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NATIONAL ADVISORYCOMMITTEE FORAERONAUTICS TECHNICALNOTE , NO. 1142 i AN ANALYSISOF THEAIRSPEEDSANDNORMALACCELERATIONS OF DOUGLASDC-3AIRPLANESIN COMMERCIAL TRANSPORTOPERATION By A. M. Peiser LangleyMemorialAeronauticalLaboratory LangleyField,Va. - .- Llt3RARYCOP{ 0 23f9s LANGLEY R&~&_ w!!!’ MPTON, VRGINIA -- Washington September1946 https://ntrs.nasa.gov/search.jsp?R=19930081795 2018-07-10T03:09:57+00:00Z

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NATIONALADVISORYCOMMITTEEFORAERONAUTICS

TECHNICALNOTE,

NO. 1142

i

AN ANALYSISOF THE AIRSPEEDSAND NORMALACCELERATIONS

OF DOUGLASDC-3 AIRPLANESIN COMMERCIAL

TRANSPORTOPERATION

By A. M. Peiser

LangleyMemorialAeronauticalLaboratoryLangleyField,Va.

- .-

Llt3RARYCOP{

0 23f9sLANGLEYR&~&_

w!!!’MPTON,VRGINIA --

WashingtonSeptember1946

https://ntrs.nasa.gov/search.jsp?R=19930081795 2018-07-10T03:09:57+00:00Z

NATIONALADVISORYCOMMITTEEFOR AERONAUTICS

TECHNICALNOTE No. II-42

AN ANALYSISOF ThW AIRSPE??DSAND NORMALACCELERATIONS

OF DOUGLASDC-3 AIRPLANESIN COMMERCIAL

TRANSPORTOPERATION

By A. M. Peiser

SUMMARY

AccelerationaridairspeeddatarecordsfromDouglasDC-3 .airplenes

.-

in the form of V-Goperatedover three‘“

transcontinental-routesin the UnitedStateshave beenanalyzedto determinethe influencesof route,forecastimand dispatchingpractices,and aperatingspe.ed_ontheappliedloadsexperiencedduringcommercialtransport”operation.The o~erational-lifeof airplkneswas fo-tid”to be directlyrelatedto the operatingspeedsmaintainedin regionsof turbulenceand to the forecastingfac$~i%16sand dispatchingpracticesof the airline. Dwing a givenperfodof operation,however,~or transcontinentaloperationin the UnitedStates,differencesin routeroughnessappearto be so compensatedfor by the fore-castingand dispatchingpracticesof the airlinesthatroute,s.sa significantparameterin airplanelife,maybe neglected. ._

INTRODUCTION .

The presentreportis the secondpreparedto givethe resultsof an analysisof V-G data--fromcommercial“-transportairplanes.The firstreport(reference1)dealtwith data obtainedfrom BoeingS-307 airfilanesflyingin the Caribbeanregion. The presentreportis concernedwith an analysisof data obtainedwith DouglasDC-3airplanesflyingover threetranscontinentalroutesin ““the UnitedStetes. The datahave been malyzed inaccordancewith themethodof reference2 to indicatethe influenceson airplanelifeof route,.dispakchingend forecastingpractices,and operatingspeed; ‘“._..__

SCO?EAND YYJJ.UATIO~OF DATA

A totalof 133 V-G recordsr&resenting5~F,210hours of’fli@~t_wereevoilablefotithepresentanelys~.s~Theserecordswere obtainedwith the NAc!AV-G recorder(reference3) fromDC-3 air~lsneso;>erateclby threeofthe principalairlinesof the UnitedStatesd’min~t::er~erlodfrom 1937 to 1~~. The rG&ordswere sunpliedto the LanKleyilemori~lAeronauticalL8bor.~toryc~ the~TAcAby ij~e airlj.ne~ ~op~~~r with the dates of installa-tionand removal,the numberof i’fi’ghthours~er record,t~le routxrsflowndurinsthe timethat the recordwesinstalledin the airnl~ne,end occ.s~icnelsupplomencaryremarksrega.rdi.ngunusual.etmos~l;ericcondition orouepetin~vrectices, Sinceno infmmetionw~s madeavailableby–theairlineson the operatingweighbendothercharacteristicsof the alrn-lanespertinenttathepresentre~ort,the design.vsluea as obtainedfromreferences4..to.6have beenused. Thesev~lues~ranresentedin table1, The limitloadfectorof ~.l]~gwas determinedfrom the atk.arairp~ne charect~risticson the basisof tl~erequirementsset rorthin reference7.Thisvaluere~resentstho accelerationtkatwouldresultvfrom an effectivegustvelQcityof:30Kf’~t :?arsecondencounteredat maximumlevel-flights:aedwhe’reK is thegust alleviation“factor;(~~ference7)., On the bssisofthe,.desi~n.~rossw~igh~c-fthe DC-3 alral?ne,& va.LueofK of’1.07has beenuse”din the prasentraport.

