Miles/Hour to Mach Number Calculator

Mach Number Formula:

\[ M = \frac{mph \times 0.44704}{\sqrt{\gamma R T}} \]

Speed:

miles/hour

Temperature:

Kelvin (K)

Ratio of Specific Heats (γ):

Gas Constant (R):

J/(kg·K)

Mach Number (M):

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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 commonly used in aerodynamics to characterize high-speed flight.

2. How Does the Calculator Work?

The calculator uses the Mach number formula:

\[ M = \frac{mph \times 0.44704}{\sqrt{\gamma R T}} \]

Where:

\( M \) — Mach number (dimensionless)
\( mph \) — Speed in miles per hour
\( \gamma \) — Ratio of specific heats (1.4 for air at standard conditions)
\( R \) — Specific gas constant (287.05 J/(kg·K) for air)
\( T \) — Temperature in Kelvin

Explanation: The formula converts mph to m/s, then divides by the speed of sound (which depends on temperature and gas properties).

3. Importance of Mach Number

Details: Mach number is crucial in aerodynamics. Flows are classified as subsonic (M < 0.8), transonic (0.8 < M < 1.2), supersonic (1.2 < M < 5), and hypersonic (M > 5). Different physical phenomena occur in each regime.

4. Using the Calculator

Tips: Enter speed in mph, temperature in Kelvin, and appropriate values for γ and R. For standard air conditions, use γ=1.4 and R=287.05 J/(kg·K).

5. Frequently Asked Questions (FAQ)

Q1: What is the speed of sound at sea level?
A: Approximately 761 mph (1225 km/h) at 15°C (288.15K) with γ=1.4 and R=287.05 J/(kg·K).

Q2: Why does temperature affect Mach number?
A: The speed of sound increases with temperature (√T relationship), so the same true airspeed corresponds to a lower Mach number at higher temperatures.

Q3: What are typical Mach numbers for aircraft?
A: Commercial jets cruise at M≈0.78-0.85, fighter jets at M≈1.5-2.5, and the Concorde flew at M≈2.0.

Q4: How does altitude affect Mach number?
A: At constant true airspeed, Mach number increases with altitude because temperature (and thus speed of sound) decreases.

Q5: What's the difference between indicated and true Mach number?
A: Indicated Mach number comes from aircraft instruments, while true Mach number uses actual atmospheric conditions. They differ due to instrument errors and non-standard conditions.