low-aspect-ratio wings for wing-ships · 2015-02-04 · and out of ground. at lower aspect ratios...

Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc.

Low-Aspect-Ratio Wings for Wing-ShipsAntonino Filippone* and Michael S. Selig*

Department of Aeronautical & Astronautical EngineeringUniversity of Illinois at Urbana-Champaign

Urbana, IL 61801-2935

AbstractFlying in ground poses technical and aerodynam-ical challenges. The requirements for compact-ness, efficiency, maneuverability, off-design oper-ation, open new areas of investigations in the fieldof aerodynamic analysis and design. A review ofthe characteristics of low-aspect ratio wings, in andout-of-ground, is presented. It is shown that theperformance of such wings is generally inferior tothat of slender wings, although in ground place-ment can yield substantial improvements in theaerodynamic efficiency. The use of tip devices, suchas winglets and endplates, or an appropirate tipdesign, can change substantially the characteris-tics of the wing. Thin and thick airfoil sectionsare designed in ground effect, by using a multi-point inverse design method based on conformalmapping, to perform best either at constant lift orat increasing ground clearance. Three-dimensionalcomputations have been performed with a panelcode (VSAERO), and compared with available exper-imental data at aspect-ratios as low as 1. Wingsof aspect-ratio 1.5 to 2.5 having the airfoil sectionspresented in this work have been computed at var-ious ground clearances. It is concluded that de-sign in ground effect is possible, and that the ex-isting computational methods are adequate for anapproximate study of low-aspect-ratio wings, al-though many flow phenomena require detailed in-vestigastions.

'Post-doctoral Fellow, Member AIAA.t Assistant Professor, Senior Member AIAA. Copyright

© 1998, by A. Filippone and M. Selig. All rights reserved.Published by the American Institute of Aeronautics and As-tronautics, Inc with permission.

Introduction

Wing-in-ground planes (wing-ships) are aircraftthat fly in near-ground. Since the lift is generatedby forward flight, the wing-ship is fundamentallydifferent from a hover-craft, which generates a jetof high pressure flow to lift itself. Due to the rela-tively low resistance of the air (1/800th of that ofthe water), the wing-ship can fly at a much higherspeed than any existing ship. Experiences madein the former Soviet Union showed that the vehi-cles traveled fast, reliably, and were insensitive torough seas.

Although ideas about hybrid ship-planes go backover a hundred years, the earliest practical designswere developed in the Soviet Union in the 1960s1.Some of the most outstanding vehicles are listedin Table 1. The prototypes were designed for mil-itary purposes, rescue operations, civil transport,and cargo services. One of the first commercialvehicles was the KM model (Korabl Maket, shipmodel), developed at the Central Hydrofoil DesignBureau at Gorkii in the early 1960s. It flew over theCaspian Sea at a top speed of 500 km/h poweredby 10 jet engines. The A-90 Orlyonok wing-ship,designed in 1979 at Gorkii, could operate at a seaState 5, travel up beach and over flat terrain. TheLun' Spasatel, a later model derived from the KMin the late 1980s, had a larger wing span and ashorter fuselage. It was propelled by 8 jet engines,and had a cruise height of 1-4 meters above calmsea, although it could fly in 3.5 m high waves! Thecruise height of other (less famous) Soviet wing-ships varied from 4 to 90 m on snow-bound terrain,flat tundra, and ocean seas. The construction ofsuch vehicles was generally preceded by

1


Datawing-span (m)total length (m)loaded weight (t)speed (Km/h)max range (Km)cruise height (m)

Korabl Maket32-4093-106

500400-500

3000—

Lun Spasatel4473

400450

30001-4

Orlyonok A903158

125-140350-400

1100-3000—

Beriev VVA-14————

8000—

Raketa 2-219.533.531180500—

Table 1: Various dimensions of existing Soviet wing-sbips. Ranges given in each box are dependent on thevehicle's version (commercial, military, cargo). Weights are intended for loaded vehicles. Some data areunknown.

experimentation on smaller ones, single- or double-seaters, although a large vehicle weighing nearly1000 tons (Beriev VVA-14) was designed andtested in 1976.

In the late 1980s it was estimated2 thatwith improved aerodynamics a wing-ship weighing300 tons would have a chord of 36 m, a wing spanof 40 m, a total fuselage length of about 100 m, andwould fly in ground effect at a cruise height of 3.5-7.0 m. Cruise speed would be about 250 km/h, andthe vehicle would require 40,000 kW thrust fromthe propulsion system. Such a vehicle could oper-ate year-around over 90% of the world seas, in par-ticular: inland waters and offshore areas (life boats,coast guard units, high speed ferries), coastal traffic(as fast passenger ferries and freight), and overland(crossing flat areas, ice and snow, along with possi-ble mono-rail vehicles). Other advantages include:reduced fuel consumption, high payload, high de-gree of comfort, easy to pilot, and low take-offspeed. The low power required by this type of craftis a result of improved lift/drag ratio of a wing-in-ground effect as compared with flight out of groundeffect.

More recently wing ships have been designedand produced in Germany, China and USA. Theseare generally much smaller units, often prototypes,with limited passenger capabilities. A preliminarydesign of a wing-in-ground aircraft was performedat the University of Illinois in 19933. A criticalanalysis of wing-ship conceptual design is presentedin4.

The experience briefly reported above has ledto the introduction of wings of various planforms(trapezoidal, rectangular, tapered, with/withoutdihedral) and the most disparate configurations.

The KM vehicle had rectangular wings mountedhigh, no dihedral, tail-wing tapered, swept, withlarge dihedral angle. The Lun' Spasatel had rect-angular wing mounted low. The Orlyonok hadwing mounted lower, small tip skegs, trailing edgeflaps. Tapered and swept tail-plane with zero dihe-dral and four elevetors/side. Raketa 2-2 had smallcanards, down-turned tips, rectangular main wingswith wing skegs, wing flaps, elevens, aspect-ratioabout 1. The Beriev VVA-14 had short anhedralwings.

Wing-ships operate on the principle that by fly-ing in close proximity to the ground the induceddrag is reduced for a given lift coefficient becausethe downwash is inhibited by physical bounds.Ground effect become significant at cruise altitudesof h/c ~ 0.1-0.3. Assuming a design ground clear-ance of h/c = 0.25 with a design cruise height of3-4 m, the wing chord becomes 12-15 m. To main-tain a compact shape, a wing-ship must have a rel-atively short semi-span. The required lift, on theother hand, can be achieved by increasing the wingchord, which — at constant ground clearance —improves the ground effect gains. There sometimesappears to be a lower limit for h/c of approximately0.1 below which the wing experiences a downforcetermed suck-down. The effect depends on the ge-ometry (in particular, on the amount of camber),and must be seriously investigated, to avoid thesinking effect on the ship. The concept of sinkinga wing is widely applied in race car aerodynamicsto increase the grip and the cornering speed of thecar. The phenomenon is caused by a Venturi-typeflow, where the acceleration below the wing leadsto a pressure drop, that is enhanced as the groundclearance decreases.

Low-aspect-ratio wings, while best suited for the


present applications, are not well suited for conven-tional aircraft transport, since the efficiency L/Dof the wing increases with the aspect-ratio. There-fore, the wing-ship performance must be comparedto that an air-cushion machine (hover-craft) flyingover water, rather than an aircraft.

The aim of this paper is to investigate the perfor-mance of ground effect performances of low aspect-ratio wings suited for wing-ship applications. Al-though high lift devices are sometimes an integralpart of a wing-ship, high lift devices (e.g. flaps) arenot addressed in this paper.

Low Aspect-Ratio Wings: AReviewAerodynamic flows past low aspect-ratio wingsare strongly three-dimensional and vorticity-dominated, with some degree of trailing-edge sep-aration. In some cases the tip vortices can interactwith each other downstream; whereas, on the wingitself the tip flow can reach the symmetry plane.

Low sweep is required to fly at high lift and slowspeeds. In fact, low-.4 wings have a high angle ofattack at Cxma., a low lift-curve slope, and (gener-ally) a longitudinal stability that deteriorates withthe increasing angle of attack and moderate to highsweep angles. Sweepback causes the load on thewing of a given A to be further concentrated out-board when the increasing sweep angle. This pro-motes undesirable tip stall.

