Overview and Intermediate's lift equation (L = ½ρV²S·CL) implicitly
assumes INCOMPRESSIBLE flow — valid at low Mach numbers, but air
genuinely compresses as speed increases, and CL itself changes as a
result, even in the subsonic regime, before any shockwave forms.

Prandtl-Glauert correction (valid roughly M < 0.7-0.8, before
transonic effects dominate):

  CL_compressible = CL_incompressible / √(1 - M²)

As M increases toward 1, the denominator shrinks toward zero, so
CL_compressible grows — meaning a wing produces MORE lift for the
same geometry and angle of attack as compressibility becomes
significant, not less. This is a real, first-order correction
engineers apply before ever reaching the transonic regime where
Fundamentals' drag-rise effects take over.

Given:  CL_incompressible = 0.5

At M = 0.6:
  CL_compressible = 0.5 / √(1 - 0.6²) = 0.5 / √(0.64) = 0.5 / 0.8
  CL_compressible = 0.625

At M = 0.7:
  CL_compressible = 0.5 / √(1 - 0.7²) = 0.5 / √(0.51) = 0.5 / 0.714
  CL_compressible = 0.700

Verified programmatically: both values computed directly from the
formula. Notice the correction grows non-linearly as M approaches
1 — going from M=0.6 to M=0.7 (a 0.1 increase) grew CL by 0.075,
noticeably more than a similar-sized Mach increase would at a lower
starting M — this accelerating growth is exactly why the correction
becomes unreliable and is abandoned once transonic effects (shocks,
flow separation) take over above roughly M=0.7-0.8.

CRITICAL MACH NUMBER (Mcr) — the free-stream Mach number at which
local airflow SOMEWHERE on the airfoil (almost always the point of
maximum curvature on the upper surface) first reaches exactly
Mach 1, even though the aircraft's own speed is still subsonic.

This is the precise, quantitative version of Fundamentals'
qualitative transonic explanation — Mcr is a specific, real number
for a given airfoil shape (not a fixed universal value), and flying
above Mcr is what actually triggers the drag-rise Fundamentals
described, because that's the point local shockwaves begin forming.

A THINNER, less-cambered airfoil generally has a HIGHER Mcr (delays
the onset of local supersonic flow, and therefore drag rise, to a
higher flight Mach number) — a real, first-order reason supersonic
and high-subsonic aircraft use thin airfoil sections, at the direct
cost of internal volume for fuel/structure that a thicker airfoil
would provide.

EFFECTIVE MACH NUMBER seen by a swept wing's airflow:
  M_effective = M_flight · cos(Λ)

Where Λ (capital lambda) is the wing's sweep angle, measured from
the perpendicular to the fuselage.

The physical idea: only the velocity component PERPENDICULAR to the
wing's leading edge actually "does the work" of accelerating flow
over the airfoil's curvature the way Mcr cares about — sweeping the
wing back reduces that perpendicular component relative to the
aircraft's true forward speed, without changing the true airspeed at
all.

Given:  M_flight = 0.85

Unswept (Λ = 0°):
  M_effective = 0.85 · cos(0°) = 0.85 · 1.0 = 0.85
  -> the wing's airflow experiences the FULL flight Mach number

Swept 35° (Λ = 35°):
  M_effective = 0.85 · cos(35°) = 0.85 · 0.8192 = 0.696

Verified programmatically: cos(35°) = 0.8192, giving an effective
Mach of 0.696 -- noticeably below the aircraft's true 0.85 flight
Mach. If this airfoil's Mcr is, say, 0.72, the UNSWEPT wing (seeing
the full 0.85) would already be well past Mcr and deep into drag
rise, while the SWEPT wing (seeing only 0.696) would still be safely
below Mcr at the exact same true flight speed -- the sweep alone is
what makes the difference between "already past drag rise" and
"not yet."