The Wright Brothers Absorbed Nt =Dimensionlesstail Volume, ´T `T0 T = V =Ightspeed Allthat Was Known in Aeronauticsbefore Them, Then Added Their Own 1

AIAA JOURNAL Vol.41,No.6, June 2003

TheWright Brothers: First Aeronautical Engineers andT est Pilots

F.E.C.Culick CaliforniaInstitute of Technology,P asadena,California 91125

Nomenclature v =translationalvelocity W C D =dragcoef cient = weight W S CL =liftcoef cient w =wingloading, = x CLt =liftcoef cient (tail) =coordinatepositive from center of gravity y CLw =liftcoef cient (wing) =coordinatepositive along starboard wing Cm =pitchingmoment coef cient ® =angleof attack ¯ =sideslipangle Cm ac =pitchingmoment coef cient (aircraft) ° = path angle Cm cg =pitchingmoment coef cient about the center of gravity c = wing chord ±c =canardde ection D = drag force ±w =warpde ection Fx = x componentof force ±’ =incrementof theproperty ’ Fy = y componentof force " =downwashangle120 g ´t =tailef ciency, qt =q [Eq. (5)] =accelerationdue to gravity 1 H V C C µ =pitchattitude angle = Nt d Lt =d L h =fractionof chord ½ =gasdensity K =gainin controllaw, proportional control Á = bank angle L = lift force `np =separationof center of gravity and neutral point Subscriptsand Superscripts `t0 =distancebetween aerodynamic centers ofcanard and wing ac= aerodynamiccenter M = mass cg= centerof gravity m =pitchingmoment cp= centerof pressure np= neutralpoint mnp =pitchingmoment about neutral point p =rateof rotation t = tail = wing qt =dynamicpressure at a horizontallifting surface w 1 2 0=zerolift condition q =dynamicpressure, 2 ½V r 1 = yaw rate 1 —=steadyvalue S = wing area T =thrustforce IRGeorgeCayley invented the conventional con guration of T theairplane at theturn of the19th century. Otto Lilienthal re- µ1 =low-frequencyfactor S Tµ2 =high-frequencyfactor alizedthat building a successfulaircraft meant learning how to y; u =averageforward translational velocity hebecamethe rsthang glider pilot and also the rst ightfatality VN S cS in1896.Beginning in thelate 1890s, the Wright Brothers absorbed Nt =dimensionlesstail volume, ´t `t0 t = V =ightspeed allthat was known in aeronauticsbefore them, then added their own 1

Fred E.C.Culick joined the facultyof the CaliforniaInstitute of Technologyafter receivinghis Ph.D in Aero- nauticsand Astronautics from the MassachusettsInstitute of Technologyin 1961. He is currently RichardL. and DorothyM. HaymanProfessor ofMechanicalEngineering and Professor ofJetPropulsion. Dr .Culick’s Ph.D. dissertationtreated combustioninstabilities in liquid rockets. Muchof his research since hasbeen concerned with problemsof unsteady motions in combustion chambers generally. He beganworking on solid rocket combustion instabilitiesin 1965; since 1979he hasbeen addressingthe problemin airbreathingsystems, with recent emphasis onfeedbackcontrol applied to combustion systems, and measurements of combustion dynamics. Dr .Culickis a Fellowof the AIAA andof the InternationalAcademy of Astronautics. In 1981, he received the AIAA Pendray Aerospace Literature Awardand in 1988 the JANNAF CombustionSubcommittee Recognition A ward.From 1977 to1986, Dr .Culickwas a memberof the AGARD Propulsionand Energetics Panel,resuming that position in 1994, untilthe destructionof AGARD. He hasbeen aconsultantto all of the majorU.S. rocket companiesas well asto variousgovernment organizations. As partof his interest inaeronauticalhistory and early aviation, since 1978 Dr.Culickhas been Project Engineerand designated First Pilotin a project sponsoredby the LosAngeles Section ofthe AIAA. The project exists tobuild a full-scalewind tunnel model of the Wright1903 Flyer (tests completed ) anda yingversion to be ownin 2003. Dr .Culickhas publishednumerous papers on aviationhistory, the work ofthe WrightBrothers, andthe AIAA project.He coauthoredthe recent book OnGreat WhiteWings— The Wright Brothersand the Race forFlight ,anillustratedhistory of the race toinvent the rst powered aircraft.Currently, he is alsocollaborating with the Chairof Aerodynamics at the MoscowA viationInstitute and the Director of TsAGI, the RussianCenter forAerodynamics and Hydrodynamics, on reviews ofRussian aerodynamics in the 20thcentury.

