Dr. Nikos J. Mourtos AE 162
A Boeing 747-SP is climbing out of San Francisco International Airport. The following
information is known for the 747:
Take-off Weight
Span
Gross Wing Area
Wing Taper Ratio
Zero-lift angle of the wing
W = 3 x 106 N
b = 60 m
S

Dr. Nikos J. Mourtos AE 162
Horseshoe Vortex Model of a Wing and its Wake
Define
An airplane with wing span b = 20 m, weight W = 10 kN just took off and is flying @ a
speed V = 100 m / sec. After 0.2 sec in flight, the vortex formation is as show

Dr. Nikos J. Mourtos AE 162 Open-Ended Problem
2 BIRDS
Two identical, low aerodynamic IQ birds are flying at the
same speed one directly behind another. If the power
required by the 1st bird to overcome its induced drag is 0.1
hp, what is app

Dr. Nikos J. Mourtos AE 162 Potential Flow Theory
Example: Determine whether a flow is rotational or irrotational
Consider a vortex flow defined by the radial and tangential velocity components:
ur = 0
and
u! = !
c
r
respectively, where c is a constant.
D

Dr. Nikos J. Mourtos AE 162 Potential Flow Theory
Example: Analyze the flow field around a Rankine semi infinite body
!
= 1.5 m 2 / s is placed at the origin and combined with a
2!
uniform flow u! = 9 m / s in the positive x direction. Calculate the follo

Dr. Nikos J. Mourtos AE 162 Potential Flow Theory
Example: Obtain the equation for the streamlines of a flow
Consider a velocity field where the x and y components of the velocity are given by
u=
cx
(x + y 2 )
2
and
!=
cy
(x + y 2 )
2
where c is a constan

Dr. Nikos J. Mourtos AE 162 Wing Theory / Aerodynamic Interference
Define
You just finished testing a wing model in a subsonic wind tunnel with a rectangular
cross-section.
Given
Wind tunnel cross-sectional area
Horizontal distance of wingtips from wind t

1
Dr. Nikos J. Mourtos AE 162 Potential Flow Theory
Example: Given the stream function, analyze the flow field
A flow field is described by the stream function:
# 25 & 628 r
! = 100y % 1 " 2 ( +
ln
$
r ' 2! 5
(1)
What is the
(a) Shape of the zero streamli

Dr. Nikos J. Mourtos AE 162 Potential Flow Theory
1
Example: Given the velocity field, analyze the flow field
The following velocity field is given:
"
r2 %
uz = umax $ 1 ! 2 '
# R &
where umax , R are const.
ur = 0
u! = 0
(a) Does it represent a real flow

Dr. Nikos J. Mourtos AE 162
Define
An airplane has a wing with elliptical planform and is flying through sea level air.
Given:
Airplane speed:
V = 45 m / s
Wing loading:
W / S = 1,000 N / m2
Wing span:
b = 10 m
Aspect ratio:
A=5
No geometric twist.
Same a

Dr. Nikos J. Mourtos AE 162 Potential Flow Theory
Example: Calculate circulation around a path
Calculate the circulation about a closed path enclosing a free vortex.
Solution
A streamline of the free vortex at distance r from the origin is illustrated in

Dr. Nikos J. Mourtos AE 162
1
Define
Consider a vortex ring shed by a bird flapping her wings in flight. Derive an expression
for the velocity at the center of this ring, induced by the vortex ring itself.
Explore
We need to apply the Biot Savart law to c

Dr. Nikos J. Mourtos AE 162 Wing Theory / Monoplane Equation
Define
Calculate the aerodynamic coefficients of an airplane wing with the following
characteristics:
Airfoil
Geometric twist
Zero-lift angle
Leading-edge sweep
Quarter-chord sweep
Trailing-edge