History

In 1887, Ernst Mach and Peter Salcher presented their paper on the supersonic motion of a projectile “Photographische Fixirung der durch Projectile in der Luft eingeleiteten Vorgänge,” in the journal Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften [Wien], Mathematisch-Naturwissenschaftliche,” one of their famous schlieren photos being shown below. They deduced theoretically and then verified experimentally the existence of a conical shock wave (called a Mach cone or Mach wave) that would form at the nose of the projectile (or any other object) that flies supersonically.

Consider the figure below, which shows a two-dimensional section of a wing with subsonic and supersonic flows. If the component is less than unity, then the chordwise pressures and wing loadings will be the same as those produced on an unswept wing in a free-stream Mach number of , i.e., in a subsonic free-stream. Point Q will be inside the Mach cone from all points such as P, and the flow about the wing will be subsonic, which is called a subsonic leading edge, i.e.,

(12)  

which means

(13)  

so . The wave drag, therefore, will be zero.

If the component is greater than unity, then the chordwise pressures and wing loadings will be the same as those on an unswept wing in a supersonic free-stream of Mach number . In this case, point Q is outside the Mach cone from all points such as P, and the wing is said to have a supersonic leading edge, i.e.,

(14)  

which means

(15)  

so . Therefore, it becomes clear that a wing flying with a supersonic leading edge will create a larger wave drag.

Therefore, a desirable design goal is to use a subsonic leading edge, forming a series of oblique shocks to gradually slow the airflow. If obtained, the result is a smoother transition and reduced drag rise compared to the abrupt changes associated with normal shocks in supersonic flow. These preceding arguments, however, only apply to a wing of infinite span, which in practice means any part of a finite span wing where the flow can be considered nominally two-dimensional, i.e., away from the wing tips.

Using wing sweepback to reduce (wave) drag is most effective for larger aspect ratio wings because using too much sweep also reduces the effective aspect ratio of the wing. The disadvantage of using sweepback is that less lift is produced at a given angle of attack because of the lower effective free-stream velocity normal to the wing’s leading edge, which increases the airplane’s stall airspeed. The lower effective aspect ratio also gives a higher induced drag on the wing during subsonic operation, but this is not a desirable flight condition. Nevertheless, the wing must fly at lower airspeeds and higher angles of attack during takeoff and landing.

The figure below, derived from wind tunnel measurements, summarizes how wing sweep angle profoundly affects high subsonic, transonic, and supersonic drag. As is now apparent, this effect arises because swept-back wings reduce the wave drag and prevent the shocks from interfering with the flow over the wings, which can create flow separation and a further increase in drag. Notice that sweep delays the rise of the transonic drag and reduces the rate at which the drag increases in the transonic regime. However, although swept wings can help delay this drag rise from compressibility effects, other aerodynamic, higher structural weight, and aeroelastic problems can also be associated with swept wings. Therefore, in practice, airplane designers tend to use as little wing sweep as possible to accomplish the aerodynamic goals, with 20 to 30 degrees of sweep being typical of modern commercial jet airliners.

The effects of sweep angle are also summarized in the figure below, which shows the lift-to-drag ratio of a swept wing versus an unswept wing as a function of flight Mach number. In light of the preceding analysis, it becomes clear why some sweepback of a wing can minimize transonic and supersonic drag. On the one hand, as an airplane with an unswept wing approaches Mach 1, its drag increases rapidly, and its lift-to-drag ratio plummets immediately. On the other hand, it can be seen that the highly swept delta wing has a much lower lift-to-drag ratio at lower Mach numbers compared to the unswept wing, but it has a much more acceptable lift-to-drag ratio in supersonic flight.

Therefore, there must be trades and design compromises when selecting the sweep angle of an airplane wing. The moderately swept-back cantilever wing with high-lift devices is the best way to fly at Mach 0.8, and the delta wing is the best for flight at Mach 2. Delta wings, in particular, are well-suited for continuous supersonic flight.  A highly swept wing with a completely subsonic leading edge will perform very well at supersonic speeds and low lift coefficient but at the cost of poorer low-speed performance, i.e., higher induced drag because of its low aspect ratio wing. A swept wing produces less lift than an equivalent unswept wing, resulting in a higher stall speed and also less maneuver capability because of the lower stall margin. This is why some airplanes, including the B-1 bomber, the F-14, and Tornado fighters, use variable-sweep wings to merge the benefits of unswept and swept wings over the full Mach number envelope of the airplane. However, this aerodynamic advantage comes at the price of structural complexity and weight, amongst other issues.

Supersonic Delta Wings

For sustained supersonic flight, it is known that a delta or triangular wing is close to the optimal type of supersonic wing planform, first theoretically defined by R. T. Jones, and has since been confirmed using wind tunnel and flight test measurements. The advantage of a delta wing is that it can have a larger sweep angle and a greater wing area than a wing just swept back. However, it has also been found that other wing platforms can give similar aerodynamic benefits of low wave drag in supersonic flight.

For a delta wing, the flow is conical from the apex of the wing at O, as shown in the figure below. The pressure is constant along any radius vector from O. Two cases must be considered:

1. Subsonic leading edge.
2. Supersonic leading edge.

With the subsonic leading edge then . In this case, as shown by the figure, there is a low leading edge pressure (suction) over AB and CD, but the average pressures are less than for a two-dimensional wing with no sweep. With a supersonic leading edge, then . It is found that the average pressures across AB and CD equal that for a two-dimensional wing with no sweep.

Lift & Drag of Supersonic Delta Wings

The key factors affecting the lift on a supersonic wing are its angle of attack, , operating lift coefficient, ,  the free-stream (flight) Mach number, , and the wing’s leading edge sweep angle, . For a delta wing, the wave drag is strongly influenced by the leading edge sweep angle, . When the leading edge is subsonic, the effective sweep angle is greater than the Mach angle, which reduces the strength of shock waves and, consequently, the wave drag. A supersonic leading edge creates stronger shock waves on the wings, increasing drag and influencing the lift characteristics. In contrast, a subsonic leading edge allows for smoother airflow and less pronounced shock effects, leading to different lift and drag characteristics as functions of angles of attack and Mach number.

Supersonic Leading Edge

For a thin delta wing with a supersonic leading edge, then . The lift coefficient can be approximated by

(16)  

where is the angle of attack (in radians), and is the Mach number of the free stream. This result has an underlying, but not unreasonable, two-dimensional assumption that each wing section operates at the same local lift coefficient.

The corresponding drag on a delta wing comprises three main components. The contributions differ based on whether the leading edge is supersonic or subsonic. For a delta wing with a supersonic leading edge, then the sources of drag are:

1. Wave drag is the dominant source of drag because of the creation of relatively strong shock waves.
2. Induced drag, or “drag due to lift,” arises from the effects of the wing tip vortices.
3. Skin friction or boundary layer shear stress drag.

The wave drag coefficient, , can be approximated by

(17)  

Corrections to the wave drag can be applied for wing thickness in the same manner as two-dimensional airfoils.

The induced drag for a delta wing can be more complex to characterize than for a high aspect ratio wing. For a thin delta wing,  the induced drag coefficient, , is often expressed as

(18)  

where is the wing’s aspect ratio, and is Oswald’s efficiency factor. As airspeed, , and flight Mach number increases, the lift coefficient for a given airplane weight, , will decrease with the inverse square of the airspeed, i.e.,

(19)  

where is the reference wing area and is the ambient air density. Therefore, the induced drag becomes an increasingly smaller fraction of the total drag. For supersonic flight, the induced drag is typically relatively low because of the low lift coefficients on the wing.

The boundary layer or viscous shear drag, , on a supersonic wing can be approximated by considering the skin friction coefficient, , and the wetted area, , of the wing, i.e.,

(20)  

so that is given by

(21)  

where is the standard wing reference area. Here, is influenced by the Mach number and Reynolds number. For a turbulent boundary layer, can be estimated using empirical correlations such as

(22)  

where the Reynolds number is based on the wing chord. For supersonic flows, modifications to account for compressibility effects are needed, such as using the van Driest transformation, i.e.,

(23)  

The viscous shear drag on a supersonic wing tends to be lower in terms of the skin friction coefficient compared to subsonic conditions. Still, the overall drag is influenced by higher dynamic pressure and complex interactions between shock waves and boundary layers.

The total drag coefficient, , is then the sum of the wave drag, , induced drag, , and skin friction drag,  , i.e.,

(24)  

Subsonic Leading Edge

A subsonic leading edge is an ideal operating condition for a supersonic wing, i.e., the leading edge of the wing is swept back behind the Mach cone, i.e., for a subsonic leading edge, then .  As shown in the figure below, the geometric goal for a supersonic airplane for a given design flight Mach number is to sweep the leading edge back behind the Mach cone just enough, with some margin, so it always has a subsonic leading edge. The design should not use too much sweep so as to reduce the lifting area and aspect ratio of the wing. In this regard, the supersonic planforms shown in the figure below all seem just about right.^[5] The idea of using a larger sweep angle near the root of the wing is to account for the slightly higher Mach numbers caused by wing/fuselage interference.

For a delta wing with a subsonic leading edge, the lift coefficient can be approximated using linear theory as

(25)  

Given that for small angles of attack, then

(26)  

For a delta wing with a subsonic leading edge, the wave drag is still present but reduced in intensity. The reduction in wave drag can be attributed to the lower Mach number at which the leading edge operates. When the leading edge is subsonic, the flow around the wing is more streamlined, and the shock waves that form are weaker, resulting in less intense wave drag.

Mathematically, the wave drag coefficient, , for a subsonic leading edge can be expressed as a function of the Mach number and the sweep angle, i.e.,

(27)  

where (>1)  is an empirical factor that accounts for nonlinear effects, viscous effects, and shock wave interactions that are outside the framework of linearized aerodynamic theory; typically, is between 1.2 and 1.4.

The total drag coefficient, , is then the sum of the wave drag, induced drag, and skin friction drag,  , i.e.,

(28)  

Again, the induced drag is typically relatively low because of the low lift coefficients on the wing at supersonic flight speeds.

Note on Supersonic Boundary Layer Characteristics

The viscous shear drag considerations mentioned earlier apply generally to supersonic wings but need further specification depending on whether the leading edge is subsonic or supersonic. When the leading edge is subsonic, the flow remains attached and behaves similarly to subsonic flow around the leading edge. The boundary layer starts forming smoothly from the leading edge, and the primary concern is the development of the boundary layer along the wing’s chord. In this case, the flow over the leading edge does not generate strong shock waves, and the skin friction drag behaves similarly to high-speed subsonic flows, with compressibility effects taken into account.

For a supersonic leading edge, the flow encounters a shock wave at the leading edge. This generates a strong shock-boundary layer interaction, which can significantly affect the viscous shear drag. The boundary layer is more prone to separation and thickening because of adverse pressure gradients introduced by the shock waves. Additionally, shock waves can induce a turbulent boundary layer almost immediately downstream of the leading edge, increasing the skin friction drag.

