US2441758A - Fluid-foil lifting surface - Google Patents

Description

y 8, 1948. M. A. GARB ELL FLUID-FOIL LIFTING SURFACE 3 Sheets-Sheet 1 Filed July 16, 1946 FIGURE l INVENTOR.

ATTOEA/FYJ y 1948-- M. A. GARBELL I FLUID-FOIL LIFTING SURFACE Filed July 16, 1946 v:5 Sheets-Sheet 2 FIGURE 2 .rZmzUF-FEOU 7 km] ZOFUwm SEMITSPAN SPANWISE STATION ROOT FIGURE 3 Wma -Z. INVENTOR.

2Z 7MML May 18, 1948. M, A, R E L 2,441,758

FLUID-FOIL LIFTING SURFACE Filed July 16, 19 46 5 Sheets-Sheet 3 SECTION .LIFT COEFFICIENT FIGURE ROOT SPANWISE SEMI-SPAN- STATION E z l,u

z 2 0 Ln. ,2 {3 FIGURE 0 O 5 LIJ m U ROOT SPANWISE SEMI-SPAN STATION WW1 M/J INVENTOR.

fatenteti Ma 1 8, 1948 FLUID-FOIL LIFTING SURFACE.

Maurice Adolph Garbell, San Francisco, Calif.,

assignor to Maurice A. Garbell, Inc., San Francisco, Calif., a corporation of California Application July 16, 1946, Serial No. 683,815 I 15 Claims.

1 o This invention relates to the design and con struction of surfaces to be driven through a fluid, intended to produce a useful force component perpendicular to the relative velocity of the fluid with respect to the surface, known in the art as lift force, side force, etc, and referred to hereinafter as lift.

In particular this invention relates to the design and construction of surfaces to be driven,

through theair, intended to produce an aerodynamic lift force perpendicular to the relative wind velocity with respect to the said surface, while. minimizing the aerodynamic drag force parallel to the relative wind. In the art such surfaces are known as wings, fins, blades, etc., and will be referred to hereinafter as lifting'surfaces. intersections of the lifting surfaces with vertical planes parallel to the relative wind will be referred to hereinafter as fluid-foil sections. The body to which the lifting surface is fastened will be referred to hereinafter as the craft.

Figure 1 illustrates the preferred embodiment of this invention comprising a lifting surface designed and constructed according to the method outlined in the subject specification.

Figure 2- illustrates the spanwise distribution of actually prevailing section lift coefficients and.

the spanwise distribution of maximumattainable section lift coefficients on a typical lifting surface designed and constructed according to the subjectmethod of this invention.

Figure 3 illustrates the typical inception and growth of the stall of a lifting surface designed andconstructed according to the subject method of this invention. I

Figure 4 illustrates the procedure employed in the finding of the optimum spanwise location of the third controlled fluid-foil section in a lifting surface designed and constructed according to the subject method of this invention,

Figure 5 illustrates the spanwise distribution of actually prevailing'section lift coeflicients and the spanwise distribution of maximum attainable section lift coefiicients on a typical lifting surface designed and constructed according to the subject method of this invention, the tip section of said lifting surface having a thickness ratio smaller than the optimum thickness ratio for absolutely maximum attainable section lift coefficient for the series of fluid-foils employed in the lifting surface.

The closed curves resulting from' more controlled fluid-foil sections I, 2, and 3,

' selected according to the method explained in the subject specification of this invention, wherein section 2, representing'the additional controlled sections 'interjacent between the root and the tip of the lifting surface, is at variance with the section 4 obtainable at the respective spanwise stations by means of-straight-line fairing between the fluid-foil sections located at the root and the tip of the lifting surface.

Another object of this invention is the elimination of the violent rolling moments ordinarily produced by the unavoidable asymmetry of the stalling process, because the aforementioned method of fluid-foil selection suppresses the stall inception at the tip of the lifting surface and induces stall inception at a more inwardly located panel ofthe lifting surface, thus reducing the rolling moments acting on the craft for a given asymmetry of lift forces on the two stalled lifting surfaces. 7

vices attached to the trailing edge of the tip Another object of this invention is the maintenance of adequate lateral-control effectiveness, together with the elimination of violent unstable control forces acting on control'surfaces and depanel, during the critical stall-inception stage of the lifting surface, because the aforementioned method of fluid-foil selection induces stall inception at a more inwardly located panel of the lifting surface, so that the fluid flow over the tippanel and hence over the said control surfaces and devices remains smooth, thus maintaining effective lateral control as well as stable ,and'smoothly varying control forces throughout the stall .of the lifting surface.

The general object of thisinvention is the at- I Another object of this invention, .through the employment of the aforementioned method of fluid-foil selection, is to reduce both the parasite drag and the induced drag of the unstalled lifting surface,'and to shift the spanwise. location of the center of drag forces. of thestalled lifting surface inwardly so that: the drag moment of. the stalled lifting surface with respect to 'a vertical axis at or near the root is reduced to a value smaller than that of a lifting surface having a stall inceptionnear the tip thereby reducing to In the art the achievement of the objects of 1 this invention is recognized as one of the great steps in advancing safety and efficiency in aircraft design. According to accident statistics of the Civil Aeronautics Boards and other aeronautical agencies most flying accidents, especially those accidents occurring while flying in proximity of the ground, during take-off, and when landing, are caused by the stall of the lifting surface, the"severityof' such accidents being attributable not so much to the loss of lift directly, as indirectly to the adverse longitudinal and lateral stability characteristics, to the loss of con; trol effectiveness, and to the violent unstable control forces produced by the stall inception near. the tip of the lifting surface;

An investigation of the fundamental reasons for unsatisfactory and hazardous stalling characteristics reveals that high plan-form taper and sweep-back of the lifting surface create three principal unfavorable effects resulting in a stall inception near the tip of the lifting surface: (1)a"reduction of the scale factor known in the art :as Reynolds number in d ct propdrtion to the decrease chord length f' root tothe tip; according tjdw nagr wa experimental evidence the Ina ximuin section lift coefficient attainabl wit iv-tn' u l t qlif' ml t e tip Panel ofv the lifting surface is smaller than the max m e tio tptfiltite t at t e Sam section would be capable of attaining wereit Pl ce in t e roo ane Where. we h r eil t nd hence e Et rntlds. n mbe r er a ilatiql f m the d a pti al spanl s ri ut o en W ease th lif lii i nts prev i n ov r th p s io i and t9.

e e h i cdsfi c ent va in ve tlit -Qtt s ct ns at a y. v n, total ift wtfii tll li' llt f in su face; (3) an. outwa dhr. irectedpam wisef id. r ss-fl w e pecia ly on. tha uttis ll id of he lif in surface; thi cr sslow at. h lift coeflicients of the lifting surface in an additional incentive for fluidefl w. se a at n and sta lnsa the tip of the, lifting surface,

In the art, prior to. invention, it; was customarily, sought to. co nteract the aforemem tioned factors that contribute. to. the stall incepr. n i the tip, anelby resortin t th foll win measures: ((1). effective. washout, that is, wash u of the zero-lift line ofjthe fluid-foil. section atthe,

tip with respectfto thefzero-lift. line of theroot section, thus. reducingthe effective, angle. of attrack of. the. tip section, below the. eifective, angle of attack of lthe'root section; (b) theemployment of a fluid-foil section with a more highly, camberecl mean line. at the. tip ofithe lifting surface. than at the root, in orderto enable the tip section to attain higher. maximum slectionlifticoefii'cients. These. measures, however, have. not been 'entirely successful in suppressing the. stallinception near the tip of the lifting'surface; the spanwise distribution of. the actually prevailing section lift coefiicient's'reaches a peak near the tip and therefore inevitably intersects the nearly line'arspanwise distribution of maximum attainable section liftcoefiicients in this most critical portion of the lifting'surface.

As. a rule the resulting stall patterns remain unsatisfactory for all but the lowest of-plan -form taper ratios, anclma'y' become dangerously critical for plan-form taper ratios in excess of 3'1 and for any highly swept-back lifting surfaces. The stall inception in the vicinity of th tip of the lifting surface and a comparatively slow inboardw'ard" p ogression of the stall'wi th any further increase h am: am qfi ttalil t ila sults in the most vicious type of tip stall, with little or no stall warning, violent rolling moments, loss of lateral control, violent unstable control forces, and unstable nose-up pitching moments throughout the stall.

It was therefore customary in the art, prior to this invention, to employ as washout and camber variations as was deemed permissible, and to transfer the further responsibility for the avoidance of the admittedly unsatisfactory stalling characteristics to the care of the pilots, or to warning signals actuated by the stalled fluid flow, or. to a limitation of the elevator control travel to pr "t the attainment of the high angles of at at'which stall occurs.

Techniques utiliaing three controlled fluid-foil sections, in which the section at the semi-span center has either greater or smaller mean-line camber than the sections at the root and tip, have alsQ f i d to. offe ny ubstan al i pro emen of t ama es til al tharet tr ttitt, Qt highly t s t a ti/0. w at-halal? i t n ti tfaoes.

prefer ed e ibed i th ol ow n aeofi a n; the. broad scope of the invention is'eigpress m lathe claims concluding the instant application.

e n nt n QQ i S i nav l met ods. and. combination of bi ds. desc i ed. hereina er, all i W th' n i ute to. Pra -lu e sa e a d. t3.- cient-lifting surface.

l ii l v 1 l stra e the. r rreutmbsu mtat of this i ven on comp i in a l g u fa e with t re or, m re. u ljq td. fl id- 91 i wh h. the tt e w h. he lea t m nlinej camber if, is located at the root of the lifting rl te; ta tt 'qn w th." e r ate t mcankl as am i ttat i' a h fl i rdv lamica lr ra r'o t e: t g uriat i the tt a ip. air n o h ift ng urfa 'amai cqmrr s fa lrtadiman ipaa tly. w t qut ail a.- tifiabla mtane x s camb ith s o a an nsequence in the nli.a,9n of th SEW-QC? nven o a out r ere. l-itr a sat uid: foil sections ate e tjttttl' ol o r fi th. ll thllt t ined s wl aid. ttr 'atelli fl idil t ta s hav n ia uts f. t e me .1 9 amera var an e. w th the. ra lg it; b ab t at he. re} stt t ra rl st's t lls bymsaa bf ai h line fairing between the fluidfoil section located, at the root and the fluidffoil a j16 atd at the tip of the liftingsurface, provided; marine ps st li alue f; t ri r -l n a e lltt telltfl -i i ns e her x' te' the inean line camber o f t lie tip 'se ction npr ej hif tei'stira i s' ihe various controlled fluid-foil se ions are fpre: sented herein for lifting surfaces 'whereinthe thickness'ratio of theroot section is the greatest,

and th ethickness ratio of'the tip section is the smallest, respectively, of any fiuid-"foil section employed in the lifting surface;

' Figure? illustrates the preferred manner in which" this invention, through the employment of the" aforementioned method of fluid-foil; selec# tion, a chievesthe establishment of a curvilinear polygon 5 describing the spanwise distribution f heritage a as as n. i t tie ts' sa tur l ar. Pol o be n o. d h t it"e'nvelop's" closelvthe curve 6 describing the tmbt lttallt. of th s nvention. s.

spanwise distribution of the actually prevailing section lift; coefflcienta'except that beyond the spanwise point I at which the highest actually prevailing section lift coeflicient'occurs-the maximum'attainable section lift-coeflicient exceeds substantially the actually prevailing section lift coeificient, so that the stall inception occurs near mid-semispan, spreads more prevalently inboardward and to a smallerextent outboardward, and does'not involve the extreme tip of the lifting surface prior tothe breakdown of the fluid flow over the entire remaining lifting surface.

As used herein the curvilinear polygon 5 describing the spanwise distribution ofmaximum attainable section lift coefficients is established by the respective values of the maximum attainable lift coeiiicients of the root section 9, the tip section 8, and the third or'additional control section II, and by the respective maximum attainable lift coeflicients 5 of the sections obtained by conventional fairing between each pair of controlled sections 9-ll, l|-8, etc.

The curve 6 describing the spanwise distribution'of the actually prevailing sectionlift coefficients at the-maximum lift coefiicient of the lifting surface is obtained by conventional methods of experimentally verified calculation for the desired lifting surface, taking into consideration the plan-form, effective aerodynamic washout, section lift-curve-slope characteristics, etc.

The term envelopment" as used herein signifies the establishment of curvilinear polygon 5 on the convex side of curveB, wherein each individual branch 9-l|, ll8, and so forth of the curvilinear polygon vti is tangent or nearly tangent to curve 6.

Figure 3 illustrates'the stallprogression resulting from the employment of the subject,

method of this invention. The curves I2, l3, l4, l5, and I6 indicate, in their orderly progression, the extent of the stalled lifting-surface area of the stalled area prevents the formation of a deep local stall in a chordwise or depthwisejsens'e' at any one spanwise station. Steep spanwise pressure differences between unstalled sections and stalled sections, and hence deep spanwise cross-flows, are thereby effectively prevented.

The prevalently inboardward development of the stalled area not only produces the desired timely stall warning in the form of a gentle tail shake at a speed slightly in excess of stalling speed, but serves also to reduce the downwash of the fluid flow aft of the lifting surface, in the space usually occupied by the horizontal stabili'zer, so that an upwardly directed lift-force in-. crement is made to act on the horizontal stabilizer, thereby imposing a nose-down pitching moment on the craft that induces the craft to return to smaller angles of attack-and brings to a halt any further progress and intensification of the stalling process by precluding any increase in angle of attack beyond the stalling angle.

