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]
- 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

Crosswind Component:

MOVED! See more about crosswinds on the crosswind landing page

Short Field Takeoff Performance:

MOVED! See more about short field takeoff performance on the Short Field Takeoff page

Load Factor:

MOVED! See more about crosswinds on the Accelerated Stalls page

Stall Speed Banked:

MOVED! See more about crosswinds on the Accelerated Stalls page

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) ÷ 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 V_a
More weight = more stable
- Formula:
- Example:
  - Follow instructions given on section 6 of the POH

True Airspeed:

MOVED! See more about crosswinds on the Airspeed Indicator page


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 — Time, Fuel, and Distance to Climb

Top of Climb:

MOVED! See more about crosswinds on the Flight Planning page

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)

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:

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
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Performance Calculations

Introduction:

Units of Measure:

Temperature Conversion:

Formula:

Example:

Calculate:

Chart

Table:

Crosswind Component:

Short Field Takeoff Performance:

Load Factor:

Stall Speed Banked:

True Vs. Magnetic North Course Conversion:

Formula:

Example:

Calculate:

Mach Number:

Formula:

Example:

Calculate:

Pressure Altitude:

Formula:

Example:

Calculate:

Chart:

Density Altitude:

Formula:

Example:

Calculate:

Chart:

Cloud Bases:

Formula:

Example:

Calculate:

60 to 1 Rule:

Takeoff & Landing Performance:

Climb Rate Required:

Formula:

Example:

Calculate:

Maneuvering Speed:

Formula:

Example:

True Airspeed:

Top of Climb:

Time to Travel Using a Whiz Wheel:

Ground Speed on Whiz Wheel:

Fuel on Whiz Wheel:

60 to 1 Rule:

Conclusion:

References: