Airspeed Calculator: IAS, TAS & CAS Made Easy

Understanding airspeed conversions is critical for aviation safety and precision. Accurate calculations involve IAS, TAS, and CAS metrics.

This article thoroughly explores formulas, tables, and practical scenarios for mastering Airspeed Calculator: IAS, TAS & CAS Made Easy.

Calculadora con inteligencia artificial (IA) para Airspeed Calculator: IAS, TAS & CAS Made Easy

• Calculate TAS from IAS=120 knots at 10,000 ft pressure altitude with 15°C temperature.
• Find CAS given an IAS of 150 knots at sea level under standard conditions.
• Determine IAS when TAS is 200 knots at 20,000 ft with an outside air temperature of -20°C.
• Compute TAS, CAS, and IAS for a flight at 5,000 ft with an indicated airspeed of 100 knots and temperature deviation of +5°C.

Comprehensive Airspeed Tables for IAS, TAS, and CAS

Key Formulas for Airspeed Calculation: IAS, TAS & CAS Explained

To convert and understand the different airspeeds, it is essential to apply the core aerodynamic and atmospheric principles using specific formulas. Below are the fundamental formulas used in airspeed calculations:

1. Calibrated Airspeed (CAS) from Indicated Airspeed (IAS)

CAS adjusts IAS by error factors primarily due to instrument and position errors.

These corrections are typically derived from aircraft-specific calibration charts and are minimal at low speeds and altitudes but can become significant at high speeds.

2. True Airspeed (TAS) from Calibrated Airspeed (CAS)

TAS accounts for changes due to air density variations at altitude and temperature. It is computed by correcting CAS for density altitude:

Where:

• ρ₀ = Standard sea level air density (~1.225 kg/m³)
• ρ = Air density at altitude and temperature

3. Air Density (ρ) Calculation

Density is derived from pressure and temperature via the ideal gas law:

Where:

• P = Static pressure at altitude (Pa)
• R = Specific gas constant for air (287.05 J/kg*K)
• T = Absolute temperature in Kelvin (K = °C + 273.15)

4. Pressure Altitude (H) to Static Pressure (P) Conversion

Using the barometric formula for the International Standard Atmosphere (ISA):

Where:

• P₀ = Sea level standard atmospheric pressure = 101325 Pa
• L = Temperature lapse rate = 0.0065 K/m
• H = Pressure altitude in meters (1 ft = 0.3048 m)
• T₀ = Standard temperature at sea level = 288.15 K
• g = Acceleration due to gravity = 9.80665 m/s²
• R = Specific gas constant for air = 287.05 J/kg·K

5. Computation of Temperature Corrected Pressure Altitude

Outside air temperature (OAT) variations impact density altitude, calculated as:

Where:

• OAT = Actual outside air temperature (in °C)
• ISA Temperature = Standard temperature at altitude (°C)

6. Simplified TAS from IAS

For practical quick calculation, pilots use the formula:

This works under assumption of standard temperature and pressure but must be modified with actual OAT.

Detailed Explanation of Variables

• IAS (Indicated Airspeed): The speed shown on the airspeed indicator directly affected by dynamic pressure.
• CAS (Calibrated Airspeed): IAS corrected for position and instrument errors.
• TAS (True Airspeed): Actual speed of the aircraft through the air mass, crucial for navigation.
• ρ (Air density): Mass per unit volume of air, decreasing with altitude and temperature rise.
• H (Pressure Altitude): Altitude corrected to standard atmospheric pressure (29.92 inHg or 1013.25 hPa).
• OAT (Outside Air Temperature): The ambient air temperature outside the aircraft.
• P (Static Pressure): Atmospheric pressure at a given altitude used in density calculations.

Real-Life Application Examples

Example 1: Calculating TAS from IAS at 10,000 ft with Corrected Temperature

An aircraft indicates an IAS of 120 knots flying at a pressure altitude of 10,000 ft. The OAT is recorded as -5°C.

Step 1: Determine standard temperature at 10,000 ft: 15°C – (6.5°C × 10) = -50°C (ISA lapse rate)

Step 2: Calculate temperature deviation: -5°C – (-50°C) = +45°C

Step 3: Calculate pressure altitude in meters: 10,000 ft × 0.3048 = 3,048 m

Step 4: Compute static pressure P (using barometric formula approximation):

P ≈ 101325 × (1 – (0.0065 × 3048)/288.15)^5.256

P ≈ 101325 × (1 – 0.0688)^5.256

P ≈ 101325 × (0.9312)^5.256 ≈ 101325 × 0.696 = 70501 Pa

Step 5: Calculate air density:

ρ = P / (R × T) where T = OAT + 273.15 = (-5 + 273.15) = 268.15 K

ρ = 70501 / (287.05 × 268.15) ≈ 70501 / 76979 ≈ 0.916 kg/m³

Step 6: Calculate TAS:

TAS = CAS × √(ρ₀ / ρ) = 118 × √(1.225 / 0.916) = 118 × √1.337 ≈ 118 × 1.156 = 136.4 knots

Final Result: The true airspeed is approximately 136 knots.

Example 2: Determining CAS and TAS from IAS on a Sea Level Standard Day

A pilot reads 150 knots IAS at sea level where both pressure and temperature are standard (15°C and 1013 hPa). What are the CAS and TAS?

Step 1: At sea level with standard conditions, IAS approximately equals CAS.

Step 2: Calculate TAS:

TAS = CAS × √(ρ₀ / ρ) = 150 × √(1.225 / 1.225) = 150 × 1 = 150 knots

Final Result: IAS = CAS = TAS = 150 knots under these standard conditions.

Additional Considerations and Best Practices

• Instrumentation Calibration: Accurate CAS requires periodic aircraft-specific calibration due to varying airframe impacts on air data measurements.
• Altitude Impact: TAS generally increases with altitude for a given IAS due to decreasing air density; pilots must compensate using calculative tools.
• Temperature Variability: Substantial deviations from ISA temperature impact density and thus TAS—monitor instrumentation for reliable temperature data.
• Use of Electronic Flight Instruments: Modern avionics simplify these calculations but understanding fundamentals is crucial for manual backup and validation.

Expand Your Technical Knowledge with Authoritative Sources

For further study and verification of airspeed calculation standards, consult the following authoritative references:

• FAA Airplane Flying Handbook (FAA-H-8083-3A)
• NASA Technical Memorandum – Airspeed Principles
• Skybrary: Airspeed Indicator and Calculations
• EASA Aircraft Performance Regulations