The Mach concept is fundamental to aeronautics, and plays an essential role in measuring aircraft speed. It quantifies the relative speed of an aircraft in relation to the speed of sound in the medium through which it travels. Knowledge of Mach speed is crucial to aircraft design, performance and safety.

Aircraft speed measurement dates back to the earliest days of aviation, but the use of the Mach concept has developed over time thanks to technological advances. Early attempts to measure speed were based on instruments such as the Pitot tube, which was later improved to take account of the effects of air compressibility at high speeds.

What is the Mach concept?

A. Definition of Mach speed and its origin

Mach speed is a relative measure of the speed of an object, usually an aircraft, compared with the speed of sound in the medium through which it is passing. It is expressed as a multiple of the speed of sound, which is approximately 343 meters per second (or 1,235 kilometers per hour) under standard atmospheric conditions at a temperature of 20 degrees Celsius. For example, if an airplane flies at Mach 2, this means it is moving at twice the speed of sound in the surrounding air.

The Mach concept was named after Austrian physicist Ernst Mach, who carried out fundamental research into wave propagation and sound speed phenomena in the 19th century. Mach studied shock waves and pressure differences associated with the speed of sound, laying the foundations for scientific understanding of fluid dynamics at high speeds.

Ernst Mach also formulated the notion of the Mach number, which is the speed of an object divided by the speed of sound. He developed experiments to study shock waves and the properties of air at supersonic speeds. His work has led to a better understanding of the effects of air compressibility and the aerodynamic phenomena that occur at high speeds, notably the formation of shock waves and the sonic boom.

Today, Mach speed measurement is essential in aeronautics to assess aircraft performance, understand flight characteristics at different speeds and guarantee flight safety. Aeronautical engineers use the Mach concept to design aircraft capable of flying efficiently in different speed ranges, taking into account the aerodynamic effects associated with each Mach regime.

B. Explaining the relationship between Mach speed and the speed of sound

The relationship between an aircraft’s Mach speed and the speed of sound is crucial to understanding the aerodynamic phenomena that occur when an aircraft reaches or exceeds the speed of sound.

When an aircraft flies at a speed below the speed of sound, it is referred to as subsonic. In this speed range, the sound waves emitted by the aircraft propagate ahead of it, without forming shock waves. Air compressibility effects are negligible, and flight characteristics are mainly influenced by air resistance and drag.

When the aircraft reaches the speed of sound, Mach 1, it enters the transonic regime. At this speed, the sound waves emitted by the aircraft begin to accumulate in front of it, forming a shock wave. A shockwave is an area of high air pressure and density variation, created by the compression of the air as the aircraft travels at speeds close to the speed of sound. The phenomena of shockwave formation and compressible flow become more important, which can lead to complex aerodynamic effects and disturbances in the airflow around the aircraft.

When the aircraft exceeds the speed of sound, it becomes supersonic. In this speed range, shockwaves form continuously around the aircraft and propagate behind it. The main shock wave, known as the Mach cone, is generated at the front of the aircraft and propagates perpendicular to the trajectory. At supersonic speeds, air compressibility effects become predominant and can have a significant impact on aircraft aerodynamics, aerodynamic drag and flight stability.

Beyond the supersonic regime lies the hypersonic regime, where the aircraft flies at speeds well in excess of Mach 5. In this regime, aerodynamic effects become even more complex, and flight characteristics are influenced by phenomena such as kinetic heating, chemical reactions in the airflow and non-linear aerodynamic forces.

C. Importance of the Mach concept for aerodynamics and flight safety

The Mach concept is essential to aircraft aerodynamics, as it influences shock wave formation, drag and aircraft stability. Knowledge of Mach speed is also crucial to flight safety, as exceeding certain Mach speed limits can lead to undesirable phenomena such as sonic boom and aerodynamic instabilities.

Knowledge of these phenomena is crucial to the design of aircraft capable of flying efficiently in these conditions, minimizing drag and maximizing aerodynamic performance.

Mach speed is also closely linked to flight safety. When an aircraft reaches or exceeds the speed of sound, it generates a sonic boom, also known as a supersonic boom. The sonic boom is a shock wave produced by the aircraft as it breaks the sound barrier. Sonic boom is generally perceived as a powerful noise, similar to an explosion, and can cause significant noise pollution on the ground.

In addition to sonic boom, high Mach speeds can also lead to aerodynamic instabilities and undesirable phenomena such as aerodynamic stall. When an aircraft flies at speeds close to the speed of sound, the airflow characteristics change considerably, which can lead to disturbances in the airflow around the aircraft and affect its stability. Understanding aerodynamic limits and behavior at high Mach speeds is essential to avoid these dangerous situations and ensure flight safety.

The different Mach values

A. Explanation of the different Mach categories (subsonic, transonic, supersonic and hypersonic)

The Mach concept covers several speed categories. The subsonic regime corresponds to speeds below the speed of sound, the transsonic regime is characterized by speeds close to the speed of sound, the supersonic regime corresponds to speeds above the speed of sound, and the hypersonic regime concerns very high speeds, several times greater than the speed of sound.

The Mach concept is used to divide aeronautical speeds into different categories, according to their relationship with the speed of sound. Each Mach category has its own characteristics and specific aerodynamic phenomena.

Subsonic regime: The subsonic regime covers speeds below the speed of sound, i.e. Mach 1. In this category, aircraft operate at speeds not exceeding the speed of sound. Typical aerodynamic phenomena in the subsonic regime include lift, drag and air resistance. Subsonic aircraft are designed to optimize fuel efficiency and flight stability, and are suited to low-altitude flight at relatively low speeds.

Transonic regime: The transonic regime corresponds to speeds close to the speed of sound, generally between Mach 0.8 and Mach 1.2. In this speed range, aircraft can experience complex aerodynamic effects associated with the transition from the subsonic to the supersonic regime. Shock waves begin to form, and air resistance increases significantly. Engineers need to take these phenomena into account to design stable, high-performance transonic aircraft.

Supersonic regime: The supersonic regime concerns speeds above the speed of sound, i.e. Mach 1. In this category, aircraft fly faster than the speed of sound, resulting in the continuous formation of shockwaves around the aircraft. Supersonic aerodynamic phenomena, such as wave drag and compressible flow, become predominant. Supersonic aircraft, such as Concorde, are designed to fly efficiently at supersonic speeds while minimizing the adverse effects of these phenomena.

Hypersonic regime: The hypersonic regime encompasses very high speeds, several times greater than the speed of sound. Hypersonic aircraft fly at Mach 5 or higher. At such speeds, aerodynamic phenomena become extremely complex, with effects such as kinetic heating, non-linear aerodynamic forces and chemical reactions in the airflow. Designing and flying hypersonic aircraft presents significant technological challenges, but it also offers potential advantages in terms of travel speed and access to space.

B. Characteristics and features of each Mach class

Each Mach category has its own distinctive features. Subsonic aircraft are suited to low-altitude flights at speeds below the speed of sound. Supersonic aircraft, such as Concorde, can fly at speeds in excess of Mach 1, while hypersonic aircraft, still under development, aim to reach speeds well in excess of Mach 5.

Subsonic :

• Subsonic aircraft are designed to fly at speeds below the speed of sound (Mach 1).
• They are suited to flying at low altitudes and relatively low speeds.
• Important aerodynamic characteristics in this regime include lift, drag and flight stability.
• Subsonic aircraft are commonly used for civil transport, low-level flight and short-haul operations.

Transonic regime :

• The transonic regime lies around the speed of sound (Mach 1).
• Aircraft operating in this regime encounter complex aerodynamic effects linked to the transition between the subsonic and supersonic regimes.
• Air resistance increases considerably in this speed range.
• The design of transonic aircraft requires particular attention to minimize adverse effects such as shock drag.

Supersonic :

• Supersonic aircraft fly at speeds above the speed of sound (Mach 1).
• The formation of continuous shock waves around the aircraft is a major characteristic of this regime.
• Supersonic aircraft are designed to minimize air resistance due to shock drag, which requires specific aerodynamic shapes and advanced design techniques.
• The Concorde, an emblematic supersonic aircraft, is an example of an achievement in this regime.

Hypersonic regime :

• The hypersonic regime concerns speeds well in excess of Mach 5.
• Hypersonic aircraft are designed to reach extremely high speeds, several times faster than the speed of sound.
• Aerodynamic characteristics in this regime include phenomena such as kinetic heating, non-linear aerodynamic forces and chemical reactions in the airflow.
• Hypersonic aircraft are still under development and represent an advanced field of research and innovation.

Each Mach category presents specific challenges and considerations in terms of design, performance and aerodynamic technologies. Understanding the characteristics of each Mach regime is essential to designing aircraft suited to these specific flying environments, and to effectively exploiting the advantages offered by each speed regime.

C. Examples of iconic aircraft in each Mach category

Examples of iconic aircraft in each Mach category include the Boeing 747 for subsonic, Concorde for supersonic and the X-15 for hypersonic. These aircraft illustrate the challenges and characteristics specific to each Mach speed category.

