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1. Units of Measurement and Flight Safety

• Significance of Unit Consistency:

  • In the 1983 Air Canada incident (the "Gimli Glider"), ground personnel computed fuel in pounds, while flight crew calculated requirements in kilograms, causing the aircraft to exhaust fuel mid-flight.

  • Unit consistency is a direct flight safety requirement, not an administrative detail.

• Fundamental Quantities (SI Base Units):

  • Length: metre ($\text{m}$$)</p></li><li><p>Mass: kilogram ($\text{kg}$$)

  • Time: second ($\text{s}$$)</p></li><li><p>Temperature: kelvin ($\text{K}$$)

• Derived Quantities:

  • Velocity: metres per second ($\text{m/s}$$)</p></li><li><p>Acceleration: metres per second squared ($\text{m/s}^2$$)

  • Force: newton ($\text{N}$$)</p></li><li><p>Energy: joule ($\text{J}$$)

  • Power: watt ($\text{W}$)

• Standard Aviation Units & Common Conversions:

  • Altitude: feet (\text{ft}$$)

  • Speed: knots ($\text{kt}$$)</p></li><li><p>Distance: nautical miles ($\text{NM}$$)

  • Mass: kilograms ($\text{kg}$$) or pounds ($\text{lb}$$)

  • Key conversion factors:

  • $1\,\text{m} = 3.281\,\text{ft}$

  • $1\,\text{kt} = 1.852\,\text{km/h}$

  • $1\,\text{NM} = 1.852\,\text{km}$

  • $1\,\text{kg} = 2.205\,\text{lb}$

  • Altitude calculation example: Bole elevation of $2334\,\text{m} \times 3.281\,\text{ft/m} \approx 7657\,\text{ft}$.

• Conversion Relay Exercises:

  1. Bole Elevation: Convert $7657\,\text{ft}$ to metres: $\frac{7657}{3.281} \approx 2334\,\text{m}$.

  2. Cruise Speed: Convert $850\,\text{km/h}$ to knots: $\frac{850}{1.852} \approx 459\,\text{kt}$.

  3. Route Distance: Convert $1360\,\text{NM}$ to kilometres: $1360 \times 1.852 = 2518.72\,\text{km}$.

  4. Fuel Load: Convert $20000\,\text{lb}$ to kilograms: $\frac{20000}{2.205} \approx 9070.3\,\text{kg}$.

2. Distance vs. Displacement

• Distance (Scalar):

  • Total length of the path traveled without regard to direction.

  • Directly determines the amount of fuel required for an operation.

• Displacement (Vector):

  • Net straight-line change in position from departure to arrival point, including directional orientation.

  • Directly influences directional tracking, navigation, and heading selection.

• Aviation Case (Addis Ababa to Nairobi):

  • Path distance traveled: $1300\,\text{km}$

  • Net displacement: $1160\,\text{km}$ South-Southwest (SSW)

3. Speed vs. Velocity

• Speed (Scalar):

  • Defined as total distance traveled per unit time:
    $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$

• Velocity (Vector):

  • Defined as total displacement per unit time, maintaining direction:
    $\mathbf{v}_{\text{avg}} = \frac{\Delta \mathbf{x}}{\Delta t}$

• Flight Application (Addis Ababa to Nairobi):

  • Given displacement $\Delta x = 1160\,\text{km}$ and elapsed time $t = 2.5\,\text{h}$:
    $\mathbf{v}_{\text{avg}} = \frac{1160\,\text{km}}{2.5\,\text{h}} = 464\,\text{km/h}$

4. Acceleration and Deceleration

• Definition & Formula:

  • The rate of change of velocity over time:
    $a = \frac{v<em>f - v</em>i}{t}$

  • SI Unit: $\text{m/s}^2$

• Takeoff Run:

  • Accelerating from rest ($0\,\text{m/s}$) to rotation speed ($80\,\text{m/s}$) in $35\,\text{s}$:
    $a = \frac{80\,\text{m/s} - 0\,\text{m/s}}{35\,\text{s}} \approx 2.29\,\text{m/s}^2$

  • Equivalent acceleration in terms of Earth's gravity ($g \approx 9.8\,\text{m/s}^2$):
    $\text{Load Factor} \approx \frac{2.29}{9.8} \approx 0.23\,g$

• Landing Rollout:

  • Decelerating from touchdown speed ($70\,\text{m/s}$) to a complete stop ($0\,\text{m/s}$) in $25\,\text{s}$:
    $a = \frac{0\,\text{m/s} - 70\,\text{m/s}}{25\,\text{s}} = -2.8\,\text{m/s}^2$

  • The negative sign signifies deceleration (acceleration vector opposing the direction of forward flight).