪

⎩⎪⎪

TW

⎛⎝⎜

⎞⎠⎟ required

= CD0

12ρV 2

WS

+

WS

⎛⎝⎜

⎞⎠⎟

πARe 12ρV 2⎛

⎝⎜⎞⎠⎟

12ρV 2 = 1

2γ PM 2 = 251.84 psf

Table 5.1 Thrust to Weight Ratios for Cruise

60 0.08027 0.32368

80 0.06541 0.24796

100 0.05768 0.20373

120 0.05352 0.17523

140 0.05140 0.15572

160 0.05056 0.14184

! WS

⎛⎝⎜

⎞⎠⎟ TO

! TW

⎛⎝⎜

⎞⎠⎟ required

! TW

⎛⎝⎜

⎞⎠⎟ TO

Figure 5.1

(T/W

) tak

e-of

f

0

0.08

0.16

0.24

0.32

0.4

(W/S) take-off / lbs/ft^250 77.5 105 132.5 160

T/W requiredT/W take-off

Discussion Boeing 787-8 Dream Liner

6. Discussion To conclude conducted evaluation it was suggested

to export final results in term of the following set of tables.

6.1. Limitations and Further Work The values were based on the assumptions, reasoned

throughout the discussion. However with respect to the further work, those should be again corrected as in a more detailed further stages, the range of required values shrinks to a specific value. This is especially imprint in terms of the engine thrust to weight ratio parameters. The scatter of the engine thrust ratio should be minimised with an aid of further constraints.

Mainly, this include a more detailed design of the aircraft structure, in terms of the fuselage, wings, tailplanes, etc. From the analysis of each individual section it is possible to arrive at relationships linking them together in a more tailed way. In particular, the height and allocation of the passenger seats determine the height of the fuselage and hence establish its minimum size.

On the other hand a detailed surrey of structural material may establish the upper boundary of the fuselage size. Same could be done to all other aircraft parts.

However in case of the power plant, it is suggested to use bottom up approach as the engine cost accounts for a major portion of total aircraft’s development costs.

As well it should be noted that applying composite materials allowed to arrive at decreased value for empty weight, however its stress properties were ignored. In practise, greater weight saving could be achieved, if the composite materials are smartly implemented into the aircraft’s structure.

In terms of the preliminary sizing, the sequence of assumptions made it possible to determine some important aircraft’s characteristics, however before the second chapter it was stated that the values based on the tables given in appendix showed a relatively poor accuracy. In case of the sensitivity analysis it is especially important as all subsequent calculations were dependent on the suggested A and B values.

Therefore, it is concluded that to arrive at more accurate results, it is essential to updated used statistical data.

Apart from that the whole mission profile could be changed to explore subsequent changes, which shell be applied to the aircraft.

References Boeing 787-8 Dream Liner

7. REFERENCES

[1] DEN6445 PRELIMINARY SIZING HANDOUT FOR JET DRIVEN AIRCRAFT

[2] Boeing 787 -8 (Dreamliner) sample analysis, (2005), web page: http://www.lissys.demon.co.uk/samp1/index.html

[3] Daniel P. Raymer, Aircraft Design: A Conceptual Approach, (July 28, 2006) Fourth Edition (AIAA Education), ISBN-13: 978-1563478291

[4] David J. Peery (November 16, 2011)Aircraft Structures (Dover Books on Aeronautical Engineering) ISBN-13: 000-0486485803

[5] Richard Von Mises (June 1, 1959), Theory of Flight (Dover Books on Aeronautical Engineering), ISBN-13: 978-0486605418

[6] John P. Fielding, (October 14, 1999), Introduction to Aircraft Design (Cambridge Aerospace Series), ISBN-13: 978-0521657228

[7] Gib Vogel (October 1, 2013), Flying the Boeing 787

[8] Federal Aviation Administration, (March 6, 2015), Boeing 787-8 Design, Certification, and Manufacturing Systems Review: Boeing 787-8 Critical System Review

http://www.lissys.demon.co.uk/samp1/index.html

Appendix Boeing 787-8 Dream Liner

8. Appendix Information given in the appendix was collected

from similar works, dedicated to the sizing and preliminary design.

