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 A0=0.2 and A1=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
cl=π(2A0+A1). So putting A0 and A1 we get cl = 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 αL=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 αL=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, αL=0 shifts to the negative side.
5. The moment coefficient for a thin cambered airfoil about the leading edge is given by______
a) cm,le=-0.5π(2A0+A1)
b) cm,le=-π(A0+A1+A2)
c) cm,le=-0.5π(A0+A1-0.5A2)
d) cm,le=-π(2A2+A1)
View Answer
Explanation: The moment coefficient for a thin, cambered airfoil about the leading edge is given by cm,le=-0.5π(A0+A1-0.5A2). We can verify that for a symmetric airfoil A1 and A2 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) cm,le=-(\(\frac {c_l}{2}+\frac {\pi }{4}\)(A1-A2))
b) cm,le=-(\(\frac {c_l}{4}+\frac {\pi }{4}\)(A1-A2))
c) cm,le=-(\(\frac {c_l}{4}\)+(A1-A2))
d) cm,le=(\(\frac {c_l}{2}+\frac {\pi }{4}\)(A1-A2))
View Answer
Explanation: The lift coefficient is cl=π(2A0+A1). When we put this in the formula for moment coefficient about the leading edge, cm,le=-0.5π(A0+A1-0.5A2) we get the desired relation.
7. Given an angle of attack 5°, A1=1.5, A2=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 cm,l/4=\(\frac {\pi }{4}\)(A2-A1) which is cm,c/4=cm,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 (cm,l/4=\(\frac {\pi }{4}\)(A2-A1)). 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 (cm,l/4=\(\frac {\pi }{4}\)(A2-A1)) 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 xcp=\(\frac {c }{4}\)(1+\(\frac {\pi }{c_l}\)(A1-A2)). 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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