This page is intended for college, high school, or middle school students.
For younger students, a simpler explanation of the information on this page is
available on the
Kid's Page.
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, small disturbances in the flow are transmitted
to other locations
isentropically or with constant entropy.
But a sharp disturbance generates a
shock wave
that affects both the lift and drag of an aircraft.
The
ratio
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.
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.
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.
The Mach number appears as a
similarity parameter
in many of the equations for
compressible flows,
shock waves,
and
expansions.
When wind tunnel testing, you must closely match the Mach number between
the experiment and flight conditions.
It is completely incorrect to measure a drag
coefficient at some low speed (say 200 mph) and apply that drag
coefficient at twice the speed of sound (approximately 1400 mph, Mach
= 2.0). The compressibility of the air alters the important
physics between these two cases.
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 Java 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 aircraft at a given speed and altitude
on 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, 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:
