Quest for Performance: The Evolution of Modern Aircraft
Chapter 10: Technology of the Jet Airplane
Wings and Configurations for High-Speed Flight
[248] The revolutionary new jet propulsion systems that had their beginnings in the 1940's are briefly described above. The potential for high speed offered by these systems, however, could in no way be realized by typical aircraft designs of the World War II era. High-speed aircraft of this period were usually characterized by straight wings having thickness ratios in the range from 14 to 18 percent. (The wing thickness ratio, expressed in percent, is defined as the thickness of the wing divided by its chord.) The aerodynamic design of such aircraft could, to a first approximation, be thought of in terms of the linear addition of various elements of the aircraft. For example, the drag of the wing, fuselage, and tall, measured separately, could be added together with only minimum consideration of interference effects to obtain the drag of the entire aircraft. As jet propulsion opened the prospects of flight in the high-subsonic, transonic, and supersonic flight regimes, however, these and other time-honored tenets of airplane design were to undergo radical change. The classic shape of the airplane of the 1940's had to be fundamentally altered to permit efficient and safe operation in these new speed ranges. Some of the new configuration concepts for high-speed flight are discussed below.
Swept Wings
The critical Mach number of a wing is the flight Mach number of the aircraft at which the local Mach number at some point of the wing becomes 1.0. At a Mach number slightly in excess of this critical value, shock waves form on the wing, and further increases in speed cause [249] large changes in the forces, moments, and pressures on the wing. The effects on the lift and drag characteristics of increasing the Mach number beyond the critical value are briefly discussed and illustrated in chapter 5. Subsonic aircraft usually do not cruise at Mach numbers much beyond the critical value. For supersonic flight, however, the aircraft must have sufficient power to overcome the high drag in the transonic speed range and be capable of controlled flight through this capricious Mach number range.
For many years, reducing the airfoil thickness ratio was the only known method of increasing the wing critical Mach number by any significant amount (ref. 139). Then in 1945, Robert T. Jones of NACA offered a fundamental breakthrough when he proposed the use of wing sweep as a means for increasing the critical Mach number (ref. 172). The use of wing sweep to increase the efficiency of aircraft intended for flight at supersonic speed was first suggested by Busemann in 1935 (ref. 142); the effectiveness of wing sweep as a means for increasing the critical Mach number had been recognized in Germany before 1945 (ref. 143), but this work was unknown in the United States until after World War II.
The way in which sweepback increases the critical Mach number is illustrated in figure 10. 11. If the swept wing is of infinite aspect ratio, the critical Mach number is related to that of the corresponding unswept wing as follows:
where wing sweepback angleis the wing sweep angle, forulais the critical Mach number of the unswept wing, formulais the critical Mach number of the swept wing, and the airfoil thickness ratio normal to the leading edge, or other appropriate spanwise element, remains constant as the wing is rotated to different angles of sweepback. This relationship is based on the assumption that the critical Mach number of the wing is controlled only by the flow normal to the leading edge and is independent of the Mach number parallel to the leading edge. Thus, the free-stream Mach number, that is, the flight Mach number of the aircraft, is resolved into components normal and parallel to the leading edge of the wing. The assumption of independence of the two components of the stream Mach number is strictly true only for invisid flow, but the assumption works reasonably well in predicting the effect of sweep on the critical Mach number of wings operating in real flows with viscosity.

sweptback wing formula
[250Figure 10. 11 - Sweptback wing showing resolution of stream velocity into components normal and parallel to leading edge.

The effect of sweepback on the critical Mach number of finite wings is usually analyzed in terms of a wing of given aspect ratio and airfoil thickness ratio in the free-stream direction. The airfoil thickness ratio normal to the leading edge varies, in this case, as the wing sweepback angle is changed. For this reason, and because the flow at the wing root and tip cannot conform to the simple resolution of components normal and parallel to the leading edge, the simple cosine relationship overestimates the magnitude of the effect of sweepback on the critical Mach number. The swept wing, however, must be regarded as a cornerstone of the aerodynamic design of modern high-subsonic-speed jet airplanes. As compared with a straight wing, the swept wing offers significant increases in cruising Mach number and, at the same time, permits the use of wings of sufficient thickness to allow aspect ratios high enough for good values of the maximum lift-drag ratio. The aspect ratio, sweep angle, airfoil thickness ratio, and wing weight necessary for adequate wing strength and stiffness are all related and require a complex series of trade-off studies to arrive at an optimum design for a given set of requirements. The internal volume required for fuel storage and landing-gear retraction also forms an important part of these trade-off studies.
Early jet fighters capable of flight at high-subsonic Mach numbers profited greatly from the use of wing sweepback. A number of such [251] aircraft were developed in the late 1940's and early 1950's. Perhaps the best known of these was the North American F-86 Sabre (described in chapter 11). Only a few years after the end of World War II, however, competitive pressures underlined the need for fighter aircraft capable of flight at transonic and low-supersonic speeds. Efficient flight at these speeds required the use of afterburning jet engines, new configuration concepts, and much reliable aerodynamic design data.
The difficulties encountered in the use of conventional wind tunnels for aerodynamic tests near a Mach number of 1.0 are briefly described in chapter 5. To overcome these difficulties, several alternatives to the wind tunnel were utilized for aerodynamic studies in the last half of the 1940's. These alternative techniques included the free fall, or drop body, and the rocket-model methods. In the free-fall technique, test wings were mounted on a heavily weighted, streamlined body that was dropped from an airplane at altitudes as high as 40 000 feet. With radio transmission of measurements made with internal balances and ground tracking by radar, the forces and moments acting on the wing could be deduced as the test body passed through the transonic speed range. A variation on this technique that offered the potential for higher speeds and longer test times was the rocket-boosted model launched from the ground.
Two other techniques, entirely different from those just described, were used for aerodynamic studies at transonic speeds. In one of these, called the wing-flow technique, a small wing model was mounted perpendicular to the top surface of the wing of a high-speed fighter aircraft. As the aircraft Mach number approached its critical value, transonic speeds developed on top of the wing to which the model was mounted. Forces and moments as measured by a small balance in the airplane wing were then recorded. In a variation of this technique, known as the transonic bump, the small test model was attached normal to a streamlined bump mounted on the floor of a conventional high-subsonic-speed wind tunnel. The high induced velocities over the top of the bump, as on an airplane wing, provided the desired transonic test environment. Several of these techniques are discussed in reference 159.
Although useful as temporary measures, the wind-tunnel alternatives just discussed were time consuming, lacked test flexibility and controllability, and, in some cases, provided results of doubtful quantitative validity. The slotted-throat transonic wind tunnel developed at the NACA's Langley laboratory provided a new dimension in transonic testing. The 8-foot tunnel at Langley was modified with slots and put [252] into operation in 1950 (ref. 138). In this facility, controlled study of large-size models could be made under a variety of test conditions and at Mach numbers that could be varied continuously through the transonic speed range. With the use of facilities such as the 8-foot tunnel, new ideas and the supporting engineering data needed for the development of transonic aircraft began to emerge.
The effectiveness of wing sweep as a means for increasing the critical Mach number of subsonic aircraft has already been discussed. Data obtained from the new facilities showed that wing sweep and airfoil thickness ratio also played a key role in establishing the drag level at transonic speeds. These effects are clearly shown in figure 10.12, which is based on information contained in reference 154. Figure 10.12(a) shows the minimum drag coefficient for a wing with 47° sweepback plotted as a function of Mach number for airfoil thickness ratios of 9, 6, and 4 percent. The dramatic reduction in drag coefficient at Mach numbers in excess of 1.0 as the airfoil thickness ratio is reduced from 9 to 4 percent is obvious. The variation of minimum drag coefficient is shown in figure 10.12(b) for a 4-percent-thick wing having sweepback angles of 11°, 35° and 47°. Increasing the sweep angle for a wing of given thickness ratio also reduces significantly the drag level at speeds above Mach 1.0. Clearly, the message portrayed in figure 10.12 is that the wings of aircraft designed to penetrate into the low-supersonic speed range should be thin and swept. These purely aerodynamic considerations for choosing a wing of low drag do not necessarily result in an optimum wing for a given airplane. Again, as in the case of subsonic aircraft, detailed trade-off studies between the various wing geometric/ aerodynamic characteristics and wing strength, weight, and stiffness must be made. Because of the requirements for very thin airfoil sections, these trade-offs almost inevitably lead to wings of low aspect ratio on fighter aircraft designed to penetrate the transonic and low-supersonic speed regimes. As compared with aspect ratios of 7 to 8 commonly found on subsonic jet transports, values as low as 2 to 3 are not unusual on fighter aircraft.
The wings illustrated in figures 10. 11 and 10. 12 are swept back, as are most of the wings seen on operational aircraft. But, according to the simple theory in which the streamwise velocity is resolved into components normal and parallel to the leading edge of the wing, the wing could just as well be swept forward. The experimental Junkers Ju 287-1, built in Germany during World War II and described in reference 201, had sweptforward wings, and one of the business jet transports described in chapter 14 also incorporates wings with forward sweep.

