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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.

1. 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.

2. Convert the sea level speed of sound, 760 mph, from units of mph to km/hr.

3. 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

4. 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

5. 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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