High-angle-of-attack (high-α) aerodynamics is inherently associated with:

• Separated flows (and thus nonlinear aerodynamics)
  • One of the key aspects is the interaction of components—vortex flows in particular (since vortex bursting is also an important effect).
• Heavy dependence on wind tunnel testing
• Flight simulation to ensure good handling qualities
  • This means that large amounts of data have to be acquired to construct the mathematical models of aerodynamics.

The key tutorials and surveys on high-angle-of-attack aerodynamics were written by Chambers and Grafton^[1] and later by Chambers on his own.^[2] Typical high-α issues and concerns for three classes of aircraft are highlighted below. Addressing them requires a good understanding of the high-α aerodynamic characteristics of the aircraft.

General aviation aircraft

• Prevention/recovery from spins. To improve spin resistance, consider the drooped outer panel (NASA LaRC) or the interrupted leading edge (NASA Ames). Do consider placing the vertical tail where it can get “good” flow during a spin, including inclining the rudder hinge line forward rather than aft. It will make it more effective. Also, placing a ventral strake ahead of the rudder, as seen on many general aviation (GA) airplanes, not only adds side area but also produces a vortex at sideslip that helps maintain the entire surface effectiveness. Finally, do not use the tail-damping power factor (TDPF) available in the old NACA literature. It is known not to work.
  Folklore has it that T-tail configurations may have a benefit; the vertical tail and rudder may not be blocked by the wake of the horizontal tail. This may or may not be true.

Fighters

• Resistance to departure from controlled flight
• Ability to control aircraft at high-α air combat maneuvering^[3]
• Allowance for unlimited α range (the F-16 requires an angle of attack limiter)
• Requirement to be able to perform velocity vector rolls^[4] (through inertial coupling, this adds additional nose-down pitching moment requirement)
• Perform the Herbst maneuver (causing a rapid change of heading but also losing a lot of energy, so in a multiple engagement, you may become a sitting duck for someone else)
• Fuselage pointing to allow missile lock-on and fire
• Use of the control system to enhance maneuver capability
• Controls enhanced using thrust vectoring (possibly especially important for stealth a/c).
  • Well known high-angle-of-attack research aircraft: F-18 HARV (thrust vectoring with vanes), X-31 (thrust vectoring with vanes), X-29 (no. 2 had nose blowing)
• Supermaneuverability and aircraft agility are of major interest for advanced fighter design. This requires the use of dynamic measures to assess performance. Supermaneuverability seeks to exploit an unsteady flow effect—the fact that you can get higher C_Lmax’s by so-called dynamic overshoot.

Transports

• As discussed previously in terms of basic transport configuration aerodynamics, the primary high-α problem is the suppression and control of pitchup and avoidance of deep stall. The case study of the DC-9’s development provides an excellent overview of the issues with the T-tail configuration and the stall issues in general.

8.1 Basic Aerodynamics of High-α

8.1.1 Longitudinal

The basic aerodynamic characteristics are illustrated in figure 8-1. This is a notional pitching moment curve. For modern airplanes, the stability may not be a major issue (within reason), but the envelope defining the maximum nose-up and nose-down moments that can be generated is critical, and the minimum value of nose-down pitching moment is a critical condition.

Wind tunnel data^[5] for the F-16 contained in figure 8-2 shows that, for this CG location, the F-16 is limited in angle of attack (AOA) at which it can be trimmed to obtain C_m = 0. Thus the control system is designed to limit the angle of attack that the F-16 can reach to prevent the airplane from encountering a problem. This reference is a classic study and includes detailed aerodynamic math model data.

The following values of suggested design criteria for nose-down pitching moment were developed by Marilyn Ogburn and John Foster at NASA Langley, supported by the Navy.^[6] These are design goals for modern maneuvering aircraft.

Table 8-1: Suggested design criteria for nose-down pitching moment

8.1.2 Lateral/Directional

The typical directional characteristics are assessed in terms of the directional stability, C_nβ. Figure 8-3 provides the generic expectation, while figure 8-4 contains wind tunnel results for an F-5.^[7] Initially the vertical tail provides the stability. However, at angles of attack where the wake from the wing prevents the tail from operating in clean flow, the vertical becomes ineffective. At higher angles of attack, the long forebody on modern fighters can be designed to provide direction stability.

Figure 8-5 shows the generic characteristics for lateral characteristics, which is examined in terms of C_lβ. Initially, wing dihedral or sweep will cause the stability derivative to decrease with angle of attack. However, in a swept-wing situation, asymmetric flow separation characteristics cause the curve to “break” and abruptly become positive.

Figure 8-6 contains actual characteristics of an F-4, with the effects of the maneuvering slats, which are seen to be extremely beneficial.^[8]

These characteristics are used to establish the basic lateral-directional static stability. One of the complications associated with canard aircraft is the wide variation in these characteristics based on canard setting. The trailing vortex system from the canard interacts with the leading-edge vortices of the main wing, forebody vortices, and also the vertical tail. Thus the lateral-directional characteristics of canard configurations play a large role in deciding if a canard configuration is practical. Recall that for classical static stability:

• Directional stability (must be in the stability axis): C_nβ > 0.0
• Dihedral effect (also promoted by wing sweep): C_lβ < 0.0

8.2 Flight Mechanics of High-α

Controllability of flight at high angle of attack can encounter several different types of problems.^[9] Here are some brief descriptions of terms you are likely to encounter.

• Departure: This occurs when the airplane departs controlled flight. It may develop into a spin.
• Wing drop: A roll-type problem caused by asymmetric wing stall (or unstall).
• Wing rock: The aerodynamic rate-damping moments become negative, and the wing starts to oscillate in roll. This is associated with an interaction of the separated flow above the wing, typically the leading-edge vortices that are above the wing.
• Nose slice: When the aerodynamic yaw moments exceed the control authority of the rudder, the airplane will tend to exceed the acceptable sideslip angle and depart through a yawing motion (making this a yaw-type problem).

The basic aerodynamic characteristics described above are often used to try to assess, at least approximately, how susceptible the aircraft is to departure. In reality, you also need dynamic aerodynamic characteristics, but these are usually not available early in the design process. Some static derivative-based dynamic criteria are available to provide guidance. Greer^[10] provided a summary of directional data for numerous aircraft, as well as a very easy-to-read description of the departure problem as it changed from piston fighters to high-speed swept-wing jet fighters. Greer’s report contains nominal characteristics of the following aircraft: XP-92, YF-102, XF4D-1, F-8, F-86D, Mig 15, Bell D-188A, X-15, A-7, F-4E, F-111, F-5, XB-58, Winged Missile, Lockheed SST, the initial Boeing SST B2707, and NASA Generic SST.

In his 1972 paper, Greer wrote:

In the late 1940s low-aspect-ratio swept-wing fighter configurations began to emerge, and it soon became apparent that they would behave very differently at the stall than their predecessor straight-wing configurations. Whereas straight-wing configurations generally experienced a roll-off type of divergence at the stall because of one wing dropping before the other and unstable damping in roll immediately after stall, the swept-wing configurations began to show a directional divergence at high angles of attack.

Thus, it appeared that both C_nβ and C_lβ were important. Greer went on to explain:

A theoretical analysis group headed by Leonard Sternfield, then of Langley, studied the problem and concluded that the divergences occurred when the C-term of the stability quartic became negative and they developed a simplified form of the C-term and called it C_nβdyn, or the directional stability parameter. The derivation of this parameter is given in the appendix.

Greer’s report shows the correlation of various aircraft data with the directional stability parameter. The reasonable correlation showed that this parameter could be used to estimate when aircraft departure would become likely. Note that Lutze et al.^[11] show how this parameter can be derived in very general terms. The discussion of C_nβdyn by Calico^[12] is also useful.

8.2.1 Directional Stability Parameter, C_nβdyn

According to Johnston and Heffley,^[13] C_nβdyn may not be a highly precise predictor of aircraft departure, only approximate. Its target value should be positive, as shown in equation (8-1).

$$C_{n_{{\beta }_{dyn}}}>0\text{(8-1)}$$

where

$$C_{n_{\beta dyn}}=C_{n_{\beta }}\cos \alpha -\left(\frac{I_z}{I_x}\right)C_{l_{\beta }}\sin \alpha \text{.}\text{(8-2)}$$

This is an open-loop parameter. To improve resistance to directional divergence, Greer suggested increasing the vertical tail size (C_nβ) and using leading edge slats (C_lβ). The vertical tail size was increased in the case of the F-100 aircraft. Just looking at pictures of the original design give the impression that the tail was too small. However, since the vertical tail loses effectiveness at high angle of attack, this by itself is not sufficient.

8.2.2 The Lateral Control Divergence Parameter (LCDP)

LCDP is a “good predictor” according to Johnston and Heffley^[14] and shown in equation (8-3).

$$LCDP=C_{n\beta }-C_{l_{\beta }}\left(\frac{C_{n_{\delta a}}}{C_{l_{\delta a}}}\right)>0\text{(8-3)}$$

Negative values imply roll reversal, where the pilot commands roll in one direction, and the plane rolls the other way!

This is a closed-loop parameter. To improve this value, the control system can be used to include the use of the rudder at high angle of attack. This approach, known as an aileron-rudder interconnect (ARI), can dramatically improve the value of LCDP at high angle of attack.

Figures 8-7 and 8-8 show the lateral-directional characteristics of the F-16 aircraft, together with C_nβdyn and LCDP.^[15] Figure 8-8 shows the significant effect the ARI has on LCDP.

Some effort has been made to correlate the values of these parameters to define regions in which something can be said about departure characteristics. These parameters have been combined to suggest the best region to operate in the design space. The original chart is derived from Weissman,^[16] but Bill Bihrle added some more details,^[17] leading to the chart shown in figure 8-9.

Other requirements:

• Dynamic derivatives (generally from forced oscillation testing):
  • C_nr < 0.0 (yaw damping) not too pro spin
  • C_lp < 0.0 (roll damping) < 0 to prevent wing rock

8.2.3 The Spin

If the departure develops into a spin, there are a few things that are known.

First, the mechanics depend on the sign of the term (Ix – Iy).

• If (Ix – Iy) > 0, the plane is said to be wing heavy (typically GA airplanes).
• If (Ix – Iy) < 0, the plane is said to be fuselage heavy (typically modern supersonic fighters).

There are also some rough guidelines to recover from a spin:

• If (Ix – Iy) > 0, ailerons are applied against the spin, elevator down.
• If (Ix – Iy) < 0, ailerons are applied with the spin.

A key survey on spins is again by Chambers^[18] and should be studied for further insight.

8.3 Control Effectiveness With Angle of Attack

Control effectiveness tends to diminish as the angle of attack increases. This is especially true for the ability to generate yawing moment. Figure 8-10 shows the reduction in control forces with angle of attack for the same F-16 wind tunnel test illustrated previously.^[19] Note that this reference is a classic study that includes detailed aerodynamic math model data.

Figure 8-11 shows a somewhat novel way of generating yawing moment for a supersonic tactical aircraft configuration (STAC) using differential canard deflections to make up for the loss of rudder effectiveness.^[20] Here, differential tail is also used to make up for the rudder.

Thrust vectoring can also play an important role in providing control power at high angles of attack. This also means that the thrust must be provided so as to create a moment arm. Sometimes this is a problem, preventing the use of deflected thrust to be used for trimmed lift.

8.4 The F-22: Putting It All Together (An Example)

The F-22 is one of the more recent airplanes to require high-angle-of-attack capability. Charles M. Wilson from Lockheed Martin gave a talk at Virginia Tech in November 1996 called “High Angle of Attack Design Considerations.” The main purpose was to give the attendees an appreciation for integrating high-angle-of-attack (high-α) flight into the F-22 external configuration (or the outer mold line). Charlie left a copy of the charts he used in his discussion of the high-α development effort. He used examples of wind tunnel data for YF-22 (the prototype configuration) to present design considerations for forebodies and vertical tails of the F-22. He showed the effect of the leading-edge flap (LEF) schedule on the lateral-directional characteristics and the nose-down pitching moment across the angle-of-attack range, including the effect of thrust vectoring. Finally, he presented the maximum roll rate as a function of angle of attack, also showing the significant benefit of thrust vectoring using comparisons with the F-15. Images and narratives from selected slides from his presentation are shown in figures 8-12 through 8-15. A related paper on the YF-22 is by Clark and Bernens.^[21]

Figure 8-12 shows a perspective view of the F-22 configuration that illustrates blended-wing body shaping for stealth with integrated propulsion for supercruise capability. The figure shows flight control surfaces, their no-load rates, and deflection limits. For example, the ailerons have a no-load rate of 70° per second and a deflection limit of ±25°. Horizontal tails are primarily for longitudinal control with considerable assistance from thrust vectoring at lower speeds. Leading-edge flap, flaperon, and ailerons are scheduled with angle of attack and Mach number to improve performance, stability, and control. Flaperon, aileron, and differential horizontal tail combine for roll control with leading-edge flap added at moderate angles of attack. Rudder power is augmented at high angles of attack by differential horizontal tail and nonsymmetric aileron/flaperon. Instead of a dedicated speed brake, the aircraft combines up-deflected aileron, down-deflected flaperon, and outboard rudder to increase drag, using horizontal tails to trim.