Experimental investigations on highly sweptwing showed that the root sections do not expe-rience high leading-edge pressure peaks5. In ad-dition, the spanwise pressure gradients cause anoutward drain of the boundary layer from the rootsections. The combined influence of these two ef-fects makes the root sections highly resistant toflow separation and therefore capable of developinglocal lift coefficients that more than compensate forthe lift losses that occur when the tip sections ofthe wing stall. As a consequence, the wing rootsections stall at very high angles, and the tip sec-tions stall at much smaller angles. The thinner thewing, the lower the angle of attack at which thevortex flow is observed5.

A combination of partial and progressive separa-tion may cause destabilizing changes in tne pitch-ing moment, frequently at low values of CL and inboth incompressible and compressible flow6. Thisbehavior is known as breakdown in the pitchingmoment, and the lift obtained at that point is theinflection lift.

Experiments carried out in Germany in the1940s7 for swept and unswept wings of aspect-ratios A = 1-5 at Re = 106 showed that the CLmaxis relatively insensitive to A for A > 2, with an al-most constant angle of maximum lift.

For smaller aspect-ratios (1 < A < 2) the an-gle of maximum lift moves upwards to 30 deg.At even smaller aspect-ratios (A < 1) experimen-tal investigations8 show that the values of the liftcoefficient are considerably larger than those pre-dicted by linear wing theory. The lift coefficientgrows at a faster rate because the tip vorticesstrongly interact with each other, while the cen-ter of the wake is pushed downwards. Some non-linear lifting line theory computations8"12 are re-markably close to the measurements for both deltawings and swept-back wings with A = 1. Exper-imental data for squared wings (^4 = 1) report'maximum lift coefficients that are extraordinarilyhigh'11 (CLmax ~ 1.3).

Another important detail is the leading-edge de-sign, especially for swept-back wings. Sharp lead-ing edges promote early flow separation (as withthe delta wing) even at small angles of attack. Anempirical correlation yielding the limiting leading-edge radius is given in5 , deduced from the analysisof a large number of wings.

The effect of aspect-ratio on lift and drag havebeen compared by Betz and Wieselsberger12 usingthe Lanchester-Prandtl correlation, given by

+A

-JA0(1)

where the index 'o' is relative to the reference data.The above expression was originally obtained for alifting surface with elliptic spanwise loading. WithEq. 1 measured polars can be transformed to aknown polar of given aspect-ratio. For wings inground effect, such a correlation does not exist.The wing aspect-ratio influences the lift curve slope


according to C'L/C'Loo = A/(A+2). The total dragof a wing consists of both the profile (viscous) dragand induced drag. The profile drag is largely inde-pendent from A. The induced drag is created bythe downwash generated by the tip vortices. Low-A wings have generally higher induced drag thanslender wings.

Rolling moment due to sideslip of rectangularwings is considerably lower than that for deltawings and swept-back wings. For aspect-ratiosin the range 2 < A < 3 experimental resultsshow an increase for the decreasing aspect-ratios(NACA measurements13). The response of rectan-gular wings, delta wings and wings with sweptbackto yawing moment due to sideslip is similar to thatof rolling moment.

Tip EffectsOnly few of the studies mentioned above has ad-dressed the influence of the tip flows on the over-all performances of the low aspect-ratio wings. Infact, as the wing becomes shorter, the geometry ofthe tip becomes essential hi determining the aero-dynamic characteristics. Round tips and fairingsincrease the effective aspect-ratio, promote or de-lay tip stall, and contribute in considerable amountto the total lift and drag forces. Tip separation oc-curs before than the wing trailing edge. The wayseparation occurs is strongly dependent on the ge-ometry.

Vertical winglets/endplates are useful in improv-ing the L/D ratio. The tip design should be a com-promise between the extra vortex lift obtainablefrom a low-,4 wing and its lateral and longitudinalstability.

Earlier Experimental WorkThere are several publications reporting experi-ments on low aspect-ratio wings. Ref14 deals withaspect-ratio 1 wings, untwisted, unswept, 11- and22%-thick, with flat tip or lower winglet, at vari-ous ground clearances. Experimental data for 11%-thick wing with winglet obtained by Carter14 andPaulson-Kjelgaard15 do not agree. Aspect-ratio 1

to 6, untwisted wings, with/without winglets atvarious ground clearances have been treated byFink and Lastinger16. Aspect-ratio 2 (or higher)whig, untwisted, at various sweep angles, 18%-thick, round tip, with without flaps and elevens,and fuselage (wing-body combination) have beentested by Paulson and Kjelgaard15. Aspect-ratio5 whig, untwisted, unswept, 12% thick, withoutother devices, out-of-ground effect17. High lift sys-tems and short aspect-ratio wings in ground ef-fect have been tested more recently at Gottingen18.Furthermore, there is a large body of experimen-tal work from Lockeed19 and Douglas Aircraft20.Other experimental data for low aspect-ratio wingsare available in some older literature21"22.

Airfoil RequirementsFor this study, two airfoils were designed using themultipoint inverse method for multi-element air-foil design documented in23. This design methodis driven by a MATLAB-based graphical user inter-face (GUI) enabling rapid, interactive design. Themethod couples an isolated-airfoil inverse designcode documented in24"25 with a panel method formulti-element airfoil analysis. In the current de-sign problem, the single-element airfoil in groundeffect is modeled as a two-element airfoil — the ac-tual airfoil and its image due to the presence of theground.

The two airfoils design here are referred to as"thin" and "thick" with design requirements listedin Table 2. The objective in setting the require-ments was to study the effects of the operationallift range — low lift for the thin airfoil, high liftfor the thick airfoil. The indicated nondimensionalchord c is a measure of the resulting chord requiredfor a whig hi ground effect ship such that the take-off gross weight remains constant which nominallyscales with c<7/. The thickness requirement wasdictated by assuming a constant span loading, andhence a desired constant physical wing thickness.The h'/c ratio was determined by the requirementof operating in the same sea state, e.g. constantheight h' — as measured from the lowest point ofthe airfoil, hi this case the trailing edge. Since h' isa constant hi the design while the chord changes,


the h'/c changes accordingly.

Parameter Thin Thick^t,designC

cd~Lt/C

h'/ca (deg)

1 0116

0.123.1

20.51

120.246.0

Table 2: Tiin and thick airfoil design require-ments and resulting design angle of attack.

The resulting airfoils at the required angles of at-tack are plotted to the design chord lengths (Table2) in Fig. 1.

The effects on the lift coefficient of operating inground effect as shown in Fig. for both the thinand thick airfoils. For the thin airfoil, the angles ofattack of 4.5, 6.5, and 8.5 deg correspond to out-of-ground effect lift coefficients of 0.938, 1.167, and1.393, while for the thick airfoil 4, 6, and 8 degcorrespond to lift coefficients of 2.316, 2.546 and2.772, respectively. What is clear from Fig.2 isthat the thin and thick airfoils behave differentlyclose in ground effect, while for h/c's values greaterthan approximately 2 a trend emerges. It shouldbe noted that h/c is measured from the 1/4 chordpoint, and the airfoil rotates about this point onthe chord line.

Some understanding of the changes in lift withproximity to ground can be gleaned from the ve-locity distributions about the thin airfoil at groundheights h/c of 0.25, 0.75, and oo for a = 6.5 degas shown in Fig. 3a. As the airfoil approaches theground from oo, the first effect on the airfoil is thatdue to the image vortex, in particular the "forward-wash" on the airfoil produced by the image-airfoilbound vortex. Thus, the "freestream" seen by theairfoil is effectively reduced, resulting in a reducedlift coefficient as ground is first approached. Thisreduction in the "freestream" is the cause for theoverall lower velocity distribution about the thinairfoil for h/c = 0.75 in Fig. 3a as compared withthe out-of-ground effect case. As the airfoil movescloser to the ground, the "forward-wash" effect in-creases as can be seen by a lowering of the uppersurface velocity (non-dimensionalized still be FQO).

A stronger effect — the ram effect — dominates,however. The lower surface flow is brought muchcloser to stagnation, and consequently this largereffect combined with the image vortex effect leadsto a net increase in lift as shown Fig. 2. Thedominant ram effect for the lower ground heightsis driven mainly by the angle of attack of the airfoil,resulting in slowing of the flow beneath the airfoil— the higher the angle, the greater the ram-effectcontribution to lift for a given ground height.

