Machmeter Operation: Mach Number, Pressure Ratios, and Speed Margins

The Machmeter displays the Mach number ($M$), which is the ratio of the aircraft's True Airspeed (TAS) to the Local Speed of Sound (LSS).

Formula

$M = \frac{TAS}{LSS}$

• LSS depends only on temperature ($LSS \approx 39 \sqrt{T_{Kelvin}}$). Warmer air $\rightarrow$ higher speed of sound.
• Since $LSS$ decreases with altitude (due to temperature drop), for a constant TAS in a climb, Mach Number increases.

Principle of Operation

The mechanical Machmeter derives the Mach number by measuring the ratio of dynamic pressure ($P_t - P_s$) to static pressure ($P_s$). $M \propto \sqrt{\frac{P_t - P_s}{P_s}}$ It combines an airspeed capsule (dynamic pressure) and an altitude capsule (static pressure) via a mechanical linkage. It does not assume any air temperature or density; the pressure ratio is sufficient.

Climb/Descent Relationships (Constant Mach)

When climbing at a Constant Mach Number (assuming standard atmosphere):

1. Temperature decreases $\rightarrow$ LSS decreases.
2. TAS must decrease to keep the ratio $M$ constant.
3. CAS/IAS decreases (due to density reduction). (Mnemonic: "Temperature down $\rightarrow$ TAS down").

Stall Margin: In a constant Mach climb, since CAS is decreasing, the margin above the stall speed ($V_s$) reduces.

Errors

• Blockage: Influenced by both pitot and static blockages (similar to ASI and Altimeter errors).
• Compressibility: The Machmeter is inherently designed to account for compressibility effects.