Full-Scale Ornithopter
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The Flight Dynamics of a Full-Scale Ornithopter Tahir Rashid A thesis submitted in confomity with the requiiements for the degree of Master of Applied Science Graduate Department of Aerospace Science and Engineering in the University of Toronto O Copyright by Tahir Rashid, 1995 National Library Bibliothèque nationale du Canada Acquisitions and Acquisitions et Bibliographie Services services bibliographiques 395 Wdliion Street 395. nie Wellington OnewaûN K1AW Ottawa ON K1A ON4 Canaada Canada The author has granted a non- L'auteur a accordé une licence non exclusive licence allowing the exclusive permettant a la National Library of Canada to Bibliothèque nationale du Canada de reproduce, loan, distribute or sel1 reproduire, prêter, distribuer ou copies of this thesis in rnicroform, vendre des copies de cette thèse sous paper or electronic formats. la forme de microfiche/fiim, de reproduction sur papier ou sur format électronique. The author retauis ownership of the L'auteur conserve la propriéte du copyright in this thesis. Neither the droit d'auteur qui protège cette thèse. thesis nor substantial exûacts ffom it Ni la thèse ni des extraits substantiels may be printed or otherwise de celle-ci ne doivent être imprimés reproduced without the author's ou autrement reproduits sans son permission. autorisation. The Flight ûynamics of a FulCScale Ornithopter Master of Applied Science, 1995 Tahir Rashid Aerospace Science and Engineering University of Toronto This t hesis investigates the non-lineaif light dynamics of a full-scale flapping-wing aircraft (ornithopter). Using simplifying assumptions, the equations of motion were developed for a 2-wing-panel and 3-wing-panel rnodel. A cornputer program was written to examine the longitudinal and lateral stability of the omithopter. The pmgram was first tested using inputs for a mode1 ornithopter known as "MI. BilP and then using the inputs for a full-scale omithopter. The results indicate that both 'Mr. Billaand the fulkscale ornithopter are longitudinally and laterally stable. The accelerations and displacements are much less for the 3-panel model than for the 2-panel case because the 3-panel design serves to balance the time-varying forces seen by the fuselage. I wouid like to thank my supervisor, Di. J.O. Delaurier, for his assistance and guidance during this research, and as well as his patience. Also, thanks to all the mernôen of the ornithopter team for their help and the Natural Sciences and Engineering Council for financially sopporüng this projed. I am also very grateful to my father(AWu1 Rashid) and my biothers Akhtar, Zafar, Nasir, and Qasir for their advice and continual encouragement. Their hard work and support has helped to make my dreams a reali. Finally, I wouîd like to dedicate this thesis to my mother, Mn. Seema Rashid, who passed away during the compilation of this research. Her love and wisdorn have benthe key reasons for my success in life. May she live on in our hearts and may God bless her. TABLE OF CONTENTS ABSTRACT 7ABLE OF CONTENTS LIST OF FIGURES UST OF SYMBOLS vtii 3. LITERATURE SEARCH 4. DEVELOPMENT OF THE EQUATlONS OF MOTION 4.1 %PanelMode1 4.1.1 Dynamic Mode1 4.12 Body EquationsûfM~ai 4.13 Wmg Equaiions ûfhaotion 4.1.4 Kincmatic Analysis 4.1 5 Complctc Equarions Of Motion (2-Pncl) 433-P-1 M*l 42.1 Bady Equakms Of Mdim 422Ccnter Psael E41mticmsOf Motion 423 Pm Wmg Equalions Of Me 42.4 SIIlbard Wmg Equations Of Motion 4.25 KineniPtic Analysis 4.2.6 Campiece EquPtim Of MoQa (3--1) 5.3 Body contributhm 53.1 Body Dmg 5.32 Body Lin 53.3 Body Pitching Momcnt SA TU)Contributho 5.4.1 Total Angle of Auck of Tail 5.42 Taü Lift 5.4.3 Tai1 Drag S.!! Canbined Body and Tdi Coiitributioa 5.4 outer wm Panel coitribotim 5.6.1 Wig Lift 5.6.2 Wing Drag 5.6.3 Wing Pitching Moment 5.7 Cmm blCOObhthll 5.7.1 Centcr Panel Lift 5.7.2 &ter Panel Drag 5.7.3 Cawr Panel Pitching Moment 6.1 My~~~tributioP 6.1.1 Body Si- FaFe 6.12 Body Yawing Mormcnt 6.13 Body Rolling Moment 6.3 Fim coatmutia 6.3.1 Fin Sideslip Angle 63.2 Fi Side Lift 6.3.3 Fi Drag 8. DISCUSSION OF RESULTS 8.1 Imgitudid Stabiüty 8.1 .l Pipr Comanche PASI-?SO 8.12 2--1 "hi.. Billa 8.13 3-Puiel "Mr. Bill" 8.1.4 2-Pncl Fd-MOrnirhagca @SO) 8.1 s 3-PnJ FiiII-Scrlt Oniihaper (FSO) 8.2 LATERAL STABILll'Y 82.1 Pipa ComiPche PA24-W) 8.2.2 2-Ponel "Mr.Bill" 8.23 3-Puicl "M.Bill" 8.2.4 2-l'ad Full-SC& Oniiw(FSO) 8.25 3-Plael FU-S~CMtbapter (FSO) 9. CONCLUSION APPENDIX A - GRAM APPENDlX B - DERIVATlON OF EQUATIONS OF MOTION FOR A RlGlD BODY APPENDIX C - 2-PANEL COMPLETE NON-UNEAR EQUATIONS OF MOTION APPENDlX D - 3-9 ANEL COMPLETE NON=UNEAREQUATIONS OF MOTION APPENDIX E - MOMENTS AND PRODUCTS OF lNERllA Of WlNGS APPENDIX F - ORDER OF MAGNITUDE ANALYSS FOR TWlSTlNG APPENDlX H - COMPUTER PROGRAMS LIST OF FIGURES Figure 1: 3-Pricl madel anithopcr. .M r. BU ........................................................................................ 