B2-13e Aircraft Systems - Navigation Flashcards

Pedagogical Definitions and Study Resources

Pedagogical Definitions:
- Define: To describe the nature or basic qualities of; to state the precise meaning of a word or sense of a word.
- State: Specify in words or writing; to set forth in words; declare.
- Identify: To establish the identity of.
- List: Itemise.
- Describe: Represent in words enabling a hearer or reader to form an idea of an object or process; to tell the facts, details, or particulars of something.
- Explain: Make known in detail; offer reason for cause and effect.
Study Resources Provided:
- Jeppesen General and Jeppesen Airframe.
- AC 43.13-1B/ AC 43.13-2A Combined – Aircraft Inspection and Repair.
- Kennedy – Davis Electronic Communication Systems.
- James Powell (Jeppesen) Aircraft Radio Systems.
- National Training Materials for the Aerospace Industry.
- Avionics Fundamentals – Jeppesen.
- Automatic Flight Control – Pallett.
- Aircraft Instruments & Integrated Systems – EHJ Pallett – 1992.
- COAs.

Fundamental Laws of Motion and Inertial Principles

Newton’s First Law of Motion:
- An object in motion will remain in motion, and an object at rest will remain at rest unless acted upon by an unbalanced force.
- In a vacuum, an object would continue at the same speed forever; in Earth's atmosphere, friction and gravity provide the opposing forces.
- Zero net force (equilibrium) results in no acceleration; the object either remains at rest or moves with uniform motion in a straight line.
Newton’s Second Law of Motion:
- \text{“The acceleration of a body is directly proportional to the force causing it and inversely proportional to the mass of the body.”}
- Mathematical Formula: $F = m \times a$ or $a = \frac{F}{m}$ .
Momentum:
- Momentum is the product of mass and velocity: $\text{Momentum} = m \times v$ .
- It is a vector quantity (magnitude and direction).
- Example: A 100-unit mass at 10 velocity has the same momentum (1000 units) as a 2-unit mass at 500 velocity.
Inertia:
- Inertia is the natural property of objects to resist changes in their state of motion or to resist acceleration.
- Mass is the measure of inertia, not weight (an object in space is weightless but still possesses inertia).
Force:
- A force applied to an object changes or tends to change its state of rest or uniform motion (pushing or pulling).

Kinematic Parameters and Navigation Definitions

Velocity:
- Unlike speed (scalar), velocity is a vector quantity describing both speed and direction.
- An object moving in a circle at a constant rate has a fixed speed but constant changing velocity due to direction changes.
Acceleration:
- The rate of change of velocity.
- Positive acceleration is an increase in velocity; negative acceleration is deceleration or retardation.
- Formula: $a = \frac{v_2 - v_1}{t_2 - t_1}$ .
- Example Calculation: If an aircraft goes from $26\,m/s$ to $35\,m/s$ in 3 seconds, $a = \frac{35 - 26}{3} = 3\,m/s^2$ .
Displacement:
- The vector from an initial position to a subsequent position, resulting from velocity and acceleration over time.
Area Navigation (RNAV):
- Allows pilots to fly direct from point to point without ground-based beacons.
- INS is an accurate self-contained RNAV system but can degrade at $1\,NM/hr$ to $2\,NM/hr$ .
Core Navigation Terms:
- Azimuth: The clockwise angle from North to the longitudinal axis (heading), $0^\circ$ to $360^\circ$ .
- Bearing (BRG): Direction from the aircraft's longitudinal axis to a point, measured clockwise.
- Track (TK): The actual path the aircraft flies over the Earth’s surface.
- Cross Track (XTK): Lateral distance left or right of the desired track.
- Track Angle Error (TKE): Angle between the actual track and the desired track.
- Drift: Lateral movement from heading due to wind.
- Elevation: Height above a datum, usually sea level.
- Great Circle: A circle whose plane passes through the Earth's center; the shortest distance between two points (Geodesic Lines).
- Rhumb Line: A line maintaining equal angles with all meridians; spirals toward the pole.

