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
Temperature Conversion Chart
Temperature Conversion Table
TemperatureWorld.com,
Temperature Conversion Table

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
Temperature Conversion Chart
Temperature Conversion Table
TemperatureWorld.com,
Temperature Conversion Table

Crosswind Component:


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
      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
      Pressure/Density Altitude Conversion Chart
    • Calculate:

      • 29.92-29.82 = .10
      • 0.10 * 1000 = 100'
      • 100' + 500' = 600'
    • Chart:

      [Figure 4]
      • 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) - (ISA Temp)])
    • Example:

      • Pressure Altitude = 600' (as calculated above)
      • OAT: 10°C
    • Calculate:

      • ISA Temp (using standard Lapse rate of -2 degrees C per 1000 ft) is 14° C
      • 600' + [120 * (10-14)]
      • 600' + (-480) = 120'
    • Chart:

      [Figure 4]
      • 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 Pilot Friend'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

60 to 1 Rule:

  • One degree of course change will put you 1 NM off course after 60 NMs

Takeoff & Landing Performance:

  • Specific charts and their instructions are contained inside the pilot operating manual/pilot information manual for your aircraft
  • The numbers provided are under specific conditions which will almost never apply exactly to your conditions
    • Determine what your personal minimums are, and add a buffer to the performance calculated

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
      Maneuvering Speed Formula
    • Example:

      • Follow instructions given on section 6 of the POH

True Airspeed:


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Maneuvering Speed Formula
Time, Fuel, and Distance to Climb

Top of Climb:

Time to Travel Using a Whiz Wheel:

  • Point the black arrow to match the expected ground speed
  • Look for the distance to travel on the outer wheel
  • Read time immediately below (inner scale) the number representing distance

Ground Speed on Whiz Wheel:

  • Line up distance over time (outer wheel over inner)
  • Find the big black arrow, it is pointing to your ground speed
  • Note that you will travel 10% of your speed in 6 minutes (6 min * 10 = 60 minutes)

Fuel on Whiz Wheel:

  • Point the big black arrow to the pounds per hour (burn rate)
  • Read time off the inner wheel
  • Look above time to get pounds burned in that time

60 to 1 Rule:

  • The 60 to 1 rule is is a technique for establishing predictable pitch changes for climbs or descents and lead points for intercepting courses or arcs
    • It allows the pilot to compute the pitch changes necessary when establishing an attitude during the control and performance concept of attitude instrument flying
    • It reduces the pilot's workload and increases efficiency by requiring fewer changes and less guesswork
    • It is an alternative to the TLAR (That Looks About Right) method of flying
  • The 60-to-1 rule gives us a mathematical equation to help you figure out all these questions, but it is almost impossible to run these calculations and fly at the same time
    • You need to use the formulas before you fly
  • Find out what your turn radius is at cruise airspeed up high and at approach airspeed down lower; find out what a 1° pitch change will do to your VVI and remember those numbers
  • The 60-to-1 Rule:
    • 1° = 1 NM at 60 NM (60 NM from the station, there is 1 NM between each radial)
    • 1° = 100 FT at 1 NM (1° climb or descent gradient results in 100 FT/NM)
  • VSI Versus Pitch Change:
    • We now know how to calculate the altitude gained or lost for each degree of pitch change over a given distance
    • Throw in a time factor using True Airspeed (TAS) expressed in NM per MIN and we can relate this pitch change to a change in VSI
    • First, lets convert speed to NM/MIN, since the 60-to-1 rule is based on TAS expressed in NM/MIN
      • NM/MIN can be obtained easily from TAS as follows: NM/MIN = TAS/60
      • Examples:
        • 120 KTAS = 2 NM/MIN
        • 150 KTAS = 2.5 NM/MIN
      • If we don't have a TAS indicator, TAS can be computed from IAS
      • TAS increases over IAS at the rate of 2% per 1,000 feet altitude increase
      • So, the following equation could be used: TAS = IAS + (2% per 1,000 FT) X (IAS)
        • Example: 3,000 FT; 150 KIAS
          • TAS = 150 + (2% X 3) (150) = 150 + (.06)(150) = 159 KTAS
      • Another easy but less accurate rule of thumb (best used above 10,000 feet) to determine TAS is: TAS = IAS + Flight Level (FL)/2 or "Add 5 kts per 1,000' to IAS"
        • Example: FL 200; 175 KIAS
          • TAS = 175 + (200/2) = 275 KTAS
        • If one degree equals 100 ft/nm, then our VSI can be calculated numerous ways:
          • VSI for 1° pitch change = NM/MIN X 100 FT
          • VSI = (Pitch Angle) X (NM/MIN X 100)
          • VSI = (Gradient) X (NM/MIN) = (FT/NM) X (NM/MIN)

Conclusion:


References: