Final Design Report - Purdue University



AAE 451

Team 3 – Project Avatar

Final Report

Professor Andrisani

Fall 2003

Purdue University

School of Aeronautics and Astronautics

1282 Grissom Hall

West Lafayette, IN 47907

Final Report

AAE 451 Aircraft Senior Design

Professor Andrisani

Fall 2003

We, the undersigned authors, hereby declare the originality of all material in this report, unless properly cited or referenced.

Team 3

Brian Chesko, Dynamics and Controls, Performance Date

Brian Hronchek, Propulsion, Structures Date

Ted Light, Team Co-Leader, Aerodynamics, Dynamics and Control Date

Doug Mousseau, Team Leader, Structures, Propulsion Date

Brent Robbins, Performance, Aerodynamics Date

Emil Tchilian, Aerodynamics, Performance Date

NOTES ABOUT THIS REPORT:

Since this project is primarily a design project, the analysis shown in the body of the report is the fundamental work relating to the overall design of the aircraft.

This design also has the possibility of being constructed at a future time. Some of the decisions made in the design of this aircraft were made in order to aid in the construction process of the plane. For that reason, there is a very important section in the Appendix relating to the construction of the plane. If there are specific configuration questions, the pictures and instructions found in the construction section may be helpful in answering them.

A CD has been included as part of this report. This CD contains the electronic copy of the Pro/E model used for some of the analysis along with electronic copies of important documentation. A good summary of the design can be found in electronic format in the CDR presentation on the CD.

Executive Summary

The plane designed for this particular mission is described as a low wing aircraft with a T-tail and a high pusher engine. The landing gear is a tricycle gear with four inch diameter wheels.

Some of the design considerations leading to this particular configuration include the pod safety and propeller shielding.

The low wing design allows more structure to be placed below the pod, and thus increasing the likelihood that the pod will survive an incident. This is a unique aspect of this design that makes it a more crashworthy aircraft than many high wing concepts.

The pusher engine ensures that the view of the camera looking forward from the pod will not be inhibited by a propeller or exhaust. Most two cycle model aircraft engines tend to purge a great deal of oil and unburned gasoline out the exhaust. It was felt that having the engine located in front of the camera could potentially cause some visibility problems even if the exhaust pipe was rerouted around the camera.

The high mounted engine allows the construction of a tail assembly that protects the prop from damage due to contact with the ground. This is an important consideration because a prop that comes into contact with the ground tends to break into many pieces. These pieces can then potentially cause substantial damage to the surrounding structure.

The landing gear design is a robust break-away concept. If the gear collapse, they will remain under the fuselage, and buffer the electronics from impact with the ground.

A T-tail approach was taken to allow the horizontal and vertical stabilizer to be behind the propeller, thus making them more effective.

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Table of Contents

Table of Contents i

List of Figures iv

List of Tables v

List of Variables vi

1 Request for Proposal and Design Objectives 1

2 Sizing 1

3 Aerodynamic Analysis 3

3.1 Wing Modeling 3

3.2 Airfoil Selection 4

3.3 Wing Performance Analysis 5

3.4 Horizontal Tail Analysis 8

4 Propulsion Analysis 9

4.1 Engine Selection 9

5 Dynamics and Controls 11

5.1 Center of Gravity 11

5.2 Aerodynamic Center 12

5.3 Static Margin 12

5.4 Dihedral Angle 13

5.5 Horizontal Tail Size 13

5.6 Vertical Tail Size 14

5.7 Control Surface Size and Trimming 15

6 Structures 18

6.1 Material Selection 18

6.1.1 Basic Building Material 18

6.1.2 Wing and Tail Covering Material 18

6.1.3 Fuselage Covering 18

6.2 Wing Spar Analysis 18

6.2.1 Bending Loads 19

6.2.2 Torsion 20

6.2.3 Final Spar Dimensions 21

6.3 Tail Beam Analysis 21

6.3.1 Bending Loads 21

6.3.2 Torsion 22

6.3.3 Final Tail Beam Dimensions 22

6.4 Landing Gear Analysis 22

6.4.1 Rear Gear Analysis 22

6.4.1.1 Energy Absorption 22

6.4.2 Front Gear Analysis 23

6.5 Tail Analysis 23

6.6 Final Weight Analysis 23

7 Performance 24

8 Cost 25

9 Summary and Recommendations 26

10 References 27

11 Appendix: - 1 -

11.1 Initial Sizing - 1 -

11.1.1 Constraints – Cruise Speed: - 1 -

11.1.2 Constraints – Stall Speed - 1 -

11.1.3 Constraints – Climb Angle - 1 -

11.1.4 Constraints – Ceiling - 2 -

11.1.5 Constraints – Endurance - 2 -

11.1.6 Constraints – Takeoff Distance - 3 -

11.1.7 Constraints – Landing Distance - 3 -

11.2 Aerodynamics - 4 -

11.2.1 General Information - 4 -

11.2.2 Sample Output from Lifting Line Code - 4 -

11.2.3 Zero lift angle of attacks determination: - 5 -

11.2.4 Sample run of the main wing with flaperons at 15° - 6 -

11.2.5 Experimental Clark Y data -- Stall at approximately 13-14° - 7 -

11.2.6 More General Information - 8 -

11.2.7 Drag Build Up at Cruise - 8 -

11.2.8 Wing Dimensions - 9 -

11.3 Propulsion - 9 -

11.3.1 Correspondence with O.S. Engines - 9 -

11.4 Dynamics and Controls - 11 -

11.4.1 Horizontal Tail versus Theta Double Dot - 11 -

11.4.2 Cm versus Angle of Attack for Landing and 15 degrees flaperons - 12 -

11.4.3 CL of Horizontal Tail versus Angle of Attack of Aircraft for Cruise and 0° Flaperons - 12 -

11.4.4 CL of Horizontal Tail versus Angle of Attack of Aircraft for Landing and 15° Flaperons - 13 -

11.4.5 Takeoff Rotation Equation - 13 -

11.4.6 Needed CL for Horizontal Tail at Specified Aircraft Angle of Attack - 14 -

11.5 Structures - 14 -

11.5.1 Material Trade Study - 14 -

11.5.2 Elaboration on Equations - 15 -

11.5.3 Forces Acting on Tail - 16 -

11.5.4 Plots of Tail Deflection and Twist - 17 -

11.6 Cost - 17 -

11.6.1 Airframe Cost - 17 -

11.6.2 Electronics Cost - 18 -

11.6.3 Propulsion Cost - 18 -

11.6.4 Total Cost - 18 -

11.6.5 Total Value - 18 -

11.7 Thoughts on Construction - 19 -

11.7.1 View of Internal Structure - 19 -

11.7.2 Fuselage - 19 -

11.7.3 Wing - 19 -

11.7.3.1 View of Internal Wing Structure - 20 -

11.7.4 Tail - 20 -

11.7.4.1 View of Tail Structure - 21 -

11.7.5 Landing Gear - 21 -

11.7.5.1 Landing Gear Buckling Analysis - 24 -

List of Figures

Figure ‎2-1: Aircraft Constraint Diagram 2

Figure ‎2-2: Constraint Diagram (zoom) 2

Figure ‎3-1: Prandtl's Lifting Line Theory 3

Figure ‎3-2: Drag Polar for Candidate Airfoils 4

Figure ‎3-3: Clark-Y Airfoil 5

Figure ‎3-6: Lift Coefficient versus a 6

Figure ‎3-7: 2-D Viscous and Total 3-D Drag Coefficient 6

Figure ‎3-8: Lift versus Angle of Attack for Wing with Flaps Deflected 7

Figure ‎3-9: 2-D Viscous and Total 3-D Drag Coefficient for Wing with Flaps Deflected 7

