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# INTRODUCTION TO AERODYNAMICS MECH 594

Rice University

GPA 3.92

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This 9 page Class Notes was uploaded by Shaina Lowe Jr. on Monday October 19, 2015. The Class Notes belongs to MECH 594 at Rice University taught by Staff in Fall. Since its upload, it has received 8 views. For similar materials see /class/224974/mech-594-rice-university in Mechanical Engineering at Rice University.

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Date Created: 10/19/15

Propeller Aircraft Performance and The Bootstrap Approach Background lof9 http www allstarfiu eduaeroBArBackgroundhtm To Javaempowered ALLSTAR Network Level 1 Level 2 Level 3 Level 1 Level 2 Level 3 Level 1 Level 2 Level 3 Hot Links Please let me remind all of you this material is copyrighted Though mrtiallp funded by NASA it is still a private site Therefore before using our materials in any form electronic or otherwise you need to ask permission There are two ways to browse the site 1 use the search button above to find speci c materials using eywords or 2 go to specific headings like history principles or careers at specific levels above and click on the utton Teachers may go directly to the TeacheIs39 Guide from the For Teachers button above or site browse as in 1 and 2 Propeller Aircraft Performance and The Bootstrap Approach J r The Bootstrap Approach Background The Bootstrap Approach The Bootstrap Approach is a parametric performance method You take the airplane out and y it for an hour or two doing very speci c climbs glides and a level speed run Those routine maneuvers must be done at known weight and altitude but it doesn t matter what that weight or that altitude is That gives you the data after you get back down to calculate the parameters making up the quotBootstrap Data Platequot BDP In all the BDP consists of nine parameters When you want to know the airplane s performance 7 say angle of climb 7 under specific circumstances weight and altitude you simply take the appropriate Bootstrap formula substitute in the BDP parameters for that airplane and the 121203 109 PM m A M 39s performance A p r r t r r number Now let39s take a look at where the Bootstrap Approach eomes from u r u Vd gvmv a u u u predret assume that propeller ef clency h ls some eonstant Commonly erteol values are h 80 and h 85 Then thrust T h P where P ls the englne power Unfortunately propeller ef clency ls m fact not eonstant rt vanes wrth arr speeol anol RPM or more preersely wrt the olrmensronless rauo of those two vanables V J 7 1 M where Jls the propeller advanee ratro As the propeller rotates through one errele the the arrplane advanl a drstane Jls then the rauo o at a anee drstanee to propeller39s drameter d Flgure l ls an example of how propeller ef clency vanes wrth advanee ratro Propeller Ef ciency vs Advance Ratio 1m PmPeHer Emmencv Advance Rama 1 e vmu Flgure l Emereney graph for MeCauley 7557 my lZlZDZIEIEPM propeller on some Cessna 172s The basl Bootstrap Approach strangely enough makes no assurnptron about propeller ef clency It has an alternate way whlch we now explam for coml g up wrtln tlnrust Be a hub moves m a sense m tw o duectlons at onee 7 long tudmally wrtln veloerty v and to tlne slde wrtln speeol m2p e tlnere A lelents L er e g lt3 14 s a E g 5 E CPL Lhrhdn rYLL Jquot wmlwmofthe propeller blaole we assume tlne propeller ls ngld enough that rt doesn39t move at all The propeller tlnrust eoemerent ls anol tlne propeller power eoemerent ls Flgure 2 shows for tlne sarne propeller as m Flgure 1 how tlnese eoemerents vary wrtln advanee rauo J Propeller ef clency ean be obtarneol knowlng tlne two eoemerents from C v 17 4 r PrnpellerThrusl and iner Cneff ems 3m lZlZDZIEIEPM my u on u an Advznce ante J the Flgure 2 All the rmportant lnformatlon about a propeller s funeuon ean be rust and power eoemerent funetrons The Bootstrap Approach uses a lrttle known but elose apprommate relatron between these two eoef elents that the sorcalled propellerpolar de ned as IT12 plotted agamst cP ls ll that C 7 lt5 The Bootstrap Ap proaeh depends upon our ndlng those parameters m and b and a few others experrmentally by means of rght tests For the same propeller as above Flgure 3 shows the propeller polar and the best t hne apprommatmg rt The Bootstrap Data Plate To predret the auplane39s performance uslng the Bootstrap method a sorcalled Bootstrap ls a Data Plate or BDP eonsrstmg of mne numbers must rst be aseertamed Table 4 sample BDP for a parueular Cessna 