Aviation Navigation, Performance, and Flight Planning Study Guide

Flight Planning and General Operating Procedures

• Flight Plan Item 10 Symbols: The letter W in Item 10 of a flight plan indicates that the aircraft is RVSM (Reduced Vertical Separation Minimum) approved.
• Flight Plan Submission Timing:
  • Submissions should occur $24\,hrs$ before ETD (Estimated Time of Departure).
  • Submissions should occur $120\,hrs$ before EOBT (Estimated Off-Block Time).
• Standard Instrument Departures (SID): Unless otherwise indicated on charts, standard instrument departure routes are provided with magnetic headings.

Aircraft Performance: Take-Off and Climb

• Climb Limited Take-Off Mass (Climb Limit):
  • The climb limited take-off mass can be increased by selecting a lower flap setting and selecting a higher $V_2$ speed.
  • Factors that increase the climb-limited TOM (Take-Off Mass) include:
    • Low flap setting.
    • Low Pressure Altitude (PA).
    • Low Outside Air Temperature (OAT).
• Take-Off Ground Run Performance: To decrease the take-off ground run, the following conditions are favorable:
  • Decreased take-off mass.
  • Increased air density.
  • Increased flap setting.
• Selection of Low Flap Setting: Favorable conditions for choosing a low flap setting during take-off include:
  • High field elevation.
  • Distant obstacles in the climb-out path.
  • Long runway.
  • High ambient temperature.
• Field Length Limited Take-Off Mass: If the field length limited take-off mass is calculated using a Balanced Field Length technique, utilizing additional clearway allows for the obstacle clearance limit to be increased with no effect on $V_1$.
• Climb Gradient Definition: The climb gradient is defined as the ratio of the increase of altitude to the distance over ground, expressed as a percentage: $\text{Climb Gradient} = \frac{\Delta \text{Altitude}}{\text{Ground Distance}} \times 100\%$.
• Variable Changes with Altitude:
  • Best Angle of Climb ($V_x$): Increases with increasing altitude.
  • Best Rate of Climb ($V_y$): Decreases with increasing altitude.
• Propeller Thrust: For a fixed propeller, the thrust decreases slightly as the aeroplane speed builds up during the take-off run.

Aerodynamics and Engine Failure

• Wind Effects on Speeds:
  • Maximum Range Speed (IAS): Increases with a headwind component compared to still air.
  • Speed for Maximum Climb Angle: Stays constant regardless of wind component.
• Critical Engine Inoperative (CEI): The failure of a critical engine increases the power required due to the greater drag caused by the windmilling engine and the need to compensate for the yaw effect.
• Minimum Control Speed ($V_{MCA}$): During flight at $V_{MCA}$ following an engine failure, the pilot must be able to maintain heading, altitude, and a positive rate of climb of $100\,ft/min$.

Mass and Balance Calculations

• Basic Empty Mass (BEM): Includes the mass of the aeroplane structure, power plants, systems, furnishings, and integral equipment. Its value is found in the latest version of the weighing schedule, corrected for modifications.
• Maximum Zero Fuel Mass (MZFM): On aeroplanes without a central fuel tank, the MZFM is related to the bending moment at the wing root.
• Center of Gravity (CG) Calculations: The position of the CG is determined by dividing the total moment by the total mass: $\text{CG} = \frac{\sum \text{Moments}}{\sum \text{Mass}}$.
• CG Limits and Aircraft Stability:
  • Forward CG Limit: Results in a decrease in range, increased stalling speed, and requires more elevator trim (increasing fuel consumption).
  • Rearward CG Limit: Results in a reduction in power required for a given speed and reduced fuel consumption due to reduced drag.
  • Longitudinal Stability: Determined by the location of the CG with respect to the neutral point.
  • Neutral Stability: An aeroplane is neutrally stable when the CG is situated at its rearward limit.
• Fuel Density and Mass Calculations:
  • Formula: $\text{Mass} = \text{Volume} \times \text{Density (Specific Gravity)}$.
  • Example 1: Fuel volume $3800\,US\,Gallons$, density $0.79$. Mass = $11364\,kg$.
  • Example 2: Volume $16500\,litres$, density $780\,kg/m^3$. If entered as $16500\,kg$, the aircraft is actually lighter than anticipated, and calculated safety speeds will be too high.
  • Example 3: If $15400\,kg$ of fuel is loaded but entered as $14500\,kg$, the pilot will notice the speed at un-stick is higher than expected.
• Payload and Traffic Load Calculations:
  • Example: BEM $3000\,kg$, MTOM/LM/MZFM $5200\,kg$, Ramp Fuel $650\,kg$, Taxi Fuel $50\,kg$. Payload available: $5200\,kg - (3000\,kg + 600\,kg \text{ takeoff fuel}) = 1600\,kg$.
  • Under-Loading: Loading an extra baggage container in the aft compartment without updating the load sheet makes the aircraft heavier; calculated safety speeds are unaffected but safety margins are reduced.
• Weighing Procedures: During weighing, it is required to drain all usable fuel and engine oil, but not required to drain chemical toilet fluid tanks.

