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C O NTRACT REP O RT N ASACR 114399
ADVANCED GENE RAL A VIAT ION
P ROPE LLE R STUDY
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_"'d f " h _'• _._ _ " ". "' P R EPARED UNDER CONTRAC.T NO . NAS2--6477 BY H A M ILTON STANDARD DIVISION OF UNITED AIRCRAFT CORPORATION ;, W I NDSOR LOCKS ,CONNECTICUT FOR i' ' _ ADVANCED CONCEPTS AND MISSIONS DIVISION ' OFFICE OF A DV AN CED R E SEARCH AND TECHNOLOGY NATIONAL AERONAUTICS AND SPACE ADMINISTRATION _ C O NT RA CT R E POR T N A SA CR 1 14 3 99 ADVANC ED GENERA L AVIA TI ON P ROPE LL ER S TUDY B y Ro s e W o ro bel MiU a rd G . Mayo De c e m be r 2 1 , 1 97 1 '_" Pre p ar e d U n der C on tract No . NAS2- 6477 By : ' ._ ' HA M ILT O N STA N DA R D ' D ivis i on o f U n ited Ai rcr a ft C o r po rati on Windsor L o ck s, Connecticut i" f o r ADVAN C ED C ON CE P TS AN D M ISSI ON S D I V IS ION O FFICE O F A D VAN CED R E S EA R CH AND TECHN O L O G Y NAT ION AL AE RON AUTICS A N D SPACE A D MIN IST R ATI ON q • rJ ,l f_ f,.. I A( , I,, ,lH,A_ ' ,,q( NOT i |I_Mr , D ABSTRA C T Unde r a p re v io us NA S A c on t ra ct and reported i n CR- 11 428 9 me t h o ds fo r pre- d icting the pe r f or ma nce , n o is e , w eig ht , an d c ost of prope ll er s f o r ad v a nc e d ge nera [ av iati o n ai r c r a f t o f th e 1980 t i me perio d w e re d ev e lo pe d an d comp ut e r i z e d . Unde r th e p r e s ent contrac t thi s b as te pro gr am w a s r e fin ed to in cor p orate a me t hod of i nc l ud - i n g th e b lade shap e pa r ame ter, in t eg r a te d desi gn lif t e o e ff icl_ :nt , T h is m e th o d a r L da r e v e r s e th r u s t c o mp u t ati o nal p ro ce d u r e w e r e i nc l ud e d i n the c omput e r p ro g ram . Th e wet g _ e q uat i on wa s re f i n ed a n d a l s o i nc orp o rated in t h e c om pu t e r p r og r a m. A U se r ts Manu a l w hich i nc l u des a c omp l et e lis tin g of th is c omputer p r og r am w i t h d et a i l ed ins tr uct io ns o n tt_ u se has b een w r it te n and wil l b e p ub lis h e d as a NA S A low n umber Co n tractor Ro p or L I ll / iv CON TE NTS , SUMMARY 1 I NTRO DUCTI O N 3 S Y M B O LS 5 TE C HNOLOGY D E V EL O PME NT 7 Me thod for V a ry i n g Integ : a t e d D es ig n L i ft Coeffic i ent, 7 I n t e gr a ted De s i gn Lift Coe f fici e nt Adju s tme n t Facto r , 9 Co m pr e ssibility Fa ct or 10 M eth o d fo r Co m puti ng Reverse Th r ust 1 1 C om putational Procedur e 1 3 R efi n ement of Wei g ht Generalizati o n 1 6 In p ut / O utput Additi o ns to the Co m puter P rogr a m 17 USE Rt S MANUAL 1 9 . _ ' C O NC LUDING R E MA RKS 2 1 R EFE R ENCES 2 3 ,. .;._ T AB LES _ . .
: ' I W e i g h t S um m ary of P r o pe ll ers S tud i es fo r 1 980 2 5 .... II Ge n era l A viation - Genera li zed P rope l ler W ei gh t Equ a t io n 2 6 !_ : _._i III Typical 1 970 P ropeller We ig hts 2 7 :. " IV O. E .M. S i ng l e U n it C o st S u mmary o f R e pr e se n tat i ve 2 9 i . i_ii, i P r o pel l ers fo r 1980 . : : FIGU R ES 1 B lade Ca m ber D ist r ibut ion 30 2 Num ber of Bl a d es C o rrection f o r Pow er C o efficient 31 3 Camber Factor Adjustment f o r Advance R atio 3 2 4 Inte gr ated Desi gn Lift Coeffic i ent Adjustment to Power Coeff i c i ent for 4 - Bladed P ropellers 33 5 N umber of B l ades Correct i on for Thru s t Co e ff i c i e n t 34 • 6 Inte g rated Desi g n Lift C o e ffi c i ent A d j ustment t o Thrust C o eff i cient f o r 4- B l aded P r o pel l ers 3 8 . : 7 Cr i t i cal Mach N umber fo r A dvance R at io s Greater than Zero 36 V i CONT E N TS (Continued) FIGURES (Con tinued) 8 C r i tica l Ma s h N um b er f o r Adv a nce R atios Equal to Zero 37 9 C om p r es _ ib i l i ty A d justme nt 38 10 E_ c ample Reve rs e Th rus t V ar i at i on w _t h L andi n g S peed and Power S et t ing 3 9 11 A c tivity F acto r Adjustment to Torq ue C o eff i c ient 40 12 I n t eg r sted Desi g n Lif t Coeffi c ie n t Ad j us t ment t o To r qu e ,.
C o _J f f l eien t 4 1 1 3 V a r i a ti o n of P er c en tag e of In te gra t ed Desig n L i ft C oe ff i c ient C or r e c tion R e quired f or Th r u st a n d Torq u e 42 14 B as ic P er for ma nc e Curve - Va r i a tio n of Eff ective Torque C oe ff i c ient w ith Adv a n ce Ra tio and B l ade A n gl e 43 15 I n t e g rate d Des ig n l i ft Co e ff ic i ent Ad ju stm ent to T or q ue Co eff ic ie nt 44 16 Ba s i c P e r f or ma nc e C ur _e - V ariat i on o f E ff ective Th rust Co e ff i c i e n t w it h Adv an c e Rat io a n d Blade Ang l o 4 5 17 Ac t iv i ty Factor A d ju s tment to Th rust Coefficient 4G 18 I n tegrated Des i gn L if t C oe f ficient A d justment to T hrust Coeff i e i ent 47 !
