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FEASIBILITY STUDY FOR A FLOATWMG WATERBORNE AIRCRAFT TYPE
Asbnf Otbmaa
A thesis submitted ii conformity with the nquiremenb for tbe degree of Muter of A p p M Science
Craduate Department of Aerospace Science and Engineering University of Toronto
O Copyright by Asbnf Othman 2001
National Libraiy "Y&"""" du
Acquisitions and Acquiaims et Bibliographie Senrices senrices biMiagraphiques 395 Wellington S i f M si ni.^ OItaw ON K1 A ON4 OCLiuûN KlAONI CaMda Cn#
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Feasibility Study for a Fbrtnisg Wrtdmrie AircrrR Type
Master of Appüed Science 2Oû1
Ashraf Othman
Craduate Department of Aerosprce Euriictrimg u d Appacd Science
University of Toronto
This thesis examines the floatwing watetbonie a i r d concept as developed by Aquavion
S ysterns Corporation. Unlike its seaplane pdecessors, wbich make use of conventional bats
as with "floatplanes" or a boat-like hull as with "fiying boats", the hat wing uses the main wing
as the prirnary buoyant volume d tk exclusive hyàrodynamic d e . The concept was
proven and analyzed through experkntation with a 72" wing spaa radio-controki prototype.
The aerodynamic properties of the WC d l wexe studied ehrough wmd tunnel experiments
conducted with a 42% scale d e l . Estimaies of the stability derivatives were obtained h m tbe
wind tunnel test results and h m anaiytiçal calculathris a d applied to the small d i i e
theory to verify the longitudinal and lateral stability of the codiguratbn.
In the narne of Go& the Beneficem the M a f i l , 1 ~~IUIIK Him 6rst and fiir mis& for î k countless
blessings 1 have received in my life, and in jmrticular, for the sttength and tbe koowledge needed
to complete this endeavour, for He is the All-Knowing Lord of the Uaiverse.
On a more Earthly level, 1 would lilce ta thank Dr. J.D. DeLaurier for taking me into his
group, and for generously giving me the W o m to c h s e a researçh path thaî most satisfkd
my interests. 1 dso thank Ray Richards, who has presenîed me with the opportunity to wotk on
a very interesthg and chailenging pro* and who bas aiways shown encouragement ad
confidence in my engineering skill.
Finally 1 would like thank my family, who's love is always a sowce of inspiraibn, a d my
dearest kiends who have been there to mice with me in times of success and to off% their
support during the more difficuh moments. I thank you ail.
Sincerely,
As hraf Othman
ABSTRACT
Ackoow ledgments
List of Figures
List of Tables
List of Symbols
Chapter 1: introduction
1.1 A Brief Synopsis of Saphmes
1.2 The Floatwing: A Modem % M o i
1.3 Floatwing Tbeory
1.3.1 Hydrodynamic P baiig
1.3.2 The Floatwing Coa&mntbm
1.3.3 The Floatwing as r Scipbw
1.4 Research Objectives
Chapter 2: Proof of Concept: Hydrodynimk Erperimenb
2.1 Earty Experimentation by Aqirvioi Syskas Corp.
2.2 Construction of r 72" W i i S p i Radio Conlraîkd Fkaitwimg Madd
2.2.1 Constructioa of the Fpiscbat r d S i a b M g Surfhm
2.2.2 Construction of the W i i
2.23 Tbe Propulsion Sysîem
2.2.4 Compktioa of tht 72" Spm Radio Coitrollrd Modd
2.3 Experimental Testiag of the 72"Span Pkr- Madcl
2.3.1 Initial Testiag in r Eldryad Sw- Pwl
2.3.2 Continued Testing om tk Scverm River
2.4 Performance Summry kPr tk 72" S p i Radïm Coottolkd
2.5 Continuing Research
2.6 Topics for Parthcr Rem-
C bapter 3: Proof of Concept: Aerodynraie Expcrbaeitr
3.1 The Wind Tunnel E x p c m t
3.2 Const~ction of tbc W'md T m d M d d
3.3 Test Equipmeet
3.4 Modiiication and Caiibntioi of the Force I k h m ~ ~
3.5 Experimental Procedore
3.6 Experimental Results
3.6.1 Lift, Drag, and Pitcbimg Moment vs. Angk of Ath&
3.6.2 The Lift-to-Dng Rehtionsbip
3.6.3 Effects of tbe StulWirg
3.6.4 Effets of tbe Eiorimit.1 Sbbiiizer
3.6.5 Lateral Measuremeob
3.6.6 Drag Buikt-Up Sîudy
3.7 Topics for Furtber Rcscrnb
Chapter 4: The Stability Analysis
4.1 An Introduction
5.2 Theoretical Modeüng
5.3 The Stability Derivatives and Morimts ofIntr@h
4.4 Longitudinal Strbility
4.5 Lateral Stability
4.6 The Location of tbe Ncmtril Poirt and Cm* of Gt8viQ Liai-
4.7 Topics for Furtbcr Rcscrrcb
Chapter 5: The Future of the Floatwimg 5.1 The Floatwing D m m
5.2 The Next Step
5.3 Potential Floatwiag Desgis
5 . An Ultralibt Fbrtwbg
5.3.2 A B u s i a ~ o u n i i g C b Fbatwïmg
5.3.3 The Fiying RV Fbaiwimg
5.4 Final Remarks
References
Bibliograpby
Appendix A: The Ciadc-Y AirIoil
Appendix B: Informrtioa Rtkviit to tbe Whd T i i d E~pcriis«it
Appendix C: Stability Aadysis MATLAB Progrna
List of Figares
Figure 1.1, The Murphy Elite in tk classic batplam cont$gud~n.
Figure 1.2. The Canadair CL-425 flying boat water bomber.
Figure 1.3, A conceptual cira* of a ao;itwmg a i r d .
Figure 1.4, The Equator AimaA Company Equator amphi'bious aircraît.
Figure 1.5, Drag-to-weight ratio plot for a fiat plate.
Figurl.6, Drag-to-weight ratio plot for a flyiug boat hull.
Figure 1.7, Drag-to-weight ratio plot fOr an airplane haî.
Figure 1.8, Drag-to-weight ratio plot for aircraft equipped with hydros)ris,
Figure 1.9, Effect of d i angk on the drag fimction for de-piercing hydrofoils.
Figure 1.10, The dihedral of the wing dbws for rollmg into tum during high speed
planing . Figure 1.11, The dynamics of stable hydroplaning.
Figure 2.1. The 19" wing span tow model m action.
Figure 2.2, The 1 1 " wing span tow model shown here in static bataiion, pian&,
and in flight.
Figure 2.3,3-View drawing of tbe 72" wing span di conüoiled floatwing model
Figure 2.4, Detail of the tùselage construction technique usiag layered ham and
fiberglass.
Figure 2.5, Detailed drawing of the wing designeci h r the radio-conirolled mxkL
Figure 2.6, Detd of the coiistnrtion techaique used for the wïng panels.
Figure 2.7. Fiberglass sheets cure to the wing panels under tbe pressure of tk
vacuum bag.
Figure 2.8, Detail of the coasmietion technique used to build the centte section
foam core.
Figure 2.9, Typical locations h r muuthg eagines on wapianes.
Figure 2.10, Use of the ducted allows for tbe thnist Liw to be lowered-
Figure 2.1 1, The waterline on tk aoaNvmg mwfel diairig static floatation,
Figure 2.12, Lateral stabiüty dut to tbe wMgs actiug as spoasoris.
Figure 2.13, The fioatwiag moàel durhg high-speed %epU plahg.
Figure 2.14, Büster spray forming off the bow ofthe wiug and pesshg through
the propellem.
Figure 2.15, The floatwing mode1 mlling iato a tum while bydroplaning.
Figure 2.16, The ducted h assembly mouutcd on a pybn to raise the tbnist üne.
Figure 2.17, Effkct of wmd on the dynamics ofiakiag-off h m water.
Figure 2.18, Modifications matic to teduce the drag of the WC midel
(November 2,2000).
Figure 2.19, Definition oftbe angles used in bngitudinal a ircd dynamics.
Figure 3.1, Set-up for wind ninnet e?qxrimentation.
Figure 3.2,3-view of wind tunnel mode1
Figure 3.3, Completed wind tunnel model,
Figure 3.4, Test stand used io suppon mode1 in the tuml and d e r Ioads to the belance.
Figure 3.5, Schematic of the hrce bdame detailing the method of measuring the
applied loads.
Figure 3.6, Modifications made to the force balance music-wire supporis.
Figure 3.7, Schematic of the force bdance caiiiration teclmique.
Figure 3.8, Relative positionmg of the force baiance axes to tbe tunnel axes.
Figure 3.9, Sample calihtion pbt fbr lift axis of htce balance.
Figure 3.10, Output of unIoaded drag axis d h g d i i o n of üft axis,
Figure 3.11, Sample calilnation plot for drag axis of force halarirP.
Figure 3.12, Sample calibration plot h r moments applied to bnx balance.
Figure 3.13, Calculation of pitching moment h m wind tuMe1 measuremeats,
Figure 3.14. Lift coefficient vs. angle of atîack pbt showhg the complete deta sei.
Figure 3.15. Drag coefficient vs, angle of amch plot showiog tbe coqlete data set.
Figure 3.16. Moment coefncient vs. angle of a ü d pbt showhg tbe amplete data set.
Figure 3.17, L a coefficient vs, angk of atîack plot showing the average oftbe dirra set.
Figure 3.18, ûrag coeEcient vs. angie of atîaxk plot showiag tbe average of the data set.
Figure 3.19, Moment coefkient vs. angle of atradc pbt showing tk average of the data set* 73
Figure 3.20, Changes in elevator trim angle causes tbe lift curve to sbift up or down. 74
Figure 3.21, Data points for Qag vs. U masmmnts.
Figure 3.22, Quaciratic fit to drag vs. lift measurements to hm a standard drag polar
(no hear term).
Figure 3.23, Another quadratic fit to tbe drag m. lift measuremeats, this tinte allowing
a linear tenn to exist m the drag ph.
Figure 3.24, Both drag polar 6ts provide reasonable drag estimates w i t h the useful
range of üft coeffici-.
Figure 3.25, La-to-drag ratio vs. angle of W k plot sbowing the complete data set.
Figure 3.26, Effect of the stubwing on lift,
Figure 3.27, Efféct of îhe sîubwing on drag.
Figure 3.28, Effit of the stubwiag oatk tifi-tdrag ratio.
Figure 3.29, Effect of the stubwing on pitcbing moment.
Figure 3.30, Efféct of the horizontal stabüizer on la. Figu re 3.3 1, Efféct of the horizontal siabilizet on drag.
Figu re 332. Effit of the horizontal stabilizer on pitching moment.
Figu re 3.33, Laterai force coefficient vs. sideslip angle,
Figure 3.34, Yawing moment vs. sideslip an@.
Figure 3.35, Mode1 configuratioris tested in the drag Md-up sndy.
Figure 336, Drag measureniertts o f various midel contigurations for drag build-up &yY
Figure 4.1, Rudimentary solid mode1 used to estmiate the mwnts of inertia fbr the
72" span d e l .
Figure 4.2, The longitudinal eigenvahm pbtted in the real-gneginary p l m .
Figure 43 , Flying handling qualities pilot opinion contour bsed on tbe short-period
mode naturai kqrieacy and damping ratio.
Figure 4.4, Another pilot opinion contour sbowhg diffeient resuiî~.
Figure 4.5, The lateral eigeavaiws pbîîeâ in the d i m a g h u y plaae.
Figure 4.6, Moment coefficient vs. augk of aUak pbt for varying CG locatioas.
Figure 4.7. The centre of gravity beation ürnits iOr the rarlio controlled floetwmg modeL
Figure 5.1, A potential bushess/tou&g ciass
Figure A.l, The Clark-Y AXoü.
Figure A.2, UIUC low-speed M o i l test resuits fOr the Chrk-Y airfoil as presented on the NASG Airfoil Databese.
Figure B.1, Lift calibration plot br set 1.
Figure B.2, Lift calibration plot tOr set 2.
Figure B3, Lift calibration plot br set 3.
Figure B.4, Lift calibration pbt &r set 4.
Figure B.5, Drag calibration plot fbr set 1.
Figure B.6, Drag caiiition plot fbr set 2.
Figure B.?, Drag caliration plot for set 3.
Figure B.8, Drag calibration pbt for set 4.
Figure B.9, Moment calibratmn plot for set 1.
Figure B.lO, Moment caliiration pbt fOi set 2.
Figure B. 11, Moment calibration pbt for set 3.
Figure B. 12. Moment calibration pbt for set 4.
Figure B.13, Sample calculation sbeet for wind tuml experiment.
Figure B.14, Statistical analysis of a wind nilwl experllnent measurements.
108
la les
108
lm 109
lm
les
116
110
110
1 le
111
112
Table 1.1, Tabulated trade-on5 br seaplane con6gurations.
Table 1.2, Drag build-up for a flying boat des'ign
Table 4.1, Stability derivatives for tbe 72" spaa floatwhg &L
Ta bte 4.2, Longitudùial eigenvectors.
Table 4.3. Lateral eigenvectors.
List of Symbols
- thrust force (or period in Chapter 4 only)
- drag force
- lifl force
- aircrafi weight
- aircrafi mass
- pitch angle
- angle between thrusi Iùie and x-aiùs in body firame (Cbaptet 2)
- angle of downwash at the h o h d siabilizer (Cbap t~ 3)
- ciimb angle
- speed
- acceieration
- power
- vohage
- electrical c m n t
- propelier efficiency factor
- lift force in the direction of the force balance lift-axis
- drag force in the direction of the brce belance drag-axis
KL, KD, K,,, - force balance caiiition sbpes for lift and drag forces, and pitcbing moment
d V - differential voltage
AR - differential resistance
a - angle of attack
4 - dynamic pressure S - reference wing area - c - mean geometric chord
M - pitching moment
CL - lift coefficient
CD - drag coefficient
C.W; - pitcbg moment coefEcient (about centre of gravity)
- distance h m centre of test stand pst to desired centre of gravity location on wind
tunnel mode1
- wing plaaform efficiency factor
- aspect ratio of wing
- drag coefficient at ENI iift (parasitic drag coefficient)
- centre of gravity position as a fraction of mean c W
- neutral point position as a ûaction of mean chod (sîick faced)
- horizontal stabilizer tail vohune
- lie coefficient of the briPonial stabil 'i
- pitching moment coefficient due to the propulsion system
- distance form the man aerodynamic centre of the wing to the mean d y n a m i c centre
of the horizontai stabilizer
- reference area of the horizontal stabilizer
- roll angle
- yaw angle
- sideslip angle
(,Y, Y, 2) - scalar components of the tesuhant force vectot in the M y refircnce ûame
(L . M, N) - scalar components of the resuhaat moment vector in the body reknce fianie
(u. v. w ) - scalar compoacnts of the resuhant velocity vector in th body reference fram
@- 4. r ) - scaiar components of the resuharit an- vebcity vector in the body ref'aence
frame
CI" - variation of x-force coefficient with angle of attack
C - variation of z-force coefficient with angle of attack
Cm* - variation of pitching moment coefficient wiih angle of attack
CI- - variation of x-force coeflt?cient wÏîh rate of change of angk of attaçk
GA - variation of z-force coefficient with rate of ckmge of angle ofattack
Cm. - variation of pitchhg niornent cuef£icient with rate of change of angle of attack
CI. - variation of x-force coefficient with speed
C; - variation of z-force coefiient wiîh sped
Cm. - variation of pitching moment axfkient wiîh speed
CU - variation of x-force coefficient with rate of change of speed
- variation of z-force ccdicient with rate of change of speed
- variation of pitcbing moment coef l ic ' i with rate of change of s p â
- variation of x-force coefiient with pikh rate
- variation o f z-force coefficient wiih piich rate
- variation of pitchhg moment caeflticient witb pitch ra!e
- variation of K-force coefficient with rate of cbange of pitch raie
- variation of z-force coefEcient with me of cbange of pitch rate
- variation of pitching moment coeûïcient with rate of change of pitch rate
- variation of lateral force coefficient with sideslip mgk
- variation of roiiing mm- coefkient with sideslip angle
- variation of yawing moment coefkient witb sideslip angle
- variation of lateral force mefiient with rate of change of sideslip angle
- variation o f roiiing moment coef[icient wah rate of change of sideslip -le
- variation of yawing rmment coefficient with rate of ctiange of sidesüp angle
- variation of lateral hrce cwfiient with roU rate
- variation of roUing moment eoefncient with di rate
- variation o f yawing moment wefiieat wath mU rate
- variation o f Iateral force coefiient with tau: of change of r d rate
- variation of roUing moment coetkient with rate of change ofrd rate
- variation of yawing momnt coefkient wah rate of change of roll rate
- variation of l a t d force coefficient with yaw rate
- variation of roiiiag mmnt coeî5cient with yaw rate
- variation of yawing moment coefkient wiih yaw rate
- variation of laterai force d i e n t with rate of cbaage of yaw rate
- variation of roihg =nient codcient with rate of chaage of yaw rate
- variation of yawing mmnt e i e n t with rate of change of yaw rate
Lx, [,TV, I= - moments of M m about the: (x, y, z) axes of the body kame
I,, I , - pmductsofinertia
Vol - voIume
P - densiîy
A - eigenvalue
-mdampednaîuraifrquency
< - damping ratio
I - time
iV - number of cycles
Cbapter 1 Introdiakn
Chapter 1: Introduction
1.1 A Brief Synopsis of Snplrncs Since the tirst days of powered fiight, designers bave been expbring the concept of watehornt
aircraft. With 75% of the earth's surke covered in water, it would provide accessibility to even
the most remte parts of the world where there are no developed runwayq only vast expanses of
lakes and waterways offerkg extremeiy bug nmways any way ihe w i d bbws.
This was the vision that spurred the devebpment of seaplanes bughout tk First Wodâ War
rig ht through to the end of the Second Workl War. Some existing tenestrial aimaft were &mg
retrofitted with pontoon-style bats, definmg the ûoatplaae class such as m Figure 1.1, while
other aircrafi were developed fmm boat hulls, defining tbe flyiag boat chss such as in Figute
1.2. Both classes of seaplanes flourished in the inter-war years, which were characterizai by the
large elegant flying b a t s used for inter-continental air services. However, îhe Second Worid
War era brought about s u W i a l devebpments in efficient wmmerciai and miiitary transport
and a global expansion of permawnt airfields close to major iniand centers. Tkse rapid changes
prematurely deemed the stilldeveloping seapiane obsoleîe within îhe decade tbbwing tbe end
of the war.
Alt hough f i h e r developrnent of seaplaaes was abendocmi, tbe chanci br such an aimait type
still existed. Even today tbere are many w b cboose to tly seaplanes ad opetate h m the
hundreds of waterdromes in Canada abne. The seaplanes used today range h m tefmbisbed
mtiques, terrestrial a ircd retrofitted with Hoats, to modem kitplane designs. However, the
technology of the modem designs dws not mer funâamentally h m tbat of tk anthpes, and
therefore stilI posses the same shortcomiags that mide the seaplrme o b s o k in tk fbt place.
The inferiority of the classic segplane design is inherent by the sacdkes d e in aerodynamics
for cornpetence in hydrodynamics. Tbe seaplane, is in actuai bct, a hybrid of a d k e - m a r k
craft and an aircraft, and this aotion is weii reflected m the six fudamntal requirements fOr a
successfùl seaplane design:
Chapter 1 htrodiedoi 2
1. Adequate buoyancy to strry qf lo~ t ùr a nirrmwr that will be stuîical& and dynomiculiy stable
on the water. This re~uiremcnt is g o v d by the well-laiow11 Arctiimedean pincipk tbat
a body must displace an qua1 weight of water in ordet to stay afloat. The srab'iiity on the
water is determined by the shape of die submcrged body, be it the fiiselagc or the pontooa
floats. FIying boats that achieve buoyancy by the partiai-submqence of the fiisclage
require additional devices to achieve lateral stability such as outboard wing floats or
sponsons, which are lateral extensions ûom the side of the fuselage to extend the bcam (the
width dimension of a hull). A coavent id floatplane uses two pntoon floats with euough
separation between them to provide lateral stability, and with suffkient length to provide
longitudinal stability.
Dynamic stability cequiremmts an much the samc as those for static stability, however ia
the dynamic scenario, the hydmdymmic and aerodyuamic forces generated while piauing
on the surface must be centered in a maaner îhat will not cause the a i r c d to nosc over. or
even submerge. Pocpising is a common accurmice with high specd planhg craft like
boars and seaplanes, and is cbatactcriped by violent longitudinal pitching oscitlations.
There are s e v d factors that can contnbutc to this dféct: premature iB due to an excessive
wing incidence angle, submergcncc of the &-body (the portion of the body dl of the
hydrodynamic step) causcd by suction fmcs due to surfacc tension, and thc relative
positioning of the hydrodynamic step and centet of gravity.
2. Low hydrodynamic &ag d the ability to achkve -ic 1Ii;li) at low speedt. As a
seaplane (or ship) travels fonvard almg the surfacc of a body of watcr, it gcneratcs a
hydrodynamic force that cm bc broicen down into a lift and drag componcnt, both of which
are proportional to the square of the spcai of the vessei, It is the drag component ihat is
responsible for the large amounts of encrgy expendecl during iaxiing and takcoff. If the
drag force is too excessive for die propulsion power availabk, the aiirraft may never k
able to achieve adequate spccd fa ta i~~~f f . Heuce, the impo-e of hy-c lift at
low speed is to reduce the dr& of the seapkc (the deph of the submergeci portion), which
in turn reduces the s u b m d am, the drag, and the cnergy nquirrd to takeoff.
Chapter 1 I i t rodreh 3
3. Maneuvembility and contiol whik tari@. As fm my d vehick, ttn seaplane must
demonstrate îhe ability to maneuver at low spccds, primady foc dackiag, avoidmg
waterway üaflic and obstacles, and to basicaüy foiiow the course that the pilot desinS.
4. Means for spray suppression and protection of the prqdlers, enghm a d other
components that may be damagai by the spray. Large amounts of sprrry are gcncra5«1 at
the high pressure point where the planing surface picrccs the d b c e of the watcr. Tbt
spray can be classified into two focms, velocitylnin spray ad blister spray. nie first is
usually a datively hannless spray that is directeci pcrpendicuiar to the path of the body,
whereas the later is more dense a d violnt, and develops in ilte fm of a blister paralel
with the body. The force of the blister spay impacthg the strucîm can bc vcry damaging
if precautions are not takm to protect sensitive compomts such as dic ppclkrs, which
are prone to Wear and damage by the impact logdiag generated by the blister spray passing
througfi the propeller slipsueam.
The exposure of the airctaft compomts to water bas long-tcrm cffects on coclosion of any
metallic components, and most criticaiiy, the mgines. This is a very scrhs problcm far
operation in a salt-water environmmt. Pmper design of tbe planhg surhcc can grcatly
rninimize the arnount of spray and help supprcss it h m causing umirccssary damage.
5 . Overail reduction in drag. Seaplancs are inhcmitly diantaged in this criterion because
of the design sacSces requireâ to achieve the ability to opcratc on water. The h g c
volume hull or fldats q u i m i fm flontation, the addition of hydradynamic sttps, chiaes,
rigging and bracing for outboard wnig floats or pontoon-styk floats arc al1 grcat sources of
parasitic and interference drag. The ~ M ~ O L I of a square hydmîymnic stcp doat cau
increase the drag coefficient of a stnamlMed body by up a 5036, or up to ody 15% if an
elfiptical step is used. Tables 1.1 aud 1.2 cleariy Qmoastiate how impoaant it is for
seaplane designers to focus on minimizing the Qag pcnahies of such rnodincaticms.
6 . Eflciency and versatiliity B r fe491'6le operation. This last aitcirioa is bastd an tûe
opnmizâtion of the previous fke to produce the lowest possiile opaathg costs.
Chapter 1 Iiriodrctki 4
1.2 The Floatwing: A Modcn SoIution Since 1996, Aquavion Systerns Corp. of Ajax, Ontario, bas kni warking on thc development of
a pioneering concept in watcrbome aimaft tcchnology called the floatwing. Tbis concept
consists of a new seaplane operathg technique, as weU as the allcraft configuration nccdcd to
make this technique work.
A generic tloatwing configuration is shown in Figure 1.3. The flogtwing is noticeabiy unique to
classical seaplane configurations in many ways, but the most obvious king the fact tbot it bas
done away with large boat-like huils and pontoon floats, and anly uîiks partiai submcrg~~e of
the main wing and horizoatal stabilizcr to achieve the requlltd buoyancy for f l d o n .
It is also noticeable that the a i d possesscs unique geomdcal charactcn*stics aud proportions,
for example: the sweep and dihcdrai of the main wing, and the s k c of thc stabilizing surfiiccs.
These are requued features for making the floatwing technique possible.
The main wing is the primary hydrodynamic d w e , and is tht bais for thc seaplanc operatkg
technique. In the static case, the root section is submergd enough to pmvide adtquaic
displacemenr for buoyancy. As fozward motion begins, the wing behaves like a Jurféct-pictcing
hydrofoil, generating hydrodynamic lift h m the submccgd mot section and -c lift
fiom the rest of the exposed wing. Sincc watcr is 830 t k s dniscr than &K, hydrodynamics
dominates at low speed. The hydroûynamic lift produccd by the root section is enough to raise
the aircrafi higher out of the water as the spced is increascd, d l hydrudynamic planing is
achieved. The aircraft is designed to plane on the üaiiing cdge of die wing mot, ushg 5 as tbt
"step". While planhg on the stcp, the aimaft accelerates to hi* spceds whm the domiaancc
of hydrodynamics transitions to amdymnics, and evcntually Boff is achicved. The takeoff
nin will be described in more detail m section 1.3.1.
The Equator Aircrafi Company uscs the tenn "fioat-wingn to dcscnk its newiy Qvclopcd
Equator amphiiious seaplane. As seen m Figure 1.4, the Equator uscs the whg as spansons for
lateral stability on the water, and aot as the main buayant v o b or hydrodyaamic siafiicc.
Therefore the Aquavion 11oatwmg is a uniqw seaplane dssign.
Chapter 1 Iiaodrttk. 5
1.3 Floatwing Tbeury Described in this section is the basic tb«mtical coaccpt of the floatwMg sirrrPff ml how it is
expected to work, aad the requinmenfs bebind dit uniqw dgraeiion.
1.3.1 Hydrodynamic hihg
To date, there is not much theary avaiiable on hyQodyMmic pianin$ duc to tbe complrxitics
involved in accmtely modclhg wavcs, spray, and tbc varying gewnctry berwmr the body and
the interface of two fluids of vas@ différent dcnsiies. Becsruse of ibis, most work in tk k l d of
hydrodynamics is done experimcntidly ushg firll size or t o w d madcls.
Figure 1.5 shows the axperimental of tbe dng-laading ratio (ratio of drag to
weight) against the Fraude numbcr ( d i c h is p p a t r i d to spsed) for a flat plate, cakca flom
Hoemer [l]. This is a vaIuabIe figure in ihat it iilwaatts the wisnec of the dmg duting tbc
takeoff m, and therefore provides an insight inîo the power and cnergy requkd ta achitvc
planing and lifi-off.
It can be seen that the drag inctc8ses most rapidiy as the p h h g suciàce begins to build up s p d
kom its rest position. During this phase, tûc p h h g s w k is pushing a luge bow w a n at thc
leading edge and is pwducing a latge amount of vclocity spray dirccted p m p d h k to the
direction of motion. It is important at this for the wing to have as much incidence as
possible so as to produce caougb hydtodynamic Lift to b q h plaaing and to c h b up over the
bow wave.
The speed at which the peak of îhc drsg-loahg ratio m e occm is h w n as tk "hump
speed". This is the point at which tht pianing su&c just c h b on tap of the b me, and
the vicious blister spray due to the bnalting of tht baw wrvt is diministKd - . . lustpriortothis
peak is the point labeled %art of planinp", s h in F i i 1.5. ï k r c is no r d d e h i t h as to
when planing is actually establishcd; howevcr, it bas Prbitlarily been d t W as tbe spccd at
which the tifi due to buoyancy is 2096 of tbe dynamic liR
Chapter l ImROdlCtjDI 6
Once the point of maximum drag is overcome at the hump speod anci the planing s\irface is
raised up out of the water, with oniy the stcp and surroiinding ana subwrged, tbe drag b@s to
drop off as aerodynamics takes over fiom the hydrodynamics. The dmg conîinues ta drop as tht
speed increases since the dependencc on hydtodyaamics is continually decreasing, uatil liftsff is
achieved and only the aerodynamic drag mnains.
Although this description d e s c r i i the takeoff nm for a fh plate, it is npcscntatin of the
performance expected by a floatwing because of the way the wing bthaves likt a surfire
piercing hydrofoil. Figures 1.6 to 1.8 show the sunilar drag-Ioading curvcs for a typical flying
boat hull, an airplane float, and an airplane mode1 on hydro skis. From tûcst figures it is seen
that the hydro ski technique is the least efficient, produchg a 70'36 drag to weight ratio @/W) at
the hurnp speed, followed by the float at approximately 25% Dm, and thc @hg boat at 22%
DtW. The flat plate produces the lowcst hump speed dmg-loading ratio a& approximately 17%
DIW, which most closely madels wbat could bc cxpectcd h m tht floatwbg design, suggesting
that the floatwing could become an efficient solution in watcrbme aircd opetat.0115.
1.3.2 The Floatwiag Configrntbi
As mentioned earlier, the floatwing design has a contiguration. Tk main whg alone
possesses a generous amount of dihcdrai and swccp back angk, both of f ich are net to k
expected on low speed subsonic but an however compromises madt for hydirodynamic
performance.
The dihedral is added to reduce the amount of the wing that is 9ubmerged in thc watcr, tbus
reducing the hydrodynamic drag, Figun 1.9 takm h m Hocrwr (Il, shows ihri tht drag-Liff
funetion (a d ~ d d ~ : ) deccaoa as the dihdnl angle Cr h c m s d for nnhoe m i n g foih Tbe
dihedrai also serves to allow for rolling mm turns during high speed planhg on the writcr as
shown in Figure 1. tO.
Chapter 1 htiaductki 7
The sweep is needed to position the acrodynamic ccntcr of the wing fiather aft, to m b i m k îhe
distance between the aerodynamic center of the wing ad the centcc of gravity, which is located
longitudinally at the trailing edge of tht whg mot. The center of gravity is situaicd so fin afk in
order to maintain dynamic stabw while planing, as illustrated in F i 1.1 1. The
hydrodynamic center of pressun should always be forward of the center of gravity, sa as to
produce a stabilizing nose-up moment. If tbc center of gcavity were allowcd to move fmatd of
the hydrodynamic center of pressure, tbcn a dangmu noscavet moment will k ptoduccd and
planing will not occur.
The center of gavity location also atldcts dat size of ik stabilizing sudices. By Icn%benrng dic
tail a m , the stabilizers could bc duced in uca; howevcr it would d u c e the allowable mîation
angle of the aircrafi before the tail woufd amtact the watcr. Because it is important to have a
margin to adjust the trim angle while Eaxiiag and p W g , it is prcfetable to kecp the tail am
short and high, meaning that the slabilizcrs must bc telatively large because of the s h
coupling. It is also advantagrnus to have a large horizontal stabilizcr for adquate control
authority if the aircraft is to be ope& in grouad e t k t
1.3.3 The Floaîwing as a Seapbre
Now that the basis of the float wing concept has kcn dcscn'bcd, it is a gaad time to nview the
six fundamental requirements for a suemsfiil scaplaw design, which w m previously dWcusscd
in section 1.1, and see how thcy arc fiilnlkd by the fl-g design. It was this c h c c ~ that
motivated the developmeatal work of this design concept.
1 . Adequate buoyans, to stay @ k t in a mrnnet that will he statically and dynranicallj stable
on the water. It was already m e u t i d that the fl- d i h s ptid suhergmce of
the main wing and the lowcr siafiifc of the horizrmtd stabili#r fot static f i d o n . Siatic
stability was assumed to bc inh«ient in the design because rockhg would rcsuit in a
stabilizig moment due to a focal Urcreasc in buloyancy whm submergcllcc oecuis.
Dynarnic stability was taken are of by the cm& positionhg of tk center of grPvity as
previously mentioned m &on 13.2.
Chapter 1 Iitrodwiiom 8
2. Low h y d r o ~ m i c drug and rtie abihly ro achieve @dv&amic li# m lm sp&.
Because the wing ha. a camkrad airfoii scctioa, tbe submcrged portion is expcettd make
good use of the high density of wata and to produce an ample amount of hydradynamic lüt at low speeds.
3. Maneuverabilis> and control while tmyng. ïhe 0oatwing a i d has no conml arfaces
on the main wing to duce the ri& of leakagt into the interd sûwîm; therefon al1 of the
controls are located on the îail surfiices. The vertical stabiiizcr uses a convcntional air
nidder for yaw-roll coupling, and ik horizontal s t a b i k uses elev011s for roll and pitch
control.
On the water, prop wash tiom the e@o(s) c d d bc blown against the ruddcr for iucning at
low speeds. As well, the elevons cauld be uscd as diffenatial water brakes for low sped
maneuvering. A twinsngine cdgutatioa wauld a h w for extra maneuverability by using
differential thnist. At hi& s p d , during the taktoff run or high speed taxiing, the ruddcr
cm be used for turning and the dilacdral built into dic main wing will allow for rohg into
hi&-speed turns as prwiously mclltiOIKd.
4. Means for spray suppression and ~ e c t r û n of the propellers, engines a d orher
components that mcs, k h a & by the spray- &fore any modcls w m actually testcd m
the water, it was not known how spray would fonn and bchavc widi this dgurat iou.
Precautions were taken by mrking sure to mount the propellets over the mi&& d o n of
wing chord, so that the wing wouid act to shield the props h m the main body of wetet.
5 . Overall reduction in h g . This is oae of the potcntiai advautsgcs tbat motivatcd the
development of the floatwing concept. S k it does wt use floats, or have a large boat l k
hull with hydrodynamic stcps, thcm W a potentiai to have an airfiramc with clcan bues
closely resembling t h of a tcmstrial aima& anà thus a Iower drag tban its traditiouai
counterparts.
Chapter 1 Introdrctki 9
6. Eflciency and versatility for jérrrible opution. As mcntiOEICd in scctiOn 1.3.1, it is
expected that the floatwing will bave a hg-loading curve for the take~ff nm similer to tbat
show for the flat plate. This, coupled wiib the low dtag, cudkicnt would maire the
floatwing a more efficient ahutive in watdmmc aircraff in temu of cnctgy
consumption.
The qualities presented in the checldist npnscnt îùe expcctations of the floatWing desii bcfm
any experimental testing was cmpleted. Thc txperimental vetiticathu and findings will be
discussed in detail in the following chaptas.
1.4 Research Objectives
The objective of this sîudy was to prove the fc85ii~iIity of the floatwing concêpt by meaas of
experinienting with rnoâels. The fl-ing was p v e n on the water and in the air. for both
hydrodynamic and aerudynamic pedonn~~:e.
The evaluation of the hydrodynamic pcrfarmsace was cwductcd with d e modcb. Tbc th
initial tests were petfonned ushg 19" and 11" wùig spsn tow modiels. The nsuhs obtaincd h m
these models were solidifkd widi expcrimmts doue using a 72" wing span tadio controlled
model. This model was also c@k of fligbt and provided a b i s for an cvdunîi~ of the
aerodynamic performance.
A more detailed aerodynamic perfbrmance cvaluacicm of the 72" WC mode1 was done using a
42% scale mode1 of the WC mode1 in tht UTIAS Submk Wind TUMC~. The mlts WCI'C used
to determine the stability derivatives foir ihis COZlfigurath, which w m imphmtd m a
stability analysis.
Both the hyûrodynamic and acrodynamic pcrformencc cvduatiolls wcre vcry critical in
detemining îhe future of this project. Wittsout adequatt hydrodyriPmic @ m e , t h ~ thm IM
"floatwing" concept, and without muate aaodynamic p a f i e and stabw, the floDtwing
would be usekss (or noncompttitiw at tbc least) as an airplane-
Chapter 1 htrduebbir
Figure 1.1, The Murphy Elitc in the classic floatplane configuration (hm Murphy Aitcraft Mg. Ltd. [21).
Chapter 1 htiodretki 11
-a aœw
Table 1.2, Drag build-up for a flying boat design (reproducd h Stinton 141).
IRM; INCREASE PER CENT
addition of nn and cabin
Chapter 1 Iitrodietki 12
Figure 13, A concepnial drawing of a floatwiog a i r c d
Cbapter 1 Iitmd.ebki 13
Drag-Lod ntio of a #a~ planing surface (32.3) 31 a- a functiun of I:mude number; for d - 5 - optimiim, b - -
300 mm. W 5 0 kg, W/ y b' = 1.85 consimt.
Figure 1.5, Dmg-to-wctght ra-tio p h for a flat p h (hm Ref [l]).
\. A--"'- SPRAY
\ \ î- - €ITIHAT€O 7TIHUM
Exampia for tht dng/wcight cati0 of typicd gy&g- bat hulk. -
Figiirl.6, Drag-to-weight r d o plot fiw a flyhg boat huil (fiom R d [l]).
Chapter 1 htrœlietki 14
Bng-wcight ratio of an a&l;me float (32s) as a iukt ion of Froudc number. Flwt data: DVL No.7, at oc - 7" - constant. I/b = 9.2. b = 0.3 m. Codhcinit CA = W/ y b3.
Figure 1.7, Drag-to-wcight ratio plot for an airplane d6at ( h m Rcf 111).
Totd (terodynarnic and hydrodyn;imic) drj s rzio of an airplme mode1 on skis (38.3)- Dimensions arc indicatcd full scde. The prersurc &tg c o r r e s p d ta the trim mgle 'sa ;ri rnarked. plus ttic an& at which the skis are sct against the fuselage.
Figure 1.8, hag-to-weight ratio plot f a uiFntt equippcd with hydroskis (hm Ref [ID.
Chapter 1 Iitndwtbi 15
Figure 1.9, Effect of dihadtal an& cm îhe drag fllnctim for surface-piercing hydmfoiis (fial Ref [ID.
Figure 1.10, The dihcdrai of thc wing a b ~ ~ fa rollhg into naru d~fbg high s p d planing.
Chapter 1 Iitrodrcaoi 16
'4" ammat- - )iriir
Fire 1.11, The dynamics of stable hydmplaning.
Chapter 2 P w f of Concept: Hydrodp.nir Expcrimcnts
C ha p ter 2: Proof of Concept: Hydrodynamic Experimenta
2.1 Early Experimentation by Aquavion Systetüs Corp.
Richards [6] of Aquavion Systems Corporation initially conceived the floatwing concept in
1996, afier which development proceeded cautiously. In the years to follow, major milestones in
the development of the floatwing were achieved during experiments conducted with two tow
models of 19" and 1 1" wing spans.
The tirst experiments were conducted with the 1Y wing span mode1 shown in Figure 2.1, which
was constmcted fiom balsa and fiberglass. This model was tested on the Severn River, Ontario,
Canada, while being towed alongside a motorboat The model demonsîraîed stable hydroplaning
and eventually managed to lifi off tiom the surface when the motorboat reached a high enou@
speed. This was a benchmark run proving that the aimaft was stable on the water and that lifb
off was possible by replacing the standard hydrodynamic step of traditional seaplanes with the
trailing edge of the wing.
One problem that was observed during this initial experiment was that if the angle of attack of
the aircraft became t w shallow during planing, such that the zero lifi angle was exceeded in the
negative direction, the a i r d would a d l y submerge itself. This was the fkst sign of this
pro blem, w hich will be discussed in tùrther detail lata on
The 11" wing span tow model shown in Figure 2.2, which was buiit only of balsa, was aiso
tested in the Severn River. Rather than king towed dong side a motorboat, expenexpenments were
conducted off the side of the boat dock with the model towed by a fishing rod- This d e l
showed the same stable planing characteristics as the 19" model. Because this model was built
much lighter, it easily lified off fiom the surface. Once it was airborne, the towline was allowed
to slacken such that the model could glide to a landing on its own, something that was not done
with the 19" model. The 1 1" model demonstraîed smodh landings on the d a c e of the water,
without signs of instability or nose over moments, bencharking artuther major achievement.
Chapter 2 P m f of Concept: Eydrodprnaic hperimeeb 18
From these experiments, confidence was built up in the floatwing concept. It was now known
that not only planing was possible with this a i r d configuration, but aiso liftsff fiom the
surface and safe landings. The next stage in development was to build a larger self-propelled
radio-controlled model that would be able to provide more insight into the characteristics of the
fioatwing design.
2.2 Construction of a 72" Wing Span Radio Controlled Floatwing Model
The purpose of building a 72" wing span radio comol model was to solidify the achievements
made with the smaller tow models. The advantage of going with radio control was that the
aircrafi would be self-propelled, and would thus demonstrate a behavior similar to what could be
expected From a tùll size floatwing.
The 72" wing span radio controlled floatwing model, shown in Figure 2.3, was built as a scaied
up version of the 11" wing span balsa model. The phiIosophy behind the design of this model
was that it would be used as a purely scientific test beù, primarily to study water handling and
secondarily to study flight handling. Aesthetics were of the least concern, and a great emphasis
was placed on keeping the design simple and modular, with a high degree of fieedom in
configuration and mounting of components. This would allow b r ease of modification, if certain
components were to be replaced or moved, and if new componems were to be added.
2.2.1 Construction of the Fusclrge and Strbilhiag Surf'es
The fuselage and stabilizing surfaces were built using a combination of conventional
aeromodeling techniques and new innovations by Richards. The fiiselage was conmcted as a
sandwich arrangement of three '/2 blue Dow Styrofoam SM foam sheets and tiberglass, as
shown in Figure 2.4. The inner two layers of fiberglass were laid-up wet with epoxy, and
allowed to cure forming the bond between the sheets of foam. An innovative technique wing
pre-cured tiberglass sheets was implemented on the outer fiberglass layers that fonn the finished
surface.
Sheets of fiberglass were laid-up on a large section of plae glass d e r k i n g thomughly saturated
with epoxy. The epoxy used for al1 fiberglass Iay-up was the West Systems 104 resin with the
Chapter 2 Pmf of Concept: Eydrodynrnik Esperiments 19
205 hardener. Any excess epoxy was removed using a squeegee, and the fiberglass/epoxy sheet
was lefi to cure on the glass surface under atmospheric pressure. Once cured, the sheet was
removed to reveal a glass-smooth finish on the side that was fâce down. The sheet was then
trimmed to size and bonded to the side of the foam structure, applying the epoxy to the backside
with the weave texture. This technique provides an extremely smooth surface finish without the
repetition of sanding and filling normally attribut4 to composite materiai constniction.
When using the pre-cured finishing sheets of fiberglass, the quality of overall finish is greatly
dependent on the surface that it is bonded to. Even very small outsf-plane displacements will
show up in the finish f ie r bonding, therefore it is important to make sure the under surface is
free frorn damage.
The top and bonom of the hselage were capped with balsa sheet and coated in epoxy to ensure
that structure would be watertight. It was very important that al1 components of the model be
watertight such that the structure would not be damaged by water or increase in weight. Tests
showed that the blue foam used as the core of whole model structure is fairly resilient to water
absorption. Small samples were submerged in a water bath for severai houm with only a
negligible change in weight, However, after long-term exposure, the pores in the foam would
begin ta fil1 with water, priming the way for the absorption of more water and causing the foam
to significantly soflen.
The horizontal and vertical stabilizers were constnicted using the same foam and fibergiass
technique used with the tùselage. Both were consvuaed from a singIe sheet of Viw blue
Styrofoam, sheeted top and bottom with pre-cured fiberglas sheets. Before the horizontal
stabilizer was sheeted, a unidirectional carbon fiber spar was added at the quarter chord location
spanning almost the entire length of the stabilizer, falling 5" short at each tip.
The leading edges were made fom half round baisa stock and baisa cap strips were bonded to
the back end of the foam stabilizers, to provide a solid kundation tOr hinging the controI
surfaces. The tips were also cap@ with balsa sheet. Epoxy was again used to provide a
waterproof seal on the wood components.
Chapter 2 Prodaf Coacepr: Hydi.odynrniic Experiments 20
The control surfaces were c o n s ~ i ~ t e d h m strips of the X' blue Styrofoam sanded down to
fom a taper at the trailing edge. Pre-cured fiberglas sheeting was again used on the upper and
lower surfaces, and a triangular balsa stock I d i n g edge was bonded to the foam for mounting
the hinges. Plastic hinges were used to mach the elevons to the horizontal stabilizer and the
rudder to the vertical stabilizer. The hinged joints were sealeci using Ultracote, a thin plastic film
used for covering model aircrafi.
2.2.2 Construction of the Wing
Construction of the main wing presented some unique challenges in structural design due to the
requirements of the mission and its unique geometry. Since the wing serves as the buoyant
volume, the planing surface, the aerodynamic sudace, and the landing gear, it needed to be
designed to hlfill the needs of each task.
To provide adequate buoyancy the wing must displace a specific volume of water, and must also
be built to be waterproof The airfoil section chosen was the Clark-Y for its flat bottam (good
for hydroplaning) and its weil-known and suitable aerodynamic performance for general aviation
aircraft. Using this cross-section, it was calculated that there would be ample volume available
to float the weight of the model.
For al1 aircraft, it is important to keep the weight of the structure to a minimum. However, in the
case of the floatwing, a compromise must be made in order to provide the wing with suficient
structural robustness needed for operating on the water. Since the floatwing hydroplanes on the
lower surface of the wing, this area musi be reinforced to withstand the impact loads that may
occur during planing or landing, since the only shock absorption for seaplanes is that provided by
the water.
The high dihedral angle and sweep angle, 15" and 10" rcspectively, pose structural design and
construction problems such as how to eady join the l& aiid right wing panels, and how to
properly transfer the loads through the structure. With O" sweep wings, it is nlatively simple to
run a main spar through the entire span of the wing, including the dihedrai angle. Wih a swept
Chapter 2 Proof of Canccpl: Hydrodynmuk Expcrimentr 21
wing, a "bent" spar would be needed if a similar construction technique was used, but this would
of course, be inferior in strength to a straight var. For this reason wept wings genedly use a
box spar, which can be rather cumbersome.
The chosen solution to the wing design problem is show in Figure 2.5. The wing is basically
composed of two panels (lefi and right wings), and a center d o n which ties the two panels
together and mounts ta the fuselage. There is no real main spar, since the panel construction
provides suficient bending stifîhess. There is, however, a pIywood joiner, which geatly
strengthens the center seçtion and serves to transfer most of the Ioads fiom the wing panels to the
fuselage.
The wing panels were cut from blue Dow Stpfoam SM using a hohHire foam cutter- Templates
of the panel root and tip airfoils were made from 1/14" sheet steel, and mounted to a block of
foam in the correct position to account for the IO" sweep back of the quartet cbrd line. Once
the basic wing panels were cut, a number of steps were taken to prepare the foam cores for the
covering stage. First, the root sections of the wing panels were tnincated at a 15" angle using a
band saw to provide the correct joining angle for the dihedral. Then the leading and trailing
edges were trimmed off. creating a square face for later bonding of the balsa leading edge and
trailing edge stock. Finally, a straight dot was cut in the spanwise direction to acconunochte the
piywood wing joiner.
The foam panels alone are quite flexible in bending and twisting, and are vulnerable to damage
on the soft surfaces. To increase the stiffhess and toughness of the foam panels, balsa sheeting is
traditionally used. In this case, a new technique was implemenîed using bristol board sheeting.
SeveraI test sections of foam core were built using combinations of balsa wood, bristol board and
fiberglass, and then compared based on strength and weight. It was found that the fioam core
sheeted with bristol board was différ than 1/16" baisa sheeted test section, and was slightly
Iighter as well. Assuming that the same adhesive is used and qua1 amunts, the 0.018" thick
bristol board sheeting is 20% lighter tfuui the 1/16'' balsa sheeting under dry conditions.
Chapter 2 Praaf of Concept: Eiydrodynrmic Erpcrimcats 22
The final arrangement for the wing skins is illustrated in Figure 2.6. Dwing the construction
process, the foam core was sheeted with bristol board on both the upper and Iower surfaces using
Southern's Sorghum nibber cernent adhesive, made by Dave Brown Products. Then the baisa
Ieading and trailing edge stock were cernented on ta the fiont and back faces of the f i wre
using the same rubber cernent used on the bristol board. Since the wing tapers dong the span
and the stock leading and trailing edges did not match the Clark-Y airfoil, they ha. to be carved
and sanded down to the final correct shape. The next step then was to increase the stiffiiess of
the wing panels by adding a sheet of pre-cured fiberglass sheet to the lower d e . The
tiberglass sheet was mounted to the lower surface so as to keep the fibers primarily loaded in
tension during most of the flight mission, and to toughen the lower surface of the wing, which
would experience impact loadings while planing on the water. Therefore, failure would be
compression on the upper surface.
The pre-cured fiberglass sheets were bonded to the wing using a vacuum b a n g technique
shown in Figure 2.7, which is commonly used in composite materials construction. The
advantage of using a vacuum bag during bonding is to apply a constant pressure across the emire
surface being bonded. If this is done properly, then al1 of the air pockets trapped between
composite material and the base structure will be removed, and any excess epoxy is dso
squeezed out, leaving a uniform surface. The standard lay-up technique had to be modifieci
slightly for use with the pre-cured fiberglass sheets, since the material is not porous and does not
provide any escape for trapped air bubbles except tiom around the edges. To overcome this
problem, it was necessary to divide up the sheet used to cover one panel into smaller sheets,
providing more edgedseams for air and epoxy to escape. Two spanwise strips were used for
each wing panel, with the seam running approximately at mid chord. Ideally, the seam should be
situated in the chord wise direction to avoid disturôing the airflow over the wing, howewr for
strengh purposes the fibers rnust be kept continuous along the span. Great care was taken in
finishing the wing such that the seam appeared to be nonexistent.
To strengthen the trailing edge, which would be taking significant loads during hydroplaning, a
reinforcing strip of pre-cured fibergiass sheeting was bonded to the upper surface of the balsa
trailing edge. The reinforcing strip was placed along the entire span of the panel, extending in
Chapter 2 P d of Coacqt: Eydrodprmic Experimtnts 23
width tiom the trailing edge to a W' overiap on the main part of the wing panel to enhance the
bond of the trailing edge to the wing.
The centre section was constmcted using the mot sections of the foam cores that were truncated
to produce the dihedral angle as illustrateci in Figure 2.8. This simplified construction since the
truncated airfoil shape of the right size was already available. The non-truncated side was
truncated at 15" to match, and both the right and leA halves were bonded together forming the V-
bottom at the center of the wing. A foam pylon was made and bonded to the top of the wing
center section, which would provide the flat base for the ftselage to sit on for mounting.
Plywood plates were bonded to the sides of the center section, which took the shape of wing
cross-section and extended up dong the sides of the pylon and above to form the bolting plates
used to mount the wing to the ftselage. A slot was the cut across the center section, where the
plywood joiner was inserted and bonded using epoxy, Like the wing panels, the leading and
trailing edges of the center section was shaped fiom balsa stock material. The stock leading and
trailing edges were not shaped until after the wing was assemblecl. to ensure that that the shapes
matched perfectly. The final step in the construction of the center section was to cover the lower
surfaces of the V-bottom with the same bristol board as used on the main wing.
Assembly of the wing was fairIy straighdorward for this particuiar design. The wing panels
were simply joined to the center &on one at a time by sliding the wing panel over the wing
joiner of the center section, using the slot cut into the core of the wing panel as previously
mentioned. The wing panel was bonded to the joiner and center d o n using epoxy, which was
applied pt-ior to the mating of the çomponents.
To solidi4 the joint of the wing panels to the center section, a layer of fiberglass was applied to
the flat bottom portion of the airfoil, covering the V-bottom and spanning to appmximately a 2"
overlap on the wing panels. A wet lay-up was us& in this case, and the finishing procedure
involved sanding and filling using a mixture of epoxy and microballoons, until a very smooth
finish was achieved. On the upper dace . a an wide mip of pre-cwed fiberglass sheet was
bonded over the bristol board at the rwt of each wing to add extra bendimg stiffness and to
provide a solid skin over the root of the wing joiner. A fillet was also formed at the intersection
Chapter 2 P r d of Concept: Hydrodyamic Ex~riments 24
of the pIywood wing mounting plates and the wings using a microballdepoxy mixture and
fiberglass cloth. The micro balloon filler was also used to stren@hen the intersection between
the wing panels and the center section.
The upper surface of the wing was finished with Cntracote to provide a waterproof coating for
the bristol board sheeting. The lower surface of the wing, which is covcred with fiberglass, was
painted with automotive paint. The exposed foam of the center section pylon, the plywood wing
mounting plates, and the balsa wood wing tip caps were sealed with epoxy before king finished
with automotive paint. The entire wing was finally given a coat of cl= sealant to provide a
final waterproof finish.
2.2.3 The Propulsion System
From the beginning of the design stage, it was uncertain whether the model would use single or
multiple power plants, and single or multiple propellers. Most seaplanes generally have a high
wing configuration, and therefore mount the engines on wing nacelles or on a pylon for the singe
engine versions, as shown in Figure 2.9. This is very helpful for protecting the propellers and the
engines from exposure to water, however this configuration ends up placing the t h s t line quite
high above the drag line, causing a strong nose over moment when power is applied. This
introduces the problem of drastic longitudinal trim changes tiom takeoe cruise flight, and
landing configurations. The ideal configuration would place the thmst Iine as close to the drag
line as possible. For this reason it was chosen to use a min-engine configuration as shown on
the model three-view in Figure 2.3. The engines were mounted on a pylon, which was made
more like a wing (known as the ab-wing) in an attempt to lighten the wing loading.
It was preferable to use an electric power plant over the tradition glow fiiel engines for simplicity
and reliability. In the past decade, great advancemems have been made in feducing the s k and
weight of electric motors, making their use on RK aircraft possible. Nickel cadmium batteries
have aiso seen advancements over the years, in terms of current deliverable to the motors and
duration of discharge. The drawbacks of using electrk power are rnainly the iiifimior power to
weight ratio in cornparison to the glow fiel counterpart, the reduced flight times, and the down
tirne required to charge the batteries, On the contrary, the advantages of using el& power are
Chapter 2 Proof of Concept: Eydrodyiamic Esperimtnts 25
the simplicity of preflight pteparation, the reliability during operation, and the low environmental
impact. Successttl operations are almost guardirteed at the flick of a switch, provideci the
batteries are fiilly charged, whereas giow fuel motors can be v g r finicky and hard to start on
occasions, and are prone to stalling. For this reason specifically, the decision was made to use
eIectric motors, since it would not be vety easy to start and restart the motors while operating on
the river fiom a small observation boat.
The specific power plants used consist of two Graupner Speed 600 ferrite magna electric
motors, powered by a total of 18 Sanyo 800AR 1.2V nickel cadmium cells. Each motor turns a
13" diameter propeller with an 8" pitch, geared down at a ratio of 2.2: 1. The manufacturer has
rated this combination to produce a total of 4 Ib of thnist.
Ducted fans were also considered as an alternative power plant. Because the diameter of the fans
is only 4". it was assumed that the thmst line could be lowered substantially by lowering the
position of the ducted fans as show in Figure 2.10. The ducted fans used are produced by
Electrojet Technologies, and are turned by electric moton using the sarne eighteen NiCd ceils
mentioned previously. Each fan is rated at 24 oz of thnist.
2.2.4 Completion of the 72" Spn Radio Coatrol Modd
The final assembled weight of the model using the propeller configuration was 8.8 Ib, and 8.4 Ib
with the ducted fans. This put the wing loading at 1.72 1bld for the pmpella coniïguntio~ or
1.57 lb/tI2 if the area of the stubwing is included, and 1.64 lbltt2 for the ducted fans
configuration. This is higher than the estimateci wing loading of 1.38 lb/ft2 due to
underestimation in component weight and the addition of other cornponeas, wtiich were not
accounted for in the initial estimate. This weight increase is traditiod in aircraft design.
2.3 Experimental Testing of the 72" Sprn Floatwing Modd With the new model complete, the experimemd testing could begin. As memioned earlier, the
objectives of this model were to ver@ the successfiil planing and lift-off h m the water that was
demonstrated by the small-sale tow models. Since this was the first f l h n g mode1 to be seif-
propelled and to use an actual airfoil on the planing wing, there were several questions that
Chapter 2 Pmf of Concept: Hydrodynrmie Experimcats 26
needed to be answered. Also because of the great site and weight difference between the WC
mode! and the tow models, there were major uncertainties such as: (1) whether the mode1 wouid
tloat as expecteà, (2) would the tail be able to break the suction of the water, and (3) would
planing on the step be achievable? mese were al1 concems that couId only be answered by
testing the model in the water.
2.3.1 Initial Testing in a Backyard Swimming Pool
The objectives of this test were to place the newly completed model in the water for the 6rst time
and to observe the static displacement, stability on the water, check for slow-speed water
handling, attempt preliminary high-power starts, and to check off any unexpected snags in the
construction such as unwanted leaks.
On September 3, 2000, the RIC floatwing was gently lowered into the waters of an 18 fi by 30 fi
swimrning pool until the buoyant forces were enough to keep the aircratt afloat. The waterline
was surprisingly low for the 8.9 lb model, as seen in Figure 2.1 1. The root d o n of the wing
submerged as expected, with the water line extending to l e s than a quarter of the semispan on
the leading edge, and less than half of the semispan on the trailing edge. The horizontal
stabilizer rested on the water, with only the underside wetted and the elevons partially
submerged. This displacement resulted in a dr& of approximately 2.5" (25% of the fiiselage
depth). which was less than initial estimations.
Static stability on the water was tested by tipping the aircrafl iongitudinally or laterally in the
water, and observing the response. There was really no question about the longitudinal statk
stability of the floatwing on the water, since there is a wide base extending tiom the leading edge
of the wing to the trailing edge of the elevons, providing a very stable platform. Tipping in the
lateral direction demonstrateci one of the floatwing's inherent s a f i feanires. Because the
winçs behave like sponsons, once tipping occus, more of the downside wing becornes
submerged increasing the local buoyancy force thus resulting in a conecting moment. This
effect is illustrated in Figure 2.12. The response was found to be oscillatory ami heavily
damped. Even with severe tipping, the oscillations would damp out within 1.5 cycles.
Chapter 2 P d of Caaecpt: Eydmïynmic Esperiaients 27
Once the static stability was satisfmorily investigated, the motors were nimed on to slowly taxi
the floatwing for the fust time. Taxiing was smooth, and control was achieved by using the
partially submerged elevons as differential brakes for W n g . A lefi stick input would produce a
right t u n and visa versa. The tuniing radius of this control technique was enough to dlow the
floatwing to perform figure-8 maneuvers within the confines of the swimming pool. It was dso
discovered that when the power is off, the elevons could be used as paddles to very slowiy propef
the floatwing forward, which may be useftl in an emergency situation.
The next step in the testing procedure was to simuiate the begiming of the takeoff run. The
model was positioned at one end of the pool, and the throttle was advanced to fUll power. The
aircrafl was then accelerated through a distance of approximately half the length of the pool,
after which the power was cut off and the aircrafi was dlowed to decelerate back to rest. Again,
the results of the testing showed the same success as demonsuated by the small tow models.
Once the throttle was advanced, the tail was observeci to irnmediately leave the water, mostly due
to the prop wash blowing past the horizontal stabilixer and generating lie. As forward motion
progressed, the submerged portion of the wing began to rise fiom the water until the floatwing
was officially planing. Directional control was maintained using the nidder, which was blown
upon by the prop wash.
This simulation was repeated several times, making adjustments in the piloting technique each
time in an attempt to optimize the performance. tt was found that the best operathg procedure
was to keep the elevons deflected up (pdI up) when the throttle was initially ad- keeping
the highest incidence angle for the main wing and thus producing the most lifi. As the forward
speed increased and the aircraft was climbing out of the water, the tail was brought out of the
water to reduce the drag and allow faste acceleration, At best, within the few seconds of the
accelerated run, the model was just shy of planhg on the step (the trailing edge of the wing). It
appeared that if there were a few more meters of travel, the model would have been planing on
the step as desired.
The taxing and takeoff simulations were repeated again using the ducted fân propulsion system.
With this configuration, the resuhs were not as successfUl as wïth the propellers. T b ducted
Chapter 2 Proof of Concept: Hydrodpim~ Experiments 28
fans produced a very focused high-speed jet of air, which was directed below the horizontai
stabilizer (due to the lower thnist line), and causeci the tail to always come up out of the water.
This reduced the incidence angie of the main wing, causing the a i r d to "dig in" rather than
climb out of the water. Because the jet of air was directed under the horizontal stabilizer, it was
very difficult to keep the tail down in order to maintain the maximum wing incidence angle.
With the tail down, the ducted fans were still not capable of making the floatwing climb out of
the water. At this point it was assumed that the low thnist line with the jet blast passing below
the horizontal stabilizer was to blame for this shortcoming in performance.
