Mach Number Calculator with Altitude

Mach Number Equation:

\[ M = \frac{v}{\sqrt{\gamma R T}} \] \[ T = T_0 - L h \]

Mach Number (M):

Temperature at Altitude (T):

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1. What is Mach Number?

The Mach number (M) 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 following equations:

\[ M = \frac{v}{\sqrt{\gamma R T}} \] \[ T = T_0 - L h \]

Where:

\( M \) — Mach number (dimensionless)
\( v \) — Velocity (m/s)
\( \gamma \) — Specific heat ratio (1.4 for air)
\( R \) — Specific gas constant (287 J/kg·K for air)
\( T \) — Temperature at altitude (K)
\( T_0 \) — Sea level standard temperature (288 K)
\( L \) — Temperature lapse rate (0.0065 K/m)
\( h \) — Altitude (m)

Explanation: The calculator first determines the temperature at the given altitude using the standard atmosphere lapse rate, then calculates the Mach number based on the speed of sound at that temperature.

3. Importance of Mach Number

Details: Mach number is crucial in aerodynamics for determining compressibility effects. Different flow regimes (subsonic, transonic, supersonic, hypersonic) are defined by Mach number ranges.

4. Using the Calculator

Tips: Enter velocity in m/s, altitude in meters, and specific heat ratio (1.4 for air). All values must be valid (velocity > 0, altitude ≥ 0, γ between 1-2).

5. Frequently Asked Questions (FAQ)

Q1: What is the speed of sound at sea level?
A: Approximately 343 m/s (761 mph) at 20°C (293 K), but it varies with temperature.

Q2: What are typical Mach number ranges?
A: Subsonic (M < 0.8), Transonic (0.8 < M < 1.2), Supersonic (1.2 < M < 5), Hypersonic (M > 5).

Q3: Why does temperature decrease with altitude?
A: In the troposphere (up to ~11 km), temperature decreases with altitude due to decreasing pressure and adiabatic expansion.

Q4: What's the difference between true Mach and calibrated Mach?
A: True Mach uses actual speed of sound, while calibrated Mach corrects for instrument errors at high speeds.

Q5: How accurate is this calculator?
A: It uses standard atmospheric model which is accurate for general purposes but doesn't account for weather variations.