f07_sp - Fluids Lecture 7 Notes 1. Elliptical Lift...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Fluids Lecture 7 Notes 1. Elliptical Lift Distribution Reading: Anderson 5.3.1 Elliptical Lift Distribution Definition and lift calculation Consider an elliptical spanwise circulation distribution given by 2 y 2 ( y ) = 0 1 b y b/2 0 b/2 where 0 is the circulation at the wing center at y = 0. The overall lift on the wing is the integral of the corresponding lift/span distribution L ( y ) = V ( y ). b/ 2 b/ 2 2 y 2 L = L ( y ) dy = V 0 1 dy = V b b/ 2 b/ 2 b 4 The integral can be evaluated via integral tables, or by inspection by noting that the area under an ellipse is / 4 times the area of the enclosing rectangle. Downwash calculation Computation of the downwash first requires knowing the trailing vortex sheet strength, which is minus the derivative of the circulation. d 4 y ( y ) = = dy b 2 1 (2 y/b ) 2 The downwash at some location y o is then b/ 2 y 1 b/ 2 ( y ) dy 0 dy w ( y o ) = = 4 b/ 2 y o y b 2 b/ 2 1 (2 y/b ) 2 y o y As in thin airfoil theory, the mathematical problem is considerably simplified by making the trigonometric substitution b y o = cos o 2 b y = cos 2...
View Full Document

This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.

Page1 / 4

f07_sp - Fluids Lecture 7 Notes 1. Elliptical Lift...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online