42. The goal of this problem is to design the camberline of an airfoil using thin airfoil theory such that the following two constraints are met:

The lift coefficient at zero angle attack a0 is 0.5.

Ce=27+

The center of pressure at zero angle attack a-0 is located at the quarter chord

) such that

the airfoil has neutral static stability.

NO Cafberca

Consider the equation of the camber line is given by the equation.*

0

YEu dI

2TL

where A & B are two constants, x and z are the Cartesian coordinates relative to the origin, and c is the chord of the thin airfoil.

Using thin airfoil theory for a uniform flow V past the airfoil with angle of attack a, please calculate:

1. Please find the constant A and B in Eq(1) that fulfill the two constraints above? (20%)
2. The lift coefficient can be expressed as C, = Boa+B1. Find the constant Bo and B,? (10%

2A+ LB

For this problem, the thin airfoil theory gives:

Lift coefficient C,=(2A0+Ai); The center of pressure location:

6B

42

2

36

(A - A)]

G

( CupcT

1

where A, = a -

c* dz

0

d0 ; 4, =

dx

2

dz cosnOde for n = 1,2,.

20

dx

attack. Useful formula:

cos 20 = (2 cos 0 - 1);

cos Ode = 0

- cos e) and a is angle of cos odo = 2 cos ode=0;

2. The goal of this problem is to design the camberline of an airfoil using thin airfoil theory such that the following two constraints are met: - The lift coefficient at zero angle attack =0 is 0.5 . cl=2(+i1[dx2 - The center of pressure at zero angle attack =0 is located at the quarter chord(cX=41) such that the airfoil has neutral static stability. where A&B are two constants, x and z are the Cartesian coordinates relative to the origin, and c is the chord of the thin airfoil. Using thin airfoil theory for a uniform flow V past the airfoil with angle of attack , please calculate: (a) Please find the constant A and B in Eq(1) that fulfill the two constraints above? (20\%) (b) The lift coefficient can be expressed as Cl=B0+B1. Find the constant B0 and B1 ? (10\%) Cl=(2A0+A1)=(2x(10x46B+22A+6B For this problem, the thin airfoil theory gives: Lift coefficient C1=(2A0+A1); The center of pressure location: cXcp=41[1+C1(A1A2)]=A23B22A where A0=10xdxdzd;An=20xdxdzcosnd for n=1,2,;cx=21(cos) and is angle of attack. Useful formula: cos2=(2cos21),[0cosd=0,[0cos2d=2,[0cos3d=0; 0cos4d=83