1 Introduction
Thiokol Final Design Report:
Design of a Stylish RC Aircraft
[pic]
AAE 451: Aircraft Senior Design
April 26, 2005
Team 2
Michael Caldwell
Jeff Haddin
Asif Hossain
James Kobyra
John McKinnis
Kathleen Mondino
Andrew Rodenbeck
Jason Tang
Joe Taylor
Tyler Wilhelm
Executive Summary
Design of a Stylish RC Aircraft
In an effort to efficiently accomplish the mission of senior design, some aircraft of the past had seemingly lacked a certain degree of style. Hence, in addition to the basic mission requirements to be discussed later, a major aspect of the design process for this group focused on styling. In as much as style can be rather subjective, for this team the attempt was in creating a unique design, yet with a theme somewhat reminiscent of more archaic fliers. Additionally, the design was to be suitable for the confines of indoor flight, specifically Mollenkopf Athletic Center. These two things led us to having a thematic airplane that would appeal to beginning RC pilots. The ability to fly indoors allows flexibility in where the plane can fly in general. This easy-to-fly airplane opens RC aircraft flying to customers previously restricted by space.
The aircraft is electrically powered with a brushless PJS 1200 motor and a 3 cell Kokam lithium-polymer battery allowing for a total flight endurance of just over 15 minutes. The motor/propeller combination used allows for enough excess power such that more advanced maneuvers are possible for the capable pilot. Weighing a total of just over 3 lbs, the aircraft is easily handled and portable. If a suitable area is not available for takeoff, it is comfortably hand launched. The 6.0 ft. wing blends into the center fuselage and has an aspect ratio of 6. Wing twist distribution and taper ratio (.7) help achieve a near elliptical span-wise lift distribution. The wing has a slight dihedral of about 5o for stability. Favorable lift to drag ratios are obtained by using the Wortman FX 63-137 high camber airfoil section, specifically designed for low Reynolds number flight. The canard configuration remains non-standard in the industry, although it was used on the first powered flier, and is a style point for the plane. Two outer fuselages act as supports for the canard and landing gear. An elevator control feedback system has also been implemented so that inexperienced pilots will have less difficulty in pitch control. The overall look of the aircraft is that of a large but docile machine, functional in form as aircraft from the earliest era of powered aviation. To amplify this effect, landing skids, rather than traditional tires, have been attached for a more antiquated look. The attachments for the skids easily allow for replacement with wheels if conditions so require.
The most recent flight tests for this aircraft revealed an error in center of gravity placement with respect to the aerodynamic center. This led to considerably violent impacts shortly after takeoff, proving the incredible robustness of the EPP foam construction. Great steering control was exhibited on the ground along with sufficient thrust and lift for takeoff. Had longitudinal stability been achieved these characteristics would have led to a great flying aircraft. Solving this problem may be of interest to future students. As designed the aircraft was to achieve relatively low speeds so that an amateur flier could be successful maneuvering indoors or in restrictive spaces. The classic, stylish appeal and versatility of this aircraft make it a great trainer, first airplane, or nice addition to an existing collection.
Table of Contents
Section 1: Introduction 1
Section 2: Concept Selection 1
Section 3: Initial Sizing 2
Section 4: Aerodynamics 2
4.1 Airfoil Selection 2
4.2 3D Wing Analysis 3
4.3 Drag Model 3
4.4 CL Max 4
4.5 Endurance 4
Section 5: Propulsion 5
5.1 Propeller Selection 5
5.2 Motor Selection 6
Section 6: Structures 7
6.1 Structural Layout & Construction 7
6.2 Landing Gear 8
6.2.1 Design 8
6.2.2 Construction & Testing 9
6.3 V-n Diagram 9
6.4 Structural Design & Wing Loading 9
6.5 Weights 10
6.6 Cost 10
Section 7: Dynamics & Controls 11
7.1 Canard & Vertical Tail Sizing 11
7.2 Center of Gravity & Aerodynamic Center 12
7.3 Trim Diagram 12
7.4 Stability 13
7.4.1 Longitudinal Modes 13
7.4.2 Lateral Directional Modes 13
7.5 Feedback Control 14
Section 8: Troubleshooting 15
Section 9: Testing 16
Section 10: Lessons Learned 17
Section 11: Design vs. As Built Comparison 20
Section 12: Conclusion 21
Appendix 23
Appendix A: Concept Selection 24
Appendix B: Initial Sizing 26
B.1 Equations 26
B.2 Figures 26
Appendix C: Aerodynamics 27
C.1 Equations 27
C.2 Figures 29
C.3 Tables 33
Appendix D: Propulsion 34
D.1 Equations 34
D.2 Figures 34
D.3 Tables 39
Appendix E: Structures 41
E.1 Equations 41
E.2 Figures 41
E.3 Tables 44
Appendix F: Dynamics & Controls 45
F.1 Equations 45
F.2 Figures 46
F.4 Class One Tail Sizing 50
F.5 Class Two Tail Sizing 51
Appendix G: Photos 54
G.1 Construction 54
G.2 Testing 59
Appendix H: Matlab Scripts 61
H.1 Twist_ConstantSAR.m 61
H.2 lline.m 63
H.3 integ.m 65
H.4 Drag_3D.m 66
H.5 nblade.m 68
Section 1: Introduction
The desired product in this endeavor was a stylish and unique airplane that could be easily flown indoors by a minimally experienced pilot. More specific mission requirements set by the instructor and team included the following: electric powered; aircraft fits on a 6’X6’ tabletop; a loiter speed of less than 25 ft/s; stall speed at or below 15 ft/s; takeoff roll of less than 60 ft; flight endurance of 15 minutes; a climb angle of 20o and descent angle greater than -5.5o; the aircraft should be capable of flying a figure 8 in the 150 ft. width of the indoor field; lastly, the airplane must implement at least one feedback controller. No additional payload is required for the flight.
Having these as guiding parameters, each team member provided several design concepts, from which a team concept design was formed. Sizing and analysis lead to a more detailed design. With the design frozen, design for manufacturing began. Naturally following was prototype fabrication. The aircraft was then flown, tested and comparisons made between the actual airplane and the design. In the following report the details of each process are discussed and include: concept selection, component design such as aerodynamics, structures, etc., the building process, and finally the flight testing and analysis. Throughout the build and testing process supplementary changes and additions were made to the design. All such decisions are noted in this report.
Section 2: Concept Selection
Generating concepts is the fundamental aspect of design. Understanding the mission requirements as a basis for generating them will result in a quality product. Selecting a concept design for this project was done using two different techniques: weighted objectives and Pugh’s method.
For the weighted objectives, twelve objectives were selected which affected the mission requirements. Rankings and percentages were then assigned to each objective (Table 2.1). Each objective was ranked either 1 – Poor, 3 – Average, or 9 – Excellent for the nine design concepts. Each objective score was then multiplied by its corresponding weighted average and added together to give a total score for each design (Table 2.2).
The next step was Pugh’s method, where the concept which scored highest in the weighted objectives was set as the datum, a standard for which all other designs were compared. To compare each design, a score of “+” (better), “-“ (worse), or “s” (same) was assigned for each objective. The sum of each scoring criteria (“+”, “-“, or “s”) was taken and design strengths and weaknesses were determined (Table 2.3). Design 6 (shown in Figure 2.1), a three fuselage design with canard and high aspect ratio wing, was selected from the weighted objectives and Pugh’s Method results.
[pic]
Figure 2.1: Design Concept
Section 3: Initial Sizing
Using Equations 3.1 to 3.3 a historical initial sizing chart (Figure 3.1) was created for both LiPoly and NiCad batteries. Three lines appear on the chart: the green line represents historical data for RC aircraft, the blue and red lines are payload versus initial weight for LiPoly and NiCad battery powered aircraft respectively. From this chart initial weight guesses were 1.97 lbs for a LiPoly battery powered aircraft and 3.87 lbs NiCad battery powered aircraft.
Once the initial sizing was completed, the constraint diagram (Figure 3.2) was created for the aircraft’s specific mission. From the constraint diagram power loading and wing loading were found. The power loading was 32.74 lbf/hp and the wing loading was 0.38 lbf/ft2. Using the initial weight from Figure 3.1 for a LiPoly powered aircraft the initial wing area was calculated to be 5.24 ft2 and the required horsepower was determined to be 0.060 hp.
Section 4: Aerodynamics
4.1 Airfoil Selection
Knowing that the aircraft would be flying relatively slow, one of the initial and very critical design processes was airfoil selection. The basic criteria for selection consisted of the following: indicated performance at low Reynolds number; high lift-to-drag ratio; large minimum drag region and/or a small increase in drag with lift ; highest possible Cl max; finally, the geometry should be easily manufactured with the materials to be used. Wind tunnel data for airfoil sections was obtained on the NASG online airfoil database: . For a selected airfoil, a drag polar with data values and a lift curve were provided for a specified Reynolds number. The section’s contour shape and coordinates were provided. This information was the basis for the airfoil study and subsequent selection.
Having a reasonably accurate range for Reynolds number was important in this selection process. This was clearer after the initial sizing where approximate weight and wing area were determined. The flight regime was already set by the initial constraints; therefore, using the basic equation for lift (Equation 4.1) and Reynolds number (Equation 4.2) a range of chord lengths could be determined. Also desirable was that these correspond to Reynolds numbers where the airfoils were known to have good performance.
Figure 4.1 in Appendix C shows the comparison between the Wortmann FX 63-137 and the Selig 1210 airfoils. Though the Selig gives a greater maximum lift coefficient, it is actually more than required as the aircraft does not need the additional lift for takeoff; furthermore, the Wortmann has a much smoother drag bucket and lower drag coefficient values for the range of lift coefficients in which the aircraft will be flying. Ultimately, the Wortmann airfoil was selected (Figure 4.2). The 3-D maximum lift coefficient (historically 90% of the 2-D value) was approximately 1.4, where the 2-D data indicates the maximum at around 1.6. The stall angle is also shifted from 10 degrees to about 14 degrees for the 3-D wing.
4.2 3D Wing Analysis
As an initial analysis for the 3-D effects of the wing, Prandtl’s lifting line theory was implemented. Mathematically, this theory models the wing as a series of horseshoe vortices in a spanwise distribution. The idea was to model the circulation at the wingtips, compute downwash, and therefore the induced drag and actual lifting capability. The method of implementation for this concurrently analyzed these values stated above and developed a wing twist distribution for a specific design point flight speed.
The MATLAB scripts developed allow the user to hold the wing area, taper ratio, and aspect ratio constant, as these were specified in other analyses. The design point was specified by flight velocity. Additionally, when total lift (total weight) is specified, the distribution is assumed to be elliptical spanwise. From here the required spanwise lift coefficient is determined for the design point (loiter velocity). Using airfoil camber data, which directly relates to zero-lift angle of attack, and the lifting line model, a twist distribution is determined to achieve elliptical loading, which when integrated spanwise, equals the total weight of the aircraft. The design point was chosen to be the loiter velocity (approximately 22 ft/s) since this is where the majority of the mission is spent. TWISTConstantSAR.m sets up the geometry and constants, lline.m (modified from Prof. Williams, AAE Purdue University) models the wing as the line of horseshoe vortices, and integ.m is the integrating function to verify total lift is as specified. Figures 4.3 and 4.4 show the required Cl and twist distribution. The drag polar of Figure 4.5 accounts only for induced drag as this is an inviscid model. This feeds into the aircraft drag model for a total aircraft drag polar. The twist of the wing also helps in stall characteristics. Since the root of the wing will always be at a higher angle of attack than the rest, it will stall first and aileron effectiveness will be prolonged in a stall.
4.3 Drag Model
The drag coefficient of the aircraft was calculated using Equation 4.3. In Equation 4.4, the viscous drag coefficient, or parasite drag coefficient, is [pic] and the induced drag coefficient is[pic]. The viscous drag (also called parasite drag) was calculated using the component buildup method found in Raymer’s Aircraft Design: A Conceptual Approach. The method uses a flat-plate skin-friction coefficient (Cf), component wetted area (Swet), the pressure drag due to viscous separation estimated by a component “form factor” (FF), and a “Q” factor to estimate interference effects on the component drag. In addition, a miscellaneous drag coefficient ([pic]) is used to account for unretracted gear and is estimated to be approximately 10% of the component parasite drag. An additional estimate for leakages and protuberances ([pic] ) can also be added; however, for the design it was considered to be negligible. The parasite drag build up is shown in Equation 4.5. The equations for individual component parasite drag buildup are located in the Appendix. Table 4.1 lists the component wetted area and parasite drag along with the miscellaneous drag, and overall parasite drag.
The induced drag coefficient ([pic]) is a function of the lift coefficient (CL), as shown in Equation 4.5. In Equation 4.5, e is Oswald’s span efficiency factor and AR is the aspect ration. Equation 4.5 can also be written in the form of Equation 4.6 where e is related to δ by Equation 4.7. An Oswald’s span efficiency factor (e) of 0.85 was used for the design.
From Equation 4.2 a drag polar can be found. The drag polar compares lift to drag for various angles of attack. It is important to note that there is no induced drag when the lift is zero; however, drag is nonzero when lift is equal to zero because the parasite drag is not dependent on the lift or angle of attack. Figure 4.6 show the drag polar for a Reynolds number (Re) of 147,820 which corresponds to the loiter phase of the mission.
4.4 CL Max
The maximum lift coefficient of the wing ([pic]) was calculated using only Raymer’s approximation for high aspect ratio subsonic wings, Equation 4.8. Equation 4.8 assumes moderate sweep and a large leading edge airfoil radius. The resulting maximum lift coefficient of the wing is [pic].
4.5 Endurance
One major constraint on the aircraft design was the endurance. This was a concern early in the design to verify that the aircraft can maintain loiter velocity for the given amount of time. To complete the analysis, a few calculations were required. First, the equations for CL and CD were used to create a function for L/D in terms of angle of attack, Equations 4.9 – 4.12. Next, L/D was calculated. Because CLo, CLα, CDo, and k are all constants for a given design, L/D is only a function of angle of attack as shown in Equation 4.13. For a given set of geometric parameters, the velocity of the aircraft is a function of the lift required and the angle of attack. For specific flight conditions, i.e. straight and level flight or for constant altitude turning flight, the velocity becomes a function of only angle of attack. The velocity as a function of angle of attack and lift is shown in Equation 4.14.
For straight and level flight the lift must be equal to the weight of the aircraft. The lift in constant altitude turning flight must offset the weight of the aircraft as well as produce an inward acceleration to create a circular flight pattern. The radial acceleration required for a given radius turn is shown in Equation 4.15. An illustration of the free body diagram is shown in Figure 4.7. The total lift required for constant altitude is a sum of the two perpendicular vectors as shown in Equation 4.16. Combining Equation 4.16 with Equation 4.14 produces an equation for turning velocity that is only dependant on angle of attack shown in Equation 4.20.
Combining this equation with the drag equation produces the thrust required by the propeller at a given angle of attack and velocity. With a set velocity and thrust, power can be calculated as shown in Equation 4.24. This is the output power of the propulsion system after the efficiencies of the motor, gearbox, and propeller have been taken into account. The input power required is more than double the output power, with an efficiency of 0.44 for the entire propulsion system. Multiplying the input power and the time at a known power setting gives the energy needed for the loiter flight (Equation 4.25). This number can then be used to determine the amount of battery power needed for the entire flight. It has been assumed that half of the 15 minute flight time will be constant altitude turning flight and the other half in straight and level flight. Equation 4.30 shows the formula for the output energy needed for loiter. Equation 4.31 shows the energy from the battery needed for loiter flight time.
Section 5: Propulsion
5.1 Propeller Selection
Goldstein’s method was used to analyze the performance of the propellers. Goldstein’s kappa factor was replaced by Prandtl’s tip loss factor to allow the computation of performance for propellers with an arbitrary number of blades. Prandtl’s tip loss factor is computed as a function of the ratio of radial station along the blades to the blade radius, r/R, and the helix angle (Equation 5.1) at the tip of the blade.
Prandtl’s tip loss factor for n blades is Equation 5.2, and it is an excellent approximation of Goldstein’s kappa factor as shown in Figure 5.1. All figures, equations, and tables are located in Appendix D.
The MATLAB script nblade.m was used to implement Goldstein’s method with Prandtl’s tip loss factor for a wide variety of propellers. A two bladed 8 inch diameter propeller with 5 inches of pitch was found to best fulfill the requirements. A three bladed 8 inch diameter propeller with 6 inches of pitch also does very well and will allow much more aerobatic aircraft performance if desired. Table 5.1 compares the two propellers for various mission phases.
Figure 5.2 compares the propeller efficiency of the propellers at loiter speed, 22 ft/s. The 2 bladed propeller has higher efficiency in the operating range where the required amount of thrust is produced. Figure 5.3 compares the thrust of the propellers at loiter speed, 22 ft/s. The three bladed propeller produces more thrust and has a much higher maximum thrust. Figure 5.4 compares the power required by the propellers at loiter speed, 22 ft/s. The 2 bladed propeller requires significantly less power to operate.
5.2 Motor Selection
Motor sizing and battery selection began with a theoretical look at the thrust requirements of the aircraft. To do this, the flight was divided into four phases: take off, climb, loiter and cruise. The thrust required was determined by calculating the lift requirement for each phase of flight (Equations 5.3-5.6) and equating that to drag with the help of a drag polar, Figure 5.5. As calculated, the climb phase required the highest thrust, 4oz, thus becoming the baseline for motor selection. Thrust requirements for the various phases of flight are shown in Table 5.2.
