Document created: 04 May 2004
Air University Review, July-August 1971

Sonic Boom and the Supersonic Transport

Major Richard M. Roberds

The planned production of a United States supersonic transport (SST) was intended as the next logical step in the evolution of space-age transportation. While there has not yet appeared to be a distinct military requirement for an SST, the Air Force nonetheless followed its progress with keen interest and anticipation. It was believed that, at minimum, spin-off from it would find valuable military application. Indeed, Dr. John S. Foster, Jr., Director of Defense Research and Engineering, seemed eminently right when he described the potential contribution of the supersonic transport to defense as “indirect but not insignificant” by “reinforcing the technological base upon which defense will be drawing for the development of military systems.”1

As the SST operates supersonically over populated areas of the globe, a sonic boom may be created that is capable of destroying property and provoking substantial public opposition. This fact is especially critical in light of the current emphasis on environmental pollution. The sonic boom from the SST looms as a possibly serious intruder into the nation’s justifiably deserved peace and quiet. The persistent lay question is simply whether the SST is worth the price of enduring its sonic boom.

Recent research has begun to shed some light on the problem. Notably, the Air Force has played a significant role in the experimental research toward an operational supersonic transport that will not be objectionable to society. To answer some of the questions concerning the impact on society of the sonic boom from the SST, the Federal Aviation Administration, in conjunction with the United States Air Force and several contracting firms, embarked on a series of sonic-boom measurement tests. These tests were the first major effort anywhere in the world to measure quantitatively the effects of the sonic boom on populated areas.

The test program was conducted at Oklahoma City from 3 February through 30 July 1964. The principal objective was to ascertain the public reaction to sonic booms of intensities on the order of 1.5 to 2.0 pounds per square foot (psf) peak overpressure. This was the predicted intensity of overpressure to be expected from an SST. Air Force B-58, F-l01, F-104, and F-106 aircraft were used to generate the booms.

A second phase of the Oklahoma City area test was conducted to study specifically the effects on structures of varying sonic-boom intensities. This test series was performed at White Sands Missile Range in New Mexico from 18 November 1964 through 15 February 1965. B-58 and F-104 aircraft were employed, and sonic booms were generated of intensities up to 38 psf peak overpressure.

A third test series was carried out at Edwards AFB, California, from 3 June to 23 June 1966 and from 31 October 1966 to 17 January 1967. In this program the Air Force was designated the implementation agency and program manager, with technical assistance from the Stanford Research Institute. Again, the determination of human reaction and structural response to the sonic boom was a prime objective. Peak overpressures up to 3.0 psf were generated by F-104, SR-71, and XB-70 aircraft. Sonic-boom ground overpressure measurements for flights at altitudes in excess of 70,000 feet and at speeds up to Mach 3.0 were provided by the SR-71.

In addition to these flight research programs, data have been made available from public complaints and damage claims from operational flights of military aircraft where sonic booms have been generated of routine necessity. The SR-71 Category III testing from 1 July to 30 September 1967 is an example of such operational stimulation of public reaction.

Another research effort is presently being conducted in which operational flights of the SR-71 are being used to generate sonic booms for study. This program is being conducted by the Environmental Science Services Administration of the U.S. Department of Commerce in the Pendleton, Oregon, and Goldburg, Idaho, areas.

Other ongoing research programs continue to study the various aspects of sonic booms. Experimental and theoretical research at NASA’s Langley and Ames research centers is being conducted on the feasibility of reducing or eliminating the sonic boom by modifying the shape of the airplane. This work may hold the eventual solution to the sonic-boom problem.

A consequence of these research efforts has been a substantial enhancement of understanding in three principal areas:

    · Generation and propagation of the sonic boom

    · Human behavioral response to the sonic boom

    · Effects of the sonic boom on structures and structural material.

It is not coincidental that these areas are the ones that were outlined in 1964 by the National Academy of Sciences’ Committee on SST-Sonic Boom as needing special study. While the gains made in each area have been extensive and certainly beyond the scope of a single article, it is interesting to review, if only in part, some of the fruits of the efforts.

