Mach Number

Team Physics -
Created by: Team Physics -, Last Updated: May 17, 2024

Mach Number

Mach Number is a dimensionless quantity in physics that describes the ratio of the speed of an object moving through a fluid to the speed of sound in that fluid. Named after the Austrian physicist Ernst Mach, the Mach number is crucial in the study of aerodynamics and fluid dynamics.

What is Mach Number?

Mach Number is a dimensionless quantity in physics that represents the ratio of an object’s speed to the speed of sound in the surrounding medium. Named after the physicist Ernst Mach, this number is crucial in the study of fluid dynamics and aerodynamics.

Mach Number Formula

The Mach Number (M) is given by:

M = v/c​


  • v is the velocity of the object relative to the medium.
  • c is the speed of sound in the medium.

Mach Number Classification

Speed below the speed of sound is termed as subsonic whereas speed above the speed of sound is termed as supersonic, although scientists practicing aerodynamics most of the time use these terms to describe a particular range of Mach values.

The various regimes of Mach values are:

Transonic0.8 – 1.30
Supersonic1.3 – 5.0
Hypersonic5.0 – 10.0
High-Hypersonic10.0 – 25.0
Re-entry speeds>25.0


Commercial aircraft with aerodynamic features such as a rounded nose and leading edges. The Mach is below 0.8.


Aircraft that are built with swept wings. The Mach value is between 0.8 and 1.3.


The aircraft designed to go supersonic have specific features such as canards, thin aerofoil sections, and sharp edges. The Mach levels are between 1.3 and 5.0.


These planes have several distinctive features, such as cooled nickel-titanium skin and small wings. The Mach values are between 5.0 and 10.0. The U.S. plane X-15 created the world record of flying at Mach 6.72.


The Mach levels are between 10.0 and 25.0. At such high speeds, thermal controls become a critical part of the design. The surface’s hotness must be considered beforehand.

Re-entry speeds

The Mach speed is above 25.0. This does not require wings and has a blunt design.

Classification of Mach Regimes

Regime(Mach)Speed (knots)Speed (mph)Speed (km/h)Speed (m/s)
Re-entry speeds>25.0>16,537>19,031>30,626>8,508

Significance of Mach number

The Mach Number plays a critical role in various fields of physics and engineering, particularly in fluid dynamics, aerodynamics, and aerospace engineering. Here’s why the Mach Number is significant:

1. Characterizing Flow Regimes

Subsonic Flow (M < 1): In subsonic regimes, air flows smoothly around objects with relatively predictable pressure and velocity distributions.

Transonic Flow (0.8 < M < 1.3): This regime is critical as it involves both subsonic and supersonic flow characteristics. It can lead to complex phenomena like shock waves and requires careful aerodynamic design.

Supersonic Flow (M > 1.3): At supersonic speeds, shock waves form, leading to significant changes in pressure, temperature, and density across the shock. This affects the design of aircraft and missiles.

Hypersonic Flow (M > 5): Hypersonic speeds introduce severe thermal and aerodynamic challenges. The heat generated due to air friction necessitates special materials and cooling techniques.

2. Aerospace Engineering

Aircraft Design: Engineers use the Mach Number to design aircraft shapes that minimize drag and withstand the stresses at high speeds.

Spacecraft Re-entry: During re-entry, spacecraft experience extremely high Mach Numbers, requiring heat shields to protect against intense aerodynamic heating.

3. Sound Propagation

Acoustics: The Mach Number helps in understanding how sound waves travel in different media, influencing the design of a equipment and structures.

Sonic Booms: When objects exceed the speed of sound, they produce sonic booms. Knowing the Mach Number helps predict and mitigate the impact of these shock waves.

4. Fluid Dynamics

Compressibility Effects: At high Mach Numbers, gases become compressible, significantly affecting their flow properties. This is crucial in designing efficient nozzles, diffusers, and turbines.

Flow Separation: The Mach Number helps predict flow separation points on surfaces, which is vital for ensuring stable and efficient aerodynamic performance.

5. Performance Analysis

Engine Efficiency: For jet engines and rockets, the Mach Number is essential in determining optimal operating conditions to maximize thrust and fuel efficiency.

Stability and Control: High-speed flight dynamics depend heavily on the Mach Number, influencing the stability and control systems of high-speed aircraft.

Uses of Mach Number

Uses of Mach Number
  • Aerospace Engineering: Mach Number is critical in aerospace engineering for designing aircraft and spacecraft. It helps engineers understand the behavior of air around the vehicle at various speeds, which is essential for optimizing aerodynamic performance and ensuring structural integrity.
  • Supersonic and Hypersonic Flight: Mach Number determines flight regimes such as subsonic, transonic, supersonic, and hypersonic. These regimes influence aircraft design, particularly the shape of the wings, fuselage, and control surfaces to minimize drag and manage shock waves effectively.
  • Jet Engine Performance: Engineers use Mach Number to optimize jet engine performance. It helps in designing engines that can operate efficiently at high speeds by managing airflow and pressure changes within the engine.
  • Wind Tunnel Testing: In wind tunnel testing, Mach Number is used to simulate the conditions an aircraft or vehicle will experience in flight. This allows for precise measurements and adjustments to improve performance and safety.
  • Meteorology: Mach Number helps meteorologists understand and predict the behavior of atmospheric phenomena, such as jet streams and shock waves created by thunderstorms. It also aids in modeling weather patterns and wind speeds at different altitudes.
  • Space Exploration: Mach Number is important for space exploration, particularly during re-entry. Spacecraft re-entering the Earth’s atmosphere experience hypersonic speeds, and understanding Mach Number helps in designing heat shields and managing thermal loads to protect the vehicle and crew.

Examples for Mach Number

  1. Aerospace Engineering: In designing aircraft, engineers use the Mach Number to determine the aerodynamic properties at different speeds. For instance, commercial jets typically cruise at Mach 0.85, just below the speed of sound, optimizing fuel efficiency and passenger comfort.
  2. Supersonic Flight: Fighter jets and supersonic aircraft, such as the Concorde, operate at speeds greater than Mach 1. The design of these aircraft, including their streamlined shapes and materials, accounts for the shock waves and increased aerodynamic heating experienced at supersonic speeds.
  3. Hypersonic Flight: Hypersonic vehicles, like certain military missiles and experimental spacecraft, travel at speeds greater than Mach 5. Understanding the Mach Number is critical for managing extreme thermal loads and ensuring structural integrity at these high velocities.
  4. Spacecraft Re-entry: During re-entry into the Earth’s atmosphere, spacecraft reach hypersonic speeds. The Mach Number helps engineers design heat shields and other thermal protection systems to withstand the intense heat generated by atmospheric friction.
  5. Wind Tunnel Testing: Engineers use wind tunnels to simulate flight conditions at various Mach Numbers. This allows them to study the aerodynamic behavior of models and prototypes, optimizing designs before actual flight testing.
  6. Meteorology: Meteorologists use the Mach Number to understand and predict the behavior of jet streams and other atmospheric phenomena. For example, supersonic jets can generate shock waves that influence weather patterns.
  7. Automotive Design: In high-speed automotive design, such as for race cars, the Mach Number helps study airflow and aerodynamic forces. This aids in optimizing the shape and performance of the car to reduce drag and increase stability.
  8. Maritime Applications: For high-speed boats and submarines, understanding the Mach Number in water, though much lower than in air, is important for reducing drag and improving efficiency.


Who introduced the concept of Mach Number?

The Austrian physicist Ernst Mach introduced the concept of Mach Number.

Why is Mach Number important?

Mach Number helps determine the behavior of objects moving through a fluid, especially in aerodynamics and fluid dynamics.

How do you calculate Mach Number?

Calculate Mach Number by dividing the object’s speed by the speed of sound in the medium.

What is the speed of sound?

The speed of sound is the speed at which sound waves travel through a medium, approximately 343 meters per second in air at room temperature.

What is a subsonic speed?

Subsonic speed is when an object’s Mach Number is less than 1, meaning it is moving slower than the speed of sound.

What is a supersonic speed?

Supersonic speed is when an object’s Mach Number is greater than 1, meaning it is moving faster than the speed of sound.

What is a hypersonic speed?

Hypersonic speed is typically defined as a Mach Number greater than 5.

How does Mach Number affect aircraft design?

Mach Number influences the aerodynamic design of aircraft, affecting wing shape, materials, and structural integrity.

How is Mach Number used in wind tunnel testing?

In wind tunnels, Mach Number helps simulate different flight conditions to study aerodynamic properties of models.

What is the Mach cone?

The Mach cone is the conical shock wave produced by an object moving at supersonic speeds.

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