The Area Rule and Transonic Flight

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Increase in wave drag at transonic Mach numbers
Effect of the area rule on overall vehicle shape
Effect of the area rule on the F-102
Whitcomb area rule test models: (a) cylindrical fuselage, (b) fuselage with wings, (c) bulged fuselage, (d) waited fuselage with wings

Volume distribution of a Sears-Haack body

The area rule is an important concept related to the drag on an aircraft or other body in transonic and supersonic flight. The area rule came into being in the early 1950s when production fighter designs began pushing ever closer to the sound barrier. Designers had found that the drag on these aircraft increased substantially when the planes traveled near Mach 1, a phenomenon known as the transonic drag rise illustrated below. This increase in drag is due to the formation of shock waves over portions of the vehicle, which typically begins around Mach 0.8, and this drag increase reaches a maximum near Mach 1. Because of its source, this type of drag is referred to as wave drag.

Since the physics of supersonic flight were still largely a mystery to manufacturers, designers had no idea how to address this problem except to provide their aircraft with more powerful engines. Even though jet engine technology was rapidly advancing in those days, the first generation of jet-powered fighters was hampered by relatively low-thrust engines which limited them to subsonic flight. The US Air Force hoped to overcome this deficiency with its first dedicated supersonic fighter, the F-102 Delta Dagger.

Since the transonic drag rise was still not fully understood, the F-102's designers chose an engine they believed would provide enough thrust to reach a maximum speed of about Mach 1.2. However, initial flight tests of the YF-102 prototype indicated that the aircraft couldn't even reach Mach 1. The Convair engineers were baffled by this lack of performance until a NACA researcher named Dr. Richard Whitcomb developed the area rule.

Whitcomb experimented with several different ax-symmetric bodies and wing-body combinations in a transonic wind tunnel. What he found was that the drag created on these shapes was directly related to the change in cross-sectional area of the vehicle from the nose to the tail. The shape itself was not as critical in the creation of drag, but the rate of change in that shape had the most significant effect. For the mathematically inclined, we can say that wave drag is related to the second-derivative (or curvature) of the volume distribution of the vehicle.

To illustrate the point, four of Whitcomb's experimental models are drawn above, representing a simple cylindrical fuselage, the same fuselage with wings attached, a bulged fuselage, and a "pinched" fuselage with wings. What Whitcomb discovered was that the addition of wings to the basic cylinder produced twice as much drag as the cylinder alone. He also found that drag rose by the same amount if a simple bulge were added to the cylinder, the bulge being of equivalent volume as the wings. However, if he reduced the cross-sectional area of the fuselage over the region were the wings were attached, shown as body "D," the total drag was about the same as that of the cylinder alone.

The conclusion of this research was that shaping the vehicle to create a smooth cross-sectional area distribution from the nose to the tail could drastically reduce the drag on an aircraft. The area rule tells us that the volume of the body should be reduced in the presence of a wing, tail surface, or other projection so that there are no discontinuities in the cross-sectional area distribution of the vehicle shape.

Whitcomb's findings are related to a more theoretical concept called the Sears-Haack body. This shape yields the lowest possible wave drag for a given length and volume. The variation in cross-sectional area for a Sears-Haack body, illustrated in the following figure, tells us that wave drag is minimized when the curvature of the volume distribution is minimized. The closer the volume distribution of an aircraft or other high-speed vehicle comes to the ideal Sears-Haack body, the lower its wave drag will be.

Whitcomb's research was a major breakthrough in supersonic aerodynamics and had an immediate effect on the design of the aforementioned F-102 fighter. Convair engineers quickly redesigned the aircraft's fuselage, taking the area rule concept into account, to create the "waisted" or "coke-bottle" fuselage. This modification, plus a new engine, allowed the aircraft to easily exceed Mach 1 and achieve a maximum speed over Mach 1.5.

Today's supersonic fighters are fitted with much more powerful engines than were available in the 1950s, so the area rule is not as essential to their design as it used to be. However, it has found greater application to subsonic aircraft, particularly commercial airliners since they cruise at the lower end of the transonic regime. A good example is the Boeing 747, known for its distinctive "hump." This hump, which houses the cockpit and upper passenger deck, increases the cross-sectional area of the forward fuselage and has the effect of evening the volume distribution over the length of the aircraft. As a result, the 747 is able to cruise efficiently at a slightly higher speed than most other airliners since the increase in transonic wave drag is delayed.

by Jeff Scott


The Whitcomb Area Rule

Area Rule and Transonic Flight


Area Rule and how the F-102 broke the Sound Barrier

The concept known as the area rule is one of the great success stories of airplane design. The area rule says very simply that the transonic wave drag of an aircraft is essentially the same as the wave drag of an equivalent body of revolution having the same cross-sectional area distribution as the aircraft. This fact, coupled with the knowledge of the shape that minimizes drag shows designers how to reshape the fuselage and other components of an airplane to reduce the drag of the total configuration.

Since the rule was formulated, and verified experimentally, attempts have been made to estimate aircraft wave drag by a theoretical analysis of the equivalent-body area distributions. It has been found that reasonably good wave drag estimates can be made near a Mach Number of 1 if the slender-body-theory is applied to the aircraft area distribution. Numerous theoretical and experimental investigations have shown that the fuselage and other components of an airplane can be reshaped in a way that will reduce the wave drag of the total configuration. A typical configuration will frequently have a fuselage with a local minimum of area near the middle of its length, sometimes referred to as "coke-bottling".

The transonic area rule was considered so valuable that attempts were quickly made to extend the results to higher Mach numbers. This theoretical effort culminated in the development of the so-called Supersonic Area Rule, which is more complicated than the transonic rule.

This procedure can be extended to higher Mach numbers with good accuracy by using the supersonic area rule to determine the equivalent-body area distributions. The area distribution for the transonic area rule can be developed with drafting techniques. The supersonic area rule depends on computing areas intercepted by oblique cuts through a configurations and requires a considerable amount of computational geometry.

While Whitcomb was conceiving and testing his area rule concept, the Convair Division of General Dynamics was developing what it hoped would be the company's first supersonic aircraft. The Convair F102 "Delta Dagger" was designed to be a long-range interceptor, with delta wings and the most powerful turbojet engine available at that time, the Pratt & Whitney J-57. Early test results of an F-102 model in Langley's 8-Foot High-Speed Tunnel, however, seemed to indicate that the design's transonic drag might be too high for the aircraft to surpass Mach One.

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The NACA had immediately classified any information pertaining to the area rule, as it had the research on the slotted throat wind tunnel that allowed the area rule to be developed. In 1952, the United States was engaged in heated and high-stakes competition for military superiority with the Soviet Union, and NACA realized the importance of transonic research in developing superior military aircraft. Although the classification was necessary, it made dissemination of information about the area rule more difficult. Fortunately, NACA's history of successful technology transfer efforts had been less a product of published writings than the various levels of informal NACA-industry cooperation and researcher-to-engineer discussions.32 The area rule would prove no exception.

In mid-August 1952, a group of Convair engineers were at Langley to observe the performance of the F102 model in the Eight-Foot High-Speed Tunnel. Shown the disappointing test results, the engineers asked the Langley engineers if they had any suggestions. Whitcomb's first research memorandum on the area rule would not be published for another month, but he had completed his tests on the various wing-body combinations using indented fuselage shapes. He explained his findings and the area rule concept to the Convair team.

Intrigued, the Convair engineers worked with Whitcomb over the next few months to experiment with modifying the F-102 design and building a model that incorporated the area rule concept. At the same time, however, the company continued work on the original F-102 prototype. The engineers may have been open to exploring a possible new option, given the uncertainty produced by the wind tunnel tests of the original F-102 model, but the company had already made a commitment to the Air Force to build two prototypes of the original F-102. In addition to any mental and institutional resistance Convair might have had to changing a design which it had touted so highly and had already made a commitment to build, the company's commitment also created an issue of cost.

