Aerodynamics Final Exam

A) List the necessary conditions to reduce the Navier-Stokes equations to the (unsteady) Euler equations.What else is necessary to have irrotational flow? (1 point)

B) The figure below shows a simple model for a F1 racing car, where the front and rear wings of the car aremodeled as point vortices of circulation in a 2D plane. Do the aerodynamic forces on the vortex modelingthe front wing result in a positive Fx (drag), or do they result in a negative Fx (thrust)? (1 point)

x

zU'

K

K

L

h 5h

C) Match airfoil numbers to the letters of the different cl() curves. The base airfoil is A1. Explain yourchoices. (1 point)

ABC

DE

cl

_

1

2

3

4

5

D) An experimental airfoil designed to fly at supersonic speeds has a flexible camber given by

zc(x)

c= "c

x

c

(1 x

c

)(xc+ a

),

where the value of a is controlled by the flight computer. Compute the function a() that needs to be pro-grammed in the flight computer so that the center of pressure of the airfoil remains fixed at x/c = 1/4 for anyM > 1. (1 point)

Dept. of Bioengineering and Aerospace Engineering 1 2012/13

Aerodynamics Final Exam

E) In order to design the airfoil for the vertical plane of the tail of a commercial airplane, we consider a thinsymmetric airfoil flying at zero angle of attack. The airfoil is equipped with a trailing edge flap, hinged atx = xB, whose deflection angle is " 1. The design specifications fix a critical Mach number M,cr = 0.9when = 0, and a distribution of perturbation velocities at cruise conditions (M = 0.5, = 0) equal to

u(x, 0) = u0x

c

(1 x

c

).

With these design criteria:

1. Compute the value of u0/U that results in the desired critical Mach number, M,cr = 0.9. (1 point)

2. Solve the inverse thickness problem to compute zt(). (1 point)

3. Is there any value of xB that yields cm,c/4 = 0, irrespective of M and ? (1 point)

F) Consider a wing flying at velocity U in air of density . The wing is made of thin symmetric airfoils, withno geometric twist. The distribution of circulation along the wing is

(y) = 0

[1

4(yb

)2].

Assume that on top of and U, we know the mass M of the wing, the span b, the aspect ratio AR and thevalue of the chord at the root cr = c(y = 0).

1. Compute the value of 0 and CL. (1 point)

2. Compute the induced angle of attack. (1 point)

3. Compute the angle of attack () and the chord distribution c(y) of the wing. (1 point)

HINT: Note that you can solve problem F without computing the coefficients An. In that case, the followingintegral might come in handy:

ydy

y0 y = y0 ln(y0 y) y + constant.

Dept. of Bioengineering and Aerospace Engineering 2 2012/13