A theoretical model of the power required for each phase of flight was necessary for battery selection. First, required energy input was calculated from Equation 5.7, where brushed motor efficiency was taken to be 60%, brushless 85%, and propeller efficiency 75%. Power required was calculated from Equation 5.8, and used directly to solve for the necessary mAh a battery would need to fly this mission (Equations 5.9 & 5.10). Endurance required for brushed motor flight was near 420mAh, while 300mAh was required for brushless motor flight (Table 5.3 & 5.4).
Local modeling experts advocated revisiting battery energy requirements when hearing the calculated value of 300mAh. They claimed that the battery capacity needed to be closer to 1300mAh. This claim was made on the grounds that model aircraft missions are never ideal. Factors such as wind, pilot experience, and control systems can cause an aircraft to quickly stray from theoretical conditions. The prop2 code was used to validate the opinion of the modeling experts. The Matlab prop2.m script (provided by Prof. Andrisani) calculated a 21 minute flight time for this configuration using a 1200mAh battery. Through iteration it was discovered that the best battery for our configuration according prop2.m was the Thunder Power 900mAh battery, as it resulted in a flight time of 16 minutes. Prop2.m however does not take into account the power requirements the servos, receiver or control system which will also be onboard. With these accounted for a battery of size 1044mAh is required according to prop2.m. This battery size is not available. Therefore the Kokam 1200mAh battery was chosen. The 1200mAh battery fits into the weight constraints set for the battery. As an added bonus, the Kokam 1200 also has about 15% more energy than required which may be necessary to account for unknown variables during flight. Motocalc[1] was used to validate this information (Figure 5.6 and 5.7). For various pre-programmed missions, Motocalc estimated between a 15 and 23 minute flight time with the chosen components.
A Model Motors Axi 2212/20 brushless motor was chosen to power the aircraft. When compared to brushed motors, the Axi motor is better in all respects. The smallest available brushed motor which met the mission requirements is overpowered by nearly 50% (it is designed to fly a 60 oz aircraft). A limited availability of batteries results in the selection of a battery that will power the aircraft for nearly 25 minutes (70% longer than constrained). This, in addition to the high temperatures at which brushed motors run, and the extreme weight difference, pointed to the Axi motor being the right choice for this mission. The pricing and weight differences can be seen in Tables 5.5 & 5.6.
Section 6: Structures
6.1 Structural Layout & Construction
The structural design consists of two outer fuselages, a main center fuselage, a canard, a rear main wing, and two vertical tails. The outer fuselages are 3 ft (36 in) long cylinders with a 0.083 ft (1 in) radius. At the tips they become conical. The distance between the outer fuselages is 1 ft (12 in). The main fuselage is a 1.75 ft (21 in) long cylinder with a 0.167 ft (2 in) radius also becoming conical at the tips. This length includes the space for the propeller and the propeller spinner. Both the canard and main wing are a blended body configuration. The canard has a span of 1.8 ft (21.6 in) with a 0.67 ft (8.04 in) chord, and an aspect ratio of 2.69. Outside of the outer fuselages the canard has a taper ratio of 0.7 and a dihedral angle of -4°. The elevator has a span of 0.33 ft (4 in) and has a 1 ft (12 in) span running the entire length between the outer fuselages. The main wing is made from three sections. The middle section has a span of 1.67 ft (20 in) and a chord of 1 ft (12 in). The outer sections of the wing have a taper ratio of 0.7 and a dihedral angle of 4°. The total span of the wing is 5.24 ft (62.88 in) with an aspect ratio of 5.24. The ailerons have a 0.20 ft (2.4 in) chord and a 2.62 ft (31.44 in) span. They start 0.25 ft (3 in) from the wing tip. The vertical tails are mounted in the very back of the outer fuselages with the rudders hanging off the end. They are each swept back at a 45°, have a chord of 1 ft (12 in), and a span of 0.64 ft (7.68 in) with an aspect ratio of 0.64. The rudders have a span of 0.82 ft (9.84 in) and a chord of 0.50 ft (6 in) each. See Figure 6.1.
EPP foam was milled using a CNC machine for the construction of the main wing and the canard. The wing was made from four pieces of foam with the center two pieces containing cylinders for the outer fuselages. The canard was milled from one piece of foam, also containing the outer fuselages. The main fuselage was constructed from balsa formers and stringers with a rib near the outer edge on both sides. The center pieces for the wing were epoxied to these ribs. The outer sections of the wing were then epoxied to the center sections. A carbon fiber rod was placed in a trough cut in the top of the wing as the spar at the quarter chord to provide additional rigidity. A slot was cut out of the bottom of the outer fuselages to house a balsa stringer (1/2 inch by 3/4 inch) running from tip to tip. Two circular sections 7 inch long were created using balsa formers and stringers and were placed on the bottom stringer and placed between the canard and wing circylar sections. The ailerons and elevator were cut out of foam and mounted using four nylon hinges on each control surface. Holes were cut into the top of the canard just big enough to fit the battery and gyro. UltraKote then covered the entire structure.
The vertical tails were constructed from balsa wood and were then covered in fiber glass. Two tabs were made on each tail that slid into slots cut into the foam and balsa stringer on the outer fuselages. The tails had large sections removed to reduce weight. The rudders were made from foam and attached using a stripe of tape running along the edge creating a tape hinge. UltraKote was also used to cover the vertical tails.
6.2 Landing Gear
6.2.1 Design
A major aspect of the aircraft design project is the selection of a launching and landing method. The design and positioning of a landing gear system is determined by the unique characteristics (mission requirements, weight, geometry) associated with each aircraft. Appropriate configurations can then be evaluated to determine how well they match with the aircraft structure and operational requirements.
One of the trade studies performed analyzed different launch and landing methods and determined which ones were best suited for the concept. Some design variables to consider were weight, cost, and performance. The gear should also be within the weight estimate and budget but the performance should not be hindered. It must also be structurally safe and rigid enough to withstand landing on the Astroturf inside Mollenkopf Athletic Center.
For launch techniques, there were several options to choose from: conventional launch, ski launch, hand launch, cart launch, or balloon launch. For landing techniques, there were several options to choose from: conventional landing, ski landing, belly landing, parachute, or hand catch.
After careful deliberation of each method’s advantages and disadvantages, the ski launching and landing methods were selected. For the building process, the parts for the gear configuration should be very easy to find and assemble. For launching, the skis can be adjusted to factor in propeller strike. For landing, the wider stance of the skis will prevent tip-over and offer a smoother landing. The skis are also relatively cheap (around $10 - $15), would not weight very much (about 1 oz.) and will add more style to the aircraft’s design.
Placement and technique for mounting the gear system on the aircraft was analyzed. It was very important to take into account how much extra weight being adding to the aircraft and how that would affect the center of gravity depending on location. A wire strut would be attached to the bottom stringer of the outer fuselage for each gear. In order to take the load on impact, the bottom stringer would be increased from 1/8 inch to 3/4 inch in width. The wires would be held in place by a mounting bracket and screws and secured to the fuselage (Figures 6.2 and 6.3). They could be cut at a length that would give enough prop clearance (approximately 6 inches) and bent at any angle.
With the results of the analysis from the second trade study, the influence of positioning of the landing gear on the center of gravity is very nominal. Moving the front and back landing gear either forward or backward 2 inches will only change the CG by 0.006 feet or 0.072 inches. The important point is to secure the wire to a point of the bottom stringer of the outer fuselage that will be most stable. As seen in the top view of the aircraft, the most stable place to put the landing gears would be at the max thickness (where the I-beam will be placed) of the canard and wing. The load on landing will then be applied to the I-beam which will give more support than anywhere else along the length of either the canard or wing.
6.2.2 Construction & Testing
Landing gear design went through several phases during the construction and testing process. 1/8 inch aluminum wires were used in the first design, but it was discovered this method was not feasible. The wires were not robust enough and broke during the construction process. 1/8 inch brass tubes were used next, but they were also too flexible and bent during subsequent drop tests. Skis were constructed using PEX (Cross-Linked Polyethylene) tubing for use with the aluminum wire and brass tube designs.
Following several outdoor tests, it was noted that the skis caused too much friction on the McAllister Park runway. They were replaced with nylon washers in the front and small wheels in the back. The 1/8 inch brass tubing was also replaced with 1/8 inch solid steel wires. These steel wires were cut to length using a hack saw and bent to specified angles using a metal bending brake.
1/4 inch plywood strips were epoxied onto the bottom stringers to prevent the gears from tearing out of the balsa. Two nylon landing gear straps were then used to secure the wires onto the plywood / bottom stringer to prevent the wires from pivoting upon landing. 1 inch flathead wood screws were used to fasten the straps in place. The washers and wheels were then attached at the bottom of the wires and secured using 1/8 inch nickel plated dura-collars.
6.3 V-n Diagram
The purpose of a V-n diagram (Figure 6.4) is to describe the relationship between an aircraft’s speed, longitudinal maneuverability, structural strength, and maximum operational load factor. The maximum lift line is the main focus of attention. It indicates how aggressively, at a given airspeed, the pilot can pitch an aircraft to change its flight path without stalling the wings or doing aerobatic maneuvers through excessive loads. The maximum lift line demonstrates how the load factor diminishes as the aircraft slows down, disappearing finally at the 1-g stall velocity.
6.4 Structural Design & Wing Loading
As the design process evolved, a new material, EPP or expanded polypropylene foam, became available. This foam had superior Young’s modulus and maximum yield stress to previous foams. Given this new material, the wing analysis was conducted again to determine if in fact a lighter wing could be constructed using EPP foam. A CAD model showed that each wing half, if constructed out of solid foam, would have an internal volume of 428.79 cubic inches, or 0.248 cubic feet. Given the density of EPP foam at 1.3 lbs/cu. ft., this gives a total wing weight of 0.6448 lbs, lower than the balsa construction wing, which was estimated to weigh 0.70 lbs. The use of this foam also simplified construction techniques, as the entire structure could be machined using a 3 axis CNC mill from large foam billets.
If a foam wing was to be used, wing loading analysis would need to be recalculated to determine if any internal stiffeners were required to reduce maximum bending stress at the wing root. Bending stress in a beam can be calculated using the Equation 6.1.
Where M is the moment on the beam, y is the distance from the airfoils center to its bottom surface, and I is the moment of inertia of the airfoil cross section. Using the elliptical load distribution given by the aerodynamics group, a lift generated by each wing half of 1.01 lbs, and the load factor due to maneuvering calculated to be 2.77, the bending moment was determined to be 52.87 inch-lbs. Given a maximum y distance of 0.95 inches, and a moment of inertia for our wing cross section of 0.1388 in4, the maximum bending stress at the wing root is 361.8 psi. Given a yield stress of EPP foam of 4000 psi, it was determined that no additional covering or internal support would be necessary with an EPP wing.
The twisting moment on the wing was determined using the Equation 6.2, based on aerodynamic loads.
The maximum twisting moment on the wing section, given Cm for the airfoil and our flight velocities of no more than 30 ft/s, is 2.328 in-lbs. The twist angle from this moment is given by the Equation 6.3.
EPP foam is quite stiff, and due to the large torsional stiffness term, EI, in Equation 6.3, the twist in the wing was found to be only 0.127 degrees.
Maximum wing tip deflection can be found using beam theory equations, if E and I are known and constant, as they are here. Integration of beam equations can be difficult for complex loading equations, such as the elliptical load distribution. A simple derivation exists for a cosine based load distribution, and manipulation of some constants allowed a cosine based loading distribution that very closely approximated an elliptical distribution (the R squared value was greater than 0.98, indicating a good curve fit). This produced a maximum wing tip deflection of 0.163 inches.
6.5 Weights
The aircraft was primarily built with EPP foam and balsa. Using the material densities shown in Table 6.1, the component weights of the wing, fuselages, tail, and canard were calculated. Weights for the motor, batteries, servos, rate gyro, speed controller, receiver, and propellers were obtained from the suppliers’ websites[2]. The weight of the landing gear was estimated from the weights of the materials that would be used. Figure 6.5 shows the component weight breakdown. The total weight of the aircraft design was 1.96 lbs.
6.6 Cost
Costs of the electronic equipment (motor, speed controller, rate gyro, receiver, servos, and battery) and propellers were also found on the suppliers’ websites. EPP foam costs[3] were calculated after estimating how much would be needed to construct the wing and canard sections. Ultrakote, balsa, and landing gear costs were approximated with regard to the prices at Hobby Time in Lafayette, IN. The cost estimation breakdown is shown in Figure 6.6.
Section 7: Dynamics & Controls
7.1 Canard & Vertical Tail Sizing
Static margin is an important indicator of aircraft stability. Positive static margin means that the aircraft center of gravity is ahead of the aircraft neutral point (aerodynamic center). If the locations of the center of gravity and the neutral point are known, the static margin can be calculated with Equation 7.3. In order to find the center of gravity, and the neutral point, the sizes of all components, including tails, must be known. In order to size the horizontal and vertical tails, a static margin must be assumed. Typical values of static margin are: fighter jets 0-5%, transport aircraft 5-10%, and model aircraft 10-15%. In order to ensure longitudinal static stability while accounting for potential weight growth, a goal of 15% static margin was chosen.
Two methods were employed for sizing of horizontal and vertical surfaces. The first method, known as the tail volume method, used historical data to size the horizontal and vertical tails. Information for this class of radio controlled aircraft proved difficult to obtain. For that reason, typical volume coefficients for a homebuilt aircraft, given by Raymer, were used. Further discussion of the tail volume method can be found in Appendix F. The volume coefficients, and the resulting tail areas, can be seen in Table 7.1. Note that this design has 2 vertical tails, and the areas listed are for each tail.
The second method for sizing the canard and vertical tail is known as class two sizing. This method uses “x-plots” to determine the areas of the tail surfaces. To size the vertical tail, Cnβ(rad-1) is plotted versus the area of the vertical tail. A second line is plotted where Cnβ is a constant 0.0573 rad-1. This is the desired value of Cnβ given by both Roskam and Raymer. The intersection of the two lines sets the area of the vertical tail.
The size of the canard was also set using an x-plot. Non-dimensionalized values of the location of the center of gravity and the location of the aerodynamic center are plotted versus canard size. The canard is sized by determining where the difference between the two lines is equal to the desired static margin. For this aircraft, the desired static margin is 15%. Table 7.2 summarizes the results of class 2 sizing.
The size of the vertical tails was investigated further by varying the moment arm of the tails, over a range of angles of attack. With the aerodynamic center of the vertical tails a maximum of 0.935 ft behind the aircraft center of gravity, and a maximum negative angle of attack of -10 degrees, the size each vertical tail becomes 0.847 ft2.
The final size of the canard was chosen from the volume coefficient method because there was less estimation in the variables used. The final design sizes of the tail surfaces are shown in Table 7.3.
[pic]
Table 7.3: Final design tail areas
With the areas of the canard and vertical tails established, the control surfaces were sized. Ailerons typically extend from about 50% to 90% of the wing span. Elevators and rudders are typical about 90% span of the horizontal and vertical tails respectively. The aileron chord is usually about 15-25% of the wing mean aerodynamic chord. The chord of the elevator and rudders are typically 25-50% of the horizontal and vertical tail chords respectively. Past AAE 451 groups complained of inadequate control authority, so control surfaces were sized using the upper limits of the guidelines. Table 7.4 shows the dimensions of the control surfaces. Note that the design has two ailerons and two rudders, with sizes listed for only one of each.
[pic]
Table 7.4: Control surface sizes
7.2 Center of Gravity & Aerodynamic Center
The center of gravity is the mass-weighted average of the component locations. The non-dimensional center of gravity is calculated using Equation 7.1. Where M is the total mass of the aircraft, m is the mass of each component, and x is the distance from the leading edge of the mean aerodynamic chord of the wing to each component.
The neutral point of the aircraft is where the aerodynamic moment remains constant. The non-dimensional total aircraft aerodynamic center, also known as the neutral point, is calculated using Equation 7.2. To have a stable aircraft, the center of gravity must be in front of the neutral point. For this aircraft, the center of gravity was designed to be 1.708 ft from the front of the aircraft, and the neutral point was to be 1.856 ft, measured from the same point. These values give a static margin of 14.8% (Figure 7.1). This is acceptably close to the desired static margin for this aircraft.
7.3 Trim Diagram
The trim diagram was found using the method outlined in Roskam’s Airplane Design Part IV. For trimmed flight, CM=0 must be satisfied. To achieve this condition, canard incidence (ic) and the elevator deflection (δc) are used. The trim diagram for the aircraft is shown in Figure 7.2. The lift and moment coefficients were calculated using Equations 7.4 and 7.5, respectfully. The effect of elevator deflection on lift was calculated using Equations 7.6 and 7.7, where [pic] is the effect of the deflection. The effect of elevator deflection on moment was calculated using Equations 7.8 and 7.9, where [pic] is the effect of the deflection.
The deflection angle definition is shown in Figure 7.3. From the trim diagram, the elevator deflection can be found for trimmed flight at any desired lift condition. For the aircraft, the maximum trimmed lift coefficient ([pic]) is 1.54 at an elevator deflection of 5o and the loiter ([pic]) elevator deflection for trimmed flight is -2o.