From these initial trials conducted in the swimming pool, several hndamental questions had
been answered. It was now solidly known that the aircraft floats as expected and demonstrates
ample static stability, and that planing can be achiwed rather quickly. This lefi the question of
whether or not the floatwing could maintain stable planing, and would it lifl off fiom the
surface?
2.3.2 Continued testing on tbe Severn River
Testing of the floatwing mode1 continued on September 9,2000, on the Severn River, northwest
of Gravenhurst, Ontario. The results tiom the swimming pool tests provided an optimistic
insight for the next series of tests, whkh involved attempting to lifi off from the surface.
September 9,2000
The mode1 was first tested in the water at low speeds to get a feel for the handling characteristics
once again. Different methods for slow speed tuming were tried and compareci. Fust, the
elevons were used as differential braices, as was done in the swimming pool tests. Then it was
attempted to perform a tum using oniy the aetodynamic rudder k i n g blown by the prop wash.
This method was successfbl, and was capable of producing a tuming radius equivaient to that of
the differential elevons method. It was found tbat for both methods, especially the latter, that a
tighter turning radius could be achieved by advancing the throttle through the tum. This had to
be done by feel for the best results. The third method aied was a combination o f the first two,
using both the differential elevons and the nidder for turning with throttie k i n g slightly
advanced through the development of the tuni. This methad was the most successfid for slow
Chapter 2 P d of Concept: Hydradynimic Experimcats 29
speed taxiing, and it was observai that the turning radius was only slightly greater than one semi
span of the main wing (36.2"). It must be noted here that the model was not equipped with
differential throttles for the twin motors. if differential throdes are used, it is expected that the
turning radius would be reduced to only a small fiaction of the semi-span.
The next stage of testing was to advance to hydrodynarnic planing at higher speeds. As done
during the pool tests. the throttie was advanced and the a i r d was accelerated to planing speed.
Planing on the step was achieved for the first time. Figure 2.13 shows the tloatwing model
during high speed planing on the trailing edge of the wing. After repeated hais, it was found
that when started from rest, planing would start after 2 seconds, and planing on the step d e r
only 5 seconds, within a distance of approximately 15 A.
During the takeoff run, it was found that the piloting technique for the particular wave conditions
was fairIy important in reducing spray through the propellers. Most times there was no
noticeable spray passing through the propellers; however on rare occaions, blister spray would
forrn off the leading edge of the wing were the bow wave is generated, and would pass through
the prop disk as show in Figure 2.14. Blister spray passing through the propeller disc is a
common problem that plagues seaplanes, and requires the aircrafi to undergo more fiequent
maintenance. This did not cause any immediate damage to the model; however, -ion would
prernaturely Wear components and maybe cause failures due to overloading. To reduce the
occurrence of this problem, it was found that the throttle should be advanced slowly during the
start up. This minimires the size of the bow wave by reducing the amount that the water is
disturbed by a rapid response to the nose-over moment introduced by an abrupt thraie advance.
Another potential problem was discovered dunng planing. It was found that the aircraA had a
tendency to rock laterally while planing on the step. It was unknown at first what was causing
this problem, but it was not found to be a regular occurrence. It appem as though the a i r d
would be stable while planing,, until a control input was applied, and then the oscillations would
begin.
Chapter 2 P d of Conccptt HyddymmK Esperiments 30
One theory as to why this occurred was that the a i r d had an unstable Dutch roll mode due to
the short-coupled stabilizers and the generous wing dihedral and sweep. This was investigated in
the stability analysis presented in Chapter 4. It was soon found that the radio control equipment
was more to blame for this problem, for two reasons. The control stick on the transmitter, used
for elevator control in the upfdown direction, and aileron conuol in the leWright direction, was
very loose to the pilot's touch. When the pilot applied what was meant to be elevatordy
inputs, the transmitter was sending a component of aileron input, and visa versa. To aggravate
this problem, the electronic control mixer onboard the model, which is used for the elevon
control, was producing some kind of error affeçting the neutrai position of the elevons. Each
time the elevons were deflected, they would not return to the neutrai position but stay deflected
to some degree.
This problem was solved for later testing by stiffening the Springs on the control stick that are
used to apply control feedback to the pilot. This helped set up a sensory definition for the pilot
to distinçuish between small elevon and aileron controt inputs. There was not rnuch that codd
be done about the control mixer, however, it seerned that was the lesser of the two problems.
Later testing showed that stable planing could be achieved without lateral oscillations being seen.
Since the lateral oscillations were not a wnsistently reoccurring problem during the tint day of
testing on the river, the program continued with prolonged planing runs and attempts to lie off
from the surface. Dunng high speed taxiing whiIe planing, it was found that the floatwing still
maintained a high degree of maneuvmbility. Using the nidder, the model would naturaily roll
into tums as shown in Figure 2-15 Aggressive turning at high speeds was made possible by the
15" of dihedral built into the main wing, which produced the V-bottom used to carve through the
tums and not skid.
In an atternpt to achieve flight, the floatwing model was set into planing for a long stra-ght nui.
Although the model was able to successfiil maintain step planing, where the aerodynamic forces
take dominance over the hydrodynamics, it was unable to aitain a high enough top speed ta Li&
off fiom the surface. The speed was enough t rnake the model Iight on the mer, which was
demonstrated several times when the mode1 wuld launch h m wave crestq and then retuni to
Chapter 2 Pmf of Concept: Hydrodynamic Experimcnb 31
planing on the surface, unable to maintain flight. As insignifiant as it seems this event
provided initial proof that the floatwing is able to break away fiom the surtàce ofthe water, and
land successfully without instability or nosing over.
Something to be noted at this point is that throughout the hydroplaning tests, no porpoising was
experienced. This is because there is no afler-body on the float wing design, meaning that no
pan of the tùselage is in the water afl of the "step", which could be repeatedly sucked d o m and
released by the surface tension of the water. In a critical sense, the event of launching off wave
crests could be categorized as porpoising, however, it is the kind caused by premature Iift and is
easily controlled, whereas the first kind can be violent and cannot be remedied since it is a
characteristic of the hulVfioat design.
In the late aflernoon, the winds had calmed down and the surface of the river had become smooth
and glassy. This provided ideal conditions to reattempt a takeoK The first attempt was a repeat
of what was seen earlier in the day, long step planing mns with no Iift off", however, the second
attempt was much more rewarding. Mer a long run, the model finally lifled off from the
surface. flying in ground effect for approximately 3 seconds before returning to the surface for a
successfùl landing. The speed at which takeoff was to occur was estimated to be about 25-30
mph. No significant altitude or flight time was recorded, however this was a benchmark fust
flight for the floatwing concept. Now, for the first time, there was concrete pfoof of a working
floatwing prototype.
-4 second attempt was made to repeat the success of the previous flight, and again lift off was
achieved. In both flights, the airspeed was so close to the stall speed of the mode1 that flight
could not be sustained for very long. In this attempt, the angle of attack was allowed CO get too
high in an attempt to increase the flight duration, causing the model to d l . The port wing
dropped as the model nosed over, plunging into the water for a rough landing. Despite the
awhward attitude of the aircraft upon impact, the mode1 managed to remain right-side up, and no
damage was sustained.
Chapter 2 Proof of Concept: Hydrodynr~iK Expenmcits 32
The results obtained fiom this first day of testing on the river suflïced to prove that the floatwing
concept works as a hydrodynamic vehicle capable of liftingsff 6om the surface, and therefore
shows potential for becoming a successfiil new class of waterbome aircraft.
September 30,2000
Testing was continued on Severn River, to now retry the ducted tàn propulsion system last tested
on September 3, 2000 in the swimming pool. During the swimming pool tests, it was found that
the t hmst line of the ducted fans was t w low and hydrodynamic planing could not be achieved.
To correct this, a pylon was made to raise the thnist line of the ducted fans to the same height as
that of the propellers. This modification is illustrated in Figure 2.16.
The wind speed on the river was measured to be on average 7 mph gusting to 15 mph, which
made for rather choppy water conditions. The ducted fans were ineffective under these
conditions and, as before during the swimming pool tests, hydroplaning was not achieved. The
fatdrnotor combination lacked the thrust necessary to overcome the drag of the water.
When the ducted fans were replaced with the propellerfstub-wing combination, planing was
achieved, but with dificulty due to the strong winds. To manage pianing, the a i r d had to be
directed crosswind so as to reduce the aerodynamic drag that hindered forward accelération.
With terrestrial aircrafl, strong head winds result in early takeoff. Although the ground speed is
reduced b y the aerodynamic drag, the relative air speed over the wing is high e m g h to achieve
flight. With the floatwing, and its seaplane relatives, the reâuced ground speed due to the high
winds results in greatly reduced hydrodynamic lift, which is crucial to the takeoff nin. In Figure
3.17 it c m be seen that the wind speed only increases the relative speed of the air over the model,
thus increasing the aerodynamic drag and lift. The aerodynamic Iift is dl1 too small to have any
significant effects; however, the drag reduces the resuitant thrust available to accelerate the
aircraft forward. This reduces the water speed of the aircraft, in tum reducing the hydrodynamic
l i f i produced. if the wind speed is high enough, the aircraî't may not achieve the speed néeded to
produce the cntical hydrodynamic lifl required to begin accelerating towards the s d h for
planing.
Chapter 2 P m f of Concept: Hydrodpamic Experiaicrîs 33
This phenornenon was exactly what occuned dunng testing on this day, and t h is why
hydrodynamic planing was only achieved when heading crosswind or downwind. Understanding
this was valuable for developing floatwing piloting technique. The procedure for takeaff during
windy conditions should be to first achieve planing on the step in a cros..nd direction, and then
turn into the wind while planing on the step. At this stage the aerodynamic lifi is quite
significant, and will be increased by the headwind, acting in favor of the t&er>E.
Xround the hours of dusk, the winds dieà down enough to attempt another mn The mode1 was
planing for a long straight run as done many times before. When la-off was not achieved, a
large radius high-speed turn was attempted to retum the model closer to the observation point
During the execution of the tum, the tail managed to come up higher than normal, making the
incidence angle of the wing too low, and causing the aircraft to dig in and stop very abruptly.
This was the same problem first discovered with small tow models. It was uncertain as to what
exactly caused the tail to come up during the tuni, but it was assumed that not enough "stick-
back" elevator input was applied, thus losing the planing rrim angle.
When this attitude is experienced, the model ties to dive undet water, however the buoyancy of
the airfrarne and the increased drag stop the a i r d immediately. Although it never nosed ova,
and remained right-side up and hlly intact, this type of accident is very dangwaus. Had there
been human passengers. the G-force of the rapid deceleration would have surely been fatal. For
this reason, a hl1 size floatwing would require a safety system that would automaticdly ensure
that the critical trim angle is never exceeded. This rnight not be such a problem for a pilot
controlling the aircraft fkom inside the cockpit; however, the safety system would be able to
respond to unexpected pitching much Faster than any human.
November 2,2000
In an attempt to increase the top speed of the model while planing, two significant modifications
were made to reduce the drag coefficient. These modifications are illustratecl in Figure 2.18.
The first modification is an acetate shroud moumed to fair the gap betweea the fmbble canopy of
the battery compartment and the ail turtle deck of the ftselage. This made for a cleaner
Chapter 2 P d of Coacept: Hydrodyarniic Esperimenb 34
aerodynamic shape uver that portion ofthe fuselage and also proteaed the d o equipment h m
the water.
The second modification was to the motor mounts, which were designed to hold two motors to
be geared together turning a single shaf't. On the flaatwing modei, only one motor was placed in
each mount. The second slot in each mount was left empty, so that second motors wuid be
added in the tbture if necessary. However leaving these dots empty exposed a rattier large
vertical flat plate on each rnount. Therefore to tùrther duce the drag cdcient, these plates
were trimrned off
With these modifications made, the testing continued. Again, the winds on the main body of the
river were high enough to make the water conditions unsuitable for Iift off attempts. It was
decided to move the test location to a secluded citannet, later dubbed " f l d n g run", which
offered shelter frorn the wind. The surface of the water in the channel was calm, and ideal for
t e d ng the floatwing.
The effects of the modifications made to the ayfiame were immediately noticeable on the tint
test run. Once on the step, the model accelerated significantly f i e r than any of the previous
tests. Lift off was achieved rather quickly at a speed just shy of the chase boat top speed (30
mp h), and maintained flight bnefly before rehirned back to the d e for a smooth Ianding on
the step.
The significance of reducing the drag coefficient was clearly demonsmited in this experirnent.
The quantitative effect of the modifications made to the clrag coefficient of the mode1 is studied
later on in Chapter 3.
A second atternpt was made, and again tbe model accelefated rapidly &er gdng up on the step.
Lateral oscillations once again plagued the nin, mostly because of the out-of-phase over-
corrections to initial smail harmless osciIlations. Despite the lateral instability, lift-off was still
achieved for a short duration, finishing with a rather hard landiig
Chapter 2 Proaf of Concept: Eydmdynrmie Esperimeats 35
Continuing with the successes of the day, îùrther attempts to gain longer flights were made. On
the third attempt of the day, as the a i r d was accelerating on the step, the tail was accidentally
allowed to get to high, causing the abrupt stop mentioned earlier. This was the second time such
an incident had occurred during the test program, stressing the importance of having an
automatic safety system dunng planing.
M e r the abrupt stop, testing continued immediately since there was no damage to the model.
Planing was reestablished and, shortly after, lift otf was once again achieved. This time the
model climbed fairly rapidly, and was leveled out at an altitude of approximately 10-15 ft. Mer
approximately 5 seconds of level flight, the model was brought back down to the sutface because
the end of the channel was rapidly approaching.
The fourth atternpt was aboned part way through due to the same lateral oscillations experienced
during the second run. Mer stopping ?h of the way down the channel, the nin was continu4
around the bend of the channel out ont0 the main body of the river. The bend was negotiated
while high-speed planing on the step Mer planing on the river for a short period, the model
once again took-off This time since it was over the main body of the river, there was no need to
bring it down irnmediately. The mode1 was left to fly low in ground effect while the airspeed
was allowed to build up. Once sufficient speed was built up, the mode1 climbed out to an
altitude of approximately 20 tt, and allowed to fly level for approximately 30 seconds and
maintaining a top speed slightly faster than 30 mph before making a very smooth powersn
landing. This was the most successtiil flight of the floatwing model, demonstrating the ability to
quickly achieve planing and then lift off fiom the surface into stable flight, finally safely
retuming to the surface.
2.4 Performance Summary for the 72" Span R/C Mode1
The expetiments performed with the 72" span R/C float wing model showed that the floatwing
was capable of the hydrodynamic performance for the mission requirements. The mode1 was
found to have the buoyancy required to stay afloat with only partial submergence of the wing and
elevons. The water line extendeà to a quarter of the semi span dong the leading edge of the
wing and to half of the semi span dong the trading edge, and the horizontal stabilizer lay fIat on
Chapter 2 Proof of Concepî: Eydrodynamic Erperimcnts 36
the surface with only the elevons submergeci. This amnide in the water proved to be rematkabiy
stable in the static mode.
The floatwing model was found to be very maneuverable at low speeds. Tuming was rnanaged
using both the aerodynamic nidder blown by the p o p wash, and by using the elevons as
differential water brakes. The application of these methods was capable of producing a turning
radius slightly longer than the semi span of the wing. ifdifferential thmst was used, the turning
radius could be reduced to a fraction ofthe semi span.
Hydroplaning was easily achievable with the floatwing model. Planing was well established
within 3 seconds afler starting tiom rest, and step planing aiter only 5 seconds within a distance
of approximately I5ft. The mode1 was naturaliy stable during planing, howwer instabilities
were occasionally introduced by the radio control system and aggravated by pilot over-
corrections. These problems were worked out during the process of testing and were non-
existent in later tests. During high speed planing, the floatwing model was still capable of
aggressive maneuvering using the aerodynamic nidder.
With the airfiame in the configuration used on November 2,2000, the floatwing model was able
to accelerate to a flight speed around 30 mph, where lifl-off tiom the s u r f i was easily
achieved. The transition fiom hyddynamics to aerodyr~unics was found to be very smooth and
graceful throughout the takeoff M.
The flights achieved with the floatwing model were mostly of short dumion; however, no
instabilities during the flights were noted. The longest of the flights lasted for approximately 30
seconds, flying level over the river and then brou@ back down to the surkce for a smooth
landing. Landings with the floatwing were always stable and there were no tendencies to nose
over, even during the roughest landings. One point to mention is that the floatwing always
remained right-side up, even &er clipping a wing in the water upon landing or nose-diving while
high speed planing.
Chapter 2 Proaf of Concept: Hydrodyarmic Experirnents 37
Frorn these results it can be seen that the floatwing model demonstraîed satisfactory performance
to prove that the floatwing concept is viable. Much was lemed about the characteristics of such
an aircraft, as well as what needs to be further developed for more success.
2.5 Coatinuing Research
The experimental work performed with the W C model thus far has been strictly qualitative.
Although the floatwing has been proven to be a viable new aircraft type, there d l remains the
goal to measure the eficiency of the floatwing during the takeoff nui. The efficiency can be u
described by studying the curve of the drag-to-weight ratio versus speed, as described in section
I . 3 . l . As also rnentioned in section 1.3.1, the eficiency of the floatwing is expected to be higher
than that of traditional floatplanes and flying boats, meaning that the floatwing is expected to
generate less hydrodynamic drag dunng the takeoff mn.
To perform the experimental measurernent of the DIW ratio, Aquavion Systems Corp. is in the
process of developing a miniaturized 8-channel data acquisition system equippeà with telemetry
to be mounted on the model. The model is to be inswmented to measure the various parameters
necessary to calculate the drag over the duration of the takeoff run using the following equations:
Where T is the thrust, D is the drag, L is the li& and Vis the speed. The angles 8, t; and yare
described in Figure 2.19. Since the thmst line of the motors is parallel to the reference body axis
of the aircraft, the angle s is equal to 0" and can be eliminated fiom the equations. The climb
ansle, 3 can also be assumed to be equal to the pitch angle 8, during the initial stiallow climb out
of the water to planing, and then O" when level planing is achieved.
The two unknowns in this system of equations are the L and D, the immeasurable quantities.
The remaining variables can be measured. Speed will be calculateci îiom the dynamic pressure
measured using a pitot tube conaected to a miniature dierential pfessure transducer.
Acceleration in the inertiai fiame X and 2-axk will be measured using a 2-axis accelerometerhiit
Chapter 2 Proof of Coectpt: Elydrodynrimic Experiaieats 38
sensor, and cm be verified by integrating the speed over time. The thnist can be detennined
either by using an experimentally detennined thrust versus speed look up table (since the throttle
is constantly at maximum during
calculating the thmst as follows:
the takeoff mn), or by measuring the elemicai power and
Where E is the voltage supplied to the motors and I is the current draw, and q is the propeller
efficiency. Although this method is simple becaw is does not require much pre-experiment
work to determine a thrust to speed curve, equation 2.4 will not suffice in accuratdy calculating
the thmst at low speeds, during the most crucial moments of the expsiment when the aircrafk is
working towards planing. For this ceason the tira method is superior, since the experimental
rneasurements would accurately describe the relationship of the thnist at low speeds for a
constant throttle setting. A third possibility would be to mount the stub wing on a specially
designed pylon. which would be a strain-gage force balance capable of measuring the net thnist
produced by both motors. This would mean raising the thnist Iine slightly, but may simplify the
experimental process.
The most difficult parameter to measure is the pitch angle. Several angle-measuring sensors are
commercially available, howwer, they are only usehl when used on a non-accelerating h e .
To use such sensors would require expensive and heavy gyros, which would not be fegsible for
this application. To overcome this problem, research work was done at Aquavion Systems Corp.
to design a Doppler shifi angular acceIeration sensor. The details of how this design works
cannot be exposed at this point in time since it is proprietary information o f Aquavion Systerns
Corp. This technique however is very unique in that it is irnpervious to inertial effects, and could
be made compact enough to be usefùl in this experiment.
With the completion of this experimem, it wilI be possible to compare the floatwing design with
the floatplane and seaplane coumerparts in tetms of efficiency in gettîng off the mer- Ef the
results are found to be as expected, then a significant improvement should be seen in the energy
Chapter 2 Prodof Conctpt: Eydmbnuie Exptrimenta 39
required to takeoff fiom the water, giving the new f l d n g a competitive edge in a market that
has rernained relatively unchaqed h r decades.