A summaryof thd“racordssuppli~dior analysisbyeach of’the airlines(r&ferredto hereinsf’t-e,r.8&.eirli.neaA, ?3,andC) is givanjn tableII-:Recordswere suppligdby airlineA from 193’7to 1~~~+and:tb.esQr~c~rd~hsvebeen separatedIn tablaII accordinvto prawm (beforeWorldWar 11) or war (durincNorl.d;er 11) oosrstion.AirlinesB and C supgliadrecordsd,prin.qonly tke.u?ewarperiod. .InasmuchSS the fliGhthoursper recordforeach airlinecoverada f’alrlywiderm::a,end sinceWemethodof ahalysiswhichhcsbeen azployodrequiresthatthe flighttimtiper recordbe held rassonablyuniform,it WS.Snecossvy t-orestrictthe.an~lysisto smsllor,~roupsof recordsfor w’~ict~tn~ ran:esof flightnourswarenot too greet. The ren~esof fli@~thours thstwereselectedfor e~ch grnu’~of records~r~.shownin tableIItofletherwith a summpmyof the recotds~het..corre.spond~dto thoseranges. The.choicaof a stiitabltiranGsof flighthours is somewh~t-arbitra.ry.The oresentchoices,howaver,

*

b—.—

—.—

--

---

—. .

.-

r

t-

*

.=

. --.

~..:

s“

NACATN NO. ll@ 3

conformto the statementgivenin reference2 of therangesthat are desirablein the applicationof thepresentmethodof ~alysis.

No attempthas beenmade in tho presentanclysisto classifyaccelerationpeaks as due to gusts,gustmaneuvers,or maneuvers. As in reference1, theassumptionhas beenmade that alllarge accelerationsin flightare due to gusts.

METHODOF ANALYSISANDRESULTS

The methodof analysisof the data obtainedwiththe DC-3 airplanesis exactlythe same as the methodused for the date.obtainedwith the S-307 airplanes(reference1). Six valuesars read from eachrecord:the flighttime,themaximumindicationairspeedVm=$themaximumpositiveand negativ~accelerati~n””increments13s=9 and the indicatedairspeeds“V. .atwhichthesemaximun~ccelerationsare experienced.The frequencydistributionsof Vm=, A%MCC? and V. fcr each ofthe airlinesare shownin tables111, m, ~d V,res?ectivoly.Becauseof the essentialsymmetryofnositiveandnegativesccolerationincrements,valuesof A%= were combinedwithoutregardto sign.

With the aid of the computedmean value.-

~ms.x~~~ax or To, and the computedvaluesof the standarddeviation ~ and the coefficientof skewness cc, PearsonType 111 probabilitycurves(reference2) c~.nbe fittedto each of the frequencydistributionsso thatestimatesmay be made of the probabilityof exceedinggiven valuesof airspeedend acceleration.By rnosnsof theseprobabilitycurvesand tho valuesof the averagerecordtime T in tableII, tha ~.veragenumberof hoursrequiredfor each of cirlinesA; B, end C to exceGddiffGrentvaluasof airspeedand accelerationhasbeen computedin the manneroutlinedin reference1.The resultsfor ~irspeedand acceleration656 shoti”infigurGs1 and.2,respectively.The curvesof fi.guros1:.nd2.cremerelyPe8rsonType 111 probabilitycurvesreferredto @ time scale. Valugstakenfrom figures1r.~cl- 2 at the nle-cp~d speed (nine.tenthsof’thomQXimumglidingspeed)of 257,milesper hour and at tho

4 NACATN NO, lti!2

limit-load-fact-orincrementof2.~g of the DC-3 airplaneare summarizedin figures3 end4.

