16.885J/ESD.35J - Sept 2003
16.885J/ESD.35J
Aircraft Systems Engineering
Aerodynamics Primer
Prof. Earll Murman
16.885J/ESD.35J - Sept 2003
Topics
?Geometry jargon
? Standard atmosphere
? Airflow variables
? Forces acting on aircraft
? Aerodynamic coefficients
? Lift curve
? Drag polar
? Reference: Anderson, John D. Jr. Introduction to Flight,
McGraw Hill, 3rd ed. 1989. All figures in this primer are
taken from this source unless otherwise noted.
? Note: other sources need to be added.
16.885J/ESD.35J - Sept 2003
Wing and Airfoil Nomenclature
t = thickness
c = chord
t/c is an airfoil
parameter
t
c
V
8
16.885J/ESD.35J - Sept 2003
More Wing Nomenclature
b
S
c
r
c
t
/
? b = wing span
? S = wing area
? AR = aspect ratio=b
2
/S
– For c
avg
= S/b, AR= b/c
avg
? O = c
t
/c
r
= taper ratio
? / = leading edge sweep angle
? Twist is the difference in the
angle of the tip and root airfoil
section chord lines .
16.885J/ESD.35J - Sept 2003
Standard Atmosphere: The Environment
for Aircraft Design
? The “standard atmosphere” is a
reference condition.
– Every day is different.
? Temperature T, pressure p,
density U are functions of
altitude h.
? Standard sea level conditions
– p = 1.01325x10
5
N/m
2
= 2116.2 lb/ft
2
– T = 288.16
0
K = 518.7
0
R
– U = 1.2250 kg/m
3
= 0.00278 slug/ft
3
? Handy calculator
http://aero.stanford.edu/StdAtm.html
16.885J/ESD.35J - Sept 2003
Flow Velocities
?V
f
called the freestream velocity
– Units ft/sec, mph (1 mph = 1.47 fps), knot (1 kt = 1.69 fps=1.151 mph)
? a = speed of sound
– Function of temperature: a
1
/a
2
= sqrt(T
1
/T
2
)
– Function of altitude (standard sea level a = 1116.4 ft/sec)
? Mach number is ratio of velocity to speed of sound, M=V/a
–M
f
= V
f
/ a
f
–M
f
< 1 is subsonic flight, M
f
> 1 is supersonic flight
–M
f
close to 1 (approx 0.8 to 1.2) is transonic flight
16.885J/ESD.35J - Sept 2003
Pressures
21
? For M < 0.3, pressure and velocity are
related by Bernoulli equation
– For M > 0.3, pressure and velocity (or Mach number)
are related, but equation is more involved
– Further restricted to no losses due to friction.
?p
1
+ 0.5 UV
1
2
= p
2
+ 0.5 UV
2
2
= p
0
– p called static pressure
– 0.5 UV
2
called dynamic pressure = q
–p
0
called stagnation pressure
– p + q somewhat like potential plus kinetic energy
16.885J/ESD.35J - Sept 2003
Pressure Coefficient
? Due to geometry of airfoil, the
velocity, and therefore the
pressure, vary.
– Manifestation of lift
? It is convenient to express this
as a pressure coefficient
C
p
= (p - p
f
)/ q
f
? From Bernoulli Eq and
assuming density is constant
(ok for M < 0.3),
C
p
= 1 - (V/ V
f
)
2
? Pick out some features on
figure at left
Lift proportional
to area under
curve
Pressure coefficient for a
conventional airfoil: NACA 0012
airfoil at D = 3
0
.
Lower surface
U
p
p
e
r
s
u
r
fa
c
e
C
p
x/c
1
0
-1
-2
+1
16.885J/ESD.35J - Sept 2003
Forces
Wing imparts downward force on fluid, fluid imparts
upward force on wing generating lift.
Lift = Weight for steady level flight.
Drag is balanced by thrust for non-accelerating flight.
Aerodynamic leverage - lift is 10-30 times bigger than drag!
For 1 pound of thrust get 10-30 pounds of lift.
Aerodynamic leverage - lift is 10-30 times bigger than drag!
For 1 pound of thrust get 10-30 pounds of lift.
16.885J/ESD.35J - Sept 2003
L, D Definitions
? Resultant force on
body resolved into
Lift L and Drag D
? By definition,
– L is perpendicular to
relative wind
– D is parallel to
relative wind
c
/4
V
8
α
L
D
Relative wind
16.885J/ESD.35J - Sept 2003
Force Coefficients
? It is convenient to use non-dimensional forms of the
forces, called coefficients
? Allows scaling between different size aircraft (wind tunnel
models vs full scale), different velocities, altitudes, etc.
? Can use different ways, e.g.
– If C
L
, S, q are known, then L = C
L
Sq
– If L=W and C
L
, S are known, then flight speed which
gives level flight is
C
L
L
qS
, C
D
D
qS
where q
1
2
U
f
V
f
2
V
f
2W
U
f
C
L
S
16.885J/ESD.35J - Sept 2003
Lift Curve
L
if
t
s
lope
=
C
l, max
α
L=0
dC
l
d
α
α
C
l
α
stall
16.885J/ESD.35J - Sept 2003
Lift Generates A Vortex
For wing to
generate Lift
Low Pressure
High Pressure
Kinetic energy in freestream redistributed to cross flow. It represents
an unrecoverable loss called drag due to lift, or induced drag.
16.885J/ESD.35J - Sept 2003
Drag Due to Friction
? Friction due to fluid viscosity acting on total
surface of aircraft causes a skin friction drag.
16.885J/ESD.35J - Sept 2003
Drag
? Independent of Lift
– Skin friction
– Pressure changes due to boundary layer
– Flow separation due to shock (lecture 5)
– Shock wave drag (lecture 5)
? Plus lift dependent
– Induced (vortex drag)
– Viscous and wave drag to do lift
? Total Drag
C
D
0
f (Re,M
f
,shape)
C
D
i
C
L
2
S AR e
, e < 1
C
D
kC
L
2
f ( D,M
f
,Re)
C
D
C
D
0
C
L
2
S AR e
kC
L
2