Module 7 - Lifting Line Theory

Question 1

What is geometric twist? Why might it be introduced to a wing?

Answer 1

Geometric twist varies the geometric angle of attack along the span of the wing.
The designer is likely trying to obtain an elliptical lift distribution to minimize induced drag

Question 2

What is aerodynamic twist? What characteristics change along the span?

Answer 2

Aerodynamic twist varies the aerofoil profile across the span of the wing.

The zero-lift angle of attack, lift slope, and profile thickness ratio may change along the span of a wing with aerodynamic twist.

Question 3

What are Helmholtz’s vortex theorems?

Answer 3

1. The strength of a vortex filament is constant along its length
2. A vortex filament can’t end in a fluid, it must extend to infinity or form a closed path

Question 4

Why is a single horseshoe vortex not used in lifting line theory?

Answer 4

It produces physically unrealistic downwash distribution, including infinite downwash at the wing tips

Question 5

What is the simple model of lifting line theory?

Answer 5

Place infinite horseshoe vortices with the bound vortices placed along the lifting line with varying lengths from 0 to b

Question 6

How are the strengths of trailing vortices related to lift distribution in lifting line theory?

Answer 6

They are equal to the change in circulation along the lifting line at that point

Question 7

What is the circulation at the wing tips in lifting line theory?

Answer 7

0

Question 8

What is the statement of the fundamental equation of lifting line theory?

Answer 8

Geometric angle of attack = effective angle of attack + induced angle of attack

Question 9

What do we assume about the form of a general lift distribution in lifting line theory? What do we solve for? What is the general solution process?

Answer 9

1. Sine Fourier series
2. Sine Fourier series coefficients
3. Sub Fourier series into fundamental equation at N points along lifting line, solve N coefficients. With N unknowns and N equations the coefficients can be solved and plugged back into the Fourier series to get the circulation distribution

Question 10

For an elliptical lift distribution wing with no twist, what do we know about the a) lift distribution b) downwash distribution c) platform area

Answer 10

a) elliptical lift distribution
b) constant downwash
c) elliptical planform

Question 11

What happens to the lift of a wing compared to its aerofoil section? What happens when the aspect ratio is increased?

Answer 11

Wing lift slope is lower, as AR increases it will approach the lift slope of its aerofoil section

Question 12

Why do gliders have long slender wings?

Answer 12

To minimize induced drag