Delta Wings in the Transonic Regime

All wings, including delta wings, exhibit unique aerodynamic characteristics because shock waves form when transitioning through the transonic regime, typically defined for a supersonic capable wing by flight Mach numbers from approximately 0.9 to 1.1, as shown in the figure below. These shock waves create wave drag and can also cause flow separation near the wing’s trailing edge, further increasing drag and reducing lift. The lift generated by delta wings in the transonic regime is influenced by the angle of attack and the strength and positions of the shock waves. It is undesirable to continuously operate a supersonic wing (or aircraft) in this transonic regime, not just because of the high drag but also because of the buffeting caused by shock wave boundary layer interactions and trailing edge flow separation.

The increase in drag and the commensurate increase in thrust required for flight led to this transonic flight regime being called the “sound barrier.” While there is no intrinsic aerodynamic barrier to flight at supersonic speeds, the significant increase in thrust required for an airplane to transition into supersonic flight usually requires an afterburner. After that, the drag coefficient (but not the drag!) diminishes somewhat, and supersonic flight can continue without the afterburner.  The overall trend of the aerodynamic characteristics in the subsonic and the supersonic flow just before and just after the transonic regime is that is proportional to before, and   is proportional to after.

While cruising at Mach 2, the Concorde could operate without afterburners because the engines were optimized for sustained supersonic flight. However, using the afterburners was essential to overcome the increased drag in the transonic regime. Furthermore, the center of pressure shifts from near the 1/4-chord to near the 1/2-chord as the wing moves through the transonic regime, affecting the airplane’s stability and control. These effects are often mitigated by re-balancing the fuel weight, as was done on the Concorde, or using an “all-flying” foreplane canard.

The transonic region is considered a transitory flight condition for these reasons, which include both performance and stability. A supersonic airplane will push through it quickly as it transitions from subsonic to supersonic flight and vice versa, minimizing the time spent in this aerodynamically complex regime.

Other Variations of the Delta Wing

Many variations of the delta wing design have since emerged in the evolution of more efficient supersonic airplanes, as shown in the figure below. The tailless delta wing is the classic design, although experience has shown it could be better from a flight handling qualities perspective. To this end, tailed delta wings have improved the airplane’s pitch control and overall handling qualities, especially when transitioning to and from supersonic flight. In addition, compound and ogival delta wings have been found to have better low-speed and high-angle-of-attack characteristics while still having all of the advantages of supersonic flight.

The closely-coupled canard delta configuration is popular because it gives better overall flight characteristics and handling qualities for both supersonic and subsonic flight. The design of supersonic fighter airplanes, including the Eurofighter Typhoon, has become standard, as shown in the photograph below. This closely coupled configuration has a smaller “all-flying” delta fore-plane or canard in front of and above the main delta wing. This canard delta configuration beneficially modifies the airflow over the wing at high angles of attack, keeping it more attached and giving the airplane lower landing speeds and better handling qualities. The all-flying delta-shaped foreplane also gives significant pitching moment authority for control, trim, and maneuverability.

Several other issues have emerged when using pure delta-wing airplanes, including:

1. Controlling the significant changes in pitching moments on the airplane relative to its center of gravity as it transitioned to and from a supersonic flight is difficult to trim with the normal use of the flight controls on the wing.

2. Concerns about the airplane’s low-speed flight characteristics, the thin wings being prone to stall at low angles of attack, and a susceptibility to develop a behavior known as wing rock. Therefore, the early delta-wing airplanes had high landing speeds, raising many operational challenges.

3. Because relatively thin wings were needed for aerodynamic reasons, obtaining the required structural strength and stiffness while ensuring the wing was free from aeroelastic twisting and flutter issues was challenging.

With a delta wing or one of its variants, the supersonic wave drag may be minimized further by employing Whitcomb’s Area Rule along the length of a slender fuselage. This rule can also be used to improve the spanwise lift distribution over the wing as it passes the fuselage; Dietrich Küchemann had originally hypothesized these ideas during WWII. The subtle use of the Area Rule is often noted when examining the fuselage shapes of supersonic fighter airplanes, which may have carefully contoured fuselage shapes to give smooth variations in the cross-sectional shape of the airplane. A constraint in this aerodynamic shaping process for a fighter is engine integration because the fuselage must contain the engine, the afterburner, and all the engine-associated systems.

Variable Sweep Supersonic Wing Designs

To widen an airplane’s flight envelope, designers strive to meld the benefits of different airplane shapes that perform well in various flight regimes. For example, combining the benefits of efficient subsonic and supersonic flight is desirable. As shown below, these benefits can be accomplished using a variable-sweep or “swing-wing” design. However, it is not always a possible engineering solution, partly because of the extra mechanical complexity and a significant weight penalty.

There can be several missions where a supersonic capability combined with good subsonic efficiency is a highly desirable characteristic. For example, a mission may require an efficient subsonic cruise over large distances, conserving fuel, followed by a shorter supersonic flight to the target, and then a subsonic cruise to return to base. The variable sweep or “swing-wing” design can also better maintain trim as the center of lift on the wing changes from subsonic to supersonic flight and back again, and there is also a center of gravity movement. On the F-14, F-111, and B-1 supersonic bombers, the wings are swept forward for takeoff and landing, significantly reducing the stall speed and improving the low-speed handling qualities.

The lift-to-drag ratio of the F-111 airplane for both subsonic and supersonic flight is shown in the figure below. Notice the improvement in the lift-to-drag ratio as the wings are swept forward, which is an expected behavior based on the corresponding increase in wing aspect ratio. A lift-to-drag ratio between 4 and 5 in supersonic flight is typical for any swept delta-wing airplane.

