AIRCRAFT WING DESIGN BY USING THE FINITE ELEMENT METHOD AND THE ANALYTICAL TECHNIQUES GRADUATION PROJECT. Emre ÜNLÜ. Aeronautical Engineering

Transcription

1 ISTANBUL TECHNICAL UNIVERSITY FACULTY OF AERONAUTICS AND ASTRONAUTICS AIRCRAFT WING DESIGN BY USING THE FINITE ELEMENT METHOD AND THE ANALYTICAL TECHNIQUES GRADUATION PROJECT Emre ÜNLÜ Aeronautical Engineering Thesis Advisor: Doç. Dr. Aytaç ARIKOĞLU January, 2019

2 ISTANBUL TECHNICAL UNIVERSITY FACULTY OF AERONAUTICS AND ASTRONAUTICS AIRCRAFT WING DESIGN BY USING THE FINITE ELEMENT METHOD AND THE ANALYTICAL TECHNIQUES GRADUATION PROJECT Emre ÜNLÜ Aeronautical Engineering Thesis Advisor: Doç. Dr. Aytaç ARIKOĞLU January, 2019

3 Emre ÜNLÜ,student of ITU Faculty of Aeronautics and Astronauticsstudent ID , successfully defended the graduation entitled AIRCRAFT WING DESIGN BY USING THE FINITE ELEMENT METHOD AND THE ANALYTICAL TECHNIQUES, which he/she prepared after fulfilling the requirements specified in the associated legislations, before the jury whose signatures are below. Thesis Advisor : Doç. Dr. Aytaç ARIKOĞLU... İstanbul Technical University Jury Members : Dr.Öğr.Üye.Özge ÖZDEMİR... İstanbul Technical University Öğr.Gör.Dr.H. Barbaros SOYER... İstanbul Technical University Date of Submission : 02 January 2019 Date of Defense : 14 January 2019

4 To my family,

5 FOREWORD As a person who has ben interested in the aeronautical since his early ages, I feel lucky for that I study in İstanbul Technical University Aeronautical Engineering Department. I have learned a lot of professional information since I was in this department. I have made many designs and analysis by using the new information and technics in my project. It is also proud to start my career by sharing my works with my future colleagues. I will continue my works in my occupational career without stopping for the aeronautical to get ahead in our country. I would like to thank to my thesis advisor Associated Professor Aytaç Arıkoğlu and all my teachers who have contributed to me. January 2015 Emre ÜNLÜ i

6 TABLE OF CONTENTS FOREWORD... i ABBREVATIONS... iii LIST OF TABLES... iv LIST OF FIGURE... v SUMMARY... vi 1. INTRODUCTION Purpose of Thesis Literature Rewiew THEORETICAL KNOWLEDGE Finite Element Method CATIA (Conception Assistée Tridimensionnelle Interactive Appliquée) ANSYS Workbench AIRCRAFT WING Wing Structure Element Spar Rib Research of Similar Design Cessna 172 Skyhawk Beechcraft Musketeer Diamond DA Grumman American AA Piper PA-28 Cherokee Selected Wing Geometry Wing Cross-sections and Aerodynamic Properties WING DESIGN STAGES Materials Used in Wing Structure Material Selection Spars Design Rib Design Wing Geometry LOADS Aerodynamic Forces Lift Drag Pressure Coefficient and Force Integration Load Factor ANALYSIS AND RESULTS ii

7 ABBREVATIONS iii

8 LIST OF TABLES Table 3.1: Properties of Cessna 172 Skyhawk... 7 Table 3.2: Properties of Beechcraft Musketeer... 8 Table 3.3: Diamond DA Table 3.4: Properties of Grumman American AA Table 3.5: Properties of Piper PA Table 3.6: Characteristics of aircrafts Table 3.7: Properties of NACA 2415 airfoil Table 4.1: Mechanical properties of aluminum iv