Table 8.01 Standar Atmosphere

! Table 8.02 Preliminary Weight Characteristics

! Table 8.03 Preliminary Fuel System

!

Table 8.04 Suggested Mission Fuel Fractions

! Table 8.05 Suggested Coefficient of Lift and Drag

! Table 8.06 Suggested Cruise Performance Chart

!

COPYRIGHT © 2013 THE BOEING COMPANY PRELIMINARY

Airplane Characteristics

CHARACTERISTICS UNITS 787-8 787-9 787-10 Max Design Taxi Weight LB 503,500 555,000 555,000

KG 228,384 251,744 251,744

Max Design Takeoff Weight LB 502,500 553,000 553,000

KG 227,930 250,837 250,837

Max Design Landing Weight LG 380,000 425,000 445,000

KG 172,365 192,777 201,848

Max Design Zero Fuel Weight LB 355,000 400,000 425,000

KG 161,025 181,437 192,777

Maximum Fuel Capacity US GALLON 33,528 33,384 33,384

LITER 126,917 126,372 126,372

TCDS No.: EASA.IM.A.115 Boeing 787 Page 13 of 18Issue: 07 Date: 07 November 2013

9. Fluid Capacities

Tanks Usable Fuel

U.S. Gallons Pounds* Liters Kilograms* Main L or R 5,570 37,319 21,085 16,868

Center 22,200 148,740 84,036 67,229 Total 33,340 223,378 126,206 100,965

Unusable Fuel

U.S. Gallons Pounds* Liters Kilograms* Drainable 32.4 217 122.6 98 Trapped 72.4 485 274.1 219

Total 104.8 702 396.7 317

* Fuel Density is 6.7 Pounds / U.S. Gallon and 0.8 Kilograms / Liter

See appropriate Weights and Balance Manual (See Section IV Note 3)

10. Airspeed Limits

VMO/MMO = 350KEAS / 0.90M. For other airspeed limits, see the appropriate EASA approved Airplane Flight Manual (See Section IV Note 1)

11. Flight Envelope

Maximum Operating Altitude: 43,100 feet See the appropriate EASA approved Airplane Flight Manual (See Section IV Note 1)

12. Operating Limitations

See the appropriate EASA approved Airplane Flight Manual (See Section IV Note 1)

12.1 Approved Operations The airplane is approved for the following kinds of flight and operation, both day and night, provided the required equipment is installed and approved in accordance with the applicable regulations/specifications: - Visual (VFR) - Instrument (IFR) - Icing Conditions - Low weather minima (CAT I, II, III operations) - RVSM - B-RNAV

Version 1 1

Data and formulae for aircraft preliminary weight estimation and sizing Typical fuel fractions for non-fuel intensive mission segments

Breguet formulas for range (R) and endurance (E):

aircraft type

engine start and

warm-up taxi take-

off

Climb and acceleration

to cruise descent

landing, taxi and

shut-down

homebuilts 0.998 0.998 0.998 0.995 0.995 0.995 single engine piston props 0.995 0.997 0.998 0.992 0.993 0.993 twin engine props 0.992 0.996 0.996 0.990 0.992 0.992 agricultural 0.996 0.995 0.996 0.998 0.999 0.998 business jets 0.990 0.995 0.995 0.980 0.990 0.992 regional turboprops 0.990 0.995 0.995 0.985 0.985 0.995 transport jets 0.990 0.990 0.995 0.980 0.990 0.992 military trainers 0.990 0.990 0.990 0.980 0.990 0.995 fighters 0.990 0.990 0.990 0.96 - 0.9 0.990 0.995 military patrol, bombers and transport 0.990 0.990 0.995 0.980 0.990 0.992 flying boats, amphibians and float planes 0.992 0.990 0.996 0.985 0.990 0.990 supersonic aircraft 0.990 0.995 0.995 0.92 - 0.87 0.985 0.992

