5.1 Speed of Sound, Mach Number & Flight Regimes

5.1 Speed of Sound, Mach Number & Flight Regimes

As aircraft approach high subsonic cruise speeds, maintenance engineers and licensed personnel working under EASA Part-66 Module 08 must abandon the incompressible assumptions used for slow training aircraft. Air becomes a compressible fluid: density, pressure, and temperature change significantly along streamlines. The single parameter that classifies compressibility behaviour is the Mach number — and it is built directly on the speed of sound in the local atmosphere.

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The Speed of Sound in Air

Sound propagates as a weak pressure disturbance travelling through a medium. For an ideal gas, the speed of sound ($a$) is:

$a = \sqrt{\gamma R T}$

Where:

• $\gamma$ (gamma) = ratio of specific heats ≈ 1.4 for diatomic air
• $R$ = specific gas constant for dry air ≈ 287 J/(kg·K)
• $T$ = absolute temperature in Kelvin (never use °C in this formula)

Critical exam point: $a$ depends on temperature only (for a given gas composition). It does not depend on static pressure, density, or the speed of the aircraft. Cold air is "slow" for sound; hot air is "fast."

At ISA sea level ($T_0 = 288.15\text{ K} = +15°\text{C}$):

$a_0 = \sqrt{1.4 \times 287.058 \times 288.15} \approx 340.3\text{ m/s} \approx 661\text{ kt}$

In the troposphere, temperature falls with altitude, so $a$ decreases as you climb. A jet cruising at a constant Mach number therefore flies at a lower true airspeed (TAS) in knots at FL 350 than at FL 200, even though compressibility effects are similar.

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Mach Number Definition

The Mach number ($M$) is the ratio of the aircraft true airspeed (TAS) to the local speed of sound:

$M = \frac{V_{\text{TAS}}}{a_{\text{local}}}$

• $M = 0.80$ means the aircraft flies at 80% of the local sonic speed.
• $M = 1.00$ means TAS exactly equals the local speed of sound (sonic flight).
• Mach is dimensionless — it is not a unit of speed.

Indicated vs true vs Mach: At altitude, pitot pressure still drives airspeed indicators, but compressibility corrections matter above roughly M 0.3. Transport aircraft display Mach on the primary flight display because structural loads, buffet margins, and engine surge limits are Mach-dependent. For Part-66 exams, always convert temperature to Kelvin before calculating $a$, then divide TAS by $a$.

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Flight Regimes (Compressibility Classification)

Aviation teaching divides compressible flow into regimes. Boundaries are approximate — aircraft design and wing section shift the exact thresholds — but EASA syllabi use the following framework:

  M = 0          0.3        0.8        1.0        1.2         5.0+
  |--------------|----------|----------|----------|-----------|---->
     Incompressible      Subsonic        Transonic    Supersonic  Hypersonic
     (Bernoulli OK)    (M < 0.8)      (0.8–1.2)     (M > 1.2)   (M > 5)

Subsonic Flight

In subsonic flight, the disturbance caused by the aircraft propagates ahead of the nose — information travels at the speed of sound, so upstream air "knows" the wing is coming and begins to divert. Below about M 0.3, compressibility effects are small and engineers treat air as incompressible (Bernoulli, constant density). Between M 0.3 and ~0.8, compressibility corrections appear in lift and drag data but shocks are usually absent on cruise sections.

Transonic Flight

Transonic flight is the most operationally significant regime for modern jet transports. The freestream Mach may be only 0.82–0.86, yet airflow over the curved upper surface accelerates to supersonic local speeds. Where that supersonic pocket terminates, a shock wave forms (covered in Section 5.2). Drag increases rapidly — the drag divergence Mach — and pilots feel compressibility buffet near the limit. This is why long-range jets have thick operational manuals defining maximum operating Mach ($M_{MO}$).

Supersonic Flight

In supersonic flight, the aircraft moves faster than the propagation of pressure disturbances. Air cannot move aside gradually; a bow shock stands off the nose, converting kinetic energy into heat and raising static pressure behind the shock. Lift and trim behave differently; wave drag becomes a major fuel penalty. Centre-of-pressure shifts can cause Mach tuck if not compensated by design or Mach trim systems.

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Worked Example 5.1.1: Local Speed of Sound at Cruise

Problem: A turbofan transport cruises at FL 350. ISA temperature at that level is approximately −54.3°C. Calculate the local speed of sound.

Solution:

1. Convert to Kelvin: $T = -54.3 + 273.15 = 218.85\text{ K}$
2. Apply $a = \sqrt{\gamma R T}$: $a = \sqrt{1.4 \times 287.058 \times 218.85} = \sqrt{87{,}860} \approx 296.4\text{ m/s}$
3. Convert: $296.4 \times 1.944 \approx 576\text{ kt}$

Result: Local $a \approx 296\text{ m/s}$ (≈ 576 kt). Any TAS above this value would imply $M > 1$ at that altitude under ISA.

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Worked Example 5.1.2: Mach Number from TAS

Problem: The same aircraft flies at TAS 470 kt at FL 350 with $a \approx 576\text{ kt}$. Find Mach number.

Solution: $M = \frac{470}{576} \approx 0.82$

Result: M ≈ 0.82 — squarely in the transonic regime for a conventional swept-wing transport, even though TAS is subsonic relative to sound.

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Exam Traps (Part-66 Module 08)

1. Using °C in $a = \sqrt{\gamma R T}$ — always Kelvin.
2. Assuming sound speed drops because pressure drops at altitude — it is the temperature lapse that matters.
3. Confusing IAS with TAS — Mach uses TAS.
4. Thinking transonic means the whole aircraft is supersonic — often only local pockets are supersonic while $M_\infty < 1$.
5. Forgetting that $M_{MO}$ is a structural/aero limit, not merely a performance preference — exceed it and buffet, trim changes, and load limits follow.