12

2008 SAE Aero Design:

Cargo Plane Preliminary Design Review

Written by:

Jeff Gibson (Team Leader)

Jennifer Allison

Dan Denmark

Ray Klingerman

Kathleen Murray

Steven Tucker

Joe Walk

Submitted to:

Dr. Sepri

Date Submitted: October 26, 2007

Course Titles:

Senior Design: MAE 4291-01

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Table of Contents

Section Title Page Number

Need .................................................................................................................................... 2

Problem Statement and Objectives ..................................................................................... 2

Goals ................................................................................................................................... 2

Evaluation Criteria .............................................................................................................. 3

Information Search.............................................................................................................. 3

Background ......................................................................................................................... 3

Aerodynamics ..................................................................................................................... 4

Wing Structure and Construction........................................................................................ 8

Fuselage and Landing Gear .............................................................................................. 15

Control Systems ................................................................................................................ 21

Economic Analysis ........................................................................................................... 24

References ......................................................................................................................... 25

Appendix A: Schedule ...................................................................................................... 27

Appendix B: Multi-Disciplinary Teams ........................................................................... 28

Appendix C: Life-Long Learning: .................................................................................... 29

Appendix D: Matlab code for take-off analysis: ............................................................... 30

Appendix E: Selig 1223 CFD Analysis: ........................................................................... 33

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Need

There are two major needs to be addressed by this project. The first need is to

compete and do well at the competition. Because Florida Tech has a sparse history in

competing in the SAE Aero Design competition, one of the purposes of the project will

be to gain more recognition for the school through participation in the event.

The second need is the indirect need to maximize carrying capacity for aircraft.

This project will act as an exercise in optimizing certain design aspects toward this goal.

Many of the concepts and techniques used to design the aircraft can be applied to other

real world design scenarios, such as military cargo planes, or passenger airliners.

Problem Statement and Objectives

This design project has several main objectives that the team will pursue which

consist of:

1. Designing and creating an RC aircraft that meets the requirements to compete in

the regular class SAE Aero Design 2008 competition.

2. Competing in the SAE Aero Design 2008 competition.

Goals

The following are the main design requirements imposed by the competition rules and

guidelines supplied by SAE [1].

1. The aircraft must operate using an unmodified OS .61FX engine and E-4010

muffler.

2. The aircraft must be able to take off within a distance of 200 feet and land within

a distance of 400 feet at maximum payload.

3. The overall aircraft dimensions (Length + Width + Height) must not exceed 175

inches.

4. The fuselage must be able to fully enclose and support the rectangular cargo box

measuring 5x5x10 inches.

5. The aircraft must have a gross weight (including max payload) of no more than 55

pounds.

In addition to the design requirements necessary to meet the competition guidelines

and rules, the team has defined several self-imposed design requirements:

1. In order to place well in the competition, the final aircraft must be able to achieve

a successful flight with at least 35 pounds of payload at sea level density. It will

be the main goal of the team to maximize this payload as much as possible while

keeping with the design limitations.

2. The aircraft must be able to make a turning radius necessary to make a full circle

of the airfield without entering any of the no fly zones.

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3. The aircraft must be easy to control, such that an experienced RC pilot can fly the

plane with little difficulty and little practice with the aircraft.

4. The aircraft must be able to sustain the extra load factors of the maneuvers

necessary to meet the mission requirements of the competition.

5. The aircraft must be able to sustain the impact of landing and maintain its

structural integrity.

6. To ensure reliability through the course of the competition, the aircraft must be

easily repaired in the event of a crash or structural failure.

7. To score well on the design category of the competition, the team must develop

an equation to predict the maximum payload based on density altitude within 2

pounds.

Evaluation Criteria

The main criterion for evaluating the success of the project will be the overall

placement in the competition. A secondary criterion will be whether or not the team's

initial goal for maximum payload is met.

Information Search

There is a multitude of sources being used throughout the research and design

phases of this project. Two major sources provided a great deal of information pertaining

to the design. The first is an AIAA journal by E.V. Laitone pertaining to the tandem wing

design ([2] Laitone, E.V. Prandtl’s biplane theory applied to canard and tandem aircraft

AIAA Vol 17, No4, April 1980 pg 233-237). This paper gave the necessary equation for

downwash angle, shown in the Aerodynamic Analysis section that allowed the team to

develop a model for the aerodynamic forces on the second wing. The second is a white

paper published by Leland Nicolai on the subject of aircraft analysis and design as it

pertains to the SAE Aero Design competition. ([3] Nicolai, Leland M. “Estimating R/C

Model Aerodynamics and Performance.” June 2002.). Using the information obtained

from these two sources, a mathematical model for the takeoff distance was developed,

and was used as a method for comparing the performance of tandem wing geometries and

configurations.

Background

The challenge that has been set before the SAE Aero Design competitors is to

design and construct a radio control aircraft that can carry a payload successfully. The

purpose of this challenge is to offer students an opportunity to apply the knowledge and

skills they have been supplied with to a real life situation. Each team entry must follow

specific guidelines for the construction of their aircraft in order to qualify for

competition. This provides experience with working in a design group atmosphere and

with following specific instructions and deadlines.

The direct need of the project involves the need for Florida Tech to enter a team

into the competition, and place well. There are other secondary needs of the project as

well, particularly those which revolve around the military and civil applications of heavy

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lifting aircraft in industry. Competing in the design competition acts as an exercise in

creating the most efficient and effective design possible, and may also spur innovation

and research into new design concepts.

The 2008 Cargo Plane team spoke with the 2007 team to discuss the difficulties

that they have faced in their project as well as what their design entailed and their

reasoning behind their design decisions.

The 2007 cargo plane team faced time constraint difficulties and failed to stick to

their schedule. The team’s construction is late and some parts are still not finished. This

is due to the fact that the designing portion was finished past the scheduled time.

The 2007 cargo plane also discussed their design for the plane. An aspect ratio of

15 has been chosen as the best compromise of various factors. The 2008 team will

reanalyze this design based on the changed 2008 requirements in order to obtain

maximum performance. For practical reasons, the center of gravity of the entire plane

should be vertically aligned with the aerodynamic center or with the pressure center of

the main wing. The nose then has to be far enough from the center of gravity; this way,

the weight which would have to be added in order to compensate the weight of the tail.

The size of the current senior team’s plane is constrained by the elements which have to

be placed inside the fuselage, such as the cargo bay, battery pack and receiver from the

RC unit, fuel tank, 2 servos for the elevator and the rudder.