Figure ‎3-10: Lift Coefficient of Tail vs. a with no Elevator Deflection 8

Figure ‎3-11: Lift Coefficient of Tail with 15o Elevator Deflection 8

Figure ‎4-1: Thrust vs. Horsepower for two and four bladed propellers at 8500 RPM 10

Figure ‎4-2: RPM vs. Efficiency for two and four bladed propellers during cruise 10

Figure ‎4-3: Zinger 4 bladed propeller 11

Figure ‎5-1: CG and AC of Aircraft 13

Figure ‎5-2: Horizontal Tail Area versus Theta Double Dot 14

Figure ‎5-3: Vertical Tail Area versus Yaw Moment 15

Figure ‎5-4: Control Surface Size 16

Figure ‎5-5: Angle of Attack versus Flaperon Deflection 17

Figure ‎6-1: Simple Cantilever Beam (Wing) 19

Figure ‎6-2: Deflection at Tip of Outboard Section of Spar (Percent of Spar Length) 20

Figure ‎6-3: Torsion of Outboard Wing Spars 21

Figure ‎6-4: Rear Gear Configuration 23

List of Tables

Table ‎1-1: Design Requirements and Objectives 1

Table ‎4-1: Performance Characteristics of Propulsion System 11

Table ‎5-1: Control Surface Sizing 15

Table ‎5-2: Control Surface Sizing Part 2 16

Table ‎5-3: Poles of Transient Response 17

Table ‎6-1: Final Spar Dimensions 21

Table ‎6-2: Final Tail Beam Dimensions 22

Table ‎6-3: Weight Analysis 24

Table ‎8-1: Cost of Airframe 25

List of Variables

a0 2D Lift Curve Slope

b Span

c Chord Length

cdi Sectional Induced Drag Coefficient

cl Section Lift Coefficient

g Acceleration Due to Gravity

k Spring Constant

q Dynamic Pressure

xAC Position of Aerodynamic Center

xCG Position of Center of Gravity

xh HOrHasdfasdfkjsahdflkjasdflkjasdflsdafDistance between wing quarter chord and horizontal tail quarter chord

xv HOrHasdfasdfkjsahdflkjasdflkjasdflsdafDistance between wing quarter chord and vertical tail quarter chord

AR Aspect Ratio

CD Coefficient of Drag

CDi Induced Drag Coefficient

CDp Parasitic Drag Coefficient

CL Coefficient of Lift

Cm fus Pitching Moment Coefficient for the fuselage

[pic] Variation of wing pitching moment with flaperon deflection

Cm Pitching Moment Coefficient for the aircraft

CLα 3D Lift Curve Slope

D Drag

E Young’s Modulus

KE Kinetic Energy

I Moment of Inertia

L Lift

PE Potential Energy

Re Reynolds Number

Sht Horizontal Tail Reference Area

Svt, Sv-tail Vertical Tail Reference Area

S, Sw, Sref Wing Reference Area

SM Static Margin

T Thrust

T Torque

Vstall Stall Velocity

VTO Takeoff Velocity

[pic] Freestream Velocity

Vh Horizontal Tail Volume Coefficient

Vv Vertical Tail Volume Coefficient

[pic] Vertical Distance to Thrust Force from Vertical Center of Gravity

W/P Power Loading

W/S Wing Loading

( Angle of Attack

αL=0 Zero-Lift Angle of Attack

αI Induced Angle of Attack

(f Flap Deflection

( Flight Path Angle

( Induced Drag Factor

(h Dynamic pressure ratio of horizontal tail to free stream

(p Propeller Efficiency

( Viscosity of Air

( Density of Air

Γ Circulation

Ф Angle of Rotation

Request for Proposal and Design Objectives

The objective of this project is to design a large-scale remote control aircraft with the capability to photograph land based objects and assign accurate GPS coordinates to the targeted object.

Several design constraints were included in this proposal. In addition to the constraints that were explicitly given by the customers, some further constraints were added by the design team in order to make the project more marketable and contemporary. The design constraints used in this project can be found in Table ‎1-1.

For the purposes of this paper, design requirements are considered minimums, both quantitatively and qualitatively, that the aircraft must meet. Design objectives are goals that are not necessary to meet, but would help in the marketability of the aircraft. These objectives will not be used as design constraints such that they will not be allowed to drive the design, however, if they are met, the aircraft will be much more marketable.

Table ‎1-1: Design Requirements and Objectives

|Design Requirements |Design Objectives |

|Maximum weight < 55 lbs | |

|Cruise speed > 50 ft/sec | |

|Stall speed < 30 ft/sec | |

|Climb angle > 5.5 degrees | |

|Operative ceiling > 1000 ft |Operative ceiling > 6500 ft |

|Flight time > 30 minutes |Flight time > 1 hour |

|Payload of 20 lbs in 14”x6”x20” pod | |

|Spending limit (for airframe only) < $300 | |

|T.O. distance < 105 feet | |

|Rough field capabilities | |

|Detachable wing |Multi-mission capabilities (adaptable wing) |

|Easy construction |Easily repairable |

|Carry pitot-static boom | |

Sizing

One of the first important processes in the design of a new aircraft is the sizing. The sizing methodology uses analytical and empirical techniques to predict the size of the final aircraft. All equations used to predict the size of the aircraft can be found in the Appendix under the appropriate category.

Figure ‎2-1 shows the aircraft constraint diagram created by the sizing results. The design space is in the lower left corner.

[pic]

Figure ‎2-1: Aircraft Constraint Diagram

Figure ‎2-2 shows a zoomed-in view of the constraint diagram. This view clearly shows the design space. The values for power loading and wing loading at the starred location are given in the plot.

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Figure ‎2-2: Constraint Diagram (zoom)

Aerodynamic Analysis

1 Wing Modeling

Based upon the initial sizing discussed above, a required wing loading of W/S=1.28 was obtained, resulting in a wing area of approximately 42 ft2. Since the stated design requirements & objectives require an aircraft that is easy to construct, a rectangular wing planform was chosen. The aspect ratio for the design was determined to be 5 through trade studies performed by individual group members examining the weight and drag of different aspect ratios. From this point, the wing was fairly well defined.

To examine the wing in greater detail, a MATLAB code implementing Prandtl’s Lifting Line Theory was used. This theory models the wing as a series of horseshoe vortices as depicted below in Figure ‎3-1.

[pic]

Figure ‎3-1: Prandtl's Lifting Line Theory

This analysis gives a distribution of circulation, Γ, along the span of the wing expressed as follows, where θ is the angular spanwise location along the wing. This distribution will eventually give a lift distribution along the span of the wing.

[pic]

Using this distribution, the problem can be formulated as a system of equations with as many unknowns as control points taken along the wing. The induced angle of attack along the span of the wing can be expressed in Equation ‎3-2.

Prandtl’s wing equation is given in Equation ‎3-3.

Substituting the above expressions for circulation and induced angle of attack into Equation ‎3-3 gives Equation ‎3-4.

Solving the system of equations gives the An terms, describing the circulation distribution along the span. From this distribution, the Cl distribution along the span can be found from Equation ‎3-3. The induced angle of attack and induced drag coefficient can also be found along the span of the wing from the expressions given above. The 3D wing CL and CDi can also be found from the expressions below.

