Designing of Automated Drone CHASER-1 Design Team (in Alphabetical Order) Aditya Desai, Ajith Kumar, Anil Kumar Nakkal, Dinesh Koya Nelamuru, Gaurav Kejriwal, Praveen Donni and Yajur Kumar A report submitted for the term project of Flight Stability and Control Supervisor: Dr. Mangal Kothari Department of Aerospace Engineering Indian Institute of Technology, Kanpur April 2015 Look deep into nature, and then you will understand everything better. -Albert Einstein 3 Contents 1 Introduction to Drones 7 1.1 The Unmanned Aerial Vehicles or Drones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Unmanned Aircraft System (UAS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Steps in Design and Development of the Drone . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.1 Analyzing the Requirement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.2 Estimating the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.3 Material Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.4 Manufacturing of the Drone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.5 Taking a Test Flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.6 Estimating the Flight Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2 Analyzing The Requirement 9 2.1 Payload Requirement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Endurance Requirement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Radius of Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Speed Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.5 Launch and Recovery 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Estimating the Model 11 3.1 Payload Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 Choice of Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.3 Wing Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.4 Horizontal Tail Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.5 Vertical Tail Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.6 Fuselage Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.7 Control Surface Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.7.1 Ailerons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.7.2 Elevator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.7.3 Rudder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.8 Selection of Airfoil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.9 Computation of Moment of Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.9.1 4 7 Using Software Tools like AutoCAD TM . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.9.2 Experimental Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Material Selection 4.1 19 Selection of Material for Drone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4.1.1 4.1.2 4.1.3 4.1.4 4.1.5 4.1.6 19 19 20 20 20 20 Selection of Extruded Polystyrene as Base Building Material Coroplast Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . Depron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Selection of Balsa Wood as Control Surface Material . . . . . Selection of Aluminum Stiffners . . . . . . . . . . . . . . . . . Miscellaneous Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Manufacturing of the Drone 5.1 16 23 Manufacturing Processes Used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Hot Wire Shaping Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 23 6 Taking the Test Flight 6.1 Test Flight and Electronics Components detail . . . . . . . . . . . . . . . . . . . . . . . . . . 27 27 7 Estimating the Flight Parameters 29 7.1 7.2 Aerodynamic Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Modelling of Aerodynamic Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 30 A NACA2412 Airfoil 33 B Drawings 35 C Drone Stability and Control Parameters 37 5 Chapter 1 Introduction to Drones 1.1 The Unmanned Aerial Vehicles or Drones Unmanned Aerial Vehicles (UAV) which are also known as drones, are unpiloted aerial vehicle or remotely piloted aircrafts. They are aircrafts without a human pilot inside. Drones are being used in many areas ranging from search and rescue, research, mapping to combat in the war fields. On the basis of their mode of operation they can be either autonomous or can be remotely controlled. The drone under this project is expected to be automated in the sense that it has autopilot installed which manages to keep it cruise on a fixed altitude, take turn with the specified attitude and climb and descent to a specfied altitude. In the developmental process of the drone, it was divided into two phases, one phase which deal with the deisgn and development of the drone, and next phase which deals with the development of autopilot and setup of remaining avionic components of the drone. This project report concentrates on the designing phase of the drone. The various designing steps included in this phase are discussed below and throughout the report. 1.2 Unmanned Aircraft System (UAS) An unmanned aircraft system or UAS includes ground stations and other elements besides the actual aircraft. A typical UAS consists of the following: 1. Unmanned Aircraft 2. Control system 3. Control link, a specialized datalink 4. Other related support equipment 1.3 Steps in Design and Development of the Drone Design and development of a drone comprises of following steps. 7 1.3.1 Analyzing the Requirement This is the very first step of the designing phase. It includes analyzing the very requirement of the operation including its required range and endurance, its maneuvering capabilities and its minimum operational time. 1.3.2 Estimating the Model After analyzing the requirements, the next step is designing the drone which includes computing the dimensions of the drone, selecting airfoil for the wing cross-section. To visualize the model, a computer-aided model can be generated. 1.3.3 Material Selection Drones are expected to be lightweight and it is hence, material selection is an important factor, since, it need to have enough strength also. A number of materials are available for making drones and after analysing the pros and cons of the different materials, particular materials were selected. 1.3.4 Manufacturing of the Drone The most practical phase in the designing process of the drone is the manufacturing processes invloved. It includes various methods like using hot wire to take cut out of the wing section, fuselage and other parts of the drone. 1.3.5 Taking a Test Flight After manufacturing the drone, it has to be tested for its capabilities of successful cruise flying, taking turning and other maneuvering capabilities with the help of remote control pilot. 1.3.6 Estimating the Flight Parameters The final step in the designing phase includes estimation of the flight parameters which will be needed for designing autopilot for the drone. 8 Chapter 2 Analyzing The Requirement 2.1 Payload Requirement The payload in the drone mostly comprises of the weight of the power source installed on board, on board processor, and the weight of the motors installed as propelling source and servo controllers for the control surfaces. The estimated payload in this case is 1.5 Kg for the drone. 2.2 Endurance Requirement Endurance refers to the maximum time an aircraft can spend in the cruise flight. The flight endurance demanded of the air vehicle can range from, say 10 minutes for a close-range surveillance system to more than 1 hr for a long-range surveillance or airborne early warning (AEW) system. The volume and mass of the fuel load to be carried will be a function of the required endurance and the reciprocal of the efficiency of the aircraft’s aerodynamics and its power plant. As per the power source availability and payload requirements, the drone is expected to have an endurance of 20 minutes. 2.3 Radius of Action The radius of action of the aircraft may be limited – by the amount of fuel that it can carry, and the efficiency of its use, its speed or by the power, frequency and sophistication of its communication links. The data rate requirements of the payload and other aircraft functions will greatly effect the electrical power and frequency range needed for the radio-links. 2.4 Speed Range The required speed range will be a dominant factor in determining the configuration and propulsive power of the aircraft that is a strong function of surveillance. 