Personal Air Vehicle by David Goligorsky

Aircraft Team GO! Presents…

The Sky2k

AM410, Spring 2006: Technical Design Final Report Joe Coombs David DeLaurentis David Goligorsky Kyle O’Brien Christopher Wummer

Stability and Control Structures Layout and Design Propulsion Aerodynamics

Prepared for Dr. Donald E. Wroblewski Department of Aerospace Engineering

ACKNOWLEDGMENTS: Aircraft Team GO! would like to acknowledge the following people for their help and support during the course of this project: Professor Wroblewski Joe Estano David Campbell Professor Nagem Family and Friends Alumni Discussions Board The CAD Lab The SCUD Lab Nub Pob Sausages Martin Hepperle

ABSTRACT: Noticing the gap in available modes of transportation, there is a need to establish a means for air travel that supersedes the existing hub-and-spoke airport system.

The market demands fewer time constraints and greater

freedom of mobility than what is available from any aircraft currently in production. The following technical report outlines the problem addressed, the consequent design drivers, and an analysis of the viability and quantitative characteristics of the air vehicle at the preliminary design stage. In brief, it has been established through a highly iterative design process that Short Takeoff and Landing (STOL) is the safest, most economic, and most convenient solution for point-to-point air transportation. With a ground roll of just over 100 ft, the Sky2k can takeoff from any runway and could make use of other paved surfaces for even more direct transport. High lift devicesdouble-slotted flaps and leading edge slats- and an overpowered piston-prop engine allow the aircraft to achieve STOL. To increase versatility, it was important to restrict the footprint of this Personal Air Vehicle (PAV). For this reason, a lifting canard was added to decrease the overall wingspan. The canard was designed to stall before the main wing, leading to a virtually stallfree aircraft. Other aspects of the design, like the pusher-prop configuration, H-tail, and fixed landing gear are all decisions driven by safety and reliability considerations. The design mission is defined for a 450 nm range and three people, each weighing 200 lb, with 50 lbs of baggage per person. This mission will begin with a short takeoff and climb to 10,000 ft, then a cruise at 175 mph, and a descent with 15 minute loiter segment before the short landing. This mission, with its necessary weight allotments and factors in the design decisions (such as the 2024-T6 aluminum structures, engine selection, etc.) give a gross takeoff weight of 3020 lbs. ii

This vehicle is unique as a pusher-prop STOL PAV. Such characteristics have always been admired, but have not yet been realized in one entity. Such effectiveness and versatility lead to multi-faceted market potential. Every step of the design stage holds safety paramount and attempts to achieve the most reliable, comfortable, and affordable aircraft within the chosen design parameters.

iii

TABLE OF CONTENTS LIST OF FIGURES

VII

LIST OF TABLES

INTRODUCTION

i.1 Motivation, and Market Applications i.2 Design Mission

1 3

CHAPTER 1: CONCEPT DRIVERS AND DESIGN EVOLUTION

1.1 Introduction 1.2 Design Drivers 1.3 Design Evolution 1.3.1 VTOL With Rotating Rear Lift Fan 1.3.2 VTOL With Body-Mounted Rotating Lift Fans 1.3.3 STOL Pusher-Prop

5 5 5 5 7 9

CHAPTER 2: WEIGHTS AND LAYOUT

2.1 Introduction 2.2 Weights 2.2.1 Layout and Center of Gravity 2.2.2 Empty Weight and Takeoff Gross Weight 2.2.3 Internal Layout 2.3 Landing Gear 2.3.1 Landing Gear Arrangement and Selection 2.3.2 Verification of Landing Gear Layout 2.3.3 Tire Sizing

13 13 13 14 15 16 16 17 20

CHAPTER 3: AERODYNAMICS

3.1 Introduction 3.2 Initial Airfoil Selection and Analysis 3.3 High-Lift Devices Creation and Optimization 3.4 Results 3.5 Safety 3.6 Conclusions

22 22 29 34 36 37

CHAPTER 4: PROPULSION

4.1 Introduction 4.2 Powerplant Sizing, Selection, and Performance 4.3 Piston-Engine Installation

38 38 42

4.4 Propeller Sizing 4.5 Propeller Performance 4.6 Takeoff Analysis 4.7 Landing Analysis 4.8 Conclusions

43 44 49 52 54

CHAPTER 5: STABILITY AND CONTROLS

5.1 Introduction 5.2 Static Stability 5.2.1 Longitudinal Stability 5.2.2 Directional and Lateral Stability 5.3 Trim Analyses 5.3.1 Longitudinal Trim at Takeoff 5.3.2 Longitudinal Trim at Cruise 5.3.3 Lateral and Directional Trim 5.3.4 Control Surface Sizing 5.4 Dynamic Stability and Automatic Control

55 55 55 59 60 60 62 63 64 66

CHAPTER 6: STRUCTURES

6.1 Introduction 6.2 V-n Diagram 6.3 Material Selection 6.4 Wing and Canard Structure 6.4.1 Spar Design – Theory 6.4.2 Spar Design - Finite Element Analysis 6.4.3 Wing and Canard – Design Details 6.5 Fuselage Structure 6.5.1 Tensile Loads and Skin Sizing on Fuselage 6.5.2 Longeron and Bulkhead Spacing 6.6 Rudderlets 6.7 Structural Weights

74 76 79 80 80 86 93 95 96 97 99 100

CHAPTER 7: COST ANALYSIS

102

7.1 Introduction 7.2 Design Mission Cost Analysis 7.2.1 Purchase Price 7.2.2 Operating Costs 7.3 Off-Design Mission Cost Analysis 7.3.1 Off-Design Mission Description 7.3.2 Operating Costs

102 102 102 103 103 103 104

CHAPTER 8: THE FUTURE FOR SKY2K

105

8.1 Introduction 8.2 Unmanned Controls 8.3 Infrastructure

105 105 105

CONCLUSION

106

APPENDIX

107

A.1 Dimensioned Three-View Drawing

107

REFERENCES

108

LIST OF FIGURES Figure i-1: Boeing’s Current Market Outlook, Commercial Air Travel History and Predictions

Figure i-2: Boeing’s Current Market Outlook, Aircraft Size and Usage in Commercial Air Travel

Figure i-3: Design Mission Profile

Figure i-4: 450 nm Great Circle Centered on Boston

Figure 1-1: “The Hammerhead” VTOL With Embedded Front Lift Fan and Rotating Rear Lift Fan

Figure 1-2: “The Guppy” Front View

Figure 1-3: “The Guppy” Left Side View

Figure 1-4: “The Guppy” Isometric View

Figure 1-5: Side View 3D Render with Perspective and Approximately 6 ft. Passenger

Figure 1-6: Sky2k Front View 3D Rendering

Figure 1-7: Sky2k Right Side View 3D Rendering

Figure 1-8: Sky2k Rear View 3D Rendering

Figure 1-9: Sky2k Top View 3D Rendering

Figure 1-10: Sky2k Quarter View 3D Rendering with Perspective

Figure 2-1: Internal Layout Side View

Figure 2-2: Tipback Angle and Verification Angle

Figure 2-3: Overturn Angle Schematic

Figure 2-4: Sky2k Overturn Angle

Figure 3-1: The NACA 3414 Airfoil

Figure 3-2: Cl Plot for the Clean NACA 3414 Airfoil

Figure 3-3: The Drag Polar for the Clean NACA 3414 Airfoil

Figure 3-4: LinAir Model of Canard, Wing, and Winglets

Figure 3-5: Inverted Drag Polar with Quadratic Fit for the NACA 3414 Airfoil

Figure 3-6: The Slat and Flap System of the Wing During Takeoff

Figure 3-7: The Slat and Flap System of the Canard During Takeoff

Figure 3-8: LinAir Lift Distribution Plot

Figure 3-9: Canard and Wing in Cruise Configurations

Figure 4-1: Propulsion System Speed Limits

vii

Figure 4-2: Wing Loading Chart for Sky2k

Figure 4-3: Effects of Turbocharging with Altitude

Figure 4-4: Updraft Scoop Cooling

Figure 4-5: Blade Element Theory

Figure 4-6: Thrust and Power Coefficients, Efficiency & Max Efficiency vs. Advance Ratio

Figure 4-7: Takeoff Distance Components

Figure 4-8: Ground Roll Thrust Profiles for Several Pitch Variations

Figure 4-9: Variable-Pitch Propeller Ground Roll Thrust

Figure 4-10: Takeoff Breakdown

Figure 4-11: Landing Distance Components

Figure 4-12: Landing Breakdown

Figure 5-1: Sky2k Weight Broken Down by Component

Figure 5-2: Trade Study Showing the Effect of Wing Position on Stability

Figure 5-3: Trade Study Showing the Effect of Wing Sweep and Wing/Canard Area Ratio on the Stability (For the Minimum Load)

Figure 5-4: Represents the Moment as a Function of Elevator Deflection at any Vertical Lift Figure 5-5: Coefficient of Lift Vs. Coefficient of Moment about the CG at Cruise

61 63

Figure 5-6: Dimensions of Rudder on Winglets Total Area Refers to Both Controls

Figure 5-7: Dimensions of Elevators on Lifting Canard Total Area Refers to Both controls

Figure 5-8: Dimensions of the Ailerons and Flaps on the Main Wing

Figure 5-9: Longitudinal Impulse Response to a 1 Rad Input of Pitch Angle, q

Figure 5-10: Lateral Impulse Response to a 1 Rad Input of Sideslip, b

Figure 5-11: The Root Locus and Dynamic Step Response of a PID Control

Figure 6-1: Block Diagram of Structural Design Plan

Figure 6-2: Canard Stall V-n Diagram

Figure 6-3: C-Beam Dimension Variables

Figure 6-4: Shear Force Diagram for the Wing and Canard

Figure 6-5: 3D CAD Model of Sky2k Wing Structure

Figure 6-6: Stress Distribution in Wing Due to Lift Loads

Figure 6-7: Deflection of Wing Due to Lift Loads

viii

Figure 6-8: Wing Safety Factor Distribution Due to Lift Loads

Figure 6-9: 3D CAD Model of Sky2k Canard Structure

Figure 6-10: Stress Distribution in Canard Due to Lift Loads

Figure 6-11: Canard Deflection Due to Lift Loads

Figure 6-12: Canard Safety Factor Distribution Due to Lift Loads

Figure 6-13: Z-shaped Stringer and Skin Profile

Figure 6-14: Wing and Stringer Configuration

Figure 6-15: Diagram of Loads on Fuselage

Figure 6-16: Shear Forces and Moment Along Fuselage

Figure 6-17: View of Longeron and Bulkhead Configuration Inside Sky2k

Figure 6-18: Rudderlet structure CAD drawing

100

LIST OF TABLES Table 2-1: Component Weight and Placement

Table 2-2: Wheel Load Geometry

Table 2-3: Static Load Verification Results

Table 2-4: Static and Dynamic Gear Loads

Table 2-5: Tire Sizing

Table 3-1: Planform Dimensions of the Canard and the Wing

Table 3-2: Flow Properties Used in LinAir

Table 3-3: Canard and Wing LinAir Section Properties at Cruise

Table 3-4: Cl,m,ax Comparison of Raymer and JavaFoil

Table 3-5: CL,m,ax Comparison of Raymer and JavaFoil

Table 3-6: CL,max values for Sky2k at Takeoff

Table 4-1: Engine Specifications

Table 4-2: Summary of Propeller Characteristics

Table 4-3: Airfoil Data for Propeller Blade at Various Stations

Table 5-1: Results From Longitudinal Static Stability Analysis

Table 5-2: The Stability Coefficients for Directional and Lateral Stability

Table 5-3: Shows the Difference in Proximity of the Canard to the CG and the Wing to the CG

Table 5-4: Coefficients Provided by LinAir and Hand Calculations

Table 5-5: The Coefficients that LinAir Doesn’t Provide

Table 5-6: The Pilot Flying Qualities During Cruise

Table 6-1: Aluminum Study

Table 6-2: Trim Theoretical Minimum Moment of Inertia

Table 6-3: LinAir Theoretical Minimum Moment of Inertia

Table 6-4: Shear Stress in Spar for Different Web Thicknesses

Table 6-5: Parametric Study of C-Beam Dimensions and Moment of Inertia (Wing)

Table 6-6: Parametric Study of C-Beam Dimensions and Moment of Inertia (Canard)

Table 6-7: Results of Parametric Study

Table 6-8: Verification of Results – Wing

Table 6-9: Verification of Results – Canard

Table 6.10: Results of Longeron Geometry and Bulkhead Sizing

Table 6-11: Structural Weight Calculations Compared to that From Refined Sizing

101

Table 7-1: Operating Costs for Design Mission (All in FY2K5$)

103

Table 7-2: Off-Design Operating Costs (All in FY2K5$)

104

INTRODUCTION I.1 MOTIVATION AND MARKET APPLICATIONS Today’s air transportation market is built around the hub-and-spoke airport model. This structure is defined by having larger aircraft feed into main cities where smaller regional aircraft provide connecting flights to less-traveled destinations. There are many inherent flaws associated with this structure. For one, the time saved by high-speed travel is lost in ineffective system architecture.

With travel to and from the nearest hub airport, security,

luggage and check-in, loading and unloading passengers, and possible flight delays, the block travel time (duration from the beginning to the end of a trip rather than simply air time) for a regional trip can easily be longer than driving, and the plane tickets are much more expensive.