CL = πAR·A1·α

A sample output for the wing at 2° at cruise conditions is shown in the Appendix.

2 Airfoil Selection

Knowing the lift coefficient over the span of the wing enables a criterion for airfoil selection. By finding an airfoil that has low drag over the required range of cl values at cruise conditions, an airfoil can be selected that results in low drag for the wing. Since the aircraft will spend most of its time in cruise, this is the most desirable condition to analyze for airfoil selection. From the construction requirements discussed above, an airfoil that was easy to make was desired. This would include a round leading edge, a trailing edge that could easily be constructed, and a relatively flat lower surface. Figure ‎3-2 shows the drag polars for several airfoils that were considered.

[pic]

Figure ‎3-2: Drag Polar for Candidate Airfoils

The above analysis was carried out using XFOIL. As can be seen, the Clark Y airfoil has low drag over the range of cl values the wing sections need at cruise and has a shape that meets the criteria for easy construction described above. A plot of the Clark Y airfoil is shown below in Figure ‎3-3.

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Figure ‎3-3: Clark-Y Airfoil

Entering airfoil-specific data such as the 2D lift curve slope and zero-lift angle of attack for the Clark Y airfoil into the lifting line code enabled an accurate analysis of the wing. The 2D airfoil analysis from XFOIL at Re = 900,000 (cruise conditions) is shown below.

3 Wing Performance Analysis

Given the distribution of cl values along the wing at a particular angle of attack and the 2D drag polar data from XFOIL above, the 2D parasitic drag coefficient, cdp could be found at each spanwise location along the wing. This was done by fitting polynomials to the 2D airfoil data above. The drag coefficients could then be integrated to give a total parasitic drag coefficient (CDp) along the wing. The induced drag coefficient (CDi) was then added, giving a total drag coefficient, including both induced and viscous drag (CD = CDp + CDi).

Using the above approach, multiple runs were conducted at various angles of attack and 3D data for the wing was found. The results are shown below. Two runs were made at cruise (Re = 900,000, V = 50 ft/s) and stall (Re = 500,000, V = 30ft/s) conditions. These results are below.

The lifting line code had input parameters that were updated depending on the conditions that we ran our wing at. The input parameters were:

AR Aspect Ratio

a0 2D lift curve slope

αL=0 Angle of attack at zero lift

α Angle of attack of the wing with respect to the free stream

Below are plots of the 3D data generated for our wing at cruise conditions.

[pic]

Figure ‎3-6: Lift Coefficient versus a

[pic]

Figure ‎3-7: 2-D Viscous and Total 3-D Drag Coefficient

To generate the lift required for steady level flight, a CL of 0.44 is needed. Figure ‎3-6 above shows that the wing needs to be at approximately 2.8° to achieve it. This sets angle at which the wing should be mounted.

To meet the stall requirement specified in our DR&O document, a CL of approximately 1.19 is needed. From Figure ‎3-8, to achieve this CL, the aircraft would have to fly at an angle of over 13°. Experimental data for a wing with the same airfoil section and similar dimensions in the Appendix shows that this would be near, if not at, the stall of the wing. To alleviate this problem, flaperons were implemented into the wing. A procedure similar to the one described above was used to analyze the wing with flaps deflected 15° (Flaps are hinged 80% chord of main wing). Plots of the lift and drag coefficients for the wing with and without flaps deflected are shown below.

[pic]

Figure ‎3-8: Lift versus Angle of Attack for Wing with Flaps Deflected

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Figure ‎3-9: 2-D Viscous and Total 3-D Drag Coefficient for Wing with Flaps Deflected

As can be seen above (Figure ‎3-8), with flaps implemented, we can attain the CL required at stall at an angle of attack of 11°. At this angle of attack the airfoil would be out of the stall region. The take off and landing characteristics are similar to the stall characteristics with the exception of the landing and take-off speed, where VTO = 1.1 Vstall. The wing with flaps deflected at 15° can achieve the CL needed for take-off at an angle of attack of 8.5°. A table with all the operating parameters for the main wing at stall, takeoff, and cruise conditions can be found in the Appendix.

4 Horizontal Tail Analysis

The horizontal tail was modeled using the same lifting line routine described above. The airfoil selected for both the horizontal and vertical tail was the NACA 0012. The tail sizing was provided from the dynamics and controls analysis. Figure ‎3-10 and Figure ‎3-11show the horizontal tail performance at cruise and at stall (15° elevator deflection). This data will be used in the dynamics and control section to decide the incidence of the horizontal tail and whether or not it produces enough coefficient of lift to trim the aircraft.

[pic]

Figure ‎3-10: Lift Coefficient of Tail vs. a with no Elevator Deflection

[pic]

Figure ‎3-11: Lift Coefficient of Tail with 15o Elevator Deflection

Propulsion Analysis

The propulsion system selection and sizing is an important part of aircraft design, and depends heavily on the size, weight, and configuration of the aircraft.

To begin the propulsion system selection and sizing, a drag and weight program was used to model the aircraft to help predict the amount of drag that would be produced during the different flight regimes. Using this MATLAB code, along with the help of the aerodynamics and structures and weights teams, the aircraft was predicted to be 53 lb with a 14.4 ft wingspan and an aspect ratio of 5. These characteristics, along with other important aircraft defining characteristics were used to make simple drag calculations. Because the amount of thrust needed during flight is equal to the drag created by the aircraft during straight and level flight (ie. cruise), having a good estimate of the drag allows a good estimate as to how much thrust will be needed. (The drag prediction done here is a good estimate, but is not as detailed as what the Aerodynamics team has done. For a detailed analysis of the lift and drag performance of the aircraft, see the Aerodynamics Section).

Simple drag prediction equations were used. The parasite and induced drag coefficients were calculated using Equation ‎4-1 and Equation ‎4-2.

where AR is the aspect ratio of the main wing and e is the Oswald’s Efficiency Factor. Drag is calculated using the dynamic pressure.

These equations gave us a drag of about 4.5 lbf under cruising conditions and about 7.5 lbf for takeoff.

1 Engine Selection

Starting with the constraint diagram, and using our estimated aircraft weight, the engine for our aircraft will need to produce about 3.5 hp. O.S. Engines makes a 1.6 cubic inch glow engine that produces 3.7 hp which is very close to the estimated power required. O.S. offers a fuel-injected version of the 1.60 engine which was chosen above the non- fuel-injected version because of the height of the engine above the fuel tank. O.S. recommends placing the fuel tank about a quarter inch above the needle valve for the non-fuel-injected version, but the fuel-injected version claims to regulate the air and fuel mixture that the engine is receiving at any altitude and attitude. The engine can be trimmed by the pilot during flight to enhance performance and give the pilot better control over the engine performance.

Since the propeller needs to be matched to the specific performance characteristics of the engine, the engine had to be chosen first. The O.S. 1.60 FX-FI engine produces 3.7 hp at 8,500 RPM and ranges between 1,800 and 9,000 RPM. This information, along with the predicted drag, was used as the input into a modified version of gold.m to start the propeller design. Wanting to keep the propeller diameter small because of the placement of the engine and tail boom led us to evaluate the performance characteristics of four bladed as well as two bladed propellers because of the inherent higher efficiencies that come with a larger number of blades. Figure ‎4-1 compares some two and four bladed propellers.

[pic]

Figure ‎4-1: Thrust vs. Horsepower for two and four bladed propellers at 8500 RPM

Figure ‎4-1 reveals that the only two propellers shown that require less than the provided 3.7 hp at the maximum throttle setting are the 18 x 7 two bladed and 16 x 7 four bladed propellers. Figure ‎4-2 compares RPM and efficiency required to turn the selected propellers during cruise.

[pic]

Figure ‎4-2: RPM vs. Efficiency for two and four bladed propellers during cruise

Figure ‎4-2 shows that, within a reasonable range, the 16 x 7 and 18 x 7 perform about the same. Seeing that there is little to no performance difference during cruise (cruise takes up most of the mission and carries the most importance in influencing the propeller design) for these two propellers, the 16 x 7 four bladed propeller was chosen to keep the engine closer to the fuselage.

Table ‎4-1: Performance Characteristics of Propulsion System

| |Cruise |Max |

|Velocity [ft/s] |50 |90 |

|RPM |5200 |8500 |

|Thrust [lbf] |4.5 |7 |

|Required hp |0.62 |3.7 |

|Efficiency |0.66 |.73 |

The final propeller selection is the 16 x 7 four bladed propeller. Table ‎4-1 lists some of the performance characteristics of the O.S. 1.60 FX-FI with a Zinger 16 x 7 pusher propeller as was predicted by this analysis.

[pic]

Figure ‎4-3: Zinger 4 bladed propeller

A picture of the final propeller selection can be seen in Figure ‎4-3.

Dynamics and Controls

1 Center of Gravity

The final center of gravity location is calculated from the computer aided design package Pro-E that was used to design this aircraft. This method was used because the program is able to calculate the center of gravity of some of the components with better accuracy by including the correct material properties. The resulting values for center of gravity are 3.2 feet in the x-direction and 0.4 feet in the z-direction from the bottom of the fuselage at the nose of the aircraft.

The only weight lost during flight is that of the fuel. In this design, the fuel tank is at the center of gravity so this point will not move from beginning to end of the flight as fuel is burned. This provides better design capability because the aircraft only has to be stable around one point. However, the aircraft will be doing test flights without the expensive payload which will alter the center of gravity of the aircraft. Without the 20 lb payload, the center of gravity moves aft to 4.3 ft. Since this is aft of the aerodynamic center, which is given later, the aircraft will need a weighted payload for stability.

2 Aerodynamic Center

The aerodynamic center of our aircraft is determined by the following Equation ‎5-1.

With the final wing area being 41.8 ft2 and the finalized horizontal tail area being 12 ft2, the aerodynamic center of the aircraft is 3.6 ft from the nose. These values were calculated using the 3-D values for the lift curve slope of both the wing and horizontal tail. The wing’s 3-D CL( is 3.9 and the horizontal tail’s 3-D CL( is 3.6. This finalized size of the horizontal tail will be explained later in this section. The aerodynamic center does not change throughout the flight of the aircraft since it is purely dependent on the lifting capabilities of the wing and horizontal tail.

3 Static Margin

The static margin of the aircraft is decided from the following Equation ‎5-2.

This value is preferably between 0.15 and 0.20 for a statically stable aircraft as shown by historical data. If the static margin is less than this range, then the center of gravity is too close to the aerodynamic center which presents problems. The aircraft has other restrictions in regards to changing the weight of the aircraft. For example, the aircraft cannot vary in weight (outside of fuel burn) because that could inadvertently move the center of gravity back to an unstable position. Also, the center of gravity would be too close to the aerodynamic center position to induce a pitch-down moment at higher angles of attack. If the center of gravity is further from the aerodynamic center than desired, then the center of gravity would induce a larger pitch-down moment and the aircraft would be too stable.

Figure ‎5-1 below gives a visible analysis of whether or not our aircraft falls within the given parameters for an aircraft to be longitudinally stable. It presents the position of the center of gravity and the position of the aerodynamic center, both as functions of the size of the horizontal tail. With these two values, the desired static margin range is shown in dashed lines. Because the slope of the lines for the center of gravity and aerodynamic center are different, it can be seen that the ideal size of the tail should be between 9 and 15.5 ft2.

[pic]

Figure ‎5-1: CG and AC of Aircraft

Since there should be an allowance with the static margin if there is a change in center of gravity, the horizontal tail was chosen to be 12 ft2 to give a static margin of approximately 0.18.

4 Dihedral Angle

The dihedral for the main wing of our aircraft was decided upon by evaluating recommendations from several sources. Tables of low-wing homebuilt and agricultural aircraft provided in Reference [9], Volume 2, have an average dihedral of around 5º. While these categories do not directly apply to our aircraft, they should serve as a good reference. An article titled “Wing and Tail Dihedral for Models” in Reference [15], recommends 0-2º of Equivalent V-Dihedral (EVD) for maximum maneuverability of remotely controlled aircraft with ailerons. For our purposes here, EVD can be taken simply as dihedral. This recommendation, however, is likely too low for our purposes here because our aircraft is desired to be more stable than maneuverable. McCombs also recommends 3-8º EVD for Free Flight Scale model low-wing aircraft. Taking all of these recommendations into consideration, a dihedral of 5º was decided upon as a good compromise for stability.

5 Horizontal Tail Size

The Class I method was the first used to calculate the approximate size of the horizontal tail. This method is taken from Equation ‎5-3 below, found in Reference [9], Volume 2.

This equation used a tail volume coefficient of 0.5. The resulting value of this equation gave a Class I horizontal tail size of 11.6 ft2. This value provides a reality check for any following values calculated using further analysis for the horizontal tail.

The first design consideration was that the horizontal tail would have the needed lifting effect only if it was placed in the prop wash so that a higher dynamic pressure would be experienced. This led to the design of the T-tail for the aircraft. Typically, the ratio of dynamic pressure of the horizontal tail to that of the free stream is only 0.9, but because of the placement of our propeller, our horizontal tail would experience a higher velocity which would raise the ratio to greater than one. Since the horizontal tail would experience a greater dynamic pressure, it will produce enough downward lift force to counter the moments produced by the other components of the aircraft, such as the high mounted engine. This will benefit in stabilizing and trimming the aircraft.

Two methods were used to size the horizontal tail of the aircraft and to determine the correct size. The first was the x-plot made from the comparison of horizontal tail sizes and static margin of the aircraft shown in Figure ‎5-1 above. This gives an initial starting point for a quantitative analysis to decipher the size of the horizontal tail. Given the size of the horizontal tail and the resulting center of gravity, this figure tells us whether not the airplane is within the static margin limits.

The second method used the takeoff rotation equation given from Reference [3]. This equation can be found in the Appendix. This gives a calculation of the available angular acceleration that is needed by the aircraft during takeoff.

Figure ‎5-2 shows the angular acceleration of an aircraft with the respective horizontal tail area. For lighter aircraft, the angular acceleration should be above 10 deg/sec2. Also, this value depends on the runway surface material as shown in the figure.

[pic]

Figure ‎5-2: Horizontal Tail Area versus Theta Double Dot

Iterations were done between these two methods to find an agreeable center of gravity and aerodynamic center value. The final value for the horizontal tail is 12 ft2 which agreed with the requirements of both methods. Using this value in a rearrangement of Equation ‎5-3, the value for volume coefficient is 0.52 which is comparable to the historical value of 0.5.

6 Vertical Tail Size

As with the horizontal tail, an initial Class I sizing was done for the vertical tail to provide a future reliability check. This is done using the following Equation ‎5-4 which is similar to the one used for the horizontal tail.

Thus, the Class I sizing of the vertical tail resulted in a value of 4.6 ft2.

The first analytical method used to size the vertical tail was obtained from Reference [9], Volume 6 and 2, to use the coefficient of yawing moment to equal a suggested value of 0.001 per degree. Using their method of equations, a vertical tail x-plot was formed and is presented in Figure ‎5-3. According to the figure, the coefficient of yawing moment of 0.001/deg yields a vertical tail value of approximately 2 ft2.

[pic]

Figure ‎5-3: Vertical Tail Area versus Yaw Moment

The third method to size the vertical tail was to place the aircraft in a landing scenario with a high sideslip angle and high angle of attack. This method was also obtained from the same reference but added values for a high sideslip angle to calculate the necessary tail size for the yawing coefficient to be zero. It also used values for rudder effectiveness using methods from Reference [9], Volume 6 and 2. This added a yawing moment due to the deflection of the rudder. However, the size of the tail to make the coefficient of yaw zero was approximately 0.5 ft2. As a result, the second method was decided upon.

Due to the configuration of the tail empennage and placement of the vertical tail behind the propeller, it will also receive a higher dynamic pressure than the free stream air because of the higher wind velocity. Thus, the effect of the vertical tail should be greater than estimated.

7 Control Surface Size and Trimming

Initial control surface sizing was done from empirical data taken from Reference [9], Volume 2, which gave percentage values of the tail areas. These suggested values are given below in Table ‎5-1.

Table ‎5-1: Control Surface Sizing

| |Aileron/ |Elevator/ |Rudder/ |

| |Wing |Horizontal Tail |Vertical Tail |

|Percentage Chord |21% |46% |56% |

|Inboard Position |45% |45% |95% |

|Outboard Position |95% |90% |37% |

Design considerations caused some of these to change. First, the aircraft needed flaperons due to the need for additional lift during landing and takeoff as explained in the aerodynamics section. To assure the size would add a sufficient amount of lift, they extend from the start of the dihedral to the wing tip as flaperons. Again, the analysis of the resulting lift is shown in the aerodynamics section.

The final values for control surfaces were decided on as a percentage of the size of our tail. The final values for the control panels are shown in Table ‎5-2.

Table ‎5-2: Control Surface Sizing Part 2

| |Aileron/ |Elevator/ |Rudder/ |

| |Wing |Horizontal Tail |Vertical Tail |

|Chord |0.58 ft |0.6 ft |0.6 ft |

|Inboard Position |0.2 ft |0.2 ft |0.1 ft |

|Outboard Position |7 ft |3 ft |1 ft |

Extending the control surfaces to the wingtip provides easier construction for this aircraft. The sizes can be seen pictorially in Figure ‎5-4.

[pic]

Figure ‎5-4: Control Surface Size

Control panel deflections and their maximum position are decided using trimming methods about the aircraft’s center of gravity. Equation ‎5-5 from Reference [2] shows how to calculate the moment about the center of gravity.

This equation was modeled in MATLAB with different values of elevator deflection.

According to Reference [2], the angle of attack at which lift is zero for the horizontal tail changes with the amount of elevator deflection. This principle was used to calculate the coefficient of lift produced as a result of different elevator deflections. These varying amounts of CL values are used to trim the aircraft at a specified angle of attack of the aircraft.

There should not be any need for elevator deflection for the aircraft to be trimmed at cruise. To assure this, the horizontal tail is given a negative incidence angle to provide constant downwards lift force which results in a positive moment on the aircraft. This counters any moments caused by the fuselage, wing and engine during stable cruise. This analysis was done by finding the coefficient of lift needed for the pitching moment of the aircraft to be zero at cruise. This data is shown in the Appendix. The CL needed is approximately -0.2 (the negative represents the downward force). Looking at Figure ‎3-11 in the aerodynamic section shows that this coefficient is given when the horizontal tail is at an angle of attack of -3°. After factoring in downwash angle, the angle of attack for the horizontal tail should be -4°.

Equation ‎5-5 was modeled in MATLAB with this tail incidence and the results are shown below in Figure ‎5-5 for cruise (no flaperon deflection). It can be seen here that no elevator deflection is needed at 0° angle of attack.

[pic]

Figure ‎5-5: Angle of Attack versus Flaperon Deflection

This same analysis is done for the aircraft at landing conditions with the thrust being 20 lbs and dynamic pressure being altered accordingly. The results are shown in the Appendix. From the figure, it is shown that for the aircraft to maintain a nose up configuration at 9 degrees angle of attack, the elevator needs to be deflected at approximately

-18 degrees. Also, figures are available in the Appendix to show the needed CL values at the respective aircraft angle of attack.

The stability of the aircraft given by the poles of a transient analysis is given below in Table ‎5-3.

Table ‎5-3: Poles of Transient Response

| |Pole |Natural Frequency (rad/s) |Damping Ratio |

|Short-Period Mode |-6.3833 ( 4.35i |7.7246 |0.82636 |

|Phugoid Mode |-0.059224 ( 0.72286i |0.72529 |0.081656 |

|Dutch Roll Mode |-0.32098 ( i0.93921i |0.99254 |0.32339 |

|Roll Mode |-19.644 |N/A |N/A |

|Spiral Mode |0.13951 |N/A |N/A |

These results were calculated using a transient analysis package coded in MATLAB, called Predator. These results show that the plane is stable in all modes except for spiral. This awareness provides reason to change the parts of the aircraft that have an affect on the weathercock stability derivative (i.e. vertical tail size, wing dihedral, wingspan) and other factors of the spiral mode. Also, the roll mode is excessively stable.

Structures

1 Material Selection

1 Basic Building Material

Many remote control aircraft use balsa as the basic framework for the aircraft. Since this aircraft is much larger than most remote control airplanes, other options needed to be explored.

A trade study was performed in order to determine the best material to make the aircraft from. The results from this trade study (which can be found in the Appendix) indicate that titanium is the best material to build the aircraft from. Lacking the availability of titanium, spruce or bass wood is the second best choice for the construction material for the airplane. For this reason, most of the structural members of the airplane will be built from spruce or bass wood (the properties are so close, either one will work).

2 Wing and Tail Covering Material

Traditionally, remote control aircraft have been covered with a tissue paper, silk, or heat-applicated plastic covering. Upon discussions with many experienced modelers, a concern was raised over whether traditional coverings had enough strength for the expected loads of this larger aircraft. For that reason, the wing and tail will be covered in an iron on fabric type material. The fabric resists tears better than the plastic, and the covering is relatively easy to apply. The recommended covering for this design is Coverite 21st Century Fabric, available from Tower Hobbies [5].

3 Fuselage Covering

The fuselage will be covered with one ply of pre-preg fiberglass material. It is very important that fiberglass is used as opposed to carbon fiber so there is no electrical interference between the fuselage and the electronics inside the pod.

Fiberglass will be used because it will be able to withstand the aerodynamic loads without requiring significant internal structure to support it. Due to this, the fuselage can be made relatively hollow, allowing easy installation and removal of the pod.

The fiberglass fuselage will be made by one of two processes, either lost foam method, or traditional molding method. This manufacturing process is best decided by the team dedicated to producing the aircraft.

2 Wing Spar Analysis

Niu’s Airframe Design book [7] recommends the use of a dual spar system for the internal structure of the wing. This system allows many possibilities as far as the attachment of other structure is concerned. In addition, a two spar system is far superior to a one spar system in resisting torsional loads.

Niu [7] recommends that the front spar be located at ~15% of the chord length from the leading edge, and the rear spar be located at ~60% of the chord length from the leading edge. These recommendations are made for much larger aircraft; however they will be utilized for this design because spar locations varying much from the recommendations severely restrict the maximum height of the spar (due to airfoil geometry).

For the purposes of this design, the spar cross section will be a rectangular beam. A rectangular beam is very easy to manufacture, and should aid in the constructability of the design. A tapered beam design is much more weight efficient than a constant cross section because the bending loads decrease outboard along the wing. Unfortunately, tapered spars are more difficult to construct. For this reason, a stepped spar will be used in the design. This can be seen in the appropriate section in the Appendix.

1 Bending Loads

The analysis used for the bending loads is a very simple analysis found in Gere [4]. Figure ‎6-1 shows the side view of a simple cantilevered beam. If the wing is taken to be a cantilevered beam with the lift acting at one point, this figure will accurately represent the forces acting on the system. For this design, the aerodynamics team determined what the a length would be, and reported back to the structures group.

[pic]

Figure ‎6-1: Simple Cantilever Beam (Wing)

Using the representation shown in Figure ‎6-1, a formula for the deflection at the tip of the spar can be seen in Equation ‎6-1.

In this equation, E is the Young’s Modulus of the material, and I is the moment of inertia of the spar.

This equation was plotted for a variety of different spar sizes. The results of this analysis can be seen in Figure ‎6-2. The green and black lines represent the thickness of the rear spar, and the x-axis shows the thickness of the front spar. If the maximum deflection is set at 5% of the wing length, then the area below the shaded region shows the allowable combinations of front and rear spar thicknesses. Note that this figure only shows the results for the outboard section of the spar. The inboard section of the spar (before the step occurs) utilized the same analysis, but included bending moments from the entire wing, instead of just the outboard section.

[pic]

Figure ‎6-2: Deflection at Tip of Outboard Section of Spar (Percent of Spar Length)

The red star shown above designates the final spar thicknesses. As shown, these thicknesses give a deflection just below 5% of the half span. This deflection is assuming a safety factor of 1.5 and a g-loading of 5.

2 Torsion

In addition to making sure the wing will not bend excessively, the torsion effects of the wing must be examined. The effects of torsion on a two spar system are detailed in Kuhn’s paper [10]. The analysis for the torsion can be seen in Equation ‎6-2.

When this equation is plotted, the combinations that make the twist go to zero can be found. The results of this can be seen in Figure ‎6-3.

[pic]

Figure ‎6-3: Torsion of Outboard Wing Spars

As described in the deflection portion of the analysis, the red star represents the finalized outboard spar dimensions.

3 Final Spar Dimensions

The above analyses determine the final spar dimensions. All dimensions are assuming a rectangular cross section, and a factor of safety of 1.5, a g-loading of 5 and a weight of 53 lbf.

Table ‎6-1: Final Spar Dimensions

| |h (in) |t (in) |t (in) (outboard) |material |location |

| | |(inboard) | | | |

|Front Spar |3.60 |0.73 |0.46 |Spruce/Bass |0.15 chord |

|Rear Spar |3 |0.25 |0.16 |Spruce/Bass |0.6 chord |

3 Tail Beam Analysis

1 Bending Loads

The analysis done for the tail beam is very similar to the analysis for the wing. In the case of the tail beam, it is assumed that the load acts at the end of the beam instead of at a location in the middle of the beam. A pictorial representation of this can be seen in the Appendix. The forces created by the horizontal stabilizer create a bending moment on the tail beams. This bending moment can be represented as a simple cantilever beam as shown in the Appendix. With the simple cantilever beam theory driving the deflections of the tail, Equation ‎6-3 can be used to solve for the actual deflections.

Using this equation, the deflections of the tail can be plotted exactly as they were for the wing spars. Due to the similarities, this result is shown in the Appendix. This equation assumes small deflections, a safety factor of 1.5 and a g-loading of 3.

2 Torsion

The analysis for the torsion of the tail was carried out in the same manner as the torsion analysis for the wing spars. Due to the similarities, this result is shown in the Appendix.

3 Final Tail Beam Dimensions

The above analyses determine the final tail beam dimensions. All dimensions are assuming a rectangular cross section, a factor of safety of 1.5, a g-loading of 3, and a weight of 53 lbf.

Table ‎6-2: Final Tail Beam Dimensions

| |h (in) |t (in) |Dist. Between (in) |mat’l |

|Left Beam |3 |0.25 |8 |Spruce/Bass |

|Right Beam |3 |0.25 | |Spruce/Bass |

4 Landing Gear Analysis

1 Rear Gear Analysis

The gear configuration is shown in Figure ‎6-4 below. The rear gear is made from 1” x 1” x 0.065” thick 6063-T6 aluminum tubing.

1 Energy Absorption

The landing gear analysis was done on the assumption that the gear would absorb all of the energy associated with the landing of the aircraft. For this analysis, it was assumed that the aircraft was flying at 1.1 times the stall speed or 33 ft/sec. The worst-case scenario was considered to be an aircraft that dropped out of the sky at an altitude of 5 feet, while moving forward at a speed of 33 ft/sec.

The associated values for kinetic and potential energy can be found in Equation ‎6-4 and Equation ‎6-5. The total energy that needs to be absorbed is the sum of these two equations.

Since it has been assumed that the rubber bungee cords absorb the impact at landing, Equation ‎6-6 shows the relationship between the energy absorbed and the bungee cord extension.

[pic]

Figure ‎6-4: Rear Gear Configuration

Based on the above analysis, the tie-down was determined to need a length of 18 inches when relaxed. In addition to the energy absorption analysis, a simple buckling analysis was done to ensure that the square tubing would not break. This can be found in the Appendix.

2 Front Gear Analysis

The front gear was analyzed in a similar manner as the rear gear. Due to the similarities, this analysis can be found in the Appendix.

5 Tail Analysis

The tail was analyzed in the same manner as the wing. Therefore, the tail results are found in the Appendix. The tail structure consists of two spars, and is a foam core structure covered in 21st Century Fabric.

6 Final Weight Analysis

The final weight estimate of our aircraft is 53 lbs. The weight analysis for the aircraft can be found in Table ‎6-3.

Table ‎6-3: Weight Analysis

[pic]

Performance

• Maximum Flight Time (at cruise) = 30 min

where Consumption of Fuel = 45.455mL/min

Volume of Fuel = 50 oz

• Maximum Range (at cruise) = 17.45 mi

where L/D = 19

Cbhp = 1.5 lb/hr/bhp

Prop efficiency = .67

Fuel Fraction = 1.043

• Maximum Flight Velocity = 90 ft/sec

A MATLAB script was written and iterated until Thrust = Drag to find the maximum velocity.

• Minimum Flight Velocity = 29.956 ft/sec

• Rate of Climb (at takeoff conditions) = 7.5 ft/sec

where D = 6.5lbf

hpengine = 3.7 hp

W = 53 lbf

V = 33 ft/sec

Prop Efficiency = 0.3

• Climb Angle

where Vv = 7.5 ft/sec

V = 33ft/sec

Cost

Since the airframe cost is the only cost shown in the design requirements, it is the only cost that will be shown in the main part of the report. This breakdown can be seen in Table ‎8-1.

Table ‎8-1: Cost of Airframe

[pic]

The cost shown in Table ‎8-1 is above the $300 limit in the design requirements; however this has been discussed with and approved by the customer.

Summary and Recommendations

This aircraft as designed would certainly be able to perform the desired tasks. The construction techniques shown are intended to make the final production of the aircraft unproblematic. Many other features incorporated into the design are intended to ensure the safety of the avionics pod, even in the event of a failure.

If this design is intended to be used, there are a few recommendations that the design team would like to convey. The pitching moment of the aircraft due to different throttle settings has not been extensively researched. An analysis of this would be helpful to the pilot.

The spiral mode of the aircraft is shown to be slightly unstable by the “Predator” code. Due to certain uncertainties in the inputs to the code, this problem deserves further attention.

All of the initial design requirements have been met or exceeded except for one. The $300 limit on the cost of the airframe has been exceeded with this design. Despite numerous attempts to lower the cost of the aircraft, no acceptable options were discovered. This inadequacy of the design has been discussed with and approved by the customer.

Apart from the aforementioned issues, this aircraft would be an excellent candidate for the described mission.

References

[1] MATLAB. PC Vers 6.0. Computer Software. Mathworks, INC. 2001

[2] Raymer, Daniel P., Aircraft Design: A Conceptual Approach, AIAA Education Series, 1989.

[3] Roskam, Jan., Airplane Flight Dynamics and Automatic Flight Controls. Part I. DAR Corporation, Kansas. 2001

[4] Gere, James M., Mechanics of Materials. Brooks/Cole, Pacific Grove, CA. 2001

[5] Tower Hobbies. 9 December 2003.

[6] XFoil. PC Vers. 6.94. Computer Software. Mark Drela. 2001.

[7] Niu, Michael C., Airframe Structural Design, Conmilit Press Ltd. Hong Kong. 1995.

[8] Halliday, et al., Fundamentals of Physics, John Wiley & Sons. New York. 1997.

[9] Roskam, Jan, Airplane Design (Parts I-VIII), Roskam Aviation and Engineering Corp. Ottawa KS. 1988.

[10] Kuhn, P., “Analysis of 2-Spar Cantilever Wings with Special Reference to Torsion and Load Transference”. NACA Report No. 508.

[11] McMaster-Carr. 9 December 2003.

[12] Pro/ENGINEER. PC Release 2001. PTC Corporation.

[13] Roskam, Jan., Methods for Estimating Stability and Control Derivatives of Conventional Subsonic Airplanes. Publisher Jan Roskam. Lawrence, KS. 1977.

[14] Zinger Propeller. 9 December 2003.

[15] McCombs, William F., “Wing and Tail Dihedral for Models”, Model Aviation. Dec. 1994. 104-112.

Appendix:

1 Initial Sizing

1 Constraints – Cruise Speed:

2 Constraints – Stall Speed

3 Constraints – Climb Angle

[pic]

4 Constraints – Ceiling

5 Constraints – Endurance

6 Constraints – Takeoff Distance

7 Constraints – Landing Distance

2 Aerodynamics

1 General Information

|  |Wing |Horizontal Tail |Vertical Tail |

|Area (ft2) |41.4 |12 |2.4 |

|Aspect Ratio |5 |3 |0.6 |

2 Sample Output from Lifting Line Code

[pic]

3 Zero lift angle of attacks determination:

[pic]

Bottom plot is the polynomial fit of the actual XFOIL data on the top plot

Cruise: αL=0= -3.5°

Takeoff no flap: α L=0= -3.8°

Takeoff 10° flap: α L=0= -7°

Takeoff 15° flap: α L=0= -7.8°

3D parasitic drag determination and plots: CDp was obtained by trapezoidal integration of the parasitic drag coefficients obtained using the cl vs. cd polynomial fit over the range of cl values from lifting line theory at a particular angle of attack. See plot below:

[pic]

4 Sample run of the main wing with flaperons at 15°

[pic]

[pic]

Above – Wing performance with different flap deflections – Stall Condition (V = 30 ft/s):

CL needed for stall is 1.19. Stall is at approximately 13°. With 15° flap deflection CL is achieved at 11°.

Below is the drag performance at the above runs.

[pic]

5 Experimental Clark Y data -- Stall at approximately 13-14°

[pic]

6 More General Information

|  |CL |α (of wing) |Flap Deflection |CD |L/D |

|Stall |1.19 |11° |15° |0.119 |10 |

|T/O |0.989 |8.8° |15° |0.084 |12 |

|Cruise |0.44 |2.8° |0° |0.018 |24 |

7 Drag Build Up at Cruise

|Component |CD |Drag |

|Wing |0.018 |2.6 lbf |

|Fuselage |0.0045 |0.6 lbf |

|Horizontal Tail |0.0043 |0.6 lbf |

|Vertical Tail |0.0017 |0.04 lbf |

8 Wing Dimensions

[pic]

3 Propulsion

1 Correspondence with O.S. Engines

11/27/2003:

From e-info@os-

Dear Sir,

We are so sorry for our late reply.

Thank you so much for your selecting our O.S. engines for your project.

We have our own technical data including power curve or others. However,

it's we think a kind of O.S.'s own way. And we would be glade to

introduce it to you future. But it's not the time yet based on company

policy, sorry.

We would appreciate your understanding.

We would like to inform that non- FI engine might be easy to operate and

maintenance.

And there is not much difference between them on fuel consumption.

We are sorry we couldn't help you enough this time.

Yours sincerely,

N. Shiomaki  O.S.

Doug Mousseau

Dear Sir or Madam,

I tried to get additional information about the O.S. 1.60 and O.S. 1.60 FI, and was directed to this e-mail address.  I would greatly appreciate any assistance on the questions posed in the original e-mail found below.  Thanks.

Doug Mousseau

mousseau@purdue.edu

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

Reply from O.S. America:

Thank you for your recent e-mail.

Unfortunately we do not have that information available.  You may want to try and contact OS in Japan.  Here is a link to their website:



Did you know that our web pages now all contain FAQs? (Frequently asked questions)  Please drop by and take a look! We hope you'll find the information helpful and valuable to you.

Sincerely,

John G.

Product Support Lead Technician

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

Original E-mail:

>>>10/17/2003 10:49:35 PM >>>

Dear Sir or Madam,

I am currently on a design team at Purdue University.  The project involves designing and building a large scale R/C aircraft.  We have decided to purchase either an O.S. 1.60 FX or an O.S. 1.60 FX-FI.  If at all possible, we would like to gather some more information about these engines. Specifically, any input in the following areas would help immensely:

Fuel Consumption (FI vs non-FI)

Reliability (FI vs non-FI)

Ease of Use (FI vs non-FI)

HP versus RPM curves (for these or similar engines)

Fuel Consumption versus RPM (for these or similar engines)

I can be reached at:

Doug Mousseau

mousseau@purdue.edu

(765) 543-9985

Thank you for any assistance you can provide.

Sincerely, Doug Mousseau

4 Dynamics and Controls

1 Horizontal Tail versus Theta Double Dot

[pic]

2 Cm versus Angle of Attack for Landing and 15 degrees flaperons

[pic]

3 CL of Horizontal Tail versus Angle of Attack of Aircraft for Cruise and 0° Flaperons

[pic]

4 CL of Horizontal Tail versus Angle of Attack of Aircraft for Landing and 15° Flaperons

[pic]

5 Takeoff Rotation Equation

[pic]

6 Needed CL for Horizontal Tail at Specified Aircraft Angle of Attack

[pic]

5 Structures

1 Material Trade Study

The results from the material trade study are shown below. This trade changed the cross-sectional area of a beam until the deflection was at the desired amount. Then the weight difference for the different types of materials was shown.

|Assumptions: |

|Small deflections (large deflection areas shown are not necessarily valid) |

|Spar located directly below aerodynamic center (no torsion effects) |

| |

|Variables |Value |

|Lift (Load) Constant |49 lbs |

|Base (b) |[0.01:0.01:20] in |

|Height (h) |3.6 in |

|Span Length (L) |7 ft |

|G Loading (Gload) |5.0 |

|Safety Factor (S.F.) |1.5 |

A list of the material properties used can be found below.

|Material Properties: |

|Material |Weight Density ([pic]) [lbf/ft3] |Young’s Modulus (E) [psi] |

|Balsa Wood |9.9 |0.49e6 |

|Bass Wood |22.9 |1.46e6 |

|Spruce Wood |22.3 |1.43e6 |

|Aluminum |180 |14e6 |

|Titanium |280 |15e6 |

|Steel |490 |28e6 |

|Brass |540 |14e6 |

[pic]

2 Elaboration on Equations

[pic]

[pic]

3 Forces Acting on Tail

[pic]

[pic]

Simple Cantilever Beam

4 Plots of Tail Deflection and Twist

[pic]

6 Cost

1 Airframe Cost

[pic]

2 Electronics Cost

[pic]

1 Propulsion Cost

[pic]

2 Total Cost

[pic]

3 Total Value

• Total Aircraft Value = (Engineering Pay) + (Cost) + (Value of Already Possessed Parts)

• Engineering Pay = 823.75 hr x $100/hour = $82,375

• Aircraft Cost = $14,016.14

• Value of Already Possessed Parts = $7,000

– Micropilot = $5,000

– E-Glass = $2,000 (estimate)

TOTAL AIRCRAFT VALUE = $103,391.14

8 Thoughts on Construction

1 View of Internal Structure

[pic]

2 Fuselage

The fuselage should be manufactured out of one ply of fiberglass. It is easiest to use a pre-preg type fiberglass, but a wet lay-up would also work. The fuselage should have a removable nose to allow the pod to slide into it, on top of the beams. The pod can then be attached to the beams with standard bolts or screws (lightweight ones of course).

3 Wing

The wing will be made with a typical built up construction. There will be 2 spars located at 15% and 60% of the chord. These spars will be cut at a location ¾ of a foot outboard from the centerline of the fuselage. Outboard of this cut, the spars will be angled up at 5o in order to create the desired dihedral effect.

The spars will be made out of either spruce or bass wood, and will have the rectangular geometry shown in the main report.

The connection between the dihedral will consist of a removable bolt attachment. Essentially, there will be two boards on the outer part of the spars at the cut locations. These boards will be affixed to the spar with removable aluminum pins.

The outer dihedral parts of the wing will be removable from the main aircraft to allow for transportation. The inner part of the wing will be permanently affixed to the fuselage ‘tail beams’. The method of joining the permanent part of the spar to the fuselage will consist of a doubler block of wood that is bolted with aluminum bolts to the tail beam.

1. View of Internal Wing Structure

[pic]

4 Tail

The tail construction will be a traditional foam core construction method. Both horizontal and vertical tails will be foam cores cut to the desired shape, and then covered with more of the 21st Century Fabric described in the structures portion of the paper. Since this fabric is not a significant load carrying structure, spars must be added to the tail structures. The spars shown in the picture below are 0.25 inches thick, and extend to the outer surface of the tail.

2. View of Tail Structure

[pic]

5 Landing Gear

The rear landing gear will be made from square aluminum tubing. A simple buckling analysis was done on the aluminum tubing, and it was determined that 1” x 1” x 0.065” thick 6063-T6 square aluminum is adequate for the front and rear gear. This tubing can be easily obtained from McMaster-Carr Supply [11].

The front landing gear will be made from the same square tubing as the rear gear. This tubing will be made such that there is a 60o angle bent in the gear. The gear will then be affixed to the main fuselage beam with an aluminum bolt to pivot on. In addition, a nylon bolt and bungee will allow the nose gear to “flop” forward on a hard landing. This concept is shown in the figure below.

A picture of the gear design can be seen below.

[pic]

The gear placement has also been determined; this can be found in the figures below.

[pic]

[pic]

1 Landing Gear Buckling Analysis

[pic]

[pic]

Buckling Results

-----------------------

[pic]

[pic]

Assumptions

[pic]

[pic]

[pic]

Assumptions

[pic]

Load (lbf)

Assumptions

Assumptions

[pic]

[pic]

Equation

6-1

L (in)

Side force from V-stab creates torsion effect on beams

‎6-1

L (in)

Side force from V-stab creates torsion effect on beams

[pic]

Assumptions

[pic]

[pic]

Assumptions

[pic]

[pic]

Assumptions

Load (lbf)

L (in)

a (in)

[pic]

Downward force from H-stab creates bending moment on beams

[pic]

Equation ‎6-3

[pic]

Equation ‎6-2

Figure ‎3-4: Cl versus a

2”

1”

.75”

.375”

.25”

.16”

Outboard Front Spar = 0.455”thick

Outboard Rear Spar = 0.16” thick

h

t

Figure ‎3-5: Cd versus Cl

h

t

Equation ‎3-6

.375”

2.8 ft

Where T = Torque (in-lbf)

L = Length (in)

λ = f(B0, A0)

A0 = f(E, I)

B0 = f(G,J)

E = Young’s Modulus (psi)

I = Moment of Inertia (in4)

G = Torsional Stiffness (psi)

J = Polar Moment of Inertia (in4)

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

Equation ‎3-5

[pic]

Equation ‎3-4

[pic]

Equation ‎3-3

[pic]

Equation ‎3-2

Equation ‎3-1

[pic]

[pic]

[pic]

6.25 ft

Equation ‎5-4

[pic]

Equation ‎5-3

[pic]

[pic]

Equation ‎5-2

Equation ‎5-1

[pic]

[pic]

[pic]

Equation ‎6-4

Equation ‎6-5

[pic]

Equation ‎6-6

Spar Step Location, also the detach point for the wing

Al tube:

1” x 1” x 0.065” thick 6063-T6

Front Gear Aluminum Tube

Designed not to break

Designed not to bend

Aluminum Bolt

Provides pivot for gear (does not break)

Elastic Band & Nylon Bolt

Elastic Band Absorbs some energy from landing

Nylon bolt breaks during hard landing

γ = overturn angle =

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L

Load

Load

For Rear Gear:

L ~ 15.3 in

Ref. Gere pg 763

Assumptions:

Pinned-Pinned Column

1st Mode Buckling

No Eccentricity

10 g-loading on landing

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Where L = Length (in)

E = Young’s Modulus (psi)

I = Moment of Inertia (in4)

A = Cross Sectional Area (in2)

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Equation ‎7-1

Equation ‎7-2

Equation ‎7-3

Equation ‎7-4

Equation ‎7-5

Required CL

Required CL at stall

1” x 1” x 0.065”

0.58 ft

0.6 ft

0.6 ft

0.9 ft

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Equation ‎5-5

Equation ‎4-1

Equation ‎4-2

Equation ‎4-3

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