Performance Calculations

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:

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

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

MOVED! See more about crosswinds on the crosswind landing page

MOVED! See more about short field takeoff performance on the Accelerated Stalls page

Crosswind Component Chart — Figure 4: Short Field Takeoff Performance

MOVED! See more about crosswinds on the Accelerated Stalls page

MOVED! See more about crosswinds on the Accelerated Stalls page

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°

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

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

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'

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

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

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

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

Also referred to V_a
More weight = more stable

Formula:

Example:

Follow instructions given on page 6 of the POH

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

Many calculations are rules of thumb that are constantly handy
Reference material such as the: Pilot's Pocket Handbook: Flight Calculations, Weather Decoder, Aviation Acronyms, Charts and Checklists, Pilot Memory Aids and Pilot's rules of thumb: Rules of thumb, easy aviation math, handy formulas, quick tips can come in handy


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

MOVED! See more about crosswinds on the Flight Planning page

Performance Calculations

Introduction:

Units of Measure:

Temperature Conversion:

Crosswind Component:

Short Field Takeoff Performance:

Load Factor:

Stall Speed Banked:

True Vs. Magnetic North Course Conversion

Mach Number

Pressure Altitude

Density Altitude

Cloud Bases

Climb Rate Required

Maneuvering Speed:

True Airspeed:

Conclusion:

Top of Climb:

References: