Problem: Need to find lift and the ratio of lift to induced drag, for a straight tapered, twisted wing.
Flight condition:
flight speed 100 m/s
freestream density: 1.2 kg/m3
freestream static temperature: 288K
Wing Geometry:
Root chord: 3m.
Span: 15m.
Taper ratio: 0.5
Twist (linear): 2 degrees washout.
Section lift curve slope: 6.0 per radian.
Section zero-lift angle of attack: -2 deg.
Geometric angle of attack at mid semi-span : 5 deg.
Solution:
Tip chord = 0.5 * root chord= 1.5m.
Wing area S = 2*(3+1.5)*7.5/2= 33.75m2.
Aspect ratio = b2/S = 225/33.75= 6.667
We’ll use a symmetric, 2-coefficient Fourier series, using only odd coefficients. Thus, our assumed distribution of bound circulation along the span is given by:
Pick 2 points on the wing, that are not the tip or the middle (these points already satisfy the equation)
The transformation from x-y coordinates to ‘theta’ coordinates is
Pick q of p/3 and p/6 as locations where we will write down the equation. This is equivalent to satisfying the equation at y =3.75m and6.495m respectively.
At q = p/6, the absolute angle of attack (the LHS of the Prandtl lifting line equation, equal to the local section angle of attack, relative to its zero-lift angle):
chord 
So, writing out Prandtl’s lifting line equation,
so that
………………….Eq.
(1)
Similarly, we write the equation atq = p/6. Note that here the chord is 2.25m, and the absolute angle of attack is 0.12217 radians.
………………….Eq.
(2)
Solve these two equations. We get
=
0.02519
=
0.0008538
The lift and induced drag coefficients can be found as follows:
Spanwise efficiency factor
Lift –to-drag is simply the ratio of the lift coefficient to the induced drag coefficient, and comes out to be 39.56.