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True Airspeed and Ground Speed Calculator

True Airspeed Formula

degrees

1. What is the True Airspeed and Ground Speed Calculator?

Definition: This calculator computes the True Airspeed (TAS) of an aircraft using a rule-of-thumb formula based on Indicated Airspeed (IAS), Outside Air Temperature (OAT) correction, and altitude. It then calculates the Ground Speed (GS) by adjusting the TAS for wind speed and direction.

Purpose: It is used in aviation to determine the actual speed of an aircraft through the air (TAS) and over the ground (GS), which are critical for navigation, flight planning, and fuel efficiency calculations.

2. How Does the Calculator Work?

The calculator uses the following formulas:

Formulas: \[ \text{TAS} = \left( \text{IAS} \times \text{OAT} \times \frac{\text{A}}{1000} \right) + \text{IAS} \] \[ \text{GS} = \text{TAS} + \text{W} \times \cos \theta \] where:

  • \( \text{TAS} \): True Airspeed (knots, km/h, mph)
  • \( \text{IAS} \): Indicated Airspeed (knots, km/h, mph)
  • \( \text{OAT} \): Outside Air Temperature correction term (% per °C or °F)
  • \( \text{A} \): Altitude of the airplane (in thousands of feet, yards, m, km, miles)
  • \( \text{GS} \): Ground Speed (knots, km/h, mph)
  • \( \text{W} \): Wind speed (knots, km/h, mph)
  • \( \theta \): Angle between the wind direction and the aircraft's motion (degrees)

Unit Conversions:

  • Speed (IAS, Wind Speed, TAS, GS):
    • 1 knot = 1 knot
    • 1 km/h = 0.539957 knots
    • 1 mph = 0.868976 knots
    • For output: 1 knot = 1.852 km/h, 1 knot = 1.15078 mph
  • Altitude (A):
    • 1 ft = 1 ft
    • 1 yard = 3 ft
    • 1 m = 3.28084 ft
    • 1 km = 3280.84 ft
    • 1 mile = 5280 ft
  • OAT Correction:
    • 1 % per °F = (5/9) % per °C

Steps:

  • Enter the Indicated Airspeed (IAS) in knots, km/h, or mph (default is 200 knots, step size 0.00001).
  • Enter the Outside Air Temperature correction term (OAT) in % per °C or °F (default is 0.02, i.e., 2% per 10°C, step size 0.00001).
  • Enter the altitude in ft, yards, m, km, or miles (default is 10,000 ft, step size 0.00001).
  • Enter the wind speed in knots, km/h, or mph (default is 20 knots, step size 0.00001).
  • Enter the wind angle in degrees (default is 0 degrees, step size 0.00001).
  • Convert IAS and wind speed to knots, altitude to thousands of feet, and OAT correction to % per °C.
  • Calculate the TAS using the rule-of-thumb formula.
  • Calculate the GS by adjusting the TAS for wind speed and direction.
  • Convert the TAS and GS to the selected speed unit and display the results, using scientific notation if the absolute value is less than 0.001, otherwise rounded to 4 decimal places.

3. Importance of TAS and GS Calculation

Calculating TAS and GS is crucial for:

  • Navigation: Pilots need TAS to calculate the actual speed through the air and GS to determine the speed over the ground, which affects flight time and fuel planning.
  • Safety: Accurate GS helps in maintaining safe separation from other aircraft and ensuring timely arrivals or departures.
  • Efficiency: Knowing TAS and GS allows pilots to optimize flight paths, taking advantage of tailwinds or minimizing the impact of headwinds.

4. Using the Calculator

Examples:

  • Example 1: Calculate the TAS and GS with an IAS of 200 knots, OAT correction of 0.02 % per °C, altitude of 10,000 ft, wind speed of 20 knots, and wind angle of 0 degrees, in knots:
    • Enter IAS = 200 knots.
    • Enter OAT = 0.02 % per °C.
    • Enter Altitude = 10,000 ft, convert to thousands of ft: \( 10,000 / 1000 = 10 \).
    • Enter Wind Speed = 20 knots.
    • Enter Wind Angle = 0 degrees.
    • TAS: \( (200 \times 0.02 \times 10) + 200 = (200 \times 0.2) + 200 = 40 + 200 = 240 \, \text{knots} \).
    • GS: \( 240 + 20 \times \cos(0) = 240 + 20 \times 1 = 260 \, \text{knots} \).
    • Result: \( \text{TAS} = 240.0000 \, \text{knots}, \text{GS} = 260.0000 \, \text{knots} \).
  • Example 2: Calculate the TAS and GS with an IAS of 300 km/h, OAT correction of 0.01 % per °F, altitude of 5 km, wind speed of 30 mph, and wind angle of 90 degrees, in mph:
    • Enter IAS = 300 km/h, convert to knots: \( 300 \times 0.539957 = 161.9871 \, \text{knots} \).
    • Enter OAT = 0.01 % per °F, convert to % per °C: \( 0.01 \times (5/9) = 0.0055556 \).
    • Enter Altitude = 5 km, convert to ft: \( 5 \times 3280.84 = 16404.2 \, \text{ft} \), then to thousands of ft: \( 16404.2 / 1000 = 16.4042 \).
    • Enter Wind Speed = 30 mph, convert to knots: \( 30 \times 0.868976 = 26.0693 \, \text{knots} \).
    • Enter Wind Angle = 90 degrees.
    • TAS: \( (161.9871 \times 0.0055556 \times 16.4042) + 161.9871 = 14.7635 + 161.9871 = 176.7506 \, \text{knots} \).
    • GS: \( 176.7506 + 26.0693 \times \cos(90) = 176.7506 + 26.0693 \times 0 = 176.7506 \, \text{knots} \).
    • Convert to mph: TAS = \( 176.7506 \times 1.15078 = 203.4357 \), GS = \( 176.7506 \times 1.15078 = 203.4357 \).
    • Result: \( \text{TAS} = 203.4357 \, \text{mph}, \text{GS} = 203.4357 \, \text{mph} \).

5. Frequently Asked Questions (FAQ)

Q: What is the difference between TAS and GS?
A: True Airspeed (TAS) is the speed of the aircraft relative to the air mass it is flying through, accounting for temperature and altitude effects. Ground Speed (GS) is the speed of the aircraft relative to the ground, adjusted for wind speed and direction.

Q: Why is the OAT correction term needed?
A: The OAT correction term accounts for temperature variations that affect air density, which in turn impacts the aircraft's true airspeed. The rule-of-thumb formula uses this term to approximate the density altitude effect on airspeed.

Q: How does wind angle affect ground speed?
A: The wind angle determines the component of the wind speed that affects the aircraft's motion. A wind angle of 0° (tailwind) increases GS, while 180° (headwind) decreases it. A 90° or 270° angle (crosswind) has no effect on GS, as \( \cos(90°) = 0 \).

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