Inertial Navigation

Before we go any further, one bit of definition is in order. An Inertial Reference System (IRS) is nothing more than something that reports your position (latitude, longitude, geometric altitude), speed, and attitude. An Inertial Navigation System (INS) adds the ability to catalog various positions as waypoints and provides a method of getting from one waypoint to another. If you have an FMS that does this for you, you don't really need an INS, so the IRS is probably what you have installed.

1 — Evolution

2 — Inertia and Newton’s First Law of Motion

3 — Mechanics of inertial navigation systems

4 — Flight Management Computer (FMC) “Fail Down” sensor logic

As I write this, the Global Positioning Satellite (GPS) system is the primary means of navigation for most of aviation. It may be useful to see the evolution of long-range navigation to understand how inertial navigation came to be:

• Pilotage relies on keeping an eye on landmarks and terrain to determine where you are.
• Dead reckoning uses some form of heading information and an estimate of speed to determine where you are going.
• Celestial navigation uses angles between the local horizon and known celestial objects (e.g., sun, moon, or stars), or between those celestial objects to determine position on the earth.
• Radio navigation uses frequency sources from known locations, such as VORs or NDBs.
• Inertial navigation uses a known initial position, attitude, and measured accelerations to determine velocity and the resulting position.
• GPS is a type of radio navigation that uses position and time signals from multiple satellites to determine the receiver’s position.

"A body at rest will remain at rest and a body in motion will remain in motion, unless acted upon by an unbalanced force."

Newton’s First Law of Motion implies that bodies have a property called inertia. Inertia may be defined as the property of a body that results in its maintaining its velocity unchanged unless it interacts with an unbalanced force. The measure of inertia is what is technically known as mass. A few points about this first law will make all that follows easier to, well, follow:

• When there are no external forces, objects move with constant velocity.
• Inertia is resistance to changes in motion.
• The amount of inertia an object has is measured by its mass; more mass means more inertia.

So how do we measure those external forces? We first need a stable platform to measure those forces against . . .

Gyroscopes

The word gyroscope comes from the Greek gyros, which means circle. In a conventional gyroscope, the gyro is a spinning wheel mounted on two bearings inside an inner ring which itself is mounted inside another ring. When rotating, the spinning wheel maintains its position according to the conservation of angular momentum.

These rings are known as gimbals. Note that the outer gimbal can be moving in various directions and the inner spinning wheel maintains its orientation in space. That becomes very useful when the outer gimbal is mounted to a moving vehicle, such as an airplane. The airplane's orientation in space can change while the inner spinning wheel's orientation remains constant.

The axle of the spinning wheel determines its axis. The ends of the axle resist any external forces exerted by the outer gimbals. They effectively “push” against the force. Measuring these forces with accelerometers provide the basis of inertial navigation.

Accelerometers

Before considering gyroscopes and other items of inertial magic, let us consider the accelerometer.

Accelerometers measure the deflection of the "proof mass" with something a bit more reliable than a spring. But the point is that we can measure acceleration in any axis.

Inertial Platform

An inertial platform is basically three gyroscopes placed at 90° angles with each other and three accelerometers to measure forces on the platform. If we find the forces in each direction over a specific time period, we can find the velocity in all three directions. By multiplying the velocity by time to find distance, a relative position can be determined. If the starting position was known, the relative position can be added to determine an ending position.

Three dimensions – “sort of”

With the three gyroscopes on our inertial platform, we have a way of tracking movement in three dimensions. But we, as pilots, don't actually operate in three dimensions, by the truest sense of the term. Our horizontal plane is aligned with the surface of the earth, which isn't flat.

Our inertial navigation must consider "level" to be parallel to the earth's surface or perpendicular to gravity's pull. The engineer calls this the "locally level frame" but for us pilots it is simply level flight. There are two major problems to tackle. First, the earth is rotating. The inertial navigation system needs to compensate for that. Second, the earth isn’t flat. We have to account for the fact “up” and “down” are technically different everywhere on the globe. Sounds complicated? It is . . .

