# 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

## 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

## Determining Rate-of-Climb Requirements:

• 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

• ### 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
• 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

## 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)