The following specification outlines the method employed in the design of the subject lifting surface of this invention, whereby to select the most opportune values of fluid-foil section mean-line camber and fluid-foil section thickness ratlo'required to achieve the objects of the instant invention: a

To apply the subject methodof this invention it is actually necessary to know only the plan form of the lifting surface and the desired stall pattern. Inasmuch as practical considerations other than those pertaining solely to the control of the stalling characteristics ordinarily predetermine certain design parameters of the lifting surface, preferred embodiments of the subject method of this invention are hereinafter explained for two typical combinations of predetermined basic design parameters:

In the first typical configuration the following design parameters, for example, are assumed to be given a priori: (a) the plan form of the lifting surface, based on structural and practical design considerations; (b) the series of fluid-foil sections to be employed, based on high-speed and other performance requirements; (0) the maximum permissible effective aerodynamic washout, based on drag considerations and structural bending-moment limitations; (d) the thickness ratio of the fluid-foil section at the root, based on the critical-Mach-Number requirements and structural weight considerations; (e) the thickness ratio of the fluid-foil section at the tip, based on practical space requirements for control-surfacebalances, etc.; (I) the mean-line camber of the fluid-foil section at the tip, based on the requirement of adequate torsional lifting-surface stiffness at high speed.

The subject method of this invention is employed firstly to design the lifting surface without any effective aerodynamic washout, that is,

with the three or more controlled fluid-foil sec-.

tions placed at such 'an angle of incidence with respect to the reference chord plane of the lifting surface that the'said'fluid-foil sections operate at their respective zero-lift angles of attack when the-entire lifting surface operates at its angle of attack for zero overall lift.

Based on fundamental experimental windtunnel data available forthe pre-selected series priate values of the Reynolds number is estimated, for example, by dividing the maximum attainable section lift coefficient of the tip section 8 (obtained from the aforementioned windtunnel data) by the highest spanwise value of the additional section lift coefficient (as defined in Army-Navy-Commerce ANC-l(1) entitled spanwise Air-Load Distribution), as,

follows C max tip 'highelt ace-135a value of mean-line camber is determined from the graph showing the experimentally determined variation of the maximum attainable section lift coefficient with varying mean-line camber, selecting that value of the mean-line camber that produces a maximum attainable section lift coefiicient 9 equal to or slightly superior to the section lift coefficient Ill actually prevailing, over the root section.

For the spanwise location of the third and additional controlled sections 2 and II, the subject method of this invention utilizes preferringly locations between the spanwise point of the highest actually prevailing section lift coeificient 1 and the root Ii! of the lifting surface; the most efficient interval wherein to locate the third controlled section lies between the spanwise point of, the highest actually prevailing section lift coeflicient I and the spanwise point located twice as distantly from the tip as point I, with a preferable optimum at the point H, where the tangent to the inboard portion of the curve of spanwise distribution of the actually prevailing section lift coefficients I8 intersects the horizontal tangent I9 to the same curve, as shown in Figure 4.

It will be understood, however, that inescapable practical design considerations may require that the additional controlled sections 2 and II be placed at spanwise stations located inside power plant nacelles or at those spanwise stations where the lifting surface is mechanically jointed for sudden changes in plan-form taper, or sweep- A back, as is the case in craft with removable or foldable outboard panels.

The Reynolds number is calculated for the third controlled section; the thickness ratio ob- 4O tainable at the third section by straight-line interpolation between the root section and the tip section is also determined. For the Reynolds number and thickness ratio thus determined, the

required value of mean-line camber is found from the graph showing the experimentally determined variation of the maximum attainable section lift coefficient with varying mean-line camber, selecting that value of the mean-line camberwhich produces a maximum attainable so section lift coefficient I I and I I equal to or slightly superior to the highest actually prevailing section lift coefilcient 1.

From the foregoing, it will be readily seen that the lifting surface obtained by the invention, and 5 6 If the required maximum attainable section lift coeificient for the interjacent section H cannot be obtained with a mean-dine camber not exceeding the mean-line camber of the tip section, a value equal to or slightly less than the 710 mean-line camber of the tip section is selected. The maximum attainable section lift coefficient of the interjacent section is then increased by changing the section thickness ratio in the proper sense, usually downward, until-eitherthe required 75,

maximum attainable section'lift' coemcient II is obtained, or untilstructural considerations interfere with the continuance of this procedure. If thisprocess does not offer a conclusive result, which is rare, a small amount of effective aerodynamic washout is then introduced, /2 to 1 in each step of the application of the method, wherein the total effective aerodynamic washout is distributed in appropriate fashion between the controlled sections and where the total washout is less than the maximum permissible washout as defined in the aforelisted initial design assumptions. The entire heretofore specified procedure including the establishment of a curve B conforming to the washout chosen, is then repeated for the selected amount of effective aerodynamic washout, until the desired results as illustrated in Figures 2 and 3 are attained.

A typical example of the application of the principles of this invention to'one well-known type of lifting surface isv as follows: Here we as.-

ness ratio of twelve per cent along the entire semi-span, the utilization of 64- series NACA low-drag fluid-foil sections, a mean-line camber of the root section I characterized by an ideal lift coefficient C1 equal to 0.1, and a mean-line camber of the tip section; characterized by an "ideal lift coefilcient C1 equal to 0.45. The term ideal lift coefficient is to be interpreted as defined by the National Advisory Committee for Aeronautics nomenclature and i herein used as a parameter characteristic of the mean line camber of a fluid foil section. Galen.- lations based on conventional methods will indicate that a lifting surface having the above general design parameters will experience, at its maximum resultant lift coefficient, a distribution of section lift coeiiicients as illustrated in curve 6.

Following the. procedures hereinzbefore described, we achieve in the above-outlined construction the desirable stalling characteristics taught bythis invention through the use Qf a controlled fluid-foil section 2 or I I at a station approximately per cent of the semi span from the root and with an effective aerodynamic washout of zero degrees with respect to the root section, wherein the mean-line camber of the interjacent controlled section .2 or II is characterized by an ideal lift coefficient C1 equal to,

0.35,. 'In this structural example the mean-line camber of the inter'iacent controlled section ,2 or I1 is greater than that of the root section ,I or :9, smaller than that of the tip section 3 or 8, and greater than that of the interpolatedsection obtainable at the .5 5per--ce nt semi-span station by means of straight-line fairing between sections I and 3, and which accomplishes the 'envelopment of curve 6" by the curvilinear polygon V In another typical example, ,a lifting surface is assumed 'as having substantially identical basic 5 design geometry as the preceding example, .ex-

cept for a structurally desirable .root thickness ratio of twenty-three per cent, a tip thickness ratio of seven ,per .cent, a total .efiective aeroynamic washout .of one degree, anda thickness, ratiooffifteen .per cent at an inter-iacent station locatedat approximately ,per cent of the semispan.

Again following the procedure of this invention we achieve in the abovedescribed-construction the desirable stalling characteristics taught 9 by this invention through the use of a controlled fluid-foil section 2 or II at the station located approximately 60 per cent of the semi-span from the root and with an effective aerodynamic washout of 0.5 degree with respect to the root section,

wherein the mean-line camber of the interjacent controlled section 2 or H is characterized by an ideal lift coeificient C1 equal to 0.12 In this structural example themean-line camber of the interjacent controlled section 2 or II is greater given a priori: (a) the plan form of the lifting surface; (b) the seriesof fluidfoil sections to be employed and their fluid-dynamic characteristics; (c) the maximum permissible effective aerodynamic washout; (d) the thickness ratio of the fluid-foil section at the root; (e) the meanline camber of the fluid-foil section at the tip.

In this case where the thickness ratio of the tip section is'not predetermined but is left to the judgment of the fluid-dynamical design engineer, the subject method of this invention employs to good advantage a peculiarity observed in the variation of the maximum attainable section lift coefficient with varying section thickness ratio. Most series of related fluid-foil sections reach their absolutely highest maximum section lift coeiiicient (for a given mean-line camber and Reynolds number) at a certain experimentally determined thickness ratio, usually between 12%1and 16%. Sections with thickness ratios greater or smaller than optimum attain less than the absolutely maximum section lift coefflcient. If, as illustrated in Figure 5, a thickness ratio smaller than optimum is used at the tip 20 of a lifting surface, where the actually prevailing section lift coeflicients are greatly below their highest spanwise value 22, the fluidfoil section with the optimum thickness ratio can be located at a spanwise station 2| a small distance inboard of the tip, near the spanwise station 22 at which the highest actually prevailing section lift coefficient is encountered. 'Here it will be understood that the mean-line camber of the interjacent controlled section 2 may be greater .or smaller than that of the aforementioned secmum lift coemcient Cr of the entire lifting surface shall be determined not on the basis of the maximum attainable section lift coefflcient of the tip section, but on the basis of the absolutely maximum attainable section lift coefficient 2|, that is, for the section of optimum thickness ratio, as follows:

Cl k: mu lb..

highs The thickness saw the fluid-foil section at the tip of the lifting surface is then so chosen that the section 2| with optimum thickness ratio for absolutely maximum attainable section lift coeflicient lies between the spanwise station of highest actually prevailing section lift coeflicient 22 and the tip 20, unless structural and other design criteria interfere by establishing a minimum section thickness ratio. j

If the designer intends to achieve positive stall inception in a certain spanwise panel of the lifting surface, the subjectmethod of this invention provides that in either of the aforedescribed design procedures the mean-line camber and thickness ratios, as wellas the spanwise location, of the sections comprised within or adjacent to the panel for which stall inception is desired be so selected that within the stall inception pane the curve of maximum attainable section lift coefficients lies slightly below the curve of actually prevailing section lift coeiiicients, without modifying the aforedescribed relationshipof the maximum attainable -.section lift coefficients and the actually prevailing section lift coefficients on the remainder of the semispan of the lifting surface outside of the stall-inception panel proper. If, in any of the aforedescribed cases, the lifting surface under consideration is modified by excrescences such as, for example, power-plant nacelles, or flaps that modify the local zero-lift angle and the local maximum attainable section lift coefficient, the calculation of the spanwise distribution of the effective washout and the maximum attainable section lift coefi'icients takes due account of the effects of these modifications by introducing "equivalent values ofthe'efiective washout and section mean-line camber into th subject method ofthis invention;

Upon completion of the procedure outlined for the subject method of this invention, the zerolift angles of the fluid-foil sections selected thusly are determined for their respective mean-line cambers, thickness ratios, and Reynolds numbers, and each fluid-foil section is set properly with respect to the reference chord plane of the lifting surface, so that the desired effective washout is achieved.