2.6 Topics for Further Reserrch One area in the hydrodynamics regime that would require fiitther -ch is the design of the
bow, or leading edge o f the submerged portion of the main wing. If properly designed, the size
of the bow wave produced, before planing is established, could be greatly reduced. If this is
done. then planing could be established much sooner and easier since there will be less of a
hump to overcome. Reduction in the magnitude of the bow wave would also be b d c i a l for
suppression of the harrnhl blister spray that occasionally passes through the propelln d i s .
The proper design of the bow would d u c e the hyàrdynamic drag and, in tum, the
aerodynamics would be directly improved. Further improvements could also be made on the
tàiring between the wing and GseIage intersection.
With al1 aircrafi and watercraft design there is always room fOr improvements. Optimization of
the design parameters is very important, and with such vehicles these parameters are many. The
floatwing is a hybrid of both an aircraft and watercraA and there are never-ending thesis topics
for iûrther research to achieve an optimum compromise between hydrodynamic and
aerodynamic performance.
Chapter 2 Proof of Compk Hydroby.imic Esperiacib 40
Figure 2.1, Tlsc 19" whg span tow mode1 in acîion.
Figure 2.2, The 1 1" wing spaa tow d l show11 h m m s!atic f l d o a , plnning, and m aight.
Chapter 2 Prwf ofCoicep8: Hydrodymanic Ehmrimmb 41
Figure 23,3-View dtawing of the 72" wing span radio controUed Qoatwing model.
Figure 2.4, Detail of the fuselage canstnaction technique using layececl form and f l .
Chapter 2 Proof of Concept: Eydmdynmic Expedmeib 42
l/am AI- PLY NOTE: DIMENSWS SHWN IN CENTIUEIERS
HMAmlws I W
A-A 8-8 TlP 0-
Figure 2.5, Detailed drawing of tbc wing desi@ fa the radîontrolled model.
Figun 2.6, Detail of the amsûucb îechnique iued fot tht wing panels.
Cbaptcr 2 Pmf of Comapt: Hydrodyumk EsptrinCrb 43
Figure 2.7, Fiberglas sheets cure to the wing panels undcr the pnsswr of tht vacuum &
Figure 2.8, Detail of the coasauction technique usui to buiiô th ceme secth Ewm corn.
Cbapter 2 Proof of Cor#pt: Hydrmdynamic Erpri i i iemb 44
MU1 TI-ENGINE
Figure 2.9, Typical locations fot mounting cngincs on scapianes.
WCm, FANS m
Figurt 2.10, Use of the ducted fans aiiows for tfie thnist Linc to k lowcrui.
Chapter 2 Proof of C e Hydrodyulaic Experiwitr 45
Firc 2.12, L W stability duc to tbe wings acting as sp6nsoas.
Figure 2.13, The floatwing mode1 durhg high-speed "step" planing.
Figure 2.14, Blister spray for* off tbe bow of the wing and passmg through the propcks.
Chapter 2 P d d C a i ~ Hydrodyuriic Erpcriwwb 47
Figure 2.16, The ducmi fjui assembiy mormtcd an a pylon to raise thc îluust hue.
Chapter 2 Roof of Corœpt: Eydrodyirmic Esptdumb
Figure 2.17 Effa of wind on the d p m k s of tskuig-off h m watcr.
Figure 2.18, Modifications made m rrduce the drsg of the WC model (Noveinkt 2,2000).
Chapter 2 PmofofCoierpt: Hydrodyrmmœ Espedm~îa 49
X - 2 BODY AXIS 1 Figure 2.19, Definition of the aiiglcs used in loagitud'aal aucraft dyuamics.
Chapter 3 Proof of Coictpt: Aemdymiric Esptiiamb
C hapter 3: Proof of Concept: Aerodynrmic Experiments
3.1 The Wind Tunnel Experimenb In the previous chapter the floatwing waxpt was proven as a hybodynamic vehicle; bwever,
as mentioned in Chapter 1, the floatwing concept would be useless as an akcrail without
adequate aerodynamic performance and stability. E e n t s to ver* these criteria for tk
tloatwing model were done ushg a 42% scale model m the 45" x 66" subsoaic wirad tuunel at the
University of Toronto InstiMe for Aerospace Stuàies.
The replica of the fluatwing RIC model was buih and then mounted on a specially designed test
stand. The base of the test stand is an electronic force balance capable of measuring two
perpendicular forces and a moment in the plane of the forces. This set-up was mounted in the
subsonic wùid tunrtel, which is capable of gemting wind speeds h m 50 kmCb to 100 kmlb.
The data fiom the electronic force balance was coiiected using a data acquisition system linked
to a lap top cornputer. Figure 3.1 illustrates the experimental set-up descn i .
One of the objectives of the wind tunnel experirnentation was to measure the L i drag, and
pitching moment over a range of angles of attack, and the laterai force and yawbg moment over
a cange of sideslip angles. The resuks were later studied to deduce iwdymmk cùawteristics
of the floatwing modei, and to obtaui the stabiiiiy derivatives C,, CI, Cm, C'fi and CmF The
stabiiity derivatives w m applied in the stab i i analysis discussed in Cbapter 4.
The second objective of the wind tunnel experiment was to obtain the Iüt-to-drag reiationship of
the model and to investigate the drag build-up due to the a i r t h e compowats. Tbe r e d k h m
this experiment were studied to derstand tk major wntni ions to the aircraft Qag and b w it
couId be reduced.
3.2 Construction of the Wind Tunnel Mode1
The wind tunnel mode1 was constnicted as a 42% sale replia of the 72" span WC rmdeL At
this scale, the span of the model is 30", which is 67% of the -1 height. Panbust and
Holder [7] suggest keeping the model span les tban 7W of the tunnel dimeasion to mmimizt
Cbapter 3 P r d of C-: Acrodyumk EIpciinmb 51
the wall interference effects on the wing tip vorticies. The smpllccrt tunnel dimeLlSioll was the
Iimiting factor since the mode1 was going to k mormtcd bath horiurntdy and v d 4 l y to
measure Iongitudial and l a t d fairces.
The 3-view drawing of the wind tunnel modcl is show in Figure 3.2. Coasûuction of the modcl
mainly consisted of balsa wood, foam and some fibcrgks. The h l a g e was constnictcd fiam
balsa wood using a built-up construction technique. Thc cail boom was originaily buüt to be
detachable; however, it was later perm~nently boadcd to increase the saucnval Wty. To
fùrther increase the strength along the narrow Eail boom, a thin laya of fibaglass was appücd to
al1 four sides along most of the lengtb, A 318" diameter steel tube was mounted into the tail
boom fiom the rear and bonded with epoxy. The addition of the sting incnased the stitIMss of
the tail boom, and was used to mount tbe mode1 to the test stand.
The wing was constructed in a manner very similar to the lacger WC m d l wing. Two f m
cores were hot-wire cut to form the two wing panels. The lower d e s of ttie pneb w m
sheeted with 1/32" plywood, and the uppcr surteces wen shceted with 1/32" balsa wood and pe-
cured fiberglass bonded wing a vacuum bagging technique. The leadhg and trajliag edges w m
made h m baba stock and sanded down to sbapc. The two panels were thcn bonded togctbet
and reinforced with a layer of îXmgiass on the lower surface over the joint. This conStniCti011
technique insured a very stiff wing to m i h i z c Qflcctions d h g the expriment.
The stabilizing surfaces and the stub-wing w m srrnded dom to sbPpe firom solid sbecrs of bolso.
The control surfaces were also made h m solid shcets of balsa, and hingcd to tht stabilizas
üsing only Scotch Tape. Thnc scrcw j e k mechauisms wcrc bu& for adjusting thc cmtml
surface angles. Two were mountcd onto the sides ofthe tail boom and linlted to dK elvoas, a d
one was mounted on the vertical stabilwt and linired to the cuddcr. The vertical sEabiliPn was
pemanentIy boaded to the f'useiage while die siubwing and horiumtal stabiliacr w m mounted
using screws to alIow for removal.
The nose cone and bubblecanopy were shaped using folun and coeted with epoxy to form a bard
surface capable of k i n g painmi. Further degils wae adQd by mouating balsa wood
Chapter 3 Proof of Comcept: Acrodyumk bpdmemb 52
battery packs to the sides of the fuselage, Md d e motor mounts and motoft w a r mack h m
wood and mounted to the stubwing.
One of the most important steps in building the wind tumnel mode1 was finishiag the surface.
The entire surface was fint prcpared by sanding srnooh, and thca painted widi several coats of
sanding sealer until the wood grain was no longer polous. After d h g , the s h wss sdd
and then painted with appmximately 2 3 coats of cleac SIG brand dope. The dqmi sutfaces
were again sanded and finally painted 4th several coats of Motor Master Saaich Fi ninser.
The primer was sanded and Lepage Po11yfW wood filler was used to fil1 in any imperfiactions in
the surface. When d l of the filiing and sanding was complete, a &ai coa! of primer was appiied
and then sanded with 600 grit saadpaper, and thcn polished to a ghssy smoath hi& uskg
Kirnwipes. The completed mode1 is b w n in Fi- 3.3.
3.3 Test Equipment
The wind tunnel mode1 was mountcd to a specially buiit test stand nipporting it in tht centre of
the tunnel test section. Figure 3.4 shows a drawing of the test stand and how the niode1 was
suspended fiom it by the steel sting pmûudbg h m the tail of the model. nie test stand consisis
primarily of an aluminurn post on top of which is a m l 1 aluminum p W o n n w h the d l is
mounted. The method for attaching the mode1 allowed for casy adjusm~nr of the mounting
angle in the horizontal plane of the tunnel. This allowcd for changes in angie of attack wb«r the
model was mounted vertically, and changes in yaw angk whcn the mode1 was moulltcd
horizontally.
The base of the tests test stand was soiidiy mountcd to the forçe balance. Tbe f m e baIance used
was designed and built by Lowen [8], to measurr forces by using a simin gage technique. A
schematic drawing of the balance is shown m Figure 3.5. The aadymmic forces gcaaatcd by
the mode[ were transferred through the test siand to the platfm of the force Mame, which was
suspended below the wind tunnel floot by thM music-wirc stnito. Tbis dbws the platform to
deflect fairIy fieely in the plane of the hmcl floor, traderring îhe losds h n tht test stand to
the three cantilever bearns. The caatilever besms wac mountcd 6 d y to the wind tunnel floot
in such a way thattwo take the lcmd in one axis, aiadthe thirdtpLcstbe lod mtbepcrpcndicuiar
Chapter 3 Proofof C- Acrodyullk E s m h m f a 53
axis. With this configuration, two perpendid far#s Pnd the moment in t k solm p h k
measured.
The forces were measured using strain gages mountcd on the m u beams. T k strain gages
change in resistance proportionally to the strainldcfkctk of tbc cantilever beams, and therefa
the thickness of beams was crucial to the sensitivity and l d limit of the balanct. Four Jtrain
gages were mounted to each beam, two on each k e measuring the Mi strain. This
arrangement allowed the gages of each beam to fonn a temperatrrrr ampamtd Whatstme
bridge. A 5V power supply was used to power the bridge circuits, and outputs were rrsessurrd
and recorded using the 12 bit FLUKE 2645A NETDAQ data acquisition system liakcd to a Sony
Vario laptop computer. The NETDAQ was set up to read and record the suppIy v o w , the
output voltage of the three bridge circuits of the force balance, and the resistance of thc angle of
attack meter.
The angle of attack meter was used to measure the geometric angle between a nfirmce lime on
the model and the Eree stream flow in the tunnel. The meter was made using a low-toque
Novotechnik Series P 2201 5 ki2 potentiometer. A A weather vane was mounted onto the
shaft of the potentiometer to always point in the direction of tbc fk strtgm flow. Tbc
mechanical sweep angle for the potentiomem is 360°; however, the electrical angk is 345' (the
angular range between zero resistaace and I11 resistance), making for a resolution of 0.069OIQ
or 14.5Wdeg, which is easily measurabk. The low toque cheractcristic of the potcntiomctcr
was very important in achievmg npeatable results. Other off-the-shelf poteatiometc~s were
tried. However the friction in the mechanisms was too high to overcome at low mgk of attack
when the forces on the weather vane arc low.
The angk of attack (AOA) meter was mounted as fst back on the sting as possible, and on a long
extension arm perpendicular to the sting, in order to position it as close as possibk into 6ne
stream conditions. When the position is too close to the -1, the angk wrs\md k
severeiy affected by the downwash of the flow past the model.
Chapter 3 Pmf of Coracpt. hmdymdc bpednmb !M
3.4 Modification and Caiibmtion of the Force W a c e
The balance in its original configurasion was designcd to mcasurc forces of the same order as the
forces expected to be produceci by the mode!. Howcver, it was aot daignai to withsrend the
magnitude of the moment grnerateci by the mdd in iis srrangcmcnt oa the test stand. The
severe moments would cause the thin music-win mpports thit wm used to suspend the balance
platfonn under the tunnel flmr to bucklt, and ovmload tbe cantilcvet bcams. TO ovtrcome this
problem, the supports had to be s t i f f d However* mer-stiffcniag would d u c e the ficeQm
of motion of the platform, and thus the sensitivity of the fom balance would be gmtly reduced
Figure 3.6 shows an illustration of the a d i f h t h made to tbt platform supports. The major
difference is in the use of the aluminurn angk brackets bondcd on both the platcotm ad uppa
surface of the balance (whd tunnel floor) for macmthg the music wire, radier than simply
wrapping the wire around screws as used ia the original design. The use of these brackets
reduced the effective length of the music wire çupporis, greatly reducing tbe risk of buckiii&
and allowed for the rapid replacement of the music wire if the stiffncss of the balance netdeâ to
be changed.
The balance was then calibcateâ by using the wcight and pulky illustratcd in Figure 3.7.
A basket of weights was suspended by a string pMsmg over the pulley of the calibration rig to
the post of the calibration rig, and was uscd to apply forces of lmown magniruric. The rig was set
up to apply loads along each axis indtpeadcntly to dctcmh die slopc of dic l ad versus output
voltage relationship. When the loads wnc applied in thc direction of one axiq the output of the
perpendicular gages was monitored to ensure thst dierr was no couphg of the two axa. It was
discovered that when loads werc appücd a a d y p d k l and perpendicular to the wind trmbei
walls, there would be cross talk in the output of the two oxcs of the balance, howcvc~~ whcn the
Ioads were skewed 5" h m the axis of tbe tuaiici, î b outpurs bccame nidepcndcnt of each ohm-
This means that the axis of the balance was r d 5' hm the axis of the tunnel as show m
Figure 3 -8, and had to be corrected for in the resufts,
Sarnple calibrations are shown m Figures 3.9 - 3.12. Thcsc grspbs sbow tht quality of the linœ
relationship between the appiied Ioads and k output vohage of dK balance. The non-loadd
Chapter 3 P m f of Corccpt: hdymnk Exp8dœmb 56
axis plot shown in Figure 3.10 vd ies tbe midcpcndence o f d wis by dcmoiwtrstiag how the
dope of the output voltage pet applied lcmd iippwehcs zrro forth mm-laded ais.
Using 0.078" diameter music wire fot the support wins ccsukcd in calibration slopes of 3.48
ib/mV in the drag direction, and 2.17 lWmV in lif? ditection. Tbis sbowëd that the balaacc
was too stiff to resolve small changes in lift ad drq, which is impartant for comparing
variations in the aircraft configuration. Tbc support wim w m later nduccd in diameter ta
0 . O 5 j W and the new slopes wete 1.88 lWmV in the cimg direction, 1 .O8 Ib/mV in the liff direction,
ruid 0.84 ft IbImV for the moment. This was a great i m p o v e m ~ ~ t over the pmious
arrangement, and allowed fot the tesolution of Imiall changes m foms, espccially m tbc h g ,
which was to be studied in detail.
3.5 Experimental Procedure The rnethods used for the executioa of thc ex- wen fairly sûaigh~onivard. The wllid
tume! model was mounted on the test stand vcrticaliy for loagihrdinal measrirrments, or
horizontally for lateral measurements. More d nin, a rm, rradmg was taken for tbc balance
offsets. Readings fiom the balance wcre Ealrcn ushg the NETDAQ, which was initially set to
take a 10 second sample of &ta. This was later changcd kcaltsc the NETDAQ was formd to
have an inconsistent sampbg rate. Insisad, the NETDAQ w a ~ kft to record data mtil 397
samples were recorded, which was approxirmitciy 10 seoonds of oampling time. It was p f d
to use the same number of siamples for eîeb run to simplify the rrductioa of tbc d t s in an
Excel spreadsheet.
Afier the zero readings were recorckd, tk wtod aumtl was turned on to geaeratt an airspecd of
14 ds. This resulted in the made1 Reynolds wmkr of 100 000, which is of the same order as
that for the R/C model. AU tests wcrc coiiducoed at 14 mls to mmim;rr fkxurc m thc mode1 and,
more irnportantly, to keep the loads in tbe isngc of tiit fÔne boluicc. Oncc the ai&w in tbe
m e 1 was fuily developeà, the NETDAQ was &vatcd to record thc ousput perrimcters w g
the nui. The results of each run werc p d m rn Exccl sp&kct . The pcn, rwdmgs and
the experiment readings of the supply voho%c, as well os the balrnçc output av=gcd- The
Chapter 3 P m f ofcaiapt: hdymmk E s p d n w m 56
average of the active readings w a tben comcîcd by tûe o f k b of the average of the zm,
readings.
The angle of attack meter resistance was also rccoréod during the rua, and an initial 0" mistance
was subtracted tiom it to obtain the change in resistancc. This was used to calculate the angle of
amck during the run using equatim 3.4 to follow.
The following equations were appiied in the Exce1 spnadsheet (see Appendix B) ta cakulate the
desired quantities:
The quantities L ' and D' are the la and drag measured dong the axis of die b c e , and an
corrected for the 5" skew in equatioas 3.7 and 3.8. The K values refcr to the instrument
calibration slopes, and the AV symbl nfCrs to the output voltage h m the balance conecttd for
the zero offsets. The subscripts "totaln and *diffczc~tcc" arc due i4 the use of two cantileva
beams in the lift direction of the force balance. Tbertfotc the sum of tbc two rerduigs, rotal*, is
used to derive the total lift force, aud and ''dinérenc-e'' is d to derivc i ! ~ moment. if tht
difference were null, then tbat would indicate a pmc lift f- and no moment, The CS with the subscript W refer ta the m m d i m c n s i i fotccs and moment gaiaatod by the
test stand alone. These are subtmctd from the masud valm to -t thosc values for the
aircraft alone. Finaiiy, equation 3.9 is dcscn'kd physicPlly in Figm 3.13.
Chapter 3 Pmf of Coircpt: 57
The process of recordhg zero mdings, and starcnig thc wind tunntl and ncording errperiimcntnl
readings, was repeated s e v d tixncs for each angle of atîack or sidesüp angle testcd in ardcr to
study the repeatabiîity of îhe results. The main c x p h m b mpid 10 runs per aagBe, while
only 5 runs were used dwirig sceondary tests on dit effects of tht sîubwing and briumtai
stabilizer.
3.6 Experimeatal Results The results obtained h m the wind tunnel experimcnt rc~cmbled what c d d be expcctad for an
aircraft. A11 of the c w e s obtained p o s s d the ü~nds aad mnaimui# that wcre expctd,
providing a confidence that the experim«iiai quipment was frmctioning pmpdy arad drt
experimental procedure was s a t i s h ~ .
For the majority of the experimentaîh, the mode1 was set up in tbc cmfigudott of dK WC
modef as it was flown on November 2, 3000. It must also be noted that tht d t s rrprrscnt
those for gliding flight without the pnscncc of the ptopclicrs.
3.6.1 Lift, Drag, and Pitciiag M o i m i n. Aylt of AICIcL
The longitudinal measurements consistai of la drag, and p h b g momtnt as a ftnctim of tbe
angle of attack. Figures 3.14 - 3.16 show thrrt ntiitionships with daio for ail tcn nins,
while Figure 3.17 - 3-19 show tht avcrage rrsults wiîh a 95% c o d e m x intemal (I2 standard
deviations). The vertical errer bars show tb thc fam mcasunmcnts ohahcd h m the Vanous
m s agree welI with each othcr, and vMfy bK repcarability of thc rcsults. Tbc angle
rneasurements aiso dernonstrate reasonable em#s tbtough tbt angk range, exocpt for the fh
data set, which has a broad spmd causmg an d t y in the position of the f3st data point.