By theprocedurein referencg2, ‘Ylightenvelopes‘Jhavebeen constructedfrom the datafor eech of [email protected],in a givennumberof flighthours,an averageof one airspeedwillexoeedtheenvelope,and an averegeof one positivemdonenegative~ccelerationincrementwill exceedtheenvelo~ewith equalprobabilityof beingex~>ariencedat any airspeed.For comparisonwith othordata,theflightenvelopescorrespondingto 10,000,20,000,and50,000hoursof flight-by airlineA durtngthe vrewarmndwar oeriodsandby eirlinesB entiCduring theprewarperiod,are shownin figures5, 6, 7, and 8,res~ectivaly.The compositeV-G onvalopesrap~sentingall the datesu~pliedby each of the Pirlinesare alsoshownin figures5 t-u8. For :mm?osesof comparisonthe 5000-hour flightenveloe has btionincludedinfiguro8, inasmuches only‘J85 hoursof recordsweresupnliedby eirlineC: On several”ofthe individualV-G recordsthe flight-accelere.tionpeeks et low speeds(100to120 milesner hour)wereex~ungedby trecesonthe reccn?dsceusedby landin[.shocks. The lendin~shocksso oxhibitodon theserecordswerenot includedin thecompositeV-G envelooesof figures5 to 8.

The flightenvelopeshave been converted,by .mosnsof the sharp-edged-gustformula(rof’erence3), to gust-valocityanveloneswhichpredict–thqtin ~ stiatednumberof flighthours,an ~ver~gaof one.upgust and ona downgushwill exceedthe envelooewithoquel prob~bilityofbein~encountered~t any ~irs?eed.:The 50,000-houreffective-gust~ve~ocityenvelopescorrespondingto-the ~O,OCIO-hourflightenvalopesof fi.Gures5 to ~sre presentedin figure9,

PRECISION

r

.-

The precisionof the NACA V-G recorderand thelimitationsof themethodof :nslysisemployedhavebeendiscussedin reference1. The inherenterrorsinthe V-G recordershouldnot exceed*0.2gfor acceler~tion ‘ ‘and 3 percentof thefull-scalevnluefor airsueed.

8

NACATN No. 1142 5

The use of the designgrossweightin the -- .calculationof effectivegustvelocitiesundoubtedlyresultsin conservativegustvelocitiessince,so”fsr as is known,the DC-3 airplmes werenot operatedat weightsgre~tarthan theirgrossweights, 9ohedulcd “----”overatingtimesthatwere suppliedby the airlineshavebeenused as the besis.ofa rough.calculatiw of theaveragegross wei~htof the airplanein flightand,on the avsrage,the effectivegust velocftyappearstobe conservativeby about5 ‘percent. —— _.

DISCUSSION

Applicationof themethodsof reference2 to thedata obtainedwith the DC-3 airplanes.has indicatedcertaintre-ndswithragard to the influencesof route,forecastingand dispatchingyractices,and operatingspe~don the lifeexpectancyof c~mmfircialtransportairplan6s.

For the enalysisit is necessaryto determine.what constitutesa significantdifferencebetweentwoprobabilities. The criterionadoptedin reference1 isemployedherein;namely,if one probabilityis greaterthan the otherby a ratioof more than 5 to 1, thedifferencebetweenthe probabilitiesmay be regsrdedas sipificant.

Route,forecasting and disptitchin.- The combinedeffectson airplanelif: of route and o forecastingand dispatchingpractices,as contrastedwitl~the “- ““separateeffectof oparp.tingspeed,may be determinedb:?eliminating,so f~r es possible,the influencesonthe data of differ~mcesh operatingspeed. Thisdeterminationmay be made by s-electinga representativeairspeedfor each airlineand reducingtlhedata to acorw.onbasisin terms of theserepresentatives~eeds.The speedselectedfor each airlineis the “probablesPeedl{Vp (reference1), which is the speedthat corre-spondsto the maximumaccelarntionincrementon thecalculatedenvelopesof figure~5 to 8. The prob~blespeedis the speedat whichthe maximumac”celcretionincrementswillmost probablybe experienced.

.-

6 NACATN No. 1~2

The influencesof’route and cf dispatch~ andforecastingpracticesara e~ress.adin termsoF theaveragenumberof flighthoursrequiradto cxcaedthoaccelerationthatwouldbe experienc~das the resultOr encounteringa gust of’giveneffectivevdlocity.atprobabl~speed. The effectivogustvelocitychosenfor thisnurposois 37.5Kfeetper second,whoroK isthe gust alleviationfactor(ref’eranco7). Thisaerticularvalueof gust velccitq”was selectedso thatthe timerequir~dto exceedthe result-ingaccelerationswouldbe roughlycomparablet-othe timercquirodtoexcoadthe”limitlo8df8ctor. Th6 averagetimerequiredto exceedthe accelerationincramantnroducedby a gu~t--velocttyof 37.5Kfeetper secon~at probeblespeedfor e~ch of airlinesA, E!,andC, as detwminedfrom f’iguro2, is shownin figurs~. Sinc5the timescaleon thisfigzgpis lo~arit:q~c$the 5-to-lcritoribnfor Si-@ific&ntdifferencesmay be rapressntedby a constantlengthand is includedin tho figurof’ornurposesof comparison.It will be notedthcttt~odif’feranczsemongthe eirlinosfor prowaroperationst?ra not significanton tho basisof the 5-to-1crltm?lon.Thus, at leastfor transcontinentaloper~tionin theUnitedSt~tes,differencesin routeroughnesse;>pesrto be so con~ensatedfor by v~riationsin the Pmre.castingsnd dispatchingpracticasof the aj.rlinasthabrouts,as a significant>aremstarof?airplanelift?,may beneglected.

For@cestinszend dispatchingover a givenroute.-The fact thPt d8tE from airlineA ~p~ ava>lab~+for bothnrewarandw~r ~ari,odssffordsti @20rtuni.tyto d~tirjtin~the effecton airplanelifec~ changesin forecastingand dispatchingtechniquesover a givenrout=. Duringthe war period,eitherbecauselesg fi.dequatefacilitiesfor foracast-ingwere availableor ljbcausodisp~tchin~techniques.wore deliber~tulyrel~~ud,thzrairplenosworeflOWnthroughturbulentair th’~t WCN.I~dhavd cm.medflightc~ic~lation in the prewarperiod. A directevaluationof the effectof ‘thesech&ngosmay bo m~dofrom tho timesrequiredto exceed~ effsctivagustvelocityof 37.5Kfeetper second&t-pP-oh.ablaspaed(fi~.~), In feet,figure ~ indicntesthat the ev~regotimeraquiredfor airlineA to exceedthisvsluaWQSdacreasodby a factorof 10 during$he war nwiod.Sincethe probablespeedfor airlineA is the same

.-

b

9

?

NACA TN NO. 11.42 7

for both periodssso that a generalsimilarityofover-alloperatingspeedsfor the two periodsmay beinferred,the indicateddecreasein timemay be attri-buteddirectlyto the greaterturbulenceexperiencedduringthe war periodas a resultof eitherless adequateforecastingfacilitiesor relaxeddispatchingpractices.Thus,forecastingand dispatchingpracticesover-a-givenrouteare of appreciableimportancein determiningair-planelife. .,—

—-Operatingspeed.-Sincethe parametersof route,

forecasting, and dispatchinghave been shownto have hadno significantinfluenceon airplanelifeduringtheprewarperiod,whateverdifferencesexistamongtheoperationallivesfor the threetirlinesmust be attri-butedto otherfactors. The o~erationallivesmay bedetermineddirectlyfromfigure3 in termsof theaveragefltghttime requiredfor each airlineto exceedthe limitloadfactor. Althoughthe valuesgivenforairlinesA and B are in essentialagreement,theoperationallifefor airlineC is significantlyhigherthanthe others. In fact,airlineC exceedsthe limitloadfactoronly aboutone-tenthas oftenas do airlinesA and B. The valuesof probablespeedin figure3 showthatthe differenceis due to the fact that the airpltiesof airlineC are flownat low speedsin regionsofturbulence.WhereasairltnesA and B have probablespeedsof 175 milesper hour and 170 milesper hour$respectively,with resultingoperationallivesof aboutequalmagnitude,the probablespeedof airlineC is only14.5milesper hour. Thus operatingspeedin turbulentatris apparentlyof primaryimportancein the determinationof the operationallife of airplanes.

Excessivespeed.-The resultsshownin figure4,,in whichthe timerequiredto exceedthe limitloadfactorin figure2 ~d the time requiredto exceedplacardspeedin figure1 are summarized,indicateadirectrelationshipbetweenthesefactors. Such arelationshipmightbe expectedif, as can be reasonablyassumed,transportairplanesare neverintentionallyflownat excessivelyhigh speedsand thesespeedsareattainedonly as a resultof the loss of controlinturbulentair.

8

CONCLUS1ONSt

.

An analy~lswas made of the V-G records obtainedfrom ?)ouglaeDC-3 airplanesduringcommercialtransportoperationoverthreetranscontinentalroutesin theUnitedStatesto determinethe effectsof route,forecastingand dispatchingpractices,and operatingspeedon the applledloadsexperiencedduringcommercialtransport0?f31%ti011.The analysisindicatedthefollowingconclusions:

1. For transcontinentaloperationin the UnitedStates,differencesin ‘routeroughnessare so compensatedfor by variationsin the forscastirigmd dispatchingpracticesof the airlinesthat route; as a significantparameter.inairplanelife,may be neglected.

2. Forecastingand d~spatchi~.practicesover agivenroute,as reflectedin differencesbetweenprewarand war operation,are of appreciableimportanceindeterminingairplanelife.

3. Operatingspeedin regionsof turbulenceisof primaryim~ortancein thedeterminationof–theo~erati.onallifeof’air~lanes.

4. The averagetime requiredto axaeedthe olacardspeedseemsto be directlyrelatedto the averagetimerequir~dto exceedthe limitloadfactor.

LangleyMemorialAeronauticalLaboratoryNat~onalAdvisoryCcmmdtteefor Aeronautics

Langl$yField,va,; April16, 1946

NACA TN NO. Il.!@

REFERENCES

9

1. Peiser,A. M., andWalkep,W. G.: An Mdysis Of theAirspeedsand NormalAccelerationsof BoeingS-307 Airplanesin CommercialTrmxsportOperation.NACATN No. 1141,Igl+6.

2. Poiser,“A.M., andWilkerson,M.: A MethodOfAnalysisof V-G Recordsfrom TransportOperations. “NACA ARR NO. L5J04,1945.

3. Rhode,RichardV.: Gust @ads on Airplanes.SmJour., vol.40, no. 3, l;arch1937,pp. 81.-88.

~~,Walker,WelterG.: Gust hads on Trmsport Airplenes.NACARB, JUIY 19J2.

5. Anon.: Interdependenceof OperatingTechniqueendAircraftStructuralDesign. DouglesAircreftCo., Inc.,Aug. 1, 1945.

6. ~on.: Priveteand CommercialAircreft. AeroDigest,vol. 38, no. 3, March194.1,p. 138.

~. ihOI1.: Airpl~neAirworthiness.Pt. 04.of Civil:tiro.Manual CAA, U.S. Dapt.Commerce$Feb.

L1, 1941,

sec.O .2121.

NACATN NO. ll@

TABLEI

?

CHARACTERISTICS5F

Grossvi~l.~t,

Wtng are~,sq

Wing span,ft

lb

ft

Mean ~.erodynamic

● ☛☛✎✌

● ☛☛☛☛

chord,ft

Slopeof liftcurva,

Aspectratio . . .

Maximumlevel-flight

Placards?eed,mph .

Limitloadfector,g

.*-

● ☛✎

99*

● **

per rndi8n

.* ...*

speed,mph

● 9 b**.

. . . . . .

9

.

DC-3 AIRPLANES

s

.

.

.

.

8

9

.

.

25,200

● 937

● *95

11.5

4*79---— .. ..-_—

● 9.1

● 211 .-

.257’ -.-?.lJ}

NATIONALADVISORYCOMMITTEEFOR AERONAUTICS

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NACATN NO. 1142

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TABLEIII

FREQUENCYDISTRIBUTIONSWD STATISTICALPARAMETERSOF Vmu

Veloclty(mph)

190to194195to 199200to204

205 tO 209210tO 24

215tO 219220to224

225to229

230to254251jto259

*O to.244245to249

250to254255to259

260to264

?requencyforal~lfqeA,prehar

1

4

34

2

1

15

229.88.31.04

FrequencyforairlineA,

. Wer

1

31

42

52

1

1

20

227.812.70.77

FrequencyforairlineB,prewar

4

76,

13

31

11

1

37

215.7

9.9

1*M

FrequencyforairlineC,prewar

1

1

332

1

11

206.68.70.79

NATIONALADVISORYCOMMITTEEFORAERONAUTICS

.

