How to Analyze an Airfoil Using Reynolds Number and Mach Number

Reynolds number is the viscous scale

The chord Reynolds number is

Re = ρ V c / μ = V c / ν

with flight speed V, chord c, and the kinematic viscosity ν of the air at the real temperature and pressure. Sea-level air has ν near 1.5×10⁻⁵ m²/s. That value is wrong at altitude: cold, thin air has a different ν, and a Reynolds number copied from a sea-level table will mis-rank your sections.

Two examples, sea level, only to show the range:

• Small UAV: V = 20 m/s, c = 0.25 m → Re ≈ 3×10⁵.
• Transport wing station: V = 230 m/s, c = 3 m → Re on the order of 4×10⁷ if you wrongly use sea-level ν. At cruise altitude the number is lower than that sea-level estimate, and it is still far above the UAV.

Between those worlds the boundary layer changes character. At a few hundred thousand, laminar flow persists, laminar separation bubbles are common, and a section designed for Re = 6×10⁶ can look mediocre. At several million, transition is earlier, bubbles are weaker, and thickness and camber trade against a different drag. Always recompute at the mission Re. A family of polars at two Reynolds numbers beats a single “representative” curve you cannot justify.

What Reynolds number moves

Mach number is the compressible scale

M = V / a, with a the local speed of sound, about 340 m/s at sea-level standard temperature and lower when the air is colder. The UAV at 20 m/s is near M = 0.06. Compressibility is a small correction. A wing section at M = 0.75 is in a different regime: the suction peak can reach sonic speed while the freestream is still subsonic. That freestream Mach is the critical Mach number. Above it, a local supersonic pocket and a shock appear, drag rises (drag divergence), and the moment can shift.

Rules of thumb, not laws:

• Below about M = 0.3, an incompressible analysis plus a careful Reynolds number is usually the right first tool.
• From there toward M = 0.6, a compressibility correction (Prandtl–Glauert and its relatives, or a Karman–Tsien-type correction inside a viscous panel code) is a screen, not a shock-capturing solution.
• Near and above drag divergence you need a method that can hold a shock, and you need sweep, which a 2D section does not include. Sweep raises the Mach number a wing can fly by lowering the component normal to the section.

How to set up the analysis

1. Compute Re from true speed, true chord and true viscosity. Write the number down.
2. Compute Mach from true speed and true speed of sound. Write that down too.
3. Choose a transition assumption that matches the atmosphere you claim: clean sailplane air is not the same as a bug-speckled UAV.
4. Sweep angle of attack wide enough to see CL max, and no wider than the method can mean.
5. If the mission has two conditions — climb and cruise, or root and tip — run two polars. A single polar cannot represent both.

HENFOIL asks for Re and Mach as explicit polar fields, and it can build a Reynolds family or a Mach family so the sensitivity is visible. The result remains a VIC polar at those inputs. It does not become a flight-test point because the inputs were careful.

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Where this sits in the series

In simple words: what this page is for

Reynolds number says how large viscosity is relative to the section. Mach number says how much the flow notices that air is compressible. State both.

This lesson exists because section decisions fail when geometry, method labels and selection reasons are scattered. How to Analyze an Airfoil Using Reynolds Number and Mach Number 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 How to Analyze an Airfoil Using Reynolds Number and Mach Number 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 How to Analyze an Airfoil Using Reynolds Number and Mach Number 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
• What Is the Aerodynamic Center of an Airfoil? Location, Meaning and Applications
• How to Identify Numerical Convergence Problems in Airfoil Analysis
• How to Build an Airfoil Analysis Database with Consistent Simulation Conditions
• All HENDOI blog articles
• HENFOIL product page
• HENSYNTH product page
• Pricing — Student, Professional & Team
• FAQ
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• 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.