Presentedas Paper2001-3385 at theAIAA/ ASME/SAE/ASEE37th Joint Propulsion Conference, Salt Lake City,UT, 8– 11 July 2001; received 3August 2002;revision received 5December 2002;accepted forpublication 9 December 2002.Copyright c 2002by F. E. C.Culick.Published by the American Instituteof Aeronautics and Astronautics, Inc., with permission. Copies of this paper may bemade° forpersonal or internaluse, on condition that the copier paythe $10.00 per-copy fee totheCopyright Clearance Center,Inc., 222 Rosewood Drive, Danvers, MA 01923;include the code 0001-1452/ 03$10.00in correspondencewith the CCC. 985 986 CULICK discoveriesand developed the rstsuccessful airplane. Technically, inventedby Benjamin Robins in 1742. Cayley himself invented theirgreatest fundamental achievement was their invention of three- dihedralas ameansfor maintaining equilibrium in roll.The vertical axisaerodynamic control. Less obviously, their success was a con- tailprovided directional stability, like the feathers on an arrow,and sequenceof style,their manner of workingout theirideas and of pro- inCayley’s viewwould also be usedfor steering, as aboat’s rudder gressingsystematically to their stunning achievements. They were serves.By analogy, the horizontal tail gave stability in pitch. It turned indeedthe rstaeronautical engineers, understanding as best they outlaterthat Cayley was half right on bothcounts. couldall aspects of their aircraft and ying.They were thinkers, de- Cayleydid not formally apply Newton’ s lawsfor translational and signers,constructors, analysts, and especially ight-testpilots. Their rotationalmotions to the airplane. He produced no mathematical powersof observationand interpretationof thebehavior of theirair- descriptionsfor the motions of an aircraft and, therefore, had no craftin ightwere remarkable and essential to their development quantitativebasis for designing his yingmachines. However, he oftheairplane. Their work in theperiod 1899– 1905 constitutes the hadthings right at the level he worked. With his rstefforts he rsttrue research and development program carried out inthe style establishedthe principle that he later explained thoroughly in a ofthe20th century. As the centenary of their rstpowered ights seriesof papers: The means of producinglift to compensateweight 2 4 approaches,the Wright Brothers’ magni cent achievements excite mustbe distinct from the means of generating thrust. ¡ It was growingadmiration and respect for their achievements. The broad arevolutionaryidea at the time. He properly shifted attention to featuresof their accomplishments have long been well known. Only articial ightfrom simple imitation of birds to development of inthe past two decades has serious attention been directed to the xed-wingaircraft. scientic andtechnicalcontent of theirwork, to explain the nature of Thoseideas dominated all attempts to inventaircraft in the19th theproblems they faced and how they solved them. After a century’s century.Three immediate predecessors of the Wrights were par- progressin aeronautics, the principles, understanding, and methods ticularlyimportant to their work. Alphonse P´ enaud(1850– 1880) notavailableto theWrights provide the basis for interpreting in mod- inFranceadopted Cayley’ s designand ewthe rstpowered me- ernterms the experiencesthat the Wrights themselves documented chanical yingmachine, a smallrubber-powered model. He had the someticulouslyin theirdiaries, papers, and correspondence. It isa cleveridea to usetwisted rubber strips as the source of powerfor uniqueopportunity in the history of technology. apropeller.In ashortpaper describing his model, P´ enaudgave the rstexplanation for the action of anaft horizontal tail to providesta- I.HistoricalBackground bilityin pitch. 5 InFrance, the surface became known as the P´ enaud Aconsiderablebody of aeronautical knowledge existed at the tail. endof the 19th century. The basic aerodynamics required to invent Themost important immediate predecessor of theWrights was asuccessfulaircraft had long been known: the lift and drag on a OttoLilienthal (1848– 1896). Educated and professionally success- surfaceplaced in a steadystream. Construction methods familiar fulas a mechanicalengineer, Lilienthal made his mark following frombridges, boats, and kites could be and were adapted for y- hisboyhood ambition to build a successful yingmachine. His two ingmachines. Finally, recent progress in the development of inter- mostin uential contributions were his realization and demonstra- nalcombustion engines and lightweight steam engines practically tionthat, to build a successfulairplane, it was necessary to learnhow solvedthe problem of havingsuf cient power. toyandhis extensive tests of airfoils,producing the rstsystem- Thusthe problem of mechanical ightcame down to oneof ge- aticdata for lift and drag of avarietyof airfoils. Less well known is ometry:Find an arrayof surfaces large enough to generate the lift thatone ofLilienthal’s resultsalso contributed to Kutta’ s rstpaper requiredand so arranged that the pilot can control stable and ma- onairfoil theory 6:Heemphasized the property of a goodairfoil neuverable ight.That was essentially the problem that the Wrights thatthe owshould be smoothat thetrailing edge. Carrying out his solvedto make possible their rstpowered ight(Fig. 1) and for owninstruction to y,Lilienthal built a seriesof successful gliders whichthey received their 1906 patent, never broken. The Wrights havingessentially Cayley’ s conguration. Lilienthal’ s resultswere knewand thoroughlyunderstood the state of aeronautics when they inuential particularly because they were widely reported and illus- begantheir work. They pro ted from the successes and failures of tratedand because of his book Birdight as theBasis of Aviation ,7 others.Someone else could certainly have been rstto inventa suc- publishedin 1889. cessfulairplane and would have in the absence of the Wrights. It Lilienthalinspired four followers: Percy Pilcher (1866– 1899), a isimportant to understand the historical context for the Wrights’ Scot,who, like Lilienthal, was killed when a glidingtest ended in a workand to appreciate the fundamental importance of their style of crash;Octave Chanute (1832– 1910), who built several gliders after researchand development in makingthem succeed rst. Cayley’s andLilienthal’ s generaldesign; Ferdinand Ferber (1862– In1799, 26-year-old George Cayley (1773– 1857) sketched what 1909),who began his gliding tests in 1899; and the Wrights. Ferber’ s wenow recognize as thefamiliar conventional con guration of an mostsigni cant accomplishment was his successful motivation of airplane:a camberedwing having dihedral, an aftvertical tail, and an agroupof enthusiasticaviation pioneers in Paris. His contacts with afthorizontal tail (Gibbs-Smith 1).Cayley’s choicefor the airfoil was theWrights led, indirectly, to theagreement the Wrights eventually basedon aerodynamic characteristics of airfoilstested by himand struckwith a Frenchsyndicate to ypublicly rstin France in 1908. hispredecessors using various forms of a whirlingarm apparatus OctaveChanute was the third predecessor of theWrights to hold animportantposition in their development program, 1899– 1905. He providedguidance to the existing literature and accomplishments byothers with his important book Progressin Flying Machines .8 Technically,his use ofthePratt truss was adapted by theWrights as theirbiplane con guration. Equally important was Chanute’ s role asakindof soundingboard during the Wright’ s intensivework from 1900to 1905.There is no evidencethat he providedany technical contributionsto theirsuccess other than the Pratt truss, but he and Wilburexchanged many informative detailed letters, particularly onmatters relating to the measurement and interpretation of lift and drag. Bythe end of the19th century, it seemed that much of thebasic knowledgewas in hand for theinvention of poweredpiloted ight. Asa consequenceof the progress achieved primarily by Cayley, P´enaud,and Lilienthal, a successfulcon guration had been established.The recent invention of thelightweight internal combustion enginesolved the problem of propulsion,although the known pro- Fig.1 First successful powered ight,17 December 1903;Wilbur is at pellerdesigns had ef ciencies well below what would soon become the rightwing, and Orville is the pilot. available. CULICK 987

However,the gap between what was known and what was re- problemsthey faced, the frustrations they must have felt, and the quiredfor a practicalairplane was larger than generally appreci- solutionsthey fashioned. ated.Only the Wright Brothers recognized the extent to which the Itis not an oversimplication to statethat ultimately the general greatproblem of controlstill remained to be solved. Solving that problemof achieving basic mechanical ightis equivalent to the problemled directly to theability to executecircles and generally problemof controlling rotations in three dimensions. Any investi- beingable to maneuver the airplane. Lilienthal had demonstrated gationof rotations of anobjectleads very quickly to considerations manysuccessful straight glides by swinginghis weight to maintain ofstabilityand, as a practicalmatter, control. Newton’ s lawsshow equilibriumin ight.Because his gliders were stable, he wasable that,corresponding to theconnection between translational motions quiteeasily, by shifting his body laterally, to “ directour course of andforces, rotational motions are the consequences of momentsor ourightto the right and totheleft” (Lilienthal, “ TheFlying Man,” torquesacting on anobject. in Chanute,8 p.285).However, he was gliding, and not soaring for At theturn of the19th century, inventors struggling to discover extendedperiods, and so hewasunable to execute circles and did the“ secret”to successful ightunderstood translational motions. notinvestigate the intricacies of turningthat the Wrights later dis- Theyknew that steady rectilinear level ightrequires that suf cient covered.Lilienthal did not require much controllability under his liftbe generated to compensate the weight ( L W )andthat the normal yingconditions. The rsttime he truly needed substan- thrustexactly equals the drag ( T D).Theyalso D had an intuitive tialcontrol in pitch, his method of hanggliding failed him, causing notion,roughly at the level of understanding D the principal of the his death. lever,that an airplane will rotate unless the net moment acting is Nearlyall of the Wrights’ predecessors and their contempo- zero.Until the Wrights began their work, would-be inventors were rarieswere preoccupied with constructing intrinsically stable air- concernedprincipally with equilibrium, that is, no rotation,of pitch- craft,essentially large model airplanes. Moreover, none progressed ingor longitudinalmotions; in particular, no rotationin pitch means farenough to becomeconcerned with maneuverability, and hence, zeropitching moment ( m 0). controllabilitywas not an issue for them. The sole exception was Noneof thepioneers of Dight,including the Wrights, wrote the Montgomery(1858– 1911), who, in the 1890s, experimented with equationarising from m 0and,therefore, had no basis for ex- wingwarping for control in roll (see Ref. 9). Hiswork was not publi- ploringits implications. Their D intuition stopped with the essentially cized,and theWrightsindependently invented their method of wing correctconclusion that for equilibrium in pitch, the “ centerof pres- warping.It isinteresting and convincing evidence of their indepen- sure”must coincide with the center of gravity. Practical problems dencethat Wilbur used a biplanedesign to incorporate warping, arisewith interpreting and locatingthe center of pressure. The state- whereasMontgomery worked only with monoplane gliders. More mentof coincidenceis trueif thecenter of pressureis that of the tothepoint, before Montgomery could construct his planned pow- entireaircraft. Incorrect conclusions follow if only the center of eredaircraft he, too, was killed in a crash.Although his aircraft pressureof the wing is understood. Failure to make and under- executedcircles, he didnot face the general problems of three-axis standthat distinction caused many dif culties for the aeronautical stabilityand control or thespecial dif culties of powered ight. pioneers. Itis theirexplicit and persistent attention to thoseproblems that Becausegravity acts in vertical planes, in the rstinstance it reallydistinguishes the Wrights from their contemporaries and pre- doesnot affect motions of an aircraft in roll and yaw (heading) decessors.They formulated and effectively solved, to the extent awayfrom steady level ight.Hence, equilibrium in rolland yaw theyrequired, problems of stabilityand controlabout all three axes. seemedsimpler than equilibrium in pitch. In fact,Cayley realized Awonderfulfeature of their style of working is their meticulous thatstability of equilibriumwas the primary matter for bothroll and documentationof their observations and progress in the best tra- yaw.Stabilityof equilibriummeans that if the aircraft is disturbed ditionof ighttesting. Parts of their diaries and letters read like froman initialstate of equilibrium,aerodynamic forces are naturally dailyreports of amodernresearch and developmentprogram. That generatedthat tend to restorethe equilibrium.Cayley concluded that iswhywe are able to puzzle out howthey encountered and reacted anaftvertical tail and dihedral provided the restoring forces in yaw totheirdiscoveries of themotions of anunstablepowered aircraft. androll, respectively. His conclusions are correct and apparently Moreover,by examiningclosely the problems the Wrightsencoun- solvedthe problems of roll and yaw motions— until the Wrights teredand the solutions they devised, we can clarifythe de ciencies recognizedthat piloted ightrequired control ofrolland yaw ,not intheirown understanding of the mechanics of ightand, hence, merelyequilibrium and stability. oftheiraircraft. Their stunning invention of the practical airplane Nevertheless,despite their brilliant successes, the Wrights never placedthe Wrights far in advance of their contemporaries. How- completelyunderstood quantitatively the problem of stability of ever,at the sametime, the backward state of thegeneral theory and rotationalmotions. They shared that de ciency with all of their understandingof ightmechanics hindered them and in factcaused contemporaryinventors, for the same reason: They never wrote or themconsiderable dif culties. Indeed, the most serious gap in their consideredequations for rotational motions. Without the bene t knowledgewas probably the basic reason for their unwitting mistake ofthat formalism, they could not understand the true essence of inselectingtheir canard con guration. stabilityof rotations.As a practicalmatter, they could not identify Thechief intent of thispaper is to interpret the technical achieve- thephysical contributions to stability, a failurethat had signi cant mentsof the Wrights in the context of aerodynamics and ight consequencesfor their work. mechanicsdeveloped in thedecades during and after their program, 1)Like their contemporaries, the Wrights could not properly solve whichbegan in 1899 and had practically ended before Wilbur’ s thesimplest problem of gliding;hence, they had only approximate deathin 1912.Limited space has been devoted purely to descrip- meansfor designing their gliders. tionof their achievements and none to their private lives. Several 2)Also like their contemporaries, they did not have the basis for booksand popular publications thoroughly cover those historical investigatingand understanding stability quantitatively. aspectsof the Wrights’ careers, in particularAnderson, 10 Combs,11 3)They could not appreciate the importance of thezero-lift pitch- Crouch,12;13 Culick,14 Culickand Dunmore, 15 Gibbs-Smith, 16;17 ingmoment and, therefore, did not realize the problem caused by Hooven,18 Howard,19 Jakab,20 Kelly,21 Walsh,22 and Wolko.23 All selectinga highlycambered airfoil. oftheseworks, except Kelly’ s book,begin with the superb collec- 4)Therefore, they were not motivated to make extensive mea- tionof theWrights’ diaries, papers, and correspondence prepared surementsof theaerodynamic pitching moment acting on an airfoil. byMcFarland. 24 5)They had no way of estimatingthe location of the center of pressureof acompleteaircraft. Hence, they could not entirely un- II.TheGreatest De ciency in EarlyAeronautics derstandthe signi cance of thelocation of thecenter of gravity. Hindsightis always a satisfyingadvantage for historical com- Thepoint, of course,is notto criticizethe Wrights. On the con- mentary.In the subject of ightmechanics, we now have essentially trary,our admiration for their marvelous accomplishments is in- acompleteand closed theory supported as wellby decades of ex- creasedwhen we understand more completely the contemporary perimentaland computational results. With all that experience, we stateof aeronautics,the context in whichthey achieved their suc- canreview the Wrights’ work and appreciateeven more deeply the cess.We can appreciate best that context and the Wrights’ progress 988 CULICK byinterpretingas far as possible their aeronautical experiences in termsof what we understand a centurylater.

