Performance Calculations
Performance numbers can be derived from charts, tables, or manually crunching the numbers yourself to predict aircraft performance.
Introduction
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:
- 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
- Determining Rate-of-Climb Requirements
- Maneuvering Speed
- True Airspeed
- Time to Travel using a Whiz Wheel
- Ground Speed on Whiz Wheel
- Fuel on Whiz Wheel
Units of Measure
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
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
Crosswind Component
- MOVED! See more about crosswinds on the crosswind landing page
Short Field Takeoff and Climb Performance
Short Field Takeoff and Climb Performance
- MOVED! See more about short field takeoff performance on the Short Field Takeoff page
Load Factor
Load Factor
- MOVED! See more about crosswinds on the Accelerated Stalls page
Stall Speed Banked
Stall Speed Banked
- MOVED! See more about crosswinds on the Accelerated Stalls page
True Versus Magnetic North Course Conversion
True Versus 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
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
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
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
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
60 to 1 Rule
- One degree of course change will put you 1 NM off course after 60 NMs
- 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
- Example: 3,000 FT; 150 KIAS
- 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)
- Example: FL 200; 175 KIAS
Takeoff and Landing Performance
Takeoff and 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
Maneuvering Speed
Maneuvering Speed
- Also referred to Va
- More weight = more stable
Formula:
Example:
- Follow instructions given on section 6 of the POH
True Airspeed
True Airspeed
- MOVED! See more about crosswinds on the Airspeed Indicator page
Time to Travel Using a Whiz Wheel
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
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
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
Conclusion
Conclusion
- Many calculations are rules of thumb that are constantly handy
- Note that while extrapolation or interpolation are skills pilots need to read charts, when you're parameters are off the chart, you're a test pilot, and performance in these regions should be treated as prohibited
- 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
- Still looking for something? Continue searching:
References
References