Project Manual 2017-2018.pdf

Project manual AE1111-I – Exploring Aerospace engineering

2017/2018

Contents About the AE1111-I project ................................................................................................ 2  Grading ............................................................................................................................ 8  2D  Pressure distributions on aerofoils ............................................................................ 9  LI  Lift and weight ......................................................................................................21  DR  Drag and Longitudinal stability ................................................................................30  TH  Thrust ...................................................................................................................37  PW  Power ...................................................................................................................42  3D  Execution of 3D Wind Tunnel Experiment on a Swept Wing .......................................47  AD  Aerodynamic Design...............................................................................................57  RE  Range and Endurance ............................................................................................62  FE  Flight envelope, climb rate and glide........................................................................65  BT  Building and testing the aerodynamic model.............................................................67  M1  Mars Mission Design I ............................................................................................70  M2  Mars Mission Design II ...........................................................................................72  M3  Mars Mission Design - Poster ..................................................................................74 

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Project manual AE1111-I – Exploring Aerospace engineering

Change sheet Date

Name

Section

Change description

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2017/2018

Project manual AE1111-I – Exploring Aerospace engineering

2017/2018

About the AE1111-I project The AE1111-I project is a first exploration of the aerospace engineering field, which means it aims to enhance knowledge taught in parallel courses by using the exploration theme. Aerospace engineers create machines, from airplanes that weigh over a half a million pounds to spacecraft that travel over 17,000 miles an hour. They design, develop and test aircraft, spacecraft and missiles and supervise the manufacturing of these products. Aerospace engineers develop new technologies for use in aviation, defence systems and space exploration, often specializing in areas such as structural design, guidance, navigation and control, instrumentation and communication, or production methods. They often use computer-aided design (CAD) software, robotics, and lasers and advanced electronic optics. They also may specialize in a particular type of aerospace product, such as commercial transports, military fighter jets, helicopters, spacecraft, or missiles and rockets and can be experts in aerodynamics, thermodynamics, celestial mechanics, propulsion, acoustics, or guidance and control systems. Almost all jobs in engineering require some sort of interaction with co-workers. Whether they are working in a team situation, or just asking for advice, most engineers must have the ability to communicate and work with other people. Engineers should be creative, inquisitive, analytical, and detail-oriented. They should be able to work as part of a team and to communicate well, both orally and in writing. Communication abilities are important because engineers often interact with specialists in a wide range of fields outside engineering. This project is focused on flying wings, which have long been a dream of many designers. The biggest problem found when building a flying wing aircraft is that such designs are inherently unstable and they do not easily stay in level flight. Yet such an all-wing aircraft would have excellent payload and range capabilities because it produces less drag than a conventional aircraft as the tail and the fuselage of a conventional aircraft are responsible for a significant amount of drag. Eliminate the tail and fuselage and you might be able to eliminate a great deal of drag, enhance performance, reduce the amount of fuel required and improved the handling capabilities of the airplane; an attractive prospect in the age of fuel running short and an increase in air traffic transportation. This manual is the general guideline for the different parts of the AE1111-I project and tells you, the student, what has to be done for this project. Most of the exercises and lab sessions will aid you in designing and building your own actual flying wing except for the part of the project called ‘Mars Mission Design’. In that part of the project you will explore, with your team, the design of a solar-powered aircraft which can map part of the surface on Mars and present the design on a poster. You will find that some of the exercises throughout the student manual also refer to Mars. They can be treated as stand-alone exercises that are not related to the Mars Mission Design. The schedule for this project can be found on the AE1111-I BrightSpace site, along with other important information for this project. It should be noted that attendance to all project parts is mandatory, according to the exam regulations, and will be registered. You can be absent for no more than two project parts per period, which must be compensated for in consultation with your tutor. If you are absent more than twice or do not compensate for being absent, you can be expelled from the project. It is recommended that you bring your own laptop with you during the project, since there are only two computers available per project group in the project rooms. As every part of this project requires a report answering all questions stated, a short description is given below about the things required in a report:  Frontpage: Frontpage, including student names, student number, group number and title.

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Project manual AE1111-I – Exploring Aerospace engineering

  

2017/2018

Introduction: shortly introduce the topic and the outline of the report Bibliography: All websites, books or information retrieved elsewhere, must be clearly and properly documented at the end of the report. The reference list at the end of this chapter can be seen as a good example. Table with contributions of each student, to keep track of what you and your colleagues have been doing during project, but it also important for the teaching assistants to keep track that work is distributed equally.

Although the course AE1110-I Introduction to Aerospace Engineering is running parallel with this course, it might occur that the project is running ahead. Nothing can be done about this unfortunately, and you, the students, are asked to do some discovery yourself. If you have any questions or suggestions about this project, please pass these on to your mentor, so he or she can further take that into consideration. We hope you enjoy taking part in this thematic project!

Aerodynamics of flying wings Designing an aircraft, such as a flying wing, consists of many steps going from preliminary to detailed design in which relevant disciplines like aerodynamics, propulsion, flight dynamics and structures are considered. With respect to aerodynamics, we will limit ourselves to the main aspects of aerodynamics of flying wings, where complicating elements like the fuselage and the tail planes (denoted as the empennage) are left out of the analysis. The wing is the main element of the aircraft that exhibits all physical aerodynamic phenomena that occur, which makes a flying wing attractive as a study object to elucidate the discussions on the basic laws of aerodynamics as discussed in chapters 1 to 5 of Introduction to Flight (Anderson, 2008). Moreover, flying wings may have some advantages when it comes to aerodynamic or performance efficiency when they are used as a simple platform to carry equipment, such as cameras, either in the Earth’s atmosphere or at remote planets.

NASA Mars Explorer (1999)

Northrop YB-49 (1948)

Blended Wing Body (BWB) design Helios, high altitude research plane (2001) Figure 1: Examples of “flying wing” aircraft with different missions. The flying wing shows remarkable similarities with the blended wing body (BWB) (Figure 1) which is being studied word-wide. In this sort of design the entire airplane (including the

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Project manual AE1111-I – Exploring Aerospace engineering

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fuselage) generates lift and is streamlined in such a way to minimize drag and produce a high lift-to-drag ratio. On conventional transport aircraft, the cylindrical fuselage is a source of drag and generates close to no lift. Therefore, the design of a flying wing can have significantly better fuel characteristics than aircraft with a traditional layout. There are however some serious drawbacks to flying wings which need to be overcome, such as the inherent aerodynamic longitudinal instability and the limited space for cargo if the wing thickness is a limiting factor (drag). You may find a lot more information that is relevant for this typical aircraft design in open literature. As the aerodynamics of wings is discussed extensively in Anderson’s book we will frequently refer to this work for further reading. Furthermore, use will be made of the sample problems at the end of the chapters to practice solving simple problems in the same manner as will be done in subsequent exams. In subsequent chapters the lift production of wings will be discussed, starting with the typical behaviour of aerofoils. This will be done through a dedicated wind tunnel test in which the pressure distribution is analysed. The results may be assumed to be typical for aerofoils in the low speed regime, i.e. the effects of compressibility are neglected (M S1+S2. Please read the practicum instructions beforehand.

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Project manual AE1111-I – Exploring Aerospace engineering

2D

2017/2018

Pressure distributions on aerofoils

This first part of the project consists of two parts, the preparation of 2D wind tunnel experiment and the wind tunnel experiment itself. As there are ‘only’ four 2D tunnels and up to eight project groups per one half day, the tasks which do not require the wind tunnels need to be completed around the measurements at the project tables. A flying wing needs lift for which you need the velocity relative to the air, also known as airflow. This airflow behaves in a certain way for which a 2D analysis provides insight. Although it is possible to calculate the flow around entire airplanes using high-performance computers, wind tunnels are still very important. Besides measurements on aircraft aerodynamics, fundamental work on specific flow characteristics is done using modern measurement methods. Experimental research and numerical research in aerodynamics are complementary as the numerical research can give more insight in flow phenomena and the experimental research is used to validate numerical calculations. In this respect there seems to be a growing demand for dedicated wind tunnels. Apart from the necessity of experimental research, wind tunnels also provide a relatively simple means to show the basic flow phenomena and offer hands on experience of aerodynamics. The wind tunnel experiment discussed in this and the following chapter is meant to provide a better inside in the airflow around a wing profile and the associated pressure distribution, which are also treated in the aerodynamics lectures (AE1110-I). The experiment will be performed on a TecQuipment AF10 Airflow Bench, a small wind tunnel equipped with a wing profile in the airflow. This profile has pressure holes to measure the air pressure and its angle of attack (  ) is adjustable.

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Project manual AE1111-I – Exploring Aerospace engineering

Learning objectives

Schedule

Deliverables

2017/2018

The student should:  become familiar with total, static and dynamic pressure.  understand the basic working principle of wind tunnels, pressure holes and manometers.  obtain insight in the behaviour of 2-dimensional aerofoils.  understand the working of a simple wind tunnel and the manometer measuring device.  have the ability to execute a 2D wind tunnel experiment.  be able to convert measurements from one quantity to the other.  (40 min.) Preparation and familiarizing with the theory, including reading the related chapters in Anderson (2008).  (15 min.) Divide the tasks over the group members.  (60 min.) Working out of the exercises.  (60 min.) Preparation and execution of wind tunnel experiment for six different angles of attack (all group members need to be present).  (30 min.) Working out the results of the wind tunnel experiment.  (30 min.) Presentation of results to tutor.     

Make sure that you write clearly on everything you hand in who has worked on it.

Worked out exercises [Task 1: 1.1-1.7] Measurement report of the wind tunnel exercise [Task 1 &2] Worked out exercises and produced graphs [Task 3] The combined wind tunnel measurements for all six angles of attack delivered to the tutor as well as to all members of the group (needed for LI). Clear table containing work and hour distributions of all team-members

Theoretical background The theory used in this chapter and during the wind tunnel experiment will also be treated in the aerodynamics lectures (AE1110-I) but for this project it is important that you know the working principle of wind tunnels, the different pressures and manometers before you start working out the results of the wind tunnels. Therefore, you should read chapter 4.10 until 4.11.1 in Anderson (2008). If after reading there are still things on these concepts unclear, please feel free to do your own investigation to find the required information. Below you will find a short summary of the most important equations, but be aware, these are only the equations in their final form. For the derivations, please read the related chapters in Anderson (2008).

Continuity equation One of the basic principles from physics is that mass can neither be created nor destroyed. If this should be applied on a flowing gas, the following equation must hold: m 1  m 2 . This means that the mass flow at point 1 in a stream tube must be equal to the mass flow at point 2 (see Figure 1). This can be written as: m 1  m 2  1  A1  V1   2  A2  V2

(1)

This can be further simplified if we assume that the flow is incompressible, which means that the density does not change within the stream tube and Equation (1) becomes A1  V1  A2  V2

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(2)

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Figure 1: Stream tube with mass conservation [Anderson (2008)]

Bernoulli’s equation The derivation given in Anderson (2008) for Bernoulli’s equation assumes a steady, incompressible, irrotational, and inviscid flow and can be written as: p1  12    V12  p2  12    V22

(3)

Using Bernoulli’s equation with a Pitot-static tube (information on the Pitot-static tube can be found in chapter 4.11 in Anderson (2008), the following equation can be formed: p  12    V12  p0

(4)

The first term is the static pressure, the second term describes the dynamic pressure and the last term states the total pressure. The total pressure is sometimes also written as pt .

Manometer During the wind tunnel experiment you will measure the pressure differences along the aerofoil using a manometer. In this section, the basic principles behind manometer measurements will be discussed. A simple manometer is a tube in an ‘U’ shape, filled with a fluid, see Figure 2. In this situation one side of the U tube is connected to a certain pressure p1 . The other side is connected to a certain pressure p2 . A difference in fluid height, h , in the U tube is a measure for the difference in pressure, p2  p1 . In equation form this looks like: (5) p 1  A  p 2  A  w  A  h Here, A is the cross-sectional area of the tube and w is the specific weight of the fluid. w is defined as the density of the fluid times the acceleration of gravity. Equation (5) can be written as: p1  p2    g  h  w  h (6)

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Figure 2: Force diagram for a manometer [Anderson (2008)] If one of the pressures is known, say the ambient pressure; and the height difference is measured, Equation (6) can be used to calculate the unknown pressure on the aerofoil. Please note that the width of the tube, A, on either side is not important, if it is equal!

Speed of sound The speed of sound, as the words already suggest, is the speed at which sound propagates through a medium. In many aerodynamic problems, the speed of sound plays an important role. How the speed of sound fulfils this role becomes clear in the coming aerodynamics lectures and during the rest of your studies. The principle is introduced in this section, but the complete derivation of the formula for the speed of sound in a gas can be found in Anderson, 2008. The most important result of this derivation is that the speed of sound in a perfect gas

depends only on the temperature of that gas:

a    R T

(7)

The parameters  and R are constants (look up their values). Next to the speed of sound, there is another widely used quantity, the so-called Mach number. It is defined as: V a See chapter 4.11 of Anderson (2008) for further details. M 

(8)

Execution of 2D Wind Tunnel Experiment For a wing to be able to fly, it must consist of a number or wing profiles which are extruded over the span. How the flow over these profiles causes changes in pressure can best be demonstrated in a wind tunnel. This chapter will cover one of the more practical sessions during the aerodynamics part of your first-year project. You will do measurements on a NACA0020 aerofoil in a small vertical wind tunnel. All preparation steps for the measurements and the measurements themselves need to be done by you and your project group. First you will get some theoretical background to be able to operate the wind tunnel. After this you will do the measurements at different angles of attack and you will have to record the measurement results. Finally, you must process the results and do some exercises related to the wind tunnel experiment.

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Project manual AE1111-I – Exploring Aerospace engineering

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Theoretical background The wind tunnel The wind tunnel we use for the experiments is the TecQuipment AF10 Airflow Bench which is a simple vertical wind tunnel (see Figure 1). The wind tunnel generates a controlled airflow for various experiments with standard equipment.

Figure 1: The TecQuipment AF10 Airflow Bench

Principle of the wind tunnel The wind tunnel has a fan that draws air from the atmosphere and generates a flow along a pipe into a settling chamber (or air box) above the test area. In this settling chamber the flow is conditioned to produce a uniform laminar flow. Any unsteadiness or unevenness of the flow is further reduced by the increase of velocity towards the test section (the air is accelerated through a contraction). The velocity of the flow can be regulated by a valve that is positioned in the pipe. The rectangular exit at the end of the contraction is provided with quick release joints to which various test sections can be coupled. In the following experiment, such a test section is used.

Operating the wind tunnel All complementary assets of the wind tunnel are breakable and very expensive. So treat everything with utmost care! The wind tunnel has two important buttons:

 

Start-button: the black button on the right side below the wind tunnel Stop-button: the red button on the right side below the wind tunnel next to the black one

The valve of the wind tunnel can be set from 0 to 1. The setting 0 means the valve is near to close (low wind velocity), while setting 1 means the valve is completely open (highest wind velocity). Neither of these settings is very good when starting up the wind tunnel, therefore the

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setting of the valve is fixed and should not be changed! When you are ready to perform the tests, just press the start button and begin with the measurements.

