Performance study of the 1911 Wright Brothers model B aircraft and propeller

Rochester Institute of Technology

RIT Scholar Works

Theses

Thesis/Dissertation Collections

1999

Performance study of the 1911 Wright Brothers

model B aircraft and propeller

Robert Egenolf

Follow this and additional works at:

http://scholarworks.rit.edu/theses

This Thesis is brought to you for free and open access by the Thesis/Dissertation Collections at RIT Scholar Works. It has been accepted for inclusion

Recommended Citation

PERFORMANCE STUDY OF THE 1911 WRIGHT BROTHERS

MODEL B AIRCRAFT AND PROPELLER

Robert Egenolf

Mechanical Engineering Department

Rochester Institute of Technology

Rochester, New York

A Thesis Submitted in

Partial Fulfillment of the

Requirements for the

Degree of

MASTER OF SCIENCE

In

Mechanical Engineering

Approved by: Professor

_

Kevin Kochesberger, Thesis Advisor

Professor

_

Dr Alan Nye, Professor

Professor

_

Dr. Ali Ogut, Professor

Professor

_

PERMISSION

TOREPRODUCE

Thesis Title.

PERFORMANCE

STUDYOF THE 1911 WRIGHT BROTHERS

MODELBAIRCRAFTAND PROPELLER

I,

Robert

Egenolf,

hereby

grant permissionto theWallace Memorial

Library

ofthe

RochesterInstituteof

Technology

toreproduce_mythesisinwholeor part.

Any

reproduction can notbe usedforcommercial use or profit.

FORWARD

Iwouldliketo take this_opportunityto thank thepeople whohave helpedme

throughout _mycollege career and_{in reaching my}goal ofgraduation.

To my advisor,Kevin

Kochesberger,

Iwouldliketoextend_mythanksinthe time

and efforthe putforward

helping

me conceivethisproject and

bring

ittofruition. I

would alsoliketo thankhim fortheplane ridesdownto thewindtunnelat

Langley,

Virginia.

To Ken

Blackburn,

Iwouldliketoextend_mygratitude andthanksforall ofhis

help

with_sortingouttheinputs forthe softwareprogramand all ofhisadvice_regarding

this thesis.Withouthistremendous effort,Iwouldstillbe inthedarkon_manyofthese

issues.

To my

family, Joyce, Bruce,

and

Eric,

Iwouldliketoextend_mygratitudefor

theirconstantsupportthroughout_myeducation,hereatRITand evenbeforehand. Icould

nothaveaccomplished_mygoals withouttheirencouragementand confidence_{in my}

ABSTRACT

Aperformance evaluation ofthe 1911 WrightBrothers Model B aircraftand

propelleristobepresented.

Background,

_contemporaryaviation

history,

andtheWright

analysis will precedetheevaluationinordertorecreatethesituation inwhichthe

Brotherswere operating.

Following

thisbrief

history,

theories _regardingpropellers will

beexaminedinordertounderstandbetteran_efficiencyevaluation.

Finally, theoretically

generateddatawillbecomparedto theknownvaluesatthetimeoftheModel B's flight.

Theoretical datawillbegatheredfromtwosources;

(1)

a software program

dedicatedto the_efficiencypredictionof_propellers,and

(2)

a

drag

_studyconductedonthe

Model B aircraftitself. The inputs forthe software programwillbe discussedaswellas

theprocedurefor operatingthe software.Outputswillinclude graphs,specifically

efficiencyandavailablepoweratcertainspeeds.

Following

thischapterwillbea

drag

studyoftheModel B aircraft, which willincorporatethesoftware graphs and producethe

aircraft's cruise speedandclimbrate.Afinalchapter will discusstheseresults and

recommendfurtheravenues of study.

Finalresults ofthe performanceevaluation ofthe 1911 Wright Model B aircraft

haveshown_relativelyclosecorrelationtotheoriginal numbers measured and calculated

by

theWright Brothersthemselves. Cruisespeed and overall_efficiencyas predicted

by

TABLE OF

CONTENTS

Pages

I. GreekLetters 7

II. Dimensionless Parameters 7

III. Variables 7-8

IV. ListofTables 9

V. ListofGraphs 9

VI. ListofFigures 9-10

Chapter 1- Introduction

1.1

Contemporary History

11-12

1.2 Background 12-13

1.3 Wright Brothers ExperimentsandAnalysisofthePropeller 14-18

1.4Objective 21-22

Chapter 2- Propeller

Theory

2.1 Simplified Momentum

Theory

23-28

2.2 Blade Element

Theory

28-34

Chapter 3- PropellerSoftware Program InputsandResults

3.1 Propeller Software Background 35-39

3.2 Selected Inputs forthePropellerProgram 41-43 3.3 Output Results fromtheSoftware Program 44-49 Chapter4- Performance Evaluation_oftheWright Model B Aircraft

4.1

Drag

Analysis ProcedureoftheWright Model B 50-55 4.2

Drag Study

NumericalAnalysisandResults 56-65

Chapter 5- Discussion_ofResults

6.1 Climb SpeedandClimbRate 66

6.2 Performanceat

CL

Max 66

6.3 Cruise Speed 66

6.4 Propeller Performance 66-67

Chapter6- ConclusionsandRecommendations

6.1 Conclusions 68-70

6.2Recommendations 70-72

VII. References 73-74

I. Greek

Letters:

Q : angular_velocity

p:

density

r\ : _efficiency

-: pi

u. : axial_velocity

a : angle ofincidence

O :blade angle

cj) :bladeangle

-angleofincidence

y:effect of profile

drag

oftheblade

II.Dimensionless Parameters:

J : advanced ratio of a propeller

III.Variables:

V: freestream velocity

v : incremental_velocity

pA : initialpressure

p'

: incrementalpressure

HA

:initial head flow

A: area

E :_energy

T: torque

Ta

: torqueavailable

Pa

:power available

r : radius

a'

: rotational interference flow

Cd

: coefficient of

drag

Cl

: coefficient oflift

M : resultant_velocity

c : chord oftheairfoil shape

s : _solidityofblade

N :number ofblades

n :

frequency

L:thrust(Wright Brothers

Theory)

K: airpressurecoefficient

SWing

: total_wingarea

S :reference area

A=AR : geometric aspect ratio

Ai :effective aspectratio

e : correctionfactor

b : wingspan

h : height betweenwingson abi-plane

W : weight

Q

: torque

CT

:coefficientofthrust

IV. ListofTables: _page

Table 1 :Tableof_{Software Inputs 42}

Table 2 :Flyer

Drag

Coefficients

60

Table3 : B

Drag

Coefficients

₆₁

Table 4: B

Velocity/Drag

Force ₆₃

Table5 :B PowerRequired ₆₄

V.ListofGraphs

Graph 1 :

Efficiency

vs. Speed 44

Graph 2 : HPvs. Speed ₄₅

Graph 3 :

Efficiency

vs. Advanced Ratio 46

Graph 4: Thrustvs. Speed ₄₇

Graph 5 :

Cp

vs. Advanced Ratio 48

Graph 6 :Ct vs.Advanced Ratio 49

Graph 7 : Flyer CLvs.

Cd (induced)

₅₉

Graph 8 :B

CL

vs.

Cd (induced)

₅₉

Graph 9 :Flyer

CL

vs.

Cd (induced/total)

₆₀

Graph 10:B

CL

vs.

Cd (induced/total)

₆₂

Graph 1 1 :Power Requiredvs. Power Available 65

VI. ListofFigures:

Figure 4 :Blade Element

Theory

Diagram 31

Figure5 : Software Program Diagram 36

Chapter

1

:

Introduction

1.1

Contemporary

History

Inordertounderstandthemagnitudeofthe accomplishmentthat theWright

Brothersset out_{to achieve,}abrief descriptionof_contemporary

history

in aviation willbe

divulgedtothe reader.Atthe timeofthe

Brothers,

no onehadyetdeterminedtheforces

in action on aerial propellers. Inmarine_propellers,mostknowledgewas empiricaland

needed experimentationtoreach perfection.

Transferring

marineknowledge intoaerial

propellerknowledgewouldbe impossibleand not reasonable.

Up

tothispointin_aviation,propellers were_onlyabout40%efficient with some

ofthebetter designs andbettercraftwork_reachingashighas55%. Thesenumbers might

seem

high,

buttheWright Brotherswishedto gohigherand surpasstheprevious designs

and goals.

Settling

forwhat other peoplehadconstructed was unacceptableto the

Brothers. For_{example, Santos-Dumont's Bird of}

Prey,

required50 HPtobecome

airborne. _{This relatively high}power numberindicatedthat thepropellers musthave been

inefficientandtheplane was_probablyoverweight.The goal oftheBrotherswastouse a

motorcapableof_{only 8 HP This}tremendousdifference inrequirements exhibitsthe

ambition and_engineeringskillpossessed

by

theBrothers.More horsepower

instantly

meant alargerandbiggerengine.

This,

in turn,meantthat theplane would_{automatically}

gainin weightfromthemotor alone.Thepredicted weight ofthe_{Flyer only}allowedfora

smallmotor,light inweight.

Casting

processesofthe

day

also preventedthelarger

motorsfrom

losing

alotofweight.Propellershadtobe more efficientthanthose

centralhubwithout

taking

intoconsiderationthecurvatureoftheupper surface which

dictates theliftandinthe case of a_propeller,the thrust.

Fortheirachievementinaviation,

including

theplane and_{the propellers, the}

WrightBrothers were considered pioneers andinnovators intheirfield. Nowthat the

readerhas abetter_{understanding} ofthetimeperiod,amorein depth lookattheWright

Brothers willbe

discussed,

as

they

arethe mainfocusofthisdocument.

1.2Background

Inthe_{early 1900's}ateamoftwobrotherswouldbethefirsttoachievethe

unreachable goal of sustainable poweredflight. OrvilleandWilbur Wrightwould

revolutionizethe

industry

with ahomemadeplane and onehistoric flightat

Kitty

Hawk.

Butthis tremendousaccomplishment was not withoutits obstacles andtechnical

challengesthat

they

wouldencounteronmorethenone_occasion,bothanticipated and

unforeseen. The lastaspect oftheplanetobedesigned beforethe flightwasthe

propulsion _system,

including

theengine/motoritselfandthemeans

by

whichtheengine

power wouldbetransformedintothrustorforwardmovement. Bothofthesecomponents

would provetobethelargestobstaclesofthemall.

Ownersandoperators of abicycleshop,theWright Brothers had littletono

experienceintheengine

building

business.

They

hadconstructed aone-cylinder engine

topowertheequipmentintheirshop butthatwastheextent oftheirexpertise. When

they

firstconsidered powerplantsfortheir plane,

they

contactedautomobile engine

manufacturersand gavethem their specifications,whichhadbeencalculated and checked

manufacturer atthe timecould meetthedemandsofthebrothersand;therefore, the

engine wouldhavetobeconstructedfromscratch andbepurpose-builtfromtheonset.

Luckily

one of_{their employees,}Charlie

Taylor,

hadabitmoreengine experienceand

almost single

handedly

builtthebrothersafourcylinder enginefor_{their plane,}andto

theirspecifications.

However,

oncethisproblem was_overcome,a_seeminglypremature assumption

made

by

thebrothers wouldturnintoa_{revolutionary idea}anddesigninthearea offlight

propulsion. Thepropellers requiredtotransformthe_energy atthe outputshaft ofthe

engineinto forwardmotionthrough theair wouldbereinvented,in everysense ofthe

word.Noonepriorto theWright Brothers hadunderstoodthedynamicsanddesignof

propellers.

"

Maxim/Langley

developed great motorsbut

terribly

inefficient

flat-bladedpropellers

"

Mostofthework completedinthisareaexisted_{only in}thearea of marinepropellersand

not airplane propellers.The brothers believed

they

couldjustsubstitute air pressurein

placewater pressureandachieve propeller performance predictions.Aquicklook into

thisassumption provedthis

theory

would notbeapplicableto theirsituation. Withall

previouswork

being

_entirelyempirical and nottheoretical,theWright Brotherswere

forcedto

develop

theirown equations andcalculations inordertoconstructthecorrect

propellersonthefirstattempt(Notethat

they

didnothavethecapitalto_relyon the"cut

and try"

methodemployed

by

other_contemporaryinventors.).With onlyone attempt at

their grasp, theircalculationshadtobecorrect and_predictingthe_efficiencyofthe

1.3 WrightBrothers'

Experiments

andAnalysisofthe Propeller

(Flyer)

Before completingtheirdesign fortheairfoilpropeller, theWrightBrothers

conducted various experiments to

help

themdetermineshapes, sizes,and speedsfortheir

design.

Specifically

they

conductedfanscrew and propeller experimentsina scaled wind

tunnel

they

hadcustombuilt forthisspecific purpose.

These,

_alongwiththe analysis of

theireventual propeller willbeundertakeninthisportion ofthechapter.

Forthefirstoftheirexperiments,

they

employedfan bladesand a motor(the

motor was_probablytaken fromtheir_{bicycle shop}where

they

usedittodrivesome of

theirpower equipment).

During

theseexperimentsthebrotherspaid close attentiontothe

Centerof

Pressure,

which is defined

differently

fromthe_meaningassociated with a

horizontalwing. This

they

defined as ablade sectionlocated 5/6oftheradius_{away from}

thehub. There

they

measuredor estimatedbladeangle,camber,rotationalvelocity, and

angleofattack.

They

usedthesecrudebladestocreate_earlymodels ofthepropeller

bladesand

help

themvisualizehowthe_propshould

finally

appear. Thesewere_{only early}

experimentsand so

they

moved ontopropellersthat_{eventually became}alotmore

sophisticatedand alotcloserto theirultimategoal.

Thepropeller experimentsagain usedthesame motor asthefanscrew

experiments,mainly duetoafailureofthelargermotor.Thepropellers were similarin

lengthto thefanscrewbut differed in bladewidth andbladeangle.The Brothersaltered

these twovariablestogain thebestthrust/liftdesignthatwould suit theirneeds.

They

determinedthatasthelengthoftheblade

increased,

theblade sections nearthehub

became.The Brothers developedanequationforthethrust/liftofthepropeller andit

appears as follows:

L

=

KxVxSxCL

(D

whereL_{is thrust,} A"

isan air pressurecoefficient, Vis the_{velocity in}mph,S isthetotal

blade area,andC/,is theliftcoefficient.

By

_{simply understanding} thatliftfora_wing

correspondstothrustfora_propeller,theBrotherswere ableto_applythisequation

directly

to theirdesigns.

Once

they

had finishedthese experiments,

they

coulddeterminethecorrect

propellerfortheplane

they

were

building

basedon some assumptions

they

hadmade at

theonset oftheproject_regardingtheirFlyer.These included:

Planeweight=755lbs

Min velocity for flight=23 _mph

Engine & propweight=200lbs

Total wingarea=500 ft2

They

above mentioneddesignrequirementsdictatedthepropeller'sdesignandits

performanceaswell asthemotor and other_necessarycomponents. The Wright Brothers

keptnotebooksontheprogressionoftheirdesignandanalysisandthe

following

analysis

has beenexcerpted from Wilbur'snotebook

H,

1902-1905.

Efficiency,

asdefined

by

the

Wrights,

becamethe

following

equation:

___ . PowerOutput

(2)

Efficiency

=

Knowing

this relationship,one candeterminethe input

by

_multiplyingthe torqueand

velocityof rotationtoobtain:

40lb

xl2l

ft/

s=

4,

S40

ft

-

lb/s

4,840

550

=

S.13hp

This givesthefirstpart ofthe_efficiencyequation.Now

by

_{understanding}that thepower

outputisproduct ofthethrustandforwardvelocity, the second portionbecomes:

90lbx24

mi/

'hr

=_2,160/m

-Ib/hr

2,160

375

=

5J6hp

where 375mi-lb/hris equaltoonehorsepower. Oncetwoout ofthreevariables have

been

determined,

the _efficiencyequation cannowbeusedtodeterminetheperformance

ofthepropeller asfollows:

__, . PowerOut 5.76

n ,,

Efficiency

= = _{x1 00}=_66% Powerln 8.73

Thiswasthe theoretical number associated withthepropellers used onthe

Brothers'

Flyer.

According

tocalculations

they

hadsurpassedtheachievements of past

aviatorsandbroughtthepropellerintoanewera.Theiranalysis would serve asthebasis

for

designing

propellers for decadestofollow. Neverbefore inaviationhadsuch an

undertakingbeen acceptedandthenovercome. The Brothers hadthelastpiece fortheir

year. Someother_{critical numbers associatedwiththepropellers oftheFlyer}

andtheB

were asfollows:

Flyer Data

Speedof machine=_23mph

Grossspeed_{(forward velocity}of_proprelative to the_air)=44 ft/s

Thrust=90 lbs

Areaofblades=5.4 sq ft

RPM=330

SpeedofCenterofPressure (locatedat5/6ofthe total_radius)= 121 ft/s

Angleofincidence=₇

deg

Normalpressure=_{25.3 lbs}

Weight :755 lbs (withone_pilot)

Wing

area:500ft2

1911 Model B Data

Speedof machine :40mph

Grossspeed: 58.6 ft/s

Weight: 1250 lbs (withtwo_pilots)

Wing

area : 472ft2

RPM :428

where gross speedisthe _{freestream velocity}withouttheadded"suck"_velocityand90lbs

ofthrustistheestimated

drag

ofthe_{Flyer according}totheBrothers.

Along

withthese

numberswere also quite afew tables, _graphs,anddiagrams fromwhichtheBrothers

propeller

design,

inan_engineeringsense ofthe word. The figures (1 and

2)

onthe

-L..A_i...L.,

\

i

./,LU.-._

/

. I--1 a sy 1 i i f1 I

1

, ^*i_ II "^Vi 1 >

_______!$ l i i i \

n

r-#v\

i _j _/

1

^

--f-h. . -.-__

09

-. pa CO .

"

-8

I

I

_. On

5

~

z o

CN

U

00

1.4 Objective

Nowthatthebackground forthe_{study has been}

documented,

the main purpose of

the_studywillbediscussed. Theoverall objective ofthis_studywasto_employcurrent

techniques of propellerdesignand_efficiencycalculationin ordertopredictthe_efficiency

ofthepropeller used ontheWright Model Baswell asthecruise speed oftheplanein flight. Thisprediction wouldbecarried outinanumberof various_ways,bothwith a

computertool and_{analytically in}ordertocapture arangeof sources andtechniques.

The firstofthesemethods wasto_employa propeller performance software

packagein

determining

theoverall_efficiency and poweroftheWright Brothers design.

Having

propellerdrawings available wouldallowdatatobe inputted

directly

intothe

software. Oncethisis complete, thesoftware program wouldbeabletorunthroughits

calculations andsimulationsand output sixperformance graphs(canbe seeninthe

ResultsandConclusionssection)

Thesecondmethod of_analyzingperformancewouldbetoconduct a

drag

_studyof

the overallplane anduseavailable equationsto transform

drag

numbersintoanoverall

drag

force. The

drag

forcewouldthenbe plottedintheformof power required against

power available.Fromthe thrust numbers,powercanbe derivedandthiscanbeusedto

directly

determinetheperformanceand cruise speed ofthe aircraft,

including

maxlevel

Thethirdsource ofdatawouldbetheWright Brothers themselves.

They

conducted an extensive analysis priorto_constructingtheFlyerandthepropeller

efficiencywas a critical part ofthis analysis.Theremethodofanalysisand_resulting

numbers willbeused as a comparisontothe two aforementioned methods.

Following

datacollection, the_efficiencyand powernumbers were compiledand

comparedtothenumber obtained

by

theWright Brothersatthetime theFlyer B was

Chapter

2

:

Propeller

Theory

In orderto better understand how the _efficiency of a propeller is

determined,

a more

in depthexplanation ofthe employed theories will nowbe given. The first two theories are used in

determining

the ideal _efficiency of a propeller. This explanation is necessary

tounderstandhowthesoftware program operatesinthenext chapter.

2.1 SimplifiedMomentum

Theory

(Rankine and

Froude)

Asevidencedin thename_alone,this

theory

of airscrewsdependson a consideration ofthemomentum aswellasthe_{kinetic energy}ofthe system

being

studied. _{Before going}

in depth intoadetailedanalysis ofthis

theory however,

_{it is necessary}tostatethe

assumptions attachedto the theory.

Assumptions:

1. the airscrewisconsideredtobe adisc

(spinning

in_{the air)} 2. thegeneratedthrust_{is distributed evenly}overthedisc

3. anyrotationoftheslipstreamdueto theaction ofthe torque isignored

Nowthat the assumptions_{have been categorically}

described,

the

theory

canthen

besetforth. Asthe fluidpassesthrough the

disc,

anincrementalpressureis added which

is equalto the thrustper unit area ofthedisc. Thiscanbeseenin Figure 3 onthe

following

page.Anothereffect ofthe disc istoformaslipstreamofincreasedaxial

velocitybehindthedisc. The fluid flow frompointAtopointB isregarded as

irrotational,

as_previously statedinthe assumptionsassociatedwiththis theory.Once

theseideas have beenestablished, it isnow properto _{apply Bernoulli's Equation}tothe

fluid flow. Bernoulli's Equationappliedto thediagrammed fluid flowyields anequation

for dynamicpressure as follows:

nA=pA+y2pv2=p+y2p{v+v)2

(3)

where V isthe_{freestream velocity}andvisthe_{incremental velocity}added oncethe

stream passesthroughtheairscrew._p0istheinitialpressurebefore

being

effected

by

the

airscrewand_{p is}thepressurejustpriorto_passingthrough thescrew.

Further,

after_passingthrough_{the prop,}

H

=P,+/2P(V+\f

=P+P

+/2P(V+vf

(4)

where p'

istheincrementalpressureadded

by

theairscrew.

And,

Ap-HB-HA_p(v+

^/vB)vB

(5)

By

consideringthis

Ap,

thethrust,

T,

thenbecomesthe

following

withA=_{area of}

thedisc. This isalso anexpression fortherateof changeinaxial momentum:

T

=

A/7(V

₊

Figure3

[image:25.538.30.509.139.460.2]

Andthisindicatesthathalfofthe added_velocityoccursbeforetheairscrew andhalfofit

afterthe airscrew.

Therefore

_equation

(6)

canberewritten

taking

thisintoconsideration,

T

=

2Ap(V

_{+ v)v}

(7)

HereVcanbeconsideredthefreestream_velocityor gross_velocity and v canbe takenas

the"suck"_velocityorthe_velocityadded

by

theairscrew.

Anexamination ofthekinetic_energyofthesystemreveals anincreaseovertime

inthefluidsystem_{corresponding}to the

following

equations:

E^A^V+v^V+vJ-V2)

(8)

Whichreducesto

E=2Ap(V+v)2v

(9)

Whichyieldsthe

following

after_usingequation

(7)

E_T(V+v)=QQ

(10)

whereQ isequated toangular_velocityoftheairscrew

(27if)

and

Q

isthetorqueofthe

airscrew.Nowthisexpression canbeusedtodefine the totalworkdoneonthefluid

by

the thrust.Oncetheactual andidealwork areboth

known,

an expressionforthe

efficiencyofthe system canbewritten asfollows:

TV

n=^Q

<>

and wherethe total workdoneis

nQ

=

T(V

₊

And if

y=aV

(13)

where ahereisusedtosymbolizea multiplier

Thenthe_{ideal efficiency is}thensaidtobe:

V V 1

rj= = =

V+ v V+ aV 1+ a

(14)

By

constructingthisequationtheassumptionismadethat the_{only loss in}the

systemis dueto the_{kinetic energy}ofthe axial_{velocity in}theslipstream.Butthereare

otherlosses in_{the system,}which areignored inthis

theory

aslisted below.

a) nofriction

drag

oftheblades

b)

nokinetic energy loss intherotationoftheslipstream

c) noloss ofthrust towardsthebladetips

Themostinfluential ofthelistedlosseswouldbe

(a)

becausethereexists alarge amount

offrictionalloss here

depending

onthebladesurfacematerial. Fora quick and

dirty

estimate ofthe_efficiencyof apropeller, one can predictwithsome_certaintythat the

actual_efficiencywillbealmost85% thatofthe_{ideal efficiency}

(#4,

H.