One disadvantage of such a swing-wing airplane is the added structural weight and complexity of the sweep pivot joint and associated actuator mechanisms. Also, variable geometry wings are more challenging to make stealthy, which is a big concern for the military.

Examining any military fighter airplane will show that wing pylons are generally always needed to carry bombs, air-launched weapons, and long-range fuel tanks. Therefore, another disadvantage of a variable-sweep wing is that pylon stations on the wing’s outer (swing) part are only possible if they can be mechanically designed to be reoriented to point into the relative flow. Pivoting pylons have been used on some airplanes with variable geometry. While they incur a weight penalty, they can significantly enhance the airplane’s capabilities in that it can now carry weapons or external fuel tanks.

Pivoting wing pylon systems for external stores and weapons carriage have been used on the General Dynamics F-111 and the Panavia Tornado to keep them facing into the flow as the wing sweeps backward and forward. Mechanically, this can be done using a form of pantograph, with one end fixed to the fuselage and the other to the pylon. The F-111’s outermost pair of pylons did not swivel and were only used while the wing was swept fully forward, restricting the airplanes to fly only subsonic flight with fuel tanks, such as for long-range ferry flights.

Engines for Supersonic Flight

Engines for supersonic airplanes have ranged from rocket engines to turbojets to turbofans. In supersonic flight, the inlet to an engine must be designed so that the intake to the compressor occurs at subsonic speeds. This goal is achieved by using a duct and/or doors or baffles to give a total pressure recovery at the end of the inlet diffuser before it reaches the compressor stage, as shown in the image below for the Roll-Royce/Snecma Olympus 593 engines used to power the Concorde.

The thrust from a turbojet engine tends to increase linearly with increasing supersonic flight Mach number because of the increased mass flow rate through the engine at supersonic speeds. Still, their relatively high specific fuel consumption can be an issue. While many supersonic airplanes have used turbojet engines with afterburners, the low bypass turbofan (with an afterburner) can be designed to give much better propulsive efficiency over a broader range of flight Mach numbers, thereby giving the airplane good fuel consumption throughout its flight envelope.

However, maintaining an efficient supersonic cruise for extended flight times is a continuing challenge with any supersonic airplane. Therefore, besides the engine requirements, there is always a need for low supersonic drag, so the airframes must be highly streamlined, and the wings have to be relatively thin with short wingspans.

Supersonic Transport (SST) Airplanes

There was much interest in developing supersonic transport (SST) airplanes during the 1960s, with significant technical efforts being led by the British and French airplane industries. The Anglo-French Concorde became the World’s first SST, which flew first in 1969 and went into operational service in 1976. The Concorde used a tailless ogival-shaped “slender-delta” wing, carefully designed to give good lift-to-drag in supersonic flight but also acceptable low-speed flight characteristics for takeoff and landing.

The Russians soon followed with the Tupolev Tu-144, which resembled the Concorde but was distinctive in its use of retractable foreplane canards. Both the Concorde and Tu-144 were designed for cruising at just over Mach 2 at 60,000 feet, which was the highest Mach number that could be obtained without excessive kinetic heating of the airframe. As a result, both the Concorde and the Tu-144 used special aluminum alloys in their construction and various other design features to allow the airframe to expand during flight. Conventional airplanes use various aluminum alloys, but these materials tend to soften and lose their strength at the temperatures produced by kinetic heating at Mach 2 and above.

Only 14 Concorde SSTs were built, and the airplane was never economically viable for broader airline service except over the North Atlantic. Nevertheless, it was a very popular airplane with both the passengers and the flight crews alike. British Airways and Air France flew the Concorde for over 25 years until it was abruptly retired in 2003 after a crash.^[6]With a take-off speed of about 220 knots (250 mph) and a cruising speed of 1,350 mph, which was just a little more than twice the speed of sound, a typical London to New York crossing was accomplished in 3-1/2 hours, compared to 8 hours for a subsonic flight. The Concorde holds many aviation records, including the fastest transatlantic airliner flight (New York JFK to London Heathrow) in 2 hours and 53 minutes. However, the Tu-144 was unsuccessful as a commercial airplane. After two crashes, including one on a delivery flight to Aeroflot, it was permanently retired after only 55 passenger flights.

In the 1970s, Boeing planned to develop an SST, initially using a variable geometry or “swing-wing” design, the final evolution of the concept shown in the figure below. The idea of the swing-wing design has already been discussed, which, for civil airplanes, could allow them to fly efficiently at subsonic speeds over land and inside terminal areas while having all the advantages of an efficient supersonic cruise.

However, despite the potential aerodynamic benefits of a swing-wing concept, the detailed engineering analyses done by Boeing proved too challenging from an airframe weight perspective. Boeing’s final 2707 SST concept was a more conventional supersonic delta-shaped wing. The Boeing design was also much larger than the Concorde or the Tu-144 and was intended to cruise at Mach 3. However, compounding the technical problems, high development costs, concern about sonic booms, and the lack of a passenger market for the airlines eventually led to its cancellation.

Slender Delta Concept

Like most delta-wing fighter-type airplanes, they do not have good aerodynamic characteristics at low flight speeds and high angles of attack, such as during takeoff and landing. Takeoff and landing speeds are high for such airplanes, requiring long runways. Concorde was specially designed to use a vortex-lift concept to improve the low-speed, high-angle of attack flight. The airplane had no high lift devices, so to reduce the landing speeds, the wing was designed to promote a phenomenon called vortex lift.