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By mid-1952, when Convair tested the F-102 model at Langley, the company had already begun setting up a production line at its San Diego, California, facility for manufacturing the aircraft. To change the design would mean not only delays and additional engineering costs, but revamping the production line, as well. Consequently, far from being receptive to a new design approach, Convair had a significant stake in proving that its new aircraft could perform just fine without it. 33

Nevertheless, the company could not totally ignore the doubtful test results of its original design, so its engineers began working on a "Plan B" with Whitcomb while production of the prototype F-102s continued. Starting in May 1953, the Convair engineers and Whitcomb began testing models of a modified, area rule-based, F-102 design in Langley's wind tunnel. By October 1953, they had developed a model that could meet the Air Force performance specifications. Convair noted the results but continued working on the original F-102 prototype, which flew for the first time on October 24, 1953. 34 The first prototype was severely damaged on its maiden flight, so test flights had to be postponed until January 11, 1954, when the second prototype flew for the first time. The results of the flight tests, however, proved to be largely the same as those predicted by the wind tunnel tests of the F-102 model in 1952. The aircraft performed below expectations and could not attain supersonic speeds in level flight. 35

Even at that point, Convair might have continued to press for production of the design as it was, given that the tooling and production line in its San Diego plant was already set, except for one crucial factor. The Air Force officials working on the F-102 design were aware of Whitcomb's area rule and the fact that a modified F-102 model, based on that concept, had achieved supersonic speeds in wind tunnel tests. Consequently, the Air Force realized that the F-102 was not the best that Convair could do. Whitcomb's experiments had proven that a supersonic airplane was possible, and the Air Force decided to settle for no less. The F-102 program manager at Wright Field in Ohio informed Convair that if the company did not modify the F-102 to achieve supersonic flight, the contract for the fighter/interceptor would be cancelled. 36

Incorporating Whitcomb's innovative design approach involved extra expense, but nothing compared to the cost of losing the entire F-102 contract. Convair immediately halted the F-102 production line and began working on the modified design Whitcomb and the company engineers had developed and tested. In only 117 working days, the company had built a new, area rule-based prototype, designated the F-102A. The F-102A flew for the first time on December 24, 1954, and surpassed the speed of sound not only in level flight, but while it was still in its initial climb. The area rule had improved the speed of the F-102 design by an estimated twenty-five percent. 37

While Convair was struggling with its F-102 design, the Grumman Aircraft Engineering Corporation was also working to develop its first supersonic carrier-based fighter, the F9F/F-11F Tiger.38 Although the area rule research was classified, the NACA released a confidential Research Memorandum on the subject to appropriately cleared aircraft manufacturers in September 1952. Just two weeks after receiving that memorandum, Grumman sent a group of its engineers to Langley to learn more about it. The information they brought back to Bethpage, New York, was immediately incorporated into the design, and in February 1953, Whitcomb was flown in to review the final design plans before construction on the prototype was begun. On April 27, 1953, the Navy signed a letter of intent with Grumman for the fighter, based on the Whitcomb-approved design. On August 16, 1954, the Grumman F9F-9 Tiger "breezed" through the sound barrier in level flight without the use of the afterburner on its Wright J-65 turbojet engine.39

The enthusiastic incorporation of Whitcomb's innovation by Grumman stands in stark contrast to the qualified experimentation and resistance that characterized Convair's response. But the two companies were in different situations. Convair had already completed a design for the F-102 and had begun construction of two prototypes and a production line. Grumman, on the other hand, was still working to design the F11F Tiger when Langley published its confidential report on Whitcomb's area rule breakthrough. It was the perfect time to incorporate a better design idea, and involved few extra costs to the company. At the same time, the Navy had not yet contracted for the fighter, and Grumman may well have recognized that its chances of winning the contract would be improved by incorporating any available new technology into its design; especially something that might improve its speed.

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In any event, Whitcomb's innovative idea was incorporated into two production military aircraft only twenty-four months after he completed his initial wind tunnel tests on the concept. This incredibly "successful" example of technology transfer was a result of two important factors. First and foremost, there was a "problem looking for a solution" 40 that the area rule was able to solve. Transonic drag was a real and seemingly insurmountable obstacle to supersonic flight. Whitcomb's area rule was not one of a number of potential solutions; it was the only approach anyone had developed that had proven itself capable of overcoming that barrier. It also had the backing of a very powerful customer: the United States military. When the Air Force decided to hold firm on its demand that Convair's aircraft fly supersonically in level flight, Convair could not simply sell its F-102s to another customer. The Air Force was its only client, just as the Navy was for Grumman.

But another important element, especially with regard to Convair, was the cooperation and individual relationships that existed between the Langley researchers, including Whitcomb, and the industry engineers. The modified F-102A model that proved to the Air Force that a fighter could achieve supersonic flight was a cooperative effort between Whitcomb and Convair engineers. Without that cooperation, or the informal discussions at Langley that launched that work, the fate of the F-102 might have been different.

The area rule undoubtedly would have been incorporated into aircraft designs eventually, regardless of the individuals involved. But that timeframe could have been different, which could have had an impact on the kind of air defenses the United States had at its disposal in the early days of the Cold War.

As it was, the success of the area rule-based F-102 and F11F was followed by the incorporation of the area rule in virtually every supersonic aircraft built after that point. The Vought F8U "Crusader" fighter and the Convair B-58 "Hustler" bomber, both of which were on the drawing board at the time the area rule was developed, were redesigned using Whitcomb's approach. The F-106, which was Convair's follow-on design to the F-102A, adhered even more to the area rule. It was able to incorporate a much deeper indentation in the fuselage than its predecessor, because it was an entirely new aircraft, unencumbered by existing design elements.

The fuselage of the Republic F-105 "Thunderchief" fighter/bomber, which flew for the first time in 1955, incorporated the area rule in a slightly different manner. It could not be indented because of its complex engine inlets, so a bulge was added to the aft region of the fuselage to reduce the severity of the change in the cross sectional area at the trailing edge of the wing. The Rockwell B-1 bomber and the Boeing 747 commercial airliner also used the addition of a cross-sectional area to reduce their drag at transonic speeds. Both the B-1 and the 747 have a vertical "bump" in the forward section of the fuselage ahead of the wing. It is perhaps more visible in the 747, where it houses the airliner's characteristic second story, but both airframe modifications were added to smooth the curve of the design's cross-sectional area . 41

The Collier Trophy

Whitcomb's Area Rule research was classified until September 1955, so he did not receive any immediate accolades or press on his discovery. But two months after his work was made public, Whitcomb received the National Aeronautic Association's Robert J. Collier Trophy in recognition of his achievement the previous year, when the Grumman F9F-9 Tiger and the Convair F-102A prototypes demonstrated just how significant the area rule was. The Collier Trophy citation read, "For discovery and experimental verification of the area rule, a contribution to base knowledge yielding significantly higher airplane speed and greater range with the same power. "


Although an engineering design approach using formulas or algorithms does not lend itself to the kind of notoriety that a project like the X-1 generated, the development of the area rule was no less significant. The X-1 proved the sound barrier could be broken. The area rule made that discovery practical by enabling production aircraft to operate at that speed.

The fact that the area rule was discovered by an engineer sitting with his feet up on his desk, contemplating a vision in his mind, also shows the importance of creativity and the individual in advancing technology. Postwar science and research projects may have been growing in complexity and size, but Whitcomb's discovery was a reminder that the

41. Whitcomb, interview, May 2, 1995; Whitcomb, "Research on Methods for Reducing the Aerodynamic Drag at Transonic Speeds," November 14, 1994, p. 3.

42. Bill Robie, For the Greatest Achievement: A History of the Aero Club of America and the National Aeronautic Association, (Washington, DC: Smithsonian Institution Press, 1993), p. 232; Richard T. Whitcomb, telephone interview with author, May 15, 1995.

