16.100 Homework Assignment # 5
Due: Wednesday, October 12, 9am
Reading Assignment
Anderson, 3
rd
edition: Chapter 5 Section 5.1 – 5.3
All of the reading will be directly useful in the problems.
In this homework, we will apply Prandtl’s lifting line to predicting the lift and induced drag of a
tapered wing.
The wing is symmetric about the root and the planform is shown below:
c
t
y
c
r
b
/ 2
The airfoil of the wing is symmetric (uncambered).
In this homework, we will specifically be
looking at the cruise performance of the wing and considering how different taper ratios,
r
t
c
c
/
=
σ
(in Problem #1), and geometric twist distributions,
)
(
y
g
α
(in Problem #2) affect the
induced drag.
Problem #1: Effect of Taper Ratio and Aspect Ratio (50%)
In this problem, we will analyze the impact of taper ratio and aspect ratio on an untwisted,
0
)
(
=
y
g
α
. We will assume that the circulation distribution can be well approximated by the
first two
odd
terms (i.e. n=1 and n=3) in the Fourier series expansion:
( )
∑
=
∞
=
Γ
N
n
n
n
A
bV
1
sin
2
θ
θ
where
θ
cos
2
b
y
−
=
Note: we will only use odd terms as the even terms are asymmetric about
.
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 Fall '03
 willcox
 Dynamics, Aerodynamics, Wing, Lift, Airfoil, Wing design

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