Figure 2: Multi-tube manometer and the principle of reading pressures [Markland (2009)]

The multi-tube manometer The multi-tube manometer (Figure 2) is a manometer with fourteen tubes that can be connected to pressure tubes. Figure 2 is only meant to explain the principle of reading measurements from a manometer, it is not the actual set-up you will be using. The manometer liquid is water coloured by a dye, this to improve the visualization of the water height. The density of the water is not significantly altered by addition of the dye. The manometer can be used inclined to a suitable angle to increase sensitivity, however this is not necessary for the experiments we are performing. The reservoir of manometer liquid can be set to different heights to adjust to the experimental situation. Know the liquid height does not tell anything about individual pressures you want to measure! The only thing that you will be able to measure is the pressure difference that can be obtained by reading the shift in liquid height in the manometer tube. The reservoir connection must be left open to atmospheric pressure during the measurement. The pressures are not read directly from the level of the manometer. It depends on what quantity is desired. First the level (in mm) is read and then the pressure difference desired is calculated e.g. h p  h pt  p  pt [mm H2O)] (Figure 2). After that the pressure difference can be calculated using the conversion factor; pressure readings taken in terms of mm of water may be converted to units of N/m2 with the relationship: 1 mm water = 9.80665 N/m2

Description of the equipment For this experiment a module that houses a tapped aerofoil profile, as shown in Figure 3, is coupled to the wind tunnel exit. The layout of the module is indicated in Figure 4, Table 1 and Table 2. The aerofoil has 6 pressure holes on the upper surface and 6 on the lower surface. All pressure holes are connected to the manifold next to the test section, the manometer is connected to this manifold. The angle of attack of the aerofoil can be adjusted by simply turning the aerofoil (NOTE: turning the aerofoil clockwise represents a positive angle of attack).

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Figure 3: The TecQuipment AF18 aerofoil module [Markland (2009)]

Figure 4: The NACA0020 aerofoil [Markland (2009)] Table 1: Aerofoil model details Aerofoil type Aerofoil chord Aerofoil wingspan Effective surface area

NACA0020 63 mm 49 mm 0.0031 m2

Table 2: Tapping positions on the NACA0020 model Tapping number 1 2 3 4 5 6 7 8 9 10 11 12

Tapping position from the leading edge [mm] 2.2 3.9 6.1 8.7 11.8 14.8 20.0 25.6 31.4 37.3 43.4 49.4

Task 1: Exercises Divide exercises 1.1 – 1.7 among the different group members. Next to calculations you are also asked to make a sketch of the situation (like Figure 5) with all relevant numbers and parameters in it. Each subgroup should prepare a short presentation about the exercise they did for the rest of the project group. The purpose of the presentation is to tell the rest of the group how you have

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solved the exercise. Use the whiteboard to explain the steps you have taken. In the preparation you should think about how you are going to explain your work to the rest in a consistent way. 1.1

Explain why the width, A, of the tube in a manometer is not relevant in the calculations.

1.2

In Figure 5 you see a simple representation of the wind tunnel you will be using next week. It consists of a settling chamber and a convergent duct. A fan generates a flow in the settling chamber and due to the contraction, the air is accelerated through the duct. In the wind tunnel there are 3 pressure holes, one in the settling chamber ( P1 ), one in the contraction ( P2 ) and one in the duct ( P3 ). The pressure at point 1 and 3 is measured using a manometer. The pressures are measured with respect to the atmosphere and given in mm H2O. At point 1 there is a difference of 25mm and at point 3 there is no difference. It is further given that 1mm H2O is equal to 9.81N/m2 and the wind tunnel is located at sea level in a standard atmosphere on Earth. Assume that the cross-sectional area of the settling chamber is very large compared to the cross section of the duct.

Figure 5: Representation of a simple vertical wind tunnel

   

  1.3

Calculate the speed of the air in the duct. What assumption did you use? What is the Mach number of the airflow? Why is it not possible to use the pressure at point 2 instead of point 1 to calculate the speed of the air in the duct? Assume the wind tunnel is placed on the planet Mars. Calculate how high the pressure should be in the settling chamber to get the same speed as calculated earlier. Use the data for the standard atmosphere for Mars given in Excel sheet MarsAtmosphere.xls that can be found on BrightSpace. How much higher is pressure in the settling chamber with respect to the atmosphere (in %), on Mars? And on Earth? What is the speed of sound on Mars at sea level in the standard atmosphere described above?

Consider the incompressible flow of water through a divergent duct. The inlet velocity and area are 1.524 m/s and 0.929 m2, respectively. If the exit area is 4 times the inlet area, calculate the water flow velocity at the exit and the pressure difference between the exit and the inlet. (Based on question 4.1 and 4.2 from Anderson (2008))

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1.4

Consider an airplane flying with a velocity of 30 m/s at a standard altitude of 3 km on Mars. At a certain point on the wing, the airflow velocity is 35 m/s. Calculate the pressure and the Mach number at this point (use the speed of sound calculated in 1.2). (Based on question 4.3 from Anderson (2008))

1.5

Consider a low-speed wind tunnel with a nozzle contraction ratio of 1:20. One side of a mercury manometer is connected to the settling chamber, and the other side to the test section. The pressure and temperature in the test section are 1 atm and 300 K, respectively. What is the height difference between the two columns of mercury when the test section velocity is 80 m/s? (Question 4.18 from Anderson (2008))

1.6

A Pitot tube is mounted in the test section of a low-speed subsonic wind tunnel. The flow in the test section has a velocity, static pressure and temperature of 241.4 km/h, 1 atm and 21.1 °C, respectively. Calculate the pressure measured by the Pitot tube. (Based on question 4.20 in Anderson (2008))

1.7

A wind meter that is to be used on Mars is tested in a wind tunnel. The wind meter can measure dynamical pressure with an accuracy of 0.03 Pa. What is the minimum wind speed at which an accuracy in wind velocity of 10% is reached? Assume that the density is known without error.

Task 2: The wind tunnel experiment During this wind tunnel experiment you are going to perform measurements on a NACA0020 profile. You will be doing pressure measurements on the aerofoil at different angles of attack. These measurements will be further processed in the following chapter. During the experiment don’t forget to measure the air temperature [K], using the thermometer attached to the wind tunnel and the barometric pressure [N/m2]. The barometric pressure can

Figure 6: Connection of the AF18 module to the multitube manometer [Markland (2009)] be taken from the KNMI website observations for the location of Rotterdam. You need these data later to determine the air density.

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Before the measurements can be done, the aerofoil pressure holes should be connected to the manometer. Check if connections are done correct. To understand the results better, you should connect tappings 1, 3, 5, 7, 9 and 11 (lower surface) to the first set of manometer tubes. Tappings 2, 4, 6, 8, 10 and 12 (upper surface) can then be connect to the next set of tubes. The 13th tube should be left open so all pressures are shown with respect to the atmosphere. The final tube is used for measuring the static pressure in the airbox and at the inlet. This set-up can be seen in Figure 6. If the manometer is set-up correctly, you can start the wind tunnel, as described earlier. The valve controlling the flow is already open and should not be changed. Now the wind tunnel is running and ready for the measurements to start. You have about one hour to complete the measurements. The angle of attack of the aerofoil can be adjusted after loosening a screw at the back of the test section. For the first measurement set the angle of attack to 0° (zero). Do not forget to tighten the screw again. For the different angles of attack the following should be done (NOTE: all pressure measurements should be done with respect to the manometer tube with the atmospheric pressure) and in the following order:



  

Measure the ambient pressure, patm , and the air temperature, Tair . Since the wind tunnel draws its air from the room, the air temperature is assumed to be the same as the temperature in the test section. Connect the static pressure tapping at the top of the wind tunnel (air box) to the last manometer tube and measure the pressure, pt . Change from the static pressure tapping at the top of the wind tunnel to the static pressure tapping in the inlet and measure this pressure, p . Measure all the pressures from the tappings at the aerofoil.

Repeat all these measurements for the following angles of attack -5°, 0°, 5°, 12.5°, 20° and 25°. This brings the amount of measurements, including the first measurement at 0°, to 6 in total. You can write your measurements down in a table like Table 3, use for every measurement a new table. The grey cell in the table should be filled out during the measurement. A sheet with tables where you can enter your measurements should be available at the wind tunnel. Also at high angles of attack, you will see that the pressure changes abruptly. Write down the angle of attack at which this happens. Also write down the pressure distribution (from the manometer) for this angle of attack. Remark: please note the behaviour of the surface mounted tuft during the measurements as this may indicate flow separation (further discussed later on)

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Table 3: Results wind tunnel measurements Angle of attack,  [] Air temperature, Tair [K] Ambient pressure, patm [N/m2] Tapping hp h p - h patm No. [mm H2O] [mm H2O]

p  patm [N/m2]

p [N/m2]

pt p 1 3 5 7 9 11 patm 2 4 6 8 10 12

Task 3: Results of the wind tunnel experiment The following questions must be worked out after the wind tunnel experiment in the project room. 3.1

For the measurements you did at the wind tunnel, you must calculate the pressure p in N/m2 for all tappings on the aerofoil, in the airbox (p0) and the inlet (p∞). Use the intermediate steps indicated in the table. This is a similar exercise as you have done in task 2.

3.2

To check the behaviour of the pressure distribution over the model you should draw the data points in a figure like Figure 7 (available on BrightSpace) or in a likewise plot. Each group should draw the pressure distribution at a different angle of attack.

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Figure 7: Sample figure for the pressure distribution over the NACA0020 profile 3.3

Calculate the Mach number in the inlet. Considering this, is it allowed to assume incompressible flow?

3.4

Where would you expect the highest Mach number at aerofoil? How high is it? At which angle of attack? How much higher is it compared to the flow at the inlet?

3.5

Calculate the Reynolds number. Can you achieve the same Reynolds number on Mars (use the excel sheet MarsAtmosphere.xls)?

3.6

What diameter should a wind tunnel for Martian conditions have, to achieve laminar flow at 10 m/s? (Note: assume that turbulent flow occurs for a Reynolds number larger than 104). Which wind tunnels (see section ‘About the AE1111-I project’) that simulate Martian conditions will likely exhibit turbulent flow?

3.7

What happens at high angles of attack? How can you see that in the pressure distribution?

3.8

Why is water and not Mercury used in the measurements of pressure differences? What are the advantages of water in comparison to Mercury? When would you use Mercury?

Now the pressure distribution has been determined along the aerofoil, it is an easy step to convert this into forces, such as lift and drag. These topics will be treated in the subsequent chapters. A well-constructed Excel sheet might come in useful, as future exercises may need to be added and that the Excel sheet may need to be updated.

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LI

2017/2018

Lift and weight

A flying wing needs lift to stay in the air. This lift is generated by a distribution of pressure over the wing. You have learned about the pressure distribution along an aerofoil in the previous chapter.

Part 1 - Lift distribution In the previous chapter, you have measured pressure distributions of an aerofoil at different angles of attack. The next step is to use these pressure distributions to determine the lift coefficient of the aerofoils. In this chapter, you will learn how this can be done. After this we will look at the relation between the lift coefficient and the angle of attack of a certain aerofoil. You will probably guess that the lift will increase when the angle of attack increases. But will this also follow from the measurements and calculations? And how will a plot of the lift coefficient as a function of the angle of attack look like? When you finished this chapter, you will have the answers to these questions.

Part 2 – Lift and weight In a few weeks you will have to design your flying wing. To be able to make choices about the design parameters of the aircraft (wingspan, chord length, thickness, sweep, etc.), you should understand what influence these parameters have on your flight performance. In this chapter, we will focus on the lift and weight of the aircraft. In this respect the main question to be answered is: will the wing generate enough lift to counteract the weight of the aircraft? If this is not the case the aircraft simply will not fly. At the end of this chapter you will be able to estimate the lift force of your flying wing.

Learning objectives

Schedule

The student should be able to:  Understand the relation between pressure distribution and lift.  Convert the pressure distributions to lift coefficient.  Get insight in the typical lift curve of 2-dimensional aerofoils.  Understand the balance between wing lift and weight.  Understand the difference between infinite and finite wings.  Build a (well structured) excel sheet for lift analysis.  (30 min.) Preparation and familiarizing with the theory, including reading the related chapters in Anderson (2008).  (15 min.) Divide tasks amongst group members.  (165 min.) Work out tasks.  (30 min.) Share results amongst group members

Make sure that you write clearly on everything you hand in who has worked on it.

Deliverables      

Worked out exercises and produced graphs [Task 1, 2, 3 and 5]. Lift curve and important values (Table 2) of NACA 0020 with the entire group [Task 3.1 and Task 4]. Worked out calculation of [Task 5]. Worked out calculation of E and the total excel sheet (lift and weight) [Task 6 and 7]. Table with the results for lift and weight [Task 8 and 9]. Clear table containing work and hour distributions of all team-members.

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Theoretical background Pressure coefficient

Start with reading Chapter 5.6 of Anderson (2008) to get familiar with the definition of pressure coefficient. You should be able to find and understand the following formula for the pressure coefficient:

C  p

( p  patm )  ( p  patm ) p  p p p      q q 1  V2   2  

(1)

Where:

Cp p p q

= Pressure coefficient (dimensionless)



= Density (kg/m3)

V

= Undisturbed free stream velocity (m/s)

= Pressure at a given point (tapping) (N/m2) = Undisturbed static pressure (N/m2) = Undisturbed dynamic pressure (N/m2)

The aerofoil is in a duct in which the boundary layer thickness over the wall increases. This gives a smaller effective area around the aerofoil, leading to a free stream velocity which is, in stream wise direction, higher at the aerofoil than it is at the inlet. This can be explained using the continuity equation as shown in Chapter 2 of Anderson (2008). To correct for this, you must find the ‘effective static pressure’ ( peff ), around the aerofoil, and then use this to find the correct free stream velocity around the aerofoil. To find the effective static pressure, you must interpolate between the duct inlet pressure (some distance in front of the aerofoil) and atmospheric pressure (behind the aerofoil). This means that you assume the pressure as a function of distance from the inlet to the outlet to be linear. Now you will be able to estimate the effective pressure at each point between the inlet and the outlet. The duct inlet tapping is 135 mm upstream of the exit of the duct. The centre of the aerofoil is 85 mm downstream from this tapping. So:

peff  p 

85  ( patm  p ) 135

(2)

where p is the pressure at the duct inlet and patm is the atmospheric pressure. For each angle of attack, you can use peff to find the correct free stream velocity ( V ) with Bernoulli’s equation:

1 pt  peff  V2 2

(3)

For each tapping point on the aerofoil, find the pressure coefficient with the equation for pressure coefficient as mentioned above using:

Cp 

p  peff 1 V 2 2 

Where p is the pressure measured at a specific tapping.

