Analysis methods
Airfoil Analysis at High Mach Numbers: Compressibility and Drag Rise
HENDOI · 27 October 2026
Above a section’s critical Mach number the suction peak goes sonic, a shock can form, and drag rises. Thickness, camber and lift all move that Mach number.
Mach number of the freestream, Mach number on the surface
Freestream Mach is M∞ = V / a, with a the local speed of sound. On the upper surface the flow is faster, so the local Mach number is higher. The critical Mach number is the freestream Mach at which the peak local Mach first reaches 1. Below that, the flow is entirely subsonic and a compressibility correction can be honest. Above it, a supersonic pocket appears, usually closed by a shock. Drag starts to rise sharply a little later: that freestream Mach is drag divergence. The gap between critical Mach and drag divergence is a design target of supercritical sections. It is not zero, and it is not something an incompressible solver can see.
What pushes the bad news to a lower freestream Mach
- Thickness. A thicker section has higher peak velocities at the same lift. Critical Mach falls.
- Lift coefficient. More CL strengthens the suction peak. The same section at CL = 0.6 reaches sonic speed earlier than at CL = 0.2.
- Nose shape and camber. A sharp suction spike is a shock waiting at a lower M∞ than a long, mild rooftop. Supercritical sections are drawn to replace the spike with that rooftop and a rear recovery.
- Sweep, which a 2D section does not contain. A swept wing sees a lower Mach component normal to the leading edge. A two-dimensional polar at M = 0.78 is pessimistic relative to a swept wing at the same flight Mach, and it is still not a wing analysis. Do not “add sweep” by a guess after the fact without a method that has sweep in it.
What a correction can and cannot do
| Tool | Honest use | Stop using it when |
|---|---|---|
| Incompressible viscous polar, M entered as 0 | Low-speed UAVs and the linear range below about M = 0.3. | You are near a known critical Mach, or the flight Mach is a design variable. |
| Prandtl–Glauert and related corrections, including corrections inside a viscous panel code | A screen for moderate subsonic Mach, to see CL and Cp amplify as 1/√(1−M²) in the small-disturbance sense. | A shock is part of the question. The correction does not capture one. |
| Euler or RANS with a proper mesh | Shock position, drag rise, and the moment break that often comes with it. | The mesh, the boundary layer and the transition treatment are unexamined. A shock in the wrong place is still a picture. |
If you must screen several sections before any of them deserve a compressible CFD run, sweep Mach at the design CL in the viscous section tool, watch CD and CM, and treat the upturn as a flag to change thickness or nose shape — not as the certified drag-divergence Mach number. Then spend the expensive method on the short list.
Where this sits in the series
In simple words: what this page is for
Above a section’s critical Mach number the suction peak goes sonic, a shock can form, and drag rises. Thickness, camber and lift all move that Mach number.
This lesson exists because section decisions fail when geometry, method labels and selection reasons are scattered. Airfoil Analysis at High Mach Numbers: Compressibility and Drag Rise 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 Analysis at High Mach Numbers: Compressibility and Drag Rise 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 Analysis at High Mach Numbers: Compressibility and Drag Rise 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
- Airfoil Design for High-Altitude, Low-Reynolds-Number Flight
- Airfoil Selection for High-Lift Aircraft: Balancing Cruise Efficiency and Takeoff Performance
- Airfoil Design for High-Lift, Low-Speed Aircraft and Short Takeoff Applications
- All HENDOI blog articles
- HENFOIL product page
- HENSYNTH product page
- Pricing — Student, Professional & Team
- FAQ
- Login · Register now
- Previous: Numerical convergence problems in airfoil analysis
- Next: Modify an airfoil without losing geometric integrity
- 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 Analysis methods. 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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