2.5 Launch and Recovery The method for air vehicle launch and recovery, as driven by the operational role, will be significant in determining the aircraft configuration, its structural design and auxiliary equipments. The drone in this 9 case is expected to have take-off by throwing into the air by hand and landing by simply gliding it using the installed autopilot (being worked by the Autopilot Design Team). 10 Chapter 3 Estimating the Model 3.1 Payload Specifications The work started with a study of aeromodels previously made within the institute. After considering similar models, we estimated the maximum weight of the model at about 1.5 Kg. The most essential payload was the aeroquad board to be used for flight data acquisition. The physical dimensions of this board were 75mm x75mm. The weight of this board was very small (120 gm) compared to the overall weight of the model. Dimensions of the battery to power the propeller were 100mm x35mm x 20mm. This set the essential payload space desired on the model. 3.2 Choice of Material A lot of different materials were considered e.g Styrofoam, Bio-foam, Balsa wood, pink foam etc. Eventually it was decided that while most of the model will be made out of Styrofoam to keep the weight on the lower side, Balsa wood would be used to achieve better surface finish and mounting for the control surfaces. 3.3 Wing Design As a standard, for Styrofoam wings are designed with wing loading usually between 4 − 8kg/m2 . We chose to keep it around 5.4kg/m2 . Wing join is shown in figure 3.1. In cruise, lif t = weight, therefore wingloading = Thus, wing are is calculated as Sw = weight area weight wingloading Typical aspect ratio for such aeromodels is 5-7. AR = 5.4 was chosen. Now we have, AR = b2 Sw Which gives us the wing span, b. In order to achieve a higher aspect ratio, we decided to use a tapered wing. The ‘Taper ratio’ is defined as 11 Figure 3.1: Wing c tip t = croot . We chose to keep t = 0.69. Area of the wing is given by 1 bcroot (1 + t) 2 Using this, we can calculate croot . To get ctip , we simply multiply it by the taper ratio t. Lastly, the Mean Aerodynamic Chord (MAC) for a tapered wing is given by Sw = M AC = 1 + t + t2 2 croot 3 1+t This can now be calculated based on the known information. The dimensions thus obtained are listed in table 3.1. 3.4 Horizontal Tail Design A very important design parameter is Tail Volume Ratio (VH ). This was chosen as 0.54 based on survey of previous models. Area of Horizontal tail is typically 20-25 per cent of wing area. It was chosen to keep this ratio as 21 per cent. This gave us the tail area (SH ). Tail aspect ratio is usually kept smaller- between 3 to 4. It was chosen as 3.25. Based on this, tail span (bV ) 12 Table 3.1: Wing Parameters Specification Symbol Wing Area Wing Span Root Chord Tip Chord MAC Aspect Ratio Taper Ratio Sw b Croot Ctip AR t Value 277777mm2 1220mm 268mm 185mm 229mm 5.4 0.69 Figure 3.2: Horizontal Tail Design Table 3.2: Horizontal Tail Parameters Specification Symbol Tail Area Tail Span Root Chord Tip Chord MAC Aspect Ratio Taper Ratio SH bH Croot Ctip AR t Value 58290mm2 435mm 175mm 93mm 138mm 3.25 0.53 was calculated using the same formula as used earlier for the wing. Taper Ratio (t) was chosen as 0.53. Once this was fixed, the root chord and tip chord were also calculated as done earlier for the wing. Lastly, the Mean Aerodynamic Chord (MAC) for the tail was calculated. All the parameters for thus calculated are listed in Table 3.2 3.5 Vertical Tail Design A very important design parameter is Tail Volume Ratio (VV ). This was chosen as 0.06 based on survey of previous models. Area of the Vertical tail is typically 50-60 per cent of Horizontal Tail area. It was chosen to 13 Figure 3.3: Vertical Tail Design Table 3.3: Vertical Tail Parameters Specification Symbol Tail Area Tail Span Root Chord Tip Chord MAC Aspect Ratio Taper Ratio Tail Volume Ratio SV bV Croot Ctip AR t VV Value 34423mm2 245mm 199mm 82mm 149mm 1.74 0.41 0.06 keep this ratio as 59 per cent. This gave us the vertical tail area (SV ). Aspect ratio for Vertical Tail is usually kept smaller- between 1.5to2.5. It was chosen as 1.74. Based on this, tail span (bV ) was calculated using the same formula as used earlier for the wing. Taper Ratio (t) was chosen as 0.41. Once this was fixed, the root chord and tip chord were also calculated as done earlier. Lastly, the Mean Aerodynamic Chord (MAC) for the vertical tail was calculated. All the parameters thus calculated are listed in Table 3.3. 3.6 Fuselage Design To accommodate the desired payloads, a space of 100mmx100mm was essential. To leave some room for the propeller and any future payloads, a margin of 75% in length was added. This fixed the length of fuselage before the wing. The length aft of the fuselage was defined by the tail arm (lt ) requirement. Based on the horizontal tail area (st ) and the desired volume ratio (vH ), lt = vH st This gave us tail arm, which is effectively the distance between aerodynamic center of the wing and aerodynamic center of the horizontal tail. This completed the description of the length requirements. The maximum width of the fuselage was determined by the payload dimension while the maximum height was kept as the thickness of the Styrofoam sheet used. Maximum width of the fuselage was maintained right above the wing, while the remaining part was tapered lo streamline the fuselage. A cross section of 50mmX50mm 14 Figure 3.4: Fuselage Geometry Table 3.4: Fuselage Parameters Specification Wing Chord Tail Arm Length of the section before wing Total length of the fuselage Maximum Height Maximum Width Value 268mm 590mm 175mm 890mm 100mm 100mm was retained at the aft end of the fuselage to support the tail. The dimensions thus arrived at are shown in Table 3.4. 3.7 3.7.1 Control Surface Design Ailerons Ailerons are usually designed with length of 25% of wing span and chord of 25% of wing chord. Using these guidelines, ailerons of 450mmX45mm were chosen. 3.7.2 Elevator Elevator area is usually kept between 20% to 30% of the horizontal tail area. This ratio was chosen as 23% and the elevator was designed as a non-tapered flap of 31mm width through the span of the tail. 3.7.3 Rudder Span of the rudder was kept 30mm shorter than the span of the vertical tail, keeping in mind the portion of the tail going inside the fuselage. The rudder was given taper to achieve area ratio of 43%. The final dimensions of control surfaces are listed in Table 3.5. 3.8 Selection of Airfoil For the wing profile, NACA2412 airfoil was selected. It’s specfications are given in Appendix 1. 15 Table 3.5: Control Surface Parameters Specification Ailerons Span Chord Elevator Span Chord Rudder Span Chord Tip Chord 3.9 3.9.1 Value 450mm 45mm 435mm 31mm 215mm 79mm 35mm Computation of Moment of Inertia Using Software Tools like AutoCADT M CAD has an option to find the properties of the model like area, volume and moment of inertia. Since these models are drafted individually, the properties of the material could not be uploaded to get Moment of Inertia. However, after literature survey and interactions with others we got a preliminary understanding to calculate the Moment of Inertia. 1. Identify the reference point before start of modeling. 2. Using that reference point make all three dimensional models. 3. Assuming the material properties to be constant for all cases, we can find out the Moment of Inertia individually and then we can add all of them. 4. Make 1:1 Model in CAD that includes all components with their properties and then a reference has to be generated for finding out Moment of Inertia. 3.9.2 Experimental Computation This experiment is to be performed in order to evaluate the mass moment of inertia of a UAV by introducing two methods: 1. The Bifilar Suspension Technique. 2. The Auxiliary Mass Method. After this step, the values obtained from the two different methods will be compared with the value obtained analytically, using the geometry and dimensions of the beam. The layout of the experiment is shown schematically, in which we have a regular rectangular cross-section steel beam of length L, total mass M , and mass moment of inertia about its centre of gravity I. The beam is suspended horizontally through two vertical chords, each of length l, and at distance b/2 from the middle of the beam’s center of gravity(cog). The system is initially balanced, and by exerting a small pulse in such a way that the beam keeps oscillating in the horizontal plane about its middle point (centre of gravity), then by virtue of the tension forces initiated 16 in the suspension chords, the beam will oscillate making an angle θ with its neutral axis, and the suspension chords will make an angle φ with the original vertical position. 17 Chapter 4 Material Selection 4.1 Selection of Material for Drone We were focusing on UAV which can be robust, reusable, having higher strength to weight ratio, durability satisfying the mission requirements. Keeping in mind the above considerations, the materials chosen for fabrication are reported below. 4.1.1 Selection of Extruded Polystyrene as Base Building Material UAV body, Fuselage and wings were made using Hot wire, and emery paper was used for finishing. Styrofoam of required length was chosen and then shaped. Later, the wing profile was drawn on the paper and pasted on the sheet. The shape was later surface finished by emery paper to get required shape. 4.1.2 Coroplast Sheet This sheet was mainly used where it requires rigidity with minimum dissection. This is used in realization where one dimensional cutting is required. This is used in Vertical Stabilizer. Figure 4.1: Styrofoam 19 Figure 4.2: Coroplast Figure 4.3: Depron 4.1.3 Depron Useful for small models and it is very light in weight. This is used where drag caused due to skin friction is low. 4.1.4 Selection of Balsa Wood as Control Surface Material Like Coroplast, Balsa wood can be cut in single dimension. In the drone, Control surfaces were made from Balsa wood since they guarantee rigidness and ensure stiffness too. 4.1.5 Selection of Aluminum Stiffners Aluminium stiffners were used in areas which are subjected to torsional and bending forces during the flight to provide strength to the concerning structure. In this case, aluminum stiffners are used to provide stiffness to the wings of the drone. 4.1.6 Miscellaneous Materials In addition to above materials, glass fiber sheet was used to provide further strength and rigidity to the drone structure. Other support materials includes adhesive films and industrial adhesives. 20 Figure 4.4: Wood of Balsa Figure 4.5: Aluminum Stiffner 21 Chapter 5 Manufacturing of the Drone 5.1 Manufacturing Processes Used The block diagram shown as figure 5.1 briefly illustrates the manufacturing process of the drone. Drone manufacturing takes sequentially the following steps: 1. Generation of CAD Models 2. Cutting of fuselage 3. Cutting of wings/tail planes 4. Cutting of balsa wood control surface 5. Attachment of control surfaces to the wings/ tail 6. Plastering the UAV either with Coroplast sheet or Tape 7. Strengthening of wings and Tail : by using balsa wood and aluminum stiffeners 8. Assembly of UAV with necessary Avionics and power plant. The electronic components used in the drone are enlisted below: 1. Thrust motor: 840 Kv 2. Servos: For Control Surface Deflection 3. Electronic speed controller: Vary Motor Speed and Direction 4. Battery: 2200 mAh Lithium Polymer Battery 5. Transmitter: 2.4 GHz 4 Channel Transmitter 6. Receiver: Receives Signals from the transmitter and passes it to servos and ECS 5.1.1 Hot Wire Shaping Method To give the drone parts their shape, hot wire cutting method was employed. In this method, a hot wire was passes through the cross section of the extruded polysstyrene mass to get it shaped into the desired shape and size. 23 Figure 5.1: Servos Figure 5.2: Motor and Propeller Figure 5.3: Li-Polymer Battery 24 Figure 5.4: Transmitter Figure 5.5: Wire Connector 25 Chapter 6 Taking the Test Flight 6.1 Test Flight and Electronics Components detail The CHASER has flown under several trials to test its flyabilty and its flight behavior. Different flyers have tested their skills on it by performing various maneuvers. The executed maneuvers were climb, cruise, turn, inverted mode flying and gliding during around ten minutes of its flight: The CHASER were equipped with the following electronics: Table 6.1: Electronics Components details Components Battery Thrust motors ESC Servos Propeller Transmitter and Reciever Details LiPo, 2.2Ah, 4-S 1050 KV, DLDC Turnigy plush 60 A Digital servo/2.2 Kg TGS sport 12 x 6 2.4 GHz with mode-1 Figure 6.1: Take off 27 Figure 6.2: Maneuver mode Figure 6.3: Landing 28 Chapter 7 Estimating the Flight Parameters 7.1 Aerodynamic Parameter Estimation An important task in the development of UAV is the modeling and identification of their aerodynamic characteristics, i.e. the stability and control derivatives. Estimation of these parameters has been done by various methods such as: analytical methods,Numerical, wind-tunnel methods and flight test methods. A basic details with some features of these methods is tabulated in the figure 7.1 At initial stages of aircraft design, analytical methods provide the only convenient way of estimating the aircraft parameters. However the accuracy of such theoretical estimates being not so high, there is a need to verify these estimates with those obtained from wind-tunnel testing and flight tests. Figure 7.1: Aerodynamic Parameter Estimation 29 7.2 Modelling of Aerodynamic Derivatives Modelling of CLα :This is lift curve slope gradient. For subsonic conditions and for wing planforms with moderate sweep angle we can findCLα for finite wing from 2D CLα of airfoil. CLα3D = CLα2D 1+ CLα2D πARe Modelling of CDα : This is the drag stability derivative with respect to angle of attack. CDα = 2CL1 πARe CLα Modelling of Cm0 , Cmα , Cmδe & Cmq : This is the pitching moment stability derivative with respect to angle of attack. C m0 = Cmα = C m δe = C mq = Xcg − Xac Cma c + CL0w + ηVH CLαt (ǫo + iw − it ) c̄ dǫ Xcg − Xac − ηVH CLαt 1 − CLα c̄ dt −ηVH τ CLαt lt −ηVH τ c̄ Modelling of Cyβ : Cyβ (v) = −kav (1 + where, K = a0 2π Sv dσ )ηv dβ S empirical parameter ηv (1 + Sv Zw dσ S ) = 0.724 + 3.06 + 0.4 + 0.009ARw dβ 1 + cosΛc/4w d Where, Zw is distance parallel to z-axis Modelling of Clβ : Clβ (v) = −kav (1 + Sv dσ )ηv Zv dβ S Modelling of Cyp Cyp (v) = Zv Cyβ (v) b Modelling of Cnβ Cnβ (b + w) Cnβ = −KN KR SB l f S b Where, KN is empirical wing body interference factor and KR is fuselage Reynolds number (Ref Bandu N. Pamadi, P-275-277) Modeeling of Cyr 30 2 Cyr = − lv cyβ (v) b (7.1) Modelling of Cnr C nr = Modelling of Cyδr Cyδr = av 2 lv cyβ (v) b2 αδ CL Svt αδ CL KKb τ = av αδ Cl S αδ Cl where, τ is ratio of the 3-D flap effectiveness parameter to the 2-D flap effectiveness parameter K=1 (ref: Roskam 10.2 and 10.7) Modelling of Clδr Clδr = Cyδr Zv b Modelling of Cnδr Cnδr = −av τ (vv )ηv 31 Appendix A NACA2412 Airfoil NACA2412 airfoil is used as the cross section of the wing of the drone. The camber line is shown in red, and the thickness – or the symmetrical airfoil 0012 – is shown in purple. Maximum thickness is 12The NACA airfoil section is created from a camber line and a thickness distribution plotted perpendicular to the camber line. The equation for the camber line is split into sections either side of the point of maximum camber position (P). In order to calculate the position of the final airfoil envelope later the gradient of the camber line is also required. The equations are: Front(0 6 x < p) Camber: yc = Gradient: M (2P x − x2 ) P2 dyc 2M = 2 (P − x) dx P Back(p 6 x < 1) Camber: yc = M (1 − 2P + 2P x − x2 ) (1 − P )2 Gradient: 2M dyc = (P − x) dx (1 − P )2 The thickness distribution is given by the equation: yt = T (a0 x0.5 + a1 x2 + a2 x2 + a3 x3 + a4 x4 ) 0.2 Figure A.1: NACA0012 Airfoil Geometry 33 Figure A.2: NACA2412 Polar where, a0 = 0.2969, a1 = −0.126, a2 = −0.3516, a3 = 0.2843, a4 = −0.1036 34 Appendix B Drawings Figure B.1: Fuselage Geometry Figure B.2: Horizontal Tail Geometry 35 Figure B.3: Vertical Tail Geometry 36 Appendix C Drone Stability and Control Parameters Table C.1: Aircraft Stability and Control Parameters Parameters CDo CLo CLα CLδe Cm0 Cmα C mq Cmδe Cyo Clo Cno Cyβ Value 0.246 0.006 4.542 1.510 -0.015 -1.204 -2.200 -0.816 0 0 0 -0.0195 Parameters Clβ Cnβ Cyp Clp Cnp Cyr Clr Cnr Cyδr Clδr Cnδr Value -0.027 0.1807 -0.005 -0.45 0 0.0188 0.0001 0.0154 0.01434 0.0008 -0.0983 37