In the early 1950s, Weber and Küchemann at the RAE (Royal Aircraft Establishment) in the U.K. published a series of papers on a new type of delta-wing planform known as the “slender delta” concept. If designed appropriately, delta wings could produce robust and stable vortex flows on their upper surfaces at low airspeeds and high angles of attack, as shown in the schematic below. The presence of these vortices creates very low-pressure zones and so causes the lift on the wing to be significantly increased. All modern supersonic airplanes are explicitly designed to take advantage of the benefits of vortex lift at low airspeeds.

Weber and Küchemann determined that the lift from the leading-edge vortex flows could be maximized by increasing the slenderness of the wing and drooping the leading-edge camber somewhat. This approach would retain good supersonic performance but also allow for high values of maximum lift at low airspeeds, as shown in the figure below, offering much lower takeoff and landing speeds. The unfortunate byproduct is also a significant increase in drag, which requires considerable thrust and power to overcome, even when landing.

However, Concorde had to be flown at an extremely high angle of attack to achieve this condition, which was a distinctive (if not rather alarming) flight attitude during takeoffs and landings. Indeed, the angle of attack on takeoff and landing was so high that the airplane was designed with a “drooped-nose” feature to allow the pilots to see over the nose of the airplane. Concorde was also distinctive because of its exceptionally tall landing gear, which was needed to enable the airplane to rotate to the required angle of attack for takeoff without the tail striking the runway.

Any Future for SSTs?

The Anglo-French Concorde remains the only successful SST so far. Although many other SST designs have been studied, it remains to be seen if any future SST concept will ever prove economically viable for scheduled airline service. The inherently much lower lift-to-drag ratios of airplanes flying at supersonic speeds, even if the wing and airplane as a whole are highly aerodynamically and structurally optimized, means that SSTs will always burn much more fuel over a given range than subsonic airplane designs. The resulting seat-mile costs are considerably higher than those of a subsonic airplane (perhaps 3 to 5 times or more), even though the advantage is that the airplane’s flight time is less because it can cover the same distance in less than half the time.

However, the maximum achievable range of a supersonic airliner will always be much less than a subsonic airliner because of the higher fuel burn. Like the Concorde, the trans-Atlantic routes for a Mach > 2 capable SST are undoubtedly technically and economically feasible. However, for longer ranges, such as over the Pacific from the USA to Asia or Australia, stops for refueling will be needed and will likely erode any speed advantage, especially for only a Mach 1.5 to 1.7 capable SST. Longer ranges may also be required using alternative routings to minimize the effects of sonic booms over land, eroding any potential speed advantage unless the SST is capable of Mach 2 or greater.

Kinetic Heating

A serious problem facing supersonic (and hypersonic) flight vehicles is the airframe’s kinetic heating caused by air friction, which, for the Concorde, was a serious concern at the design stage. The graphic below illustrates just how hot the different parts of the Concorde became at its cruise speed of Mach 2.1. The skin temperature ranged from a peak of 130C at the nose to 93C at the tail, which caused the airplane to expand about 18 cm or 7 inches in length during its flight. The airframe expansion meant that some special structural design features were needed to allow the airframe to expand without setting up high structural stresses.

Traditional aluminum alloys cannot survive these high temperatures, so unique materials had to be developed to build Concorde. To this end, high-temperature aluminum alloys were used for its construction, including light alloy Hiduminium RR58, high-temperature steel, stainless honeycomb, and resin-bonded glass composites. Hiduminium RR58, which has a much higher melting point than conventional aluminum alloy, was used for most of Concorde’s structure. In addition, steel was used for sections subjected to even higher temperatures and the highest loads, and resin-bonded glass fiber was used for regions with the highest skin temperature, such as at the nose.

Sonic Booms

A problem facing SSTs (as well as any other type of supersonic or hypersonic flight vehicle) is the production of sonic booms. The leading and trailing shock waves formed by a supersonic airplane (one shock at the nose called the bow shock and another at the tail) appear to an observer on the ground as a pressure pulse in the form of an overpressure and an under-pressure, as shown in the schematic below. This pressure change is heard (and felt) by an observer on the ground as an impulsive “boom-boom” noise. Besides being annoying, if not startling, the intensity of the pressure pulse from Concorde produced noise levels over 135 dB, enough to rattle or break windows on buildings. Nevertheless, research continues into ways of mitigating sonic booms.

In 2017, NASA issued a draft request for proposals for developing its Quiet Supersonic Transport (QueSST) low-boom flight demonstrator. This program called for designing and testing a new X-plane to support the development of future-generation SST concepts. The contract was awarded to Lockheed Martin, and its Skunk Works X-59 supersonic demonstrator, as shown in the artist’s rendering below, is expected to cruise at 55,000 feet and Mach 1.4. One purpose of the flight tests will be to help quantify community response to supersonic flight over land. Still, this demonstration will unlikely change the public’s opinion after the psychoacoustic supersonic flight tests done over London and Oklahoma City in the 1960s. As of December 2023, the X-59 airplane had been constructed and readied for its first flights in 2024.

Smaller supersonic transport airplanes, such as supersonic business jets (SSBJs), have received more recent attention than larger commercial SSTs. Several companies are proposing SSBJ concepts, intending to transport as few as 10 to as many as 80 passengers. Typically, SSBJs would be about twice the size of a typical subsonic business jet but much smaller than Concorde.