The characteristics of die lifi curve follow the î d i t h d teaiplaie. Tirtough the range ofangks,
the reiationship is quite Iinear, roUing off at the highcr agies of ateeck befm d. The Iost data
points are at approximately 1 Io, whicb appcar to k at maximum sügbdy b e b d. Tufés
mounted on the main wing of the mode1 i d k a i d that bit flow over the rwt d o n of tbe wing
was still attacbed and not yet stolkd. Altbough the maximum liA is achkvd, the cuve wül
Chapter 3 Pmof of Corccpt: Aerodynmic Espdmmbi 511
gently roll over before fuUy stalling. The beginning of this is iüuscroted by the curve as it g d y
rolls off fiom a steady linear incieasc to the maximum lift cafncicnt of 1.4.
The lifl coefficient representtd hm is the net rcsuh for the fiil aircrafk, including the lift
produced by the tail. The results are fot the ekvator trim Pngk set to 4 = -3" (or 3' up). 'ibis
particular trim angle was used to exactiy nprrsent the configmîion of the WC modtl.
Changing the trim angle would tninslete the lift curve up or down as showa in F i i 320,
dependhg on the changes in tail lift. The drag and moment nlationships woukl aiso k a f f d
by changes in the elevator trim angle.
The drag cuve is seen to rise in an exponential féshion, 'itsrting out rchtively low, incrrasing
non-linearly with the liR and f i d y Ulcnasing rapidly as tbe aircraft approaches stall. The
results corn the drag measurements wiii be discussed in greater detail in section 3.6.2.
The relationship between the pitching moment coefficient and the an& of attack is vcry
important in the analysis of aircraft pitch stability. From the mlts it is seca thas the aircraft has
a positive pi tch-seess (-ve dChlc$da) and, at rm, üff (approximaîeiy a = 4 O ) , has a positive
moment coefficient about the CG (nose up). The positive pitch-stüks indicatcs ihat the
aircraft will return to the trimmed pitch angle if distiakd. The k t that the moment c d k i c n t
at zero l i f l is positive in conjunction wiîh the negative dope indiCates dut at some angle ofattack
the moment is going to be zero, meanhg that thc ahwatt is trimmbd: acither pitcbnrg up nor
d o m . In this case, the aVctaft achiews trinu& gliding flight at an angk of at&k of
approximately a = 2.5'. Again this would change if the trim an& of the ckvatcw were to
change; however, the slopc would rcmain the same.
3.6.2 The Lift-to- Dng Rcûtiorsbip
The lie-to-drag relationship for an aimsft cai typicaüy be .nimniatizcd by tbe dng ph and the
Iift-to-drag ratio. The drag polar is shown in Figure 321 as the plot of CD agakt CL. The
typical relationship of lifi-toldrag is gcaedy descrihi by thc hllowmg cquation:
Chapter 3 P d d C w : AcradyrrmkExpdmntr 9
Where K is an efficiency factor dependant on the wing planfm (K=l for an eiliptical planf~l~ll),
and AR is the aspect ratio of the wing. 'ibis equation shows thed the dmg bas a quadraîk nbth
with the lifl, with the coefficient of th lincar tcrm king ano. In Figure 3.22, a line is fit
through the plot of Co against C: to vhim the followhg expression f a îhe dng as in quatim
3.10:
CD = 0.036c + 0.047 (3.1 1)
In Figure 3.23, a standard poiynomid was fit to the daîa points dlowing a linear term to bc
present. The following expmsicm fm the dcag polar was ohinad:
Both equations fit the &ta points nssonably weii. Equation 3.1 1 poduccr an R' nhw of 0.%1
while equation 3.12 is siightfy bettn with au R' value of 0.m. The poaibiliry of ùaving th
linear term present is explaineci by DeLarina [9] to be due to a phcnomc~lot~ d e d p a d
leading edge suction, which occm with airfoils at low Reynok nimibers. Both of the equations
used to describe the drag polar ptovide aàquate estimates of tht dmg coefficient for a &CIL lift
coefficient. As seen in Figure 324, the diffemicc ktween the two curves is smoll.
The lift-to-drag ratio is presented in Figure 3.25. The Iift-todmg ratio incrrtses to a maximum
of approxirnately 12 at an angle of atûuk of 7' k f m droppmg off. This means îhat a maximum
glide slope of 12:l could be achieval, at a glidt slopc angk of 4.8". For the configuration testcd
(with 3" of up-elevator), the W-to-dmg ratio at the trimmebfli@t an& of aüsk is
approxirnately 9, which givcs a @de ratio of 9:l at a glide dope of 6.4'. Agaia it is tb
note here that the nsults for the drag of the wind ninncl model m q k sligh@ optimistic sime
the model does not inchde the effects of the propellers.
Chapter 3 PraololCmcepî: Atrodyumk Eqedmmîs 60
3.6.3 Effects of the S t u b W ' i
Studying the effects of the stubwing on tht lift and dmg was important kfawc it is prt of the
unique floatwing configuration. It was originaüy assumcd that forming the motor pylons into a
wing would help produce extra Li& howevct, in Figun 326 it can bc seen that the appositc
effect has occuned. The lift is acnially sli&t!y hi* with the absence of tbe stubwing uutil
just before reaching maximum iift, whm the curvu cross. This rrductioir in liff c d d be a
result of the position of the stub-wing. ïhe high-pressure region genctated on the lowcr siirf8ce
of the stub-wing may be reducing the m@tudc of the p u r e diffemtiai at the root of the
main wing, causing a decrease in la. At the higk angks of attack the main wing shadows the
srub-wing, and the effect is no longer prisent. Relocation of the ab-wbg to a position fiadier
aR may remedy the situation if it w m nquiml. if it is certain that the analysis of tbis
phenomenon is exact, then an cxtreme trial solution may k to use an invertcd aidoil on the stub
wing, with the suction side face-@face with the sucticm side of the main Wiag, thus incrcasing
the pressure differential.
The effect of the mb-wing on dtag is shown in Figure 3.27. As expected, tbc addition of the
stub-wing with the motors resulted in an incmise m the dmg. The drag curves arc identicai, d y
transiated by the drag of the stubwing.
The reduction of lift and the incrcasr in ckag dut to the stub-wing have a doublt impact on the
lifi-to-drag ratio as shown in Figure 328. The addition of the stubwing mhices the gli& slapc
from a maximum of approximately 16 Qwn to 12.
From the moment rneasutpments show m Figure 3.29, it was f o ~ d that the prrscnce of the
stub-wing had negligibk cffects on the ahmît pitching moment.
3.6.4 Effmb of the Horàoibl SbW)rcr
Studying the characteristics of the wing-body cdgPrat i0~1 is usefiil in adyzhg thc stabiiity of
the aircraft and for opthking the &si* of the baPitDatol stabikr. The d g
configuration in thii case consists oftk enth mode1 Save the horinwtd Mi.
C hapter 3 P r d of C-. Acrodyuiik ErpcriiiHib 61
Figure 3.30 shows the effcct of the horizontal stobilizcr on thc slope of tht Liff curve. The
maximum l i f i coefficient is reduced to appmxinintcly 1.2. This is quai to the C M - Y
maximum section liA cafficient a! a Reynolds numbcr of ld , as pmmed on tbe NASG M i l
Database 11 11 (see Appendix A for Clarit-Y data). The lüt coefficient of a finitt wing is
generally lower than the section lift coefficient; however, in this case the fiiseiagt CO CL^^^
enough li ft to make the wing-body 1% coefficient cquivalmt to tâat of the section. The efht of
the horizontal stabilizer on drag is shown in Figure 3.31, and will be diScusseci M e r in s e c t h
3.6.6. The most important effect caused by the horizontai stabilizcr is, of course, the siope of the
moment curve shown in Figure 3.32. W i the tail, the pitch stiffncss is ncgatbe @mitive
dope), rneaning the aircrafl is unstable. The size of the horizontai stabi lk and its mament arm
are very important for achieving longitudinal stability as show11 by tht foUowing cquatim from
Etkin and Reid [I l ]:
Where,
And h and h, are the locations of the centre of gravity and the a d pomt nspcctivcly, based
on percent mean aedynamic chord. ïhe syrnbol ê nprrsenîs tht gametric &rd ofthe
wing, Cm, is the propulsion contribution to tbe rncnnent coefficient, U tbc disiancc h the
mean aerodynarnic centre of the wing to that of iùe tail, Sr is the tail a m , and h d y E is thc
angle of the downwash off the wing. Using thW nia thdp , ths tioriumtal stabilwr could bc
optimized to achieve the desircd pitch stabiiity.
3.6.5 Lateral Measunmeab
The experirnents perfomed to mcasurr the lateral p c r h m w of tbc airaaft WCKC done midy
to obtain values for the latemi s t a b i i daivasivcs. The only tcsuhs that could k mcamtcd with
the set-up used were the lateral force Y, and thc yaw moment N. Figure 3.33 shows the ümar
relationship between the laiemi force and die sideslip angle, and Figurr 3.34 S&OWS a similar
Chapter 3 P r ~ f of Cowcpt: AtroBgrimk Exptriiwib 62
linear relationship between the yaw moment a d tk sideslip Mgle. Tbt yaw moment is not
exactly zero at O" sidesiip angic due to possible aspmtrk in the model. This offset is not a
problem, since the important infoltllidiion hm tbe rrsults an the rates of chau8c, which are used
for the stability analysis in C h a p 4.
3.6.6 Drag Build-Up Study
This study focuses on analyzing the majar souras of drag on the airûame and how it cm be
reduced. Because the floatwing has a unique COILfjgurOtiOai, it was of interest to detemine the
drag contributions fiom adding major compol~tlts such as die relatively iarge horizontal
stabilizer and the stub-wing. For this cxperiment, the mdd was mouutcd at an angle of attack
sirnilar to the cruise angle, and the drag was mcrisund fot scveral configurations. uiitislly ihe
model was stripped of the horizontal s t ab ih and sîub-wing, kaving only the fiisclage and wing
(which were permanently bonded to each a). Then tht components w m added one by one
to determine the drag build-up h m the base& wing-body configuration.
Figure 3.35 shows the results of these tXpCrimeats f a tbe madel configmatioas hm in
Figure 3.36, It is seen here that the addition of thc stub-wmg c o n t n i substmtiaity to the
overall airccaft h g . This can be blamtd on thc latge bluff-bodicd motors mouutcd on the upper
surface of the stub-wing. The incrcasc in dtag by adding the borizoatal stabilizer is oniy a
fraction of that due to the stubwing. For the augk of a i ~ k siudied, the change in CD !hm
adding the stub-wing was appmximaieiy 0.012, CO@ to 0.ûû2 for adding the horizontal
stabilizer (after the stub-wing was alnsdy in p k ) . W i the aidition of the horizontal
stabilizer, the aircraft was Ui the same coafigiaation h w n on Novcmkr 2,2000. It is irnpommt
to recall that these results arc for the aircrafk at thc cruk mgle, and thaî the drag différence
Uicreases substantiaiiy at higher angles of aîîack as shown by F i i 327.
Fairings were fitted to the butt face and back of dw box fhclsge as shown in configurations 4
and 5 of Figure 3.36. The fairing for the fise was munded aiad resembled the Ieading edge of a
wing. The addition of this fairing, &me, was s u d in &hg tbt CD to tbt kfm tbc
horizontal stabiiizer was added. Tht h i h g for th bsclrsidc of the k l a g e was triangular, and
when mounted on the model (along with thc fiout f8iring) poduced negligik changes in the CD.
Chapter 3 Pmf of C-. h r o d p r i t -b 63
It was also attempted to add wing filkg to fàir t h mterscctioa at the wiag niot; however, tky
proved to increase the drag. This was most l k i y c d by the incrtese in h t a i and wctted
areas due to the improper design of the Mets. It is clear tbet thc design of the wiag fille& is very
critical and may inttoduce dtag penahics i f h impropetiy.
One of the highlights of this study W the comperison of the dmg coefficient for the aircraft as
tested on September 9,2000, to îhat test& on Novcmba 2,2000, after making the modifications
discussed in Chapter 2. The origiaoi cairfigumtion ptbduced a CD of appmximatcly 0.079,
whereas the modifications were able to nduce the CD to approximatcly 0.062, a savings of
almost 22%. From these results it is easy to irisdrrstand the grcat inmase in perfosrrrrmce drrriag
the November 2 tests.
3.7 Topics for Further Researcb
The wind tunnel experiment presented in this chapta simulated the mode1 in gliding flight,
without the presence of any propcilcr effects. It would be beneficial to study the same
characteristics with the presence of the propeUen and slipsttesar. Sincc the popcIIers arc
rnounted above the wing, it would bc mtmsting to sec how this o f f i the flow ova the wing.
It would also be interesting to h o w if the stubwing khaves, or could k designcd to kbave,
like a blown flap to increase the Iift at low speeds.
As the mode1 used in this experimcat was a tcplim of the scientific test-bed WC modci, it is not
very representative of what a real floafwing moy look m. AWaugh tbe general configuratb
would remain relatively the same, the body would bt wm tbrrt dimensionai ami aerodynrunic
in nature. A combination of accurate sccik modcling sind propa scaling of the ptopcllcf
slipstream would provide great insight in@ the rictodyaemcs and stabiliry for devclopamt of a
full size version in the future.
Chapter 3 Pmf af Co-: Aerodyimie Experhwts 64
WlND l4m/s n
WlND NNNEL FLOOR
FORCE BKANCE
v POWER SUPPLY MTA MUlSmûN UPrOP COUPUTER
MTA ANKrSlS
Chapter 3 P d of C o i c c ~ Aer#tyumir Eriurimerb 66
MoDaSCKE: 42/lûû WiNG SAN: 50.47. (77.4 cm)
f i -
-\
Chapter 3 Pmof of Co-. h d m 66
Figure 3.4, Test stand used to support mode1 m tht tunnel ad transfer loads to the balance.
Figure 3.5, Schematic of the farce balance dctailing tbc method of m e ~ j the applied Id.
Chapter 3 67
Fiun 3.6, Modificatioas made to tht force balance music-wh supports.
STRING
PUUY
TEST STAND
I I "" t FOR WElGHlS
Figure 3.7, Schematic of the fom balance caliWon technique.
Chapter 3 Pmof of C m A t d y n i n k IbptrirCib 68
D D' Figure 3.8, Relative positionhg oftbc forc~ bahce axes to the tunael axes.
Figure 3.9, Sampk c a l h a t h plot fot îifk axis off- balance.
Chapter 3 P w f of Corapt. Atmdynamk Esperimcits 69
Figure 3.10, Output of doadcd drag axh diiting c a l i i o n of lift axis. Note the dope of output voltage to kmi is two fold lcss than the lüt axis slope* thecefore, the cross-ioading is ncgligile.
Fire 3.11, Samplc c a ü i plot fw drag axis off- bahce.
Chapter 3 Proaf of Cm-: Aeilodyusik -b '18
Figure 3.12, Sample caiibration plot for moments applied to force baiance.
MCG = Mm - (L COS a + D sin a) lc, - M,
Figure 3.13, Calculath of pitchiag moment t'rom wmd nmibcl m w m m t s ,
Chapter 3 Proof ofCompt= Awlodyumic Experiaemb 71
4 2 - - - ----
-6 4 -2 O 2 4 6 8 10 12
Anok@fA-b(ckg)
Figure 3.14, Lie coefficient vs. angle of attack plot showiug the complcte data set.
-1
4 4 -2 O 2 4 I 8 10 12
kiOl.dAdElck,ddrgl
Figure 3.16, Moment coefficient vs. angle of anack plot stiowing the complcte data set
a -4 -2 O z 4 6 8 IO 12
kiOidAtlrdCddrg) Figure 3.17, Lift coefficient vs. angle of attack plot showhg the avaegc of the data set.
Chapter 3 Proof of Co- A m à y m d c Expdmnb 73
Figure 3.18, Drag coefficient vs. angle ofattack plot showing the average of the data set.
-1 .O
8 4 -2 O 2 4 @ 8 10 12
kiOkd-a(6g) Figure 3.19, Moment coefficient vs. angle of attack plot showing the avcmgc ofthe data set.
Chapter 3 Praof of Corecpt: A-& Erpcriacrb 74
Figure 3.20, Changes in e k v m trim angie causes thc liA c m to shifl up or dawu.
O
4.2 O 0.2 0.4 0.8 0.8 1 12 1.4 1.8
m-CL Fium 3.21, Data points fotdrag vs. üft masmmak
Chapter 3 Proof of C m . Aemdynmk ExptriWib 73
Figure 3.22, Quadratic fit to dmg vs. la mca~uccmcnts to fonn a standard Qag polar (no tincar term). The curve was fit to the dani points befon maximum lifk was achievcd.
Figure 3.23, Another quadratic fit to ihe cùag vs. üA masmments, this t h e dowing a Lincu term to exist iu the drag poiar.
Chapter 3 Proof of Concept: Aerodyirmk E x p e h b 76
Compariron of Polynomirl F b for t h Dng Pokr
Figure 3.24, Both drag polar fits provide ceasonabie dtag estimwes widiin the usefiil rangc of Iüt coefficients.
4
4 4 -2 O 2 4 6 8 10 f2
md-a:(drig)
Figure 3.25, La-to-drag ratio vs. angle of at&k plot showhg the compktc data set-
Cbapter 3 Proof of Coiœpt: Aerodyumic Eqdmtnb n
F imre 3.26, Effkt of the stubwmg on lift.
Chapter 3 Proof of C w Aemdyumic Eqœdmmb 78
Figure 3.28, E f k t of the shibwhg on the lif€-cudmg ratio.
-2 O 2 4 8 8 10
k i g l i d r n a t d r g l
Firt 329, Effect of tbe stubwllig on pitching moment
Chapter 3 Pmf of Co- Aerodyumk Experimemb 79
_.-- ._.-
O œ.---.-.
4 -2 O 2 4 8 8 10 12
kighof AtCidr, a
F i u n 3 3 , Effect oftûe horizontal stabilizer on M.
0.18 -- mioriorrcir 0.16 - 8 mrikr.#.
6 . 1 , --.-.- y'. Pory.cmriwi.ru).
% 0.1 8 O 0,08
p 0.06
a 0.04
Cbapter 3 Proof of Coicrpt: Aedyurk Erperiwib !Ml
Figure 3.32, Effect of the horizoidal stabilizer on pitching moment
0.05 -2 O 2 4 8 8 I O
--B(drg)
Figure 333, Lateral f m cocfncicnt vs. sideslip an&.
Chapter 3 PrdofConccpt= Aerodynmk Esperiœemb 81
-1.2
.2 O 2 4 6 8 10
SidrrHD kigk, fi Idrg)
Fkrrt 334* Yawing moment vs. sideslip angie,
1 2 3 4 6 6 7
Cori(lguntlon -m-W1
Figure 3.35, Modd c o ~ o m tcsted in the drag build-up stdy
Chapter 3 P r d of Con-. Acrodyiuiisic Eqdmab 82
eD - Cumnt Co*.
Figure 336, Drag measurements of various mode1 conîiguratio~ls for drag Md-up stirdy.
Chapter 1 T k Stribiüty Andyds
C ha pter 4: The Stability Adysis
4.1 An Introduction
The objective of this study was to analyze the dynamic stability of the floatwing madel. The
uni que configuration of the floaniring design has brought about questions regarding aerodynamic
stabil ity , warranting this investigation. In this analysiq the stability derivatives were obtained
from the results of the wind tunnel experiments, or calculated analytically for those thaî could
not be measured. The stability derivatives were employai in the equations of motion, which
were solved to determine the response of the aircraft to srnall disnubances in the longitudinal and
lateral directions.
4.2 Theoretical Modeling
The model used in this study was the well-known small-disturbance theory described in detail by
Etkin and Reid [ I l ] . This theory treats the flight path of an a i r e as a series of small
disturbances from equilibrium flight. A condition for this model is that the aircraft is in
unaccelerated flight, and that the response of the a i r d to the srnaIl distutbances is linear. The
response of the aircrafi is obtained by the solution of the linearized equations of motion.
The longitudinal equations can be prescnted as follows
Which is of :he form
M+Nx+AFc=O (4.2)
Which can also be expressed in the form
Chapter 4 The Stabiiity Aadysis 84
And the lateral equations are expresseci in a similar matter
- (m - Y.) ri Yi
-(L- L p ) (In+ L;) L I 1 Nv ( L + N @ ) - ( L - N , ) Nr l 1 O l
O O
L " O -secab
Inherent in these equations are the following assumptions:
1. The equilibrium flight condition is symmetric with no angular velocities, and the stabilii
axes (or body axes) are used such that:
v o = p o = q o = r,= & = O & w, = O , uo =jtight~jpeedund8~ =climbangle
2. The effects of spinning rotors are negligible, representing gliding flight or counter
rotating propelfers.
