Low Aspect Ratio Wings Research Articles

A Consideration on the Hydrodynamic Normal Forces Acting on the Bilge Keel

A brilliant development of the theory of waves generated by a body oscillating in the free surface has remarkably improved theoretical prediction of ship motion in waves. However, there is yet room for improvement of the accuracy of predicting the rolling motion, because the damping coefficient for rolling is still estimated by a semi-empirical formula. This paper is devoted to improving the estimation of roll-damping force for real ships with usual hull-forms. By the way, Yuasa et al. investigated the hydrodynamic forces acting on an oscillating flat plate immersed enoughly in the fluid in both cases where the flat plate has forward speed and not.On the contrary, this paper deals with the hydrodynamic normal forces to the surface of bilge keel, which damps the rolling motion of a ship. However, for bilge keels attached to three-dimensional bodies, some effects which need not be considered for an oscillating flat plate should be taken into consideration. Among such effects, the effect of mirror image of a bilge keel with respect to the hull surface and the effect of increase of relative flow speed at the bilge are especially important. By taking account of both effects, the authors succeed in relating the damping force acting on the bilge keel without forward speed to that on an oscillating flat plate, and also estimating approximately the damping force of the bilge keel with forward speed by low aspect ratio wing theory for uniform motion.

Spanwise cambered delta wing with leading-edge separation

Smith's method of calculating flow with leading separation on plane delta wings in subsonic flow is extended to the case of spanwise cambered delta wings, through the use of a system of conformal transformations. A numerical procedure to develop the required transformation is described. Using the transformations, a study of the effect of spanwise camber on the flow characteristics such as vortex core location and strength, sheet shape, pressure distribution, and normal force is made on a conically cambered delta wing. It is found that, at a given incidence measured from the respective zero lift angle, the core vortex on the cambered wing lies more outboard towards the leading edge and closer to the wing surface than that on the plane wing. Core and sheet vortex strengths of the cambered wing are less than those of plane wings. Significant changes in sheet shape and the location and magnitude of suction peaks are observed as a function of spanwise camber. However, with increase in incidence, the camber wing characteristics approach those of the plane wing, indicating the diminishing influence of spanwise camber on the flow details at large incidence. Since the theoretical flow model is based on the assumption of conical flow in the separated flow field and slender wing theory for attached flow, the method is applicable in the forward region near the apex of low aspect ratio wings.

New Approach to Hydrodynamic Forces on Oscillating Low Aspect Ratio Wings

A new approach to calculating the hydrodynamic forces acting on harmonically oscillating low aspect ratio wings is presented. This approach is based on free streamline theory and lifting surface theory. The hydrodynamic forces can be represented by a linear combination of the inertia force, the first order damping force, that is to say “lift”, and the second order damping force, that is to say “drag”. Each component of these forces estimated by the model of lifting surface with free stream is compared with the experimental results obtained by the forced oscillation of rectangular low aspect ratio wings. And chordwise pressure distribution estimated by the model is compared with that of measurement.As the results of these comparisons, the following conculsions are derived :1) Although the equivalent total drag coefficient, Cdt, of estimation increases monotonously with the inverse of reduced frequency, that of experiment is not so much varied with reduced frequency, k, for fixed period parameter, P. P., and aspect ratio, A. R. In the range of small 1/k the experimental Cdt becomes less than that at the time when 1/k equals to zero.2) The result of the chordwise pressure distribution shows that as 1/k increases drag forces decrease and lift forces increase, so Cdt is not so much varied then.3) The added inertia coefficient, Cm, of experiment is remarkably dependent on k however, that of estimation is close to 1.0 and less dependent on k in low aspect ratio wings. In the range of small 1/k experimental Cm is much greater than 1.0 and it becomes close at estimated Cm as 1/k increases.

Slowly Oscillating Pointed Low Aspect Ratio Wings at Sonic Speed with Thickness Effect

Slowly Oscillating Pointed Low Aspect Ratio Wings at Sonic Speed with Thickness Effect

A Theory for Rectangular Wings with Small Tip Clearance in a Channel

SummaryEquations are derived for the total lift about low aspect ratio wings in an inviscid, incompressible, uniform flow. The analysis extends Bollay’s analysis, which followed the line suggested by Prandtl, and it is shown experimentally that Bollay’s simplifying assumptions can still be applied. Agreement is good between the present theory and the author’s experiment for values of total lift with small tip clearance.

