Chapter 5 Flashcards
Dimensionally speaking, what is the difference between an airfoil and a finite wing.
An airfoil has 2D geometry while a finite wing has 3D geometry.
Ref: Anderson Pg. 427
How do tip vortices affect streamlines above and below the wing?
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
What is the equation for the effective angle of attack?
alpha_eff = alpha - alpha_induced
Ref: Anderson Pg. 429
Does d’Alembert’s paradox occur for a finite wing? Why or why not?
No, the reason is that drag (induced) is predicted by inviscid incompressible theory.
Ref: Anderson Pg. 430
Can induced drag be considered a type of pressure drag?
Yes
Ref: Anderson Pg. 430
The total drag is a combination of what?
Induced drag, skin friction drag, and pressure drag (due to flow separation).
Ref: Anderson Pg. 431
What components of the total drag are due to viscous effects? What is the common name of the sum of these two drag components?
Skin friction drag and pressure drag.
Profile Drag
Ref: Anderson Pg 431
True or False
If the circulation is taken about any path enclosing a vortex filament, a constant value of circulation is attained.
True
Ref: Anderson Pg. 432
What are the three Helmholtz vortex theorems?
- The strength of a vortex filament is constant along its length.
- 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.
- A fluid that is initially rotational remains rotational and vv unless non-conservative forces act.
Ref: Anderson Pg 435
Define washout with respect to geometric twist.
The tip is at a lower geometric angle of attack than the root.
Ref: Anderson Pg. 435
Define washin with respect to geometric twist.
The tip is at a higher geometric angle of attack than the root.
Ref: Anderson Pg. 435
True or False
For a finite wing, the lift distribution will b zero at the tips.
True
Ref: Anderson Pg. 435
What is the difference between a bound vortex and a free vortex?
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
Give the equation for lift from the Kutta-Joukowski (KJ) theorem.
L’=rho_infifnityV_infinityGamma
Ref: Anderson Pg. 440
True or False
A vortex filament can end in a fluid.
False
Describe the “lifting line.”
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.
For an infinite number of horseshoe vortices along a lifting line, what is the total strength of the sheet integrated across the span?
Zero.
Ref: Anderson Pg. 438
What is the effective angle of attack?
The angle of attack actually seen by the local airfoil section.
Is the effective angle of attack a variable? Why?
Yes. Since downwash varies across the span, the effective angle of attack varies with span unless the wing is elliptic.
When will the angle of attack at zero lift be a variable?
When there is aerodynamic twist.
Ref: Anderson Pg. 440
When will the angle of attack at zero lift be constant?
When there is no aerodynamics twist in the wing.
Ref: Anderson Pg. 440
For an elliptic wing what two properties are constant with respect to the chord?
Downwash and induced angle of attack.
Ref: Anderson Pg. 443
The induced drag coefficient for an elliptic wing is directly proportional to what other important parameter? Inversely proportional to what other parameter?
Directly: C_L^2
Inversely: A_R (aspect ratio)
Ref: Anderson Pg. 444
The power required from an aircraft engine to overcome the induced drag is ______.
The same power required to generate the lift of the aircraft.
Ref: Anderson Pg. 445
To reduce induced drag, what should be done to the aspect ratio?
Make it as high as possible (see eq 5.43 in the book)
Ref: Anderson Pg. 445
In order for a lift distribution to be elliptical, what must the platform of the wing look like?
An ellipse.
Ref: Anderson Pg. 446
What is the difference between geometric twist and aerodynamic twist?
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
Important!
How does the lift slope of a finite wing compare to an airfoil?
The airfoil’s lift slope is higher than the finite wing. The difference is due to induced drag.
Ref: Anderson Pg. 454
For an elliptic wing with no geometric twist what factors are constant?
- Induced angle of attack
- effective angle of attack
- c_l
- C_L
Ref: Anderson Pg. 454
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)?
Equal.
Ref: Anderson Pg. 454
At zero lift what values do the induced angle of attack and induced drag ratio take on?
Zero.
Ref: Anderson Pg. 454
In what scenario will the angle of attack at zero lift be the same for both an airfoil and a finite wing?
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
As the aspect ratio approaches infinity, what happens to the lift slopes for the airfoil and finite wing?
They start to become equal.
Ref: Anderson Pg. 456
What actually induces downwash at the lifting line? The lifting line itself or the trailing vortex sheet?
The trailing vortex sheet.
Ref: Anderson Pg. 457
Can a discontinuous change in tangential velocity theoretically cross a vortex sheet? In real life, do such discontinuities exist?
Yes
No
Ref: Anderson Pg. 457
What lift distribution yields a minimum induced drag?
Elliptic
Ref: Anderson Pg. 449
Define the taper ratio:
TR = ct/cr
Ref: Anderson Pg 450
A plot of the lift coefficient vs the drag coefficient is called the_____.
Drag Polar.
Ref: Anderson Pg 452