By practicing my invention a lifting surface can be designed and constructed to achieve the objects heretofore stated.

Numerous flight tests and wind-tunnel tests in reputable wind-tunnels such as the California Institute of Technology, the Massachusetts Institute of Technology, the various wind tunnels of the National Advisory Committee for Aeronautics, and elsewhere have demonstrated convincingly that each of the objects of this invention has been fully achieved. 7 The tests were performed, on numerous wing models, on sailplanes; and on models of at-least five aircraft designs of; widely varying design scope employing a wide varietyof airfoil series. Force-test records, photographic records, and cinematographic records of the tests substantiate the attainment of the objects of this invention.

The inventor wishes it to be clearly understood that the. greatly improved and generally judged satisfactory stalling characteristics of thewings (and other lifting surfaces) designed and constructed according to the subject method *of this invention are directly attributable to the use of three (or more) controlled fluid-foil" sections selected according to the her'einbefore specified method of this invention, and to the aforedescribed method employed in the design of such lifting surfaces.

This invention accomplishes important improvement in the art, and the discoveries herein disclosed are of great value toa'll types of air craft (as well as to craft operating in other fluids), throughout their entireloperating range, and especially in the critical low-speed operation where steadiness of lift and lift variation, stability of the craft, control efiectiv-enessand smoothness and stability of control forces are of vital importance for the safety and efiicien-cy of the craft; also in violent maneuvers at high speeds when high lifting-surface lift coefficients com parable with those occurring at the low-speed stall are encountered and even temporarily surpassed. r

I claim:

1; A lifting surface with three or more controlled fluid-foil sections, in; which the first section with the smallest mean-line camber is located at the root, the second section with the greatest mean-line camber is locatedat the fluiddynamically effective tip, and the third or additional fluid-foil sections are located at stations interjacent between the root and the tip, wherein the values of the mean-line camber of the interjacent fluid-foil sections are greater than the values of the mean-line camber obtainable at the respective spanwise stations by means of straight-line fairing between the fluid-foil section located at the root of the lifting surface and the fluid-foil section located at theti-p of the liftin surface.

2. A lifting surface with three or more controlled fluid-foil sections, in which thefirst section with the smallest mean-line camber is located at the root, the second section with the greatest mean-line camber is located at the fluiddynamically effective tip, and the third or additional fluid-foil sections are located at stations interjacent between the root and the tip, wherein the values of the mean-line camber of the interjacent fluid-foil sections are at variance withthe values of the mean-line camber obtainable at the respective spanwise stations by means of straight-line fairing between the fluid-foil section located at the root of the lifting surface and the fluid-foil section located at the tip of the lifting surface, said three or more controlled fluid-foil sectionshaving values of the mean-line camber selected in such manner that the resulting spanwise distribution of maximum attainable section lift coeflicients of the three or more controlled sections forms a curvilinear polygon enveloping a curve representing the spanwise distribution of section lift coefficients for a given planform actually prevailing at the maximum foil sections are at variance with the values of the mean-line camber obtainable at the respective spanwise stations by means of straight-line fairing between thefluid-foil sectio'nlocated at the root of the lifting surface andthefluid-foil section located at the tip 5 of the lifting surface, said three or more controlled fluid-foil sec o s a ing values of the mean-line camber selected in such manner that the resulting :spanwise distribution of maximum attainable section lift coefficients of the three or more controlled sections forms a curvilinear polygon enveloping a curve representing the spanwise distribution of section lift coeflicients actually prevailing at the maximum attainable lift coefiicient'of the lifting surface, and that thesaid resulting spanwise dis tribution of maximum attainable section lift coefficients for a given planform be so shaped that the first intersection with the spanwise distribution of actually prevailing section lift coefficients occurs in that interval of'spanwise stations for which stall inception isto be obtained.

4. A lifting surface with three or more controlled fluid-foil sections, in which the first section with the smallest 'mean-line camber and greatest thickness ratio is located at the root, the second section with the greatest mean-line camber and smallest thickness ratio is located at the fluid-dynamically effective tip, and the third or additional fluid-foil sections are located at stations interjacent between the root and the tip, wherein the values of the thickness ratio of the interjacent fluid-foil sections are greater than the values ofthe'thickness ratio obtainable at the respective spanwise stations by means of straight-line fairing between the fiuid fo'il section located at the root of the'lifting surf-ace and the fluid-foil section located at the tip of the lifting surface.