1 9 Sample C a se I of C om puter Progra m O utput 48 2 0 S a mple Case II o f Com pu te r Pr ogra m Ou tput 49 SUMM ARY A m ajor outc o m e of th e s tud y s po ns or ed by the Advan ce d Co n cept and mi ssi o n . D i v i s i o n, A . C . M.D. o f N AS A u n der C o n tr a c t N o. N A S2_ 58 8 5 da t e d 30 J a nua r y 1970 an d r e p o rted in CR 114289 ha s been th e d e v elo pn mn t of a c o mputer pr ogra m fo r e val u- a t i n g pr o pe ll e r p e r f orman c e, n o ise , w e ig ht an d co s t f or gene r a l a vi at ion aircra f t pro - p o ll e r s as a fu nc t ion o f t h e pri mo g e o m e tr i c and a e ro d y namic vari ab l es . Thi s pr o g ra m p r ovi d e s for ch ang e s i n t h e a c t ivi t y f a ct o r pe r blade an d n umb e r of bl a d e s , but i t w a s li mi t e d t o a s i n g le valu e of inte gra ted desi g n lif t c oe ff icien t . Th is s tu d y , C on t r a c t No.
NAS 2 -6 4 7 7 d a ted fl M ay 1971 a nd a lso s p onso r ed b y t he A. C . M. D., e xt en ds t h i s c om- p u t e r pro g r a m t o in c o rp o r at e t he i nt e gr a t ed deMg n l i f t coeff i c ien t as a pr o p e l le r bla de sh a p e v a ri ab l e . Add iti on a l ext e n s ion s t o t he c o m p u t e r pro gram wh ic h a re do cume nt e d i n th i s r e port a r e the ea p abi l i W o f c alcula t i ng prop e ll e r r e ver se thru s t a nd t he r efi n e - - mea t o f t he p r opel l e r w e ight eq uat io n. A f in a l r eq u i r em ent of C on tract N o . NAS 2 -6 477 was t o de s c ri b e th e com p l et e co m puter pr o gr am . This manuM i s r e p o rted in a s e p - a r ate l ow number NAS A Co n tra c t o r Rep o rt.
In th i s rep o rt the te c hn ology i s deve l oped fo r i nc l ud ing the c ap abili t y of vary i ng inte g rated d e sig n lift coefficient. An existing reverse thrust method ha s bee n adapted f o r the general aviati o n aircraf t app l ication. The weig h ts for 36 add i tional prope ll ers over th o se used i n the original s tu dy have been defined an al yt i c all y and u sed in re f ining the we i ght equation. These technology a dd iti ons and revisi o n s are i n c orporated i nto the : co mputer program.
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INTRODUCTION Aviation fo r ecasts f o r the next ten to fifteen year tim e per i od, i ndicate t h e eon- if tinne d stea d y g r owth o f gene r a l a viat i on. Fu rt he r mo r e , it is ap p a r en t t ha t m os t of [ the s e aircraft, even int o the 1980 time pe r i o d will be pr o peller d r iven utilizing p r ima- I ril y reeipr o eating eng i nes with tu r bi n e e n gi n es c o ming o n as their ec o n o mies im p ro v e .
T h e at ta i n men t of th is fo r ecas t e d g rowt h is d e p enden t up o n th e eontl 1ned i mprov e ment 1
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in the saf e ty , u tility, pe r f o rmance and c o st o f gene r al aviati o n si r e" , fit .
| In v iew o f t h is, a s t udy was u nde rt aken u nde r NA S A sp o nso rsh i p t o de r ive and 1 c o mput e riz_ app ropr iate p r opeller pe r fo r mance , noise, weight and cost c r it e r ia to p e r mit s e nsitivity studies of these factors to b e ma d e fo r adwmee propelle r c o n fi g ur a - tions des i g n e _ f or gene r al aviation ai r c r aft of t he 1 9 8 0 time pe r i o d. The r es ul ts o f this stu d y we r ,_ p r es e nt e d in C o n tr a c t or Repo rt NA S A Cfl 114289, "A d va n ced G en e r al Aviation Stud : ¢ , t Ap r il 1971 ( ro f. 1). A t NA_AIs re qu e st a contrac t study was un de r- " taken to p r ovi d e a Us e r ts M an n ed w h i c h includes a c omp let e li st i n g of t hi s co m p t_¢ er pro g ra m w i th det a il ed i nstruc ti ons o n i ts use. Furth e rm o r e th e s c o p e of the co mpu ter pr og r a m has b e en e xt e nded to inc orpor a te th e f oll ow in g: 1 . Method f o r var yi n g i ntegrated des i gn l i ft coeff i c i ent (the o nl y pr i me blade shape var ia ble not i nc lu ded i n the or i g i n a l p rog r am ) _ . 2 . Method for comput i n g reverse thrust : 3 . R efinement of the we i ght e q uat i on Th us a re liabl e co m put e r progr am has been developed for pred i ct i ng propel l er p erfor - ma nce (stat i c , fl i ght and reverse), no i se , we ig h t a nd cost f or the complete general :i_ aviat i on airc ra ft r an ge .
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'_' A d et ail ed d i sc us s i on of the technolo gy developments and i ncorporat i on i nto the .:_ compu t at i onal proce d ures o f the a bove extens i ons to the computer pro g ram are d i scussed i n the follow i ng text. The User t s Manual wh i ch i ncludes F OR T R AN I V l i st i ngs an d I nput / output I nstruct i ons wtl l be publ i shed under s e parate c over as a NAS A lo w number Contrac to r R eport.
3 / 4 SYMB O LS AND ABBREVIATIONS i.0 O. 15 b bl a d e aa e t i on widt h , ft B n tm lb e r of bl a d e fl C LD b l ade B_ c tl o n d e s ig n li ft coe f fi ci en t 1 . 0 EL I propeller bln d e integ rated dest i ne Ill% coe ff i c ien t 4 f CL D x 3 d , _ 0 . 18 SHP( P o /P ) I0II C p pow er c o ef f icie n t, 2N 3 D 5 CQ t o rque co e f fic i ent for J_ 1.0 , SH P ( ____._Po / P). 1011 47r N 3D 5
1 . 514 x 10 6T.. ( Po /p )
CT thrust coefficient , N 2D 4 D propeller diameter, ft h max i mum blade sec t ion thickness 101.4 Vk J adva n ce rat i o , ND M free stream M ach n um ber N pr o peller speed, rpm PN L percei v ed n oise level , P NdB . . ....... .,........... . , ... .... ;>.
Qc t or que coe ffi c i ent fo r J;. 1 . 0 , SHP( Po /P ) 1011 I 4_r N 3 D 5 j2 ' i R blade ra d ius at propeller t i p , ft r r adius a t b l a d e eleme n t , f t S HP _ h aft horse p o w e r T p rope l le r t h rus t , pou n d _ TC t h r ust coe f fi c ient fo r J_ 1. 0 , 1._14 x 106 T( Po/p ) X 1 N2 D 4 j2 VK f r e o s tr c _u n v e l oci t y , lmots x f r a cti on o f p r op e ller t i p r _l i us, r / R _ 3 / 4 prope ller b la de ang le at 3 / 4 r a d ius P d e n s ity , lb sec 2 / f t 4 P c den sit y at sea leve l standa r d day, 0 .00 2 3 78 l b. sc c 2 / f t 4
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.= ' ' 6 TE C li NOLOGY DEVELOPMENT Me t h od for V ar yin g I n t eg rat e d D es i gn Lift Cae ff ia i e nt In the o r igin al r e p o rt ( r ef. 1 ), a p er fo r ni ane e m e th o d g e ne r al i za tio n wa s deve l_.
o p ed fa r pr ed i c t ing s t a t ic a nd fo rw ard fl ight p erf o r mance for g e n e ral avi at i o n ai r cra ft p r o pell e r s . Th e h o rse p o we r, t h ru st , pr o pe lle r r o ta tion al spe_ d, v e l oci t y a n d d i a_ mo tor a r e includ ed I n th e non - dimens i onal f a r m o f po w e r c oe ff i c i e n t , C p , t hrust ao cffi ei o n t , C T , an d a d va n c e ratio , J def ined as fal l ow s: fdliP ( P o /P ) 1 0J] C p _ ....
2N 3D 8 1.514. x i06T ( Oo/p ) (' T _ - _ ....
N2D d 101. 4 V K J = ' N D whe r e : S lIP - shaf t horsep o wer P o /P - ratio of dens i t y at s e a l evel s t andard da y t o den s i t y ' fo r a speci fi c oper a ti n g c on ditio n _, , N - prop ell e r speed , rpm , , D - prope l ler diameter _ ft T - prope U er thrust , pounds VK - forwa rd speed velocity, knots Base c u rves were defined in this non-di m ensional form presenting the perf o r- m an ce of 2 , 4, 6 and 8 bladed p ro pellers re f erenced t o an activity f act o r o f 150 an d 0.5 integrated design li f t coefficient.
. In o rder to minimiz e the n umber o f curves and c on seque n tly the size an d c o mp l ex- ity of the computer p ro gram , th e t e rms effective power coeffi c ient , C P E , and effective : thrust c o effic i ent , C TE wer e intr o duced. The effective p ow er c o effic i e n t and thrust C TE _ C TxTAFxTCLI wh e r e = Cp .- p a war aoe ff i ete n t P AF - n a ti v ity f acto r l u iJus t m t _n t t o pow e r eoofflal o nt (r o f. 1, fig 3A) P CL l - i n t eg r a t e d des i gn l ift coeff i c ient, e L l ra l Jtmt m o n t fimto r to l)ower aoe f fiato n t (do_ o t_llmd in subt_o q uoat text) ( 2 T - - th r u . _t aooffiektnt TAF - activity f a t Jtor adjustment factor to thrust t,)offt c l_a_ ( r ift. 1, fig. 3A) T C L l - integrated d es i gn lift c oeff ici en t , eL i a d j u s t m e n t f a ct o r to thr u st '.'i c oe ff i c i e n t (d escr i b e d i n s u b s eq uent te x t ) I In t he or igina l r e p ort, t he ba s e pe rf or m a n ce c u rv e s a nd the act i v i ty f actor i ,_ a dj us t men t factors , PA F a n d TAF were deve lop ed a nd i nc l uded i n th e c o mputer p r o- ,, gr a m . F urther mo r e, a lim it ed an m u nt o f wo r k w as done t o estab li s h th e feasi b i li t y • of gen er _i z ing the in tegrated de s i gn l i.f t c o e ffi c i ent ef fe ct . U nder t h e present stud y c on tract , the i nt e grated d es i g n li ft c oef fi c i ent a djustment factor was deve l oped for a . '_ r ang e of 0 . 3 _ CLt _ 0 .8 . Bl a d e c ambe r dist r ibutions for t h is r a nge of CL! a r e sh own : '_ ' i: i n f i gu r e 1. T h us, t he ba s e curv e s whil e re fe r e nced to a basi c a ct ivity f ac t b r and .: :, in t e gr a t ed d e s i g n l i f t coeffi c ie n t , a re applicable to t he compl et e r ang e of 2 to 8 blades, 80-200 ac tiv i t y f a c tor a nd O. 3 to O. 8 int e g r ated de s i gn lift co e ffici en t.
Since it h a s been p r o jected th a_ g eneral avi at i o n a ircr a f t wil l be op er at in g at si gni ficantly , hig her speeds by the 1980 _tm e per i od , a co mpress i b i l i ty factor , Ft for the base curv e s of 0.5 i nte g r a ted des i gn l i f t coeff i c i ent was der i ved for u s e w i th the ba s e p lots pr e s e nt e d i n re f er e nce 1. Th e thrust i s m ult i pl i ed by t h e Ft to correct f or co m press i b ili ty l osses . Under t he pres e nt contr a ct, the Ft correct i on was e x p a nded t o a pp ly to th e comp l ete r a n ge of inte g r a t ed desi gn l if t c oe fficient o f 0. - _t o 0 .8.
The d e v e l o pme n t of th e in t e g r ated d esi gn l i ft coe ff icient adj us tm en t facto rs , : P C Lt a nd TC L t a n d the c o m p r e ss ibility corr ectio n , F t, a s w e ll as thei r i n c or p or ati o n " ' ' L / ., 8 into the compu t ati o nal pr o cedu r es are described in the following text Integrated design lift coefficient adiustmen_ factors - Using the propeller compu- ta t ional procedure based on the work of Goldstein _ defined in reference 1, calcula - tions were made for integrated design lift coefficient between 0.3 and 0.8, number of blades ranging from 2 to 8 , and activity factor from 80 to 200. These calculations were utilized in deriving the adjust m ent factors, PC Lz and T C L l for the power ,_ A ld thrust coefficients respectfully. These adjustment factors are dependent on advance ratio, number of blades, activit y factor : ro d integrated design lift coefficient. The detailed step - by-step procedure incorp_ , rated in the computer program is presented below for the ease where thrust is calculated for a known shaft horsepower.
1 . CPE 1 - ealetflate = C p x PAF ( P AF - r ef. 1,fi g . 3A) 2. P BL - r ead [_ o m f i gu r e 2 f o r t h e C PE 1 o f ite m I ab ove an , ! t h e p roper number of blades 3. PFCLi - read from fig_tre 3 for the app r opriate J (revision of fig. 12A in ref° 1) 4. CPE2 - calculate = CPE 1 x P BL x PFCLI 5. PCLI - read from figure 4 for the CPE 2 of item 4 and the CLi (expansion of fig. 13A in ref. 1) 6. CPE - calculate = CPE 1 x PCLi Now, the corresponding blade angle, _3 / 4 and thrust coefficient, C T are obtained as foUows: ,i_; °j 7 . _3 / 4 - r ead f or C P E , J an d a p p r o p r i at e numbe r o i b lad es ( re f . 1 , _:?_ fig. 4A , 6A, 8A, 10A ) , , 1 _:_ ° J 8. - rea d f o r J and fl 3 / 4 fo r t he prop er num be r of b l a de s _ _ ( re f . 1, fig. 5 A_ 7A, 9A, l lA) _, CTE The following iteratio n is required to defi n e the thrust coefficient si n ce ,, C T = CTE / (TAF x TCLi) and TCLi is a fu n ctio n of CT.
_o 9. C T - assume 4_mr v ) , -, 10. CTE 1 - calculate = CT x TAF (TAF ref. 1, fig. 3A ) - • L i 9 ,.i__ o 11. TBL - r ead f r om f i gu r e 5 f o r CTE 1 and the appropr i ate number o f b l ad e s , . 12. TFC L i - r , _ad f r om figure 3 for appr o p r iate J (revisi o n o f fig. 12A in r ef. 1) 1 , - calculate x TFC L I x 13. C I_E2 = C TE1 TBL 14. TCLI _ read from f i g u re 6 for CTE 2 and CLI (expansion of fig.
14A in ref. 1) 15, CTE - calculate= CTE I x TCLi I tems 9 thr o ugh 15 are repeated until the CTE in item 1 6 equals the CTE in item 8. Compute the thrust corresponding to the final a ssumed CT of item 9 .
A similar procedure has been included in the computerization for the case where shaft horsepower is c alculated for a known thrust with th e lte r ative proeesg required to define CP and subsequently the c orr e sponding S L I P , Compr essibility factor. - The c om pr e ssibi l i t y c o r re c tio n in cl u de d i n r e fe r e nc e 1 was extendedto span thecomplete integrated de s ig_ lift coeffi c ient range. The same c omputationsas those u s e d indevelopingthe integrated design lift coe ff icient adju s t- ..... m e n t facto r we r e us ed i n dev e loping t he c o mpr es si b ilit y fa ct o r . A c ritioal Ma ch numbe r , MCRIT for ea c h val u e of adva nc e r atl.o, J , has been defi n ed as the limiting f r ee st r eam Mach n u mber at which n o compr e s s ibility losses are e n co u ntere d • • (fig. 7) . Simila r M C RI T limit s :for J eq u al s z ero a r e s h own on f i gl_ r e 8 . If th e f r e e ::: st rea m Ma c h numb er exceed s t h e c r iti c al Maeh number, the compressibility factor , : F t is o b t ained ( fig. 9 ) . Ft h as bee n de riv ed as a fu n ction of C T in stead o f C p as defi n ed originally ( r ef. 1 ) sin c e it simplifies the c o mputational proce d ures whe n , ,' : .'
the thrust input option is used. The compressibility factor, Ft is obtained as follows.
: :::!: ' ::i.: 1 . M- airplane Mac h nu m ber , compute • -! • : 7r ND M - fc J = 0 ' .. 6 7, 200 M - V K fc J >0 661.2 whe re: N - prop e ll er rpm " D - propelle r diamete r , ft.
•" 10 fc - r a ti o o f speed o f sou n d a t st anda r d d ay sea le v el to s p e e d of sound at o p e r at i ng condi t ion VK - fr ee s tr e am v e lo ci t y, k not s tr ue ai r s p eed 2. MC R IT - read from figu r e7 fo r J > 0 a nd f i gu r e 8 fo r J = 0 for C LI ( expansion of f i g, 1 5 A i n ref. 1) 3. A (M_McRIT ) - ca l culate whe r e M i s t he f r ee _t r eam Much numbe r 4. CTE 3 - calculate = CT x TAF x TBL x TCL I 5 , F t - read fr o m fig_are 9 for CTE 3 a n d A (M - M c I_ I T ) Met h od fo r Computing Reverse Th r ust Airc r aft i ncorporating propellers with the reve r s e thrust feature have the capa - b i lity to l i m i t the _and i ng ground run to significantly shorter distances than w i th _he e l brakes alone . The propelle r nor m ally operates at a f i xed r eve r s e blade a n gle sett i ng : thr o u gho u t t he g round run op erat io n and the r e verse an gl e is se le cted to ab sorb normal rated power and spe e d a t zero vel ocity. O ccasion al ly, the reverse bl a de an g le setting , :, . i s bas ed o n a par tial thro ttle se t tin g inst e a d of f u ll t hro ttl e. T her efo re , the opt io n .
o f co mput in g r e ve r se angle and the c or r e s po n di n g r eve rs e thr u st, h orse powe r a n d propeller s peed f o r a range o f velocities s pa n n in g the gro un d r un s p e ed s ba s ed on '_ o p e ra ti n g a t sev e r al t hro t t le s ett in g s i s i n cl u d e d in t he compu t er p r og r am . Wit h th i s "'. ,T .:, da ta ( f i g . 1 0), th e corre sp ondi n g land in g d ist an c e s c an b e co m pute d and a c cor di n gly : . the ap pr o pri a te revers e a n gl e and pow er se t ti ng c a n be o btai ned .
• .: T h e analyti c al met h o d fo r co mpu ting r e verse t h rus t i s b a s e d o n an e xi s t in g H a milto n S tandard pr o cedur e wh i ch was obta i n e d by g e ne r al i zi n g all available p r opell e r . . .'
. , t e st d ata . The sh aft horse p ower , thrust, p ro p e ll er ro ta tion al sp ee d , ve l oci ty an d ' d i a m et er ar e i n clu d e d in t h e non - dim e n s ional fo r m of torque coefficient , C Q o r Q C , _. thrus t coefficient, CT o r TC, an d ad van ce r at i o , J d e fin e d a s foll o w s: j = !01.4 VK ND SHP ( Po /P ) 1011 for J _ 1.0 C Q =.
41r N3D 5 • 11 = x - - fo r J>l. 0 Q c Slip ( Po / P ) 1 0 1 4 v N 3 D 5 j2 1.514x106 T ( Po/P) C T ..... for J_ 1 .0 N2D 4 T C = -I'B14xl06T(p° /P). x --- f o r J >l.0 N2D 4 j 2 where: SH P - shaft ho r s e pow er P o / P - rati o of density at s e a l e v e l standard day to density for a sp ec ific op e rating condition N - p rd p ei.l er s p ee d ., rpm D - p ro p ell e r d iam e t e r , f t T - p rope l ler thrust, pounds :, VK - fo rwa rd speed ve l ocit y , k nots Base c urve s hav e b een d e f in ed in th is ma nn er fo r a 3 blad e d, 100 a c t i vity fact o r, :: 0 . 4 int eg r a te d desi gn lif t coeffi c i en t prope ll er . The t erms e ff ective tor q ue coefficient, :_. CQE o r Q C E , a n d e ff ec ti v e t h rus t co eff i c i e nt, CT E or TC E, a re us ed. A s with t he "., forwa r d fl i ght g ener al iz ati on , the se ba se cu rv e s w i th app r opr i at e adju s tment s f o r AF, ... C L i an d n umber of b la des can be used in predic t ing reverse thrus t ch a racteristics .. f or the fa mi ly o f pro p e ll e r s sp a nning 2 to 8 number o f b lad es, 8 0 - 2 0 0 AF , and 0.3 to • 0 .8 CLi . The eff ec tiv e torque coeff icien ts and thru s t co e ffi ci e n t s are defined as follows : C QE = ..... Q C E = [Q c x ( 3 / B) 0 o 8 3 x QAFJ - AQCE2 ( PC R / 1 0 0) for J • 1° 0 CTE = [C T x (3 / B) 0. 83 x TAF 1 - ACTE 2 ( P CR / 100) f o r J _ 1.0 TC E = IT c X ( 3 / B ) 0.83 x T A F ] - ATCE 2 ( P CR / 1 00) for J • 1 .0 wh e r e : !: CQ - t or que c o efficien t fo r J _ 1.0 ( 3 / B)0 .83 - numbe r o f blades, B , adjus t ment QAF - act i v i ty factor adjustm e n t fact o r to torque (fig . 11) A C QE 2 - i n tegrated desi g n l if t c o e ffi cien t adj u stme n t fac tor to torque fo r J < 1 . 0 (fig. 12) P CR - pe r cent a ge o f i nteg r ated design lift coefficie n t adJu n tment fact o r to use (f i g. ].3) Q C - t o rque coeff ic ie n t for J _ - 1 . 0 The base torque perfor n m n ce curves are sh o w n on f i gure 14 .
