Mach Regimes & Compressibility

Defining the Mach number and the limits of incompressible assumptions.

Aerospace EngineeringCompressible FlowFree preview
⏱️ About 15 min
Mach Regimes & Compressibility — illustration
Decorative illustration.

When aircraft approach the speed of sound, the air itself changes behavior, violating standard aerodynamic assumptions.

💡
The big idea: The Mach number \(M\) is the master parameter for compressibility, governing aerodynamic response across subsonic, transonic, and supersonic regimes.
🎯 By the end, you'll be able to
  • Calculate the Mach number and classify flow regimes.
  • Understand the density limits of incompressible assumptions.
  • Apply the Prandtl-Glauert rule for compressible pressure coefficients.
📎 Helpful to know first
  • Aerospace Engineering Module 3: Aerodynamics II

The Speed of Sound

The speed of sound \(a\) represents the speed at which pressure disturbances propagate through a medium. When an aircraft flies, it continuously generates sound waves. The relationship between the aircraft's freestream velocity V_infinity and the speed of sound \(a\) determines how those waves interact, a concept quantified by the Mach number \(M\).

Mach Regimes

Aerospace flows are categorized by Mach number: subsonic (M < 0.8), transonic (0.8-1.2), supersonic (1.2-5), and hypersonic (M > 5). Below a Mach number of approximately 0.3, density changes are negligible (under 5%), allowing engineers to safely use incompressible flow assumptions. Above this, compressibility effects must be accounted for.

\[ M = \frac{V_\infty}{a} \]
🔑 Compressibility Correction

As Mach number increases in the subsonic regime, the pressure coefficient \(C_p\) on an airfoil changes. The Prandtl-Glauert rule corrects incompressible data for compressible effects up to critical Mach.

\[ C_p = \dfrac{C_{p,0}}{\sqrt{1-M^2}} \]
🎮 Mach Regime Explorer LIVE
Predict first: How does the flow regime change as Mach number crosses 0.3, 0.8, and 1.0?
Visualizing flow regimes and compressibility effects with varying Mach number.
📝 Worked example: At sea level a = 340 m/s. Aircraft flies at V_infty = 270 m/s. Find M and classify.
  1. 1. M = 270/340 = 0.79
  2. 2. 0.79 < 0.8 so subsonic (high subsonic).
✓ M = 0.79 (subsonic)
✏️ Practice: Incompressible airfoil reads Cp0 = -0.40. Estimate compressible Cp at M = 0.6 (Prandtl-Glauert).
Solution
  1. Hint: sqrt(1-0.36)=0.8
  2. Answer: Cp = -0.40/0.8 = -0.50

Check your understanding

1. An aircraft is flying at Mach 0.5. Which regime is it in?
Mach 0.5 falls in the subsonic regime (M < 0.8) but requires compressibility corrections.
2. If Cp0 = -1.0, what is Cp at M = 0?
At M=0, the Prandtl-Glauert denominator is 1, so Cp = Cp0.
🔎 Related lessons
Isentropic Flow Relations · soon
✅ Key takeaways
  • Mach number is the ratio of freestream velocity to the speed of sound.
  • Incompressible assumptions break down above Mach 0.3.
  • Prandtl-Glauert corrects pressure coefficients for subsonic compressibility.
➡️ Now that we understand Mach regimes, we can explore how pressure, temperature, and density vary isentropically with Mach number.
Want to test yourself on this? Try the Aerospace Engineering Aptitude test →
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