9 LIST OF FIGURE Figure 2.1: Physical System and f.e. model... 3 Figure 2.2: Example of a aircraft wing designed in catia program... 4 Figure 3.1: Basic wing structure... 5 Figure 3.2: Structural parts on the wing... 6 Figure 3.3: Cessna 172 Skyhawk... 7 Figure 3.4: Beechcraft Musketeer... 8 Figure 3.5: Diamond DA Figure 3. 6: Grumman American AA Figure 3.7: Piper PA-28 Cherokee Figure 3.8: Wing profile components Figure 3.9: Selected wing profile Figure 3.10: Cessna 172 Skyhawk sketch Figure 4.1: Material assigned wing geometry Figure 4.2: Technical drawing of front and rear spars Figure 4.3: Designed spars Figure 4.4: Technical drawing of rib Figure 4.5: Designed ribs Figure 4.6: Designed rib and spar structure Figure 4.7: Designed wing Figure 5.1: Forces on aircraft Figure 5.2: Center of Pressure Figure 5. 3: Pressure coefficient Figure 5.4: NACA 2412 coefficient of pressure distribution Figure 5.5: 0 of angle attack force integration Figure 5. 6: 5 of angle attack force integration Figure 5.7: 10 of angle attack force integration v

10 SUMMARY Aircrafts are one of the most popular and most interesting vehicles as a vehicle that is now one of the most preferred transportation vehicles. In this respect, it is known that aircraft are becoming widespread today.in short, the plane is defined as the vehicle that can fly in the air. Airplanes can fly through the lifting force produced by the wings. In this case, one of the most important processes in aircraft design is the wing design process. A good design targets maximum durability and minimum cost. This is especially important for wing design. During flight, most of the forces on the plane cover the wings. The material used for a good wing design, the selection of the inner and outer structure of the wing is very important. The material used must be able to withstand the loads on the wing and be able to withstand the deflection and to be very light when achieving this. Wing interior design is also important for minimizing material use. In this study, structural analysis, which is an important process of wing design, has been done. The analyzes were performed by using the finite element method. Finite element method is a method used in most engineering applications. In the finite element method, an approximate solution is reached with the sum of the separate solutions made at each node point after being separated into simpler and smaller geometries with the help of complex geometry nodes. Thus, a complex problem can be easily solved by solving simple problems. In the first part of the study, the aim of the study and the finite element method used were introduced. In the second part of the study, an important step in the design process is the study of similar designs. The characteristics of similar designs and their similarities were compared. As a result of the examinations, the characteristics selected for the design were determined and the wing aerodynamic profile was selected according to these characteristics. In the third part of the study, wing structure and wing structure elements are examined. The reasons and designs of the elements such as rib and spar were investigated. In the fourth part of the study, the geometry and structural elements of the study were performed using CATIA V5R21 CAD program. All elements were drawn separately and dimensioned and then assembled to each other to achieve the desired wing structure and geometry. In the fifth part of the study, aerodynamic forces were examined. The distributions of these forces on the wings were transformed into force integration. vi

11 In the sixth part of the study, the drawn geometry was prepared for the analyzes to be made by participating in ANSYS program. Structural analyzes on the wing were performed by using ANSYS STATIC-STRUCTURAL program. The solution network in the wing structure, especially sparlara and solution networks at the connection point of the wing has been considered. Before the analysis, the materials selected for the elements in the wing structure are assigned. Aluminum alloy for ribs and spars, composite material inside the outer surface is selected. The analysis was performed by entering the required boundary conditions. In the last part of the study, the results of the analysis were evaluated. According to the results of the analysis, it was decided not to make any changes in the design status and design. Keywords: Aircraft wing, finite element method, structural analysis 7

12 1. INTRODUCTION The aircraft is a motorized vehicles which can be lifted in the air due to the pressure difference between the upper and lower surfaces of the wing profile parts, especially the wings. Many aircraft with propellers or jet engines, fixed and heavy aircraft are included in the aircraft category. Today, while the most basic types of aircraft are known as passenger aircraft, fighter jets, cargo aircraft, there are also planes that are customized according to different geographical conditions. The main parts of the aircraft are the wings that allow to hold in the air, the tail to keep the wings in balance, the control surfaces that change the position and position of the aircraft and the motor and propeller elements that provide the necessary push. It is one of the main parts of the cockpit plane that hosts passengers and cargo and the flight crew and flight controls. The most important structure that lifts and holds the aircraft in the air is the wing. This is because the wings provide control of the aircraft during the flight as well as the production of the lifting force to keep the aircraft in the air with the help of wings. The wings carry both the air and the weight of the whole plane in the air and do the works that it takes with various different forces such as diving, slowing with flaps. All of the maneuvers made during landing and take-off, while in the air, are controlled via the wings. Therefore, wing design is one of the most important processes in aircraft design. The designed aircraft wing must be able to withstand the total weight of the aircraft upon flight, fuel loads, and various forces such as forces during maneuvering. One of the important processes in the wing design is the selection of the material to be used in the wing design. It is important that the selected material is able to withstand long periods of time under various forces on the wing and without being damaged. The material chosen in the wing design should be light because the lighter the weight of the airplane wing the better the impact on the bearing force. 1