172 auplane Buntstr ap Value Units Aircraft Data Plate Subsystem Item lzlzmz l 9 PM 5m ng area S 174 ti All39frame ng aspeet ratro A 7 38 Alrframe Rated MSLtorque1Iu 311 2 rlbf Englne Altatuole droproff 0 12 Englne parameter c Propeller dlameter d o 25 ft Propeller Parasrte drag eoemererrt 0 037 Alrframe c Alrplane ef clency factor 0 72 Alrframe 2 Propeller polar slope m 170 Propeller Propellerpolarrrrtereept b 70 0564 Propeller Table 4 Bootstrap Data Plate for a partleular Cessna 172 Propeller Polar and Linear Approximation 151 1 1 1 1 1 1 1 V1 1212113 1 my PM crmz cpmz Flgure 3 For rnost propellers the best flt llne to rts polar dlagram as a goodnessrofrflt parameter R1 0 95 or better Where do these mne BDP rterns eorne fr0m7 Flve eorne from the Prlots Operatrng Handbook POH or eornrnon knowledge Those are 1 Reference ng area S174 fcz 2 Wlng aspeet ratro A BZS 7 38 3 Wlng span 35 83 a Mean sea level MSL fullethrottle rated torque MD P 2an PD rated power ltelbf But m rnost of our formulas though rt rnakes thern a lrttle longer we39ll retarn PD and nn 4 The proportronal mechanlcal power loss rndependent of altrtude c whlch ean alrnost always be taken as 0 12 Thls governs fullrthrotde torque at alutude through the power droproff factor Greek eaprtal Phl39 Mo qgtltagtx Mn 5 Relauve atrnosphenc denslty Greeksrnall Slgma s rm where r ls aunospherlc denslty and standard denslty rn o o 7 son lZlZDZIEIEPM my slugrt3 The leerhonored form Gag g and Fanar 193 4 for thrs drop off ractor rs t7 C w 7 17C Ur Propeller drameter 1 5 25 rt To slmpllfy later calculauons rt39s conyenrent to assume a standard werghtquot for the arrplane For our sample Cessna 172 we choose we 24001bf maxrmum cemfled gross werght Standard relauye arr densrty rs taken to be unrty Gllde testfor Drag Parameters or the four remarnrng harderrmrgeL EPD ltems two typrry drag and two charactenze thrust The drag numbers are the usual 5 Parasrte drag coefflclent Cm and 7 Arrplane emcrency factor 2 Getung cDEI and g by the usual method lrnear regressron analysrs of many glldes rs oyerldll Instead srmply nd by tnal and enor the speed s and rts makes s 0 85157 and Fs 0 84281 For conyenrence of the checldng reader we carry more decrmal places than makes strrct sense Consrder that we ume glrdes from 5100 rtto 4900 L Dh 200 rt wlnd rs shallowestwhen product vTth true arr speed umes elap flnd thatmaxrmrzrng V one can Justas well use calrbrated arr speed Vc IS lamr calculamd from Em A 8 Vm A The relatron between true and calrbrated arr speeds rs Gllde angle m calm sed lee rs greatest To Best glrde angle 7 lzlzmz l my PM my 9 J 0 For oursarnp1e Cessna take vcha 58 9 KCAS 115 29 Uses and D1 15 95 see From Eq 91 vTh5 743 KTAS 125 3 Uses From Eq 8 ghs 5 40 deg The two reqmred drag pammeters are obtamed from Wsm Car 7quot lt10 K nVcogS and E 7 mm 75 11 Eqs 10 M11 1 We Ae0720 w1Lh sorne naps extended Chmb and Level thhLTests for Thrust Parameters Our lasttwo BDPnerns are 8 Slope of the hnear propeller polar m 9 Inmrceptof the hnear propeller polar b or severa1 a11ernauve mghttest regrrnens for eva1uaung m and b we choose malrandrenor o 1 an r r urnu VX o r rnaxrrnurn level Ughtspeed VM and Lhen m VX m in m m quot rvhs r negauve ghde ang1e you can aehreve Accordmgly when product VXDL 1s smallest one has found VX For oursarnp1e Cessna 172 assume vex 50 5 KCAS 1021 sec The Lrue va1ue 1s Lhen VTX v TAS 110 0 Uses The Bootsme formula whreh 1dnds polar 1nLercepL 715 S CDn 2 b 2d2 ozszwAV 12 mm 1 my PM SubsLlLuLlng oul sample values Into Eq 12 glves 17 41 0554 We conclude oul fllghttests wth a fullrspeed level lun sull aLSOOO fL sull at 2200 lbf and rlnd VCM 104 8 KCAS 175 9 Used ln the hue Elms n ded ln oul f0 mulas VTM VM 112 9 KTAS 190 5 Used The BooLsLlap rolmula rol polal slope m ls m Jam 7 la mainlpSrrct In K Subsumung oul values Into Eq 13 glves us In 170 The BooLsLlap Data Plate of Table 4 ls complefE Go to next secuoanoosLlap Approach Folmulas and Glaphs The ALLSTARneLwolk would llke to Lhank Dl John T Low of Fllght Physlos rol plondlng ths seouon of narenal and glVlng ALLSTARpelmlsslon to use IL Dl Lowly ls the 1999 l Fll m 12 M h lull 1 ard Wlnnel Th n u m edlted Lhe matenal rol clamy and malnlalns Lhe oopyllghlovel the format of Lhe matenal presentation the marenal ls wholly Dl Lowly s and ls oopyllghled to hlm Aplll 1999 Any quesuons about th5 narenal should be dlleoled to Dl Lowly Send all comments to W o mums ALLSTAR Newark A nexus xzsmled munla Funded n pan by Updaced FequaIy 04 2002 my lZlZDZIEIEPM

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