The history of the area rule research also illustrates that even a "breakthrough" discovery does not always win immediate acceptance by those who might implement it. As opposed to projects that were wholly funded, developed and implemented by the NACA and its successor, the National Aeronautics and Space Administration (NASA), or other government agencies, Whitcomb's breakthrough was just an idea. It may have been developed at a NACA laboratory, but it was not up to NACA to apply it. In order for the innovation to have any impact at all, industry had to agree to use it, which is not always as simple a process as it might seem. Whitcomb's area rule was the answer to a tremendous problem that industry needed to solve, but the enthusiasm with which it was received differed greatly between Convair and Grumman. The advantages offered by the innovation were the same; the costs of implementing it differed.

But even in the application of the area rule concept, individuals played an important role. An Air Force demand was the primary reason Convair incorporated the area rule into the F-102, despite the added cost. But the Air Force might not have had the confidence to make that demand if it had not been for the model work performed by a small number of individuals at Langley and Convair. As scientific and engineering research and projects became more expensive, complex, and systems-oriented, it was easy to lose sight of the individuals that made those systems work. Richard T. Whitcomb, in developing and helping to win acceptance for a concept that revolutionized high-performance aircraft design, was a reminder that the individual still mattered.

Another way to visualize the principle is that the energy deposited in the air by the aircraft depends almost completely on the work done on the air by the virtual two-dimensional "piston." What made the piston's time history isn't that important. It's the expansion and contraction that matters. The aircraft might as well be an expanding and contracting circular cross section (a body of revolution) as long as the rate of expansion and contraction is the same. The effects of the cross section being something other than a circle get smoothed out as the disturbance propagates away. Just like it doesn't matter much what the shape of a stone is when you drop it in the water. As the disturbance expands, it becomes circular.

Another important point .... We are talking about "wave" drag not "friction drag." Aircraft experience both kinds. The aircraft's propulsion system must add energy to (do work on) the air to overcome drag forces. Energy that overcomes skin friction generally just heats the air. (Isn't that what happens whenever there is friction?) Energy that overcomes wave drag actually sets the air in motion. For the flight regimes of F-102's and similar aircraft, wave drag is much greater than skin friction.   

Although it's a stretch, induced drag might also be considered a form of "wave" drag. The vortices shed by a lifting surface of finite span induce a downward velocity on the wing which diminishes effective incidence (angle of attack), tilting the ideal lifting force, some of which is still upward but some of which actually resists forward motion. Skin friction dominates at "high" speeds, but induced drag dominates at low speeds. This is what leads to the "power curve," with both a low speed and a high speed equilibrium for a given propulsion input. The aircraft will climb at any speed between the low and high speed equilibrium. (More propulsive power than required for equilibrium.) The aircraft will descend at speeds lower than the low speed equilibrium point -- or higher than the high speed equilibrium point. That is what it means to be "behind the power curve." In both cases, power input is not sufficient to overcome drag (induced draat low friction at high speeds). (It is kind of non-intuitive that if you keep going faster and faster at a given altitude, eventually you will descend! You're just increasing frictional drag more rapidly than you can add power.)


The Area Rule and the F-102 Story

 The Cold War and the Korean War were stark realities in the early 1950s. The U.S. Air Force urgently needed a supersonic fighter to maintain air superiority. In 1951 several purportedly supersonic aircraft were on the drawing boards. Engineers had sketched out smooth, sleek fuselages with thin wings and powerful jet engines. These craft looked supersonic, and the data from rocket-propelled models suggested that they would be supersonic in actual flight. In reality, the so-called transonic region from Mach 0.9 to Mach 1.1 had not yet been explored systematically in wind tunnels. Bulletlike aircraft, as it turned out, were not the sole answer to supersonic flight.

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The YF-102 and YF-102A side by side. The narrowing of the YF-102A fuselage near the wings was dictated by the Area Rule and enabled the craft to become supersonic. Without the Area Rule, the YF-102 prototype never attained supersonic speeds in level flight.

To remedy the acknowledged deficiency in transonic research, the NACA had begun operating its 8-foot high-speed wind tunnel with a slotted wall at Langley Field in early 1950. This newly modified tunnel, which attained transonic speeds, arrived on the scene at an opportune moment.

