#### Transcript AE 301 Aerodynamics I

```Swept wings
• You have probably already noticed the swept wings
used on high speed airplanes.
• Wing sweep has two beneficial aerodynamic
purposes:
– It increases the critical Mach number in subsonic aircraft,
– and it decreases the wave drag in supersonic aircraft.
• The first effect can be seen by comparing the flow
across both an unswept and swept wings
Mt
M
M
L
AE 301 Aerodynamics I
Mn
L
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Swept wings (continued)
• Only the flow component normal to the leading edge,
Mt
Mn, sees the shape of the wing.
• The tangent component, Mt,
simply flows along the wing and
doesn’t contribute to pressure
variations.
M
Mn
L
• As a result, the Mach number on
the wing is effectively reduced by cos(L)
• Thus, theoretically, the wing critical Mach number is:
M cr,airfoil
M cr,wing 
cos(L)
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Swept wings (continued)
• In reality, the normal and tangent flows are not
completely independent, but interact with each other.
• As a result, the full theoretical benefit of sweep can
not be achieved. Thus:
M cr,airfoil  M cr,wing 
M cr,airfoil
cos(L)
• Still, sweep is very effective. Typical values for large
transports are in the range of 25 to 35.
and poor stall behavior.
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Swept wings (continued)
• The other use of wing sweep is to reduce the wave
drag of supersonic aircraft.
• Consider the two swept delta wings shown below
M

M



• The main difference between them is whether the
leading edge of the wing lies inside or outside of the
Mach cone originating from the point of the delta.
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Swept wings (continued)
• When the leading edge is outside the Mach cone:
– the velocity normal to the leading edge is supersonic
– thus each segment of the leading edge produces its own
shock wave
– the result: high wave drag.
• When the leading edge is inside the Mach cone:
– the normal velocity is subsonic.
– no shock are formed at the leading edge, except for the
point of the delta itself.
– the result: low wave drag.
• Using this design philosophy: the higher M, the
smaller , the greater the desired sweep, L!
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Variable Sweep
• Adding sweep for better high speed performance
inevitably hurts low speed performance like L/D ratio
• One fix is to consider
variable sweep:
• Of course, variable sweep wings are structurally
challenging!!
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High Lift Devices
• So far, we have seen that the faster we want to fly,
the thinner and higher swept we want our wing to
have in order to avoid wave drag.
• Both of these have a negative impact on the
maximum lift coefficient, CL,max , the wing can reach.
• Also, the faster our flight velocity, the smaller the
wing area we need since L=W=½V2S CL.
• Both of these effects act to increase the slowest
speed we can fly at: the stall speed
Vstall 
AE 301 Aerodynamics I
2W
  SC L ,max
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High Lift Devices (continued)
• Since we will still want to be able to fly slow at takeoff and landing, most wing designs include so called
high lift devices to help during these flight phases.
• The simplest of these devices is called the single
hinged flap.
d
• By deflecting this surface downwards, the camber of
the wing is effectively increase, thus increasing the
lift coefficient.
• The greater the deflection, the greater the lift: but,
too much deflection leads to separation and reduced
effectiveness and high drag!
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High Lift Devices (continued)
• Other type of flaps are:
Split flap: a little more effective
than a hinged flap, but very high
in drag.
Single slotted flap: moves aft and
down. Wing area is increased, and
flow through slot reduces separation.
Multiple slotted flap: like the one
above, but better and more complex.
Leading edge slat: works a lot like
the single slotted flap, but in front,
not back.
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Circulation Theory
• Circulation theory is an alternate conception of how
lift is produced by airfoils and wings.
• In reality, this theory is more a mathematically based
then physical, but the concepts developed are very
valuable.
• The theory is based upon some very basic flow
elements which are superimposed to emulate real
bodies:
Uniform Flow
AE 301 Aerodynamics I
Source (or Sink)
135
Vortex
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Circulation Theory (continued)
• Combining sources and sinks with a uniform flow
results in flow patterns similar to those around bodies
- in this case, an ovoid.
Uniform Flow
Source
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Sink
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Circulation Theory (continued)
• When a vortex in the center is added, lift is created
by the difference in pressure between top and
bottom:
Faster local
velocity
Source
Sink
Vortex
Uniform Flow
AE 301 Aerodynamics I
Slower local
velocity
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Circulation Theory (continued)
• The magnitude of the lift is given by the the KuttJoukowsky theorem:
l  V 
or
2
cl 
cV
• Where  is the circulation around the vortex. In
terms of the vortex velocity, u:
 
u 
2r
• For a sharp ended body, like an airfoil, the amount of
circulation is dictated by the need to have the aft
stagnation point at the trailing edge.
• This is known as the Kutta condition.
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```