Mach Number Calculator

Aircraft Speed (

v

Temperature (

T

) at Altitude:

1. What is Mach Number Calculator?

Definition: This calculator computes the Mach number ( $M$ ), a dimensionless quantity that represents the ratio of an aircraft's speed to the speed of sound in the surrounding medium.

Purpose: It is used in aerodynamics to determine the flight regime of an aircraft (subsonic, transonic, supersonic, or hypersonic), aiding in aircraft design, performance analysis, and safety assessments.

2. How Does the Calculator Work?

The calculator uses the following formulas:

Formulas: $M = \frac{v}{c}$ $c = 331.3 \sqrt{1 + \frac{T}{273.15}}$ Where:

$M$ : Mach number (dimensionless)
$v$ : Aircraft speed (m/s, km/h, mph, ft/s, km/min, ft/min, mile/min)
$c$ : Speed of sound (m/s)
$T$ : Temperature at altitude (°C, °F, K)

Unit Conversions:

Aircraft Speed ( $v$ ):
- 1 m/s = 1 m/s
- 1 km/h = 0.277778 m/s
- 1 mph = 0.44704 m/s
- 1 ft/s = 0.3048 m/s
- 1 km/min = 16.6667 m/s
- 1 ft/min = 0.00508 m/s
- 1 mile/min = 26.8223 m/s
Temperature ( $T$ ):
- 1 °C = 1 °C
- 1 °F = (°F - 32) × 5/9 °C
- 1 K = K - 273.15 °C

Steps:

Enter the aircraft speed ( $v$ ) with its respective unit (m/s, km/h, mph, ft/s, km/min, ft/min, mile/min).
Enter the temperature ( $T$ ) at the given altitude with its respective unit (°C, °F, K). Default is -46.42°C (typical at 31,000 ft).
Convert the aircraft speed to m/s.
Convert the temperature to Celsius.
Calculate the speed of sound using $c = 331.3 \sqrt{1 + \frac{T}{273.15}}$ .
Calculate the Mach number using $M = \frac{v}{c}$ .
Display the result, using scientific notation for values less than 0.001, otherwise with 4 decimal places.

3. Importance of Mach Number Calculation

Calculating the Mach number is crucial for:

Flight Regime Classification: Determining whether an aircraft is flying at subsonic ( $M < 1$ ), transonic ( $M \approx 1$ ), supersonic ( $M > 1$ ), or hypersonic ( $M > 5$ ) speeds.
Aircraft Design: Ensuring aircraft are designed to handle aerodynamic effects like shock waves at high speeds.
Safety and Performance: Assessing compressibility effects that impact lift, drag, and stability during flight.

4. Mach Number Ranges and Flow Types

The Mach number determines the type of flow and the typical objects operating within that range:

Mach Number Ranges:

$M < 0.8$ - Subsonic Flow
- Type of Objects: Passenger aircraft and helicopters
- Common Examples: Dornier 228, Boeing 747-400, Airbus A330-300
$0.8 \leq M \leq 1.2$ - Transonic Flow
- Type of Objects: Military trainers
- Common Examples: M346 Master, T45 Goshawk, B-1B Lancer
$1.2 < M \leq 5.0$ - Supersonic Flow
- Type of Objects: Military aircraft
- Common Examples: MiG 21 Fishbed, F 16 Fighting Falcon, Mirage 2000H
$5.0 < M \leq 10.0$ - Hypersonic Flow
- Type of Objects: Ballistic missiles, experimental vehicles
- Common Examples: Bramhos-II, NASA X15

5. Using the Calculator

Examples:

Example 1: Calculate the Mach number for a commercial aircraft (Boeing 787) flying at 490 knots (252.1 m/s) at 31,000 ft, where the temperature is -46.42°C:
- Enter $v = 490$ knots (convert to km/h: $490 \times 1.852 = 907.48 km/h$ ).
- Convert to m/s: $v = 907.48 \times 0.277778 = 252.1 m/s$
- Enter $T = - 46.42$ °C.
- Calculate speed of sound: $c = 331.3 \sqrt{1 + \frac{- 46.42}{273.15}} = 331.3 \sqrt{0.8301} = 301.84 m/s$
- $M = \frac{252.1}{301.84} = 0.8352$
- Result: $M = 0.8352$
Example 2: Calculate the Mach number for an aircraft flying at 15000 ft/min at an altitude where the temperature is -50°F:
- Enter $v = 15000$ ft/min.
- Convert to m/s: $v = 15000 \times (0.3048 / 60) = 15000 \times 0.00508 = 76.2 m/s$
- Enter $T = - 50$ °F.
- Convert to °C: $T = (- 50 - 32) \times 5 / 9 = - 45.56 °C$
- Calculate speed of sound: $c = 331.3 \sqrt{1 + \frac{- 45.56}{273.15}} = 331.3 \sqrt{0.8332} = 302.37 m/s$
- $M = \frac{76.2}{302.37} = 0.2520$
- Result: $M = 0.2520$

6. Frequently Asked Questions (FAQ)

Q: Why does the speed of sound depend on temperature?
A: The speed of sound in air depends on the temperature because it affects the average speed of air molecules. Higher temperatures increase the speed of sound, as described by the formula $c = 331.3 \sqrt{1 + \frac{T}{273.15}}$ .

Q: What does a Mach number less than 1 indicate?
A: A Mach number less than 1 indicates subsonic flight, meaning the aircraft is traveling slower than the speed of sound.

Q: Can this calculator be used for objects other than aircraft?
A: Yes, the Mach number can be calculated for any object moving through a fluid (e.g., a car, a projectile, or a spacecraft), as long as the speed and temperature of the medium are known.