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Bruno Pacheco

This course starts with a theoretical overview of the famous Navier-Stokes equations and how to simpllify them in order to get easier, yet insightful, potential equations for fast analysis.

Then we will focus in using these equations to derive the Vortex Panel Method (we'll cover all maths aspects also) and code it in Matlab. With that in hands, we will perform several analysis of generic airfoils to better understand how key design characteristics affect the overall results.

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This course starts with a theoretical overview of the famous Navier-Stokes equations and how to simpllify them in order to get easier, yet insightful, potential equations for fast analysis.

Then we will focus in using these equations to derive the Vortex Panel Method (we'll cover all maths aspects also) and code it in Matlab. With that in hands, we will perform several analysis of generic airfoils to better understand how key design characteristics affect the overall results.

On the next section, we'll go from 2D world to 3D, analysing wings now. Similarly, we'll start with a theoretical review of the Weissinger method for general wings (we'll cover all maths aspects also) and then we'll create a Matlab code to simulate the designs. We'll invistigate how several key parameters, such as sweep, aspect ratio, twist and others, can affect the overall behavior of wings.

Finally, we'll include viscous effects on the Weissinger method for a more robust analysis, including flow separation and stall.

This course is filled with real examples and is a more hands-on approach on the analysis of airfoils and wings. If your are an engineering student, aviation enthusiast, industry or academic engineer or just want to learn more about how to apply Aerodynamic theory, this is the right course for you.

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What's inside

Learning objectives

  • In-depth knowledge on aerodynamcs topics, supported by the coding of your own airfoil and wing analyzer
  • How to evaluate the characteristics of arifoils
  • Matlab coding applied to aerodynamics analysis
  • Design, simulate and optimize your own airfoil and wing designs
  • Vortex panel methods
  • Weissinger method
  • Estimate the stall angle of your wing designs
  • Vortex lattice method

Syllabus

Model and analyze your own airfoils

Hello and welcome. Let's get to know each other and take a look what we will learn in this course.

References for further studies:

Fundamentals of Aerodynamics - John D. Anderson Jr.

Aerodynamics for Engineers - John J. Bertin

Foundations of Aerodynamics: Bases of Aerodynamic Design - Kuethe and Chow

The Matlab version used in this course is 2020a. But if you follow the step by step instructions you can use any version after 2012a.

Read more

We'll learn how to simplify the famous and difficult Navier-Stokes equations to more simple maths in order to allow a fast approach in analyzing airfoils.

Irrotationality of the velocity potential

There are several elementary flows (source, sink, uniform, vortex, etc). In this section will learn how to derive and work with the uniform and vortex flow. Those are the ones that will be used in the future Vortex Panel Method we'll derive.

In part 1 of the airfoil theory, the goal is to introduce the geometric characterisitcs and explain the physiscs behind lift generation.

We'll also introduce the pressure coefficient concepts to pave the way to the airfoil analysis to be done on part 2.

This part 2 will focus on the viscous theory and in the analysis of several design characteristics of airfoils.

- NACA airfoils characteristics

- Camber

- Thickness

- Leading edge radius

- Flap deflection

We will work on the theoretical derivation of the linear varying Vortex Panel Method. A lot of maths in this section, but it will greatly help our coding in the next lesson.

The main sources for this section derivations are:

1- Foundations of Aerodynamics: Bases of Aerodynamic Design - Arnold M. Kuethe / Chuen-yen Chow - 4th Ed - section 5.10

2- Fundamentals of Aerodynamics - John D. Anderson - 3rd Ed - section 1.5


After the paved theoretical background from last lesson, let's get into Matlab and code our Panel Method for airfoil analysis.
The first part is dedicated to the airfoils' drawing. We'll cover NACA 4 and 5 digit airfoils as well as general shapes that can be loaded via an Excel spreadsheet.

The second part is dedicated to defining and checking the panel geometry as defined in out theoretical lesson.

