# Inertial Navigation Systems: Gyroscopes and accelerometers

Oct. 1, 2002

By Jim Sparks

Gyroscopes and accelerometers

Inertia shows its presence in a variety of ways on a daily basis. Being pressed back into your seat as you go down the runway or having your coffee cup spill over as the pilot applies maximum braking. Inertia is almost always the property that contributes to the fact that any time a tool slips out of hand; it will end up in the most inconvenient place possible. Sir Isaac Newton’s first law of motion states that an object set in motion tends to stay in motion unless acted upon by external forces.

Sensors can be used to measure different types of motion and by applying some mathematics accurate position calculations can be made from a specific starting point. The two most conclusive types of motion are acceleration and rotation. Gyroscopic sensors are used for measuring degree of rotation, while rate gyros measure the speed of rotary motion.

Accelerometers on the other hand are devices used to measure acceleration. The "G" force is the main unit for measurement of acceleration and is calculated as 1G = 32 feet per second per second.

Both gyroscopes and accelerometers use an inertial reference frame, which is a means of providing a fixed point from which measurements can be made. An accelerometer in free fall has no detectable input therefore no measurement can be made. The input axis of an inertial sensing device defines what it can measure and inertial navigation uses gyros and accelerometers to maintain an estimate of position. These inertial navigation systems (INS) not only provide a reliable means of position sensing for aircraft but have also found uses in spacecraft, missiles, ships, submarines, and even surface vehicles. An Inertial Navigation System is comprised of some type of inertial measuring unit (IMU) or inertial reference unit (IRU).

This type of navigational system includes a group of sensors including gyroscopes and accelerometers. All sensing devices contained within are secured to a common base which ensures all sensing devices have the same reference orientation. These sensing units supply acquired information to a microprocessor where integration of all available data is initiated and only then an estimated position is formulated based on applied motions and initial position.

"Gimbaled" and "strap down"

Even though there are numerous designs, INS with different capabilities fall into two groups, "gimbaled" and "strap down."

A gimbaled device is one that includes a rigid frame with rotating bearings. If the bearings could be made frictionless and the frames perfectly balanced then the supported body will be free of rotational inertia. When a gyroscope is mounted in the frame it can sense any torque from bearing friction or instability due to frame balance. A feedback can be made to zero out all the forces not having an applicable effect on the gyroscope. At least three axes or gimbals are required to isolate a supported body and are referred to as roll, pitch, and yaw. The earliest INS appeared around 1960 and computers of the day were unable to keep up with all the equations of motion which meant a stable platform or "stable table" was required to keep the accelerometers and gyroscopes oriented to the appropriate axis.

The inertial sensors in a strapdown system are just like those in a gimbaled device with one significant exception. There is no mechanical system of correction. The supported gimbaled framework is missing. All sensors are anchored or "strapped down" to the object being monitored. In this type system the computer is performing all the calculations to satisfy the full six degrees of motion. Strapdown platforms are more susceptible to shock and vibration than gimbaled units. It is necessary to take special precautions when installing these devices in areas where vibration may influence the system operation.

Only human imagination and the laws of physics limit the designs of inertial sensors, there are thousands of designs for gyroscopes and accelerometers. Not all are used for navigation, gyroscopes are used for steering and stabilizing ships, torpedoes, missiles, and even for cameras and binoculars. Acceleration sensors can be used to measure the effects of gravitational impacts, leveling, and even measuring vibrations.

Gyroscope designers have employed many concepts to resolve sensing problems. The Momentum wheel gyroscope uses a spinning mass similar to a child’s toy top. When this device is mounted in a gimbaled ring frame it tends to remain in an inertially fixed direction. By monitoring the gimbal position, a readout of angular displacement can be determined. Drift characteristics of the momentum wheel requires specialized bearing supports and in some cases magnetic or even electrostatic bearings are used.

Momentum wheel gyroscopes also exhibit the tendency to precess or drift. This is caused by a shift of the center of the spinning mass from the center of the gyro support. The torque produced will be at a right angle to the spinning mass.

Laser gyroscopes free us of dealing with the hazards and pitfalls of their mechanical predecessors. The ring laser is a device that works on a principle of smoke and mirrors, literally! A gas-filled triangular laser tube with mirrors in each corner is charged with two counter-rotating laser beams.

A photo detector is located behind one of the mirrors, which is designed to allow a certain percentage of light to leak through. As the laser platform moves in conjunction with one axis of the aircraft the effective length of one of the laser cavities will increase while the other shortens. This will result in a relative frequency change at the photo detector. The result is a fringe frequency that is directly proportional to the input rotation rate.

Newton’s second law

Accelerometers used for inertial navigation employ Newton’s second law which says, an applied force is a result of accelerating a specific mass or Force = Mass x Acceleration.

Pendulum accelerometers use a hinged arm to support the mass. This type device can be very effective in two dimensions. As the hinged platform begins to move, the mass being supported on the arm will try to remain constant. The deflection angle will be directly proportional to the applied acceleration.

Because an INS operates in a world with gravitational effects, incapable of measuring yet has significant bearing on the ultimate results, a precise gravity model is needed. These must realistically mimic the centrifugal forces generated by the earth’s rotation as well as the gravitational pull.

Determining alignment

INS, even though they are able to calculate where an aircraft is going, have no ability to determine initial position without a bit of external help. Several means of alignment are used. The most basic is line of sight reference using a ground-based direction.

Gyro compass alignment is one of the more common means of providing an INS with initial positioning. To accomplish this the device senses the earth’s direction of rotation to determine North. After that latitude and longitude can be entered manually.

Another means includes the ability to transfer alignment data from one operating INS to one that is being initialized.

Global position sensing (GPS) is a popular means for providing alignment variables. Using this type of programming can in some cases even be accomplished while the aircraft is moving.

The accuracy of the alignment is a function of time as well as the lack of movement of the INS. Another factor in alignment time is latitude location; an alignment occurring at zero to 60 degrees latitude may require from two to 10 minutes. As location gets further away from the earth’s center the alignment time increases. Above 70 degrees the alignment time may be closer to 15 minutes. Once alignment is complete and the aircraft is underway position drift may occur. This is an acceptable condition providing the degree of drift is within the prescribed limits of the system. The acceptable amount of drift will by and large increase with the duration of the flight. In other words, the longer the flight, the greater the allowable amount of drift. About two nautical miles per hour is considered normal.

Pitch and roll

In addition to calculating aircraft position, information from inertial sensing devices is used by a variety of systems including attitude displays such as pitch and roll. IRS data is also used to compute heading, ground speed, and even wind direction. Most automatic flight control systems rely on inertial information to provide feedback as well as guidance for steering and otherwise maneuvering the aircraft. Most flight guidance systems have a maximum roll rate as well as a specific degree per minute yaw. Yaw damping devices would not be able to function without inertial input of some type.

Attitude information used to provide a pitch compensation to fuel quantity indicating systems and acceleration data may be included as a factor to regulate automatic wheel braking systems.

Inertial reference units generally have an independent control head with selections such as NAV, ALIGN, and ATT. When any one of the modes is selected from the OFF position a self-test is initialized. Successful completion of a BITE check will result in automatic transfer of the system to ALIGN. It is in this configuration that external data is needed to tell the inertial unit where it is. When selected to ATT, all sensors are capable of recognizing any movement, however, the system may not have any input on its current position.

As these devices include high-speed microprocessors in addition to all the motion sensors, a backup battery is often considered a standard component in the installation. In the event of a short-term loss of aircraft electrical power the battery should be capable of keeping the reference unit alive without having to be re-aligned for duration of the power outage.

With all the internal electronics involved in proper operation next to vibration, heat is probably the No. 1 killer of inertial sensing devices. This being the case most units are often fit with internal blower fans or at least require a constant flow of air from an airframe source. Often overheat indicators will inform the flight crew as well as maintenance personnel about impending overheat conditions. Many systems include filters in the airflow path and when this is the case, like most filters, a scheduled replacement interval is essential.

Inertial navigation, which relies on knowing initial position, then sensing velocity and attitude to calculate aircraft position, is the only navigation system that does not rely on any external reference. It does however require us to pay attention to things like proper installation and verification of proper airflow and backup battery integrity.

The basis of operation for inertial sensing systems is Newton’s Laws of Motion and as I recall one of Sir Isaac’s laws said something about "a body at rest tending to stay at rest," Hmm, what a concept!