Second, flight

frequency is limited by runway space, which tends to be an issue with a high flight density airport. The amount of flights per day that a “hub” airport can handle is a limiting factor for the amount of flights that can depart to a “spoke” destination. The essence of air travel is in the ability to get from point-to-point directly and at high speed, but the hub-and-spoke airport system does not allow air travel to meet its ultimate potential. A study on air travel trends done by Boeing has shown that regional travel represents 90% of all commercial air traffic (3). The same study has shown that passenger air traffic has been growing at approximately 4.8% and this growth is expected to continue, as can be seen in Fig. i-1. Note that RPK is short for Revenue Passenger Kilometers- the number of passengers multiplied by the number of kilometers they fly.

Figure i-1: Boeingâ&#x20AC;&#x2122;s Current Market Outlook Commercial Air Travel History and Predictions

Furthermore, the types of aircraft that are predominantly used in passenger air travel today are small aircraft. Aircraft on the order of the Boeing 747 and larger compose only 4% of this market (3).

Figure i-2 presents the

breakdown of aircraft size and usage.

Figure i-2: Boeingâ&#x20AC;&#x2122;s Current Market Outlook Aircraft Size and Usage in Commercial Air Travel

The hub-and-spoke airport system is not only inefficient with regard to time and money, but the market analysis implies that this infrastructure does not effectively cater to the common need. The motivation for the aircraft design that will be discussed in this document is in finding an effective solution to the aforementioned issues focusing on versatility, accessibility, and safety. The particular design drivers and ultimate mission that define the Sky2k also create a multifaceted market potential. It could become a major player in providing regional point-to-point transport for people interested in traveling between small cities. The versatility of Short Takeoff and Landing allows this aircraft to be useful for island hopping or for any other theater where runway length and availability is a limiting factor. The hope is that the passengers would be the pilots, but it would be possible to use this aircraft to run an air taxi service as well.

This does limit ownership to the upper-class and

companies interested in providing a rental or taxi service. I.2 DESIGN MISSION The Sky2k was designed for two passengers and a pilot, each weighing 200 lbs and carrying 50 lbs of baggage per person. This totals 750 lbs of nonexpendable payload. After a short taxi, the aircraft will takeoff over a 50 ft obstacle (a FAR 23 requirement) in 600 ft, which corresponds to a ground roll of about 130 ft (compare to the Boeing 747-200 wingspan of 211 ft). The Sky2k will then climb to 10,000 ft and cruise at 152 knots (175 mph) for a distance of 450 nm. After this segment, the aircraft will descend, loiter for 15 minutes, and land clearing a 50 ft. obstacle in a distance of 1040 ft, which incorporates a total ground roll of 530 ft. See Fig. i-3 for a mission profile schematic and Fig. i-4 for an image representing the range capacity of the aircraft.

Figure i-3: Design Mission Profile

Figure i-4: 450 nm Great Circle Centered on Boston (http://gc.kls2.com)

CHAPTER 1: CONCEPT DRIVERS AND DESIGN EVOLUTION 1.1 INTRODUCTION Throughout the design process, several conceptual aspects of the desired aircraft were used to drive the technical details. This chapter outlines the decisions made to fulfill the conceptual design as well as the course of the aircraft evolution towards the final configuration that is documented by this report. 1.2 DESIGN DRIVERS There is a list of considerations set forth by NASA and the CAFE Foundation in their joint competition for Personal Air Vehicles (PAVs) that lists the most important features to be optimized when designing such an aircraft. This list includes balance field length, landing distance, cabin noise, community noise, fuel consumption, and ease of use (4). Our aircraft was designed with these in mind as well as special considerations for safety and minimal aircraft footprint. The process of establishing a layout solution to elegantly solve the conceptual problem that has been posed was a highly iterative process. Three major designs have been extensively scrutinized before one was selected as the best approach. These three layouts are described in the following section. 1.3 DESIGN EVOLUTION 1.3.1 VTOL WITH ROTATING REAR LIFT FAN: â&#x20AC;&#x153;THE HAMMERHEADâ&#x20AC;? The thought of a personal aircraft conjures images of a vertical takeoff and landing (VTOL) machine. It has been a long-standing human desire to have

small, affordable, and easy to use aircraft and this ideal is generally paired with the notion of being able to takeoff and land within the footprint of the vehicle.

Figure 1-1: â&#x20AC;&#x153;The Hammerheadâ&#x20AC;? VTOL With Embedded Front Lift Fan and Rotating Rear Lift Fan

With a VTOL aircraft, the propulsion system is the kingpin of the design. For this concept, two large lift fans allow vertical maneuvers. These lift fans were placed along the central axis of the aircraft for stability purposes at the terminal phases of the mission. For cruise, the lift fans had to provide forward thrust, so the rear lift fan would rotate to power this segment. There are many flaws associated with this. First, the front lift fan plays no role in cruise and acts as a deadweight and waste of space. Next, the fuselage substantially blocks airflow to the rear lift fan in cruise position, basically eliminating performance. Furthermore, the mechanical systems required to drive and rotate such lift fans are enigmatic and likely to be very heavy and mechanically inefficient.

The proposed engine was a 630 horsepower

turboshaft engine estimated at $1.5 million (FY2K5$).

This design proved to be more ideological than technically feasible, but did lay the foundation for our future decisions- namely the dual wing configuration for a small footprint and twin vertical tail for improved pilot visibility. Facing the problems associated with this design early on helped us avoid those mistakes in the following iterations. 1.3.2 VTOL WITH BODY-MOUNTED ROTATING LIFT FANS: “THE GUPPY” Part of the proposal for the “Hammerhead” design incorporated the extensive use of composite materials to reduce weight. It seemed counterproductive to design a composite aircraft with a heavy, useless front lift fan, so the design described in this section mainly tried to ameliorate that issue as well as solve the problem of blocked airflow. Figures 1-2 through 1-4 illustrate this concept. Many of the problems associated with lift fans on the longitudinal axis of the aircraft could be averted by locating lift fans on the side of the fuselage. Flow to the fans would not be blocked as in the former design and both fans could be used during cruise. Also, the transition from VTOL to cruise could be analyzed more easily than with “The Hammerhead.” However, there was still a problem with the mechanics required to spin the lift fans and to rotate the nacelles. These transmissions are complicated, add a large amount of weight, and reduce mechanical efficiency. Furthermore, the nacelles and pylons add considerable amounts of drag and there are inherent stability problems relating to the shifting CG during any mission. Lastly, the turboshaft engine required over 955 HP to achieve VTOL.

Figure 1-2: “The Guppy” Front View

Figure 1-3: “The Guppy” Left Side View

Figure 1-4: “The Guppy” Isometric View

On reviewing the preliminary analysis and comparing the aircraft’s qualities to the conceptual guidelines, it was clear that a better solution had to be reached. “The Guppy” had an estimated civil purchase price of $7.7 million (FY2K5$) where the engine alone cost $1.8 million (FY2K5$). Besides the restrictive cost, it seemed especially unsafe to place a 955 HP turboshaft engine several feet from the cabin and the noise levels emitted from the engine and lift fans would be extremely high. Another solution was necessary to meet safety and cost objectives. 1.3.3 STOL PUSHER-PROP: “SKY2K” The conceptual convenience of VTOL led to performance and cost specifications that were unrealistic for our target market. By eliminating VTOL and opting for Short Takeoff and Landing (STOL), our air vehicle can finally take on all the characteristics that our concept laid out: versatility, accessibility, and safety. The rest of this report documents the analysis of the layout, aerodynamics, propulsion, stability, controls, structures, and cost of the Sky2k, but the general aspects of this design will be touched upon in this section. A pusher-prop has many benefits centered on simplicity and safety. Pistonprop engines are more readily maintainable- piston engines are commonly serviced by auto mechanics. This arrangement allows for a shorter fuselage, which reduces wetted area. With the propeller at the back of the aircraft, the pilot’s view is unhindered. Engine noise and vibration is reduced in the cabin. Another benefit is that the aircraft does not fly in the propeller’s wake. Conversely, the propeller operates in the fuselage wake, which increases the noise that the propeller produces. A general necessity of pusher-props is to have a highly swept wing to maintain stability. Frequently, the swept main wing is paired with a control canard. In the case of the Sky2k, the canard functions in both lift and control.

A benefit of having a canard on such an aircraft is the ability to design for a â&#x20AC;&#x153;stall-freeâ&#x20AC;? vehicle. The canard can be designed such that it will stall before the main wing, so the aircraft as a whole will not loose control authority. Another function of the highly swept main wing is that it allows for the placement of control winglets.

Configured as rudderlets, they reduce the

induced drag, create ample turning moments, and using two effective vertical tails reduces the overall height of the aircraft. As the aircraft progressed, a Computer Aided Design (CAD) model was updated and enhanced. Autodesk Inventor 10 was the CAD package used for these models and it proved to be very powerful with its 3D rendering capability and built-in Finite Element Analysis (FEA) software, which was heavily used in the structural analysis of the aircraft. Figures 1-5 to 1-10 provide a scaled image of the Sky2k.

Figure 1-5: Side View 3D Render with Perspective and Approximately 6 ft. Passenger

Figure 1-6: Sky2k Front View 3D Rendering

Figure 1-7: Sky2k Right Side View 3D Rendering

Figure 1-8: Sky2k Rear View 3D Rendering

Figure 1-9: Sky2k Top View 3D Rendering

Figure 1-10: Sky2k Quarter View 3D Rendering with Perspective

CHAPTER 2: WEIGHTS AND LAYOUT 2.1 INTRODUCTION Perhaps the most critical factor in an aircraft design is the gross takeoff weight.

It determines the lift needed for aerodynamic analysis and the

subsequent power plant to provide adequate thrust. The structural loads are based on these factors and the distribution of weight throughout the aircraft determines its stability. The following section reports the layout of component placement. Also, before the plane can take flight, it must be stable on the ground. Landing gear selection and tip over analysis can be found in this chapter. 2.2 WEIGHTS 2.2.1 LAYOUT AND CENTER OF GRAVITY The final relative positioning of components is the result of design iterations that regard each technical aspect of the aircraft. That said, having a statically stable configuration was a major safety consideration for this PAV. It was important to place the canard and wing to provide adequate control moments as well as keep the center of gravity (CG) in front of the neutral point. Having a pusher-prop configuration generally requires that the engine be placed at the tail end of the aircraft. The engine is the heaviest single component in the vehicle and its aft placement requires careful wing design and component placement to retain static stability. Table 2-1 summarizes the component CG and the total CG in the X (position from nose) and Z (position from ground) directions for the design mission. Also, refer to Figure 2-1 to visualize their placement.

Wing Canard V Tail Fuselage Main Gear Nose Gear Engine Rest Pilot Passengers Carry-on No Fuel Fuel Center Fuel Wing Fuel canard Fully Loaded

Weight (lb) 245.7 116.3 13.2 233.6 125.8 37.5 588.0 422.8 200.0 400.0 150.0 2532.8 514.0 0.0 0.0 3071.9

Position From Nose (ft) 22.7 3.7 27.6 9.3 14.0 1.3 20.0 8.0 4.0 6.0 7.0 11.7 11.9 0.0 0.0 11.8

Height From Ground (ft) 7.0 3.3 7.0 5.5 0.6 0.5 6.0 5.5 5.5 5.5 5.5 5.4 5.0 0.0 0.0 5.3

Table 2-1: Component Weight and Placement

2.2.2 EMPTY WEIGHT AND TAKEOFF GROSS WEIGHT The estimation of an accurate takeoff weight is very important throughout the conceptual and preliminary design of an aircraft. Misjudging the gross takeoff weight can set the design into a weight spiral. This occurs because as an aircraft gets heavier, it needs more propulsive power driving it, which increases the structures, engine weights, and fuel needs- all of which directly increase the weight and require another iteration of this unstable loop. It is difficult to decide on a gross takeoff weight at the conceptual design stage because nothing is known about the aircraft except its general mission. This proves to be enough, however, as it is possible to compare the conceptual aircraft to a historic air vehicle with relatively similar specifications. The Sky2k has characteristics of existing aircraft like the Cessna variations and Burt Rutanâ&#x20AC;&#x2122;s Varieze and Longeze canard pusher-props. It was possible

to assume a takeoff weight of 3000 lbs and perform Newtonian iterations based on assumed weight fractions resulting from the mission description. As the design acquired technical details, more complete weight estimates could be calculated. Throughout the course of this design, the weight was iterated through an initial sizing (based on the mission), updated sizing (based on W/S HP/W selection), and refined sizing (based on approximation formulae for component weights (6)). Each stage is the weight estimation process is iterative and relies on the convergence of these gross takeoff weights. For the Sky2k, the initial sizing gross takeoff weight (GTOW) was 2527 lbs. The updated GTOW based on a W/S of 21.7 and HP/W of 0.1 is found to be 3020 lbs. The refined sizing iterations of the GTOW give a value of 3075 lbs. The breakdown of this weight is discussed later on in relation to aircraft stability. 2.2.3 INTERNAL LAYOUT The Sky2k is a personal air vehicle and it is important that its passengers feel comfortable. The seating configuration is a “one by two” where the pilot’s seat is forward of the passengers’ seat, where they sit side by side. In the interest of luxury, each seat is twenty inches wide, making them an inch wider than normal first class seats. They are spaced at a three-foot seat pitch, meaning that there are three feet from the beginning of the pilot’s seat to the same point on the passengers’ seat. This is four inches longer than first class pitch on a Boeing 737-800/900 (2).

Engine

Fuel

Seating

Avionics

Baggage

Figure 2-1: Internal Layout Side View

2.3 LANDING GEAR 2.3.1 LANDING GEAR ARRANGEMENT AND SELECTION The Sky2k makes use of a tricycle gear configuration. This is characterized by having two main wheels aft of the CG and a nose wheel fore of the CG. Several safety and ease of use factors make this arrangement superior to others. First and foremost, this configuration is stable on the ground. In addition, it allows the plane to land at a large “crab” angle (i.e. the nose is not aligned with the runway).

This is especially useful in crosswind landing.

Furthermore, this configuration allows the cabin floor to be parallel to the ground for simple loading of passengers and cargo. It is also the landing gear arrangement that maximizes the pilot’s graze angle for a given fuselage design. The Sky2k makes use of fixed landing gear. On such a small aircraft, the implementation of retractable landing gear would require additional structures on the fuselage to house them. Retractable gear mechanisms are heavy to begin with and adding gear housing would further increase structural weight.

With these extra structures required for retracting gear, the drag savings are not worth the added weight, increased cost, and reduced reliability. Solid spring shocks were chosen for the main gear. This type of shock is commonly used in general aviation aircraft.

They are very simple and

extremely reliable. Oleopneumatic shocks (“oleo”) are the most common type of shock currently in use (16). They employ a combination of the spring effect in compressed air with the damping effect of driving fluid through an orifice by a piston. An oleo is implemented in the nose gear for extra comfort. For oleo shock sizing, internal pressures are generally 1800 psi (16) and the diameter of the piston is a function of internal pressure and maximum static load (which is discussed later). This gives a shock piston diameter of 0.15 ft. Both the main gear and nose gear have aerodynamic struts and the wheels are covered by speed fairings to reduce drag as much as possible. 2.3.2 VERIFICATION OF LANDING GEAR LAYOUT The two critical angles for landing gear placement are the “tipback” angle and the “overturn” angle. The gear on the Sky2k was analyzed using a method proposed by Raymer (16). The tipback angle is a measure of the maximum aircraft nose-up attitude with the tail touching the ground. To be sure that the aircraft won’t tip backwards, the angle between the vertical and the CG should be greater than the tipback angle or 15 degrees (whichever is larger). Fig. 2-2 shows the tipback angle of 35o and the angle to the CG is 45o, which is a positive check.

Figure 2-2: Tipback Angle and Verification Angle (Not to Scale)

The overturn angle affects whether the aircraft will tip when taxied around a turn. The angle must be viewed from a position where the nose wheel and one of the main wheels are in the same line of sight. The overturn angle is from the line through the wheelâ&#x20AC;&#x2122;s center horizontal to the ground up to a line that goes through the CG location. This is best described in Fig. 2-3. It should be less than 63o and it can be seen in Fig. 2-4 that the angle is 61o.

Figure 2-3: Overturn Angle Schematic (12)

Figure 2-4: Sky2k Overturn Angle (Not to Scale)

The longitudinal positioning of the landing gear was based on static loads encountered by the gear. Recommendations made by Raymer (16) guided this process of finding ratios between fore and aft CG locations, wheel placement relative to these CG locations, and the wheelbase dimension. The method is based on finding a ratio between the distance from the main gear to the forward CG (i.e. fully loaded) and the length of the wheelbase as well as a similar ratio for the aft CG (i.e. when the plane has no luggage, passengers, or fuel). These ratios gauge if the main gear are taking too much of the static load. If so, they may collapse, and if the nose gear doesnâ&#x20AC;&#x2122;t take some of the static load, there may not be enough normal force to provide steering authority. Table 2-2 lists the dimensions in variables proposed by Raymer (16). Na is the distance from the nose gear to the aft CG, Nf is the distance from the nose gear to the forward CG, H is the height from the ground to the CG, B is the wheelbase, while Ma and Mf represent the difference between the respective N-value and the wheelbase. Table 2-3 presents the results of the landing gear position validity check. The numerical values for the static load calculations as defined by Raymer are given in Table 2-4.

Dimension Na Nf Ma Mf H B

Length (ft) 14.34 13.13 1.16 2.37 5.3 15.5

Table 2-2: Wheel Load Geometry

Ma/B Mf/B

0.075 0.153

>0.05 <0.2

Table 2-3: Static Load Verification Results

Max Static Load Max Static Load, Nose Min Static Load, Nose Dynamic Braking Load, Nose

Load (lbs) 2843.9 2604.0 230.1 1072.6

Table 2-4: Static and Dynamic Gear Loads

2.3.3 TIRE SIZING The tires were sized using coefficients from a table in Raymer (16). The diameters and widths of the wheels are based on the weight on that wheel set (nose or main wheels) and two coefficients defined for various types of aircraft.

The coefficients used for this analysis are for general aviation

aircraft. Table 2-5 summarizes this analysis. To test the validity of these calculations, they were checked against the method used in Corke (6) and matched well. Since the rest of the landing gear analysis was done using Raymerâ&#x20AC;&#x2122;s methods, tire-sizing calculations also followed that text.

Main Tires Diameter (ft) Width (ft) Nose Tire Diameter (ft) Width (ft) Table 2-5: Tire Sizing

2.1 0.7 1.2 0.5

CHAPTER 3: AERODYNAMICS 3.1 INTRODUCTION As an STOL aircraft, aerodynamics is arguably the most important and technically challenging aspect of the Sky2k PAV. In order to allow the aircraft to takeoff and land in such short distances (500 and 1000 feet, respectively), high-lift devices need to be used. Although there are several forms of high-lift devices, such as triple slotted or externally blown flaps (which will increase the maximum CL of the aircraft so much that even shorter takeoff distances can be achieved) these devices will add much more complexity, weight, and cost to our aircraft, significantly detracting from our converging on a light, small, and affordable personal air vehicle. For these reasons, no high-lift devices more complicated than double slotted flaps were placed on the aircraft. This chapter details how an initial airfoil was chosen, which high-lift devices were chosen, how analysis was performed on these devices, and the subsequent optimization of those devices to obtain the maximum lift possible from them. 3.2 INITIAL AIRFOIL SELECTION AND ANALYSIS First, an airfoil was chosen. By taking the wing loading at cruise and dividing that by the dynamic pressure at cruise, we obtain a CL, cruise = 20.976 / 57.8 = 0.363 (22). This means that we should choose an airfoil with a design Cl of 0.4. For this reason, the NACA 3414 airfoil was chosen. With a thickness-tochord ratio, t/c = 0.14, a maximum thickness location xt/c = 0.3, a maximum camber of f/c = 3, and a maximum camber location of xf/c = 0.4, the NACA 3414 is a nice, thick airfoil which becomes a good choice for a STOL aircraft

such as Sky2k. The airfoil in its clean configuration is shown below in Fig. 31.

Figure 3-1: The NACA 3414 Airfoil Next, the properties of this airfoil were found using JavaFoil. JavaFoil is a program written to analyze 2D airfoil sections using potential flow analysis and boundary layer analysis (11). First, the ClÎą plot was found, shown in Fig. 3-2 and the drag polar was also calculated and can be seen in Fig. 3-3.

Figure 3-2: ClÎą Plot for the Clean NACA 3414 Airfoil

Figure 3-2: Clα Plot for the Clean NACA 3414 Airfoil From Figure 3-2, the lift-curve slope is found to be 0.121 for the airfoil section. It can also be seen that the zero-lift angle of attack for the airfoil is -3.3°, and that that Cl,max value is 1.7. These values are used extensively in determining the planform shape of the wing for the conceptual design of the aircraft. In Figure 3-3, the cruise Cl is marked with a green vertical line along with ±0.3 from that Cl. These markers represent the probable values of Cl our aircraft will observe during cruise, and from the drag polar, it is shown that during these Cl values, Cd is kept to a minimum, which means that total drag will also be kept to a minimum during cruise. In the conceptual design phase of Sky2k, these values from the NACA 3414 airfoil were used to create the planform dimensions, including planform area, of a single-lifting surface that would be able to lift the aircraft. This area was then taken and divided into two separate areas each for the canard and the wing. The chosen wing to canard area ratio was 2.2. This value is optimized for stability and control purposes and is detailed later in this report. The 24

planform dimensions were then worked around this area ratio.

The final

dimensions can be seen below in Tbl. 3-1. Dimension

Canard

Wing

Aspect Ratio

7.6

Planform Area (ft2)

43.45

95.59

Wing Span (ft)

18.17

26.95

ΛLE (deg.)

6.44

35.0

Taper ratio, λ

0.4

Root chord (ft)

3.42

5.07

Tip chord (ft)

1.37

2.03

Table 3-1: Planform Dimensions of the Canard and the Wing

Next, once the planform dimensions had been set, the 3D wing and canard were modeled in LinAir. LinAir is a vortex panel method used to analyze three-dimensional lifting surfaces. While it is possible to place models of the fuselage into LinAir as well, only the canard, wing, and rudderlets were placed in LinAir for the Sky2k. To complete this task more efficiently, as the planform of the aircraft changed throughout our design process, a spreadsheet was set up which took planform dimensions from the conceptual design spreadsheet and converted them into the necessary LinAir coordinates for each the canard, wing and winglets. First the flow properties of the model needed to be input. The reference area, span, and chord values come from the planform dimensions of Sky2k as if it had only one lifting surface.

The reference locations (X and Z) are the

coordinates of the center of gravity location of the aircraft. A summary of the flow properties in LinAir can be seen below in Tbl. 3-2. It should also be noted that these values remain constant and that any values not listed here are zero. However, Mach number and α do change, but here they are shown during cruise conditions.

Flow Property

Value

Reference Span (ft)

32.51

Reference Area (ft)

139.04

Reference Chord (ft)

4.28

Ref. X (ft)

11.78

Ref. Z (ft)

5.29

Mach

0.238

α (deg.)

-1.504

Table 3-2: Flow Properties Used in LinAir

Next, each lifting surface is placed into LinAir.

Aside from the physical

placement coordinates described above (these can be found in the Aerodynamics e-ppendices’ spreadsheet LinAir.xls, but can be seen below in Fig. 3-4), LinAir also needs section properties of the airfoil, including drag polar, moment, and lift coefficients at the root and tip of the lifting surface. JavaFoil was used to find all these coefficients.

Their specific airfoil

configurations, including slats and flaps (whose design will be detailed later in section 3.3), were placed into JavaFoil and analyzed there. For a list of the airfoil coordinates and their corresponding analysis in JavaFoil, see the aerodynamics e-ppendices. The three drag polar coefficients (CDp0, CDp1, and CDp2) LinAir asks for come from the coefficients in a quadratic equation that fit an inverted drag polar plot, as seen in Fig. 3-5. The actual coefficients can be seen in the plot, where CDp0 is the constant term, CDp1 is the linear term, and CDp2 is the quadratic term. The lift coefficients are taken from Figure 3-2 (for the wing only), by reading off the value of Cl when α = 0°, and when the airfoil reaches Cl,max. The moment coefficient is determined by finding Cm when α = 0°. These results are tabulated below in Tbl. 3-3 for the canard and wing. It is important to note that although LinAir asks for these section properties at both

the root and tip, only one set of values are listed in Tbl. 3-3. This occurs because there is no airfoil change in either the canard or the wing and there is no twist to either lifting surface.

Therefore, these section properties will

remain the same regardless of spanwise location on either lifting surface.

Figure 3-4: LinAir Model of Canard, Wing, and Winglets

Figure 3-5: Inverted Drag Polar with Quadratic Fit for the NACA 3414 Airfoil

Canard

Wing

cdp0,root

0.0035

cdp1,root

-0.0041

cdp2,root

0.0069

cm0,root

-0.075

cl,max,root

1.848

1.7

cl0,root

0.846

0.4

Table 3-3: Canard and Wing LinAir Section Properties at Cruise

The differences in lift coefficients for each lifting surfaces are a result of differences in flap configuration and incidence angles. These values come from trim conditions determined by stability and controls, and can be found in the e-ppendices. These values for the rudderlets can also be found in the LinAir.xls spreadsheet in the e-ppendices, but are not listed here, as not too much analysis was performed on the rudderlets. 28

Once a procedure for analyzing both the 2D airfoil sections using JavaFoil and 3D platform using LinAir was setup, the analysis of high-lift devices used to takeoff and land in short distances could begin. 3.3 HIGH-LIFT DEVICES CREATION AND OPTIMIZATION In determining what types of high-lift devices to use to the aircraft, many questions must be asked. First, what CL,max do we wish to obtain, and what high-lift devices can reach that value? Second, how much added weight, cost, and complexity do these high-lift devices add to the aircraft? Although the latter consideration isnâ&#x20AC;&#x2122;t looked into with as much detail as the former, it still must be taken into account to design a marketable and technically feasible PAV. Initially, the decision was made to attempt to have a maximum CL greater than 4.0 during takeoff. Once it was realized that this is only possible using very complicated high-lift devices, we decided to try and reach a maximum CL of 4.0 exactly, which was also met with problems. When researching what type of high-lift devices to use, initially we wanted to use full-span slats and a flap system, based on other STOL aircraft (9). At first, junker flaps were analyzed, but as those did not produce the lift required, a double-slotted flap system was chosen for the wing. This was based on the Cl,max it would yield as well as its relative simplicity (1). The canard, however, was given a plain flap system to help reduce the complexity of the aircraft. Next, a system for the leading edge of the airfoil was chosen. Again, this was chosen based on other STOL aircraft (9) and recommendations based on Raymer (16) and Anderson (1). A full-span slat was chosen for its ability to increase the effective camber of the wing and thus the Cl,max of the wing,

delay flow separation at high angles of attack, and do so without producing a significant increase in drag (1). Once these systems were chosen, a basic idea of how to create them was needed. For that, the book Aerofoil Sections by Riegels (17) was referenced. By searching through various types of slat and flap configurations and their corresponding CL,max values as listed, a form for the slat and double-slotted flap was converged upon (17).

This design was modeled as closely as

possible when splitting up the NACA 3414 airfoil to have a detachable leading edge slat and flaps that would be able to fold up into the original airfoil shape. By manually editing the coordinate files of the airfoils, a slat and flap configuration was made for both the wing and the canard. They can be seen below in Figures 3-6 and 3-7, respectively.