For the thick airfoil, the lift close to the groundas indicated in Fig. 2 does not rise as it did withthe thin airfoil for two reasons. First, the imagevortex effect dominates largely as a result of thehigher lift coefficients of the thick airfoil. This ef-fect dominates the velocity distributions shown inFig. 3b for an angle of attack of 6 deg for h/c of0.25, 0.75, and oo. Second, the ram effect is not aslarge because the angle for a given lift coefficient isnot as great as it is for the thin airfoil.

Another ground effect not appreciably displayedin these results for lifting airfoils is the venturi ef-fect. This latter effect is present with inverted air-foils, such as those employed in auto racing, e.g.Indy cars. In this case, the flow is greatly accel-erated between the airfoil in the ground resultingin a suck-down effect, or in motorsports terminol-ogy, downforce. Also, the "forward-wash" effectbecomes a "rear-wash" leading to a locally higherfreestream and hence greater downforce.

The effect of the ground on the maximum liftcoefficients of the thin and thick airfoils can bededuced from the velocity distributions shown inFigs. 4a and 4b, which correspond to respectiveconstant lift coefficients, rather than constant an-gles of attack as in Fig. 3a and Fig. 3b. For the thinairfoil since the lift at h/c = 0.75 is less than thatout-of-ground effect (Fig. 2), the angle of attackmust increase for this height. For h/c = 0.25, how-ever, the gain in lift with ground proximity leadsto a lowering of the angle of attack. In particular,the constant lift coefficient of 1.167 yielded corre-sponding angles of attack of 6.5, 6.83, and 5.45 degfor h/c values of oo, 0.75 and 0.25 respectively. Ascan be seen, while the angle of attack is less nearthe ground (h/c = 0.25), the suction-side pressuregradient on the airfoil changes very little. Thus, itcan be expected that for this airfoil the maximum


lift coefficient is hardly changed by ground effect.For the thick high-lift airfoil, however, the trends

are reversed. To compensate for the dramatic lossin lift, the angle of attack must be increased sub-stantially. Specifically, to maintain the constantlift coefficient of 2.186, angles of attack of 2.9, 6.4and 12 deg were required for h/c values of oo,0.75 and 0.25 respectively. From Fig. 4b it canbe seen that the high angle of attack in groundeffect leads to a strong adverse pressure gradienton the leading-edge upper surface. When this iscompared with the out-of-ground effect case, it canbe deduced that the out-of-ground effect maximumlift coefficient will be greater than that in groundeffect. Thus, the maximum lift characteristics ofairfoils in ground effect as compare with the out-of-ground effect conditions depends strongly on theairfoil geometry — the maximum lift coefficient ofhighly cambered airfoils will decrease with decreas-ing ground clearance owing to the occurrence of astrong leading-edge suction peak.

The Low Aspect-Ratio WingsMethods used to predict the performance of wingsin ground range from 2-D potential flow meth-ods, with/without boundary layer displacementeffects18, to 3-D steady/unsteady lifting surfacemethod26. Approximated linear methods, suchthat of Multhopp9, Betz11 and Truckenbrodt17 aresometimes used for wings with moderate sweeps.

In the present work the low-order panel methodVSAERO27"28 has been used for the calculationsshown in this paper. Currently, problems describedby several hundred body and wake panels requireno more than a few minutes per run on a personalcomputer. The low computing cost makes VSAEROa practical tool for solving complex non-linear aero-dynamic problems. An interface is provided toVSAERO to compute entire polar characteristics of agiven wing. This computer code has been validatedin the present work by computing low-aspect ratiowings in- and out of ground. The results have beencompared with experimental data.

Figure 5 shows the results for the computed po-lar of an aspect-ratio A = 5 wing having a con-staint airfoil section NACA 2412. The computed

data are compared with experiments with a wingout of ground. The computation was performed byusing a free wake analysis and a boundary layer it-eration, that works very well under mild pressuregradients. The computed polar is very close to theexperimental data for a wide range of angles of at-tack.

Wings of aspect-ratio as low as one, Fig. 6, havebeen computed both in- and out of ground ef-fect, after the wake separation line has been ad-justed. The results are generally satisfactory, al-though problems of tip flow separation are very dif-ficult to handle. Also the results of Fig. 7 have beenobtained with a free wake analysis and a boundarylayer interaction.