3 Figm 2: Conventid notation............ .................................................................................... .........5 Fi- 3: 2-pluukl ......... ............. .. ................................................................................................8 Figure 4: 3-panel m&i .................................*........................................ .. .........................................-9 Figure 5: Schemstic 2-panel mode1 with reaction farces and moments .... ......................................... 11 Fiipiie 6: Ax* sysiem ofwhg and body ....................................e................................ ...................... 12 Figure 7: Axes sysmns ..................... ...... ....................................................................................15 Figure 8: 3-plm&l with mction faa~and manaus ........................ .......... ..... Figure 9: Cenm panel ...................... ..................................................................................................... 22 Figure 10: Pœî wing ...............................................................................................................................23 Figure 11: Sirboud wing ......... ................. ..... .. ........... ................................................................a Figure 12: Axes fa body ad whg ....................................................................................................25 Figure 13: Axcs fa body and ccnia pl................... .... ....... .......................................................27 Figure 14: Lift ~IMIârag trmsfdon .................... .... ............... ... Figure 15: Tdtd lift vscuiru, producc i)w9................ .....................e.......... ...................................38 Figure 16: Changes in angle of aasdr due to a roll p ............................ .... .......... .......................4 Figure IR Chrigcs in angle of ritrk due to a yaw r................... ... .... ... ..... ....................... 47 Figure 18: 'Ihiide-view drawing of the Piper ComPndie PA24-250........................................................ 51 LIST OF SYMBOLS f - fin cp - centei panel wl - port wing w2 - starboard wing a - angle of attack fl - sideslipangic e - downwash angle Q - mUmgie 0 - pitchangle Y -yawmgle Y - WPing angle P - dcnsity of air - aspect ratio - "ng span - mean wing chord - drsg coefficient - drag coefficient at zero angle of attack - lia coefficient - lifl - CUNC slope - pit~hing- m~mc~~t- cuive dope - side - force stability dcrivative - yawing - moment stabiiity denvative - rohg- moment stability denvative - dragforce - x distance from body cg. a centa panel cg (3 - panel) x distance fiwi body cg. to point on mtof wing alignai with wing cg (2 - pand) - y distance frwi body cg. a center pand cg (3 - panel) y distance from body cg. 1~ point on root of wing aiigned with wing cg (2 - pand) - z distana hmbody cg. to centa pand cg (3 - panel) z distance hmbody cg. to point on mot of wing aligneci with wing cg (2 - pand) - x cunponent of œnta panel vdocity W. r. t. body (3 - panel) - y cmponmt of cuiter pand vdocity W. r. t. body (3 - peî) - z canponent of center panel vclocity w.r. t. body (3 - pd) - x canponent of anter pand acœleratim w.r. t body (3 - panel) - y component of anter panel occcleration W. r. t. body (3 - pand) - z cornpaient of anter pand ~c#xIeretionW. r. t body (3 - pand) - x distance fiom wing cg to pivot point - y distance frwi wing cg to pivot point - z clistana fiom wing cg to pivot point - x distana frwi mot of wing to cg of wing pand - y distance from root of wing O cg of wing pmd - z distana fnw mot of wing O cg of wing panel - Osdddfich~y factor - x dinction rcaction fcnce at wing pivot point - y direction rwction farce at wing pivot point - z cikation r#iction farce at wing pivot point - x distance frwi body cg to pivot point on wing - y distance hmbody cg to pivot point on wing - z distance ninn body cg to pivot point on whg I,I,I,I,I - momaitofinertias ~&,&Jyz - derivatives of moment of incrtias JL - xdiisoionlWCtimmnnitatwingpiwtpant J, -ydirccti011donmamtatwingpi~t~ JN - zdirixtiond011mmmtat~g~vapant L - liftfolice L, L, -idlingmnrnt L- - tdeaodynanicmb(lltlltsinthexdircctim m -IIliiSS M - pitchingmniwu ML -x~011rmctiaimmntbawmitheaioawingpsndandmiapsnel(3-pand) xdiribctiailCaCtionmmrntbaws#ithcwingandbody(2-pand) MM - ydinctiairitactiai~tbaweaidieaitadgpaadandmi~p~l(3-panci) y~onrc8ctimmonientbetweaithcwingandbody(2-panel) MN - z diiccticm dmmmnt bawcen the wing panel ami anter panel (3 - panci) zdiribctioniacrionmnmnbetwknthewingaadbody(2-pand) M, -taPlamdynamicrrmmtntsintheydiribctim