sweep angle measured at quarter-chord line
[253Figure 10. 12 - Conceptual effect of wing sweepback angle and airfoil-section thickness ratio on variation of wing drag coefficient with Mach number.

Sweptforward wings, however, have a fundamental aeroelastic problem that has mitigated against their use. Simply stated, an increase in load on the wing twists the outer portions of the sweptforward wing to higher angles of attack. When the dynamic pressure reaches a critical value, the increment in aerodynamic twisting moment associated with an incremental change in angle of attack is equal to the corresponding incremental change in torsional resisting moment provided by the structure. Any further increase in dynamic pressure will result in the wing twisting off the aircraft. The critical condition at which this catastrophic failure occurs is termed the divergence speed, or divergence dynamic pressure. Structural studies of wings constructed of conventional metal alloys have shown that a sweptforward wing of a given aspect ratio will be heavier than a sweptback wing of the same aspect ratio and sweep angle. The additional weight results from the increased torsional stiffness required to prevent divergence within the flight envelope of the aircraft. The advent of composite materials, however, seems to offer the possibility of constructing sweptforward wings with little or no weight penalty (ref. 166). A number of studies of the possible [254] advantages of such wings on fighter aircraft have been made, and a research-type fighter with sweptforward wings is now (1982) under development.
Delta Wings
A variation on the swept wing theme is the delta wing first proposed by the German aerodynamicist Alexander Lippisch in the years prior to World War II (ref. 175). This wing derives its name from the Greek letter , which describes the planform shape. Sweep of the leading edge varies with the application but usually falls in the range between 70 and 40. Shown in figure 10.13(a) is a simple 45° delta wing; three variations of the simple delta planform are shown in figures 10.13 (b), (c), and (d). Many other variants are possible. In fact, the wings of some modern fighter aircraft defy classification as simple delta....

simple delt wing form

cropped delta wing form

(a) Simple delta

(b) Cropped delta

notched delta wing form

double delta wing form

(c) Notched delta

(d) Double delta

Figure 10.13 - Four delta-wing planforms.


[255]....or swept wings since they have some of the geometric characteristics of both. Typical wing-planform shapes of fighter aircraft are illustrated in chapter 11.

The delta wing is particularly well suited to tailless, all-wing configurations since the flap-type longitudinal controls can be located on the wing trailing edge, far behind the aircraft center of gravity. Other advantages of the delta wing as compared with the swept wing are its large internal storage volume, relatively good characteristics at high angles of attack, and lessened susceptibility to aeroelastic problems. On tailless applications, however, trailing-edge high-lift devices cannot be used because of the large pitching moments generated by these devices. Further, the high drag due to lift inherent in the low-aspect-ratio delta wing must be carefully evaluated in relation to such aircraft characteristics as wing loading, as well as cruise speed and altitude. Again, as mentioned previously, the choice between swept, delta, straight, or some hybrid wing planform must rest on the results of trade-off studies for a given application. A good discussion of such studies is presented in several of the papers contained in reference 155.
Variable-Sweep Wings
Thin swept wings of low aspect ratio are part of the aerodynamic ingredients of a low-drag supersonic aircraft but, at the same time, yield an aircaft with a relatively low maximum lift-drag ratio at subsonic speeds, as well as certain undesirable handling characteristics in the low-speed, high-angle-of-attack regime. (Even so, the poor subsonic maximum lift-drag ratio is higher than that at supersonic speeds; flight in the low-supersonic speed range is not very efficient.) There are several types of mission, however, in which a supersonic capability coupled with high subsonic efficiency is highly desirable. For example, an attack mission may be comprised of a long-range, high-efficiency subsonic segment followed by a supersonic dash over enemy territory to the target, after which subsonic cruise is used for the return trip home. Many military-mission profiles combining efficient subsonic cruise with a supersonic capability have been postulated. In the civil arena, the supersonic transport not only requires good supersonic cruising efficiency but must also be able to fly efficiently at subsonic speeds for route segments over land (such aircraft are forbidden to fly at supersonic speeds over land because of the sonic boom) and for holding in the terminal area.
[256] These multimission requirements suggest a wing whose sweepback angle, and thus aspect ratio, can be mechanically adjusted in flight to the optimum position for each speed regime. A model of' a conceptual variable-sweep aircraft with its wings set in three different sweep positions is shown in figure 10.14. The increase in wing span, and thus aspect ratio, that accompanies movement of the wing to lower sweep angles is obvious. The maximum lift-drag ratio at subsonic speeds increases, of course, with the aspect ratio, as quantitatively shown in....

photo of a variable-sweep aircraft model
Figure 10. 11 - Model of a conceptual variable-sweep aircraft with the wing in three different sweep positions. [NASA] [Original photo was in color, Chris Gamble, html editor]


[257] ....appendix C. The near-zero sweep angle with accompanying high aspect ratio would be appropriate for landing, takeoff, and climb; whereas the intermediate sweep could be used for normal cruise at subsonic speeds. Flight at high-subsonic and supersonic speeds would call for the wing to be swept fully back.

Aircraft with variable sweep wings have been discussed since the concept of wing sweep was first introduced. Some of the aerodynamic problems introduced by the variable sweep concept together with possible solutions, based on material contained in reference 184, are illustrated in figure 10.15. Figure 10.15(a) shows a wing that changes its sweep angle by rotating about a single inboard pivot located on the fuselage center line. At the bottom of the figure the rearward movement of the wing center of lift with increasing sweep angle is shown for both subsonic and supersonic speeds. The slight rearward shift of the aircraft center of gravity is caused by the rearward shift of the wing weight. Indicated by the cross-hatching is the distance between the center of gravity and the center of lift. This distance is a measure of the longitudinal stability of the aircraft and greatly increases as the sweep angle increases. A small amount of longitudinal stability is highly desirable, but the large increases with sweep angle shown in figure 10.15(a) cause reductions in aircraft maneuverability and large increases in trim drag. (Trim drag is associated with the large negative lift load that must be carried by the tail to balance the pitching moment induced by the distance between the centers of gravity and lift.) A single pivot wing of the type shown in figure 10.15(a) is accordingly unacceptable, and no aircraft utilizing this concept has ever been built.
A solution to the problem highlighted in figure 10. 15(a) is illustrated in figure 10.15(b). Here, the wing translates forward as the sweep angle increases so that the stability remains essentially the same at all sweep angles. The increase in stability at supersonic speeds is not related to variable sweep but is characteristic of all wings as they pass from subsonic to supersonic speeds. The rotating and translating variable-sweep wing has been explored on two experimental aircraft. First was the Bell X-5 research airplane, which made its initial flight in 1951. The sweep angle on this aircraft could be varied from 20 to 60, as shown by figure 10.16. No problems were encountered with the variable-sweep mechanism on the X-5, and flight characteristics of the aircraft were fairly good at all sweep angles. At a somewhat later date, the Grumman XF10F variable-sweep fighter entered flight testing. Like the X-5, the Grumman fighter had a wing that combined rotation and [258] translation to control the relationship between the centers of lift and gravity. Because of problems entirely unrelated to the variable-sweep feature, the XF10F was not a success and was never put into production. Both the X-5 and the XFIOF were subsonic aircraft in which the variable-sweep feature was intended to increase, as compared with a fixed-wing aircraft, the critical Mach number at high-subsonic speeds and reduce the landing speed at the other end of the scale. These goals were accomplished in both aircraft. The translating and rotating variable-sweep wing, however, is heavy and leads to undesirable mechanical complications.
Shown in figure 10.15(c) is the basic solution to the variable-sweep stability problem employed in the design of all operational variable-sweep aircraft in use today. The wing pivot is located outboard of the fuselage with a highly swept cuff extending from the pivot to the side of the fuselage. In this concept, developed at the NASA Langley Research Center, the fixed and movable components of the wing are configured so that the wing span-load distribution varies with sweep angle in a manner to minimize the rearward shift in the center of lift. As illustrated in figure 10.15(c), the distance between the centers of lift and gravity are the same at subsonic speeds for two sweep angles - one low and one high.

