AAE 334, Fall 2011, Homework 11 SOLUTIONS
Due Monday, September 26 at the beginning of class.
1.
Consider a single horseshoe vortex of span
i
b centered on the origin of the coordinate system,
0
,
0
,
y
x
, in the z=0 plane as shown below in a view from above the wing.
The strength of the vortex
is
i
.
What is the induced velocity at a point
j
j
y
x
y
x
,
,
, in the z=0 plane?
It may be handy to write the answer in terms of
i
A
sin
,
i
B
sin
,
i
A
cos
, and
i
B
cos
, and then list what
these four trig functions are in terms of
j
j
i
i
y
x
y
x
,
,
,
.
You can assume that the point
j
j
y
x
,
is not on
the head of the horseshoe vortex.
The induced velocity at
j
j
y
x
,
is the sum of induced velocities from the three parts of the
horseshoe vortex:
j
j
tip
j
j
tip
j
j
Head
j
j
i
y
x
w
y
x
w
y
x
w
y
x
w
,
,
,
,
where the three parts are
the head, the tip at positive
b
i
/2
and the tip at negative