lec30 - Aerodynamics Lecture 30 Prandtls Lifting Line...

Info icon This preview shows pages 1–7. Sign up to view the full content.

Aerodynamics Prandtl’s Lifting Line Theory 30.1 Lecture 30 Aerodynamics Wing: Prandtl’s Lifting Line Theory AE311 Aerodynamics Manoj T. Nair IIST
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Aerodynamics Prandtl’s Lifting Line Theory 30.2 Agenda 1 Prandtl’s Lifting Line Theory
Image of page 2
Aerodynamics Prandtl’s Lifting Line Theory 30.3 Prandtl’s Lifting Line Theory I Fundamental equation of Prandtl’s lifting line theory α = Γ( y 0 ) π V c ( y 0 ) + α L = 0 + 1 4 π V Z b / 2 - b / 2 ( d Γ / dy ) dy ( y 0 - y ) The solution yields Γ = Γ( y 0 ) y 0 ranges along the span from - b / 2 to b / 2 The aerodynamic characteristics of a finite wing are then obtained The lift distribution from Kutta-Joukowski theorem L 0 ( y 0 ) = ρ V Γ( y 0 ) The total lift is L = Z b / 2 - b / 2 L 0 ( y ) dy L = ρ V Z b / 2 - b / 2 Γ( y ) dy
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Aerodynamics Prandtl’s Lifting Line Theory 30.4 Prandtl’s Lifting Line Theory II The lift coefficient is C L = L q S = 2 V S Z b / 2 - b / 2 Γ( y ) dy Induced drag D 0 i = L 0 i sin α i D 0 i = L 0 i α i The total induced drag D i = Z b / 2 - b / 2 L 0 ( y ) α i ( y ) dy D i = ρ V Z b / 2 - b / 2 Γ( y ) α i ( y ) dy The induced drag coefficient is C D , i = D i q S = 2 V S Z b / 2 - b / 2 Γ( y ) α i ( y ) dy
Image of page 4
Aerodynamics Prandtl’s Lifting Line Theory 30.5 Prandtl’s Lifting Line Theory III Elliptic Lift Distribution Before discussing the general solution, lets discuss a special case Consider the circulation distribution given by Γ( y ) = Γ 0 s 1 - 2 y b 2 Γ 0 is the circulation at the origin Circulation varies elliptically with y along the span
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Aerodynamics Prandtl’s Lifting Line Theory 30.6 Prandtl’s Lifting Line Theory IV
Image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.
  • Fall '14
  • Manoj
  • Aerodynamics, Lift, Airfoil, dy, lifting line

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern