Supersonic Travel

The speed of sound at STP (Standard Temperature and Pressure, 0°C and 1 atmosphere of pressure) is 331 m/s which is approximately 740 mph. The speed of sound is the speed at which sound waves propagate or move through the air. The speed of sound in air varies with temperature and pressure, although temperature has a significantly predominate effect on the speed of sound.

As temperature increases the speed of sound in air increases by 0.6 m/s per degree Celsius increase in temperature. The speed of sound is greatest at sea level, where temperature is greatest. The speed of sound for the most part tends to decrease as altitude increases, since as altitude increases, temperature decreases.

It should be noted that air temperature does not always decrease as altitude increases. A study conducted by NACA and published in Technical Note 4352 Tables and Graphs of Normal-Shock Parameters at Hypersonic Mach Numbers and Selected Altitudes recorded an initial decrease as expected in temperature as altitude increased. However, surprisingly at a certain altitude the temperature increases again. The study showed that when the temperature was 15°C at sea level (altitude of 0 ft.), the temperature decreased at a linear rate from 15°C to -56°C at 36,000 ft. The temperature then remained constant at -56°C from 36,000 ft. to 82,020 ft. Then from 82,020 ft to 154,200 ft. a change occurred, the temperature increased from -56°C to 10°C. The temperature then remained at 10°C from 154,200 ft. to 173,885 ft. Then as expected temperature began to decrease again as altitude increased from 173,885 ft. to 246,000 ft., the temperature went from 10°C to -76°C. After 246,000 ft. the temperature remained at -76°C till an altitude of 295,280 ft. at which altitude no more data was collected.

The speed of sound in air can be calculated based on the temperature in degrees Celsius. The equation used is:

v = 331 + 0.6T                where v is in m/s and T is in °C

An aircraft moving at a speed less than the speed of sound is said to be traveling subsonic. An aircraft traveling at the speed of sound is doing just that. An aircraft traveling faster than the speed of sound is said to be traveling supersonic.

An aircraft’s speed is sometimes measured in Mach numbers. Mach 1 is equal to the speed of sound in the atmospheric conditions that the aircraft is flying in. Mach 1 will have a different value at different temperatures. Subsequent Mach numbers are multiples of Mach 1. Thus Mach 2 is twice the speed of sound, Mach 3 is three times the speed of sound, and so on. Speeds of Mach 6 or higher are said to be hypersonic.

When an aircraft travels less than the speed of sound (between Mach 0 and Mach 1) the sound waves emanating from the front of the aircraft travel in front of the aircraft and move forward away from the aircraft at a speed equal to the speed of sound minus the speed of the aircraft. Sound can only travel at the speed of sound, it will travel no faster and no slower, regardless of the speed of the source emanating the sound. Only changes in atmospheric conditions such as varying temperature can change the speed at which sound travels at. Sound waves consist of a series of consecutive alternating compressions (regions of higher air pressure) and rarefactions (regions of lower air pressure) of air, that oscillate parallel to the direction of propagation of sound. The distance between consecutive compressions, or the distance between consecutive rearfractions is the wavelength. The frequency is the rate at which the wave oscillates. Velocity, frequency and wavelength form the relation:

 v = f(wavelenght)      where v is velocity in m/s, f is frequency in hertz, and wavelength is in meters.

When an aircraft travels at the speed of sound the sound waves emanating from the front of the aircraft stay with the aircraft and pile up on the front of the aircraft. This causes extreme turbulence and buffeting of the aircraft. As the aircraft travels faster than the speed of sound, the aircraft travels faster than the sound it emits. The airplane actually moves ahead and away from the sound it emits at a speed equal to the speed of the aircraft minus the speed of sound. This creates pressure disturbances in the air resulting in the formation of shock waves. Shock waves produce sonic booms which are loud thunder-like sounds. Sonic booms can be extremely disturbing and irritating to people. They have also been none to cause damage to buildings, glass windows and other fragile items.  The diagram below shows the shapes of sound waves emited by an object at rest, an object traveling at the speed of sound, and the sound waves of an object traveling faster than the speed of sound.

To learn more about sonic booms click here.

Bibliography

Huber, Paul W., Technical Note 4352: Tables and Graphs of Normal-Shock Parameters at Hypersonic Mach Numbers and Selected Altitudes. Langley Aeronautical Laboratory.

Levinson, Nancy S., Chuck Yeager - The Man Who Broke the Sound Barrier.  Walker and Co., 1988.

Yeager, Charles E., and Janos, Leon, Yeager.  New York: Bantam, 1985.