U.S. patent number 3,712,564 [Application Number 05/089,415] was granted by the patent office on 1973-01-23 for slotted diffuser system for reducing aircraft induced drag.
Invention is credited to Scott C. Rethorst.
United States Patent |
3,712,564 |
Rethorst |
January 23, 1973 |
SLOTTED DIFFUSER SYSTEM FOR REDUCING AIRCRAFT INDUCED DRAG
Abstract
A wing assembly for increasing lift and reducing drag is
disclosed comprising (1) an inboard conventional primary wing
panel, and (2) an outboard secondary wing panel which is aft-swept
and comprised of a cascade of airfoil elements. The inboard panel
is provided with a constant lift distribution which is dropped
sharply at the knee or juncture with the outer panel, shedding a
substantially concentrated vortex at the knee rather than at the
wing tip. The sweep of the outer panel deflects the flow carrying
this vorticity outboard, and its cascade airfoil elements then
operate in the upflow outboard thereof. The cascade elements of the
outer panel are stacked vertically above to the rear, so that the
vorticity shed from each element generates a spanwash providing an
incremental lift and thrust on the next element aft and above,
which, in turn, because of its sweep deflects the vorticity
underneath outboard, providing a greater effective span. The
cascade splits the vortex into a vertical stack of vortex sheets,
which laminate into an expanded size, slowly turning vortex core.
The energy and corresponding induced drag of the vortex pair shed
from this improved wing assembly is less because the vortex cores
are (a) expanded, and (b) displaced outboard.
Inventors: |
Rethorst; Scott C. (Pasadena,
CA) |
Family
ID: |
22217510 |
Appl.
No.: |
05/089,415 |
Filed: |
November 13, 1970 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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792872 |
Jan 21, 1969 |
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Current U.S.
Class: |
244/199.4;
244/200 |
Current CPC
Class: |
B64C
23/06 (20130101); Y02T 50/162 (20130101); Y02T
50/10 (20130101) |
Current International
Class: |
B64C
23/06 (20060101); B64C 23/00 (20060101); B64c
003/00 () |
Field of
Search: |
;244/41,40 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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303,117 |
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Jul 1918 |
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DD |
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434,540 |
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Sep 1926 |
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DD |
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49,524 |
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Oct 1940 |
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NL |
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Primary Examiner: Buchler; Milton
Assistant Examiner: Rutledge; Carl A.
Parent Case Text
This application is a continuation-in-part of application Ser. No.
792,872 filed Jan. 21, l969, now abandoned.
Claims
Having thus described my invention what I claim as novel and desire
to secure by Letters of Patent of the United States is:
1. An aircraft wing comprising a primary solid portion and a
secondary slotted portion, said secondary portion trailing said
primary portion including a cascade of airfoil-shaped elements
extending aft and swept outboard of the primary solid portion so as
to be parallel to, along side of, outboard of, and in close
proximity to any residual vorticity shed from said primary solid
portion, and having a negative or lesser angle of attack than the
inboard primary solid portion such that when the said primary
portion of the wing is operating at a positive amgle of attack, the
vector sum of the upwash generated by the residual inboard
vorticity and the free stream flight velocity provides a resultant
upflow giving a positive angle of attack on the outboard secondary
portions, thereby providing a force normal to the resultant
velocity which has both a lift and a forward thrust component.
2. An aircraft wing comprising an inboard solid portion and an
outboard slotted portion, said outboard portion comprising a
plurality of airfoil-shaped elements with the aft ends of said
elements swept outboard in a direction beyond said inboard portion,
said elements having leading and trailing edges, said leading edges
being rounder, thicker, and having a larger radius than said
trailing edges which have a thinner, sharper, and lesser radius,
said elements having upper and lower surfaces, said upper and lower
surfaces being smoothly faired from said leading edges to said
trailing edges, said elements being disposed with their centroids
stacked vertically above to the rear, said inboard solid portion
and said outboard slotted portion being joined in a smoothly faired
juncture region, said juncture region having a sharp decrease in
angle of attack, or washout, so as to shed the lifting vorticity
inboard from the wing tip, the aft sweep of the outboard slotted
portion then deflecting the air flow outboard, transporting outward
the shed wing tip vortex, said vortex generating an upflow for said
outboard slotted wing portion, providing a lift force with a
reduced induced drag component.
3. An aircraft as in claim 2 said solid portion having center of
lift forward of the aircraft center of gravity, said slotted
portion having center of lift aft of the aircraft center of
gravity, said aft portion including a cascade of airfoil-shaped
elements with the aft ends of said elements swept outboard towards
the trailing edge of said wing, the inboard edge of said elements
being displaced down and being reflexed in providing passages from
the upper to the lower surface of said wing.
4. An aircraft as in Claim 2 said solid portion having center of
lift forward of the aircraft center of gravity, said slotted
portion having center of lift aft of the aircraft center of
gravity.
5. An aircraft wing as in claim 2, said slotted portion including a
cascade of airfoil-shaped elements with the aft ends of said
elements swept outboard towards the trailing edge of said wing,
said elements having chord lengths substantially less than the
chord of the wing itself, thereby providing lower Reynolds number
and laminar flow.
6. An aircraft wing as in claim 2, said slotted portion including a
cascade of airfoil-shaped elements, said elements having chord
lengths substantially less than the chord of the wing itself,
thereby providing lower Reynolds number and laminar flow.
Description
This application pertains to improvements in the vortex generating
and diffusing system disclosed in my U.S. Pat. No. 3,369,775,
issued Feb. 20, 1968, and in my continuation application, Ser. No.
706,480, filed Feb. 19, 1968 now U.S. Pat. No. 3,523,661.
My prior U.S. Pat. No. 3,369,775 disclosed a vortex generation and
diffusion system comprising a series of vortex diffusers defined by
ribs or ridges asymmetric in spanwise cross section on the surface
of the wing, and disposed so as to utilize the spanwise flow over a
finite span wing to generate and diffuse the normal trailing
vorticity within the wing planform into pressure on the backside of
the wing.
My continuing application, Ser. No. 706,480, filed Feb. 19, 1968,
disclosed an improvement over that of U.S. Pat. No. 3,369,775
consisting of a particular shape and arrangement of the vortex
diffusion structure. That is, that the aforementioned ridges are
shaped to provide a diffuser concave to the spanwise flow to
generate a vortex flow on the underside of the wing providing
positive pressure or lift, as well as thrust, and further providing
a turned flow on the upper surface of the wing, thereby causing, in
one region, reduced pressure and suction lift, and in another
region, positive pressure and thrust.
The further improvement of the present invention over that of U.S.
Pat. No. 3,369,775 and application Ser. No. 706,840, consists of a
particular wing assembly to increase lift and reduce induced drag.
This assembly is comprised of (1) a forward conventional primary
wing generating lift principally due to the chordwise flow, and (2)
an aft secondary wing system having a cascade of swept slotted
airfoil-shaped diffuser elements generating lift principally from
the spanwise flow and providing a set of air passages leading from
the upper to the lower surface of the wing. The terms outboard,
inboard, leading edge, trailing edge, forward and aft refer to the
primary wing coordinate system even when the secondary wing system
is being discussed.
The forward primary wing generates a reduced pressure on its upper
surface causing a spanwise inflow, which if unchecked will continue
off the trailing edge of the wing assembly, meeting up with a
spanwise outflow from the underside, producing trailing vorticity
and induces drag. The aft secondary wing system, comprised of
slotted and swept-wing elements (trailing edge outboard of leading
edge), utilizes the pressure asymmetry on the leading edge of the
upper surface of a swept wing to provide an outboard component to
the flow. This corrects, to some extent, the inboard component
caused by the pressure gradient due to the suction lift on the
forward part of the wing. Thus the flow off the trailing edge of
this improved wing assembly will be at least partially free from
the opposing upper and lower surface spanwise components leading to
trailing vorticity and induced drag. It should be noted that the
requirement for sweep is relative to the resultant flow, being the
vector sum of the chordwise and spanwise flows. Thus, in the
presence of a spanwise flow component, the airfoil elements may be
oriented directly aft or parallel to the chordwise flow, thus
providing sweep with respect to the resultant flow. Therefore,
sweep as used in this document is always to be understood as with
reference to the resultant flow.
The swept and slotted airfoil-type diffuser elements are arranged
to act as wings with respect to the spanwise flow, thereby
developing both suction lift on their upper convex surface and
positive pressure lift on their lower concave surface. The air
thereafter proceeds inward, downward, and aft through the cascade
and diffuses into higher pressure as the air emerges on the lower
side of the wing, thereby providing additional lift on the under
surface.
On the upper surface of the wing, the gap provided by the swept
diffusers faces forward. On the lower surface of the wing, the gap
faces aft. Hence, on the upper surface dynamic pressure is imposed
on the gap, whereas the pressure on the lower surface is mostly
static pressure. To force the air through the diffuser slots from
the upper to the lower wing surface, the upper dynamic pressure
must exceed the lower static pressure.
The under surfaces of the elements may have straight or reflexed
inboard edges to aid in correcting the outboard spanwise component
developed by the high pressure on the lower wing surface, thereby
further reducing the trailing vorticity.
Thus the spanwise flow, or the spanwise component of the total flow
over the upper surface of the wing, performs four functions: (1)
the flow passes over the upper convex surface of a small secondary
swept wing and in so doing generates lift, (2) the pressure
asymmetry due to the sweep of these small secondary wings provides
an outward component to the flow, thus correcting the inward
component already provided to the air by the primary suction lift
over the basic wing, (3) the air continues inward, downward, and
aft under the next adjacent inboard diffuser element in the
cascade, developing positive pressure lift on the underside of this
element due to its concave underside curvature, and (4) in
continuing in the direction of the resultant flow the air
preferably encounters an expanded slot cross section, thereby
further diffusing the velocity energy into pressure as the air
emerges on the under and backside of the wing, thus providing
further positive pressure lift on the underside and thrust on the
backside of the wing elements and cancelling the outboard lower
surface spanwise flow component.
The total lift is increased by functions 1, 3, and 4. The induced
drag is decreased by functions 2 and 4 . The logic is not to put up
a barrier or fence to stop the flow, but rather to recognize that
the pressure gradient of the primary wing produces both (1) lift,
and (2) adverse spanwise flows leading to induced drag. Therefore,
the secondary airfoil system is designed to (1) retain the pressure
gradient providing the lift, while (2) utilizing the energy of the
spanwise flows to correct themselves, thus reducing the induced
drag.
The aft secondary wing system also acts as a tail with regard to
the forward primary wing, and thereby provides a longitudinally
stable lifting assembly. A conventional wing is unstable
longitudinally, and requires a lifting surface aft of the center of
gravity to provide a stable system, as is well known in
aeronautics. In the present wing assembly, the aft secondary swept
wing system performs the function of a tail by providing a lift
force located aft of the primary wing and the center of gravity,
thereby introducing a moment whose changes with angle of attack
make the overall wing assembly stable. This stable wing assembly
also eliminates the induced drag produced by lift on the tail.
Furthermore, the slotted structure of the aft secondary wing system
prevents flow separation at high angles of attack, i.e., when the
aircraft is landing, by enabling the flow to pass in reverse from
the bottom surface of the wing up through the slots to the top
surface, thereby energizing the boundary layer on the upper side of
the wing and preventing flow separation. In a sense, the wing
structure at very high angles of attack thus acts as a vented
parachute, with the flow through the slots from the bottom high
pressure region generating further lift on the airfoil elements in
passing through the slotted passages.
Another mechanism for reducing the spanwise flow could be obtained
by adjusting the characteristics of the secondary wing system
elements so that the flow progresses from the lower to the upper
wing surface in all phases of flight. In this case, the high
pressure air on the lower wing surface overcomes the spanwise
dynamic pressure gradient on the upper wing surface and allows the
flow to pass through the wing with the velocity opposing the upper
surface inward spanwise flow component. The outward spanwise flow
on the lower wing surface provides dynamic pressure to aid in
forcing the flow through the slots. Lift is still provided on the
convex upper surface of the airfoil elements and the differential
spanwise flow between the upper and lower wing surfaces is still
eliminated.
The aft, secondary, slotted, and swept wing system also helps
maintain the boundary layer laminar on the upper surface of the
wing. On a conventional airfoil, it is very difficult for the air
flow to negotiate the adverse pressure gradient on the aft portion
of the upper surface of the wing, and as a result, the laminar flow
generally makes a transition to turbulent flow, with a
corresponding higher frictional drag. The aft secondary swept wing
system, on the other hand, has a series of short chord wings,
providing a low Reynolds number, thereby assisting in maintaining
the boundary layer laminar. Furthermore, the cascade-like
structure, coupled with the sweep, provides a series of ridges
which the spanwise flow must negotiate, and the up and down path
over these ridges produces accelerations in the spanwise flow which
are large as compared to the accelerations of the chordwise flow,
with the result that the boundary layer is dominated by the
spanwise flow. This spanwise flow has a very low velocity and hence
a low Reynolds number as compared with the chordwise flow, thereby
again assisting in maintaining the flow laminar. In addition, the
reduced pressure on the upper surface of the airfoil element causes
a suction trough extending towards the trailing edge of the wing,
providing a favorable pressure gradient route within the adverse
primary wing pressure gradient field to assist in maintaining the
boundary layer laminar on the aft part of the upper surface of the
wing assembly. In the case of the secondary airfoil system elements
having reflexed inboard edges, the air flowing into the suction
trough diffuses and thereby provides thrust against the concave
surfaces of the elements, with the tubular portion of the
overlapping s curve airfoil elements acting as jet tail pipes, with
the spanwise air thus diverted aft providing thrust as a rate of
change in momentum acting on the walls of the tubes which provided
the deflection of the flow aft.
The airfoil elements of the slotted and swept aft secondary wing
system, in conjunction with the spanwise flow, produce a lift
force. Because of the angle of attack of these elements, due to
their inclination from the upper to the lower surface of the wing,
the resultant force normal to the surface is tilted inboard. The
vertical component of this force is lift, and the inboard component
is analogous to the induced drag component of the resultant force
due to the chordwise flow. This inboard component, however, is
nearly normal to the direction of motion of the aircraft, and hence
represents almost zero work. Hence, this force is primarily an
internal stress or compression on the structure, as with other
types of diffusers.
The aft secondary wing system as described above is particularly
effective on the outboard section of the wing, including the wing
tip region itself. The inboard component of the resultant force
generated on the airfoil elements, as described above, is the
reaction to a change in momentum outboard of the flow past the
secondary wing system. Any residual vorticity remaining in this
outward deflected flow will then produce an upwash outboard
thereof. The secondary wing system in the neighborhood of the wing
tip is thus most effectively swept outboard, extended aft, and
inclined downward so as to lie parallel to, along side, outboard
of, and in close proximity to the residual vorticity, to thereby
extract further lift from its upwash.
The lift on the forward primary wing may thus most effectively be
reduced inboard of the aft swept tip region, thereby concentrating
most of the residual vorticity at the knee or apex where this aft
swept tip elements begins.
The airfoil-shaped elements of the aft slotted and swept wing
system in acting as airfoils generate an irrotational flow field
extending (theoretically) above the surface to infinity. Hence, the
outboard flow deflection caused by the pressure asymmetry due to
the small swept wing elements is felt in the entire flow field
above the wing, not restricted simply to the boundary layer. Other
types of flow deflectors (fences, ridges, barriers, end plates,
etc.) produce a force only in the plane of the wing and the flow is
influenced only over the physical extent of the structure, thereby
necessitating large structures to produce appreciable flow
changes.
The angle of flow outwards produced by the slotted secondary wing
system is greatest at the bottom of the boundary layer, because of
the reduction of chordwise velocity near the wing surface, with the
angle of flow then decreasing rapidly upwards through the boundary
layer. The magnitude of the outward component given to the flow by
the pressure asymmetry, however, falls off slowly above the
boundary layer, as does the inward component due to the suction
lift of the primary wing, so that the rates of decay of these
opposing components in the outer flow field are of the same
order.
The foregoing and other readily apparent features of my present
invention will be better understood by reference to the following
more detailed specification and accompanying drawings in which:
FIG. 1 is a perspective view of the preferred embodiment of the
aircraft wing assembly, including a forward primary wing and an aft
secondary wing system comprised of a cascade of slotted swept
diffusers concave to the windward side of the upper surface and
extending from the upper to the lower surface of the wing;
FIG. 2 is an enlarged sectional view taken along the line 2--2 of
FIG. 1, illustrating the slotted passages from the upper to the
lower surfaces of the wing formed by the airfoil-shaped cascade
elements;
FIG. 3 is a top plan view of the wing showing sweep, particularly
of the outer wing panel, and the resulting outflow of the air over
the upper surface;
FIG. 4 is a bottom plan view of the wing showing the outboard
spanwise flow component and its cancellation by the inboard
component of the upper surface flow passing through the slots;
FIG. 5 is a sectional view along the line 5--5 of FIG. 1, showing
the downward deflection of the airflow over the wing;
FIG. 6 is a schematic view, looking forward, of an unslotted wing
showing the pressure distribution and resultant spanwise flow on
the wing;
FIG. 7 is a schematic rear view of the flow and pressure
distribution over an element of the secondary wing system when the
elements are arranged such that the flow passes from the upper to
the lower wing surface;
FIG. 8 is a perspective view of the slot between two elements
increasing in cross section from the forward to the aft ends of the
elements;
FIG. 9 is a perspective view of the flow over two airfoil
elements;
FIG. 10 is a schematic, looking inboard, of a wing/horizontal tail
system used for longitudinal stability on conventional
aircraft;
FIG. 11 is a schematic view, looking inboard, of the primary
wing/secondary slotted diffuser system, showing the mechanism by
which longitudinal stability can be achieved without a horizontal
tail;
FIG. 12 is a schematic view of the flow and pressure distribution
over an element of the secondary wing system when the elements are
arranged such that flow passes from the lower to the upper surface
of the wing;
FIG. 13 is a plan view of the outboard region of the wing system,
showing the aft swept, outboard, extended wing tip;
FIG. 14 is a vertical section along the line 14-14 through the
outboard tip region of FIG. 13;
FIG. 15 is a set of diagrams comparing the features of both a
conventional wing and the present improved wing;
FIG. 16 is a plan view of the improved wing system, showing the
vortex paths provided by the aft swept, slotted structure;
FIG. 17 is a vertical section view along the line 17--17 through
the outer tip region of FIG. 16, showing the pressure profiles on
the wing elements;
FIG. 18 is a plan view of the improved wing system, showing a more
general view of the outward deflected flow streamlines generated by
the aft swept, slotted structure;
FIG. 19 is a schematic view of an aircraft wing, illustrating the
vortex patterns provided both by conventional wings and by the
outflow of the present improved wing, including a table showing the
induced drag reductions thereby provided; and
FIG. 20 is a schematic view of a wing represented by a paired
vortex model, the upper set of vortices representing the upper
surface of the slotted wing structure and the lower set
representing the lower surface of the wing.
In the drawings, like numerals refer to like or corresponding parts
throughout the several views. Referring FIG. 1, a wing is
illustrated having a forward primary wing 20, and an aft secondary
wing system 21 comprising several airfoil-shaped elements 22
arranged in a cascade with their outboard edges 23 pitched higher
than their inboard edges 24 to produce positive angles of attack 25
relative to an inboard spanwise flow component 26. The elements are
swept at angles 27 relative to the resultant 28 of the chordwise
velocity 29 and the spanwise velocity 26.
The flow 30 through the passages 31 between the airflow elements 22
is illustrated in FIG. 2. The low 32 and high 33 pressure regions
resulting from this flow are illustrated by minus and plus signs,
respectively. The inboard edges 24 may be airfoil-type trailing
edges or may be reflexed to form the element cross section into an
s shape.
The flow turning mechanism by which the inward spanwise velocity
component 26 is cancelled is illustrated vectorially by FIG. 3. The
elements 22 are swept at angles 27 relative to the resultant
velocity vector 28. The sweep produces pressure gradients toward
the trailing edges 34 of the elements, thereby providing a
resultant velocity vector 35 which is in the chordwise direction of
the total wing. This eliminates the vortex producing spanwash on
the upper wing surface.
The flow turning mechanism operating on the lower wing surface 36
is illustrated in FIG. 4. The free stream velocity 37 is diverted
outboard 38 by the positive lower wing surface pressure gradient.
Some of the inward turned flow from the upper surface 39 passes
through the slots 31 between the airfoil elements 22 and opposes
the outward flow, eliminating the lower surface spanwash.
The mechanism by which the free stream flow 37 is diverted around
the wing section 40 is illustrated in FIG. 5. At some distance in
front of the wing, an upwash 41 occurs because of the acceleration
of the fluid over the cambered upper surface of the wing. The flow
directly behind the wing experiences a downwash 42 and then returns
to the free stream direction 37 at some distance downstream.
The mechanism by which the spanwise flow over the primary wing 20
is produced is illustrated by FIG. 6. The low pressure area 43
created on top of the wing by the acceleration of the flow, as
shown in FIG. 5, is at a lower pressure than the free stream 44,
resulting in an inboard spanwise flow 26. The pressure on the lower
wing surface 45 is higher than the free stream pressure 44,
resulting in an outboard spanwise flow 46. The inboard 26 and
outboard 46 components are not necessarily equal, but, if
uncorrected on the wing surface, will result in a trailing
vorticity 47 with the rotation direction as shown. A schematic
fuselage 48 is shown between the two halves of the wing.
The mechanism by which lift is generated in the secondary airfoil
system is illustrated schematically in FIG. 7. The flow 30 passing
through the slot 31 produces low pressure 32 over the convex upper
surface of the airfoil elements 22. In addition to the high
pressure 45 on the lower side of the total wing as shown in FIG. 6,
high pressure 33 is generated on the concave underside of the
elements. This combination of pressure produces a component of lift
49 on each element. Because of the angle of attack 25 of the
elements, the resultant force vector is tilted inboard, allowing
its resolution into a lifting component 51 and an inboard component
50. This component 50 is nearly perpendicular to the resultant flow
and, therefore, does not create a drag energy loss over the wing.
FIG. 7 also illustrates the reflexed inboard edge configuration 24
of the airfoil elements. The flow over the reflexed edges creates
an area of lower pressure inboard on the underside of the elements
which aids the dynamic pressure gradient in driving the flow from
the upper to the lower surface of the wing.
A perspective view of two airfoil elements is illustrated in FIG.
8, showing the slot size increasing toward the trailing edge, i.e.,
the distance 52 between the tip sections is greater than the
distances between more forward sections 53. This increasing slot
size acts as a diffuser or jet tube, i.e., the flow expands as it
is swept toward the trailing edge, creating a region of higher
pressure at the aft end of the slot which acts as a thrust in the
chordwise direction 54.
In FIG. 9, a view similar to FIG. 8 shows streamlines 55 of the
flow as it is diverted over the secondary wing system. The flow
enters the secondary wing system with the resultant velocity 28
imparted by the primary wing. The flow is swept down and aft by the
slotted diffuser system and leaves the wing in a chordwise
direction 56.
The mechanism by which the primary and secondary wing systems are
longitudinally stable as if the assembly were a wing/horizontal
tail system on a conventional aircraft is shown in FIG. 10 and 11.
A conventional wing 57 usually has a center of lift 58 ahead of the
aircraft center of gravity 59 which produces a nose-up moment 60
when the angle of attack 61 is increased. The horizontal tail 62 is
added to provide a nose-down moment 63 due to the center of lift of
the tail 64 being aft of the center of gravity 59. The horizontal
tail has a component of induced drag 65 similar to that of the
wing. The primary wing/aft slotted diffuser system of FIG. 11, on
the other hand, eliminates the need for a horizintal tail by
providing lift both forward and aft of the center of gravity. The
lift 66 at the primary wing center of lift 67 produces a nose-up
pitching moment 68, while the lift 69 at the secondary wing center
of pressure 70 produces a nose-down moment 71 about the center of
gravity 72. Since the secondary wing system cancels the primary
wing induced drag and has its own angle of attack induced force
component directed inboard, both the wing and horizontal tail
induced drags are eliminated.
The pressure distribution and resultant lift produced when the
angle of attack of the primary wing or the arrangement of the
slotted diffusers is such that the flow 30 passes from the lower to
the upper surface is illustrated in FIG. 12. Low pressure 32 is
generated on the convex upper surface of the elements and high
pressure 33 on the concave lower surfaces. The flow, moving
outboard, opposes the inward spanwise component 26 of the flow on
the upper surface. The inboard edges 24 of the airfoil elements
illustrate the straight or nonreflexed element configuration.
The elements of the aft secondary wing system as described above
and illustrated in FIG. 1 are further shown in FIG. 13 as they
appear in the neighborhood of the wing tip.
A vertical section view taken in the direction of flight through
the outboard tip section of FIG. 13 along the line 14--14
illustrates how the vector sum of the upwash 73 generated by the
residual inboard vorticity and the free stream velocity 29 provides
a resultant upflow 74. The secondary wing elements 22 in this
region can then be inclined at a negative angle of incidence 75,
thereby providing a force 77 normal to the resultant velocity 74
which has both a lift 78 and a forward thrust component 79. Thus
thrust or a reduction in induced drag is obtained from the upwash
energy of the residual vortex system.
Conventional planar wings, such as illustrated 80 in the left side
of FIG. 15, are designed to minimize induced drag by distributing
the downwash resulting from trailing vorticity uniformly across the
span. These wings are based on an approximate mathematical model
that (a) represents the wing in the x-- y plane, and (b) includes
no structure to recover the trailing vortex energy into either
increased lift or reduced drag. The minimum induced drag for such
an approximate model is produced by elliptic lift distribution 81,
and has been shown to correspond to a uniform spanwise downwash
distribution 82, and a single horseshoe pattern 83, as shown on the
left side of FIG. 15 for such a conventional wing.
The right side of FIG. 15 illustrates the improved new wing system
of the present invention which is designed to recover the upwash
energy, and showing in a corresponding set of diagrams from the top
down (a) wing geometry 84, (b) spanwise lift distribution 85, (c)
vertical induced velocity distribution 86, and (d) a reverse vortex
diagram 87. This improved wing shown in the right side of this
figure is designed to maximize lift on its inboard panel 88 with a
uniform distribution 89 generating no trailing vorticity, and to
dump most of its vorticity at a selected point 90 outboard of the
uniform lift but inboard of the wing tip in such a manner as to
enable a specifically designed swept and slotted panel 91 outboard
thereof to recover a large part of the energy associated with the
vorticity dumped from the inboard panel.
The mechanism of energy recovery from upwash is further illustrated
in FIGS. 16 and 17. This method employs swept and slotted structure
in the outer panel comprising a cascade in the chordwise direction
successively providing a short swept element 92 to unload vorticity
inboard at its tip 93, a long swept element 94 to transport this
vorticity outboard in its upper surface suction trough 95, and a
second long element 96 located above and aft to further deflect
this vorticity outboard by its lower surface pressure mount 97.
FIG. 16 further shows that the vorticity 98 transported outboard in
the upper surface suction trough 95 gradually trails off and under
the next aft long element 96 whose lower surface pressure mound 97
in turn deflects the free vortex 98 below further outboard. FIG. 17
illustrates the adverse pressure gradients 99 on both, the upper
99u and lower 99 surfaces of each tip element which in combination
with sweep 100 causes the flow to deflect outboard.
Thus, each aft swept element transports vorticity outboard by two
mechanisms, a suction trough 95 on its upper surface, and a
pressure mound 97 on its lower surface. This improved wing 84 is
thus designed specifically for energy recovery and drag reduction,
in providing a two element wing, comprising (a) an inboard element
88 having a constant lift distribution 89, with a sharp drop 90 in
its lift distribution and therefore a concentrated dumping of its
vorticity at a selected point 90 outboard of the uniform lift but
inboard of the wing tip 101, and (b) a specifically designed panel
91 outboard thereof to recover a large part of the energy
associated with the vorticity dumped from the inboard panel 88.
The paired vortex model illustrated in FIG. 20 represents the
improved wing 84 not by the conventional single set of horseshoe
vortices 83 in the x- y plane, but rather a pair of horseshoe
vortices, one above the other. The upper horseshoe vortex set 102
then represents the upper wing surface and slotted structure,
including chordwise diffuser structure and outboard swept elements
having a chordwise component, as bound vortices. The lower
horseshoe system 103 represents the lower wing surface as free
trailing vortices, which generate the inboard spanwash 104 over the
upper surface of the wing and its diffuser structures or aft swept
elements.
An incremental lift .DELTA. L is then generated by this inboard
spanwash 104 over the chordwise portion 105 of the upper bound
horseshoe vortex system 102, and a forward thrust .DELTA. T is
similarly generated by this inboard spanwash 104 over the vertical
legs 106 of the upper bound horseshoe system, where in both cases
the incremental force is provided by the Kutta-Joukowsky Law,
namely:
.DELTA. F = p v .GAMMA.
where v is the spanwash velocity and .GAMMA. is the circulation of
the chordwise bound vortex.
Although the vortex strengths shown in FIG. 20 are each .GAMMA./2,
the model is sufficiently general so that (a) the strength of the
upper and lower portions may be arbitrarily specified and (b) the
upper chordwise portion may be bound and the lower chordwise
portion free.
This model thus employs the lower free vortex portion to provide
the inward spanwash flow over the circulation strength of the upper
bound portion, providing an upward lift force. The upper bound
portion, in turn, provides an outward deflection of the lower free
vortices. Thus, any residual vorticity shed from both the upper and
lower system is deflected outboard, and would lay along side,
adjacent to, and parallel to the bound vortices of an aft swept and
downward inclined outer wing tip portion such as illustrated in
FIG. 16, thus, maximizing the additional lift from the induced
flow, as illustrated in FIG. 20.
With vortex model, thus, representing the wing by such a horseshoe
system, conventional airfoil theory can then be employed to
calculate the incremental lift .DELTA. L and incremental thrust
.DELTA. T as a function of the wing geometry. Thus, the vortex
model is a tool for (a) representing a wing modified in a
particular way to recover the spanwash energy with secondary
structure such as diffusers or outboard aft swept elements, (b)
identifying such modified wings with conventional vortex theory,
and (c) enabling the forces and pressures to be calculated by the
well developed and test confirmed means of conventional airfoil
theory.