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Lift coefficient The next step is to use pressure distributions to calculate the lift coefficients of the different aerofoils under different angles of attack. The definition of lift coefficient should have been treated in the lectures, but if the meaning of lift coefficient is still a bit vague for you, start with reading Chapter 5.3 of Anderson (2008). Read Chapter 5.7 of Anderson (2008) as well. Here you can find that the area between the two curves (upper and lower surface) in the pressure distribution graph is equal to the normal force coefficient. In other words, the integral of the upper surface Cp-curve minus the lower surface Cp-curve gives the normal force coefficient. This is represented by the following formula: c

cn 

1 x C p ,l  C p ,u  dx    C p ,l  C p ,u d     c0 c 0 1

where cn is the normal force coefficient, c the chord length, coefficient curve and

(5)

C p ,l the lower surface pressure

C p ,u the upper surface pressure coefficient curve. The next step is to

convert this normal force coefficient into a lift coefficient. In Anderson (2008) you can find that these terms relate as follows: cl  cn cos   ca sin  (6)

cl is the lift coefficient,  is the angle of attack and ca is the axial force coefficient (also often symbolized as ct ). In Anderson (2008) it is stated that for small angles of attack Where

(   5 ) you can assume that 0

cl  cn , since then cos   1 and sin   0 . Although some of

your measurements were performed at angles of attack higher than 5 degrees, for simplification you can assume cl  cn in all your calculations. Know this assumption is not allowable in more advanced aerodynamic experiments, since it can differ greatly from the real case! In the previous chapter, you have learned to determine the lift coefficient of an aerofoil from its pressure distribution. The next step is to convert this lift coefficient to a lift force. In Chapter 5.3 and 5.4 of Anderson (2008) you can find the following relation:

L  CL

1 V 2 S 2

(7)

Where:

L 

= Lift force [N] = Air density [kg/m3] (varies with altitude)

V CL S

= Flight speed [m/s] = Lift coefficient [dimensionless] = Wing area [m2] Figure 1: A380 in cruise flight

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Tasks Task 1: Compute the pressure distributions of the wind tunnel experiment Perform the following two subtasks for all 6 different angles of attack that where measured in the wind tunnel. Use Excel for your calculations and plots. A typical form of a pressure distribution on an aerofoil can be found in Chapter 5.7 of Anderson (2008). Make sure that eventually all angles of attack are covered, since they are needed in Task 3.

 

Calculate the pressure coefficients of all measured points along the surface Make one graph of the pressure distributions over both the upper and lower surface. Plot negative C p in the positive y-direction. Connect the points with straight lines.

Task 2: Exercises Now you should have 6 graphs of pressure distributions of the aerofoil measured in the wind tunnel, each for a different angle of attack. Answer the following questions: 2.1

Why do we plot C p (negative) instead of

2.2

At which Mach number did you perform the wind tunnel experiment? What would happen with the pressure distribution graphs if your measurements where performed at (a) half this speed and (b) Mach 0.8?

2.3

Is there a relation between the location of the thickest part of the aerofoil and the lowest pressure (in your data)? Explain.

2.4

What is the highest value of

C p (positive) upward?

C p that is to be found in the test and why? How do we call

this point on the aerofoil?

Task 3: Compute the lift coefficients and the lift curve 3.1 



Wind tunnel experiment In Task 1 you have produced graphs of the pressure distributions over the upper and lower surface of the aerofoil, at six different angles of attack. Use the theory above to determine the lift coefficient at each angle of attack. Combine the results to plot these 6 lift coefficients as a function of the angle of attack, using Excel.

3.2 MH44 with use of the Trapezoid Rule Download the file ‘PressureDistributionMH44.xls’ from BrightSpace (AE1-100 -> Course Documents). In this file you will see the following column titles: Table 1: Part of ‘PressureDistributionMH44.xls’

Upper Surface x/c 0 0.00505 0.01449 0.0282 ………..

Cp 0.99093 0.58711 0.20079 -0.06389 ………..

Step size

Average height

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As you can see the first two columns are already filled in. The first column represents the tapping position from the leading edge, divided by the chord length. The second column is the pressure coefficient at that tapping position. The pressure distribution can be plotted with this information. Further down the excel sheet (not visible in the table above), also the pressure coefficients of tapping points on the lower surface are given. This pressure distribution will be integrated using the Trapezoid Rule, which is explained in Appendix A of this reader. Be aware that the step size between the tapping points (referred to as h in Appendix A) is not constant! Therefore Equations A.5 and A.6 are not valid.



Plot the pressure distribution from the provided data in excel. Upper and lower surfaces should be plotted in the same graph.



Use the Trapezoid Rule to find the lift coefficient of the MH44 aerofoil. The three column titles are given to point you in the right direction.

3.3

Pressure distribution given by a function

In some cases, it is useful to evaluate theoretical pressure distributions which are given by a function. By integration of that function it is then possible to get an exact result for the lift coefficient, instead of an estimation by using the Trapezoid Rule or another method. Consider an aerofoil under zero angle of attack with chord length c and the running distance x measured along the chord. The leading edge is located at x / c  0 and the trailing edge at x / c  1 . The pressure coefficient distributions over the upper and lower surfaces are given, respectively, as: 2

 x C p ,u  1  200   c x C p ,u  2.47  2.63   c  x C p ,l  1  0.84   c 

x  0.13 c x for 0.13   1.0 c x for 0   1.0 c for 0 

Calculate the lift coefficient. Type out your calculation steps clearly.

Task 4: Determine important values from the lift curve From a lift curve, some important characteristics of an aerofoil can be determined. One is the angle of attack at which no lift is generated (  L 0 ). Another one is the lift slope ( dcl / d ) When these two values and the angle of attack are known, the lift coefficient can easily be calculated:

cl   

dcl (   L 0 ) d

(8)

Of course, this function only holds for the linear part of the lift curve! Another important property of an aerofoil is the maximum lift coefficient ( cl ,max ). This is the top of the lift curve. Evaluate the lift curve of the aerofoil tested in the wind tunnel to determine the three characteristics mentioned above.



Fill in the table on the next page.

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Table 2: Lift curve characteristics NACA 0020 (Wind tunnel)

cl 0 dcl / d clmax Task 5: Exercises Answer the following questions:



Does the NACA 0020 profile have a lift curve which is going through the origin? Explain why lift curves of certain aerofoils go through the origin and others do not.



Which phenomenon occurs when the angle of attack gets too high? Make a sketch of the flow of this for a sample aerofoil.



What is the ratio of the lift coefficients on Mars and on Earth for an aircraft with the same mass, wing surface area and cruise speed?



Search your book and the internet for the theoretical value of the lift slope ( dcl / d ) for thin aerofoils. Does this value agree with the value you have found for the NACA 0020 aerofoil?

Task 6: Determine the lift coefficient of a solar airplane on Mars in cruise flight Consider the Sky-Sailor autonomous solar powered Martian airplane with characteristics given in the paper Noth et al. (ASTRA proceedings, 2004):



Draw the forces acting on an aircraft in flight. Determine the relations between those forces in steady horizontal flight.



Calculate the lift coefficient of the Sky-Sailor in cruise flight.

Theoretical background Infinite and finite wings

In the Wind Tunnel Experiment 2D you tested a so-called infinite wing, since the wing was clamped between the walls of the wind tunnel. However, the flying wing will be a finite wing, since it has wing tips. Chapter 5.13 of Anderson (2008) explains the difference between the lift coefficient of an infinite and a finite wing. Read this chapter before you continue. With the aerofoil lift coefficients found in the previous chapter we can calculate the lift per unit

span:

L ( per unit span) 

1 V 2cl c 2

(9)

where c is the chord length. You should understand now that we cannot just multiply the lift per unit span with the wingspan to find the total lift:

L  L ( per unit span)  b 26

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L

1 V 2cl S 2

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(11)

Figure 2: Representation of a lift distribution over an infinite wing (left) and a finite wing (right) The only difference between equations 7 and 11 is the lift coefficient. The aerofoil lift coefficient (Cl) is not equal to the wing lift coefficient (CL). As we will see later the lift distribution of a straight finite wing can sometimes be approximated by an elliptical distribution (see chapter 5.14 of Anderson (2008)). This elliptical lift distribution can now be used to model the actual lift distribution over your wing. We can use this model to estimate the relation between the aerofoil lift coefficient and the wing lift coefficient. Shown on the left side of Figure 2 is the case when a section of an infinite lift distribution is assumed. On the right side an elliptical lift distribution is shown. This is a far more realistic representation of the actual lift distribution over a finite wing. Note that the maximum lift per unit span lift (in the middle of the wing) of the elliptical lift distribution is equal to the lift per unit span of the infinite lift distribution. Let us define E as a factor that relates the area of the elliptical lift distribution to the infinite lift distribution:

E

Ainfinite Aellipse

(12)

Where Aellipse is the surface area of the elliptical lift distribution and Ainfinite the surface area of the infinite lift distribution (dashed area in Figure 2). Since the surface of the lift distribution represents the total lift of the wing, the following relation can be found (using Equation 9):

1 V 2bc c  l E 2 1 CL V 2 S CL 2

cl

(13)

So, if we can determine a value for E and the aerofoil lift coefficient (cl) is known, the wing lift coefficient (CL) can easily be calculated. For reference, further information about the relations between infinite and finite wing can be found in Chapter 5.13 and 5.15 of Anderson (2008).

Weight After you finished the design your flying wing will be cut out from a block of foam. This is not the usual foam used to isolate houses, but a special engineered plastic foam material which is a lot stronger and less brittle than the usual foam. This very light weight material is called EPP (Expanded Polypropylene) and has a density of 20 kg/m3.

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Next to the weight of the wing itself the following items should be added to calculate the total weight of the aircraft: - Battery - Propellers - Electronics The total mass of these three items is 17 grams. Keep in mind that it could be possible that more weight must be added to the aircraft in a later stadium, i.e. stabilizing fins or duct tape.

Task 7: Build an Excel sheet which calculates the total lift force

V∞

c

S

b Figure 3: Top view of the flying wing

Chord line

c

V∞ α 

Figure 4: Side view of the flying wing In this task, you will have to build an Excel sheet which calculates the total lift of the flying wing when all parameters are known. Consider your aircraft as a rectangular wing with a certain airspeed under a certain angle of attack, as shown in Figure 3 and Figure 4. Your Excel sheet should contain only the following input variables: - Factor between elliptical and infinite lift distribution (E) [dimensionless]

Dimensional characteristics -

Chord length (c) in [mm] Wingspan (b) in [mm]

-

Zero-angle-of-attack lift coefficient (cl(α0)) [dimensionless] Lift slope (dcl/dα) in [rad-1]

Aerofoil characteristics Flight characteristics -

Airspeed (V∞) in [m/s] Angle of attack (α) in [rad] Air density (ρ) in [kg/m3] Gravitational acceleration (g) in [m/s2]

With these variables, the following parameters should be calculated: - Wing area (S) in [m2] - Wing lift coefficient (CL) [dimensionless] Perform the following subtasks:

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 

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Build the excel sheet capable of calculating the total lift force in Newton. Make sure your sheet is well structured; it should be clear which values are input variables and which values are calculated. Calculate E using Equation 12.

Task 8: Extend your Excel sheet with weight calculation Add the following input variables to your excel sheet: - Area of aerofoil (Aaerofoil) in [mm2] - Density of EPP (ρEPP) in [kg/m3] - Weight of battery, propellers and electronics (Wbpe) in [g] - Extra weight (Wextra) in [g]

Figure 5: NACA 0020 aerofoil To estimate the area of the aerofoil ( Aairfoil ) you can use the ratio between the maximum thickness ( tmax ) and chord of the aerofoil. The ratio is given by the aerofoil name: NACA 0020 means that the percentage of thickness to chord is 20%.



Extend your Excel sheet so it calculates the weight of the aircraft in Newton.

Task 9: Calculate lift and weight with use of excel sheet Consider two rectangular wings flying in a standard atmosphere on sea level with the characteristics as stated in Table 3. Table 3: Characteristics of two flying wings Flying Wing 1 Flying Wing 2 Aerofoil NACA 0020 NACA 0020 Wingspan 600 mm 400 mm Chord 120 mm 75 mm Airspeed 3 m/s 6 m/s Angle of attack 3° 3°



Calculate the lift and weight (in Newton) of both flying wings, using your Excel sheet. Check with your fellow group members if everyone has found the same results.

Lift and weight have now been discussed thoroughly, but how about the drag an aircraft has to overcome? Furthermore, lift and drag may also contribute to the longitudinal stability of the aircraft. This will be treated in the next chapter.

References Noth, A, Bouabdallah, S, Michaud, S, Siegwart, R, Engel W, 2004, The design of an autonomous solar powered Martian airplane, In: Proceedings of the 8th ESA Workshop on Advanced Space Technologies for Robotics, (ASTRA 2004), Noordwijk, Netherland,2004

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DR

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Drag and Longitudinal stability

As discussed in the previous chapter, there are four forces acting on an aircraft. Lift and weight have been treated already and in this chapter, drag and thrust will be discussed. On aircraft, such as flying wings, drag is considered unwanted as it needs to be overcome by thrust. Thrust is generally created by either a piston engine or a jet/turbofan engine. Both come in many different variants, but that is not the scope of this chapter. The student should be able to:  become familiar with the concept of drag and be able to Learning explain which contributions make up the drag on a wing objectives  Calculate the total drag of a wing  Get insight in the drag behaviour of a 3-dimensional wing  Be familiar with the concept of (longitudinal) stability.  Describe how longitudinal stability can be achieved.  (30 min) Preparation and familiarizing with the theory, including reading the related chapters in Anderson (2008) Schedule  (15 min) Divide the tasks over the group  (45 min) Extend the excel sheet with drag and thrust calculations  (120 min) Working out the exercises.  (30 min) Present results.

Make sure that you write clearly on everything you hand in who has worked on it.

Deliverables    

Excel sheet with the drag/thrust calculations (hand in digitally) [Task 1 & 2] Worked out exercises [Task 3] Worked out exercises and produced graphs per sub group [Task 4]. Clear table containing work and hour distributions of all team-members.

Theoretical background of drag Let us first consider drag. The more drag an aircraft experiences, the more thrust is needed to propel the aircraft. So, for an aircraft designer it is important to try to minimize the drag of an aircraft. But what is drag, which components does drag have? In the next section only a short summary on drag will be given. The related chapters in Anderson (2008) where more information can be found, are indicated in the text.

Infinite wing In the previous chapter the step has been made from an infinite to a finite wing, here we first take a step back and consider again an infinite wing, the drag for such a wing consists of three parts. D  D f  D p  Dw (1) where:

profile drag

D

= total drag

Df

= skin friction drag

Dp

= pressure drag due to flow separation

Dw

= wave drag

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The wave drag can be neglected at subsonic speeds, it only plays a role at transonic and supersonic speeds. The remaining drag components are called the profile drag, because both heavily depend on the shape of the object. The skin friction drag (Df) is present because the airflow over a solid object creates a boundary layer. For a detailed explanation, please read the related Chapters (3.15 – 4.17) in Anderson (2008) on viscous flows and laminar- and turbulent boundary layers.

