Inertial Navigation Systems (INS)

Inertial Navigation Systems (INS)

• An object in motion stays in motion, and an object at rest stays at rest unless acted upon by an unbalanced force, as stated in Newton's 1st Law of Motion
• Zero net force is equivalent to no force, leading to equilibrium
• The acceleration of a body is directly proportional to the force causing it and inversely proportional to its mass, according to Newton's Second Law of Motion
• When forces on a body are balanced, the object maintains a constant velocity
• Force = mass x acceleration (F = ma)
• Momentum is the product of an object's mass and velocity
• An object with 100 units of mass moving at 10 units of velocity has 1000 units of momentum
• An object at rest has no momentum
• Momentum increases when a force acts on an object, giving it motion
• Momentum is a vector quantity
• Force to stop or accelerate an object relies on its momentum, mass, and required velocity
• Momentum = mass times velocity
• Velocity tells you something about both speed and direction and is therefore a vector quantity
• Velocity differs from speed because it considers how fast a body moves and the direction it is moving at any given point in time.
• Speed is distance covered per unit time without direction
• Velocity is distance covered per unit time in a specific straight-line direction
• Acceleration is the rate of change of velocity
• Positive acceleration means the rate of movement is increasing and negative acceleration means it's decreasing
• A body has no acceleration when stationary or moving at a constant rate in a straight line
• Aeroplane with a constant velocity of 25 meters per second is not accelerating
• Acceleration is calculated by subtracting initial velocity from final velocity and dividing by the time period
• a = v2 - v1 ÷ t2 - t1
• Inertia is the natural property of objects to resist changes in motion
• Mass, not weight, measures inertia
• Larger mass equals more inertia
• Force changes or tends to change an object's state of rest or uniform motion
• Force describes pushing or pulling objects to change their movement
• Displacement: A vector or the magnitude of a vector from the initial position to a subsequent position assumed by a body, i.e. a result of velocity and acceleration
• With velocity and time, displacement increases

RNAV and INS

• RNAV lets pilots fly direct without needing ground-based navigation beacons.
• RNAV is simply the route an aircraft takes from one point to the next
• INS is used for RNAV that create an accurate self-contained navigation system
• With INS, pilots can disregard ground-based radio navigation and program many waypoints
• INS programmed waypoints are able to navigate aircraft on autopilot
• INSs are subject to errors
• Degradation of 1-2 nautical miles per hour is possible to maintain precision
• Many INS incorporate an updating facility corrected by a visual fix, VOR/DME, VORTAC, or GPS
• INS systems are approved as RNAV systems on their own or with other systems

Coordinate systems and Flight Path

• Align is Platform: leveling and orienting a platform to its co-ordinate system
• Azimuth: angle from north to longitudinal axis, commonly called heading, from 0° to 360°
• Bearing (BRG): Direction of a point or navigational aid measured clockwise from the aircraft's longitudinal axis
• Co-ordinate System: A system of two or more magnitudes used to establish a position or point
• Geographical co-ordinate system: Coordinate values referencing lines of longitude and latitude
• Grid co-ordinate system: Coordinates using grid lines for north-south and east-west measurement
• Flight Path Course (CRS): Planned flight direction on earth, expressed as magnetic, true, or grid course
• Flight Path Heading (HDG): Course angle measured clockwise from the reference to the course
• Track (TK): Line defining aircraft's direction over the earth's surface
• Cross Track (XTK): Distance left/right from desired track, measured perpendicularly
• Track Angle Error (TKE): Angle between aircraft's track and desired track. Error is left when the actual track angle is less than the desired track angle, and right when the actual track angle is greater than the desired track angle.

