Beginner's
Guide to Rockets
Mach Number
Activity
If so instructed
by your teacher, print out a worksheet page for these problems.
Open the slide called Mach Number
and read the definition of Mach number.
As a rocket is launched into
space, the Mach number of the rocket goes from zero to almost 25.0.
Do you know what that means?
The unitless Mach
number was named after the Austrian physicist Ernst Mach.
The Mach number is the ratio of the speed of the rocket to the
speed of sound .
When the rocket is
flying at less than Mach 1 is traveling at
subsonic
speeds; at about Mach 1, or
transonic ,
it is at the speed of sound,
and greater than Mach 1 is
supersonic .
A rocket traveling
at Mach 2 is traveling at twice the speed of sound.
The Mach number can also be used to define the speed of exhaust flows
leaving the nozzle of a rocket engine.
The speed of sound on an average day at sea level is 760 mph. The
speed of sound depends on the composition and temperature of the air
and it
decreases with altitude.
 Use the definition
of Mach number obtained from the Mach Number slide
and the information above to determine the speed of a rocket flying at Mach 3
at sea level.
 Convert the sea level speed
of sound, 760 mph, from units of mph to km/hr.

Let's perform a little study to determine how the velocity of
a rocket changes during its flight into orbit.
We've installed a small device on the side of the rocket to measure
the free stream Mach number. The data is presented below in terms of
time after launch and measured Mach number. Convert this data to
velocity (km/hr) assuming the speed of sound remains the same
as the velocity you computed in problem #2:
Time s

Mach

Speed, km/hr

60

1.0


120

2.8


180

4.5


240

6.5


300

9.0



We know that the temperature and speed of sound change with
altitude, so let's correct our data for that effect.
We have some additional radar data that gives the altitude of
our rocket during its ascent. Use the
AtmosModeler simulator to determine
the actual speed of sound at each altitude and calculate a more accurate
value of the rocket's velocity:
Time s

Mach

Altitude m

Speed of Sound, km/hr

Speed of Rocket, km/hr

60

1.0

1000



120

2.8

2500



180

4.5

5000



240

6.5

15000



300

9.0

30000




The
RocketThrust computer simulation was used to model the exhaust from
the Space Shuttle Main Engine (SSME) nozzle. The exit Mach number is
4.54, and the exit velocity is 12,250 feet/sec.
A. What is the speed of sound in the exhaust (feet/sec)?
Exhaust Speed of Sound = __________________
B. How does that compare with the speed of sound in air at sea level,
expressed in feet/sec?
Air Speed of Sound = __________________
C. Why do you think they are different?
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