The third part is dedicated to calculating the linear coefficients from the A matrix and solve for zero normal velocities at the panels to determine the circulation and therefore, the lift, drag and moment coefficients.

The last part is just to help the flow visualization by computing the streamlines around the airfoil.

Derivation of the general flow integral outside the airfoil
Checking the results
Exam 1

If you have a MATLAB version newer then 2016, you can open the live script (.mlx), otherwise, use the normal script (.m) VPM_lin

Model and analyze your own wings
Wing Theory

This lesson focus on the derivation of the Weissinger Method ofr the commputation of general planform wings. The references used are:

BERTIN, J. J.; CUMMINGS, R. M. Aerodynamics for engineers. 5. Ed. Englewood Cliffs, NJ: Pearson Prentice Hall, 2009.

PHILLIPS, W. F.; SNYDER, D. O. Modern adaptation of prandtl's classic lifting-line theory. Journal Of Aircraft. v.37, p. 662-670. Jul. 2000.


After the paved theoretical background from last lesson, let's get into Matlab and code our Weissinger Method for wing analysis.

Weissinger Method Coding - Part 2: Lift Calculation
Weissinger Method Coding - Part 3: Drag Calculation

Let's use our code to analyze several design characteristics of wings.

- Aspect Ratio

- Taper Ratio

- Sweep angle

- Geometric twist

- Aerodynamic Twist

Aspect ratio effect on CL x Alpha curve
Wing Design - Linear Characteristics

This section aims in constructing a numerical optimizer for the wing geometry (Aspect Ratio, taper, twist and sweep) in order to minimize drag and other constraints.

If you have a MATLAB version newer then 2016, you can open the live script (.mlx), otherwise, use the normal script (.m) WEISSINGER_MAIN

Let's get more realistic and analyse non-linear effects such as flow separation and stall.

In this lesson we'll learn how to use a potential method to compute viscous flows of wings.

The refetence used in the decambering method is:

Mukherjee, Rinku & Gopalarathnam, Ashok & Kim, Sung. (2003). An Iterative Decambering Approach for Post-Stall Prediction of Wing Characteristics from Known Section Data. 10.2514/6.2003-1097.

Modifying the Weissinger Code and Analysing the Results
Optimize wing planform to maximize CLmax
Final Exam
COURSE REFERENCES

References for further studies:

Fundamentals of Aerodynamics - John D. Anderson Jr.

Aerodynamics for Engineers - John J. Bertin

Foundations of Aerodynamics: Bases of Aerodynamic Design - Kuethe and Chow

PHILLIPS, W. F.; SNYDER, D. O. Modern adaptation of prandtl's classic lifting-line theory. Journal Of Aircraft. v.37, p. 662-670. Jul. 2000.

Mukherjee, Rinku & Gopalarathnam, Ashok & Kim, Sung. (2003). An Iterative Decambering Approach for Post-Stall Prediction of Wing Characteristics from Known Section Data. 10.2514/6.2003-1097.

The Matlab version used in this course is 2020a. But if you follow the step by step instructions you can use any version after 2012a.

Bonus Section

Good to know

Know what's good
, what to watch for
, and possible dealbreakers
Covers the fundamentals of aerodynamics and builds a solid foundation for further study in the field
Takes a practical approach by guiding learners through coding their own airfoil and wing analyzers, providing hands-on experience
Provides a comprehensive understanding of key design characteristics and their impact on airfoil and wing performance, equipping learners with valuable knowledge for practical applications
Utilizes multiple teaching methods, including theoretical explanations, coding exercises, and real-world examples, to enhance learning
Covers advanced topics such as vortex lattice methods and viscous effects, catering to learners seeking deeper knowledge in aerodynamics
Requires proficiency in MATLAB, which may limit accessibility for learners without prior coding experience

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Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Applied Aerodynamics - Airfoils and Wings with these activities:
Read Fundamentals of Aerodynamics
This book provides a comprehensive introduction to the fundamentals of aerodynamics and will help you understand the concepts covered in this course.
Show steps
  • Read the chapters on the basics of fluid mechanics.
  • Read the chapters on the aerodynamics of airfoils and wings.
Review Calculus
This course requires a solid foundation in calculus to fully understand and apply the Navier-Stokes equations.
Browse courses on Calculus
Show steps
  • Review the basics of differential and integral calculus.
  • Practice solving calculus problems.
Watch Aerodynamics Tutorials
Watching aerodynamics tutorials will help you supplement the material covered in this course and gain a deeper understanding of the concepts.
Show steps
  • Find aerodynamics tutorials online or on YouTube.
  • Watch the tutorials and take notes.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Solve Aerodynamics Problems
Solving aerodynamics problems will help you apply the concepts you learn in this course and improve your problem-solving skills.
Show steps
  • Find practice problems online or in textbooks.
  • Solve the problems using the concepts you learn in this course.
Volunteer at an Aerospace Museum
Volunteering at an aerospace museum will help you learn about the history of aviation and see real-world applications of aerodynamics.
Show steps
  • Find an aerospace museum in your area.
  • Contact the museum and inquire about volunteer opportunities.
Build an Airfoil Model
Building an airfoil model will help you visualize the concepts you learn in this course and gain a deeper understanding of how airfoils work.
Show steps
  • Design the airfoil using the concepts you learn in this course.
  • Build the airfoil model using materials such as foam or cardboard.
  • Test the airfoil model in a wind tunnel or using CFD software.
Find a Mentor in the Aerospace Industry
Finding a mentor in the aerospace industry will help you learn about the field and gain insights into career opportunities.
Show steps
  • Attend industry events and meet professionals in the aerospace field.
  • Reach out to professors or alumni in your field.
Design an Airplane Wing
Designing an airplane wing will help you apply the concepts you learn in this course and gain a deeper understanding of how wings work.
Show steps
  • Research different types of airplane wings.
  • Design the wing using the concepts you learn in this course.
  • Build a model of the wing and test it in a wind tunnel or using CFD software.