Glauert)

fromthe

aboveequation, whichindicatesthata_studyofthe_{ideal efficiency is}a good guideto

determining

actual efficiency.Anotherversionofthe_efficiencyequation

involving

power, speed,andthe airscrewdiametercanbe derivedwhen one considers power output

versus powerinputtoa_propeller,withthefinalresult

being

the

following

1-7

2P

rj npND

Itcan_{be deduced fromthisequationthatthe}

efficiency falls quicklyasthepower

coefficient

increases,

such as_attemptingtoput alotof powerthrougha_relativelysmall

propeller.

2.2 Blade Element

Theory

(ExtensionofMomentum

Theory)

Asa continuation ofthesimplified momentum_theory,thebladeelement

theory

providesfora moredetailedanalysis ofthepropeller

by

_exploringtheforcesexperienced

by

theairscrewblade. Aswiththemomentum_theory,thereare several assumptions made

by

this

theory

inordertoconduct an analysis and

they

are asfollows:

1. Therotationalvelocityofthe tipsoftheblade doesnot approachthe

speedofsound.

2. The blade isplacedinauniform streamof_{velocity V}parallelto the

axis ofrotation.

Thereexistalso someterms thatneedtobedefined inorderforafullexplanationto

becomeuseful in

helping

oneanalyze a propeller.

Inflow- Flow

immediately

in frontofscrew

Outflow- Flow

immediately

behindthescrew

Wake- Flow in_slipstreamfar behindthe _screw

Interference Flow

-Velocity

fieldof system of

trailing

_{vortices which acts as an}

interference ontheblade elements

Nowthatsomeimportanttermshave been defined forthe reader, a morein depthlookat

the_{activity surrounding}apropellerblade canbe discussed. Inthis _theory,asinthe

timeitissubjecttointerference flowrepresented

by

helicalvorticescreated

by

tip

and

rootblade elements. (Inthis case, theexact effect ofthevorticesis difficulttoanalyze

andthemean valueis_{generallysubstituted.)}

To begintheanalysis,thetorqueofthe airscrew mustbeexaminedand

understoodtocreate rotation abouttheaxis offlow intheslipstream. Notethatthis

rotationdoesnot occurinfrontoftheairscrew or outsidethe

boundary

layer. This

rotationthen transformsintovortices and circulation aroundtheblades. Dueto the

trailing

vortices,theflow intheplane ofthe screwwillhavean angular_{velocity in}the

same sense astherotation ofthescrew. Thecirculation aroundthe screwbladeswill

cause equal and opposite angularvelocities oftheinflowandoutflow.Oncethe flow

motionis understood, theangular momentum oftheoutflow can beexaminedandknown

to_{be closely}relatedto the torqueofthe screw.

Consider bladeelementdrat radialdistancerintheFigure 4. Fromthis figurethe

following

variables andequationscanbe derived. Equation

(16)

showsthatthe

accelerationoftheflow inthe directionofthebladetravelresultsintorque.Equation

(17)

isthentheincrementalthrustforanelement_alongthepropellerblade.

dQ

=torque of this element

u=axial _velocity thru the airscrew annulus

torque=_rate of increase of angular momentum

dQ

=

2-xp

u-2--r2dr

(16)

^

=

4-r> VQ(l+

a)a'

(17)

andais theaxialinterferenceflowwhile afistherotationalinterference flow.

Theaxial_{velocity is}consideredtobecontinuousthrough theairscrew and ubecomes the

axial_velocityattheinflowand outflow. _{In estimating}theaxialinterference flow

magnitude one importantassumption mustbe made:the

trailing

vortices movein helices.

Theinterference flowexperienced

by

thebladesatdistancerfrom theaxis

doesn't dependonbladeelements at otherdistances. Forthisstatementtobe true,

considerthebladeelementdratrfromthecenter whentheremainderoftheairscrewis

not present. The

trailing

vortices which _{spring from}theends oftheelementlieon the

surfaces ofthe twocircular cylinders of radius randr+dr. The vorticity isresolvedinto

twoparts:

1. Axis paralleltothescrew axis

2. Circumferential

The firstoftheseparts acts as a

bearing

betweenthe_rollingshell of airbounded

by

the

cylindrical surfacesandthe generalair.Thistranslates intothe factthat thegeneral mass

of aircannot acquire circulationabouttheaxis andhencetherotationduetothetorqueof

theblade elementis confinedto theregionbetweenthe twocylinders.Thereforethe

rotational interference duetothevortexsystemisexperienced_only

by

thoseblades that

causethevorticity.

Discovering

this

fact,

ageometricanalysisofthevelocities andtheoverall effect

Figure4

Blade

Element

Theory

Diagram

Resultant Force

rQ(l-a').

Rotational velocity

M

Resultant

velocity

V(l+a).

[image:31.564.22.519.133.458.2]

where

a V (1+a) tand=

-(20)

rQ(l-a')

Cl

and

Co

aredefinedastheliftand

drag

coefficients, respectively.These applytoairfoil

intwo-dimensionalmotion.Thesecanberesolvedintothrustandtorque_accordingto the

following

equations:

\

=

CLcost#-CDsin^

(21)

/*2 =

CL

sin<p+

CD

cos_tp

(22)

Theelements ofthrust andtorquegiven

by

thebladeelement of area_cdr,wherecisthe

chord oftheairfoil shape,thenbecome:

dl=AiyipM1cdr

(23)

Theseexpressions arethenmultiplied

by

the numberofbladestoobtaintheelements of

thrustandtorquefortheentire airscrew. Inplace ofc,sisusedforthepropellerblades

whichisequaltofollowing:

Nc

(25)

s= 2-r

whereN isthenumberofblades inthe airscew. srepresentstheratio ofbladeelementsto

Andthe advanceratioforthescrew canbegivenas:

. V r V r

1-a'

,

(26)

rjD R rQ R 1+ a

There existtwoextremities forthisanalysisthefirstof whichis thefollowing:

(27)

sCL=4^2

where

C_

istaken atanangle ofincidenceequalto 0

-<f>. Thiscorrespondstoa normal

positive value of</>forapropulsive screw. Thesecond_extremityoccurs whenthe thrust

disappearsatapoint given

by

thefollowing:

CL=CDtan<*

(28)

Thetorqueispositivebutvanishes at ahigherrate of advancewhen

(29)

CL

CD

cot<j>

Betweenthesetwopoints, theairscrewis actingas abrakeandbeyondthepoint where

torqueis negative, theairscrew isthen_actingas a windmill.

For efficiency utilizingthemethodfound intheNotesinthe appendix and

correspondingtoanincrementalelementat

dr,

theequationbecomesthe following:

VdT

_

V

\

tan^

(30)

T,~

where

CD-CLtanr

(31>

Note : yis definedas theeffect of profile

drag

ofthe

blades and

a1

is theeffect of rotation onthe slipstream.

Profile

drag

is definedastheskinfrictionandinduced

drag

on an airfoil shaped section.

Inthefirstoftheseequationstherearetwoadditional sources of_{energy loss} andthese are

thefollowing:

1.

a'

: effect of rotation ontheslipstream

2. _y: effect of profile

drag

oftheblades

. The first loss issmall overthe

workingrange ofthepropeller,butthe secondloss

becomes importantwhenthebladeelement approachestheattitudeofnolift.

Nowthat thebladeelement

theory

has been introducedand_{explained,showing}

thateachbladeelementcontributesto theperformanceofthepropeller, anothertechnique

employingtheuse of a computer softwareprogramwillnowbecovered. Thissoftware

programtakesinto account a numberofbladeelements andthedesignofthepropellerin

ordertopredicttheperformance and_efficiencyoftheoverall prop.This eliminatesthe

needtoperformtedioushandcalculationsinorderto get afasterestimate ofthe_prop

performance without construction ofthepropelleritself. As

long

as_geometryat certain

Chapter

3

:

Propeller Software

Program

3.1 Propeller

Software

Background

Modern

Prop

andDuct

Design, by

Martin HollmannandMark

Bettosini,

is a

written guide thatfirstexplainsthe

theory

ofdesign behindpropellers and ductsandthen

proceedsto analyze potentialdesigns with anincludedprogram.But beforetheprogram

canbe_properlyutilized,a general_{understanding}oftheauthors'

knowledge concerning

thesubject mustbe undertaken.Tothisend,the

theory

inthemanualwillbeexplainedin

detailandthentherelativeinputsrequiredfornumeric predictionswillbe divulged.

Thetheoreticalbackgroundon whichthesoftwareprogramis basedwillnowbe

discussed. The geometryofthebladetobeusedonthe aircraftmustbe

fully

described in

ordertoderivemathematicequationsthatpertaintothrust,power,and efficiency.The

mostbasicofthesequantitiesincludethebladepitch angle 0,theradius ratwhicha

bladesectionis described alongthe

blade,

the totalradiusRofthe

blade,

andthe

rotational speedoftheblade Q. IfoneconsultsFigure 5on thenextpage, these

quantitiesare more_easilyreferenced. It isalso_necessarytoknoworhave an

understandingoftherelativewind speedseen

by

boththeplane andthepropeller.This

quantity isgiven

by

:

v

=

Vv>(nr)!

<32>

where

V_

is thefreeair

flow,

whichin anycaseisthesameforthe_prop andtheplane

being

that thepropellerisattachedto theplane. Itcan alsobeseenthat thepitch angleis

thesumoftwootheranglesasfollows:

0

=_a+

O

Figure5

Blade Element Diagram

for Program Input

Blade

section

Qr

J

- <> +

<^

[image:36.584.28.551.179.505.2]

where

O =

tan"1

-z-(34)

Clr

It isobviousthat thepitch ofthebladevaries _alongtheradius and so O is determinedat

eachbladesection _alongtheradius(note thatit isrecommendedtousetensectionsfora

betteranalysis),fora certain _speed,and certainfree flowof air. Thevariablea however

remains a constantbetween 2and4 degreeswhich givesthemostlift forthe leastamount

of powerforcertain_wingsections.

Oncean_{understanding}ofthesequantitieshas beenacquired,it isnowrelevantto

discuss efficiency 7ofapropeller which canbe definedas :

P 77=7"

(35)

Inthis equation, theefficiency is simply describedasthepower availablefromthe

propellerovertheshaftbrakepowerdeliveredto thepropeller

by

the engine orthedrive

systemitself. Butthisequationneedstobe broken down intoa moredescriptiveequation

withknownquantities andmeasurablevalues such as:

TV

77

"

p

(36)

wherethepower available atthe_{prop has been}equatedto thefreestreamflowmultiplied

by

theavailablethrust. Frompast

theory

andextensiveexperimentation,it has been

determinedthat the_efficiencyisafunctionof adimensionless quantity

J,

theadvanced

where nisthe

frequency.

Agraph canbegenerated

depicting

the_efficiencyversus

various values ofJ in orderto

directly

readthe_efficiencynumber,butthis technique

cannotbeusedforbladesthatdonothaveafixedpitch. Inthiscase a more complex

techniquemustbe employed whichiswherethe software programbecomesmostuseful.

Twoother quantities ofinterest are also analyzed and graphed

by

thesoftware

program. Theseinclude

Ct,

thecoefficient of_thrust, and

Cp,

thecoefficientof power.

Thecoefficient ofthrustfora propellerdependsonthreeseparatefactorswhichinclude

theshape ofthepropeller, the advance_ratio, andtheReynold'snumber.Thepropeller

thrustisequalto thefollowing:

T

=

pnld*CT

(38)

whered isthediameterofthepropeller andn istherotationalspeed ofthepropellerin

revolutionsper second. Thepower coefficient alsodependsonthesame_{factors affecting}

the thrustcoefficientanditcanbeequatedto thefollowing:

CP

=

2nCQ

(39)

where

Cq

isthecoefficientoftorque. Thepower equationstarts asthefollowing:

P

=

pn3d527rCQ

(40)

and canbereducedtothefollowing:

P =

When_callingupontheaid of a softwareprogramfor

help

inan_engineering

problem,it isalways good practicetounderstandtheinputsrequiredoftheuser andthe

correspondingoutputstobeinterpreted

by

theuseraswell.Forthisparticular program

thereare alargenumber ofinputsneededinorderto_{correctly describe}thepropeller

geometricallyas well astheenvironmentinwhichitwilloperate. This assiststhe

computerin

determining

a more accurate resultintheschemeofthings.The listofinput

variables canbefound intheNotessection.The otherinputsrequiredforthecorrect

analysis ofthepropeller canbe foundwiththeTableofInputs inthenext section.These

3.2 Selected InputsForthePropellerProgram (withcollaborationfrom Ken

Blackburn)

After

defining

and

listing

the inputsto thesoftware_program,one mustbe ableto

inputthecorrect valuesfortheparticulartypeofpropeller

being

usedfortheevaluation.

This willtell thepotential propellerdesignerandbuilderwhetherthebladesare adequate

enough forthepurpose intended. Forthisparticular_analysis, reverse_{engineering is}used

todeterminethe_efficiencyoftheWrightBrothers'

propeller. Sincetheblade_{is already}

inexistence, thevalues must_{simply be determined from}thesectionsprovidedonthe

propeller

drawing

itself.

Inordertoacquirethe_{necessary inputs}requiredforthesoftware program, the

propellerandinturn eachbladesectionmust_{be carefully}analyzed.Forthistask, an

Eppler

boundary

layerprogramisemployed. Informationonthe

drawing

is transferred to

thisprogramfortheanalysis whichoccursintwosteps. The firstofthesestepsis an

inviscid flowanalysiswhichlooksattheairflowaroundthe airfoil. Itproduces a_velocity

distributionandpressuredistribution tobeusedinthe second step.Importanttonoteis

thatthisprogram assumes no

boundary

layer. Thesecond _stepoftheprogramis an

integral

boundary

layersolverthatintegratesindividualeffects on small sections ofthe

airfoil. Thisis apiecewiseintegratorand,intheend, this program can producethe

requiredinputs forthe analysisofthepropeller_usingthe_efficiencyprogram.

Analyzing

thesesections_accordingtoKen

Blackburn,

the

following

values wereinputted intothe

M: 10

THETA75: 28.875

RPM: 428 rpm

VMPHBEGIN:0

VMPHEND: 50

VMPHSTEP: 1

D: 8.5'

N:2

RHO: .002378

CLP: 2.0

MINCL: 1.2

ALPHAMINCL: 22

Theaforementionedvariablesdescribethe_operatingconditions fortheWrightBrothers'

propeller.Thevariable THETA75 specificallyrefersto theangle of attack atthespan

75%outfromthe centerhubofthepropeller. Thesoftwareprogramusesthisvlaueto

determine allothervalues,

by

assumingtheangle oftwistas afunctionof radiusis ideal.

Anothernoticeable variableis theRPMofthepropeller.The value of428 rpm was

retrievedfroma

drawing

oftheWrightpropeller.Thisrpm waskeptconstantthroughout

the analysisbecausethepropellerturnedata constant rpm ontheModel B.

Nowadays,

propeller rpm canbe altered

during

flight butthisis notthecase withtheModel B. The

nextset ofvariables takesintoaccountthesections oftheblade andtheirspecific

characteristics andproperties.Thiswillensuretheprogramhasthecorrect propeller

[image:42.538.55.480.142.485.2]

Table 1

TableofInputs

Column 1 Column 2 Column 3 Column 4 Column 5 Column 6 Column 7

.1 .1401 .0103 0 1.21 .105 -8.89

.2 .1401 .0103 0 1.21 .105 -8.89

.3 .1404 .0103 0 1.21 .105 -8.89

.4 .1594 .01 0 1.25 -8.95

.5 .1805 .00935 0 1.295 .11 -7.43

.6 .21372 .0087 0 1.34 -5.91

.7 .2301 .0075 0 1.36 -6.345

.8 .2258 .0063 0 1.38 -6.78

.9 .2235 .00615 0 1.39 -6.6

.95 .2164 .0060 0 1.40 -6.42

Column 1 : Midelement spanwiselocationasa percent ofthe total

Column 2: Widthofthebladeairfoilsection as given

by

the

following

Width=_Chord/Radius

Columns 3 & 4: Coefficientsofthe_followingequation

CD

=

A,

+A3

xa2

where_A*isobtained_bysettingtheangle of attacktozero and_readingthe_{correspondingCD}and_A3is obtained

by

_readingthe_{CDcorresponding}toa

knownangle of attack.

Column5: MaxCLforeach section

Column6: Liftcurve slopeforeach section(enteredper_degree)

Thetableonthe_precedingpage completestherest oftheinputs necessary forthe

output ofthegraphs and_efficiencynumbers

by

thepropeller program.

By

_alteringthese

numbers, one can changetheperformance characteristics ofthepropellerandinturnthe

plane towhichthepropeller will beattached.Thesenumbers were_carefullycalculatedin

ordertoobtainthecorrecttraitsoftheWrightBrothers'

propeller. Graphical

3.3 Output

Results

from

Software

Program

Graph1- 428

rpm

Efficiency

vs.Speed

1 1

09

-OR^

07

-o

n r

-_.

i>

>>

c

05-0)

'5

m

04-i>

no

-0<?

10 15 20 25

Speed_(mph) 30

?_Efficiency

Graph2- 428

rpm

HPvs.Speed

18

16

14

12

10

a.

z

<>

n

o

<>

o

10 15 20 25

Speed_(mph)

?HP

Graph3- 428_rpm

Efficiency

vs.Advanced Ratio

0.9

0.8

0.7

^0.6

>>

c 0.5

a,

'5

UJ

0.4

0.3

0.2

0.1

?

?

?

?

<> 1 1

0.2 0.4 0.6

AdvancedRatio

0.8 1.2

Graph4- 428 rpm

Thrustvs.Speed

120

100

80

|

60

40

20 o

V. a

<?

o

10 15 20 25

Speed_(mph)

?Thrust

Graph 5- 428_rpm

Cp

vs, Advanced Ratio

0.3

0.25

0.2

0.15

0.1

0.05

?

?

?

_

0.2 0.4 0.6

Advanced Ratio

?_Cp

0.2

0.18

0.16

0.14

0.12

0.1

0.08

0.06

0.04

0.02

0.2

Graph6- 428_rpm

CTvs.Advanced Ratio

?

? _?

?

<

0.4 0.6

AdvancedRatio

0.8

?CT

These graphscannowbeusedinan overall performance evaluationoftheWright

ModelB aircraftin Chapter 4. Notethat thediscussionofthesesix graphs willbeundertaken

Chapter

4

:

Performance

Evaluation

of

the

Wright

Model

B

Aircraft

Nowthat thecomputer software programhas beenutilized and produced

performance_graphs, a

drag

_studywillbeconductedtobeusedinconjunction withthe

performance graphsin ordertopredictthecruise speed oftheWright Model B aircraft. In

this section,datafromtheWright Flyer willbe usedand correctedtofittheWright

Model B. Thismethod was chosendueto thelackofdata inexistence ontheModel B.

4.1

Drag

AnalysisProcedureoftheWright Model B

The first step in conductinga

drag

_studyoftheWright Model B wastoobtain _any

drawingsavailable oftheplaneinordertoaidinthecalculationoftheequivalentfrontal

area oftheplane. Inthis caseboth drawingsfortheFlyerandtheBwere obtained(for

reasonstobe discussed later). These drawingswere presented asFigures 1 and2 inorder

forthereadertobetterviewthe available material. Oncethescale ofthe

drawing

was

established, measurementsweretakenof cable

length,

strut

length,

approximate engine

size,and approximatepilotsize.

Following

the measurements,a

drag

coefficientforeach separate piece was

determinedwith

help

fromaFluid Dynamic

Drag

textbook(Hoerner,S 1965). Cableand

strutcoefficientsweretaken

directly

fromthe

book,

while a

Cd

forthepilothadtobe

calculated_usingejection seatdataprovidedinthebook (Note:thefrontalarea ofthepilot

wasassumedtobe equivalenttotheejectionseatbecausebothwerein a_sittingposition.

Thisanalysis willbeshowninthenumerical results section.).In_{the end,}thetotal

equivalentflatplate_{area, the}overall

drag

coefficient oftheplane wasthencalculated

accordingtothefollowing:

(42)

C.plane=

S.

wmg

where

Swing

is thetotal area ofthewing,notjustthefrontal area.Now eventhis

coefficientis not

totally

accurate so thata correctionfactormustbeappliedtoboostthe

coefficienttomatch windtunneldata. Becausea

l/8th

scalemodel oftheFlyer hasbeen

inthewind_tunnel,thetotal

drag

coefficients oftheplane are_{already known. These}will

beusedto

help

determinethe

drag

coefficients ofthemodelB.Theinherentassumption is

that theplanes are_relativelysimilarin flight. Basedondatato

date,

thisappearstobe a

good assumptiondueto thefactthat theplaneswere nottoodifferent in design. There

wassome differenceinthenumberof_pilots,

landing

_gear,andtailbooms buttheoverall

planeappeared similarenoughtomakethis assumption.

The first stepwastodeterminethe totalcoefficientof

drag

oftheplaneinorderto

further carryontothe_{final step}of

determining

thepowerrequiredto

keep

theplanein

flight. Thetotalcoefficientof

drag

can_{be determined according}to thefollowing:

(43)

C Total =C'Parasitic₊C. Induced

da a

whereparasitic

drag

is due to theflatplate areaandtheinduced

drag

is duetolift

generated

by

thewingsandtheangle of attack oftheplane.Sinceparasitic

drag

_{is merely}

the_onlypart_{requiring further}analysis.The

following

equation canbe

directly

appliedto

determinetheinduced

drag

coefficient:

C2

C'induced=

(^4)

-e

(AR)

where

Cl

is theliftcoefficient,eisa correctionfactor

(approximately

equalto0.9forthe

Wrightaircraft), andAR istheaspect ratio fortheplane. Since

Cl

willbeplotted against

Cd,

Cl

isthengiven andisnot neededtobecalculated.As with

Cl,

eand ;rare_already

knownvalues

leaving

ARtobe determined foreach respectiveplane.

Theaspect ratiowouldbe easily determined fora_monoplane,butchanges forthe

case oftheWrightplaneswhichwerebi-planes. Inthiscasethewingspan andheight

betweenwings mustbe known. Oncetheratio ofheighttowingspan was

determined,

it

wasfoundon agraph(canbeseenintheResultsandDiscussion

Chapter)

andtraced

overto the_{corresponding}Ai/A value.Thiswas_merelyanintermediate step in

determining

theultimate aspectratio- Ai.The _valueAR_wasthen_calculated

by

the

following:

b2

(45)

AR

=

wing

wherebis thewingspanand

Swing

isthetotalarea ofthewings.Oncethiswas

determined,

theoverallAi foreachplanewasfinalized.

This stepwas repeatedfor boththeFlyerandtheBmodels. (Notethatseparate plots

were created andthesewillbeshownintheResultsandDiscussion

Chapter.)

The

inducedplotfortheFlyerwasthencombined withtheoverall

Cd

fortheFlyer. This

meansthatthe inducedplot couldbe subtractedfromtheoverall plotinordertoisolate

theparasitic

drag

_only,which wasdone_accordingto thefollowing:

Cd

parasitic=_Cdoverall

-Conduced

The resultingnumbers werethenadjusted

by

_multiplyingthem

by

the

following

correctionfactor: (Thecorrectionfactor accountsforalloftheparasiticdifferences

betweentheFlyerandBso

CdB(parasitic)

canbe

found.)

cf=

Y,CdS(B)

(47)

Y^CdS

(Flyer)

CdB(

parasitic)=cfx

CdFlyer{

_parasitic)

(48)

where

CjS(B)

isthe totalequivalent flatplate area ofB aircraft and

CdS(Flyer)

is the total

equivalentflatplate areaforthe Flyer. Thesenew _numbers, alsoknownastheparasitic

drag

fortheBplane,werethenaddedto theinducedcurvefortheB inordertogetthe

combined

drag

coefficient fortheB plane_accordingto thefollowing:

Cd

(B total)=

Cd

(B induced)+_cf*Cd

(flyer

_parasitic)

'4")

Anew curvewas thenplottedtodepictthe

Cl

vs.

Cj

totalfortheB plane.Thiscanbe

Oneofthelaststeps ofthisanalysis wastodetermine the

drag

force atcertain

speeds ontheplane.Thiswas conducted

by

first

determining

the_velocityat whichthe

plane was

flying

_accordingto the

following

equation:

CL=

, W

(50)

y2pv2swing

where Wisthe weight oftheplane,_{p is}theair

density,

V isthevelocity,and

SWig

is the

total _wingarea.

Knowing

Cl, W, S,

and_{p, theonly}unknown valueis thevelocity.

After rearrangingtheequationthe_velocitycanbe found from:

W

(51)

V C S1

wing

Knowing

this_quantityandthecoefficient of

drag

at each

CL,

the

drag

forcewasthen

calculatedasfollows:

1/ 2

(52>

Drag

Force =

C,

x _V,

'

xpxV x₅

whereall oftheabove quantities have been previously definedand areknown inthe

equation. From heretotherequiredpower was _onlya matter of_{plugging into}the

following

equation:

Powerrequired=

Drag

Force_x

Velocity

(")

Thiswasthenconvertedinto horsepowerthrough a series of conversions which were

ontheplot of power available vs. speed obtainedfromthesoftware analysis. Thepower

obtainedfromthesoftware program neededtobe doubledinordertoaccountforthe two

propellers present ontheplane.

The final_stepwasto determinetheclimb speed

by

_readingthespeedoff ofthe

graphthatcorresponds to theleastamount ofHPrequired.Thentherate ofclimb,

R,

can

befound_accordingto thefollowing:

P -P

R=

(54)

Weight K }

where

Pa

is theavailable power and

Pr

istherequired power attheclimb speed.

4.2

Drag Study

Numerical

_AnalysisandResults

According

to theanalysisdescriptiongiveninthe

Theory

Chapter,

the

following

drag

studyoftheWright Brothers

Planes,

the Flyerandthe

B,

was undertaken and

completedand exhibitedthe_proceedingresults.

Total Equivalent FlatPlate Area

Flyer: 2.69

(cables)

+ 13.54

(struts)

+ 1.8 (chain_tubes)+2.205

(engine)

+7.65

(wing)

+6.48 (person+ radiator +fueltank)=34.365

Model B :

(1.91+.32) (cables)

+ 12.85

(struts)

+2.21 (chaintubes)+ 1.42

(motor)

+.385

(wheels)

+7.08

(wing)

+ 12.96 (pilot+ radiator +fuel _tank)=39.135

Cd

ofPerson in

Sitting

Position (from Fluid- Dynamic

Drag

Book)

The_{first step in}

determining

theequivalentflatplate area oftheWright

planeswas tofindthe totalprojectedfrontal areafromthedrawings. Thenthe

Cd

wasfound intheFluid Dynamic

Drag

bookand appliedto thefrontalarea. Inthe

caseofthepilottherewasnoclear-cut

drag

coefficient.The frontalareahadto

assumedandthe

drag

coefficient wascalculated_accordingto theinformation

foundinthebook (theexample was foran ejection seatbutthe

drag

coefficient

was appliedtotheWrightpilot).

=

V~oV2SC

(55)

Drag

force=

where

5 =

6ft2(asumed)

V=500 knots=843.9-^/

p=.00238

Drag

force=5500lbs

Knowing

this

information,

the

Cd

oftheejection seat/personisequivalentto 1.08.

Aspect Ratio Determination (from Fluid- Dynamic

Drag

book)

Figure4 :AspectRatio Diagram

ATA _(C^ ()

> ae a (e,) ()

A C II (C,) (<)

A> k/l m

Gap

Ratio=h/b

EffectiveAspect Ratio =Ai

GeometricAspect Ratio=A=

y^

[image:57.538.113.444.296.626.2]

Flyer Analysis:

B Analysis:

Plotof

Cd

Induced

Gap

Ratio=

h/

=

6/A

n

=0. 15

40

A=

40Xio

=3-137

Ai=1.25x3.137=3.921

Gap

Ratio=

h/b=

5'4%s

5

=0.141

A/A

=l.23

A= =3.140

'472

Ai=_1.23x3.140=3.8622

C 2 C,induced = , .

d

n{0.9)Ai

Oncetheaspectratiohas been determined fromtheprevious _analysis,theinduced

drag

coefficientcan beplotted versusthecoefficientoflift. Theresults canbeseeninthe

Flyer

induced

drag

plot

C C.induced = _, .

'

^-(0.9)3.921

Graph7- Flyerinduced

drag

CL

vs.

Cd

Flyer

n

(

1 <

) 8 ?

<

<

1 R ?

1 A. ?

1*? ?

n i?

-0.01 0.01 0.03 0.05 0.07 0.09 0.11 0.13 0.15

Cd

?Cd induced

B induced

drag

plot

C

C,

induced

=-, .

'

^-(0.9)3.3.8622

Graph 8-- Model B induced

drag

r>

CL

vs.

Cd

B

(

(

I

i ?

i p ?

J.Q

1fi ?

1 A ?

\i ?

J.c fl .

*

-0.01 0.01 0.03 O.I35 0.07 0.09 0.11

Cd

0.13 0. 15

PlotofFlyer

Induced

Drag

+Parasitic

Drag

(takenfrom_existing

data)

Graph9- Flyer induced

andtotal

drag

CL

vs.

Cd

Ryer 1.2 0.8 0.6 0.4 0.2 ? ? ? *t

1

?

,, B

0.05 0.1 0.15

Cd

0.2 0.25 0.3

?Cd induced Cd induced+parasite

Parasitic

Drag

CoefficientDeterminationoftheFlyer

Cdparastic=

Cd

(measured)

-Conduced

Using

theabovedescribedequationandthecurves presentedintheprevious

section,theparasitic

drag

coefficient oftheFlyerwasdeterminedat eachdatapoint and [image:60.538.101.463.92.332.2]

placedintothe

following

table:

Table 2- Flyer

Drag

Coefficients

Cd

induced

Cd

total

Cd

parasite

0 0.13 0.13

0.000902009 0.12 0.119097991

0.003608035 0.11 0.106391965

0.008118079 0.11 0.101881921 0.014432141 0.11 0.095567859

Determination

oftheParasitic

Cd

fortheB

Nowthat theparasitic

drag

coefficienthas been determined forthe

Flyer,

itcanbe

appliedtotheB with afewadjustments as _{follows using}acorrectionfactor:

YC.S(B)

39.135 cf =

__^

d v J

= =_1.1388

2^CdS

(Flyer)

34.365

Thetotalcoefficient of

drag

fortheB isasfollows:

Cd(B total)=_Cd(B

induced)

+_cfx.Cd

(flyer

parasitic)

[image:61.538.185.352.379.569.2]

This yieldsthe

following

tableof values andthegraphonthe

following

page:

Table 3- Model B

Drag

Coefficients

Cdinduced Cdtotal

0 0.148044522

Graph 10- Model B induced

andtotal

drag

CLvsCd

B

O

1

1 _ ?

?

Ofi

?

\J.KJ

04

ut

OP

A?

\J.C

n;

\

.

0

?

Cd

induced

Cd

irduced+parasite

Drag

Force

Determination

fortheB

Oncetheabove plothasbeencompleted, a

drag

forcecanbeobtained

by

_applying

the

following

equationsin theorder presented:

V =

W

/₉ L wing

Drag

Force =C.x

]/xpxV2xS

Inthiscasetheunknown_{velocity is found first}

by

_pulling

CL

valuesfromthegraphs and

then_applyingthe second equationfor

drag

force. Fromthese twoequations the

following

tablewas produced:

Table4- Model B

Velocity

/

Drag

Force

cd

Total

Velocity

ft/s

drag

force

Lbs

CL

0 0.148045 471.747814 18505.51

0.1 0.136545 149.179757 1706.808

0.2 0.124823 105.486018 780.1388

0.3 0.124265 86.1289731 517.7702

0.4 0.123485 74.5898787 385.8893

0.5 0.125329 66.7152157 313.3209

0.6 0.12695 60.9023809 264.4775

0.7 0.131194 56.3846484 234.2751

0.8 0.14091 52.743009 220.1719

0.9 0.156098 49.7265858 216.8015

1 0.193838 47.1747814 242.2965

[image:63.538.168.374.351.562.2]

Power Required for Flight

Nowthat the

drag

forcehas beencalculated, theoverall power requiredto

keep

theplanein flightatdifferentvelocities canbe determined. Oncethishas been

found,

it

canbeplotted onthe same graph as power available produced

by

the softwareprogram.