Subsonic :

• The emblematic example of a subsonic aircraft is the Boeing 747, also known as the Jumbo Jet. This jetliner, widely used in commercial transport, is designed for speeds below the speed of sound.
• The Boeing 747 is characterized by its imposing size, high passenger capacity and ability to fly long distances economically. It embodies the characteristics and performance typical of subsonic aircraft.

Supersonic :

• The most famous example of a supersonic aircraft is the Concorde, a supersonic transport plane developed jointly by France and the UK.
• The Concorde was capable of speeds in excess of Mach 2 (around 2,180 km/h), more than twice the speed of sound. It was mainly used for high-speed transatlantic flights, linking destinations such as Paris and New York.
• The Concorde had specific aerodynamic features, including a sleek tapered shape, delta wings and an afterburner engine configuration. It paved the way for commercial supersonic travel, although it was withdrawn from service in 2003.

Hypersonic regime:

• In the hypersonic field, a notable example is the X-15, an experimental rocket plane developed by NASA and the US Air Force.
• The X-15 was capable of flying at hypersonic speeds of up to Mach 6.7 (about 7,273 km/h). It performed suborbital flights and played a key role in hypersonic flight data collection and aerodynamics research at extremely high speeds.
• The X-15 was an innovative research vehicle, featuring an advanced aerodynamic design and powered by a rocket engine. It provided invaluable information on aircraft performance in the hypersonic regime.

These examples illustrate the diversity of iconic aircraft in each Mach category. Each aircraft represents the technological advances and challenges specific to the corresponding speeds, whether flying efficiently in the subsonic regime, managing supersonic shock waves or exploring hypersonic environments at extremely high speeds.

Mach speed measurement and calculation

A. Instruments used to measure Mach speed

Mach speed measurement requires specific instruments such as static pitot tubes and total pressure probes. These instruments measure atmospheric pressure and total pressure at different positions on the aircraft to determine Mach speed.

Accurate Mach speed measurement requires the use of specific instruments that can collect the necessary atmospheric and total pressure data. The two main instruments used for this purpose are static pitot tubes and total pressure probes.

Static pitot tubes:

• Pitot tubes are devices that measure the dynamic pressure of the surrounding air. They generally consist of a forward-opening tube, which captures the air flow.
• Static Pitot tubes are used to measure static air pressure, which is the ambient atmospheric pressure. These instruments are mounted on the aircraft and are designed to collect static pressure at a specific position, usually outside the aircraft structure.
• The difference between the dynamic pressure measured by the pitot tube and the static pressure measured by the static pitot tube is used to calculate the aircraft’s speed relative to the speed of sound.

Total pressure probes :

• Total pressure probes are used to measure total air pressure, which includes both static and dynamic pressure.
• These probes are designed to collect total pressure at specific positions on the aircraft, usually at the front of the airframe or on the control surfaces.
• By measuring the difference between total pressure and static pressure, total pressure probes can be used to determine the aircraft’s Mach speed.

These instruments are essential for accurately measuring an aircraft’s Mach speed. The data collected by the static pitot tubes and total pressure probes are then used to calculate Mach speed as a function of the speed of sound in the given atmospheric conditions.

Modern aircraft are equipped with sophisticated Mach speed measurement systems, which integrate these instruments with other sensors and electronic devices to obtain accurate and reliable Mach speed measurements. This enables pilots and engineers to monitor and control aircraft speed relative to the speed of sound in real time, helping to ensure safety and optimum flight performance.

B. Factors taken into account for accurate Mach speed calculation

The precise calculation of Mach speed requires the consideration of several factors that influence the speed of sound in air. Here are some of the main factors taken into account

Air temperature: The speed of sound in air depends on temperature. The higher the temperature, the higher the speed of sound. Mach speed measurement systems must therefore take air temperature into account to calculate Mach speed accurately.

Air density: Air density, which is influenced by atmospheric pressure and temperature, also affects the speed of sound. As air density decreases, the speed of sound increases. Mach speed measurement systems use pressure sensors to assess air density and adjust Mach speed calculations accordingly.

Atmospheric conditions: Variations in atmospheric conditions, such as altitude and temperature changes, can affect the speed of sound. Modern Mach speed measurement systems use temperature and pressure sensors to collect real-time data on atmospheric conditions for use in Mach speed calculations.

Instrumental errors: The measuring instruments used to calculate Mach speed may introduce errors or inaccuracies. Consequently, Mach speed measurement systems are designed to take these instrumental errors into account and make adjustments to obtain more accurate Mach speed measurements.

Modern Mach speed measurement systems use temperature, pressure and other sensors to collect the necessary data on the factors mentioned above. This data is then used to accurately adjust and calculate the aircraft’s Mach speed, taking into account variations in temperature, density and other atmospheric conditions.

Accurate Mach speed measurements are essential to ensure flight safety, particularly at high speeds. Pilots and engineers rely on these measurements to monitor and control aircraft speed relative to the speed of sound, ensuring optimum performance and effective management of Mach-related aerodynamic factors.

C. Limits and challenges of Mach speed measurement

Accurate Mach speed measurement presents certain limitations and challenges that are important to consider. Here are some of the main ones:

Air compressibility effects: At high speeds, air compressibility effects become significant. These effects can cause density and pressure variations that affect Mach speed measurement. The airflow around the aircraft may become compressible, making Mach speed measurement more complex.

Measurement errors: The instruments used to measure Mach speed can introduce errors, such as inaccuracies in pressure or temperature sensors. Measurement errors can affect the accuracy of Mach speed measurements and require regular calibration to maintain the accuracy of results.

Atmospheric density variations: Air density can vary according to altitude, temperature and other atmospheric factors. These density variations can influence Mach speed measurements, as the speed of sound is directly dependent on air density. Appropriate compensations must be applied to account for these variations and obtain accurate Mach speed measurements.

Non-ideal effects: In real-life situations, non-ideal conditions can affect Mach speed measurements. For example, turbulence, local temperature variations and other aerodynamic phenomena can interfere with accurate Mach speed measurement. These effects need to be taken into account and, where possible, compensated for to obtain more reliable measurements.

To meet these challenges and overcome these limitations, aeronautical engineers and instrument designers are working closely together to develop more accurate and reliable Mach speed measurement systems. This may involve improving sensors, implementing advanced calibration techniques and using sophisticated aerodynamic models to correct measurement errors.

Accurate Mach speed measurement is crucial to ensuring the safety and optimum performance of aircraft at high speeds. Despite the challenges and limitations, ongoing advances in measurement techniques and associated technologies are making it possible to obtain increasingly accurate Mach speed measurements, thereby contributing to the advancement of aeronautics and flight safety.

Practical applications of the Mach concept

A. Aircraft design and development.

Mach speed plays a crucial role in aircraft design and development. It has a direct influence on aerodynamic characteristics and engine performance, as well as on wing and airfoil design. Here are some important points to consider:

Aerodynamic characteristics: Mach speed determines the behavior of the air around the aircraft. At high speeds, aerodynamic phenomena such as shock waves and drag become significant. Aircraft design must take these effects into account to ensure optimum performance and aerodynamic stability.

Engine performance: Mach speed influences engine performance. At supersonic speeds, air compression can become a challenge for engines, affecting their efficiency and power. Designers need to take these factors into account when designing engines to maximize their performance in different Mach speed ranges.

Wing and airfoil design: Mach speed influences the shape and characteristics of wings and airfoils. At supersonic speeds, wings must be designed to manage shock waves and minimize induced drag. Specific airfoils, such as supersonic or delta wing airfoils, can be used to enhance performance at high Mach speeds.

Stability and control: Mach speed affects aircraft stability and control. At high speeds, variations in Mach speed can have an impact on the aircraft’s directional and longitudinal stability. Designers need to take these factors into account to ensure optimum handling and safety at different Mach speeds.

Taking Mach speed into account in aircraft design and development helps optimize aircraft performance, stability and safety. Aeronautical engineers use simulation models, wind tunnel tests and advanced analysis techniques to assess the effects of Mach speed on various aspects of aircraft design. This enables the development of aircraft adapted to specific speeds, while guaranteeing optimum aerodynamic performance and enhanced safety.

B. Aircraft performance and capabilities

Mach speed has a direct impact on aircraft performance and capabilities, particularly in terms of take-off and landing distance, cruising speed and fuel consumption. Here are some important points to consider:

Take-off and landing distance: Mach speed affects aircraft take-off and landing distance. At high speeds, the aircraft needs more distance to accelerate and decelerate, due to increased aerodynamic forces. Braking and propulsion performance must be matched to Mach speed to ensure safe and efficient operation.

Cruising speed: Mach speed determines the aircraft’s optimum cruising speed. Aircraft are designed to achieve their best efficiency at specific speeds. At high Mach speeds, some aircraft may have a higher cruising speed, which can reduce flight time and increase range. However, it’s important to find the right compromise between Mach speed and fuel consumption to optimize overall performance.

Fuel consumption : Mach speed affects aircraft fuel consumption. At high Mach speeds, aerodynamic drag increases, which can lead to higher fuel consumption. Aircraft designers must strike a balance between Mach speed and fuel efficiency to minimize fuel consumption and maximize aircraft range.