Navigation: Time, Distance, and Points of Change

• Critical Point (CP) / Point of Equal Time (PET):
  • The CP is the decision point in the event of an engine failing before reaching the mid-point.
  • If Ground Speed (GS) is less than expected, the PET moves into wind.
• Point of No Return (PNR):
  • If flight fuel is increased, the distance to PNR ($D_{PNR}$) will increase (e.g., an increase of $200\,kg$ shifts $D_{PNR}$ from $500\,nm$ to $520\,nm$).
• Distance Calculations:
  • Still Air Distance: With a sector distance of $450\,nm$, TAS $460\,kt$, and a $50\,kt$ tailwind ($GS = 510\,kt$). Still Air Distance = $\frac{450}{510} \times 460 = 406\,NAM$.
  • Climb Distance with Wind: If climb to cruise takes $36\,min$ over $157\,nm$ (zero wind), with a $60\,kt$ tailwind, additional distance = $60 \times \frac{36}{60} = 36\,nm$. Total distance = $157 + 36 = 193\,nm$.
• ADF and Relative Bearings:
  • Time to Station: If an OBS rotation of $10^{\circ}$ takes $8\,min$ to center the CDI, time to station is $48\,min$.
  • Distance to Beacon: Relative bearing change from $045^{\circ}$ to $090^{\circ}$ (a $45^{\circ}$ change) in $5\,min$ with TAS $120\,kt$. Distance Calculation results in $6.7\,min$, $13.4\,nm$, and $0.6\,Gal$ fuel used.

Air Data and Altimetry

• Speeds and Corrections:
  • Calibrated Airspeed (CAS): Defined as Indicated Airspeed (IAS) plus the pressure error correction.
  • CAS and Altitude: At a constant Mach number, CAS increases when altitude increases.
  • CAS and Temperature: For a constant CAS in level flight, a fall in ambient temperature results in a lower True Air Speed (TAS) due to the increase in air density.
  • TAS Corrections: To produce TAS from IAS, one must correct for altitude and temperature.
• Altimeter Settings:
  • QNH Change: If QNH changes from $1013\,hPa$ to $1022\,hPa$, it does not affect field elevation, but the altimeter reading will change.
  • QFE Change: Changing QFE from $1013\,hPa$ to $1022\,hPa$ will increase the field elevation reading on the altimeter.
  • Pressure Altitude Calculation: If elevation is $25000\,ft$ and QNH is $999\,hPa$. Offset = $(1013 - 999) \times 30 = 420\,ft$. Pressure Altitude = $25000 + 420 = 25420\,ft$ (approx. $25400\,ft$).
• Air Data Computer (ADC): Transforms air data measurements (pitot/static) into electric impulses for instrument servos.

Magnetism and Compass Systems

• Earth's Magnetic Field:
  • Directive Force: The horizontal component of the Earth's magnetic field ($H$) which aligns the compass; it is greatest at the magnetic equator.
  • Red Pole: The Earth's magnetic "Red Pole" is situated in North Canada.
  • Magnetic Dip: The angle between the total magnetic field and the horizontal plane.
  • Field Strength: The horizontal component weakens as one moves from the magnetic equator toward the nearer magnetic pole.
• Compass Errors and Design:
  • Aperiodic (Dead Beat) Compass: Made stable by using a pendulous suspension system and damping wires.
  • Variation: Charted values change annually due to magnetic pole movement. It does NOT depend on aircraft heading.
  • Turning Errors: In the Northern Hemisphere, northerly turning error is steepest on headings of $000^{\circ}$. In the Southern Hemisphere, turning right from $320^{\circ}$ to $050^{\circ}$ results in the compass under-indicating the turn.
• Remote Indicating Compass (Flux Valve):
  • Advantage: Usually mounted in the wingtip to minimize magnetic interference from the aircraft. This reduces deviation.
  • Flux Valve Mounting: It is fixed to the aircraft and senses the Earth's magnetic field.
  • System Components: The master unit is ideally positioned in the center of the aircraft to minimize deviation from internal circuits.

Earth Geometry and Chart Projections

• Standard Measurements:
  • The Earth rotates about its Polar diameter.
  • $1\,minute$ of arc varies in length because the Earth's radius varies (it is an oblate spheroid).
  • Great Circle Track: The shortest distance between two points (e.g., from $56^{\circ}N\,070^{\circ}W$ to $62^{\circ}N\,110^{\circ}E$ is approximately $5420\,nm$).
• Chart Projections:
  • Lambert Conformal Conic: Great circles (other than meridians) are curves concave to the parallel of origin. The distance between parallels increases between and reduces outside of the standard parallels.
  • Transverse Mercator: Scale is exactly correct along the Meridian of tangency and meridians at $90^{\circ}$ to it.
  • Graticule: The network of meridians and parallels on a map.

Time and Astronomy

• LMT and UTC:
  • Local Mean Time (LMT): The time elapsed since the transit of the mean sun over its meridian.
  • Standard Time: The legal time established by a country for a specific zone.
  • International Date Line (IDL): Crossing from $150^{\circ}E$ to $108^{\circ}W$ at $0000\,UTC$, the destination LMT is behind and the date is ahead.
• Sunrise Calculations: Sunrise at $50^{\circ}N\,025^{\circ}E$ is $0254\,UTC$. At $50^{\circ}N\,040^{\circ}W$, the longitudinal difference is $65^{\circ}$. $65^{\circ} \times 4\,min/deg = 260\,min = 4\,hrs\,20\,min$. $UTC \text{ time} = 0254 + 0420 = 0714\,UTC$.