no wing translation

with wing translation

no wing translation

(a) No wing translation.

(b) With wing translation.

(c) No wing translation.

Figure 10. 15 - Aft movement of center of lift with increasing sweep angle for three variable-sweep concepts.


aerial photo of variable sweep wing Bell x-5
[259Figure 10.16 - Bell X-5 research aircraft equipped with variable-sweep wings. [NASA]

Three variable-sweep aircraft employing the outboard pivot concept are in operational use or under development in the United States today. These are described in chapters 11 and 12. Several variable-sweep aircraft are also in operational use in Europe. Interesting accounts of the development of' variable-sweep concepts and aircraft are contained in references 155 and 184.
The Area Rule
[260] The large number from subsonic to supersonic values is clearly indicated by the Curves in figure 10.12 for wings of different sweep angle and thickness ratio. The formation of shock waves on the wing and body as the aircraft passes through the transonic speed range is responsible for this large increase in drag. Both aerodynamic theory for this speed range and early experimental results obtained from tests in the slotted-throat transonic wind tunnel indicated that the wave drag of a wing-fuselage combination would be significantly higher than the sum of the drag of these two elements measured separately.
In the early 1950's, Richard T. Whitcomb of the NACA Langley Memorial Aeronautical Laboratory first experimentally demonstrated an aerodynamic principle that has had a profound and far-reaching effect on the entire process of airplane configuration synthesis. Known as the transonic area rule (ref. 202), this principle is illustrated in figure 10.17(a). According to Donlan, from whose 1954 paper (ref. 153) the sketch in figure 10.17(a) was taken, "the basic tenet of the area rule ... states that the wave drag of an airplane configuration depends primarily on the longitudinal distribution of the total cross-sectional area. This concept results in the proposition that the wave drag of a simple equivalent body of revolution (that is, a body having the same longitudinal distribution of total cross-sectional area) would be the same as that of the more complex wing-body arrangement." As shown in figure 10.17(a), the cross-sectional area distribution is determined from planes passed through the configuration perpendicular to the longitudinal axis of the body. This procedure is correct only for a Mach number of 1.0, but with a relatively simple modification it can be applied at supersonic speeds (ref. 203).
Figure 10.17(b) shows the variation of drag coefficient with Mach number for a smooth body and the same body having a bump corresponding to the cross-sectional area of a wing. The dramatic increase in drag associated with the addition of a bump to the body is apparent. An obvious conclusion to be reached is that the cross-sectional area distribution of a low-drag wing-body combination should be the same as that of a smooth body of optimum shape. Thus, at transonic speeds, the time-honored principle that the drag of the individual elements of an airplane could be added in a linear manner to give the approximate drag of the entire configuration was forever ended, and the era of the "wasp waist" or "Coke bottle" airplane with indented fuselage began.

1954 sketch of the Transonic  Rule
(a) Equivalent body concept.
diagram illustrating the difference in drag coefficients of different body designs
(b) Variation of drag coefficient for two bodies.
[261Figure 10.17 - The transonic area rule.

The first aircraft to which the area-rule principle was applied was the Convair F-102 delta-wing fighter. With its relatively low-thrust engine, the prototype of this supposed supersonic fighter was unable to pass through Mach 1.0. At the top of figure 10.18 is the total cross-sectional area distribution of the aircraft, together with that of the...

graph of aircraft speed, Mach vs drag coeffecient
[262Figure 10. 18 - Effect of area-rule modifications on drag of Convair F-102 delta-wing fighter.