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Figure 1: flow separating at high angle of attack

The final contribution to the drag comes from the separation of the flow over a surface. If you look at a wing with a high angle of attack, it is possible the flow is not able to follow the shape of the aerofoil and separates at a certain location (Figure 1). This separation causes a large decrease in lift and an increase in drag and is something that should be avoided. More on pressure drag can be found in Chapter 4.20 in Anderson (2008). Measurements on drag of a wing can easily be done in a wind tunnel, but exact calculations are much harder to perform. For the skin friction in a laminar boundary layer, there are formulas from laminar boundary layer theory to calculate the drag. But for turbulent boundary layers there is no such theory. Turbulent boundary layers and their drag can only be estimated by approximate formulae, derived from experiments. Also, pressure drag due to separation cannot be calculated exactly. Although it must be said that nowadays numerical calculations can approximate the reality very well.

Finite wing If we now go back to the finite wing, there is another contribution to the total drag. This is caused by the fact that a wing is finite and that there is a pressure difference between the upper and lower surface. Due to this pressure difference some air will flow around the tips from the high pressure to the low-pressure side. This flow will create a circular motion that trails down from the wing tips. This motion is called a vortex. Due to these vortices, the oncoming flow of air near the wing will be tilted slightly down, this is called the downwash. This has two effects, the angle of attack of the aerofoil is reduced, with respect to the undisturbed flow, due to the downward component of the oncoming flow. The second effect is an increase in drag, called the induced drag. This induced drag has at least three physical interpretations:

  

The vortices change the pressure distribution over the wing, which leads to an increase in drag Due to the downwash and the change in stream direction the lift vector is tilted back slightly. Therefore, a contributing component in the drag direction occurs. The circular motion of the vortices themselves contain a certain amount of energy, which has to come from somewhere and thus is a source of drag

More on induced drag can be found in Chapters 5.13 and 5.14 in Anderson (2008), please study this carefully. The derivation of the formula for induced drag coefficient is given in Chapter 5.14 and will not be repeated here, only its final form will be given.

CD,i 

CL2  eAR

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In this formula, the e is the span efficiency factor and is an indication how much induced drag a wing has. For wings with an elliptical lift distribution this e equals 1 and it is smaller than 1 for all other wings. Wings with elliptical lift distribution therefore have the lowest induced drag. For typical subsonic airplanes e ranges from 0.85 to 0.95. AR stands for the aspect ratio, which is defined as b2/S, where b is wingspan and S the total wing area. So a slender wing (high AR), like a glider, has a low induced drag. Another important conclusion that can be drawn from the equation is that the induced drag coefficient varies with the square of the lift coefficient. This means that at high lift coefficients the induced drag will be very significant. To conclude, the total drag coefficient for a finite wing at subsonic speeds is

CL2  eAR

(3)

D  12 V 2 SCD

(4)

CD  cd  The total drag is defined as

Figure 2: A practical NASA study on the effects of wing tip vortices

Theoretical background of longitudinal stability If you have ever flown with a model aircraft, you will know that stability is a very important issue. The best pilot in the world could not fly an unstable airplane without the help of an autopilot. Although some fighter aircraft are made intentionally less stable to achieve high manoeuvrability, your flying wing should be stable if you would like to fly with it. In this chapter, some basic topics concerning stability will be treated. To get some insides into the longitudinal stability of aircraft, three concepts are introduced in this chapter. Much more information on (longitudinal) stability can be found in Anderson (2008), other books in the library and on the internet. Although this subject is not an aerodynamics subject, you should know something about stability to be able to make a good design for your flying wing. Stability of aircraft will be further treated during the rest of your studies.

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Centre of mass In general, the centre of mass (or when in a uniform gravitational field, the centre of gravity) of a system of particles is a specific point at which, for many purposes, the system's mass behaves as if it were concentrated. When the system consists of different particles, the position of the centre of mass is only a function of the mass and relative position of all the particles. When the system is a rigid body, the position of its centre of mass is fixed in relation to the object. But because the mass within the rigid body may not be uniformly distributed, the centre of mass does not need to coincide with geometric centre of the body. The centre of mass is very important for the design of aircraft. The centre of mass must lie within certain limits, because when it is outside these limits the aircraft may become unstable. L

Mac

ac cg

D

cp

W Figure 3: Typical position of Aerodynamic center, center of gravity and center of pressure on a flying wing

Aerodynamic centre Consider the pitching moment of an aircraft. For the aircraft to pitch, the forces on the aircraft need to create a moment. This moment can be taken around any arbitrary point on the aircraft, for example the nose of the aircraft, the leading or trailing edge of the wing. However, there is a point on the aircraft around which the (pitching) moment is independent of the angle of attack. This point is defined as the aerodynamic centre of the wing (Figure 3). The aerodynamic centre is a very important point when considering the stability of an aircraft. More information can be found in chapter 7.3 of Anderson (2008).

Longitudinal stability Any vehicle moving in a direction and with a certain speed will be subjected to forces that will change that direction and speed. If after such a disturbance the vehicle has the tendency to return to its original direction and speed, the vehicle is called statically stable. If the disturbance causes the vehicle to further change direction and speed, the vehicle is called statically unstable. If none of the above happens and the vehicle doesn’t change direction or speed, it is called statically neutral (Figure 4). For aircraft, it is very important that they are statically stable, otherwise the pilot will have a great deal of trouble keeping the aircraft in the air.

Figure 4: Illustration of static stability; from left to right: stable, unstable, neutral Longitudinal stability is considered in this chapter. Longitudinal motion is the pitching motion about the y-axis of an aircraft (Figure 5). If an aircraft is longitudinally stable a positive change in angle of attack will create a negative pitching moment and will decrease the angle of attack. There is a lot of information on the internet on longitudinal stability of flying wings. This is a good website which offers you some more insight in the subject (http://mh-

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aerotools.de/aerofoils/flywing1.htm), but you can of course also look for yourself or read Anderson (2008) chapter 7.5.

Figure 5: Definition of the airplanes axis and the translational and rotational motions (Anderson (2008)) Besides having longitudinal stability, the airplane should also be stable about its other axes. This is called roll stability and yaw stability. These will not be treated here, but when you are going to choose your final design and during the production of your flying wing, you will be supplied with hints and tips on how to improve your roll and yaw stability.

Pitching moment coefficient You should have done some more research on stability of aircraft by now and you should have seen that the pitching moment coefficient is very important for longitudinal stability. For most aerofoils this moment coefficient is negative and that has certain consequences for the layout of your airplane. As you could have seen on the website mentioned before, an aerofoil with positive pitching moment coefficient is preferred for a flying wing in order to create longitudinal stability. This is very important to remember, as some exercise below cover this. You should also remember this for the final design of your flying wing.

Tasks Task 1: Extend the excel sheet from the previous chapter so it can calculate the total drag In the previous chapter, you have created an excel sheet with which you can calculate the total lift your flying wing will produce. Now you are going to extend this sheet, using the formulas in this chapter, so it can also calculate the total drag. You will need some extra input variables and others that are already in your Excel sheet. Add the following input variables to your Excel sheet and make sure that it stays well structured: - Add the average profile drag ( cd ) [dimensionless]

cd = 0.03

-

Add the average span efficiency factor ( e ) [dimensionless] e = 0.95

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Perform the following subtasks:  Calculate the aspect ratio (AR)  Now you have all the variables to first calculate CD [dimensionless] and then the total drag in Newton. To make the calculations not too complicated, you have been given a single average value for the profile drag. In real life, this is of course not the case and the profile drag is dependent on several variables, like the aerofoil itself, the surface quality, the lift coefficient etc. It should also be noted that the selected profile drag coefficient of 0.03 is an approximated value. You will see in later lectures that the estimation of aerofoil characteristics at low Re-numbers (below Re = 150000) is extremely difficult; both numerically and experimentally. Be aware of this and remember that for now the profile drag is constant only to keep the calculations manageable.

Task 2: Incorporate thrust in the Excel sheet Your flying wing will be powered by two small electro motors that drive two propellers. These are the same as being used in model aircraft you can buy in the store. These engines are powerful enough to fly your flying wing at 50% throttle. Measurements have shown that these propellers give approximately 15 gr. of thrust in total. This is the maximum value (full throttle) in cruise flight. The thrust can be significantly different. For example, when the batteries are not fully charged, the propellers are not optimally mounted, or the thrust is influenced by other external variables. For now, it is important that you include the thrust in your Excel sheet, so that you can compare the amount of thrust with the amount of drag to see if your flying wing will be able to fly.

Task 3: Exercises 3.1

For the two wings in Task 8 of Lift and Weight calculate the total drag using your Excel sheet. Check your results. Is the difference between the two wings in the same order as it was for the lift? Why or why not? Try to explain which parameters influence drag.

3.2

If you look at the equation for induced drag, you see that there are two ways to control the induced drag. Either you lower the lift coefficient, but if you lower it too much, you will not be able to fly. The other thing you can do is to increase your aspect ratio. You can see this effect in glider planes, these have very slender wing to decrease the drag. Why isn’t the same being applied to commercial aircraft? Mention at least three issues in different areas.

3.3

Estimate the wing span of a Boeing 747 if it would have the same aspect ratio as a glider (take AR=20), but still produced the same amount of lift. Use calculations to demonstrate your estimation.

3.4

The Cessna Cardinal, a single-engine light plane, has a wing area of 16.2 m2 and an aspect ratio of 7.31. Assume the span efficiency factor is 0.62. If the airplane is flying at standard sea-level conditions with a velocity of 251 km/h, what is the induced drag when the total weight is 9800N? How much is the induced drag when the considered Cessna is flying at stall speed, flaps down at sea level (85.5 km/h)? (Question 5.21 and 5.22 from Anderson (2008))

3.5

Consider a finite wing with an area of 21.5m2 and an aspect ratio of 5 (this is comparable to the wing on a Gates Learjet, an executive twin-jet). Assume the wing has an NACA 65-210 aerofoil, a span efficiency factor of 0.9, and a profile drag coefficient of 0.004. If angle of attack, calculate CL and CD . the wing is at 6 (Question 5.23 from Anderson (2008))

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Task 4: Exercises How is in a conventional airplane the longitudinal stability achieved? 4.1

What problems with longitudinal stability arise when designing a flying wing?

4.2

How can these problems be solved? Focus especially on different kind of aerofoils. Also make a free body diagram to show why certain aerofoils can’t provide longitudinal stability and others can.

4.3

Can a tailless aircraft be made longitudinally stable by applying sweep? Explain why or why not.

4.4

How is a canard used to achieve longitudinal stability in a delta wing aircraft like the Eurofighter Typhoon (Figure 6)?

4.5

Draw a swept flying wing in a (3-dimensional) body fixed reference frame and indicate the following points  Centre of gravity  Aerodynamic centre  Centre of pressure Also draw the weight- and lift forces and the moment coefficient around the y-axis at the correct location. Use this figure to indicate how longitudinal stability is achieved.

Lift, weight, drag and lateral stability have been explained and questions have been answered about these topics. The only force yet to explore is the thrust force. This will be explored in the next chapter, closing the sequence of chapters on forces.

Figure 6: The Eurofighter Typhoon with its delta wing and full movable canards (www.eurofighter.com)

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TH

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Thrust

Your flying wing uses an electrically driven propeller for thrust and control. The amount of thrust and power the propeller generates depends on the airspeed, the rotational speed, the size and pitch of the blade. For this practical the group will perform wind tunnel measurements on propellers powered by an electrical engine, in order to create performance diagrams of the propellers. Additionally, the measurement results will be compared to theoretical results which are obtained using the blade element method, combined with momentum theory.

Learning objectives

Schedule

The student should be able to:  Know the following parameters; Power available (Pa), Shaft power (Pbr) and propulsive efficiency.  Understand the relations between Thrust, propulsive efficiency, Pa, Pbr and the airspeed.  Gain understanding in the effects of changes in key propeller design parameters, such as blade pitch and rotational speed, on the performance of propellers.  Use blade element theory to perform basic performance calculations on propellers.  (15 min) Preparation and familiarizing with the theory.  (15 min) Divide the tasks over the group  (90 min) Do measurements in the wind tunnel.  (90 min) Work out the exercises (could be before tunnel).  (30 min) Discuss results.

Make sure that you write clearly on everything you hand in who has worked on it.

Deliverables   

Propeller performance diagrams o theory and o measurement results Answers to the questions of Task 3. Clear table containing work and hour distributions of all team-members.

Tasks Please follow the instructions of the student-assistant/mentor during the wind tunnel measurements. For the theoretical analysis, a brief explanation of the blade element method is given below. However, you are encouraged to look up the given reference, or any other source of information for more detailed information.

Task 1: Wind tunnel measurement You are asked to produce: (1) Thrust vs. Velocity, (2) Power available vs. Velocity, and (3) Propeller efficiency vs. Velocity graphs for the combination of propeller and motor used in the test set-up. To do so, you can either record the values of the different variables by hand, or input them directly into a program like Microsoft Excel, if you have a laptop available. The plots are to be created for different engine settings, e.g. 20%, 40%, 60%, 80% and 100% of maximum shaft rotational speed. The parameters measured are the velocity [m/s], the thrust [g], the voltage [V], the current [A] and the propeller speed [rpm]. Please keep in mind that some of the parameters need to be converted to the correct units for some of the calculations. The propulsive efficiency of a propeller is defined as the ratio of power available over shaft power (Ruijgrok, 2009).

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j 

2017/2018

Pa T  V0  Pbr Pbr

(1)

In which Pbr can be calculated using:

Pbr  M  

(2)

Where M is the torque [Nm] applied to the propeller and ω is the shaft speed [rad/s]. For the motor used, the output torque can be approximated by rewriting the following formula (Maxon Motor, 2008), see also Figure 1.

n  n0 

n M M

(3)

Rotational speed n

n0

n

U>Un

M

U=Un Torque M

Figure 1: Speed-Torque line provided by Maxon Motor (2008) Where n and n0 are the shaft speed and the shaft speed at zero torque, respectively. Their units are in [rpm]. The units of

n are [rpm/Nm] and those of M are in [Nm] respectively. M

Furthermore, the following relation is given (Maxon motor, 2008):

n0  U  kn

(4)

Here, U [V] is the applied voltage and kn [rpm/V] is the speed constant. Data for the motor, provided by the manufacturer, is summarized in Table 1, including the constants needed in the previous equations. Table 1: Motor data, supplied by Manufacturer Maxon Motor RE 310007 Max permissible speed 12000 [rpm] Stall torque 1020 [Nm] Speed constant 369 [rpm/V]

n M

8.69x103 [rpm/Nm]

As a final step, you are asked to calculate the maximum possible theoretical propeller efficiency, by using the measured thrust. To do this you can use the momentum theory, as explained in

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(Ruijgrok, 2009, p140-143). To obtain a value for the density, you can assume ISA conditions along with the assumption that the wind tunnel is situated at sea level.

Task 2: Theoretical Calculations

The method you are going to use for the theoretical calculations is the blade element theory, combined with momentum theory, as explained in (Ruijgrok, 2009, p140-143). The blade element method is a numerical integration technique; meaning that in order to calculate the thrust (=component of the lift) generated by a propeller blade, the propeller blade will be divided into several smaller sections; each considered to have its own constant wing section. Lift and drag of each element are calculated using two-dimensional aerodynamics. Next, the lift and drag of all blade elements, are summed up (numerical integration) to obtain the thrust and torque of the complete propeller blade. So instead of performing calculations on the entire blade, which has variable chord lengths, variable twist, variable wing profiles, etc; we simplify the blade by assuming that it can be modelled by several separate sections with constant parameters. Of course, this means that we are approximating the actual thrust and that there will be a difference between the calculated and actual thrust. This difference can be reduced by increasing the number of sections. More on numerical integration techniques will follow in 2nd and 3rd year courses. For more information on the blade element method and momentum theory, please consult the book of Ruijgrok. The data needed for this task can be found on BrightSpace in a file called slow_fly1.xls and slow_fly2.xls. If your group is performing the theoretical calculations before doing the wind tunnel measurement, use slow_fly1.xls. Alternatively, if your group has already done the wind tunnel measurement, use slow_fly2.xls.

Figure 2: Propeller blade section (Ruijgrok, 2009) To begin with the blade element method, the propeller blade should be divided into separate sections, as shown in Figure 2. The section location and width can be found in the excel file.

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Figure 3: Section Angles, Velocities and Forces (Ruijgrok, 1996) Figure 3 gives an overview of the angles, velocities and forces for a section. It is possible to calculate the induced velocity Vi by using momentum theory. However, the induced velocity is a function of the thrust of the propeller whilst the thrust depends on the induced velocity. The induced velocity can therefore only be calculated through an iterative process. For this task, you can assume that the induced velocity Vi is equal to zero. Thus, the angle of attack α, is equal to the geometric pitch angle β minus the ‘flight path’ angle Φ. Please also note that usually the Greek letter Φ is used for the pitch angle. Calculate, for each section, the angular velocity (R), and the total velocity (Vr) for the combinations of rpm and flight speed given in Table 2. As a next step, calculate the ‘flight path’ angle and the angle of attack. Table 2: Combinations of rpm and flight speed Rpm [-] Flight speed [m/s] 8000 10 8000 15 8000 20 10000 10 10000 15 10000 20 Now that you know the angle of attack, you can use the CL and CD data given in the excel file to calculate the lift and drag for each aerofoil section. You may need to use interpolation to find a correct value for the calculated angle of attack. Knowing CL and CD, you can now calculate dL and dD for the sections by applying the standard lift and drag formulas to each section.

1 L  cL  V 2  S 2 1 D  cD  V 2  S 2

(4) (5)

Here, S is the area of the section. Now calculate dT and dK for each section and then calculate the thrust and torque produced by the entire propeller for all combinations of the flight speed and rpm. Please note that you only calculated the contribution of one propeller blade. Can you now predict how the thrust varies with flight speed and rpm?

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On BrightSpace you will also find several Excel sheets with names starting with ThrustCalc. You can use these to check if your prediction was correct. Please note that this program uses an iterative process to calculate the induced velocity Vi.

Task 3: Compare results Each group has measured different propellers during today’s wind tunnel test and subsequently has different plots. Today’s final assignment is to present your plots to the other groups and compare your results with theirs. Answer the following questions:

    

How do the theoretical results compare to the wind tunnel measurements? Can you explain the differences? What is the effect of changing the propeller pitch? Does changing the diameter of the propeller have any effect? Can you explain what the benefit of a variable pitch propeller is? What is the main reason why variable pitch propellers are not always used in propeller aircraft? Can you think of another reason to use a fixed pitch propeller?

Next time Up to this point the focus was on forces on an aircraft and how an aircraft is able to overcome its own weight and gravity and how it propels itself forward. The calculations performed in the previous chapters are all regarded to a 2D configuration of an aircraft. However, in real life, it is not in two dimensions, but in three dimensions. For 3D experiment will be carried out at the big wind tunnel facility in building 64. Make sure you have read it thoroughly!

References Maxon Motor 2008, ‘Maxon Motor key information’, Switserland, viewed 13th of August 2009, url: Ruijgrok, G.J.J. 2009, Elements of airplane performance, VSSD, Second Edition, Delft.

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PW Power The power subsystem is a crucial element of any space mission. Requirements on the power subsystem are, among others (Fortescue, Stark and Swinerd 2003): - to supply a continuous source of electrical power - to provide for average and peak power. Most spacecraft use photovoltaic solar cells to convert solar energy in electric power. Their main advantage is that they are lightweight and very reliable. This type of power generation works well for satellite missions requiring up to 20 kW of energy (next-generation communication satellite, Iida 2003) and have a lifetime of up to 15 years. Design issues include (Fortescue Stark and Swinerd 2003):  the type of solar cell (e.g. silicon, gallium-arsenide, indium phosphide)  radiation environment (solar flares, Van Allen belts)  thermal environment (a solar cell’s output decreases with increasing temperature)  orientation of the solar cell (are the solar cells actively pointed towards the Sun?)  illumination (satellites in eclipse or solar cells in shadow; in these cases, the solar cells become high resistors, effectively shutting down other solar cells on the same ‘string’)  degradation (what is the average power to be delivered at the end-of-life?)  mass In this exercise, we will focus on distance, orientation and efficiency. The power delivered by a single solar cell will be measured for different voltages, distances to and orientation with respect to the light sources (LEDs will be used as light source). Also, the efficiency will be calculated. You will learn more about solar power generation in the course Aerospace Design and System Engineering Elements 1 (AE1201). It is helpful to read Nelson (2003, .pdf can be downloaded), chapter 1, up to and including section 1.4.3.

Learning objectives

Schedule

The student should be able to:  Explain the influence of distance from the Sun on power generated by the solar cell.  Explain the influence of incidence angle on power generated by the solar cell.  Explain the influence of power extracted from the solar cell on the power generated by the solar cell.  Explain how to determine the efficiency of a solar cell.  (30 min.) Preparation and familiarizing with the theory.  (180 min.) 1 morning/afternoon for each instruction group of 40 students. The smaller project groups of 10 students are split into 3 subgroups of two or three students per setup.  (30 min.) The last half hour of the project session will be used to present the results to the other group members.

Make sure that you write clearly on everything you hand in who has worked on it.

Deliverables      

I-V curve for varying distance in Excel. I-V curve for varying incidence angle in Excel. Numerical results for maximum power vs distance. Numerical results for maximum power vs incidence angle at fixed distance. Numerical result for efficiency of this solar cell. Report of [Task 4] answers.

Maximum power and Efficiency The maximum power that can be extracted from the solar cell depends on the instrument and other subsystems that are connected to the solar cell. A plot of voltage versus current (or I-V

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curve) illustrates this, see Figure 1. The power is found as the rectangular area under the curve, and the peak power point is at the ‘knee’ of the curve. Given the solar energy that is received, the efficiency of the solar cell determines the available power per area of the solar cell. The efficiency of the solar cell is defined as (e.g. Nelson 2003 p. 12):



Pmax Preceived Figure 1: Current-voltage (I-V) curve and power-voltage curve. SC: short circuit (no resistance), MP: maximum power, OC: open circuit (infinite resistance) (http://zone.ni.com/).

(1.1)

where Preceived is the energy of the light that hits the solar cell. Factors that influence the efficiency include (Nelson 2003, chapter 2):  solar cell material (specifically, the separation of the energy bands in the semiconductor)  energy spectrum of the incoming radiation  temperature (higher temperature decreases efficiency)  resistance losses inside the solar cell  reflection of the solar panel

Lumen Lumen (lm) is the international standard unit for luminous flux. In other words, it is a measure of the total amount of visible light, emitted by a source. One lumen is related to the unit candela as follows:

1lm  1cd  sr Or in words, one unit lumen corresponds to one unit of candela times one steradian. Where candela steradian stands for the power times solid angle. A steradian or solid angle is used to describe two-dimensional angular spans in three-dimensional space. If a light source would uniformly radiate one candela in a full sphere (being 4π), this would equal to:

cd  sr=1  4  12.57lm In today’s world, the unit lumen is frequently used in lighting and projectors. Since 2010, the EU has forced manufacturers of light bulbs to primarily display the amount of lumens, instead of the consumed watts. Luminus Flux As the unit of lumen already indicates, light intensity is not the same in all directions. So to calculate the luminous flux, you will need to use the following integral.

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(1.2) As you can see the luminous flux is build up out of luminous intensity, position and direction dependencence.

Tasks

Figure 2: Set-up consisting of LEDs (left), solar cell on turn table (middle) and universal meters (right). The measurement set-up is shown in Figure 2. The light-source is an array of LEDs which can be blue, yellow or white. The solar cell is built into a hard case. A metal cover (which is provided) can be placed on top of the solar cell, partly shielding it from sun- and room light. The switch on top of the case that contains the solar cell selects different resistors. In this way different combinations of current and voltage are obtained. Take measurements at settings 1 through 10 to produce an I-V curve and visually derive the maximum power point, as described in Figure 1. The current and voltage can be measured by the universal meters that are provided. To measure voltage, set the meter to 2000 mV, to measure current, set it to 20 mA. If an ‘H’ appears in the display, measurements are blocked. Press ‘HOLD’ to remove the block. Please turn off the meters after measuring to save battery life.

Task 1: Distance Vary the distance from the solar cell to the LEDs from 5 cm to 40 cm in 4 realistic (not necessarily equidistant) steps. At each distance, measure the voltage and the current for different resistors. Produce a graph of maximum power vs. distance in Excel. Pay special attention the to graph(s) you produce! How would you compare different measurements?

Task 2: Incidence angle What is the relation between incidence angle θ and power per unit area of the solar cell that you expect? Vary the incidence angle (at constant distance, e.g. 40 cm) from the solar cell to the LEDs from 0 to 80 degrees in at least 6 steps, and measure the voltage and current at each angle. Produce a graph of maximum power vs. incidence angle in Excel.

Task 3: Efficiency

Calculate the efficiency as in equation (1.1) by using your own measurements for Pmax. For Preceived you can use data from the manufacturer of the LEDs provided in Table 1, Figure 3 and Figure 4. Figure 3 and Figure 4 show how the luminous intensity varies with respect to a direction turned away from the LED, this represents the direction dependence or relative luminosity. The values in Table 1 correspond to 1.0 or 100% in Figure 3 and Figure 4. Note that equation (1.2) and figure 5 can also help you to find Pmax. It will be necessary to make some assumptions or approximations.

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Table 1: LED characteristics (NICHIA corporation). luminous intensity (millicandela) blue led 11000 white led 18000 yellow led 9200

Figure 3: Luminosity of the blue LED as a function of direction (NICHIA corporation).

Figure 4: Luminosity of the white and yellow LEDs as a function of direction (NICHIA corporation).

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Figure 5: Luminous efficiacy of the eye sensitive spectrum.

Task 4: Presentation and discussion Discuss your results and answer the following questions:  Are the I-V curves the same for all LEDs and solar cells? Why (not)?  Is the effect of distance and orientation what you expected to see? Why (not)?  Do you find a difference in efficiency for the different colours of the LEDS? Why (not)?  Describe what you need to do to determine the efficiency for the solar cells in sun light?  Could you use a light meter to measure the luminance (unit: lux) to calculate the efficiency of the solar cell? Why (not)?

References Iida T 2003, Cost consideration for future communication satellite, Acta Astronautica 53, 4-10, pp. 805-810. Nelson J 2003, The physics of solar cells, Imperial College Press, London, England. (most of the material of the book is available on google books, and a pdf of the first two chapters is available at: http://www.worldscibooks.com/physics/p276.html. Schubert E F 2003, Light-emitting diodes, Cambridge University Press, Cambridge England. (limited preview is available on google books). Slides for lecture notes available on: http://www.ecse.rpi.edu/~schubert/Light-Emitting-Diodesdot-org/ http://www.gizmology.net/LEDs.htm (computation of solid angle) Fortescue P, Stark J & Swinerd G 2003, Spacecraft System Engineering 3rd Ed., John Wiley and Sons, Chichester.

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3D

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Execution of 3D Wind Tunnel Experiment on a Swept

Wing Of course, a real flying wing is 3D, not 2D. During this part of the project you will perform wind tunnel measurements on a typical swept wing set up in a low speed wind tunnel. From the forces that will be measured using a 6-component external balance, you will analyse the most important aerodynamic characteristics: C L , CD and Cm . Furthermore, typical flow phenomena, like vortex formation and flow separation that occur throughout the range of angles of attack, will be shown and discussed. Additional information about the tests will be provided on a separate hand-out. The results for the wind tunnel are measured by a 6-component external balance and the output of the balance was forces and moments in Newton and Newton-meters. There is physically nothing wrong in expressing forces and moments in these units, but for you as aerospace engineer there are more convenient units or coefficients. For the second part of this day you will convert the measurements in lift, drag and moment coefficients. Next you will plot these coefficients and compare the measurements with your calculations in your Excel sheet.

Learning objectives

Schedule

The student should:  Be familiar with wind tunnel testing on 3-dimensional wings.  Be able to identify flow phenomena on a 3-dimensional swept wing.  Be able to demonstrate simple flow analysis techniques for wind tunnel testing.  Be acquainted with lift and drag characteristics of a finite swept wing.  Be acquainted with pitching moment characteristics of a finite swept wing.  Be able to compare experimental and theoretical characteristics.  (30 min.) Preparation and familiarizing with the theory, including reading the related chapters in Anderson (2008).  (15 min.) Divide tasks amongst group members.  (15 min.) Preparation of the test and familiarization with the test setup.  (45 min.) Conduction of the experiments. Part 1, Determination of loads.  (45 min.) Conduction of the experiments. Part 2, Presentation of typical flow phenomena.  (60 min.) Working out of exercises.  (30 min.) Discuss the results.

Make sure that you write clearly on everything you hand in who has worked on it.

Deliverables   

Measurement report of the wind tunnel exercise [Task 1 and 2]. Worked out exercises and produced graphs [Task 3, 4, 5 and 6]. Clear table containing work and hour distributions of all team-members

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Theoretical background Before the test can be accurately performed it is mandatory to familiarize yourself with the test setup. For this purpose, a description is given of the wind tunnel, the model and the measurement procedure.

Wind tunnel and balance The wind tunnel that is used for this experiment is the Open Jet Facility of the Faculty of Aerospace Engineering. This wind tunnel was officially brought into service at the beginning of 2009. Its layout is given in Figure 1. The use of an open jet makes this facility very well suited for the aerodynamic research on models with large blockage like model wind turbines. Thanks to its large test section that surrounds the jet, large groups of students can join experiments very close to the model whilst the wind tunnel is running.

