AAE 451 – Aircraft Senior Design

Spring 2008

Conceptual Design Review The Next generation DC-3 Aircraft

Team 4: Skyborne Technologies

Brian Acker

Lance Henricks

Matthew Kayser

Kevin Lobo

Robert Paladino

Ruan Trouw

Dennis Wilde

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Table of Contents

I. Executive Summary……………………………………………………………………..3

II. Mission Statement……………………………………………………………………...5

III. Three Use Cases……………………………………………………………………….6

IV. Aircraft Design Missions……………………………………………………………...7

V. Major Design Requirements………………………………………………….………10

VI. Selected Aircraft Concept……………………………………………………………11

VII. Advanced Technologies…………………………………………………………….13

VIII. Aircraft Sizing/Carpet Plots………………………………………………………..18

IX. Design Trade-offs Via Sizing Code………………………………………………….24

X. Airframe Description…………………………………………………………………24

XI. Power Issues…………………………………………………………………………28

XII. Aerodynamic Design………………………………………………………………..29

XIII. Performance……………………………………………………………..…………34

XIV. Propulsion………………………………………………………………………….37

XV. Structures……………………………………………………………………………38

XVI. Stability and Control……………………………………………………………….43

XVII. Costs………………………………………………………………………………47

XVIII. Environmental Impact……………………………………………………………49

XIX. Reliability & Maintainability………………………………………………………52

XX. Summary……………………………………………………………………………54

Appendix…………………………………………………………………………………56

References………………………………………………………………………………..68

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I. Executive Summary

In the year 2058, the National Aeronautics and Space Administration (NASA), expects

air traffic to have increased significantly. This design is an answer for the expected

problem stated by NASA. Major hubs all over the world are expected to be very crowded

and overused in the future. The problem with extremely busy hubs is that flights get

delayed and passengers miss connecting flights. NASA asked for the design of a smaller

commercial aircraft that has the ability to takeoff and land in extremely short distances.

The aircraft is expected to carry between 125 and 250 passengers. The takeoff and

landing distances need to be less than 3,000 ft.

At Skyborne Technologies, it was decided that to design a smaller aircraft with the

capacity to carry up to 126 passengers. Based on existing airport data, it was discovered

that 80% of the highest traveled airports are located within 1000 nmi from each other.

Using this data the estimated range for this aircraft is 1000 nmi. In order to solve the

problems facing overcrowded airports, two major factors had to be incorporated in the

commercial aircraft transportation. The first is to be able to utilize smaller airports around

large hubs to reduce traffic. The second is to increase the traffic capability of large hubs,

by using a split runway approach. The split runway approach is possible using extremely

short takeoff and landing (ESTOL) aircraft in conjunction with a non-interfering spiral

decent. Some future technologies that Skyborne Technologies looked at for takeoff

included blown flaps, composite materials for lighter weight, thrust vectoring, morphing

wings and possibly liquid-fueled rockets. On the other hand, the aircraft will also have to

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land in less than 3,000 ft. The lighter materials and low stall speed allow the aircraft to

stop using reverse thrust, spoilers, and a combination of wheel and speed brakes.

The team needed to pick a concept, so that the sizing would be more specific. Pugh's

method was used to generate concepts and finally to select one. Skyborne Technologies

found that a tandem wing, elliptical fuselage, would solve the requirement problems. The

concept had to be analyzed and further developed. A sizing code was written from

scratch in order to incorporate all the future technologies, and also to fit the tandem wing

design. Triple slotted fowler flaps on the front wing and a single flap on the rear wing

allowed for a CL max of 2.77. This is enough to get the aircraft off the ground in 3,000 ft

and clear a 35 ft obstacle. Other future technologies such as composite materials were

also incorporated for weight savings. The aircraft will cruise 35,000 ft at Mach 0.8.

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II. Mission Statement

“Using innovative solutions to design a short-medium range

aircraft that is efficient, eco-friendly, and cost-effective, capable

of ESTOL along with advanced technology, to increase

passenger traffic.”

6

III. Three Use Cases

1. Single Class Passenger Aircraft

2. Two Class Passenger Aircraft

3. Combination Passenger/Cargo Aircraft

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IV. Aircraft Design Missions

Mission 1: One way trip up to 1000 nmi

Segments: E-G Optional

A: Taxi/Takeoff (

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Mission 2: Round trip without refueling (2x 500 nmi legs)

Segments: J, K Optional

A: Taxi/Takeoff (

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Mission 3: Regional short hops of approximately 300 nmi

Segments: L-N Optional

A: Taxi/Takeoff (

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V. Major Design Requirements

The major design requirements are listed in Table 1.1 below. Many of these

requirements come from the guidelines suggested for the NASA ARMD competition.

Some items, such as the price per seat mile and sale price are targets established by

Skyborne Technologies. A copy of the compliance matrix is located in the Appendix

showing whether or not these values were attained.

Table 1.1: Aircraft Design Requirements

Passengers & Crew 125 + 5

Payload (lbs) 30,000

Range (nmi) 1,000

Take-off Distance (ft) ≤ 3,000

TOGW (lbs) ≤ 80,000

Cruise Speed (Mach) 0.82

Sale Price (2007 USD millions) ≤ 30

Price per seat mile (2007 USD) 0.06

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VI. Selected Aircraft Concept

Walk Around Chart

Figure 1.1: Walk Around Chart of Aircraft Design

Main Design Features

Figure 1.1 above is a visual depiction of the final chosen concept. The most important

feature incorporated in the design of the aircraft is the use of tandem wings. To satisfy

the ESTOL constraint posed by the NASA competition it was necessary to create a

design which produces a large amount of lift. It was deemed that a conventional tube-

and-wing design would be infeasible as the wing would have to be very large. The aft

wing serves a dual purpose as both a lifting device and a horizontal tail. As such, it is

designed with both elevators and flaps. To achieve the necessary lift the fore wing uses

triple slotted Fowler flaps. Both wings use winglets to reduce the vortices generated by

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the wingtips. The fuselage is made out of titanium reinforced composites for strength

while decreasing the overall weight of the aircraft. The shape of the fuselage to was

chosen to be an oval in order to provide more shoulder room for window seat passengers

when compared to a traditional circular design. Connected directly to the fuselage

structure are the two advanced turbofan engines. The position of the engines over the

fuselage and wings guarantees that a significant portion of the engine noise will be

shielded from the ground. The downside of this placement is that the passengers aft of

the engine placement will be subject to an uncomfortable amount of noise. To counteract

this, the aircraft will make use of advanced noise absorption in regions near the engines.

The final important design feature is the retracting landing gear. The landing gear is

connected to and retracts into the fuselage. The positioning of the gear was necessary in

order to make sure the aircraft was stable.

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VII. Advanced Technologies

Automated Control Systems

By 2038 unmanned vehicles will have taken over most of the front lines. Unmanned

vehicles are already in military service today performing many high risk tasks. The

technology is already in use in the military, so why not for commercial transport? Since

the F/A-18 was first designed to be statically unstable, computers have been used to help

pilots to control the aircraft. Computer systems are used in flying wing designs to control

the complex system of controls. Soon it will be possible for an automated system to take-

off and land commercial jets. Such a system can already be implemented but fear over

computer error or outside interference are holding the technology back.

The remote pilot system would be used in conjunction with two other systems to provide

multiple redundancies. These other systems would be having one pilot and one

technician/engineer. The pilot would be fully capable to operate the aircraft while the

technician/engineer would be able to fly the airplane using its automated controls and

computer flying system. The remote system would have to be activated by a person on

board, and then a pilot at the airport or nearby hub could control the plane. This would

prevent the system from being able to be hacked in flight and then a high security

encryption would be used to communicate with the plane during take-off or landing.

This would eliminate a large portion of the plane’s operating cost. This would cut

airlines’ pilots cost by about 35 to 40 percent. It would also benefit the pilots because it

would reduce the effects of jet lag and reduce time spent away from their families.

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Advanced Materials

Titanium has become the premium metal of our age. It offers the all the benefits of steel

while being lighter and less dense. Titanium has only one drawback when compared to

steel, its cost. Cambridge University has recently discovered a process to

electrochemically produce titanium. The FFC Cambridge process reduces titanium

oxides to produce a pure metal alloy with much less energy and is much simpler than the

currently used Kroll process. The Kroll process uses lots of energy to melt the metal and

is very complex. It takes a few days for just one batch of titanium. Another new

development for titanium is powdered titanium. The United States government is

funding the development. Titanium powder would allow the creation of complex shaped

parts; this would reduce the need for machining the parts. This would drastically reduce

the amount of wasted metal and the cost of machining the part to its desired shape. Metal

prices double about every 15 years, but with all the new developments for titanium its

price will increase slower and double closer to 30 years. This will allow commercial

aircraft to stop using heavy steel components. However, aluminum still has a weight

savings advantage over titanium and will continue to be used in the fuselage skin of

future airplanes.