The Earth's Coordinate System

Geographical Coordinates:
- Uses Latitude and Longitude referencing the spherical Earth.
- Latitude (Parallels):
  - Angular distance North or South of the Equator ( $0^\circ$ ).
  - Poles are at $90^\circ$ .
  - $1^\circ$ of latitude = $60\,NM$ or $111\,km$ ; $1\text{ minute}$ of latitude = $1\,NM$ .
  - Key Lines: Tropic of Cancer ( $23 \frac{1}{2}^\circ\,N$ ), Tropic of Capricorn ( $23 \frac{1}{2}^\circ\,S$ ), Arctic Circle ( $66 \frac{1}{2}^\circ\,N$ ), Antarctic Circle ( $66 \frac{1}{2}^\circ\,S$ ).
- Longitude (Meridians):
  - Angular distance East or West of the Prime Meridian (Greenwich, England, $0^\circ$ ).
  - Meridians converge at the poles; the distance between them is greatest at the Equator ( $1^\circ = 60\,NM$ at the Equator).
  - International Dateline is at $180^\circ$ .
- Coordinate Formats:
  - DMS: Degrees, Minutes, Seconds (e.g., $27^\circ 24' 59'' S$ ).
  - DMM: Degrees and Decimal Minutes (e.g., $27^\circ 24.9833' S$ ).
  - DD: Decimal Degrees (e.g., $-27.41638^\circ$ ).
Grid Coordinate System:
- Uses Eastings (horizontal axis) and Northings (vertical axis).
- Does not have converging lines; used for polar navigation.

Inertial Navigation System (INS) Fundamentals

Overview:
- A self-contained dead reckoning system requiring no external radio or satellite inputs.
- Tracks all movements from a known starting position by measuring accelerations.
Accelerometers:
- Devices that measure the magnitude of acceleration.
- They are sensitive only along a specific "sensitive axis."
- Navigation requires two accelerometers (North-South and East-West).
- Pendulous Accelerometer: Uses gravity to center the mass; output is often non-linear and suffers from Cross-Coupling Errors (sensing unintended axes when tilted).
- Torque Rebalanced Accelerometer:
  - Uses capacitive pickoffs and rebalance torquers (coils/motors) to keep the mass at null.
  - The current required to hold the mass at null is proportional to acceleration.
  - Extremely linear and eliminates cross-coupling by keeping the sensitive axis constant.
- Capacitive Accelerometer: Uses a metallized ceramic disc as a torque-restrained pendulous element.
Mathematical Integration in INS:
- Primary process: integrating acceleration to find velocity, then integrating velocity to find distance.
- Integration is the process of finding the area under a signal curve.
- Operational Amplifier (Op-amp) Integrators:
  - Uses negative feedback with a capacitor instead of a resistor.
  - The capacitor acts as a short circuit initially (zero gain) and builds resistance as it charges.
  - Rate of change: $\frac{\Delta V_{out}}{\Delta t} = -\frac{V_{in}}{RC}$ .
  - The op-amp must stay in its linear region; High input impedance allows the capacitor to hold its charge during constant velocity (cruise).

INS Components and Operation

Inertial Navigation Unit (INU): The "black box" containing the navigation computer and stabilized platform.
Control Display Unit (CDU):
- Displays Lat/Long, XTK/TKE, HDG/DA, TK/GS, Wind, and Waypoint data.
- Contains keyboard, data display select switch, and annunciators.
- WARN lamp triggers for power failure, abnormal gimbal torque, computation errors, abnormal accelerometer outputs, or over-temperature.
Mode Selector Unit (MSU):
- OFF: System powered down.
- STBY: Warm-up mode; aircraft can be moved.
- ALIGN: Aligns gyros to Earth rotation and local vertical; aircraft must not be moved.
- NAV: Active navigation mode using waypoints.
- ATT: Attitude only (pitch, roll, and azimuth); no navigation provided.
Battery Unit (BU):
- Provides emergency power for up to 30 minutes.
- Usually 19-cell, $15\,Ah$ Nickel-Cadmium.
- If power is lost for even a fraction of a second, the INS data is corrupted.