Leading-edge force features of the aerodynamic finite element method.

Description of a practical procedure for computing the wing leading-edge thrust distribution by the finite element method. When incorporated into a wing-body aerodynamic computer program, the technique is capable of predicting (at subsonic and supersonic speeds) the leading-edge thrust distribution (and therefore, the lateral-directional stability derivatives due to roll) and the nonlinear aerodynamic characteristics of low aspect-ratio wings with leading edge separation due to the application of suction technology.

Concept and conduct of proof test of F-111 production aircraft

F-111 aircraft are in service with both the Tactical Air Command and the Strategic Air Command in the USAF. The aircraft performs primarily in the fighter-bomber role for TAC and as a strategic bomber capable of high and low altitude penetration with SAC. Over 100 000 flight hours have been accumulated by the F-111 fleet including a limited amount of combat flying. The broad spectrum of service requirements for the F-111 include short field take-off and landing capability, all weather and deep interdiction, close air support with large payloads, high altitude high speed air defence, and world-wide deployment with minimum tanker support. Major technical advancements were necessary in meeting these requirements, including most notably a variable-sweep wing. The unswept high aspect ratio positions provide for maximum range and endurance and short take-off and landing distances. The wing in moderate sweep positions provides an efficient configuration for sustained high subsonic and high altitude supersonic flight. Supersonic flight at sea level at speeds in excess of the capability of any other aircraft plus supersonic speeds at altitude in excess of Mach 2.0 are achieved in a most highly swept low aspect ratio wing position.

Recent Work on Radio Frequency Ion Thrusters

1 Pitts, W. C., Nielsen, J. N., and Kaattari, G. E., Lift and Center of Pressure of Wing-Body-Tail Combinations at Subsonic, Transonic and Supersonic Speeds, Rept. 1307, 1957, NACA. 2 Alien, H. J., Estimation of the Forces and Moments Acting on Inclined Bodies of Revolution, RM A9126, March 1951, NACA. 3 Alien, H. J. and Perkins, E. W., of Flow Over Inclined Bodies of Revolution, RM A50L07, March 1951, NACA. 4 Flax, A. H. and Lawrence, H. P., The Aerodynamics of Low-Aspect-Ratio Wings and Wing-Body Combinations, Rept. CAL-37, Sept. 1951, Cornell Aeronautical Lab., Buffalo, N. Y.; also Proceedings of Third Anglo-American Aeronautical Conference, Brighton, England, Sept. 1951, London, Royal Aeronautical Society, 1952. 5 Eaton, P. T., A Method for Predicting the Static Aerodynamic Characteristics of Low-Aspect-Ratio Configurations, Rept. 2216, June 1966, David Taylor Model Basin, Washington, D. C. 6 Gersten, K., Calculation of Non-Linear Aerodynamic Stability Derivatives of Aeroplanes, Rept. 342, 1961, 1962, Advisory Group for Aeronautical Research and Development, Paris. 7 Franz, G. E., Lift Curve Slopes of Low Aspect Ratio Wings at Transonic Speeds, Applied Mechanics TN AM-TN-2-63, June 1963, North American Aviation, Columbus, Ohio. 8 Douglas Aircraft Co., USAF Stability and Control DATCOM, Rev. W-P AFB, June 1969, Vol. 2, Wright-Patterson Air Force Base, Ohio. 9 Hoerner, S. F., Fluid Dynamic Drag, 2nd ed., Sighard F. Hoerner, Midland Park, N. J., 1958. 10 Dommasch, D. O., Sherby, S. S., and Connolly, T. F., Airplane Aerodynamics, Pitman, New York, 1961. 11 Beil, W. J. et al., Major Developments for the Jet Vane Controlled Bomber Defense Missile, BE-754-S-24, March 1955, Cornell Aeronautical Lab., Buffalo, N. Y.