Composite materials are quickly becoming the material of the future. Composites are

stronger and lighter than their metal comparisons. Carbon fiber is 6 times stronger than

aluminum with a weight savings of 40 percent. They also can offer better resistance to

both heat and vibrations. They also require less maintenance. Composites will probably

never fully replace all the metal on an airplane, but they can be used in conjunction with

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metals to further strengthen them. Composites have already been used in the Boeing 787

and are planned for the new Airbus 350. They can even be used in critical structures like

the wings. Both Boeing and Airbus are claiming a 14 to 15 percent decrease in empty

weight due to composites. Carbon nanotubes are the newest and most promising

composite material. Carbon nanotubes are almost 70 times as strong as titanium and half

the density of Aluminum. They have already been used to reinforce the winning Tour De

France bicycle by using extremely small carbon fibers woven together to reinforce other

materials and metals. New manufacturing processes are also helping to cut the empty

weight of the aircraft. One piece fuselage sections are reducing the number of rivets and

fasteners. In the future these sections will be able to be built bigger and longer reducing

the number of rivets and fasteners even more.

Sweep was one of the original solutions to problem of the increased drag at higher

speeds. The graphs below in Figure 1.2 show this problem by illustrating how the ideal

wing sweep changes as the Mach number is increased. The second graph shows how the

huge increase in drag can be offset by sweeping the wing proving this systems benefit.

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Propulsion

Current turbofan advancement is happening at an alarming rate. The turbofans on the

original 747 produced around 25,000 lbs of thrust. When the engines were updated 20

years later the new engines produced 5,000 more pounds of thrust and saved 14 percent

more fuel. The GeNx program took only 10 years to replicate the same amount of

progress, a savings of 15 percent off of the specific fuel consumption. The decrease of

specific fuel consumption over the last fifty years is charted in Fig. 1.3 below. Based on

the graph, a specific fuel consumption value of 0.3 has been used for design analysis.

Fig 1.2: Optimal Wing Sweep and Wing Drag Coefficient v. Mach

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Figure 1.3: Turbofan SFC v. Year

Reusable energy sources like solar power could be harnessed to provide power to run the

compressor or power the fuselage. Getting rid of or drastically reducing the size of the

APU would cut the costs and weight of the aircraft. Powering the compressor with

electrical energy not coming directly from the engine would greatly increase the specific

fuel consumption. The energy extracted by the turbine stage of the engine could be

reduced and more of the power from combustion can be extracted. The solar panels and

batteries required to hold the charge would add weight and complexity, but it could

greatly reduce operating costs and environmental impact. Solar power is already in use

and has proven to be effective.

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VIII. Aircraft Sizing/Carpet Plots

The sizing process began by considering the tools available to successfully design an

aircraft. Both FLOPS and Daniel Raymer’s RDS software were considered at the start of

the sizing process. FLOPS was ruled out, mostly due to a lack of experience with the

software and also because of the difficulty presented in altering FLOPS to allow for

futuristic design technologies. Raymer’s software was ruled out since the team felt the

software would resemble FLOPS and because the team did not actually have a copy of

the software. The team decided to write a sizing code in Matlab (Appendix), to fit the

needs of the project. The sizing code used an iterative method to find the empty, gross

takeoff and fuel weights required for a certain mission. Table 1.2 below shows all the

fixed parameters and inputs to the iterative code.

Table 1.2: Inputs for the Matlab Script

AR = 11 % Aspect ratio of the main wings

T_to_W = 0.36 % desired thrust to weight

W_S =115 % desired wing loading

Wpay = 27500 lb % Weight payload

Wcrew = 1000 lb % Crew weight

weight_saving = 0.8*Wo % Weight saving from new tech

AR_for = AR % Aspect Ratio Front

AR_aft = AR % Aspect Ratio Rear

e = 0.8 % Oswald efficiency

g = 32.2 ft/s2 % Gravitational Constant

mew = 0.05 % Ground rolling friction

mewbrake = 0.2 % Brake Coefficient

M = 0.8 % Cruise Mach number

SFC = .3 1/hr % per second

Sweep = 32 degrees % Wing sweep

Engine_moment_arm = 4.5 ft % Distance from the engine to centerline

AR_tail = 1.5 % Aspect ratio for the vertical tail

L_fus = 132 ft % Length of the fuse

Depth_f = 13 ft % Depth of the fuse

Width_f = 11 ft % Width of the fuse

momentarm_for=0.5 ft % Moment arm ft (need to update) (Xacw-Xcg)

momentarm_aft=39.5 ft % Moment arm ft (need to update) (Xacw-Xcg)

momentarm_tail=58 ft % Moment arm from tail to cg (Xacv-Xcg)

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The code started with an initial guess for the gross take-off weight. The empty

weight was then calculated using the following equation:

0.1399 0.0923 0.1829 -0.5685 0.4260 (1.7766* * *( / ) *( / ) * )* * _We Wo AR T W W S M Wo weight saving

(Equation 1)

The fuel weight fraction calculation was derived from a flight mission. The

mission consisted of the following parts:

Take-off

Climb

Cruise

Land

Take-off (Missed Approach)

Climb (Missed Approach)

Cruise (Divert)

Hold

Land

The take-off, climb and landing fractions were taken from Table 3.2 in the

Raymer text2. The cruise fuel weight fraction was calculated from an equation found in

box 3.1 in the Raymer’s text2. The equation is stated as follows:

-Range*SFC

V_cruise_kts*L_D_cruise(k)W3 = e

W2

(Equation 2)

The loiter fuel weight fraction was calculated in a similar fashion to the cruise

weight fraction, but with a different range and velocity. The script then added the weight

of the payload, crew and fuel to the empty weight estimated, to yield a new gross take-off

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weight. The new gross take-off weight was then compared to the previous guess and if

they were not very close to each other, the program would start over with the new value

as the initial guess. Other calculations were incorporated in the above mentioned script in

order to ensure that the whole aircraft changed as the weight of the aircraft changed.

A separate function was written for the sizing of the vertical tail. The reason for

having this separate function was to allow for the main script to call the function during

each iteration. Three types of criterion were used to size the vertical tail. The first

scenario was for one engine out during flight. The second scenario was for landing in a

crosswind. The third condition was a check to make sure that the values found in the

previous two cases compared realistically to historical data. The three cases are explained

in detail below.

The moment applied to the aircraft resulting from the thrust of one engine out case

needed to be counteracted with a rudder deflection. The maximum rudder deflection was

taken to be 20 degrees or less. This case predicted a very small surface area, since the

moment arm of the engine to the centerline of the fuselage is very small for fuselage

mounted engines.

A few assumptions were made for landing in a crosswind. The first is that the wind is

constant and does not consist of irregular gusts. The second is that the aircraft is not

rolling due to the crosswind. The maximum rudder deflection for landing in a crosswind

is taken to be the same as for one engine out. The angle that the wind makes with the

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aircraft, Beta, is set to be approximately 11.5 degrees2. The 11.5 degrees comes from

vector addition with the crosswind consisting of 20 percent of the approach speed, acting

perpendicular to the flight path.

The last case simply compares the vertical tail areas found in the previous two cases to

the wing reference area. Historical data suggested that the vertical tail area should be

approximately 20 percent of the wing reference area.

The engine design method picked for the aircraft is the rubber sizing method. This

method allows for the designer to specify the thrust to weight and the specific fuel

consumption. One positive aspect of this approach is that historical trends can be used to

find predictions, which allows for the advancement of technology.

Carpet plots were generated by specifying arrays for the wing loading and thrust to

weight in the input section of the sizing script. The matrices were generated by varying

the thrust to weight for each wing loading. This was done using two for loops in Matlab.

Matrices were created for the gross take-off weight, fuel weight, landing distance and

take-off distance. These matrices were put together in a carpet plot. The gross take-off

weight along with the thrust to weight and wing loading were used to make a carpet. The

other three matrices were used to generate constraint line that intersects carpet. The plot

generated can be seen below:

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Figure 1.4: Carpet Plot used to pick design point

The carpet plot helped to the team to pick a design point. The area below the fuel line,

and above the landing and take-off distance lines were considered acceptable. The

constraint governing take-off distance was less than 3,000ft. The design constraint

imposed on the landing was chosen to be less than 2,500 ft. The landing constraint was

picked in order to allow the aircraft to land at an even smaller airport. This should only be

done in case of extreme emergencies, since the aircraft will not be able to take off with

full payload and fuel. The last constraint was a fuel constraint. A direct correlation was

made on the operating cost, to ensure that customers receive a fuel efficient aircraft. The

take-off distance curve should curve more upward, restricting the wing loading of the

aircraft. The team decided to pick the point where the wing loading is 115 pounds per

square foot and a corresponding thrust-to-weight value of 0.36. This specific design

point was entered in the original script (without the arrays), and the following results

summarized in Table 1.3 were obtained:

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Table 1.3: Sizing Code Outputs

Gross Take-off Weight 63634 lbs

Empty Weight 26954 lbs

Fuel Weight 8180 lbs

Thrust Installed 22910 lbf

L/D Take-off 9.1

L/D Cruise 27.5

Take-off Distance 2915 ft

Landing Distance 2404 ft

S total 553 ft2

S front wing 332 ft2

S rear wing 221 ft2

S tail 130 ft2

V stall 187 ft/s

V cruise 778 ft/s

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IX. Design Trade-offs Via Sizing Code

The biggest trade-off made during the sizing project was accuracy. There are several

other software programs available for sizing an aircraft, which may be more accurate than

the self-generated code. The self-written code includes less detail than the other sizing

codes, but was more applicable more to the current design.