13 1.1 Purpose of Thesis In this study, aircraft wing design and structural analysis will be done by using finite element method and analytical methods. The effect of the load and aerodynamic forces on the aircraft wing and its effects on the materials used in wing production will be examined and the structural behavior of the designed wing under the influence of these loads and forces will be observed. The aim of the study is to design a wing that can withstand the various forces on the flight during flight, produce the required lift force for the flight, and mix the structural behavior of the aircraft wing using the finite element method and analytical methods. 1.2 Literature Rewiew In this study, considering the working time, it was decided to use a wing profile belonging to the front propeller and two-person training aircraft. For this purpose, the characteristics of aircraft similar to the design process and the wings used in these planes were investigated. In this way, using the experimental data of similar aircraft, observations were made more easily in the new wing design. Considering the characteristics of the different airplanes examined, a fair airplane wing will be designed and aerodynamic profile will be selected according to these characteristics. The structural geometry of the wing geometry drawn in a design program will be examined using different analysis programs. 2

14 2.THEORETICAL KNOWLEDGE 2.1 Finite Element Method It is a numerical solution that seeks solutions to various engineering problems with an acceptable approach. Finite Element Analysis is a mathematical expression of a physical system. This system can be subdivided and has material properties and applicable boundary conditions. Finite element method; It is a solution form where the complex problems are divided into simpler sub-problems and solved in each one. The method has three basic characteristics: I-) The geometrically complex solution zone is divided into geometrically simple subregions called finite elements. II-) It is accepted that continuous functions in each element can be defined as the linear combination of algebraic polynomials. III-) The values of the definition values that are continuous within each element are enough to solve the problem by obtaining values in certain points (nodes). Figure 2.1: Physical System and f.e. model 3

15 2.3 CATIA (Conception Assistée Tridimensionnelle Interactive Appliquée) CATIA is a computer program that is widely used in computer-aided design and computeraided manufacturing. The CATIA program is one of the most frequently used programs for CAE (computer aided engineering) thanks to its many superior commands and features. CATIA, which does not only have a drawing program, supports the user at every stage from the beginning of the design to the production phase thanks to its additional features. Figure 2.2: Example of a aircraft wing designed in catia program 2.3 ANSYS Workbench ANSYS; It is a computer aided engineering program that can be done by computer aided engineering studies and analysis and simulations. The ANSYS program enables effective studies in different disciplines such as mechanical, structural analysis, computational fluid dynamics and heat transfer. ANSYS program uses the finite element method. The finite element method can be used to analyze the objects in complex geometry which are very difficult to analyze in a single piece by dividing them into small and multiple pieces. The results obtained from the analysis of a finite number of elements are combined to obtain a single and consistent analysis. 4

16 3. AIRCRAFT WING 3.1 Wing Structure Element The aim of this section is to introduce wing design and construction types in many aircraft. The most important structure that lifts and holds the aircraft in the air is the wing. Wing types according to their structure; monospar (single spar), multispar (multi-spar) and boxbeam (box beam) are divided into three. Monospar wings could not find much use. However, these wings can be used in some aircraft with the support made by web and other beams that can be added to single spared wings. In multispar wing application, more than one carrier beam extends in the wing section. This type of wings are equipped with ribs connecting each spar and independent pressure chambers. This reduces the load per spar. Figure 3.1: Basic wing structure Spar The basic load-bearing element constituting the inner structure is spar. According to the aircraft type, one, two or three pieces can be found in the wing structure. Spar production also varies according to aircraft type. Small aircraft are made of wood or aluminum, while larger aircraft use steel alloy advanced materials. Spars depend on ribs. 5

