Document
NATIONAL ADVISORY COMM I TTE E
FOR AERONAUTICS
REPORT 988
COMP ARATIVE DRAG MEASUREMENTS AT TRANSONIC
SPEEDS OF RECTANGULAR AND SWEPT BACK
NACA 65- 009 AIRFOILS MOUNTED ON A
FREELY FALLING BODY
By CHARLES W. MATHEWS and JIM ROGERS THOMPSON I< 'or sale by tbe Superintendent of Documents. U. S. Government Printing Office, Washington 26, D. C. Yearly subscription, $3,50; forell/n, $4.50; single copy price varies accordln ll to ~I.ze ••••• - • - - Price 15 cents AE RON AUTIC SY MBOLS 1. FUNDA M ENTAL AN D DE R IVED UNITS Metric English Symbol Abbrevia- Unit Ab br eviation Unit tion meter _________________ _ Length _____ _ foot (or mile) ____ __ _ l m ft (or mi) second ________________ _ T ime _______ _ second (or hour) ____ _ s sec (or hr) t Force _______ _ weight of 1 kilogram ____ _ weight of 1 pound __ _ F kg Ib P ower ______ _ hor~epower (metr ic) _ _ _ _ _ __ __ _ __ ___ horsepower _ _ __ _ __ _ _ hp p kilom eters per hOUL _ _ _ __ kph miles per hour _ _ _ _ _ _ mph Speed ______ _ V { meters per seconcL _ _ _ __ _ mps feet per second_ __ _ _ _ fps 2. GENERAL SYMBOLS v Kinematic viscosity
w Weight=mg
p Density (mass per unit volume) g Standard acceleration of gravity=9.80665 m/s 2 2 Standard density of dry air, 0.12497 kg-m- -s at 15° C or 32.1740 ft/sec 4 2 and 760 mm; or 0.002378 Ib- ft- sec
Mass = ~
m g Specific weight of "standard" air , 1.2255 kg/m or Moment of iDcrtia=mk2. (Indicate a:S(1S of I 0.07651 lb/cu ft radius of gyration k by proper subscript .)
Ooefficient of viscosity 3. AERODYNAMIC SYMBOLS Angle of setting of wings (relative to thrust line) S Area Angle of stabilizer setting (relative to thrust Area of wing
Sw
line) G Gap Q Re sultant moment Span b n Resultant angular velocity Ohord c Vl b R Reynolds number, p- where l is a linear dimen-
A Aspect ratio, S
J.L sion (e.g., for an airfoil of 1.0 fL chord, 100 V True air speed mph, standard pressure at 15° 0, the cone-
q Dynamic pressure, ~ p V
Eponding Reynolds number is 935,400; or for an airfoil of 1.0 m chord, 100 mps, the cone -
L Lift, absolute coefficient GL=:S
sponding Reynolds number is 6,865,000) Angle of attack
Drag, absolute coefficient GD=;:S
D Angle of downwash Angle of attack, infinite aspect ratio
Profile drag, absolute coefficient G = ~s
DO Angle of attack, induced Angle of attack, absolute (measured from zero-
Induced drag, absolute coefficient G = ~S
D , lilt position) Flight-path angle 'Y
Parasite drag, absolute coefficient GD1J=~S
o Oross-wind force, absolute coefficient G = q~
c
REPORT 988
COMP ARATIVE DRAG MEASUREMENTS AT TRANSONIC
SPEEDS OF RECTANGULAR AND SWEPTBACK
NACA 65 - 009 AIRFOILS MOUNTED ON A
FREELY FALLING BODY
By CH ARLES W. M A THEW S and JIM RO G ER S THOMP SON Langl ey ':" A er onautical Laboratory Langley Field, Va .
ational d lor y Committ ee for e ronautic
Headquarter, 1724 F Street mv., Washington 25, D. C.
Created by act of Congre s approved March 3, 1915 , for the upel"vi ion and lirection of the scientific tucly of the problem of fljght (U. . Code, title 50, ec. 15). It memb r hip wa increased from 12 to 15 by act approved March 2, 1929, and to 17 by act approved May 25, 194 Th e memb ers are appointed by the Pre id nt, and serve a such without compen ation.
JEROME C . Hu SAKER, Sc. D., Mas achusett In titute of Technology, Chairman LEXANDER WETMORE, Sc. D., ecretary, mithsonian In Litution, Vice Chairman DETLEV W . BRONK, PH. D., Pr esident, J ohn Hopkins Unive r- DONALD L. P UT'!', ~Iajor General, United tates Air Force, i ty. Director of Research and Development, Office of the Chief of J OHN H. CASSADY, Vice dmiral, Un i ted tate Tavy, Deputy taff , D evelopment.
Ch ief of Naval Operation.
ARTHUR E. RAYMOND, C. D., Vice Pr e id ent, Engineer ing, EDWARD U. ON DO , PH. D., Director, Nationa l Bureau of Dougla Aircraft 0., I nc.
tandards.
FRANCIS W . REI II ELDERFER, C. D ., Chief, United States HO I . THOM AS W . . D AV I S, A i tant ec r etary of Commerce. W eather Bureau.
J AMES H. DOOLI'l"l'LE, C. D., Vice Pr e id ent, hell Union Oil HO N. DELO W. RJ,NTZEL, Administrator of ivil Aeronautics, Co rp .
Department of Comme r ce.
R. 1. H AZEN, B. ., Director of Engineering, Alli on Divi ion, GORDON P. St\.VILLE, Major General, United tates Air Force, General :Mo tor Co rp.
Deputy Chief of tafl'-De l 'elopment .
WIL LIAM LI TTLEWOOD, 1. E., Vice Pr esident, Engineering.
WI LLIAM W EBS'l ' ER, ~1. ., Chairman, Research and Develop- American Airlines, Inc. ment Board, Department of Defen e.
THEODORE C. L ONNQUEST, Rear Admiral, United tates T avy , TH EODORE P. WHI GH'!', C. D., Vice President for Re earch, D eputy and A si tant Chief of the Bureau of Aeronautics. oro ell Unive r sity.
H UG n L. DRYD EN, PH. D ., Director JOlI F. VrCTORY, LL. D., Executive Secretary J OHN W. CROWLEY, JR. , B. ., Associate Director for Re earch E. I-I. CnAMBEHLIN, Executive Officer HENHY J. E. REID, D. Eng., Director, Langley Aeronautical Laboratory, Langley Field, Va.
~IIT:H J. DEFRANCE, B. ., Director, Arne Aeronautical Laboratory, Moffett Field, Calif.
EDWARD R. HARP, C. D., Director, Lewi Flight Propulsion Laboratory, Cleveland Airport, Cleveland, Ohio TECHNICAL COMMITTEES AEHODYNA~lICS OPERATI '0 PROBL E~ J S PO WER PL ANT FOR AIRCRAFT IND USTRY Co 'SULTING AIRCRAFT CON TRUCTIO Coordination of Research Needs of J.Iilitary and Civil Aviation Preparation of Research Programs Allocation of Problems Prevention of Duplication Consideration of Inventions L ANGLEY AERO NAUTICAL LABORATORY, LEWIS FLIGHT PROPULSION LABORATORY, AMES AERONAUTICAL LABORATORY, Langl ey Field, Va. Cl eve land Airport, Cl eveland, Ohio Moffett Field, Ca lit Conduct, under unified control, for all agencies, of scientific research on the fundamental problems of flight OFFICE OF AERONAUTICAL I NTELLIGE CE, Washington, D. C.
Collection, classification, C01n1Jilation, and dissemination of scientific and technical information on aeronautics II
REPORT 988
COMPARATIVE DRAG MEASUREMENTS AT TRANSONIC SPEEDS OF RECTANGULAR AND SWEPTBACK NACA 65 - 009 AIRFOILS MOUNTED ON A FREELY FALLING BODY By HARLE W. M ATH E WS and J n l ROGE R S T HO ~ 1PSON SUM iJA R Y wer e fitt ed with a po inted nose, simil ar to th at of the bodi es of re fer ence 1, an 1 wiL h a m all fairu lg at th e ta il in ord er D ir ectly compamble dmg measurements ha ve b ee n made oj an to r ed u ce t he bo ly dr ag at high p eed. Th e b odie wer e airjoil with a con ve nt i onal rectangular plan jorm and an airfoil ball asted b y ad diti on of l ead in th e no se to a to ta l weight of , wi th a swe pt b ac k plan form mounted on fr eely f alling b od ies .
a ppro x im at ely 1,3 00 pound s in o rd er to at L a in th e de u'ed B oth airjoil had N A CA 65 - 009 se ctions and were ide nt i ca l in ve 10 ci ty a nd to ins ur e a tab le config ur at ion .
pa n , jrontal area, a nd ch oTel perpendicular to the leading edge.
Th e te t airfoil , whi ch were mou nte d n c ar th e r e ar The weptb ac k plan jorm incorpomted a sw ee pb ac lc angle oj of th e cy l indri ca l par t of th e bod y , en tered th e b od y tlu-ough 45° . The data obtained hav b ee n u se d to es tabl is h the re lcLt i on rec ta ngul ar slo t 9 }~ in che long an d 1 inch wid e. Th ey , ve re betw ee n the ai1 :foil drag co e fficients and the fr ee -stream l d ach tagger ed 0 th at each pa ir of ai rfoil co uld be m o un ted on num b er o ve ? ' a range of }. ,f ac h num bers from 0.90 to 1.27.
separ at e balan ce whi ch m ea ur ed t he r eact ion b et ween Th e r es ult of th ese meas ur em 71t i nd i cat e that the drag of the e ac h pa ir of a U'f oil a nd the b ody. Thi s y tem h as th e swe pt b ac lc plan form is less th an 0.3 that oj the rectangular pl an a ddi ti on al ad va n tage of r e cl uein o- in te rf erence e ff ect of the jorm at a M ac h num ber of 1.00 and is les than 0.4 t ha t at a r ea r airfoil on th e fro nL airfo il.
lvlach num ber of 1.20 .
I N TROD UC TIO N R ece nL int ere t in ae rod yna mi c !J apes a nd config ur at ion whi ch will afi'ord minimum dr ag at tr ansoni c velo cit ie h as 1 cl to Lh e pr e en t seri e of tesLs in whi ch L he va ri at ion of dr a c- o coe ffi cien t wi th M ach number is d tel'min ed lutin g t he free Ja Il of a test bod y from high a lti t ud e. Th e fi r t e ri e of t ests on freely falling b o di e wa r epor te d in ref erence 1 .
Th e pr e en t re por t pr e e nt r e ult of t wo fr ee -fall te L s CO n- du cted in Jun 1945 a an ini tial expe rim en ta l check on Ut e lovi -dra c- ch a ra cte ri stic of we pL win g at t ran so ni c p ee d a ugge te d by Jon es in r efe rence 2. rrb e da ta ob ta ined from the e te t pro vide a di r ect co mp ar i on of the dra g of a n airfoil ha vin g a r ect an g ular plan fo rm with th at of a similar (a) H CcLa ngular pla n (0 1 Dl.
airfoil h avin g a wee pb aek angle of 45°.
Th r e ul t of till in ve L i gaL ion ar e pr esen te d a c ur ves howing L he v a ri at ion of dra g coe ffi cien L with ),J ach numb e r.
APPARAT S AND ME THOD Tes t airfoils and bodies.- Th e gen era l arran gem en L s of th e L wo test bodi es ar e hown in L h e photo gra ph ( fi g. 1) and the d et ails and dim ension arc ho wn in th e lin e c1rawin c- o ( fi g . 2) . Bo th the airfoil with t he con ve nt io nal r ecta ngula r pl an fo rm and th e ai rfoil wi th th e wep tb ack plan fo rm h a d.
ual fron ta l ar ea and span a nd inco rp or ated K AC 65 - 009 sec Lio ns of e qu al ch or d perpe ndi c ul ar to th e l ea din g edg . Till a u-f oil ection wa cl c Led a re pr e en LaL iv e of t ho e now b ein g c on ider ed for u e on hi gh- peed aU·cra fL .
Th e bo dies on which t h e te L airfoil were moun te d wer e (b) we p ibac k plall fo rm.
mad e cy lind ri ca l, b ot h for ea e of fabric at ion and for r e du cin o- int e rf er en ce e ff ect of th e bod y on th e au'foil drag. Th e; F,G UHE I. - Gc ll cral v icws of .lirfo il test bodies.
8 97 74 0-- 51 REPORT 9 - rAT IO rAL ADVISORY COMMITTEE FOR AERO AU'l'ICS ~-----------------26--------------------------~ ~-----40--------~ , Center -ol-gra vity - - - Sweplbock p lan form lacalion _ - - - Antenna IO~ • B--~--~.-~----25----~ f------30------~-----------55----------~~ Airfoil seeLio ll coordinates _ -Rectang ulor plan form (N ACA 65-009 airfoil) x y x V :r Y ---- --- -- --- --- --- 0.000 0.29 5.200 0.266 0.000 1.600 .040 .056 2.000 .321 5.600 .22 .
. 000 .068 2.' 1 00 . :l42 fi.OOO .1 87 .100 .0 5 2.800 .354 fl. 400 . H4 . 114 3 .200 .360 6.800 .1 01 .200 .400 .157 .35 8 7.200 .059 3.600 .600 .191 4.000 .347 7.f>OO .0 22 .219 4.400 .327 8.000 .800 .000 I5R .264 4.800 .299 1.200 \ Section A-A L. E. radius: 0.044 -'---T~8 ~ 1 F1 G R£ 2.-Gcncral a l"r a n. gcm~nlS and dinlcnslons of a irf o il test. bodies. (AU dim nsio l lS ar l.:. m lII Ch\!S .} Measurements.- The force ex rted by each pair of ai r- Reduction of data . -- Th e vel city of the body during free foil on the body, as mea ured by a spring balance, and the fall was obLained both by differenLi at ion of the fliaht path total retardati.on of body and ai rfoil ,a measured by a as recorded by the radar and phototh eoclolite equipment and sensitive accelerometer alined with the longi tudina l axis by in tegrat ion of the vector sum of the aravitational accelera- of the body, 'were reco rd ed at two eparate gl'ound station tion and the directed retardation mea urecl by the acceler- during the fall of the te t body by mean of the N ACA ometer. Tb directly mea ured value of auJoil dra g D , the radio-telemetering sy tern. A time hi tory of the po ition static pre' llre p, the Lcmperature T , a nd the airfoil frontal of the body in pa ce wa r ec orded during the fa il by use area F wet' e co mbin ed with the velocity V to obtain Mach of radar a nd photot heoclolite equipment. The drag fo[,ce numhe r All and the n.on. cii men ional param eter D/ Fp. In the D act ing on each pair of airfoi l wa 01 tained from the L ran onie speed range , w] )ere the clraa i clete rmin ed pr i ma- ril y hy ;'I ach Humber raUlet' thall air peecl, cur ve howing relation the variation of D/ Fp wilh Mach numb r provide the mo. L D=R+Wrae where convenien t way or pecifying the drag a a function of iz e, measlU'ec\ rea ct ion b tween airfoil and body , p und , altitude, and Mach number. Values of conventional drag R weight of aU'foil , pound s coefficient ba ed on the frontal area of the airfoil were then W 7• reading of accelerometer, g obtain d from imultaneou value of tbcse param eter by a.
usc of the relation A sUTvey of the atmospheric co nclition applying to each te t \Va obtained from ynchronized observations of static pr es ur e, te mp e ratur e, and actua l altitude during the descent of the aU'plane after each te t.
•
DRAG MEASUREMEN'l' AT TRANSONIC SPEED OF RECTANGULAR AKD WEPTBA CK NACA 65-009 AIRFOIL for L h econvenLional rectangular plan form , thedragp I'square where the ratio of pecific h eat 'Y wa taken a 1.4. Th e fooL of frontal arca increa cd abrupt ly from 0.05 of atmo - conveutional-ail"foil drag codfieient D ba cd on plan area \Va obtained by mUltiply in g the values of (YD by the ,.atio ph ri pre sure at a ~1 ach number of 0.90 to 0.35 n,L a ':'1ach F number of 0.9 and Lhen incl'ea cd at a much slo\\·er rate to of the frontal area to pl an area. The area used did not app roximaLely 0.63 of a.lmo phcric pre ure n,t a ;,1ach num- include al"Nl w. ithin the body.
ber of 1.20. imilarly, figure 5 show LhaL lhe drag per unit RESULTS A D DI S USS ION fronLal a rea for the \\ r eptback plan form iner a eel almo t linea rly from 0.04 of atmo phcric pre ure n,L a :"Iach number Time hi stor ic of the importan t quantities obtai1H'd of 0.9 to 0.29 a a ~1a ch number of 1.27. The drag throughout each ill'op are given in figure 3 and 4.
per squa r e foot of frontal area for the weptback plan A ch eck on th e over-all aCClil'acy of the velocily and tolal form i 1 ss than 0.3 that for the eonvenlionalrecLangular d ra g-force measurements.i provided by a compa ri son oJ the pl an form at a :"1 ach number of 1.0 and is Ie than 0 .4 Lhat wloeity letermmed by cliiTel"enLiation of the flight-path data aL a 11 ae11 J1l l mber of 1.2. A theoretical explanation of th e with t he velocity obtained from tep-by-step int egrat ion o[ low-drag cha r acter istic of the wepLback plan form appears the resultant acceleration obtained from the accelerometer.
in J'C£erence 2.
It will be noted. that the two velocity C urv es on each time An ind ependenl Ye lin cation of Lhe lower drag o[ the hi tory agr ee within 5 to 10 mile per hour. A cli , c ,. ('paney wepLback plan form i provided by the diO'cl'ence in Lhe o[ this magnitude COlTe pond to a mean error of 0.005g to loLal drag of the t,, -o to L boclie. At a ::'I1ach numb r of 1.2 O.Olg in the mea ured acceleration. This mran ('I" ,. or is the dil'ectl~ · mea ured airfoil drag indicat e a diffcrence in within the expected limits of acclll"acy of the ac('rk,.ometr,..
D/Fp bet" -een tll rectangular and weptback airfoils of The nlocity curve representing the difrerentiation of tIle about 0.40. ('ee fiO". 4. ) Thi elifferenc'e in D/Fp, when fl ight-path data wa u eel in co mputin g the ~1a c h number.
independcntl ~· computed from Lhe total drag measurement, TI H' accelerometer daLa werc lIsed a a guide in fairing tll is wa indicated to be about 0.54. Ina much a the dis- clll've over the fmal 3 seconcis of the elrop. For these 3 sec- crepancy bel" ·een the e va lu e i about t,,-ice a large a th(' ond , the radar and phototheociojiLe data became les aCCl/- um o[ the uncel'lainti('s of the indiyidual drag measur('- raJe because grOlU) 1 haz e obscu red the te t body on the m ents, at lea L a parL of the eli cr epancy 111usL ]'e ull from phototheoclo li te cOlTection photograph and gr ound ignal difference in the inLerferenc effect of the two airfoil pl an interfered with the radar-range i gna J.
fOI'111 on the bod)' drag. Th e body cL'ag for the model wiLh The I'e ult of the airfoil-ell'ag tests for both the conven- the rectan ular plan form wa eyidently greater than that tional rectangular plan form and thc weptback plan form with the weptback pla.n form . The rca on for the sudden arC' Sllmmariz cl in figure 5 b:v CUl"ve howing the yariation drag ri e eyidenL in the cUrYe of figLu'e 5 for the front airfoil ",jth . Mach number of D/Fp ratio and drag coefficient of the conyention al rectangular plan form at a ).1ach number ba cd on both frontal and plan area eparate curve are of l.07 is not apparent. Future te t arc expected to clar if y prc 0ntecl for thc front and rear ai doil of each type.
thi phenomenon.
Th e mall difference beLween Lhe drag values for Lh fronL It may be noted from figure 3 t hat the Lotal drag of the and rear airfoils may be caused by interf erence e fr e Ls body equipped with the re ctangu lar airfoil showed a sh ort- beLween the airfoils or between Lhe body and airfoil . B e- pcriod 0 cillation of sma ll amplitUde. The fir t vidence cau c of Lhese e ff ects the data for th e fronL airfoil should be of t bi oscillation appeared at a 11ach number of 0.98 wi th th e more r eli ab le.
a negligible amplitude and a frequency of 2 cycle per Th e maximum po sible inaccuracie in th e elraO" parameters econd. The 0 cillation became appreciable and regular aL decrea e " ' ith increasing 11aeh numbe r because of th in- 1\1" = l.05 and inc rca I l o\dy to an ampli tude of ± 20 crea e in tat ic pre lU" and air peed t hr oughout the fall. pound and to a frequ ency of 3 cycles per econel at the im- Th e maximum po sible inaccuracy in D/Fp clecrea e fro111 pact ;,1 ach number of ] .20. It appeal's likely that thi mall ± 0.020 at a Ma ch number of 0.9 to ± 0.009 at a ~1 ac h num- o cillation of the tota l lra Q" 1'e ulted f1'om a light ya wing ber of 1.2. Co rr esponding uLl ce r La in tie for CD are ± 0.0033 and a ro tation of the body during the de cent. Th e body was at a, Ma ch number of 0.9 and ± 0.0015 at a Ma ch number of obser ved to rotat e but did not appear to yaw visibly dur in g l.2 . Th e errol' in Mach number is less t han ± 0.01. the fall. Th e bod y 'with the sw eptback airfoil neither yawed Fro m th e ClU"ve fo r D IFp of fi gul'e 5, i t may b seen thaL, nor rotated during the fa ll, according to report of observers.
97740-51-2 • 4 REPORT 988 - NATIONAL ADVISORY C OMMITTEE FOR AERO I AUTICS 40xl0 f-- I-
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t: V / ~ .P'
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-t: \J ;:f l,oo ,/ .9 800 ~ ,.(!{ ~ ~ oA ~ Vf" p'P Total drag-- /' ... ", .8 8'600 VI--' pi>-' .r' ,r
is
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-4 o 4 B 12 16 20 24 28 32 36 40 44 48 56 Time after releas e) sec FIGURE 3. -' l'ime history of fr ee fa ll of 1, 2a5-pou nd t cs t body e quipped with airfoils cf conventional rectangul ar plan form (N ACA 65-009 section) .
• DRA G MEASUREMENTS AT T R AN SONIC SPEEDS OF RE CTANGU L AR AN D SWEP T B AC K NACA 6 5- 00 9 A IRFOILS I 40x 10' I 100- ~
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Y ./ / rt' .8 0;600 ./' Cl ./ JJ
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- 300 200~
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/ 1-'2 1 ci' o Airfoil drag .......
----- lOOt ;;.,..
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V f
O~ -4 o 4 8 12 16 20 24 28 32 36 4 0 44 48 52 56 Time after release, sec FIG U IIE 4. - '1'ime history 01 fr ee fa ll of 1 ,3 10-pound test bod y e qttipp ed with airfoils olswcptback pl an form (N A CA 65-009 section.)
' .. .,·""~H· RE POR T 988 - ATI ONAL A DYI O RY COMM I' J' T EE F OR A ERO r AUT I CS . 06
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p-- o I. I 1 .2 1.3 .8 .9 1. 0 .7 Ma c h n umber, M FIGURE 5.-Variation with M ach number of air foil drag coefficients and DIFp for ai r foils of conventional rectangu lar plan form and swcptback pl an form.
DRAG MEASUREME T S AT TRA T SONIC SPEEDS OF RECTANG U LAR AI D SWEPTBA CK ACA 6 5- 009 A IRFOILS CONCL UDING REMA RK S Th e appr eciable magnitud e of the dra g re du ction e ff ected by th e swe ptba ck plan form indicate t ha t continu ed re- Dir e ctly comparable drag mea ur emen t hav e been mad e se ar ch is de irable to impr ove fLU· ther Lh e aerod ynamic of an airfoil with a conventional re tangubr plan form and c haractcri ti cs of uch config ur ati on.
an airfoi l ,,, ith a we ptba ck plan form mount d on a freely falling body. Th e e mea m e ment s indic at e that th e drag of th e we ptba ck plan form i Ie than 0. 3 that of the rec tangu - lar plan form at a Ma ch numb er of 1.00 and is Ie than 0.4 L ANG L EY A E RO NAUT I CAL L AB OR AT O RY, tha t at a lIa ch numb er of 1.20. N A TIO NA l , ADV! OR Y COMMI'l' TEE F OR A ER OKf\ UT I CS, For the c onv entional r ectangular plan form, th e drag per L ANG L E Y FIELD , V A., A ug us t 9, 1 9l,.5.
s quar e foot of frontal ar a increased abruptly from 0. 05 of atmo ph ri c pr s ur e at a Ma ch numb er of 0.90 to 0. 35 at a lI ach numb er of 0.9 and th en in cr ea d at a mu ch lower REFE R ENCES rat e 1,0 approximat ely 0.63 at a Ma ch numb er of 1.20.
1. Bailey, F . J. , Jr ., \[a thew , Cha rles \V., an d T ho mp on, Jinl R oge r s: Th e drag per s quar e foot of frontal ar ea for th e airfoil Dra g M eas ur me nt a t Tr a n onie peeds on a Fr eely Fa lli ng wi th swep tba k pI an form inc rea ed almo t line arly from 0.04 Body. N AC A ACR L5E03, 19 45 .
of atmo s ph e ri c pr es m'e at a Ma ch number of 0.90 to 0.29 at 2. Jon e, R obert T .: Wi ng Pla n F o rm fo r Hi gh-Speed Fli gh t.
N CA R ep . 63, 1947.
a Mach number of 1.27 .
U. S. GOVERNMENT PRINTING OFFICE: 1 951
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Positive directions of axes and angles (forces and mom ents ) are shown by arrows Velocities Moment about axis Angle Axis Force (parallel Linear to axis) (compo- Designa- Sym- Sym- Sym- Positive Angular symbol Designation Designation bol nent along bol direction tion bol axis) RolL _______ LongitudinaL _______ Rolling _____ __ p Y~Z u X X L cJ> Pitch. ____ _ __ LateraL _ ____________ Pitching _ _____ () q Z~X v Y Y M N ormaL _____________ Yawing _ ______ r X~y Yaw to Z Z N -------
'"
Angle of set of control surface (relative to neutral Absolute coefficients of moment position),o_ (Indicate surface by proper subscript.)
L M N On=qbS 0 = qbS Om= qcS (yawing) (rolling) (pitching) 4. PROPELLER SYMBOLS Diameter D p Power, absolute coefficient Op= fD5 pn p Geometric pitch Pitc h ratio plD
:j V6
O. Speed-power coefficicnt= ~n2 Inflow velocity V' Slipstream velocity V. Efficiency Revolutions per second, rps n
T Thrust, absol ute coefficient OT= ;D4
pn Effective helix angle = tan-{> V ) <fl ~7rrn
Q Torque, absol ute coefficient OQ= ~[)5
pn 5. NUMERICAL RELATIONS 1 Ib=0.4536 kg 1 hp=76.04 kg-m/s=550 ft-Ib/sec 1 kg=2_2046 lb 1 metric horsepower=O.9863 hp 1 mi= 1,609. 35 m=5,280 ft 1 mph=O.4470 mps 1 m = 3.2808 It 1 mps=2.2369 mph