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As an aircraft moves through the air, the air molecules near theaircraft are disturbed and move around the aircraft. If the aircraft passesat a low speed, typically less than 250 mph, the densityof the air remains constant. But for higher speeds, some of theenergy of the aircraft goes into compressing the air and locallychanging the density of the air. This compressibilityeffect alters the amount of resulting force on the aircraft.The effect becomes more important as speed increases. Near and beyondthe speed of sound, about 330 m/s or 760mph, small disturbances in the flow are transmittedto other locationsisentropically or with constant entropy.But a sharp disturbance generates ashock wave that affects both the lift and drag of an aircraft.
Theratioof the speed of the aircraft to the speedof sound in the gas determines the magnitude of many of the compressibilityeffects. Because of theimportance of this speed ratio, aerodynamicists have designated itwith a special parameter called the Mach number in honor ofErnst Mach, a late 19th century physicist who studied gasdynamics. The Mach number M allows us to define flight regimes in whichcompressibility effects vary.
- Subsonic conditions occur for Mach numbers less than one, M < 1 . For the lowest subsonic conditions, compressibility can be ignored.
- As the speed of the object 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 object, 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. Because of the high drag associated with compressibility effects, aircraft do not cruise near Mach 1.
- Supersonic conditions occur for Mach numbers greater than one, 1 < M < 3. Compressibility effects are important for supersonic aircraft, and shock waves are generated by the surface of the object. For high supersonic speeds, 3 < M < 5, aerodynamic heating also becomes very important for aircraft design.
- 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 object 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.
sin(b) = 1 / M
There is no upstream influence in a supersonic flow; disturbancesare only transmitted downstream.
The Mach number appears as asimilarity parameterin many of the equations forcompressible flows,shock waves,andexpansions.When wind tunnel testing, you must closely match the Mach number betweenthe experiment and flight conditions.It is completely incorrect to measure a dragcoefficient at some low speed (say 200 mph) and apply that dragcoefficient at twice the speed of sound (approximately 1400 mph, Mach= 2.0). The compressibility of the air alters the importantphysics between these two cases.
The Mach number depends on the speed of sound in the gas andthe speed of sound depends on the type of gas andthe temperature of the gas. The speed of sound varies fromplanet to planet. On Earth,the atmosphere is composed ofmostly diatomic nitrogen and oxygen, and the temperaturedepends on the altitude in a rather complex way.Scientists and engineers have created amathematical model of the atmosphere to helpthem account for the changing effects of temperature with altitude.Mars also has an atmosphere composed ofmostly carbon dioxide. There is a similarmathematical model of the Martian atmosphere.We have created anatmospheric calculatorto let you study the variation of sound speed with planet andaltitude.
Here's another JavaScript program to calculate speed of sound and Mach numberfor different planets, altitudes, and speed. You can use this calculatorto determine the Mach number of a aircraft at a given speed and altitudeon Earth or Mars.
To change input values, click on the input box (black on white),backspace over the input value, type in your new value, andhit 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 numberor the speed by using the menu buttons. Just click on the menu button and click on yourselection.If you are an experienced user of this calculator, you can use asleek versionof 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:
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