CV Fan Drive

Corner Vanes (CV)

Fan

CV

Jet Settling chamber

Open test section

CV Figure 1: Overview of the Open Jet Facility (OJF) The wind tunnel, which is largely build out of wood, is equipped with a 600 kW electrical motor which drives a 3.2m diameter fan. Through guiding vanes in the corners of the channel, the airflow reaches a settling chamber which contains 4 anti-turbulence screens and a flow straightener. Through the contraction ratio (4:1) the airspeed is increased and leaves the mouth into the open test section. The maximum air speed that can be attained is about 30 m/s. The wind tunnel is operated from a separate control room next to the test section. Here, the wind speed can be set and relevant flow parameters can be read from a dedicated wind tunnel control program. In our experiment, some of the equipment will be read manually from within the test section itself.

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2850

Side View V

2850 model angle of attack mechanism

2950 6 component balance

1710 windtunnel cross section

support table

Figure 2: Wind tunnel cross section and side view of test set up. Dimensions are in mm. The external balance is positioned underneath a reflection plate to prevent the air from washing the balance directly. This balance is pre-calibrated and a separate utility is available to perform the acquisition of the force data. To determine the wind speed during the tests a Pitot-static tube is mounted in the jet which gives a direct reading of the local dynamic pressure. Under normal circumstances the presence of the model close to this Pitot-static tube may disturb the static pressure reading which leads to an error in the dynamic pressure (and thus wind speed) reading. However, in our case the wind tunnel is very small compared to the jet dimension and the pressure probe is assumed to produce valid readings.

Model The model is a 30 degree swept wing constructed out of wood. It has been used in the past for ground effect measurements in the low speed wind tunnel LTT. The layout of the swept wing model is given in Figure 3 while the main characteristics are summarized in Table 1: Table 1: Characteristics Parameter/Feature Span, b Chord (constant), c Wing area, S Sweep angle,  Aerofoil Material

of swept wing model. Value/Description 1.2 m 0.2 m 0.236 m2

30 NA Reinforced wood

The model is supported in the wind tunnel by three struts. The main front support members are spared by means of an aerodynamic shield. The tail strut however is completely washed by the wind. Please note that no correction for the support forces is applied which means that all aerodynamic coefficients are disturbed. Since the thickness of the struts is rather small these effects may be regarded as negligible for the moment. In later experiments, during forthcoming projects, the support interference effects will be accurately considered.

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Figure 3: Top view of the swept wing model. Dimensions are in mm. The angle of attack of the model can be set manually by sliding the tail support up or down. In case the wind tunnel is running at moderate speed angle of attack changes may be applied by approaching the model carefully from the back.

V

x y z Figure 4: Definition of balance axis system

6-Component balance The forces and moments acting on the wing during the wind tunnel experiment have been measured by a six-component balance. A detailed description of the balance can be found in the hand-out “OJF-balance-forces.pdf” presented on the project’s BrightSpace site under Course Documents. In Figure 4 you see the definition of the balance axis system. Using this definition of the axis and the measurements, you will be able to calculate the lift- and drag coefficient. Information on the moment definition of the balance can be found on BrightSpace as well.

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Lift- and drag coefficient If you look at the definition of the axis in the balance in Figure 4 you can define the following coefficients:

CFx  CFy  CFz 

Fx 1 V 2 S  2

Fy 1 V 2 S  2

Fz 1 V 2 S  2

 

Fx q S Fy q S Fz q S



(1)

(2) (3)

Which in words means that the coefficient of the force in x-direction is the actual force in xdirection divide by the dynamic pressure times the wing area. If you now once again take a good look at Figure 4 and remember that lift is always perpendicular to the free stream velocity vector and drag is parallel to the free stream velocity vector, you can find the following relations: CFx  CD (4)

CFz  CL

(5)

Moment coefficient The moment that we are interested in now is the moment around the y-axis, also known as the pitching moment. Like with the forces, you can also define a moment coefficient based on the measurements.

CMy 

My 1 V 2 Sc  2



My q Sc

(6)

This coefficient is related to the moment around the pivot point of the model in the wind tunnel. In the hand-out “OJF-balance-forces.pdf” a drawing describes how this pivot point relates to the centre of balance. The measurements are made with respect to the balance centre as shown in the hand-out. With this you can calculate the moment coefficient around the pivot point.

Test Matrix The characteristics of the model will be determined in an angle of attack range between 4 and 20 for different velocities of V  10,15, 20 m / s to enable verification of Reynolds number effects. For the analysis of the flow phenomena a wind speed of V  15 m / s is selected.

Flow Phenomena After the force measurements have been performed, some time will be used to visualize typical flow phenomena. In case you need additional information on the given topics refer to Anderson (2008) or other sources in open literature.

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Figure 5: Generation of wing tip vortices (Credits: US Cent. of Flight, Civil Air Patrol)

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Tip vortices Tip vortices are the result of flow washing over the wingtips caused by the pressure differences between the upper and lower side of the wing (Figure 5). For more information refer to section 5.13 of Anderson (2008). The visualization of the vortices can be done easily using a probe with a small wire at the end (called a tuft) of by placing a tuft grid in the flow directly behind the model. lift increase due to leading edge vortex

C

L

no vortex lift

alpha

Figure 6: Effect of leading edge vortex on wing lift coefficient of a highly swept wing.

Leading edge vortex and vortex lift Under certain circumstances (high sweep angle and high angle of attack), the flow may separate at a wing’s leading edge to form a so-called leading edge vortex (LEV, see Figure 7). Since the static pressure in and close to the vortex is smaller than the undisturbed (ambient) pressure the static pressure over the upper surface leads to an increase in lift (Figure 6). Whether the effect is found for the given model is to be determined in the case with the help of surface mounted tufts and/or a tuft probe. In case vortex lift exists on your model this should be clearly visible in the lift curve.

Flow separation In case the local wing surface is inclined to a large angle the local adverse pressure gradient becomes so large that the flow may separate. This separation process is not only determined by the pressure distribution but is affected by the Reynolds number and the surface roughness of the wing as well (refer to Section 4.20 of Anderson (2008) for more information). Although many methods are available to visualize flow separation, the easiest way is to use surface mounted tufts (Figure 8).

=0 deg

V

=12 deg

LEADING EDGE VORTEX

TIP VORTEX

attached flow

flow separation

Figure 7: of a leading edge vortex on a highly swept wing at large angle of attack. Figure 8: Visualization of flow separation on52 the upper side of a powered Fokker 27 wind tunnel model using a line of tufts; LTT Faculty of Aerospace Engineering, TU Delft.

Project manual AE1111-I – Exploring Aerospace engineering

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Boundary layer transition Boundary layer transition is a very important phenomenon as it determines the extent of the laminar flow part on the model. The further downstream this occurs, the lower the profile drag of the wing may be. Extensive information on this topic can found in Sections 4.15, 4.16, 4.17 and 4.19 of Anderson (2008). To find the location of transition a stethoscope is used. It consists of a microphone positioned directly behind a small tube that is mounted on a support. In case the stethoscope is moved over the wing from the laminar into the turbulent part of the boundary layer a clear and loud white noise is heard once the turbulent flow is reached. The stethoscope can be positioned in the flow manually. turbulent flow signal

laminar flow signal

Stethoscope (microphone)

Figure 9: Stethoscope (microphone) for transition detection.

Tasks Task 1: Determining the loads on the model Set the model in the given angle of attack range (steps of 2 ) and determine the balance forces in x, y and z -direction. For the definitions of the axis system and the registration of the forces refer to the hand-out “OJF-balance-forces.pdf” presented on the project’s BrightSpace site under Course documents. Since at a later stage the aerodynamic coefficient will be determined (polar), the dynamic (reference) pressure should be noted for all data points. To calculate the wind speed , the air temperature, Tair , and the barometric pressure, Pbar should be registered. The monitoring table for all data may look as presented in Table 1. Date: Model: Configuration: Tair : Data point #

Table 1: Sample table for the registration of model forces. Group:

 ()

Pbar : q ( Pa )

Fx ( N )

1 2 3 4 … etc.

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Fy ( N )

Fz ( N )

M y ( Nm)

Project manual AE1111-I – Exploring Aerospace engineering

2017/2018

To check the data, you can make a quick sketch in a graph. This will enable you to find out whether the data set contains erroneous data points. In the next chapter the force data will be worked further to obtain the relevant coefficients. As noted earlier the undisturbed reference velocity for the flow can be obtained through:

V  where the air density, pressure,



2q

(1)



, is found from the air temperature,

Tair (in C ) and the barometric

Pbar (in mBar )with:   1.225

Pbar 273.15  15 1013.25 273.15  Tair

(2)

In case you need the dynamic viscosity of the air,  , Sutherland’s formula may be used: 1.5

 273.15  Tair    273.15  15 

  1.7894  105 

273.15  15  110.4 (kg / ms ) 273.15  110.4

(3)

Task 2: Presentation of typical flow phenomena Take a closer look at the flow phenomena after the force measurements are performed. Now, try to draw conclusions on:

   

Tip vortices Leading edge vortices Flow separation Boundary layer transition

To perform this task in a meaningful manner, incorporate the following steps: 1. Make sketches / figures in which you show how the tufts behave for given angles of attack. 2. Try to follow the tip vortex in stream wise direction, as far as possible. Sketch the path and explain what happens at large distance behind the model. 3. Describe how the surface tufts behave when the angle of attack is changed. What happens when you position your hand directly behind the model? Explain this behaviour. 4. Sketch how the boundary layer transition line behaves with changing angle of attack and provide an explanation for this behaviour. What happens when small disturbance element (transition strip) is positioned at the upper surface, close to the model leading edge? Does this affect the local flow separation? If so, can you explain this?

Task 3: Exercises After you have performed the task described above try to solve the following problems. 3.1

First calculate the Reynolds number based on the wing chord (in stream wise direction) for the highest dynamic pressure that you used during the force measurement. Compare this Reynolds number with the one that is obtained for a free flying wing model with the same layout at V  30m / s and reference chord of c  0.25 m under Mars standard atmospheric conditions. What will be the effect of this difference in the Reynolds number with respect to:

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  3.2

2017/2018

The extent of laminar flow on both models? The lift curve and the maximum lift coefficient?

Assume you could fly the free flying model up to a speed of V  220 m / s , by using very powerful jet engines. What would happen to the forces on the model that were found at V  20 m / s and   4 ? Provide numeric values (Hint: look at the so-called “PrandtlGlauert correction”. How does the drag coefficient change in this case?

For the conversion of the measurements you should split up in sub groups and equally divide the work amongst the sub groups. To make the plots, every sub group needs all the data, so make sure you all work in the same way and that the results are compatible and interchangeable.

Task 4: Convert the measurements into coefficients 

The results from the 3D wind tunnel test need to be converted into coefficients using the equations in this chapter and in the hand-out. Remember that you have to find the lift, drag and moment coefficient for all angles of attack that were measured during the wind tunnel experiment. You should use Excel to calculate the coefficients as you will also plot the coefficients.

Task 5: Plot the lift-drag polar and moment coefficient graph

CL

CL Cm

CD

a

Figure 10: Example coordinate system such as need to be produced in task 2



To complete this, you need all the coefficients from the last task. Now, you have to plot the lift coefficient and moment coefficient against angle of attack (in one plot) and in another plot the lift coefficient against the drag coefficient. See Figure 10 for how the coordinate system could be defined.



After you have produced the graphs you should look for similar graphs of the NACA0012 and the profile you have selected for the Martian airplane in LI task 6 on the internet or in books (the NACA0012 has a similar shape as the wing you have tested in the Wind tunnel). Now you can compare the graphs made from your measurements and the NACA0012 and Martian airplane profile graphs from literature. What differences do you see and how can you explain these differences (hint: look at the Re-numbers)? Pay special attention to o The lift slope o The ‘zero angle of attack’ – drag coefficient

Task 6: Compare your calculations with the measurements With the Excel sheet you have been building up in the last few weeks, you are able to calculate the total values for lift and drag. Now you have the possibility to check how accurate your calculations are. To do so, enter the relevant input variables of the wing you tested in the wind tunnel into your Excel sheet. Most of these parameters can be found in the previous chapter. Next to that you also need the information from the lift slope (2.83 cl / rad ). You can assume a span efficiency factor of 0.95 and a profile drag of 0.00735.

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When you have entered all required input variables, you can compare the calculated lift and drag with the actual measured drag. Do this for multiple angles of attack along the entire range of angles of attack. Answer the following questions:  Is there a difference between the calculated and measured values? If so, how big is the difference?  Is the difference constant among all angles of attack?  How do you explain these differences?  How would you improve your Excel sheet to produce better results?

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Project manual AE1111-I – Exploring Aerospace engineering

AD

2017/2018

Aerodynamic Design

In these four hours you will finalize the aerodynamic design of your flying wings. Later in the project you will do the final assembly of the flying wings and in the final week you will compete against other teams in a flying competition. As a project group, you will design and build two distinct flying wings, with different properties that are the most important for the competition, such as speed, stability, manoeuvrability and weight. Today you should split up your group in two sub groups; each sub group is responsible for the design of one flying wing.

Learning objectives Schedule Deliverables

The student should:  Be able to perform necessary steps to use experimental data and theoretical calculations for a final design.  Experience the relation between optimal aerodynamics and production constraints.  (30 min.) Preparation and familiarizing with the theoretical background.  (105 min.) Working out Task 1, 2 and 3.  (45 min.) Performing Task 4

 

Make sure that you write clearly on everything you hand in who has worked on it.

The mission requirements, selected aerofoil and wing design (Table 1) together with a thorough explanation of your choices, per sub group [Task 1, 2 and 3]. Review of the trade-off including your choices and final design selection, entire group. [Task 4].

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Theoretical background Dimensional constraints Your flying wing will be cut out from a block of special foam (EPP), with an automated wire cutting machine. The dimensions of the block for the standard design are given in Figure 1.

Figure 1: Dimensions of the block of EPP

Each group will get two EPP blocks. One of the mentioned size, which can be used for the standard design, and a slightly larger block, of 300 by 200 by 70 mm, which gives you more freedom for your own design. In Figure 2 a top view of the flying wing is given. Both halves of the flying wing will be separately cut out from the block of foam, and glued together afterwards. One half of the wing will be cut out from the top side of the block and the other half will be cut out from the bottom side.

Figure 2: Top view of the flying wing The above procedure limits the thickness of your wing to 20 mm, the extra 20 mm ( 60  2  20 ) is needed for sufficient cutting space.

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You must make a choice about the orientation of your wing with respect to the block. The two (realistic) options are given in Figure 3.

Figure 3: Two possible orientations of the wing w.r.t. the block You can see in Figure 3 that orientation A gives possibilities for a large chord length and sweep angle, but your wingspan is limited to 300 mm ( b / 2  150mm ). Orientation B gives you a maximum wing span of 600 mm ( b / 2  300mm ), but your chord length and sweep angle are limited. Of course, you can also choose for a wingspan of i.e. 500 mm, by using orientation B and cutting a piece of the wing off yourself afterwards. Due to constraints of the wire cutting machine, it is not possible to orientate the block at another angle than 0° or 90° (orientation A or B).

Aerofoil selection In LI you have produced the lift curve of the NACA0020 aerofoil, making use of measurements done in the 2D wind tunnel experiment. Also, some calculations on a MH44 aerofoil were done. Three important characteristics which can be found from a lift curve are the maximum lift coefficient ( cl ,max ), the angle of attack at which no lift is generated (  L 0 ) and the lift slope ( dcl / d ). These three characteristics are used in your Excel sheet (LI and DR) to calculate the total lift of a rectangular wing. In ‘Drag and Longitudinal stability’ you have learned that not only the amount of lift produced by an aerofoil is important. The shape of the aerofoil also influences the longitudinal stability of the aircraft. On BrightSpace you will find the lift curve and pitching moment coefficient graph of three different aerofoils, including the NACA 0020 and MH44. For each flying wing, you have to choose one of those three aerofoils, based on this data and what you have learned about stability and lift characteristics.

Tasks In general, flying wings of roughly the size (and with about the same available power) that you are designing have the following flight characteristics: ‐ Airspeed ( V ): 3-4 m/s ‐

Angle of attack (  ): 2°-5°

Know these numbers only give an indication of the range you should think of. The values will be different for extreme manoeuvres/designs. But you can use these values for estimations during your design process.

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Task 1: Mission requirements Before the design process can start you have to know exactly what you are designing it for. Think about speed, manoeuvrability, stability, lift to drag ratio, etc.



Discuss your mission requirements with your team. Make a list with the most important requirements on top. Explain for each requirement why it is (not) important.

Task 2: Select an aerofoil Each team should select an aerofoil for their flying wing. Compare the four aerofoils and discuss the differences within your team. Keep your mission requirements in mind.



Select one of the four aerofoils most suitable for your flying wing. Explain why you have chosen this aerofoil, and why the other three aerofoils are less suitable. Mention lift, drag and pitching moment coefficient in your explanation.

Task 3: Finalize your flying wing design In this task, you have to make choices on the dimensions of the flying wing. Since the shape of the aerofoil is now fixed, the thickness only depends on the chord length. Looking at Figure 2 you can see which parameters still need to be fixed: the wing span ( b ), sweep angle (  ), root chord length ( croot ) and tip chord length ( ctip ). Designing the flying wing (which means finding the ideal values for the four parameters) is a complex process and cannot be prescribed in a few steps. The reason for this is that all input variables influence multiple output variables, i.e. a larger wingspan increases lift, but also weight and drag. Your mission requirements are the starting point of this process. Use the excel sheets you have made in LI and DR to ‘play’ with the dimensions and lift, drag, weight and thrust. Keep the following things in mind: ‐ ‐ ‐

The minimum tip chord length is ( ctip ) 65 mm. Be aware of the constraints due to the dimensions of the block EPP. Make sure it fits! Think about the influence of sweet and taper on the wing area, lift, etc.

In Table 1 you can find the variables in which you have to express your flying wing design. For the wingspan, you must choose between orientation A (300 mm, Figure 3) and orientation B (600 mm, Figure 3). As stated before, it is possible to cut a piece of the wing off afterwards to adjust the wingspan, but for the cutting process you must choose between A and B. The sweep angle (  ) en de root chord length ( croot ) are defined in Figure 2. The taper ratio is defined as follows:



ctip croot

The last parameter which has to be filled in is the aerofoil type. Table 1: To be filled in characteristics of the flying wings Parameter Flying Wing #1 Flying Wing #2 Wingspan (300/600), b [mm] Sweep angle,

 [°]

Root chord length, croot [mm] Taper ratio,  [dimensionless] Aerofoil

 

Fill in Table 1 with the characteristics of the final designs of your flying wings. Make a document in which you explain why you made the choices you have made.

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Project manual AE1111-I – Exploring Aerospace engineering

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Task 4: Trade-off In engineering, it is very common to have multiple designs. In the end only one design can be manufactured. A way of selecting which design suits best is a trade-off. A trade-off is a discussion in which certain criteria get a weight factor, adding the grades multiplied by the weighting gives different final results for different designs. The design that comes out best in the trade-off is the design that will be manufactured by your mentor. Use the requirements as written down in Task 1 as criteria and try to think which criteria are important and give a reasonable weighting to it. Discuss with the group how well each criterion is fulfilled within the designs and come up with the best design. Note: if the aspect of a trade-off is not clear try to find examples on the internet or ask your mentor. Your mentor will cut out your flying wing somewhere the coming weeks. This won’t be done during official project hours. If you want to help or have a look you can arrange this with your mentor.

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Project manual AE1111-I – Exploring Aerospace engineering

RE

2017/2018

Range and Endurance

When designing a large flying wing for a mission, the most important requirements are the range and/or the endurance. Today the group will be split up to analyse two missions, both performed on Earth, as well as Mars. Suppose you are part of an exploration mission and are about to explore a large canyon. Part of the team will remain at the base camp and a small exploration-team is going to descend into the canyon. For communication, the teams are equipped with FM-radios which require line of sight to work. To guarantee communication an Unmanned Aerial Vehicle (UAV) is used as a flying relay station. When the UAV is used for this purpose, endurance is the key-word, as it will have to remain airborne for as long as it can. For the second mission, suppose that due to a landslide, the trail back to base camp got blocked off, which means that a different and longer route back to base has to be found. As a result, the UAV reached its maximum endurance and had to return to base to recharge. Now suppose that after the second launch of the UAV, communications cannot be re-established, basically meaning that the exploration-team is missing. This makes the new mission of the UAV one of search (and rescue). The goal: cover as much ground as possible (maximum range).

Learning objectives

Schedule

The student should:  Be able to calculate range and endurance for a given aircraft with constant aircraft weight.  Understand the influence of design parameters on the range and endurance of aircraft.  Obtain insight in the effects of environmental parameters on aircraft performance.  (30 min.) Preparation and familiarizing with the theory  (150 min.) Divide into groups of two or three students. Each sub group will then analyse a specific mission on a Mars by performing the tasks 1-3.  (30 min.) Work out task 4  (30 min.) Discuss results.

Make sure that you write clearly on everything you hand in who has worked on it.

Deliverables  

Results of task 1-3 per subgroup. Results of task 4.

Tasks Suppose that the aircraft you are going to analyse was designed with the following parameter values: Span: Empty/Structural mass: Payload mass: Battery mass: Battery energy available: Propeller efficiency: Electric motor efficiency: Equation for Pbr: Aero data:

3 [m] 3.5 [kg] 4.5 [kg] 4 [kg] 800 [Wh] 0.79 [-] (assumed constant over range of cruise speeds) 0.87 [-] Pel·ηmotor [W] (Note that Pel here is the electric power provided by the batteries) You will find an Excel file on BrightSpace containing the relevant aerodynamic data (you may need to perform

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calculations on the provided data to obtain the correct data/graphs) Furthermore, the environmental data for Earth and Mars can be taken from the information collected during your literature survey in the beginning of the project. Also, to make the calculations easier, it is assumed that we can ignore the effects of a changing environment and increases in speed on the aerodynamic data. I.e., the given aerodynamic curves can be applied at various altitudes, speeds and even different planets. Please keep in mind that in reality the aerodynamic curves depend on the Reynolds- and Mach number.

Task 1: Determination of velocity and altitude Find the optimum combination of altitude and velocity to maximize (1) the range and (2) endurance of your aircraft in the chosen environment. You may use a program like Excel to help determine the optimum combination if necessary. Since the aircraft weight is constant, there is one optimum flight condition which does not change during the mission. For these calculations, you can therefore assume steady, straight, symmetric and level flight conditions. Furthermore, it is noted that electric motors do not consume fuel in the traditional way. That is, the “fuel flow” is zero, since the battery mass remains equal; instead, batteries have an “electric energy consumption”. You will need to derive the new range and endurance equation. To do this, you can follow the derivation presented in Ruijgrok (p283-287), noting that cp=1/ηmotor and that you are no longer integrating with respect to the weight of the aircraft. Be sure to clearly indicate the steps taken in the calculations. Plot the optimum velocity as a function of altitude. Does the optimum velocity change over time? Why/Why not? How far/long can the aircraft fly? Neglect the power needed for the climb or descent.

Task 2: Effect of design parameters Calculate the effect of doubling the following design parameters on the range and endurance: a. The span b. Battery mass (and thus battery energy available) c. The payload mass

Thoroughly explain your results.

Task 3: Requirements for indefinite flight Now let’s assume that we wish to install solar cells on the wings of the aircraft. Calculate the area of solar cells needed to allow the aircraft to operate indefinitely. Here you can interpret ‘indefinitely’ as continuously during daylight hours. Furthermore, the inclination of the sun can be assumed constant. You do not need to consider operating the aircraft at night. Consider two cases: 1. Using state-of-the-art solar cells with a total efficiency of 33% 2. Using the efficiency measured during the solar cell practical (In case you have not done the practical yet, assume a total efficiency of 15%) Indicate the steps taken in the calculation and indicate whether or not the number of solar cells required can be installed on the wings of the aircraft.

Task 4: Compare results [Entire group] Compare your results with those of the other students in your group. What are the differences between the results on Earth and the results on Mars? What are the main reasons for these differences? Do the results obtained for the missions on Mars seem realistic? Does it make sense to use aerofoils, designed for use on Earth or on Mars? Why/Why not?

Task 5 (optional): Model aircraft With what you know now, can you calculate the optimum velocity to maximize the endurance or range of your model aircraft?

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References Ruijgrok, GJJ 2009, Elements of airplane performance, VSSD, Second Edition, Delft.

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FE

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Flight envelope, climb rate and glide

The velocity and altitude your aircraft operates at influences your drag and thus your performance. Fly too slow and you will stall. Fly too quickly, and you will not have enough thrust available to maintain altitude. During the previous assignment, you evaluated the optimum flight velocities and altitude for either an endurance or a range oriented mission. Today several other flight performance parameters will be analysed for the same aircraft in the same environments.

Learning objectives Schedule

The student should:  Understand which parameters influence the (thrust limited) operating limits.  Understand which parameters influence the Rate of Climb and the glide slope.  (30 min.) Preparation and familiarizing with the theory  (180 min.) As for the previous assignment, the group will be divided into groups of two to three students. Each group will then analyse a specific mission on a specific planet by performing the tasks 1-4.  (30 min.) Comparing the results and answering the questions of Task 5.

Make sure that you write clearly on everything you hand in who has worked on it.

Deliverables  

Thrust limited flight Envelope of model for the atmosphere of the Earth or Mars. Answers to questions of [Task 1,2,3 and 4].

Tasks As with the previous assignment, suppose that the aircraft you are going to analyse was designed with the following parameter values: Span: Empty/Structural mass: Payload mass: Battery mass: Battery energy available: Propeller efficiency: Electric motor efficiency: Equation for Mission time: Aero data:

3 [m] 3.5 [kg] 4.5 [kg] 4 [kg] 800 [Wh] 0.79 [-] (assumed constant over range of cruise speeds) 0.87 [-] Pbr: Pel·ηmotor [W] (Note that Pel here is the electric power provided by the batteries) 2 hours You will find an Excel file on BrightSpace containing the relevant aerodynamic data (you may need to perform calculations on the provided data to obtain the correct data/graphs)

Furthermore, the environmental data for the Earth and Mars can be taken from the information collected during your literature survey in the beginning of the project. Also, to make the calculations easier, it is assumed that we can ignore the effects of a changing environment and increases in speed on the aerodynamic data. I.e., the given aerodynamic curves can be applied at various altitudes, speeds and even different planets. Please keep in mind that in reality the aerodynamic curves depend on the Reynolds number and Mach number.

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Task 1: Performance diagram Plot Pr and Pa as a function of velocity for 2 different altitudes, i.e. sea/ground level and 1000 m above sea/ground level. Determine the maximum Rate of Climb (also indicate this in the performance diagram) at both altitudes, at what velocities are they achieved? What is the ratio of CL/CD? Does this correspond with the theoretical value for the RCmax for a propeller aircraft?

Task 2: Flight Envelope Here you are going to explore the performance limits of the aircraft. That is, the minimum and maximum flight velocities will have to be determined as a function of altitude. Plot the altitude versus minimum and maximum velocities. What is the thrust limited ceiling for the aircraft? Please note that the limits derived in this task are performance limits. In practice, there can be additional operational limits which cannot be exceeded.

Task 3: Glide slope Suppose the aircraft suffers an engine failure at 1500m above ground level, calculate how far the aircraft can fly (relative to the ground) with: a) no wind b) a constant tail wind of 10 m/s To answer question b, you should derive a kinematic equation for the speed of the aircraft relative to the ground first. This equation is a function of the airspeed and the wind speed. Furthermore, it can be assumed that the air density is constant (equal to the air density at 750 m) throughout the glide.

Task 4: Influence of design variables Repeat the previous 3 tasks for the same aircraft with a. a span which is twice as large b. a total mass which is 1.5 times as large Thoroughly explain your results.

Task 5: Compare results [Entire group] Compare your results with those of the other students in your group. What are the differences between the results on Earth and the results on Mars? What are the main reasons for these differences? Also discuss the results of the influence of the changes in design parameters as calculated in Task 4. Which of the two changes has the largest influence on the performance results?

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BT

2017/2018

Building and testing the aerodynamic model

It is time to produce the flying wings! This section is a guide on how to produce the flying wings. Please work carefully and precisely as all the parts are fragile.

Learning objectives

The student should:  Be able to build a flying wing model.

Schedule



(180 min.) Building of both flying wing models.

Deliverables



Two flying wing models.

Tasks The following materials are present to build the wing:  4 wings cut-out of EPP  1 balsa sheet  Duct tape  Double sided tape  Glue

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The following steps describe how the wing, using the proven design which was handed to you, can be built. After you have completed the first wing, you can follow the same steps to build your own design. The dimensions of the proven wing design are shown in Figure 1.

Step 1 The first step is to cut off a piece of each wing, to attach the outer part of the wing at an angle. Figure 1 also shows where it should be cut off. Make sure to always cut away from you to

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avoid injury. The reason that the last part of the wings is attached at an angle of 350 is to increase roll stability. If you would make the entire wing dihedral, the yaw effect would cause the wing to start pitching down whilst turning, as the centre of gravity is at the front of the wing. Step 2 Glue the main parts of the two wing halves together at the root. As the glue hardens very quickly, avoid getting glue on your fingers and gluing them to each other or objects. Use a wooden mould to attach and glue the dihedral outer side of the wing under the right and same angle for both wing halves. Cut the end of this dihedral part slantwise, with an angle of 350, so you can glue it together with a flat connection. Step 3 As we want the centre of gravity in front of the aerodynamic centre for pitch stability, the engines should be placed as far to the front as possible. You also want the distance between the engines to be large to increase the moment arm, as you use a difference in turning speed of the two propellers to steer. The position of the engines is a compromise between these two requirements.