However, the potential SST players face immense technical, certification, and economic challenges, including a hefty dose of public skepticism. One startup, Boom Supersonic, claims to have a Mach 1.7 capable SST in development and will fly with airlines by 2029. One major technical issue is finding engines in a civil market with no engine manufacturers, making engines suitable for supersonic flight, at least for civil applications.^[7]Maintenance and repair costs for an SST are also likely to be considerably higher because of the stresses imposed on the airframe and engines during high-speed flight, potentially increasing downtime and the availability of the airplane.

Gaining certification from civil airworthiness authorities is a significant issue for an SST, and it is likely to be a protected affair. For example, Concorde required over 4,000 hours of certification testing over seven years and 1,000 hours of route-proving in typical airline service conditions. Considering that the U.S. and European airworthiness authorities currently prohibit supersonic aircraft from flying over land, all other issues may be moot.

Several groups believe that the technical issues, economic concerns, sonic booms, emissions, certification, etc., can be solved at a smaller scale, potentially opening up a significant future supersonic market for airlines and others. However, it remains to be seen if this will come true in the decades to come. To make a supersonic airplane commercially viable, airlines will likely have to charge higher ticket prices than subsonic airplanes, limiting the market to passengers willing to pay this premium. Nevertheless, the appeal of vastly reduced traveling time by flying at supersonic speeds remains attractive to some passengers, not least for the novelty value of flying supersonically. Still, the overall economics remain questionable for the airlines, even for the business jet market. It is fair to say that it is unlikely that passengers will be flying supersonic anytime soon.

Hypersonic Flight

Hypersonic flight is defined as flight at speeds at or beyond Mach 5. However, unlike what happens as the aircraft approaches Mach 1, there are no distinctive changes in the flow characteristics as an aircraft reaches hypersonic Mach numbers. Such high Mach numbers have only been achieved by rockets, re-entry spacecraft, and special high-altitude research aircraft. Theodore von Kármán was one of the first to analyze the problems of hypersonic flight, stating: “At such speeds, even in rarified air, the surface will be heated to the temperatures none of the known materials can withstand. The problem of the thermal barrier is much more complicated than the problem of the sound barrier.”

Challenges

When flight vehicles begin to fly at hypersonic Mach numbers, many additional aerodynamic and other technical challenges occur, a summary of which is shown in the figure below. The main issues include the proximity of the shock waves to the vehicle, kinetic heating, viscous interactions, chemical reactions, and surface erosion.

In more detail, these effects at hypersonic flight Mach numbers include, but are not limited to, the following:

1. The Mach angle is small (see Eq. 11), so the shock waves bend back to steep angles and can begin to interact with the airframe, which causes disruptions to the flow in the boundary layer. Usually, the boundary layer is relatively thin, even laminar. Still, the resulting flow field becomes very complex at hypersonic speeds as the shock waves touch the boundary layer, and flow separation is likely.

2. The shock waves are very strong at hypersonic speeds, and the air undergoes significant temperature changes that affect its chemistry. The need to include chemistry in any aerodynamic analysis of hypersonic flows significantly raises the complexity of the needed predictive methods.

3. The proximity of shock waves to the body and the effects of skin friction causes a large amount of aerodynamic heating on vehicles flying at hypersonic speeds. Even high-temperature aluminum and titanium commonly used for supersonic aircraft construction will melt.

4. The flow over the vehicle can strongly interact with the propulsion system. In this regard, the propulsion system design must be tightly integrated into the entire vehicle design. Usually, a hypersonic vehicle must be designed so that its shape pre-compresses the air before it enters the engine.

5. The sonic booms from aircraft flying at Mach > 3 and hypersonically will be loud enough to likely damage structures on the ground and permanently damage human ears. It is unlikely that a hypersonic flight vehicle of any significant size could be allowed to fly over populated areas. Nevertheless, this technical challenge will remain in the future.

History

The issues associated with hypersonic flight first became apparent in the 1950s with the further development of WWII ballistic missiles capable of flying at Mach 5. However, for such missiles to have an intercontinental range, it was necessary to launch them out of the Earth’s atmosphere into space and then re-enter the atmosphere much nearer to the target. When tests on the first of such missiles were made based on the German designs, which had very pointed nose shapes, they completely melted during the re-entry phase from the intense shock waves and aerodynamic heating at Mach 5 and higher.

The answer to this problem, which was research led by H. Julian Allen & Alfred Eggers at the NACA, was opposite to that expected based on conventional aerodynamic wisdom, which was to make the nose of the missile much more rounded, as shown in the schlieren visualization images below. This “blunt body” design created a shock wave that stood off the nose and caused a boundary layer to flow over the nose cone’s surface, preventing the excessive heat of re-entry from melting the structure. In contrast, pointed nose shapes allowed the shock wave to touch the surface with a boundary layer that was too thin to offer much thermal protection. Tests with the modified missiles confirmed the validity of this method, although the nose still needed to be made of high-temperature resistant materials.

The information gained about high-speed flight and hypersonics in the wind tunnel and through flight tests contributed significantly to the development of the Mercury, Gemini, and Apollo space flight programs. Flight test work on hypersonics was first conducted by the U.S. Air Force and NASA during the 1950s. The X-15 research airplane flew for nearly ten years from 1959 and set the world’s unofficial speed and altitude records of 4,520 mph (Mach 6.7) and 354,200 feet during a program to investigate all aspects of piloted hypersonic flight.

The X-17 was a missile program that used a three-stage rocket to get the nose section to reach conditions between Mach 10 and 20 in the lower atmosphere. The nose cones survived briefly before vaporizing but long enough for valuable measurements to be made. Ultimately, the solution of minimizing kinetic heating effects on re-entry vehicles was also to use ablative materials to help shed the heat buildup.