⎛ ⎞η ⎛ ⎞⎛ ⎞= ⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎝ ⎠ ⎝ ⎠⎝ ⎠

⎛ ⎞ ⎛ ⎞⎛ ⎞= ⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎝ ⎠ ⎝ ⎠⎝ ⎠

p startprop

cruisep endcruise

startjet

cruisej endcruise

WLR . ln

g.c D W

WV LR . ln

g.c D W

⎛ ⎞ ⎛ ⎞⎛ ⎞= ⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎝ ⎠ ⎝ ⎠⎝ ⎠

⎛ ⎞η ⎛ ⎞⎛ ⎞= ⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎝ ⎠ ⎝ ⎠⎝ ⎠

startjet

loiterj finishloiter

p startprop

loiterj finishloiter

W1 LE . ln

g.c D W

WLE . ln

Vg.c D W

Version 1 3

Maximum lift coefficient values for different a/c categories (clean configuration, take off and landing with deployed high-lift devices)

Takeoff parameter definition for jet and propeller a/c

Statistical relationship between landing distance and stall speed

Data and formula for preliminary polar drag estimation Parasite drag definition as function of the equivalent skin friction coefficient and the wetted area/reference lifting surface area ratio:

CLmax clean CLmax take-off CLmax land aircraft type min max min max min max

homebuilts 1.2 1.8 1.2 1.8 1.2 2.0 single engine piston props 1.3 1.9 1.3 1.9 1.6 2.3 twin engine props 1.2 1.8 1.4 2.0 1.6 2.5 agricultural 1.3 1.9 1.3 1.9 1.3 1.9 business jets 1.4 1.8 1.6 2.2 1.6 2.6 regional turboprops 1.5 1.9 1.7 2.1 1.9 3.3 transport jets 1.2 1.8 1.6 2.2 1.8 2.8 military trainers 1.2 1.8 1.4 2.0 1.6 2.2 fighters 1.2 1.8 1.4 2.0 1.6 2.6 military patrol, bombers and transport 1.2 1.8 1.6 2.2 1.8 3.0 flying boats, amphibians and float planes 1.2 1.8 1.6 2.2 1.8 3.4 supersonic aircraft 1.2 1.8 1.6 2.0 1.8 2.2

⎛ ⎞ ⎛ ⎞= ⎜ ⎟ ⎜ ⎟ σ⎝ ⎠ ⎝ ⎠max

jetTO TO L

W W 1 1TOP . . .

S T C⎛ ⎞ ⎛ ⎞= ⎜ ⎟ ⎜ ⎟ σ⎝ ⎠ ⎝ ⎠

max

propTO TO L

W W 1 1TOP . . .

S P C

= →

= →land

land

2L s

2L s

s 0.5915* V CS23

s 0.5847* V CS25

0wet

D feSC CS

=

Version 1 2

Reference data for Breguet formulas: Cruise data

aircraft type L/D Cj

[lbs/hr/lbs] Cp

[lbs/hr/hp] ηp

homebuilt 8-10 - 0.6 - 0.8 0.7

single engine piston props 8-10 - 0.5 - 0.7 0.8

twin engine props 8-10 - 0.5 - 0.7 0.82

Agricultural 5-7 - 0.5 - 0.7 0.82

business jets 10-12 0.5 - 0.9 - -

regional turboprops 11-13 - 0.4 - 0.6 0.85

transport jets 13-15 0.5 - 0.9 - -

military trainers 8-10 0.5 - 0.9 0.4 - 0.6 0.82

fighters 4-7 0.6 - 1.4 0.5 - 0.7 0.82 military patrol, bombers and transport 13-15 0.5 - 0.9 0.4 - 0.7 0.82 flying boats, amphibians and floatplanes 10-12 0.5 - 0.9 0.5 - 0.7 0.82

supersonic aircraft 4-6 0.7 - 1.5 - - Loiter data


[lbs/hr/lbs] Cp

[lbs/hr/hp] ηp

homebuilt 10-12 - 0.5 - 0.7 0.6



Agricultural 8-10 - 0.5 - 0.7 0.72

business jets 12-14 0.4 - 0.6 - -


transport jets 14-18 0.4 - 0.6 - -


fighters 6-9 0.6 - 0.8 0.5 - 0.7 0.77

military patrol, bombers and transport 14-18 0.4 - 0.6 0.5 - 0.7 0.77

flying boats, amphibians and floatplanes 13-15 0.4 - 0.6 0.5 - 0.7 0.77

supersonic aircraft 7-9 0.6 - 0.8 - -


Table 8.07 Suggested Loiter Data Performance Chart

! Table 8.08 Equivalent skin friction coefficient values

for different aircraft categories

! Table 8.09 Drag Correction Coefficients

!

