How to Calculate Mach N

Mach number is a dimensionless quantity that represents the speed of an object relative to the speed of sound in the surrounding medium. It's commonly used in aerodynamics, aviation, and fluid dynamics to describe how fast an object is moving compared to the speed of sound.

What is Mach number?

The Mach number (M) is a ratio of the speed of an object to the speed of sound in the medium through which the object is traveling. It's named after Austrian physicist Ernst Mach. The Mach number is used to describe the speed of aircraft, rockets, and other high-speed objects.

When an object moves at subsonic speeds (M < 1), it's traveling slower than the speed of sound. At M = 1, the object is traveling at the speed of sound (sonic speed). When M > 1, the object is traveling faster than the speed of sound (supersonic speed).

Mach number formula

The Mach number is calculated using the following formula:

M = v / c Where: M = Mach number v = velocity of the object c = speed of sound in the medium

The speed of sound (c) varies depending on the medium through which the object is traveling. In dry air at 20°C (68°F), the speed of sound is approximately 343 meters per second (1,125 feet per second).

How to calculate Mach number

To calculate the Mach number, follow these steps:

Determine the velocity of the object (v) in meters per second (m/s).
Find the speed of sound (c) in the medium through which the object is traveling. For dry air at 20°C, c ≈ 343 m/s.
Divide the velocity of the object by the speed of sound to get the Mach number.

For example, if an aircraft is traveling at 400 m/s, the Mach number would be calculated as follows:

M = 400 m/s / 343 m/s ≈ 1.166

This means the aircraft is traveling at approximately 1.166 times the speed of sound.

Mach number examples

Here are some examples of objects and their approximate Mach numbers:

Object	Velocity (m/s)	Mach Number
Commercial airliner	250	0.73
Concorde (supersonic airliner)	680	1.98
Fighter jet (e.g., F-16)	540	1.57
Bullet	340	1.00
Space shuttle re-entry	7,000	20.40

These examples show how different objects can have varying Mach numbers depending on their speed relative to the speed of sound.

Mach number chart

The following chart shows the relationship between Mach number and speed for different media:

This chart illustrates how the Mach number increases as the speed of the object increases relative to the speed of sound in the medium.

FAQ

What is the speed of sound in different media?: The speed of sound varies depending on the medium. In dry air at 20°C, it's approximately 343 m/s. In water, it's about 1,482 m/s, and in steel, it's around 5,960 m/s.
What happens when an object reaches Mach 1?: When an object reaches Mach 1, it's traveling at the speed of sound. This creates a sonic boom, which is a loud noise caused by the shock waves created by the object breaking the sound barrier.
How is Mach number different from knots?: Mach number is a dimensionless ratio of an object's speed to the speed of sound, while knots are a unit of speed (nautical miles per hour). One knot is approximately 0.514 m/s.
What are the effects of high Mach numbers?: High Mach numbers can cause significant aerodynamic heating, compressibility effects, and shock waves. These effects must be considered in the design of high-speed aircraft and spacecraft.
How is Mach number used in aviation?: Mach number is used in aviation to describe the speed of aircraft relative to the speed of sound. It helps pilots and engineers understand the performance characteristics of aircraft at different speeds.