Navigation and Location

• Using speed and time to approximate position is dead reckoning
• The point in the sky reached by an aircraft following a specific route is A ‘fix'
• Drift is defined as lateral movement of an aircraft due to wind effect
• Drift Angle (DA): Angle between aircraft's longitudinal axis and ground track
• Drift angle is right when ground track angle is greater than true heading and left when ground track angle is less than true heading
• Gyrocompass is the process by which the stable element of an Inertial Refence Unit (IRU) becomes aligned to its north reference
• Ground Speed is speed of an aircraft over the surface earth, along the track angle
• Heading (HDG): Aircraft heading is angular direction of aircraft's longitudinal axis, with respect to magnetic or True North
• Heading indicates the direction the aircraft is pointing on the earth's surface
• Local vertical: A line coincident with or parallel to the gravity vector
• Latitude and longitude provide positional reference through angular distance from the center of the Earth
• Degrees, minutes, and seconds represents DMS formatting
• Degrees and decimal minutes (DMM) represent minutes in decimal format
• Decimal degrees (DD) represent decimals with southern latitudes & westerly longitudes as negative
• Parallels of Latitude has the equator representing the zero-latitude reference
• Longitude lines circle the Earth from north to south like orange segments
• lines of longitude all have the same circumference and intersect at the poles
• International Dateline: Located at both 180° east longitude and 180° west longitude
• Orthogonal is reference lines being right angular or intersecting lines
• Polar coordinates are made up of radius vector and its angle of inclination
• Rhumb line maintains equal angles with each meridian (equator, meridians of longitude, & parallels of latitude)

Inertial Navigation System (INS) Mechanics

• Self-contained dead reckoning system that tracks movements in all directions called Inertial Navigation System (INS)
• INS constantly calculates the aircraft's present position in relation to a known starting point
• Requires no external inputs
• INS calculates present position based on measurements of speed, heading, time, therefore performing the same function as a pilot navigating via dead reckoning
• Measurement of accelerations due to forces altering aircraft inertia is the basic principle of INS
• INS constantly monitors the aircraft's position in terms of latitude and longitude
• Navigation requires acceleration measurements in both N-S and E-W directions, so two accelerometers are required
• INS accurately detects induced accelerations and calculates groundspeed, heading, and time for reliable dead reckoning
• Pendulous accelerometers use gravity, not springs, to center the mass
• A Pendulous accelerometer is affected by cross-coupling error with accelerations along the original sensitive axis senses accelerations to right angles to that original axis.
• Torque Rebalanced Accelerometer eliminates cross couple error because the sensitive axis is mostly constant
• Capacitive Accelerometers measure acceleration along a sensitive axis uses capacitors included in an AC bridge circuit and act in conjunction with a differential amplifier to develop a phase sensitive signal proportional to angular displacement.
• Torquer arrangement uses permanent magnet and coil, providing an extremely linear relationship between torque and current
• Gyros stabilize a “platform” and maintain accelerometers’ sensitive axis with acceleration direction being measured
• Displacement (rotation) of platform creates electrical signal (output) applied to a torque motor, driving the platform back to the reference position
• Gyro has single output axis, called Single Degree of Freedom (SDF) Gyro or two output movements called Two Degrees of Freedom (TDF) Gyros.
• Gimbal Lock occurs when gimbal orientation is such that the spin axis becomes coincident with one or other of the axes of freedom
• Integrators: The position transmitter provides an electrical output proportional to acceleration. Velocity is calculated with these.

INS Components

• Computer in the INS contains integrators, amplifiers, processing circuits, and power supplies
• Gyroscopically stabilized platform
• Primary functions include computing aircraft velocity/distance from acceleration data, outputting navigational signals, and providing platform correction signals
• Two accelerometers are needed to measure acceleration in the horizontal plane, with one measuring north/south acceleration and the other measuring east/west acceleration
• Heart of INS is Inertial Navigation Unit (INU), which contains the INS computer and stabilized platform
• INU calculates present position, groundspeed, true heading, track, wind speed/direction, distance/time to next waypoint, cross track distance and track angle error
• Typical INS Control Display Unit (CDU) is the main point to which the Inertial Navigation System can be accessed
• On the CDU, all waypoint data is entered and displayed, the aircraft's position is displayed, and all aircraft data is displayed to the flight crew
• WARN lamp indicates internal failure of INU power supplies or abnormal gimbal torque motor current
• Ready / Nav lamp indicates the INS has completed its aligning process. Bat light is a battery warning light.
• Mode select switch used to control INS computer with control for OFF, STBY, ALIGN, NAV, ATT
• INS Battery Unit provides a backup power source.