As pilots we don’t need to be concerned with it because the designers have done that for us. So too with the non-flat earth. Since we reference everything on earth to the surface of the earth, the inertial platform must be moved to agree with the "flat earth" concept. If we didn't do this, for example, an airplane flying from Hawaii to Switzerland would show itself inverted at the end of the journey.

Strapdown Systems

Gimballed inertial navigation systems are easy to understand, since each gyroscope maintains its orientation in space no matter what the vehicle is doing. These are called “stable platform systems” since the platform itself is constant. The problem, however, is the gimbal arrangement is mechanically complex and the bearing, motors, and sliprings generate heat and friction. This makes them somewhat expensive to maintain.

Since we are using computers to do much of the work, it isn’t really necessary to keep the platform stable, only to measure the forces on each axis. Most inertial navigation systems today eliminate the gimbals and simply strap the gyroscope to the system case, which is itself strapped to the airplane. Getting rid of the gimbals certainly reduces the number of moving parts and that increases reliability.

The problem is that the sensors used to detect forces on the gyros now have to compensate for the movement of the vehicle itself. But this isn't a problem with modern computers and so the strapdown inertial is pretty much the standard solution today.

Drift errors

With earlier inertial navigation systems, it wasn’t uncommon for the system to wander from its initial position just sitting in the chocks or to develop an error while taxiing to the end of the runway. Friction in gyro bearings, heat in various moving parts, and even the rotation of the earth could introduce errors known as drift. Not too many years ago, a total drift of 3 to 7 miles per hour was not unusual. Replacing the mechanical gyros with light greatly reduced drift.

Ring Laser Gyros (RLGs)

In its most basic form, the RLG body is a solid glass block with three narrow tubes drilled to form a triangle. The tubes are filled with a helium-neon gas mixture and a mirror placed at each end. A neon lamp is used to cause the gas to generate laser light which circulates through the tubes in light particles known as photons. The light beam is split into two and the photons travel in opposite directions. Any movement of the glass block will cause the photons in one direction to arrive sooner or later than the photons going the other direction. The time difference can be used to determine the exact movement of the RLG body.

Hybrid Systems

A new feature for modern inertial navigation systems adds an embedded GPS receiver module, becoming a hybrid system. The result is a system that automatically knows where it is when first initialized, as well as a way to align itself inflight. By constantly checking with GPS, drift errors can be continuously corrected.

Your FMC will navigate according to what it considers its most reliable sensor, usually GPS. Each system varies and it is important to know which sensor “comes next” in the hierarchy, when the switch is made, and when the system can restore itself to a more reliable source.

A typical system, for example, might have the following hierarchy:

• GPS
• DME/DME
• VOR/DME
• IRS

It may be as simple as saying if the GPS fails, the FMC will revert to DME/DME, if that fails then VOR/DME, and if that fails, finally to the IRS.

Some systems may place margins of accuracy to prevent nuisance switching. If the GPS, for example, is no worse than 5% than DME/DME, the GPS remains the sensor of choice.

With Hybrid Inertial Reference systems, however, it could be that the IRS is considered more reliable, shaking up the hierarchy:

• GPS
• Hybrid IRS
• DME/DME
• VOR/DME
• IRS

It is vitally important to understand what sensors your FMC is using and how the “fail down” hierarchy works.

Basic Principles of Inertial Navigation, Seminar on inertial navigation systems, Tampere University of Technology, undated.

Honeywell Direct-To Newsletter, New FMS Sensor Logic, December 2012.

Honeywell Laseref VI, Micro Inertial Reference System, Product Description, March 2012.

King, A. D., B.Sc, F.R.I.N., Inertial Navigation - Forty Years of Evolution, General Electric Company Review, Vol 13, No 3, 1998.

Stoval, Sherryl H., Basic Inertial Navigation, Naval Air Warfare Center Weapons Division, September 1997.

Wikimedia Commons, Public Domain Artwork