.

NACA TN No. 1142 *

TABLEIV

FREQUENCYDISTRIBUTIONSANDSTATISTICALPARMETERSOF AM=

AoceleretionFrequencyfor Frequenayfor Frequencyfor FrequenoyforIncrement airlineA, airlineA, airlineB, airlineC,(gunits) prewar war $rewar prewar

0.30to 0.39 10.40to 0.49 2

0.50to 0.59 1 2

0.60to0.69 1 3 10.70 to 0.79 1 2 1. 30.80to 0.89 2 9 30.90 to 0.99 2 2 6 2

1.00to 1.09 4 5 8 31.10to 1.19 4 2, 4 2

1.20to 1.29 6 5 91.30to 1.39 4 4 61.40to 1.49 2 5 5 31.50 to 1.59 1 31.60to1.69 k- 2

1.70 to 1.79 3 1 2

1,8otO 1.89 3 2

1.90 to 1.99 1 32.00 tO 2.09 1 1

2.10 tO 2.19 2

2.20to 2.29

2.30 to 2.39 1

z.l+o tO 2.h9 1Total 30 40 74 22A—ii= L23 1.45 1.21 0.89u 0.30 0.39 0.34 0.32a 0.46 0.48 * 0.74 0.25

,–

,

\-

NATIOIJALADVISORYCOMMI!WEEFORAERONAUTICS

NACA TN No. 1142 14

TABLE v

FREQUENCYDISTRIBUTIONSANDSTATISTICALPARAMETERSOF V.

VelocityFrequencyfor Frequencyfor Frequencyror Frequencyfor(mph) airlineA, airlineA, airlineB, airlineC,

prewar w= prewar prewai

.100to 109 3 1

110 to 119 1 3 4

120 tO 129 6 3130 to 139 1 2 8 2

40 to49 3 1 5 8

15050159 3 3 13 4160to~69 4 5 9 3170to179 6 6 13 1

180to189s

7 6- 8

190 to 199 2 “4 5 1

200 tO 209 “3 7 2

Total 30 40 74 22I

To 172.0 168.5 158.9 U9.5 ~a 21.2 30.9 24.2 16.4

a -0.57 -0.75 -o ●22 0.73\

N&l?IONALADVISORY .COMMITTEEFOR AERONAUTICS

.

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NACA TN No. 1142

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IISORY

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COMMITTEEFORAERONAUTICS

230 ‘ 2%0 250 Z60,.. -

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robe ~f cwqpeed.-

NACATN No. 1142 Fig. 2

,

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Limit-l~d-fuc+o~ _/ncremeni %

AAm e A (brewut-) Iij,o’?<‘l-

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NATIMAI.ADVISORY z

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NACATN No. 1142

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/05

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.Fig.4

Averiget~meb exceedlmvt-&d-&c for/ncremgnfihr.

figure4 .— Relation kt..een uremige time requmed toexceed hjt-bud- 7%TC+OP~ncrement und averagefm7e reqw-ed ib exceed phcurd speed

NATIONALADVISORYCOMMITTEEFORAERONAUTICS

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.31 I I I I 1 I I I

/00 /28 /’ /a? /80 m 220 240 Z’60lncitca?%d airspeed, mph

figure 5.- Coqournon of culcu)uteo’ fljgh+ ewelope~ w% complti of V-G

envelopes obfamed by a/r/lne A dur)ng pre w or open.v+on.

● ✎ ✎ ✎ ✎

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F/gure 6’.- Comywr/son of mlcuiu+ed f//ghten~e/opes WI+h composn% of V-G 1-m“

Mvehjoes obtwned by mrllne A during wur opero??on..(n

.

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<~ I I I 1 I I I I

Aw /25 /?0 /60 MO m (m 240 Ztii9/na’/cuh’ mrspeeo’, mph

F/gure 7.-Compur/~on of colculutid flight envelopes wlfh composite

envehpe.s obiimeo’ by cmlhe B uimng pre WUT opru170n.

. . . .

1 1,.

of Y-G

.

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I \ NATIONAL ADVISORY

C@YMW!e of 4485h(XrIfJ WMMTE FOR#fMUUTICS

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/nd/cu+ed arqoeed, myvi

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Figure @ .- fftedwe -gust- vekwfy envelqoes tbr 50, I&W hum of oprohm .

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