Mach Number Calculator Altitude

Mach Number Equation:

\[ M = \frac{v}{a} \] \[ a = \sqrt{\gamma R T_{alt}} \]

Velocity (v):

m/s

Temperature at Altitude (T_alt):

Ratio of Specific Heats (γ):

Gas Constant (R):

J/(kg·K)

Mach Number (M):

Speed of Sound (a):

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1. What is Mach Number?

The Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound. It's a critical parameter in aerodynamics and fluid dynamics, especially for high-speed flows.

2. How Does the Calculator Work?

The calculator uses the Mach number equation:

\[ M = \frac{v}{a} \] \[ a = \sqrt{\gamma R T_{alt}} \]

Where:

\( M \) — Mach number (dimensionless)
\( v \) — Velocity of the object (m/s)
\( a \) — Speed of sound in the medium (m/s)
\( \gamma \) — Ratio of specific heats (1.4 for air)
\( R \) — Specific gas constant (287.05 J/(kg·K) for air)
\( T_{alt} \) — Temperature at altitude (K)

Explanation: The Mach number compares an object's speed to the speed of sound in the surrounding medium, which depends on temperature and gas properties.

3. Importance of Mach Number

Details: Mach number is crucial in aerodynamics for classifying flow regimes (subsonic, transonic, supersonic, hypersonic) and predicting compressibility effects, shock waves, and aerodynamic heating.

4. Using the Calculator

Tips: Enter velocity in m/s, temperature at altitude in Kelvin. Default values for γ (1.4) and R (287.05) are provided for air but can be adjusted for other gases.

5. Frequently Asked Questions (FAQ)

Q1: What are the different Mach number regimes?
A: Subsonic (M < 0.8), Transonic (0.8 ≤ M ≤ 1.2), Supersonic (1.2 < M < 5), Hypersonic (M ≥ 5).

Q2: Why does temperature affect the speed of sound?
A: Speed of sound increases with temperature because molecules move faster and transmit sound waves more quickly in warmer conditions.

Q3: What's the speed of sound at sea level?
A: Approximately 343 m/s (1,235 km/h) in air at 20°C (293.15 K) with γ=1.4 and R=287.05.

Q4: How does Mach number affect aircraft performance?
A: Near Mach 1, compressibility effects cause drag divergence. Above Mach 1, shock waves form, requiring specialized aircraft design.

Q5: Can Mach number be greater than 1 in liquids?
A: Yes, though the speed of sound is much higher in liquids (about 1,480 m/s in water), making supersonic flow rare.