During the 1980s, NASA began considering a single-stage hypersonic flight vehicle to replace the Space Shuttle. The National Aerospace Plane (NASP) was intended to take off from a standard runway used by airliners. Once the aircraft had reached sufficient airspeed, scramjet engines would power the aircraft into hypersonic flight. Finally, a rocket system would take the NASP into orbit. The NASP eventually became the Rockwell X-30 research vehicle. While the project did not reach the flight stage, a one-third-scale demonstrator, the X-43, was built. Three were built, the first being destroyed after an in-flight malfunction, but the other two flew successfully with the scramjet operating for approximately 10 seconds.

Hypersonic “Newtonian” Theory

Like all flight vehicle design aspects, the ability to predict quantitatively aerodynamic forces for the right (physical) reason is fundamental. To this end, a relatively parsimonious but validated method must often be used, providing the necessary focus to establish initial designs from which more detailed analysis can follow. Isaac Newton did not know about shock waves or supersonic or hypersonic flows. Still, in his Principia of 1687, he hypothesized some simple hydrodynamic principles, which have seen application to hypersonic flows in recent decades.

Isaac Newton proposed that fluid flow forces exerted on a surface consisting of a uniform stream of “particles” in which the time rate of change of the normal component of the momentum of each particle would be transferred to the plate, whereas the tangential component would be preserved. He assumed that the upper surface always remains in the “shadow” of the flow and is hence uninfluenced by the free-stream flow.

The figure below shows a hypersonic flow impinging on a thin body, resulting in a shock wave close to the surface and a thin shock layer. In a supersonic flow, disturbances cannot be propagated upstream, so there is no streamline curvature as the flow approaches the wing. Indeed, the resulting flow field looks remarkably like that proposed by Newton more than three centuries ago, despite the physical disparity in detail. Indeed, although the so-called Newtonian aerodynamics theory is flawed for several reasons, it is a reasonably good model to describe the lift and drag of bodies in hypersonic flows.

It can be shown that the lift coefficient in the “Newtonian theory” on a flat surface at an angle of attack to the flow is given by

(29)  

and the corresponding drag coefficient on the surface is

(30)  

The resulting lift-to-drag ratio is, therefore,

(31)  

While the Newtonian “hypersonic” theory is elementary, at least in terms of predicting the lift and drag coefficients, the question is how well it might work in practice, i.e., can it be used to predict anything useful? To this end, the results shown in the figures below compare the Newtonian theory with NASA wind tunnel measurements on a hypersonic body at Mach numbers of 6 and 10; measurements are available for angles of attack of -5^o to 35^o at Mach numbers from 1.5 to 10.

Despite its simplicity, the Newtonian theory is in remarkable agreement with the measurements. The drag is underpredicted because the Newtonian theory does not account for wave drag and viscous effects. However, the drag equation can be modified empirically to

(32)  

where is the wave drag and is the viscous shear stress drag, both of which will depend on the specific body shape. One approximation used for the wave drag of a body in hypersonic flow is

(33)  

which is attributed to Nonweiler.  Notice that for = 10 then = 0.02. Furthermore, it is often assumed that high-speed bodies have a viscous friction drag proportional to their wetted area times a known constant, i.e., the skin friction coefficient, , which comes from boundary layer theory or the von Driest equation, i.e.,

(34)  

Therefore, approximately, for the upper and lower surfaces, then

(35)  

Naturally, there are flow interference effects to consider, too. In this case, a value of aligns well with the wind tunnel measurements. The corresponding lift-to-drag ratio now becomes

(36)  

which again is seen to be in good agreement with the wind tunnel measurements. Notice that in the absence of viscous effects, the Newtonian theory becomes singular at exactly zero angle of attack, but this is of no practical significance.

It can be concluded that despite its limitations, Newtonian “hypersonic” aerodynamics can still be used in some instances to provide reasonable estimates and initial approximations for aerodynamic lift and drag. Therefore, it can be useful in conceptual design studies or in situations where a rapid assessment of the aerodynamic characteristics of a hypersonic vehicle is required.

Other Methods

To obtain more accurate predictions for hypersonic flow about various bodies, researchers and engineers rely on more advanced approaches such as shock-expansion theory, computational fluid dynamics (CFD), and wind tunnel testing. CFD methods consider the complexities and non-idealities of hypersonic flows, including shock wave interactions, boundary layer effects, chemical reactions, and high-temperature gas dynamics. If properly conducted, wind tunnel testing represents the datum or benchmark against which CFD methods can be tested and validated.

Shock expansion theory is another popular method, which involves the analysis of fluid flow containing both shock and expansion waves. On the one hand, shock waves are abrupt changes in a fluid’s pressure, temperature, and density caused by the propagation of a disturbance through the fluid. On the other hand, expansion waves are gradual changes in these properties caused by the spreading out of the fluid. The oblique shock relations and the Prandtl-Meyer function can be used to find the pressures on the body, allowing lift and drag forces to be obtained by integration.

Hypersonic Aircraft Design

A thin, flat plate is known theoretically to be the most efficient aerodynamic shape for hypersonic flight, its lift-to-drag ratio being the highest achievable. However, a plate is an unrealistic design solution for a practical flight vehicle because of the need to contain engines, fuel, systems, payload, etc. Wind tunnel measurements of candidate hypersonic shapes have shown that their maximum achievable aerodynamic efficiency in terms of lift-to-drag ratio, , decreases with increasing flight Mach number according to

(37)  

which is often referred to as Küchemann’s equation. The conclusions to be drawn here are that the aerodynamic efficiency is relatively low in hypersonic flight and that increasing the lift-to-drag ratio will be challenging.

