Pressure distribution over an airfoil section with a flap and tab

REPORT No. 574

PRESSURE DISTRIBUTION OVER AN AIRFOIL

SECTION WITH A FLAP AND TAB

By CAR L J . W ENZING E R Langl e y M emo r i a l Aeronautica l La b ora t ory 78301--36 I N ATI ONA L A DV ISO RY C O MMI TTEE FO R AE R ON A UTICS HE A DQU A RTERS, NAVY BUILDING , W A SHINGTON, D. C.

LAB ORA TORIES, L A NGLEY FIELD, V A.

C reated by act of Congress apl , _roved March 3, 1915 , for the supervision and dire c tion o f the scientific study of the problems of fligh t (U. S. Code , Title 50 , See. 151). Its membership was increased to 15 by act approved March 2 , 1929. The members are appointed by the President , and serve as such wit h out compensation.

,]0,SEPI{ S. A M ES , Ph.D ., Ch air m an , CHAIILE$ A. LINDBERGlt , LL.D . , !

Baltimore, Md. New York City.

DAVID W. T&YLOR, D. Eng. , Vice Chairma n , }VILL1AM P. MACCR a kCKEN , Jr., LL.D., Washington, D.C. Washington, D. C.

CIIAR L ES G . ABB0q' , SO . D. , AUOUS ' rlNF_ " W . Rom_xs , Brigadier General, United States Army, Secretary, Smithsonian Institution. Chief Mat6riel Division, Air Corps, Wright Field, Dayton, LYMAIg J . BI_I G GS , Ph.D. , Ohi o.

Director, National Bureau of Standards. EUGENF L . VIDAL , C . E., AI_ T ItUR ]3. COOK, Rear Admiral, United States Navy, Director of Air Commerce, l)epartment of Conunerce.

Chief, Bureau of Aeronautics, N avy Department. EDWARD P. WAI_NER, M. S' . , WIL L IS RAY GR3_ GG , ] _ . A., New Y ork Ci t y .

Chief, United Sta t es Weather Bm'emL Os o A_ " W _'ST0_E'_, Major General, United States Army, HARRY F . GUGGI_ N HEIM , M . A., Chief o f Air Corps, War Department.

Port Washington, Long Island, N.Y. ORVILLE W_GH T , SC. D., SYI)_BY M. KI_US, Captain, United States Navy, Dayton, Ohio.

Bureau of Aeronautics, Navy Department.

GEORGE W. LEWIS, Directo r of Aeronauticol R esearc h JOHN F . VI C T O R Y , Secreta r y HENRY J. E. REn), Engineer i n Charge , Langley M e mo r ial Aeronautical Laboratory, Langley Field , V a.

JOttN J. iDE , Tech n ica l Assistant in E urop e, P ar is , F rance TECHNICAL COMMITTEES • AERODY N AMICS AIRCRAFT ACCIDE N TS POWER PLANTS FOR AIRCRAFT INVENTIONS AND DESIGNS AIRCR A FT STRUCTURES AND MATERIALS Coordi/nation o f Rese a rc h Needs of Militar y' and C iv il Aviatio n Preparation of Research Programs Allocation of Problems Prevention of Duplication Consi d e r ation of Inventions LAN G LE Y M EMORIAL A E RONAUTICAL LABORATORY O FFICE OF AERONAUTICAL INTELLI G ENCE LA N GLEY FIELD, V A . WA SHINGT ON , D. C.

Unified conduct, for all agencies, of C ollection classificati o n , c o mpilation, scientific research on the fundamental and dissemination of scientific and tech- problems of flight° nical informati o n on aeronautics.

II

RE PO RT No . 574

PR E S S UR E DI S T R IBUTION OVER AN AIRFOIL SECTION WITH A FLAP AND TA R By CAI_L J. _¥ENZI N GER i SUMMAR Y included from tests o f a tail surface of average proper - Pressure - distribution t ests o f a Clark Y air f oil with a tions with several different tabs . t fl a p and a n inset tab were made i n the N . A . C . A . 7 - Because of the rapidly increasing use of tabs , par- by lO -f oot wind tunnel . The p ress u res were measured ticular]y on tail surfaces where they replace the ad- o n both the up per and lower surJaces at one chord section , iustable fin and stabilizer , there is a demand for in- Calculations were made o J the no r mal - Jorce and pitching - formation that can be used for stress-analysis purposes.

moment coe ffi cients of the airJoil section with fla p and In this connection, the designer desires to know the tab, the nor m al -f orce and hinge - moment coe ffi cients o] the magnitude and distribution of the air forces acting on flap section w it h, tab, and the normal - force and hinge - the various surfaces and the moments about the hinge m ome n t coe ffi cients oJ the tab section alone . In addition, axes so that the structure , supports , and control comparisons were made of the theoretical and experimental mechanism can be designed for maximum efficiency.

values for a n a i r foil with a multiply hinged fl a p syste m. The present investigation was therefore undertaken to It w as . found that peak values o f the increments o f re - make available information that would be of immediate sultant pressures due to flap or to tab deflection occurred use in the foregoing design problems.

at the flap and tab hinges, respectively . Also, the varia - The tests consisted of pressure-distribution measure- tions oJ incre m ents o .i ai r Joil section normal - force and ments over one chord section of an airfoil with a flap pitching - moment coe ffi cients a n d oJflap n ormal -f orce and and a tab: From the data obtained , calculations were made of normal-force and pitching-moment coefficients hinge - moment coe ffi cients, due t o . flap deflection with a give n tab setting, w ere practically independent o f the tab for the airfoil section with flap and tab; both normal- de fl ection . I n addition, the variation of increments o J force and hinge,moment coefficients were computed tab normal - Jorce and hinge - moment coefficients with tab for the flap section with tab and for the tab section deflection for a given flap setting w as practically i nde - alone.

pendent o f fla p deflectio n. Comparisons of the theoretical APPARATUS AND TESTS with the experimental forces and m o m e n ts f or the a i r f oil The N. A. C. A. 7- by 10-foot wind tunnel , in which section w ithfla p and tab show that the theory agrees fa i rly the tests were made , is described in reference 2. A half- well wi th experiment f or small flap deflections with the span Clark Y airfoil (fig. 1) that had originally been tab ne u tral, b u t that the theory indicates much greater built for pressure-distribution tests of high-lift devices effects than are actually obtained when the fla p and tab was used. The model was altered by installing at the are simultaneously deflected , tip a flap having a chord 30 percent of the airfoil chord and a span 40 percent of the half-span model. An inset INTRODUCTION tab was mounted at the trailing edge of the flap , the A considerable number of airplanes are fitted with a tab size and location being selected as representative small flap on one or more of the movable control sur- of the average. The tab chord was 20 percent of the faces. Such an auxiliary flap is ordinarily referred to flap chord and its span was 50 percent of the flap span.

as a "tab" and is usually set into the trailing edge of the The gaps between the flap and the airfoil and those control surface. When the tab is used to reduce the between the tab and the flap were sealed with plasticine hinge moments of a control surface , it is known as a for all tests.

"balancing tab"; when used to trim the airplane in The airfoil , flap , and tab were all constructed of lam- place of an adjustable stabilizer or fin , it is referred to inated mahogany to within _0.010 inch of the specified as a "trimming tab." ordinates. A row of small orifices was installed in the The chief aerodynamic characteristics of tabs are upper and lower surfaces at one chord section located at covered in reference 1, which describes an investigation the center of the span of the flap and tab. (See fig. 1.)

of a wing with serveral arrangements of ailerons and This location was 20 percent of the semispan of the tabs , alone and in coniunction with other types of model inboard of the rectangular tip so that satisfac- balancing arrangements. In reference 1 data are also tory section characteristics could be obtained which 2 REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAIJTICS would be outside the influence of the usually high local RESULTS tip pressures. The half-span model was set up in con- The results of the investigation, in their original junction with _ reflection plane at its inboard end , the form, consisted of pressm'e diagrams for the section as plane extending from top to bottom of the air stream tested at different angles of attack and for different and some distance ahead of and behind the model, tab and flap deflections. In order to facilitate the ' A multiple-tube alcohol manometer photographically interpretation and - application of these results, the recorded tile pressures on the airfoil section, pressure diagrams are presented in the form of "incre- Pressures were measured for flap settings of 0 °, ment" diagrams, which represent the changes iX. pres- _%15°, and _:30 ° with the tab neutral. With the sure distribution due to changes in the significant i flap neutral, pressures were measured for tab settings of variables. The pressure diagrams for the basic section :t: 10 °, ±20 ° , and ±30 °. The pressures were then (i. e., neutral tab and flap) are also given so that the measured for various combinations Of flap up with tab resultant diagram for any ease may be obtained by down and of flap down with tab up. The angles of addition of the increment and the basic-section dia- attack used in the tests (--5 °, 0°, 10 °, and 15 °) covered grams. The principal advantage of the increment Or - / C- le es l o c a t e d/ n fh/ _, )la ne C O . O0 " I Or/ - I f, - om A_ g _T d -d o _ flee I L . [ ., _2. ood - _. o _ o /4.5 oo 0 H /K_'25 e t =/.20,, K 18. 000 J 18. 8 75 " . _2 P _L /9.s2's Plan v/ew of hG /f - sp G f 7 model _-- /2.00 "_ £ ) /9.8 7 5 24. O0" H Ald PU AU 8U C U OU EU FU GU HU JU KU M U, " OU i OU Seale d ,i, ?i! / ' " .... .

:. .. . pla s //c/n e- 1 ) DL EL FL OL HL JL / f L /YfL]OL tot 20 . O0 " NL PL t Set/lanai v/ew Show/r T g OF/f/d e /coo/i o ns on airfoil , flap , a nd l a b .

FIGUBE 1.--Clark Y airfoil with tab and flap arranged for pressure-distribution tests.

approximately the range h'om zero lift to maximum diagrams is that they may, by the principle of super- lift. position, be applied to pressure diagrams for any other Angles of attack and flap deflections were measured basic airfoil section, including the symmetrical section, with respect to the airfoil chord ; tab deflections were that does not depart too greatly from the C lark Y see- measured with respect to the flap chord. Positive flap tion on which the tests were made. The diagrams of or tab angles indicate a downward deflection with resultant-pressure distribution for the basic airfoil see- respect to the airfoil or flap chord. The tests were tion are given in figure 2. The increments of resultant made at a dynamic pressure of 16.37 pounds per pressure for various tab and flap deflections are pre- square foot, eorrespondir N to an air speed of 80 miles sented in figures 3 to 6. The figures give the results for per ham' under standard sea-level conditions. The a low-angle-of-attack condition , a=0 °, and for a high- average Reynolds Number was 1,220 , 000 , based on angle-of-attack condition, c _=t5 °.

the airfoil chord of 20 inches as the characteristic The important characteristics of the section as a length, whole and of the tab and flap, as functions of tab and PRESSURE DISTRIBUTION OVER AN AIRFOIL SECTION WIT H A FLAP AND TAB 3 I Flap section normal-force coefficient , ----- n -z Cn _ f [ C y h r • _ ! _ _ Flap section hinge-moment coefficient , c _,s== qc/ 2 7 _t ' I Tab section normal-force coefficient , c _ _-- ..... _ ---!_ - Tab section hinge-moment coefficient , c h,T qc ,2 3 .O ........ --_.- in which / ........ ! row, the corresponding pitching moment about !___ airfoil chord.

.... [ " t_ i -i nw istheresultantpressurefol'cenormalto the ........ _-_ L i n r , the resultant pressure force normal to the flap chord.