Table 8.10

! Figure 8.01

!

Version 1 2

Reference data for Breguet formulas: Cruise data


[lbs/hr/lbs] Cp

[lbs/hr/hp] ηp

homebuilt 8-10 - 0.6 - 0.8 0.7



Agricultural 5-7 - 0.5 - 0.7 0.82

business jets 10-12 0.5 - 0.9 - -


transport jets 13-15 0.5 - 0.9 - -


fighters 4-7 0.6 - 1.4 0.5 - 0.7 0.82 military patrol, bombers and transport 13-15 0.5 - 0.9 0.4 - 0.7 0.82 flying boats, amphibians and floatplanes 10-12 0.5 - 0.9 0.5 - 0.7 0.82

supersonic aircraft 4-6 0.7 - 1.5 - - Loiter data


[lbs/hr/lbs] Cp

[lbs/hr/hp] ηp

homebuilt 10-12 - 0.5 - 0.7 0.6



Agricultural 8-10 - 0.5 - 0.7 0.72

business jets 12-14 0.4 - 0.6 - -


transport jets 14-18 0.4 - 0.6 - -


fighters 6-9 0.6 - 0.8 0.5 - 0.7 0.77

military patrol, bombers and transport 14-18 0.4 - 0.6 0.5 - 0.7 0.77

flying boats, amphibians and floatplanes 13-15 0.4 - 0.6 0.5 - 0.7 0.77

supersonic aircraft 7-9 0.6 - 0.8 - -

Version 1 4

Equivalent skin friction coefficient values for different aircraft categories

Correction factors for ΔCD0 and Oswald factor at take off and landing ΔCD0 Δe

Clean configuration 0 0

Take-off flaps 0.010 - 0.020 0.05

Landing flaps 0.055 - 0.075 0.10

Undercarriage* 0.015 - 0.025 0

Climb rate formulas Climb rate : c = V(T-D)/W = Pa-Pr/W For propeller aircraft: For jet aircraft:

maximum for and

CD0=Cfe Swet/S Cfe - subsonic

Civil transport 0.0030

Bomber 0.0030

Airforce fighter 0.0035

Navy fighter 0.0040

Clean supersonic cruise aircraft 0.0025

Light aircraft – single engine 0.0055

Light aircraft – twin engine 0.0045

Propeller seaplane 0.0065

Jet seaplane 0.0040

η= −

ρ

p br3 /2L

D

W . 2.P ScW C

.C

= π0L DC 3C Ae =

0D DC 4C3 /2L

D

CC

⎛ ⎞= −⎜ ⎟ ρ⎝ ⎠

D

L L

CT W 2 1c .

W C S C

Version 1 4

Equivalent skin friction coefficient values for different aircraft categories

Correction factors for ΔCD0 and Oswald factor at take off and landing ΔCD0 Δe

Clean configuration 0 0

Take-off flaps 0.010 - 0.020 0.05

Landing flaps 0.055 - 0.075 0.10

Undercarriage* 0.015 - 0.025 0

Climb rate formulas Climb rate : c = V(T-D)/W = Pa-Pr/W For propeller aircraft: For jet aircraft:

maximum for and

CD0=Cfe Swet/S Cfe - subsonic

Civil transport 0.0030

Bomber 0.0030

Airforce fighter 0.0035

Navy fighter 0.0040

Clean supersonic cruise aircraft 0.0025

Light aircraft – single engine 0.0055

Light aircraft – twin engine 0.0045

Propeller seaplane 0.0065

Jet seaplane 0.0040

η= −

ρ

p br3 /2L

D

W . 2.P ScW C

.C

= π0L DC 3C Ae =

0D DC 4C3 /2L

D

CC

⎛ ⎞= −⎜ ⎟ ρ⎝ ⎠

D

L L

CT W 2 1c .

W C S C


Figure 8.02

! Figure 8.03

! Figure 8.04

! Figure 8.05

!

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