Operating conditions
Compressibility Effects on Airfoils: Critical Mach Number and Drag Divergence
HENDOI · 26 October 2026
Critical Mach number is when the peak local speed first reaches sonic. Drag divergence is the later freestream Mach number where drag actually rises. They are not the same Mach number.
Two Mach numbers worth not mixing up
The compressibility lesson set the scene. The definitions are sharp enough to keep on a data sheet:
- Critical Mach number, Mcr. The freestream Mach number at which the highest local Mach number on the surface reaches 1.0, at a stated lift coefficient. Below Mcr the flow is entirely subsonic. Above it there is a supersonic pocket, usually closed by a shock.
- Drag-divergence Mach number, Mdd. A freestream Mach number, again at a stated CL, where the drag rise becomes rapid. A common engineering marker is a slope of CD with Mach of about 0.10, or a stated number of drag counts above the low-speed level. Say which marker you used. Mdd is typically higher than Mcr. Supercritical sections exist to widen that gap and to keep the shock weak.
Neither number is a property of the airfoil name alone. Both fall as CL rises, because the suction peak is stronger. Both fall as thickness ratio rises, for the same reason. Sweep, which a 2D section does not include, raises the flight Mach number at which the normal-to-leading-edge section reaches these limits.
A screening picture
| Freestream Mach | What the section is doing |
|---|---|
| Below about 0.3 | Compressibility is a small correction. An incompressible viscous polar is the right first tool. |
| From there up to Mcr | Speeds and lift coefficients amplify. A compressibility correction can be an honest screen. There is still no shock. |
| Between Mcr and Mdd | A supersonic pocket and a shock may exist while the drag rise is still mild. This is a design region for supercritical sections, and it is outside a pure correction. |
| Above Mdd | Wave drag and often a moment break. Do not operate a cruise point here by accident. |
Preliminary design sometimes uses a correlation, such as Korn’s relation, to estimate Mdd from thickness, design CL and a technology factor that is higher for a supercritical section than for a conventional one. Treat that estimate as a start. It is not a computed shock. Confirm the short list with a method that can hold a shock, at the CL you will actually fly, and remember that a 2D Mdd is pessimistic relative to a swept wing at the same flight Mach.
Where this sits in the series
In simple words: what this page is for
Critical Mach number is when the peak local speed first reaches sonic. Drag divergence is the later freestream Mach number where drag actually rises. They are not the same Mach number.
This lesson exists because section decisions fail when geometry, method labels and selection reasons are scattered. Compressibility Effects on Airfoils: Critical Mach Number and Drag Divergence 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 Compressibility Effects on Airfoils: Critical Mach Number and Drag Divergence 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 Compressibility Effects on Airfoils: Critical Mach Number and Drag Divergence 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: Crosswind and yawed flow
- Next: Shock waves and wave drag
- 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.
Both products live
Use this lesson in the HENDOI workspace
This page sits in Operating conditions. HENFOIL and HENSYNTH are both live on one account. These articles are screening lessons — not certification reports.
Live · section
HENFOIL
Turn this lesson into a section you can draw, check, analyse and compare. Run the polar at the Reynolds number of the vehicle. The method name stays on the result.
To Know MoreLive · aircraft
HENSYNTH
After the section is chosen, set geometry and mission requirements, run screening, read compliance, synthesize candidates and download or mail the report.
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