Thoikol_Final_BX.doc

8/18/2019 Thoikol_Final_BX.doc

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Thiokol Final Design Report AAE 451: Purdue University Senior Airra!t Design

Pro!essor Do"inik AndrisaniFall #$$$

Ryan BeechMatt BasilettiMike VanMeter Oneeb Bhutta

Team

Boiler Xpress


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Executive Summary...........................................................................................................5

1 Introduction.....................................................................................................................6

2 Concept Selection and Initial Siin!............................................................................."

*.+ Mission Reuirements...............................................................................................-*.* %oncept generation and /aluation...........................................................................-

*.0 %onstraints.................................................................................................................1

*.2 3nitial )i4ing...............................................................................................................5

# $erodynamics..................................................................................................................%

0.+ 3ntroduction................................................................................................................5

0.* !ift 'roduction.........................................................................................................+6

0.0 $rag 'rediction........................................................................................................+*

0.2 Wing $esign............................................................................................................+2

0.7 )tability....................................................................................................................+2

& Structures......................................................................................................................16

2.+ 3ntroduction..............................................................................................................+8

2.* 'hysical 'roperties...................................................................................................+8

2.0 Wing.........................................................................................................................+-

2.2 9uselage...................................................................................................................+5

2.7 ail )ection..............................................................................................................*6

2.8 !anding :ear...........................................................................................................*+

5 'ropulsion system.........................................................................................................22

7.+ 3ntroduction..............................................................................................................**

7.* $esign 'rocess.........................................................................................................**

7.0 Motor and )peed %ontroller )election....................................................................*0

7.2 'ropeller )election...................................................................................................*0

7.7 )ystem esting.........................................................................................................*2

6 (ynamics and Control..................................................................................................25

8.+ 3ntroduction..............................................................................................................*7

8.* #nalysis....................................................................................................................*7

8.0 9light characteristics................................................................................................*-


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" Economics......................................................................................................................2)

-.+ )tructural %ost Breakdown......................................................................................*1

-.* 'ropulsion and lectronic %ost Break down...........................................................*1

-.0 Marketability............................................................................................................*1

) *eferences......................................................................................................................#+

$ppendix $ , Concept Selection and -ei!ted /b0ectives etod...........................#2

$ppendix B , $erodynamics etodolo!y...................................................................#"

$ppendix C Structural $nalysis etodolo!y...........................................................&)

$ppendix ( , $T3$B 'ropulsion System $nalysis Code........................................5%

$ppendix E , 'ropulsion Tests *esults..........................................................................6"

$ppendix 4 , odel Electronics Corporation Turbo 1+ T otor..........................."+

$ppendix , (ynamics and Stability etodolo!y...................................................)1

$ppendix , Economic (etails.....................................................................................%+


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Executive Summary

he Boiler ;press aircraft is designed as a /ariable stability platform forinstruction in aircraft dynamics and control. he electrically powered aircraft isconfigured to be structurally and aerodynamically efficient, using materials that easeconstruction and repair. he modular design allows aircraft and support euipment to be

disassembled for transport or storage in a space 7< by 0< by * found in many small remotely piloted aircraft.he stall speed is only +0 mph, allowing easy take&off and maneu/ering within aconfined space such as the Mollenkopf #thletic %enter. #n indoor or outdoor area withdimensions of a football field is sufficient for operation of the Boiler ;press aircraft. heelectric power plant is uiet, adaptable, and /ery easy to operate and maintain. Very littlesupport euipment is necessary to operate the aircraft.

%ost is always an important consideration, and the ;press is designed to use lowcost materials for most of its construction. he total cost for airframe materials is ?usto/er @*56. he styling is attracti/e, gi/ing it good market appeal for schools anduni/ersities desiring a useful tool for instruction in aircraft stability and control theory.Variable stability allows studies as to the dynamic response of the aircraft in the rollmode both with only open&loop control, and with a pilot&selectable gain enabled. he in&flight data recorder allows the time response of the aircraft roll rate to be downloadedafter each flight. his can then be compared to mathematical models, pro/idinginstructional /alue pre/iously unobtainable.

#ll of the design goals for the Boiler ;press were met in the prototype. he take&off run of around 86 ft. is followed by good climb and the ability to cruise for +* minutes

at ?ust o/er half throttle. /en at slow flight speeds, the control authority is good, and theaircraft remains solid and maneu/erable. he aircraft demonstrated the ability to carry atleast 1 ounces of additional payload, allowing eApansion of the mission en/elope in thefuture. 9lights may be accomplished outdoors as well, when the winds are moderate withonly a small field reuired. his further demonstrates the /alue and fleAibility of theBoiler ;press remotely&piloted aircraft.


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1 Introduction

he Boiler ;press aircraft represents a large effort on the part of four 'urdueni/ersity students. he fifteen&week design process began in late #ugust and wascompleted in early $ecember with the successful test flight of the Boiler ;press aircraft.his report will detail identification of mission reuirements, the initial concept selection

and si4ing, and then outline the preliminary design process.he preliminary aircraft design was di/ided into four primary areasC

aerodynamics, structures, propulsion and dynamics and stability. 9light testing results areincluded as /erification of the design analysis, and to indicate the effecti/eness of theBoiler ;press aircraft to complete the mission. conomics are an important constraint on producing and operating an aircraft, and summary of these considerations are gi/en in thefinal section.

9igure +.+ presents /iews of the Boiler ;press aircraft with dimensions and performance specifications of the final aircraft gi/en in able +.+.

able +.+ D #ircraft 'arameters

-in! eometry)pan ++ ft * in

croot + ft 7 in

ctip ++.7 in

)ref +0.7 ft*

$ihedral angle *°

#spect Ratio 5.6

oriontal Tail eometry

)pan * ft 1 in

#rea +.10 ft*

7ertical Tail eometry)pan + ft + in

#rea +.+1 ft*

4usela!e

!ength * ft +6 in

Width 0.7 in

(eight 8.6 in

Tail Booms

!ength E to F * ft +6 in

$iameter 6.77 in

Wall hickness 6.60* in

-ei!tsWto +6.*7 lb

Wempty 5.6 lb

4li!t Speeds

)tall )peed Eest.F +5 ft"s

%ruise )peedEmeas.F

*1 ft"s

9igure +.+ #ircraft layout


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2 Concept Selection and Initial Siin!

2.1 ission *e8uirements

he mission reuirements for the 9all *666 senior design pro?ect includeconstraints on climb rate, turn rate"radius, stall speed, cruise speed, take&off ground roll

and endurance. he o/erall mission is to design and build an aircraft that will carry +.2 pounds of flight test euipment. his includes the feedback rate gyroscope system, thedata logger, and the interface circuitry. $uring the twel/e&minute endurance mission, thedata acuisition system will record roll rates and use the control augmentation system to/ary the aircraft dynamics.

$esigning the aircraft for flight within the 2+6< A **6< confines of the indoorfootball practice field presents uniue problems. 9light speeds must be slow enough forcomfortable maneu/ering, and to allow time to turn the feedback controller on and offduring the straight&and&le/el portions of the flight. lectric power is reuired to reducemess and noise. 3t will be seen that the result is an aircraft with generous wing area,high&lift aerodynamics, and careful attention to good flying ualities. he specifics of the

mission constraints are discussed in the =$esign Reuirements and Ob?ecti/es> documentG+H.

2.2 Concept !eneration and Evaluation

#ny design process must be dri/en by the needs and reuirements outlined by themission specification G-H. he ;press team spent se/eral sessions studying anddiscussing these reuirements before initiating analysis of any particular design solution.#fter becoming comfortable with this foundation for the design, a brain storming sessiongenerated the concepts shown in 9igure *.+. he concepts considered encompass a rangeof configurations. hey include a twin&boom pusher, a con/entional tractor monoplane, a biplane tractor, a flying wing, and a biplane pusher.

9igure *.+ D %oncepts considered for further analysis.

+

*

2

0

7


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he process continued by listing the ob?ecti/es of the mission. en areas ofconcern were noted. hey were Ein ranked order of importanceFC

+F !ight weight*F urning Radius ERef. +F0F Marketability Ewill the plane sellF

2F Build within three weeks Eease of constructionF7F Maintainability Eaccess to inside, ease of repairF8F Robustness to crashes-F wel/e minute endurance Emission reuirementF1F ase of analysis Eaerodynamic, dynamics and structuralF5F ransportability Emust fit in mid&si4e carF+6F !anding abilityhe fi/e concepts were e/aluated using the weighted ob?ecti/es method. %oncepts

+ and * scored nearly eually as the best conceptsI the twin&boom pusher configurationwas finally selected by the team to eAplore the potential efficiency of this design.

2.# Constraintshe reuirements for take&off distance, climb angle, stall speed, minimum turn

radius, and cruise speed were modeled mathematically to relate each performance parameter with power loading W"' and wing loading W"). hese each are plotted bymeans of a Matlab code, with /arying aspect ratios. his result is shown in 9igure *.*.9rom this diagram it is possible to choose a design target to define the power loading andthe wing loading. his is indicated on the figure. he dashed regions show the side ofthe plots which are not allowable /alues for the design wing and power loadings.

0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.1

0.2

0.3

0.4

0.5

0.6

W/S [lb/ft2]

W / P

[ l b / f t - l b / s ]

AR=7

AR=8AR=9AR=10

9igure *.*C %onstraint $iagram showing feasible design space.

'ower loading J 6.** lb"ft&lb"s

Wing loading J 6.81 lb"ft*


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2.& Initial Siin!

stimates of the weight of the aircraft for the mission were made on the basis of acomponent break&down method. %omponents whose weights are known were listed in a

spreadsheet. #irframe components were si4ed iterati/ely to allow enough room to carrythe euipment. Wing and tail si4e are related by stability considerations, and the wingreference area )ref is constrained by the wing loading obtained from the constraintdiagram analysis. he weights for the wing and tail were initially found from a databaseof eAisting model aircraft designs on a per&suare foot basis. his was later changed toreflect the make&up of our chosen construction method. esting and weighing of samplecomponents built during the design analysis allowed this method to more accurately predict the finished weight than a historical database approach.

he si4ing process is iterati/e. %hanging the si4e of any component which is nota fiAed uantity will of course change the weight of the aircraft. his in turn alters thestall speed, reuiring the wing area Ehence weightF to be ad?usted further. Motor and

battery weights were determined from the target power loading using a database ofelectric motor systems. he spread sheet approach allowed con/ergence on thecomponent si4es and aircraft weight /ery uickly. he engineers could uickly see theeffect of /arying any components si4e.

# $erodynamics

#.1 Introduction

he mission reuirements for the Boiler ;press aircraft are the starting point inthe design of the aircraft. #erodynamic considerations stemming from the reuirementsareC

+. )low flight capabilities& *6 ft"s maA stall speed, *1 ft"s maA cruise.*. !oad carrying capabilities& +.2 lb payload for the computer andinterface"feedback control system

0. %ontrol and flying ualities& easily maneu/erable within the confines of Mollenkopf #thletic %enter, gentle stall characteristics, good stability on all aAes.

he aerodynamics problem is broken down into three main areasC!ift production$rag prediction)tability and %ontrol characteristics

Within theses three areas the design and performance of the aircraft will be defined. #ll

three areas are interrelatedI changing the wing design, for instance, will impact lift production, with the conseuence of affecting the drag and stability. 3t is necessary to prioriti4e the desired characteristics, setting some as constraints, and some as desiredtargets.

#s the goal for the aircraft is flight, lift production, specifically high %!maA is theforemost design goal. !ower drag, or higher lift&to&drag ratio !"$, reuires less power,and thereby lower weight motor and batteries. his results is smaller si4e and less cost


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for the aircraft, both /ery important design goals. !ow drag therefore is the second mostimportant consideration.

:ood flight characteristics are also /ital. he stability of the aircraft can be easilyad?usted once the basic configuration has been set by specifying the center of gra/ity toattain the desired pitch stability, introducing dihedral or washout in the wing to tailor the

roll stability, and ad?usting the si4e of the /ertical stabili4er to achie/e proper directionalstability. 3n general, these ad?ustments ha/e only minor impact on lift and drag.

#.2 3ift 'roduction

he heart of the aircraft is the airfoil. 'roper airfoil design and selection willallow the wing to produce the reuired lift with minimum drag during cruise, and allow alow stalling speed. he maAimum section lift coefficient %lmaA of the wing largelydetermines the si4e, and conseuently weight and cost of the wing. )election of theairfoil for the Boiler ;press aircraft began with analysis of the range of Reynoldsnumbers ERnF at which the wing will operate. his is an iterati/e process, as Rn is defined by the flight conditions EknownF, as well as the characteristic length Echord of the wing,

unknownF.Research began with the assumption that the aircraft will be operating in the low

Rn regime. his is generally defined as the range below RnJ166,666. 3n regime, theflow is generally assumed to be laminar o/er a significant portion of the body. !aminarflow /elocity profiles are =less full> than those for turbulent flow, as illustrated in9igure 0.+. he conseuence is that the laminar flow has less momentum near thesurface of the airfoil, and is more prone to separation in an ad/erse pressure gradient.his is the danger of an improperly designed airfoil operating at low RnC formation of alaminar separation bubble, with the attending dramatic loss of lift, and increase in drag.

9igure 0.+C !aminar and urbulent boundary layer /elocity profiles.

#irfoils designed for larger aircraft, such as the K#%# series do not generally perform well at low Rn. 9igure 0.* illustrates the trend in lift performance as the Rn

decreases.

!aminar9low

urbulent9low


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9igure 0.*C rend of %!maA with Reynolds number for /arious airfoils from reference +2.

he uest for better performance in small aircraft has led to families of airfoilsdesigned to o/ercome these trends. he work of $r. Michael )elig and his colleagues atthe ni/ersity of 3llinois has produced both a number of good airfoil designs, as well asrigorously obtained eAperimental data on their performance. Aamining this data led tothe selection of three candidate airfoilsC the )+**0, the )+*+6, and the Wortmann 9; 80&+0-. hey were chosen for their high %lmaA /alues, and resistence to laminar separationdown to RnJ +66,666. he drag polars for these three aircraft are compared in 9igure0.0.

9igure 0.0C $rag polars for candidate low Reynolds number airfoils.

he )+*+6 airfoil was chosen for its good lift capability without the sharp drag increasefor %l L 6.5. sing the approAimation for whole wing lift coefficient from Raymer, the predicted lift coefficient of a high aspect ratio wing with this airfoil is as followsC

%!maA J 6.17%lmaA EairfoilF J +.70 E)+*+6 airfoilF

Re = 150e3

0

0.01

0.02

0.03

0.04

0.05

0.06

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

Cl

C d

FX63-137

S1210

S1223

)+**0

)+*+6

9;80&+0-


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sing an iterati/e process to estimate the total weight of the aircraft, including the wingweight, the stalling speed reuirement sets the plan form area of the wing at +0.7 s.ft.

%omputer flow simulation is an increasingly useful tool in preliminary design. 3norder to /erify the lift prediction, the computer program %M#R% was utili4ed to model

the wing pressure distribution, lift, drag, and moment characteristics. sing this method,the lift coefficients and moment coefficients for a range of angles of attack werecompaered to the computed /alues. %M#R% uses a low&order panel method to computethe flow o/er the paneli4ed model, and does not accurately predict flow ualities when/iscous effects dominate. herefore predicting %!maA in this way would gi/e erroneousresults. (owe/er, the lift coefficients at lower angles of attack correlated well with those predicted using Raymer


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∑=ref

wetiii fi

DS

S FF QC C

6 E0.*F

he terms N Einterference factorF and 99 Eform factorF make allowance for theconfiguration and shape of the components, commonly known as form drag, while theskin friction is accounted for by the %fii term. he skin friction for any gi/en component

is dependent on the local Rn, and the condition of the flow. he flow was assumed to beturbulent for all components, a conser/ati/e assumption. he work on aerodynamics byMc%ormick * references the increase in skin friction drag with surface roughness. Ouraircraft prototype will be assumed to ha/e less&than&ideal surface finishes, andMc%ormick suggests that eAperimentally determined /alues of the skin friction should beincreased by *6 o/er that predicted by Blasius< correlation0C

77.*+6 FElog

277.6

Rn f C = E0.0F

he Rn for each component is found from its characteristic length, and is computed at theactual flight condition for which that drag point is being produced.

)tudying the work of (oerner G+7H and Mc%ormick guided the design of the

aircraft to produce fuselage and pod shapes which will produce the minimum drag. hewing tip was also patterned by (oerner


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0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16Aircraft Drag Polar

CL

CDCDi

CDo

9igure 0.7C Whole&aircraft drag polar for the Boiler Xpress o/er the eApected range of flight speeds.

#.& -in! (esi!n

Wing design began with the si4ing of the planform area based on lift coefficient predictions and the reuired total lift. With the pod and boom arrangement, the centersection of the wing was chosen to be untapered to ease manufacturing, and pro/idemaAimum torsional stiffness. he aspect ratio # is defined asC

ref S

b A

*

= E0.7F

(igher aspect ratio wings produce lower induced drag, as seen from euation 0.2.(owe/er, a longer wingspan will increase the bending moment at the wing root,necessitating a stronger, hea/ier wing spar design. %onsideration of the slow flight

speeds, in which the induced drag is a high percentage of the total drag, led the team tochoose an aspect ratio of 5. With remo/able outer wing panels, this is a goodcompromise to keep the si4e of these components manageable. he total wingspan thenis ++ ft.

)ome taper is desirable to produce a more elliptical lift distribution. #n iterati/e process allowed ad?ustment of the tip chord to keep the local Rn of the tip from becomingsub&critical, which may lead to laminar separation. he inner wing tip in a turn at theslowest flight speed gi/es the condition for lowest Rn of any flight condition. )etting thelowest allowable Rn at +66,666 Edetermined from airfoil dataF, the wing tip chord was setat 6.57 ft, gi/ing an a/erage taper ratio of 6.8 for the wing with a +.7 ft. root chord.

#.5 Stability

he Boiler ;press is designed to be a stable aircraft with trainer&like handlingualities. 9oremost in this effort is the determination of pitch stability and controllability.3t is desired that the aircraft not be too sensiti/e in pitch, reuiring constant attention fromthe pilot to maintain flight euilibrium, while at the same time gi/ing the reuired


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maneu/erability. #dditionally, it is desirable to minimi4e the trim drag. he methodfrom Raymer was again followed to analy4e the static stability of the aircraft G+5H.

he trim condition in steady le/el flight results in 4ero net pitching moment aboutthe center of gra/ity. #d?usting the position of the ele/ator changes the lift coefficient ofthe hori4ontal tail. his is the mechanism to pro/ide both maneu/ering capability and

trim ability in pitch.9or any gi/en ele/ator position and angle of attack, there is a gi/en lift coefficientand pitching moment produced. hese can be plotted for a range of ele/ator deflectionsand wing angles of attack to produce the plot shown in 9igure 0.8C

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

CL

C m

c g

elev deflect=-8 deg

-404

8

9igure 0.8C 'itching moment /ersus lift coefficient for ;c.g. J 00 M#%.

his plot is produced for a particular center of gra/ity location. he neutral point for theaircraft is found, and the resulting static margin is used as the measure of stability aboutthe pitch aAis. 9ollowing the guideline from Raymer for less maneu/erable aircraft, thedesired minimum static margin was set at +6 M#%. he ad/antage of keeping close tothis figure is that the hori4ontal tail is less hea/ily loaded during cruise. his produceslower trim drag and more efficient operation. hough Mark 'eters< thesis on modelaircraft stability suggests larger static margins G+-H, the author


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& Structures

&.1 Introduction

he structural design of the aircraft was dri/en by se/eral key missionreuirements. he fi/e categories of design reuirements that applied to this mission

wereC mission reuirements, airworthiness, cost, manufacturing, maintenance andaccessibility. he mission


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&.# -in!

o retain the highly cambered shape of the airfoil and its lift characteristics,styrene foam was used for the construction of the wing. 9our balsa spars of si4e 6.*7

inches A 6.*7 inches each were embedded in the foam close to the uarter chord of thewing as shown in 9igure 2.+ below.

9igure 2.+ Wing cross section showing four main spars and one sparat the trailing edge used for the control surface hinges.

he spars were designed to support the bending loads applied at the maAimum loadingcondition during flight that is at the maAimum thickness point of the wingI uarter chord.he si4e of each of the spars was obtained by multiplying the wing loading factor by *.7gand +.7 safety factor and approAimating the distributed lifting load on the wing asrectangular rather than elliptical for ease of calculation. 9urther more, it was assumed thatthe spars carried the all bending stresses and the foam and Micafilm did not carry anyload. he dimensions and distance between the spars is shown in figure 2.* below.

9igure 2.* %onfiguration of the balsa spars at the uarter chord of the wing.

With the gi/en dimensions and configuration of spars, the mathematical model predictedthe spar will eAperience a maAimum bending stress of about *+66 psi at the root of the

wing. his suggests that the spar would break as the σyiel& for balsa was eAperimentally

found to be +-*7 psi. Our conser/ati/e assumption that foam and Micafilm does not

carry any bending loads, for simplicity of calculations, is not true. 3n reality, foam andMicafilm do carry bending loads. 3n order to test this assumption, a sample model of thewing of about +.7 ft was constructed from foam, Micafilm and four 6.*7


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9igure 2.0 his figure eAhibits the loading on the wing test section performed at #)!.

he sample wing was clamped at one end with hea/y weights and a constant loading of*.76 lb"ft was applied with the aid of sand bags along the +.7ft span. # resultant force ' of about 8.6 lb, which is the sum of all constant loading on the rest of the wing subtractingthe downward force from the weights of ser/o, wires, boom, landing gear, half of thehori4ontal and /ertical tails, was applied at the end of sample wing. 3t was obser/ed thatthe wing did not break. (ence, this pro/ed that not only the wing will not break at themaAimum loading condition but also that the styrene foam and Micafilm do carry someof the bending loads. Micafilm was employed as wing skin that pro/ided the torsionalrigidity and stiffness. )ince the trailing edge of the wing was /ery thin, it was reinforcedwith fiberglass that is lightweight, strong and durable.

he wing of our aircraft was made up of three parts. he mid&wing section wasabout 0ft in length and the two outer wing sections were 2.6 ft each. he reason for thistype of configuration was that the wings could be easily detached allowing for ease intransportation. 8


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he connectors were made to be a tight fit so that the wing tips don


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9igure 2.- !ayout of euipment inside the fuselage.

#s seen from the abo/e 9igure 2.-, the fuselage was hollowed out to make room for theeuipment and payload. Most of the payload was placed close to the nose of the fuselageso as to center of gra/ity may be shifted forward. 9uselage was mounted in the center ofthe mid section of the wing with two plastic blots that were located underneath the wingand were fiAed to blocks of balsa +


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he si4es of each of the four balsa spars needed to carry the hori4ontal tail aerodynamicloads were +"1 inches A +"+8 inches. he critical stresses in the hori4ontal tail were well below the yield stress of balsa. Both the tail sections were attached to the carbon fiber boom that in turn was connected to the wing. he carbon fiber booms were hollow, 0.6 ft

in length with an outer diameter of about 6.8


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5 'ropulsion system

5.1 Introduction

9or this pro?ect, the term propulsion system, refers to the entire arrangement of batteries, speed controller, motor, gearboA and propeller. he design of a suitable

propulsion system for the Boiler ;press aircraft began early in the design process, whenthe first constraint diagram E9ig. *.*F was de/eloped. he largest constraint on the propulsion system came from the reuirements for climb. his year


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With efficiencies chosen for the propeller and gearboA it is possible to determine howmuch power the motor must supply.

F57.6Q76.6"Erequired required aircraft motor

P P = E7.+F

he power reuired by the motor then became the dri/ing parameter for motor selection.

5.# otor and Speed Controller Selection

3n addition to the power reuired, the Boiler ;press team felt a re/ersible motorwas also reuired since the concept was a pusher type aircraft. here are pusher type propellers, which allow a motor to run in the normal direction, but the number of pusher props a/ailable was /ery limited. he team felt that by limiting the propeller selectiondatabase to these few propellers, the aircraft would ne/er achie/e the desired performance. he aircraft might also be unable to complete the endurance mission if the propeller were not appropriate matched to the motor and gearboA, due to the decreasedefficiency.

Very few motor manufacturers produced, or ad/ertise, re/ersible motors. heBoiler ;press team did, howe/er, find one manufacturer who sold a re/ersible motor thatmet the power reuirements of the aircraft, Model lectronics %orp. he specific motorselected was the urbo +6 : E9ig. 7.+F. he urbo +6 : E#pp. 9F motor came with agearboA, called the =monster boA>, which could accept multiple gear ratio wheels. hemanufacturer was generous enough to send se/eral gear ratios along with the motor,including -C+, 8C+ and 5.8C+. With a large range of ratios to choose from, the team felt/ery sure that the motor, gearboA and propeller could be reasonably matched for eAcellent performance. he M;&16 digital speed controller, supplied with the motor, is small Elessthan +.7 o4.F and includes built&in battery eliminator circuitry to power the recei/er andser/os from the motor pack.

9igure 7.+ urbo +6 : Motor and :earboA from Model lectronics %orporation.

5.& 'ropeller Selection

he twel/e&minute endurance mission reuires that the propulsion system be as

efficient as possible. herefore, the Boiler ;press team chose a 9reudenthaler propellersystem E9ig. 7.*F. he 9reudenthaler propellers are specifically designed for electricflight. hey are also designed into three parts, the blade, the center yoke, the spinner andan optional propeller shaft adapter. he ad/antage to this system is that the center yokeand spinner can be used with multiple blades, allowing for an added degree of freedomo/er con/entional, wooden propellers. he two blade si4es that the Boiler ;press teamchose to use and analy4e were +8A+7 and +2A1.


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9igure 7.* 9reudenthaler 'ropeller )ystem

5.5 System Testin!

# series of wind tunnel test were completed in the Boeing Wind unnel at 'urdueni/ersity E9ig. 7.0F. he tunnel was run at the anticipated *2 ft"s cruise speed tosimulate flight conditions. %ombinations of propellers, battery packs and gear ratios were

tested with the urbo +6 : motor E#pp. F. he primary focus of these tests was to/erify that the endurance mission could be met.

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

00000 00712 01424

Time (h:mm:ss)

T h

r u s ( l ! )

9igure 7.0 hrust time histories for propulsion tests in the wind tunnel.

he battery packs, one ten cell +.* /olt nickel cadmium EKi%adF pack and one tencell, +.* /olt nickel metal hydride EKiM(F pack, eAhibited different beha/ior during thetests. Only two complete tests were eAecuted with the nickel metal hydride battery pack.Both tests were promising, ha/ing endurances right at the twel/e&minute missionreuirement. Kickel metal hydride batteries also don


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widely. ndurances with the Ki%ad batteries ranged from ten minutes up to siAteenminutes. his is likely due to older cells degrading o/er time and disuse.

9urther testing with all combinations of batteries, gear ratios, and propellers isrecommended. he limited preparation time prior to the pro/ing flights did not permitthe full range of testing which was desired. 3nterests in the results of additional testing

has been indicated by other design teams for the purpose of M#!#B®

code /erification,in the prediction of propulsion system performance.

6 (ynamics and Control

6.1 Introduction

he dynamics and control analysis of an aircraft is computational proof that theaircraft will not only fly, but do so with eAceptional flying ualities. #n aircraft that canremain in the air is useless unless it can be controlled and can demonstrate dynamicstability. he dynamic stability of an aircraft is go/erned by the main wing, thehori4ontal and /ertical tails, and the control surfaces associated with each wing, namely

the ailerons, rudderEsF, and ele/atorEsF. he dynamics and control of an aircraft isessentially a study of how changes in the control surfaces si4e and deflection effects theway an aircraft performs during flight.

6.2 $nalysis

he design process of an aircraft reuires interaction of all the disciplines that arenecessary to concei/e an aircraft concept. 9or the dynamics and control analysis, weneeded certain information pertaining especially to the geometry of the main wing. hisinformation came from the aerodynamic aspect of aircraft design.

o calculate the si4e of the hori4ontal and /ertical tails, we used the %lass 3

method for empennage si4ing as described by Roskam G*H. We needed the reference areaof the wing, S ref , the chord of the wing, c, the span of the wing, b and the distance fromthe aerodynamic center of the wing to the aerodynamic center of the hori4ontal and/ertical tails, xh and x, respecti/ely. ! and ! h are the /ertical and hori4ontal tailcoefficients. hese /alues are based on the geometrical layout of the aircraft. We foundthese /alues based on historical data taken from tables E1.+aF and E1.+bF by Roskam G*H.9rom this method we found our hori4ontal tail area, S h J *.* ft* and our /ertical tail area,S J +.-7 ft*. )ince we are incorporating a dual rudder system, historical data suggeststhat we increase our /ertical tail area by *7 to make up for the loss of effecti/eness dueto a dual rudder configuration. his /alue already includes this increase.

!ater in the design process we used a more detailed si4ing method also described

in Roskam G*H called ;&plot si4ing. o si4e the /ertical tail, the $irectional A&plotmethod was used. his method in/ol/es the yaw&aAis stability deri/ati/es of our aircraft.We first determined that our aircraft was inherently< directionally stable. his meansthat we did not need to implement a rate feedback system to obtain stable flightconditions. 9igure 8.+ shows a graphical representation of this method.


26/91

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Vertical tail area [sq ft]

CnBeta

Weathercock Stability Curve

Prototype target

9igure 8.+. ;&plot for directional stability.

he !ongitudinal A&plot, also described in Roskam, is the method used todetermine the hori4ontal tail area of our aircraft. )imilar to directional A&plot si4ing, the

longitudinal A&plot incorporates pitch&aAis stability deri/ati/es. 9igure 8.* shows a graphof this method.

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

-0.5

0

0.5

1

x/c

cg locationneutral point loction

9igure 8.*. ;&plot for longitudinal stability.

9igure 8.* shows how the center of gra/ity and neutral point change when we change thesi4e of the hori4ontal tail. he distance between these two lines is called the staticmargin, which 3 will discuss later. here is an acceptable range for the static margin toensure stability of the aircraft. 9rom this method we calculated our hori4ontal tail area to be +.10 ft* . his ga/e us a static margin of 6.65. $r. Roskam G*6H suggests the staticmargin to be between 6.+6 and 6.+7. We decided on this /alue partially based on centerof gra/ity location concerns. (owe/er, during the flight our aircraft demonstratedeAceptional pitch stability.

he si4es of the control surfaces were also found using historical data from $r.Roskam G*H tables E1.+aF and E1.+bF. hese tables gi/e ratios of the area of the controlsurface to the area of the corresponding wing. We took the a/erage ratio from homebuiltaircraft and single engine aircraft and then used our wing areas to calculate the area ofour control surfaces. We calculated our aileron area, S a J +.07 ft*, our rudder area, S r J6.16 ft*, and our ele/ator area, S e J +.66 ft*. $uring the flight, the pilot commented that


27/91


28/91

" Economics

".1 Structural Cost Brea;do


29/91

@*66 design goal, the cost is proportionally better for its si4e than other remotely piloted/ehicles with less performance.

# key marketing feature of this aircraft is the ease with which the plane could beassembled. he Boiler ;press aircraft reuires less than 7 minutes to make it flight ready.he use of fiberglass for the fuselage and for the thin trailing edge of the wing made it

/ery durable and robust to handling and crashes. he pusher design helps in protectingthe motor in case of a head&on collision. 3f the motor is switched on inad/ertently, thesurrounding airframe helps keep the propeller from in?uring crew or operators. his is animportant safety feature for high&powered electric aircraft.

$ue to its large wing, the aircraft was /ery stable in flight. 'ower&off flight isglider&like, with continued ease of handling to landing. his is an especially helpfulfeature in case the motor fails during flight or if the propulsion battery pack has beendepleted before landing. Battery recharging can be accomplished in *6 minutes.Replacement of the power pack is easily accomplished within 7 minutes reuiring only ascrewdri/er.

'esti#!

4%

Build

55%

Pelimi#a( )esi!#

41%

9igure -.* !abor $istribution for 'rototype $esign and Build


30/91

) *eferences

G+H Roskam, Pan, Airp"ane Desi#n Part $% Pre"iminar& Si'in# of Airp"anes,$#Rcorporation, ansas, +55-.

G*H Roskam, Pan, Airp"ane Desi#n Part $$% Pre"iminar& Confi#uration Desi#n and

$nte#ration of the Propu"sion S&stem, $#Rcorporation, ansas, +55-.

G0H Roskam, Pan, Airp"ane Desi#n Part $$$% La&out Desi#n of Coc(pit) Fuse"a#e) *in#and +mpenna#e% Cutawa&s and $nboard Profi"es, $#Rcorporation, ansas, +515.

G2H Roskam, Pan, Airp"ane Desi#n Part $!% La&out Desi#n of Landin# ,ear and S&stems,$#Rcorporation, ansas, +515.

G7H Roskam, Pan, Airp"ane Desi#n Part !% Component *ei#ht +stimation,$#Rcorporation, ansas, +555.

G8H Roskam, Pan, Airp"ane Desi#n Part !$% , $#Rcorporation, ansas, +55-.

G-H #ndrisani, $., -ission Specification for A.A+/01 Aircraft Desi#n) Fa"" 2333, 'urdueni/ersity, 3ndiana, *666.

G1H )un %., -echanics 4f Composite -ateria"s and LaminatesI 'urdue ni/ersity,)ring+555.

G5H $oyle Pames 9., #l/arado 9.!., Static and D&namic Ana"&sis of StructuresI luwer#cademic 'ublishers, +55+.

G+6H #rcher R. R. T !ardner . P., -echanics of So"ids% An $ntroductionI Mc:raw (ill,3nc, +552.

G++H Basiletti, M., Beech, R., Bhutta, O., and VanMeter, M., 5eam Desi#n Requirementsand 4b6ecties, ##27+ )enior $esign, 'urdue ni/ersity, West !afayette, 3K, )ept.+2,*666.

G+*H )elig, M., $ono/on, P., and 9raser, $., Airfoi"s at Low Speeds, )oarech'ublications, Virginia Beech, V#, +515.

G+0H )chmit4, 9. W. , Aerod&namics of the -ode" Airp"ane, translated from the :erman

language by .). #rmy Missile %ommand, Redstone #rsenal, #labama, +58-.

G+2H )elig, Michael )., :uglielmo, Pames P., 7i#h8Lift Low Re&no"ds 9umber Airfoi" Desi#n, Pournal of #ircraft, Vol. 02, Ko. +, Panuary&9ebruary +55-.

G+7H (oerner, )ighard 9., F"uid D&namic Dra#:) (oerner 9luid $ynamics, Bakersfield,%#, +55*.


31/91

G+8H #. %ook, . 3ndermuehle, :. !abuda, P. Rui4, . )chmidt&!ange, #. )hurtleff, !.Valentini, 5hio(o" Fina" Desi#n Report AA+ /01% Purdue ;niersit& Senior Aircraft Desi#n, )pring +555, 'urdue ni/ersity.

G+-H 'eters, Mark, Dee"opment of a Li#ht ;nmanned Aircraft for the Determination of

F"&in# Qua"ities Requirements, Masters hesis, 'urdue ni/ersity, May +558

G+1H ohn. Pean, Properties and ;ses of


32/91

$ppendix $ , Concept Selection and -ei!ted /b0ectives etod

%oncept selection takes place as the design mission and reuirements are wellunderstood by all team members. # group of canditate design configurations is formed asa result of brainstorming"discussion. %reati/ity is encouraged in this stage to produce awide range of ideas and solutions to the =problem>.

Ob?ecti/es the design must address adeuately are drawn from the missionstatement and ob?ecti/es as the team understands them. ach member of the design teamwas then asked to di/ide, among the ten ob?ecti/es, one hundred points. he point /aluesfor each ob?ecti/e gi/en by each team member were then summed and the percentage, oftotal points, for each ob?ecti/e was calculated. Eable *.+F.

able 9.+ & Weighted Ob?ecti/e 'rocess

4b6ectie Score = of 5ota"

ndurance 06 +6.6

Build within 0 weeks *-.7 5.+8!ight weight 76 +8.88urning radius 76 +8.88Robustness 06 +6ransportability +* 2ase of analysis **.7 -.7!anding ability 1 *.88Maintainability 06 +6Marketability 26 +0.00

he ob?ecti/es were then ranked in order of importance to the mission. When

ob?ecti/es matched percentiles, a team discussion ensued to determine which would

recei/e the higher ranking. he ten ob?ecti/es were ranked from one to ten, one being the

most important of the ob?ecti/es Eable *.*F.

able 9.* & Ob?ecti/e Ranking Result

Ran( 4b6ectie

+ !ight weight* urn radius

0 Marketability2 ase of construction7 Maintainability8 Robustness- ndurance1 ase of analysis5 ransportability+6 !anding ability


33/91

he final step in the weighted ob?ecti/es method, e/aluated each of the fi/econcepts, on each of the ten ob?ecti/es. ach concept was gi/en a score of D0, &+, 6, + or0 based on how well team members felt the specific concept would meet the gi/enob?ecti/e. he e/aluation was determined by group discussion Eable 9.0F.

able 9.0 & %oncept /aluation

Ran(ed 4b6ecties

>1?5win 2? Re#u"ar

>@? F"&in# *in#

>/?


34/91

he con/entional tractor monoplane style aircraft, as seen abo/e, is the highestscoring by the weighted ob?ecti/es method. (owe/er, due to the close scoring of theregular and twin boom concepts, and the enthusiasm of the design team for the twin

boom design, the final concept choice was to build the twin boom concept. his wouldalso gi/e the group the chance to further eAplore the weight sa/ings potential of thedistributed wing load characteri4ed by this layout.

Constraint (ia!ram

%****************************************************%% 451 Design Sizing Code% By Oneeb Bhutta%%****************************************************%****************************************************% Parameter used by us for Climb Rate%****************************************************rho !"!!#$1 %slugs&ft'$C(ma) 1"5$ %ssum+tionC( C(ma) & +o,er-1"#. "5/gamma 5"5*+i&10! %Climb ngle in RadiansCf !"!!Ratio2S,et2Sref $"435stall #! %ft&s Stall S+eedCdo Cf*Ratio2S,et2Sref

R 6161!7e !"5 %Os,ald 8ffi9en9y :a9tor;S !"16"!1617dummy. a?e@off Roll%****************************************************meu !"!5 %Around :ri9tion Coeffi9ient?1 !"!$3sigma !"10D( 00"03$ %lbf@ft&s@ft'#?# 4"3!*+o,er- -sigma&D(/. 1&$ /Stog 5 %ft of >a?e@off ground%****************************************************% Parameter used by us for >urn Rate%****************************************************g $#"# %ft&s'# -graity/+si !"313 %rad&se9 >urn ngleel #0 %ft&s Cruise elo9ity%****************************************************% ++lying loo+ for different R alues%****************************************************


35/91

% ere ;S ;&S E ;P ;&Pfor z 16= F 1&-+i*R-z/*e/ %**************************************************** % % Cal9ulating Rate of Climb % %**************************************************** for ? 16< term1 - #*;S-?/*9os-gamma/ / & -rho*C(/

term# ;S-?/*sin-gamma/ G ;S-?/*9os-gamma/*- Cdo G F*+o,er-C(.#//&C( ;P-?/ ;S-?/*+o,er- term1. @"5 /*+o,er- term#. @1 / end %**************************************************** % Plotting Different R alues for Climb Rate %**************************************************** if R-z/ +lot-;S. ;P.H?H/ hold on

elseif R-z/ 0 +lot-;S. ;P.HgH/ hold on elseif R-z/ +lot-;S. ;P.HbH/ hold on else

+lot-;S. ;P.HrH/ +lot-;S. ;P/ hold on end %**************************************************** % % Cal9ulating >a?e@Off Roll % %**************************************************** for ? 16< term$ ?1*;S-?/

term4 Stog*rho*- C(ma)*meu G !"#*Cdo/term5 Stog*rho*C(ma)*?#;P-?/ +o,er - - - term$ G term4 /&term5 / . @1 /

end %**************************************************** % Plotting >a?e@Off Roll %****************************************************

+lot-;S. ;P/

hold on %**************************************************** % % Cal9ulating >urn Rate % %**************************************************** for ? 16< term3 ;S-?/*F&- !"5*rho*+o,er- el. #/ / term +o,er- +si. #/*+o,er- el. # /&+o,er- g. # / G 1 term0 !"5*rho*+o,er- el. #/*Cdo&;S-?/


36/91

term el*- term3*term G term0 / ;P-?/ +o,er- term. @1 /

end %**************************************************** % Plotting Different R alues for >urn Rate %**************************************************** if R-z/ +lot-;S. ;P.H?H/ hold on elseif R-z/ 0 +lot-;S. ;P.HgH/ hold on elseif R-z/ +lot-;S. ;P.HbH/ hold on else

+lot-;S. ;P.HrH/ +lot-;S. ;P/ hold on

end %**************************************************** % % Stall S+eed % %**************************************************** 9ounter ! %Counter to form a straight line for ? 16<

;S21-?/ !"5*rho*+o,er- stall. #/*C(ma) ;P21-?/ 9ounter 9ounter 9ounter G "13 end %**************************************************** % Plotting stall s+eed %**************************************************** +lot-;S21. ;P21. HrH/ hold onendgrid)label-H;&SH/ylabel-H;&PH/legend-HRH.HR0H.HRH.HR1!H.!/


37/91

$ppendix B , $erodynamics etodolo!y

he component build&up method of drag prediction uses the wetted area )wet andform factor 99 to calculate the each airframe components contribution to the total parasite drag. 3nterference between bodies is accounted for in the interference factor N.hey are summed to gi/e the total 4ero&lift EparasiteF drag coefficient asC

∑=ref

wetiii fi

DS

S FF QC C

6 EB.+F

9orm factors for the components are based on empirical formulas. he formfactors for fuselage and nacelle components are found from the following relationshipsC

EB.*F

Where f is the fineness ratio of body length l and diameter d.he formulation of for the wing form function is gi/en byC

Where t is the thickness and c is the mean chord. he Mach number M is of course/ariable with flight conditions.

