Speed and Mach Number in Navigation

Understanding Speed and Mach Number in Navigation

Airspeed in aviation is measured in several forms: Indicated Airspeed (IAS), Calibrated Airspeed (CAS), and True Airspeed (TAS). IAS is what the pilot reads on the instrument, but navigation and performance calculations require TAS, which accounts for atmospheric conditions and instrument errors.

Mach number is the ratio of TAS to the local speed of sound (LSS). The LSS depends on the outside air temperature (OAT) and is calculated as:

• LSS (knots) = 38.96 × √(Temperature in Kelvin)
• Temperature in Kelvin = Temperature in °C + 273

So, Mach number (M) = TAS / LSS. Conversely, TAS = M × LSS. These conversions are performed either by direct calculation or using a navigation computer (flight computer/E6B/CRP-5).

Relationships During Flight

• In a climb at constant CAS, both TAS and Mach number increase as air density decreases.
• At cruise, many high-altitude aircraft fly at a constant Mach number rather than a constant CAS because the Mach number is directly related to compressibility effects and aircraft limitations.
• When descending at constant Mach, TAS decreases as the local speed of sound increases (warmer air at lower altitudes).

Practical Navigation Calculations

• To convert CAS to TAS, corrections for instrument and position errors, plus a density correction, are applied. A rule of thumb: TAS increases by about 2% per 1,000 ft of altitude gain.
• To find Mach number from TAS (or vice versa), use the OAT and the formulas above, or a navigation computer.
• Groundspeed (GS) is then determined by correcting TAS for wind, using the aircraft's track and wind vector.

Example

If an aircraft at FL350 (OAT -55°C) must maintain 480 KT TAS, calculate the Mach number:

• Absolute temperature = -55 + 273 = 218 K
• LSS = 38.96 × √218 ≈ 575 knots
• M = 480 / 575 ≈ 0.83

This demonstrates the direct relationship between TAS, Mach number, and temperature.