Aerodynamics

The wing design is extremely important to how an aircraft performs and a great

deal of time must be spent to perfect the design. Everything from the shape of the airfoil,

the length to surface area ratio of the wing, the twist in the wing, and even how far back

the wings are swept must be taken into account for the design.

The decision to choose an airfoil for the main wing would be based on

characteristics that were considered most important to the design. The airfoil’s Lift-to-

Drag ratio, maximum lift and ease of construction. However, the main characteristic

examined was the airfoils’ coefficient of lift (cl) vs. both the coefficient of drag (cd) and

the angle of attack (α). Through the comparison of data analyzed using the XFLR5

program, which is based off of the XFOIL program, the s1223 airfoil was found to be the

superior airfoil design.

The aerodynamic coefficients of the Selig 1223 airfoil, as modeled in XFLR5, can

be found in Appendix E. This data was used during the analysis and design of the wings,

and will be used to precisely model the aerodynamic performance during future design.

The Selig 1223 airfoil, which is shown in Figure 1, has been chosen by the team

as the airfoil that is to be used . The team compared several different airfoils typically

used at the competition; two of these are the Selig 1223 airfoil and the FX63-137 airfoil.

A plot comparing the coefficients of lift at a Reynolds number of 300,000 of the Selig

1223 airfoil to the FX63-137 airfoil, shown in Figure 2 clearly shows that the Selig 1223

has a higher section lift coefficient, as well as better stall performance.

5

Figure 1: Selig 1223 airfoil [4]

Comparison of cl at Re = 300,000

0

0.5

1

1.5

2

2.5

0 2 4 6 8 10 12 14 16 18 20

Angle of Attack (degrees)

Secti

on

lif

t co

eff

icie

nt

Selig 1223

FX 63-137

Figure 2: Comparison of the Selig 1223 and FX63-137 airfoils

As part of the rule changes for the 2008 regular class competition, there is no

longer a restriction on wing planform area. Instead, the sum of the overall aircraft

dimensions (Length + Width + Height) is limited to 175 inches. Because of this change in

requirements, the initial design concept has been altered to a tandem wing aircraft. A

tandem wing aircraft is one which has a second lifting surface for added lift and stability.

This is similar to a canard design, however the front surface is meant to significantly add

to the lift of the aircraft. Figure 3 below shows the Rutan Quickie, an example of a

tandem wing aircraft.

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Figure 3: Rutan Quickie [5]

By adding a tandem wing, the aircraft will have greater lifting capacity, while not

significantly increasing the overall dimensions.

The team plans to have the front wing mounted under the fuselage, and the rear

wing mounted on top, as far back as possible. This will minimize the effects of

downwash from the front wing, and allow the rear wing to produce more lift.

Aerodynamic Analysis

In order to determine the best dimensions for the aircraft, we designed a program that

optimizes the chord length and wing area based on the take-off performance. In

particular, the program analyzes the effect the forward wing has on the aft wing. The

forward wing causes downwash on the aft wing, which reduces the aft wing’s lift and

increases its drag. The following equation 1, from E. V. Laitone’s paper [6] describes the

downwash angle (w) on the aft wing.

2

1

2

1

1

2

1

2

1

1

1 /2/21

/21

)/2(/21

/21

2

1

bgby

by

bgby

by

AR

CVw

L

-------------------(1)

The longitudinal distance between the trailing edge of the forward wing and the leading

edge of the aft wing is denoted as “y” in the above equation. The height difference

between the tandem wings is given by “g” in the equation and “b” is the wingspan. The

subscript “1” denotes the forward wing.

J.H. Crowe, in his paper titled “Tandem-Wing Aeroplanes,” states that the lift to drag

ratio on a tandem-wing aircraft is greater than that of a single wing plane. Further, he

concludes that the maximum lift to drag ratio will occur when the tandem wings are

furthest apart. This is due to the fact that the downwash on the aft wing is lessened the

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further the wings are from each other [7]. Due to this analysis, we have decided that the

forward wing will be as close to the nose of the aircraft as possible, and the aft wing will

be placed as far to the rear of the craft as possible.

To determine the optimal wingspan and chord length, we analyzed how the take-off

distance varied with an increased wingspan and increased chord length. The take-off

distance is given by the following equation 2, according to Leland Nicolai [8]:

mean

TOG

a

VS

2

---------------------------------------------------------------------------------------(2)

where 21

8.0/2 lTO CSWV -----------------------------------------------------(2a)

and LWFDTWga C / -------------------------------------------------------(2b)

The mean acceleration is taken at 70% of the take-off velocity. This affects the total lift

and drag within the equation, given by the following two equations.

lTO SCVL 2

2

1 ----------------------------------------------------------------------------------(3)

and dTO SCVD 2

2

1 --------------------------------------------------------------------------(4)

The coefficients of lift and drag are determined by the aerodynamic properties of the

Selig 1223 airfoil we chose. The program solves for the induced angle of attack, which is

subtracted from the angle of attack of the wing. This new effective angle is then used to

determine the actual coefficient of lift for a finite wing. The coefficient of lift on the aft

wing is solved in the same way, except that the downwash angle must also be subtracted

from the angle of attack.

To determine the optimal chord length of the wing, the program places the leading edge

of the forward wing and the trailing edge of the aft wing at a fixed position predetermined

by us. These positions are based off the total length of the fuselage. The program

assumes that both wings are rectangular and identical in size. Each chord length is

increased linearly at the same rate. Because the leading edge of the forward wing is

fixed, as the chord length grow the trailing edge moves closer to the aft wing. This

occurs in the other direction for the aft wing, where the leading edge moves closer to the

forward wing. As the chord length gets larger, you reach a point where the downwash on

the aft wing causes the lift to decrease more than the increased chord length causes the

lift to increase.

For each wingspan, there is an optimal chord length that maximizes the lift and

minimizes the take-off distance. The following graph shows how the effect on the take-

off distance as the chord length grows. The data was taken at a wingspan of 8ft and a

weight of 45 pounds.

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Figure (4): Take off distance vs. chord length for 8 foot wingspan

The optimal chord length changes as the wingspan changes as well. We iterated our

program to find the optimal chord length at a range of wingspans between 8 and 10 feet

and found that take-off distance decreased as the wingspan increased. The chord length

also increased as the wingspan increased. We have decided on a nine foot wingspan due

to structural constraints and machining difficulties as the wingspan is increased even

higher. At a wingspan of 8.5 feet, the optimal chord length is about 1.21 feet or about

14.5 inches.