X. Airframe Description

Dimensioned 3-views

Figure 1.5: Side View of Aircraft

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Figure 1.6: Front View of Aircraft

Figure 1.7: Top View of Aircraft

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Internal Layout

Figure 1.8: Cross-Sectional View of Fuselage

Figure 1.9: Layout of Seats within Cabin

Figures 1.8 and 1.9 above show the internal seating arrangement of the aircraft. For the

best size and smallest weight aircraft it was decided to go with a two-class single-aisle

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aircraft. The green seats represent first class, blue seats are the economy class and the

pink seats are for the crew. There are three lavatories with two located at the middle of

the plane and an additional one located within the first class cabin. The middle

lavatories double as space for extra structural support for the engines. There is an

economy galley at the rear of the plane and a first class galley at the front. The aircraft

features three emergency exits with one at the front of the aircraft and two more at the

rear. The fuselage cross-section shape is oval with a vertical height of thirteen feet and a

width of twelve feet. The oval cross-section allows for more shoulder room for window

seat passengers. Information about the specific seat dimensions are available in the Table

1.4 below.

Table 1.4: Seat Dimensions

Class Pax

Arrangement Seat pitch (in)

Seat Width

(in)

Aisle Width

(in)

1st 3 rows, 4

seats/row 39 24 24

Economy 19 rows, 6

seats/row 34 18 18

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XI. Power Issues

Instead of a conventional APU, a fuel cell was chosen to provide the necessary power for

the aircraft. Solar panels were also considered, but due to the fact that they cannot run at

night and there is not enough area for the power needed, this option was eliminated as a

potential, source of power. By eliminating the APU the environmental impact of the

aircraft may be reduced by not burning fossil fuels and releasing harmful emissions.

Another advantage of the fuel cells is that the overall weight is less. Finally, the only

byproduct of a fuel cell is only water if hydrogen is used. Sizing of the fuel cell was done

based on historic trends, but a specific fuel was not selected. Due to the recent advances

in fuel cell technology, it will be difficult to gauge what new options will be available in

2038.

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XII. Aerodynamic Design

The Boeing 737C transonic airfoil, shown in Figure 1.10 was selected for both the fore

and aft wings in order to generate the high lift required to make our aircraft capable of

ESTOL. The decision was made to incorporate triple-slotted Fowler flaps on the fore

wings. To further reduce the stall speed of our aircraft during takeoff and landing the

team chose to employ the use of single flaps on the aft wings. For the tail, the NACA

0012 symmetrical airfoil was selected. For both the wings and tail the airfoil wind-tunnel

test data was produced using XFOIL and Aerofoil. From these programs the required

two-dimensional airfoil data to be used was generated. This was necessary in order to

eventually calculate the three-dimensional lift generated by each wing for the different

flight conditions. It was discovered for the fore wing that the angle of attack associated

with zero lift was (-1.5) degrees. The change in lift coefficient associated with a change

of alpha was calculated to be 0.0888 /degree. Finally, the angle of attack where

maximum lift occurs was found to be about 17 degrees. These values are the same for

the aft wing due to the use of the same airfoil for both wings. Figure 1.11 below contains

the lift curve generated using MATLAB based upon this data.

Figure 1.10: The Boeing 737c Airfoil Section

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Figure 1.11: Lift Curve generated with MATLAB

Drag Buildup

Several major components help to create the drag buildup of an aircraft flying at a high

velocity, similar to this aircraft design plane. It was important to consider the parasite

drag, induced drag, and the compressibility drag of our aircraft at the different flight

configurations.

Parasite drag was predicted by breaking the airplane down into its various parts. In this

case the aircraft was broken down into the fuselage, nacelles, tail, fore and aft wing

components. For each part the drag buildup calculation began by finding the Reynolds

Number. Then the friction coefficient for turbulent flow found in equation 12.27 in

Raymer’s textbook was calculated. Turbulent flow was assumed for the entire surface

because as the plane ages small imperfections will begin to accrue in the aircraft’s surface

and trip the flow, so this is a conservative prediction. The Reynolds number used for

calculations was the smaller of the actual Reynolds number and the cutoff Reynolds

-5 0 5 10 15 20-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Alpha (deg)

cl

Lift Curve for Boeing 737C Airfoil

31

number found in equation 12.29 in Raymer’s textbook. Next the form factor for each

component found in Raymer’s textbook was calculated by using equations 12.30-12.33.

Finally all of these components were tied together to for the parasite drag coefficient

listed in Equation 3 below:

Cdo=Q*FF*Cf*Swet/Sref (Equation 3)

In Equation 1, Q is the interference factor, which is usually assumed to be approximately

one depending on the overall location of the component. For the other variables in

Equation 3, FF is the form factor, Cf is the coefficient of friction, Swet is the wetted area,

and Sref is the reference area of the entire aircraft. The parasite drag for all of the

components was then summed in order to determine the total parasite drag. For takeoff it

was found that the parasite drag coefficient was 0.0559 and for cruise this value was

found to be 0.0571.

Next, the induced drag coefficient was calculated based upon the lift coefficient CL using

Equation 4 below.

Cdi=(CL^2)/(pi*AR*e) (Equation 4)

In Equation 4, AR is the aspect ratio and e is the Oswald efficiency factor which was

assumed to be equal to 0.8. This value was calculated for the fore and aft wings and then

summed. For takeoff it was discovered that the induced drag coefficient was about 0.54

and for cruise it was found to be about 0.00066.

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The next step was to calculate the compressibility drag coefficient. In order to do this

first it is necessary to calculate the critical Mach number. This was found to be 0.08 less

than the drag divergence Mach number, which was found using Professor Crossley’s

prediction based upon ideas from Raymer, Anderson, and Shewell. This can be found in

the MATLAB code attached in the Appendix at the end of this report. The drag

divergence Mach number was found to be 0.825 and the critical Mach number was

calculated as 0.745. Finally, the Mach number associated with the maximum

compressibility drag was found to be 1.034 using an equation provided from Professor

Crossley. During takeoff and landing compressibility drag is negligible but during cruise

the compressibility drag coefficient was found to be about 0.00095. The three different

drag coefficients were added together to find the overall drag coefficient at the different

flight coefficients. The total aircraft drag was then found by taking the product of these

drag coefficients, the reference area, and the dynamic pressure of the free stream air at

the different flight configurations.

From this the drag polar for both the takeoff and landing configurations was generated,

which are shown in Figure’s 1.12 and 1.13below. A line connected to these curves from

the origin will show the point where the maximum lift-to-drag for the aircraft occurs.

Another notable aspect of these plots is that the zero lift drag is at the point where this

curve intersects the horizontal axis.

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Figure 1.12: Drag Polar for the Takeoff Configuration

Figure 1.13: Drag Polar for the Landing Configuration

0 0.05 0.1 0.15 0.2 0.25 0.3 0.350

0.5

1

1.5

2

2.5

3

Cd

Cl

Drag Polar (TO Conditions)

Cl-Cd Curve

Max L/D

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Cd

Cl

Drag Polar (Cruise Conditions)

Cl-Cd Curve

Max L/D

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XIII. Performance

Flight Envelope

Figure 1.14: Flight Envelope, W=86,000 lb, 100% fuel load, max. thrust

Figure 1.14 above shows the performance envelope for Skyborne’s aircraft for zero

excess power. The leftmost limit is the stall velocity at each altitude. The far right limit

is velocity at which aircraft drag becomes equivalent to thrust at each altitude. Service

ceiling was chosen because this is a common 100ft/min climb ceiling for aircraft in this

airliner’s competition class.

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The absolute ceiling of roughly 70,000 feet seems extreme for this aircraft. This is the

altitude at which stall velocity curve levels off. Propulsion system performance will

likely lower the absolute ceiling when a power plant is chosen. As this has not yet taken

place, this constraint cannot be included. The aircraft can be operated in controlled flight

within the solid curve. No safety margins (never operating below 1.1Vstall, for example)

were included. The cruise conditions of Skyborne’s airliner (470 knots, 35,000 feet) fall

within this curve and below service ceiling, allowing for 100 ft./min climb rate at altitude

if necessary.

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V-n Diagram

Figure 1.15: V-n Diagram for Aircraft Design

The V-n diagram shown in Figure 1.15 represents the load factor which the airplane can

safely experience. The red line shows the envelope the aircraft can maneuver in during

normal conditions. During especially windy conditions the blue dotted line represents the

envelope for a gusty condition. It was decided that the aircraft should be able to keep up

with or exceed current transport standards so the positive load factor was set to 4 and the

negative load factor was set to 1.5. The black star represents the stall speed calculated by

sizing code. The aircraft stall speed is 110 knots and the cruise speed is 461 knots. The

aircrafts speed during approach is 140 knots.