Figure 3-6: The Slat and Flap System of the Wing During Takeoff

Figure 3-7: The Slat and Flap System of the Canard During Takeoff

Now that the flap system had been created, it needed to be optimized. First, approximations for the ΔCL,max that the high-lift systems provided were found by sets of equations from Raymer. Equation 12.21 is #S & "CL,max = 0.9"Cl,max %% flap (( cos( ) H .L. ) $ Sref '

(eq. 3.1)

where Sflap/Sref is the flapped planform area over the entire planform area of the lifting surface, ΛHL is the sweep of the hinge line where the flap connects ! to the main body of the airfoil (17). On the Sky2k, the flaps on both the wing and canard are 34% of the chord length, and the hinge line sweep was determined using the following equation that was determined based on the geometry of the wing: $ 0.66(c r # c t ) # b 2 tan( " LE ) ' " HL = tan#1& ) b % ( 2

(eq. 3.2).

To determine ΔCl, first Raymer’s approximations were used, and then these were compared to the results of JavaFoil. Raymer’s approximations come ! from Table 12.2 and are composed of coefficients which are multiplied by the effective distance they increase the chord length of the airfoil (17). These values are used in the e-ppendix spreadsheet Flap Analysis.xls. To compare Raymer’s approximations to Javafoil, first the clean airfoil was analyzed in JavaFoil and its Cl,max value was determined. Next, the dirty configuration was placed in JavaFoil and again the value of Cl,max was found. These two values were subtracted, and the results are shown below for both Raymer’s approximation and the JavaFoil analysis. Raymer

JavaFoil

Wing

2.296

2.148

Canard

1.332

1.577

Table 3-4: ΔCl,max Comparison of Raymer and JavaFoil

This shows that the two analysis methods yield very similar results. This is good and shows that we are most likely analyzing the flap/slat system correctly so far or have designed the system well. Once this was done, the ΔCl,max values were converted into ΔCL,max values using the previously stated equation from Raymer (16), the results of this work on both Raymer’s approximations and in JavaFoil can be seen in Tble. 3-5. Raymer

JavaFoil

Wing

1.618

1.513

Canard

1.010

1.195

Table 3-5: ΔCL,max Comparison of Raymer and JavaFoil

Again, these values are very close together and verify our analysis. Next, a base value of CL for each lifting surface is needed in order to add the computed ΔCL values to in order to determine the CL,max values for each lifting surface and then for the entire aircraft. To do this, LinAir was used, and each lifting surface was placed in LinAir by itself to determine the CL for each planform. These LinAir .xml files are found in the e-ppendices. It was found that the CL of the wing was 1.68, while the canard had a value of 1.62. Now, the ΔCL values were added to base CL to find the CL,max values to each lifting surface, again this was done with both the Raymer approximations and the JavaFoil results. However, to combine these values to analyze the Sky2k, we need to combine the area ratio of the wing and canard. The proper equation to use is as follows:

Sw S CL,max,w + c CL,max,c = CL,max Sref Sref

(eq. 3.3).

This will reduce each CL term by the appropriate area ratio. When this is all completed, we have values of CL,max for takeoff and landing using both the !

Raymer and JavaFoil methods. We also placed the takeoff model into LinAir and can compare the results of each method shown below in Tbl. 3-6. Method

CL,max

Raymer

3.089

JavaFoil

3.075

LinAir

3.097

Table 3-6: CL,max Values for Sky2k at Takeoff

Again, all these values are very close to each other, and when averaging them out, we obtain 3.087. Initially, a CL,max of 4.0 was to be obtained, but after realizing the limitations of our design due to flap selection, a closer look was needed to determine what CL,max value we really needed to get off the ground at takeoff.

This involved looking at the power provided by our

propeller in the vertical direction during takeoff and climb to determine that we need a CL,max of 3.1 to takeoff in the 500 ft. Our slat and flap system was then optimized to hit this target CL,max as closely as possible.

Many variations of slat and flap placement were made in

JavaFoil to determine the largest Cl,max values that could be obtained from these high-lift devices. The values seen in all the tables and figures in this section are the post-optimized values of all lift coefficients. While no specific trade study was performed on Cl vs. placement of slats or flaps, these values have been optimized to determine the proper fit, given it was a reasonable configuration. Meanwhile, there is no reason to believe that this is a suboptimal configuration, considering how closely all the calculation methods are agreeing.

3.4 RESULTS Now that there are suitable models for analyzing both cruise and takeoff configurations, we can begin to take resultant data from our analysis and use it in other aspects of the Sky2k. In this section, how the lift distribution curves and stability derivatives were obtained and used will be described. First, the lift distribution for LinAir was obtained for the cruise configuration. An image of it can be seen in Fig. 3-8. While this lift distribution works well, it does not tell us exactly what we want to know. Since the structure of the wing will need to be able to support the total force from the lift, we need to convert the output of the lift distribution curve into pound force.

Figure 3-8: LinAir Lift Distribution Plot

To do this, we need to multiply each point on the y-axis by q and cref. The value cref is described in the previous section as one of LinAirâ&#x20AC;&#x2122;s flow property inputs. The dynamic pressure, q, is also needed since the definition of lift is L=

CL qS

(eq. 3.4).

To do this, an Excel spreadsheet was created (see LiftDist.xls in the eppendices). Once a curve fit was applied to the lift curve slopes, they could be integrated to be analyzed for a structural analysis of the wing and canard. The stability derivatives were even simpler to derive using LinAir. Once the cruise condition model was placed into LinAir, all that needed to be done was ensure that all the input conditions were correct and LinAir would automatically solve for these derivatives. However, they were mainly used for stability and control analysis, and will be discussed later in the report. 3.5 SAFETY Since our aircraft is a personal air vehicle, safety is a major factor in the design decisions. As mentioned earlier, safety was one of the major factors that drove us to design an aircraft with a lifting canard.

To reiterate, an

optimal design of a lifting canard aircraft will force the canard to stall first, so that if the aircraft pitches up too far, a stall from the canard will cause the aircraft to fall back to its normal cruise condition. This creates an essentially “stall-less” aircraft. In choosing our high-lift devices and in configuring the trim condition (including incidence angles) during cruise, we can show that the canard does indeed stall first. To do so, the wing and canard, in their cruise configurations are placed in JavaFoil. When the two Clα plots are compared in Fig. 3-9, it can be clearly seen that the canard does indeed stall first. This confirms the added safety benefit of having a canard.

Figure 3-9: ClÎą Plots Canard (Green) and Wing (Red) in Cruise Configurations

3.6 CONCLUSIONS In conclusion, we see that although the most complicated high-lift devices were not chosen, the Sky2k was still able to attain a large enough CL,max value to meet its STOL requirements.

While there may still be room for

improvement of the slat and flap design, specifically in the actual shape of these high-lift devices, it is hard to determine which shapes are optimal. However, this is the optimal configuration for the Sky2k. While meeting the high CL,max necessary, we were able to keep the additional cost, weight, and complexity of adding a high-lift device onto the aircraft down to a minimum. It can also be said that although all our analysis methods did not completely agree, they were very close; so close that we can be very confident in the accuracy of our results. While designing a high-lift system to allow an aircraft with a double lifting surface to achieve STOL capabilities is quite a challenge, we have done so as well as possible with the tools we have and the assumptions made. 37

CHAPTER 4: PROPULSION 4.1 INTRODUCTION Several unique design challenges are associated with Sky2k with respect to the propulsion system. Factors such as cruise conditions, weight, size, cost, and reliability affect the particular engine selection.

The pusher-prop

configuration presents a challenge in propeller sizing and weight limits on the engine to allow static stability.

The short takeoff and landing (STOL)

requirement poses a design challenge in producing enough thrust at slow velocities from a propeller optimized for cruise velocities.

The following

sections describe the methods to overcome such challenges. 4.2 POWERPLANT SIZING, SELECTION, AND PERFORMANCE The primary motivation behind choosing a particular type of engine for the Sky2k is the cruise Mach condition.

Raymer gives a recommendation of

engine selection in terms of cruise Mach number and specific fuel consumption (SFC): in general, aircraft maximum cruise speed limits the choices, as shown in Fig. 4-1 (16).

Figure 4-1: Propulsion System Speed Limits

The cruise Mach number for Sky2k is 0.24, so Raymerâ&#x20AC;&#x2122;s recommendation indicates that either a piston-prop or turboprop engine should be used. To decide between a piston-prop or turboprop engine, further design requirements are considered. A piston-prop engine has the advantage of being substantially cheaper and having lower fuel consumption than a turboprop.

On the other hand, a turboprop has the advantage of being

substantially lighter, more reliable due to fewer moving parts, and quieter. However, in consideration of cost and fuel-weight savings, a piston-prop engine was chosen. This decision also reinforces the design ideal that the aircraft would be a personal air vehicle (PAV); piston engines can be serviced and repaired by a wider range of mechanics and customers would be more comfortable operating a familiar engine. In terms of choosing a particular piston-prop engine, required horsepower must be defined. Below is a figure of the wing loading chart for Sky2k:

Figure 4-2: Wing Loading Chart for Sky2k

At the chosen wing loading (where the cruise, landing, and takeoff lines intersect), the horsepower-to-weight ratio (HP/W) is about 0.1 HP/lb. Therefore, for a takeoff weight of about 3100 lbs, a correctly-sized engine should have about 310 hp. However, piston-engine performance suffers as altitude increases.

For

design purposes, the most important characteristic of piston engines is that the power produced is directly proportional to the mass-flow of the air into the intake manifold, which in turn is affected by the freestream air density and intake manifold pressure (16). The following equation relates power to the air density (16):

& ( 1 ' ( (0 P = PSL $$ ' 7.55 % (0

# !! "

(eq. 4.1)

This equation indicates that at the cruise altitude of Sky2k (which is 10,000 ft), a piston engine can provide only about 70% of its sea-level power. Therefore, for a piston engine to provide 300 hp at a cruise altitude of 10,000 ft, it would need 389 HP of sea-level power.

Research among engine

manufacturers shows that such an increase in power typically corresponds to an increase in weight of about 100 lbs. A turbocharger can overcome this obstacle because it can maintain sea-level performance without a significant increase in weight. It works by recovering energy via a turbine in the engine exhaust that compresses the intake air, thus increasing the manifold pressure.

The following figure shows that

typically, sea-level pressure can be maintained up to an altitude of 30,000 ft with a turbocharger (16):

Figure 4-3: Effects of Turbocharging with Altitude

The Lycoming TSIOL-540 provides the necessary horsepower.

Itâ&#x20AC;&#x2122;s a

turbocharged, fuel-injected, 540 cubic-inch reciprocating piston engine; its significant specifications are listed below (19): Power Weight Dimensions Compression Ratio Price

350 HP 402 lbs 33.50X42.50X42.57 inches 7.5:1 $60,000

Table 4-1: Engine Specifications

It is slightly oversized so that the short takeoff and landing (STOL) requirement can be met, because STOL requires very quick acceleration and thus engine power. 4.3 PISTON-ENGINE INSTALLATION The most common type of air-intake for a pusher-prop aircraft is a scoop mounted below the fuselage to provide updraft cooling.

Figure 4-4: Updraft Scoop Cooling

As a rule of thumb given by Raymer, the capture area of the scoop should be about 30-50% of the engine frontal area.

Therefore, with the chosen

Lycoming engineâ&#x20AC;&#x2122;s frontal area of 9.89 ft , 30% of that area is about 2.97 ft2. If the scoop is about 4 ft wide, then it will be approximately 8.9 inches tall.

4.4 PROPELLER SIZING The first step in designing a propeller is to define the number of blades. Hepperle remarks that a propeller with more blades will generally perform better because it distributes its power and thrust more evenly in its wake (11). Weik also provides recommendations for the number of blades. Three or more are used when the diameter needs to be minimized or if vibration is a problem. â&#x20AC;&#x153;If there is an unsymmetrical airflow through a two-bladed propeller [due to gusts or high climb angles associated with STOL aircraft], ordinarily one blade is at its highest angle of attack and load at the same time that the other is at its lowest, and this is likely to cause undesirable vibrations. With three or more blades the uneven load distribution is spread more evenly around the propeller disc and the vibrations are greatly reducedâ&#x20AC;? (21). Therefore, in consideration of the practical limits on diameter with the physical size of Sky2k in terms of ground interference (especially during takeoff and landing) and the high power loading due to the STOL requirement, a threebladed propeller was chosen. Next, an initial estimate of propeller diameter is made with an historical relation between diameter and power input (16):

d = 1.44 hp ft.

(eq. 4.2)

With an input of 350 HP, an initial diameter sizing gives 6.5 ft. However, practical limits and safety considerations due to ground strike during takeoff and landing angles limits the propeller diameter 5.5 ft, so this diameter was chosen.

The next step in propeller design calls for the rotational velocity limits. At cruise, the tip of a propeller follows a helical path through the air; therefore tip speed is the vector sum of the rotational speed ( Vtip = !nd , where n is the rotational rate in Hz, and d is the diameter) and cruise speed ( V ), i.e.,

Vtip ,helical = Vtip2 + V 2 .

(eq. 4.3)

Corke recommends that the tip speed stay below Mach 0.85 to avoid compressibility effects on propeller efficiency and to minimize noise (6). Therefore, with a propeller at 5.5 ft diameter, cruise velocity of 257 ft/s, and a tip Mach limit of 0.85, the rotational speed comes to 3050 rpm. Table 4-6 characterizes the propeller. No. of Blades Propeller Diameter Cruise Speed Cruise Altitude Tip Mach Limit Rotational Limit

3 5.5 ft 257 ft/s 10,000 ft 0.85 3053 rpm

Table 4-2: Summary of Propeller Characteristics

4.5 PROPELLER PERFORMANCE A software tool called JavaProp (11) was used to analyze the performance of the propeller for Sky2k. It implements the standard method of blade-element theory (21), depicted in Fig. 4-5 below.

Figure 4-5: Blade Element Theory

A propeller is basically a rotating wing. Blade element theory splits each blade into radial strips of width dr and treats each resulting cross-section as an airfoil element on which calculations such as lift and drag are analyzed due to local flow properties such as rotational speed, cruise velocity, air density, diameter, etc. These elements are then integrated from root to tip to give useful performance characteristics like thrust, power loading, and efficiency.

However, the physical geometries of the propeller, such as airfoil shape, angle of attack, and size along the radius, must initially be defined to analyze its performance. JavaProp provides predefined airfoil shapes that can be modified at several sections of the blade. The propeller for the Sky2k is comprised of four different airfoils. The MH126 is ideal for the root section of a propeller; it covers a wide angle of attack range without flow separation and is thick to withstand high tensile forces. The MH112 is designed to follow the root section of a propeller; it covers the typically needed range of lift coefficients for this region. The MH114 is designed for the middle part of the propeller. Finally, the MH120 is designed for the tip of a propeller; it can be used at high subsonic Mach numbers. The following figure summarizes the airfoil type, angle of attack ! , coefficient of lift C l , coefficient of drag C d , the lift-curve slope ( C l vs. ! ), and the drag bucket ( C d vs. ! ) for the airfoil chosen at each station along the blade.

Table 4-3: Airfoil Data for Propeller Blade at Various Stations

The general trend of the airfoils is that they become progressively sharper from root to tip, as the helical velocity increases to Mach 0.85 at the tip. The twist, or incident angle of attack, is chosen so that each airfoil achieves high lift coefficients without coming close to stall and remaining well within the drag bucket. The angles were optimized for cruise conditions by incrementing the angle of attack, performing the analysis, and checking the change in overall propeller efficiency. Note that typical lift coefficients for propellers are usually about 0.5; the lift coefficients for the propeller on Sky2k are all above this, with an average of 0.954. High lift coefficients are needed to provide the thrust required by the STOL requirement. The figure below shows the thrust coefficient CT , power coefficient C P , propeller efficiency ! , and the maximum possible efficiency ! * as functions

of advance ratio for the propeller over the full range of advance ratios designed for cruise conditions.

Figure 4-6: Thrust and Power Coefficients, Efficiency & Max Efficiency vs. Advance Ratio

The advance ratio at cruise is shown by the vertical line in red. Since thrust is inversely proportional to the flight velocity (except for zero velocity), the coefficient of thrust decreases to zero as the velocity increases until there is no thrust and the propeller â&#x20AC;&#x153;windmillsâ&#x20AC;? and is essentially propelled by the oncoming wind rather than the shaft input. This propeller is optimized for cruise. Notice that at cruise conditions, a good balance between propeller efficiency (well before the point at which efficiency dramatically drops off) and maximum thrust is achieved.

4.6 TAKEOFF ANALYSIS A standard method of takeoff analysis is given by Corke (6). Takeoff analysis is done assuming the total takeoff distance is comprised of four component distances: a ground roll, rotation, transition, and climb over an obstacle. The sum of these distances is the takeoff distance, as shown below:

Figure 4-7: Takeoff Distance Components

The ground roll occurs between zero and takeoff velocity where the landing gear initially leaves the ground to begin the roll phase. According to Federal Aviation Regulations (FAR) Part 23, for civil aircraft, takeoff velocity must be at least 10% greater than stall velocity. Therefore, takeoff velocity for Sky2k is VTO = 74.3 ft / s (equivalently 22.7 m/s).

FAR Part 23 also specifies an

obstacle height to be at least H OBSTACLE = 50 ft .

As mentioned before, an inherent characteristic of propellers is that they provide less thrust as velocity increases.

The propeller airfoil and pitch

distribution for the Sky2k has already been optimized for cruise conditions (where most of its flight time occurs); however, this means it will not be optimized for takeoff conditions. A unique challenge of Sky2k is the high thrust at takeoff conditions required to meet the STOL requirement. One solution is to design a variable pitch propeller in which the individual blades can be rotated within the shank. This allows thrust optimization over a wide range of velocities. The figure below shows thrust profiles for velocities in the ground roll segment as the propeller pitch is varied.

Figure 4-8: Ground Roll Thrust Profiles for Several Pitch Variations

At a blade angle change of 0° (i.e., that of the fixed-pitch, cruise-optimized propeller), thrust performance is poor at low velocities and drops to about 7500 N at 5 m/s. However, as the blade pitch is changed to 4°, the thrust rises to about 10000 N at 5m/s. A blade angle change of -5° is good for midrange ground-roll velocities, and angles between 0° and 4° produces high

thrust for velocities close to takeoff. If the maximum thrust is chosen for each profile over the range of ground roll velocities, the thrust provided by the variable-pitch propeller is obtained. It is plotted in the following figure.

Thrust vs. Velocity for Blade Angle Variations Takeoff Velocity

Optimal y

Ave Ground Roll Thrust

Poly. (Optimal)

3 2 -0.0009x + 0.039x - 0.4203x + 10.849

Thrust (kN)

10 9

8 7 0

Velocity (m/s)

Figure 4-9: Variable-Pitch Propeller Ground Roll Thrust

The optimal thrust data is fit to a third-order polynomial whose equation is boxed. The ground roll distance is dependent on the average thrust over the duration of the ground roll. To find this average, the average-value integral relation is used:

f ave =

1 b f (x )dx b " a !a

(eq. 4.4)

The limits a and b are taken to be zero and the takeoff velocity, respectively, and the integrand is taken to be the polynomial fit equation. The average thrust is then found to be 10097 N.

The figure below summarizes the takeoff breakdown:

Takeoff Breakdown Climb 45 ft 8%

Ground Roll 128 ft 21%

Rotation 74 ft 12%

Transition 351 ft 59%

Figure 4-10: Takeoff Breakdown

The transition is the most expensive takeoff component at 351 ft, or 59%, of the total takeoff distance. Climb is considered to be at an angle of ! CL = 22 o , which was defined from trim analysis at takeoff. The angle seems steep, but is typical of many STOL aircraft including the 260SE/STOL designed by Todd Peterson. The ground roll for Sky2k is 128 ft and comprises only 21% of the takeoff distance, which is 598 ft.

4.7 LANDING ANALYSIS A standard method of landing analysis is given by Corke (6).

The total

landing distance, like the takeoff distance, is comprised of four component distances: an approach over an obstacle, a transition, a free roll, and ground roll. The sum of these distances is the landing distance, as shown below:

Figure 4-11: Landing Distance Components

FAR Part 23 civil requirements call for a minimum obstacle height of H OBSTACLE = 50 ft

and a breaking friction coefficient of Âľ = 0.30 . Assuming an

o approach angle of ! APP = 3 , which is typical of transport aircraft, the landing

breakdown is shown in the following figure.

Landing Breakdown Braking, 375ft, 24%

Transition, 59ft, 4%

Free Roll, 233ft, 15%

Approach, 925ft, 57%

Figure 4-12: Landing Breakdown

The total landing distance comes to 1040 ft. Weik notes that the braking distance can be reduced with a variable pitch propeller by drastically altering the pitch to create an â&#x20AC;&#x153;air brake,â&#x20AC;? which has been experimented with by the Army and Navy. 4.8 CONCLUSIONS As is discussed above, several unique design challenges are associated with Sky2k with respect to the propulsion system. With tools such as JavaProp, trade studies, and recommendations, a propulsion system was chosen, designed, and optimized for cruise while giving the takeoff performance required for short takeoff and landing.

CHAPTER 5: STABILITY AND CONTROL 5.1 INTRODUCTION The most notably unique aspects of the Sky2k are the duel lifting surfaces and the ability to takeoff in a short distance. A lifting canard requires modifications to the methods used in analyzing the static stability for traditional aircraft. An inherent issue with canard aircraft is that the location of the neutral point is brought forward. This, along with center CG, being pushed further back due to the rear placement of the engine limits possible configurations to maintain static stability. In order to achieve STOL, a large lift must be attained at low speed while providing a pitching moment to reach a suitable climb angle. Also, stability must be maintained at maximum and minimum payloads. The relatively low weight of the Sky2k causes significant CG movement between maximum and minimum loads. The greatest challenge in resolving all of these issues is that solving one problem usually led to a new problem. 5.2 STATIC STABILITY 5.2.1 LONGITUDINAL STABILITY In order to attain a statically stable aircraft the neutral point of the plane must be aft of the CG. The neutral point is calculated by determining the location on the aircraft where the moment is not affected by changes in the angle of attack (16). The location of the CG for each major component on the Sky2k was already presented in Table 2.1 along with their weights. From these values the CG location of the entire plane can be calculated by determining the point at which its moment formed from the weight of each component is zero (16).

By knowing the locations of the neutral point and center of gravity, the static margin is known. Table 2-1 represents the maximum allowed load on Sky2k, with and without fuel. Figure 5-1 shows how great an effect the passenger and baggage weight has on the total weight of plane. A large drop in this weight would drastically change the location of the CG towards the rear of the vehicle. Since a more aft CG means a less stable aircraft, the minimum load scenario is used to determine the configuration of the Sky2k. The light configuration consists of 200 lb in the pilotâ&#x20AC;&#x2122;s seat, 0 lb in the passenger seats and 50 lb in the carry on compartment. Deadweight must be added if these specifications are not met.

Weight Distribution Fuel 16.7%

Rest 14.0%

People & Baggage 24.6%

Wetted Engine 19.3%

Nose Landing Gear 1.2% Main Landing Gear 4.2% Fuselage 7.7%

Wing 8.2% Vertical Tail 0.4%

Canard 3.9%

Figure 5-1: Sky2k Weight Broken Down by Component Note the Large Contribution From People and Baggage

By placing the aerodynamic centers of the wing and canard at appropriate locations along the length of the plane a suitable static margin can be obtained. Layout restraints do not allow for much movement of the canard so

only the wingâ&#x20AC;&#x2122;s aerodynamic center is adjustable. The static margin is adjusted by altering the wingâ&#x20AC;&#x2122;s location and sweep as well as the wing to canard area ratio. Figure 5.2 shows the effect of wing placement on static margin. The further back the wing is placed, the more stable the aircraft becomes. The initial reaction is to place the wing as far back as possible but trim conditions limit the extent of this placement. A leading edge location of 16.8 ft was ultimately chosen.

Wing Placement 0.0%

Static Margin

-20.0%

-40.0%

-60.0%

-80.0%

-100.0% 15

Wing Leading Edge Position (ft)

Figure 5-2: Trade Study Showing the Effect of Wing Position on Stability For the Minimum Load

Wing Design Wing /Canard 1

Wing /Canard 1.3

Wing /Canard 1.6

Wing /Canard 2

20.0%

0.0%

Static Margin

-20.0%

-40.0%

-60.0%

-80.0%

-100.0% 0

Wing Sweep @ 1/2 Chord (Degrees)

Figure 5-3: Trade Study Showing the Effect of Wing Sweep and Wing/Canard Area Ratio on the Stability (For the Minimum Load)

With the wing location chosen, the wing sweep and area ratio must be adjusted to obtain a stable plane at the minimum load. Figure 5-3 represents the static margin as a function of sweep and area ratio. Sweeping the wing backward brings the wing’s aerodynamic center to the rear, stabilizing the plane. However, a very large sweep also reduces the effective lift of the wing. Changing the areas of the wing and canard so that the wing is larger and the canard is smaller moves the net lift and therefore the neutral point back. The resultant wing dimensions, CG travel, and static margins are presented in Table 5-1. DIMENSIONS Canard Leading Edge Position Canard Leading Edge Sweep Canard Area Wing Leading Edge Position Wing Leading Edge Sweep Wing Area

Heavy With Fuel Heavy Without Fuel Light With Fuel Light Without Fuel

2.00 6.44 43.94 16.80 35.00 96.67 CG TRAVEL 11.78 11.76 12.87 13.11

ft Degrees ft2 ft Degrees ft2

ft ft ft ft

STATIC MARGIN 32.5 33.1 8.6 3.3

% % % %

Table 5-1: Results From Longitudinal Static Stability Analysis

5.2.2 DIRECTIONAL AND LATERAL STABILITY The directional stability is expressed through the use of Cnβ, the derivative of the yawing moment coefficient with respect to sideslip angle, β. This value can be obtained by determining the Cnβ’s for the vertical tail, fuselage, canard and wing. The sum of each component of Cnβ equals the total Cnβ for the aircraft (6). Using approximations for the Cnβ components from Corke, the directional stability coefficient for the airplane is given in Table 5-2. According

to recommendations given by Corke, the directional stability of the Sky2k is acceptable. The lateral stability coefficient, Clβ, determines the ability of the aircraft to resist rolling out of control when a cross wind is applied. By convention, a negative value of Cl applies a restoring moment for a positive β; therefore, a negative value of Clβ is desired. Using Etkin and Reid’s method, the value for Clβ is shown in Table 5-2 (7). Vertical Tail (1/Rad)

Fuselage (1/Rad)

Canard (1/Rad)

Wing (1/Rad)

0.206

-0.080

0.005

0.001

0.131

1/Rad

-0.042

1/Rad

Cnb CnbA/C ClbA/C

Table 5-2: The Stability Coefficients for Directional and Lateral Stability

5.3 TRIM ANALYSES 5.3.1 LONGITUDINAL TRIM AT TAKEOFF During takeoff, a net pitch up moment about the center of gravity must be generated in order to rotate the aircraft to an appropriate angle of attack and climb angle. Moments that pitch the aircraft upwards are designated as positive. In order to achieve this for the short takeoff requirement, a takeoff velocity of 74.4 ft/s (50.4 MPH) is used. The moment about the center of gravity is obtained by using terms from Raymer’s equation for the coefficient of moment about the center of gravity and additional terms that account for the lifting canard (16). Equation 5.1 is the expression derived to calculate the pitching moment about the CG

M CG = C Lwing (X CG ! X ACwing )qTO S wing + C Lcanard (X CG ! X ACcanard )qTO S canard + FP (Z CG ! Z P )+ C Mwing qTO S wing cwing + C Mcanard qTO S canard ccanard + C Mwing , flaps qTO S wing cwing + C Mcanard , flaps qTO S canard ccanard + C M"fuse"qTO S total ctotal + FPnormal (X CG ! X P ) (eq. 5.1) The elevator and ailerons on the Sky2k will also act as flaps during takeoff and landing. Hence, they can be referred to as flapervators and flaperons respectively. The flaps on the wing make up 40% of the chord and span the entire length of the exposed wing. During the ground roll these flaps will be deflected 35o. The flaps on the canard are 34% of the chord and span the entire length of the canard. Trim, Takeoff Elevator Angle 20 Deg.