17 3.1.2 Rib The ribs shape and shape the outer ribs of the wing. The ribs are also connected to the stringers along the wings. The load transfer takes place from the surface coating to the stringer and ribs from there to the spikes and finally to the center wing box. Figure 3.2: Structural parts on the wing 3.2 Research of Similar Design Similar designs are initially explored in all design processes. In order to minimize the error rate in this study, previously designed designs were examined. In the previous designs, information such as errors, common features of the designs are obtained and the idea for preliminary design is obtained. Thus, the loss of time due to errors in the preliminary design process can be prevented. 6

18 3.2.1 Cessna 172 Skyhawk Cessna 172 Skyhawk is a 4 person, high-wing, single engine cessna model. It is also the most popular training aircraft in the world. It was first produced in Cessna used the tricycle landing gear system for the first time on this plane. It is one of the rare models with windows behind it. Thus, the pilot can see the back. Figure 3.3: Cessna 172 Skyhawk Table 3.1: Properties of Cessna 172 Skyhawk Crew Maximum Take-Off Weight Wingspan Wing Area Cruise Speed Stall Speed one pilot, three passengers 1113 kg 11.0 m sq m 123 knot 89 km/h Wing Profile NACA

19 3.2.2 Beechcraft Musketeer Beechcraft Musketeer is a low-weight aircraft and single-engine aircraft. Produced by Beechcraft and has many models. Some of these models are Model 19 Musketeer Sport, the Model 23 Musketeer and Model 24-R Sierra. This aircraft was produced from 1963 to Figure 3.4: Beechcraft Musketeer Table 3.2: Properties of Beechcraft Musketeer Crew Maximum Take-Off Weight Wingspan Wing Area Cruise Speed Stall Speed Wing Profile one pilot, three passengers 1089 kg 9.98m m sq m 102 knot 63 knot NACA 63A415 8

20 3.2.3 Diamond DA40 This aircraft is a 4-seater, single-engine austria aircraft made of composite materials. The aircraft is lightweight as it is made of composite material. The aircraft has a low wing, a T- tail and a tricycle landing gear. Figure 3.5: Diamond DA40 Table 3.3: Diamond DA40 Crew Maximum Take-Off Weight Wingspan Wing Area Cruise Speed Stall Speed one pilot, three passengers 1198 kg 11.9 m 13.5 sq m 150 knot 49 knot Wing Profile FX

21 3.2.4 Grumman American AA-5 Grumman American AA-5 is a four-seat and light aircraft, used as tour and training aircraft. Figure 3. 6: Grumman American AA-5 Table 3.4: Properties of Grumman American AA-5 Crew Maximum Take-Off Weight Wingspan Wing Area Cruise Speed Stall Speed one pilot, three passengers 1090 kg 9.6 m 13 sq m 128 knot 54 knot Wing Profile NACA

22 3.2.5 Piper PA-28 Cherokee The Piper PA-28 Cherokee is used as training aircraft produced by Piper Aircraft. This aircraft is quite light because of the materials used in making the aircraft. The PA-28 aircrafts have single engine, low-wing and tricycle landing gear. Figure 3.7: Piper PA-28 Cherokee Table 3.5: Properties of Piper PA-28 Crew Maximum Take-Off Weight Wingspan Wing Area Cruise Speed Stall Speed one pilot, three passengers 915 kg 9.2 m sq m 108 knot 47 knot Wing Profile NACA

23 3.3 Selected Wing Geometry The characteristics of the aircraft were compared in Table 3.6. It was decided that the characteristics of the aircraft to be designed will be designed considering the average values. The design of our new aircraft wing will be formed as a design similar to the wing of Cessna 172 Skyhawk considering the analyzes to be made within the scope of the project. When analyzing the new design Cessna 172 Skyhawk's previously taken experimental data will be taken into account. Table 3.6: Characteristics of aircrafts Grumman Properties Cessna 172 Beechcraft Diamond American Piper PA-28 Skyhawk Musketeer DA40 AA-5 Crew one pilot, three passengers one pilot, three passengers one pilot, three passengers one pilot, three passengers one pilot, three passengers Maximum Take-Off Weight 1113 kg 1089 kg 1198 kg 1090 kg 915 kg Wingspan 11.0 m 9.98m m 11.9 m 9.6 m 9.2 m Wing Area sq m sq m 13.5 sq m 13 sq m sq m Cruise Speed 123 knot 102 knot 150 knot 128 knot 108 knot Stall Speed 89 km/h 63 knot 49 knot 54 knot 47 knot Wing Profile NACA 2412 NACA 63A415 FX NACA NACA

