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Performance Calculations

Introduction:

• Math is always going to be more accurate than charts
• Charts provide a quick reference, that is based off of math, but subject to inaccuracies, due to its simplicity and human error
• When calculating performance referencing a pilot information manual and ALWAYS read the notes associated with the chart
• Calculation Examples:

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:

• 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]

• 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

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
• 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'
• 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) &divide; 2 = 2,500' MSL

• (50-41) &divide; 4 = 2,250' MSL

60 to 1 Rule:

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

Climb Rate Required:

• Used to determine rate of climb for a given departure/climb out
• Formula:

• Ground Speed (GS) (knots) &divide; 60 * Climb Gradient (Feet Per Mile)
• Example:

• Ground Speed = 75 knots
• Climb Gradient Required = 200 feet per mile
• Calculate:

• 75 &divide; 60 * 200 = 280 feet per minute climb rate required

Maneuvering Speed:

• Also referred to Va
• More weight = more stable

• Example:

• Follow instructions given on section 6 of the POH

True Airspeed:    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

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