The slotted, aft swept, negative dihedral wing 84 illustrated in
FIG. 15 and 16 employing the advanced lift distribution and energy
recovery mechanism described will locate the vortex core 87 at the
knee 90 of the aft swept wing portion 91 and not at the wing tip
101 as in a conventional wing 80. As a result, the air flow inboard
of this vortex will be directed inwards 107, and outboard of this
vortex will be directed outwards 108, on both sides of the
wing.
This flow field, described in detail in FIG. 16, is further
illustrated in a more general manner in FIG. 18, showing in
particular how the slotted and swept structure of the outboard
panel 91 produces an outflow 108 which the free vortices 98 must
follow. The induced drag reductions corresponding to such outboard
vortex displacement are shown in FIG. 19, which are oversimplified
in being based on elliptic lift distribution and no vortex energy
recovery, but yet are still illustrative of the gains associated
with the effective increase in span provided by deflecting the
vorticity outboard.
FIG. 19 also illustrates the well known face (Milne-Thomson, L.M.:
"Theoretical Aerodynamics," MacMillan and Company, Ltd., Third
Edition, 1958, Section 10.4, page 182 and Section 11.7, page 206)
that the dominant inboard spanwash on the upper surface of a
conventional wing 80 having elliptic lift distribution 81 reduces
the effective span, as determined by the resulting vortex location,
to the fraction .pi./4 of the span b. The outflow 108 provided by
the improved lift distribution and aft swept, slotted structure
illustrated in FIG. 18 not only corrects this inboard spanwash, but
extends the outflow 108 and its transported vorticity 98 to or
beyond the wing span 101 itself, providing the greater effective
spans and reduced drags shown in FIG. 19. Thus, the effective span
of conventional wings 80 with elliptic lift distribution 81 is less
than the actual wing span, while the present improved wing 84 can
develop an effective span greater than that of the structure
itself.
The outboard slotted structure 91 in the wing tip region is for the
purpose of recovering otherwise dissipated vortex energy and
reducing the induced drag. The slotted structure accomplishes this
objective in two steps, namely (a) deflecting the vorticity
outboard, and (b) locating this vorticity below the lifting
elements so that its spanwash and upwash over these elements above
produces a force with lift and forward thrust components. The
vortex model of FIG. 20 illustrates the inboard spanwash 104
generated from the vortex 103 located below, and shows both the
incremental lift .DELTA. L and the incremental thrust .DELTA. T.
The corresponding flow model of FIG. 14 shows the thrust 79
generated from the upwash 73. FIG. 16 shows the vortex outflow
sliding below the aft panel elements. It is clear that this
mechanism requires the cascade to be stacked above to the rear, so
that the free vortices 103 are below the lifting elements 105. The
forward elements may then be oriented with a negative angle of
incidence, tilting the resulting force forwards, producing a thrust
component 79, as shown in FIG. 14.
The term cascade as used in this application refers to a plurality
of airfoil-shaped elements located outside of a common airfoil
envelope, so that each element of the cascade operates essentially
as an independent airfoil, generating positive pressure on its
lower surface and negative pressure on its upper surface, although
in sufficient proximity so that each airfoil element operates in
the induced flow field of neighboring elements.
These cascade elements as shown in FIG. 14 split the shed vorticity
into a corresponding set of vortex sheets, which are shed in a
vertical stack, and which then laminate into an expanded size,
slowly turning, vortex core. The energy of a pair of vortices such
as are shed from a finite span wing is given by [Durand, Wm.
Frederick (Editor-in-chief), Aerodynamic Theory, Vol. II, Dover
Publications, Inc., New York, 1963] :
where
.rho. = air density
.GAMMA. = circulation strength
b' = semi-span distance between vortex centers
r' = vortex core radius.
In the square brackets the first term is the energy of the outer
field and the second term is the energy of the vortex core.
This expression shown that the energy shed into the wake in the
vortex system, which is manifest as induced drag, is reduced as the
vortex core is (a) expanded, and (b) displaced outboard.
It is clear from this disclosure and its accompanying set of
figures that the means of reducing induced drag have been described
in detail, and the magnitude of the provisions disclosed may be
varied according to engineering considerations for different
conditions as required. 22
While the preferred form and method of employing the invention have
been described and illustrated, it is to be understood that the
invention leads itself to numerous other embodiments without
departing from its basic principles.
* * * * *