5. A lifting surface with three "or more controlled fluid-foil sections, in which the first section with the smallest mean-line camber and greatest thickness ratio is located at the root, the second section with the greatest mean-line carnber and smallest thickness ratio is located at the fluid-dynamically effective tip, and the third or additional fluid-foil sections are located at stations interjacent between the root and the tip, wherein the 'values'of the thickness ratio of the interjacent fluid-foil sections are at variance with the values of the thickness ratio obtainable at the respective spanwise' stations by means of straight-line fairing between the'fiuid-fo'il section located at "the root of the lifting surface and the'fiuid-foil section located at the tip of the lifting surface, said three or more controlled fluid-foil sections having values of the thickness ratio selected in such manner that'th'e'resulting spanwise' distribution of maximum attainable section lift coefiicients of the three or more controlled sections forms a curvilinear polygon enveloping a curve representing the spanwise distribution of section lift co'efi'icients for a given planform actually prevailing at themairimum attainable lift coefficient of the lifting surface.

6. A lifting surface with three or more controlled fluid-foil sections adapted to provide stall inception within a predetermined interval of spanwisestations, in which the first section with the smallest mean-line camber and greatest thickness ratio is locatedat the root, the second section with the greatest mean-line camber and smallest thickness ratio is located at the fluiddynarnically effective'tip, and the third or additional fluid-foil sections are located'at stations interjacent between the root and'the tip, wherein the values of the thickness ratio of the interjacent fluid-foil sections are at variance with the values of the thickness ratio obtainable at the respective spanwise stations by means of straightline fairing between the fluid-foil sectionlocated at the root of the lifting surface and the fluid- 'foil section located at the tipof thelifting surface, said three or-more-controlled fluid-foil sections having values of the thickness ratio selected in such manner that the resulting spanwise disemcients for a given planform be so shaped that the first intersection with the 'spanwise distribution of actually prevailing section lift coefficients occurs in that intervalof spanwise stations for which stall inception is to be obtained.

7. A lifting surface'with three or more controlled fluid-foil sections, in which the first section with the smallest mean-line camber is'located at the root, the second section with the greatest mean-line camberis located at the fluiddynamically effective tip, and one of the interjacent fluid-foil sections is located near a spanwise point where a tangentto the inboard portion of a curve representingthespanwise distribution of actually prevailing section lift coeflicients for a given planform intersects a substantially horizontal tangent to the highest point of the same curve, wherein the values of the mean-line camber of the interj acent fluid-foil sections are greater than the values of the mean-line camber obtainable at the respective spanwise stations by means of straight-line fairingbetwecn the fluidfoil section located at the root of the lifting surface and the fluid-foil section located at the tip of the lifting surface. v j p 8. A lifting surface with three or more controlled fluid-foil sections, in which the first section with the smallest mean-line camber. and greatest thickness ratio is located at the root, the second section with the greatest mean-like camber and smallest thickness ratio is located at the fluiddynamically effective tip, and one of the interjacent fluid-foil sections is located near a spanwise point where a tangent to the inboard portion of a curve representing the spanwise distribution of actually prevailing section lift coefficients for a given planform intersects a substantially horizontal tangent to the highest point of the same curve, wherein the values of the thickness ratio of the interjacent fluid-foil sections are greater than the values of the thickness ratio obtainable at the respective spanwise stations by means of straight-line fairing between the fluidfoil section located at the root of the lifting surface and the fluid-foil section located at the tip of the lifting surface.

9. A lifting surface with three or more controlled fiuid-foil sections and having a highest actually prevailing section lift coefficient at a predetermined spanwise station, in which the first section with the smallest mean-line camber and greatest thickness ratio is located at the root, the second section with the greatest mean-line cambeer and smallest thickness ratio is located at the fluid-dynamically effective tip, and the third or additional fluid-foil sections are located at stations interjacent between the root and the tip, wherein the values of the mean-line camber of the interjacent fluid-foil sections are at variance with the values of the mean-line camber obtainable at the respective spanwise stations by means of straight-line fairing between the fluid-foil section located at the root of the lifting surface and actually prevailing section lift coefficient at a predetermined spanwise station, in which the first 14 the fluid-foil section located at the tip of-the lifting surface, and wherein the aforesaid fluid-foil section at the tip of the lifting surface has a thickness ratio smaller than the optimum thickness ratio for absolutely maximum attainable section lift coefiicient of the fluid-foil series employed, so that a fluid-foil section having the optimum thickness ratio obtained by conventional interpolation between two of the controlled sections lies a short distance inboard of the tip of thelifting surface, near the spanwise station at -which the highest actually prevailing section lift coefiicient occurs;

10.- A lifting surface .with three or more controlled fluid foil sections and having a highest section with the smallest mean-like camber and reatest thickness ratio is located at the root, the

second section with the greatest mean-line camber and smallest thickness ratio is located at the fluid-dynamically effective tip, and third or additional fluid-foil sections are located at stations interjacent between the root and the tip, wherein the values of the thickness ratio of the interjacent' fluid-foil sections are greater than the values of the thickness ratio obtainable at the respective spanwise stations by means of straightline fairing between the fluid-foil section located at the root of the lifting surface and the fluidfoil section located at the tip of the lifting surface, and wherein the aforesaid fluid-foil section at the tip of the lifting surface has a thickness ratio smaller than theoptimum thickness ratio for absolutely maximum attainable section lift coefficient of the fluid-foil series employed, so that a fluid-foil section having. the optimum thickness ratio obtained by conventional interpolation between two of the controlled sections lies a-short distance inboard of the tip of the lifting surface, near the spanwise station at which the highest actually prevailing section lift coefficient occurs.

11. A lifting surface with three or more controlled fluid-foil sections, in which the first section with the smallest mean-line camber is located at the root, the second section with the greatest mean-line camber is located at the fluiddynamically effective tip, and the third or additional fluid-foil sections are located at stations interjacent between the root and the tip, wherein the values of the mean-line camber of the interjacent fiuid-foil sections are smaller than the values of the mean-line camber obtainable at the respective spanwise stations by means of straightline fairing between the fluid-foil section located at the root of the lifting surface and the fluidfoil section located at the tip of the lifting surface.

12. A lifting surface with three or more controlled fiuid-foil sections, in which the first section with the smallest mean-line camber and greatest thickness ratio is located at the root, the second section with the greatest mean-line camber and smallest thickness ratio is located at the fluid-dynamically effective tip, and the third or additional fluid-foil sections are located at stations interjacent between the root and the tip, wherein the values of the thickness ratio of the interjacent fluid-foil sections are smaller than the values of the thickness ratio obtainable at the respective spanwise stations by means of straightline fairing between the fluid-foil section located at the root of the lifting surface and the fluidfoil section located at the tip of the lifting surface.

13. A lifting surface with three or more conasemoe 15 trolled fluid-foil sections, in which the first section with the smallest mean-l ne camber is located at'the root, the second section Wi h th greatest mean-line camber is located at the fluiddynamically eifective tip, and one of the interjacent' fluid-foil sections is located near a spanwise point where a tangent to the inboard portion of a curve representing the spanwise distribution of actually prevailing section lift coeflicients for a given planform intersects a substantially horizontal tangent to the highest point ofthe same curve, wherein the values of the mean-line camber of the interjacent fluid-foil sections are smaller than the values of the mean-line camber obtainable at the respective spanwise stations by means of straight-line fairing between the fiuidfoil section located at the root of the lifting sur face and the fluid-foil section located at the tip of the liftin surface.

14. A lifting surface With three or more controlled fluid-foil sections, in which the first section with the smallest mean-line camber is 10- cated at the. root, the second section with the greatest mean line camber is located at the fluiddynamically effective tip, and one of the interjacent fluid-foil sections is located near a spanwise point. where a tangent to the inboard portion of a curve representing the spanwise distribution of actually prevailing section lift coefficients for a given planform intersects a substantially horit zontal tangent to the highest point of the same curve, wherein the valuesof the thickness ratio of the interiacent fluid-foil sections are smaller than the values of the thickness ratio obtainable at the respective spanwise stations b means of straighteline fairing between the fluid-foil section located at. the root of the lifting Surface and the fluid-foil section located at the tip of the liftlng surface.

15. A lifting surface with three or more controlled fluid-foil sections and having a highest actually prevailing section lift coefficient at a predetermined spanwise station, in which the first section with the smallest mean-line camber is located at the root, the second section with the greatest mean-line camber is located at the fluid- :dynamically effective tip, and the third or additional fluid-foil sections are located at stations interjacent between the root and the tip, wherein the values of the thickness ratio of the inter- J'acent fluid-foil sections are smaller than the values of the thickness ratio obtainable at the respective spanwisestations by means of straightline fairing between the fluid-foil section located at the root of the lifting surface and the fluidfoil section located at the tip of the lifting surface, and wherein the aforesaid fluid-foil section at the tip of the lifting surface has a thickness ratio smaller than the optimum thickness ratio for absolutely maximum attainable section lift coefficient of the fluid-foil series employed, so that a fluid-foil section having the optimum thickness ratio obtained by conventional interpolation between two of the controlled sections lies a short distance inboard of the tip of the lifting surface, near the spanwise station at which the highest actually prevailing section lift coefficient occurs,

MAURICE ADOLPH GARBELL.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS Focke W Dec. 6, 1932

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