...various components that make up the complete area distribution. At the bottom of the figure is the variation of drag coefficient with Mach number for the original configuration and for the aircraft with modifications made in accordance with the transonic area rule. The modified aircraft easily passed through Mach 1.0 and entered the supersonic speed regime. The way in which the appearance of the F-102 aircraft was altered by application of the area rule is illustrated in figure 10.19. At the upper left is the experimental Convair XF-92A delta-wing research aircraft. At the upper right is the prototype F-102 delta-wing fighter that was unable to penetrate the supersonic speed range. Incorporating area-rule principles, the F-102A is shown at the lower left with its obvious fuselage indentation. The definitive form of the Convair delta-wing fighter, the F-106, is shown at the lower right and clearly displays the application of the area-rule concept. The reason for the appellation "wasp waist" or "Coke bottle" for aircraft designed according to area-rule concepts is obvious from figure 10.19.

The area-rule principle is now an accepted part of aircraft configuration synthesis and must be regarded as one of the cornerstones....

delta wing design aircraft

delta wing design aircraft

delta wing design aircraft

delta wing design aircraft

[263] Figure 10. 19 - Convair delta-wing aircraft with and without area-rule design. [mfr via Donald D. Baals]


....of transonic and supersonic aircraft design. It clearly differentiates these aircraft from their subsonic ancestors.

Stalling of Swept Wings
The advantages of wing sweep for aircraft designed to fly at high-subsonic, transonic, and supersonic speeds have been discussed above. Along with such advantages, however, these wings can pose serious....

Bell L-39 prop plane
[264Figure 10.20 - Bell L-39 research aircraft intended to explore the problems of low-speed flight with swept wings. [NASA]


....stability, control, and handling problems at high angles of attack in the stalled flight condition; such problems can occur at both high and low speeds. An early NACA flight study of the handling characteristics of an aircraft with swept wings was carried out in 1947 with a modified Bell P-63 propeller-driven fighter. This aircraft, fitted with wings of 35 sweepback, was redesignated the L-39 and is shown in figure 10.20. Note the wool tufts that are attached to the wing surfaces to indicate areas of unsteady or stalled flow. Extensive wind-tunnel studies of the high-angle-of-attack behavior of swept wings and of aircraft configurations equipped with such win s were also made in the years following World War II.

The nature of the problem is illustrated in figure 10.21, in which the variation with spanwise position of the wing aerodynamic load is shown for wings of aspect ratio 4.0 and different sweepback angle and....

graph displaying wing shape vs span load distribution
[265] Figure 10.21 - Effect of wing-planform shape on span load distribution.


....taper ratio. The relative amount of aerodynamic load at each spanwise station is expressed by the span loading parameter GC/GLC, which is the product of the local section lift coefficient at a particular spanwise station and the wing chord at that position, divided by the product of the wing lift coefficient and the mean aerodynamic chord. The curves in figure 10.21(a) indicate that an increase in sweepback angle from 20 to 60 results in a large increase in the value of the loading parameter near the tip relative to that at the root for wings of aspect ratio 4.0 and taper ratio 0.4. Reducing the taper ratio from 0.6 to 0.25 on wings of aspect ratio 4.0 and 40 of sweepback causes a corresponding increase in the relative amount of load carried near the wingtip, as shown by figure 10.21(b). Variations in the aspect ratio for a given sweepback angle and taper ratio also have an important influence on the shape of the span loading curve.