3. The wind velocity is zero.
4. The density of the atmosphere daes not very with altitude.
For this analysis only controls-6xed stability was considered, and therefore the vector &, which
represents the control force equations, was non-existent. Therefore, the resulting equations have
the form
X = Ax (4-5)
Which has the solution of the fonn
N t ) = x,yU (4.6)
Substituting this solution back in to 4.5 gives the following system
(A-AI)z=O (4.7)
There is a nonzero solution for x, when the system daenninant equals zero,
Chapter 4 Tùe Strbiiity A d y s i s $5
which, in this case, produces a fourth order poIynomiai in 5. The solutions of the polynomial
may be real values or wmplex conjugates. Each eigenvaiue, k, represents a naturai mode for the
system. The final solution for each variable is a sum of al1 of the natural modes; for example
where the coefficients, a,, are determinecl by the initial conditions. What are of most importance
in this study are the eigenvalues determining the natural modes. The characteristics of these
modes, being oscillatory, non-oscillatory, convergent or divergent represent the response of the
aircraft to the small disturbance. In the longitudinal case k e are generally two oscillatory
modes: the lightly damped phugoid mode and the heavily damped short-period mode. In the
lateral case there are generally three modes: the spiral and rolling modes, which are non-
oscillatory, and the Dutch roll mode, which is osciilatory. The eigenvaiues determine if the
modes are stable or unstable, the modal natural fiequency, damping ratio, oscillation and
response time.
The non-dimensionalized system of equations can be used to obtain a set of eigenvectors
corresponding to the natural modes obtained &om the dimensional system. The eigenvectors
show the relative impact on the state variables for each mode, as well as their phase
relations hi ps, and provide great insight into the modai characteristics. The longitudinal non-
dimensional system is given by
i i i+&+Ak=o (4. IO)
Where
Chapter 4 The Strbiüty Anaiysis 84
and tinally
The lateral equations can be written in a similar form where
Cr# Cr, (-2p+Crr) mgcos& O
Cl8 Cb ct O O
C w C, c* O O
O 1 tana O O
O O sec& O O
- ( 2 - C r ) Cr, -
Cr O O
CM -(î=-cc) (L+G) O O
Cm ( Î , + c ~ ) -(L-c*) O O
O O O - 1 O
O O O O - 1 -
and findly t (4.18)
(4.15)
Chapter 4 Tbe Stabm A d y s i s 87
4.3 The Stability Derivatives and Momenîs of Iaertir To complete the stability analysig much information is neeàed to be known about the 72" W C
model. The equations require the input ofthe stability derivatives and the moments of inertia for
the aircrafi. The stability derivatives used in the small disûhance theory equations were
determined from both experimentai results and calculations. The derivatives Cz, C'8 and Cng were reduced fiom the wind m e 1 results. The remaining derivatives were caiculated
tiom the method provideds by Roskam [12]. The final results are given in Table 4.1.
Table 4.1, Stability derivatives for the 72" span floatwing model.
Ali of the derivatives with respect to rates of change are assumeci to be negligible except for Ca
and Cm, . As well, at the low subsonic speeds, it was safe to assume that the derivatives wit h
respect to changes in speed are also negligible.
To obtain estimates for the moments of inerùa ofthe air&, a solid 3D model representing the
major components of the a i m e was created using AutoCAD R14. This rudimemary model is
s hown in Figure 4.1. The mass propeities for the d e l with a unit density were detennined by
the software to be
Chapter 4 The Stabiiity Aaaîysu 88
With the mas of the aircraft known to be 4.08 kg, the density could be caiculated and used to
scale the moments of inertia. The final results are
The accuracy of the model used to obtain these results was verified by examining the location of
the centroid of the model. The location of the centroid was found to be located almost over the
trailing edge of the wing in the longitudinal direction, and approximately mid-way up the depth
of the fiiselage at that location, which is in the proximity of the actual centre of gravity.
The estirnates of the stability derivatives and the moments of inertia were implemented in the
stability analysis descnbed in section 4.2, which was solved using MATLAB.
4.4 Longitudinal Stability
The eigenvalues obtained fiom the longitudinal equations of the small disturbance d y s i s were
found to be
+As expected, two conjugate pairs were produced, insinuating oscillatory naturai modes. in
Figure 4.2, the eigenvalues are plotteâ on the real-imaginary plane to easily show that both
conjugate pairs have negative real components, implying that both modes are stable. The tint
sec of eigenvalues corresponds to the Iightly damped phugoid mode. The second set, which is
wideIy spaced along the imaginary axis and has the greater negative reai component, corresponds
to the heavily damped short-period mode.
Chapter 4 Tbt Sîabiiity Anrlysis 89
The response characteristics for eigenvaiues of the form A. = n * ai were obtauied using the
fol lowing relationships
-n Damping ratio: = - (4.20)
B1i
2K Penod: T =- (4.2 1)
W
0.693 0.693 Time to double or half t u * = tw = - = - (4.22) M 14..
W Cycles to double or half NbUbh = Nw = 0.1 1 - (4.23)
In1
üsing these equations, the characteristics of the phugoid and short-period modes were found to
be as follows
The Phugoid Mode: Natural ûequency a = 0.67 tIz
Damping ratio c= 0.39
Period of oscillation T = 10.2 1 s
C Y C ~ S to half Nhaq= 0.26 cycles
Time t0 hdf thav= 2.65 S
The results show that the phugoid oscillations are adequately darnpeâ, with the magnitude of the
amplitude reac hing half the maximum value in less than 3 seconds.
The Short-f eriod Mode: Natural 6equency = 4.81
Damping ratio c= 0.6 1
Period of oscillation T = 1-64 s
Cycles to half Nhq= O. 14 cycles
Time to haif tw= 0.24 s
Chapter 4 T k Sîability Andysis 90
The results show that the short-period made is relatively highly damped, as expected. The short-
period natural frequency and damping ratio can be used to characterize the handiiig qualities of
the floatwing model. Figure 4.3 and 4.4 show pilot opinion contours given by Eutin and Reid
[ l I ] and MacKenzie [13] respectively. The first figure shows the floatwing to fàil aimost in the
centre of the "best tested bounclary", indicahg good handling quaiities. On the second figure,
the floatwing lies on the upper bordedine between acceptable and poor handling qualities, in the
region of quick response and high sensitivity.
The reference figures used can only be regardeci as a "first guess" at the handling qualities. The
information given contains biases because much of the tabulation of pilot-opinions was done for
tighter aircraft in the past. As weil ttiere are many fictors involved in the handling qualities, and
their interactions can be overlooked. For example, the pilot may experience difficulties in
controlling the laterai modes, which could influence his rahg of the longitudinal handling.
Therefore assessment of the handling characteristics should be iürther investigated by actual
flight-testing.
Using the non-dimensional longitudinal system matrix to observe the corresponding
eigenvectors, the effects of each mode on the flight path can be observed. The eigenvectors
obtained for both modes are presemed in Table 4.2.
Ta blt 4.2 Longitudinal eigenvcctors.
n i f i d Short-&nad M ~ i ~ d e Phare M ~ I L L Phase 0.958 122.1" O. 192 7 3 . 9 O
Looking at the results for the long-period phugoid mode, it can be seen that the for a unit change
in pitch angle, only the speed was affected approximately 90" out of phase with cIimb angle.
This is a typical response since the phugoid oscillations are large and graduai, with no abrupt
changes in angle of attack or pitch rate- On the other hami, the short-piad eigenvector shows a
Chapter 4 The Strbility Anrhfsis 91
major change in the angle of attack for a unit change in pitch angle, with similar amplitude and
phase. Again, this is typical due to the rapid changes in the pitch angle. The amplitude of the
velocity provides an insight to the magnitude of the damping ratio for the short-period mode.
Generally, the short-petiod mode is so heavily damped such that the impact on the speed is
negligible; however, in this case the amplitude of the speed variable is approximately 1/10 that of
the pitch angle, suggesting a relatively low damping ratio for the short-period mode and
therefore, the occurrence of speed changes.
1.5 Lateral Stability
The eigenvalues obtained fiom the lateral system of equations for the small disturbance analysis
were found to be
RI = 0.041
;11 = -0.735
= -0.608 * 3 S87i
The two reaf values correspond to the spiral and rolling modes respectively, and the complex
conjugate pair corresponds to the Dutch roll mode. Figure 4.5 shows the relative location of
these eigenvalues on the real-imaginary plane. It is important to note that the spiral mode root
lies on the positive real mis, meaning that it is unstable. The characteristics of each mode are
detemined using equations 4.19 - 4.23.
The Spiral Mode: Time to double t a l e = 16.98 s
Since the spirai mode root consists only of a positive real component, the response is known to
be exponentially unstable. Since the time to double is f d y long, 16.98 seconds, it can be noted
that the instability is mild, and easily correcteci by the pilot.
The Rolling Mode: Time to half t h p 0.94 s
The rolling mode also experiences an exponential response, however because the toot is nqptive
real, it is stable. The response time is quick, with only 0.94 seconds required to haifamplitude-
Chapter 4 The Stabüity Anrlysii 92
The Du tch Roll Mode: Natural fiequency =3.64 Hz
Damping ratio C= 0.17
Period of oscillation T= 1.75 s
Cycles to half Nhq= 0.65 cycles
Tirne to half thor= 1.14 s
The study of the Dutch roll mode was of panicular interest. f i n g the hydrodynamic
experiments discussed in Chapter 2, it was mentioned that it was suspected that the floatwing
model may poses an instability in this mode because of the generous sweep and dihedral of the
main wing. However it is shown here that it is stable and oscillatory. The oscillations are fairly
fast with a period of 1.75 seconds, and die out relatively quick with a haif time of 1.14 seconds,
which may cause the pilot to input corrections out of phase with the natural oscillations. This
could be a potential source of instability induced by the pilot; however this is dependant on the
skill level ofthe pilot.
Table 4.3, Lateral eigenvectors.
Spimi Dut& Rol .\.lugnitude Phase bfagnitude Phare ~U(4pnioide Phme
P i O.OOa1 0" 0.042 180" 12.59 0.6'
The lateral stability of the floatwing model becornes v g r interesthg when the nonnalized
eiçenvectors of the non-dimensional lateral system of equations are studied in Table 4.3. The
results for the spiral mode are as expected, mainly consisting of yawing with minor rolling. This
is characteristic of a truly banked turn. Howarer the yaw-roll-sideslip mpling of the floatwing
configuration is highiighted in the mlling and Dutch-roll modes.
Chapter 4 The S t a b i Aaaiysis 93
Traditionally the rolling mode consists of nearly pure rolling, with no changes in yaw angle;
however, in this case the yaw angle is affecteci to the same degree as the roll angle. This would
suggest that calling this mode the "rolling mode" is a misnomer in this case.
For the Dutch-roll mode, the sideslip angle and the yaw angle are excited significantly for a unit
roll angle. Although al1 of the angles are typically excited in the Dutch-roll, it is not typical to
see such extreme magnitudes as shown by Etkin and Reid [Il]. This suggests that the impact of
this mode on the roll angle is negligible relative to the impact on the sideslip and yaw angles.
4.6 The Location of the Neutrai Point and the Cenîre of Gravity Limits
Finding the location of the stick-fixed neutral point for the floatwing configuration is crucial in
determining the centre of gravity limis for the aircraft. There was a high degree of concern that
the location of the neutral point would impose a very tight boundary on the location ofthe centre
of gravity due to the shon coupling of the stabilizing surfaces.
A graphical method using the experimental measurements of the pitching moment was used to
determine the location of the neutrai point. It is known that when the centre of gravity is located
at the neutral point, the aircraft has neutral pitch stability, meaning the dope of the pitching
moment versus the angle of attack gues to zero (Cm, = O). Therefore, by plotting a tàmily of
pitching moment curves for diffuent C.G. locations, the critical location at which the slope goes
to zero can be determined. This was achieved by adjusting the C.G. location variable in equation
3.9, which was used to d u c e the pitching moment 6om the wind tunnel data The results are
shown in Figure 4.6.
The dope of the pitching moment curve goes to zero when the centre of gravity is located 4.75"
aft of the trailing edge at the wing root or, in 0 t h terms, when h = 1.32 as defined in Figure 4.7.
This presents the afi-most boundary for the centre of gravity. The forward boundary is not
limited by the aerodynamics, but t8ther the hydrodynamics. As memioaed in Chapter 1, the
centre of gravity must be positioned dl of the hydrodynamic centre, which is located at the
absolute trailing edge of the wing root during high-speed planing. This &es a relatively wide
C.G. range of approximately 4.75" without the implementation of any d k t y margin.
Chapter 4 The Stabüity An- 94
4.7 Topics for Furtber Rcscrrcb The stability study performed in this chapter providcd a good first look at the stability
characteristics to be expected fiom the floatwing configuration. It is sufficient at this stage to
just know that the natural modes are stable for the model. Future development of a hll-size
floatwing would require a similar study, with a higher degrec of detail and accutacy.
The accuracy of the stability analysis is limited to the accuracy of the stability-derivative
estirnates and the theoretical modeling. Recall that the stability derivatives for the mode1 were
obtained partially by experimental measurements and partially by analytical methods. The
accuracy of these mettiods cwld be verified by reducing experimental values of the stability
derivatives from flight test data, obtained fiom the instmrnented model, and cornparhg those
values with the initial estimates. Flight test data obtained fiom the instnimented W C model
could also be used to veri@ the results obtained fiom the small disturbance theory.
As mentioned in Chapter 3, it would be beneficial to perform a wind tunnel experiment with a
scale model of a fiil1 size floatwing prototypel including the effects of the propeller slipstream.
Ln this event, the expriment c d d be set up to measure more of the stability derivatives by using
a six-degree of fieedom force balance. The control-force derivatives should also be measured
and applied in the stability analysis. This would allow the dynamic response to control inputs to
be studied. and would be usefitl in the design of any automatic flight conml or stabilization
systern.
Chapter 4 T k S b # l t t y A i m 95
Figure 4.1, Rudimenmy soiid mode1 uscd to e s t h t e Pbe moments of inertia for the 72" spm rnodel.
Longitudinal Stibility Roots
Figure 4.2, The longinidiaal e@& plotted in the d-haghacy plane.
4
3
2
X
Y,
\
1
O
-1
-2
-3
4 - X
-3 -2.5 -2 -1.5 -1 -0.5 O Red
Short Period Mode X
,/ ! r
Pbugoid .Mode
Chapter 4 n e * m A i i l y 3 6 %
Figure 4.3, Flying handling qualities pilot opinion contour bascd on the short-pcriod mode naturai ûquency aad damping ratio (fiam Edtin and Reid [l II).
Figure 4.4, Another pilot opinion contour showiag diffèrent nsuhs (hm MacKeaPc [12T).
Cbapter 4 Tk*bwYAiirlyrb 97
Latenl Strbility Roots
Figure 4.5, The laterai eigmvalues plottcd in the ceai-- plant.
-1 -6 3 4 1 3 6 7 @ 11 13
kigkdAtldr,a(drg)
Figure 4.6, Moment coefficient vs. @e ofattack plot for vPying CG bcahs .
Chapter 4 98
I
----- NFUTRAL POINT DO NOT LOCATE CG AT OR AFT OF THIS POINT
h, = 1.32
Figure 4.7, The centre of gravity locaîion tirnits for tbe radio ~(~troiied floatwing mode1
Cbapter 5 The Futrnc of îhe Fba-
Chapter 5: The Future of the Floltning
5.1 The Floatwing D m m
The ultimate goal of Aquavion Systerns is to devebp thE ûoatwïng as an amphibious @kg
recreationai vehicle (RV). The flying RV would b capable of accommniating a family of four,
and would be ideal for joumeys to ternote locations or as an island-bopping aixplane. The cabii
would feature the luxuries of a gdey for cooking, seating, and even a washnn,m, wbile mside
the cockpit the pilot would enjoy the computaid instrument panel and fly-by-wire control
system. Although this is a beautiftl dreatn it is still a bug ways away. Tk question aow is:
how to get there?
5.2 Tbe Next Step
The work that has been completed in this study was crucial in proving tbe fbatwing comept
worthy of tùrther development. It is now kw,m that the Eloatwing is plausiMe as a
hydrodynamic vehicle and an aircraft, however, it is a long step to go h m the ptoofsfancept
72" span EüC model to the dream of an RV size floatwing. At this stage it must be k i d e d what
the next step will be: shouki another large-de R/C mode1 be buih to continue snidying tbe
floatwing design, or would it be more advantageous to study a manwd prototype?
Choosing to develop another RIC model would mean hr tk deiay of the developnmt of a
manned prototype. It would be the safer pathway since there would be no risk of pibt injliry in
the event of an accident; but, on the other band, how much more is there to learn h m an WC
mode1 that could not have k n learned h m the 72" d e l ?
W ith the use of a manned floatwhg prototype, an experienced pilot wouki be able to provide
much more valuable insight ïnto the a h a f s performance a d bandlMg characteristicS. ïk
results obtained would in actual î k t represent a real fhtwing aircdl, whereas with remoteiy
pi10 ted models, there is always the qwstion of whether or mit the aitcraft would baad)e the same
if piloted kom the cockpit where the pilot would have a greater fée1 hr wbat the agcraft is
doing.
5.3 Potential Floatwing M i s With the intentions of building a fidi-size Qoa- aYrraft Aquavim Systcms Corp. has
proposed several possible designs ranging 6nwi a d single-scat ultralight, to the flying RV
previousiy mentioned.
53.1 An Ultraligbt Flolitwiig
A small, single-seat, ultralight version would bc ideal for a first pidt6type. Since it would be the
fmt aircraft ever developed and built by Aquavion Systcms Corp., the scale of the ultraligbt
would be a more manageable challenge in tcrms of costs and ski11 developwnt. A projcct of ihis
size wouId be much more forgiving for au inexper id design team.
.4 very appeding aircraft could be designed rmdcr the new Canadian uhraiight ngulatiolls, which
allow a maximum gros weight of 1200 lb, This would mean that the prototype design could
also be sold as an ultralight kit, and be the tht aitcraft oa the AquaMon Systcms Corp. praduct
1 ine.
The newly revived Schneider's Trophy seapiane race* which was fast heId in 1931, would be an
ideal proving ground for this ulEraligbt version. The new race is to take place in Italy, officially
beginning in the year 2002, ahhough prelimin8ry races have alrcady been uIsQctway each year
since 1998. The new race is aimed at the ultralight class aimaft, which compiy with the
ultralight regdation as defïned by the Federatioa Acmmîique htrniationale (Fm and tht
ttalian Act 106. Competing in nich a~ cvcnt would k sue to muse interest in the ncw
floatwing design and would be a pcrfect medium to establish public relations and sponsors.
5.3.2 Busindooriag Chss Florîwimg
The conception of this version was to prrseat a mid-siP compromise ktwcen tk uhdigbt
floatwing and the RV floatwing. It was intmdcd to k a four place busincss/corporatt cornmuter
aircraR which would feanue a vcry comfortabk and ckgMt intrrior, or a two place torrring
aimafi with a cabin area suitable for camp*. Figure 5.1 shows an illustration of whst this
floatwing version rnay look Like.
Chapter 5 Tk Frîmic of the Fbitiirh 101
A project of this scak would bt m m chaltcnging tban the ultralight version; however, it could
still be manageable. The weight of such a design wuuid be in the pro* of2500-3500 lb,
st il1 within the aIlowable limits for hamtbuih cKperimentai ai& This mcans tbs# the aircraff
could be matketed as a kitplane befm going through the costly ccrtincatim pmcess. The àesign
and construction techniques leamcd in die developmcnt of this airaaft would be d i
applicable to the design of the flying RV.
5.3.3 The Flying RV Floatwing This is the dream of Aquavion Sysîcms Corp., wbich was m e n t i d at die beginning of this
chapter. This would indeed be a iargc-de project, and is mone suitabk as a long-term goal duc
to the developmenîal work required, the costs, and the certifion pmçess.
With certification, the Ftying RV wodd not be lirnited to privatc use d y . It could perform
many commercial d e s such as touring, fcrrying bctwœn i s l d s , and üght ûamport. As a bush
plane, it may compete with the classic Beava and Otter stiii in use today. For hurnluitauian . .
missions, the Flying RV could bc cmv& into a mobile medical unit capabk of rrrtching the
most remote of locations, which may ody be accessible by waterways. It may dso serve weil as
a flying boardroorn in the business sectoc, aliowing tix board mecrings to takc p k e at aay
beautifut port location. The neads ofeach rok arc met by the task-dtfmed intctior of tbc cabm
section making the possible applications of the Fiyiog P,V endless.
