The Machmeter and the Air-Data Computer

Mach number and the local speed of sound

The Mach number is the aircraft's true airspeed divided by the local speed of sound (LSS): the speed at which pressure disturbances travel through the air the aircraft is actually flying in. The LSS depends on temperature alone: in knots, about 38.94 times the square root of the absolute temperature, roughly 661 kt in ISA sea-level air and about 573 kt at the tropopause's −56.5 °C. Cold air is slow air, acoustically.

That construction answers the syllabus's why-question. The ASI's compressibility error exists because that instrument converts dynamic pressure into a speed through a fixed sea-level calibration, and compression at high speed feeds it more pressure than the calibration expects. The Machmeter never makes that conversion: Mach is itself defined by the pressure ratio the instrument measures, compression included, so what corrupts the ASI is simply part of the Machmeter's answer. No compressibility error exists to correct.

Displays, blockages and leaks

Displays follow the altimeter's family: a pointer on a dial, a drum rolling the digits, the vertical straight scale sharing the electronic speed tape, or a plain digital readout. And because the Machmeter drinks from the same two lines as the ASI, its blockage behaviour rhymes with the ASI's:

Blocked pitot line — traps the total pressure, and a climb widens the apparent ratio, over-reading Mach.
Blocked static line — traps the case pressure, under-reading Mach in a climb and over-reading it in a descent.
Leaks — pull the leaking line toward the pressure around it: a pitot leak bleeds away total pressure and the Mach reading falls, and a static leak inside a pressurised cabin feeds the case the cabin's higher pressure, so the Machmeter under-reads badly, again the worst offender.

CAS, TAS and Mach: who moves against whom

Three speeds describe one flight, and the exam loves how they move apart. The anchors: at a given pressure altitude, a CAS corresponds to a fixed Mach number (both are functions of the same pressure ratio), while TAS depends additionally on temperature. From that, the rules of motion:

Climb at constant CAS — the static pressure falls, so the pressure ratio for the same CAS grows: Mach rises, and TAS rises with the thinning air.
Climb at constant Mach — the ratio is held, so CAS falls; TAS falls slowly while the air cools (the LSS shrinks) and holds steady in the constant-temperature stratosphere.
Descent — mirrors each rule.
Level flight — temperature moves only TAS: warmer air at the same level and CAS means a higher TAS, but the Mach number, tied to the pressure ratio, does not move.

VMO and MMO, and their indications

Transport aircraft carry two maximum operating speeds, met in Principles of Flight's limitations module:

VMO, the maximum operating speed in IAS terms.
MMO, the maximum operating Mach number.

On analogue panels their combined limit rides the ASI as the barber's pole of the last lesson, driven to whichever of the two currently binds; on electronic displays the same limit is the red-and-black band descending from the top of the speed tape, with the overspeed warning wired to it.

Which limit binds: altitude, and the margins in climb and descent

Because Mach rises with altitude at any fixed IAS, the two limits trade places: low, VMO binds; high, MMO binds, the trade happening at the altitude where flying at VMO would just reach MMO. The climb has its own switch point below that: the crossover altitude, where the constant climb IAS corresponds to the operator's chosen climb Mach. The margins follow the CAS-Mach rules above. Climbing at constant IAS, the Mach number rises toward MMO: the margin to MMO shrinks even though the ASI needle never moves, which is why the climb switches to constant Mach at the crossover. Descending at constant Mach, the mirror image: IAS rises toward VMO and the margin to VMO shrinks, so the descent switches to constant IAS partway down.

The other edge: the stall margin

The same climbs squeeze the envelope's other side. Climbing at constant Mach, the CAS falls, and the stall's own speed does not: the margin to the stall shrinks from below while MMO stands still above, until at the aircraft's ceiling the two margins meet in the narrow corridor the buffet-onset chart draws. Descending at constant IAS relaxes both: Mach falls away from MMO, and the constant CAS holds the stall margin. The instrument-side lesson is the same one the whole module teaches: each speed watches a different edge, and only reading them together shows where the aircraft actually sits in its envelope.

The air-data computer

The air-data computer (ADC) replaces the capsule-per-instrument museum with arithmetic: it receives the raw sensor signals, applies every correction digitally from stored aircraft data (the calibration curves the mechanic once read from tables), computes the full set of air-data quantities, and distributes them on a data bus to every consumer at once:

Inputs — TAT, static pressure, total pressure, measured temperature, angle of attack, flap position, landing-gear position, and the stored aircraft data.
Outputs — IAS, TAS, SAT, TAT, Mach number, angle of attack, altitude, vertical speed, and the VMO/MMO pointer.

The road to TAS, computed

The correction chain the mechanical instruments could only approximate, the ADC simply calculates, honouring the promise the temperature lesson made. From the raw pressures it forms indicated airspeed; the position error is removed using the stored calibration for the current flap and gear position (the static source error correction, SSEC), giving CAS; the instrument error barely exists, there being no mechanism to be imperfect; the compressibility correction is a formula, giving EAS; and the density correction uses static pressure with the SAT computed from TAT and Mach, delivering TAS: the quantity navigation actually wants, and the reason the FMS, the autopilot, the transponder, the ground-proximity system and the flight-envelope protections all drink from the ADC's bus rather than from any dial.

The ADIRU, and the switch that must not be guessed

Modern aircraft integrate further: the air-data inertial reference unit (ADIRU) packages the ADC together with the inertial reference unit (IRU), the accelerometer-and-gyro unit the inertial-navigation module of this course introduces. One box, but two separable functions with separate cockpit controls: the air-data part and the inertial-reference part can each be selected, switched or shut down on its own. That separation is where the syllabus places its warning: in a failure drill, selecting the wrong control has consequences that may be irreversible. Shut down a misbehaving air-data channel and the pressures return when it is restored; shut down the inertial part and its alignment is gone, and realignment needs a stationary aircraft, which no failure drill at cruise can provide. The discipline is the module's cross-checking habit in its sharpest form: identify which half is actually failing before touching either switch.

Losing an ADC, versus losing an instrument

The architectures fail differently, and the syllabus wants the comparison made. A stand-alone instrument fails alone: a broken ASI takes one needle, and every other indication stands. An ADC failure takes its whole suite at once: one side's speed, altitude, vertical speed, Mach and their dependents all go together, a much larger single loss. The system's answer is the redundancy of the pitot-static lesson carried into the computers: multiple independent ADCs with switching so either pilot's displays can be fed from the surviving computer, and the standby instruments on their own sensors as the floor beneath it all. The trade is deliberate: rarer, larger failures with better corrections and comparison monitoring, against the stand-alone panel's many small, uncorrected, uncompared ones.