. 2 . 0 _ ! -!--! ......... h ,, the corresponding moment about the flaPhinge. nt, the resultant pressure force normal to the q h i , the corresponding moment about the tab - P -_ _ -_-I tab chord.

° hinge.

The subscript w refers to the airfoil section with flap / . o and tab ; the subscript j to the flap section with tab; the subscript t to the tab section alone.

section are plotted in figure 7 against angle of attack.

'_ The integrated coefficients for the basic airfoil z _ Curves giving the increments for various tab and flap deflections are presented in figures 8 , 9 , and 10.

Figures 11 and 12 are plots of theoretical parameters o taken from reference 3 and modified so as to apply __ directly to N. A. C. A. absolute coefficients. Com- parisons of theoretical with experimental values of the forces and moments for the Clark Y airfoil tested with several different deflections of tile tab and flap are shown in figures ] 3 , 14 , and 15.

- / .0 J DIS CUS SI O N Pressure distribution.--The effects on the distribu- ! tion Of resultant-pressure increments due to tab or flap i deflection are shown b y figures 3 and 4. Deflections - _ of the tab or of the ftap produce peak values of the F IG_JRE 2 .-- D istributi o n of res u ltant pressure oii airfoil se ct i o n w i th flap a n d t ab pressure increments at the tab hinge or at the flap neutral, a =0°and 15 °. hinge , respectively. If the tab and flap are deflected flap deflection , are also plotted as increments. These simuItaneously (tab deflection opposite to that of flap) , increments were obtained by deducting• the basic- then peak values of the pressure increments occur at section characteristics from those for the section with both hinge axes but the resultant pressures act in deflected flaps , the characteristics being determined in opposite directions. (See figs. 5 and 6.)

Section characteristics.--The characteristics of the each case b y integration of the original pressure basic airfoil section given in figure 7 (tab and flap diagrams. Calculations were made of the following neutral) exhibit no unusual tendencies. For a given quantities in which l o wer-case letters are used to indi- cate section coefficients: setting of the tab, the flap and tab may be considered as a flap unit. Then the effect of deflection of such a % w Airfoil section normal-force coefficient, c _--_ unit will be similar to that for an ordinary flap (e. g., aileron , elevator, or rudder). Increments to the basic Airfoil section pitching-moment m . values of airfoil section normal-force and pitching-me- coefficient , c' _j4-- qc ,_2 ment coefficients are given in figure 8 for various flap 6 REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS deflections with given tab settings. With the tab Lift coefficient of airfoil: deflected it will be noted that the curves are displaced _. dCJ , ba ba parallel to the curve for the undeflected tab. This U _=_L a d-bs / a / d-_ tt a_ ) (1) parallel nature of the curves shows that the variation f of increments with flap deflection , considered with respect to any given initial tab deflection , is independ- Pitching-moment coefficient: ent of tab deflection. A t 30 ° deflection of the tab, _ C, _ b C m _ .

however , the effectiveness of the tab appears to have Umc/ 4: Um o- _- _ f (_. f -d--_ t 8 t (2) .

been considerably reduced so that tab deflections of _' 20 ° should not be exceeded with the arrangements tested. H inge - moment coefficient of flap: Increments to the basic values of flap section normal- C C 5 C hs C b C hs b C h f force and hinge-moment coefficients are plotted in hs= hS0+ _ L+_-1_s+_-t _ (3) figure 9 for various flap deflections with given tab settings. The curves for the tab-deflected condition Hinge-moment coefficient of tab: are displaced parallel to the curve for the undeflected tab , as was the case for the airfoil s ection increments. C C bC _ t bC h t _ C _,t The variation of the flap increments with flap deflec- s_,= _,t0 + _ C L + _- / _ / + _ _t (4) -x- Omc / 4 t _ - ×_ _×-- Chf --×-_ ×-----_ Oht _. 1 _ I -. 10 -. 10 L£O --- x / × / . 80 / " e nw / ....

. 40 I / . /I0 ........... . 40 --

/i p : -t

0 tx' T__X__ _x-

o 8 / 6 - ° 8 o - °D D 8

d, o'eqree _ _ , de g lr - ee _ c _ , o' eg r - ee _ FIGURE 7.--Characteristics of the basic airfoil section. Tab and flap neutral.

tion for a given tab deflection are likewise independent a ' is the angle of attack of the main portion of the of tab deflection, airfoil measured from zero lift of the un- Increments to the basic values of tab section normal- deformed section. (All angles are measured force and hinge-moment coeffÉcients are given in in radians.)

figure 10 for various tab" deflections with given flap settings. The curves for the flap-deflected condition C ,£, C _ ,l o , and C h t 0 are moment coefficients at zero lift of the undeformed airfoil.

are also displaced approximately parallel to the curve for the undeflected flap , over the range of tab deflec- 5 a ba bC _ bC _ bC hf bC ht bC h l _ C ht tions from --20 ° to 2 0 °. The curves show that the Parameters _ , _t ' _ ' -5-_t ' b _ ' 5_ ' _: ' _ ' variation of increments with tab deflection for a given are given in figure 11.

flap deflection is practically independent of flap deflection. 5 C _ s b C _ t Comparison with theory.--Theoretical expressions Parameters -_ and _ are given in figure 12.

for the lift , pitching moment , and hinge moment for a thin airfoil with any multiply hinged flap system have The curves given in figures 11 and 12 correspond to been derived by Perring (reference 3). The following those given in reference 3 except that the values have relationships apply to a thin airfoil with a flap and been calculated and the curves redrawn on the basis of a tab , N. A. C. A. absolute coefficients being used: N.A.C.A. absolute coefficients.

PRESSURE DISTRIBUTION OVER AN AIRFOIL SECTION WITH A FLAP AND TAB 7 i • 80 .2 0 I -- -: - '_ i ! # ,40 I _ _..__ __ -- __ . / 0

o_ ; --< { . _ ' _/ I i _- o I o

__"_ " IIII : . 4 - __.U ' f'! . '_ . _ _ -- -. I0 "

-4 ° _i . < .- I I i I k i Po_ n i , , <---- , v_' g o , ' ; vc I i I I I I't_'_

- - I _ : :_ o ° - _l. . -!-. . I I i I I

[] =- dU ° ' _ , h\ ",_ , I I . I0 '

X'.s " , ' } , ! -'< ?i '_-_\

• "< P ; _ 1 1 i

o i '!I "' _x_<<_ _ , , o _"i.'.'_.h- o

_.. o L i -.2 o

-, 90 - 2 0 - I0 0 I0 20 30 -, 90 - 20 - I0 0 I0 2 0 30 d /, d e gi - ee s d /, deg r ees I_ ] _ V RE 8.--Increments of airfoil section normal-force and pitching-moment coefficients for various tab and flap deflections.

8 REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS The theoretical and experimental values of airfoil air near the trailing edge of the airfoil and is therefore section normal-force and pitching-moment coefficients unable to produce its full effect.

are compared flu figure 13. The data show that the theory agrees fairly well with experiment for flap de- CONCLUSIONS flections from 0 ° to± 15 ° with the tab neutral. Similar Based on the arrangement of airfoil section, flap, agreement was found in comparing data from reference and tab tested, the following conclusions may be drawn: 4 which deals with tests of a 30 percent chord flap. i. Peak values of the increments of resultant pres- Reference 5 also shows good agreement of theory with sures due to flap or to tab deflection occurred at the experiment for small angular deflections with flaps 20 flap and tab hinges , respectively.

percent of the airfoil chord. With the tab and flap 2. The variation of increments of airfoil section both deflected , however , the present investigation normal-force and pitching-moment coefficients and of shows that the theory indicates considerably greater flap normal-force and hinge-moment coefficients, due to, .20 -- _ -- %. • /© 0 ec: O ° _ %" < 0 \