Sonic-Boom Generation

An airplane traveling at supersonic speed is creating shock waves that will manifest themselves as a sonic boom if they reach the ground. The generation of the shock waves and their subsequent propagation through the atmosphere are well understood and substantiated by measurement. In fact, all the factors entering into the formation and final intensity of the boom can conveniently be placed in three categories: how the airplane is flown (flight conditions), atmospheric conditions, and airplane design. The fundamentals of each category are relatively simple.

flight conditions

An airplane that is creating a sonic boom will be flying at a particular altitude and Mach number and may or may not be maneuvering. These three flight conditions determine the magnitude of the sonic boom that is felt on the ground.

It is probably intuitive to the reader that as the altitude of the airplane increases, the sonic-boom intensity on the ground decreases. This is indeed the case; in fact, the altitude is the one single variable that has the greatest effect on sonic-boom reduction. The reason is twofold:  the magnitude of the shock wave diminishes with the distance traveled, and the intensity of the shock wave as it is generated decreases with the decreasing air density.

The variation of boom intensity with flight Mach number is not as intuitive. The peak overpressure of the sonic boom increases slowly with aircraft speed up to about Mach 1.4. As velocity increases above this point, the accompanying decrease in aircraft angle of attack becomes the predominant factor, and the boom intensity begins to decrease slightly. For practical purposes, this decrease is insignificant, and the boom intensity above Mach 1.4 may be regarded as remaining constant. 

If an airplane traveling at supersonic velocity maneuvers by turning, porpoising, or accelerating, the effect is to focus the sonic boom at points on the ground. The sonic booms so focused are known appropriately as superbooms. Recent French studies have indicated that magnification may be as high as five times under focusing conditions. Fortunately, such points encompass only 100 to 200 feet.

atmospheric conditions

Sonic-boom measurement tests have revealed variation in recorded peak overpressures from a single aircraft flying at constant speed and altitude. These variations are attributed to nonuniformities in the atmosphere. Clouds, turbulence, wind, and sharp temperature inversions are inhomogeneities in the atmosphere that alter the intensity of the sonic boom. Such atmospheric perturbations rarely cause a variation of more than 0.3 psf, however, and can be neglected in analyses of boom effects on communities.

An important phenomenon in the atmosphere that cannot be neglected is the refractive effect of the normal atmospheric temperature change on the shock-wave front. Since the speed of sound increases with increases in air temperature, as the shock-wave front nears the tank and enters warmer air, it bends forward. If the airplane is not moving at too high a supersonic speed (the shock front is not swept back too far), this refraction may cause the direction of travel of the shock front to become parallel with the ground. Under this condition, the sonic boom will not reach the ground and will not be heard. This phenomenon gives rise to the threshold Mach number effect. (Figure 1) The threshold Mach number is a speed above which an airplane must be flying for its boom to be felt on the ground. Under standard atmospheric conditions, the threshold Mach number for an airplane above 35,000 feet is around Mach 1.2.

Figure 1. Threshold Mach number.

Figure 1. Threshold Mach number.

The effect of temperature refraction acts on the sonic boom in another important way. It limits the area of ground that is exposed to the boom in the lateral direction (perpendicular to the airplane flight path). The term “lateral cutoff point” is used to describe the lateral distance from the flight path where the shock front has been refracted to move parallel with the ground. This, of course, is the border of the sonic-boom path. The boom path, or “bang zone,” will grow wider as aircraft altitude and Mach number increase. For an SST flying at 65,000 feet, the boom path will be 65 miles wide.

airplane design

The third general area under which the variables that affect the intensity of the some boom can be grouped is that of airplane design. Within this category fall such variables as aircraft weight, length, and what are known as design parameters. “Design parameters” means the details of the shape of an airplane.

The weight of the airplane has a very simple relationship to the intensity of the sonic boom generated. The sonic-boom peak overpressure varies directly with weight. The maximum takeoff weight of the American SST was expected to be around 750,000 pounds, more than twice the original design objective of 350,000 pounds prescribed in 1963. At this heavy weight, difficulty would certainly be expected from the overpressures generated if it were the only design consideration.

A factor that tends to affect the peak over-pressure is the length of the aircraft: the longer the airplane, the less intense is the sonic boom. The length of the projected Boeing 2707 SST was 298 feet, a length which would have offset, somewhat, the intensity of the sonic boom generated. However, the longer aircraft are also the heavier aircraft, so that, in general, larger airplanes generate larger booms.

A problem on which a significant amount of effort is currently being expended is that of determining how airplane design parameters affect the size of the boom. It has turned out to be one of the most difficult aspects of the sonic-boom problem, almost on a scale with determining how people will react to the boom. Yet it is a tremendously significant area in which a breakthrough may mean a solution to the entire boom problem.