To maximize the aerodynamic efficiency of a flight vehicle in hypersonic flight, it is recommended by experts in the field that some general design rules should always be followed. Such vehicles should generally be blended with body shapes with integrated forebodies, propulsion systems, and afterbodies. More specifically, they should have as small a frontal area as possible, with a highly streamlined overall shape to minimize surface area. A short-span, low aspect ratio wing should be used to keep the airplane behind the Mach cone, with the fuselage suitably shaped to generate lift, i.e., as a lifting body. The propulsion system must be well-integrated into the vehicle’s overall shape to prevent shock waves from one component from adversely interfering with the flow at another component.

Waveriders

A waverider is another type of hypersonic wing design with an improved lift-to-drag ratio relative to other shapes. This goal is accomplished using the shock waves generated by its flight as a lifting surface, a phenomenon known as compression lift. The waverider concept originated from the work of Terence Nonweiler on winged atmospheric re-entry vehicles in the 1950s. A waverider is a delta wing with some anhedral, often called a caret wing. With the advent of computational fluid dynamics (CFD) and advanced hypersonic prediction methods, various optimized waverider shapes have been developed, as shown in the figure below. However, heat dissipation is an issue with such optimized designs because of the closer proximity of the shock waves to the surfaces.

Propulsion Issues

Achieving combustion and propulsion is another major problem at hypersonic speeds, and the most likely candidate is a variation of a ramjet engine called a scramjet, i.e., a supersonic ramjet, as shown in the figure below. A scramjet (Supersonic Combustion Ramjet) engine works on the principle that the shock waves on the vehicle can slow down and compress the air to support combustion inside the engine.

A scramjet cannot start or operate at low airspeeds because it requires the incoming air to be at supersonic speeds to start the combustion. Typically, a scramjet must be accelerated to speeds near Mach 4 by another propulsion system, such as a rocket, turbojet, or ramjet. Rocket engines can provide significant thrust and quickly accelerate the scramjet to the required operational Mach number, although they are inefficient compared to air-breathing engines. Turbojet or ramjet engines can also be combined with scramjets, operating efficiently at lower speeds and transitioning to scramjet operation at higher speeds.

Maintaining continuous combustion in supersonic flow is complex because of several factors. The fuel/air mixture has an extremely short residence time within the combustion chamber, just a few milliseconds. This rapid transit makes achieving efficient fuel/air mixing and complete combustion challenging before the flow exits the engine. The supersonic airflow can also create shock waves and complex boundary layer interactions within the engine, potentially disrupting the flow needed for efficient combustion. The high-speed airflow through a scramjet also results in significant aerodynamic heating, requiring advanced materials and cooling techniques to manage the thermal load on the engine components.

Airframe/Engine Integration

One feature of a hypersonic airplane is the need for carefully integrating parts of the aircraft that provide volume, i.e., for payload and fuel, with those for propulsion, i.e., an engine such as a scramjet. The figure below shows the basic idea for a “two-dimensional” configuration.  An externally carried scramjet separately attached to the airframe (body) on a pylon would have an unacceptably high drag. However, properly integrating the body and the propulsion system could be expected to reduce the wave drag on the body and much of the external nacelle drag. The penalties paid for this achievement are a slight loss of useful volume and the ingestion into the intake of some of the boundary layers on the body surface. Studies have shown that careful aircraft/propulsion can be expected to increase maximum lift-drag ratios by about 1.5 higher relative to a non-integrated design.

The Boeing X-51A scramjet demonstration aircraft was a waverider concept tested from 2011 to 2013, as shown in the artist’s impression below. The X-51A was used to demonstrate scramjet engine operations at hypersonic airspeeds and other aspects of hypersonic flight. The aircraft sustained Mach 5 flight for 200 seconds during its longest tests. Measurements made during these test flights have been used to compare measurements made in hypersonic wind tunnels and predictions made using CFD.

Summary & Closure

Humans have always sought to fly faster, which has led to the development of aerodynamically optimized flight vehicles and advanced propulsion systems for supersonic and hypersonic flight. However, the development and practical implementation of these technologies still involve complex engineering challenges and much research. Solving these challenges requires optimizing vehicle shape to minimize drag and shock wave interactions and developing efficient engines for supersonic and hypersonic flight.

Continued advancements in aerodynamics, propulsion systems, and materials science will eventually lead toward potential future breakthroughs in high-speed flight capabilities. The design of hypersonic engines remains a significant challenge, with scramjets showing some levels of success. Kinetic heating on the airframe at high speeds produces high surface temperatures, requiring unique “high-temperature” materials. The future of hypersonic flight is likely to involve waverider vehicles., which use the shock waves generated by their flight to create lift and reduce drag. By “riding” their shockwaves, these vehicles can potentially achieve better hypersonic efficiency.

Technical issues aside, the economics of a supersonic or even hypersonic aircraft are complex and depend on many factors. Research, design, testing, and certification expenses for such aircraft can be high, and they will need to be recouped through sales and operations. Manufacturing costs are also likely to be much higher than for subsonic aviation because specialized materials and production methods are required. Supersonic aircraft will consume significantly more fuel per passenger and incur higher maintenance and repair costs. Therefore, airlines will likely charge higher ticket prices to make a supersonic airliner commercially viable. The success of any future commercial supersonic transport (SST) aircraft will ultimately depend on passenger demand and competition from existing subsonic options.