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XIV. Propulsion

Figure 1.16: Thrust available and required for cruise at 35,000 feet.

Figure 1.16 above shows thrust available and thrust required for cruise. Vehicle mass

was assumed to be 82000 pounds (half fuel load). The cruise velocity for this aircraft is

470 knot. At this velocity, thrust available is 25% higher than thrust required. The

vehicle is capable of cruising at 510 knot if no excess thrust is desired.

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XV. Structures

Configuration Layout

Aircraft structural risk and reliability analysis is an important consideration in the area of

aircraft structural and component integrity. It is essential to discuss the probability and

avoidance of failure due to fatigue and its implications on components such as the

airframe, wings and material selection. This obviously is an important factor in the

determination of the total aircraft cost and has been carefully considered. The structural

configuration impacts the general arrangement of the aircraft. The primary forces to be

resolved are the lift of the wing and the opposing weight of the major parts of the aircraft,

such as engines and payload. The size and weight of the structural members will be

minimized by locating these opposing forces near to each other. The weight of the

structural members can be reduced by providing the shortest, straight load path possible.

As wings provide the lifting force, load-path distances can be reduced by locating the

heavy items as near to the wing as possible. The weight can be reduced by locating

structural cutouts away from the wing. Required structural cutouts include the cockpit

area, and a variety of doors. Bulkheads are used to carry a number of concentrated loads.

Ribs carry the loads from the control surfaces, store stations and landing gear to the spars

and skins. Flutter is an unfortunate dynamic interaction between the aerodynamics and

the structure of an aircraft. Finite element analysis can be used to simulate the stress

distributions and deflections, using a large number of nodal points, it is easy to produce

an accurate estimate and reduce flutter. Since the shape of control surfaces should never

be convex, the attempt was made to employ flat-sided control surfaces on this aircraft

design. It is desirable to have a beveled trailing edge, and a control surface that is

39

flattened at the hinge line, this will tend to reattach flow, improving flutter characteristics.

It is bad for flutter if the natural frequency of the vibration of the aileron about its hinge is

nearly the same as the wing natural bending frequency. To increase the relative torsional

stiffness, a rigid torque tube is connected to the elevators. Vulnerability areas such as the

pilot, computers, fuel and engine will be reinforced with a stronger material. Hydraulic

lines and reservoirs are located away from the engines. Care is taken so as to avoid

production breaks, if required a routing channel is used by careful placement.

Skyborne Technologies made use of a single elliptical cross-section cylinder co-cured

with the wings, tail and other components; this was the basis of the airframe. Eight

equally spaced I-beams were attached to the inside of the fuselage, which gives it rigidity

and support from bending. For means of providing an easy load path, frames co-located

with bulkheads are used to transfer engine loads to our fuselage. This structure is well

suited to support the fuselage mounted engines. With the fuselage configuration layout

pressurization issues are easily handled. For the wings and empennage section a multi-rib

design was decided upon. This structure only has two spars and multiple ribs supporting

the structure, therefore adding to our weight savings. This wing carry through box is

attached to our fuselage. Pylons, along with vibration isolators attached to fuselage

frames are used as our engine mounts, these provide some shielding of noise for people

on the ground and are relatively simple to integrate. They also help with weight and

balance. The shock absorbing retractable landing gear is integrated to fit our fuselage

design by means of downlocks, drag braces and retraction actuators together with

bulkheads. Rotation actuators, axle beam folds, struts and compensating actuator

40

assemblys attach the wheels to the rest of the landing gear. Laser-beam welding (LBW)

and friction-stir welding (FSW) are two modern techniques used as our fasteners.

Material Selection

In order for the aircraft to have a lifespan of more than 50 years, the use of advanced

materials and new processing technology is required. The selection of materials was

based on research which took into account material performance, manufacture of

components and associated costs at the same time. Major aircraft components and

material selections, along with their advantages and disadvantages are summarized below

in Table 1.5.

Table 1.5: Major aircraft components and material selection

Materials were chosen that have the most desirable characteristics for the aircraft. These

would include carbon nano-tubes and carbon fiber reinforced plastics (CFRP’s) that have

high tensile strengths but are light as well. Other components such as the fuselage and

skins are made out of advanced materials like composites such as GLARE ("GLAss-

REinforced" Fiber Metal Laminate) and aluminum-lithium alloys. The landing gear uses

41

components made out of titanium alloys. The use of these advanced materials gives the

aircraft a technology weight saving factor of around 20%.

Figure 1.17 – Material distribution (weight breakdown) based on the A380

Factors considered in the selection of materials were based on their ability to withstand

cyclic and tension loading, crack propagation, yield strength, stiffness as well as fracture

toughness. Areas that were more prone to damage such as bird strike impact require

material with more damage-tolerant characteristics. Another important criterion was the

corrosion and fire resistance of these materials. According to an Airbus1 advanced

materials study, the major achievements in the use of aluminum alloys are the

introduction of a very wide sheet material on the fuselage panels which has made

possible the reduction of joints and resulted in weight reduction. Titanium alloys have

been selected to replace steels in numerous applications due to their high strength, low

density, damage tolerance and corrosion resistance, however high price of these materials

can be a factor in some cases. The use of CFRP’s on the A380 composite center wing

box, gives a weight savings of up to one and a half tones compared to most advance

aluminum alloys which is well represented in the case of our aircraft. Other advanced

42

methods of assembling structure and materials together include the concepts of Resin

Film Infusion (RFI), Automated Fiber Placement (AFP), Resin Transfer Molding (RTM)

and Automated Tape Laying (ATL) technology.

43

XVI. Weight, Stability and Control

Weight Breakdown

Table 1.6: Breakdown of Components Weights and Positions

Components density multiplier weight

est weight(lb)

Estimated location (percent total length)

Actual Location

All else empty

0.017 2000 1715.3 0.45 0.3905303

Fore wing 10 0.8 10000 2584 0.5 0.5

Aft Wing 10 0.8 8000 1720 0.8 0.8

Pilot/engineer

400 400 0.08 0.08

Fore gear 15% of total

0.8 2000 520.644 0.1 0.1

First class pax

2400 2400 0.4 0.4

Coach pax

23000 23000 0.6 0.6

Frame 5 0.8 27500 19000 0.45 0.3905303

Fore wing fuel

10000 8000 0.5 0.5

Aft gear

0.8 4000 2950.316 0.74 0.74

Aft wing fuel

0 0 0.8 0.8

Engines installed 1.3 0.8 6000 6000 0.5 0.5

Tail 5.5 0.8 5000 276.32 0.9 0.8901515

Crew

600 600 0.45 0.3905303

gear (sum)

0.043 0.8 6000 4338.7

engines (sum of all)

6000 6000

Table 1.6 shows the location of the various major airframe components. The table

presents the overall weight of the component, based on values taken from Raymer’s

textbook. The location of the component was then calculated as a percentage of the total

aircraft length. Data from this table was fed into another program to calculate the overall

center of gravity of the aircraft.

Longitudinal Stability

The method to determine static stability was closely tied in with the overall weight

estimation. After selecting the design point from the carpet plot the values were run

44

through our sizing code to produce the important sizing values of the aircraft. Even

though this did include an aircraft total weight this was based on many broad equations

and assumptions. A weight breakdown was used to get a more accurate total weight.

Equations for the wing, fuselage, and tail were used from Raymer’s textbook. Other

important features like power cells for the APU, avionics, and landing gear were also

estimated from historical trends or similar aircraft. These weights and their positions

relative to the nose were input into an Excel spreadsheet to produce the center of gravity.

Weighted values of position multiplied by weight were calculated, totaled and then

divided by the total weight to find the center of gravity.

The data in Figure 1.18 shown below is the C.G. operating envelope. It plots the center

of gravity against various important weights. This gives an accurate representation of

how the aircraft’s center of gravity changes from refueling and loading on the ground to

flying in the air. The lowest point represents an unloaded aircraft with no fuel on board.

Moving clockwise, first the fuel is added; then the crew and pilot board the aircraft. The

fourth point represents the payload and passengers being loaded while the fifth represents

the fuel being burned during normal operation. Finally the aircraft is fully unloaded and

it returns back to its original starting position.

45

Figure 1.18: Location of CG Based on Aircraft Weight

The aerodynamic center of the aircraft (neutral point) was found through a code designed

in Matlab for our aircraft. The aerodynamic centers of the tandem wings were taken at

the quarter chord. The code used extra parameters for a tandem wing design, like the

downwash incurred on the aft wing and the lower air velocity the aft wing experiences.

A ratio for the two wing’s area and their total combined coefficient of lift were also used.

The aerodynamic center was found to be at 58 percent of the length away from the nose,

which ends up being 76.6 ft.

Since the neutral point is aft of the center of gravity the aircraft is statically stable.

The static margin of the aircraft was also calculated in the same Excel spreadsheet as that

used for weight breakdown and center of gravity. The static margin was again based

CG Operating Envelope

0

10000

20000

30000

40000

50000

60000

70000

80000

0.495 0.5 0.505 0.51 0.515 0.52 0.525 0.53 0.535

CG Location (%)

Weig

ht

of

Air

cra

ft (

lbs)

46

upon the special conditions cause by the tandem wing. The static margin was found to be

negative 13.1, where negative indicates a downward pitching moment and thus the

aircraft being statically stable.

47

XVII. Costs

In order to predict the total cost of the aircraft, Skyborne Technologies made use of the

DAPCA-4 cost model, outlined in Raymer’s textbook. This cost model proved to be

inadequate for an aircraft of this type. The DAPCA-4 model is primarily based on the

empty weight of the aircraft. Due to the extremely low empty weight of the aircraft, the

cost predictor initially indicated a sale price for the aircraft in the $16 million range. In

order to ensure the cost model was functioning correctly, the cost of a Boeing 737 was

estimated. The DAPCA-4 model provided a cost within $4 million of the Boeing 737

(based on available data) and was therefore assumed to be functioning as intended.

To produce a more realistic aircraft cost, the empty weight of the aircraft was input,

however no technology factors were applied. This nearly doubled the input weight,

however the sale price of the aircraft was still out of line, based on historical data for

similar aircraft. The anticipated sale price of the aircraft should be in the $40 million

range. Based on the output from the DAPCA-4 model, the production cost of the aircraft

is $16.9 million (2007 USD) and the sale price of the aircraft is $25.7 million (2007

USD). The total RDT&E cost as predicted by Skyborne Technologies is $8.5 billion

(2007 USD). Based on the business case previously established, a total production run of

5,000 aircraft is anticipated. The goal of the initial production run is 500 aircraft over a

five year period. After this time, the remaining 4,500 aircraft will be produced over a

fifteen year period, at a rate of twenty-five aircraft per month. This production quota is

very attainable, as Boeing currently produces roughly thirty 737s each month. Based on

the DAPCA-4 model, the number of aircraft required to break even is 766, when a

seventeen percent profit margin is assumed. This number is very much out of line, and

48

can be attributed to the DAPCA-4 model not being suited to aircraft with extremely low

empty weights and subsequent low sale prices.

Direct operating costs were also a main concern of Skyborne Technologies. The goal

was to have a price per seat mile less than ten cents. Several factors come into play when

calculating the direct operating cost. Crew salaries, maintenance and depreciation of the

airframe account for roughly two-thirds of the direct operating costs. High fuel prices

lead to higher direct operating costs and are the single largest influence on the overall

direct operating cost. Based on a fuel price of $3.00/gallon, the direct operating cost was

calculated. An insurance value of two percent was added on to the yearly cost of the

aircraft. This produced a price per flight hour of $3628.51. Based on the number of

passengers and the target range of the aircraft, the price per seat mile was calculated to be

$0.07, well under the target value set by Skyborne Technologies.

49

XVIII. Environmental Impact

Noise

Aircraft noise can be of great concern to those living near, or just traveling to and from,

an airport. Current aircraft similar in size and mission to Skyborne’s new airliner have a

noise level of 70-85 dBA upon takeoff and landing at a distance of 6500 meters from end

of runway. While these values are well below FAR criteria, consumers often find this

level of noise quite agitating, and Skyborne feels they can be improved upon. Current

generation turbofans have seen a 20 dB decrease in noise level from the preceding

generation. Skyborne will be using propulsion systems that are no less than one

generation ahead of those currently in use. Thus, if a similar drop in noise level is seen in

the next generation of engines (as those at Skyborne predict), and given the fact that

Skyborne’s aircraft exhibits turbofans mounted atop the fuselage, noise levels will be

reduced to 55-65 dB for this airliner. This is well within the range of comfortable

hearing (equivalent to a personal conversation with someone in the same room). Thus,

Skyborne believes aircraft noise will no longer be a major concern when its aircraft

becomes operational.

Engines mounted directly to the fuselage in an area which encloses the cabin can create

noise issues for passengers. Skyborne intends to neutralize cabin noise from engines by

introducing the same engine noise into the cabin artificially. This second engine noise

will be 180 degrees out of phase from the actual engine noise, effectively neutralizing it.

This technology is already in use and has shown great promise.

50

Emissions

The effects of global warming are widely recognized as a threat to the climate of the

entire planet. Emissions from transportation play a large part in this. NASA estimates

that a full four percent of total annual carbon dioxide emissions (which are second only to

water vapor in trapping heat on Earth) come from aviation sources. Skyborne

Technologies believes this number can be reduced. Engineers at Skyborne are seeking

ways to lower carbon dioxide output while limiting adverse effects upon aircraft

performance and economic efficiency. The correct choice of power plant may help in

this search. Researchers at NASA’s Glenn Research Center are testing materials that will

allow engines to withstand higher temperatures than ever before. This may lead to a

reduction in carbon dioxide emissions of up to fifteen percent. While increased

combustion temperatures may lead to a reduction in carbon dioxide emissions, they may

actually lead to an increase in other hazardous emissions. Nitrous oxide production, for

example, will likely increase as a result of higher engine core temperatures. At cruise

altitudes, these oxides contribute to ozone production and the greenhouse effect. Thus,

trade studies between the two pollutants and others that may be affected by engine

temperature must be performed when selecting a power plant for this aircraft.

Fuel efficiency increase will help lower overall emissions, as they are directly related to

the amount of fuel consumed. NASA is currently developing technology (the details of

which are not fully available at this time) that would permit aircraft in the same class as

Skyborne’s new airliner to burn 25% less fuel by the year 2018. If the trend of 25%

reduction in fuel usage per decade is extrapolated to 2038 (when this aircraft enters

51

service), aircraft will be using only 42% of the fuel volume they currently require. This

fact, combined with a fifteen percent reduction in carbon dioxide emissions due to higher

combustion temperatures, suggests that it may be possible for aircraft to produce only

36% of the current carbon dioxide emission levels when Skyborne’s airliner enters

service. While this figure may not be attainable in reality (all conditions would have to

be perfect for such a reduction), it is evident that considerable lowering of carbon dioxide

and other hazardous combustion byproduct levels is very possible. With consumers

finally beginning to think ‘green’ and consider their impact upon the world around them,

it may not be long before engine manufacturers begin to do the same.

52

XIX. Reliability & Maintainability

Recently, customers have demanded better, faster deliveries of products and services, all

at lower costs. This is the ideal request, but very difficult to achieve. One step to reach a

higher level of availability is to increase the reliability of products. Methods such as

probability theory, basic reliability measures, mission reliability measures, maintenance

free operating period (MFOP), failure free operating period (FFOP), hazards, and mean

time between overhaul (MTBO) can be used to assess the reliability of our aircraft. At

Skyborne Technologies common belief is that the designed aircraft is reliable, as it meets

all of the customer requirements such as range, take-off distance and cruise speed all

while maintaining passenger comfort and low airfare. The current required FAA

regulations such as having the required number of crew for available passengers,

lavatories, emergency exits are met. Other requirements such as the ability to withstand

forces up to the maximum limit load factor, oxygen supply, required tail and nose wheel

runway clearance have also been addressed. An attempt has been made to limit

environmental issues such as NOx and CO2 emission by using alternate renewable fuels.

A goal of Skyborne Technologies is to use hydrogen fuel cells and an alternate APU to

power our aircraft. The use of smart materials such as CFRP’s, titanium alloys and

GLARE, together with latest manufacturing technologies ensures that our aircraft will

have a long lifespan and reliability in terms of having low wear, corrosion, fatigue, better

collision damage and fire resistance. Internal cabin noise is a major issue with aircraft

that has been addressed by fitting the cabin with a microphone that detects noise and

employs a speaker that sends a signal 180 degrees out of phase, therefore cancelling

unwanted noise. This aircraft features a comfortable two class configuration. ‘Elite First

53

Class’ and ‘Premiere Economy’ are enough to suit the needs of most passengers with

state of art ergonomics such as a comfortable seats that have a large seat pitch, built in

audio and video entertainment and extra leg room making it one of the most reliable

aircraft in its class.

Maintaining a repairable system can be a complex task from economical and reliability

standpoint. The cost of maintenance in the aviation industry is high and there is always a

continuous process of cutting costs, which has to be done without compromising safety

and airworthiness. Maintenance is a multidisciplinary task which consists of management

planning, equipment, facilities, inventory and human resources. Skyborne Technologies

is comfortable with implementing a rigorous structure to maintain service and dispatch

the aircraft fleet. The scheduled maintenance of an aircraft contains hundreds of timely

inspection and replacement of parts. Easy access to fueling ports, luggage bins, de-icing

and catering services are possible with our aircraft design configuration. However, some

issues may arise when it comes to maintainability with respect to inspecting our fuselage

mounted engines due to their location. However, this is not expected this to be a problem

by 2038 since there will presumably be better ramp and on-site field services available.

Savings can be made by using the knowledge of previous maintenance data and the use

of software would be more effective. A simpler and cheaper method can improve logistic

tasks like maintenance planning and management of spare parts which will also affect

positively on aircraft availability and unpredicted expenses. We intend to use methods

such as mean time to repair (MTTR), mean down time (MDT) and maintenance man

hour (MMH) to measure maintainability of our aircraft.

54

XX. Summary

Skyborne Technologies has successfully designed the next generation short-to-medium-range

airliner. This aircraft will be lightweight, reliable, and cost-efficient. To help solve airport

congestion problems of the future, the aircraft has been designed primarily with ESTOL

capabilities in mind. The aircraft will utilize a range of no less than 1,000 nmi. Airlines and

cargo carriers will be the primary customers for our aircraft. The aircraft will be designed

with several different missions in mind, including direct flights between major city pairs and

shorter regional hops.

Skyborne Technologies selected the tandem-wing aircraft with an elliptical cross-section

design after considering many alternate aircraft designs. Current sizing sees this aircraft

carrying 126 passengers and 5 crew at Mcruise of 0.8 with a range of 1,000 nmi. Gross

takeoff weight is currently 63,600 pounds.

Advances in titanium production technology may make this metal economically practical

by the time this aircraft enters service. Composites are already in use in airliners but this

aircraft will take make use of advances in composite technologies, allowing for a

significant decrease in empty weight. Carbon nanotubes are seventy times stronger than

steel and will be a viable option when this aircraft enters production.

There are a few minor details which need to be completed at this time. Elevator trim

diagrams will need to be completed for the aircraft. At the present time the aircraft will

forgo the use of an APU. However, the total power drawn from all sources is unknown at

55

this time. Decisions will need to be made regarding power extraction from the aircraft,

and an APU may be installed if the needs are unable to be met. Completion of these

steps will allow production of a futuristic, commercially viable aircraft which Skyborne

Technologies will be proud to associate their name with.

56

Appendix

Sizing Code

clear all, close all, clc

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Initial design weights

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

AR = 11; % Aspect ratio of the main wings

T_to_W = 0.36; % desired thrust to weight

W_S =115; % desired wing loading

M_max = 0.8; % Inputs for the weight function

Wpay = 27500; % Weight payload

Wcrew = 1000; % Crew weight

weight_saving = 1; % Weight saving from new tech

AR_for = AR; % Aspect Ratio Front

AR_aft = AR; % Aspect Ratio Rear

e = 0.8; % Oswald efficiency

g = 32.2; % Gravitational Constant

mew = 0.05; % Ground rolling friction

mewbrake = 0.2; % Brake Coefficient

M = 0.8; % Cruise Mach number

SFC = .3; % per second

Sweep = 32; % Wing sweep

Engine_moment_arm = 4.5; % Distance from the angine to centerline (ft)

Tail_moment_arm = 60; % Distance from the tail mount to the cg (ft)

AR_tail = 1.5; % Aspect ratio for the vertical tail

L_fus = 132; % Length of the fuse

Depth_f = 13; % Depth of the fuse

Width_f = 11; % Width of the fuse

momentarm_for=0.5; % Moment arm ft (need to update) (Xacw-Xcg)

momentarm_aft=39.5; % Moment arm ft (need to update) (Xacw-Xcg)

momentarm_tail=58; % Moment arm from tail to cg (Xacv-Xcg)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Empty weight Prediction

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Woguess(1) = 0;

Woguess(2) = 100000; % Initial guess

k = 2;

while Woguess(k) > 1.0001*Woguess(k-1) || Woguess(k) < .9999*Woguess(k-1)

%%%%%%%%%%%%%%%%%%

%% Wing Geometry

%%%%%%%%%%%%%%%%%%

S_tot(k) = Woguess(k)/W_S;

S_for(k) = .6*S_tot(k);

S_aft(k) = .4*S_tot(k);

57

Sweep_Effect = cos(Sweep*pi/180);

b_for(k) = sqrt(S_for(k)*AR);

b_aft(k) = sqrt(S_aft(k)*AR);

c_for(k) = S_for(k)/b_for(k);

c_aft(k) = S_aft(k)/b_aft(k);

c_tail = 4;

%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Altitude

%%%%%%%%%%%%%%%%%%%%%%%%%%

cruise_alt = 35000;

rho_0 = 0.002377; %Density at 0 ft, slug/ft^3

Viscocity_0= 0.3745e-6; %Viscocity at 0ft slug/ft s

rho_35 = 0.0007382; %Density at 35,000 ft, slug/ft^3

Viscocity_35= 2.995e-7; %Viscocity at 35,000 ft slug/ft s

%%%%%%%%%%%%%%%%%%%

%% Lift

%%%%%%%%%%%%%%%%%%%

CL_and_L = Lift_coef(AR_for,AR_aft,S_for,S_aft,S_tot,e,Sweep_Effect);

CL_for_max(k) = CL_and_L(1);

CL_for_cruise(k) = CL_and_L(2);

CL_aft_max(k) = CL_and_L(3);

CL_aft_cruise(k) = CL_and_L(4);

CL_max_TO(k)= ((CL_for_max(k)*S_for(k))+(CL_aft_max(k)*S_aft(k)))/(S_for(k)+S_aft(k));

CL_max_cruise(k)= ((CL_for_cruise(k)*S_for(k))+(CL_aft_cruise(k)*S_aft(k)))/(S_for(k)+S_aft(k));

%%%%%%%%%%%%%%%%%%%

%% Velocities

%%%%%%%%%%%%%%%%%%%

Knots_ft_s = 1.6878;

Vstall(k) = sqrt((2*Woguess(k))/(rho_0*CL_max_TO(k)*(S_for(k)+S_aft(k))));

Vstall_knots(k) = Vstall(k)/Knots_ft_s; %knots

%Take off Velocity

V(k) = 1.2*Vstall(k); % ft/s

Vk(k) = V(k)/Knots_ft_s; % knots

a_TO = 1116.4; % ft/s

M_TO = V(k)/a_TO;

% Landing Velocity

Vl = 1.3*Vstall(k);

VL_70 = 0.7*Vl;

% Cruise Velocity

58

a = 973.1434; % ft/s at 35k

V_cruise = M*a; % ft/s

V_cruise_kts = V_cruise/Knots_ft_s; % knots

q_0 = (1/2)*rho_0*(V(k)^2); %slug/ft s^2

q_0_L = (1/2)*rho_0*(Vl^2);

q_35 = (1/2)*rho_35*(V_cruise^2); %slug/ft s^2

Lift_TO(k) = CL_max_TO(k)*q_0*(S_tot(k));

Lift_cruise(k) = CL_max_cruise(k)*q_35*(S_tot(k));

%%%%%%%%%%%%%%%%%%%%

%% Installed Thrust

%%%%%%%%%%%%%%%%%%%%

Thrust_installed(k) = T_to_W*Woguess(k);

%%%%%%%%%%%%%%%%%%%%%%%

%% Vertical Tail

%%%%%%%%%%%%%%%%%%%%%%%

%Drag_failed_engine*Engine_moment_arm

F_tail = (Thrust_installed(k)*Engine_moment_arm)/Tail_moment_arm;

Sweep_Effect_tail = cos(35*pi/180);

chordx = 1-0.25*cos(20*pi/180); % Change in chord x at 20 degrees deflection

chordy = 0.25*sin(20*pi/180); % Change in chord y at 20 degrees deflection

alpha_zero_lift = -12*pi/180;

Cl_alpha_tail = (1.726-0)/(17*pi/180);

CL_alpha_tail = Cl_alpha_tail/(1+(Cl_alpha_tail/(pi*AR_tail)));

CL_tail_20 = (CL_alpha_tail*(0-alpha_zero_lift))*Sweep_Effect_tail; % Might have to be the effective

alpha instead of zero

S_tail = F_tail/(q_0*CL_tail_20);

b_tail = sqrt(AR_tail*S_tail);

c_tail = S_tail/b_tail;

%Landing in a crosswind

S_tail_cw =

Vertical_tail(AR,Sweep,momentarm_for,momentarm_aft,momentarm_tail,CL_for_max(k),CL_aft_max(k),

CL_alpha_tail,L_fus,Depth_f,Width_f,S_for(k),S_aft(k),b_for(k),b_aft(k));

b_tail_cw = sqrt(AR_tail*S_tail);

c_tail_cw = S_tail/b_tail;

%%%%%%%%%%%%%%%%%

%% Drag

%%%%%%%%%%%%%%%%%

cdo =

Drag_Buildup(rho_0,Viscocity_0,V(k),c_for(k),c_aft(k),c_tail,S_for(k),S_aft(k),S_tail,M_TO,b_for(k),b_a

ft(k));

59

cdo_cruise =

Drag_Buildup(rho_35,Viscocity_35,V_cruise,c_for(k),c_aft(k),c_tail,S_for(k),S_aft(k),S_tail,M,b_for(k),b

_aft(k));