Wing Structure and Construction

The structure of the wings is an area where significant weight can be taken off by

choosing the correct material, but the manufacturing methods also have to be weighed

into the material decision. The first material that was considered was a foam which

would have had carbon fiber skin and a carbon fiber spar. This material had the lower

weight that the team was looking for, but it is also a very complicated manufacturing

process. The second material that was considered was balsa wood for the ribs,

prefabricated carbon fiber tube for the spar, and plastic sheeting called MonoKote for the

skin. This method is also light weight, but the manufacturing for it will be much simpler.

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The team has made the decision to use the second set of materials because of the

manufacturability.

Ribs

Manufacturing the ribs for the wing structure out of balsa wood will be done

using a method that has been followed at this institute many times before. The ribs will

be constructed out of pieces of balsa wood cut to the chosen airfoil shape. The shapes

would be cut out by tracing the shape off of a piece of paper using a pen, and then could

be cut out of the main sheet of wood using a simple razor blade. A pen (not a ball point

pen though) has to be used when tracing the shape because the ink will be able to pass

through the paper, and a pencil will leave impressions in the balsa wood that could cause

weaknesses in the structural integrity of the part. After the frame is assembled it would

be covered with MonoKote by simply tacking the sheet down and then applying heat to it

with an iron. The MonoKote provides several advantages over the composite lay up that

was discussed previously. First, the MonoKote has a simpler manufacturing process then

the composite lay up. Secondly, the composite material is very hard to repair if there is a

problem with it, but with the MonoKote all that has to be done is reapplying the heat. If

there are wrinkles it is just apply heat, for a hole there is pressure activated MonoKote to

apply in the field, and then a patch can be made of the original MonoKote which is then

applied with heat.

This material choice was made based on the ease of manufacturing, and it allows

for varying the spacing between the ribs as the team sees fit. This spacing between the

ribs can be determined by several methods including but not limited to the stress that the

ribs will experience and the tension needed from the skin to hold it taunt. After a

literature search it was determined that the first failure that the ribs will cause is the

buckling of the skin as shown below in figure 4.

Figure 4: Primary failure mode caused by rib spacing

This failure will occur before the spacing becomes large enough that the ribs will

individually support enough force to cause failure. Presently, the rib spacing has been

estimated to be between one and a half to two inches, but once we have a sample of the

Ribs

Skin

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plastic sheeting a simple test can be preformed to determine if the spacing can be larger

resulting in a lower weight.

Spar

The design of the spar started with determining an estimation of the loading and

size in conjunction with compiling a list of desired behavior characteristics. Estimates

for the size and loading came from the constraints placed on us by the SAE competition

guidelines for the regular class competition. Those being, that the maximum weight of

the loaded plane, including fuel and payload, would not exceed 55 lbs. From this a

simple force balance for the plane during cruise will show that the lift on the wings will

be 55 lbs. We increased this estimate to 60 lbs to account for the increased lift needed for

take off to accelerate the plane up to cruise altitude. This is a rough estimate that has

been recently modified but as of yet hasn’t been taken into account for the spar analysis.

Then we estimated the maximum wing span available to us using the new

dimensional constraints given by the competition guidelines. The rules now require that

each plane not exceed a 175 inch sum of the height, width and length of the plane,

excluding the prop-length. From this a minimum height was estimated based on

clearance for our already existing propeller length, giving an approximate height of 18

inches. This left a maximum wingspan of 9 feet, and gave our maximum length for the

spar design constraints.

Next we compiled a list of goals we felt it necessary to achieve the best

performance of the wings. The list consists of the following goals for the spar behavior:

Maximize strength

Maximize rigidity

Minimize weight

Maximizing strength is necessary to withstand the most lift force in order to lift

the most weight, which is the entire point of the competition. This strength constraint is

mainly addressed by material selection but certain configurations also affected this goal

and will be discussed later. Because of the long wingspan in order to decrease any

vibrations and flapping of the wings, which decreases the lift efficiency, we realized that

the spar design would have to maximize the rigidity of the spar geometry and material

composition.

Additionally the overall design factor of safety 1.2 had to be considered and to

increase the conservative nature of our estimations it was decided that we would model

the spar based on the assumption that all the lift would be produced by a single wing even

though we had previously decided on a tandem wing configuration. Also, the lift would

absorbed by a single spar even though a secondary spar will be necessary to handle the

torque experienced by the wing and servo/control surface placement.

Using these constraints several geometries were discussed as possible candidates

for the spar geometry. Such discussion included the idea for an I-beam configuration

manufactured using carbon fiber strands, which was rejected because we felt our

fabrication experience was to low to produce something reliable within the time need to

complete construction. Also, the I-beam configuration is generally used when the

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bending direction is fixed to maximize the I-beam properties, but our wing will be

bending due to drag and lift and the resultant bending plane will shift as velocity is varied

and the I-beams behavior will be difficult to predict. Another possibility considered was

a square wooden beam with carbon fiber re-enforcement, which was rejected because the

square would create stress concentrations at the corners and wouldn’t minimize weight.

Also, the square wouldn’t be a perfect square and would there fore have a preferential

bending direction where it would be less resistant to bending and such a direction may

not be immediately known and could result in a weak wing.

Finally, a tube/cylinder design was decided upon for several reasons. First, the

tube maximizes the moment of inertia (I) of the spar while allowing less weight, which

both increases strength, rigidity and reduces weight. Secondly, a tubes bending

characteristics, namely the moment of inertia (I) is axially uniform, which is great

because of the previously mentioned changing directions of the overall bending moment.

The cylinder geometry exhibits similar uniform behavior but doesn’t minimize weight,

however some materials, like wood, can’t be made into a 9 foot tube.

Then several configurations were considered for how the spar would be attached

to the fuselage. Two main configurations were considered; rigidly fixed, and a pinned-

simply supported. It became immediately apparent that the rigidly fixed configuration

produced more stress but less displacement and the pinned-simply supported type of

configuration was rejected. Below in Figure 5 the final configuration model can be seen.

