CA1120452A - Annular wing - Google Patents

Abstract

ABSTRACT OF THE DISCLOSURE

An annular wing particularly suited for use in support-ing in flight an aircraft characterized by the absence of direc-tional stabilizing surfaces. The wing comprises a rigid annular body of a substantially uniformly symmetrical configuration cha-racterized by an annular positive lifting surface and cord line coincident with the segment of a line radiating along the surface of an inverted truncated cone whereby a decalage is established for the leading and trailing semi-circular portions of the body, relative to instantaneous line of flight, and a dihedral for the laterally opposed semi-circular portions of the body, relative to the line of flight, the direction of flight and climb angle or glide slope angle being established by selectively positioning the center of mass of the wing ahead of the aerodynamic center along a radius coincident with an axis for a selected line of flight.

Description

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The inven-tion generally relates to a unique wing and more particularly to a unique wing for aircra-ft characterized by the absence of directional stabilizing surfaces, such as empen-nage fins and the like, The prior art is replete wi-th wings o~ various configu-rations adapted to be employed in supporting air cra~-t in flight.
Included among the wings previously employed and suggested ~or use are disk shaped bodies having paddle wheels mounted therein whereby rotation is imparted to the bodies about their axes to produce li-ft. For e~ample, see the U.S, patent to Lemberger No.
3,182,929. Additionally, disk shaped bodies emp~oying propellers and the like for producing required lift have been proppsed, see U.S, patent No. 3,432,120, In each instance, the con~iguration of the disk shaped body is not relied upon to produce lift.
Most conventional aircraft equipped with lift-producing wings are characterized by directional stabilized flight proper-ties resulting froma ~use of non-planar lateral stabilizing sur-faces. Unfortunately, with the use of such surfaces there is an attendant loss in simplicity and efficiency.
It is therefore, the general purpose of the instant invention to provide a highly maneuverable wing particularly suited for supporting powered flight aircra~t, as well as for use as a free floating body or tethered kite which is si~ple in con-cept, economic to fabricate, characterized by the absence o~ di-rection stabilizing sur~aces and by stable horizontal -flight pro-perties at subsonic speeds, in all directions and capable of flight at large angles of attack under powered flight conditions.
It is the general purpose of the instant invention to provide a unique wing adapted for use in operational environments requiring a high degree of maneuverability.
It is another purpose to provide a unique statically stable wing particularly suited for use in supporting aircraft in f'light caracterized by -the absence of directional stabili~ing surfaces, the wing-~ having a high degree of maneuverability at subsonic speeds and capable of achieving uniform stabilized flight in all peripheral directions of :flight, depending only on adjust-ment of a center of gravity location -for glide slope and direction of' flight control.
~ Furthermore the wing is particularly suited for use in - supporting a flight power aircraft although not necessarily res~
tricted in use thereto since the wing of the instant invention possesses similar utility when employed as a free floating body or a tethered kite.
These and other purposes and advantages are achieved through the use of an annular- wing comprising a rigid annular body o-f a substantially uniformly symmetric configuration charac-terized by a decalage for the leading and trailing semi-circular portions o-f the body, relative to an instantaneous line of flight, and a dihedral for the laterally opposed sèmi-circular portions of the wing and a variably positioned center of gravity for con-trolling direction of line of flight.
The present invention provides a statically stable wing characterized by the absence of directional stabilizing sur aces comprising: a rigid annular body of a substantially uniform sym-metric configuration having an annular positive lifting surface and a chord line coinciding with a segment of a line radiating along the surface of an inverted right circular truncated cone.
The present invention also provides in combination with a tailless aircraft, a wing comprising an annular body of substan-tially rigid, uniformly symmetric configuration characterized by a decalage for the leading and trailing semi-circular portions of the body, relative to an instantaneous line of flight, and a di-hedral for the laterally opposed semi-circular portions of the wing relative to the line of flight, In drawings which illustrate embodiments of the invention, Fig. 1 is a top plan view, not to scale~ of a tailless aircraft supported in fligh-t by an annular wing which embodies the principles of the instant invention. -Fig. 2 is an elevational view of the aircraft shown in Fig. 1.
Fig. 3 is an elevational view of an aircraft of another category supported by annular wing embodying the principles oi' ; 10 the instant invention.
Fig. 4 is a top plan view diagrammatically depicting one manner in which the location of the center of gravity for the wing is varied.
; Fig. 5 is a cross-sectional view taken along line 5-5 of Fig. 4.
Fig. 6 is a diagrammatic view of the wing shown depicting forces acting thereon during flight.
Fig. 7 is a fragmented diagrammatic view employed in calculating the lift curve slope for the wing.
Figs. 8, 9 and 10 are diagrammatic views employed in calculating the aerodynamic center for the wing.
Fig. 11 is a diagrammatic view employed in calculating the longitudinal static stability for the wing.
Fig. 12 is a diagrammatic view employed in calculating the lateral static stability for the wing.
Fig. 13 is a graphic view depicting efficiency o-P the wing.
; Figs. 14 and 15 are graphic views illustrating lift-drag characteristics of the wing.
Referring now to the drawings with more particularity, wherein like reference characters designate like or corresponding parts throughout the several views~ there is shown in Fig. 1 an 4~'~

aircraft, generally designated 10, supported by a statically stable wing 12 which embodies the principles of the instant invention.
It is important to appreciate that the particular mission for which the aircr~f* 10 is designed is varied as desired. Consequently, it is to be understood tha-t the utility of the wing 12 is not limited to any specific aircraft. More-over, it should be further unders-tood that the clepiction of the aircraft 10, as shown in Figs 1, 2 and 3, is for the purposes of exemplifying the utility of the wing and not the ; aircraft. For example, the alrcraft 10 may, where desired, comprise a sail plane or the like, as illu~trated in Figs. 1 and 2, or a powered aircraft as illustrated in Fig. 3 Turning now to Fig. 4, it can be seen that the wing 12 is of an annular configuration and includes a uniformly curved out~r edge 14 and a uniformly curved inner edge 16. As best illustrated in Fig. 5, the structure of the wing 12 is symmetrical in all vertical planes and *he chord, designated 18, is coincident with a segment of a line extending from the apex o~ an imaginary truncated right cone circular to the per-iphery of its base.
In flight the wing 12 may be considered to include a leading semicircular portion and a trailing semicircular portion, relative to the line of flight. The chords 18, Fig.
5, of the leading and trailing semicircular portions of the wing are in flight set at different angles of inGidence, as illustrated in Fig. 6. The angular difference between the chords of the leading and trailing semicircular portions of the wing is herein re~erred to as decalage.
Since the chords 18 are, as aforementioned, coinci-dent with segments of lines extending from the apex of an imaginary truncated right circular cone, the lateral semi-B

s~ ~

circular portions o~ the wing 12, relative to the line o~
flight, impart a transverse inclination to the lower surface of the wing, herein referred to as dihedral.
The wing, as shown, is provided with a pair of trans-verse beams 20 diametrically related to the opening de~ined by the inner edge 16 o~ the wing, the purpose o~ which is to support an annular track 22 for a pivotal ballast arm 24 While the track 22 is of any suitable design, as shown, the track includes a supporting surface for a track 26 ~rom which 10 is suspended a hanger 28 connected to the ballast arm 24 As a practicalmatter, the ballast arm 24 also is supported at its inboard end by a pedestal 30 mounted on the beams 20 at the center of the wing 12 As shown, the ballast arm is connected I with a motor 32, ~or example, which serves to drive the arm Z in pivotal displacement along a circular path.
; The ANGLE OF ATTACK, as illustrated in Fig. 6, for I the wing IZ 2 iS established in a manner readily understood by Z those familiar with the design of aerodynamic bodies including -l wings and the like. As depicted in Fig. 6, the wing 12 is in flight with the RELATIVE WIND VELOCITY acting in opposition to the directlon of flight, or in the direction of DRAG. The center of mass, cg, is disposed in leading relation with the aerodynamic center, ac, o~ the wing, while the aerodynamic center leads the geometric center of -the wing, indicated by aD axi~s of symmetry~ no-t designated, projected through the annular wing 12. Hence 9 it can be appreciated that the resultant LIFT tends to pitch the wing 12 is a positive direc-tion about a pitch axis, not designated, while WEIG~T acts at the center o~ gravity cg in opposition to LIFT. It should now be apparent that the ANGLE OF ATTACK for the wing 12 is stabil-ized when the pitching moment for the wing acting about the pitch axis equals zero.

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In order to control -the angle of attack and flight path angle for the wing 12, there is mounted on the ballast arm 24 a bal`last 34 of mass sufPicient to vary the location of the center of mass, cg, of the wing 12 as the position of the ballast is varied. Since the arm 24 is displaceable along a circular path the mass of the ballast 34 also is displaceable so that the wing's center of mass cg may be repositioned along a circular path, de-signated 36, to a series o-f posi$ions located in spaced relation with the aerodynamic center ac of the wing. Of course, while the position of ~he wing's center of mass cg may be fixed by fixing the position of the ballast arm 24, relative to the track 22, where so desired, the ballast arm 24 may be permitted to swivel freely, in which case the position of the center of mass is free to shift.
In order to control fligh-t path angle, it is desirable to provide -for a reposi-tioning of -the ballast 34 relative to the radius of the wing. The particular manner in which such reposi-tioning of the ballas-t 34 is accommodated is deemed to be a mat-ter of convenience only, particularly since various mechanisms are available for this purpose, For example, the mass 34, where desired, is displaced by an extensible hydraulic ram, not shown, connected with the ballast and employed for advancing and retract-ing the ballast along the length of the arm. In any event, it should be apparent that in order to ashieve directional control for the wing 12, control o-f the location of the center of mass for the wing along the path 36 must be facilitated. Similarly, in order to achieve control of the flight path angle for the wing, control must be established over the position of the ballast 34 along the radius of the wing. Hence, control of the flight path angle and direction of flight for the wing is accomplished solely by controlling the location of the center of mass for the wing relative to its aerodynamic center ac.

As shown ln the drawi.ngs J for illustrative purposes, a glass canopy 38 is mounted on ~he pedestal 30 and i5 employed as a payload carrylng compartment. However, where desire~, the aircraft comprises a powered aircra~t 40 suspended from the pedestal. Since the partic~lar manner in which the payload compartment is mounted and employed forms no specific part of the instant invention, a detailed description thereof is omitted.
The various properties of the wing 12, herein desig-nated as lift curve slope, lift-to-drag ratio~- aerodynamic center, longitudinal static s~ability and lateral static stabil-ity and may be computed for demonstrating feasibility, accord-ing to the ~ollowing calcula-tions:
Lift Curve Slope The lift curve slope, as depicted in Fig. 14, can be mathematically determined as -follows wi~h reference particu.larly to Fig. 7. Reference: DATCOM, USAF Flight Dynamics Laboratory, Wright-patterson Air Force Base, Dayton, Ohio.

C - 2 ~ A
L r~ _ _ ~7\ ~ ~ ~ Cl ~ ~

~2 b~
A- ~ - ~ ( R

b = span = 2Ro Ro = wing outer radius Ri = wing inner radius = Mach number S = wing area = effective sweep angle of midchord line ' Approxlmated as ~ollows:
Cc~S (/1c/~ 4 ~ CoS/\~S ds 5 ~olro(l~
O ,~; .

~C~_51~
~ 2 ~

- ~ - . 63 ~rr , 1~
t~n ~
~ ~A
C _ ~
Loc 2~ [I t ( ,~

~ ~ ~ . , ~q~ 2~ 4)Z L~ 4 ~,.
L = lift q = dynamic pressure For low speeds ( A ~b~ CL~deg~
0 1 . 273 1 . 301 . 0289 , 5 1 . 7 1 . 178 . 034g , 6 1 . 99 1 . 100 . 0382 , 7 2 . 50 . 981 . 042 .8 3.54 ,794 .0491 , 9 6, 70 , 49d~ , 0578 B

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Li~t--to~drag Ratio The lift~to-drag ratio as plotted in Fig. 15, can be mathemat~cally determined as follows:
Lift-to-drag ratio (L/D): ~
L ~1~
D ~ ~ C ~ 2 ) Do = zero lift drag = qS~Cf Sw = wetted area~ 2S
Cf = skin friction coefficient e = Vswald ef~icienc~ factor For nominal siz~ sin~le-place aircraft, Reynold~s number is ~ ~~ 3 to ~ x l~
From reference ~ATCO~
C$ ~ ~3~ ( ~pp~x ) ~ence ~ ~ ~ ~ C ~ r~
b~ ~ ~ $
550 ~
For parabolic polar -zo ( D )~

Assuming e~ .8, following results are obtained ~ A ~ ~ (q~ L (CL~ L ( ~ ~o~

0 1.273 .00550 10.7 .1176 .150 5,19 1.7~ .00413 1~.4 .1017 .173 4.96 6 1,9g ,0035Z 13,4 .0940 ,187 4.90 ~B

45;~

. 7 2 . 50 . 00281 15 . 0 . 0~39 . 210 4 . 90 . 8 3. 5~ . 00198 17 . ~ . 0705 . 250 5 . 09~
. 9 ~. 70 . 00105 24. S . 0512 . 343 5 . g3 * CL

C~

Aerod~namic Center The aerodynamic center can be mathematically determined approximately as follows with re~erence being made particularly to Figs. 8, 9 and lOo Let wing consist of forward (1) and rear t2~ elements having ind~vidual aerodynamic centers (ac) located -distance ~ from wing center (Fig. 8).

Assume the span loading on each element to be elliptical -L?~= d7~ = LO~ L= L~

Assume also the downwash angle at element (2) due to element (1 to have an average value ~ -Ll = d.~ OC ~ L~ ~ L2-- ~æ ~DC~

The moment of lift about central axis then is: -L ~ 2. L,J (~ - ~) where L=L~ oC = L, ~ L2 _g _ 0g~5~

The lift slopes of elements (1) and (2) are identical (see DATCOM expression for lift slope) and hence half the value for the complete wing, Then - ~ [ 5 ~ ~

Since the span loading is identical for both elements -- _.
Z
d An approximate estimate for d~/d~ is as follows:
The average downwash velocity at element (2) due to element (1) is assumed to be ~ully imparted immediately downstream from element (1) such that ~r = ave downwash velocity and ~ _ ~Uf :20 Using Prandtl's approximation for momentum transfer L = n~ ~r where n~ is the mass ~low rate through the circular streamtube intercepted by the wing span b (Fig. 9) it fo].lows that L ~ r b~s~ ~ ~r ~ = air density q bZ '2_ ~ = '2_ ~

d ~ dLid~
Hence d ~ ~ q b It follows that ~ . - ~ C L
~rr~

4~2 An estimate of ~ for the assumed elliptic loading on the semi-circular plan form is found by taking the lift moment of element ~1) abou-t the lateral axis through the wing center (Fig. 10):
d~ -L~I-L~

r L ~ ~ L~ d Then ~I L ~ L~ d f I " --_ ~ ~1-~ d~

The aerodynamic center location therefore is given by 8 X --- _ 8 ( L~ 2.73).
~- 31r ~fA 311~ qb~ J- 9 Typical values are as ~ollows:
~o ~
0 1.301 .351 .5 1.17~ .318 .6 1.100 .297 .7 .981 .265 .~ .794 .214 ,9 .494 .133 Longitudinal Static Stability The longitudinal static stability for the wing can be mathema*ically determined a~ follo~s, by reference being made to Fig. 11.

The lift moment about the la~eral axis is given by L ( ~ C9~ b t ~lo D~ ~eYo 11~ mon~ent The stability der~vative becomes d L ~ ~3 The zero-lift moment (Mo) is as ~ollows:
Summing the lifts and moments about the lateral axis ~or elements (1) and (2) gives L- Lo~ I) t Lo~z (oC~

~ ~, b ~L~, (~ 2. b L~
As before ~ z ~ L ~1 ~ L~ ~ ~~ 2 L ~ ( win~
And Subs~ituting ~ ~ ~ ' 'bi' ~ ~r- 4 b ~ ( ~ t- i) ~ ' 1 L ~
Gives L= Z L~ ~ ~r 9k~ )J

For ~ = 0, G~ , where Loc C4 ~ 9 ~ ~ ~ . .

2.--1 ~, 2-- CL,~, ~ q~)~ ~A
And Mo becomes /~O = 3lr bLo,~ b~ ~;o~

Lo~ ~
Mo _ ~ j r ( L~)-- (~ ) ~ 1 b L ~C, 3~ ~ ~q ~ ~ J

Or M L~ ~ C L~. ~ ( lrA~
b Lo~ i 3 rr ~ ,4 'æ - C La~;
T~im angle of attack thcn is a~;T --~C; O
i b Lo~

Represent~tives values are as follows (low speed):

~T -O~o ~; LO~
RO ~9 b1 I b LO~ 9- . lO . 15 ~ . 25 0 . 4141 1 . 070 10 . 70 7 . 13 S ~ 35 4 . 2 . 5 . 3750 1 . 0~5 10 . ~5 6 . ~7 5 . 28 . 4 . 1 - . ~ . 3501 1~ 029 10. 29 6. ~6 5 . 15 4 . 12 7 . 3123 1 . 006 10 . 06 6 . 71 5 . 03 4 . ~2 . 8 . 2527 . 972 g . 72 6 . ~8 4 . ~6 3 . 89 ~ 9 . 1572 . 921 9 . 21 6. 14 4 . 61 3 . 68 : 20 Lateral_Static Stability The lateral static stability for the wing can be determined as follows, reference being made to Fig. 12.
For positive sideslip angles ( ~) , the induced rolling moment is ~ = rolling moment - -~ b ~ir\~3 x L
Assuming ~ to be small sln~

- 3~ And d ~ ~ bL

Letting C ~

Then C ?~ ~ C L (dihedral effect) The dihedral effect ls negative hence stabilizing.
The directional stability deriva~ive(C ~ )is zero without a vertical tail.
The Dutch Roll stability( W ~)is as ~ollows:

~n2 - I C~ ~ (C,;;3~ C~

~ 9~ ~ CL >

Ix, Iz are wing moments of inertia about longitudinal and vertical axes respectively.
~Jn~ is always positive, hence the wing i9 statically stable.
As an aid to understanding the various calculations herein set ~orth, the symbcls employed are defined as follows:
Q ~, designates aerodynamic center A aspect ratio, b2/S
b wing span, 2Ro CD drag coefficient, D/qS
C ~ O drag coefficient at zero lift C ~ skin friction coefficient, friction /qsw ~ designates center of gravity CL lift coefficient, L/qS
C LOC~ dCL/dD~
C ~ rolling moment coefficient, ~/qsb C l~ dihedral effect, d C 2/d ~

30 Cn yawing moment coefficient, yawing moment / qSb C n ~ directional stability derivative 9 dC~ 1~
C ~ Dutch roll stability, ~ ~ n~

5~

d designates derivative of variable D drag force ~o drag force at zero lift D/4~)~ C~ /~ I
e~ Oswald e~ficiency factor, = ~A
unity for elliptic span loading j angle of incidence of wing airfoil section ~ aircraft moment of inertia about longitudinal axis T æ aircraft moment of inertia about vertical axis 10 ~ representative length for determining Reynolds nUmber~ 0 - Ri in present case L lift force L~ lift at zero angle of attack I o~ d L/~
L~ d Ll d Llqb~ C~
_D rolling moment d~
-~,3 d~/d~
n~ air ~ass flow rate, ~ b~
20 ~ pitching moment pitching moment at zero lift Mach number q dynamic pressure 7 1 p~ ~
radial distance from center of wing : R Reynolds number, V~
F~ radius of inner wing edge R radius of outer wing edge S wing area wetted area of wing Sw average downwash velocity across aft wing span ~r aircraf-t velocity longi-tudinal, lateral distance from wing center angle of attack at zexo lift r angle of attack at ~ero pitching moment angle of sideslip average downwash angle across aft wing span,ton wing spanwise coordinate, ~ ~ ~o ~ Z ~/b wing chordwise coordinate, ~ / ~o- ~ X /b distance of ac from wing center ~ ~ distance of cq from wing center 10 ~ ~2 sweep angle at points along midchord line of wing e~F wing effective sweep angle (mean value for fore and aft wing semispans) ~ kinematic viscosity of air at 59F
p mass density of air at 59F

U~ Dutch roll static stability expressed in terms of undamped natural frequency Subscripts:
1, 2 designates fore and aft wing segments ~respectively) max. maximum value Other terms:
I CLI absolute value of CL
Parabolic polar means drag is proportional to s~uare of lift, t~)/qb2 - ~ol,~b~ t ~e ( L/~b~)necalage angle = incidence of fore~wing half minus incidence o~
aft-wing half, i,e. 2i Elliptic loading means wing section lift varies elliptically across span, While not shown, it is to be understood that where so desired, the annular wing can be employed in a configuration in which the position of the center of mass is fixed. In such ins-tances, the wing is fitted with flaps for use in establishing con-trol over the pitch and roll angles for the wing. Also, while not z shown, it is to be understood that where the configuration includes a fixed center of mass, it is highly desirable to accommodate wi-th-drawal of low energy boundary layer air at the aft end of the wing, by ingestion in ~jet engine exhaust or a propeller slip stream, as -the case may be, In summary, wi-th the wing 12 attached in supporting re-'ation to an aircraft 10, as illustrated in Figs. 1 through 3, la-teral stability is provided for solely by the wing~s dihedral effect which is uniform in all directions. The ratio of the in-ner to outer radius of the wing determlnes the ef-ficiency of the wing, while the angle o~ incidence -for the airfoil section provi-des a positive zero lift pitching moment for extablishing longi-tudinal stability at the desired lif-t coefficient. Control of the flight path angle and direction of flight is achieved simply by repositioning the ballast 3~, relative to the center of the wing, It is believed that in practice later~l boundary layer flow will enable large angles of attack to be reache~ prior to wing stall, provided, of course, low energy boundary layer air is ingested at the aft end of -the wing. Abrupt changes of flight direction are, of course, limited only by the occurrence of wing stall. Due to the annular shape of the wing, the wing possesses lift properties which may be approximated in theory by a circular lifting line. Finally, down-wash from the forward semi-circular element produces sufficien-t dihedral effect for lateral stability without a need for vertical directional stabilizing surfaces.
In view of the foregoing, it should be apparent that the wing 12 provides a practical solution to the problem of achieving directional control of an aircraft without employing s-tabilizing surfaces.

Claims (3)

The embodiments of the invention in which an exclusive property or privilege is claimed are defined as follows:

1. In combination with a tailless aircraft an im-proved wing capable of achieving in-flight longitudinal and lateral stability and abrupt changes in direction of flight while remaining substantially stabilized relative to its axis of yaw, comprising:
an unitary annular air foil characterized by wing sections of uniform size and shape, the chord of each section being coincident with a segment of a line radiating from the apex of an inverted cone and said section being substantially symmetric relative to the chord, said air foil being symmetri-cal to all planes passing through the geometric center thereof, and when in flight being longitudinally stabilized, and later-ally stabilized by a dihedral effect uniform in all directions.

2. In combination with a tailless aircraft an improved unitary wing capable of achieving in-flight longitud-inal and lateral stability and abrupt changes in direction of flight while remaining substantially stabilized relative to its axis of yaw, comprising:
an unitary annular air foil characterized by wing sections of uniform size and shape, the chord of each section being coincident with a segment of a line radiating from the apex of an imaginary inverted cone and said section being sub-stantially symmetric relative to the chord, said air foil being symmetrical to all planes passing axially through the geometric center thereof, and when in flight, being character-ized by leading and trailing semi-circular portions, said wing in flight being longitudinally stabilized in response to the effects of a difference in angles of incidence for the leading and trailing portions of the air foil, and laterally stabilized relative to the direction of flight by a dihedral effect uniform in all directions.

3. In combination with a tailless aircraft an improved wing capable of achieving in-flight longitudinal and lateral stability and abrupt changes in direction of flight while remaining substantially stabilized relative to its axis of yaw, the improved wing when in flight having a direction of flight, a climb angle, a geometric center, an aerodynamic center, and a center of mass located forwardly of the aero-dynamic center of the wing, relative to the direction of flight, comprising:
an unitary annular body defining an annular air foil symmetrically related to all planes passing through the geometric center thereof, and characterized by wing sections of uniform size and shape, each of said sections having a chord coincident with a segment of a line radiating from the apex of an inverted cone, said sections being symmetric relative to the chords, said annular body, when in flight, being longitudinally stabilized by a decalage effect and laterally stabilized by a dihedral effect uniform in all directions; means for altering the direction of flight including means for repositioning the center of mass circumferentially relative to the geometric center of the wing; and means for varying the climb angle in-cluding means for repositioning the center of mass relative to the radius of the wing.