Flight performance: Mach speed influences aircraft flight performance, particularly in terms of maneuverability, stability and operational capabilities. At supersonic speeds, for example, aircraft can benefit from a greater ability to perform rapid maneuvers and avoid threats. However, this may also require advanced stability and control systems to maintain aircraft safety and control.

Taking Mach speed into account in aircraft design helps optimize performance, fuel efficiency and flight safety. Aircraft engineers use simulation models and flight tests to evaluate aircraft performance at different Mach speeds and optimize flight characteristics accordingly. This enables the development of aircraft capable of meeting the specific needs of flight operations in different Mach speed ranges, while ensuring optimum overall performance.

C. Respecting Mach speed limits is essential for flight safety

Compliance with Mach speed limits is of paramount importance to flight safety. When aircraft exceed the speed of sound, a phenomenon known as sonic boom occurs. Sonic boom is a shock wave produced by aircraft flying at supersonic speeds, creating an intense pressure wave.

Sonic boom can cause significant noise nuisance for people living near flight zones. The sudden loud noises associated with sonic booms can disrupt the surrounding calm, causing sleep disturbances and affecting the quality of life of those concerned.

Sonic booms can also affect nearby structures. The pressure waves generated by sonic booms can damage buildings, windows and other infrastructure in the vicinity. This underlines the importance of respecting the specific Mach speed limits set by aviation regulations to minimize negative impacts on the environment and communities.

In addition to noise and structural damage, exceeding Mach speed limits can also lead to aerodynamic and aircraft stability problems. Aircraft are designed to operate efficiently within specific speed ranges, and excessive Mach speeds can cause aerodynamic instabilities, excessive vibration and reduced aircraft maneuverability. This can jeopardize flight safety, and requires strict adherence to Mach speed limits set by manufacturers and aviation authorities.

Evolution and future of the Mach concept

A. Technological advances and the new challenges of high Mach speeds

Technological advances continue to push back the limits of high Mach speeds, opening up new perspectives and challenges for aeronautics. Here are some important aspects to consider:

Materials and structures: High Mach speeds impose significant constraints on aircraft materials and structures. Traditional materials may not be suitable for the temperatures and aerodynamic stresses encountered at supersonic or hypersonic speeds. Research is focusing on the development of lightweight, heat-resistant composite materials capable of withstanding extreme aerodynamic forces.

Propulsion: High Mach speeds require advanced propulsion systems to deliver the necessary power. Conventional jet engines can reach their limits at supersonic or hypersonic speeds. Emerging technologies, such as hypersonic supersonic combustion propulsion, closed-cycle jet engines and ramjet engines, are being explored to meet these challenges and improve aircraft efficiency and performance at high Mach speeds.

Aerodynamics and control: Aircraft at high Mach speeds have to overcome complex aerodynamic challenges, such as supersonic drag and shock wave formation. Managing these phenomena is essential to ensure aircraft stability, maneuverability and safety at high Mach speeds. Advances in modeling and simulation techniques, as well as in flight control systems, enable us to better understand and control these aspects.

Human factors: High Mach speeds also pose challenges for pilots in terms of human factors. The g-forces exerted on the human body, the effects of gravity, vibrations and pressure variations can have an impact on pilots’ health and performance. Research is being carried out to understand and mitigate these effects, developing protective systems and environments suitable for pilots of aircraft at high Mach speeds.

Costs and regulations: High Mach speed aircraft can represent significant investments in terms of development, manufacturing and maintenance. In addition, regulatory considerations, such as restrictions on supersonic flights over populated areas, can limit the commercial operation of these aircraft. Assessing the costs, benefits and regulations associated with high Mach speed aircraft is therefore an essential aspect of the development of these technologies.

B. Supersonic and hypersonic aircraft development projects

Supersonic aircraft are those that fly faster than the speed of sound, which is around 1,235 km/h at sea level. Examples of supersonic aircraft include the Concorde, a commercial aircraft developed jointly by France and the UK that operated from 1976 to 2003, and military aircraft such as the F-22 Raptor and the Russian SU-57.

Hypersonic aircraft, on the other hand, are those that travel at more than five times the speed of sound. These aircraft have the potential to revolutionize air transport, as they could considerably reduce travel times between continents. Examples of hypersonic aircraft include the experimental X-15 and the Boeing X-51 Waverider.

Several projects are currently underway to develop supersonic and hypersonic aircraft. For example, NASA is working on the X-59 QueSST, a supersonic jet designed to produce a quieter sonic boom, while the US Air Force is developing the X-60A, a hypersonic research vehicle. Companies such as Boeing and Lockheed Martin are also developing hypersonic weapons for the military.

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