SP-367 Introduction to the Aerodynamics of Flight

VI. SUPERSONIC FLOW

[119] The previous discussion has centered mainly on the transonic drag rise and how, through proper design, it may be delayed. Many of the techniques used also are directly applicable in designing the airplane to fly with minimum wave drag in the supersonic regime.

If one returns to the discussion of shock formation, it was shown that a bow shock wave will exist for free-stream Mach numbers above 1.0. (See fig. 88.) In three dimensions, the bow shock is in reality a cone in shape (a Mach cone) as it extends back from the nose of the airplane. Figure 99 demonstrates that the Mach cone becomes increasingly swept back with increasing Mach numbers. As long as the wing is swept back behind the Mach cone, there is subsonic flow over most of the wing and relatively low drag. A delta wing (fig. 100) has the advantage of a large sweep angle but also greater wing area than a simple swept wing to compensate for the loss of lift usually experienced in sweepback. But, at still higher supersonic Mach numbers, the Mach cone may approach the leading edge of even a highly swept delta wing. This condition causes the total drag to increase rapidly and, in fact, a straight wing (no sweep) becomes preferable. Figure 101 shows qualitatively the drag advantage that a straight wing has over a swept or delta wing at higher Mach numbers.

Sweepback has been used primarily in the interest of minimizing transonic and supersonic wave drag. At subsonic Mach numbers, however, the disadvantages are dominant. They include high induced drag (due to small wing span or low aspect ratio), high angles of attack for maximum lift, and reduced effectiveness of trailing-edge flaps. The straight-wing airplane does not have these disadvantages. For an airplane which is designed to be multimission, for example, subsonic cruise and supersonic cruise, it would be advantageous to combine a straight wing and swept wing design. This is the logic for the variable sweep or swing-wing. Figure 102 shows (L/D)max, a measure of aerodynamic efficiency, plotted against Mach number for an optimum straight-wing and swept-wing airplane. Although not necessarily equal to the optimum configurations in their respective speed regimes, it is evident that an airplane with a swing-wing capability can in a multimissioned role, over the total speed regime, be better than the other airplanes individually. One major drawback of the swing-wing airplane is the added weight and complexity of the sweep mechanisms. But technological advances are solving these problems also. Figure 103 shows a variety of modern airplanes employing a swing-wing.

[120] In addition to low-aspect-ratio wings at supersonic speeds, supersonic wave drag may also be minimized by employing thin wings and using area ruling. Also long, slender, cambered fuselages minimize drag and also improve the spanwise lift distribution.

Figure 99.- Mach cone and use of sweep.

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Figure 100.- Delta-wing airplane (F-106).

Figure 101. - Wing design drag coefficients as functions of Mach number.

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Figure 102. Variation of (L/D)max with Mach number. Variable sweep airplane.

[From left to right, top to bottom]
(a) Mirage IIIG.
(b) Fitter B.
(c) F-111A
(d) F-14A

Figure 103.- Modern variable-sweep airplanes.

[123] The SST

On June 5, 1963 in a speech before the graduating class of the United States Air Force Academy, President Kennedy committed this nation to "develop at the earliest practical date the prototype of a commercially successful supersonic transport superior to that being built in any other country in the world ...." What lay ahead was years of development, competition, controversy, and ultimately rejection of the supersonic transport (SST) by the United States, and it remains to be seen whether the British-French Concorde or Russian TU-144 designs will prove to be economically feasible and acceptable to the public.

NASA did considerable work, starting in 1959, on basic configurations for the SST. There evolved four basic types of layout which were studied further by private industry. Lockheed chose to go with a fixed-wing delta design; whereas, Boeing initially chose a swing-wing design.

One problem associated with the SST is the tendency of the nose to pitch down as it flies from subsonic to supersonic flight. The swing-wing can maintain the airplane balance and counteract the pitch-down motion. Lockheed needed to install canards (small wings placed toward the airplane nose (fig. 104(a)) to counteract pitch down. Eventually, the Lockheed design used a double-delta configuration (fig. 104(b)) and the canards were no longer needed. This design proved to have many exciting aerodynamic advantages. The forward delta begins to generate lift supersonically (negating pitch down). At low speeds the vortices trailing from the leading edge of the double delta (fig. 105(a)) increase lift as shown in figure 105(b). This means that many flaps and slats could be reduced or done away with entirely and a simpler wing design was provided. In landing, the double delta experiences a ground-cushion effect which allows for lower landing speeds. This is important since three-quarters of the airplane accidents occur in take-off and landing. Figure 106 shows the British-French Concorde and the Russian TU-144 prototypes. They use a variation of the double delta wing called the ogee wing. It, too, uses the vortex-lift concept for improvement in low-speed subsonic flight.

(a) Lockheed CL-823.
(b) Lockheed double delta.

Figure 104.- Lockheed SST configurations.

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(a) Vortices on double delta wing.
(b) Lift coefficient increase due to vortices.

Figure 105.- Lifting vortices of double delta wing.

Ultimately, Boeing with a swing-wing design was selected as the winner of the U.S. SST competition. Figure 107 shows the evolution of this design originally derived from one of the NASA designs. The size of the airplane grew to meet airline payload requirements. Major design changes were incorporated into the Boeing 2707-100 design. The supersonic cruise lift-drag ratio increased from 6.75 to 8.2 and the engines were moved further aft to alleviate the exhaust impinging on the rear tail surfaces. Despite the advantages previously quoted for a swing-wing concept, technological advances in construction did not appear in time. Because of the swing-wing....

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(a) British-French Concorde [top]
(b) Russian TU-144.

Figure 106. British-French, and Russian SST airplanes.

Figure 107.- Evolution of Boeing SST design.

[126] ....mechanisms and beefed-up structure due to engine placement, incurable problems in reduction of payload resulted. Boeing had no recourse but to adopt a fixed-wing concept. Figure 107 shows the final configuration adopted-the B2707-300. Political, economic, and environmental factors led the United States to cancel the project in 1972.

While the British-French Concorde and Russian TU-144 fly, research is still continuing into advanced supersonic transports in the United States. Whereas, the Concorde and TU-144 cruise at M = 2.2 to 2.4, and the Boeing design cruised at M = 2.7, configurations with a cruise speed of M = 3.2 are being analyzed. One such design tested at the NASA Langley Research Center is shown in figure 108.

Figure 108.- Langley advanced SST design.

[127] Sonic Boom

One of the more objectionable of the problems facing any supersonic transport is commonly referred to as the "sonic boom." To explain sonic boom, one must return to a description of the shock-wave formation about an airplane flying supersonically. A typical airplane generates two main shock waves, one at the nose (bow shock) and one off the tail (tail shock). Shock waves coming off the canopy, wing leading edges, engine nacelles, etc. tend to merge with the main shocks some distance from the airplane. (See fig. 109.) The resulting pressure pulse changes appear to be "N" shaped as shown. To an observer on the ground, this pulse is felt as an abrupt compression above atmospheric pressure followed by a rapid decompression below atmospheric pressure and a final recompression to atmospheric pressure. The total change takes place in one-tenth of a second or less and is felt and heard as a double jolt or boom.

Figure 109.- Sonic-boom generation.

The sonic boom, or the overpressures that cause them, are controlled by factors such as airplane angle of attack, altitude, cross-sectional area, Mach number, atmospheric turbulence, atmospheric conditions, and terrain. As shown in figure 110, the overpressures will increase with increasing airplane angle of attack and cross-sectional area, will decrease with increasing altitude, and first increase and then decrease with increasing Mach number.

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Figure 110.- Factors affecting sonic-boom overpressures.

Turbulence in the atmosphere may smooth the "N" wave profile and thus lessen the impact of the boom or, on the other hand, may in fact amplify the overpressures. Reflections of the overpressures by terrain and buildings may cause multiple booms or post-boom aftershocks. In a normal atmospheric profile, the speed of sound increases with decreasing altitude. Figure 111 shows that the directions in which the overpressures travel are refracted in this normal case and that they will at some point curve away from the Earth. The strongest sonic boom is felt directly beneath the airplane and decreases to nothing on either side of the flight path. It is interesting to note that a turning supersonic airplane may concentrate the set of shock waves locally where they intersect the ground and produce a superboom.

Figure 111.- Refraction of shock waves.

[129] Perhaps the greatest concern expressed about the sonic boom is its effect on the public. The effects run from structural damage (cracked building plaster and broken windows) down to heightened tensions and annoyance of the citizenry. For this reason, the world's airlines have been forbidden to operate supersonically over the continental United States. This necessitates, for SST operation, that supersonic flight be limited to overwater operations. Research for ways in which to reduce the sonic boom continues.