Inertial Principles and Systems

This lesson asks what module 4's solid-state ingredients can do when they are built to a far higher standard of accuracy. The answer is inertial navigation: a system that, given nothing but a starting position, feels every acceleration applied to it and adds them up into velocity, position, track and speed over the ground. The lesson builds the principle, the corrections it cannot live without, the two generations of hardware, and the light-based gyro at the heart of the modern one.

The self-contained navigator

Everything met so far in this course leans on something outside the aircraft: the pressure instruments on the atmosphere, the compass on the Earth's magnetic field. An inertial system leans on nothing. It measures its own accelerations, inside its own box, and computes attitude, velocity and position from them alone. That self-sufficiency is why, in commercial air transport aeroplanes, inertial navigation and reference systems are the main source of attitude and one of the main sources of navigational data: the attitude shown on an airliner's primary displays comes from its inertial units, not from a spinning artificial horizon.

The self-sufficiency has exactly one stated exception: true airspeed (TAS). To determine attitude and navigational data the system requires no external input except TAS, which it takes from the air-data computer for one product in particular: wind. The inertial side knows the aircraft's motion over the ground; TAS and heading give its motion through the air; the difference between the two is the wind. Without TAS the box would navigate perfectly well, but it could not tell you what the air mass was doing. The position entered before flight does not break the rule: it is a starting datum handed over once, not a running feed.

From acceleration to position

The principle fits in one sentence: measure acceleration, and everything else is arithmetic. An accelerometer is, at bottom, a small mass on a spring: accelerate the case and the mass lags behind, and the force needed to hold it in place measures the acceleration. Integration is summing over time: acceleration summed over time is a change of velocity, and velocity summed over time is distance gone. Doing both, double integration, turns measured acceleration into distance travelled, and distance counted from a known starting point is position.

One accelerometer serves one direction only, so acceleration must be measured, or mathematically extracted, along three components: north–south, east–west and vertical. The two horizontal chains do the navigating; the vertical chain serves height and is dominated by gravity, which is one of the reasons the next section exists.

Keeping the sums honest: four corrections

Left alone, the chain would integrate every error as faithfully as every truth. Four effects must be corrected for, and the first two are old acquaintances: they are the apparent and transport wander of the gyro-principles lesson, met again at navigation accuracy.

Earth rate precession — the Earth turns under the system, about fifteen degrees per hour. A reference that held itself rigid in space would appear to tilt and swing round as the planet rotated beneath it, exactly like module 4's apparently wandering gyro. The level, north-aligned reference must therefore be steadily precessed, or rotated in the computer, to stay level and north-aligned on a turning Earth.

Transport precession — carrying the system across the curved Earth changes which way is down and which way is north. The reference must be turned to follow the local vertical as the aircraft travels; otherwise straight-line arithmetic is being done on a curved surface.

Coriolis — a body moving over a rotating Earth follows a curved path through space, and the accelerometers dutifully sense the sideways acceleration that curve involves. It says nothing about motion over the ground, so it is computed and removed.

Gravity — an accelerometer cannot tell being accelerated from being held against gravity. The vertical channel must subtract gravity itself, and any tilt of the reference leaks a slice of gravity into the horizontal channels, where double integration would grow it into a position error. Keeping gravity out of the horizontal sums is the sharpest reason the reference must stay exactly level.

INS and IRS: two generations

The hardware comes in two generations, and the syllabus is precise about a naming habit. The earlier generation kept its sensors on a gyro-stabilised platform: a small table hung in gimbals, held level and north-aligned by gyros, with the accelerometers riding on it so each stayed pointed along its own axis whatever the aircraft did around it. These platform systems are conventionally, though technically incorrectly, called inertial navigation systems (INSs). Technically, anything that navigates this way is an inertial navigation system; convention reserves the name for the old mechanical-platform boxes.

The modern generation has no moving platform at all. A strap-down system is fixed to the structure of the aircraft and normally consists of three ring laser gyros and three accelerometers. The accelerometers turn with the aircraft, so their readings arrive in aircraft axes; the ring laser gyros measure every rotation, and the computer uses that attitude to rotate the readings mathematically into the steady, level, north-aligned frame the old platform provided physically. The platform still exists; it is made of arithmetic now. These strap-down units are conventionally called inertial reference systems (IRSs).

The names also mark how much company each system keeps with the rest of the aircraft. An INS can be considered stand-alone: it carried its own control panel and its own waypoints and navigated by itself. An IRS is integrated with the flight management system (FMS), the aircraft's navigation and flight-planning system, which this course meets properly in its own module: the IRS supplies the raw motion data, the FMS does the navigating. And here the line module 4 deferred gets drawn: the AHRS shares the strap-down recipe of gyros plus accelerometers, but it stops at attitude and heading and leans on a magnetic sensor; an IRS carries sensors accurate enough to navigate by, and adds the position and velocity outputs an AHRS never attempts.

The ring laser gyro

The gyro that made strap-down possible contains no gyroscope in module 4's sense at all. A ring laser gyro (RLG) is a closed triangular light path drilled through a single block of very stable glass, with a mirror at each corner. The gas in the bores is made to lase (to generate laser light), and two beams run round the triangle in opposite directions. While the block is still, both round trips are the same length. When the block rotates with the aircraft, the beam running with the rotation has slightly further to go to complete its loop and the beam running against it slightly less, so their frequencies split apart. One mirror leaks a trace of both beams to a detector, which counts the interference between them: the frequency difference is proportional to the rate of turn.

What the systems deliver

A stand-alone INS, given its start position and left to integrate, can determine the aircraft's navigational data in full:

Present position — latitude and longitude, continuously.

Velocity over the ground — groundspeed, true track, and the drift angle between heading and track.

True heading and attitude — the directions the platform or computed frame holds anyway, handed to the flight instruments.

Steering data — distance, time and desired track to the next waypoint, and the cross-track distance off the planned leg.

Wind — the one output that needs the TAS input, as the first section explained.

On a modern aircraft the inertial position is a contribution, not the final answer. Where an IRS and an FMS are fitted, the FMS's own computer holds the answer: the flight management computer (FMC) position is normally derived from a mathematical analysis of IRS, global positioning system (GPS) and distance measuring equipment (DME) data, together with VHF omnidirectional radio range (VOR) bearings and localizer (LOC) beams where they are received. The blend plays to each source's strength: the IRS is continuous and needs no reception at all, while the satellite and radio fixes are anchored to the outside world, and the FMC uses them to trim away the slow drift the inertial sums accumulate.

All of it depends on one thing this lesson has quietly assumed: that before the first integration the system knew exactly where down was, where north was, and where it was parked. Teaching it that is a ground ritual with strict rules, and it is the next lesson.