Trim Drag Research Articles

Canard/tail comparison for an advanced variable-sweep-wing fighter

Equivalent canard and tail control surfaces are compared on an advanced, carrier-based fighter/attack aircraft featuring variable wing sweep and vectorable, two-dimensional nozzles. Evaluations of stability and control characteristics, trimmed drag due to lift, minimum takeoff rotation speeds, and carrier approach speeds are presented. The results show that the canard configuration has substantially less supersonic trim drag and a lower carrier approach speed, which can yield appreciable takeoff weight savings, but the tail configuration exhibits better stability and control characteristics with less development risk.

New Shape in the Sky

Currently undergoing NASA flight testing is the Grumman X‐29 forward swept wing (FSW) demonstrator aircraft which was built under a contract sponsored by the Defence Advanced Research Projects Agency (DARPA) and funded through the Air Force. The FSW aircraft first took to the air in December, 1984 and after four flights with the manufacturer was handed over to NASA for a verification programme involving all the benefits of this design. Advanced technology features which will be demonstrated are the forward swept wing for improved aerodynamic efficiency and good control at high angles of attack; tailored composite wing structure that resists the tendency towards structural divergence inherent in this configuration; thin supercritical aerofoil for improved transonic performance at high lift coefficients; variable camber trailing edge to reduce drag at all lift coefficients and avoid supersonic drag associated with aerofoil camber; canard longitudinal control for efficient trimming of variable camber pitching moments and favourable canard‐wing interactions; highly relaxed static stability for very low trim drag at all Mach numbers; and a digital fly‐by‐wire flight control system.

Aerodynamic canard/wing parametric analysis for general-aviation applications

Vortex panel and vortex lattice methods have been utilized in an analytic study to determine the two- and three-dimensional aerodynamic behavior of canard and wing configurations. The purpose was to generate data useful for the design of general aviation canard aircraft. Essentially no two-dimensional coupling was encountered and the vertical distance between the lifting surfaces was found to be the main contributor to interference effects of the three-dimensional analysis. All canard configurations were less efficient than a forward wing with an aft horizontal tail, but were less sensitive to off-optimum division of total lift between the two surfaces, such that trim drag could be less for canard configurations. For designing a general aviation canard aircraft, results point toward large horizontal and vertical distance between the canard and wing, a large wing-to-canard area ratio, and with the canard at a low incidence angle relative to the wing.

Effects of displacement and rate saturation on the control of statically unstable aircraft

Methodologies are presented for the analysis and design of stability augmentation control laws for aircraft in which hard displacement and rate limiting are significant. Candidate control laws are derived using the linearquadratic (LQ) regulator. Analytical and computational estimates of the stability limits imposed by control saturation are presented using state trajectories, as well as describing functions and eigenvalue computation. Analysis also includes an investigation of the interaction of the state-space saturation and stability boundaries for various choices of LQ weighting matrices. For minimum energy control, the saturation and stability boundaries are shown to be parallel. In this case, there is a direct relation between the solution to the matrix Riccati equation and the aircraft's open-loop dynamics. V IRTUALLY all aircraft control system actuation mechanisms possess hard limits on deflection and rate of deflection, and accounting for these limits is particularly important for aircraft designed with relaxed or negative static stability. Relaxed static stability generally leads to reduced weight and trim drag, both of which enhance the aircraft's performance.1 Relaxed static stability also may lead to increased control activity.2 For such aircraft, consideration must be given to the effects of control saturation on the initiation and, more importantly, the arrestment of dynamic motions, if departure from controlled flight is to be prevented. It may be possible to provide hardware actuation limits large enough so that normal disturbances and command inputs do not force the controls and to their mechanical, hydraulic, or electrical stops; however, there is no guarantee that commanded control deflections or rates will not exceed any established limit. Therefore, it is important to define the region within which stability and satisfactory response can be assured. This paper explores the effects of deflection and rate saturation on the stability of a statically unstable aircraft. This paper also reports on the development of methodologies for the analysis and design of stability augmentation control laws, with emphasis on response to initial conditions. (Command response is presented in Ref. 3 is the subject of a separate paper.11) Candidate stability augmentation system (SAS) control laws are derived using optimal control theory, with the linear-quadratic (LQ) regulator taken as the fundamental solution. Analytical and computational estimates of the stability limits imposed by control saturation are presented.

Comment on "Ideal Tail Load for Minimum Aircraft Drag"

P E. V. Laitone's Engineering Note on ''Ideal Tail Load for Minimum Aircraft Drag, [J. Aircraft 15, 190-192 (1978)] is interesting in its use of the basic biplane equation and Munk's stagger theorem for estimating trim drag. However, there are errors in the conclusions and some of the basic assumptions of the note. First, in modern high-speed transport aircraft the contribution of compressibility drag to the total trim drag problem is very significant. The download on the tail increases the total lift that the wing must carry and if the airplane is operating near the Mach number for drag divergence the required increase of wing angle of attack will cause an increase in compressibility drag. This compressibility contribution is of the order of half of the total trim drag. On the other hand, when compressibility drag is not present the interference term in the biplane equation introduces a negative drag term which compensates to a large degree for the obvious induced drag penalties on the tail due to its download and on the wing due to the greater wing lift. Second, even with compressibility drag, trim drag is generally much less than the 5% mentioned by Professor Laitone. Figure 1 shows the variation of trim drag with center-of-gravity position for various lift coefficients and Mach numbers for a DC-8-54 aircraft. Typically, the DC-8 flies at a CL of about .35. At the original design cruise Mach number of 0.82 and at an average center-of-gravity position of about 26% of the mean aerodynamic chord, the trim drag is 2.2% of the total drag. With some consideration of aft loading cargo the average center of gravity might be moved to about 29%. The trim drag will then be 1.6%. Since the dramatic rise in fuel prices, cruise Mach number has been reduced to 0.8 to reduce compressibility drag. The trim drag penalties are then 1.4% at 26% center-of-gravity position and 0.9% at 29% e.g. position. These representative numbers are well below 5%. Only at high CL and Mach number and at far forward center-of-gravity positions can trim drag approach such high values. Third, Professor Laitone concludes that large trim drag savings could occur if only transport aircraft were designed with larger tails. An aircraft design is a matter of complete integration and a savings in trim drag would have to be weighed against the weight and parasite drag penalty of the larger tail. If we accept the possibility of a 1% decrease in induced drag from the zero tail load case with tail upload this corresponds to something like a 0.4% reduction in total drag since induced drag is approximately 0.4 of the total drag in cruise. Then the total trim drag gain from current practice is of the order of 2.0% of total drag. To gain this 2.0% one would have to move the center of gravity well aft and to do that would require significant increases in the horizontal tail size. Since the horizontal tail contributes about 8% of the total parasite drag or about 4.8% of the total drag it can be seen that a significant increase in this tail size would quickly

Aerodynamic Design of a Mach 2.2 Supersonic Cruise Aircraft

The McDonnell Douglas Corporation has conducted numerous Mach 2.2 supersonic aircraft design and in- tegration studies in support of the NASA Supersonic Cruise Aircraft Research (SCAR) program. This program traces the evolution of a baseline study configuration and an improved performance configuration through several aerodynamic design and trade study cycles. The impact of real-world constraints on configuration design is discussed. Previous studies have not addressed the Mach 2.2 cruise design condition and this work has resulted in a structurally feasible configuration capable of achieving £/D's in excess of 9 at this cruise Mach number. The purpose of this paper is to present the resulting design and wind-tunnel test results for two configurations. The wind-tunnel test results are compared to the analysis methods. N 1972, interest was renewed both at NASA and in the industry in conducting technology assessment studies on supersonic cruise aircraft. The NASA Supersonic Cruise Aircraft Research (SCAR) program emerged late in 1972, charged with the task of identifying, through aircraft design studies, key technologies whose pursuit would lead to im- proved aerodynamic efficiency, reduced operating costs, and environmental compatibility for typical next-generation supersonic cruise configurations. McDonnell Douglas (MDC) reassessed the entire spectrum of supersonic travel beginning with a market analysis and a review of technology available at various design Mach numbers. Results of these preliminary design studies indicated that a 273-passenger, Mach 2.2 aircraft offered the best mix of low operating costs, productivity, near-term technology materials, and reduced program risk for typical supersonic transport con- figurations. 1 Using this as a starting point, McDonnell Douglas conducted numerous aerodynamic studies, trade studies, and sizing studies in support of the SCAR program.2'3 A baseline study configuration, shown in Fig. 1, emerged, which was a structurally feasible arrow-wing configuration promising good cruise L/D's. Subsequent studies indicated that improved performance was available through wings optimized to reduce configuration trim drag. In 1975, a cooperative MDC-NASA wind-tunnel test program was conducted in which the performance of the study baseline configuration and an improved-perf ormance configuration was substantiated, and the analytical techniques used in their design were validated. Methods of Analysis The primary analytical tools used in the aerodynamic design and analysis of the McDonnell Douglas advanced supersonic cruise aircraft configuration have been the Woodward program4 and the Douglas Arbitrary Body Wave Drag Program.5 The McDonnell Douglas version of the Woodward program has been extensively modified to im- prove its versatility. In the SCAR studies it was used in both the inverse (optimization) and direct (analysis) modes. Wings were designed by optimizing the wing camber distributions for minimum drag due to lift at specified CL's, with and without specified pitching moments. Wings were primarily optimized as wings alone extended to the fuselage centerline, but some optimizations were done in the presence of the fuselage. Drag due to lift and wing-body pitching moments were computed by direct analysis of wing-body combinations including wing thickness effects. Wing panels were spaced equally spanwise and chordwise on both wings alone and wings exterior to the fuselage. All wings were represented by 9 spanwise and 12 chordwise panels, which is sufficient for converged solutions. Biquadratic interpolation was used to determine exterior wing camber distributions from wing-alone optimizations, and vice versa. A typical Woodward wing-body paneling scheme is shown in Fig. 2. Although not depicted on Fig. 2, the Woodward program was used in the full configuration mode to calculate wing-body pitching moments, including the ef- fects of forebody lift. Configuration zero-lift wave drag was calculated using the McDonnell Douglas-developed Arbitrary Body Wave Drag Program which calculates, based on the area rule theory,6'7 the wave drag of completely arbitrary configurations. All analyses were performed on full wing-body and wing-body- nacelle configurations at their cruise attitudes. While the program can accept cambered fuselages with exact cross sections, it has been determined that cambered fuselages with

Optimising the shape

THE ECONOMIC and operational efficiency of any supersonic airliner depends on the successful reconciliation of two conflicting aerodynamic requirements: good control and handling characteristics at subsonic and transonic speeds and low trim drag at supersonic speeds. Years of aerodynamic research have established the slender delta wing as the optimum shape for mach two cruise. In the Concorde design, the basic slender delta was modified by cambering the profile and tapering the forward part of it, refining the wingtips and leading edges to give improved low speed controllability without detriment to supersonic performance. Thousands of hours in different wind tunnels have enabled optimisation of the shape of the aircraft. Some results which were not available in time for incorporation on the prototypes have already been embodied on the pre‐production and production planes. Even though some of these modifications, such as elongation, redesigned nose vizor and tail shape were not applied for aerodynamic improvements, they have nevertheless affected aerodynamics.

Some Trim Drag Considerations for Maneuvering Aircraft

The results of a preliminary analytical and experimental study of trim drag characteristics at maneuvering lift coefficients have been summarized. The study included aft-tail configurations at subsonic and supersonic speeds and canard configurations at subsonic speeds. It is shown that the tail load required to minimize trim drag is highly dependent on the wingbody drag-due-to-lift characteristics with examples presented for both the full and zero leading-edge suction cases. For the high drag case (corresponding to zero leading-edge suction), which tends to be typical at high maneuvering lift coefficients and high speeds, rather large uploads on the tail are required to reduce the trim drag problem. The analytical predictions of trim drag characteristics compare well with the experiment for the aft-tail configuration. At supersonic speeds, reductions in down tail load required to trim, obtained by increasing tail volume and thereby allowing a favorable rebalancing of the aircraft, result in relatively large reductions in trim drag for aft-tail configurations. At subsonic speeds, the experimental studies for the canard configuration exhibit considerably higher trim drag than the analytical prediction as a result of canard stall.