A Q C E 2 - integrated des i g n l i ft coeffic i ent adjustme n t facto r t o t or que for J > 1.0 (fig. 1 5 ) CT - t h rust c o efficien t f o r J _ 1. 0 i:i: • _ T he base thrust per f ormance curv e is shown o n fi gu re 16.
' .. TAF - activity factor adjustment factor to t hru st (fig. 17) : AC T E 2 - in t e gr ated desi g n lift coeffic i ent adjustment f actor to : thr u s t for J _ 1.0 ( f i g . 18) : : :_ :' i! T C - thrust coefficient f o r J > 1.0 i: .... A T C E 2 - in tegrated des i g n lif t co eff i c i e n t ad j ust_c_lt factor t o • thru s t for J > 1 . 0 ( f i g. 1 8) Co mp uta tional p rocedure. - Usin g the m e t h od d e scribed ab ov e , t h e reverse an gle is c o mp u ted for zero vel o c i t y and a S HP a n d R PM c orr es pond i ng to a s pec i fi c throttle setting and the pre ss ure a n d temp er atu r e cond i t i o n as so c i ated with the airport . With the angle so def in ed, the SHP and RP M and the c o rre s ponding reve rse thru s t s are c o mp u t e d for the rang e o f grou n d run velocitie s. It is reasonable t o a ssu me that fo r rec i pr o ca t i ng e ngine i n s talla ti o n s S H P / N rem a i ns con s t an t t hr o u g h out t he co m pl e t e r e ver s e range and that for power turbine in s tallation s , S B P rema i ns con s tant for the turb i ne s p e ed range encountered dur i ng landing .
:i F o r each thr o ttle setting at zero velocity the f o ll o wing calcu l ati o ns are made t o compute the corresponding reverse angle.
• .. 1. CQ - o alculate f o r given SHP and RPM 2. QAF - read fr o m figure 1 1 for th e s p ecified AF and CLI 3. (3 / B)0.83 .- n u mber of blades , B adjustment, c o mputed 4. ACQE 2 - read fr o m figur e 12 f o r J =0 an d s pecifie d CLI 5 . PC R - 100 f o r J = 0 6. CQE - calculate ( ( 2Q x QAF x ( 3 / B) 0" 83 ) _ A C QE 2 x (PCR / 100) 7 . _ 3 / 4 - re a d from fig u re 14 for CQE and J -_ 0 F o r a r ang e of J ' s th e fol . l owing ca lc u l at i ons a r e made t o defi n e t h e R P M and powe r r e latio ns h i p s ov er the landing r un ra n ge.
8 . J - adva nce r a tio , a ssume a r ang e of JT s 9. CQE o r - IfJ $1 . 0 , re ad CQEIO r J(Item 8 ) a n d re v er s e '_' QCE 1 33 / 4 (item 7) and if J >1. 0, QCE from figure 14 •i_ / :-i '__ 10 . ACQE 2 o r - if J _ 1. 0, rea d ACQE 2 f rc m fi gur e 12 or AQCE 2 fr o m • . AQCE 2 f i g ure 1 5 if J >1. 0 f o r C L i a nd J : 11 . P C R - r ea d from fi gur e 1 3f o r f _ 3 / 4 a ndJ_ 0 .9; for J>0. 9 , .... • ..,_ P CR = 0 : :: _i • i_ : : < '.; .:.:, 12. CQ - c al c ulat e wh e r e .+. CQ E + -: : _:i_ CQ = - ACQE _ x (PCR/1 00) fo r J _ 1 . 0 ! ' QA F x (3 / B) 0. 83 no ti n gt ha t C Q = Q C x j2 CQ = (QCE+AQCE2X (PCR / 1 00 ) fo rJ > l. 0 • ,,, ' ii QA F x (3 / B ) 0. 83 c )_) , 1 4 ...._ . _.............. : . . _ . .... _ , - - , : . - _ _ . _ " " _'_.!_ _: - ' - _ _ : ' _' - _ Fo r tu rb ine eng i ne installa t i o ns, go to item 15. Fo r a ir c r aft with r eci pr oca t ing eng i nes , SHP / N r emains a ppr ox im at ely c o nstant thr o ugh o ut the complete r eve r s i ng c a nge. Theref o re , 1 / 2 13. N - propeller rpm is ca l culated = RPM 1 / C_O-_ where s ubscription 1 refers to item land subscript 2 to i tem 12 SHP1 x R PM 2 14. flH P - ca l c u late - RPM 1 whe r e s u bscript 1 refe r s to i t em 1 m_d s u bsc r ipt 2 t o i t em 1:]. Go to it e m 17.
Fo r ai r craf t w ith t u r b i ne e ngi n e s, SlIP r emains appr o ximately co ns ta nt a nd th e r e i b r e
N
w here t he s u bscr ip t 1 refers t o it em 1 a nd subscr i pt 2 refers to it e m 1 2 .:_. 16. SH P - sa me a s us e d i n item 1 Th e c o rres pond i ng vel oci t ies and r e ve rs e th rus t s a r e com p u t e d a s f o l lo w s .
JxNx D 17. VK - f o rwa r d s peed v e l oc ity in kno ts - - 1 0 1. 4 :_i:_!_ for J ( item 8) , N (i tem 13 fo r r ec ipr o ca t i ng e n gi n e an d :i i te m 1. 5 f or t ur b i ne ins talla tion s) , and D i s prope ll er _. dia meter a ssum e d i n it e m 1 .
18 . C T E o r - i f J_ 1 .0, re a d CT E f o r J (ite m 8) a nd rev e r s e TC E f _ 3 / 4 (i tem 7 ) a nd f o r J > 1 . 0, TCE from figu re 16 19. T A F - rea d fr o m figure 17 f or appropr i ate AF and CL i 2 0. ACTE 2 Or - i fJ _ l. 0, re adAC TE 2 and if J > l. 0 , readATCE 2 A TCE 2 f rom f igu re 1 8 f or C L L 2 1 . CT - c a lc u late wh e re CTE + ACTE 2 x (PCR / 100) CT = forJ_l. 0 TAF x (3 / n) 0. 83 Noting that C T = TC x d2, then / TCE + ATCE2 x (PCR / 10 0 )_ j2 for J _ 1 . 0 C T = ....... --
t )
0.661 x 10-6 N2D 4 CT 22. Thr u st - calculate = , Po / p Thus , f ro m t he eompu t atlons desc ri bed ab o ve, r e v e r se t hrus t, p ro peller speed, th e horsepower can b e plo t ted versus ground run veloc l tle_ for r e verse angles cor_ respoi,ding to specific throttle netti n gs similar to the plots on figur e 1 0 . Then , utilizing standard methods the corr e sponding l m Mlng runway distances c a n be computed a n d the , tpp r opri a te r e vers e angle a n d th r ottle setting s elected .
It e flnem c nt o f Weight Generalizatio n Th e gener_dized weight equation used ill th e previous general aviittlon study (rcf. 1) wits d e rived using w e ights of current high tip speed propellers 'i s a basis.
Five classes o f aircraft arc defined in r eference 1, and the p r opeller categories that 1 correspond to each are as follows: category I - fixed pitch; category II - con s tant speed; category III- constant speed, full feather, deicing (for light twin engine air- .... craft); category IV - constant speed, full feather, deicing (for medium twin engine _ aircr_'t); category V - constant speed, full feather, deicing, rever s e. Comparison of calculated design weights of a low tip speed 1980 technology propeller in each of .... categories II, IV and V with equation weights revealed sufficient discrepancy to make : eq ua tion weight suspect ove r a wide tip sp e ed r ange. As a r esult, this study was :.
' conducted to refine the generalized weight equation to provide reasonable accuracy for propellers encompassing a wide range of tip speeds.
. ,. . , .
...... ; Des i gn weight s w e r e e s tim a t e d for twelve 1 9 8 0 te c lmol o gy propellers i n each of :: _:: ca teg or ie s II , IV and V f o r a total of thirty-six propellers. These propellers were s ele c ted to span tipspe e d, activity fact o r and number of blade s range s shown i n Table :. I. P ropeller diam e t e r, shaft ho rse pow e r and maximum flight M uch nu mb er w e r e held const an t for e a ch c ategor y . P rope l l er weight s were dete r mi ne d by calc u lati n g the weight of e a ch sub- ass embly us ing empiri c al equatio ns and judgeme n t b as ed on expe r ience w i th exi s ting propelle r families. Th e s ub-as s emblie s included b l ade s , blade retentions, barrel, hitch c hange dome and mechanism and f l uid.
The s e propell er weights wer e plotted versu s a ctivit y facto r and tip s peed . The a ppropriate equ a tio n co n stant s w er e modified to provid e correl a t i on o f equation weights with th e calculated wei g hts within te n p erc ent a_,curac y . The expone n ts generalized for the 1980 propellers are a l s o applicable to the 1970 prop e ll e r s w i th the differe n ce in technology for the two e ra s bei n g r efl ec ted i n the con s tant . C o n s tant s were derived fo r ca tego ries I an d III ba s ed on a ct ua l 1 970 p r opel l e r weights _-mdthe gen er alizations for the other c a tegories.
The m o dified gene r aliz e d w eight equa ti o n wi th v a r iati o ns in constan t s and exponents for the five a i rcraft cat e g o ries is sh o wn o n Table II. The s i gnif i cant m o difi- cati o ns to the equation are: (1) in c r e as e d value of the activity fact o r exp o nent in categ o r i es I m_d II reflecting the greater p r oporti o n o f blade we i ght in t o tal weight of the simpler prop e llers_ (2) de c reased vahm o f the tip spe e d exponent in all categ o r i es and (3) th e addition of exp o nents t o the counterwe i ght equati o n f o r greate r ac c uracy .
A c o mpa ri s o n summary of r ep r esentatiw_ 1.0 7 0 ac t ual p ro peller w eights ve r sus weights c alculated from the gen o rMlzed equation is shown in Table III. A summary of 1980 prop e ller calculated w e ights versus generalized equation weights is shown in Table I , It can be seen from Tabl e s I and III thaI; generally there is v e ry good agr e e - m e nt b o tweenweights computed by the weight gen e ralization equation and the actual w e t ghts.
Th e revised w e ight g e neralization deviates the furthest from the previous w e ight generMlzation for c ategory ll propellers since as was shown on Table X in r e feren c e 1, the gen e ralization was the weakest for that classification. Therefore, the weights and coasoquently the costs for the s e nsitivity studies for category II (r_f. 1) s hould be significantly higher. Furthermore , the weight _md cost versus tipspeed curves should have less slope for M1 five categories.
I n th e p r e v ious s tudy ( r ef. 1 ) a g en e r ali ze d c os t e qu ation was de r i v ed which is a functi o n o f pr o pell e r weight. Three p r op e ll er s r epr e se n tative of the 1 9 8 0 tim e p e ri o d were de s ign co s ted. A comparison of the c o st s b a sed o n the s e defi n ed by the w ei ght generaliz a tion a n d those on the d es ig n cost we re made and tab u lated on Table XIII (r e f . 1). Th e ag r eement b e tween the two sets of cost s rang e d fr o m 6 % low to 21 % h i gh. Th e c o sts baseu on the weight equation we re recalculated due to th e revi s ed w e ight e quat io n and a similar compari s on wa s made. An inspe c ti on of Table IV s h o w s th a t the c o st s computed with the generalized cost eq u ation now agree from 7 to 1 5% low and thu s the c ost compar i son has been significantly i mpr o v e d .
The re f i ned gene r alized wei ght equat io n of Tabl e I I p r ov i de s a u se ful tool fo r estim a ting propelle r weight fo r any general a v iation aircraft in s tallation in this de c ade with reasonable accuracy. However i t mu s t be remembe re d that paramet e rs othe r than the ba s ic geometric and pe r fo r mance characteristic s used in thi s eq u ation effect prop e ller w e ight s. Th es e a re variatio ns i n propeller environm e ntal temp er atures, type of control system and the d egree to which individ u al man u f a cturer s design for m i nimum w ei ght.
I n put / Output Addit ion s t o t h e Co mpute r P ro g r am It i s not t he i n ten t t o r epea t t h e d e t ailed inpu t / output i ns tr u cti ons fo r t h e c o mp u t e r program presented in refe r ence 1 but to d e fine t h e additional input required to use the extensions to the compute r program develop e d under th i s c ontract and to p r esent sample output sheets for demonstration purpose s .
q + _ The fo l low in g ad di tiona l input i s r eq u ired to I nc l ude the i n tegrated design li ft c o e fficient v ariati o n o pti o n.
1 . Initial integrated design lift coefficient, CLi 2. Inc r ement of C L I if a range of CLi is to be computed 3. Numbe r o f C Li'S The input for th e weight gene r al, lzat | : an a r emain the _ a me .
To use t h e option of computing rever_ e angle and reverse thrust , the following ll_put Is requi r ed 1 . O p tio n :: 3 2 , S pecify engine - r eciprocating o r l,u r bino 3. Opt i on of includ i ng reverse anglo or ca l culating It 4. SHP at zero velocity , full th r ottle set t i n g 5. Re ve r se an gle at 3 / 4 ra di us i f th i s op t io n i s se l ected i n 3 6 . R P M a t z er o v e l oc ity , f u ll t hro ttle se tti n g " : 7 . I n i ti al thrott l e s et ting i 8. Increment of th r o t t l e s etti ng i f a r ange is to b e cal cu lated 9. Numbe r of thr o ttle s etti ng s [ . ' . :: 10. La n ding touc h down s p eed , kno t s 11. Temperatu r es, °t ' i 1 2 . A lt itud e, ft .
S p e cific i n put instructio ns are i nclud e d i n the Us e r's M anual ,a n d will be discussed i n the fo l lowi n g s ec t i on .
A s ampl e o u tp u t f or a f o rward flight pe r f or manc e c o nd iti o n w e r e integrated design lift c oe fficient , and tipspeed are varie d is s h o w n o n figur e 19. A typi c al r ever s e thru s t computation for a ra nge o f th ro ttle se tt in gs i s p r e se nted on figur e 20 .
1 8
............, .... ..... ¸ - , •
r
USE Rt S MA NU AL
19 / 2o
C O NCLUDIN G REMAR K S ,i.: ; i 2 1 / 22 R EFE R EN C ES 1. Wo rob el , R . and Ma yo , M . : Advan c ed Ge ner al Av iation Pro pell er Study .
NA S A R e port C R 114289, April 1 9 7 1 2 . Wo r obel, R , : Co mputer Pr o gram Use r' s Manu al fo r A d v an c ed Gen er al Aviat i on P ro peller St u dies. T o be p ub l is h e d as a NASA l ow n umber C o ntra ct o r R e port.
23 / 24 TABLEI W EIGHT SUMMA R Y OF PROPELLERS STUDIED FOR 198 0 Math N o. D l a Weight (Lb s ) Class No. Blades (Ft) A , F, SHP RPM Est. Eq,mtion II 0.2 6 2 4 8 I 00 300 955 103 94 1310 111 104 16 7 0 12 0 113 150 955 134 134 1310 148 150 1670 1 6 7 I _3 200 9 56 173 174 13 10 202 194 1670 2 3 1 211 q 1 80 9 5 5 109 11 0 1310 122 123 1670 130 133 IV 0.328 3 9 100 340 95 8 104 104 I Z 30 1 10 112 1480 1 16 1 21 1 5 0 9 5 5 14 3 148 1230 151 1 59 1480 15 9 169 200 9 55 195 195 1230 206 208 1480 218 218 i 4 150 9 5 5 189 184 123 0 20 0 19 7 1 480 211 208 : V 0.368 4 lO 100 6 5 0 860 171 164 1190 180 180 182 5 193 1 95 1 5 0 860 216 218 1190 2 34 240 1525 2 5 9 259 200 860 2 6 3 267 1 190 287 294 15 2 5 318 317 3 1 5 0 860 171 178 1190 1 8 6 196 1525 2 14 21 2 TAB LE II GENERAL AVIA TION Gene ralized Propeller Weight Equation: W ' r _ Kw ('i-_) _t0n2 ] ( M + 1 )0. + c w Where: WT Pz' op . Wet Weigh t , l b s , ( e x cl u des s p in n e r, d ele in g & g o v e r n or ) D = Prop, Die, Ft, B _ N o. o f B l ad o s A . F . Blade A c ti v i t y F ac tor N - P r op . Spee d , R PM ( ta k e- off) S H P S haft Ho r sepower, lt P ( t ake- o ff) M = Nl ac h N o. ( D e s i gn Con di t ion: Max P o we r Crui s e) CW : Y _1--_ ) 2 . - 0 = C o u n t erw eight Wt,, lb s.
K W, C W: u , v and y valu es fo r use in the w e ight equatlo:a a r e t ake n f ro m tabl e bel o w: A i r c r a f t [ '- -¥ e _ o l o gy C la ss I 1970 1 980 Kw u v y --"_ ]_ (1) [ ( 1) ( 1) 1 7 0 0 .9 0.35 0 I {
::_ _i I (2) I ( 2 ) (2) 200 0 .9 0 .3s 0
' ::. III Ii (3) Ii ( 3 ) (3) 22 0 O. 7 0.,4 0 5 . 0 I I
iv I ( 3 ) I (4) (4 > 19 0 0 . 7 0 . 4 0 3 .B
I I . . " VV _ J (5) (5) 190 O.7 O . 30 0 ? .. : P ro pel ler ty p e s a _s o c i a t e d w it h ab o ve Kw a nd C w a re a s foll ows: "..k • :i:,. ( 1) A l l fix e d - pit c h props .' 2 ( 2) Me C auley n o n - eot m ter we ig h te d, non- fe at h er ing , co n st a n t s p eed pro ps (3) All H artzell, all Hamilton Standard small prop s , and feat h ering M c Cauley (4) Fibergla ss -bladed , con s tant s peed, c ounterwetght e d, full feathered (5) Fibe r gla s s-blade d , constant-spe e d, do u ble-acting (non-count e rweighted) , fall feathe r ed, r e v er s t, • 26 t_ I _ . t O tO to tO I0 I0 _0 tO iO _ i f ) iO I0 I0 0 I0 0 L r _ _ D _ I _@ ? _ ,_ _ 2?
TABLE IV O. E.M. SINGLE UNIT COS T SUMMARY OF REPRESENTATIVE _ROPELLEtiS FOR 1980 Ge n e ra li z ed C al mlla t e d E qu at i on D e s l l_l Cost Cost Cost V ariation C at eg ory $ / lb $ / l b % I I 27 29. 1 + 7 IV 35 38.5 +1 0 V : 3 5 41.2 +15 •. : _ o Q 8 1 FIGURE 3. CAMBER FACTOR ADJUSTMENT FOR AD V ANCE RATIO C PE 2 =CP x PA F X PBL X PFCLI 00 0.2 0.4 0.6 0. 8 1.0 EFFECTI V E P OWER COEFFI C IENT, C P E 2 FIGURE 4o INTEGRATED DESIGN LIFT COEFFICIENT ADJUSTMENT TO POWER COEFFICIENT FOR 4--BLADED PROPELLERS 3 3 , ° • ......... , ........... _ ... _ .. _ . _ : _ .... ' :. : .... _ . _ - _ -- _ -- _ - _ .- . . : -. ._: / , -.- t k. _. ; v -.......... _ - -._ . _-_ ...... " _ ' _ -- b , _ ,,, , " _ ' - ' ' _ - --_-_ .___ i C TE 2 = C T X T AI . - X TB L X TF C L i 2 . 8; 0 0 , 1 0. 2 0 , 3 0.4 EFFECTIVE THRUST COEFFICIENT t CTE 2 FIGURE 6 , INTEGRATED DESIGN LIFT COEFFICIENT ADJUSTMENT TO THRUST COEFFICIENT FOR 4--BLADED PROPELLERS ....... _ .. - " - - : ,.... : _ . _ . _ __- _ ,1 II " " --- ' - I FIGURE 8. CRITICAL MACH NUMBER FOR ADVANCE RATIO EQUAL T O ZERO 3 8 _ , _ _ . .___ _ __ . _ / 3 =-12 ' 9 ° , 100 % THROTTLE SET T ING
5 00
b' ) • 40C I
I
__ I " /3 3 / 4 -----9.2° ' 60 % • __ _: 300 _ : £ IL n,
22oo
bl O 2100 a.