Drag_TO(k)

=(cdo*q_0*S_tot(k))+(((CL_for_max(k)^2)*q_0*S_for(k))/(pi*e*AR_for))+(((CL_aft_max(k)^2)*q_0*S_

aft(k))/(pi*e*AR_aft)); %lbf

Drag_L(k) =

(cdo*q_0*S_tot(k))+(((CL_for_max(k)^2)*q_0*S_for(k))/(pi*e*AR_for))+(((CL_aft_max(k)^2)*q_0*S_a

ft(k))/(pi*e*AR_aft)); %lbf

Drag_cruise(k) =

(cdo_cruise*q_0*S_tot(k))+(((CL_for_cruise(k)^2)*q_0*S_for(k))/(pi*e*AR_for))+(((CL_aft_cruise(k)^2)

*q_0*S_aft(k))/(pi*e*AR_aft)); %lbf

Cd_ac_TO =Drag_TO(k)/((q_0*S_for(k))+(q_0*S_aft(k))); %Aircrafts drag coefficient; note, when

eda is found need to revise with different q's

%%%%%%%%%%%%%%%%%

%% L/D

%%%%%%%%%%%%%%%%%

L_D_TO(k) = Lift_TO(k)/Drag_TO(k);

L_D_cruise(k) = Lift_cruise(k)/Drag_cruise(k);

%%%%%%%%%%%%%%%%%%

%% Empty Weight

%%%%%%%%%%%%%%%%%%

We(k) = (1.7766*(Woguess(k)^0.1399)*(AR^0.0923)*(T_to_W^0.1829)*(W_S^-

0.5685)*(M_max^0.4260))*Woguess(k)*weight_saving;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Mission weight fractions

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

% 1 --> Take-off

% 2 --> Climb

% 3 --> Cruise

% 4 --> Land

% 5 --> Missed aproach (TO)

% 6 --> Missed aproach (Climb)

% 7 --> Divert (Cruise)

% 8 --> Hold

% 9 --> Land

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

climb_angle = 20*pi/180; % radians

Naut_to_feet = 6076.115; % conversion factor

climb_dist = cruise_alt/tan(climb_angle); % ft

Range_pri = 1000 - climb_dist/Naut_to_feet; % ft

Range_sec = 150; % ft

Loiter = 0.75; % hr

% 1 --> Take-off

W1_Wo = 0.97;

60

% 2 --> Climb

W2_W1 = 0.985;

% 3 --> Cruise

W3_W2 = exp((-Range_pri*SFC)/(V_cruise_kts*L_D_cruise(k)));

% 4 --> Land

W4_W3 = 0.995;

% 5 --> Missed aproach (TO)

W5_W4 = 0.97;

% 6 --> Missed aproach (Climb)

W6_W5 = 0.985;

% 7 --> Divert (Cruise)

W7_W6 = exp((-Range_sec*SFC)/(V_cruise_kts*L_D_cruise(k)));

% 8 --> Hold

W8_W7 = exp((-Loiter*SFC)/(L_D_cruise(k)));

% 9 --> Land

W9_W8 = 0.995;

W9_W0 = W1_Wo*W2_W1*W3_W2*W4_W3*W5_W4*W6_W5*W7_W6*W8_W7*W9_W8;

Wf_W0 = 1.01*(1-W9_W0);

Wf(k) = Woguess(k)*Wf_W0;

k = k+1;

Woguess(k) = We(k-1) + Wf(k-1) + Wpay + Wcrew;

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Takeoff Distance

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

V_70 = (0.7*1.2)*Vstall(k-1); % 0.7*1.1 = 0.84 (70% VTO)

q_0_70 = .5*rho_0*V_70^2;

Lift_70 = CL_max_TO(k-1)*q_0_70*(S_tot(k-1));

Drag_70 =(cdo*q_0_70*S_tot(k-1))+(((CL_for_max(k-1)^2)*q_0_70*S_for(k-

1))/(pi*e*AR_for))+(((CL_aft_max(k-1)^2)*q_0_70*S_aft(k-1))/(pi*e*AR_aft)); %lbf

Distance_TO = (1.44*Woguess(k)^2)/(rho_0*S_tot(k-1)*CL_max_TO(k-1)*g*(Thrust_installed(k-1)-

Drag_70-mew*(Woguess(k)-Lift_70)));

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Landing Distance

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

V_70_L = (0.7*1.3)*Vstall(k-1); % 0.7*1.1 = 0.84 (70% VTO)

q_0_70_L = .5*rho_0*V_70_L^2;

Lift_70_L = CL_max_TO(k-1)*q_0_70_L*(S_tot(k-1));

Drag_70_L =(cdo*q_0_70_L*S_tot(k-1))+(((CL_for_max(k-1)^2)*q_0_70_L*S_for(k-

1))/(pi*e*AR_for))+(((CL_aft_max(k-1)^2)*q_0_70_L*S_aft(k-1))/(pi*e*AR_aft)); %lbf

Distance_L = (1.69*(0.85*Woguess(k))^2)/(rho_0*S_tot(k-1)*CL_max_TO(k-1)*g*(Drag_70_L +

0.5*Thrust_installed(k-1) + mewbrake*(0.85*Woguess(k)-Lift_70_L)))

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

61

%% External Calculations

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

M1 = 0.5; % Start of acceleration

V1 = M1*a;

delta_V = V_cruise-V1;

delta_He = 30000; %Cruise flight level

density_ratio = rho_35/rho_0;

Ps_cruise = (V_cruise*(Thrust_installed(k-1)*(density_ratio)-Drag_cruise(k-1)))/(0.97*.985*Woguess(k));

% .97, 0.985 is the weight fractions for takeoff and climb

Ps_TO = (V(k-1)*(Thrust_installed(k-1)-Drag_TO(k-1)))/(0.97*Woguess(k)); % .97 is the weight

fractions for takeoff

Ps_avg = (Ps_cruise +Ps_TO)/2;

t_climb = (delta_He/Ps_avg)/60;

Flight_time = 1150/V_cruise_kts

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Output

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Gross_Takeoff_Weight = Woguess(k)

Empty_Weight = We(k-1)

Wfuel = Wf(k-1)

Thrust = Thrust_installed(k-1)

Wingloading = W_S;

Thrust_weight = T_to_W;

Lift_Drag_TO = L_D_TO(k-1)

Lift_Drag_Cruise = L_D_cruise(k-1)

Take_off_Distance = Distance_TO

Specific_Power_cruise = Ps_cruise;

Specific_Power_TO = Ps_TO;

Time_Climb = t_climb

62

Drag Buildup

function [dragvec] = Drag_Buildup(rho,Viscocity,V,c_for,c_aft,c_tail,S_for,S_aft,S_tail,M,b_for,b_aft)

%%%%%%%%%%%%%%%%

% Drag Buildup

%%%%%%%%%%%%%%%%

%Variables

l_nac=11; %length of necalle ft

l_fus=130; %length of fuselage ft

k_skin=2.08E-5; %skin fric coeff for smooth paint in ft

d_fus=13; %diameter of fuselage in ft

d_nac =8; %diameter of nacelle in ft

x_c_m=0.457; %chordwise location of max thick point

t_c=0.104; %thickness to chord of wings

x_c_m_tail=0.3; %chordwise location of max thick point of tail

t_c_tail=0.12; %t_c for the tail

%Reynolds Numbers

Re_for_wing=rho*V*c_for/Viscocity;

Re_aft_wing=rho*V*c_aft/Viscocity;

Re_fuselage=rho*V*l_fus/Viscocity;

Re_tail=rho*V*c_tail/Viscocity;

Re_nac=rho*V*l_nac/Viscocity;

Re_x_cr=500000; %Re # where transition from lam to turb occurs

%%%%%%%%%%%%%%%%

% Parasite Drag

%%%%%%%%%%%%%%%%

%fuselage

R_cutoff_fuselage=38.21*((l_fus/k_skin)^1.053);

if (R_cutoff_fuselage < Re_fuselage)

R_fuselage=R_cutoff_fuselage;

else

R_fuselage=Re_fuselage;

end

Cf_fuselage=0.455/((log10(R_fuselage)^2.58)*(1+(0.144*M^2))^0.65);

%for wing

R_cutoff_for=38.21*((c_for/k_skin)^1.053);

if (R_cutoff_for < Re_for_wing)

R_for=R_cutoff_for;

else

R_for=Re_for_wing;

end

Cf_for=0.455/((log10(R_for)^2.58)*(1+(0.144*M^2))^0.65);

%aft wing

63

R_cutoff_aft=38.21*((c_aft/k_skin)^1.053);

if (R_cutoff_aft < Re_aft_wing)

R_aft=R_cutoff_aft;

else

R_aft=Re_aft_wing;

end

Cf_aft=0.455/((log10(R_aft)^2.58)*(1+(0.144*M^2))^0.65);

%tail

R_cutoff_tail=38.21*((c_tail/k_skin)^1.053);

if (R_cutoff_tail < Re_tail)