24 3.3.1 Wing Cross-sections and Aerodynamic Properties Specially designed standard wing sections consist of two curved surfaces. The lengths of the sections are called the wing cross-section length (chord) and are indicated by c. The vertical length between the two surfaces is called the wing section thickness and is indicated by t. The front part of the section, which meets the flow, is given the front (leading) edge and the other part is called the (trailing) edge. Combining these two ends is called the true cross-sectional beam line (chord line). Figure 3.8: Wing profile components Figure 3.9: Selected wing profile 13

25 Table 3.7: Properties of NACA 2415 airfoil Thickness 12.0 % Max CL 0.82 Camber 2.0 % Max CL Angle 11.5 Trailing edge angle 20.4 % Max L/D Lowe Flatness 7.6 % Max L/D Angle -0.5 Leading edge radius 2.7 % Max L/D CL Efficiency 30.2 Stall Angle 12.0 Zero-lift Angle WING DESIGN STAGES The dimensions of the new aircraft wing are based on the wing dimensions of the Cessna 172 Skyhawk aircraft. Figure 3.10: Cessna 172 Skyhawk sketch 14

26 4.1 Materials Used in Wing Structure The most important structure that lifts and holds the aircraft in the air is the wing. As the wing carries both its own weight and the weight of the entire aircraft in the air, it is exposed to various forces such as landing, take-off, deceleration, forces during air maneuvers. On the motor-connected wings, forces such as shaking, vibration or buckling are involved in the connection of the motor to the wing. The vortex in the air causes shocks at the end of the wing. In this case, the materials to be used in the wings require flexible. Thus, vibrations and vibrations on the wing are not transferred to the body. Wing trunk connections are exposed to fatique due to these continuously changing loads. Light weight, elasticity, toughness, resistance to external factors, ease of production and cheapness can be shown as the most important criteria in the selection of materials used in aircraft wing. In view of these criteria, aluminum alloys, titanium alloys, nickel-based alloys, steel and composite materials are used in modern aircraft Material Selection In accordance with this information, it was decided to use aluminum when making the aircraft wing. Aluminum is the most commonly used engineering material owing its weight capacity suitable to high strength values. Reasons for selection of aluminum alloys; middle cost, lightness, ease of fabrication, high strength, fracture toughness, fatigue resistance, ductility, mechanical and heat treatment and good control of properties. The disadvantages of using Al alloys can be expressed as follows; shows low mechanical properties at high temperature and corrosion conditions. Aluminum alloys have been one of the most commonly used materials in the aerospace industry due to their light, high strength and ease of manufacturing. 15

27 Table 4.1: Mechanical properties of aluminum Modulus of Elasticity (E) 71.0 GPa Poissons Ratio (ν) 0.33 Mass Density (ρ) kg/m 3 Tensile Strength, Ultimate Tensile Strength, Yield (σy) Shear Modulus 485 MPa 435 MPa 23 GPa Figure 4.1: Material assigned wing geometry 16

28 4.2. Spars Design The following figure shows the detailed dimensions of the front and rear spar. Front spar shape is designed in the form of I profile. Figure 4.2: Technical drawing of front and rear spars Figure 4.3: Designed spars 17

29 4.3. Rib Design Ribs are in the form of a wing profile naca 2412 and the dimensions of the part are shown in detail below. 7 holes were drilled on the profile. Each ribs thickness is 2 mm. Figure 4.4: Technical drawing of rib Figure 4.5: Designed ribs 18

30 4.4 Wing Geometry Figure 4.6: Designed rib and spar structure Figure 4.7: Designed wing 19