 

       

 

As the propellers are in a pull configuration, but the motors are fragile, the motor and propeller must be integrated into the wing, even though the motor has to be behind the propeller. When pushing the propeller onto the wing, please support the back plate of the motor, or you will push the back plate out. If you do push the back plate out, please do not try to push it back yourself. This is also a reason why the propeller should be mounted into the wing as the back plate will tend to come out when the propeller hits something. The distance between the holes should be reduced to about 120mm (60 mm from the centre), or the wires will not be long enough. Please check the length of the wires before cutting! The distance from the from the nose to the propeller cut-outs should be reduced to about 35mm to move the engines (and thus especially the centre of gravity) forward. For your own design, you need to decide where to place the engines, but consider wire and centre of gravity limitations! The width of the hole should be at least 60mm, as the propellers are 56mm wide. A 20mm long and 5-6mm wide cut out should be added to the cut outs cut outs in a T shape, to fit the motors in (this should be a snug fit). The motors should still be tilted upwards, but are now sunk into the wing and fixed with black tacky tape. A 5cm piece of Velcro should be stuck to the front centre of the underside to fix the battery and the receiver. Note that the total centre of gravity will have to be at about 20% of the average cord. This usually means the battery must be mounted right at the front of the wing. Shifting the battery position will change the speed of the aircraft (forward means faster) and influence the stability. More forward (usually) means more stable. The motor connector on the side of the battery connector should be on the left when seen from below. Please hand back the transmitter receivers and batteries at the end of the session. You will be handed a new set for the flight test.

Step 4 Now it is time to attach the electronics, battery and propellers onto the lower side of the wing. Be careful with these fragile electronic parts! Make sure you do not bend the wires close to the circuit board! Again, we want to place the weight as far forward as possible. In figure 2 it is shown where to put the electronics and battery. The grey rectangle has a (green) circuit board attached on the other side. Two parts are sticking out of the circuit board: cut away some foam to sink them into the wing. After this you

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can glue it onto the wing, but only put glue on the plastic parts (If you put glue on the metal parts the electronics might fail)! Use double sided tape to stick the battery onto the electronics,

Figure 4: Picture of engine and Velcro placement

so you can easily change the position of the centre of gravity by repositioning both at the same time. Use tacky tape to fix the engines into the wing. Check with the transmitter whether the left and right engine are correct and if the propellers are rotating in the right direction. Change the engine connector if not. To bind the receiver and the transmitter (only needed to be done once): • Connect to receiver to a battery • Wait till the led starts flashing quickly. • Push down on the left stick of the receiver and hold it down • Turn the receiver on and let go after three seconds. View the video on this page: http://deltang.co.uk/rx31d-34.htm There is also an instruction there on how to change the steering mix (default is 25%) Now that your wing is finished it is time to test it and see if it flies properly! When you start flying, you will probably notice that you only have to use little power to sustain steady horizontal flight. If it then pitches up or down, you can adjust the thrust angle of the engines to compensate for this. You can now follow the same steps to build the second aircraft with your own design.

Deliverables 

Two flying wings

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M1

2017/2018

Mars Mission Design I

The project up to this point has focused primarily on aircraft (think about endurance and range, longitudinal stability, and forces). The focus, however, of the course Introduction to Aerospace Engineering has also been put on spacecraft. The next parts will be about a mission design to take a closer look at the Hellas Basin. Mars is home to giant dust storms, that start in a small region but can grow to planet-size storms within days. In 2001, a giant dust storm was captured by the Mars Global Surveyor and the Hubble Space Telescope (http://science.nasa.gov/science-news/science-atnasa/2001/ast16jul_1/). Dust storm season starts when Mars is closest to the Sun, but it is not clear in detail how dust storms develop, with feedback mechanisms from temperature and clouds (http://www.thunderbolts.info/tpod/2005/arch05/050324dustmars.htm). Recent research focuses on how regional dust storms emerge in topographic basins (Hinson et al. 2012). Dust storms pose a threat to the life of spacecraft on Mars. They can double atmospheric drag (Johnston et al. 1998), and reflect up to 25% of the incoming sunlight (http://science.nasa.gov/science-news/science-at-nasa/2003/09jul_marsdust/). It is also known that most dust storms start in specific terrain. The 2001 dust storm developed in the Hellas basin, a 2300 km wide impact basin on the southern hemisphere. A solar airplane could offer a closer look at the terrain of the Hellas basin and provide insight in the local topography and composition of the surface. The objective of M1 and M2 is to design the solar airplane and determine some mission parameters. There is no unique solution for the design and iteration will be necessary to meet the requirements. The table below provides parameters for the scientific payload and several subsystems. Diameter of cylindrical container containing airplane Power for camera Mass of the camera Power for communication (average over day and night) Night duration Effective incidence angle Battery energy density Mass density of the solar cells Chord Electric motor efficiency Propeller efficiency

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2.65 m 6.5 W 1 kg 5W 13.2 h 45˚ 200 Wh/kg 0.32 kg/m2 0.30 m 0.87 0.79

Project manual AE1111-I – Exploring Aerospace engineering

Learning objectives Schedule

The student should be able to:  Produce a mission design within constraints/requirements.  Work in a team towards a design solution.

 

2017/2018

scientific

(210 min.) Working out of [Task 1,2 and 3]. Some tasks can be executed in parallel. (30 min.) Discuss and combine results.

Make sure that you write clearly on everything you hand in who has worked on it.

Deliverables  

Answers to all questions, including calculations (equations and numerical values) for [Task 1, 2 and 3]. The results should be presented in the poster to be produced during M3.

Task 1: Launch configuration For launch and successful delivery of the airplane to Mars, it should fit into a cylindrical container with diameter specified in the table. Describe possible solutions to fit an airplane with large wingspan in the container and derive the maximum wing span from these. Drawings of the configuration can be used for the poster presentation (M3).

Task 2: Cruise flight Calculate the power that needs to be delivered during the day (camera operating) and night (camera not operating). At night, the power needs to be delivered by the batteries. Calculate how much power needs to be generated by the solar cells (during daytime) for daytime operation and for charging the batteries. You can assume the following: ‐ The mass of the structure (without solar cells, batteries and camera) is 0.25 kg; ‐ The surface area outside the wings is 0.3 m2 (thus the total area is b  c + 0.3m2); ‐ The cruise altitude is 1500 m; ‐ The Sun and the airplane are on the equatorial plane of Mars. The effective incidence angle of the Sun is given in the table. Calculate the surface of the solar cells, the mass of the solar cells and the mass of the batteries. Use the efficiency for the solar cell that was determined in PW. The efficiency of the propeller is defined as the power delivered to the airplane divided by the electric power delivered by the batteries

Pbr  Pel motor

Assume the power used by the propeller is 15 W. Is this sufficient for cruise flight? It will be necessary to select a wing profile suitable for flight on Mars. For drag and lift calculations, you can use the excel sheet developed earlier in the project.

Task 3: Iteration of the Design Improve the design of the airplane so that the conditions for cruise flight can be met. Choose from the following options: different efficiency for the solar cells or propeller, different wing profile (CD and CL), different mass density for the batteries. Proceed by implementing one or a combination of these improvements in the design and repeat the calculations in Task 2.

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Project manual AE1111-I – Exploring Aerospace engineering

M2

2017/2018

Mars Mission Design II

To contribute to the knowledge of dust storms the following requirements for a solar powered Mars mission are derived: - collect 1 minute of video footage at 30 frames per second during daylight - a ground resolution of 1 m is required. The objective of this assignment is to complete the design of the solar powered Martian airplane so that the science objectives can be achieved.

Learning objectives

The student should:  Produce a mission design within constraints/requirements.  Work in team towards a design solution.

Schedule

  

scientific

(60 min.) dividing tasks and literature survey (150 min.) Working out of [Task 1-5]. (30 min.) Discuss and combine results

Make sure that you write clearly on everything you hand in who has worked on it.

Deliverables  

Answers to all questions, including calculations (equations and numerical values) for [Task 1-4]. The results can be used in the poster to be produced in MD3.

Figure 1: Hellas Basin (http://en.wikipedia.org).

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Figure 2: topography model including cross section of the Hellas Basin (http://www.solarviews.com).

Project manual AE1111-I – Exploring Aerospace engineering

2017/2018

Task 1: Resolution Calculate the cruise height of the airplane so that the minimum ground resolution of the video is achieved. Use data from heritage satellite instruments for the viewing angle of the camera. (for example, see http://nssdc.gsfc.nasa.gov/imgcat/html/object_page/vo2_428b61.html). Is this a reasonable cruise height? If not, select a new viewing angle and new cruise height using reasonable assumptions on the aircraft's flight envelope.

Task 2: Transmitting the video Design the orbit of the orbiting spacecraft so that the 1 minute movie can be transmitted from the solar powered airplane to the orbiting spacecraft during each orbit, with an antenna that can handle a bit rate of 200 kbit/s. Assume that the resolution is 720x480 pixels, the colour depth is 24 bits per pixel and MPEG2 compression is used for the movie. Start by assuming a certain orbit height and calculate the contact time between the airplane and the orbiting spacecraft taking into account the rotation of Mars. Calculate the bit rate after compression when the airplane is in contact with the orbiting spacecraft. If the bit rate is too high for the antenna, lower the bit rate by adjusting one of the parameters and discuss the effect of this adjustment. Note that other mission requirements for the satellite impose a maximum altitude below the orbit of Phobos.

Task 3: Dust storm Calculate how long it takes to cover the area in figure 1 by the airplane. When the airplane flies through a dust storm, the solar flux reduces by 25% and the aerodynamic drag doubles. Calculate how long it takes before the batteries run out. Assume steady, straight, symmetric and level flight conditions.

Task 4: Rate of climb The centre of Hellas Basin is 7 km deep, see Figure 2. Can the airplane fly across the crater while maintaining the same ground resolution?

Task 5: Deployment Describe how the airplane can be brought from the spacecraft orbit height found (assumed) in Task 2 down to the flying altitude calculated in Task 1. Quantitative simulations are not required, but the scientific literature should be consulted.

References Fortescue P, Stark J & Swinerd G 2003, Spacecraft System Engineering 3rd Ed., John Wiley and Sons, Chichester. Johnston, M.D., Esposito, P. B., Alwar, V., Demcak, S. W., Graat, E. J., Mase, R. A., Mars Global Surveyor Aerobraking at Mars, 1998. AAS/AIAA Space Flight Mechanics Meeting, Paper AAS 98112, Monterey, CA. Jon D. Pelletier, Kelly J. Kolb, Alfred S. McEwen, and Randy L. Recent bright gully deposits on Mars; wet or dry flow? 2008. Geology, 36(3):211-214.

Kirk,

Hinson, D.P., Wang, H. & Smith, M.D, A multi-year survey of dynamics near the surface in the northern hemisphere of Mars: Short-period baroclinic waves and dust storms, 2012. Icarus, 219:307-320.

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Project manual AE1111-I – Exploring Aerospace engineering

M3

2017/2018

Mars Mission Design – Poster/screen presentation

The design of a Mars mission (M1 and M2) is to be presented in a poster. Some parts of the design were straight forward, other parts involved weighing several alternatives. The poster should present the aspects that are most interesting in the design of the Mars airplane.

Learning objectives Schedule

The student should be able to:  Summarize the main items in the design.  Produce a poster with scientific content in an attractive layout.

    

Deliverables 

(30 min.) Read instructions and examine template (30 min.) Define and divide tasks (150 min.) Work out parts of poster (20 min.) Discuss and finalize poster. (10 min.) Upload poster to BrightSpace

Make sure that you write clearly on everything you hand in who has worked on it. Poster according to the template provided on BrightSpace, uploaded to the groups file exchange.

Task 1: Poster/screen presentation Some examples of what the poster could contain: ‐ Text and images explaining the Mars mission design (wing area, power requirements, power delivered, cruise speed, altitude) ‐ Text on the design and how it meets the requirement of indefinite cruise flight. ‐ iteration of the design to meet the requirement of the antenna bit rate. ‐ Images of how the Mars airplane is folded in the launch cylinder. ‐ Images of the flight pattern across Figure 1 or Figure 2. ‐ Images of the deployment. A PowerPoint presentation can be found on BrightSpace, containing instructions that have to followed. Furthermore, a template is provided and the grading sheet is shown.

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Project manual AE1111-I – Exploring Aerospace engineering

2017/2018

Appendix A – Numerical Integration Usually, the application of integration, involves the definite integral: b

I   f (x)dx

(1)

a

Many techniques of integration have been developed, however not every technique can be used in every situation. When trying to find an “anti-derivative” of f (x) , two obstacles can prevent you calculating from I in this way: 1. Finding an anti-derivative of f in terms of familiar functions may be impossible, or at least very difficult. 2. We may not be given a formula for f (x) as a function of x, for instance, f (x) may be an unknown function whose values at certain points have been determined by experimental measurements. When values are determined by experimental measurements, we can investigate the problem by approximating the value of the definite integral I using numerical integration. We can make use of many methods for evaluating definite numerical integrals. For example: Upper and Lower sums, the Trapezoid Rule, the Midpoint rule, Simpson’s Rule and the Romberg Method. For numerical integration, the Trapezoid Rule, as illustrated in Figure 1, is an easy and quick way to make an approximation. It is assumed that f (x) is continuous on [a,b]. Divide [a,b] into n subintervals of equal length h  (b  a)/ n using n  1 points x0  a x1  a  h xn  a  nh  b (2) If the value of f (x) at each of these points is known; y0  f ( x0 ) y1  f (x1 ) yn  f ( xn )

(3)

the curve can be replaced by straight lines between the points of the small intervals (figure A.1). The area beneath a straight line segment represents a trapezoid. Now, the first trapezoid has vertices (x0, 0), (x0, y0), (x1, y1) and (x1, 0). The two parallel sides are vertical and have lengths y0 and y1. The perpendicular distance between them is h = x1 − x0. And the area of this trapezoid is h times the average of the parallel sides: x1 y0  y1 (A.4) x f (x)dx  h 2 0 It follows that the original integral, I, can be approximated by the sum of these trapezoidal areas; b yn1  yn   y0  y1 y1  y2 (5) a f (x)dx  h  2  2  ...  2  1  1 (6)  h  y0  y1  y2  ...  yn1  yn  2  2

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Project manual AE1111-I – Exploring Aerospace engineering

2017/2018

Figure 1: The trapezoid rule The sum of the differences between the areas enclosed by the curve and by the trapezoids is the error made by this method. A much smaller error is given by Simpson’s Rule, which will be introduced in later courses in the first-year curriculum.

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