Sonic Boom Propagation

Basics to Know About Supersonic Flight

• Supersonic and subsonic speeds are relative to the speed of sound in the atmosphere.
• 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.
• Since temperature varies as altitude above ground level increases, the speed of sound varies as altitude increases.

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

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

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.

What is a sonic boom?

A sonic boom is a thunder-like sound produced when an aircraft travels faster than the speed of sound. Air is a fluid and is pushed apart with great force as an aircraft traveling at supersonic speeds cuts through the air, forming a shock wave of compressed air, similar to the bow waves created by a boat as it cuts through the water.

Photo shows pressure density of shock waves emitted by a T-38.  Dark regions indicate higher pressure, while lighter regions indicate lower pressure.

Haering, Edward A., Jr. Dryden Fact Sheet: Schlieren Photography - Ground to Air. [online]. Available: www.dfrc.nasa.gov/PAO/PAIS/HTML/FS-033-DFRC.html, June 1, 1997.

• Shock waves have the shape of a cone with its vertex located at the nose of the aircraft and pointing in the direction of travel of the aircraft.
• The cone spreads out behind the aircraft and increases in diameter as distance behind the aircraft increases.
• The cone shaped shock wave moves along with the aircraft at the same speed as the aircraft.
• The shock wave creates a sonic boom at each point in space that it passes.
• The air pressure within the shock wave at ground level is usually only a few pounds per square foot greater than normal atmospheric pressure. This is about the same pressure difference experienced by a change in elevation of about 20 to 30 feet. It is the rate of change in air pressure, or the amount of time during which the air pressure is released that makes the sonic boom audible.

• The additional pressure above normal atmospheric pressure is called overpressure.
• If the overpressure were released slowly it would produce little sound. When this overpressure is quickly released during a very short time interval it generates a sonic boom. This can be compared to a tank containing pressurized air. If the air is slowly released only a slight hissing noise will be heard. If on the other hand, the tank suddenly bursts open, instantly releasing all the pressurized air inside it, it will create a loud explosion. Thus it is the rate of change of air pressure, the instantaneous change in air pressure from normal pressure to overpressure and back again to normal air pressure that creates the sonic boom.

These photos show the pressure structure of shock waves for T-38, SR-71, F-18 aircraft.

Stacy, Kathryn  Digital Enhancement of Schlieren Photography. [online] Available: davl-www.larc.nasa.gov /stacy/Focused_schlieren, June 1, 1997.

This diagrams shows the cone shaped shock wave emanating from a vehicle.

Brown, Fred A. Hyper-X Hypersonic Experimental Research Vehicle. [online]. Available: www.dfrc.nasa.gov/Projects/HyperX/index.html, June 1, 1997.

Why are Sonic Booms and Shock Waves Worth Studying?

Shock waves seem to be an unavoidable aspect of supersonic transport. Shock waves and sonic booms can be disturbing to humans, and the environment. They also have the potential to damage buildings and structures. This could be a negative side-affect of HSCT (High Speed Civil Transport), if this aspect is not properly diagnosed, and a solution presented. The HSCT program objective is to develop a supersonic civilian transport vehicle that will be environmentally friendly with low levels of noise pollution at ground level.

Factors Affecting Sonic Boom Intensity

• The intensity of sonic booms are affected by :
• Weight, size and shape of the aircraft.
• Altitude.
• Attitude—orientation of the aircraft’s axes relative to the its direction of motion.
• Flight path.
• Atmospheric and weather conditions.
• As the size and weight of the aircraft increases, the intensity of the sonic boom increases. This is because a larger aircraft displaces more air, and a heavier aircraft needs a greater force of lift to sustain flight. Thus creating a louder and stronger sonic boom.
• As the altitude of the aircraft increases the intensity of the sonic boom at ground level decreases. The shock cone gets wider as distance behind the aircraft increases.
• The sonic boom cone spreads out beneath the aircraft about one mile for each 1000 feet decrease in altitude. Thus an aircraft flying faster than the speed of sound at an altitude of 60,000 feet will produce a sonic boom cone 60 miles wide at ground level.
• As the cone gets wider the force contained in it is spread over a larger area. Thus by the time the shock wave reaches the ground, most of the pressure has been dissipated, and therefore the sonic boom produced at ground level is less intense.
• The lateral spreading of the sonic boom is dependent only upon altitude, speed and the atmospheric conditions.
• Increasing altitude is the most effective method of reducing sonic boom intensity at ground level.
• The longer and more slender the aircraft, the weaker the shock waves. On the other hand the fatter and more blunt the aircraft is the stronger the shock wave produced.
• At speeds just over Mach 1, the direction of propagation and strength of shock waves are affected by wind, speed, direction, air temperature and pressure. But their affect is small at speeds greater than Mach 1.3.
• Distortions in the shape of the sonic boom signatures can also be affected by air turbulence near the ground. This will cause variations in overpressure levels.
• The motion of the aircraft can cause distortions in shock wave patterns. Maneuvers such as pushovers, S-turns and accelerating can amplify the intensity of the shock wave. Hills, valleys and other topographic features can create multiple reflections of shock waves thus affecting intensity.

Sample Overpressure Data

Overpressure in pounds per square foot is used to measure sonic booms. Overpressure is the amount of pressure above normal atmospheric pressure.

• Normal air pressure is 2,116 psf or 14.7 psi.
• At 1 psf of overpressure, no damage to structures occurs.
• 1 to 2 psf of overpressure occur at ground level from aircraft flying at supersonic speeds at normal operating altitudes. Overpressure above 1.5 psf is irritating to people.
• At 2 to 5 psf some minor damage can occur to structures.
• As overpressure increases, the chance of structural damage increases. Structures in good condition can withstand overpressures of up to 11 psf.
• 20 to 144 psf are experienced at ground level when aircraft fly at supersonic speeds at altitudes of less than 100 feet. Such levels of overpressure have been experienced by humans without injury.
• At 720 psf damage to eardrums results. At 2160 psf lung damage occurs.

The following over pressures at ground level have been measured for several aircraft:

• 0.8 psf for the F-104 at Mach 1.93 and 48,000 feet.
• 0.9 psf for the SR-71 at Mach 3 and 80,000 feet.
• 1.25 psf for the Space Shuttle at Mach 1.5 and 60,000 feet during landing approach.
• 1.94 psf for the Concorde SST at Mach 2 and 52,000 feet.

The SR-71 Experiment on Propagation of Sonic Booms

Haering, Edward A., Jr. Preliminary Airborne Measurements For The SR-71 Sonic Boom Propagation Experiment. [online].  Available: www.dfrc.nasa.gov/DTRS/1995/HTML/TM-104307/index.html, June 1, 1997.

• The purpose of the experiment is to study the propagation of sonic booms. The data collected from the experiment will be used in the development of a high speed civil transport (HSCT). Such a transport vehicle is not anticipated until the next century.
• The experiment consisted of: The SR-71 aircraft flying at 3 different altitudes and 2 different speeds. An F-16XL aircraft was used to gather overpressure data at different vertical separations below the SR-71. A YO-3A aircraft was also used, but its data will not be discussed here.

Haering, Edward Jr.  SR-71 Experiment on Propagation of Sonic Booms. [online]  Available: www.dfrc.nasa.gov /DTRS/1996/HTML/DRC-95-32/index.html, June 1, 1997.

• It was necessary to gather sonic boom signatures above the turbulent atmospheric layer near the ground, since this section of the atmosphere can distort sonic boom signatures.

• It was also necessary to gather the data at an altitude above the level where the shock waves coalesce or merge and form N-waves.

• In the experiment, an F-16XL aircraft would fly at several vertical separations below the SR-71 while the SR-71 would fly at a constant altitude and Mach number. The F-16XL would start behind the shock waves of the SR-71 and fly at a speed faster then the SR-71, so as to fly through the shock waves. As it passed through the shock waves, pressure instrumentation for signature measurement recorded the changes in atmospheric pressure created by the shock waves emanating from the SR-71. The F-16XL would then slow its speed slightly and allow the SR-71 to past it, recording additional data.

• Shock wave pressures can be amplified by the shape of the sonic boom probe used to record the data.

• The ratio of the overpressure measured by the probe to the actual overpressure is called the reflection factor.

• The preliminary measurement of the F-16XL reflection factor is 1.0, therefore the reflection factor should not affect the data, and all measurements are actual overpressure.

• Below is a graph of the sonic boom signature for an F-18 recorded at ground level by the F-16XL. This data was compared to other ground sensors, and used to determine the reflection factor. Notice that at ground level there are only two main shock waves. Data collected at higher altitudes will show several shock waves.

Haering, Edward A., Jr. Preliminary Airborne Measurements For The SR-71 Sonic Boom Propagation Experiment. [online]. Available: www.dfrc.nasa.gov/DTRS/1995/HTML/TM-104307/index.html, June 1, 1997.

Results of the Experiment

• When the F-16XL probed within a 1000 ft. vertical separation of the SR-71 there were apparent indications that the shock waves were being crossed. These indicators were:
• Feeling the change in cabin pressure by the pilot.
• Hearing the SR-71 engines when aft of the tail shock.
• Aircraft being slightly jostled by the shock waves.
• When the F-16XL probed shock waves at vertical separations greater than 1000 ft., the pilot was unaware when the shock waves were being penetrated. However the sensors on the F-16XL did measure shock wave signatures.
• Previous experiments have shown that overpressure should be a function of vertical separation to the -3/4 power, and this experiment confirms this relationship.

