This set of Aerodynamics Question Paper focuses on “The Cambered Airfoil – 3”.

1. The lift curve slope for a thin, cambered airfoil is 2π.

a) True

b) False

View Answer

Explanation: The lift curve slope for cambered airfoils is also equal to 2π. This comes from the thin airfoil theory, irrespective of the shape of airfoils.

2. The coefficient of lift for a thin, cambered airfoil with A_{0}=0.2 and A_{1}=1.12 is____

a) π1.52

b) π1

c) π0.52

d) π2

View Answer

Explanation: The lift coefficient from the thin airfoil theory for a cambered airfoil is given by

c

_{l}=π(2A

_{0}+A

_{1}). So putting A

_{0}and A

_{1}we get c

_{l}= π1.52.

3. Which of the following does not hold for the zero-lift angle of attack?

a) It is a negative value

b) Denoted by α_{L=0}

c) It is zero for a symmetric airfoil

d) Does not depend on the slope of the camber line

View Answer

Explanation: The zero lift angle of attack is the value of angle of attack where the lift is zero. It is a negative quantity and depends on the shape of the airfoil (slope of the camber line). It is zero for a symmetric airfoil.

4. The zero-lift angle of attack for a thin, cambered airfoil increases in magnitude with the increasing camber of the airfoil.

a) True

b) False

View Answer

Explanation: Using the formula for α

_{L=0}=\(\frac {-1}{\pi}\int_0^{\pi}\frac {dz}{dx} \)(cos∅-1)d∅, the dependence of the zero-lift angle of attack on camber can be seen. It is clear that for higher cambered airfoils, α

_{L=0}shifts to the negative side.

5. The moment coefficient for a thin cambered airfoil about the leading edge is given by______

a) c_{m,le}=-0.5π(2A_{0}+A_{1})

b) c_{m,le}=-π(A_{0}+A_{1}+A_{2})

c) c_{m,le}=-0.5π(A_{0}+A_{1}-0.5A_{2})

d) c_{m,le}=-π(2A_{2}+A_{1})

View Answer

Explanation: The moment coefficient for a thin, cambered airfoil about the leading edge is given by c

_{m,le}=-0.5π(A

_{0}+A

_{1}-0.5A

_{2}). We can verify that for a symmetric airfoil A

_{1}and A

_{2}are both zero giving the moment coefficient about the leading edge for a symmetrical airfoil, which is not satisfied by other options.

6. The relation between lift coefficient and moment coefficient about the leading edge is_______

a) c_{m,le}=-(\(\frac {c_l}{2}+\frac {\pi }{4}\)(A_{1}-A_{2}))

b) c_{m,le}=-(\(\frac {c_l}{4}+\frac {\pi }{4}\)(A_{1}-A_{2}))

c) c_{m,le}=-(\(\frac {c_l}{4}\)+(A_{1}-A_{2}))

d) c_{m,le}=(\(\frac {c_l}{2}+\frac {\pi }{4}\)(A_{1}-A_{2}))

View Answer

Explanation: The lift coefficient is c

_{l}=π(2A

_{0}+A

_{1}). When we put this in the formula for moment coefficient about the leading edge, c

_{m,le}=-0.5π(A

_{0}+A

_{1}-0.5A

_{2}) we get the desired relation.

7. Given an angle of attack 5°, A_{1}=1.5, A_{2}=2 and the chord length is 5m, the moment coefficient about the quarter-chord is_____

a) \(\frac {\pi }{8}\)

b) \(\frac {\pi }{4}\)

c) \(\frac {-\pi }{8}\)

d) –\(\frac {\pi }{4}\)

View Answer

Explanation: The coefficient of moment about the quarter-chord is given by c

_{m,l/4}=\(\frac {\pi }{4}\)(A

_{2}-A

_{1}) which is c

_{m,c/4}=c

_{m,le}+\(\frac {c_l}{4}\). In this question, it comes out as \(\frac {\pi }{8}\).

8. The quarter-chord moment coefficient for a cambered airfoil depends on______

a) Chord length

b) Angle of attack

c) The shape of the airfoil

d) Center of pressure

View Answer

Explanation: The coefficient of moment about the quarter-chord is independent of angle of attack and chord length. It depends on the shape of the cambered airfoil (slope of the camber line (\(\frac {dz}{dx}\))).

9. The quarter-chord is the center of pressure for a cambered airfoil.

a) False

b) True

View Answer

Explanation: The coefficient of moment about the quarter-chord is not zero for a cambered airfoil (c

_{m,l/4}=\(\frac {\pi }{4}\)(A

_{2}-A

_{1})). The center of pressure is the point about which the total moment is zero. Therefore, this statement is false.

10. The quarter-chord is the aerodynamic center for a cambered airfoil.

a) True

b) False

View Answer

Explanation: The coefficient of moment about the quarter chord (c

_{m,l/4}=\(\frac {\pi }{4}\)(A

_{2}-A

_{1})) is independent of angle of attack α, thereby making it the aerodynamic center (moment coefficient independent of angle of attack) for a thin cambered airfoil.

11. For a cambered airfoil, the center of pressure does not vary with_____

a) Chord length

b) Angle of attack

c) The shape of the airfoil

d) Location of the aerodynamic center

View Answer

Explanation: This solution is best answered from the formula for the center of pressure which is x

_{cp}=\(\frac {c }{4}\)(1+\(\frac {\pi }{c_l}\)(A

_{1}-A

_{2})). Moreover, the aerodynamic center is located at the quarter-chord but the center of pressure keeps changing with the other three parameters.

12. When the lift becomes zero, the center of pressure of the cambered airfoil is at which point on the airfoil (consider given lengths are from the leading edge)?

a) Quarter-chord length

b) Mid-chord length

c) 0 (i.e. at the leading edge)

d) ∞ (i.e. the point does is not on the airfoil)

View Answer

Explanation: The center of pressure of a cambered airfoil will leave the airfoil and move at a very large distance away from the airfoil. This is one reason why the aerodynamic center is preferred over the center of pressure since it is always at the quarter-chord but the later keeps on changing with the angle of attack.

13. The aerodynamic center for all the airfoils lies exactly at the quarter-chord always for all the given angle of attacks.

a) True

b) False

View Answer

Explanation: The aerodynamic center is always near the quarter-chord for airfoils with linear lift and moments but it is not exactly the quarter-chord always.

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