3nterference drag prediction is also based on empirical estimations. %omponentorientation and layout Ehigh&wing, mid&wing, low&wing for eAampleF determine the /alueof N as followsC

Component Confi!uration @ factor value

Wing (igh wing +.6!ow wing +.+&+.2

Mid wing +.6

Kacelle On wing +.7

L Kacelle $ia. 9rom wing +.0

Kacelle $ia from wing +.6

9uselage

Kacelle

d

" f =

+++=266

+6686

+0

f

f FF

f FF

07.6++=

( ) [ ]+1.62 02.++668.6+ - ct

c

x

ct

FF

++=

EB.0F


38/91

)ee Raymer


39/91

)h $"5

S2horz h*Sref*9bar&)h)bar2a9h #"$ele2ratio !"# % 9hord of eleator&9hord of h"stab

eta2h !"05 % tail dyami9 +ressure ratio @Raymer +" 41#:+ ! % assume no turning of flo, by +ro+eller:+a !)bar2a9, !"$ % S1#1! aifoilal+ha2!( @0*+i&10! % radCla 5"44 % from airfoil 9l s al+ha +loteta1 Cla&-#*+i/C(!h !C(ah $"# %1&rad from thin symmetri9al airfoilal+h2!(2h ! %symmetri9al h"stab se9tion

%% Stability eKuations6

> !Lbar2t "15 %erti9al distan9e of thrust line from 9"g"

d8u2da 1"$ % u+,ash deriatie ,ith al+ha from Raymer fig 13"11d82da "$$ % do,n,ash deriatie from fig"13"1#del2h 1@d82da % 9hange in horiz"stab angle of atta9? ,ith ,ingangle of atta9?

: 1"!*-1G"#5&11"1/'# %fuselage lift fa9tor Raymer 1#"i, $*+i&10! % ,ing in9iden9e angleih @3*+i&10! % tail in9iden9e angleCm, Cm!*-*-9os-lamda//'#&-G#*9os-lamda///delta2al+ha2C(ma)#*+i&10! %:rom airfoil dataC(a2, -#*+i*/&-# G -4G--'#&eta1'#/*-1G-tan-lamda//'#///'"5/*Se)+&Sref*: %,ing only Raymer 9h 1#al+ha2C(ma) C(ma)&C(a G al+ha2!( G delta2al+ha2C(ma)C(h2deC(ah&+i*-a9os-1@#*ele2ratio/ G #*-ele2ratio*-1@ele2ratio//'"5/ % =ar? Peters "1#C(a C(a2, G C(ah*eta2h*-S2horz&Sref/*-1@d82da/ % ,hole air9raft :romRos?am eK $"#4Cmfus ! % assume no +it9hing moment from fuselageCma2fus !)bar2+ !del2+ !

CmK@#"#*eta2h*-S2horz&Sref/*C(ah*-)bar2a9h@)bar29g/'# %Pit9h dam+ingderiatie -Raymer 13"5#/K+rime$#"#*-n@1/&9ruise %+it9h rate as related to load fa9tor for+ull@u+ manueer -Raymer 13"5/

i!al+ha @46#61#7al+haal+ha*+i&10!

for de@106610


40/91

if de @10 stringH?*@H else if de@ string Hr*@H else if de! string Hg*@H else if de string Hb*@H else stringHm*@H end end end end

dede*+i&10! %9onert to radians iiG1

de2dummy-i/ de

al+ha2h -al+haGi,/"*-1@d82da/ G -ih@i,/ % effe9tie angle of atta9?of horiz"stabC(h C(!h G C(h2de*de G C(ah"*al+ha2h % lift of h@stabC(,ingC(a2,*-al+ha Gi, @ al+ha2!(/ %,ing aloneC( n*-C(a2,"*-al+ha G i, @ al+ha2!(/ G eta2h*-S2horz&Sref/*C(h/

Cm9g C("*-)bar29g@)bar2a9,/ G Cm, G Cmfus @eta2h*-S2horz&Sref/"*C(h"*-)bar2a9h @ )bar29g/""" G >&-K*Sref/*Lbar2t G :+&-K*Sref/*-)bar29g @ )bar2+/G CmK*K+rime

Cma C(a2,*-)bar29g @ )bar2a9,/ G Cma2fus @eta2h*-S2horz&Sref/*C(ah*-del2h/*-)bar2a9h @ )bar29g/"""

G :+a&-K*Sref/*del2+*-)bar29g @ )bar2+/

)bar2n+ -C(a2,*)bar2a9, @ Cma2fus Geta2h*-S2horz&Sref/*C(ah*del2h*)bar2a9h G :+a&-K*Sref/*del2+*)bar2+/""" &-C(a2, G eta2h*-S2horz&Sref/*C(ah*del2h G :+a&-K*Sref//

%Cma @C(a2,*-)bar2n+ @ )bar29g/

%sub+lot-1.#.1/figure-1/

+lot-al+ha*10!&+i. Cm9g.string/hold onfigure-#/+lot-C(. Cm9g. string/hold onend

C(h2manueer -Cm9g @-C("*-)bar29g@)bar2a9,/G Cm, G Cmfus G >&-K*Sref/*Lbar2t G :+&-K*Sref/*-)bar29g @ )bar2+/G CmK*K+rime//""" "&-@ eta2h*-S2horz&Sref/*-)bar2a9h @ )bar29g//


41/91

(2horz C(h2manueer*"5*"!!#$1*S2horz*9ruise'#

figure-1/grid on)label-Hal+ha -rad/H/ylabel-HCm9gH/legend-Hele defle9t@0 [email protected]!H.H4H.H0H/hold off

figure-#/grid on)label-HC(H/ylabel-HCm9gH/legend-Hele defle9t@0 [email protected]!H.H4H.H0H/

hold offC(2de C(h2de*-S2horz&Sref/Cmastati92margin@-)bar29g@)bar2n+/

figure-$/+lot -al+ha*10!&+i. C(,ing/)label-Hal+ha deg7H/ylabel-HC( ,ing onlyH/grid on

(ra! $nalysis

%************************************************%% >his 9ode +redi9ts the total Drag Cdo and lift% 9oeffi9ient Cl of the air9raft at different% flight elo9ities"%% Programmer6 Oneeb Bhutta% Dated6 !&!!% =odified by =atthe, Basiletti 1!#&!!%%************************************************

%Clearing =atlab memory and s9reen9lear9l9

%************************************************% :light Conditions%************************************************

meu $"1e@ %slugs&ft@se9 M 1!!!ftel 16165!7 %ariuos flight elo9itiesrho !"!!#$1 %slugs&ft'$ -density/tem+2air 515"1# %tem+ of air in R M1!!!ftgamma2air 1"4R2air 110 %Aas 9onstant for air


42/91

%S+eed of sound M 1!!!fta +o,er- tem+2air*gamma2air*R2air. "5/

%Size of the elo9ity =atri9edummy otal ,etted area of ,ing -ft'#/

%************************************************% >ail horizontal E erti9al surfa9es%************************************************b2horz $"! % s+an of horizontal stabilizer -ft/S2horz #"#92horz S2horz&b2horz %Chord of the horizontal stab -ft/

)292horz !"4 %Chord,ise lo9ation of ma)imum thi9?ness +ointt292horz !"!3 %Pre9ent of thi9?ness of the airfoilS,et2horz S2horz*#*1"!# %,etted area -ft'#/

N2horz 1"44 %Com+onent Jnterferen9e fa9tor92er2root 1"! %Root Chord of the ert" stab"-ft/92er2ti+ !"3 %>i+ 9hord of ert" stab -ft/92er -92er2rootG92er2ti+/ %aerage 9hord of ert tailS2er 1"5 %area of both ert tails -ft'#/h2er !"5*S2er&-!"5*-92er2rootG92er2ti+//


43/91

S,et2er S2er*#*1"!# %,etted area -ft'#/ -BO>/)292er !"4 %Chord,ise lo9ation of ma)imum thi9?ness+ointt292er !"!3 %Pre9ent of thi9?ness of the airfoil

%************************************************% :uselage%************************************************

92fuselage $"$ %length in ftd2fuselage +o,er- 4*"#&+i. "5 / %Diameter in ft

%rea of the fuselage in ft'#S,et2fuselage !"*+i*d2fuselage*92fuselage

%************************************************% +od --


44/91

%************************************************

% Drag Cal9ulation for main ,ing %************************************************

% Reynolds number R2,ing rho*el-?/*92,ing&meu

%S?in fri9tion Coeffi9ient ->urbulent flo,/ %-Ref" Raymer eK"1#"#/ tem+1 log1!-R2,ing/ Cf2,ing -!"455&+o,er-tem+1. #"50//*1"# %s?in fri9tion 9oeffi9ientadusted for rough surfa9e

%Com+onent :orm fa9tors%-Ref" Raymer eK"1#"$!/

=a9h el-?/&a

tem+# 1 G !"3*t292,ing&)292,ing """

G 1!!*+o,er- t292,ing. 4 / tem+$ 1"$4*+o,er-=a9h. !"10/

::2,ing tem+#*tem+$

% Drag 9do %-Ref" Raymer eK"1#"#4/ Cdo2,ing Cf2,ing*::2,ing*S,et2,ing&Sref

%************************************************ % Drag Cal9ulation for horizontal E erti9al % surfa9es %************************************************

% Reynolds number R2horz rho*el-?/*92horz&meu

%S?in fri9tion Coeffi9ient ->urbulent flo,/ tem+3 log1!-R2horz/ Cf2horz -!"455&+o,er-tem+3. #"50//*1"# %oriz"stab" fri9tion9oeff" adusted for rough surfa9e

%Com+onent :orm fa9tors

tem+ 1 G !"3*t292horz&)292horz """

G 1!!*+o,er- t292horz. 4 / tem+0 1"$4*+o,er-=a9h. !"10/

::2horz tem+*tem+0

% Drag 9do Cdo2horz Cf2horz*::2horz*N2horz*S,et2horz&Sref

% Reynolds number


45/91

R2er rho*el-?/*92er&meu

%S?in fri9tion Coeffi9ient ->urbulent flo,/ tem+ log1!-R2er/ Cf2er -!"455&+o,er-tem+. #"50//*1"# %ert"stabl fri9tion 9oeff"adusted for rough surfa9e


tem+1! 1 G !"3*t292er&)292er """ G 1!!*+o,er- t292er. 4 / tem+11 1"$4*+o,er-=a9h. !"10/

::2er tem+1!*tem+11

% Drag 9do Cdo2er Cf2er*::2er*S,et2er&Sref

%************************************************

% Drag Cal9ulation for :uselage %************************************************

