Measuring Horizontal Acceleration
The key to a successful inertial system is absolute accuracy in measuring horizontal accelerations. A slight tilt of the stable platform introduces a component of earth’s gravity as acceleration on the aircraft and results in incorrect distances and velocities. [Figure 16-4] Keeping the accelerometers level is the job of the feedback circuit. The computer calculates distance traveled along the surface of the earth and moves the accelerometer through an equivalent arc.
Several factors affect aligning the accelerometer using this method. The earth is not a sphere, but an oblate spheroid or geoid. Because the earth is not a smooth surface, there are local deviations in the direction of gravity. The feedback circuit operates on the premise that the arc traversed is proportional to distance traveled. Actually, the arc varies considerably because of the earth’s shape; the variation is greatest at the poles. The computer must solve for this irregularity in converting distance to arc.
The accelerometers are kept level relative to astronomical rather than geocentric latitude. Using the astronomical latitude, the accelerometers are kept aligned with the local horizon and also with the earth’s gravitational field. Feedback from the computer keeps the accelerometers level, correcting for two types of apparent precession. If the inertial unit were stationary at the equator, it would be necessary to rotate the accelerometers to maintain them level because of the earth’s angular rotation of 15° per hour. Also, movement of the stabilized platform would require corrections to keep the accelerometers level. When using a local horizontal system, in which the accelerometers are maintained directly on the gyro platform, the gyro platform must be torqued by a signal from the computer to keep the platform horizontal. Apparent precession is illustrated in Figure 16-5.
A slight error in maintaining the horizontal would induce a major error in distance computation. If an accelerometer picked up an error signal of 1/100 of the G-force, the error on a 1-hour flight would be 208,000 feet (over 34 nautical miles (NM)). In 1923, Dr. Maxmillian Schuler showed a pendulum with a period of 84.4 minutes could solve the problem of eliminating inadvertent acceleration errors.
If a pendulum has a period of 84.4 minutes, it indicates the vertical, regardless of acceleration of the vehicle. He demonstrated that a device with a period of 84.4 minutes would remain vertical to the horizon despite any acceleration on the device. The fundamental principle of the 84.4-minute theorem is that if a pendulum had an arm equal in length to the radius of the earth, gravity would have no effect on the bob. This is because the center of the bob would be at the center of gravity (CG) of the earth, and the pendulum arm would always remain vertical for all motions of the pivot point. While it would be impossible to construct this pendulum, devices with an 84.4-minute cycle can be constructed using gyroscopes. The Schuler pendulum phenomenon prevents the accumulation of errors that would be caused by platform tilt and treating gravity as an acceleration. It does not compensate for errors in azimuth resulting from the precession of the steering gyro. The amplitude of the Schuler cycle depends upon the overall accuracy of the system. Figure 16-6 shows the Schuler-tuned system.
A spinning, untorqued gyro is space-oriented and appears to move as the earth rotates underneath it. This is undesirable for older systems because the accelerometers are not kept perpendicular to the local vertical. To earth-orient the gyro, we control apparent precession. If a force is applied to the axis of a spinning gyro wheel that is free to move in a gimballing structure, the wheel moves in a direction at right angles to the applied force. This is called torquing a gyro and can be considered as mechanized or induced precession. A continuous torque, applied to the appropriate axis by electromagnetic elements called torques, reorients the gyro wheel to maintain the stable element level with respect to the earth and keeps it pointed north. An analog or digital computer determines the torque to be applied to the gyros through a loop that is tuned using the Schuler pendulum principle. The necessary correction for earth rate depends on the position of the aircraft; the correction to be applied about the vertical axis depends on the velocity of the aircraft.
It is important that the stable element be leveled accurately with respect to the local vertical and aligned in azimuth with respect to true north. Precise leveling of the stable element is accomplished prior to flight by the accelerometers that measure acceleration in the horizontal plane. The stable element is moved until the output of the X and Y accelerometers is zero, indicating that they are not measuring any component of gravity and that the platform is level. Azimuth alignment to true north is accomplished before flight by starting with the magnetic compass output and applying variation to roughly come up with true north reference. From this point, gyrocompassing is performed. This process makes use of the ability of the gyros to sense the rotation of the earth. If the stable element is misaligned in azimuth, the east gyro sees the wrong earth rate and causes a precession about the east axis. This precession causes the north accelerometer to tilt. The output of this accelerometer is then used to torque the azimuth and east gyro to ensure a true north alignment and a level condition.
In the more modern gyroscopes, the gyro cannot be physically torqued, because the gyro is either not moving or the gyro is electronically suspended. In these systems, the stable platform is leveled mathematically using gyro data. The precise orientation of the X and Y accelerometers on the stable platform is less critical since the computer can mathematically correct for any orientation. The next generation of INS may work without a stable platform, with orientation and stability maintained mathematically from accelerometer inputs.
Simply stated, the processing of acceleration is done with an integrator. An integrator integrates the input to produce an output: it multiplies the input signal by the time it was present. Accurate navigation demands extremely accurate integration of both acceleration and velocity. One of the most used analog integrators is the DC amplifier, which uses a charging current stabilized to a specific value proportional to an input voltage. Another analog integrator is the AC tachometer-generator that uses an input to turn a motor, which physically turns the tachometer-generator, producing an output voltage. The rotation of the motor is proportional to an integral of acceleration.
The computer changes the integrator’s outputs into useful navigation information. To do this, one accelerometer is mounted aligned to north and another is mounted 90° to the first, to sense east-west accelerations. Any movement of this system indicates distance traveled east-west and north-south. The INS maintains a local vertical reference and measures distance traveled over a reference spheroid perpendicular to the local vertical. On this spheroid, the latitude and longitude of the present position are continuously measured by the integration of velocity. In Figure 16-7, Ө represents latitude and λ represents longitude. The axes are designated X, Y, and Z, corresponding to east, north, and local vertical. This defines their positive directions. References to velocities, attitude angles, and rotation rates are about the X, Y, and Z axes. The local vertical (Z) is established by platform leveling. This is the most fundamental reference direction. To complete platform alignment, the INS uses gyrocompassing to establish true north (Y). Gyrocompassing establishes platform alignment to the earth’s axis of revolution or North Pole. The INS is capable of doing this to an accuracy of 10 minutes of arc or less. After alignment, the platform remains oriented to true north and the local vertical, regardless of the maneuvers of the aircraft.
Groundspeed components of velocity in track (V) are measured by the system along the X and Y axes. [Figure 16-8] These components, VX and VY, include all effects on the aircraft, such as wind, thermals, engine accelerations, and speed brake decelerations. Some form of digital readout usually displays the groundspeed (V).
The angles between the aircraft attitude and the platform reference attitude are continuously measured by synchros. The aircraft yaws, rolls, and pitches about the platform in a set of gimbals, each gimbal being rotated through some component of attitude. TH is measured as the horizontal angle between the aircraft’s longitudinal axis and platform north. Roll and pitch angles are measured by synchro transmitters on the platform roll and pitch gimbals.
INS technology has advanced very rapidly within the past few years. Advanced navigation systems are commonly designed with INS as an essential component. INS reliability is exceptional and INS accuracies are second only to GPS. Traditional INS design has capitalized on the advances of the digital computer to increase system responsiveness.