__ ____ _-. "'<-_%-

-2 0 Po z //-/v e -- A/egof/ve _ --1_.< _-=x - . /0 __,._× = oo A c _ t _ /5 ° hc _ 20 ° t ...........................

i

o /5 o \_ , . o

, <-%-. - / 0 • - 30 - 20 - /0 0 /0 20 30 - 30 - 20 - /0 0 I0 20 , 90 6t, degrees dr , degrees FIGURE 10.---Increments of tab normal-force and hinge-moment coefficients for various tab and flap deflections.

effects on the airfoil section normal-force and pitching- flap deflection with a given tab setting , was practically moment coefficients than are actually obtained by independent of the tab deflection.

experiment. 3. The variation of increments of tab normal-force Theoretical and experimental values of the flap and hinge-moment coefficients with tab deflection for hinge-mo m ent coefficients are compared in figure 14. a given flap setting was practically independent of flap As in the case of the airfoil section coefficients , good deflection.

agreement is shown between theory and experiment 4. Comparisons of the theoretical with the experi- when the tab is neutral. With the tab deflected in a mental forces and moments for the airfoil section with direction opposite to that of the flap , however , only flap and tab shows that the theory agrees fairly well one-half to two-thirds of the theoretical effect is ob- with experiment for small flap deflections with the tab taflued. Similar effects were shown by comparisons neutral, but that the theory indicates much greater made in reference 6. effects than are actually obtained when the flap and Values of the theoretical and experimental hinge- tab are simultaneously deflected.

moment coefficients of the tab are compared in figure 15. This comparison shows a very poor agreement between theory and experiment , probably because of LANGLEY MEMORIAL AERONAUTICAL LABORATORY , the smallCchord tab (6 percent of the airfoil chord) , NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS, which is operating in a somewhat turbulent region of LANGLEY FIELD , VA. , December 10, 1935.

i i ]0 REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS Ct v ord of f/ Gp f oF wh/ ' ch h / b ge morr T en/ / '_ sougt T_ per c en/ o/ _ fo/ 7 ct T o F d 0 I0 20 30 40 SO 80

.j

_ _ "_ C h o r d of odd/ C lone/ Flop,

\\ -- .5 o

\\\ \ \ \_ o _\

°' - ..... > iL-- - ......

O Che [ t - 7_ - I , 40 I flap hinge moment tab hinge moment FIGURE ]2 . --Iih]ge-moment parameters. Izlereil2ents in ratio of - or tal_ angle flap angle

PRESSURE DISTRIBUTION OVER AN AIRFOIL SECTION WITH A FLAP AND TAB 11

? 7 < \ \ .... / o # 40

/ _ : 20° _\ _\ \-2o' "_ X \ \., 0 • ,. @I / ._d / - .......o: o o _........ , o , \_\ -_\ \, / /o ° I Theo - -. 10 -.40 --; _ ............... " F eb ' - .... - col i -. 80 ............... -. 20 I ...... I t - 1 . 20 - 30 - 20 - I0 0 I0 20 30 - 30 - 20 - I0 0 I0 20 30 = 80 6 _ , deg r ee s dy , deg r ees FI G UR E 1 3 .--C o mparison o f the or etical, and experimental values of airf o il Beotion n ormal-force and p i tching-moment c o efficients. Clark Y section with flap a nd tab. _ =0° . 30 -- ", _ I I I I ' "" \ T heo r e//col - i

. 2 o _, " =-_S:-

< .l\ I d_ zx = 20 ° _ 20 ° _ x = 15 t-_ _\ T/ v eore h' col , "-_\ --_ \_ _ ° l _ ,,., , , _ "_ ", _ = - /5 o

" ° C \ ,- . ,o ,-__ \,, o o

\ "-.<_ .,xX. o o _= 1 5°

_ _ %\

- . i o \ oa"-. \

\ ' \\_ ' _-..

N -

25: < \ I \,_

, ,, I \ a -' a 5 o

" aO - ZO - I0 0 I0 20 30 - 2 0 - I0 0 I0 20 30 S y , degrees d e , degre e a FIGUIIE 14.--Comparison of theoretical and experimental hinge-moment coefficients FIGUI _ E 15.--Comparison of theoretical and experimental hinge-moment coefficients of flap with tab. Clark Y airfoil section. CL =0.3. Oftab . Clark Y airfoil section with flap and tab. C L = 0.3 .

REFERENCES 4. Smith, 1%. H.: Lift, Drag , &nd Elevator Hinge Moments of Handley-Page Control Surfaces. T. 1%. No. 278, N. A.

1. Harris , Thomas A.: Reduction of Hinge Moments of Air- C.A. , 1927.

plane Control Surfaces by Tabs. T. 1%. No. 528 , N.A. 5. Jacobs, E_stman N., and Pinkerton , Robert_ M.: Pressure C. A. , 1935. Distribution over _ Symmetrical Airfoil Section with 2. Harris , Thomas A.: The 7 by 10 Foot Wind Tunnel of the Trailing Edge Flap. T. It. No. 360, N. A. C. A., 1930• National Advisory Committee for Aeronautics. T. 1%. 6. Lombard , A. E.: Control Surface Flaps for Trim _nd Bal- No. 612, N. A. C. A. , 1931. anee. Jour. Aero. Sei. , Vol. 2 , No. 1 , J_nuary 1935 3 . Perring, W. G. A.: The The o retical Relationships for an pp. 10-15.

Aerofoil with a Multiply Hinged Flap System. It. & M.

No. 1171, British A. 1%. C., 1928.

U,S, GOVERN M ENT PRIN T ING OFF I CE: 1 9 3 6 # ¢ P o s itiv e d ire ctio ns of a xe s and an gle s ( forces and mome n ts) are s hown by arr ow s A xis " _ Moment a bout a xis ' _ Angle, Ve l ocities • ' Fo rc e [ " (parallel .I • -" " ........ Linear / bol symbol Po sitive De s ig na - . Sy m- (coInp o- t n _' u l ar "-D es ign a t ion Sy m- t o a xi s) D es ign a ti on Sb _ o _" di r ection' tion bo l n e n talo n g • ,, '.1 ' a xi s) - L ongitudin a l.__ X X R olling ..... L Y --= - -_ Z Roll ........ _ u . p Latera l ....... Y Y P it chin g___ . ,- M Z ----* X Pitch .... 0 v q Nor ma l ..... _:__ Z Z Y a wing ..... N X ----_ Y Yaw_ .... _ h _ w ' r A b s olute coeffici e nts of-mome n t Angle of set of control surf a ce .(rel a tive to n e utral L . G _ -- qb - S G _ _ qc _ G - N position) , _. (Indic a te surf a ce b y prope r s ub scr ip t .)

", qbS (rolling) (pitching ) , (y a wing ) 4. PROPELLER SYMBOLS p • 2 9 , Di a meter P, P ower , a bsolute coefficient Gp_ pn - r D _ T, Geometri c pitch i o/ . / 9 , Pitch ra tio G, , Speed-power coefficient --- 5 / _- V --_ V', Infl o w velocity V ,, Slipstream vel o city n , Efficiency T, Thrust , a bsolute co e ffi c ient G r--- T n, Revolutions per second, r.p.s.

pn _ D ' 4_, =Effective helix a ngle= tan-' (_ n ) Q _ To r que , a bsolut e coeffici en t ff q _ 5. N UM E R I CA L R EL A TIONS 1 hp. = 76.04 kg-m / s--550 f t-lb. / se c . 1 lb. = 0.4536 kg.

1 metric horsepower = 1.0132 hp. 1 kg = 2.2046 lb.

1 m.p.h. =0.4470 m.p. s . 1 mi. = 1 , 609.35 m = 5 , 280 f t.

1 m.p.s. = 2.2369 m.p.h 1 m = 3.2808 ft.

L