2 0 00 L 0 10 20 30 40 50 60 70 LANDING SPEEDS, KNOTS FIGURE 10. EXAMPLE REVERSE THRUST VA R IATION WITH LANDING SPEED AND POWER SETTING • ._. FIGURE 11 . A CTIVITY FACTOR ADJUSTMENT TO TORQUE COE F FICIENT " : 4 o J<_. 1 . 0 FIGURE 12. INTEGRATED DESIGN LIFT COEFFICIENT AD IUSTMENT TO TORQUE COEFFICIENT 100 .............
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• " _I- • ( D n, 2 0 _, Q::: Q:: .. ' : Q- 0 , : 10
o _
-- 30 --20 -- 10 0 1 0 BLADE ANGLE, / 3 3 / 4 • 4 , .: F I GURE 13 . V A R IA TIO N OF PERCENTAGE OF INTEGRATED DES I GN LIFT • COEFFICIENT CORRECTION REQUIRED F OR THR U ST A ND TORQUE - 3 0 - 20 --10 0 10 B LA DE ANGLE, / 3 3 / 4 FIGURE 14. BASIC PERFORMANCE CURVE V A RIATION OF EFFECTIVE TORQUE COEFFICIENT WITH ADV A NCE RATIO & BLADE ANGLE 4 3 _ : _ "_ ,. / 7 ,_ ;, ; ; , • , . r_ ,. , ' :_ ................ _ . , % ' _= t_ , . - , ,, _w , =_= --- "_ '---- _ --' _ ' _"_"_ , _ ._ ' " - -- -- _ , _ Y ' _, ; ,_ . jj{ + #_ -_ ...... 4 . ,= ., 'J_ ; _=; ' C=_=_ , ,. .
FIGURE 15. INTEGRATED DESIGN LIFT COEFFICIENT ADJUSTMENT TO TORQUE COEFFIC I ENT , t , t 3 BLADES / IO OAF / 0. 4 C Li -0 . 4 . - . . -- 3 0 - 2 0 -10 0 1 0 -- 0. 4 - - J .0 ' _ I. d -0 . 3 . _ I- _" _ _ : I Z O _ n o - 3 0 - 2 0 -10 0 1 0 ' BLA D E ANGL E , /3 3 / 4 !
FIGURE 16. BASIC PERFORMANCE CURVE VARIATION OF EFFECTIVE THRUST COEFFICIENT WITH ADVANCE RATIO & BLADE ANGLE , t5 80 1 00 1 20 1 40 160 180 200 ACTIVITY FACTOR, AF' : ;t ' FIGURE 17. ACTIVITY FA C TOR ADJUSTMENT TO THRU6T COEFFICIENT '" 4 6
_ T c E 2 = A CTE 2x0 / J) 2 ( J> 1 . 0 )
F- ( J 0,0 4
q
0 . 03 J < 1 .0 __ O.02 ,.. _ 0.01 • m i h 0 h h l ;' 0 , 0 -0.0 1 • . - .o n_ : Z: 0.3 0.4 0.5 0.6 0.7 0.8 INTEGRATED DESIGN LIFT COEFFICIENT, CLi FIGURE 1 8 . INTEGRATED DESIGN LIFT COEFFICIENT ADJUSTMENT TO THRUST COEFFICIENT - H AM I LT O N STANDARD COM PUTER DECK NO. H6 3 2 CO MPUTE S PERFO R M A NC Ep N OTS F t H E| GHT t AND COS T F O R G E NE RAL AVIAT IO N PR OPE L L E R S 1 C LA S SI F I CATI O N 5 AIR P LANE SAMP L E CASE II 2 REVERSE TH RU ST O PTION R EV ER SF THRUST CO H P U T AT IO N E FCIPR O C AT I NG ENGINE N O F M AL RA _ E C S H P = 550, N ORMAL R ATEO RPM = 2 2 00 .
T OU CH DOHN V-KNOTS = 7 2 .
NU N BER OF BLADES = 3 . A C TIVITY F A CTOR = t09. INTEGRATED CE S IGN CL=.509 THR O TTLE REVERSE REVERSE D TA;_ T S FTT I NG ANG L E V-KNCTS THRUST S HP RP N .... K . _ 100. -1 2.9 C.O 5 24 . 550. 2199, 10. 0 615. 547. 2 188.
? 0.0 71 4 . 54 3. 2172.
3 0. 0 822. 5 38. 2 151.
4 0. 0 93 8. 53 1. 212 4 .
50. 0 10 5 9. 523. 2092.
" 6 0 .0 117 q . 5 1 4 . 20 5 6.
7 0.0 1 3 1 3. 5 0 3. 20 13 , 7 2.0 1 342. 501 . 2004.
8 .5 80. - 11 .2 0.0 380. 46 0. 2 1 q8.
IO. O 4 68. 437. 2187, 20.0 56 5 . 4 34. 2 1 70.
3 0 . 0 67 3 . 4 3 0 . 21_ 9.
6 0.0 790. 4 2 5. 21 24 .
50.0 9 1 3. 4 1 9 . 209 3.
60.0 1 035. 6 12. 2 059.
7 0. 0 1 1 7 3. 406. 201 9, 72.0 1 20 4 . 4 02. 20 10.
8. _ 60. - 9 .2 0.0 208. 330 . 220 0 .
1 0. 0 2 9 3 _ 32 8 . 21 8 4 .
2 0 .0 388. 325. 2 165 .
30.0 4q5 . 3 2 1. 21 4 3 .
40.0 6 1 2. 31 8. 211 7.
_0 .0 737. 313. 2087.
6 0. 0 861. 308. 20 5 4.
7 0 .0 1 0 0 2. 303. 2 018.
7 2.0 10 3 _ . 302. 2 01 0, FIGURE 20. SAMPLE CASE II O F COMPUTER PROGRAM OUTPUT 49 / 50