System Errors, Alignment, and Corrections

Stabilized Platforms:
- Gyroscopes (SDF or TDF) detect platform rotation and drive gimbal torque motors to keep the platform level relative to gravity.
- This prevents the accelerometers from sensing gravity instead of aircraft motion.
- Gimbal Lock: Occurs when the spin axis becomes coincident with an axis of freedom, causing the gyro to topple.
Earth Rate and Transport Rate:
- Earth Rate ( $W_e$ ): Earth rotates at $15^\circ$ per hour ( $360^\circ$ in $23\,HR\,56.4\,MIN$ ).
- Apparent Drift: The perceived movement of a gyro on Earth due to rotation; calculated as $15^\circ \sin(\lambda)$ .
- Transport Rate: The apparent tilt of a gyro when moved across the Earth's curved surface; corrected by torqueing the gyro by $\frac{V}{R}$ ( $V = \text{Velocity}$ , $R = \text{Earth's Radius}$ ).
Coriolis and Centripetal Effects:
- Coriolis Force: Caused by the Earth's rotation; aircraft must crab left in the Northern Hemisphere and right in the Southern Hemisphere to follow a Great Circle.
- Centripetal Force: Force required to hold an object in circular motion ( $F = \frac{mv^2}{R}$ ); corrected mathematically by the INS computer.
Schuler Tuning:
- Prevents gravity-induced oscillation errors in the platform.
- The platform is governed by the principles of a Schuler Pendulum with a length equal to the Earth's radius.
- The period of oscillation is $84.4\text{ minutes}$ . This tuning keeps the platform normal to the local vertical.
Alignment Process:
1. Coarse Alignment (Caging): Gimbals driven to null; takes approx. 30 seconds.
2. Fine Alignment (Levelling): Accelerometers used to level the platform; takes approx. 2 minutes.
3. Gyrocompassing: Alignment to True North by sensing Earth's rotation; takes approx. 6 minutes.
Wander Azimuth System:
- Unlike North-pointing systems, the platform does not physically point North at high latitudes.
- Calculates a "Wander Angle" (Alpha) to allow navigation in Polar Regions where North-pointing torquing rates would be too high.

Inertial Reference Systems (IRS) and Ring Laser Gyros (RLG)

Evolution to Strapdown Systems:
- Modern IRS (Strapdown) has no moving gimbals; components are "strapped down" to the aircraft chassis.
- Eliminates mechanical complexity and improves reliability.
- Total sensors: 3 RLGs and 3 linear accelerometers per IRU (18 total in triple systems).
Ring Laser Gyro (RLG):
- Acronym: Light Amplification by Stimulated Emission of Radiation.
- Construction: Solid triangular block of temperature-stable glass with gas-filled cavities (Helium-Neon).
- Operation: Two laser beams (CW and CCW) travel in opposite directions. Rotation changes the effective path length and frequency of the beams (Sagnac Effect).
- Sensitivity: Detects frequency differences as small as a few Hertz (Light frequency is $4700\,THz$ ).
- Dithering: A piezoelectric dither motor vibrates the RLG block at $400\,Hz$ to prevent "Lock-in" (where beams couple and fail to sense rotation at low rates).
Air Data/Inertial Reference System (ADIRS):
- Combines Air Data Reference (ADR) and Inertial Reference (IR) into a single ADIRU.
- A320/A340 Displays: Includes ON BAT, FAULT, and ALIGN indicators. FLashing ALIGN indicates alignment fault, no position entered, or large position discrepancy (> 1^\circ).
Maintenance and Updates:
- IRS Updating: In-flight updates via GPS, VOR, or DME to remove accumulated drift accuracy loss ( $0.6\,NM/hr$ is typical for RLG systems).
- Calibration: IRS systems use automatic calibration programs to estimate drift and modify gyro bias factors after every flight.
- Embedded GPS: Modern IRUs often contain an internal GPS moduel for "in-flight alignment" and continuous calibration, removing the 10-minute stationary requirement.