An increase in the value of the span loading parameter from root to tip indicates that the amount of load carried by each section of the wing increases as the tip is approached. If the wing is tapered, the section lift coefficients increase at a greater rate than the loading parameter. Thus, for untwisted wings equipped with airfoil sections having the [266] same maximum lift coefficients, the initial wing stall would be expected to occur near the wingtip at the spanwise location at which the loading parameter is a maximum. Further increases in angle of attack would cause an inward progression of the stall. A loss in load near the wingtip may, depending on the sweep angle, taper ratio, and aspect ratio, cause a forward shift in the wing aerodynamic center of sufficient magnitude to cause the aircraft to become unstable and pitch up to a higher angle of attack and further into the stalled and poorly controlled flight regime. This behavior is in contrast with that of a straight-wing aircraft that has inherent stability at the stall and pitches down to a lower angle of attack and into an unstalled and fully controllable flight condition. Pitch-up at the stall is considered to be a highly undesirable flight characteristic. In the development of a new aircraft, much attention is given to wing design and configuration arrangement to avoid pitch-up. Electromechanical devices (described later) must be used in some cases to provide acceptable flight characteristics at high angles of attack.
The approximate boundary shown on the left side of figure 10.22 delineates the combinations of wing sweep and aspect ratio that show reduced stability, or pitch-up, at the stall from those combinations that show increased stability at the stall. Combinations of aspect ratio and sweep angle that give reduced stability at the stall are in region II to the right of the boundary. The types of pitching-moment curves that might be expected in region 11 are indicated at the top right side of figure 10.22. Combinations of sweep and aspect ratio that are characterized by positive stability at the stall are in region I to the left of the boundary, and the corresponding shape of the pitching-moment curves is shown at the lower right side of the figure. If positive stability at the stall is desired, the curve in figure 10.22 indicates that the aspect ratio must decrease as the sweep angle is increased.
The stability boundary given in figure 10.22 was taken from reference 183 and is for untwisted wings with a taper ratio of 0.5. The results given in reference 189 indicate that increasing the taper ratio from 0.5 to 0 raises the stability boundary; that is, the limiting aspect ratio for stability at the stall is increased for a given sweep angle. Highly swept and tapered delta wings as used on many fighter aircraft generally do not have a pitch-up characteristic, which is one of the attractive features of this planform. Twisting the wing so that the geometric angle of attack of the tip is less than that of the root (termed 11 "washout") may be used to reduce the tendency toward tip stall, as can various types of leading-edge high-lift devices. Some of these devices are briefly discussed in the next section. The spanwise flow along the....

graph of sweepback wing angle affect on stall position
[267Figure 10.22 - Effect of wing-planform shape on static longitudinal stability at the stall. Tall off; taper ratio of 0.5.


....wing that results from the sweepback causes the boundary layer on the outboard sections of the wing to thicken, as compared with an unswept wing. The thicker boundary layer near the tip of the wing causes the maximum lift capability of these sections to be reduced, as compared with the two-dimensional value. The fences seen on the upper surface of many swept wings are intended to limit the spanwise boundary-layer flow and thus increase the maximum lift capability of the outboard sections; at the same time, the boundary layer builds up inboard of the fences and reduces the maximum lift coefficent of that part of the wing. Both these effects of the fence reduce the tendency toward pitch-up.

The discussion so far has dealt only with wing-alone stalling behavior. The stalling and subsequent pitching characteristics of the aircraft, however, are highly dependent upon the details of the aircraft configuration. The longitudinal and vertical position of the horizontal tail with respect to the wing is particularly important. A detailed development of the relationships involved is beyond the scope of the present discussion but may be found in references 189 and 195.
[268] Some indication of the flow phenomena involved in the wing-tail relationship, however, may be gained from figure 10.23. At the top left side of the figure is an aircraft configuration on which the horizontal tail is slightly above or below the chord plane of the wing. At position I the wing is Just beginning to stall and the tail is immersed in the wake. The hypothetical pitching-moment curve in the lower portion of figure 10.23 shows that a reduction in stability is beginning at point 1. At position 2 the aircraft is at a higher angle of attack, and the wake from the wing passes above the chord plane of the tail. The contribution of the tail to the positive stability of the aircraft is therefore increased at point 2, as compared with point 1, because the tail is operating in a flow field characterized by smaller downwash angles and higher dynamic pressure. The pitching-moment curve shown at the bottom of figure 10.23(a) shows the higher stability of the aircraft at position 2 and indicates that there is no real pitch-up, although a small reduction in stability occurs at the stall. The pitching-moment curve for the aircraft configuration with the tail mounted in the low position would be considered acceptable, although not as desirable as that of a design that showed no reduction in stability at the stall.

diagram contrasting low tail and hight positions
Figure 10.23 - Effect of horizontal-tail position on static longitudinal stability.

[269] An aircraft configuration in which the horizontal tail is mounted high above the chord plane of the wing is shown in figure 10.23(b). A greater portion of the wing is stalled on this type of configuration, as compared with the design with the low tail, before the tail encounters the stalled wake. The wake is therefore broader in width and of a lower dynamic pressure for the high tail position. Position I in the upper part of figure 10.23(b) shows the high tail immersed in the wide, low-energy wake. The hypothetical pitching-moment curve at the bottom of the figure indicates the large reduction in stability that accompanies an increase in angle of attack as the tail passes through the wake. Following emergence of the tail from the wake, the aircraft again becomes stable and with further increases in angle of attack reaches a second trim point as indicated by point B on the pitching-moment curve. If the longitudinal control surfaces are in the full nose-down position and the pitching-moment curve appears as depicted in figure 10.23(b), no recovery is possible if the aircraft is allowed to reach the second trim point B.
Although fighter aircraft have in the past been configured with a high tail position, the requirement for fighter-type aircraft to engage in high-g maneuvers at high-subsonic and transonic speeds makes the use of a low tail position very desirable to avoid the possibility of pitch-up into an uncontrolled flight condition. The consequences of such an uncontrolled maneuver in a combat situation can well be imagined. The low tail position as employed on the Grumman F11F fighter, introduced in the mid-1950's, is shown in figure 10.24. The good handling characteristics of this aircraft are evident from its use for many years by the U.S. Navy Blue Angels demonstration team.
Since high-g maneuvers are not required on large transport aircraft, acceptable pitching-moment characteristics can usually be obtained with a high tail position by careful tailoring of the wing and tail designs and their relationships to each other. For configurations that employ engines mounted on the aft portion of the fuselage, careful attention must be given to exact placement of these engines since the wake from the engine nacelles at high angles of attack may combine with that of the wing and contribute to the loss in effectiveness of the horizontal tail. In some cases, acceptable pitching-moment characteristics cannot be achieved by aerodynamic refinements alone. In these cases, mechanical devices such as stick shakers or stick pushers, sometimes both, are employed to prevent the aircraft from entering a potentially dangerous angle-of-attack region. A stick shaker is a mechanical device that causes the control column to vibrate violently as the aircraft....

tail end view of F11F
[270Figure 10.24 - Grumman F11F with all-moving horizontal tail mounted in the low position. [NASA]

....approaches a restricted angle-of-attack range. The vibration is intended to alert the pilot to an approaching stall and to make him take corrective action to reduce the angle of attack. A stick pusher causes the control column to be pushed forward mechanically with a considerable force, perhaps 100 pounds, as the critical angle-of-attack range is approached. Sometimes the devices are employed together, in which case, the stick shaker is first activated, and if the pilot ignores the warning and permits the aircraft to continue pitching to a higher angle of attack, the stick pusher comes into action. Both the stick pusher and the stick shaker are activated by signals from instruments that sense parameters such as angle of attack, rate of change of angle of attack, attitude and its rate of change, or some combination of these parameters.

The preceding discussion deals with the major aerodynamic problem of the swept wing. Other aerodynamic problems of a less fundamental nature are also associated with the use of the swept wing. There are also problems in the areas of structures and aeroelasticity. While these problems are beyond the scope of the present discussion, an indication of the nature of the structures and aeroelastic problems is suggested in figure 10.21(a) by the wings with an aspect ratio of 4 and sweepback angles of 20, 40 and 60°. Increasing the sweepback angle for a given aspect ratio results in an increased length of the wing panel. The length-to-width ratio of the panel, sometimes referred to as the panel aspect ratio, is increased by the factor 1/cos wing sweepback angle for a given aerodynamic aspect ratio. For a given aerodynamic aspect ratio and airfoil thickness ratio, increasing the sweepback angle increases the wing length and causes a reduction in wing bending and torsional stiffness. As a consequence, the problems of aeroelasticity, flutter, and dynamic loads can be intensified by the use of sweepback.