R_tail=R_cutoff_tail;

else

R_tail=Re_tail;

end

Cf_tail=0.455/((log10(R_tail)^2.58)*(1+(0.144*M^2))^0.65);

%nacelles

R_cutoff_nac=38.21*((l_nac/k_skin)^1.053);

if (R_cutoff_nac < Re_nac)

R_nac=R_cutoff_nac;

else

R_nac=Re_nac;

end

Cf_nac=0.455/((log10(R_nac)^2.58)*(1+(0.144*M^2))^0.65);

%%%%%%%%%%%%%%%%%%%%%%%%

%%Component Form Factors

%%%%%%%%%%%%%%%%%%%%%%%%

FF_for=(1+(0.6*t_c/x_c_m)+(100*t_c^4))*(1.34*(M^0.18)*(cos(32*pi/180)^0.28));

FF_aft=FF_for;

FF_tail=(1+(0.6*t_c_tail/x_c_m_tail)+(100*t_c_tail^4))*(1.34*(M^0.18)*(cos(37*pi/180)^0.28));

f_fus=l_fus/d_fus;

FF_fus=(1+(60/(f_fus^3))+(f_fus/400));

f_nac=l_nac/d_nac;

FF_nac=1+(0.35/f_nac);

%Component Interference Factors

Q_nac=1.3;

Q_for=1.0;

Q_aft=1.0;

Q_tail=1.04;

Q_fus=1.0;

%Swet Calculations

Swet_nac=pi*d_nac*l_nac;

64

lambda_fus=l_fus/d_fus;

Swet_fus=pi*d_fus*l_fus*((1-(2/lambda_fus))^(2/3))*(1+(1/(lambda_fus^2)));

Swet_for=2*1.02*S_for;

Swet_aft=2*1.02*S_aft;

Swet_tail=2*1.02*S_tail;

%Cdo Calculations

Cdo_for=(Q_for*FF_for*Cf_for*Swet_for)/S_for;

Cdo_aft=(Q_aft*FF_aft*Cf_aft*Swet_aft)/S_aft;

Cdo_tail=(Q_tail*FF_tail*Cf_tail*Swet_tail)/S_tail;

Cdo_nac=(Q_nac*FF_nac*Cf_nac*Swet_nac)/(l_nac*d_nac);

Cdo_fus=(Q_fus*FF_fus*Cf_fuselage*Swet_fus)/(l_fus*d_fus);

Cdo=Cdo_for+Cdo_aft+Cdo_tail+(2*Cdo_nac)+Cdo_fus;

%%%%%%%%%%%%%%%%%%%%%%%

% Compressibility Drag

%%%%%%%%%%%%%%%%%%%%%%%

Mdd=((-0.82*t_c)+0.849)+(((-0.00323*t_c)+0.00135)*32)+(((-0.00184*t_c)+0.000017)*(32^2))

Mcrit=Mdd-0.08

M_Cdo_max=(cos(32*pi/180))^-0.2

Amax=((pi*(d_fus)^2)/4)+((b_for-d_fus)*t_c*c_for)+((b_aft-d_fus)*t_c*c_aft);

k=0.4;

Ldim=k*l_fus;

Swet_tot=(2*Swet_nac)+Swet_fus+Swet_for+Swet_aft+Swet_tail;

C_DW_SH=((9*pi)/(2*(Swet_tot)))*((Amax/Ldim)^2);

EWD=1.6; %optimistic emperical wave drag efficiency

Cdw_max=EWD*(0.74+(0.37*cos(32*pi/180)))*C_DW_SH;

if (M

65

Lift Calculation

function [xvec] = Lift_coef(AR_for,AR_aft,S_for,S_aft,S_tot,e,Sweep_Effect)

%%%%%%%%%%%%%%%%%%%

%Lift

%%%%%%%%%%%%%%%%%%%

% 2-D case take-off

cl_alpha_for= 0.0888; %/degree based on wind tunnel data

cl_alpha_aft= 0.0888; %/degree based on wind tunnel data

alpha_Lo_for= -1.5; %alpha L=0 based on wind tunnel data

alpha_Lo_aft= -1.5; %alpha L=0 based on wind tunnel data

alpha_Lmax_for= 17; %alpha Lmax based on wind tunnel data in degrees

alpha_Lmax_aft= 17; %alpha Lmax based on wind tunnel data in degrees

% High Lift Devices

chord_extension = 0.15; %Chord extension with chord = 1

chord_extension_aft = 0.1;

zerolift_deflection = -10; % degrees

dCL_max = 0.9*2.5*(1+chord_extension)*cos(zerolift_deflection*pi/180);

dCL_max_aft = 0.9*0.9*(1+chord_extension_aft)*cos(zerolift_deflection*pi/180);

% 3-D case take-0ff

CL_alpha_for=cl_alpha_for/(1+((57.3*cl_alpha_for)/(pi*e*AR_for))); %/deg pg131 reference 10

CL_alpha_aft=cl_alpha_aft/(1+((57.3*cl_alpha_aft)/(pi*e*AR_aft))); %/deg pg131 reference 10

CL_for_max = (CL_alpha_for*(alpha_Lmax_for-alpha_Lo_for) + dCL_max)*Sweep_Effect; %pg

123 of reference 10

CL_for_cruise = (CL_alpha_for*(0-alpha_Lo_for))*Sweep_Effect;

CL_aft_max = (CL_alpha_aft*(alpha_Lmax_aft-alpha_Lo_aft) + dCL_max_aft)*Sweep_Effect;

%pg 123 of reference 10

CL_aft_cruise = (CL_alpha_aft*(0-alpha_Lo_aft))*Sweep_Effect;

xvec = [CL_for_max CL_for_cruise CL_aft_max CL_aft_cruise];

66

Tail Sizing

function [S_tail] =

Vertical_tail(AR_wing,sweep_wing,M_arm_for,M_arm_aft,M_arm_vert_tail,CL_for,CL_aft,CL_tail,l_fus,

D_f,W_f,S_for,S_aft,b_for,b_aft)

d_bv_db_nv=.55; % crude estimate for wing interference on the dynamic prsseure and

beta_effective equation 16.51

D_fus = (W_f+D_f)/2; % Average Diameter of the fuseZwf = 6; % Height of wing

above center line

sweep_wing = sweep_wing*pi/180;

b_tot=(b_for*S_for+b_aft*S_aft)/(S_for+S_aft);

M_arm_for = M_arm_for/b_tot;

M_arm_aft = M_arm_aft/b_tot;

M_arm_vert_tail = M_arm_vert_tail/b_tot;

S_totwing=S_for+S_aft;

Volume_fuselage=pi*((D_fus/2)^2)*(l_fus+10);

Cn_beta_for = (CL_for^2)*((1/(4*pi*AR_wing))-

((tan(sweep_wing)/(pi*AR_wing*(AR_wing+(4*cos(sweep_wing)))))*(cos(sweep_wing)-(AR_wing/2)-

((AR_wing^2)/(8*cos(sweep_wing)))+((6*M_arm_for*sin(sweep_wing))/AR_wing))))*(S_for/S_totwing);

%eq 16.44

Cn_beta_aft = (CL_aft^2)*((1/(4*pi*AR_wing))-

((tan(sweep_wing)/(pi*AR_wing*(AR_wing+(4*cos(sweep_wing)))))*(cos(sweep_wing)-(AR_wing/2)-

((AR_wing^2)/(8*cos(sweep_wing)))+((6*M_arm_aft*sin(sweep_wing))/AR_wing))))*(S_aft/S_totwing);

%eq 16.44

Cn_beta_fus=((-1.3*Volume_fuselage)/(S_totwing*b_tot))*(D_f/W_f); %eq 16.50

Cn_beta_vt=-Cn_beta_fus-Cn_beta_aft-Cn_beta_for;

S_tail=Cn_beta_vt*S_totwing/(CL_tail*d_bv_db_nv*M_arm_vert_tail);

67

Current Compliance Matrix

63,600

68

References

1. Airbus, “Advanced materials and technologies for the A380 structure”, Airbus Industrie, Toulouse, France 2008.

2. Raymer, Daniel P. Aircraft Design: A Conceptual Approach, 4th Edition. Reston, VA.

3. Lednicer, David and Selig, Michael, UICC Airfoil Database - The Incomplete Guide to Airfoil Usage, Analytical Methods, Inc, Redmond, WA, 98052, 2007.

4. Hepperle, Martin. JavaFoil©, , Myrtenweg 1, D-38108 Braunschweig, Germany, 1996-2006.

5. Bureau of Transportation Statistics. January 31, 2008. < www.bts.gov >

6. Jane’s All the World’s Aircraft. January 20, 2008.

7. National Aeronautics & Space Administration. February 2, 2008. www.nasa.gov

8. Ott, James. “Combating Congestion.” Aviation Week & Space Technology. Jan 7, 2008: 41.

9. American Institute of Aeronautics & Astronautics, Inc., 2006.

10. Brandt, Steven A. “Introduction to Aeronautics: A Design Perspective.”2nd Edition. Reston, VA