Figure 5: Cantilever beam with uniform load [9]

The uniform load was used as an approximation of the lift distribution on the

wing even though the actual lift will be more parabolic and be more concentrated towards

the half-spar’s center. The stress and vertical displacement behavior for this

configuration are:

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σmax = (0.5ωl2c)/I ymax = - (ωl4)/8EI [9]

ω = distributed load of the lift approx. 0.56 lbs/in (30 lbs/54 inches)

l = length of the half-spar (54 in)

I = moment of inertia ((π/64)*(Do4-Di

4))

E = Modulus of elasticity (Young’s modulus)

Using this simple model the next stage was deciding the material selection which

we selected based on our goal criteria; strong, rigid, and light weight. For a comparison

we decided to compare the performance of three different materials; Carbon Fiber,

Aluminum 7075-T6, and Ponderosa Pine wood. The Carbon Fiber and Aluminum can

both be found in tube configurations and because we want to minimize weaknesses due to

poor construction techniques it was decided that the Carbon Fiber would need to be

purchased. Therefore it was necessary to run our calculations using cross-sections that

are commercially available. Based on the 9 foot wing span and the initial cord-length it

was determined that the outer diameter of the tube would have to be around 0.5-0.8

inches. A vender was found that supplied Carbon Fiber tubing with an outer diameter

and inner diameter of 0.625 x 0.500 inches and with published material properties. This

configuration was modeled for both Aluminum and Carbon Fiber as a comparison.

The wood couldn’t be made into a tube so the cylinder configuration was selected

and an outer diameter was determined based on the loading constraints, materials

properties and design factor of safety. The results of the overall comparison are as

follows:

Table 1

Half-spar Material Comparison Results

Material Properties

Carbon Fiber [10] Aluminum 7075-T6 [11] Ponderosa Pine [12]

Yield Strength [kpsi] 200 73 6.29

Allowable Stress [kpsi] 167 65.5 5.2417

Young's Modulus [Mpsi] 17.8 10.4 1.26-1.31X10-3

Density [lbs/in3] 0.054 0.098 0.0145

Estimated cost $400 $60 $50

Half-spar Analysis Results

Stress [psi] 57.7 57.7 5.2417

Maximum deflection [in] 7.566 12.95 1.787

Weight [lbs] 0.3221 0.5845 0.83

All of the above materials would be capable of bearing the anticipated loading

conditions assumed for the comparison, but the wood weighs the most and the diameter

needed to sustain the structure was found to be 1.16 inches; greater than our 0.5-0.8 in

outer diameter constraint. The Aluminum is also heavier than the Carbon Fiber and

experienced almost twice the deflection. Following up the analysis we generated a

comparison matrix as seen below.

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Str

en

gth

Rig

idity

We

ight

Cost

Availa

bili

ty

Tota

l

Carbon Fiber 5 5 5 1 3 19

Aluminum 7075-T6 3 1 2 2 2 10

Ponderosa Pine 1 4 1 5 4 15

5-1: 5 Best

The selection criteria for the material selection matrix was based on our goals of

maximizing strength, rigidity, minimizing weight and additionally the cost and our ability

to obtain the material commercially (Availability). The end result was that the Carbon

Fiber, even though most expensive, performed the best overall.

In order to remain flexible in our design and in case our budget doesn’t allow for

the cost of the Carbon Fiber our potential fall back options are:

A wooden cylinder core with carbon fiber re-enforcement

An internally tensioned bow spar made from Aluminum

Aluminum tubing with a “Blue foam” core

The problems associated with the wood core and carbon fiber re-enforcement

would be modeling the behavior under loading. How the carbon fiber would affect the

woods strength and rigidity would be difficult to estimate and testing would be our best

option to determine the performance of such a combination. Also, manufacturing would

be more difficult and take more time in addition to the time taken up by the testing.

ANSYS analysis may be possible but there wouldn’t be any comparison for the results to

determine if they were valid. The use of Aluminum with a “Blue foam” core would have

the same complications.

The internal bow spar design is a concept that could increase the performance of

either the Carbon Fiber or the Aluminum. The main concept behind the bow spar is the

presence of a wire running through the hollow tube core diagonally from the bottom

center the wing to the upper top of the wing tips. The wire will hopefully diminish the

deflection of the wings tip under loading and it is anticipated that it may change the

bending behavior from that of a cantilever beam with one fixed end to that of a cantilever

beam with one fixed end and one simply supported end. This should produce a bending

in the middle of the spar that will considerable less than the deflection experienced with

out the wire. Figure 6, seen below, is a rough diagram of a half-spar using the bow spar

concept.

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Figure 6: Bow spar concept diagram

The wire in bow spar (seen here as the red line) will resist the deflection in the tip

caused by the lift on the wing. However, the angle theta (θ) is very small (about 0.53o for

our current geometry) and results in high levels of tension in the wire. In order to get a

maximum level of possible tension in the wire we assumed that the half-spar was totally

rigid and pinned at the connection to the fuselage, transferring all the lift force to the

wires tension. From a simple static analysis of the spar the maximum possible tension

was found to be:

ΣMo = 0 = Lift*27 in – T*sinθ*54 in

o T = 1620 lbs

This is a considerable amount of tension and would require an especially strong

cable. Fortunately in our research we found a vender (Fibraplex Corp.) that sells Carbon

Fiber Tow; a string made from carbon fiber that has a 750 lbs [13] breaking point and

very low weight for $0.40 per foot. Three sets of this cable would allow for over 2100

lbs of tension in the bow spar. The use of this material is expected to allow no

displacement of the end point of the spar and can hopefully be modeled using the fixed-

simply supported cantilever beam with uniform loading model. Also, it may be possible

to analyze the behavior of the spar using ANSYS in comparison to the cantilevered beam

model. In the end the best thing to do will be to test the spar and determine if its behavior

is the best fit for our plane.

If the half-spar does behave the way we expect the model will be similar to that of

Figure 7, seen below, and the maximum displacement will become approximately 0.0326

inches in comparison to 7.566 inches.

T θ

Lift Force

o

15

ymax = (ωx

2/48EI)*(l-x)*(2x-3l)

Figure 7: Bow spar approximate behavior – fixed-simply supported Cantilever beam [9]

What’s not taken into account by this modeling is the axial component of the

tension acting on the spar. Realistically the tension in the Carbon Fiber Tow won’t even

approach the 1620 lbs maximum tension but will be much lower and will hopefully not

greatly affect the integrity of the design. In order to determine if it will have a great

impact the static analysis needs to be redone with the beam fixed and then solved using

the combined displacement of the wire and beam to determine the overall behavior.

Then next phase of design will be the tensioning mechanism and the attachment

to the fuselage. Initially the tensioning mechanism seems like it would need to be able to

with stand a very large tension in the string, but our intention is to connect the Carbon

Fiber Tow to both ends of the wing so only a single tension will run through the entire

string and this will be slightly tensioned at the center of the wing. For a quick mental

comparison take a string and place it under high tension; it’s then possible to increase the

tension without much effort by placing your finger on it and slightly displacing it.

Essentially that will be the same thing being done by the tensioning mechanism. The

displacement will be almost perpendicular to the tension so only a small component of

the tension will be absorbed by the tensioning mechanism. Also, initially we won’t

tension the string beyond removing slack out of the line to help inhibit vibration and

jerking of the wing. Further schematics of how the whole spar will look like and operate

will created in the next phase of the design.

Fuselage and Landing Gear

The fuselage provides the majority of the aircraft’s structure and integrity. The

fuselage also houses all the control systems, the engine, and the cargo bay. Due to the

weight of the items within the fuselage, as well as the weights due to the wings and tail, it

is necessary for the fuselage to be constructed out of a durable material. The location of

the center of gravity is therefore estimated to be located within the cargo bay. The exact

location shall be determined once the mass of the components held within the fuselage

are known or can at least be approximated based on comparison to similar components.

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In accordance with the requirements from SAE, the cargo box being employed for

the plane will be an enclosed rectangular box measuring 5x5x10”, the minimum allowed

parameters for the box. During the competition, the box will be measured and tested to

prove that it can be removed and re-inserted easily. This is done to show that the cargo

box does not add any strength or integrity to the structure of the airframe, but that it can

be secured to the airframe to prevent the box from falling out during flight. Another

requirement is that the box supports the weights placed inside it as a homogeneous mass.

This can be done either by having the weights wedged in the box or having holes cut into

the weights and securing them with posts to the box structure.

The design that is being considered is a box with two interlocking pieces made of

either balsa or basswood. Each piece in a simple half box form that will slip together and

be locked into place by aluminum posts that screw into the bottom half and stick out the

top half, where they will be secured with wing nuts. The basic designs for the top and

bottom half can be seen in figure 8 below with the approximate locations of the post

holes.

Figure 8: Model of the top and bottom half of the cargo box

designed in Pro-E by Jennifer Allison

The choice of material for the cargo box is still to be finalized, but the thickness

of the material has been determined to be 3/16”. Taking this into consideration, the wood

used for the cargo box must be durable enough to be able to support approximately 25

pounds while having a 3/16” thickness and being light enough for flight. Although the

balsa wood is much lighter than the basswood, the basswood is a more logical choice

based on general durability and strength, despite being thin. For example, the

compressive strength of balsa is 3.5 – 27 MPa while the compressive strength of

basswood is between 32.4 – 33 MPa parallel to grain. The flexural modulus should be

considered, although it is assumed that flexing will be prevented by the support of the

airframe against the cargo box.

The support posts for the weights are to be aluminum based on machinability and

availability. To aid in the anchoring of the posts, an additional basswood block can be

added to the base of the box beneath the holes or these blocks can be attached to the

airframe only. This second option would require for perfect alignment between the box’s

17

holes and the locations of the blocks. The full assembly can be seen in Figure 9, without

the posts and wing nuts.

Figure 9: Model of fully assembled cargo box

Designed in Pro-E by Jennifer Allison

Payload plates

Another key part to this project is the payload plates. These plates are to be the

weights carried in the cargo box inside the plane. According to Section 30.2.6.1 in the

SAE AeroDesign Rules for 2008, every team must provide their own plates. [1] This

allows for some flexibility when designing the box and plates themselves. Our team has

decided upon a simple rectangular design that will fit snuggly into the cargo box. They

will also have two holes drilled in them to allow for the support pegs to hold them in

place.

The approximate surface dimensions of the plates, for now, are 4.625”x9.625”.

The thickness of the plates will vary according to the type of material used and which

weight increment each plate is to have. The material type for the plates is going to be

metal, but the type of metal has yet to be determined according to availability and price.

The different weight increments are four 1lb plates, two 5lb plates, two 10lb, and one

20lb. The reasoning behind the different increments is so that during testing, each flight

can have small increments of weight added on. This will assist in testing the fuselage

structure’s stability and the overall aircraft performance.

Landing Force Calculations

The force that the plane will experience upon landing is much higher then the

force that it will experience while resting on the ground. This dynamic force was the

force that was used to model the landing gear in ANSYS, because this should be the

highest force that the plane will experience. A Matlab program was created using

equation 5 so that the various parameters could be altered easily.

18

x

hmFl 1 -------------------------------------------------------------------------(5)

Where Fl is the force upon landing, m is the weight of the aircraft, h is the altitude that

the aircraft is landing from, and x is the distance that the plane travels on the ground.

This equation assumes that the force felt upon landing is absorbed over a distance x

rather then all at one point. This will be accomplished by the flex in the landing gear and

the damping associated with the rubber of the wheels on the landing gear. Below in

figure X is a sample output from the Matlab program that shows how the landing force

dissipates the longer the x component is.

Figure 10: Theoretical landing force as a function of landing distance

This landing force was used in the ANSYS calculations by taking x = 100ft so that we

have a conservative number since the allowed landing distance is 400 ft.

Landing Gear

Three design concepts have been produced for the landing gear. All of the

concepts are of a semi-circular design in order to reduce the number of sharp angles. The

decrease in number of sharp angles prevents having more areas of concentrated stress.

The bowed shape of the landing gear also allows the structure to flex when force is

applied as the aircraft lands. All three of the concepts are to be made of aluminum.

ANSYS analysis was done in order to determine the displacement and the von Mises

stress of the landing gears when an upward force, the force created during the aircraft’s

landing, is applied.

Design concept 1, shown in figure 11 is designed to be attached to the top of the

fuselage. This concept was designed in order to provide a 24in wide spacing between the

wheels and maintain a constant radius of 12in and is 1in wide. It is 12in high in order to

leave clearance between the propeller and the ground. The fuselage is going to be 6in

from top to bottom and then the propeller will reach another 4in below that, leaving a

clearance of 2in between the ground and propeller tip. Since the wingspan of each of our

19

wings is approximately 9ft in length a wide wheel separation is needed in order to keep

the plane stable while it is touching the ground. Also the constant radius is necessary to

evenly distribute the load that is applied to the landing gear as it contacts the ground. The

maximum displacement of this concept is 0.175675in and its maximum von Mises stress

is 11913psi. This concept however has several flaws. One of these flaws is the fact that

when attached to the fuselage, the large cross sectional area will cause more drag. It also

weighs 2.122lbs which is a significant weight addition that is not needed. Also,

placement of a top mounted landing gear is more difficult than a bottom mounted gear.

