hw5 - 16.100 Homework Assignment 5 Due Wednesday October 12...

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 .