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.
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 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.
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.
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
Input
Press->
Output
Speed
Speed of Sound
Mach
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:
