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Our friends aerodynamicists, have
given us a quite simple expression for
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drag coefficient, CD = CD0 the constant
term called parasitic drag
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plus Ki CL square a term dependent
on the lift and called induced drag.
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A simplistic explanation
to this dependence on lift,
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comes from the fact that to create lift.
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The wing pushes down on the air.
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This creates a downwash behind the wing.
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Of course, we cannot have
a discontinuity between the downwash and
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still air of the wing.
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And as you can see on this
beautiful picture from NASA,
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a vortex appears at the wingtip.
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This large motion of the mass
of air around the airplane,
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requires a significant transfer of kinetic
energy from the airplane to the air,
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which is obtained through
an increase of the drag.
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The corresponding theory called
the lifting line theory,
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has been developed by Ludwig Prandtl.
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He has shown that the induced
drag coefficient Ki should
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be equal to 1/ Pi lambda
with lambda z aspect ratio.
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This is true for an elliptic lift
distribution along the wing.
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Later, if the additional e0 efficient,
called the Oswald efficiency factor,
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was proposed to account for
non elliptic lift distribution.
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Practically speaking, those
coefficients may vary from the theory.
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as CD0 will capture all
the constant rate contributions, and
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Ki all the contributions dependent
on lift and angle of attack,
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even if not directly induced by lift.
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The constant parasitic drag coefficient,
CD0.
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accounts for friction drag,
a direct effect of air viscosity and
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pressure drag, due in particular
to boundary layer separation.
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Obviously ,this drag is formed
not only on the wing, but
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all over the wet surface
of the entire airplane.
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This "wet" surface is the one that
would be covered with paint,
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if I dip the
whole airplane in a paint bucket.
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This includes wings, fuselage,
empennage, landing gear antennas, etc.
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For this reason, wet area must be kept
to a minimum, to reduce parasitic drag.
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The last contribution to CD0 is wave drag,
due to sonic shock.
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As wave drag is due to sonic shock,
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it does not exist below
the critical Mach number.
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It appears in the transonic domain,
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when a pocket of supersonic flow forms
on the upper surface of the wing.
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However, it remains relatively small, up
to Mdd, the drag-divergence Mach number,
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where it starts to increase
dramatically with Mach number.
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The precise definition of Mdd may vary,
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depending on the threshold value retained
for the gradients CD over delta M.
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A great improvement of airliner wings
in the last decades, has been to
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increase the separation between Mc and
Mdd and push the last closer to Mach one.
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While keeping a thick wing,
which is lighter to design and
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hosts more fuel, on supersonic
airplanes fitted with thin wings.
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The way of drag increase is less
dramatic and reduces above Mach 1.
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Reasonable values are recovered
above typically Mach 1.3.
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But it is never interesting
to fly close to Mach 1.
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[SOUND]
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