Airfoil Compressibility Corrections: Prandtl–Glauert and Its Limitations

The factor

For a slender body in subsonic flow, linearized theory says disturbances scale with

β = √(1 − M²)

The Prandtl–Glauert rule then reads an incompressible solution and stretches it:

Cp ≈ Cp,inc / β and CL ≈ CL,inc / β

At Mach 0.3, β is about 0.95, so the correction is a few percent. At Mach 0.6, β is 0.8, so lift and suction are about 25% stronger than the incompressible values. At Mach 0.8, β is 0.6 and the factor is large. The formula does not know whether a shock has already appeared. It will keep growing as Mach approaches 1, which is the formula leaving its assumptions, not the airfoil reaching an infinite lift.

What it is allowed to correct

How to apply it without fooling yourself

1. Compute the incompressible, or the low-Mach viscous, polar at the right Reynolds number.
2. If the flight Mach number is below about 0.3, you may be done. Write Mach = 0.1 anyway so the case is explicit.
3. If you apply the factor, apply it to lift and to the pressure, and do not also apply a second compressibility switch inside the solver. Double-counting is a common 10% error.
4. Check the corrected minimum Cp against the sonic Cp at that Mach. If the corrected suction is already past sonic, the factor has announced its own failure. Move to a transonic method for that point, and read the critical-Mach lesson before you quote a drag rise.

---

Where this sits in the series

In simple words: what this page is for

The Prandtl–Glauert rule stretches incompressible lift and pressure by 1 over the square root of 1 minus Mach squared. It is a small-disturbance, subsonic correction. It is not a shock model.

This lesson exists because section decisions fail when geometry, method labels and selection reasons are scattered. Airfoil Compressibility Corrections: Prandtl–Glauert and Its Limitations helps you keep a clean trail from shape to polar to choice.

Why the topic matters

Engineers lose time when a title sounds clear but the page only sketches the idea. This article expands Airfoil Compressibility Corrections: Prandtl–Glauert and Its Limitations so you can answer three questions without jargon: what is the idea, when do you use it, and how do you check it in a HENDOI product.

Read the sections above for the core definitions. Use the steps below to move from reading into a real project trail you can share with a teammate.

How to apply this in HENDOI

In practice: create a HENDOI account or log in, open HENFOIL, bring a section in (create, import DAT, or digitize), pass the geometry gate, climb the analysis ladder only as far as the decision needs, then compare and archive. Every calculated number should keep its method label.

When the section choice is ready for the aircraft, continue in HENSYNTH for mission, compliance and trades. Same account. Same plans.

What this page will not claim: a teaching polar or geometry note is not a flight-Re certificate. HENFOIL labels methods so you know what you bought. Tunnel data and professional judgement still sit outside any single software run.

Checklist before you leave this page

• Can you state the idea of Airfoil Compressibility Corrections: Prandtl–Glauert and Its Limitations in one sentence?
• Do you know which product owns the next action — HENFOIL or HENSYNTH?
• Will every number you keep carry a method label or a stored-run source?
• If you are new here, have you opened Register or Login?

Related reading on this site

• Active Flow Control on Airfoils: Suction, Blowing and Synthetic Jets
• How Adverse Pressure Gradients Affect Airfoil Boundary Layer Separation
• What Is the Aerodynamic Center of an Airfoil? Location, Meaning and Applications
• What Is Airfoil Aerodynamic Efficiency Across a Range of Flight Conditions?
• All HENDOI blog articles
• HENFOIL product page
• HENSYNTH product page
• Pricing — Student, Professional & Team
• FAQ
• Login · Register now

• Previous: Camber, zero-lift angle and lift distribution
• Next: Reynolds-number similarity
• Index: all HENFOIL airfoil lessons

These pages teach the ideas. They are not wind-tunnel data and not a certification analysis. When a number matters, compute it at a stated Reynolds number, Mach number and transition setting, and keep the method label on the result. In HENFOIL that production polar is a VIC polar — see the analysis ladder and the polar field guide.