The location of the center of gravity may place the landing gear at the same point as the

lower wing, which it cannot pass through.

Figure 11: Landing gear concept 1

designed in Pro-E by Raymond Klingerman

To remove the problem that the top mounted landing gear provided, a bottom

mounted, constant radius alternative was designed. Concept 2, shown in figure 12, is 6in

high, in order to leave the necessary 2in of clearance between the ground and the

propeller. This concept is much lighter than the previous, weighing at approximately

0.8lbs. The flaw to this concept is the fact that in order to keep a constant radius of 6in

the separation between the wheels is only 12in, causing the aircraft to be rather unstable

while on the ground. The ANSYS analysis performed on this concept gave a maximum

displacement of 0.07744in and a maximum von Mises stress of 15685psi. This tells us

that the this design deforms less than the taller and wider design but the stresses are

greater in the landing gear due to less area to disperse the stress through.

20

Figure 12: Landing gear concept 2

designed in Pro-E by Raymond Klingerman

Concept 3, as shown in figure 13, is a combination of the two previous designs. It

is 6in high, 1in thick and has a separation between the wheels of 24in. This allows it to be

mounted anywhere under the fuselage but still gives us a wider separation, which allows

for better stability of the aircraft while on the ground. This concept weighs the least

amount at approximately 0.2lbs. This concept however does not have a constant radius

causing it to have higher stresses acting on it as the ANSYS analysis shows. The analysis

showed that the concept will experience a maximum von Misses stress of 48196psi,

which is much higher than the other two concepts but still under the breaking stress of the

aluminum. The displacement of this concept was also greater, at 0.822355in. This

displacement is allowable due to the fact that there is 2 inches of clearance that allows for

such bending of the landing gear. This concept even though it has a higher stress and

deflects more appears to be a good choice as far as stability and attachment reasons. Also,

the larger displacement will allow the shock of the landing to be absorbed by the landing

gear instead of dispersed mostly into the aircraft protecting it from possible damage.

Figure 13: Landing gear concept 3

designed in Pro-E by Raymond Klingerman

21

Our third wheel design has not yet been determined. More analysis of where the

center of gravity of the aircraft is located is going to be done in order to determine

whether to have a nose wheel or a tail wheel design. At this time it is anticipated that a

tail wheel will be used due to the fact that our second wing will be attached directly to the

top of the vertical stabilizer, putting a large amount of mass at the back of the aircraft.

Control Systems

In all remote controlled planes the control systems are very important for the

propulsion and maneuverability of the aircraft. The control system of an RC plane is the

mechanical and electrical (see Figure 6, below) parts that control the throttle, and the

movement of the ailerons, elevators, and rudder. The control systems are a set of

electronics and mechanisms including:

Remote controller

Digital servos

Pushrods/linkages

Battery packs

Wires/switches

Figure 14: Electronics for the control system [14]

The remote controller will be a typical RC plane four channel controller that has a

channel each for all three degrees of freedom (pitch, up/down, left/right) experienced by

the airplane and a final channel controlling the throttle. It will be necessary to make sure

that the joystick motions for flying are setup in a typical manner to make it familiar for

the pilot to operate. The standard setup used in the US is currently ailerons and elevators

controlled by the right joystick and throttle and rudder controlled by the left joystick.

22

The competition rules require that the controller transmit according to the FCC and

Academy of Model Aeronautics 1991 standards and recommend a 2.4 GHz system to

avoid interference. The standards consist of a list of frequencies for different channels in

the 72 MHz, and 2.4-2.48 GHz bands, while the average controller available for purchase

is generally in the 72 MHz band. The controller will determine the rotation of a set of

servos controlling each degree of freedom for the aircraft. There will need to be one

servo for the throttle, two for the rudder, one for each elevator, and one or two for each

aileron depending on the size and expected forces working the ailerons, the total being 7-

9 servos depending on aileron size.

Servos are small electric motors than can be digitally programmed to have an

output rotation of a specific degree and are controlled by the joysticks on the remote

controller. This means that if an object to be moved, such as a rudder, which has no need

to fully rotate, it is not necessary to have a motor that rotates a complete 360 degrees. If

a motor that rotates 360 degrees is used, a complicated four bar crank rocker mechanism

would have to be designed in order to get a small output motion. The servos that are

going to be used can be programmed to rotate a certain degree setting to provide the

small output movement of the rudder. The servos are programmed by a handheld servo

programmer that allows the user to easily and digitally set the specific rotation angles of

the servos.

The servos will most likely be purchased from or donated by a local hobby shop.

The servos available for purchase have a torque output range of 76-333 oz-in for

operation using a six volt battery. The respective weights for the servos are respectively

1.4-2.2 oz and are of varying dimensions and prices. The placement of the servos and

which size will depend on how much torque needs to be used and for how long that

torque needs to be applied. For instance the rudder will be operating a lot of the time

during flight and as the power drains from the batteries the torque output will drop

considerably. It will probably be necessary to test the actual torque output and its change

over time using a setup similar to that seen below in Figure 15.

Figure 15: Servo torque test setup [15]

Servo placement will consist of one servo connected to the engine’s throttle,

which will open and close the intake valve to increase or decrease the power output of the

engine. The servo for the throttle will be located inside the fuselage directly behind the

motor. The servos for the elevators will be located on the underside of each of the

horizontal sections of the tail and will be connected to the elevators using pushrods and

linkages. The two servos for the plane’s rudder will be located low, on both sides of the

Servo

Scale

23

vertical section of the tail. The rudder needs two servos in order to allow it to cover the

full area of rotation necessary for the planes handling. Two or more additional servos will

be necessary for ailerons and will have to be located within the wing’s cross-section,

most likely on a fortified rib.

Pushrods are metal dowels, of a small diameter, that are used to convert the

rotation of the servo to the output motion needed for the object it is attached to. The

pushrods that are going to be used are going to be made using a small diameter aluminum

dowel that well be cut to the necessary size. The pushrods are connected to the servos

and the flaps by linkages. The pushrods are bent at the end where they connect to the

servo and are placed in a hole in the linkage that is glued to the output shaft of the servo.

The other end of the pushrod is glued into the linkage that is connected to the flap.

The linkages that are going to be used on the plane are going to be prefabricated, store

purchased, or donated, typical RC plane linkages. They are typically made of plastic and

are connected to the plane by screws, adhesive or a combination of the two. The

connection of the flap, by the use of linkages and pushrods, to the servo are shown in

Figure 8.

Figure 16: Connection of a flap to a servo using linkages and a pushrod [16]

The battery packs and wiring are going to be store bought or donated and have to

be at least 500 mA-h, as stipulated by the SAE requirements. For the initial design it is

expected that two 6 volt, NiMH battery packs will be used to power the five servos. The

battery packs will be located in the fuselage and will be connected to the servos by the

wiring harness. It is also expected that a third battery pack of a different voltage will be

used in the remote controller.

Design considerations that will need to be taken into account to prevent failure

will be the possible overload of the batteries when multiple servos are operated together.

For instance when turning the rudder and ailerons will be used simultaneously, and draw

a load for four to six servos at the same time. If the batteries are over loaded the servos

won’t operate correctly and loss of control could occur. Also, the placement will have to

be precise in order to have balance and minimize vibrations. Because there is also a

“slop” test performed by the judges prior to each flight to make sure that there is no give

in the controls the linkages will have to be tight and properly put together. There is also a

24

requirement for servo testing in the design report that will be turned into SAE prior to

competition.

Note: Some of the items discussed in this section, as stated, are going to be prefabricated,

store purchased, or donated items in order to save the team time and money.

Economic Analysis

Current Budget:

Registration fee $450.00

Control systems/electronics $600.00

Carbon Fiber Spars $400.00

Balsa/Bass wood $150.00

MonoKote Film $100.00

Miscellaneous supplies $300.00

Travel cost $700.00

TOTAL $2,700.00

Sources of funding:

Because this project is being fully funded by the university, pursuit of financial

sponsors has been put on hold.

25

References

[1] Society of Automotive Engineers. “SAE Aero Design 2007 Rules and Guidelines.”

<http://www.sae.org/students/aerorules.pdf>

[2] Laitone, E.V. Prandtl’s biplane theory applied to canard and tandem aircraft AIAA

Vol 17, No4, April 1980 pg 233-237

[3] Nicolai, Leland M. “Estimating R/C Model Aerodynamics and Performance.” June

2002.

[4] Pisano, Jessica. “Heavy Lift Cargo Plane.” Stevens Institute of Technology.

2004.

<http://www.stevens.edu/engineering/me/fileadmin/me/senior_design/2004/grp13

/graphs.html>. 23 April, 2007

[5] Wikimedia Commons. “Image: Rutan Quickie.”

<http://upload.wikimedia.org/wikipedia/commons/d/de/Rutan_quickie_q2.jpg>.

September 10, 2007.

[6] Laitone, E. V. “Prandtl’s Biplane Theory Applied to Canard and Tandem Aircraft.”

Journal of Aircraft. Vol. 17, No. 4. April, 1980.

[7] Crowe, J. H. “Tandem-Wing Aeroplanes: An Examination of the Characteristics of

this Type of Wing Arrangement.” Aircraft Engineering. October, 1935.

[8] Nicolai, Leland M. “Estimating R/C Model Aerodynamics and Performance.” SAE

White Paper. June, 2002.

[9] Budynas, Richard: Mechanical Engineering Design, 8th ed., McGraw-Hill Book

Company, NY, 2007.

[10] GraphiteStore.com. <http://www.graphitestore.com>. Copyright 2002-107.

September, 23rd 2007.

[11] Beer, Ferdinand: Mechanics of Materials, 4 ed., McGraw-Hill Book Company, NY,

2006.

[12] Automations, Inc.

http://www.matweb.com/search/SpecificMaterial.asp?bassnum=PTSAJ Copyright

1996-2007. September 25th

2007.

26

[13] Fibraplex Corp.

<http://www.fibraplex.com/Carbon%20Fiber%20Rope%20String.as>. Copyright

2007. October, 22nd 2007.

[14] Fieldman, Jim. "Great Planes Patty Wagstaff's Extra 300S ARF Product

Review.” Great Planes Homepage. June 2003.

<http://www.greatplanes.com/reviews/gpma1305-rcm.html>.

September 12, 2007.

[15] Troy Built Models. "TBM Servo and Servo Extension Testing.”

<http://www.troybuiltmodels.com/servo_testing.htm>.

September 12, 2007.

[16] Aero Protect Corporation.

<http://www.aeroprotect.com/Workbench/CUDA/Images/Wing46.JPG>.

Copyright 1999-2006. April 24, 2007

27

Appendix A: Schedule

Table A-1: Schedule

28

Appendix B: Multi-Disciplinary Teams

The following chart shows a breakdown of current roles on the team, and the

people fulfilling them:

Volunteer Team Member:

Sarah Lagerquist

The team members have the following majors:

Name Major

Jeff Gibson Aerospace Engineering

Steven Tucker Aerospace Engineering

Jenn Allison Aerospace Engineering

Joe Walk Aerospace Engineering

Ray Klingerman Mechanical Engineering

Dan Denmark Mechanical Engineering

Kathleen Murray Mech+Aero Engineering

Sarah Lagerquist Aerospace Engineering

Tim Arbeiter Business

The mechanical engineers on the project are responsible for the structural and

control systems design, as well as drafting. The aerospace engineers are responsible for

the design related to aerodynamic performance, stability, and control. Students from both

Team Leader

Jeff Gibson

Drafts

Person Resource

Manager

Communica

tor Technical

Engineer

Researcher Master

Builder

Daniel

Denmark

Ray

Klingerman

Kathleen

Murray

Tim Arbeiter

Daniel

Denmark

Jeff Gibson

Jen Allison

Tim Arbeiter

Aerodynamic

s

Steve Tucker

Joe Walk

Jeff Gibson

Structures/

Electrical

Jen Allison

Daniel Denmark

Ray Klingerman Kathleen Murray

Jen Allison

Steve Tucker

Jeff Gibson

Kathleen

Murray

29

majors must apply knowledge in their respective fields, and be able to communicate their

design ideas and analysis to the other team members. Additionally, one team member is a

business major, and is responsible for resource management, communication with

external parties, and website development. By dedicating themselves to their particular

tasks, the team members are able to work together effectively, and the team as a whole

can progress toward its final goal.