5.4 Final Remarks
At the beginning of this project, it was not certain whetber or not the f-g coibccpt wouid
work, and if the mode1 would evca float or p h e the way it was supposad to. Only a f k
intensive experimentation with the pnoofof'cooeept mode1 and carrful otudy of the rrmhs was
confidence ensued m this new concept, to the point w k it was desirobk to carry on wiîh
further development work.
The major barrier preventing the fidm devciopment of tbt fioptwing is, as with many pjccts,
the funding. Most of the w d done to date hm becn assis& wiîh grcaits povirCcd fbm the
National Research Corncil of Caaada (NRC) Fiwkr tûe W Resaxch AssisÉsnce Rograni
Chapter 5 TLcF~tmrrdtbeFbmtnliq 102
(IRAP). To continue âevelopment on a full& hmtwbg, adin sources of ibnhg must k
found in order to quaiify for a kgc-scak poject lRAP grant.
For any project to be successfiil work must k done nut only m cnginedg developmcnt, but
also on the marketing front. This is the pathway to sttracting intenst in tfie projcct and, with a
little luck, potential investors. With the maiktting mi#crial available today for die aoatwing,
which is nothing fancy, it was vcry casy to atîwt thc Mtmst of mmy aviation enthusiasts and
even some non-enthusiasts. It is this enbshm sud apport fidm the aviation cornmimi@ tùat
has reinforced the motivation of AqUanm Systems Corp. to continue pursuhg the k t w h g
dream with confidence that one dsy it will keame a succcss a d dream fiiüilled.
Chapter 5 Tk Frtrndtk Fbatwimg ldb
1. Hoerner, S. F. Fluid-Dpmic Dtag. By Author, New Yorlc, 1958, pg 11-22 - 11-29.
2. Murphy Aircraft Mfg. Ltd. web page: ~www.murphyaU.com>, Sepîembcr 5,2001.
3. Bombardier Aerospace web page:
<http:/lwww . a e r o n a u t i q u e . ~ b a r d i ~ . ~ ~ m ~ i n d c x . j s p ? i ~ -
O.html> September 2001.
4. Stinton, D. Aero-Marine Design and Flying Qualities of Floatplanes and Fiyiag-Boais.
Aeronauticaf Journal, W h 1987, pg. 97427.
5. Equator Aircrafl Company web page: <http://mcmbeft.aol.com/EquatorAC>, Sepembtr
2001.
6 . Richards, R. G. Personal communications.
7. Pankhurst, R. C., & Helder, D. W . Wid-Tratnel Technique. Sir Isaac Pitman & Sons,
Ltd., London, 1952, pg 589.
8. Lowen, D. C. An Experimental Invtstigation of Closcly Spaced Membrane Mails.
University of Toronto, B.A. Sc. Thmis, 1991, pg. Al-AS.
9. DeLaurier, J. D. Drag of Wings with Camknd Airfoils and Partial L d i g Edge
Suction. Journal ufAirwaj2, Vol. 20, No. 10, Octokr 1983, pg. 882-886.
10. NASG Airfoil Database web page: <bttp'Jhvw.nasg.comlafdWshow-plat-
e.phtml?id=o>, Septembcr 2001.
1 1. Etkin, B., & Reid, L. D. DyMniics u,fFïight - Shibilip md Conbd. 3d cd. John WÜy &
Sons, Inc., 1996, pg. 15,32, 107-1 18.
1 2. Roskam, J. Methods for Estimating Stabw and Cmtroi Dctivatives of Conventional
Su bsonic Airplanes. Published by Author, Kansas, 197 1.
1 3. MacKenzie, R.B. Longitudinal Handling Quaiiîies. AER 1214 Fiight Lab Course
Manuai, UTIAS.
1 . Barfield, N., & Jarreîî, P . B @ h to hdi~rioplrme Airc~Development 1919-1939.
Putman Aeronautical Books, London, 1997, Chapter 5.
2. Etkin, B., & Reid L. 0. qnuinks of Ffighr - Stability anù Coidrul. 3" (d John Wücy &
Sons, Inc., 1996.
3. FLUKE NetDAQ Networlced Data Aupisition UNts 2640A & 254SA USA Manual.
Rev. 2, May 1994.
4. Hoemer, S. F. Fluid-Dynanric Drug. By Autbot, New York, 1958.
5 . Pankhurst, R. C., & Holdcr, D. W. Wind-Twael Technique. Sir Isaac Pitman & Sons,
Ltd., London, 1952.
6 . Pavian, H. C. Experimental Amdymdcs. Pi- Publishing Corporation, New York &
Chicago, 1940.
Appendir A
Clrrk-Y M o i 1 Ihta
A. 1 The Airfoil Coordinates
Figure Al, The Clark-Y Airfoil,
Appendix A 167
A.2 Clark-Y Aerodyaamic Cùamcteristb The Clark-Y is a cIassical aidoil, and then is much id- arailable about it. Many of the
experirnents performed on the Clark-Y airfoii w m duae at RcyiPo16 nimrkn much higk t h
the Reynolds number of in- in ttiis study. The ApplKd Acrodynamiw Gtoup ab the
University of Illinois at Urbu-Cham- bas daae Iowspcd wind aroincl tests on thc Clark-
Y, and the results can be found prcscntcd cm the Nihon UaEvnsity Am, Students' Cimup M o i 1
Database o d i e (see ref [IO]). ïhe nsults art fot a Rcyn01ds manber of 102 d00, wbich is
equivaient to the wiad tunnel test described in Chqter 3.
Figure A.2, UnrC low-spted airfoil test nsuhs for tk Clark-Y airfoi as prrscnted on thc NASG Airfoi1 Databsise.
Appendb B 108
Information Relevant to the Whd Tunnel Esptriment
B. 1 Force Balance Calibtltion
B.l.l Calibration for Lift
Figure B. 1, Lift calibration plot for set 1. Figure B.2, Lift calibration plot for set 2.
Figure 8.3, Lift calibraîicm plot for set 3. Figure R4, LiA c a i i i o n plot for set 4.
The linearity of the lift c a i i i o n pl@ was f d to be amptable, with an awragt of
4838.7 NN. This was convcRed into Imp«ial uaits for the calcplations, i.c. KL = 1084 I W .
O 4.M31 4.m 'I- I
- v o i i i r A V m
Figure B.5, Drag calibration plot for set 1. Fipm Rd, ilmg c o l i i m plot fm set 2.
Figure B.7, h g calihion plot f a set 3. F i p t B.8, Drag caiibtatioa plot fm set 4.
The linearity of the drag cali'bration plots was fwnd to bc accepühle, with an avcragc slopc of
83 59.5 NN. This was converrcd into Imperial unb fot the cakularians, i.t. KD = 1880 1bN.
-
B.1.3 Calibraiion for Mommt
Figure B.9, Moment cdibration plot fat set 1. Figmrt 810, Moment calibration plot fa set 2.
4.6 - 4 - Y i - l l Y l l l i l n l ) A r
€3.6 ---- n'il f, ,
Figure B.11, Moment calibration plot for set 3.
Figwe B.12, Moment calibration plot fa m 4.
The linearity of the moment caiiiration plots was found to bt acceptable, with an average dope
of 1 135.7 N mN. This was convcrled into Impmal Mits for the catcdations,
i.e. K,rr = 839.2 fi IW.
B.2 Sample Data and Cdculrtion Shed
. aOPinv n m a
Note: A cornpletc mord of al1 of the - wuidnmnelcxpctiincatrwultsislccpt on file m eledmk farmat at the Univcrsiry of Toroato Institue for Actospaec Studiw.
.arc l i t s a .l reo, UbOI s- 4- 1- 4- 2- lm 4- 1- Z t w 17- L M 4QlDS 1- 4mE.M tOC4) SYHQ 4- 11- a l m a ZQLQS a m rmms 1144) I zow r a m 1- -1- LIE^ UIQI 4 1- ?164imcaUQB .am 1- 2- 2- a Q B r m i c w a .r- z v o r s w .arc 1- Zn- 2- - 4- UEQS 7- 2- UllQ
1- 4- 2- )lZC.0 1 w 2ltc.a 2- n r a t ( &Sa 1.- 2- a- r ima i- 2- a- 4 1 1 0 a zPIQ aOEa su.a
Figure B.13, Sample caiculrttMn shcct for wind ntnnel experiment.
Figure B.13 shows a sample Excel sprcadskî uscd far d g and anob.sing the exphenta i
data obtained during one run of tht wmd ûmel arperiniicnt. For each mgle of atta~k asted,
there would be 10 such wotkshars to ensure rcptabiiity in tht r d t s , Th followhg section
shows a statistical analysis of tbc nsults.
Appendix B 112
Figure 6.14, Staristical malysis of a wiud tunnel expcriment measunmentS.
Each set refen to the results of h 10 workshtcts pet angle Scttiag. T h e r e k angle seaiag 1
corresponds to a = -3.891 O 0.851°, CL = -0.047 f .UN, CD = 0.042 f 0.005, Pnd C- = 0.278
= -020 at the 95% confidence IeveI.
Stabiüty Andysb MATLAB Program
C. 1 The Stability Analysis Prognm These MATLAB program werc developed to solve the smalldistuibance theory quatim of
motion outlined in Chapter 4. Th- cirr two sirnilar progmns, 1ong.m and k m , ta solve the
longitudinal and lateral equatioas respecgVeiy. The begllinin~ of each pogtom consists a section
in which al1 of the input paramctpft are &&cd, such as: the stabii daivatives, aircraft
physical properties, and flight conditions such as spccd, air dcasity and climb angle. The
remaining sections of the program deal with solvhg the dimensional and nondimensional
system matrices to obtain the eigeavalues and nomai id eigcuvtct~s as discussed in Chgprcr 4.
The graphical outputs are shown in Chapter 4, Figures 4 2 and 4.5.
C.2 Program Outputs
C.2.1 Longitudiaal Stability Reaab f i m bmgm
*** PHUGOID MODE ***
Eigenvalues: Lamdal = -0.25992 + 0.62063i L a m u = -0.25992 t -0.62063i
Norrnalized Eigenvector for Phugoid Made: u = -0.5 1403 + 0.80847i dpha = 0.02875 + -0.017571 q = -0.00232 + 0.00554i theta = 1 .O0000 + 0.00000i
*** SHORT PERIOD MODE *'O
Eigenvalues: Lamda3 = -2.92601 + 3.821 12i Lamda4 = -2.92601 + -3.821 12i
Norrnalized Eigenvector for Short Pcriod Mo& u = 0.05346 + O.lM74i alpha = 0.5 17 18 + 0.87469i q = -0.02613 + 0.03412i theta = 1 .O0000 + 0.00000i
C.2.2 Latenl Sîability Resrits tmm k m *** S P W MODE "'
Normalized Eigenveçtor for Spirai Mode: beia = 0.oooI 3 + 0.00000i p = 0.00001 + 0.00000i r = 0.00027 + 0.0ûûûûi
phi = 0.05834 + 0.0ûOûûi psi = 1 .O0000 + 0.ûûûûûi
*+* ROLLING MODE '**
Normalized Eigenvector for Rolling Modt. bera = -0.04191 + 0.ûûûûûi
p = -0.00500 + 0.00000i r = 0.00377 + 0.00000i
phi = 1.00000 + 0.ûûûûûi psi = -0.98733 - 0.00000i
D L W H ROLL MODE ***
Eigenvalucs: Lamda.3 = 4.60753 + 3.58726i Lamda4 = -0.60753 + -358726i
Nomdized Eigenvcctor for Dutch Roll M6dt: beta = 12.58969 + 0.13018i
p = -0.00233 + 0.033% r = -0.04750 + -0.29835
phi = 1 .O0000 + 0.00000i psi = - 1 1.97901 + 4.04484
42.3 The Codes
'i.:r.--;ix:.er.si~nal :?.put5 CxaLpha = -0.26; Czalpha = -4.698; Cmalpha 9 -5.51; Cxu = 0.0; Czu = 0.0; Cmu = 0.0; Cxq = O I Czq = -12.6; Cmq = -32.42; Cxdalpha = 0.0; Ctdalpha = -2.82; Cmdafpha = -9.59; Exdu = 0 . 0 ; Czdu = 0.0; Cmdu = 0.0; Zxdq = 0 . 0 ; Czdq = 0.0; Qndq = 0.0;
I x x = 0.703; I y y = 3 . 5 3 7 ; Itt = 4 . 1 5 4 ; 1x2 0 0.206; ixx = I x x / (rofS* (b/2) ̂ 3 ) ; iyy = I y y / ( r o f S * (c/2In3) ; itz = Izz / [ ro*S+ (b/2) - 3 ) ;
Xdu = Zdu = Mdu =
Xdw = Zdw = Hdw =
Xdq = Zdq = X a q =
Cxdq* ( l / 8 ) *ro*S*cn2; Czdq* (l/8) *ro*S+cA2; Cmdq* (l/B) *ro*S*cA3;
Uo 3 14; ro = 1.19; thetao = 2*pi/l00; Clo = 0.4; Cxa = -0.35; Caio = 0 . 0 0 ; Czo = -Ch;
g = 9.81;
muc = m/ (O.S*ro*S*c); mub = m/ (0.5*ro*S*bI ; mg = m*g/ (O.5*ro*Uoa2*Si ;
Aoaendù C
- 3 : x r z ç i u m ; Xatrix Y i ? , l ) = m - Xdu; M(117) = -Xdw; M(1,3) - -Xdq; M ( 2 , i l = -Zdu; M(2,2) = m - Zdw; M(2,3) = -Zdq; Yi3,1) = +du; M(3,2) = +du; M(3,3) = fyy - Mdq: ! 4 [ 4 , 4 1 = 1;
N(1,1] = Xu; N(1,Z) = XW; N(l,3l r Xq; N(L4) = - rn*g*zos !thetao) ; N ( 2 , l ) = Zu; N(2,21 = Zw; N(2,3) = m*Uo + Zq; N(2,41 = - m*g*sin(thetao) ; M ( 3 , l ) = Mu; N(3,2l = MW; N(3,3) = Mq; N ( 4 , 3 ) = 1;
A = i n v (Ml *N;
figure (1) ¢if compass ( lamdal )
f i g u r e ! 2 c l f p l o z c r e a l (lamdal), imag(larndal), '::-:' x l a b e l t ' : 1- : . ' 1 y l a b e i ( ' y - : ::r. : r . : . ' ) - 4 L - L l e [ ' , - - : - - . , : : :~.%- - - A L - : - - : . -.. rd.- - - - y ? ' ]
j r i d on
S . - - ,r, -:i.er.sizxL Ma:r;x Xhat (1,l) = 2*muc- Cxdu; Mhat (l,2) = -Cxdalpha; Mhat(l,3) = - Cxdq; Xhat i2,1] = -Cidu; Mhat (2,2) = 2*muc- Czdalpha; Mhati2,3) = - Czdq; Mhat (3,l) = -Crndu;
Nna t C:q; Yhat Nhat
Ahat
[v2 1
Nhat ( 2 , 4 ) = -mgtsin (thetaol; 3,l) = Cmu + 2*Cmo; Nhat(3,2) = Cmalpha; NhatI3,3) = Cmq; 4,3) = 1;
= inv(Mhat) *Nhat;
amda21 = e i g (Ahat) ;
, - .-- - - . -,cg - . z h e eigenvector for i = 1:4
vnorm(:,i) = v2(:,i) ./v2(4,i); end
and
, %.---i:-+-.-..-~ . -.. a-...-..=--..a: :RpG:s
Zybeta = -1.35; Cnbeta = 5.6; Clbeta = -0.38; Cyr = 0 . 5 1 6 ; Cnr = -0.186; Clr = 0.229; C y p = -0.228; Cnp = 0.027; Clp = -6.766; Cydbeta = 0.0; Cndbeta = 0.0; Cldbeta = 0.0; Cydr = 0.0; Cndr = 0.0; Cydp = 0.0; Cndp = 0.0;
Cldr = 0 .O; Cldp = 0.0;
O 0 - 14; ro = 1-19: thetao = 2*pi/180; Clo = 0.4; Cxo = -0.35; Cm0 = 0.00; Cr0 = -Clo;
g = 9.81;
muc = m/ (O.S+rotS*c) ;
Appeadix C 118
Ydv = Cydbeta*0.2S*ro*S*b; Ldv = ~lcibeta+0.25*ro*S*b~2; Ndv = Cndbeta*0.25*ro*S*b"2;
Idp - Cydp* (l/8) *ro+S*bn2; Ldp = Cldp* (l/8) *ro*S*bA3; Ndp = Cndp* (l/8) *ro*S*b63;
Ydr = cydrc ( l / @ ) *ro*S*bh2; 3 d r = ~ldr*(l/B)*ro*S*b"3; Ndr = Cndr*(l/81*ro*S*bA3;
E I ( 1 , 1 ) = \IV; N(1, î ) = Yp; N ( 1 , 3 ) = -(m*Uo - Y r ) ; N ( 1 , 4 ) = mtg*cos ( the tao) ; ~ ( 2 ~ 1 ) = LV; N(2,2) = Lp; N(2,3) = Lr; N(3,l) = Nv; N(3,21 = Np; N(3,31 = Nr; x ( 4 , 2 ) = -1; N(4,3) = -tan(thetao); N!5,31 = -sec(thetaol; N(5,5) = 0;
f i g u r e ( 1) cl f compass (lamdal)
Appendu C 119
Yhat (l,l) = 2*mub - Cydbeta; Mhat (l,2: = -Cydp; Mhat Hhat Rhat Pihat Mhat Mhat Mhat Mhat
1 , 3 ) = - ~ y d f ; 2,1) = -Cldbeta; 2,2) = ixx - Cldp; 2,3) = -(lx2 + Cldr); 3 1 1) = -Cndbeta; 3,2) = -(ixz + Cndp); 3,3) = izt - Cndr; 4 , 4 ) = 1;
Nhat (1,i) - Cybeta; Nhat(l,2) = Cyp; Nha: ( il 3 = -2*rnub + Cyr; Nhat(l,4) = rng*cos( the taol ; Nhat(2,Tl = CLbeta; !ihat(2,2) = Clp; Nhat(2,3) = C l r ; ~ h a t ( 3 , l ) = Cnbeta; Nhat(3,tI = Cnp; !Ihac!3,3) = Cnr; Nhat(4,2) = 1; Nhat ( 4 , 3 ) = tan ( t h e t a o ) ; Nhat ( 5 , 3 ) - s e c ( t h e t a o 1 ; Nhat (5,j) = 0;
Ahat = inv [Mhat) *Nhat;
[ v2,larnda2 1 = e i g (Ahat 1 ;
Appendix C 120
f p r i n t f ( ' -. '
f p r i n t f ( ' - ' - - . . - .. . . - - . * - - r.,y -c . . - - ' - - - ... . < -- . .- -- ... .. - ' I r f p r i n t f ( ' < . ;e:.:?. ic:: 7.' ); - - . - - - . f p r i n t f ( ' l i- 2.: 3 = - - 7 _ _ - _ - . - - - - - - .
-. + - - r',real(lamda1(4,41) ,imag(lamdal(Q,4) 1 ) ; . - - . .
f p r i n t f ('lc:?.: = - - -. - - - - - - = . - r i -. zi,reaL(lamdal(5,5) ),imag(lamdal(5,5)) 1; - - , - . -CF.-----.. . - - f p r i n t f ( ' . : :Y: : - - ~. IL! - . . , Y . - - - - f z r L::::. ? ~ i l >!CE: .?.'); . . - - . _ - _ ,_ _ * . f ~ r i n t f ( ' : - 2 - j : :. * - - - - L i .. . . - - a
-',real(vnarm(l,3) ) ,imag(vnorm(l,3) 1 ) ; f - r i n t f ( ' r .: - - . - - . - _ ._ -.--A _ - . ..
. . - A -
-',real(vnorm(2,3) ),imaq(vnonn(2,3)) ) ; f p r i n t f ( ' - -
. _ - - _ - . - - - .~ .;.;r;.n',real(vnarm(3,3)),imag(vnonn(3,3)));
- - . f p r i n t f ( ' 7-: = - - . - - - * _ ._ . - - . . - _ - , .. . .
*',real(vnorm(4,3) ),imag(vnom(4,3) 1 ; f p r i n t E ( ' :: .: _ = - - - . - - - . A , - ! .. - - - . - - - ..... ,real(vnorm(5,3)),imagivnorm(5,3))1;
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