Operation and Error Mitigation

• Gyros run up to speed and the platform aligns with respect to gravity, and detects the earth's rotation then corrects gyro drift for earth and transport rate
• The INU requires a local or present position Lat/Long so it can correct gyro drift for earth and transport rate
• Uninterrupted power supply to an INU is critical
• Gimbal: the gyroscopically stabilized platform
• Accelerometers are mounted on the platform and provide outputs of acceleration in the N-S and E-W directions. The computer calculates the resultant direction of acceleration, velocity, and distance travelled
• As the inertially stable part of a gyro (float) is displaced from the case, an error signal is developed at the pick off. This signal is then amplified, resolved, and sent to the torque motor which drives the gimbal and the case of the gyro to a new position nulling the pick off
• Coriolis effect, centripetal effect, transport rate, and earth rate are factors to solve in regard to INS for navigation around a rotating globe
• Rhumb Line A Rhumb line is a line which is formed when it maintains equal angles with each meridian as it intersects them and are also complex curves that spiral towards the pole
• Maintaining platform alignment keeps the accelerometers aligned N-S and E-W
• Aircraft attitude changes involve transmitting friction torque to the stable element through the gimbal bearings
• Azimuth resolver splits portions of pitch/roll from east and north gyros to produce pitch/roll outputs on display
• INS drifts typically around 1 to 2 NM per hour
• Many INS systems can be updated with visual landmarks, radio navigation transmitters, or GPS
• Outputs from the gyros are processed by the computer, which also provides the N-S and E-W platform correction
• Aircraft roll attitude is derived from a synchro mounted on the outer roll gimbal.

Azimuth and Wander

• INS will rotate about the azimuth gyro's input axis by signal to an amplifier that conditions a torque motor
• Wander azimuth compensation uses a computer to maintain the platform at the right attitude as the aircraft flies through latitude and longitude changes -Alpha Angle system is where gyro isn't True North
• Wander Angle with an INS not necessarily pointing at True North
• The amount of rotation needed to correct the gyro related to Earth and the effect its has in Inertial Guidance systems
• Transport rate (or wander) is what a uncorrected gyro would display.
• Coriolis force produces acceleration known as the Coriolis force.

Corrections

• To eliminate earth rate, space gyro can be precessed at 15° per hour
• For horizontal axis gyroscopes the following methods can be used to compensate for the apparent drift
  • calculating corrections using the earth-rate formula given in a table form and applying them apply fixed torques which unbalance the gyroscope
  • apply torques having a similar effect to that stated in above, but which can be varied according to the latitude.
• Schuler Tuning can minimize erroneous accelerometer oscillations caused by gravity INU platforms
  • Output of the accelerometer integrated to supply velocity signal, multiplied by I/R (R is earth's radius)
• To level the stabalized platform in the INS, after the accelerometer outputs do drop to zero. At this point the computer will set the velocity to zero to set the initital refrence point.
• INS systems use computer (i.e. card stack), gyros, synchro (a signal transmission device).
• INS references: against movement about the verticle axis (what direction its spinning towards), Pitch, Yaw, Roll
• Earth Rate (We) is the earths rotation in association with gyro dynamics. Earth Rate (We) = 15° per hour
• Correctly calculating the apparent drift requires knowledge of its latitude and the orientation of its spin and input axes.

Initialisation, Alignment, and Functions

• Alignment: process in which a inertial systems gyros are spun up over which time the system is coarsely and finely aligned
  • Course Alignment- provides starting point for alignment phases, lasts for 30 seconds
  • Fine Alignment - repositions the stable element this levels outputs for a approximate tow minutes to complete then intiates next stage
  • Gyrocompasing- aligns stable element to true north, which switches the computers into gyrocompass phase