Appendix C: Life-Long Learning:

In order to achieve the goals of this design project, the team must actively engage

in gaining knowledge and insight that is not part of the normal curriculum. By doing a

literature search, as well as performing other research, the team can find the information

they need to succeed with the project. Design concepts unique to this project, such as the

tandem wing designs, and the “bow” spar design, are not specifically taught in

classrooms. The team members working on these elements of the project needed to use

the skills they already possessed, but also pursue additional knowledge into these

subjects. Only after participating in this continued learning, were the team members able

to apply their skills toward the design of these particular components to the aircraft.

Though knowledge of these two aspects of the design has been obtained, there will be

future instances during the course of the project where team members will have to learn

additional information on the subject.

30

Appendix D: Matlab code for take-off analysis:

function [x,y]=sgy() clear all; clc; %% Define values rho=0.002378; %density (slugs/ft^3) g=32.2; %gravity acceleration (ft/s^2) Fc=0.03; %coefficient of rolling friction T=20; %static thrust (lb) z=1; %height difference between wings (ft) Clmax=2.25; %maximum lift coefficient Cf=0.0059;

b1=8; %wingspan first wing (ft) b2=8; %wingspan second wing (ft) e1=.7; %wing efficiency first wing (rect.) e2=.7; %wing efficiency second wing (rect.) c1=0.5; %Chord length first wing (ft) c2=0.5; %Chord length second wing (ft) W=55; %weight (pounds) alpha=0; %angle of attack (degrees) alphamax=14; i=1; startdist=13.083-b1-8/12; %distance between LE of forward

wing %and TE of aft wing %% Begin While loop while c1<=2.0

S1=b1*c1; %Area (ft^2) first wing S2=b2*c2; %Area (ft^2) second wing AR1=b1^2/S1; %aspect ratio first wing AR2=b2^2/S2; %aspect ratio second wing y=startdist-c1-c2; %distance between TE of forward wing %and LE of aft wing (ft) %% Solve for Fuselage Drag lF=49/12; %length (ft) dF=6*sqrt(2)/12; %diameter (ft) Swet=1300; %Wetted area (ft^2) FR=lF/dF; %fineness ratio FF=1+60/FR^3+.0025*FR; %Fineness Factor cdF=FF*Cf*Swet/(1440); %Drag coefficient due to fuselage %% Solve for Wing Drag L=1.2; R=1.05; tc=.13; FF=(1+L*tc+100*tc^4)*R; cdW=FF*Cf*4; %Additional *2 for second wing %% Additional Drags and solve for Cdmin (taken from Nicolai paper)

31

cdLG=0.0042;

cdE=0.002; cdVT=0.00039; cdTB=0.00009; cdmin=cdTB+cdVT+cdE+cdLG+cdW+cdF; %Minimum drag %% Solve for lift and drag coefficient of first wing cla1=1.09+0.0933*alpha; %coeff. of lift (infinite) alpha_ind1=2*cla1/(pi*AR1)*(180/pi); %induced angle of attack cdi1=2*cla1^2/(pi*e1*AR1); %induced drag coefficient alpha_eff1=alpha-alpha_ind1; %effective angle of attack cl1=1.09+0.0933*alpha_eff1; %coeff. of lift (finite) cd1=2*cl1^2/(pi*e1*AR1); %coefficient of drag %% Solve for maximum lift on first wing clamax1=1.09+0.0933*alphamax; alphamax_ind1=2*clamax1/(pi*AR1)*(180/pi); alphamax_eff1=alphamax-alphamax_ind1; clmax1=1.09+0.0933*alphamax_eff1; %% Solve for downwash angle on second wing eps2=(cl1/(2*pi*AR1)*(((1+2*y/b1)/((1+2*y/b1)^2+(2*z/b1)^2))+((1- 2*y/b1)^2)/((1-2*y/b1)^2+(2*z/b1)^2)))*180/pi; %% Solve for lift and drag on second wing (same analysis as first)

cla2=1.09+0.0933*alpha; alpha_ind2=2*cla2/(pi*AR2)*(180/pi); cdi2=2*cla2^2/(pi*e2*AR2); alpha_eff2=alpha-eps2-alpha_ind2; cl2=1.09+0.0933*alpha_eff2; cd2=2*cl2^2/(pi*e2*AR2); %% Solve for maximum lift on aft wing clamax2=1.09+0.0933*alphamax; alphamax_ind2=2*clamax2/(pi*AR2)*(180/pi); alphamax_eff2=alphamax-alphamax_ind2; clmax2=1.09+0.0933*alphamax_eff2; %% Solve for Take-off Velocity Vto=(2*W/((S1*clmax1+S2*clmax2)*0.8*rho))^.5;

%% Solve for Mean Acceleration D=0.5*(cd1+cdmin)*rho*(.7*Vto)^2*S1+0.5*(cd2+cdmin)*rho*(.7*Vto)^2*S2; L=0.5*cl1*rho*(.7*Vto)^2*S2+0.5*cl2*rho*(.7*Vto)^2*S2; a=(g/W)*(T-D-(Fc*(W-L))); %% Solve for Take-off Distance todist(i)=Vto^2/(2*a); %%Take-off distance chord(i)=c1; %%Chord length

32

%% Increment chord lengths c1=c1+0.01; c2=c2+0.01; i=i+1; end %end while loop %% Plot take-off distance vs. chord length plot(chord,todist); grid on; title('Take-off Distance vs. Chord Length'); xlabel('Chord Length (feet)'); ylabel('Take-off Distance (feet)'); [x,j]=min(todist); y=chord(j); end

33

Appendix E: Selig 1223 CFD Analysis:

The graphs are attached directly following this page.

34

Appendix F: Team Work Division:

Jeff Gibson – Need, Problem Statement and Objectives, Goals, Evaluation Criteria,

Information Search, Schedule, Multi-Disciplinary, Life-Long Learning, Economic

Analysis

Jennifer Allison – Fuselage and Landing Gear (Fuselage, Cargo Box), Economic

Analysis

Dan Denmark – Wing Structure and Construction (Spar), Control Systems, Economic

Analysis

Ray Klingerman – Fuselage and Landing Gear (Landing Gear), Control Systems,

Economic Analysis, Report Editing

Sarah Lagerquist – Background, Fuselage and Landing Gear (Payload Plates), Economic

Analysis

Kathleen Murray – Wing Structure and Construction (Ribs), Fuselage and Landing Gear

(Landing Force Calculations), Economic Analysis

Steven Tucker – Aerodynamics (Aerodynamic Analysis), Economic Analysis, Matlab

code for take-off analysis

Joe Walk - Aerodynamics, Economic Analysis, Selig 1223 CFD Analysis