Mach Numbers Explained: The Speed of Sound and Beyond

Breaking Through the Invisible Wall

On October 14, 1947, at an altitude of 43,000 feet over the Mojave Desert, Captain Chuck Yeager pushed the throttle of his Bell X-1 rocket plane and did something many engineers had declared impossible. As his aircraft, nicknamed "Glamorous Glennis," accelerated past 700 miles per hour, it punched through an invisible barrier that had killed pilots and destroyed aircraft. Yeager became the first human to travel faster than the speed of sound, achieving Mach 1.06.

But what exactly is a Mach number? Why do we measure aircraft speed this way instead of using familiar miles or kilometers per hour? And how does sound itself work as a speed limit that can be broken? Understanding Mach numbers opens a fascinating window into the physics of flight and the engineering marvels that allow humans to outrun sound itself.

What Is a Mach Number?

A Mach number is a dimensionless quantity representing the ratio of an object's speed to the local speed of sound. Named after Austrian physicist Ernst Mach (1838-1916), this measurement tells us how fast something is traveling relative to sound waves in the surrounding medium.

The simple formula:

Mach Number = Object Speed / Speed of Sound

When an aircraft travels at exactly the speed of sound, it is moving at Mach 1.0. At half the speed of sound, it travels at Mach 0.5. At twice the speed of sound, it achieves Mach 2.0.

Who Was Ernst Mach?

Ernst Mach was a brilliant physicist and philosopher whose work on shock waves and supersonic motion laid the groundwork for modern aerodynamics. Working in the late 1800s, long before powered flight existed, Mach used special photography techniques to capture images of bullets traveling faster than sound.

His photographs revealed the cone-shaped shock waves that form when objects exceed sound speed. These "Mach waves" demonstrated fundamental principles that would prove essential to aviation engineers decades later. In recognition of his pioneering work, the ratio of speed to sound speed was named the Mach number in his honor.

The Speed of Sound: Not a Fixed Value

Here is where Mach numbers become more interesting than simple speed measurements: the speed of sound is not constant. It changes based on the properties of the medium through which sound travels.

Temperature Is the Key Factor

In air, the speed of sound depends primarily on temperature. The relationship follows this principle:

Speed of Sound = 20.05 x square root of (Temperature in Kelvin)

At different temperatures:

• At 59 degrees F (15 degrees C / sea level standard): 761 mph (1,225 km/h)
• At 32 degrees F (0 degrees C): 742 mph (1,193 km/h)
• At -40 degrees F (-40 degrees C / typical cruise altitude): 660 mph (1,062 km/h)
• At -67 degrees F (-55 degrees C / stratosphere): 614 mph (988 km/h)

Why Altitude Matters

As aircraft climb, air temperature generally decreases until reaching the tropopause (around 36,000 feet), after which temperature stabilizes or slightly increases in the stratosphere. This means:

At sea level (standard day): Mach 1 = 761 mph (1,225 km/h) At 35,000 feet: Mach 1 = approximately 660 mph (1,062 km/h)

This is precisely why pilots and engineers use Mach numbers instead of miles per hour at high altitudes.

Conversion Examples at Different Altitudes

At sea level (standard conditions, 59 degrees F):

• Mach 0.80 = 609 mph (980 km/h)
• Mach 1.00 = 761 mph (1,225 km/h)
• Mach 2.00 = 1,522 mph (2,450 km/h)

At 35,000 feet cruise altitude (-56 degrees F):

• Mach 0.80 = 530 mph (853 km/h)
• Mach 1.00 = 663 mph (1,067 km/h)
• Mach 2.00 = 1,326 mph (2,134 km/h)

The Speed Regimes: Subsonic to Hypersonic

Subsonic (Below Mach 0.8)

Most everyday aviation occurs in the subsonic regime. Commercial airliners, general aviation aircraft, and helicopters all operate here.

Examples:

• Cessna 172: Mach 0.18 (140 mph)
• Boeing 737 approach speed: Mach 0.24 (180 mph)
• Turboprop airliner cruise: Mach 0.50 (380 mph)

Transonic (Mach 0.8 to 1.2)

The transonic regime is the most challenging for aircraft designers. The "sound barrier" refers to the dramatic increase in drag that occurs in this regime.

Examples:

• Boeing 747 cruise speed: Mach 0.855
• Modern fighters in afterburner: Pass through transonic rapidly

Supersonic (Mach 1.2 to 5.0)

Once fully supersonic, airflow behaves more predictably than in the transonic range.

Examples:

• Concorde cruise: Mach 2.04 (1,354 mph at altitude)
• F-22 Raptor supercruise: Mach 1.82
• SR-71 Blackbird cruise: Mach 3.2 (2,193 mph)

Hypersonic (Above Mach 5.0)

At hypersonic speeds, new physical phenomena emerge.

Examples:

• X-15 rocket plane maximum: Mach 6.7 (4,520 mph)
• Space Shuttle reentry: Mach 25 (approximately 17,500 mph)
• Ballistic missiles: Mach 20+ during reentry

Why Aviation Uses Mach Numbers

Aerodynamic Consistency

Aircraft behave according to their Mach number, not their speed in miles per hour. An aircraft at Mach 0.85 experiences the same aerodynamic conditions whether flying at sea level on a cold day or at 40,000 feet.

Critical Mach Number

Every aircraft has a critical Mach number, the speed at which airflow somewhere on the aircraft first reaches Mach 1.0. Commercial airliners have a maximum operating Mach number (Mmo) that pilots must not exceed.

Famous Mach Speeds in History

Bell X-1: Breaking the Barrier (Mach 1.06)

Chuck Yeager's historic 1947 flight reached Mach 1.06 (700 mph at 43,000 feet).

SR-71 Blackbird: The Ultimate Spy Plane (Mach 3.2+)

The Lockheed SR-71 Blackbird remains the fastest air-breathing crewed aircraft ever. Its official speed record stands at Mach 3.3 (2,193 mph).

X-15: To the Edge of Space (Mach 6.7)

On October 3, 1967, William Knight reached Mach 6.7 (4,520 mph) at 102,100 feet.

Space Shuttle Reentry (Mach 25)

When the Space Shuttle reentered Earth's atmosphere, it began at approximately Mach 25 (17,500 mph).

Concorde: Commercial Supersonic Travel (Mach 2.04)

From 1976 to 2003, the Concorde gave passengers the experience of supersonic flight, cruising at Mach 2.04 (1,354 mph at 60,000 feet).

The Sonic Boom

When an aircraft exceeds Mach 1, it creates shock waves that produce the distinctive "sonic boom" heard on the ground.

How Sonic Booms Form

Sound travels as pressure waves radiating outward from their source. When an aircraft exceeds the speed of sound, it outruns its own pressure waves. The waves pile up into a cone-shaped shock wave trailing behind the aircraft.

Characteristics of Sonic Booms

• A sonic boom continues as long as the aircraft flies supersonically
• The boom follows the aircraft like a carpet unrolling across the landscape
• Intensity depends on altitude, aircraft size, and atmospheric conditions

Converting Mach Numbers: Practical Guide

For quick conversions at sea level standard conditions:

Quick mental math for sea level:

• Multiply Mach number by 760 to get approximate mph
• Multiply Mach number by 1,225 to get approximate km/h

Conclusion

From Chuck Yeager's historic flight to modern hypersonic research, Mach numbers have defined the cutting edge of human achievement in flight. Whether you are calculating flight times or simply curious about the physics of speed, Mach numbers provide the essential framework.

Ready to convert between Mach numbers and conventional speed units? Use our speed conversion tools to instantly convert Mach to mph, kph, or any other speed unit.