Elevator Angle 40 Deg.

Elevator Angle 60 Deg.

0.50

0.00

Cm, cg

-0.50

-1.00

-1.50

-2.00 2900.00

3000.00

3100.00

3200.00

Vertical Lift (lb)

Figure 5-4: Represents the Moment as a Function of Elevator Deflection at any Vertical Lift (Used to Determine the Elevator Deflection and Angle of Attack, in Order to Takeoff)

Given these flap sizes and deflections, Figure 5-4 plots the coefficient of moment against lifting force at various elevator deflections, Î´e. This lifting

force consists of the lift created by the wing and canard plus the lift in the vertical direction generated from the propeller when the plane is at an angle of attack, α. Since a positive moment is needed at takeoff, an elevator deflection of 60o is chosen. As the plane accelerates to takeoff, a positive moment develops about the CG and causes the nose of the plane to pitch up. Given the takeoff weight and chosen flap deflections, the minimum angle of attack of 10.85o is needed to leave the ground. At this angle of attack there is still positive moment acting on the plane that can rotate the vehicle to a suitable climb angle. 5.3.2 LONGITUDINAL TRIM AT CRUISE Trim at cruise requires that that total moment acting on the center of gravity is equal to zero. There also must be sufficient lift to maintain level flight. Table 5-3 shows that based on the locations of the canard and wing, the canard’s aerodynamic center is closer to the CG than the wing’s aerodynamic center. As a result, the wing needs to either move forward or the lift on the canard must be greater than the lift on the wing. In section 5.2.1, the wing was placed towards to rear of the aircraft to achieve static stability. Therefore, the wing cannot be moved forward or the aircraft will become unstable with minimum loads. XAC,wing

XAC,canard

XCG

21.49 ft

2.86 ft

11.76 ft

Table 5-3: Shows the Difference in Proximity of the Canard to the CG and the Wing to the CG

Deflecting the elevators on the canard produces a greater lift on the front of the aircraft. By using Equation 5.1 at cruise conditions, the moment can be calculated for various elevator deflections and angles of attack. Figure 5-5 shows the moment coefficient as a function of δe and the lift coefficient. The lift coefficient is a dependent upon α. Choosing the lift coefficient that is 62

required at cruise and setting the moment equal to zero produces a Î´e of 5.26o and an Îą of -1.5o. Trim, Cruise Elevator Angle 0 deg

Elevator Angle 4 deg

Elevator Angle 8 deg

0.60

Cm, cg

0.30

0.00

-0.30

-0.60 0.10

0.30

0.50

0.70

Figure 5-5: Coefficient of Lift Vs. Coefficient of Moment about the CG at Cruise (Used for Determining Elevator Deflection and Angle of Attack)

Longitudinal trim at cruise is analyzed at maximum payload and low fuel because the CG position is at the most forward position. For all other situations the CG is closer to the main wing and a smaller elevator deflection is required. 5.3.3 LATERAL AND DIRECTIONAL TRIM The lateral trim defines the minimum roll rate that an aircraft must obtain at maximum aileron deflection. Both Corke and Nelson define that transport aircraft need a minimum helix angle of 0.07 rad (6). The helix angle is a function of velocity, wingspan, and steady state roll rate at maximum aileron deflection (14). Both velocity and wingspan are already defined so that the 63

helix angle defines the roll rate. Nelson relates the helix angle to aileron deflection, location and aileron size. By choosing a maximum deflection angle the ailerons can be sized. This will be done in section 5.3.4 Directional trim sizes the rudder so that it is affective during a worst case yawing moment. Corke suggests the case of an 11.5o sideslip angle with a 20o rudder deflection during landing (6). For analysis, the vertical tail is treated as a single tail with the same aspect ratio as the winglets and a total area equal to the sum of the two winglet areas. This results in a total rudder area of 2.24 ft2. 5.3.4 CONTROL SURFACE SIZING As a result of the trim analysis, the size requirements are determined for each control surface to affectively balance the aircraft. Figures 5-6, 5-7 and 5-8 show the placement and dimensions for the rudder, elevator and aileron respectively. Figure 5-8 also shows the dimensions for the flaps that do not function as ailerons.

Figure 5-6: Dimensions of Rudder on Winglets Total Area Refers to Both Controls (Not Drawn to Scale)

Figure 5-7: Dimensions of Elevators on Lifting Canard Total Area Refers to Both controls (Not Drawn to Scale)

Figure 5-8: Dimensions of the Ailerons and Flaps on the Main Wing Total Area Refers to Both Controls (Not Drawn to Scale)

5.4 DYNAMIC STABILITY AND AUTOMATIC CONTROL After sizing and placing all of the components of the aircraft in a statically stable configuration, an analysis of the aircraftâ&#x20AC;&#x2122;s dynamic behavior is needed. Using LinAir, the stability coefficients of the aircraft are determined based on its configuration. The coefficients that have been previously calculated by hand are used as a verification of the program. Table 5-4 shows the results that LinAir computed based on the Sky2kâ&#x20AC;&#x2122;s dimensions. Also in Table 5-4 are values for some of the same coefficients that already were determined. All of the values are the same sign and on the same order of magnitude. Since LinAir calculated its results using the entire configuration of the Sky2k, while the numbers calculated by hand are based off of general approximations found in various texts, the LinAir results are the numbers that are used in the dynamic analysis.

CLa CDa Cma CLq Cmq CLM CDM CmM Cyb Cyp Cyr Clb Cnb Clp Clr Cnr Cnp

LinAir

Hand Calculation

4.2975

4.5346

0.1544 -3.6068

-2.3985

14.1810 -55.0441 0.0428 0.0032 0.0947 -0.3805 -0.2460 0.4038 -0.0952

-0.0423

0.1736

0.1310

-0.3109

-0.5938

0.1347 -0.1887 0.1071

Table 5-4: Coefficients Provided by LinAir and Hand Calculations

The

Matlab

codes,

Sky2k_Longitudinal_Cruise.m

and

Sky2k_Lateral_Cruise.m, found in the E-ppendix use the stability coefficients given from LinAir in addition to the control coefficients in Table 5-5 that are calculated from Nelsonâ&#x20AC;&#x2122;s text or are results from trim analysis (14).

CL CD CLδe Cmδe Cyδa Clδa Cnδa Cyδr Clδr Cnδr CLα,dot

0.362 0.038 3.542 1.125 0.000 0.232 -0.021 0.124 0.047 -0.073 0.000 12.691

Cmα,dot

Table 5-5: The Coefficients that LinAir Doesn’t Provide (14, 16)

Figure 5-9: Longitudinal Impulse Response to a 1 Rad Input of Pitch Angle, Î¸

Figure 5-10: Lateral Impulse Response to a 1 Rad Input of Sideslip, Î˛

Figures 5-9 and 5-10 show the uncontrolled impulse response of the Sky2k. For all cases except the roll angle, Ď&#x2020;, the aircraft is dynamically stable. In order to make this vehicle safer, an automatic control for the roll angle is designed. Figure 5-11 shows the root locus of the Sky2kâ&#x20AC;&#x2122;s roll angle with the aileronâ&#x20AC;&#x2122;s control surface applied to it. The figure also shows the dynamic response with the designed PID control in place. On the root locus plot, the light blue line does go into the positive real plane. Positive real numbers are unstable values; this shows why the roll angle is unstable when no control is applied. Choosing a stable point on the root locus provides a proportional control constant, K that is used in the automatic control. The left-most point on either the green or dark blue lines are chosen because the larger the magnitude of the negative real number, the faster the response damps out. This produces a K equal to 0.1637. According to the dynamic response graph the control system works, providing a dynamically stable aircraft.

Figure 5-11: The Root Locus and Dynamic Step Response of a PID Control The Ailerons are Used to Control the Roll Angle

Class I Airplane Cruise Category B

Phugoid Short Period Spiral Roll Dutch Roll

t1/2 (s)

Eigen Value -0.013+0.166i -6.733+6.394i 0.015 -3.099 -.663+3.869i

ω n (rad/s)

0.17 9.29

0.08 0.73

τ (s)

47.36 0.05 3.93

0.17

Quality Level 1 Level 1 Level 1 Level 1 Level 1

Table 5-6: The Pilot Flying Qualities During Cruise Class I is Small Aircraft, Category B Encompasses Cruise Segment

The flying qualities as defined by Nelson are presented above in Table 5-6. They are determined from the eigenvalues derived in MatLAB from the differential equation of motion of the Sky2k. The phugoid and short period modes are from the longitudinal motion and the others are from the lateral motion. According to Nelson, Level 1 flight is the most user-friendly flying quality. Since this aircraft is marketed toward the general population, the flying qualities are a very significant aspect of the performance.

CHAPTER 6: STRUCTURES 6.1 INTRODUCTION The structure of this personal air vehicle needs to be designed to ensure safety in worst-case scenarios. During flight, the aircraft will experience lift loads and gust loads, which need to be accounted for in the structural design. A standard aircraft safety factor of 1.5 will be used to ensure structural integrity. The wing and lifting canard configuration divides the lift on the aircraft between their two surfaces. Thus, a detailed structural analysis of the wing and canard needed to be done. The wing has rudderlets, which, along with the effects of the canard, create abnormal lift distributions that also affect the structural design of the lifting surfaces. Other challenges faced were with the spar designs and configurations required for the lifting surfaces that are needed for STOL.

Sky2k Structural Design

FAR 23

Mission Requirements V-n Diagram

Wing/Canard

Fuselage

Material Selection

Material Selection Shear Force

Shear Forces

Moments Moments Tensile Loads

Spar Design

Skin Thickness

Stress/Deflection

Finite Element Analysis

Figure 6-1: Block Diagram of Structural Design Plan

Compressive Loads Bulkhead Spacing

6.2 V-N DIAGRAM The first step in the structural design of the Sky2k was to determine the maximum loads experienced by the aircraft at various flight conditions. The greatest loads in these situations would be gust loads, which are aerodynamic loads produced by turbulent air. A V-n diagram is then used to plot the load factors, +n, as a function of equivalent air speed and show where they fall with respect to the aircraft’s flight envelope. As previously discussed, it is desirable for the canard to stall first so that the nose will pitch down and the aircraft can recover. For this reason, the V-n diagram for the Sky2k will be done with the canard stalling first. The Sky2k will experience the greatest loads at cruise and dive conditions. Therefore, the next step is to determine the aircraft’s equivalent airspeed at these conditions. The equivalent airspeed (EAS) is defined as: 1/ 2

VEAS

# $ ! =V % & ' ! Sea " Level (

(eq. 6.1)

where ρ is air density. Once all the speeds are referenced to the same air density, the aircraft’s flight envelope can be found and plotted. The flight envelope consists of a positive and negative stall line, limit load factor lines, and the dive velocity line. The positive and negative stall lines are defined as: "1 # CLMAX ± $ ! SLVEAS 2 % &2 ' Stall Line(±) = W /S

(eq. 6.2)

The limit load factors vary for different types of aircraft. The Sky2k can be classified as a general aviation aircraft, so the FAR 23 sec. 23.337 was used to determine its limit load factors to be nMAX(+) = 3.8 and nMIN(-) = -1.52.

Finally, to close the flight envelope the dive velocity line is solved with the following equation: (eq. 6.3)

VD = 1.5VCRUISE

With the flight envelope completed, the maximum gust loads need to be found. The first step in calculating the gust loads is to find the equivalent mass ratio, µ.

µ=

2 (W / S )

" gcCL*!

(eq. 6.4)

Where CLα* is found by combining the CLα of the wing and canard using their area ratios (S).

CL*! = CL!WING "

SWING S + CL!CANARD " CANARD STotal STotal

(eq. 6.5).

Next, the gust alleviation factor for a subsonic aircraft is found by:

0.88µ 5.3 + µ

(eq. 6.6)

Then, the normal component of the gust velocity for cruise and dive are calculated using the following method: u = Kuˆ

(eq. 6.7)

where û is found from plots that relate the aircraft’s flight altitude to a value of û. Next, the change in the load factor can be found by:

1 " uVCL*! #n = 2 W /S

(eq. 6.8)

Finally, the two maximum load factors are found by adding/subtracting Δn to/from 1. The V-n diagram for the Sky2k is shown in Fig. 6-2 and the gust loads fall within the flight envelope so that the Sky2k can handle the maximum gust loads at any flight condition.

nMAX(+)

VCR

+ﾎ馬CR

+ﾎ馬D

nMIN(-)

Figure 6-2: Canard Stall V-n Diagram

Knowing that the maximum gust load factors fall within the flight envelope at cruise and dive speeds, the design load factor was determined. The structure for the Sky2k was analyzed according to the positive FAR 23 load factor and the standard aircraft safety factor of 1.5. Total Load Factor = 3.8 x 1.5 = 5.7

6.3 MATERIAL SELECTION The first thing to do when designing any structure is to find the best material for the job. A study was done to find the best material for the design of the Sky2k. A wide range of materials was considered and then narrowed down to one class of materials. Due to the fact that the Sky2k is a personal air vehicle and that safety and low weight are design goals, composites were initially considered.