One of the hopefully supersonic fighters being built in 1951 was the Convair delta-wing YF-102, with the world's most powerful jet engine, the Pratt and Whitney J-57, and knife-edge delta wings. Convair aerodynamicists were sure their projectile-shaped plane would easily penetrate the Mach 1 barrier. By mid-1952 Convair and the Air Force were committed to the construction of two YF-102 prototypes. A production line was being set up in San Diego for the manufacture of hundreds more. The newly modified Langley 8-foot high-speed tunnel, however, was generating disturbing data suggesting that transonic drag (air resistance) for the YF-102 might be much higher than expected. In August 1952 a scale model of the YF-102 was mounted in the tunnel. To Convair's dismay, the model displayed such high drag in the vicinity of Mach 1 that there was serious doubt that even the powerful J-57 engine could push the YF-102 through the sound barrier.

Following the YF-102 model tests, NACA and Convair engineers went over the data together at Langley. At this time, NACA aerodynamicists described some of the surprising discoveries they had been making concerning transonic drag. Richard T. Whitcomb and his team at the 8-foot high- speed tunnel had been studying various aircraft configurations at transonic speeds in their slotted- wall tunnel. As the high-speed air flowed around the models, they expected to see shock waves forming near the noses of the models, but they were startled to find additional strong shock waves established behind the trailing edges of the wings. Obviously, the unexpected high drags being measured were [63] caused by the planes having to overcome the energy losses created by these extra shock waves. The YF-102s being built in San Diego would never go supersonic burdened with these aerodynamic anchors.

Happily, Whitcomb's tests also provided a way out that was almost as surprising as the original discovery of the extra set of shock waves. The YF-102's smooth, streamlined fuselage should be replaced with a wasplike waist and a bulging tail in such a way that the total cross-sectional area of wings, fuselage, and tail (not just the fuselage area) should be that of an ideal streamlined body. Thus the fuselage should be constricted where the wings were attached and then expanded at their trailing edges. Aircraft designed according to Whitcomb's Area Rule looked almost grotesque and were dubbed "flying coke bottles." Nevertheless, the wind tunnel data were convincing, and the Convair engineers went back to San Diego to incorporate the suggested changes into their YF-102 model.

Convair returned to Langley in May 1953 with a modified YF-102 model. New wind tunnel tests showed substantial drag reduction. Additional changes were suggested to follow the Area Rule more closely. The model was revised once again, and in October 1953, checked again in the high-speed tunnel. These tests promised that the YF-102 designed according to the Area Rule, would now meet Air Force supersonic requirements.

At this time, it was too late to change the YF-102 prototypes and the first aircraft on the production line. Besides, there was still some hope that the drag problem might not be as severe as the Langley wind tunnel tests had indicated. The first YF-102 prototype roared down the runway at Muroc Air Force Base, California, on October 24, 1953. Unfortunately, the J-57 engine flamed out on takeoff and the craft was damaged beyond repair on landing. On January 11, 1954, the second prototype flew successfully. But as flight tests proceeded, it became clear that the Langley wind tunnel data were indeed correct-the YF-102 would not go supersonic in level flight.

The Air Force was in a quandary; it needed the new aircraft in its inventory but it also wanted them to be supersonic. Hugh Dryden, Director of NACA, assured Air Force General Nathan Twining that NACA had the answer to transonic drag reduction and had already passed the information on to Convair and other aircraft companies. With this knowledge, the Air Force halted the Convair F-102 production line.

Convair had not been idle following the wind tunnel revelations at Langley. In just 117 working days during 1954 they redesigned the YF-102 according to the Area Rule and built a new prototype. The new aircraft, designated the YF-102A, had the prescribed wasp waist, bulbous fairings on the tail, a sharper nose and canopy, and a more powerful version of the J-57 jet engines. On December 20, 1954, at Lindbergh Field near San Diego, the prototype left the runway and, while still climbing, pierced the sound barrier. Using the Area Rule, the top speed of the YF-102A increased by about 25 percent. With flight success, the Air Force restarted the Convair production line, this time to build 870 F-102As and 340 "advanced" F-102As, designated F-106s. The F-106s have become the primary interceptors defending the continental United States into the early 1980s.




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