% Reynolds number R2fuselage rho*el-?/*92fuselage&meu

%S?in fri9tion Coeffi9ient ->urbulent flo,/ tem+4 log1!-R2fuselage/ Cf2fuselage -"455&+o,er-tem+4. #"50//*1"#

%Com+onent :orm fa9tors %-Ref Raymer eK"1#"$1 E eK"1#"$$/ f2fuselage 92fuselage&d2fuselage ::2fuselage - 1 G 3!&+o,er-f2fuselage.$/ """ G f2fuselage&4!! /

% Drag 9do Cdo2fuselage Cf2fuselage*::2fuselage""" *S,et2fuselage&Sref

%************************************************ % Drag Cal9ulation for +ods %************************************************

% Reynolds number R2+ods rho*el-?/*92+ods&meu

%S?in fri9tion Coeffi9ient ->urbulent flo,/ tem+5 log1!-R2+ods/ Cf2+ods -!"455&+o,er-tem+5. #"50//*1"#



46/91

f2+ods 92+ods&d2+ods ::2+ods 1 G !"$5&f2+ods

% Drag 9do@ for ea9h +od Cdo2+ods Cf2+ods*::2+ods*N2+ods*S,et2+ods&Sref

%************************************************ % Drag Cal9ulation for boom %************************************************

% Reynolds number R2boom rho*el-?/*92boom&meu

%S?in fri9tion Coeffi9ient ->urbulent flo,/ tem+1# log1!-R2boom/ Cf2boom !"455&+o,er-tem+1#. #"50/

%Com+onent :orm fa9tors f2boom 92boom&d2boom ::2boom - 1 G 3!&+o,er-f2boom.$/ """ G f2boom&4!! /

% Drag 9do for ea9h boom Cdo2boom Cf2boom*::2boom*S,et2boom&Sref

%************************************************ % >otal Parasite Drag

%************************************************

CDo2tem+ Cdo2,ing G Cdo2horz G Cdo2er G""" Cdo2fuselage G #*Cdo2boom G #*Cdo2+ods

% 1! +er9ent of mis9ellaneous drag CD2mis9 !"1!*CDo2tem+

%>otal Parasite Drag CDo-?/ CDo2tem+ G CD2mis9

%************************************************ % >otal Drag of the air9raft

%************************************************

CDi-?/ ?1*+o,er- C(-?/. # / CD-?/ CDo-?/ G CDi-?/ Drag-?/ CD-?/*"5*rho*el-?/"'#*Sref Dragi-?/ CDi-?/*"5*rho*el-?/"'#*Sref end


47/91

S,et2total S,et2,ingGS,et2horzGS,et2fuselageG#*S,et2+odsGS,et2erG#*S,et2boomPo,er Drag"*el

figure-1/+lot-el. CD.Hr@"H/hold on+lot-el. Drag.Hg@H/

title-Hirfoil Selig 1#1!H/)label-Helo9ity ft&sH/gridlegend-HCDH.H>otal DragH.!/figure-#/+lot-C(. CD. Hb*@H/hold on+lot-C(. CDi.Hg*@H/+lot-C(. CDo.Hr*@H/hold off

title-Hir9raft Drag PolarH/)label-HC(H/gridlegend-HCDH.HCDiH.HCDoH.!/figure-$/+lot-C(. CDo/)label-HC(H/ylabel-HCDoH/title-Hirfoil Selig 1#1!H/gridfigure-4/+lot-el.Drag.Hr@"H/hold on+lot-el. Dragi.Hb@H/title-Hirfoil Selig 1#1!H/)label-Helo9ity ft&sH/gridlegend-H>otal DragH.HJndu9ed DragH/

figure-5/+lot-el. CDi/)label-Helo9ity ft&sH/ylabel-HCdiH/title-Hirfoil Selig 1#1!H/grid

figure-3/

+lot-CD"'#. C("'$/)label-HCD'$H/ylabel-HC('#H/

figure-/+lot-el. Po,er.Hr*@H/grid)label-Helo9ity ft&s7H/ylabel-HPo,er ReKuired ft@lb&s7H/


48/91

$ppendix C Structural $nalysis etodolo!y

(isplacement and oment E8uations for te -in! SectionA

(isplacement and oment E8uations for te oriontal Tail

SectionA

( ) ( ) ( ) *W

W

*W

**

FE L* L

Lx* L x* L

x - oo

o −

+−−−

=

( ) L x P x - −=FE

( ) ( ) ( )2

.8

.*2

FE**W0W2W x L* L x* L x* L

x +$ ooo −

+−

−−

=

( )

( ) L xa for

a x Pa x +$

a x for a x Px

x +$

≤≤−

=

≤≤+−

=

..8

0FE

6.8

0FE

*

*

*i#!

wo

!ift

'


49/91

(isplacement and oment E8uations for te BoomsA

FEFE L x P x - −=

( ) ( ) ( )+*

.**

FE*WW*W

L* L Lx* L x* L x - ooo

+−

++

+−=

( ) ( ) ( )*2+**2

FE**W0W2W x L* L Lx* L x* L

x +$ ooo +

−+

++

−=

8F0EFE

*

x L Px x +$ −=

!ift

wo

P

Boom


50/91

Matlab %ode Output

6.*7> A 6.*7> spars for Wing )ectionCMoment_maA J 2+.-+25 lbf"ft)igma_maA J *.66*0eS660 psi

)igma_critical J +-*7 psi

+"1> A +"+8> spars for (ori4ontal ail )ectionCMoment_maA J .1*1* lbf"ft)igma_maA J 121.6012 psi)igma_critical J +-*7 psi

%***************************************************% >his +rogram 9al9ulates the =oments and% defle9tions for half of the ,ing of the% Boiler@+ress air9raft%% ******* I+dated ersion *******% By Oneeb Bhutta% Dated6 1!&!!%%***************************************************

9lose all9lear9l9

%***************************************************% =oment of Jnertia 9al9ulation of 4 stringers%***************************************************

ma)29amber # %in9hes,idth "#5 %in9hesheight "#5 %in9hesrea ,idth*height %in9hes'#

Jnertia 4*rea*+o,er- ma)29amber. # / %in9hes'4Jnertia2ft Jnertia&+o,er- 1#. 4/ %ft'4

%***************************************************% Pro+erties of S+ar -Balsa/%***************************************************

sigma29riti9al 1#5 %+si8 3#5e$ %+si82ft 8*+o,er- 1#. # / %lbf&ft'#

%***************************************************% Pro+erties of the ,ing%***************************************************

balsa2density 11"! %lbf&ft'$


51/91

Q29entroid 1 %in in9hessaftey2fa9tor #"5*1"5 %#"5g and S:1"5,o !"#$0 %,eight loading lb&ft( 5"5 %lenght of half of

%the ,ing in ft;2e)tra 1"!*saftey2fa9tor %;eight of sero. ,ires. boom.

%half of the tail. landing gear andmis9(2+rime $"4!3 %-lbf&ft/ ,ing loading aluelength2a 1"5 %distan9e of the

%e)tra ,eight from%root of the ,ing

%***************************************************%% Cal9ulation of the bending =oments and Defle9tion% on the ,ing se9tion%%***************************************************

) !6"16(7dummy


52/91

else =oment2#-?/ ! end %>otal Bending =oments =oment2total-?/ =oment21-?/ G =oment2#-?/

%*************************************************** % Cal9ulation of defle9tions %***************************************************

%Part1 defle9tion21-?/ - -(2+rime @ ,o/*+o,er- )-?/. 4/ G """ C1*+o,er- )-?/. $/&3 G C#*+o,er- )-?/. # / G C$*)-?/ """ G C4/&- 82ft*Jnertia2ft/ %Part# if )-?/ 1"5

defle9tion2#-?/ ;2e)tra*+o,er- )-?/. #/*- )-?/ @ $*length2a/&-3*82ft*Jnertia2ft/ else

defle9tion2#-?/ @;2e)tra*+o,er-length2a. #/*- $*)-?/ @length2a/&-3*82ft*Jnertia2ft/ end %>otal Defle9tions defle9tion2total-?/ defle9tion21-?/ G defle9tion2#-?/end%***************************************************%% Cal9ulation of the =a)imum Stress from =a)% Bending =oment%%***************************************************

=oment2ma) dummy#7 ma)- abs-=oment2total/ /sigma2ma) =oment2ma)*1#*Q29entroid&Jnertiasigma29riti9al>otal2s+ar2,eight 13*- balsa2density*4*rea*(*#&144/

%***************************************************%% :igures and +lots%%***************************************************

figure-1/+lot-). lo/hold on

+lot-). lo1. Hr@"H/title-H(oading on half of the ;J


53/91

+lot-). =oment21.Hr)H/hold on+lot-). =oment2#.Hbo@H/title-HBending =oments for the ;ingH/)label-Hlength ft7H/ylabel-H=oment lb&ft7 H/gridlegend-H>otal BendingH.H(ift loading =omentH. HPod ;eight =omentH. !/

figure-$/+lot-). defle9tion2total*1#.Hg*H/hold on

+lot-). defle9tion21*1#.Hr)H/hold on

+lot-). defle9tion2#*1#.Hbo@H/title-HDefle9tion for the ;ingH/)label-Hlength ft7H/ylabel-HDefle9tion in7 H/

grid

legend-H>otal Defle9tionH.H(ift loading defle9tionH. HPod ;eightdefle9tionH. !/

0 1 2 3 4 5 60

0.5

1

1.5

2

2.5

3

3.5Loading on half of the WING

Length [ft]

w i n g l o a d i n g [ l b / f t ]

Actual Wing loading

Mathematical Model Employed

0 1 2 3 4 5 6

-10

0

10

20

30

40

50Bending Moments for the Wing

length [ft]

M o m e n t [ l b / f t ]

Total Bending

Lift loading Moment

Pod Weight Moment

0 1 2 3 4 5 6-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5Deflection for the Wing

length [ft]

D e fl e c t i o n [ i n ]

Total Deflection

Lift loading deflection

Pod Weight deflection


54/91

%***************************************************% >his +rogram 9al9ulates the =oments and% defle9tions for the orizontal tail se9tion%%% By Oneeb Bhutta% Dated6 1!&!!%%***************************************************

9lose all9lear9l9

%***************************************************% =oment of Jnertia 9al9ulation of 4 stringers%***************************************************

ma)29amber $&4 %in9hes

,idth "1#5 %in9hesheight "!3#5 %in9hesrea ,idth*height %in9hes'#

Jnertia 4*rea*+o,er- ma)29amber. # / %in9hes'4Jnertia2ft Jnertia&+o,er- 1#. 4/ %ft'4

%***************************************************% Pro+erties of S+ar -Balsa/%***************************************************

sigma29riti9al 1#5 %+si8 3#5e$ %+si82ft 8*+o,er- 1#. # / %lbf&ft'#


balsa2density 11"! %lbf&ft'$Q29entroid -$&4/*!"5 %in in9hessaftey2fa9tor 1"5 %S:1"5( $"! %lenght of horizontal >ail in ft,o 5"!&-13*(/ %>otal ,eight loading -lbf&ft/(2+rime !"333*saftey2fa9tor %-lbf&ft/ ,ing loading" #"5 safetyfa9tor

%is already in9luded in the ,ingloading

%***************************************************%% Cal9ulation of the bending =oments and Defle9tion% on the orizontal >ail se9tion%%***************************************************


55/91

) !6"!56(7dummy otal2s+ar2,eight 13*- balsa2density*4*rea*(*#&144/

%***************************************************%% :igures and +lots%%***************************************************

figure-1/


56/91

+lot-). =oment21.Hg*H/title-HBending =oments on the orizontal >ailH/)label-Hlength ft7H/ylabel-H=oment lb&ft7 H/grida)is eKuallegend-H>otal BendingH. !/

figure-#/+lot-). defle9tion21*1#. Hr*H/title-HDefle9tion of the orizontal >ailH/)label-Hlength ft7H/ylabel-HDefle9tion in7 H/grida)is eKuallegend-H>otal Defle9tionH. !/

0 0.5 1 1.5 2 2.5 3

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Bending Moments on the Horizontal Tail

length [ft]


Total Bending

0 0.5 1 1.5 2 2.5 3

-1

-0.5

0

0.5

1

Deflection of the Horizontal Tail

length [ft]


Total Deflection

%***************************************************% >his +rogram 9al9ulates the =oments and% defle9tions for one of the boom rods"%%% By Oneeb Bhutta% Dated6 1!&!!%%***************************************************

9lose all9lear9l9

%***************************************************% =oment of Jnertia 9al9ulation for the hollo,% boom rod%***************************************************

ro "5$# %inner radius in in9hesri "5! %outer radius in in9hes

Jnertia -+i&4/*- +o,er- ro. 4 / @ +o,er- ri. 4 / / %in9hes'4


57/91

Jnertia2ft Jnertia&+o,er- 1#. 4/ %ft'4

%***************************************************% Pro+erties of Carbon@8+o)y rod%***************************************************

8 1"4e3 %+si82ft 8*+o,er- 1#. # / %lbf&ft'#


S: #"5*1"5 %Safety fa9tor( $"5 %lenght of 1 boom in ft2tail 5&13 %;eight of @tail in lbf2tail #"0!&13 %,eight of @tail in lbfP !"5*- 2tail G 2tail /*S:R 1"5 G P %1"5lbf is the load on the

%half on the @tail in9luding S:

%***************************************************%% Cal9ulation of the bending =oments and Defle9tion% on the orizontal >ail se9tion%%***************************************************

) !6"!56(7dummy


58/91

%%***************************************************=oment2ma) dummy#7 ma)- abs-=oment/ /%***************************************************%% :igures and +lots%%***************************************************figure-1/+lot-). =oment.Hg*H/title-HBending =oments for the boomH/)label-Hlength ft7H/ylabel-H=oment lb&ft7 H/gridlegend-H>otal BendingH. !/

figure-#/+lot-). defle9tion*1#. Hr*H/title-H Defle9tion of the boomH/)label-Hlength ft7H/

ylabel-HDefle9tion in7 H/grid

axis e8ual

le!endTotal (eflection? +D

0 0.5 1 1.5 2 2.5 3 3.50

1

2

3

4

5

6

7

8

9Bending Moments for the boom

length [ft]


Total Bending

0 0.5 1 1.5 2 2.5 3 3.5

-1.5

-1

-0.5

0

0.5

1

Deflection of the boom

length [ft]


Total Deflection


59/91

$ppendix ( , $T3$B 'ropulsion System $nalysis Code

% =>(B COD8 :OR PROPI(SJO< SQS>8= S8(C>JO<% 8451 :(( #!!. =JC8( 8R% S8P>8=B8R $! #!!!

9lear all9lose all

drag+ro+%9lear N2+ods f2+ods R2air foil21 CD2mis9 R2boom foil2# R2fuselage%9lear R2horz ? CDo2tem+ R2+ods R2er Cdo2boom R2,ing meu%9lear Cdo2fuselage Cdo2horz S,et2boom t292horz Cdo2+ods S,et2fuselage%9lear t292er Cdo2er S,et2horz t292,ing Cdo2,ing S,et2+ods tem+1Cf2boom%9lear S,et2er tem+1! Cf2fuselage S,et2,ing tem+11 Cf2horz tem+1#Cf2+ods%9lear tem+# Cf2er 92boom tem+$ Cf2,ing 92fuselage tem+4 92horz tem+5Dragi

%9lear 92+ods tem+3 ::2boom 92er tem+ ::2fuselage 92,ing tem+0::2horz d2boom%9lear tem+ ::2+ods d2fuselage tem+2air ::2er d2+ods ::2,ing dummy)292horz%9lear =a9h eo )292er < f2boom )292,ing N2horz f2fuselage R

% I CO


60/91

te)[email protected]/G1!/.HBest 8nduran9e S+eed6 H.num#str-e/.H ft&sH7/grid on: Pr"&elfigure-/+lot-el.:[email protected].:e.Hm)H/te)t-e.-:eG!"1/.HBest 8nduran9e >hrust6 H.num#str-:e/.H lbH7/title-H>hrust ReKuired CureH/)label-Helo9ity -ft&s/H/ylabel-H>hrust -lb/H/grid on

% PROP8((8R P8R:OR=


61/91

if [email protected]/!/[email protected]/!// G1 endend dummy7 size-etai/for i16 if -ma)-etai/ etai-i// etaistar etai-i/ Uistar Ui-i/ end

end startabi--1!*?@4/.16$/ ? Uistar etaistar7

figure-/+lot-Ui.etai.string/title-HPro+eller 8ffi9ien9y at Best Jndoor S+eed

-H.num#str-ideal/.H ft&s/H7/)label-HUH/ylabel-HetaH/

grid on hold on

endfigure-0/legend-H>au !"5H.H>au !"3H.H>au !"H.H>au !"0H.H>au !"H.H>au 1"!H.$/hold offfigure-/legend-H>au !"5H.H>au !"3H.H>au !"H.H>au !"0H.H>au !"H.H>au 1"!H.$/hold offdis+-H H/dis+-H H/dis+-H for H.num#str-e/.H -ft&s/H7/dis+-H tau Ustar etastarH/dis+-H @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@H/dis+-startabe/dis+-H H/dis+-H H/dis+-H for H.num#str-ideal/.H -ft&s/H7/dis+-H tau Ustar etastarH/dis+-H @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@H/dis+-startabi/dis+-H H/dis+-H H/dis+-H H/

% 8=JJO;88< RO>>JO


62/91

+lot-RP=.De-6.1/.Hb@@H.RP=.De-6.#/[email protected]=.De-6.$/.Hb@"H.RP=.De-6.4/.Hb"H.RP=.De-6.5/.Hm@@H.RP=.De-6.3/.Hm@"H/title-HPro+eller Diameter for Best 8ffi9ien9y for H.num#str-e/.H-ft&s/H7/legend-H>au !"5H.H>au !"3H.H>au !"H.H>au !"0H.H>au !"H.H>au 1"!H/)label-HRP=H/ylabel-HDiameter -in/H/grid onfigure-11/+lot-RP=.Di-6.1/.Hb@@H.RP=.Di-6.#/[email protected]=.Di-6.$/.Hb@"H.RP=.Di-6.4/.Hb"H.RP=.Di-6.5/.Hm@@H.RP=.Di-6.3/.Hm@"H/legend-H>au !"5H.H>au !"3H.H>au !"H.H>au !"0H.H>au !"H.H>au 1"!H/title-HPro+eller Diameter for Best 8ffi9ien9y for H.num#str-ideal/.H -ft&s/H7/)label-HRP=H/ylabel-HDiameter -in/H/grid on

% C(CI(>8 < JD8( DJ=8>8Rdis+-H H/dis+-H H/dis+-H H/dis+-H;RRJC =O>OR orKue and etam are the% de+endent ariables%


63/91

% 22222222222222% RP= @@@@@@@XV V@@@@@@@X in% V V@@@@@@@X Jin% V R8( =O>OR V@@@@@@@X Pin% Pout @@@@@@XV V@@@@@@@X >orKue% V22222222222222V@@@@@@@X etam%

% >he +oer reKuired by the air9raft must be eKual to the% +o,er out+ut by the +ro+eller% P+ro+ >* Pa&9 *rho*-n*D/'#*D'#*Ctstar

%9lear deg#rad h+#ftlbs h+#,att ftlbs#, CDe CDi CDo CDoe CDstar%9lear C(e C(star CDto D Drag :e ( Prto Sref > e el stall%9lear to a gamma2air ?1 ?,h#ftlb lift rho ma) min ,eight CD C(

'ropeller analysis codefun9tion CP.C>.U.eta.>7 goldfun9-Din.Pin.RP=.in+ut/

% Pro+eller nalysius :un9tion Ising AoldsteinHs orte) >heory%% Isage6% CP.C>.U.eta.>7 goldfun9-D.P.RP=./%% Jn+uts6% D @ Pro+eller Diameter% P @ Pro+eller Pit9h% RP= @ Pro+eller S+eed% @ :light S+eed

%% Out+uts6% CP @ Po,er Coeffi9ient% C> @ >hrust Coeffi9ient% U @ dan9e Ratio% eta @ 8ffi9ien9y% > @ >hrust

e9ho offformat 9om+a9t

%dis+-H H/

%dis+-HStart ne, runH/%dis+-HPro+eller nalysis using Aoldsteins Classi9al orte) >heoryH/%dis+-H >his 9ode ,or?s for t,o bladed +ro+ellers only"H/%dis+-H H/

% Jn+ut 9onstantsm+h in+ut*"3010 %in+ut elo9ity -m+h/%m+h! % airs+eed in m+hrho !"!!#$1


64/91

% Pin gies geometri9 angle to the flat +art of the% rear of the +ro+elleraoldeg@3 % angle of zero lift of the +ro+eller -degrees/ % measured from mean 9hord line -ty+i9ally negatie/beta!deg"5 % angle from flat +art of the +ro+ to mean 9hord linea#*+i % lift 9ure slo+e of +ro+ellerCd!"!!355 % #@d minimum drag 9oeffi9ient?"!1 % Cd Cd!G?*Cl*ClB# % number of blades -# for standard ty+e +ro+eller/

% in+ut nondimensional +ro+erties at ea9h radial lo9ation% 9R9&R. )r&R)"$."$5."4."45."5."55."3."35."."5."0."05."."5.1"79R"!*ones-size-)//% 8


65/91

%%dis+-H H/%dis+-H) is r&R and is nondimensional. 9R9&R. 9in is the 9hord inin9hesH/%e9ho on%dis+-)H. 9RH. 9inH7/%e9ho off%dis+-H H/

beta1atan---Pin&Din/&+i/"&)/betabeta1G-beta!deg@aoldeg/&r#dsigmaB*9&-+i*R/r)*Rrt*sKrt-)"*)Glamda*lamda/+hiatan-lamda"&)/;tt"!#*ones-size-9// %initial guessnrlength-9/nr1nr@1aioldzeros-size-9//for ii164!

;at-16nr1/"5*-@lamdaGsKrt-lamda*lamdaG4*;tt-16nr1/"*-)-16nr1/@

;tt-16nr1////ai-16nr1/atan-;tt-16nr1/"&;at-16nr1//@+hi-16nr1/%ai-16nr1/atan--G;at-16nr1/*t/"&-omega*r-16nr1/@;tt-16nr1/*t//@

+hi-16nr1/esum-abs-ai-16nr1/@aiold-16nr1///iterH(oo+ inde) H.num#str-ii/.H error H.num#str-e/7%dis+-iter/if e"!!!1 brea? endaiold-16nr1/ai-16nr1/Cl-16nr1/a*-beta-16nr1/@ai-16nr1/@+hi-16nr1//et-16nr1/sKrt--lamdaG;at-16nr1//"'#G-)-16nr1/@;tt-16nr1//"'#/gamma-16nr1/"5*9-16nr1/"*Cl-16nr1/"*et-16nr1/*tsin+hial+-16nr1/sin-+hi-16nr1/Gai-16nr1//?a++a-16nr1/?a++a#-)-16nr1/.sin+hial+-16nr1//;tt-16nr1/B*gamma-16nr1/"&-4*+i*t*r-16nr1/"*?a++a-16nr1//

endCl-nr/!ai-nr/beta-nr/@+hi-nr/rtsKrt-lamda*lamdaG1/;at-nr/rt*sin-ai-nr//*9os-ai-nr/G+hi-nr//;tt-nr/rt*sin-ai-nr//*sin-ai-nr/G+hi-nr//et-nr/sKrt--lamdaG;at-nr//'#G-)-nr/@;tt-nr//'#/?a++a-nr/!

CdCd!G?*Cl"*ClL>-+i&0/*-U*UG+i*+i*-)"*)//"*sigmaLP+i*L>"*)

dC>d)L>"*-Cl"*9os-+hiGai/@Cd"*sin-+hiGai//dCPd)LP"*-Cl"*sin-+hiGai/GCd"*9os-+hiGai//% Oerall +ro+eller +erforman9eC>tra+i-dC>d).)/CPtra+i-dCPd).)/etaC>*U&CP>C>*rho*n'#*D'4P-CP*rho*n'$*D'5/&"5PP&55!P,att1"$53*P


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torKueP&omegaClma)ma)-Cl/>oz>*13Pest;atts1"$1*D'4*-Pin&1#/*-RP=&1!!!/'$% >he aboe a++ro)imate formula ,or?s for% >o+ :lite. Linger and =aster irs9re,s reasonably ,ell"% :or Re I+ +ro+s subra9t "5 in from the +it9h"% :or PC +ro+s use 9onstant 1"11 instead of 1"$1"% :or thin 9arbon fiber folding +ro+s use 1"10 instead of 1"$1"% Ref6 8le9tri9 =otor andboo?. by Robert U" Bou9her.% stro:light. Jn9"%e9ho on%dat )H. betaH. +hiH. ?a++aH. aiH. ;ttH7%dis+-H H/%dat#)H. ;atH. etH. ClH. dC>d)H. dCPd)H7%e9ho off%dis+-H H/%dis+-HS+eed H.num#str-/.H ft&se9H7/%dis+-HRP= H.num#str-RP=/.H r+mH7/%dis+-HDiameter Din H.num#str-Din/.H in9hesH7/

%dis+-HPit9h Pin H.num#str-Pin/.H in9hesH7/%dis+-HPro+eller effi9ien9y eta H.num#str-eta/7/%dis+-H>hrust > H.num#str->/.H +oundsH7/%dis+-H>hrust >oz H.num#str->oz/.H oun9esH7/%dis+-HPo,er used P H.num#str-P/.H ft*lbf&se9H7/%dis+-Horse+o,er used P H.num#str-P/.H PH7/%dis+-HPo,er used P,att H.num#str-P,att/.H ,attsH7/%dis+-H>orKue used N H.num#str-torKue/.H ft*lbfH7/%dis+-H>orKue used N H.num#str-torKue*1#/.H in@ozH7/%dis+-HPo,er Coeffi9ient CP H.num#str-CP/7/%dis+-H>hrust Coeffi9ient C> H.num#str-C>/7/%dis+-Hdan9e Ratio U H.num#str-U/7/%dis+-HClma) H.num#str-Clma)/7/%dis+-H H/%dis+-H8stimated +o,er used. Pest;atts H.num#str-Pest;atts/.H ,atts.Ref6 Bou9herH7/%dis+-H H/%sub+lot-#11/%+lot-).dC>d)/%za)is%a)is-!.1.!.z-4/7/%)label-Hnondimensional radial lo9ationH/%ylabel-HdC>d)H/%sub+lot-#1#/%+lot-).dCPd)/%za)is%a)is-!.1.!.z-4/7/

%)label-Hnondimensional radial lo9ationH/%ylabel-HdCPd)H/%dis+-H :or model air9raft +ro+ellers this 9ode underestimatesH/%dis+-H the +o,er reKuired" >he underestimation is ,orse forRP=X1!.!!!H/%dis+-H ,here it may underestimate by a fa9tor of "5H/%dis+-H :or RP= 1!.!!! the fa9tor is about "5H/


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$ppendix E , 'ropulsion Tests *esults

Atm%eric 9re%%!re 2.287 i":#

"ae #$ %aeries &r#pulsi#' "sem

Am!"t Car#e& ;)"


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Am!"t Car#e& 3.613 A 9reller 16X15

9ea) =lta#e 15.04 @lt% ear .61

>ime t Car#e 0561 mm%%

Car#e C!rre"t 4 am

Car#e Met& Fa%tattery 9ac) ?iM:

Test # Thrust (istory

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0+00+00 0+02+53 0+05+46 0+08+38 0+11+31 0+14+24 0+17+17

Ti "e %h:"":ss &



Am!"t Car#e& 1.87 A 9reller 14X8

9ea) =lta#e 16.46 @lt% ear 8.01

>ime t Car#e 0212 mm%%

Car#e C!rre"t 4 amCar#e Met& Fa%t

attery 9ac) ?iCa&

Test ) Thrust (istory

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0+00+00 0+02+53 0+05+46 0+08+ 38 0+11+31 0+14+ 24 0+17+ 17 0+ 20+10

Ti "e %h:"":ss &




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$ppendix 4 , odel Electronics Corporation Turbo 1+ T otor


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$ppendix , (ynamics and Stability etodolo!y

uations 8.+ and 8.* show Roskam


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-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20-80

-60

-40

-20

0

20

40

60

80

Real Axis

I m a g A x i s

De-stabilizing feedback

9igure 8.7. Root locus plot of destabili4ing feedback.

Frequency (rad/sec)

P h a s e ( d e g ) ; M a g n i t u d e ( d B )

Bode Diagrams

-100

-80

-60

-40

-20

0Gm=25.428 dB (at 63.759 rad/sec), Pm = Inf

100 101 102 103-300

-200

-100

0

9igure 8.8. Bode diagram corresponding to k J 6.0877


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plot for oriontal Tailglobal ShSh !6"1647)bar9g ---#40G10!*Sh/"&-"0*13G$"*Sh//@1#"5/&1)barn+ -1"40533G!"4$40*Sh/"&-4"5##G!"1545*Sh/

figure-1/+lot-Sh.)bar9g.H*H/hold on+lot-Sh.)barn+.H@H/legend-H9g lo9ationH. Hneutral +oint lo9tionH/)label-Horizontal tail area sK ft7H/ylabel-H)&9H/a)is eKualgrid onhold off

plot for vertical Tail% +lot the ,eather9o9? -ya,/ stability +arameter

%>arget alue 9hosen based on the =asterHs thesis of =ar? Peters -seeProf" ndrisani/%

global SS !6"16#7

Cnb,f @!"!!4Cla 1"4*+iS 1$"5b 11"1) $"5Cnb Cnb,f G Cla*-S&S/"*-)&b/

S+roto1"15 %area of +rototy+eHs erti9al tails -total for both/sK"ft"Cnb+rotoCnb,f G Cla*-S+roto&S/"*-)&b/

+lot-S.Cnb/hold on+lot-S+roto. Cnb+roto.H*H/legend-H;eather9o9? Stability CureH. HPrototy+e targetH/)label-Herti9al tail area sK ft7H/ylabel-HCnBetaH/grid on

(ynamics $nalysis% =atlab S9ri+t to 9om+ute Aanin and Phase =argins for the roll a)is ofthe 8451 air9raft% >his s9ri+t uses the simulin? blo9? diagram 9alled% S140(inear"mdl% and o+tionally uses the Simulin? blo9? diagram 9alled sero


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a.b.9.d7linmod-HS140(inearH/ % get linear model from linearsero model in state s+a9e form%a


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Am.Pm.;9g.;9+7margin-mag.+hase.,/ % (Bs definitions of thefreKuen9ies ;9g and ;9+"dis+-HBe 9areful that you understand the =>(Bs definitions of thefreKuen9ies ;9g and ;9+"H/dis+-H(oo? 9arefully at the gain and +hase margins on the +lotH/Amdb#!*log1!-Am/ % Aain morgin e)+ressed in db

Pm

% Com+ute the his ,or?s" >his a++roa9h ,as +robably the best ,ayto +ro9ede"

Simulin? Data :ile -,e thin?/

=odel Y ime W1!"!W Soler ode45 Rel>ol W1e@$W bs>ol W1e@3W Refine W1W =a)Ste+ WautoW JnitialSte+ WautoW

:i)edSte+ WautoW =a)Order 5 Out+utO+tion RefineOut+ut>imes Out+ut>imes W7W (oad8)ternalJn+ut off 8)ternalJn+ut Wt. u7W Sae>ime on >imeSae

8/18/201

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