Beginner's
Guide to Rockets
Mach Number
Answers
- Use the definition
of Mach number obtained from the Mach number slide
and the information in the activity to determine the speed of a rocket
flying at Mach 3 at sea level. ~2280 mph or 3669 km/hr.
- Convert the sea
level speed
of sound, 760 mph, from units of mph to km/hr. ~1223 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
|
1223
|
|
120
|
2.8
|
3424
|
|
180
|
4.5
|
5504
|
|
240
|
6.5
|
7950
|
|
300
|
9.0
|
11007
|
-
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
|
1211
|
1211
|
|
120
|
2.8
|
2500
|
1190
|
3332
|
|
180
|
4.5
|
5000
|
1154
|
5193
|
|
240
|
6.5
|
15000
|
1062
|
6903
|
|
300
|
9.0
|
30000
|
1098
|
9882
|
-
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 = 2698 ft/sec
B. How does that compare with the speed of sound in air at sea level,
expressed in feet/sec?
Air Speed of Sound = 1115 ft/sec
C. Why do you think they are different?
The exhaust from the rocket nozzle is at a much higher temperature.
The exhaust is not air (nitrogen, oxygen, etc), it is mostly steam (H2O)
which has very different chemical properties than air.
Related Sites:
Teaching Standards
Activity
Worksheet
Rocket Index
Rocket Home
Exploration Systems Mission Directorate Home
|
