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Mach number equals object speed divided by speed of sound. Pictures
 of rocket at subsonic, supersonic and hypersonic Mach numbers

As a rocket moves through the air, the air molecules near the rocket are disturbed and move around the rocket. If the rocket passes at a low speed, typically less than 250 mph, the density of the air remains constant. But for higher speeds, some of the energy of the rocket goes into compressing the air and locally changing the density of the air. This compressibility effect alters the amount of resulting force on the rocket. The effect becomes more important as speed increases. Near and beyond the speed of sound, about 330 m/s or 760 mph at sea level on Earth, small disturbances in the flow are transmitted to other locations isentropically or with constant entropy. Sharp disturbances generate shock waves that affects the drag on the rocket. Within the nozzle of the rocket engine, gases are expelled at speeds much greater than the speed of sound to generate thrust.

The ratio of the speed of the rocket, or the speed of the nozzle flow, to the speed of sound in the gas determines the magnitude of many of the compressibility effects. Because of the importance of this speed ratio, engineers give it a special name, the Mach number, in honor of Ernst Mach, a late 19th century physicist who studied gas dynamics. The Mach number M allows us to define flow regimes in which compressibility effects vary.

  1. Subsonic conditions occur for Mach numbers less than one, M < 1 . For the lowest subsonic conditions, compressibility can be ignored.
  2. As the speed of the rocket approaches the speed of sound, the flight Mach number is nearly equal to one, M = 1, and the flow is said to be transonic. At some places on the rocket, the local speed exceeds the speed of sound. Compressibility effects are most important in transonic flows and lead to the early belief in a sound barrier. Flight faster than sound was thought to be impossible. In fact, the sound barrier was only an increase in the drag near sonic conditions because of compressibility effects. During launch, a rocket often encounters its highest dynamic pressure , or "Max Q", at transonic conditions.
  3. Supersonic conditions occur for Mach numbers greater than one, 1 < M < 5. The flow through the expansion bell of the nozzle is typically in this regime. Compressibility effects are also important for the external rocket because shock waves are generated by the surface of the rocket. For high supersonic speeds, 3 < M < 5, aerodynamic heating also becomes very important for rocket design.
  4. For speeds greater than five times the speed of sound, M > 5, the flow is said to be hypersonic. At these speeds, some of the energy of the rocket now goes into exciting the chemical bonds which hold together the nitrogen and oxygen molecules of the air. At hypersonic speeds, the chemistry of the air must be considered when determining forces on the object. The Space Shuttle re-enters the atmosphere at high hypersonic speeds, M ~ 25. Under these conditions, the heated air becomes an ionized plasma of gas and the spacecraft must be insulated from the high temperatures.

For supersonic and hypersonic flows, small disturbances are transmitted downstream within a cone. The trigonometric sine of the cone angle b is equal to the inverse of the Mach number M and the angle is therefore called the Mach angle.

sin(b) = 1 / M

There is no upstream influence in a supersonic flow; disturbances are only transmitted downstream within the Mach cone.

The Mach number depends on the speed of sound in the gas and the speed of sound depends on the type of gas and the temperature of the gas. The speed of sound varies from planet to planet. On Earth, the atmosphere is composed of mostly diatomic nitrogen and oxygen, and the temperature depends on the altitude in a rather complex way. Scientists and engineers have created a mathematical model of the atmosphere to help them account for the changing effects of temperature with altitude. Mars also has an atmosphere composed of mostly carbon dioxide. There is a similar mathematical model of the Martian atmosphere. We have created an atmospheric calculator to let you study the variation of sound speed with planet and altitude.

Here's another JavaScript program to calculate speed of sound and Mach number for different planets, altitudes, and speed. You can use this calculator to determine the Mach number of a rocket at a given speed and altitude on Earth or Mars.

Mach and Speed of Sound Calculator

Speed of Sound

To change input values, click on the input box (black on white), backspace over the input value, type in your new value, and hit the Enter key on the keyboard (this sends your new value to the program). You will see the output boxes (yellow on black) change value. You can use either English or Metric units and you can input either the Mach number or the speed by using the menu buttons. Just click on the menu button and click on your selection. If you are an experienced user of this calculator, you can use a sleek version of the program which loads faster on your computer and does not include these instructions. You can also download your own copy of the program to run off-line by clicking on this button:

Button to Download a Copy of the Program

Guided Tours
  • Button to Display Previous Page Compressible Aerodynamics: Button to Display Next Page
  • Button to Display Previous Page Rocket Thrust: Button to Display Next Page
  • Button to Display Previous Page Speed of Sound: Button to Display Next Page
  • Button to Display Previous Page Scalars: Button to Display Next Page
  • Button to Display Previous Page Atmosphere Simulator: Button to Display Next Page
  • Button to Display Previous Page Mach & Speed of Sound Calculator: Button to Display Next Page

Mach Number Activity: Grade 9-12

Related Sites:
Rocket Index
Rocket Home
Beginner's Guide Home


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Editor: Tom Benson
NASA Official: Tom Benson
Last Updated: Apr 05 2018

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