On October 3, 1967, pilot William J. "Pete" Knight set a world record that still stands to this day for the fastest flight by a crewed, powered aircraft by flying the North American Aviation X-15 as fast as Mach 6.7 at an altitude of 102,000 ft above sea level. Mach number is the ratio of an object’s velocity to the local speed of sound. Using the table for atmospheric properties with respect to altitude, calculate the speed of sound at an altitude of 100,000 ft. What must have been the velocity of the X-15? U.S. Standard Atmosphere Air Properties - Imperial (BG) UnitsGeo-potentialAltitude aboveDynamicViscosityAcceleration ofAbsoluteDensityTemperature- t-Gravity- g -(ft/s?)PressureSea Level-p -(104 slugs/it)- р-(107 Ib s/t?)(107 slug /(ft s))- h-CF)(Ib/in?)(Ibs/ft3)(ft)-500076.8432.18917.55427.453.8365932.17414.69623.773.737500041.1732.15912.22820.483.6371000023.3632.14310.10817.563.534150005.5532.1288.29714.963.43020000-12.2632.1126.75912.673.32425000-30.0532.0975.46110.663.21730000-47.8332.0824.3738.913.10735000-65.6132.0663.4687.382.99540000-69.7032.0512.7305.872.96945000-69.7032.0362.1494.622.96950000-69.7032.0201.6923.642.96960000-69.7031.9901.0492.262.96970000-67.4231.9590.6511.392.98480000-61.9831.9290.4060.863.01890000-56.5431.8970.2550.563.052100000-51.1031.8680.1620.333.08715000019.4031.7170.0200.0373.511200000-19.7831.5660.0030.00533.279250000-88.7731.4150.0000.000652.846 A "Standard Atmosphere" can be regarded as an average pressure, temperature and air density for various altitudes.The "U.S. Standard Atmosphere 1976" is an atmospheric model of how the pressure, temperature, density, andviscosity of the Earth's atmosphere changes with altitude. It is defined as having a temperature of 288.15 K (15°C, 59°F) at the sea level 0 km geo-potential height and 101325 Pa (1013.25 hPa, 1013.25 mbar, 760 mm Hg, 29.92 in Hg).The atmosphere are divided in• the Troposphere - ranging 0 to 11 km (36.000o ft) altitude• the Stratosphere - ranging 11 to to 51 km (167.000 ft) altitude• the Mesosphere - ranging 51 to 71 km (232.000 ft) altitude• the lonosphere - ranging above 71 km (above 232.000 ft) altitude

Answered: On October 3, 1967, pilot William J.…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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On October 3, 1967, pilot William J. "Pete" Knight set a world record that still stands to this day for the fastest flight by a crewed, powered aircraft by flying the North American Aviation X-15 as fast as Mach 6.7 at an altitude of 102,000 ft above sea level. Mach number is the ratio of an object’s velocity to the local speed of sound. Using the table for atmospheric properties with respect to altitude, calculate the speed of sound at an altitude of 100,000 ft. What must have been the velocity of the X-15?

U.S. Standard Atmosphere Air Properties - Imperial (BG) Units
Geo-potential
Altitude above
Dynamic
Viscosity
Acceleration of
Absolute
Density
Temperature
- t-
Gravity
- g -
(ft/s?)
Pressure
Sea Level
-p -
(104 slugs/it)
- р-
(107 Ib s/t?)
(107 slug /(ft s))
- h-
CF)
(Ib/in?)
(Ibs/ft3)
(ft)
-5000
76.84
32.189
17.554
27.45
3.836
59
32.174
14.696
23.77
3.737
5000
41.17
32.159
12.228
20.48
3.637
10000
23.36
32.143
10.108
17.56
3.534
15000
5.55
32.128
8.297
14.96
3.430
20000
-12.26
32.112
6.759
12.67
3.324
25000
-30.05
32.097
5.461
10.66
3.217
30000
-47.83
32.082
4.373
8.91
3.107
35000
-65.61
32.066
3.468
7.38
2.995
40000
-69.70
32.051
2.730
5.87
2.969
45000
-69.70
32.036
2.149
4.62
2.969
50000
-69.70
32.020
1.692
3.64
2.969
60000
-69.70
31.990
1.049
2.26
2.969
70000
-67.42
31.959
0.651
1.39
2.984
80000
-61.98
31.929
0.406
0.86
3.018
90000
-56.54
31.897
0.255
0.56
3.052
100000
-51.10
31.868
0.162
0.33
3.087
150000
19.40
31.717
0.020
0.037
3.511
200000
-19.78
31.566
0.003
0.0053
3.279
250000
-88.77
31.415
0.000
0.00065
2.846

A "Standard Atmosphere" can be regarded as an average pressure, temperature and air density for various altitudes.
The "U.S. Standard Atmosphere 1976" is an atmospheric model of how the pressure, temperature, density, and
viscosity of the Earth's atmosphere changes with altitude. It is defined as having a temperature of 288.15 K (15°C, 59
°F) at the sea level 0 km geo-potential height and 101325 Pa (1013.25 hPa, 1013.25 mbar, 760 mm Hg, 29.92 in Hg).
The atmosphere are divided in
• the Troposphere - ranging 0 to 11 km (36.000o ft) altitude
• the Stratosphere - ranging 11 to to 51 km (167.000 ft) altitude
• the Mesosphere - ranging 51 to 71 km (232.000 ft) altitude
• the lonosphere - ranging above 71 km (above 232.000 ft) altitude

Expert Solution

Step 1

Given,

M = 6.7

For 100000 ft altitude, from given table,

$T = - 51.1 ° F = 227 K$

Ratio of specific heat = $γ = 1.41$

Gas constant of air = R = 287 J/kg-K

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