Thepower required canbefoundviathefollowing:

Power required =

Drag

Forcex

Velocity

Aftertheequation was appliedto thedata intheprevioustableand

following

some

conversionstogetto theultimate _goal,

HP,

the

following

tablewas produced:

Table 5- Model B Required Power

Velocity

Ft/s 471.747814 149.179757 105.486018 86.1289731 74.5898787 66.7152157 60.9023809 56.3846484 52.743009 49.7265858 47.1747814 44.9793892 295.255

drag

force Lbs 18505.51 1706.808 780.1388 517.7702 385.8893 313.3209 264.4775 234.2751 220.1719 216.8015 242.2965 power_req HP 15872.63 462.9482 149.6252 81.08196 52.33359 38.00599 29.28605 24.01734 21.11372 19.60148 20.78236 24.14619

ThisshowstheHPrequiredagainst speed and

drag

force. Inthenext section theplot of

HPrequiredvs. Speed

(mph)

willbe presented_alongwiththeHPavailable vs. Speed

HP

Required/Available

vs.

Speed

This isthe_{last step in}theoverall

drag

_studyoftheWright Bplane. Fromthis

graphthestall speed canbedeterminedas well as regions ofliftandsinking.The

following

graph willbe further discussedinthenext section ofthis chapter.

60

50

40

_ 30

20

10

Graph11

Power Required/ Power Available

'*-7<21.1vi.vc--.

A

A

/

/

/

*

10 20 30

Speed(mph)

40 50

PowerRequiredB

-Power Available

60

ClimbSpeedand Climb Rate

According

tothegraphabove, theclimbspeedis_{approximately} 34mph andthe

climb rateisthefollowing:

,,06107-107")

,,

Chapter

5

:

Discussion

of

Results

5.1 Climb Speed

and

Climb Rate

Fromtheprevious chapteritwas shownthat thebestclimb speed occurred at34

mph andthiscorrespondedtoa climb rate or almost4.26ft/sor255 ft/min. These values

compare_closelywiththeknowndata fromtheModel Bperiod of200 ft/min. Theclimb

in ft/sisoften referredtoasthespecific excess energy. Atsealevelanaircraftperforms

differently

thenathigheraltitudes. Ascomparedtosea

level,

anaircraft'sengine loses

power athigheraltitudesdueto the thinnessoftheair. Theenginecannotingestenough

airtomaintain performance andthereforeitcannot climb over a certain altitude.

5.2

Performance

at

CL

Max

Theaircraft specific excess_energyatCLmaxis 2.26 ft/s . This indicatesthat the

aircraft canstillclimbwhileontheedge of a_stall,whichisadesirabletrait. Apilot can

usethisadvantagewhen_abortinga

landing

or_{clearing high}terrain.

5.3 Cruise Speed

Thecruise speed was readfromthepowercurve whichdepictedtheavailable

powerandtherequired power atspecificvelocities. Thetwocurvesintersectedat41

mph. This becomesthecruisespeed oftheaircraft. Availabledata fromthe period ofthe

ModelB aircraftindicatethatitscruise speedwas around40mph.This compares_very

closelyto thatofthedatagenerated

by

thesoftwareprogram andthe

drag

study.

5.4 Propeller Performance

Efficiency

of apropellerisvital to theperformanceof an aircraftinflight bothin

istoproducethrustand act against a

body

of airin ordertopropeltheplanein aforward

direction. Thepropellersatthe timeoftheWrights were

hardly

efficient andtherefore

theirgoal of66%seemed out of_reach,butthroughperseveranceandhardwork

they

succeeded.Theanalysis ofthepropeller conductedhere wastoconfirmtheirdesignand

theirnumerical outputs. Becausethepropellerturnedat one speed most ofthe_time,the

analysis was run at a constant rpm of

428,

being

thisis a published numberlinkedtothe

Model B aircraft.

Thehorsepowergraph

(2)

fromthesoftware programindicatethepowerinputto

propeller(which ismultiplied

by

2forthedualpropeller_set-up) and should notbe

confused withthepower_{resulting from}the thrust._{The efficiency factor}reducesthe

power_propellingthe aircraftforward.

Asitturns out,the428 rpm resultsin 28 totalHPrequired atthe_propellers, which

isaboutrightforthevertical4engine.Thisenginewascapable of35

HP,

butthe

transmissionlossesand

density

of air will reducethispower.

SincetheWright Brothers first designedtheirpropeller,therehave been

enormousimprovements andrefinementsmadeon propellerdesign

itself,

andinturnthe

efficiencyofthepropeller. As a result ofthese

improvements,

today'spropellers canbe

Chapter 6

:

Conclusions

&

Recommendations

6.1

Conclusions

Intheprevious_chapter,the results obtainedthrough thesoftware analysis andthe

drag

studywere presented and discussedasfarastheircorrelationto thedataor

measurements obtained

by

theWright Brothers. Thischapterwill attempttodraw

conclusionsfromtheseresults andthe

following

chapter willmake recommendationsin

ordertoeasefurther studyofthissubject matter. Fromthefirstchapter, theobjective of

thisresearch wastodetermine the_accuracyand correctness oftheWright Brothers in

theirquesttodesignapropellerfortheirairplane.

Thefirstareaof concern was the_efficiencyofthepropeller_{itself. From observing}

the presenteddataand graphsintheResultsandDiscussion

Chapter,

it isclearthatboth

studies producesimilar enoughresultstoconcludethattheir theorieswere correct and

theirpropeller performedinthemanneritwasintended.

Taking

thecross sections and

inputting

their_{corresponding}geometricaldataintothesoftware program wastheultimate

testofthepropeller.Thesoftware wasdesignedtoconduct_efficiencystudies giventhe

shape ofthepropelleras well asthe_operatingcircumstances ofthepropeller, orinthis

casetheplaneitself. Thistranslatesintoa_relativelyprecise physical model ofthe

propellerandtheresults canbeconsideredasaccurateastheinputtedmodel. Outofthe

softwarecame an_efficiencyof70%thatis notfaroff ofthe66%predicted

by

theWright

be acceptable

including

theavailablehorsepoweratdifferentspeeds

(

agraphthatwas

presented intheResultsandDiscussionChapter). Thenext_stepoftheanalysiscouldbe

completed

knowing

thisinformation.

Thesecond objective ofthisresearch wastodeterminepower requiredto

keep

the

planeinflight.Thecalculated powerdatacouldbeplotted againstthepredicted power

dataretrieved fromthesoftware and a cruise speed couldbe determined. Fromscale

drawingsofboththeFlyerandthe

B,

a

drag

_studywas conducted_accordingtothe

procedureinthe

Theory

Chapter (theresults of whichcanbeseenintheResultsand

Discussion Chapter). This

drag

_studyyieldedbothspeeds andthe

drag

forcepresent at

each speed.

Using

thisdataandthepowerequation_{presented, the}power-requiredcurve

wasthendiscovered.

Overlaying

bothplots yieldeda cruise speed of around42mph

which_closelymatchesthatgivenatthe time theplanewas constructed. Thecombined

powercurvefulfilledthis objectiveintheresearchand showedthat the technique

employedtoconductthe

drag

_studycould_actuallyproduceviable numbers with a

relativelysmall amountofknowledgeatthe start. Evenwith_onlycrude scaledrawingsof

the planes, thefinalnumberswere_onlyafewunitsofffromtheirsupposedtargets(as set

by

theWright Brothers).

Asmentionedpri