The Sonic Boom Signatures

As vertical separation below the SR-71 increases, the shock waves move behind the SR-71 in a cone shape this is shown in the diagram below:

Haering, Edward A., Jr. Preliminary Airborne Measurements For The SR-71 Sonic Boom Propagation Experiment. [online]. Available: www.dfrc.nasa.gov/DTRS/1995/HTML/TM-104307/index.html, June 1, 1997.

Haering, Edward Jr.  SR-71 Experiment on Propagation of Sonic Booms. [online]  Available: www.dfrc.nasa.gov/DTRS/1996/HTML/DRC-95-32/index.html, June 1, 1997.

Below are sonic boom signatures measured at 3 different altitudes, and 2 different speeds:

Haering, Edward A., Jr. Preliminary Airborne Measurements For The SR-71 Sonic Boom Propagation Experiment. [online]. Available: www.dfrc.nasa.gov/DTRS/1995/HTML/TM-104307/index.html, June 1, 1997.

The data from the above graphs has been translated into simplified cross sectional diagrams of shock wave pressures. These cross sectional pressure diagrams are shown below, and are in the order corresponding to the above graphs:

Several Trends can be noted from these diagrams:

• As vertical separation increases:
• Overall signature length increases.
• The overpressures decrease.
• Inlet and canopy shocks move toward bow shock.
• Tail shock moves aft.
• Exhaust plumes cause gradual decrease in pressure after the tail shock.
• Tail and inlet/wing shocks create the highest overpressure.
• As altitude of SR-71 increases from 31,000 to 48,000 ft. overpressures decrease.

The ground level recorded signatures are shown below:

Haering, Edward A., Jr. Preliminary Airborne Measurements For The SR-71 Sonic Boom Propagation Experiment. [online]. Available: www.dfrc.nasa.gov/DTRS/1995/HTML/TM-104307/index.html, June 1, 1997.

• As the weight of the SR-71 increases, a greater force of lift is needed to maintain flight. This has an affect on the merging of shock waves.
• At a gross weight of 77,000 lbf. bow and inlet shocks are separate.
• At a gross weight of 96,000 lbf. bow and inlet shocks are separate, but less distinct.
• At a gross weight of 106,000 lbf. bow and inlet shocks coalesce and form a single higher pressure shock wave.

Conclusion:

This data shows why shock waves are so destructive to buildings. Each high pressure region of a shock wave is followed by a rarefaction. The greater the initial pressure rise, the greater the rarefaction and the more negative the overpressure. At ground level usually only two shock waves are experienced. The rapid change in air pressure from positive overpressure to negative overpressure and back to normal air pressure caused by a sonic boom causes a series of imploding forces followed by exploding forces to be applied to a building, since the air pressure inside the building remains at 1 atmosphere while the pressure outside rapidly fluctuates. This causes the walls and windows of a building to be pushed in and out by the changing forces exerted by rapid changes in air pressure.  This causes the structure to resonate at destructive frequencies. At 31,000 ft, the temperature is about -43°C. The speed of sound at this altitude is 287 m/s or 941 ft./s (Mach 1). At this altitude Mach 1.25 is 1,442 ft./s, or 983 mph, and the length of the sonic boom signature at ground level is about 200 ft. Thus at this speed and altitude, it takes only 0.14 seconds for the entire sonic boom signature to sweep over a point on the ground. During this short instant in time the rapid fluctuation in air pressure occurs at ground level.

Refined and corrected data will be published by NASA’s Dryden Flight Research Center in the near future.

This webpage has been produced and published by David Gallo, for educational purposes.

Special Thanks to NASA for providing freely distributable resources on the internet.

Also Special Thanks to Mr. Haering at NASA's Dryden Flight Research Center for his explanation of tail shock signatures.

Bibliography:

Haering, Edward A., Jr. Sonic Booms Fact Sheet. [online]. Available: www.dfrc.nasa.gov/PAO/PAIS/HTML/FS-016-DFRC.html, June 1, 1997.

Haering, Edward A., Jr. Dryden Fact Sheet: Schlieren Photography - Ground to Air. [online]. Available: www.dfrc.nasa.gov/PAO/PAIS/HTML/FS-033-DFRC.html, June 1, 1997

Haering, Edward A., Jr. Preliminary Airborne Measurements For The SR-71 Sonic Boom Propagation Experiment. [online]. Available: www.dfrc.nasa.gov/DTRS/1995/HTML/TM-104307/index.html, June 1, 1997.

Haering, Edward A., Jr. SR-71 Experiment on Propagation of Sonic Booms. [online]. Available: www.dfrc.nasa.gov/DTRS/1996/HTML/DRC-95-32/index.html, June 1, 1997.