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


As an object moves through the air, the air molecules near the object are disturbed and move around the object. If the object passes at a low speed (typically less than 200 mph) the density of the fluid will remain constant. But for higher speeds, some of the energy of the object goes into compressing the fluid and locally changing the density of the air. This compressibility effect will alter the amount of resulting force on the object. The effect becomes more important as speed increases. Near and beyond the speed of sound (about 330 m/s or 700 mph), the compression waves merge into a strong shock wave, which affects both the lift and drag of an object. (You can investigate the formation of shock waves with an interactive Java applet. Use the "Back" command of your browser to return to this page.)

As we have seen, the ratio of the speed of the source to the speed of sound determines the presence of shock waves. Because of the importance of this speed ratio, aerodynamicists have designated it with a special parameter called the Mach number in honor of Ernst Mach, a late 19th century physicist who studied gas dynamics. The Mach number allows us to define flight regimes in which compressibility effects vary.

  1. Subsonic conditions occur for Mach numbers less than one; and for the lowest subsonic conditions, compressibility can be ignored.
  2. As the speed of the object approaches the speed of sound, the Mach number is nearly equal to one and the flow is said to be transonic. (At flight speed exactly equal to the speed of sound the conditions are said to be sonic and the Mach number equals one.) Compressibility effects are most important in transonic flows and lead to the early belief in a sound barrier above which velocity flight would be impossible. In fact, the sound barrier was only an increase in the drag near transonic conditions because of compressibility effects.
  3. Supersonic conditions occur for Mach numbers greater than one. (A Mach 3.0 aircraft flies at 3.0 times the local speed of sound.) Compressibility effects are important for supersonic aircraft, and shock waves are generated by the surface of the object.
  4. For speeds much greater than the speed of sound (typically greater than Mach 5.0) the flow is said to be hypersonic. At these speeds, some of the energy of the object now goes into exciting the chemical bonds holding the nitrogen and oxygen molecules together. So the thermo-chemistry of the gas must be considered when determining forces on the object.

The Mach number depends on the speed of sound in a gas. The speed of sound in air depends on the temperature which, in turn, 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 compressibility with altitude. Here's a Java program based on this mathematical model that you can use to determine the Mach number of a vehicle at a given speed and altitude.

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.

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Guided Tours


Beginner's Guide to Aerodynamics
Beginner's Guide to Propulsion
Beginner's Guide to Model Rockets
Beginner's Guide to Kites
Beginner's Guide to Aeronautics

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byTom Benson
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