31 5. LOADS It is defined as any shape structure system that can carry loads and transfer these loads to other parts of the object. Such building systems; beams, plates, shells or combinations thereof. A structural element is generally used for externally acting loads; bending, axial, shear, and torsion; or against internal loads of various combinations of these four. Each aircraft is designed to perform its special duty safely. This results in a wide range of structures, depending on size, construction and performance. Commercial transport aircraft are specifically designed to carry passengers from one airport to another. No sharp maneuvering of such aircraft is possible. Hunting and bombers are designed to withstand sharp maneuvers. Design conditions are generally determined by the greatest acceleration that the pilot will not lose consciousness before the load coefficient, which causes the collapse of the aircraft structure, is reached and the human body can withstand. In addition to the optimum design, both civilian and governmental bodies have established certain specifications and requirements for the severity of loads to be used in the design of various aircraft, in order to ensure aircraft safety, structure integrity and reliability. Boundary loads determined by civilian or military organizations are the maximum loads that the vehicle will be exposed to during its entire life. Compression, tension, torsion, bending and shear forces are the forces acting on the aircraft and its elements. Figure 5.1: Forces on aircraft 20

32 5.1 Aerodynamic Forces Aerodynamic force is the force effect of the flowing gas on the bodies. They are the main forces of aerodynamics. Aerodynamic force is applied to every object exposed to the moving flow. The aerodynamic force is a force exerted by the gas molecules in the air to the moving objects of the air Lift The effect on the plane is the component of the aerodynamic force acting towards the top of the plane in a direction perpendicular to the free flow. By "upwards" is meant the direction of the pilot's head. Rocket and so on can not be defined exactly as up or down. The direction of the transport in the objects must be well described. However, the main point is that the transport is perpendicular to the free flow direction. L = 1 2 x ρ x V2 x S x Cl ρ = density kg/m 3 V = velocity m/s S = wing surface area m 2 Cl = coefficient of lift 5000 ft level flight conditions for Cessna 172 Skyhawk, V = 62 m/s ρ 5000 = 1.06 S = 16.5 m 2 g = 9.81 m/s 2 L = 1100 x 9.81 = N = 1 2 x 1.06 x 822 x 16.5x C L CL =

33 2d to 3d C l C L,3D = 2π C l x AR (AR + 2) AR = b2 S, for b = 11m, S = 16.5 => AR = = 2π C l x 7.3 ( ) C l = rad => α = 3.7 the wing's angle of attack is 3.7 degrees, while providing level flight conditions. When analyzing on the wing, the position of the wing should be placed at 3.7 degrees. The center of pressure is given by x cp = c 4 (1 + π C l (A 1 A 2 )) For NACA 2412 A1 = , A2 = Applying the Jutta Joukowski expression for lift and moment versus vortex strength yields, x cp = c 4 (1 + C l = 2πα π ( ))

34 x cp = 0.35c, the center of pressure point = 0.35 x 1.5 m = 0.52 m Figure 5.2: Center of Pressure Drag It is the force component in the direction of movement of the aircraft and in the opposite direction to movement. It is the resistance force of air to the movement of the aircraft. D = 1 2 x ρ x V2 x S x Cd ρ = density kg/m 3 V = velocity m/s S = wing surface area m 2 Cd = coefficient of drag 5.2 Pressure Coefficient and Force Integration Aerodynamic studies often deal with the distribution of pressure around the wing. However, in these investigations it is preferred to use the expression in the form of a coefficient instead of the absolute value of the pressure. 23

35 General definition of pressure coefficient: show the free flow conditions, ρ is the static pressure at the point. Figure 5. 3: Pressure coefficient Figure 5.4: NACA 2412 coefficient of pressure distribution Cp distribution of a NACA 2412 wing profile experiment as shown in the figure above. 10 points were selected at equal intervals over the x-axis and cp values were found for each angle of attack. Computed load interaction on the wing profile was calculated by making pressure calculation at each point. This integration was made with the help of the Wolfram Alpha Mathematica program. 24

36 For 0 of attack angle CpU={{0c,1},{0.15c,0},{0.3c,-0.5}, {0.45c,-0.6},{0.6c,-0.55},{0.75c,-0.6},{0.9c,- 0.45},{1.05c,-0.3},{1.2c,-0.3},{1.35c,-0.2},{1.5c,-0.2}}; CpL={{0c,0},{0.15c,-0.1},{0.3c,-0.4},{0.45c,-0.3},{0.6c,-0.25},{0.75c,-0.2},{0.9c,- 0.2},{1.05c,-0.05},{1.2c,-0.1},{1.35c,-0.05},{1.5c,-0.05}}; CpUf=Expand[InterpolatingPolynomial[CpU,x]]; CpLf=Expand[InterpolatingPolynomial[CpL,x]]; 1 c = 1 ( (y 5.5))1.5; PU=1/2 ρ V 2 CpUf PL=1/2 ρ V 2 CpLf Upper : Lower: Figure 5.5: 0 of angle attack force integration 25

37 NIntegrate[PL, {y, 0,5.5}, {x, 0, c}] NIntegrate[PU, {y, 0,5.5}, {x, 0, c}] = N For 5 of angle attack CpU={{0c,0.5},{0.15c,-1.2},{0.3c,-1.4}, {0.45c,-1.3},{0.6c,-1.1},{0.75c,- 1},{0.9c,-0.7},{1.05c,-0.5},{1.2c,-0.45},{1.35c,-0.3},{1.5c,-0.3}}; CpL={{0c,0.75},{0.15c,0.4},{0.3c,0.1},{0.45c,0.09},{0.6c,0.1},{0.75c,0.09},{0.9c,0.1},{ 1.05c,0.09},{1.2c,0.1},{1.35c,0.1},{1.5c,0.1}}; Upper : Lower: Figure 5. 6: 5 of angle attack force integration NIntegrate[PL, {y, 0,5.5}, {x, 0, c}] NIntegrate[PU, {y, 0,5.5}, {x, 0, c}] = N 26

38 For 10 of angle attack CpU={{0c,-2.4},{0.15c,-2.7},{0.3c,-2.3}, {0.45c,-1.7},{0.6c,-1.4},{0.75c,- 1.1},{0.9c,-0.7},{1.05c,-0.5},{1.2c,-0.4},{1.35c,-0.3},{1.5c,-0.3}}; CpL={{0c,0.75},{0.15c,1},{0.3c,0.7},{0.45c,0.45},{0.6c,0.4},{0.75c,0.35},{0.9c,0.3},{1. 05c,0.2},{1.2c,0.15},{1.35c,0.1},{1.5c,0.1}}; Upper: Lower: Figure 5.7: 10 of angle attack force integration NIntegrate[PL, {y, 0,5.5}, {x, 0, c}] NIntegrate[PU, {y, 0,5.5}, {x, 0, c}] = N 27

39 5.3 Load Factor The aircraft has to perform certain maneuvers while flying in the air and thus change the position at certain speeds. When performing these maneuvers, the aircraft's wing is loaded with extra weight depending on the maneuvering situation. This wing is responsible for carrying this weight. This is one of the biggest factors in the design process and it is necessary to make an account and examine it carefully. A design maneuver diagram is needed to determine this in the design phase. Figure 5. 8 : Example of maneuver diagram The most important burden here is the ultimate load. This load is obtained by multiplying the maximum load that the aircraft may encounter during the flight time by the safety factor. Wing design is made according to this ultimate load. The safety factor indicated here is different for different types of aircraft. The limit load is the greatest burden the aircraft may encounter during the flight process. Load Factor(n) = Lift Weight 28

40 Figure 5. 9: Change of load factor according to maneuvering angles Table 5.1: Information for aircraft types of the limit load factor Aircraft types n positive n negative General Aviation-Normal 2,5-3,8 (-1) - (-1,5) General Aviation-Aid 4,4-1,8 General Aviation-Acrobatics 6-3 Passanger Aircraft 3,0 4,0 (-1) (-2) Strategic Bombers 3-1 Tactical Bombers 4-2 War Aircraft 6,5-9 (-3) (-6) The safety factor is getting 1.25 for fighter planes while 1.5 is getting for traditional airplanes. This means that traditional combat aircraft are more durable than combat aircraft. 29

41 6. ANALYSIS AND RESULTS 30

42 31