Career center

Learners who complete Applied Aerodynamics - Airfoils and Wings will develop knowledge and skills that may be useful to these careers:
Flight Test Engineer
Flight test engineers conduct tests on aircraft and other vehicles to ensure that they meet safety and performance requirements. They need to have a good understanding of aerodynamics, as well as other engineering disciplines. This course can help flight test engineers build a solid foundation in aerodynamics, which will enable them to be more effective in their roles.
Aerodynamicist
Aerodynamicists design, analyze, and modify aircraft and other vehicles. They need a deep understanding of how air interacts with objects, which is the core focus of this course. The mathematical principles taught in this course can help an aerodynamicist build a solid foundation in the field.
Computational Fluid Dynamics Engineer
Computational fluid dynamics engineers use computer simulations to analyze the flow of air and other fluids. They use their knowledge of aerodynamics and fluid dynamics to design and optimize aircraft, vehicles, and other products. This course can provide computational fluid dynamics engineers with a strong foundation in aerodynamics, which is essential for success in the field.
Aerospace Engineer
Aerospace engineers are responsible for designing, developing, testing, and maintaining aircraft, spacecraft, and other vehicles that fly. They use their knowledge of aerodynamics, structural mechanics, and other engineering disciplines to ensure that these vehicles are safe and efficient. This course can provide aerospace engineers with a strong foundation in aerodynamics, which is essential for success in the field.
Aircraft Structural Engineer
Aircraft structural engineers design and analyze the structural components of aircraft. They need to have a good understanding of aerodynamics, as well as other engineering disciplines. This course can help aircraft structural engineers build a solid foundation in aerodynamics, which will enable them to be more effective in their roles.
Avionics Engineer
Avionics engineers design, develop, and test electronic systems for aircraft, spacecraft, and other vehicles. They need to have a good understanding of aerodynamics, as well as other engineering disciplines. This course can help avionics engineers build a solid foundation in aerodynamics, which will enable them to be more effective in their roles.
Propulsion Engineer
Propulsion engineers design and develop the engines that power aircraft and other vehicles. They need to have a good understanding of aerodynamics, as well as other engineering disciplines. This course can help propulsion engineers build a solid foundation in aerodynamics, which will enable them to be more effective in their roles.
Flight Controller
Flight controllers are responsible for monitoring and controlling the flight of aircraft and other vehicles. They need to have a good understanding of aerodynamics, as well as other engineering disciplines. This course can help flight controllers build a solid foundation in aerodynamics, which will enable them to be more effective in their roles.
Mission Specialist
Mission specialists are responsible for the operation and maintenance of spacecraft and other vehicles during space missions. They need to have a good understanding of aerodynamics, as well as other engineering disciplines. This course can help mission specialists build a solid foundation in aerodynamics, which will enable them to be more effective in their roles.
Systems Engineer
Systems engineers are responsible for integrating the various subsystems of an aircraft or other vehicle into a single, functioning system. They need to have a good understanding of aerodynamics, as well as other engineering disciplines. This course can help systems engineers build a solid foundation in aerodynamics, which will enable them to be more effective in their roles.
Pilot
Pilots fly aircraft and other vehicles. They need to have a good understanding of aerodynamics, as well as other engineering disciplines. This course can help pilots build a solid foundation in aerodynamics, which will enable them to be more effective in their roles.
Air Traffic Controller
Air traffic controllers are responsible for managing the flow of air traffic in and out of airports. They need to have a good understanding of aerodynamics, as well as other engineering disciplines. This course can help air traffic controllers build a solid foundation in aerodynamics, which will enable them to be more effective in their roles.
Meteorologist
Meteorologists study the atmosphere and its effects on the weather. They use their knowledge to forecast the weather and to warn people about severe weather events. This course can help meteorologists build a solid foundation in aerodynamics, which will enable them to be more effective in their roles.
Science Writer
Science writers write about science and technology for a variety of audiences. This course can help science writers build a solid foundation in aerodynamics, which will enable them to write more accurately and informatively about this complex topic.
Teacher
Teachers teach students about a variety of subjects, including science, math, and engineering. This course can help teachers build a solid foundation in aerodynamics, which will enable them to be more effective in teaching their students about this important topic.

Reading list

We've selected 11 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Applied Aerodynamics - Airfoils and Wings.
This advanced textbook provides an in-depth exploration of the theoretical foundations of aerodynamics, with a focus on the design of aerodynamic systems.
Provides a foundational understanding of the fundamental principles of aerodynamics, covering topics such as fluid mechanics, potential flow, viscous flow, and compressible flow.
Provides an in-depth examination of compressible flow, including its history, governing equations, and applications in various fields. It valuable resource for advanced students and researchers.
This textbook provides a comprehensive overview of viscous fluid dynamics, covering topics such as Navier-Stokes equations, boundary layer theory, and turbulence. It valuable resource for both students and professionals.
Offers a comprehensive overview of aerodynamics, addressing topics such as airfoil theory, wing theory, and aircraft performance. It is an excellent reference for understanding the practical applications of aerodynamics.
This specialized textbook provides a comprehensive overview of the aerodynamics of helicopters, covering topics such as rotor aerodynamics, helicopter performance, and helicopter control.
This textbook provides a practical introduction to computational fluid dynamics (CFD), covering topics such as CFD methods, turbulence modeling, and CFD applications. It valuable resource for both students and professionals.
This specialized textbook examines the aerodynamics of vertical and/or short takeoff and landing (V/STOL) aircraft, covering topics such as V/STOL flight mechanics, propulsion systems, and aircraft design.
This textbook offers a comprehensive introduction to the fundamental principles and computational methods used in aerodynamics, providing a strong theoretical foundation for further study.
This textbook provides a comprehensive introduction to the principles and practice of flight dynamics, covering topics such as flight mechanics, stability and control, and aircraft performance.
This textbook provides a comprehensive overview of numerical methods for heat transfer and fluid flow, covering topics such as finite difference methods, finite volume methods, and finite element methods.

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