What is Mach Number?

The Mach number (M) is a dimensionless unit representing the ratio of an object’s speed to the speed of sound in the medium through which it moves. Named after Austrian physicist Ernst Mach, it’s a fundamental concept in high-speed travel, particularly in aviation and astronautics.

Definition and Formula

Mach number is defined as: M = V / a

where:

• M is the Mach number,
• V is the velocity of the object (like an aircraft’s speed),
• a is the speed of sound in the given medium (e.g., air, water, or any gas).

The speed of sound is not constant; it varies with the temperature and composition of the medium (air). In standard conditions (at sea level, at 15°C, and in dry air), the speed of sound in air is approximately 343 m/s or 1235 km/h (768 mph). As altitude increases and temperature decreases, the speed of sound decreases, which means Mach 1 at higher altitudes is slower than Mach 1 at sea level.

A Brief History of Mach in Aviation

The study of Mach number became significant in the 1940s as engineers faced the challenge of breaking the sound barrier. In 1947, Chuck Yeager became the first person to fly faster than the speed of sound (Mach 1) in the Bell X-1 aircraft. This breakthrough demonstrated that aircraft could be designed to withstand the shockwaves and aerodynamic stresses near the sound barrier, paving the way for the development of supersonic and even hypersonic aircraft.

Types of Mach Regimes

Mach number is often classified into various regimes based on the object’s speed relative to the speed of sound:

1. Subsonic (M < 0.8): At subsonic speeds, the object’s speed is less than the speed of sound. This includes most commercial aircraft, which typically operate at Mach 0.7-0.8 to optimize fuel efficiency and passenger comfort.
2. Transonic (M ≈ 0.8 – 1.2): In the transonic regime, the speed of the object is close to the speed of sound, where portions of airflow around the object may exceed Mach 1 while others remain subsonic. This range presents unique aerodynamic challenges, such as shock waves that form as an aircraft approaches Mach 1, creating increased drag and instability.
3. Supersonic (M > 1.2 – 5): Speeds above Mach 1.2 but below Mach 5 fall in the supersonic regime. Aircraft operating in this range, such as fighter jets and certain experimental aircraft, encounter significant shock waves and aerodynamic heating. Extensive engineering is required to manage the effects of these forces.
4. Hypersonic (M > 5): Speeds greater than Mach 5 are considered hypersonic. In this regime, intense aerodynamic heating becomes a major challenge, and specialized materials and thermal protection systems are required. Hypersonic speeds are typically achieved by spacecraft, rockets and experimental aircraft, as well as atmospheric re-entry vehicles.
5. High-Hypersonic & Re-entry Speeds (M > 10): Speeds above Mach 10 are extremely high-hypersonic or re-entry speeds, where aerodynamic forces and heating are extremely intense. These speeds are encountered by spacecraft re-entering Earth’s atmosphere.

Mach Number and Speed of Sound

The speed of sound (a) in the atmosphere depends on the temperature:

a = √(γ * R * T)

where:

• γ is the adiabatic index or ratio of specific heats (for air, typically 1.4),
• R is the specific gas constant (287 J/kg·K for dry air),
• T is the absolute temperature of the air in Kelvin (K).

As the temperature changes with altitude, so does the speed of sound, affecting the Mach number for a given true airspeed (TAS). Therefore, at higher altitudes, where the air is cooler, an aircraft can achieve Mach 1 at a lower true airspeed than it would near sea level.

How Mach Regimes Influence Aircraft Design

The Mach regime in which an aircraft operates directly influences its design:

• Wing Shape: Subsonic aircraft often have rounded, larger wings, while transonic and supersonic aircraft use supercritical and delta wings respectively to reduce drag and manage shockwaves.
• Materials: Supersonic and hypersonic aircraft require heat-resistant materials to endure the increased aerodynamic heating that occurs at higher Mach numbers.
• Engines: Jet engines designed for supersonic speeds often include afterburners to provide additional thrust, while hypersonic engines use advanced propulsion systems, like scramjets.

Environmental Impact of Different Mach Regimes

Mach regimes also impact the environment:

• Sonic Booms: Supersonic speeds generate loud sonic booms, limiting supersonic flights over land due to noise pollution concerns. Efforts are underway to develop quieter supersonic aircraft.
• Fuel Efficiency: Subsonic and transonic aircraft are optimized for fuel efficiency. Supersonic and hypersonic speeds consume more fuel and produce higher emissions per mile.

Applications of Mach Number in Aviation

The Mach number is particularly important in aviation because it helps determine performance, stability, and control characteristics of aircraft flying at high speeds. Here are some specific applications and uses in aviation:

1. Performance and Efficiency

• Commercial jets typically operate at subsonic speeds (Mach 0.7–0.85) because of fuel efficiency and passenger comfort. Operating at a fixed Mach number allows airliners to maximize fuel efficiency by balancing speed and fuel consumption.
• Modern passenger jets are often designed to operate near the transonic range to take advantage of the higher speeds without fully entering supersonic speeds, which would increase drag and reduce efficiency.

2. Transonic Aerodynamics

• The transonic range (Mach 0.8-1.2) presents unique challenges due to the formation of shock waves. These shock waves can lead to increased drag (known as wave drag) and compressibility effects on control surfaces.
• During World War II, aircraft like the Bell X-1 were designed specifically to study transonic effects and were among the first aircraft to exceed Mach 1. Modern commercial and military aircraft now use specialized wing shapes, like supercritical airfoils, to reduce shockwave formation and drag near transonic speeds.

3. Supersonic and Hypersonic Flight

• Military aircraft, like the F-22 Raptor, operate at supersonic speeds, often employing afterburners to reach speeds above Mach 1.5.
• Hypersonic research focuses on missiles and re-entry vehicles, with agencies like NASA exploring materials and designs that can withstand extreme temperatures and pressures.

4. Avoiding Mach Buffet

• Commercial airliners are designed to operate below the critical Mach number (M_cr), where a portion of the airflow over the wings first reaches Mach 1, leading to buffeting (vibrations due to shock waves). This phenomenon, known as Mach buffet, can affect control and stability. Staying below M_cr helps airliners avoid these issues, providing a smoother flight.

5. Mach Meter in Cockpits

• High-speed aircraft are equipped with a Mach meter, which displays the current Mach number. This helps pilots maintain optimal speeds, avoiding critical thresholds that could lead to structural stress or inefficiencies.

Practical Example of Mach Number in Commercial Flight

A Boeing 747 cruising at 35,000 feet with a true airspeed (TAS) of approximately 570 mph would operate around Mach 0.85. At this altitude, due to the reduced air temperature, the speed of sound is roughly 660 mph (compared to 768 mph at sea level). This makes it easier for the aircraft to achieve higher Mach numbers without actually increasing its TAS proportionally.

Practical Uses for Pilots

For pilots, Mach number is more than a measure of speed; it’s a critical tool in flight operations:

• Mach Number vs. True Airspeed: At higher altitudes, pilots often fly at a fixed Mach number instead of a fixed airspeed to optimize fuel efficiency and stability.
• Mach Limits in the Flight Manual: Exceeding recommended Mach limits can compromise an aircraft’s stability, so pilots are careful to maintain speeds within prescribed ranges for each phase of flight.

Conclusion

Understanding Mach number is crucial for high-speed aerodynamics, allowing engineers to design safe, efficient, and high-performing aircraft. For pilots, Mach number indicates critical speed thresholds for various flight regimes, ensuring that aircraft can handle the aerodynamic forces at each phase of flight. For industries and organizations working on the next generation of aviation and space technologies, Mach number will continue to be a key metric in developing faster, more efficient, and safer systems for transportation and exploration.