Composites, though very high strength and light, are too

expensive for the proposed market. Research was then done on metals used in aircraft structures. Steel is a high strength material, but far too heavy for aircraft applications and titanium is very expensive. Aluminum was the chosen metal for the Sky2k. Table 6-1 shows the results of the research done on different aluminum alloys.

Material Aluminum 2024-T3 Aluminum 2024-T6 Aluminum 7075-T6 Aluminum 7050-T74

Max. Strength (ksi) 50 50 73 63

Elastic Modulus (ksi) 10,600 10,500 10,400 10,400

Density (lb/in3) 0.100 0.100 0.102 0.102

Table 6-1: Aluminum Study

The types of aluminum studied in Table 6-1 are all common aircraft metals. The material chosen for the Sky2k was Aluminum 2024-T3. This was chosen because it was found to be the most commonly used aluminum alloy on aircraft, it has a high strength to weight ratio, low material and machining costs, excellent fracture toughness and crack propagation resistance, and favorable corrosive properties. All these material characteristics fit the design goals of the Sky2k and make Aluminum 2024-T3 the best choice.

6.4 WING AND CANARD STRUCTURE 6.4.1 SPAR DESIGN - THEORY The structural design of the lifting surfaces begins with beam theory. The wing and canard are treated as cantilevered beams with rectangular crosssections. The largest moment on the beam would be at the root, and from this, the minimum moment of inertia can be found. The spars and wing box can then be designed. The minimum moment of inertia was found in two ways.

The first way

involved information on the percentages of lift on the wing and canard. This information was gathered from the stability and control engineer and used to get the total lift on the wing and canard. Knowing the lift, the root bending moments can be found using the following relation:

(eq. 6.9) Where b is the span of the lifting surface, L is the lift, and λ is the taper ratio of the lifting surface. The minimum required moment of inertia at the root is then calculated by multiplying MR by the gust load factor of 3.8 and safety factor of 1.5 and then using the following equation:

I MIN =

M R z MAX ! MAX

(eq. 6.10)

Where zMAX is half the maximum thickness of the airfoil and σMAX is the yield strength of the material. Table 6-2 shows the results for the wing and canard minimum moment of inertia.

Root Bending Moment (ft-lb) Zmax (ft) Max. Stress Al 2024-T3 (lb/ft2) Imin (ft4)

Wing

Canard

21,326.80

19,001.45

0.355

0.239 6

7.2 x 10

7.2 x 106

0.00105

0.000632

Table 6-2: Trim Theoretical Minimum Moment of Inertia

The second way the minimum moment of inertia was calculated was from analysis done in LinAir by the aerodynamicist. Lift distributions for the wing and canard were taken from LinAir, which plots lift per unit span vs. half span. By integrating these curves, the lift and moments along the lifting surface can be found. The minimum moment of inertia was then calculated using the same method from above. The results from LinAir are shown in Table 6-3.

Root Bending Moment (ft-lb) Zmax (ft) Max. Stress Al 2024-T3 (lb/ft2) Imin (ft4)

Wing

Canard

19,344.26

19,942.13

0.355

0.239 6

7.2 x 10

7.2 x 106

0.000954

0.000663

Table 6-3: LinAir Theoretical Minimum Moment of Inertia

It can be noticed that the two methods give similar, but slightly different results. Therefore, the conservative decision was made to use the values that gave the largest root bending moments. These correspond to the trim moment for the wing and the LinAir moment for the canard. The next step is to design the spar cross-section. For the Sky2k, the spar cross-section shape is important because it is a short takeoff and landing aircraft and has multiple slat and flap configurations. Also, because weight needs to be at a minimum, an I or C beam should be used. The C crosssection was chosen because C-channel beams provide flat surfaces for

control surface separation. The moment of inertia for a C shaped spar about the axis of bending is:

(eq. 6.11)

Figure 6-3: C-Beam Dimension Variables

After the spar cross-section is defined, the C-beam dimensions can be varied to match the previously found minimum moment of inertia required. However, it was found that using the moments of inertia from Tables 6-2 and 6-3 were too large because they assumed the height of the spar was equal to the maximum height of the airfoil. The spars are actually spread apart leaving enough room for the flaps and slats, and due to the camber of the airfoil, their height is smaller than the maximum thickness of the airfoil. This resulted in smaller zMAX values in the IMIN equation. For these reasons the moments of inertia of the C-beams could be decreased. The spar height is constant due to the placement in the airfoil shape, and the moments from LinAir are constant, so the only variable to change in the stress equation is the moment of inertia. Thus, the new process employed in the spar design was to conduct a parametric study where the spar cross-section dimensions were varied until

a combined moment of inertia of the two spars yielded a safety factor of about 1.5 from beam theory. This was done for both the wing and the canard. Before the parametric study can be done the minimum web thickness of the spars should be found. The minimum gauge for the web thickness is 0.06 inches and a shear force plot was done for the wing and canard to check is this thickness is large enough to handle the shear stress. See Figure 6.4. 6000

Shear Force (lb)

5000

4000

Wing Canard

3000

2000

1000

0 0

Span/2 (ft)

Figure 6-4: Shear Force Diagram for the Wing and Canard

The maximum shear force occurs at the root and this needs to be compared to the shear buckling stress of the beam. The shear buckling stress of beam can be found in the following way: FShear Buckle = KE(t/b)1/2

(eq. 6.12)

Where K is found from statistical data, E is the elastic modulus of the material, t is the web thickness, and b is the height of the beam. Table 6-4 shows the results of the shear analysis for the web.

t=0.07 Wing Canard t=.06 Wing Canard

Stress shear Buckle (psf) 1754415 3578989 Stress shear Buckle (psf) 1288960 2629461

Stress Actual (psf) 1181835 3272849 Stress Actual (psf) 1378808 3818324

Table 6-4: Shear Stress in Spar for Different Web Thicknesses

Table 6-4 shows that the minimum web thickness for the spar is .07 inches, which was used in the parametric studies of the spar moments of inertia found in Tables 6-5 and 6-6.

Wing C Beam 1 Dimension h (ft) s (ft) t (ft) b (ft) d (ft) 4 Moment of Inertia (ft ) Dimension h (ft) s (ft) t (ft) b (ft) d (ft) 4 Moment of Inertia (ft ) Sum of MOI

0.250 0.29167 0.05833 0.04167 0.005833 0.0167 0.133 0.225 0.375 0.375 0.00040 0.00056 C Beam 2

0.3083 0.0333 0.0167 0.225 0.375 0.00048

0.29167 0.04167 0.00667 0.225 0.375 0.00054

0.250 0.05833 0.005833 0.133 0.375 0.00040

0.29167 0.04167 0.0167 0.225 0.375 0.00056

0.3083 0.0333 0.0167 0.225 0.375 0.00048

0.29167 0.04167 0.00667 0.225 0.375 0.00054

0.00080

0.0011

0.00093

0.00099

Table 6-5: Parametric Study of C-Beam Dimensions and Moment of Inertia

Canard C Beam 1 Dimension h (ft) s (ft) t (ft) b (ft) d (ft) 4 Moment of Inertia (ft )

0.1833 0.1833 0.0333 0.033 0.00833 0.0167 0.125 0.125 0.25 0.25 0.00010 0.00011 C Beam 2

0.167 0.04167 0.0167 0.125 0.25 0.00012

0.1167 0.075 0.005833 0.19167 0.267 0.00028

Dimension h (ft) s (ft) t (ft) b (ft) d (ft) 4 Moment of Inertia (ft )

0.1833 0.0333 0.00833 0.125 0.25 0.00010

0.1833 0.033 0.0167 0.125 0.25 0.00011

0.167 0.04167 0.0167 0.125 0.25 0.00012

0.1167 0.075 0.005833 0.19167 0.267 0.00028

Sum of MOI

0.00021

0.00024

0.000556

Table 6-6: Parametric Study of C-Beam Dimensions and Moment of Inertia

Knowing the moments of inertia from Tables 6-5 and 6-6 and the moments from LinAir the theoretical maximum stress can be calculated using the following method:

! MAX =

M R z MAX I

(eq. 6.13)

Table 6-7 shows the results of the parametric studies for the wing and canard from beam theory. A full span analysis can be found in Lift and Moments Along Span in the structures E-eppendices.

Wing

Canard

Root Moment of Inertia (ft4)

0.00080

0.00056

Maximum Stress at Root (psi)

31,268.99

33,175.79

Deflection (in)

25.08

8.40

Safety Factor

1.599

1.507

Table 6-7: Results of Parametric Study

The goal here is to get the safety factor close to 1.5 in theory and then input these moments of inertia into the finite element analysis (FEA) software and see how the results compare.

6.4.2 SPAR DESIGN - FINITE ELEMENT ANALYSIS It is also necessary to use finite element analysis software to also analyze the wing/canard design because the lifting surfaces are not straight solid beams on the actual aircraft. The software used to get a more detailed analysis was Autodesk Inventor 10.

Inventor is a computer aided design program, which

allows an engineer to create 3D models of a structure and then uses ANSYS, an FEA package, to analyze stresses in the structure. A very realistic model of the wing was created with exact planform dimensions in Inventor and is shown in Figure 6-5.

Figure 6-5: 3D CAD Model of Sky2k Wing Structure

Figure 6-5 shows a full picture of the wing, but for stress analysis only half the span will be analyzed. After the wing is modeled, the root can be fixed and forces can be applied. The forces were found from LinAir and placed along the span according to the lift distribution. Note that the forces when placed on the wing in the FEA were only multiplied by a gust load factor of 3.8 because the FEA outputs a minimum safety factor, which should be close to the safety factor from theory. The wing model was then analyzed in the ANSYS package and the outputs are shown in Figure 6-6 through 6-8.

Figure 6-6: Stress Distribution in Wing Due to Lift Loads

Figure 6-7: Deflection of Wing Due to Lift Loads

Figure 6-8: Wing Safety Factor Distribution Due to Lift Loads

Table 6-8 shows the comparison between the theory and FEA analyses. It is clear that the wing designed from theory matches the FEA very well and gives a safety factor just above 1.5.

This verifies the hand calculations done

previously.

Wing Maximum Stress at Root (psi) Deflection (in) Safety Factor

Hand Calculations 31,268 25.08 1.59

Table 6-8: Verification of Results â&#x20AC;&#x201C; Wing

FEA Analysis 32,520 20.56 1.54

A similar FEA analysis was done on the canard. The canard is straight wing with taper and was modeled according to its actual planform in Inventor. A picture is shown in Figure 6-9.

Figure 6-9: 3D CAD Model of Sky2k Canard Structure

The canard lift distribution was used to find the lift forces on the canard along the span and they were modeled in the FEA software accordingly. The output of ANSYS can be found in Figures 6-10 through 6-12.

Figure 6-10: Stress Distribution in Canard Due to Lift Loads

Figure 6-11: Canard Deflection Due to Lift Loads

Figure 6-12: Canard Safety Factor Distribution Due to Lift Loads

The comparison of the theory and FEA analyses is in Table 6-9. Again the results are verified and the safety factor is 1.5. Hand Calculations 33,175 8.40 1.507

Canard Maximum Stress at Root (psi) Deflection Safety Factor

Table 6-9: Verification of Results â&#x20AC;&#x201C; Canard

FEA Analysis 33,230 10.60 1.506

6.4.3 WING AND CANARD â&#x20AC;&#x201C; DESIGN DETAILS The wing will contain six ribs for each half span spaced 2.25 feet apart and the canard will contain six ribs per half span spaced 1.5 feet apart. The ribs are placed in this way to maintain airfoil shape and prevent buckling. The wing and canard will also incorporate the use of stringers. There will be six z-shaped stringers for each half span in each structure that will be installed along the span. Stringers help prevent skin buckling, and reduce deflection of the wing.

Figure 6-13: Z-shaped Stringer and Skin Profile

Figure 6-14: Wing and Stringer Configuration (Only 3 of 6 shown)

The skin on the wing and canard will be 0.06 inches thick. This thickness is larger than the minimum gauge, but it provides safety in the event of lightning strike. The Sky2k is a personal air vehicle and safety during lightning storms is desirable.

6.5 FUSELAGE STRUCTURE The fuselage structural design begins by analyzing the fuselage as a beam supported at the location of the center of lift of the aircraft. For the Sky2k the center of lift lies between the canard and wing and the center of gravity of the plane is just forward of the center of lift. The fuselage has multiple loads of varying magnitude along its length. These loads cause shear forces and bending moments about the center of lift. The magnitudes and locations of all the major components on the aircraft are modeled as constant loads along the fuselage length. Figure 6-15 shows a schematic of these loads applied to the beam model of the fuselage.

payload fuel

Structure canard wing

engine center of gravity center of lift 0

Distance from the Nose (ft)

Figure 6-15: Diagram of Loads on Fuselage

From the diagram in Figure 6-15 shear force and bending moment plots can be made. Figure 6-16 shows the moment and shear force distribution along the length of the fuselage.