Each of the variables that is known to affect the creation of a sonic boom can be mathematically represented and combined into an equation. This allows for the calculation of the peak overpressure of a sonic boom produced by an aircraft of varying size, shape, and weight under different flight conditions. Such theoretical determination of sonic-boom intensity has been developed to a high degree of dependability.

From a nomograph presented by John H. Wiggins, Jr., in his book Effects of Sonic Boom,2 I have constructed a nomograph depicting determination of overpressure. (Figures 2a and 2b) This nomograph is a product of present-day theory on the generation and propagation of the sonic boom. It can be used for reliable peak overpressure determination for the supersonic transport under varying flight conditions and weight. For illustrative purposes, a determination has been presented for an SST weighing 750,000 pounds and flying at 60,000 feet at Mach 2.7. The length of the SST was taken as 300 feet. As can be seen, the nominal peak overpressure under these conditions is 1.9 psf.

Figure 2a. Determination of nominal peak overpressure. Figure 2b. Continued measurement peak overpressue

Figure 2a. Determination of nominal peak overpressure. Figure 2b. Continued measurement peak overpressue

The other two areas where understanding has increased as a product of sonic-boom research are (1) human behavioral reaction to the sonic boom as it interrupts ordinary living activities and (2) damage to property from the sonic boom. Investigation within these two areas has been pointed toward answering one question: What level of sonic-boom intensity will be acceptable to society, considering both noise annoyance and boom damage?

On the basis of the data gained from the sonic-boom measurement tests, the permissible level of sonic-boom intensity may now be known. However, the maximum intensity level short of property damage is not necessarily the level that is acceptable to the public. Each area must be considered independently.

Human Behavioral Response

The most difficult part of the sonic-boom problem associated with the supersonic transport is determining how people will react to the boom. The variables in the problem are practically infinite in number and particularly elusive to measurement. The problem was stated in 1963 by Headquarters USAF:

. . . the effect that sonic booms will have on the general public remains an open question . . . Early work has served mainly to point out the extreme complexity of the problem. Not only must the magnitude of the sonic boom be considered, but also the complaint potential of the community being studied. It has been found that community tolerance depends on such factors as an awareness of what causes the booms, people’s feelings toward the Air Force and aircraft industry in general, neighborhood pride, and the presence or absence of other community problems.3

The Oklahoma City area tests revealed that other factors should be added to those cited above. The daily number of booms to which a community is subjected is an important consideration in determining how people will react to the sonic boom. Another factor to weigh is that a community with a history of exposure to sonic booms will tend to gain a degree of acclimation to their occurrence.

As a result of the work performed during the Edwards AFB test series, a method now exists whereby the public reaction to sonic booms of a particular intensity, occurring at a certain frequency per day, can be predicted. The method was devised by Karl D. Kryter and associates at the Stanford Research Institute. Dr. Kryter was the director for the psychological portion of the Edwards AFB experiments.

Kryter and his associates based their work on the “perceived noise decibel”(PNdB) of a sonic boom. The PNdB is a rating applied to aircraft noise that describes its annoyance or unacceptability. It is necessarily a subjective rating, for what may be extremely irritating to one person may not be so disturbing to another. An increase of ten PNdB is normally equivalent to doubling the “noisiness” of a sound.

Kryter established his PNdB levels from the subjective ratings by individuals of the noise from subsonic jet aircraft (KC-135) flying overhead at varying altitudes and engine power settings. This provided a good base to which sonic booms could be compared, since public reaction to subsonic aircraft noise is fairly well known. At Edwards, test subjects rated the acceptability of the noise from sonic booms of varying intensity against subsonic engine noise of known PNdB level. Kryter was thus able to correlate the noise from sonic booms with specific PNdB values. The results from this correlation are shown in Figure 3.4

The lower boundary of the affected zone in Figure 3 represents the noise rating assigned to sonic-boom overpressures by a community that had been acclimated to sonic booms. The upper boundary represents the reaction of a community that had had infrequent previous exposure to sonic booms.

An accurate prediction of the public reaction to sonic booms must not only consider the overpressure of the booms but should also take into account their frequency of occurrence. This is done by use of a rating called the “composite noise rating” (CNR). The CNR value for a noise is obtained from a mathematical relationship which includes the PNdB level and the number of noise occurrences (N). It is expressed by the relationship:

CNR = PNdB - 12 + ƒ

where ƒ is a number that increases as the number of occurrences per day increase (ƒ=10 log10N).5

Figure 3. Perceived noise levels of sonic boom nominal peak overpressure.

Figure 3. Perceived noise levels of sonic boom nominal peak overpressure.

Several studies have been made of the acceptability of subsonic jet noise, and the public reaction has been fairly well determined. The results of these studies are presented in Figure 4,6 which depicts the public reaction for a particular CNR value. The range of reactions depicted is to be expected, since each community’s reaction depends upon its particular complaint potential.

Since PNdB values have been assigned to sonic-boom overpressures by Kryter, et al., from the Edwards AFB experiments, a method is complete whereby public reaction to sonic-boom exposure can be predicted. From Figure 3 the PNdB can be obtained that corresponds to the average peak overpressure of a series of sonic booms. A CNR value can be calculated from the PNdB value and number of sonic booms occurring per day. From Figure 4 the CNR value can be converted to a range of public reactions; to determine which reaction within that range should be chosen, such factors as community motivation toward aviation and people’s feelings toward the activity creating the sonic booms should be weighed. The center line of the figure represents an average community.

Figure4. Relation between noise and corresponding community response.

Figure 4. Relation between noise and corresponding community response.

Damage to Property

Recorded incidents of damage attributed to sonic forces are not new to history. In fact, the first recorded occurrence took place thousands of years ago at the ancient Palestinian city of Jericho. The event was the Battle of Jericho, where, purportedly, Joshua, with a mighty blast of trumpets and shout of voices, tumbled the Jericho walls. However, a more recent investigation of the event by Major Tollack, chief engineer of the Allenby invasion of Palestine in World War I, suggested that the wall was not felled by the blast of horns and shouting. Major Tollack proposed that the wall felt because of the undermining of the foundation stones by tunneling operations while the defenders of Jericho were distracted by Joshua’s horn blowing.7 Such an explanation might seem more plausible than that originally claimed.

It is interesting that this event is strangely analogous to the present-day sonic-force problem—the boom from a supersonic airplane. For while there are many damage claims, purportedly due to sonic-boom forces, further investigation often reveals that other causes of the damage were more probable. Additionally, it is often military investigators who arrive at the correct explanation.

A major question posed by the advent of the supersonic transport concerns structural response to sonic booms: At what level of sonic-boom intensity can damage be expected? The answer to this question will not only aid in assessing legitimate sonic-boom damage claims; it will also serve to predict damage from the sonic boom of the anticipated SST.

The precise determination of the response of a structural element to a sonic boom is a good deal more complicated than just measuring the peak overpressure of the boom. The myriad of variables affecting the sonic boom as it is generated and propagated, plus the complexity of the response by a structure, make it difficult, if not impossible, to predict exactly the damage that will be caused by a particular supersonic overflight. To answer the question of damage expectancy, two further questions must be posed: Can the variation in boom intensity be predicted from what is known about the generation of the sonic boom? And is there some simple quantity, such as peak overpressure, to which a corresponding structural response can be predicted to an acceptable degree?

The book by Wiggins outlines a statistical method that circumvents the complexities of the problem and offers answers to these questions.8 The many variables involved in determining both the maximum value of over-pressure and the structural response cause them to behave like random variables. In fact it is reasonable to assume that the sonic-boom phenomena have a normal bell-shaped distribution, which renders the problem amenable to a statistical approach. The use of statistics provides a means to predict the variation in the sonic-boom intensity. It also allows the use of peak overpressure as an index for a corresponding damage probability.

variation in sonic boom intensity

As the SST flies supersonically at a particular altitude and speed, it will generate a sonic boom whose peak overpressure can be theoretically determined by, for example, a nomograph (as in Figure 2). This value of peak overpressure is called the nominal peak overpressure. In practice, however, because of the many unpredictable variables such as non-uniform atmospheric conditions, the peak overpressure actually experienced rarely corresponds exactly to the nominal peak over-pressure predicted by theory.

A meaningful analysis of the damage to be expected from a supersonic transport must include the higher levels of overpressure that often occur. The highest peak overpressure likely to occur when a nominal peak over-pressure has been calculated is expressed by the equation.

Pmax = Pnom (1 + NCv)

where Pmax is the highest likely peak overpressure, Pnom is the nominal peak overpressure, Cv is the coefficient of variation (Cv = .20 on a normal day), and N is the significance factor. (For N 2.3, 99% of the time the peak overpressure will be at or below the Pmax.)

It should be clear that use of the Pmax in damage prediction will provide a conservative result, since this high value of peak over-pressure will occur only rarely. However, since there is a reasonable probability of a peak overpressure occurring at or near the Pmax value, the use of Pmax is warranted.

damage probability

The damage that will be inflicted by a sonic boom of particular peak overpressure cannot be precisely stated. Instead, a statistical analysis must be employed that will predict the probability of damage. The highest likely peak overpressure determined by the above method should be used as the intensity of the boom.

Since glass is the material most susceptible to damage from sonic booms, it can serve as a convenient threshold index for predicting the sonic-boom intensity level that will begin to cause damage. Fortunately, glass damage data are of sufficient quality and quantity that a model for predicting glass damage can be constructed. Just such a representation is shown in Figure 5, which presents the probability of damage to a glass pane from a single boom of particular peak overpressure.9 A probability of 1 means the pane is certain to break; a probability of 10-1 (or 1/10) means one pane out of ten will break, and soon.

At first sight, the curve in Figure 5 appears to be overly conservative. For instance, at 10 psf, which represents an unusually loud boom, there is only one chance in a thousand that a particular pane will break. Yet the probability of glass damage to one pane does not have to be very large to have one pane break when literally millions of panes are exposed to a certain overflight.

Figure 5. Probability of window pan breakage

Figure 5. Probability of window pan breakage

The sonic-boom intensity level at which damage begins to occur is not a fine, precise point. It can be taken as that boom intensity where glass breaks. But this intensity is a hazy range of values that depends upon the chosen probability of glass breakage. There is no problem here, however, since at the lower sonic-boom levels where community reaction is acceptable the probability of glass breakage is entirely negligible, even when millions of panes are considered.

We have seen that recent sonic-boom research programs have provided real strides toward the amelioration of an unfortunate problem: that an SST, with its many benefits, would also bring a formidable sonic boom, with its unpredictable social and economic consequences. The sonic-boom measurement programs have provided quantitative information for a better knowledge of the effect of the sonic boom on society. Indeed, because of light shed on the probable public reaction to the boom, the first-generation SST will most likely be restricted from supersonic flight except over the oceans.

The current acceptable level of sonic-boom magnitude has been reasonably well established. Advancing technology shows promise that the sonic boom can be reduced below the critical level and that a second-generation supersonic transport, unlimited in its operation, may lie in the future.

Air Command and Staff College


1. Edgar E. Ulsamer, “The SST Is Vital to the National Interest,” Air Force and Space Digest, Vol. 53, No. 2 (February 1970), p. 52.

2. John H.Wiggins, Jr., Effects of Sonic Boom (Palos Verdes, California: J. H. Wiggins Company, 1969), pp. 14, 15.

3. The Sonic Boom Problem, Office of the Director of Development Planning, Hq USAF, March 1963, p. 26.

4. Figure 3 has been constructed from data presented in K. D. Kryter, P. J. Johnson, and J. R. Young, Psychological Experiments on Sonic Booms Conducted at Edwards Air Force Base, Final Report (Menlo Park, California: Stanford Research Institute, August 1968), p. 16.

5. Karl D. Kryter, “Sonic Booms and Supersonic Transport,”  Science, Vol. 163, No. 3865 (24 January 1969), p. 365.

6. Ibid. (Reproduced courtesy K. D. Kryter.)

7. Wiggins, p. 96.

8. Ibid., pp. 133-36.

9. Ibid., p. 87. (Reproduced courtesy J. H. Wiggins.)


Major Richard M. Roberds (M.A., Kansas University) is an Air Liaison Officer, III DASC Task Force, Vietnam. He has been a research physicist, Air Force Weapons Laboratory; a T-38 flight instructor in Undergraduate Pilot Training, where he taught Applied Aerodynamics; and an F-102 pilot in Air Defense Command. Major Roberds is a 1970 graduate of Air Command and Staff College.


The conclusions and opinions expressed in this document are those of the author cultivated in the freedom of expression, academic environment of Air University. They do not reflect the official position of the U.S. Government, Department of Defense, the United States Air Force or the Air University.

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