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):
- Temperature decreases $\rightarrow$ LSS decreases.
- TAS must decrease to keep the ratio $M$ constant.
- 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.