1500.0000

1000

1000.0000

-1000

500.0000

-3000

-4000

0.0000 0.00

-5000 0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00 -6000

-500.0000

-7000

MxCL = -8098.75 ft-lb

-8000

-1000.0000

-9000

x/L

Figure 6-16: Shear Forces and Moment Along Fuselage

The moment MxCL shown in Figure 6-16 is the maximum bending moment on the fuselage and corresponds to the center of lift (CL). This value sets the maximum stress condition for the structural design and dictates the internal structural layout of the fuselage. In a semi-monocoque design of a fuselage, the skin is sized to handle the tensile loads and the longerons are sized to take the compressive loads.

6.5.1 TENSILE LOADS AND SKIN SIZING ON FUSELAGE

Moment (ft-lbs)

Shear Force (lbs)

-2000

The tensile force acting on the fuselage skin is due to the moment at the center of lift. The tensile stress is then found by: M xCL R (eq. 6.14) I

!T =

Where R is the half height of the fuselage at the center of lift and I is the bending moment of inertia. For a circular cross-section with a very small skin thickness, t, the moment of inertia can be approximated to be: I=

! 3 Rt 2

(eq. 6.15)

The stress in the skin must be less than the maximum strength of the material divided by the design load factor, ndesign. Combining that with the above two equations the minimum skin thickness is found by: t min =

2 M xCL ndesign

!" T max R 2

(eq. 6.16)

Using the allowable stress for aluminum 2024-T3 the minimum skin thickness for the fuselage was found to be: tmin â&#x2030;&#x2C6; 0.01 inches This is a smaller than the minimum gauge of 0.03 inches for low speed aircraft, but a skin thickness of 0.06 inches was again used for the safety of a personal air vehicle in a lightning strike. 6.5.2 LONGERON AND BULKHEAD SPACING In a semi-monocoque design, the longerons are designed to withstand the compressive loads.

Structural failure under compression for longerons

usually occurs due to buckling. The buckling is derived from the Euler column formula:

FE =

C! 2 EI (eq. 6.17) L2

Where F is the buckling load, L is the unsupported length, and C is a factor that depends on how the column is fixed. In the case of the Sky2k, the

columns will be pinned at both ends and C is equal to 1. The Sky2k will have fourteen longerons set at 22.5ยบ around the circumference of the fuselage. Knowing this information, the maximum allowable stress for the material, and the radius of gyration, the maximum spacing between bulkheads is determined by:

LMAX =

C" 2 EIlongeron R 0.154n design M xCL

(eq. 6.18)

Where Ilongeron for a circular column with an inner radius r and outer radius R can be found by: !

" 4 4 (R # r ) 4

(eq. 6.19)

All the other variables in the Lmax equation are known so a parametric study was done where the inner and outer radius of the longeron was varied to find ! the most efficient longeron and bulkhead design. Table 6.10 shows the results of this study.

Longerons R (in) r (in) Moment of Inertia 4 (in ) Lmax (in) Lmax (ft)

0.028981 37.76007 2.57

Bulkheads Inner Radius (in) Outter Radius (in)

26 27

0.5 0.4

Table 6.10: Results of Longeron Geometry and Bulkhead Sizing

Figure 6-17 shows part of the longeron and bulkhead configuration inside the body of the Sky2k.

Figure 6-17: View of Longeron and Bulkhead Configuration Inside Sky2k

6.6 Rudderlets The rudderlet structure consists of two spars with rectangular cross-sections and four ribs to keep the shape of the NACA 0012 airfoil. The spars in the rudderlet structure are placed along the chord to leave enough space for the rudder, which takes up 16% of the chord. Figure 6-18 shows a computer aided design (CAD) drawing of one of the rudderlet structures for the Sky2k.

Figure 6-18: Rudderlet structure CAD drawing

6.7 Structural Weights The final weights of the structural components of the Sky2k were calculated by drawing them to scale in Autodesk Inventor, specifying aluminum 2024-T3 as the material, and then using a tool in Inventor to get an estimation of the mass.

It can be seen in the drawings of the wing and canard from the

previous sections that weight reduction was done to minimize the weight with out reducing the structural strength. Table 6-11 shows the results of the weight calculations and compares them to what was calculated during refined sizing.

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Wing Spars and Ribs (lb) Stringers (12 total) (lb) Skin (lb) Total (lb) Weight - Refined Sizing (lb)

94.2 19.2 130.2 243.6 249.14

Canard Spars and Ribs (lb) stringers (lb) Skin (lb) Total (lb) Weight - Refined Sizing (lb)

76 12 55 143 117.9

Fuselage Bulkheads (lbs) Longerons (lb) Skin (lb) Total (lb) Weight - Refined Sizing (lb)

96 22.3 114 232.3 234.64

Tail Total weight (lb) Weight - Refined Sizing (lb)

15.5 13.38

Total Structural Weight (lb)

634.4

Table 6-11: Structural weight calculations compared to that from refined sizing

The weights for all the structural pieces are under the weight from refined sizing except for the tail and canard. This tail is only two pounds over weight and the canard is twenty-six pounds over weight. This could be due to the fact that the canard is really holding more of the lift during cruise and needed to be designed stronger than previously estimated. Also, the estimates from refined sizing are just crude values found by fudge factors, so they can be slightly off.

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CHAPTER 7: COST ANALYSIS 7.1 INTRODUCTION Efforts were made in the design of this aircraft to bring down the purchase price. The VTOL concept was scrapped because of its astronomical costs (over $7 million!) in addition to safety considerations. Composite and titanium structures were not included for their costs. Instead, a commonly used, relatively inexpensive, 2024-T6 aluminum alloy was incorporated into the structural design. Simplicity and reliability were chosen over complexity and costliness at many stages of the design and this translated into the costs described in the following sections. 7.2 DESIGN MISSION COST ANALYSIS 7.2.1 PURCHASE PRICE A major driver in the aircraft cost analysis is the number of units in a production run. This is mainly because the manufacturing process can overcome an initial learning curve after making several aircraft and production becomes streamlined. The Sky2k is similar to most Cessna models in its payload capacity and range, so the cost analysis uses a low Cessna production run of 2,000 units to perform the cost analysis. The flyaway cost for a Sky2k based on a cost analysis method outlined by Wroblewski (22) comes to $618,895 and the corresponding civil purchase price is $647,989 (FY2K5$).

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7.2.2 OPERATING COSTS

Fuel Fuel Price (per gal) Fuel Density (lb/gal) Mission Fuel Weight (lb) Approximate Mission Time (hr) V,block (nm/hr) Cost, fuel, per cycle (2006$) Cost, fuel, oil per cycle (2006$) Maintenance Cost, labor, per fl hr Cost, Material maintenance per flight hour Total Maintenance Cost per cycle Depreciation Depreciation per year Depreciation per cycle Fees Fees per cycle Fees/nm Direct Costs Total per trip Insurance Costs per trip Finance Costs per trip DIRECT OPERATING COSTS TOTAL INDIRECT OPERATING COSTS TOTAL Total operating costs per cycle

$2.68 6.74 515.4 3.5 128.6 $204.92 $0.46 $11.41 $5.70 $59.89 $20,664.28 $0.06 $6.15 $0.01 $271.48 $2.71 $19.00 $288.81 $202.17 $490.97

Table 7-1: Operating Costs for Design Mission (All in FY2K5$)

7.3 OFF-DESIGN MISSION COST ANALYSIS 7.3.1 OFF-DESIGN MISSION DESCRIPTION The same method was used to perform a cost analysis for a mission where just a 200 lb pilot with 50 lbs of luggage flies for 200 nm. This leads to an iteration of the gross takeoff weight to 1867 lbs. The flyaway cost clearly doesnâ&#x20AC;&#x2122;t change because the aircraft is designed and produced to accomplish

103

the design mission. The operating costs for such an off-design cycle are tabulated in the next section. 7.3.2 OFF-DESIGN OPERATING COSTS Fuel Fuel Price (per gal) Fuel Density (lb/gal) Mission Fuel Weight (lb) Approximate Mission Time (hr) V,block (nm/hr) Cost, fuel, per cycle Cost, fuel, oil per cycle Maintenance Cost, labor, per fl hr Cost, Material maintenance per flight hour Total Maintenance Cost per cycle Depreciation Depreciation per year Depreciation per cycle Fees Fees per cycle Fees/nm Direct Costs Total per trip Insurance Costs per trip Finance Costs per trip DIRECT OPERATING COSTS TOTAL INDIRECT OPERATING COSTS TOTAL Total operating costs per cycle

$2.68 6.74 251.5 1.3 153.8 $100.00 $0.50 $10.00 $5.00 $19.50 $13,891.59 $0.04 $3.73 $0.02 $126.51 $1.27 $8.86 $134.59 $94.21 $228.80

Table 7-2: Off-Design Operating Costs (All in FY2K5$)

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CHAPTER 8: THE FUTURE FOR SKY2K 8.1 INTRODUCTION PAVs embody the dreams of people interested in technology. The “flying car” has captured the imagination of millions over the last few decades and each new concept that goes public gets a lot of media attention. The goals for the future are laid out and the research to incorporate them is taking place now. Ideally, PAVs will be self-operated, easily affordable, reliable, comfortable, and safe (13). Safety, comfort, and reliability in small aircraft are all here today. Automatic control systems, however, are not on the market, but are being heavily researched.

It is hoped that these aircraft can become

affordable to the point where they rival automotives, but that is mere speculation. 8.2 UNMANNED CONTROLS Unmanned Aerial Vehicles (UAVs) have provided a booming research and technology field. The elements required to remotely control aircraft already exist in vehicles like the Predator and Global Hawk. Tuning these existing systems for use in a PAV would be a matter of time and market interest. 8.3 INFRASTRUCTURE As the PAV phenomenon would be bypassing an infrastructure that is already in place, it seems natural to question the feasibility of creating a new system. Fortunately, NASA has been developing a “Highway in the Sky” that makes air

traffic

control

similar

105

driving

regulations

(5).

CONCLUSION By now, it is hopefully easy to see that the Sky2k PAV is not just a unique aircraft based on its physical characteristics, but one which will shift the paradigm of transportation entirely. Going along with the current trend of air travel shifting away from the hub-and-spoke model, the Sky2k would undoubtedly be the catalyst for new fliers and old pilots alike to begin taking air travel into their own hands. With its design optimized for a short takeoff and landing, a lifting canard which stalls first to create an essentially “stall-less” aircraft, enough space for a small family, and the reminiscent looks of your older brother’s muscle car, the Sky2k clearly is capable of bridging the gap between the light sport aircraft of today with the ease of use and public acceptance of the automobile. The Sky2k PAV focuses on safety while providing the flier with a comfortable and enjoyable ride several times faster than most other modes of transportation. However, safety is not the only positive feature of the aircraft. With a take-off distance of 500 ft., Sky2k can take-off from virtually anywhere. Combined with a tricycle landing gear system to increase the pilot’s visibility and passengers’ comfort, the Sky2k truly becomes the fore-runner in a new class of hybrid land/air craft. While not completely roadable, it is easy to assume that if successful, Sky2k would help to pave the way for future point-to-point travel methods that are becoming more and more practical in today’s world. Sky2k delivers unparalleled performance in a radical new class of aircraft, which will no doubt continue to grow in the future. By taking the first leap forward to that future vision, it is entirely possibly that the Sky3k will be the world’s first truly roadable flyer.

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APPENDIX A.1 DIMENSIONED THREE-VIEW DRAWING

107

REFERENCES 1. Anderson, Jr., John D. Aircraft Performance and Design. McGraw Hill, 1999. 2. http://www.airliners.net/info/stats.main?id=96, 2006. 3. Boeing, http://www.boeing.com/commercial/cmo/pdf/cmo2005_OutlookReport. pdf, 2005. 4. CAFE Foundation, www.cafefoundation.org, 2005. 5. CBS, Highway in the Sky, www.cbsnews.com/stories/2005/04/15/60minutes/main688454.shtml, 2005. 6. Corke, Thomas C. Design of Aircraft. Prentice Hall, 2003. 7. Etkin, Bernard and Reid, Lloyd Duff. Dynamics of Flight: Stability and Control, 3rd ed. John Wiley and sons, Inc., 1996. 8. Great Circle Mapper, http://gc.kls2.com/, 2006. 9. Heintz, Chris, Anatomy of a STOL Aircraft, http://www.zenithair.com/stolch801/â&#x20AC;Ś design/design.html, 2005. 10. Hepperle, Martin, http://www.mhaerotools.de/airfoils/jp_propeller_design.htm, 2006. 11. Hepperle, Martin, http://www.mh-aerotools.de/airfoils/javaprop.htm, 2006. 12. Jackson, David, http://www.unicopter.com/A073_B.gif, 2006. 13. Moore, Mark, http://cafefoundation.org/v1/documents/PAV-aiaawhitepaper.pdf, 2005. 14. Nelson, Robert C. Flight Stability and Automatic Control, 2nd ed. McGraw-Hill, 1998. 15. RASC, rasc.larc.nasa.gov/rasc_new/PAVE/PAVE_HQ_97.pdf, 1997. 16. Raymer, Daniel P. Aircraft Design: A Conceptual Approach. 3rd ed. AIAA, 1999.

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17. Reigels, Dr. Friedrich Wilhelm. Aerofoil Sections. Trans. D. G. Randall. Butterworths, 1961. 18. Roskam, Jan. Airplane Design. DARcorporation, Kansas, c1988. 19. Teledyne, http://www.tcmlink.com/producthighlights/ENGTBL.PDF, 2000. 20. Webb, Sandy, http://www.epa.gov/oms/regs/nonroad/aviation/faaac.pdf, 2006. 21. Weik, Fred E. Aircraft Propeller Design. 1st ed. McGraw-Hill, 1930. 22. Wroblewski, Don E. AM 409 and AM 410 Lecture Slides. 2005-2006.

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Aircraft Team GO!

2006

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