Fluid Mechanics

Drag coefficient vs Mach number plot
Sketch of scaled drag (CD) vs freestream Mach number (M). The quantity Mcr < 1 is the critical Mach number, i.e., the freestream Mach number at which transonic flow effects first appear. The curve labeled "Supersonic Wave Drag" is the wave drag computed in the classical theory of supersonic flows.

Sonic Boom, Sound Barrier, and Condensation Clouds
Sound Barrier

The idea of a sound barrier is something that has caught the public's imagination and has been represented in many ways. Even in relatively modern films such as "The Right Stuff", the world becomes hazy and distorted as the brave test pilot pushes through the speed of sound. Perhaps the influence of Star Trek and popular discussions of the theory of relativity (and the impossibility of traveling faster than the speed of light) have influenced the view of the sound barrier.

The truth of the matter is that there is a sound barrier, but it is not as exciting or mysterious as the popular view would have us think. The sound barrier can be seen in the sketch at the right which depicts a scaled version of the drag force acting on objects traveling at speeds near the speed of sound. Aerodynamicists refer to flow or travel at speeds near that of sound as transonic speeds. As the speed of of an object increases, the drag force, and therefore the power required to maintain or increase the speed, suddenly and strongly increases as the sound speed is approached.

There are two reasons for this increase. The first reason can be seen by considering the drag at supersonic speeds, i.e., at speeds which exceed the speed of sound. At supersonic speeds, shock waves are inevitably present; see also my discussion of sonic boom. Just as in the case of water waves generated by a boat, the existence of these shock waves generate a type of drag called "wave drag". Because the shock waves and their drag are not present in subsonic flight, i.e., flight at speeds below the speed of sound, there will be an additional source of drag and power loss which will need to be accounted for when the aircraft is designed.

Sketch of a typical transonic flow including shock-induced separation. Here the freestream is taken to be subsonic
Sketch depicting the flow around a wing at a speed which is just slightly below the speed of sound. The symbol M denotes the local Mach number which, in turn, is just the ratio of the local flow speed to the local sound speed.
A second contribution to the drag associated with the sound barrier is due to the fact that the disturbance due to the wing and even the generation of lift will cause shock waves to appear in the flow. An example of these shock waves is seen in the sketch at the left. If the flight speed is less than the ambient speed of sound, these shocks will terminate somewhere in the flow and will normally not extend to very large distances from the aircraft. These shock waves contribute their own wave drag, now at subsonic speeds. More importantly, these shock waves frequently cause the flow near the wing or body to separate forming the wake sketched at the left. This wake is a second source of drag. In fact, wake drag is the principal source of drag for non-streamlined bodies, even at low speeds. In essence, the shock waves that form in transonic flow convert a streamlined wing or body into a non-streamlined wing or body.

The shock does not only create additional drag. It changes the force distribution around the wing leading to the "compressibility tuck" observed in the early 1940s by test pilots on the Lockheed P-38. If the control surfaces for the wing or aircraft become buried in the wake, they can become ineffective. This lack of effectiveness comes at an awkward time because of the aforementioned pitching problem and the fact that the wake causes considerable vibration and variation of the forces on the wings. The overall aircraft design certainly needs to be modified to account for the physics of transonic flow. Some have recognized that one can always overcome the transonic drag with more powerful engines and have said that the real barrier is a control barrier.

When the speed of the aircraft is sufficiently far above the speed of sound the shock wave moves to the rear of the aircraft or wings and the adverse effects of a shock in the middle of the wing is no longer a problem. At these higher speeds the only drag is the wave drag mentioned above. Thus, the additional drag at transonic speeds leads to the hump seen in the sketch at the top of the page.

It should be noted that the transition from a speed which is just below the sound speed to one which is just above the sound speed is smooth and inconsequential. In fact, the flow picture near the wing or body at a slightly supersonic speed is essentially the same as that at a slightly subsonic speed. The primary difference is in the global flow picture where a (new) bow shock appears far ahead of the wing or body. The shock sketched above may have already moved to the tail of the shock. Both it and the bow shock will extend to infinity, i.e., to large distances from the wing or body.

Historically, the concepts presented here were well understood by engineers and scientists working on high speed aircraft in the first half of the 20th century. By the late 1940s, no competent engineer or test pilot thought that there was anything mysterious (beyond the mysteries of complex aeronautical design itself) about the sound barrier.

The term "sound barrier" arose when a reporter was interviewing W.F. Hilton (a British aeronautical engineer). Hilton showed the reporter the above hump in the drag curve and remarked that it presented a barrier to achieving higher speeds. In his story, the reporter coined the term sound barrier and it has been part of the language ever since.

In conclusion, nothing physical is "broken" when an aircraft accelerates the from subsonic to supersonic speeds. Nor is it the source of sonic boom.


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