As an aircraft moves through the air, the air molecules near the
aircraft are disturbed and move around the aircraft. If the aircraft 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 aircraft goes into compressing the air and locally
changing the density of the air. This compressibility
effect alters the amount of resulting force on the aircraft.
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, small disturbances in the flow are transmitted
to other locations
isentropically or with constant entropy.
Sharp disturbances generate
that affect both the lift and drag of the aircraft, and the flow
conditions downstream of the shock wave.
of the speed of the aircraft 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, 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 M allows us to define flight regimes in which
compressibility effects vary.
conditions occur for Mach numbers less than
one, M < 1 . For the lowest subsonic conditions, compressibility can
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
At some places on the object, the local speed exceeds the speed
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.
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
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
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.
For supersonic and hypersonic flows, small disturbances are transmitted
downstream within a cone. The trigonometric
of the cone angle b is
equal to the inverse of the Mach number M and the angle is therefore called the
sin(b) = 1 / M
There is no upstream influence in a supersonic or hypersonic flow; disturbances
are only transmitted downstream.
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.
We have created an
to let you study the variation of sound speed with planet and
Here's a Java program to calculate speed of sound and Mach number
for different altitudes and speed. You can use this calculator
to determine the Mach number of a aircraft 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. Then hit
the red COMPUTE button to
send your new value to the program.
You will see the output boxes (yellow on black)
change value. You can use either Imperial 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
If you are an experienced user of this calculator, you can use a
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: