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Performance Calculations

Introduction:

Units of Measure:

  • Statute Mile: the same as a standard mile as you would see driving a car
  • Nautical Mile: defined as one minute of arc along a meridian of the Earth. Using the widely accepted WGS84 ellipsoid model, this averages a nautical mile to 6,076 feet (1,852 meters), or 1.15 statute miles

Temperature Conversion Chart
Figure 1: Temperature Conversion Chart

Temperature Conversion:

  • The U.S. is used to operating on the Fahrenheit scale for day to day life but aviation standard is Celsius
    • Formula:
      • °C = [(°F - 32) x 5/9]
      • °F = [(°C x 9/5) + 32]
    • Example:
      • 70°F day
    • Calculate:
      • °C = ((70°F-32) x 5/9)
      • You should come out with 21.1°C
    • Chart [Figure 1]
      • Start at your initial temperature on the Fahrenheit scale
      • Move across until you hit the reference line
      • Move down and read the temperature off of the bottom
      • In this example it comes out to be roughly 22°C
    • Table: [Figure 2]
      • Find the temperature you need and read across the appropriate column
      • Notice this table is more designed for Celsius to Fahrenheit but we still come out just over 21°C
Temperature Conversion Chart
Figure 1: Temperature Conversion Chart
Temperature Conversion Chart
Figure 2: Temperature Conversion Chart
Temperature Conversion Chart
Figure 2: Temperature Conversion Chart

Crosswind Component:


Short Field Takeoff Performance:

Crosswind Component Chart
Figure 4: Short Field Takeoff Performance

Load Factor:

Stall Speed Banked:

True Vs. Magnetic North Course Conversion

  • Used primarily for flight planning when converting a chart (always true north) to a course to fly in the aircraft (magnetic north)
    • Formula:
      • "East is least, west is best"
      • Magnetic Course (MC) = True Course (TC) - East Variation
      • Magnetic Course (MC) = True Course (TC) + West Variation
    • Example:
      • True course is 270°
      • Variation is 14° east
    • Calculate:
      • MC = 270° - 14°
      • MC = 256°

Mach Number

  • Most high-speed aircraft are limited to a maximum Mach number at which they can fly
  • This is shown on a Machmeter as a decimal fraction
    • Mach 1 vs. Altitude
      Figure 6: AerospaceWeb.org. Mach 1 vs. Altitude

    • Formula:
      • Mach Number = Aircraft Speed/Speed of Sound (dependent on altitude)
    • Example:
      • Aircraft is flying at 30,000'
      • Speed of sound at 30,000' = 589.4 knots
      • The airspeed is 489.3 knots
    • Calculate:
      • 489.3/589.5 = 0.83 Mach


Pressure Altitude

  • As altitude increases pressure will decrease in a standard atmosphere
    • Formula:
      • Pressure Altitude = [(29.92 - current baro) * 1000] + Current field elevation
    • Example:
      • Current baro: 29.82
      • Field elevation: 500'
      Density Altitude Conversion Chart
      Figure 7: Pressure/Density Altitude Conversion Chart
    • Calculate:
      • 29.92-29.82 = .10
      • 0.10 * 1000 = 100'
      • 100' + 500' = 600'
    • Chart: [Figure 7]
      • Using the chart on the right of the graph, look for the current altimeter setting
      • To the right of it there will be an altitude in feet, and that is your conversion


Density Altitude

  • Pressure altitude corrected for non-standard temperature
  • Used for performance calculations
    • Formula:
      • Pressure Altitude + (120 x [Outside Air Temperature (OAT) - 15°C (ISA Temp)])
    • Example:
      • Pressure Altitude = 600' (as calculated above)
      • OAT: 10°C
    • Calculate:
      • 600' + [120 * (10-14)]
      • 600' + (-480) = 120'
    • Chart: [Figure 7]
      • From the temperature on the bottom move up to your pressure altitude
      • Next move left and read your density altitude off the scale
  • Other tools are available to help you calculate density altitude such as NOAA's Density Altitude Calculator


Cloud Bases

  • Used for VFR planning or when icing is a concern
  • This is a very rough formula as cloud bases are not always flat and can change rapidly
    • Formula:
      • Temperature-Dew Point (°C) divided by 2 = Base of clouds
      • Temperature-Dew Point (°F) divided by 4 = Base of clouds
    • Example:
      • Temperature: 10°C / 50°F
      • Dew Point: 5 °C / 41°F
    • Calculate:
      • (10-5) ÷ 2 = 2,500' MSL

      • (50-41) ÷ 4 = 2,250' MSL


Climb Rate Required

  • Used to determine rate of climb for a given departure/climb out
    • Formula:
      • Ground Speed (GS) (knots) ÷ 60 * Climb Gradient (Feet Per Mile)
    • Example:
      • Ground Speed = 75 knots
      • Climb Gradient Required = 200 feet per mile
    • Calculate:
      • 75 ÷ 60 * 200 = 280 feet per minute climb rate required


Maneuvering Speed:

  • Also referred to Va
  • More weight = more stable
    • Formula:
    • Maneuvering Speed Formula
      Figure 8: Maneuvering Speed Formula





    • Example:
      • Follow instructions given on page 6 of the POH


True Airspeed:

  • The general rule of thumb is to increase TAS by 2% for every 1,000' increase in the altitude
    • Example:
      • Indicated airspeed = 100 knots
      • Altitude = 5,000'
    • Formula:
      • 5 * 0.02 = .1
      • .1 * 100 = 10 knots
      • 100 (IAS) + 10 = 110 knots TAS


Conclusion:


Pilot's Pocket Handbook: Flight Calculations, Weather Decoder, Aviation Acronyms, Charts and Checklists, Pilot Memory Aids
Pilot's rules of thumb: Rules of thumb, easy aviation math, handy formulas, quick tips
Pilot's Pocket Handbook: Flight Calculations, Weather Decoder, Aviation Acronyms, Charts and Checklists, Pilot Memory Aids
Pilot's rules of thumb: Rules of thumb, easy aviation math, handy formulas, quick tips


Maneuvering Speed Formula
Figure 9: Time, Fuel, and Distance to Climb

Top of Climb:

References: