SME
Aerodynamics · Problem type
Prandtl–Glauert correction of Cₚ
Use this for “At low speed, a point on a wing has a pressure coefficient Cₚ = −0.4. What is Cₚ at that point when the wing flies at M = 0.6?”
Chart
Cₚ(0.6) = −0.5
This is an example. Type your own values to start a new problem.
Cₚ
=
Cₚ₀
1
−
M
2
β
Compressibility factor
calculated
Formulas
β
=
√
1 −
M
2
0.8
=
√
1 −
0.6
2
Cₚ
=
Cₚ₀
β
−0.5
=
−
0.4
0.8
Assumptions
•
Thin airfoil at small angle of attack in subsonic flow, so the disturbances stay small.
•
Cₚ₀ is the pressure coefficient at the same point in low-speed (incompressible) flow.
•
Good to about M 0.7; it fails near M 1, where shocks form.
Step-by-step
WE KNOW
Cₚ₀ = −0.4, M = 0.6
FIND
compressibility factor (β), pressure coefficient (Cₚ)
Step 1 · Find compressibility factor (β)
Use β = √(1 − M²)
Square
M
,
take
it
from
1,
then
take
the
square
root.
β
=
√
1 −
0.6
2
β
=
√
1 − 0.36
β
=
√
0.64
β
=
0.8
Step 2 · Find pressure coefficient (Cₚ)
Use Cₚ = Cₚ₀ ÷ β
Divide
the
low-speed
Cₚ
by
β
;
it
grows
as
M
rises.
Cₚ
=
−
0.4
0.8
Cₚ = −0.5
Check
Put the numbers back in. Both sides should match.
0.8
=
√
1 −
0.6
2
✓
−0.5
=
−
0.4
0.8
✓
Topic check
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