7.4 Stability
The dynamics and control stability analysis was performed on the design to help ensure longitudinal and lateral-directional stability of the chosen configuration. To ensure dynamic stability, a control system was designed to incorporate rate feedback to the pitch axis of motion. Through feedback analysis, a gain was calculated that could be implemented in a feedback loop in order to augment the stability in the pitch axis.
7.4.1 Longitudinal Modes
Aircraft starting from straight and level trimmed flight at small angle of attack experience only small perturbations experiences two independent natural motions acting about an aircraft’s pitch axis. It can be represented by a single fourth order differential equation. Taking the Laplace transforms and converting to standard second order differential equations, the terms become:
[pic] and [pic]
The first characteristic equation exhibits heavy damping and high frequency call the short period mode. The other characteristic equation exhibits less damping and lower frequency call the phugoid mode.
7.4.2 Lateral Directional Modes
Lateral directional equation of motion can also be expressed by a single fourth order differential equation. Factoring and taking Laplace transforms the equation can be converted to a standard second order differential equation and two first order differential equations. These terms represent Dutch roll, roll and spiral modes respectively.
[pic], [pic], and [pic]
The flat earth predator software was used to compute the natural frequency and damping ratio of the Short period, Phugoid and Dutch roll modes. They are tabulated in the Table 7.5.
|Modes |Natural frequency, [pic](rad/sec) |Damping ratio, [pic] |
|Short Period |[pic] |[pic] |
|Phugoid |[pic] |[pic] |
|Dutch Roll |[pic] |[pic] |
Table 7.5: [pic] and [pic]of Short period, Phugoid and Dutch roll modes.
7.5 Feedback Control
A feedback control system was designed to incorporate rate feedback to one of the axes of motion using a mechanical rate gyro. The dynamic model for the design was extensively analyzed in the pitch axis. The choice of implementing the feedback control in the pitch axis of motion was selected because it’s important to keep the plane level at all flight. Due to the canard configuration, there can be instability in the pitch axis due to nose heavy configuration. Another choice was to implement the feedback control in the roll axis to prevent unwanted rolling. This choice was ruled out because the present design has two large vertical tails which would correct rolling instability and give enough control authority to the pilot to correct any inadvertent rolling motion.
A diagram of this loop closure is shown in Figure 7.4. Each component was analyzed individually and combined to obtain the overall model. There were three major components of interest for the analysis and gain determination, the rate gyro, the servo, and the aircraft model. The transfer function for the rate gyro was a single constant ‘k’.
From this diagram, it can be seen that the pilot enters an elevator command to the transmitter, which passes the signal through the air to the receiver located in the aircraft. This signal then travels to the servo, which deflects the elevator. The deflected elevator then acts to produce a pitch rate through the aircraft transfer function. This pitch rate is measured by the rate gyro, and then fed back to the control loop after being amplified by the gain.
The feedback gain of the design was calculated using SISO analysis. Flat earth predator software, code provided by Prof. Andrisani, was used to calculate the transfer function of the aircraft; pitch rate to the elevator deflection. That transfer function was then used to perform feedback analysis using MATLAB SISO tool. A gain of 0.0857 was implemented to make the aircraft more stable in the pitch axis. To ensure that the closed loop poles of the system did not move into the right half plane, the region of instability, the implemented gain had to conform to gain and phase margin requirements
The final transfer function calculated for the chosen design configuration was found to be (Equation 7.10):
Equation 7.10: [pic]
[pic]
q = pitch rate
(e = elevator deflection
The mathematical model used for the rate gyro, also provided by Prof. Andrisani, was simply (Equation 7.11):
Equation 7.11: [pic]
k = rate gyro feedback gain
qm = pitch rate measured by the rate gyro
Section 8: Troubleshooting
In the course of building the airplane numerous modifications were made to solve problems encountered along the way. Modifications were made involving the tails, canard, wings, landing gear, motor, propeller, speed controller, and batteries.
Originally the vertical tails were made from 1/8 inch thick balsa. However, this proved too fragile and flexible, breaking during construction and handling and bending with small loads such as the servo might apply. Each tail was reinforced on both sides with one layer of fiberglass. This stiffened them but also doubled the weight. The tails were originally mounted with tabs that were pinned to the outer fuselages. This allowed for too much bending due to twisting of the fuselage when a load was applied to the tail. Fishing line was used to secure the tails to the wing with collars, putting tension on each side of each tail and preventing this rotation.
The wings were built in four sections with the inner sections attached by epoxy to the main fuselage and the outer sections attached by epoxy to the inner sections. When assembled, the foam compressed near these joints, causing unacceptable wing deflection. To stiffen the wing, a 1/4 inch thick balsa stringer was inserted through a hole drilled in the main fuselage and a channel cut in the lower surface of the wing. On the upper surface, a 3/8 inch aluminum tube was similarly inserted through the main fuselage and into a channel cut in the upper surface of the wing. These additional components strengthened the wing sufficiently but also added weight.
The landing gear were originally skis made from plastic tubing. The skis were secured to support wires with a collar and a set screw. The wires, bent into a Z shape, supported the weight of the plane and were attached to the ½ inch balsa stringers in the outer fuselages. Several different wires were tested, and it was found that 1/8 inch solid stainless steel wires worked best.
Ultimately, the skis were abandoned in favor of wheels, because they caused excessive friction that prevented the plane from attaining enough take off speed. The front wheels were manufactured from nylon washers and extra servo components. The rear wheels were found in surplus supplies from earlier projects. The wheels were secured with washers, collars, and set screws and weighed approximately the same as the skis.
Due to added components and underestimation of the weight of some components the total weight increased from about 2 lbs to about 3 lbs. Six ounces of material was removed from the tails, the wing, nose and tail cones, balsa stringers, and the canard by cutting holes in these pieces. Four ounces of UltraKote was added as well as a great deal of packing tape that had not been anticipated. This increase in weight necessitated a change of motor and propeller. The more powerful motor driving a larger propeller in turn required larger batteries and a larger speed controller.
The outer fuselages required repair due to a hard nose dive into the
ground during flight testing. Both 3/4 inch by 1/2 inch balsa stringers broke
at the vertical tail attachment. This damage was repaired with epoxy; 1/16 inch thick aluminum strips on the lower surface, and two strips of carbon fiber on the top surface. The repair held through 4 subsequent crashes.
Finally a second rear access panel was added to the main fuselage to allow increased flexibility in the placement of the electronic components. This was done to easily adjust the CG.
Section 9: Testing
Due to the limited amount of time given for flight testing, the aircraft saw minimal testing before the official flight on the evening of Tuesday, April 19. On Sunday afternoon (April 17), the aircraft was taken to McAllister Park with the landing gear configuration of nylon wheels (front) and skis (back). After starting everything and throttling up the motor, it was quickly noted that the skis prevented the plane from moving forward smoothly. Also, the speed controller cut off when the plane was at full throttle due to a programming glitch.
Changes were made to the landing gear (Figure G.11) and a 4-cell NIMH battery (Figure G.12) was added to power the receiver. New stainless steel landing gear wires were fabricated and nylon washers were kept in front while small foam wheels replaced the skis in the back. Plywood strips were epoxied onto the bottom stringers to reinforce the landing gear and prevent them from tearing out. The aircraft was flight tested again on Monday afternoon (April 18). After a couple unsuccessful attempts down the runway without a takeoff, the batteries were shifted aft (Figure G.12) to move the center of gravity closer to the aerodynamic center, decreasing the static margin. The last flight of the day started with an abrupt takeoff at the end of the runway and ended with the front of the aircraft crashing into the ground. This caused the bottom stringers on the outer fuselages to snap between the balsa and foam sections (Figure G.13). Repairs were done that night in preparation for the official flight the following evening. Aluminum strips were epoxied to the bottom of the broken stringers and supported by carbon fiber strips on the top of the outer fuselages.
At 6:00pm, on Tuesday, April 19, with the aircraft reinforced and the CG aft even further the aircraft was still unable to get off of the ground. Up until this point the pilot had assured the team that the problem was CG and elevator sizing, not inadequate thrust. Unfortunately there was no certain way of determining where the actual aerodynamic center was located. If the actual AC location was known the team would have been able to determine that the problem was power and that the CG was at this point too far aft. Instead, the team doubled the chord of the elevator. Unfortunately, the modification did not correct the problem of inadequate thrust. Finally, a battery was attached with a discharge rate of 15C. This modification provided the power required to immediately take off. Flight testing commenced at Mollenkopf Athletic Center at 7:30pm. Once in the air, with the elevator too large, and a CG too far back the aircraft did several violent rearward loops due to a major static longitudinal stability problem. The elevator issue was fixed immediately by reducing the chord back to its original length. However, with the CG still too far aft the aircraft was not stable in flight, resulting in similar loops.