On the Characteristics of Wing with Tip Clearance : Part 3, The Force Acting on a Rectangular Wing of Low Aspect Ratio

On the Characteristics of Wing with Tip Clearance : Part 3, The Force Acting on a Rectangular Wing of Low Aspect Ratio

板翼の超音速フラッター速度の一計算法

A method to calculate the supersonic bendingtorsion flutter speed of cantilever plate wings of low aspect ratio is presented. The deflection mode is assumed in a double power series expansion of spanwise and chordwise variables, and the flutter determinant is derived with the aid of the principle of minimum potential energy of the dynamic problem. The chordwise variable is measured from the midchord line along the stream direction for swept-back wings. For the aerodynamic force, the piston theory including the effect of wing thickness is used. Numerical computation is carried out for a cantilever trapezoid tested at the National Aerospace Laboratory. It has been observed that the ten terms approximation yields a good result in comparison with the twenty terms approximation. It has been clarified that the effect of aerodynamic damping on the flutter speed is very small. Reasonable results are obtained in comparison with the experimental results. Furthermore the present method is extended to cantilever plates partially clamped at the root.

Lateral motion of a slender body between two parallel walls

The method of matched asymptotic expansions is used to determine the lateral flow of an ideal fluid past a slender body, when the flow is constrained by a pair of closely spaced walls parallel to the long axis of the body. In the absence of walls, the flow field would be nearly two-dimensional in the cross-flow plane normal to the body axis, but the walls introduce an effective blockage in the cross-flow plane, which causes the flow field to become three-dimensional. Part of the flow is diverted around the body ends, and part flows past the body in the inner cross-flow plane with a reduced ‘inner stream velocity’. An integro-differential equation of identical form to Prandtl's lifting-line equation is derived for the determination of this unknown inner stream velocity in the cross-flow plane. Approximate solutions are applied to determine the added mass and moment of inertia for accelerated body motions and the lift force and moment acting on a wing of low aspect ratio. It is found that the walls generally increase these forces and moments, but that the effect is significant only when the clearance between the body and the walls is very small.

The Calculation of Aerodynamic Forces and Pressures on Wings Entering Step Gusts

SummaryLifting surface computer programs now exist for calculating the air forces on oscillating wings of general planform. These have made it practicable to evaluate the transient forces on wings entering step gusts by using a long-established relation between oscillatory and indicial forces. As examples, the indicial forces on a low aspect ratio wing in incompressible flow and the indicial pressures on a delta wing at a low subsonic Mach number are calculated. In the latter case the calculated results, which are based on attached flow, are compared with measurements on the same wing in conditions of separated flow. Despite the differences in flow, surprisingly similar development histories are found.

Hydrodynamics of Screw Propellers Based on a New Lifting Surface Theory (The 2nd Report)

Recently, the auther has developed a new lifting surface theory for low aspect ratio wings, in which the bound vortices representing the wing are distributed not over the projected surface on the stream plane but over the wing surface itself, while the free vortices are trailed along the locus of the moving wing under the category of linearized theory.In the present paper, the application of this new lifting surface theory to screw propellers is discussed theoretically. The bound vortices representing the screw blade are distributed over the helical surface of the blade itself, while the free vortices are trailed along the helical locus of the moving blade. It is desirable to treat the problem three-dimensionally, in order to investigate the form of load distribution, not only in the radial direction but in the chord direction, in relation with the blade shapes and the working conditions. A two-dimensional integral equation that relate lift and downwash distributions on the screw blade is formulated. The numerical method of solution of the equation is obtained, considering the singularity of the kernel functions.Besides, some numerical calculations are made to examine the characteristics of the kernel functions.

A New Integral Equation of the Lifting Surface with Low Aspect Ratio and its Approximate Analysis

In this paper, the approximate analysis of the low aspect ratio wing is carried out, getting a new integral equation of the lifting surface being oblique in the plane of free stream in order to estimate the lift distribution on the wing with low aspect ratio.The bound vortices are herein assumed to be distributed over the wing surface that is considered as the lifting surface and hence the induced free vortex filaments extend over the infinite down. stream having reasonable small angle to the wing surface.Applying this integral equation to the extreme case of the lifting surface, it is shown that Munk's Integral Equation is derived in case of the infinite span, and on the other hand, in case of the infinite chord wing the same result is given as that being obtained by Newton's momentum theory. The integral equation identical with that by Prandtl is further derived from the author's equation, putting aspect ratio high as the approximate treatment.

Experimental study of vortex flow about low aspect ratio wings and circular cones at M = 2

Characteristic of the flow about wings of low aspect ratio with subsonic leading edges and bodies of revolution at angles of attack is the formation of spiral vortices as a result of rolling-up of the transverse flow, which separates near the wing leading edge and on the lateral generator of the body. The vortices, concentrated in a pair of free vortex cores, interact with the boundary layer, causing a complex flow pattern on the surface of the model in question.

Estimation of Stability Derivatives and Indices of Various Ship Forms, and Comparison With Experimental Results2

The analytical method of reference [1]3 for estimating stability derivatives, and hence stability on course, which combines Albring's empirical modifications of simplified flow theory with low aspect-ratio wing theory, is extended to take into consideration the effects on course stability of higher aspect-ratio fins as well. The method, which has been applied in the earlier report to a family of eight hulls of 0.5 block coefficient, is tested further by application to eight Series 60 forms differing in block coefficient as well as in beam, draft, and displacement—with and without rudders; to an extreme vee modification of a Series 60 model; and to three other forms—a Mariner Class model, a destroyer, and a hopper dredge. Comparison with experimental results shows that the values of stability derivatives and indices determined by the analytical method are of the right orders of magnitude and indicate correct trends. Application to a variety of ship forms has demonstrated that the method can predict relative effects of changes in the geometry of a ship form, as well as the effects of changes in skeg and rudder area.

Hydrodynamics of Screw Propellers based on a new Lifting Surface Theory (The 1st Report)

Recently, the auther has developed a new lifting surface theory for low aspect ratio wings, in which the bound vortices representing the wing are distributed not over the projected surface on the stream plane but over the wing surface itself, while the free vortices are trailed along the locus of the moving wing under the category of linearized theory.In the present paper, the application of this new lifting surface theory to screw propellers is discussed theoretically. The bound vortices representing the screw blade are distributed over the helical surface of the blade itself, while the free vortices are trailed along the helical locus of the moving blade. It is desirable to treat the problem three-dimensionally, in order to investigate the form of load distribution, not only in the radial direction but in the chord direction, in relation with the blade shapes and the working conditions. A two-dimensional integral equation that relate lift and downwash distributions on the screw blade is formulated. The numerical method of solution of the equation is obtained, considering the singularity of the kernel functions.Besides, some numerical calculations are made to examine the characteristics of the kernel functions.

Lift fan vstol concept for future applications

The lift fan concept encompasses basically a V/STOL propulsion system consisting of a high bypass ratio jet engine. Jet engine thrust is installed in the aircraft for conventional flight, and this thrust is utilized as an energy source. Lift fans are sized for VTOL. Studies indicate that low aspect ratio wings suitable for fan installations compare very well with variablegeometry winged aircraft from a mission standpoint. In addition, vertifan aircraft can achieve V/STOL at nearly the cost of STOL only. Vertifan aircraft powered by lift fan propulsion systems are equally applicable to high subsonic or supersonic applications.

A Linear Approximation for the Lifting Surface with Low Aspect Ratio

A linearized theory is developed for obtaining the lift distribution on the wing with low aspect ratio. The theory is based on the assumption that, in the case of low aspect ratio wing, it is rather important to adopt not the projected surface into the plane of free stream but the wing surface itself as the lifting surface than to treat it from the non-linear theory. A linear approximation method useful in predicting the chordwise lift distribution on the rectangular wing with low aspect ratio is deduced from the present theory. The computed results from this approximation are compared with test data and show satisfactory agreement. From this fact, the propriety of the above mentioned assumption is proved. The lifting surface theory presented in this paper may be widely applicable in predicting the hydrodynamic forces on so kind of low aspect ratio wings, because of linearization of the theory.

Method of predicting course stability and turning qualities of ships1

An analytical method combining simplified potential flow theory and low aspect-ratio wing theory with empirical modifications for a real viscous fluid is used to predict the stability derivatives (first order hydrodynamic force and moment derivatives