Mach Number. As an aircraft’s speed approaches the speed of sound, the airflow around the aerofoils goes through a change, which is due to formation of shock waves. The onset of these shock waves and their subsequent effects occur, for a given aircraft type, when the true air speed is a certain proportion of the local speed of sound. For convenience, the ratio of true air speed to the local speed of sound is considered as a single entity. It is called Mach number and is usually expressed as:
Mach No. = TAS / LSS (Local Speed Of Sound) = TAS / 39√T (Temperature in deg Kelvin)
Machmeter measures the ratio of the TAS and LSS and displays it as Mach No.
Basic Principle Of Machmeter
Certain points need to be kept in mind before discussing the principle
- Speed of sound varies only with temperature.
- As the temperature increases the LSS increases and vice versa
- The precise relation is that LSS is directly proportional to square root of absolute temperature
- Sea level temperature is +15ºC = 15 +273 = 288ºK
- Speed of sound at sea level is 661.7 kts
- therefore speed of sound i.e 661.7 = const x √188
- therefore the constant = 38.94
- hence speed of sound at any level = 38.94√Absolute temperature (39√T)
Since Mach no. is the ratio of TAS and LSS it can also be written down in terms of pitot and static pressures
- TAS is a function of dynamic pressure and the local density and dynamic pressure is of course the difference of pitot and static pressure i. e. P-S.
- According to gas law temperature is also a function of static pressure and density.
Therefore, V = Dynamic pressure/ρ = P-S/ρ————(1)
and LSS ∝ ºK = S/ρ —————(2)
we know Mach No. = TAS / LSS
so combining equation 1 and 2 we get
Mach No. = P-S/S ( Considered to be combination of ASI and altimeter)
Working of Machmeter in brief
- Pitot pressure is fed to the air speed capsule
- static pressure is fed to the instrument case
- capsule contracts and expands as per change in air speed or pitot pressure
- Altitude capsule is partly evacuated ( As in altimeter)
- Altitude capsule expands/ contracts as per change in static pressure
- The ratio/ ranging arm mechanism captures the ratio of dynamic pressure to static pressure and therefore indicates the ratio of TAS to LSS on the face of the instrument
Certain V values
Vmo = Velocity max operating
Mmo = Max Mach no. operating
At lower altitude, the Vmo pointer retains a fixed position, which indicates the max operating IAS permitted
As altitude increases Vmo corresponds to an increase in Mach No. until Mmo is reached. What it simply means that at lower altitudes its the IAS which has to be kept in check and ensured that Vmo is not crossed, Mmo is not so important because the velocity at which Mmo will be reached will be much higher than Vmo.. At higher altitudes the Mach No. starts increasing with IAS, so It has to be ensured that Mach no. has to be checked as at a velocity lower than Vmo Mmo may be reached.
Errors in Machmeter
Instrument Error Like all instruments machmeter aso is subject to manufacturing tolerances, although these are extremely small
Pressure Error The Machmeter operates from the same pressure source as the air speed indicator and is therefore subject to the same pressure errors. However, the effect of pressure error is relatively greater on the machmeter as the ratio of pitot excess pressure (Pt – P) to static pressure (P) is being measured rather than just the pitot excess pressure (Pt – P) in the case of the ASI. These errors are very small at high altitudes and speed ranges where machmeter is used.
Density, temperature and compressibility errors These errors are eliminated because density changes does not alter the dynamic/ static pressures.
Blockages and Leakages
Blockages and leaks have the same effect as they have in ASI, but the effects are increased due to the z capsules
A blockage in the static system will cause the machmeter to over read during descent and under read during climb
Accuracy Machmeter accuracy is within 0.01 to 0.02 M during normal operating range.
M.No. increases TAS increases LSS Reduces
M. No. Reduces TAS Reduces LSS Increases ( At a given altitude)