Aero II

1
Aero II Lifting Line Theory Lecture 36
J. E. Brandenburg EAS 3010 Spring 2007
2
Agenda

• Horseshoe Vortex
• Lifting Line Theory

3
Vortex Ring
4
Circulation
5
Bernoulli Equation
6
Vortex Ring Shooter
7
Trailing Vortex
At end of wings vorticity does not end but spills
off end of wing
8
Downwash
9
Induced angle of attack
Induced angle of attack
Geometric angle of attack ?
Effective angle of attack ?eff ? - ?i
10
Infinite versus Finite wings
CL is reduced by finite wing effects
11
Pressure Drag
Backwards lift component
12
Space Shuttle Landing
13
Horseshoe Vortex
14
Starting Vortex
15
Lift Distribution
16
Lifting Line Theory
We can define ?(x) on wing surface
17
Lifting result
18
Biot-Savart Law
Caution ! Do not grab electric wires!
19
Biot-Savart Law
20
Biot-Savart Law
21
Biot-Savart Law
22
Biot-Savart Law
23
Horseshoe Vortex
Free Vortex
Bound Vortex
We can define ?(x) as a collection of horseshoe
vortices
24
Horseshoe Vortex
yb/2
Free Vortex
Evaluation point
Effect of distant vortex motion
y-b/2
25
Horseshoe Vortex Effect
26
Horseshoe Vortex Effect
27
Lifting Line Theory
We can define ?(x) on wing surface
28
Lifting Line Theory
?(y)
Lifting line
We can define ?(x) on wing surface as a
distribtion of horeshoe vortices
29
Horseshoe Vortex Contribution
30
Induced Angle of Attack
31
Induced Angle of attack
32
Lift Per Unit length
33
Lift Per Unit length
34
Lift Per Unit length