Figure 8 shows the computed CL and the effi-ciency CL/CD versus aspect-ratio for the two wingsat a = 0 at the design ground clearances. The val-ues obtained for the thick wing are considerablyhigher.

The lift characteristics of two wings, having thethin and the thick airfoil sections, respectively,have been computed as shown in Fig. 9. The thinwing was at the design clearance of h/c = 0.12, hasan aspect-ratio A = 2.0, with a unit chord (designconditions of Table 2), while the thick wing wasplaced at the design clearance h/c = 0.24, had thesame span, but half the chord, hence an aspect-ratio A = 4.0. The lift values of the thick wing aremuch larger, showing a gap ACx of about 0.75 inground effect.

With the airfoils section described in this pa-per we have computed rectangular wings of aspect-ratios A = 1.5, 2.0, 2.5, at the design ground clear-ances h/c = 0.12, 0.24 and out of ground, withround tips and endplates. Figure. 8a shows thelift characteristics for the thin wing, FigSb showsthe corresponding aerodynamic efficiency CL/CD-The angle of attack was a = 0.0. The values ob-tained for a wing with a rectangular endplate areconsiderably higher than the values obtained wih asimple round tip. The ffect of the plate is to diffurethe tip vortex and reduce the loss of lift at the outerboard. The effect of the spanwise lift distributionis shown in Fig. , at ground clearance h/c = 0.12and out of ground.


ConclusionsIt is possible to design airfoils in ground effect, us-ing multi-point design techniques, that include ge-ometrical constraints and specified pressure distri-bution. The method features the possibility of de-signing an airfoil with a flap system (also in groundeffect).

The inverse design method is very useful toanalyze finite wings (an inverse design methodfor finite wings in ground effect does not exist).The analysis has been carried out with a three-dimensional panel method, for both simple wingsand wings with tip devices (endplates).

For the airfoil in ground effect is was found thatthe airfoil loses lift (with respect to an airfoil out ofground) at high lift, and gains lift at low lift. Thisis due to the negative effect of the mirror imageairfoil with the airfoil itself is highly loaded. Neg-ative ground effects have been found on camberedairfoils in ground placement.

The lift curve slope increases in ground effect forboth the thin and thick wing. At some negativeangles of attack there is an inversion in the liftgenerated, since the wing-in-ground becomes lesseffective than the wing out of ground.

Low aspect-ratio wings in ground effect havebeen computed with a three-dimensional panelmethod (VSAERO). The results have been comparedwith experimental data. At relatively high aspect-ratios (A ~ 5) the results are encouraging, both in-and out of ground. At lower aspect ratios tip sep-aration occurs. If the separation line is known, theresults are in excellent agreement with the experi-mental data for aspect ratios as low as 1 (squaredwings).

The wing CL increases slightly with the increas-ing aspect-ratio, and shows values sensibly higherfor the thick wing. The lift coefficients are in bothcases much lower than the values computed for the2D airfoils in the design stage. This is clearly dueto the three dimensional effects.

The thick wing has also a larger aerodynamic ef-ficiency, both hi- and out-of-ground. At the aspect-ratios considered the thick wing is about threetunes as efficient.

Three-dimensional effects on the lift can be re-duced by using endplates of appropriate shape and

size. Computations performed on the thin wing atall aspect-ratios, in and out-of-ground effect, haveshown a substantial reduction in the loss of lift dueto end-effects, and tip vortex roll-up. Other tech-nical solutions may include boundary layer fencesto reduce the three-dimensionality of the flow.

The nature of the tip geometry is essential hidetermining the characteristics of the wings of lowaspect-ratio. It is not possible to compute flow sep-aration with inviscid methods; however, separationaffects the wing characteristics in a stronger degreethan in slender wings.

Main problems are believed to be the tip effects(which can change consistently the wing charac-teristics, in and out of ground), the stability of thewing, both static and dynamic, the take-off condi-tions, and the behavior during banking flight.

AcknowledgementsThe authors with to thank Ashok Gopalarathnamfor his help in developing the MATLAB-GUI in-terface used extensively in the airfoil design partof this effort.

