Aircraft

Abstract

Stability of a delta-shaped lifting body is improved by compensating for excessive rolling moment due to sideslip that results from high sweep angle. The compensation is achieved by providing outboard surfaces disposed at negative dihedral angles or by shaping the lifting body itself so that there exists an effective negative dihedral. Where outboard surfaces are used, they can be swept forward to decrease the rate of change of dihedral effect with respect to angle of attack, and to produce the additional advantage of greater ground clearance at high angles of attack.

Description

BACKGROUND OF THE INVENTION

This invention relates to aircraft and particularly to delta-shaped lifting bodies having high sweep angles. A delta-shaped lifting body is described in U.S. Pat. No. 3,486,719 issued Dec. 30, 1969, to John R. Fitzpatrick and Juergen K. Bock. Typically, a delta-shaped lifting body is characterized by a substantially triangular or delta-shaped planform, a nose at one corner of the triangle and a trailing edge opposite the nose and extending between a pair of lateral extremities, each at one of the remaining corners of the triangle. The sides of the triangle which meet at the nose form leading edges, and vertical, longitudinal sections of the lifting body are thick airfoil sections which may be either cambered or uncambered. The lifting body preferably comprises an enclosed hull substantially symmetrical about a central vertical plane extending from its nose to a mid-point at the wide end opposite the nose. The transverse cross-section throughout substantially all of the length of the lifting body are preferably elliptical on either side of the central vertical plane. From the nose to the point of maximum vertical dimension in the central vertical plane, the elliptical cross-sections become progressively higher and progressively wider, with width increasing more rapidly than height. From the point of maximum vertical dimension toward the trailing edge, however, the elliptical cross-sections continue to increase progressively in width, but decrease progressively in height.

Minor deviations from the above-described relationships may exist, for example with respect to the location of the nose and lateral extremities, without substantial effect on the flying characteristics of the aircraft.

Such lifting bodies possess favorable stall characteristics and are capable of relatively high cruising speeds and relatively low landing speeds. They can be made to carry a large payload efficiently, and may be operated heavier than-air, or, with helium, either lighter-than-air of slightly heavier-than-air.

Delta-wing lifting bodies having sufficiently high sweep angles to possess the favorable characteristics mentioned, are also subject to certain unfavorable characteristics. For values of wing sweepback angle .LAMBDA. in excess of a determinable critical amount, certain important aircraft characteristics tend to deteriorate to the point where the flying qualities of the lifting body become unacceptable. In particular, a fundamentally important characteristic in the handling qualities of a lifting body is the lateral-directional, short-period oscillatory mode known as the "Dutch Roll" mode. The damping of this mode must be maintained at a suitable level for the pilot and passengers to deem the aircraft's handling qualities satisfactory. A lightly damped Dutch Roll mode is inherent in a delta-shaped lifting body having a high sweep angle.

In a delta, or a near-delta, assuming only the length of the root chord C.sub.root is varied, effects due to changes in C.sub.root can be discussed and interpreted in terms of the sweep angle .LAMBDA. , defined as .LAMBDA. = tan.sup..sup.-1 (x)/(b) where is the longitudinal displacement in the chordwise direction of the 25 percent C.sub.tip point behind the 25 percent C.sub.root point.

A reasonable approximation to the damping of the Dutch Roll mode can be given (for lightly damped motions) as

N.sub.r - (N.sub.p)/(L.sub.p) .sup.. L.sub.r - (N.sub.p)/(L.sub.p) .sup.. (L.beta.)/(L.sub.p)

where:

N.sub.r is the yaw acceleration due to yaw velocity (yaw damping);

N.sub.p is the yaw acceleration due to roll velocity (yaw due to roll);

L.sub.p is rolling acceleration due to roll velocity (roll damping);

L.sub.r is rolling acceleration due to yaw velocity (roll due to yaw); and

L.beta. is rolling acceleration due to sideslip angle (dihedral effect).

The expression for the damping of the Dutch Roll mode is independent of directional stability N.beta..

In the following development it will be shown that, as the root chord C.sub.root increases, the dihedral effect (that is, the rate of change of rolling moment due to sideslip) increases and the Dutch Roll mode damping tends toward zero. Thus, at some determinable level of sweep angle .LAMBDA. (or of A , the aspect ratio, or .lambda. , the taper ratio), it becomes necessary to compensate for the loss of damping.

Dependent representations of the lateral-directional stability derivatives, or at least the principal parts of those representations are given as follows:

N.sub.r = (1)/(I.sub.z) .sup.. (1)/(2) .rho. V S.sub.v l.sub.v .sup.2 a.sub. v

where:

I.sub.z = yaw inertia;

.rho. = air density;

V = air speed;

S.sub.v = vertical surface area;

1.sub.v = distance of vertical tail aerodynamic center from aircraft center of gravity; and

a.sub.v = lift curve slope of vertical tail.

It is sufficient to determine the ratio of (N.sub.p)/(L.sub.p) as follows:

(N.sub.p)/(L.sub.p) = (C.sub.L)/(a ) .sup.. (I.sub.x)/(I.sub.z)

where:

I.sub.x = roll inertia;

C.sub.l = aircraft lift coefficient;

a = 2-dimensional lift curve slope; and

I.sub.z = yaw inertia. ##SPC1##

where:

.GAMMA. = lifting surface geometrical dihedral;

.alpha. = trim angle of attack; and

b = the span.

Combining the expressions for L.sub.p and L , we obtain:

(L )/(L.sub.p) = - (V)/(b) (.GAMMA. + 2.alpha. tan .LAMBDA.)

Examining the signs of the above terms, it will be seen that the first two terms (N.sub.r - (N.sub.p)/(L.sub.p) .sup.. L.sub.r) of the expression for Dutch Roll made damping contribute negatively to the Dutch Roll damping, having a stabilizing effect. The last term

contributes positively, having a destabilizing effect. Thus, the damping will tend toward zero as

A neutrally stable Dutch Roll mode exists when:

Substituting, we have a neutrally stable condition when:

For typical directionally stable aircraft, the first term on the right is at least an order of magnitude larger than the second, and thus this expression can be further reduced to

From this final expression, it can be seen that as the root chord C.sub.root is increased and .LAMBDA. increases correspondingly, a sweep angle will be reached where the Dutch Roll damping is zero.

SUMMARY OF THE INVENTION

In accordance with this invention, stability is restored by reducing the effective geometric dihedral angle .GAMMA. to compensate for the large value of the term resulting from the large sweepback angle.

The geometric dihedral .GAMMA. is reduced either by the provision of drooping outboard tips at the lateral extremities of the aircraft or by drooping the entire center-line or outer extremities of the center-line of the delta-wing.

Where drooping outboard tips are used, they are preferably swept forward in order to decrease the rate of change of the dihedral effect with the angle of attack.

The invention is applicable to any delta-shaped lifting body having a large sweep angle .LAMBDA. such that under typical operating conditions

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a top plan view of a delta-shaped lifting body having drooping tips in accordance with the invention;

FIG. 2 is a side elevation of the same lifting body;

FIG. 3 is a front elevation of the same lifting body;

FIG. 4 is a diagram illustrating a derivation of a lifting body shape having a decreased effective geometric dihedral angle; and

FIG. 5 is a front elevation of a delta-shaped lifting body having its shape modified to produce a decreased effective geometric dihedral.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIGS. 1 through 3 show a delta-wing aircraft 10 comprising a hull 12 which is enclosed, and which is substantially symmetrical about a vertical plane extending from nose 14 to the center of trailing edge 16. The hull is also substantially symmetrical about a horizontal plane.

The cross-sections transverse to the vertical plane just mentioned are substantially elliptical throughout the length of the aircraft from the nose almost to the trailing edge.

The position of the maximum vertical dimension of the hull is preferably between 40 and 60 percent of the chord length from the nose.

From the nose to the point where the vertical dimension of the aircraft reaches a maximum, the elliptical cross-sections increase both in width and height with width increasing more rapidly than height. From the point of maximum vertical dimension to the trailing edge, the elliptical cross-sections continue to widen, but their vertical dimensions decrease progressively.

The drawings show a cockpit 16, an engine 18 with a propeller 20, horizontal control surfaces 22, vertical stabilizers 24 and 26 and rudders 28 and 30. Landing gear are shown at 32, 34 and 36.

The geometric dihedral .GAMMA. of the hull is substantially zero. The sweep angle .LAMBDA. , however, is approximately 60.degree.. At this value, even at small angles of attack, instability will occur because:

Thus, it is necessary to introduce a negative dihedral. This is accomplished by providing, at the lateral extremities of the lifting body, drooping outboard surfaces 38 and 40. The effect of these surfaces is to produce a negative overall dihedral angle .GAMMA. so that

Under these conditions, the aircraft will not exhibit instability in the Dutch Roll mode.

In applications where a certain amount of Dutch Roll instability can be tolerated, the compensation need not be complete, but may only be partial.

Drooping tips 38 and 40 are preferably swept forward as seen in FIGS. 1 and 2. This provides greater ground clearance during take-off and landing at high attack angles. More importantly, the forward sweep of the tips reduces the rate of change of dihedral effect with respect to the lift coefficient, thus producing similar performance at various attack angles.

Referring to FIGS. 4 and 5, an embodiment of the invention is illustrated in which compensation is achieved in part by modifying the hull shape to produce a negative dihedral.

In FIG. 4, which is merely illustrative, there is shown an aircraft hull 42 symmetrical about a horizontal plane with an imaginary wedge 44 removed to produce the shape of hull 46 shown in FIG. 5. Hull 46 has a large sweep .LAMBDA., but exhibits a substantial negative dihedral .GAMMA.. Small dropping tips are provided at 48 and 50 to decrease .GAMMA. still further. Here again, .LAMBDA. is sufficiently large to give rise to a lightly damped or unstable "Dutch Roll." That is, even if .GAMMA. were zero, ##SPC2##

and the aircraft is stable.

The hull shape may, of course, be modified in various alternative ways to produce a negative dihedral. Tips 48 and 50 may be eliminated if the modification to the shape of the hull is sufficient to overcome instability.

In the embodiment shown in FIG. 5, the increased overhead arch permits better load support internally. In addition, the flattened underside produces an increased ground effect. Also, in the case of a large, cargo-carrying aircraft, the flattened underside gives rise to improved access to the interior of the aircraft.

It will be apparent that the required decrease in the effective dihedral angle can be accomplished in various alternative ways including drooping only the outer extremities of the center-line rather than the entire center line, and that various other modifications can be made in accordance with the invention.

Claims

What is claimed is:

1. A lifting body comprising an enclosed hull having a delta-shaped planform substantially symmetrical about a plane perpendicular to the direction of the maximum lateral dimension of the lifting body and extending from a nose at one corner of said planform to the mid-point at the wide end opposite the nose, the cross-sections transverse to said plane, on either side being substantially elliptical throughout substantially all of the length of the lifting body, a maximum dimension in said plane and perpendicular to the chord in said plane at a point spaced from said wide end and spaced from the nose, the transverse cross-sections of the lifting body progressively increasing in width and decreasing in height from the cross-section at the point of maximum height toward the wide end, and having a large sweep angle .LAMBDA. such that

under typical operating conditions, and including means providing a surface disposed at a negative dihedral angle .GAMMA. whereby the roll instability resulting from the large sweep angle .LAMBDA. is reduced.

2. A lifting body according to claim 1 wherein the negative dihedral angle .GAMMA. is such that

whereby the roll instability resulting from the large sweep angle .LAMBDA. is substantially eliminated.

3. A lifting body according to claim 1 in which said means providing a surface comprises a pair of outboard surfaces disposed at either lateral extremity and drooping in the direction from root to tip.

4. A lifting body according to claim 1 in which said means providing a surface comprises a pair of outboard surfaces disposed at either lateral extremity and drooping in the direction from root to tip and wherein said outboard surfaces have a forward sweep.

5. A lifting body according to claim 1 wherein the surface disposed at a negative dihedral angle is the hull itself.