Unfortunately after that point no further flight testing took place. The team is confident that with a few more tests, an appropriate CG location for stable flight could be determined. However, the aircraft’s robustness was demonstrated during the flight testing on April 19th. The aircraft underwent multiple hard landings in which little to no damage was sustained. This made flight testing a quick, smooth, and relatively pain free process.
Section 10: Lessons Learned
Many lessons have been learned from this project, especially during the construction and flight testing phases.
• Schedule / Pilot Availability
Due to the tight scheduling of this course, very little time was left for component and flight testing. There was sufficient time for construction, but due to the weather and availability of the pilot (Sean Henady), not much time was left for equipment modifications when a problem or conflict was discovered. Teams could have been created in the first days of the semester and the official first flights moved back a couple days to provide for more time for flight testing and modifications.
• Underpowered Motor / Batteries, Inconsistent Product Information
Much of the information obtained from hobby- and was either very vague or inconsistent with other sites.
The motor proved to be a tricky and rather frustrating problem. First due to manufacturing miscalculations the total aircraft weight was greater than originally estimated. In turn the new aircraft weight demanded more thrust. Because brushless motors are designed for aircraft within a 5-6 ounce weight range this proved to be a big problem. The motor originally chosen was underpowering the overweight aircraft. For this reason it would be beneficial for the motor selection take into account a 25% weight increase during build.
All single engine rotorcraft experience a rolling moment due to the prop spinning (p-force). Many commercial RC aircraft will pitch the motor slightly down and to the right (forward looking aft) to lessen this effect. This can be achieved by adding a washer or two beneath the mounting bracket in the upper left-hand corner or by manufacturing a mounting shaft with this angle integrated.
Batteries can be a critical factor in whether an aircraft flies. The most common mistake in choosing a battery is the assumption that capacity (mAh) determines the life of a battery. One must also figure in discharge rate. The larger the discharge rate the shorter your battery life will be. Manufacturers tend to not advertise discharge rates online. Extra research is needed to factor discharge rate into endurance calculations. A high discharge rate enabled the aircraft to fly, while the original, lower discharge rate batteries simply did not give us the power that was needed.
Two batteries should always be used for RC flight; one battery to power the servos, gyro, receiver etc, and another battery to power the motor. The reasoning behind this lies within speed controller technology. A speed controller that could regulate all of the power demands was not to be found. Also, when four servos, a gyro and a motor were running, it was too much for one battery and one speed controller to handle. For this reason, the team opted to switch to a two battery configuration, one battery (high discharge high mAh) to the battery and speed controller, and one battery (low discharge, low mAh) to the servos and gyro. Having 2 batteries enabled longer flight and full power to the motor at all times, full power to the servos at all times, and better performance through the speed controller.
When wiring the batteries to the speed controller it is also important to use the proper gauge wire to reduce the resistance in the wiring. Reducing the resistance in the wiring allows the batteries to work at peak performance
• CNC Issues
A majority of the class had probably never used a CNC machine until this class. It would have been helpful if there would have been a lecture to review how to use it. There were also issues with the equipment itself. The computer took very long to restart and log in. CATIA also had issues connecting to the network to retrieve the license information.
• Aerodynamic Center / Center of Gravity
The MATLAB code provided (flathearth.m) may have miscalculated the aerodynamic center of the aircraft because it assumed a conventional aircraft. This caused many problems when determining the static margin. Batteries were moved from the canard to the back part of the main fuselage to compensate for this.
In addition to the miscalculations, when addressing problems related to being nose heavy it is important to address the thrust line and amount of thrust produced before moving the CG aft. Adjusting the thrust line of the aircraft will allow the wing to “fly where it wants to.”
• Weight Issues (Epoxy / CA Glue / Packing Tape)
Epoxy, CA glue, and packing tape added a considerable amount of weight to the aircraft. Although a buffer was added to account for this weight, the actual amount of these materials was much more than estimated. This caused issues with weight, static margin, and the motor being underpowered.
• Landing Skis Don’t Work Well Outside
Although the trade study determined that skis were more stylish and fit the requirements for landing and taking off, it yielded many problems during flight testing. During outside flight testing, the skis produced a lot of friction and prevented aircraft from moving. Since the landing gear system was built to be interchangeable, it was very easy to swap out the skis with nylon wheels in the front and small wheels in the back.
• EPP Foam vs. Balsa Construction
While the EPP foam was nearly indestructible, the material properties given by the manufacture were incorrect. After construction, the wings (which were made completely out of EPP foam) flexed a considerable amount when the aircraft was lifted at its wingtips. Aluminum arrow shafts were placed in the wing to prevent this, but also added more weight. During the construction process, the EPP foam did not produce as smooth of a surface as the EPS foam. There was an inconsistency in the sizes of the wings, which may have been caused by the foam or the CNC machine. Although the machine was zeroed correctly, the trailing edge of the wings was cut off during the milling process.
Balsa construction would have produced a much more consistent aircraft compared to a foam design. The main problems with building an aircraft out of balsa are construction and repairs. Cutting out and sanding down all the different pieces of the aircraft (formers, ribs, etc.) can be very time consuming but will produce much better results.
• Material Property Availability
The metals, adhesives, and composites used in the aerospace industry all have very well documented engineering properties that can be easily obtained. Finding such properties as the Young’s Modulus of balsa in the cross grain direction, the density of balsa, the shear strength per square inch of hardware store epoxy, or the Young’s Modulus of EPP foam is much more difficult. Although the team was able to find values for all the properties required, some of the sources available were contradictory in the values given, and many hobbyists described properties such as stiffness in qualitative terms, but did not have any quantitative data available. The value that were obtained for the Young’s Modulus of EPP foam was in fact falsely high, thus calculations that initially showing an all foam wing to be of adequate stiffness were incorrect. To make the wing stiff enough for flight additional aluminum stiffeners were required, increasing aircraft weight and thus forcing additional changes.
• Airfoil Selection
Choosing an airfoil with a thicker trailing edge would have been preferable. However, when the airfoil selection was made, the aircraft was entirely made from balsa ribs, spars and stringers. This construction technique vs. milling foam allows for a more precise airfoil section. When the change from balsa to foam was made, the airfoil shape was never reexamined. A few solutions to this problem could have been to artificially enlarge the trailing edge so when it was milled the desired airfoil shape was present.
• Communication is Key
Notifying the entire team of the progress of the project was very important. This kept the team on track and let everyone know what has been done and what still needs to be completed. However, a more thorough building plan early in the design process would have beneficial and may have averted some of the manufacturing problems encountered. Also, having several meetings every week helped during the designing phase of the project. Presentations could be rehearsed and critiqued by team members.
Section 11: Design vs. As Built Comparison
Due to complications during construction or troubleshooting during flight testing the dimensions and specifications of the aircraft changed between the design and build phases. Table 11.1 lists the design values for various parameters and features of the aircraft along with the as built values.
[pic]
Table 11.1: As Design vs. As Built
Section 12: Conclusion
With this aircraft Team 2 set out to design a stylish aircraft that would be easy to fly for an amateur RC pilot in an indoor setting. This truly unique design had a style that was all its own, drawing much attention during runway trials not only from the public, but other modelers. It is unfortunate that the flying qualities were never able to be determined as there was not ample time to solve the center of gravity and aerodynamic center problem. There were, as stated throughout this analysis, many lessons well learned, lessons that can only be experienced by engaging one’s self in a project of this nature. Most notably these were in the areas of aerodynamics, propulsion, and manufacturing.
Based on flight tests, this team can say with conviction that the most important value in aerodynamic analysis is finding the true aerodynamic center. Finding center of gravity is almost trivial, but knowing the AC location precisely is much more difficult. These fundamentals of longitudinal stability will determine success or failure. Motor selection is at least just as important. Because of inexperience with this kind of project, weight growth was virtually unpredictable. This led to a heavier than expected machine and thus an underpowered motor. Special care must be taken in weight accountability and having accurate motor information, which would be best gathered by one’s own wind tunnel testing. Successfully manufacturing this unique design on the first attempt was a challenge. Supplementary additions and changes were made along the way as progressive evaluations would dictate. For example, the addition of a spar when it became evident that the EPP foam would not provide satisfactory wing rigidity.
With many of these apparent shortcomings, most conspicuously the lack of sustained and controlled flight, it might seem reasonable to claim complete failure. However this is not the consensus amongst the team. The aircraft was manufactured on time and able to become airborne, it was greatly robust to violent impacts, steerable on the ground using only rudder, and was most uniquely stylish. Had the CG problem been solved the aircraft would likely have flown well. Nonetheless, this has been an invaluable learning experience, if nothing else, refining our engineering judgment. Quoting the author Fred Brooks, “Good judgment comes from experience and experience comes from bad judgment”. With the knowledge gained from this experience, it is with confidence that this team claims success.
Appendix
Appendix A: Concept Selection
[pic]
Table 2.1: Objectives Ranking
[pic]
Table 2.2: Weighted Objectives
[pic]Table 2.3: Pugh’s Method
Appendix B: Initial Sizing
B.1 Equations
Equation 3.1 [pic]
Equation 3.2: [pic]
Equation 3.3: [pic]
B.2 Figures
[pic]
Figure 3.1: Historical Sizing
[pic]
Figure 3.2: Aircraft Constraint Diagram
Appendix C: Aerodynamics
C.1 Equations
Equation 4.1: [pic]
Equation 4.2: [pic]
Equation 4.3: [pic]
Equation 4.4: [pic]
Equation 4.5: [pic]
Equation 4.6: [pic]
Equation 4.7: [pic]
Equation 4.8: [pic]
Equation 4.9: [pic]
Equation 4.10: [pic]
Equation 4.11: [pic]
Equation 4.12: [pic]
Equation 4.13: [pic]
Equation 4.14: [pic]
Equation 4.15: [pic]
Equation 4.16: [pic]
Equation 4.17: [pic]
Equation 4.18: [pic]
Equation 4.19: [pic]
Equation 4.20:
[pic]
Equation 4.21: [pic]
Equation 4.22: [pic]
Equation 4.23: [pic]
Equation 4.24: [pic]
Equation 4.25: [pic]
Equation 4.26: [pic]
Equation 4.27: [pic]
Equation 4.28: [pic]
Equation 4.29: [pic]
Equation 4.30: [pic]
Equation 4.31: [pic]
C.2 Figures
[pic]Figure 4.1: Comparison between the Wortmann FX 63-137 and the Selig 1210 airfoils
[pic]
Figure 4.2: Wortmann FX 63-137 airfoil
[pic]
Figure 4.3: Sectional lift, Cl, required for elliptical loading at CLdesign
[pic]
Figure 4.4: Required twist distribution
[pic]
Figure 4.5: Drag polar
[pic]
Figure 4.6: Theoretical drag polar with twist
[pic]
Figure 4.7: Radial acceleration required for a given radius turn
C.3 Tables
[pic]
Table 4.1
Appendix D: Propulsion
D.1 Equations
Equation 5.1: [pic]
Equation 5.2: [pic]
Equation 5.3: [pic]
Equation 5.4: [pic]
Equation 5.5: [pic]
Equation 5.6: [pic]
Equation 5.7: [pic]
Equation 5.8: [pic]
Equation 5.9: [pic]
Equation 5.10: [pic]
D.2 Figures
[pic]
Figure 5.1: Radial thrust and power distribution
[pic]
Figure 5.2: Effect of advance ratio on propeller efficiency
[pic]
Figure 5.3: Effect of advance ratio on thrust coefficient
[pic]
Figure 5.4: Effect of advance ratio on power
[pic]
Figure 5.5: Drag polar produced by Wortmann FX63-137 airfoil with twist
[pic]
Figure 5.6: Airspeed and Amps vs. time for Motocalc 'Sedate' mission with brushless motor and components
[pic]
Figure 5.7: Airspeed and Amps vs. time for Motocalc 'Trainer' mission with brushless motor and components
.
[pic]
Figure 5.8: Comparison between brushed & brushless motors running on nickel and Li-Poly batteries
D.3 Tables
|2 Blades |8 in Diameter |5 in Pitch | | | |
|Phase |Flight Speed [ft/s] |Thrust [oz] |% Throttle * |Propeller Efficiency |Power [W] ** |
|Take-off |18 |3.15 |50% |63% |10 |
|Climb |18 |4.00 |55% |59% |14 |
|Level Flight |22 |2.93 |51% |70% |10 |
|Turn |23 |3.24 |54% |70% |12 |
|Aerobatic |25 |8.00 |77% |59% |38 |
|3 Blades |8 in Diameter |6 in Pitch | | | |
|Take-off |18 |3.15 |40% |65% |10 |
|Climb |18 |4.00 |44% |61% |13 |
|Level Flight |22 |2.93 |41% |72% |10 |
|Turn |23 |3.24 |43% |69% |12 |
|Aerobatic |25 |16.00 |83% |49% |92 |
|* max motor RPM is 9350, direct drive | | | |
|** power required from the battery (assumes75% motor efficiency) | |
Table 5.1: Comparison between 2 and 3 bladed propellers
[pic]
Table 5.2: Thrust required for various flight phases
[pic]
Table 5.3: Energy required for brushed motors for various flight phases
[pic]
Table 5.4: Energy required for brushless motors for various flight phases
[pic]
Table 5.5: Brushed motor & components weight and pricing
[pic]
Table 5.6: Brushless motor & components weight and pricing
Appendix E: Structures
E.1 Equations
Equation 6.1: [pic]
Equation 6.2: [pic]
Equation 6.3: [pic]
E.2 Figures
[pic]
Figure 6.1: Aircraft 3-View
[pic]
Figure 6.2: Landing Gear and Mounting Block
[pic]
Figure 6.3: Fuselage and Wheel/Ski/Float Attachments
[pic]
Figure 6.4: V-n Diagram
[pic]
Figure 6.5: Weight Estimation Breakdown
[pic]
Figure 6.6: Cost Estimation Breakdown
E.3 Tables
| |Density (lbf/ft3) |Young’s Modulus (ksi) |Yield Stress (psi) |
|Balsa |11 |625 |1725 |
|Spruce |34 |1500 |8600 |
|EPS Foam |1.5 |320-360 |72.5 |
|EPP Foam |1.3 |1000 |4000 |
|Epoxy |0.0625 lb/ft2 |500 |14500 |
|Ultrakote |0.0156 lb/ft2 |N/A |N/A |
Table 6.1: Material Properties (Values from Fall ’04 AAE 451 projects and )
Appendix F: Dynamics & Controls
F.1 Equations
Equation 7.1: [pic]
Equation 7.2: [pic]
Equation 7.3: [pic]
Equation 7.4: [pic], where [pic] and [pic]
Equation 7.5: [pic], where [pic] and [pic]
Equation 7.6: [pic]
Equation 7.7: [pic]
Equation 7.8: [pic]
Equation 7.9: [pic]
Equation 7.10: [pic]
Equation 7.11: [pic]
Equation 7.12: [pic]
Equation 7.13: [pic]
Equation 7.14: [pic]
Equation 7.15: [pic]
Equation 7.16: [pic]
Equation 7.17: [pic]
Equation 7.18: [pic]
Equation 7.19: [pic]
Equation 7.20: [pic]
Equation 7.21: [pic]
Equation 7.22: [pic]
Equation 7.23: [pic]
F.2 Figures
[pic]
Figure 7.1: Center of Gravity, Aerodynamic Centers, and Neutral Point
[pic]
Figure 7.2: Trim Diagram
[pic]
Figure 7.3: Elevator Deflection Definition
[pic]
Figure 7.4: Block Diagram of Feedback Loop
[pic]
Figure 7.5: Root Locus with k=0
[pic]
Figure 7.6: Root Locus with gain of 0.0857
z[pic]
Figure 7.7: Bode Diagram
F.3 Tables
[pic]
Table 7.1: Class one tail sizing
[pic]
Table 7.2: Class two tail sizing
F.4 Class One Tail Sizing
Class one tail sizing uses historical data to set the sizes of both horizontal and vertical tails. Tail “volume coefficients” are based on the ratio of tail effectiveness (tail area times moment arm) to wing area, and then non-dimensionalized by some quantity with units of length. This leads to equations 7.24 and 7.25 for vertical tail volume coefficient and horizontal tail volume coefficient respectively.
[pic] (7.24)
[pic] (7.25)
Where SVT is the area of the vertical tail, SHT is the area of the horizontal tail, and LVT, LHT, SW, bW, [pic] are as defined in Figure 7.8.
[pic]
Figure 7.8: Definitions for tail volume coefficient method
Often the tail volume coefficients are assumed in order to find tail areas. Equations 7.24 and 7.25 can be re arranged to give equations 7.26 and 7.27.
[pic] (7.26)
[pic] (7.27)
In the case of a control-type canard aircraft, historical data suggests a horizontal tail volume coefficient of around 0.1. For small radio control aircraft, a larger volume coefficient may be used to ensure adequate control authority. The volume coefficient method does not apply to aircraft with a lifting canard. For this type of aircraft, lifting area is split between the wing and the canard. A lifting canard is typically around 25% of the total lifting area, but can be up to 50% of the lifting area, which would create a tandem wing aircraft.
F.5 Class Two Tail Sizing
Class two tail sizing uses “x-plots” to size the horizontal and vertical tails. In order to size the vertical tails, yawing moment due to sideslip, Cnβ, is plotted as a function of tail area. A second line is plotted at a constant goal value of Cnβ. The goal value of Cnβ is 0.0573 rad-1 given by Figure 7.9.
[pic]
Figure 7.9: Yawing moment due to sideslip versus Mach number from Raymer pg. 510
The vertical tail x-plot for this design is given in Figure 7.10.
[pic]
Figure 7.10: Vertical Tail X-plot
The horizontal tail is also sized using an x-plot. Non-dimensional values of the location of the center of gravity and the location of the aerodynamic center are plotted versus horizontal tail size. The horizontal tail is sized by determining where the distance between the two lines is equal to the desired static margin. For this aircraft, the desired static margin is 15%. Figure 7.11 shows how the canard for this design was sized. Note that with a conventional tail, the center of gravity and the aerodynamic center would be pulled back as the horizontal tail size increase, which is opposite of this canard design.
[pic]
Figure 7.11: Horizontal Tail X-plot
Appendix G: Photos
G.1 Construction
[pic]
Figure G.1: Milling the tail and former sections with the CNC machine
[pic]
Figure G.2: Balsa sections of the outer fuselages
[pic]
Figure G.1: Tail section during the fiberglass process
[pic]
Figure G.2: Comparison between brushless (Axi 2212/20) and brushed (Graupner Speed 600) motors
[pic]
Figure G.3: Basic layout of the canard, outer fuselages, inner sections of the wing, and tails
[pic]
Figure G.4: Creating the dihedral angle into the wing using the radial arm saw
[pic]
Figure G.5: Attaching the wing sections to the main fuselage
[pic]
FigureG.6: Push rod attachment connecting the aircraft's rudders
[pic]
Figure G.7: Original landing gear attachment to fuselage
[pic]
Figure G.8: Adding an aluminum rod into the wing to reduce deflection
G.2 Testing
[pic]
Figure G.9: Aircraft with new landing gear configuration
[pic]
Figure G.10: Extra battery added to power speed controller and move center of gravity aft
[pic]
Figure G.11: Broken stringers on the outer fuselages during the first test flight
[pic]
Figure G.12: Final design during the official flight tests at Mollenkopf Athletic Center
Appendix H: Matlab Scripts
H.1 Twist_ConstantSAR.m
% AAE 451
% New twist code for specified WING AREA, AR, Weight and Taper Ratio
% Modified by Jeff Haddin
% Updated Feb. 15, 2005 (Kathleen Mondino)
clc
clear all;close all
%Data input---------------------------------------
L = 1.97; % input('Enter most recent aircraft weight(lbs): ');
S = L/.375;
AR = 5.24; %input('Enter best Aspect Ratio: ');
b = sqrt(AR*S);
tr = .7; %input('Enter desired taper ratio: ')
cr = 2*S/(b*(1+tr));
ct = tr*cr;
e=0.85; % Oswalt efficiency
h = 1000;
gam = 1.4;
p_inf=2040.86;%stadard atm. pressure in Pa at 10km.
Vdp = input('enter the velocity at this des. point(ft/s): ');
M_inf = Vdp/1112.8; %Velocity
qinf = .5*gam*p_inf*M_inf^2; %dynamic pressure
bet=sqrt(1-M_inf^2); %P-G factor
Cl_alf = 5.2; %2*pi/bet; %Cl alpha 2d*****5.2 from FX graph***********************
CL_des=L/(qinf*S); %design point CL
disp(['Design point lift Coeff: ',num2str(CL_des)])
%wing definition--------------------------------------------
n=40;
th=linspace(0,pi,n+1); %cosine spacing
y=-b/2*cos(th); %y coordinates of strip edges
ym = .5*(y(1:end-1)+y(2:end)); %y midpoint of strips
c = cr + (ct-cr)*abs(2*ym/b); %chord
alf_zl = -9.2*pi/180; %zero lift angle of attack (from HW7)
%==================================================================
% Part 1:
% Twist needed for design point:
%==================================================================
CL=CL_des;
Cl=4/pi*CL*(S/b./c).*sqrt(1-(2*ym/b).^2); %sectional lift needed for elliptic loading
alfi=CL/(pi*AR); %induced aoa for elliptic loading
alf= alf_zl + alfi + Cl/Cl_alf; % aoa
figure
plot(ym,Cl,ym,CL+Cl*0,'--')
xlabel('y');
ylabel('Cl')
title('sectional lift, Cl, required for elliptic loading at CL_{design}')
figure
plot(ym,alf*180/pi)
title('twist distribution')
xlabel('y');
ylabel('\alpha (deg)')
%==================================================================
% Part 2:
% Get drag Polar:
%==================================================================
CLt=[];CDt=[];
for ang =[ -15:20]*pi/180;
Cl_2d = Cl_alf.*(alf-alf_zl + ang);
[ym,cl,cdi]=lline(y,c,Cl_2d,Cl_alf);
[CL,CD]=integ(cr,0,0,y,c,cl,0*cl,cdi);
CLt=[CLt;CL];
CDt=[CDt;CD];
end
figure
h=plot(CDt,CLt,CLt.^2/(pi*AR),CLt,'--');
legend(h,'lifting line','elliptic loading')
xlabel('CD')
ylabel('CL')
hold on
plot(CL_des.^2/(pi*AR),CL_des,'o');
title('Drag Polar')
%************************
figure
ang = [-15:20]*pi/180;
plot(rad2deg(ang),CLt)
xlabel('\alpha (deg)')
ylabel('C_L')
title('Wortmann FX 63-137 Theoretical CL vs. \alpha With Twist')
%************************
CL_alf=(CLt(16)-CLt(6))/(rad2deg(ang(16))-rad2deg(ang(6)));
i=find(ang < 0);
i=length(i)+1;
CLo=CLt(i);
[CD,CDo,CDi,Swet]=Drag_3D(CLt);
[LD_max Alpha_max]=L_D(CLo,CL_alf,CDo,L,S,AR,e);
figure
plot(CD,CLt)
xlabel('C_D')
ylabel('C_L')
title('Wortmann FX 63-137 Theoretical Drag Polar With Twist')
fprintf('\n\nW = %g lbf\n',L)
fprintf('AR = %g\n', AR)
fprintf('S = %g ft^2\n',S)
fprintf('Design Point Velocity = %g ft/s\n',Vdp)
fprintf('CLalpha = %g deg^-1\n',CL_alf)
fprintf('CLo = %g\n',CLo)
fprintf('CDo = %g\n',CDo)
% fprintf('CDi = %g\n',CDi)
fprintf('L/Dmax = %g\n',LD_max)
fprintf('Angle of attack for L/Dmax = %g deg\n',Alpha_max)
fprintf('Swet = %g ft^2\n\n',Swet)
% figure
% plot(CLt,CDt-CLt.^2/(pi*AR))
% xlabel('CL')
% ylabel('CD-CD_{min}')
% title('Drag Penalty')
H.2 lline.m
function [ym,cl,cdi] = lline(y,c,cl2d,clalf2d)
%LLINE usage: [ym,cl,cdi]=lline(y,c,cl2d,[clalf2d])
% purpose: correct strip theory loads for finite span effects
%
% INPUT: (row vectors)
% y(j) = span coords of strip edges ,j=1:n+1
% c(j) = chord at center of j'th strip
% cl2d(j) = 2d lift coeff on j'th strip
% OR: cl2d(k,j)... if you want multiple
% solutions
% clalf2d(j)= 2d lift curve slope on j'th strip
% (optional:default 2*pi with omit or [] input)
% OUTPUT: (row vectors)
% ym(j) = y at center of j'th strip
% cl(j) = lift coeff on j'th strip
% cdi(j) = induced drag coeff on j'th strip
% IF cl2d is a matrix then cl and cdi will
% be matices of the same size as cl2d.
%
% author:
% Marc H. Williams
% AAE
% wiliams@ecn.purdue.edu
%SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
if nargin==0
help lline
disp('hit any key to see an example');pause
disp('example INPUTS:')
disp('strip edge coords')
y=[-1:.1:1]
disp('hit any key to continue');pause
n=length(y)-1;
disp('strip center chords')
c = ones(1,n)
disp('hit any key to continue');pause
disp('strip theory loads')
cl2d = 2*pi*.1*ones(1,n)
disp('hit any key to continue');pause
disp('sectional lift curve slopes')
clalf2d=2*pi*ones(1,n)
disp('hit any key to see OUTPUT')
pause
[ym,cl,cdi]=lline(y,c,cl2d,clalf2d);
disp('ym:strip centers');ym
disp('hit any key to continue');pause
disp('Cl: sectional lift');cl
disp('hit any key to continue');pause
disp('Cdi: sectional induced drag');cdi
return
end
n=length(y)-1;
b=y(n+1)-y(1);
if nargin ................
................
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