Figure 8-13 illustrates enhancement of YF-22 maneuvering capability by thrust vectoring. The longitudinal benefits of thrust vectoring are substantial at high angles of attack, where control power can be maintained equivalent to that achieved at low angles of attack. As AOA increases, aerodynamic controls such as the horizontal tail lose effectiveness. Jet-induced effects contribute a significant portion of the pitching moment due to vectoring. Since the YF-22 propulsion system does not have afterburning (A/B) capability, thrust vectoring supports pitch rates of at least 20° per second to be generated even when initiated from 120 KEAS and 24° per second, whereas an F-16 can only generate 4° per second nose-up pitch rate. Typical pitch characteristics break stable at some AOAs. The nose can no longer be held above the AOA where full nose-up control crosses the pitch axis to the nose-down side. Without A/B, thrust vectoring extends the controllable AOA range by about 20°. However, if you rely on thrust vectoring, remember that the engines may be at idle thrust and you need confidence that the engine will keep running, which isn’t always a sure thing at high-α.

Figure 8-14 provides strong evidence that leading-edge flaps (LEFs) are indispensable for high-α flights. With proper scheduling, they smooth out nonlinearities in pitch characteristics, as shown in figure 8-14(a). This helps decrease gains in longitudinal control laws. LEFs can be scheduled to improve lateral-directional stability, as shown in figures 8-14(b) and (c). They provide additional roll and anti-spin control power at moderate-to-high angles of attack. In addition, LEFs allow the wing camber to be tailored to maximize performance and improve control effectiveness of trailing-edge devices. They can also be a resource at higher speeds to control wing loads in order to change pressure distributions or to decrease buffet energy. During the F-22 configuration development, leading-edge flaps improved stability and control characteristics more than any of the vertical tail locations.

The impact of thrust vectoring on the F-22 roll rate can be illustrated by data from the YF-22 configuration shown in figure 8-15. For fighter aircraft at high angles of attack, stability axis roll rates are limited by the available yaw control power. That is why augmented aerodynamic rudder power and yaw thrust vectoring was used on the following demonstrators:

1. The Rockwell-Messerschmitt-Bölkow-Blohm experimental jet aircraft X-31 was designed to test fighter thrust vectoring technology, demonstrating significantly more maneuverability than most conventional fighters.
2. The General Dynamics (now Lockheed Martin) F-16 MATV (multi-axis thrust vectoring) demonstrated effective maneuvering beyond its 25° angle of attack limit to almost 100° AOA.
3. The McDonnell Douglas F-18 HARV (High Alpha Research Vehicle) demonstrated stable flight at approximately 70° angle of attack and rolling at high rates at 65° angle of attack, which would have been nearly impossible above 35° without thrust vectoring.

The F-22 blends use of differential horizontal tail from primarily rolling moment below 20° AOA to primarily yawing moment at high AOA. Pitch thrust vectoring relieves some of the demand for longitudinal control from the symmetric horizontal tail position, which allows it to be positioned for more effective yaw command. Figure 8-15 shows that the F-15 runs out of roll capability around 30° AOA, but the innovative use of the YF-22 horizontal tail provides the pilot with the ability to continue controlling the plane of the lift vector and to out-maneuver the adversary to higher AOAs. Thrust vectoring allows the F-22 to counter higher levels of inertial pitch coupling due to roll rate. This is evidenced near 20° AOA, where roll rates for the YF-22 are comparable to the smaller F-16 and more than twice that of the F-15.

8.5 Some Configuration Issues: Amazing Stories

8.5.1 Story No. 1: Flow Asymmetries at High Angle of Attack

In many cases, as the angle of attack increases, the flow develops asymmetrically even though the body is as nearly symmetric as possible, and the body is not yawed! The effect is to produce a side force over the nose of the body and therefore a yawing moment for the vehicle. This is particularly important for fighter aircraft with long forebodies.

In fluid mechanics terms, an axisymmetric body can produce an asymmetric flow at certain angles of attack. This is not too surprising, as the flow is simply unstable (recall the Kármán vortex street). Perhaps the key study relevant to fluid mechanics of aircraft at high-α was a fundamental study by Lamont^[22] in the NASA Ames Research Center low-turbulence 12-foot pressure wind tunnel. An ogive cylinder was studied over a range of angles of attack (20° to 90°) and Reynolds numbers (0.2x10⁶ to 4.0x10⁶). More importantly, the model was tested at numerous different roll angles, which should not have resulted in any changes in the results. However, the results showed large variations in the side force with roll angle at angles of attack starting at about 30° or 35°. Reynolds number effects were also identified. For our purposes, it turns out that the low and high Reynolds number results were similar, but there was a large Reynolds number range, which unfortunately includes most of the wind tunnels, which saw significant variation in the Reynolds number effect. This could explain something I used to hear from engineers at the Full-Scale Tunnel at NASA Langley, who would claim, “We get the right answer, the one found in flight.” Turns out they were operating at a very low Reynolds number, and it was lucky they got the right answer! The problem of Reynolds number scaling effects applied to high-angle-of-attack flow has received continuing attention.^[23]

To address flow asymmetry, small nose chines were added to fix the separation location at the nose in the X-29 aircraft. The F-22 and F-35 also have chined forebodies.

8.5.2 Story No. 2: The Role of the Forebody on Stability at High-α—The F-5 Nose Story

At low angle of attack, the vertical tail provides directional stability. However, as the angle of attack increases, its effectiveness decreases. Typically this occurs because it’s operating in the wake of the wing flow field. However, some aircraft start to exhibit increasing stability at higher angles of attack. In particular, the F-5 was tested at NASA’s Langley Research Center, and a novel investigation was made.^[24] Directional stability was found for the entire configuration. Then the vertical tail was removed. Finally, the forebody alone was tested. As expected, at low angle of attack, the tail provided directional stability. The contribution of the tail started to disappear at about 17° or 18° α. The vertical tail-on and -off data were essentially the same starting at 30° α. However, at this angle of attack, directional stability was becoming positive and increasing rapidly. When the forebody was tested alone, the results agreed with the other configurations beginning at about 30° α. Thus, the conclusion was that the forebody was responsible for creating a stable configuration even though it had significant side area ahead of the center of gravity.

The reason for this phenomena? The vortices shed from the nose developed asymmetrically with sideslip. The vortex on the lee side left the surface, while the vortex on the windward side remained close to the surface (in effect, it was blown onto the surface). The low pressure under the windward vortex in effect “sucked” the forebody back toward the zero-sideslip condition, the condition for stability. The forebody result was simulated computationally by Mason and Ravi.^[25]

As a result of the favorable forebody characteristics found in the wind tunnel data, many investigations have been made to find good forebody shapes.^[26] Chines have also been of interest due to their good stealth characteristics. However, there is a problem, as forebodies with too much directional stability tend to lack yaw damping and want to “swing past” the unyawed position. Hence, a combination of directional stability and yaw damping must be found. The F-22 forebody reflects this trade. The forebody was set to have minimum basic flow asymmetry while maintaining reasonable yaw damping and directional stability.

8.5.3 Story No. 3: The Complexity of Component Interaction at High Angle of Attack

The Research Fighter Configuration (RFC) was a joint project between Grumman and NASA’s Langley Research Center to understand high-angle-of-attack aerodynamic design within the context of a supersonic cruise-maneuver and transonic-maneuver airplane. Anticipating success based on a previous program with a smaller canard,^[27] the configuration was designed and several wind tunnel models were built. The design was tested at NASA Langley and at Grumman. Essentially, the results for the different models and different facilities agreed.

It was found that the directional stability of the model was extremely sensitive to the canard setting and that the twin vertical tail version of the airplane had a significantly lower maximum lift because of an adverse interaction with the vortices from the wing. This configuration showed complicated interactions between the forebody vortices, the canard trailing vortex system, the wing leading-edge vortices, and the vertical tail. No open literature report was ever published on this work.

Figure References