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Our friends aerodynamicists, have
given us a quite simple expression for

drag coefficient, CD = CD0 the constant
term called parasitic drag

plus Ki CL square a term dependent
on the lift and called induced drag.

A simplistic explanation
to this dependence on lift,

comes from the fact that to create lift.

The wing pushes down on the air.

This creates a downwash behind the wing.

Of course, we cannot have
a discontinuity between the downwash and

still air of the wing.

And as you can see on this
beautiful picture from NASA,

a vortex appears at the wingtip.

This large motion of the mass
of air around the airplane,

requires a significant transfer of kinetic
energy from the airplane to the air,

which is obtained through
an increase of the drag.

The corresponding theory called
the lifting line theory,

has been developed by Ludwig Prandtl.

He has shown that the induced
drag coefficient Ki should

be equal to 1/ Pi lambda
with lambda z aspect ratio.

This is true for an elliptic lift
distribution along the wing.

Later, if the additional e0 efficient,
called the Oswald efficiency factor,

was proposed to account for
non elliptic lift distribution.

Practically speaking, those
coefficients may vary from the theory.

as CD0 will capture all
the constant rate contributions, and

Ki all the contributions dependent
on lift and angle of attack,

even if not directly induced by lift.

The constant parasitic drag coefficient,
CD0.

accounts for friction drag,
a direct effect of air viscosity and

pressure drag, due in particular
to boundary layer separation.

Obviously ,this drag is formed
not only on the wing, but

all over the wet surface
of the entire airplane.

This "wet" surface is the one that
would be covered with paint,

if I dip the
whole airplane in a paint bucket.

This includes wings, fuselage,
empennage, landing gear antennas, etc.

For this reason, wet area must be kept
to a minimum, to reduce parasitic drag.

The last contribution to CD0 is wave drag,
due to sonic shock.

As wave drag is due to sonic shock,

it does not exist below
the critical Mach number.

It appears in the transonic domain,

when a pocket of supersonic flow forms
on the upper surface of the wing.

However, it remains relatively small, up
to Mdd, the drag-divergence Mach number,

where it starts to increase
dramatically with Mach number.

The precise definition of Mdd may vary,

depending on the threshold value retained
for the gradients CD over delta M.

A great improvement of airliner wings
in the last decades, has been to

increase the separation between Mc and
Mdd and push the last closer to Mach one.

While keeping a thick wing,
which is lighter to design and

hosts more fuel, on supersonic
airplanes fitted with thin wings.

The way of drag increase is less
dramatic and reduces above Mach 1.

Reasonable values are recovered
above typically Mach 1.3.

But it is never interesting
to fly close to Mach 1.

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