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8


thin airfoil: Cl = 1, alfa = 3.1 ——thick airfoil: Ci = 2, alfa = 60 •-••••

AC,/C,

-0.5

Figure 1. : Designed airfoils sections. Design Figure 2. : Lift characteristics of the thin andpoints are: thin airfoil CL = 1.0, a = 3.1 deg, thick ajrfOJ7<j <& a function of the angle of attackh/c = 0.12; thick airfoil: CL = 6.0, a = 2.0deg, h/c = 0.24.

ground clearance.

v2

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

Thin Airfoil [alfa = 6.5]

h/c = 0.25h/c = 0.75h/c = inf

a.)

0.2 0.4. 1X/C 0.6 0.8

2

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

Thick Airfoil [alfa = 6 deg]

b.)

0.2 0.4 X/C 0.6 0.8

Figure 3. Computed velocity distributions on the thin a.) and thick airfoil b.), as functionof the ground clearance.v2

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0 I

Thin Airfoil [Cl = 1.167]

h/c = 0.25, alfa = 5.45h/c = 0.75, alfa = 6.83h/c = inf, alfa = 6.5

2.5Thick Airfoil [Cl = 2.106]

1.5

0.5

a.)

h/c = 0.25, alfa =12.h/c = 0.75, alfa = 6.4h/c = inf, alfa = 2.9

b.)0.2 0.4. 0.6 0.8 0.2 .0.6 0.8^-/ v X/C

Figure 4. Computed velocity distributions at constant Ci on the thin a.) and thick airfoilb.), as function of the ground clearance.


CL

1.5

0.5

22.4

CalculationExp. Data

1.5

0.5

20.0 deg

Wing in Ground (calculated)Wing out of Ground (calculated)

0.05 0.15 0.2 0.05 0.1 0.15 0.20.1CD CD

Figure 5. Computed polar for a NACA 2412 wing with A = 5 having a round tip. Graphicof the left shows comparison between the calculated polar and the experimental data. Thegraphic on the right shows a comparison of predictions between in- and out-of-ground effectfor the same wing.

CL1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

CalculatedExp. data

-5 10 15 20

CL1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

Calculated -*-Exp. data *

-5 10 15 20

Figure 6. Computed CL-curve for a rectangular wing of aspect-ratio 2 with fiat tip, Glen-Martin 22 airfoil section (22%-thick), out- and in-ground effect (left and right graphic,respectively). The present results are compared with the experimental data of Ref. 14.

10


CLi

0.8

0.6

0.4

0.2

0 -

CalculatedExp. data

-5 5a

10 15 20

CLI

0.8

0.6

0.4

0.2 •

0 -

CalculatedExp. data

-5 10 15 20

Figure 7. Computed CL -curve for a rectangular wing of aspect-ratio 1 with Hat tip, Glen-Martin 11 airfoil section (11%-thick), out- and in-ground effect (left and right graphic,respectively). The present results are compared with the experimental data ofRef. 14.

1

0.9

0.8

0.7

0.6

0.5

0.4 •

0.3 •

0.2 •

0.11.4

Thin WingThick Wing

ground

1.6 1.8 2.2 2.4 2.6 1.4 1.6 1.8 2.42 23A A

Figure 8. Computed CL (left) and CL/CD (right) versus wing aspect-ratio for two rectan-gular wings having round tip. Angle of attack a = 0 deg. Ground clearances: h/c = 0.12,0.24, and oo.

11


-0.2-4 -2 0 2 4 6 8 10

Figure 9.: Computed lift curves for wings in- andout-of-ground effect. Thick wing A = 4.0 and h/c =0.24; thin wing A = 2.0 and h/c = 0.12.

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

in ground: h/c = 0.12out of ground

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 12y/b

Figure 10.: Computed Ci(s] spanwise distribu-tion for a rectangular thin wing of aspect-ratioA = 1.5 at a = 0 deg, with round tip and end-plate, in- and out-of-ground.

0.4

0.35

0.3

0.25

0.2 -

0.15

0.11.4

EndplateRound Tip

1.6 2.2 2.4 2.6

30

25

20

15

10

1.4

EndplateRound Tip

1.6 1.8 2.2 2.4 2.6

Figure 11. Computed CD and CL/CD versus aspect-ratio for rectangular wings having athin airfoil section with and without endplates Ground clearances: h/c = 0.12, 0.24, oo.

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low-aspect-ratio wings for wing-ships · 2015-02-04 · and out of ground. at lower aspect ratios...

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