Chapter 5

Question 1

Dimensionally speaking, what is the difference between an airfoil and a finite wing.

Answer 1

An airfoil has 2D geometry while a finite wing has 3D geometry.

Ref: Anderson Pg. 427

Question 2

How do tip vortices affect streamlines above and below the wing?

Answer 2

The streamlines on the top are pushed toward the root while the streamlines on the bottom are pulled toward the tips.

Ref: Anderson Pg. 428

Question 3

What is the equation for the effective angle of attack?

Answer 3

alpha_eff = alpha - alpha_induced

Ref: Anderson Pg. 429

Question 4

Does d’Alembert’s paradox occur for a finite wing? Why or why not?

Answer 4

No, the reason is that drag (induced) is predicted by inviscid incompressible theory.

Ref: Anderson Pg. 430

Question 5

Can induced drag be considered a type of pressure drag?

Answer 5

Yes

Ref: Anderson Pg. 430

Question 6

The total drag is a combination of what?

Answer 6

Induced drag, skin friction drag, and pressure drag (due to flow separation).

Ref: Anderson Pg. 431

Question 7

What components of the total drag are due to viscous effects? What is the common name of the sum of these two drag components?

Answer 7

Skin friction drag and pressure drag.
Profile Drag

Ref: Anderson Pg 431

Question 8

True or False

If the circulation is taken about any path enclosing a vortex filament, a constant value of circulation is attained.

Answer 8

True

Ref: Anderson Pg. 432

Question 9

What are the three Helmholtz vortex theorems?

Answer 9

1. The strength of a vortex filament is constant along its length.
2. A vortex filament cannot end in a fluid; it must extend to the boundaries of the fluid (which can be +/- infinity) or form a closed path.
3. A fluid that is initially rotational remains rotational and vv unless non-conservative forces act.

Ref: Anderson Pg 435

Question 10

Define washout with respect to geometric twist.

Answer 10

The tip is at a lower geometric angle of attack than the root.

Ref: Anderson Pg. 435

Question 11

Define washin with respect to geometric twist.

Answer 11

The tip is at a higher geometric angle of attack than the root.

Ref: Anderson Pg. 435

Question 12

True or False

For a finite wing, the lift distribution will b zero at the tips.

Answer 12

True

Ref: Anderson Pg. 435

Question 13

What is the difference between a bound vortex and a free vortex?

Answer 13

A bound vortex is fixed to a geometric body while a free vortex moves with the same fluid elements throughout a flow.

Ref: Anderson Pg. 436

Question 14

Give the equation for lift from the Kutta-Joukowski (KJ) theorem.

Answer 14

L’=rho_infifnityV_infinityGamma

Ref: Anderson Pg. 440

Question 15

True or False

A vortex filament can end in a fluid.

Answer 15

False

Question 16

Describe the “lifting line.”

Answer 16

A line upon which a large number of horseshoe vortices, each with a different length of the bound vortex, but with all the bound vortices are coincident.

Question 17

For an infinite number of horseshoe vortices along a lifting line, what is the total strength of the sheet integrated across the span?

Answer 17

Zero.

Ref: Anderson Pg. 438

Question 18

What is the effective angle of attack?

Answer 18

The angle of attack actually seen by the local airfoil section.

Question 19

Is the effective angle of attack a variable? Why?

Answer 19

Yes. Since downwash varies across the span, the effective angle of attack varies with span unless the wing is elliptic.

Question 20

When will the angle of attack at zero lift be a variable?

Answer 20

When there is aerodynamic twist.

Ref: Anderson Pg. 440

Question 21

When will the angle of attack at zero lift be constant?

Answer 21

When there is no aerodynamics twist in the wing.

Ref: Anderson Pg. 440

Question 22

For an elliptic wing what two properties are constant with respect to the chord?

Answer 22

Downwash and induced angle of attack.

Ref: Anderson Pg. 443

Question 23

The induced drag coefficient for an elliptic wing is directly proportional to what other important parameter? Inversely proportional to what other parameter?

Answer 23

Directly: C_L^2
Inversely: A_R (aspect ratio)

Ref: Anderson Pg. 444

Question 24

The power required from an aircraft engine to overcome the induced drag is ______.

Answer 24

The same power required to generate the lift of the aircraft.

Ref: Anderson Pg. 445

Question 25

To reduce induced drag, what should be done to the aspect ratio?

Answer 25

Make it as high as possible (see eq 5.43 in the book) Ref: Anderson Pg. 445

Question 26

In order for a lift distribution to be elliptical, what must the platform of the wing look like?

Answer 26

An ellipse. Ref: Anderson Pg. 446

Question 27

What is the difference between geometric twist and aerodynamic twist?

Answer 27

Geometric twist changes the geometric angle of attack through a geometric in-wash or out-wash. Aerodynamic twist occurs then the angle of attack at zero lift changes as a function of span (due to chamber change). Ref: Anderson Pg. 446

Question 28

Important! | How does the lift slope of a finite wing compare to an airfoil?

Answer 28

The airfoil's lift slope is higher than the finite wing. The difference is due to induced drag. Ref: Anderson Pg. 454

Question 29

For an elliptic wing with no geometric twist what factors are constant?

Answer 29

1. Induced angle of attack 2. effective angle of attack 3. c_l 4. C_L Ref: Anderson Pg. 454

Question 30

For an elliptic wing with no geometric twist, is the local lift coefficient (c_l) equal, greater, or less than the total lift coefficient (C_L)?

Answer 30

Equal. Ref: Anderson Pg. 454

Question 31

At zero lift what values do the induced angle of attack and induced drag ratio take on?

Answer 31

Zero. Ref: Anderson Pg. 454

Question 32

In what scenario will the angle of attack at zero lift be the same for both an airfoil and a finite wing?

Answer 32

When C_L=0 and the geometric angle of attack (alpha) is equal to the effective angle of attack (alpha_eff). Ref: Anderson Pg. 454

Question 33

As the aspect ratio approaches infinity, what happens to the lift slopes for the airfoil and finite wing?

Answer 33

They start to become equal. Ref: Anderson Pg. 456

Question 34

What actually induces downwash at the lifting line? The lifting line itself or the trailing vortex sheet?

Answer 34

The trailing vortex sheet. Ref: Anderson Pg. 457

Question 35

Can a discontinuous change in tangential velocity theoretically cross a vortex sheet? In real life, do such discontinuities exist?

Answer 35

Yes No Ref: Anderson Pg. 457

Question 36

What lift distribution yields a minimum induced drag?

Answer 36

Elliptic Ref: Anderson Pg. 449

Question 37

Define the taper ratio:

Answer 37

TR = ct/cr Ref: Anderson Pg 450

Question 38

A plot of the lift coefficient vs the drag coefficient is called the_____.

Answer 38

Drag Polar. Ref: Anderson Pg 452