Mach Number - Answers - NASA

1. 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.
2. Convert the sea level speed of sound, 760 mph, from units of mph to km/hr. ~1223 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	1223
   120	2.8	3424
   180	4.5	5504
   240	6.5	7950
   300	9.0	11007

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	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

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 = 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

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