III.The Wrights’ Early T ests: AKite (1899) anda Kite/Glider (1900) Fromobservationsof birds, Wilbur conceived the idea of control- lingrolling motions of ayingmachine by warpingthe wing. His practicalrealization was based on thePratt truss, a bridgedesign, a) b) modied to thebiplane con guration. At thesame time, he invented themethod of controllingmotions in pitch by using a secondaryhor- Fig.3 Intrinsic stabilitywhen the c.g.lies forwardof NP. izontalsurface, arranged so thatits lift could be changed by rotation abouta hingeline. He rstincorporated both ideas in a 5-ftkite thathe ewin August 1899. It was no ordinarykite, already having muchof thegeometry of the gliders the Brothers built in the follow- ingthree years. Figure 2a is a photographof arecentrecreation. 25;26 Theafternoon’ s testprogram convinced Wilbur that his basic ideas werecorrect: He had the rst yingmachine controllable about two axesby actuating surfaces to exert appropriate aerodynamic forces andmoments. Wilburand Orville were then faced with the problem of scaling fromthe kite to a glidersuf ciently large to carrya 145-lbpilot. As youngboys, the Brothers had tried unsuccessfully to build a larger versionof a tinytoy helicopter (P´ enaud’s design)their father had giventhem. Thus, building a successfullarge glider based on the kitedesign likely seemed less obvious to themthan to us.The nal 24 1 craft,shown in Fig. 2b, hada wingspanof about17 2 ft, a wing areaof 165ft 2,anda controlsurface with an area of 12ft 2. Inthis rstphase of their ight-testprogram, the Wrights were concernedprimarily with two questions: W ouldthe pilot be able tooperate the pitch and roll controls effectively to maintain the machinein an equilibrium state of steadylevel gliding? Would the biplanecon guration produce suf cient lift to sustainsteady gliding witha pilot?The Brothers sought the answer to thesecond question bymakingmeasurements of liftand drag using a springscale with theglider tethered as a kite.The lift-to-drag ratio was a low6, but moredisappointingly the lift was less than what they had calculated withLilienthal’ s data.It wasa largedifference. Wilbur noted in his

Fig.4 Forces andmoment for the elementarygliding problem.

1901 paper27 that“ Wefoundthat while it was supported with a manon itin awindof about25 miles,its angle was much nearer twentydegrees than three degrees.” What they didn’ t knowwas that at20-degangle of attack,the glider was on theverge of stalling—if notalreadyin the far side of stall see Fig. 3a. Because of uncertainties inestimatingvalues in the full-scale tests, the angle Wilbur cites is notthe same as thatused in the graph: The true angle of attackin hiscase was probably less than 20 deg. Morepositively, 2 minof gliding convinced Wilbur that his methodof control worked well in ight,de nitely superior to a) 1899 kite26 Lilienthal’s techniqueof shiftingthe pilot’ s position.He was able to executea fewshort glides, experience far short of themany minutes orhourshe hadhoped for, and he did not tryto turn. IV.TheElementary Problem of Gliding TheWrights apparently left no notes explaining the details of theircalculations relating to the gliding problem. However, it is clearfrom their letters and entries in their diaries that they (most likelyWilbur) determined the sizes of their 1900 and 1901 gliders bymakingestimates, rather than carrying out a thoroughanalysis. Theyused Lilienthal’ s dataand considerations of lift and drag only. Theirignorance of the equation for pitching moments necessarily causedtheir calculations to be approximate. Considerthe elementary problem of steady rectilinear gliding shownin Fig.4. Themachine is treatedas a pointmass M moving inaverticalplane. Its motion is the result of actionsby theforces oflift, drag, and gravity, as well as the pitching moment m. By ) 24 b 1900kite/ glider convention,the lift L and drag D act,respectively, perpendicular Fig.2 First demonstrationsof two-axiscontrol. andparallel to the direction of motion at velocity V .Thevelocity 1 CULICK 989 liesat thepath angle ° tothe horizontal. Let x and y beorthogonal fordesigning their gliders in 1900 and 1901, the Wrights might axes xedto the glider as shown in Fig.4, withorigin at thecenter haveused the following computational scheme: ofgravity(c.g.). For steady gliding, the net forceand moment must 1)The functions C L .®/ and C D .®/ aregiven by experimental vanish.In the x–y coordinatesystem, the three conditions are results;in 1900and 1901, the Wrights used Lilienthal’ s data. 2)Choose a valueof theglide speed V .TheWrights seem to i 1 ¼ havesought a groundspeed of about 4– 6 mph.One of thereasons F 0 : L cos ® D cos® Mg sin.° ®/ 0 xi D 2 ¡ ¡ C ¡ D theychose Kitty Hawk as theirtesting ground was their expectation ³ ´ ofsteadywind speeds of 15–20 mph.Hence, V 20–25 mph. X 1 (1a) 3)Select a valueof w: (grossweight)/ (wing¼ area). Equa- D i tions(3a) and (3b) are then nonlinear algebraic equations in ® and ¼ Fy 0 : L sin ® D sin ® Mg cos.° ®/ 0 linear in q .Withsome dif culty, they can be solved numerically i D 2 ¡ ¡ ¡ ¡ D 1 ³ ´ (trialand error if nocomputer is available) or graphically. X (1b) 4)For the value of ® foundfrom solution to Eqs.(3a) and (3b), i thelift coef cient and lift can be calculated and compared with the dataused in step 1. If the value is too close to the value for stall mi 0 : m 0 (1c) D D ofthe wing, then a newvalue must be set for V or w and the process(1– 3) repeated. 1 Forsmall angles, these Xequations are Chanute’s paper 28 andcorrespondence suggest that the Wrights usedthe preceding scheme or acomparablemethod, to estimatea L® D Mg.° ®/ 0 (2a) ¡ C ¡ D reasonablesize for their gliders in 1900 and 1901. In subsequent L D® Mg 0 (2b) years,their experience probably gave them the basis for estimates ¡ ¡ D withoutextensive calculations. ¤ m 0 (2c) Partof thepoint here is toemphasize a difculty unavoidable if D (asthe Wrights did) one failsto account for the moment equation. In 1 2 Let S bethewing area, c thewing chord, and q 2 ½V the thecorrect view of the gliding problem, satisfaction of thecondition 1 D 1 dynamicpressure and divide the three equations by q c to nd forzero total moment, Eq. (3c), is ensured by appropriate setting of 1 thehorizontal tail (or the canard). That is, the moment of the tail lift CL ® C D w=q .° ®/ 0 (3a) aboutthe center of mass exactly compensates the moment generated ¡ C 1 ¡ D bythelift of thewing imagined to be actingat the center of pressure. CL CD ® w=q 0 (3b) ¡ ¡ 1 D Thisanalysis of thegliding problem, represented by Eqs. (3a– 3c) canbe conrmed quite well by testswith a simplehand-launched Cm 0 (3c) D sheetbalsa glider. Even if Eqs. (3a– 3c) for equilibrium are solved where w Mg=S isthe wing loading. The lift, drag, and moment correctly,the question of stability does not arise; it must be posed coefcients D are separately.T odeterminestability, a specialanalysis is required. Consistentwith ignoring the condition of zeronet moment, the Wrightsassumed that in equilibriumthe canard carried no loadand CL L=q S; C D D=q S; Cm m=q Sc (4) D 1 D 1 D 1 servedonly as a controldevice. Hence, their view of equilibrium inpitchrequired that the center of pressure of thewing alone must Forthe speed range of gliding,the coef cients CL , C D , and Cm dependonly on the angle of attack ®.Hence,for a specic glider, coincidewith the center of gravity.In practice, it was quite possi- Eqs.(3a– 3c) contain three unknown quantities: ®, ° , and q or, for blethat the canard carried a netload, but whether it actually did agivendensity (or altitude), glide speed V .Ifthe moment 1 equa- ordid not would likely be obscured by the operational dif cul- 1 tiesof piloting an airplane not only unstable in pitch, but possibly tion, Cm 0,expressing what is usually called the trim condition, isignored,D one is left with two equations for the three unknowns— alsountrimmed. path angle ° ,angleof attack ®,andgliding speed V . A unique 1 V.TheCenter ofPressure,Aerodynamic Center , C solutionto thatproblem does not exist. For a properresult, m must andNeutral Point beexpressedin termsof itscontributions from the wing, tail, and Fromthe earliest investigations of theforce acting on anobject otherstructural components; then Cm 0becomesthe third equa- tionneeded to solve the simple gliding Dproblem uniquely. inmotion, before Newton’ s Principia,itwas recognized that the Evidentlythe Wrights must have found themselves in a quandary pressureon theobject’ s surfaceis continuous and nonuniform. The becausethey appealed only to Eqs.(3a) and (3b) or equivalent forms. integralof thepressure over the surfaceis the net force. By analogy Theonly way out istoguessthe value of one of theunknown quan- withthe center of gravity,it is natural to introduce the idea of the titiesand solve the two equations for the remaining two unknowns. centerof pressure.If the object is imaginedto be supported at the Althoughwe do not knowexactlywhat the Wrights did, we can infer centerof pressure,the aerodynamic forces generated by the motion withnearly complete con dence that they assumed the glide speed, causeno rotation:Its moment is zerowhen the net forceis imagined leavingthe path angle and the angle of attackto becalculated. In his toactat thecenter of pressure. marvelouspaper “ SomeAeronautical Experiments” prepared after Inthe case of afreely yingwing, the weight is the only other his yingseason of 1901, Wilbur 27 stated,referring to thematter of forceacting besides the net aerodynamic resistence. Thus the “ sup- gainingextended gliding practice, “ Itseemed feasible to dothis by port”is at thecenter of gravity, and ifwe neglect drag, there is no net buildinga machinewhich would be sustainedat a speedof 18 miles momenton the wing when the center of pressurecoincides with the perhour, and then ndinga localitywhere winds of this velocity centerof gravity.If drag is accounted for, the statement still holds, werecommon.” He never clari ed why he chose 18 mph, but it butas shown in Fig. 4, the gravity force is decomposed into two seemsreasonable that he arrivedat thenumber through a combina- components,one ofwhichis compensated by thelifting part of the tionof estimatesand review of averagewind conditions in various aerodynamicforce, and theother acts as athrustforce compensating locations.In any case, his reasoning led the Brothers to Kitty Hawk. thedrag. It is asimpleand correct idea, but extremely dif cult to Chanute28 inhisarticle in Moedebeck’s handbook 29 alsoassumed applyin practice to a complexaircraft. Much of theWrights’ confu- thevelocity to beknown for his solution to the gliding problem. That sionand problems with motions in pitch owfrom their incomplete articleprobably represents the accepted contemporary method for understandingof thematter. analyzingand “ solving”the problem of gliding.Letters exchanged inJanuary 1902 between Chanute and Wilbur con rm that they ¤Ina letter (1906)to the British Military Attach e´ inWashington, D.C., the Wrightsallude to the possibility that they may haveworked out a method sharedthe dif culty of ndinga wayto solvethe gliding problem. fordesigning a poweredaircraft forlevel ight,and possibly had prepared Evenwith the velocity speci ed, solution to Eqs. (3a) and (3b) tables andcharts fordesign (McFarland, 24 p.721).There isno evidence that aspart of the design process still requires iteration because the theirmethods had progressed beyond that just described in thetext, except wingloading w isnot known initially. Hence, we speculate that thatthrust generated by propellers replaced theaction of gravity. 990 CULICK

Alsoin Fig.5b, the dashedline shows the movement of thecenter ofpressurethat the Wrights believed to be thecase, early in their workat least, until their gliding tests in 1901 showed otherwise. Thatsupposed behavior is based on the following reasoning. When theairfoil (cf., the limit of aatplate)is placednormal to the stream, thecenter of pressureis ator closeto the midchord. As the angle of attackis reduced, the center of pressure evidently moves forward. TheWrights, following the beliefs of previous researchers sum- marizedby Chanute, 8 assumedthat the center of pressure moves continuously forward as ® is reduced froma largevalue, reach- ingthe leading edge for ® 0.Equivalently,the center of pressure shouldmove continuously Daft from the leading edge as the angle of attackincreases from zero. However, for an actual airfoil cambered concavedown, the center of pressure moves forward from a position fardownstream at zero lift, moves forwardcontinuouslyas theangle of attack increases untilstall occurs. Then the direction of motion reverses,and the center of pressure moves aft as theangle of attack isincreasedfurther. Problemswith controlling pitch, while gliding in 1901and during sometests of theglider as akite,led Wilbur to conclude that his pre- viousnotion of continuousforward motion of thecenter of pressure Fig.5a Centers ofpressure forthe Wright1903 airfoil 30 and the NACA astheangle of attackis reducedwas wrong. What he did not realize 4412airfoil. 30 wasthat the most forward location of the center of pressureoccurs whenthe airfoil is stalled in the vicinity of maximum lift. Hence, thecorrect view is that under normal yingconditions the center ofpressuremoves continuously forward astheangle of attack(and lift) increases uptothe value for stall, where reversal of the motion occurs. Theparticular way in which the center of pressuremoves with changeof angleof attack depends on the shape of theairfoil: There isnouniversal representation. Even if theWrights, or anybodyelse, hadinvestigated use of themoment equation for pitch, they would, therefore,have encountered unexpected complications when the ideaof the center of pressureis used.In fact those complications are apparentin the literature of ightstability until the late 1930s when thedistinguished English applied aerodynamicist. Gates introduced theidea of the neutralpoint (NP) foran aircraft.The neutral point is the aerodynamiccenter (a.c.)for a completeaircraft. Von Mises33 and,later, independently, Tchaplygin 34 discovered thatevery airfoil possesses an a.c. having location xedas theangle ofattackchanges. It isa remarkableproperty valid for incompress- iblesteady owif the airfoil has xedshape and if the Kutta condition(smooth owat the trailing edge) is satised. The a.c. is dened asthatpoint on anairfoilsuch that if thenet lift is imagined to act there,the aerodynamic moment about the supporting axis passing throughthat point is independent of angle of attack.For airfoils nor- mallyused in practice,the a.c. is close to the quarter chord. Also, for Fig.5b Centers ofpressure: ——,atplateand – – – accordingto an theusual airfoil having camber line concave downward, the moment earlybelief. aboutthe a.c. is negativein the conventional sense, acting to rotate theleading edge down. Thepractical dif culty with that interpretation of thecondition Asa practicalmatter, in writingthe equationof pitchingmoment forzero pitching moment is thatthe position of the center of pressure foran aircraft, assuming existence of thea.c. for a liftingsurface usuallydepends quite strongly on the orientation of the wing, that meansthat, if drag is ignored, the surface is simply represented by is,on the angle of attack. Moreover, the motion of the center of thelift acting at itsa.c. and a pitchingmoment (or better, a pitch- pressurewith angle of attackcauses a destabilizingpitching moment ingmoment coef cient Cmac / independentof angleof attack.The forthe usual case of a camberedwing having xedgeometry. That difculty associated with accounting for the motion of the center of is,the state of equilibrium existing when the centers of pressure pressureis eliminated. In fact, for a camberline concave downward, andgravity coincide is unstable for angles of attack less than the theforward movement of thecenter of pressureas thelift increases valuesfor stall. Figure 5 showsgraphs of the center of pressure towardits maximum is a directconsequence of theexistence of the measuredas functionsof angle of attackfor two airfoils, the Wright a.c.Reversal of theforward motion occurs when the owseparates 1903(see Ref. 30) airfoil and the NACA 4412airfoil, 31 popular fromthe surface somewhere and ceases to have the ideal form re- forlight aircraft, and a atplate. 32 Forboth airfoils, the center of quiredfor existence of thea.c. The difference in the shapes of the pressurereaches its most forward location at anangleof attackin twocurves in Fig. 5a is due to differences in theway in which ow thevicinity of thevalue for maximum lift. Details of owseparation separationoccurs. On the NACA 4412,the separation occurs rst dominatemuch of thebehavior, which is more complicated for the onthe upper surface near the trailing edge and moves forward as Wrights’highly cambered thin airfoil. Closer examination of the theangle of attack increases. The owis always attached on the owis requiredto explain why the measured center of pressureon underside.In contrast,due to thehigh camber and thin section of aatplatedoes not show reversal of its motion (Fig. 5b). 30 Viscous theWright airfoil, owseparation occurs on theunderside at low effectsresponsible for the owseparation cause the form of the anglesof attack. oweld in the immediate vicinity of the plate to vary strongly Thede nition of the NP isthe extension, to anarrayof surfaces, withangle of attack so that the plate effectively does not have a ofthe idea of the a.c. for a singlesurface. Thus the aerodynamic xedshape. That result is largely due to the in uence of a sharp forcesand moments acting on the various parts of anaircraft can leadingedge. bereplacedby asingleforce acting at the NP anda momentabout CULICK 991 theNP thatis independentof angle of attack. † Itisan immediate bettercontrol with the canard, and it was both instructive and com- consequenceof itsde nition that as theangle of attackis increased fortingto see the control surface during ight.According to Engler theadditional lift can be imagined to appear at the NP .Themost (privatecommunication, 2002), Wilbur believed that he hadmore importantconsequence of that behavior is that for static stability ‡ pitchcontrol of his1899 kite when the smaller surface was forward ofan aircraft, the center of gravity must lie forward of the NP . ofthebiplane cell. However, he waslikely misled by the fact that Thatproperty is easilyestablished with the help of Fig.3 andthe thecon guration with tail in front was unstable and, hence, very followingargument. sensitiveto his control inputs. Assumethat the NPdoesexist (we have not proved it is true,but it Becausethe theoretical basis was not yet established to under- is)having the property that the aerodynamic moment mnp about the standthe importance of forward location of thecenter of gravity, NPisconstant as theangle of attack changes. In Fig.3a, the aircraft is theWrights simply had to learnfrom their testing how to deal with assumedto be inequilibriumin level ightand so L`np mnp. Now theserious pitch instabilities of theircanard aircraft. Contrary to the supposethat the aircraft receives an external disturbance D causing viewthat has appeared in some accounts, there is no evidencethat thenose to rise, a changeof pitchingmoment about the center of theWrights intentionally designed their aircraft to be unstable—they mass, ±mcg > 0accordingto the usual sign convention; the angle justturned out thatway. In fact,without paying attention to rotational ofattackis also increased, ±® > 0.Hence, the lift is increased by motionsin some detail— and that means understanding moments at ±L.Byassumption, ±L maybe imagined to act at the NP ,and adeeperlevel than the Wrights did— no one can have a rmgrasp 35 mnp isunchanged. If the center of mass is forward of the NP ,the ofwhatstability is really about. Bryan and Williams publishedthe additionallift exerts a negativemoment ±m `np±L < 0 about rstpaper correctly analyzing aircraft stability. They showed that thecenter of mass,tending to opposethe external D ¡ disturbance and forthe centerof gravity xedrelative to the larger surface, the con- restorethe aircraft’ s initiallylevel orientation. The con guration is, gurationhaving a smallersurface aft is relativelymore stable than therefore,stable. thatwith a smallersurface forward, but both con gurations could be Thisis a perfectlygeneral result, true for any aircraft, of which madestable. The paper was unknown to those constructing aircraft theWrights were unaware— and could not be.In fact, no oneknew atthetime and of course appeared after the Wrights’ commitment thissimple argument until more than 30 yearslater with the work of tothecanard. Bryan 36 laterpublished his classical work forming the Gates,although the stabilizing effect of moving the center of gravity basisfor all subsequent work on aircraftstability. forwardwas already known with the work of Bryanand Williams 35 Elementaryanalysis of the wing/ tailcon guration may be found and Bryan.36 instandardtexts of appliedaerodynamics (e.g., Etkin 37 and Perkins In1904, the Wrights decided to try to reduce the amplitude of and Hage38).Themain results needed for present purposes are given pitchingoscillations (undulations) they encountered by movingthe inT able1. For simplicity we treat a singlewing and secondary centerof gravity.Actually, they may have been dealing with a sit- surfaceand assume that corrections for the biplane are absorbed in uationin which the oscillating motion was stable, but combined theformulas for the aerodynamic coef cients. witha secondmotion exponentially unstable with a growthrate Thecoef cients of lift, CL ,andpitching moment, Cmac , about the troublesomelyrapid (described in Sec.IX). In any case, they rst a.c.sare weighted values for the wing/ tailcon gurations: movedthe center of gravityaft— exactly the wrong direction— by movingthe engine. One ightwas enough to reveal the error; a CL CLw ´t .St =S/C Lt (5a) secondcon rmed it. For most of theremainder of theirwork with D C C C ´ .c S =cS/C (5b) canardcon gurations, the Wrightscarried ballast as far forward on m ac D macw C t t t m act thecanard as theycould, as much as 70lbonsomeoccasions. That’ s roughly8% ofthegrossweight of the aircraft. Anef ciency ´t isde ned equal to the actual dynamic pressure atthesurface divided by q .Locationsaft relative to the leading 1 VI. RelativeStability of Canardand Aft edgeof thewing are denoted by the symbols h,distancesdivided by TailCon gurations thewing chord. Thus, hac isthe dimensionless distance of the a.c. of Muchhas been written about the Wrights’ problems of stability, thewing from its leading edge, and h isthe dimensionless distance orrather instability, of their canard aircraft. Occasionally, writers ofthe center of gravity from the leading edge, being positive for anaftlocation. If h h > 0,thecenter of gravityof the aircraft is haveincorrectly claimed that a canardcon guration is necessarily np ¡ unstable.By analogy with bicycles, that has been cited as the reason forwardof thea.c. of thewing, representing a positivestatic margin. 2 4 Notethat the lift curve slope of thetail d C Lt =d® iscomputed with whythe Wrights purposely avoided the known method (Cayley ¡ and P´enaud5/ forobtaining stability by usingan afthorizontal tail. respectto the angle of attackof the wing; it isbetter interpreted as WithWilbur’ s testsof his 1899 kite and their 1900 kite/ glider,the dC dC d® Brothersknew that the machines would ywiththe tail forward Lt Lt t (6) oraftof themain lifting surfaces. How muchthey had learned of d® D d®t d® therelative stability of thetwo con gurations is notknown. Orville in which dC =d® isthe actual lift curve slope of the tail (ap- notedin a letterhome (McFarland, 24 p.38), “ Wetriedit withtail Lt t proximately2 ¼,reducedby theeffect of aspectratio according to infront,behind, and every other way. When we got through, Will liftingline theory) and d ® =d® isdue tothe downwash for an aft tail wasso mixed up he couldn’ t eventheorize. It hasbeen with con- t andupwash for a canard,representing the aerodynamic interactions siderableeffort that I havesucceeded in keepinghim in the ying businessat all.”What is fairly clear is that Wilbur did not choose the canardcon guration after considerations of stability,but rather for Table1 Someresults forcanard and conventional con gurations two reasons§ relatedto Lilienthal’s deathdue to inadequate control ofhis conventional con guration: Wilbur thought he would have Conguration Result Momentabout c.g. Canard Cm Cm CLt Vt CL .hac h/ †Thestatement remains trueif both lift and drag are accountedfor. cg D ac C N ¡ ¡ Aft tail Cm Cm CLt Vt CL .hac h/ ‡Inthis and the following two sections we are concernedonly with static cg D ac C N C ¡ Positionof NP H Vt .dCLt =dCL / stability.No considerations are givento dynamics and rates ofchangeare D N Canard hnp hac H absent. D ¡ Aft tail hnp hac H §Inhis 1901 paper, 27 Wilburremarked “: : : we nallyconcluded that tails D C were asourceof troublerather thanof assistance, andtherefore we decided todispense with them altogether.”He refers here toboth horizontal and vertical tails.During his nal ightsof 1901, Wilbur encountered unforeseen difculties while trying to turn(Sec. VIII.B)Sometime after Wilbur’s paper, Orvillerealized thatthey could overcome the dif culties by installing a vertical tail,which became partof their 1902 glider. Not until 1910 did the Wrights nallyadopt the horizontal tail (Sec. XI). 992 CULICK betweenthe wing and the secondarysurface: Table2 Canardlift coef cient fortrim of the Flyers, Eq. (11) <0 aft tail d®t d"t Flyer d® D d® >0 canard » (7) Parameter 19031905 1909 V 0.1340.355 0.320 Ifweassume that the wing and tail have lift curve slopes nearly the Nt Cm =Vt 1.050.394 0.438 same,we can approximate d C Lt =dCL by ¡ ac N hac h 0.0500.120 0.050 C¡ V h h 0.2200.203 0.094 N L = Nt . ac / dC Lt dCLt d® d®t d"t C¡ ¡ 1.270.597 0.532 N Lt dC D d® dC d® ¼ d® L ³ t ´³ L ´ Then H dened in T able1 canbe written VII. Importanceof the Zero-LiftPitching Moment Cm0 Considerationof the formulas for the pitching moment about the d" <0 aft tail H V t c.g.leads to a pleasinggraphical interpretation of therule that for Nt ¼ d® >0 canard (8) stabilitythe c.g. must lie forward of the neutral point. Simultane- » ouslywe will ndthat the pitching moment at zero lift has spe- cialimportance not anticipatedwith the discussion in thepreceding where V ´ .` S =cS/ isthe dimensionless tail volume, ` is Nt D t t0 t t 0 section. thedistance between the a.c.s of the wing and tail, and "t is the conventionalsymbol for upwash or downwash. The formulas in FromT able1, thecoef cient for the pitching moment about the Table1 thengive the results for thepositions of the NP: c.g.of acanardis C C C V C .h h/ (10) mcg D m ac C Lt t ¡ L ac ¡ hac H aft tail h h H C j j Thelift coef cient C Lt ofthecanard depends on the setting (de ec- np D ac ¡ D h H canard » ac ¡ j j (9) tion)of thesurface and, due to upwashcreated by thewing, on the liftcoef cient of theaircraft. In general, it cannotbe taken equal and H maybe approximatedby Eq.(8). tozerobecause for trim Cm cg 0andEq. (10) gives the condition D Hence,the NP fora conventionalcon guration lies aft of the (stablecon guration) wing’s a.c.,but the NP ofacanardlies forward.¶ Thatis the explicit CLt Vt CL .hac h/ Cm > 0 (11) realization,in modern terms, of Bryanand Williams’s 35 conclusion N D ¡ ¡ ac With C normallynegative, C V mustbe positivefor stability, thatthe aft tail con guration is relativelymore stable than the canard mac Lt Nt ifthesame surfaces are used. The more forward is the NP ,themore andthe canardis aliftingsurface. ¤¤ difcult it isin practice to getastableaircraft: The natural tendency Theslope of themoment curve is duringdesign and construction of an aircraft is for the c.g. to lie dCmcg dC Lt fartheraft than desirable. Often then, either ballast must be added Vt .hac h/ dCL D dCL N ¡ ¡ forwardor the location of thewing is shifted,a commonpractice formodel aircraft. dCLt h V h .h h/ (12) TheWrights’ choice of thecanard con guration was, therefore, D ¡ ac ¡ Nt dC C D ¡ np ¡ alreadyleading to a possibleproblem with pitch stability. That is an ³ L ´ unavoidableconsequence of the geometry and the aerodynamics. where hnp isgiven by Eq. (9) and H isde ned in T able1 and Acanardcan of coursebe designedto be intrinsicallystable if the approximatedby Eq. (8). For stability, reasoning similar to that c.g.is farenough forward. In thecase of the Wrights’ canard, the accompanyingFig. 3 showsthat the slope must be negative for problemis particularly dif cult because of the mass distribution stabilityin pitch. Hence, the moment curve for a stablecanard is dictatedby their design: The large weights (biplane cell, engine, likethat shown in Fig. 6a. For linear aerodynamics the graph Cm cg andpilot) are all located such that their c.g. are close together and vs CL isstraight only if the lift coef cient of the tail is constant. aftof the leading edge. Including the propellers and pilot, 94% of Equation(10) gives the value for the moment coef cient at zero thegross weight of the 1903 airplane was contained in the biplane lift: cell.That characteristic combined with the upperlimit to theliftthat Cm cg Cm0 Cmac CL t0 Vt (13) thecanard could produce (due to stall) meant that the 1903 Flyer 0 D D C N C couldnot be trimmed as astableaircraft. Tohavea stable¡ moment ¢ curve with a trimcondition, m0 must In the1903 Flyer,thec.g. is about30% of thechordaft of thelead- bepositive.In any case, for positive static stability Cm0 cannot be ingedge and the NP iscloseto theleading edge. The aft vertical tail negativebecause that would cause the graph to crossthe axis at some isalreadylight and haslittle effect on thelocation of thec.g. There pointbetween the origin and the trim condition shown in Fig.6a. areonly two ways toshift the c.g.signi cantly: add ballast to theca- Thesecond intersection would represent an unstabletrim condition, nardand movethe engineand pilot as far forward as possibleon the notallowedunder the circumstances enforced here. wing.Estimates suggest that nearly 40% of thegross weight carried Table2 showssome estimated results for trim of the 1903, 1905, Flyers 39 asadditional ballast will move the c.g. to the leading edge of the and 1909 ,usingthe measured (Bettes and Culick ) value C 0:14for the 1903 Flyer andassuming C 0:6. Those 1903 Flyer ifthepositions of the pilot and engine are not changed. mac D ¡ N L D Whenballast is added,the yingspeed of theaircraft increases valuesare not accurate for the later aircraft but are close enough for andmore power is required. Moreover, the canard must carry in- thepurpose here. C Flyer creasedload to trim the airplane. By trial and error, the Wrights did Theresults for N Lt showthat the 1903 probablycould asmuchas theycould so faras movingthe c.g. is concerned. They notbe trimmed because the canard would stall before reaching the simplyaccepted their Flyers asunstable aircraft. Later models in liftcoef cient 1.27. Its moment curve is qualitatively like that in 1908–1909 had the c.g. about 15% of thechord aft of theneutral Fig.6b, but the trim point cannot be reached. Because of their larger pointaccording to Hooven. 18 Hence,their emphasis on control was absolutelynecessary if their canards were to succeed. ¤¤Duringthe past 20– 30 years, thisresult has oftenmotivated enthusiastic supportfor canard congurations. The lifting surface relieves thewing, and, therefore,it is argued, reduces totalinduced drag. However, the argument ¶ Thelocation of theNP foran array ofsurfaces can be(roughly) visualized is awed, andthe conclusion is incorrectbecause itdoes not account for as theweighted average ofthelocations of theNPs (a.c.) ofthe individual interference between thelifting surfaces. Thecorrect conclusionfollows surfaces. Itis asimple calculationfor rectangular planforms, but otherwise fromMunk’ s staggertheorem: For xedtotal lift, the induced drag depends, themean aerodynamicchord must be foundfor each surface; forexample, togood rst approximation,only on thefront view of thecon guration and see Perkinsand Hage. 38 is independentof thefore-and-aft location of thesurfaces. CULICK 993

Wilburand Orville arrived at their camp on 10Julyand departed on20August1901. All of their ighttesting was conducted during threeweeks, ending on 16August.It was a remarkablyproductive period.The Brothers made three discoveries fundamental to their success—all were results of carefultests and acute observations. Apparentlyonly Wilbur ewin 1901.During his rstday’ s ying onSaturday,27 July1901 (“ Madeabout 17 glides,”McFarland, 24 p.71), he encountered his rstserious problems of dynamics. At leasttwo ightsterminated in full stalls; he was unaware of the phenomenonand could not interpret correctly why the glider had “lostall headway. ”Inresponse,he quicklymoved forward to shift thec.g.— on bothoccasions the machine then settled horizontally tothesand, with no damage. Wilburthought that part of theproblemwas an oversized canard, causingcontrol to be toosensitive. However, ighton the following a) Staticallystable Mondaymorning showed that reduction of the area to 10 ft 2 did notcure the problem. In theafternoon the Brothers ewthe glider asakite,with and without a personon board.Using spring scales attachedto the restraining cords, they could infer values of thelift anddrag. They made two important discoveries: As in their 1900 tests,the aerodynamic forces were much less than they had pre- dictedwith Lilienthal’ s tables,and the center of pressure did not movecontinuously forward as the angle of attackwas reduced. The unexpectedlylow values of lift and drag motivated the Wrights’ famouswind-tunnel tests carried out in Dayton after they returned fromtheir 1901 yingseason. Thematter of the center of pressurewas an immediate concern becauseit in uenced directly the pilot’ s operationof the canard forpitch control and especially affected the response to unexpected disturbancesof pitch attitude. T oclarifythe confusion, Fig. 8 is areplottingof the behavior shown by the dashed lines in Fig. 5. b) Staticallyunstable Ratherthan accept the apparently strange motion of thecenter of pressure,Wilbur tried at rstto modify the wing to produce the Fig.6 Momentcurves foran aircraft. behaviorhe wanted, continuous motion of the center of pressure forwardas the angle of attack is reduced. He correctly surmised thathe could at least reduce the severity of the control problem byreducingthe camber of the airfoil, even though this would also reducethe lift generated at a givenangle of attack. First he tried reducingthe camber by installing an additional spar between the leadingedge and aft spar on theupper wing. Tests on Wednesday, 31July,showed improved yingqualities. Thenthe Brothers spent vedays making further modi cations, ofwhichthe most signi cant was introduction of additionalspars on bothwings and king posts with additional truss wires connecting the wings.That system, just visible in thephotograph, Fig. 9, 24 allowed substantialadjustment of theairfoil, to give “ : : : ashapewhich we hopewill cause center of pressureto moveforward like a planeat allangles” (McFarland, 24 p.81).See also Fig. 7 fora clearerview ofthemodi cation. Wilbur was determined to getthe behavior he initiallyassumed. Figure 10 shows Wilbur’ s sketchesof theairfoil on27Julyand after the modi cations, on 7August.

Fig.7 Approximatepro les ofthe Wrights’airfoil 1900 –1903: 1903 wing rst tohave fabric covering on boththe topand bottom surfaces. tailvolumes, the 1905 and 1909 Flyers couldbe trimmed, although theequilibrium states would be unstable. Their pitching moments aresimilar to that shown in Fig.5b forwhich there is anunstable trim point. VIII. 1901:Y earof SeminalDiscoveries Basedon theirexperience in 1900,the Wrights returned to Kitty Hawkin July 1901 with a gliderdesigned primarily to solve the problemof developingmore lift and, hence, allowing extensive glid- ingtests. It was larger, having wing span 22 fttotal,wing area 290 ft 2, andcanard area 18 ft 2.Signicantly, to conform more closely to Lilienthal’s bestpro le, the Brothers used an airfoilshape having maximumcamber in the range 1 =12–1=18along the span, in con- a) b) trast to 1=25in1900.Figure 7 showsthe airfoils. The total weight Fig.8 Motionof the center ofpressure withangle of attack,data from wasabout 240 lb with pilot on boardand the c.g. was initially 29 in. Fig. 4: a) Wrights’incorrect expectationfor a atplateand, by assump- fromthe leading edge, about 37% of thechord. tion,for an airfoiland b ) measuredbehavior of the Wright1903 airfoil. 994 CULICK

Fig.9 Glider of1901after modications to reduce the motionof the center ofpressure: ellipses identifytwo king posts (McFarland24 ).

a) b) Fig.10 Wilbur’ s sketches ofthe airfoilshape on the 1901glider Fig.11 Motion of the center ofpressure asthe angleof attack is (McFarland24 ): a) initialhighly cambered pro le (27 July) and b) pro le changed:aerodynamic origin of the twostalls on 27July 1901. modied bytrussing (7 August).

Theimprovement in performance and yingqualities was tothepoints I and Ia inFig. 11. The point Ia identies the actual †† immediate. FromW ednesday,August 7, to Friday, August 16, locationof the center of pressure on the true graph xcp (®); I is Wilburexecuted approximately 25 glides, of whichthe longestwas onthegraph of xcp (®)thatWilbur anticipated. Now supposethat 389ft. However, one ightdid end with the wings stalled. adisturbance,that is, a windgust, causes the angle of attack to increase by ±®.Hence,the center of pressure in the actual case A.Interpretationof Wilbur’s Difculties withMotion movesforward, but Wilbur thought that it moved aft, as shownin ofthe Center ofPressure theinserts. Hence, while in reality the pilot must exert a nose-down Thereis nodoubtthat Wilbur’ s initialincorrect expectation for momentto restore the initial state, Wilbur rotated the nose of the themotion of the center of pressure contributed to the trouble he canardupward, intending to exert a nose-upmoment, compensating experiencedduring his rstday of ying.Figure 11, based on the thenose-down (he thought) rotation caused by an aftdisplacement dataplotted in Fig. 5, showsthe graphs of centerof pressure versus ofthecenter of pressure. angleof attack for a atplateand the1903 Wright airfoil, which we Inshort, because he expectedthat the center of pressure would usehere for illustration.Any detailed differences from the behavior alwaysmove aft if the angle of attackincreased, Wilbur’ s planned oftheWrights’ rst1901 airfoil are not germane to the reasoning. strategyfor control in pitchwas that, to maintainequilibrium, the Accordingto entries in his diaryand remarks in his 1901 paper, 27 pilotmust cause a nose-upmoment if the angle of attackincreases, Wilbur’s idealizedapproach to understanding gliding proceeded thatis, if the nose appears to rise.If the initial operating point I is roughlyin the following way: atanangle of attackclose to stall(but ® < ®stall),thenthat control 1)With the approximate scheme for solving the gliding problem strategycould cause the glider to stall— and that is apparently what (Sec.IV), estimate the angle of attackat whichthe lift is suf cient to happenedtwice on the rstday of testsin 1901. compensatethe total weight in steadygliding at the assumed ying WhatWilbur and Orville called the “ reversalof motion”of the speed.For simplicity here, assume that the canard carries no lift. ‡‡ centerof pressurewas their discovery of the correct motion of the 2)For that angle of attack, locate the position of the center centerof pressurebelow the angle of attackfor stall. It was clearly a ofpressure of the wing assuming the graph for a plane(Figs. 5 crucialdiscovery allowing them to continuetheir test yingsuccess- and 11). fully.Although eventually the Brothers had suf cient information 3)When disturbances, that is, gusts of wind,occur, the angle of topreparegraphs such as those in Fig. 11 (seeFig. 12 24 here), they attackchanges and the center of pressure moves according to the didnot document the reasoning just described. Indeed, it is notan graphfor the plane in Fig. 5. Thelift then generates a momentabout exaggerationto note that the Wrights truly understated this discov- thecenter of mass and the canard must be actuatedso itslift creates eryof behavior fundamental to airfoils in general and especially acompensatingmoment to maintain equlibrium. crucialto continuationof their successful gliding tests. Itis the last step that contains the explanation for Wilbur’ s difcul- tiesbecause the sense in whichthe canard is actuatedis determined B.Wilbur’s Discoveryof Adverse Yaw bythedirection of motion of the center of pressure.Before his glid- Cayleyand others before the Wrights, Lilienthal and Mont- ingtests, Wilbur had assumedthe behavior of aatplateand based gomerybeing the exceptions, assumed that turning in ightcould hisplanned control strategy on that assumption. A simpleexample beachievedby useof thevertical tail or rudder,in exactly the same showshow that strategy caused him to stall the glider. waya boatis turned. Probably from his observations of birds in Supposethat the state of (more-or-less)steady ightis suchthat ight,Wilbur knew better. His correct idea was that, to generate the theangle of attackand locationof thecenter of pressurecorrespond centripetalforce required to set the airplane on acircularpath, the airplaneshould be rolled to tilt the lift force (perpendicular to the wingsurface) so thatpart of thelift would act toward the center of †† Almostcertainly the apparent re ex in the airfoil shown in Fig. 10b had theintended circle. What he didnot recognize until later was that, to muchto do withthe improvement. It was apointmissed bythe Wrights, causethe nose to turn in the direction of thedesired turning motion, andfrom 1902 to the end of their work they used highly cambered thin airfoilswithout re ex. The signi cant andfavorable consequences of reex theremust be averticaltail to causerotation in yaw.Withoutit, the were later shown rst experimentallyby Turnbull. 40 Itis possibleto design airplanewould begin to executea circularpath, but the nose would areexed airfoil having xedlocation of its center ofpressure,but at the continueto pointnearly in itsinitial direction. expenseof poorlift-to-drag ratio. However,the situation is worse, as Wilbur discovered in his rst ‡‡Aliftingcanard is easily accommodated withinthis scheme. attempts.T orollthe airplane, the lift on one wing is increased and CULICK 995

Fig.12 Wrights’ data for the center ofpressure ontwoof their airfoils (McFarland,24 p. 503). decreasedon theother, in Wilbur’ s caseby warpingthe structure. whichthe center of pressuremoves as theangle of attack is changed, Thatcontrol generates a rollmoment. However, the drag on awing theywere satis ed because it wasthe basis for a correctstrategy of hasapartproportional to the lift. Hence, one wing has greater drag pitchcontrol. Their incomplete understanding of momentsdid not thanthe other. The differential drag causes the aircraft to yaw ,and allowthem to investigate the quantitative nature of equilibrium, thenose actually swings in the sense opposite to that desired in stability,and control of pitchingmotions. It was enough for them theturn. That is what Wilbur discovered, a verykeen observation toknowthat when their aircraft began to “ loseheading” as iten- indeed.Attempting to correctthe unwanted motion tends to com- tereda stalledcondition, they should use the canard to generatea plicatethings further, and the maneuver falls apart. nose-downmoment and gain airspeed. That understanding became Heentered his observation with the brief remark in his diary on akeypart of the nalstep in development of theirpractical aircraft Thursday,15 August:“ UpturnedWing seems to fallbehind but at in 1905. rstrises.” Then, in a letterto Chanute a weeklater, he reported, Wilbur’s identication of adverse yaw, possible only because he “Thelast week was without very great results though we proved wasa testpilot yinghis own creation, was the third of theWrights’ thatour machine does not turn (i.e. circle) toward the lowest wing greatdiscoveries in 1901. The solution to the problemof executing underall circumstances, a veryunlooked for result and one which correctturns rested on having a controlmoment about the yaw completelyupsets our theories as tothe causes which produce the axis.Sometime later, during their design of the1902 glider, Orville turningto right or left.” realizedthat their aircraft needed a verticaltail to give them the Thus,when the symmetry of the aircraft is broken,by warping necessaryyaw moment. thewing, lateral motions are induced. After 1901, as they developed theirmethod of turning,the Wrightswere forced to address problems IX.TheWrights Discover Longitudinal Dynamics oflateralmotions as wellas thoseof longitudinalmotions. The Wright Flyers hadlimited exibilityto exercise control, for Wilburmade a fewglides on the day following his experience example,with wing warping. However, because of thearrangement withadverse yaw. The Brothers then closed camp and returned to oftruss wires, the Flyers canbe approximated as rigid structures Dayton.In three weeks, test yingfrom 27 July to 16 August,they whenthe controls are xed.That assumption has a wonderfulconse- hadmadethree basic discoveries whose deep signi cance they could quence:A century’s progressin thescience of the ightmechanics notfullyappreciate at thetime. Their con rmation of measured val- ofrigidaircraft is immediately applicable to understandingthe be- uesof liftand drag well below those reported by Lilienthalcaused haviorof theWright Flyer. §§ themto build their wind tunnel andto carry out extensive tests Arigidaircraft has six degrees of freedom.For small departures ofairfoils,wing planforms, and struts. When they ended the tests, froma stateof steady ight,the time-varying motions of asymmetri- theyhad the rstsystematic compilation of aerodynamicdata suit- calaircraft can be separatedinto two uncoupled forms: longitudinal ablefor designing aircraft. Those results served them through their motionsin the plane of symmetry and lateral motions out of that entireprogram until Wilbur’ s deathin 1912 brought their design plane.The variables for the longitudinal motions are two transla- anddevelopment program to itsend. Less well known is their con- tionalvelocities u and w intheforward and vertical directions and clusionthat Lilienthal’ s datawere actually very good and that their onerotationalvelocity q forpitching motions. lowvalues for the aerodynamic forces were due to their use of the incorrectvalue of Smeaton’s coefcient ¶¶ generallyaccepted at that time(Culick and Jex 41).Theirdata gave them the correct value. A.NormalModes for Longitudinal Motions Stabilityof the translational motions is guaranteed by the pres- Incontrast to their quantitative understanding of liftand drag, the enceof aerodynamic damping due to drag. If the aircraft is also Wrightsseem to havebeen quite satis ed with qualitative results for staticallystable in pitch— the c.g. lies ahead of the NP— then the motionof thecenter of pressureon acamberedairfoil— their sec- aircraftpossesses two oscillating modes of motion:the “ phugoid” ondgreat discovery in 1901. Having established the correct way in orlong-period(low-frequency) mode and theshort-period mode. If aconventionalaircraft is rendered unstable by improper distribu- tionof thepayload, the common case is that the short-period mode §§Thewind tunnel had been invented by FrankH. Wenham in1871. In the 1890s,Albert Wells at Massachusetts Instituteof Technologyused the idea degeneratesto two exponential motions, one of whichis unstable, tomeasure thecorrect valueof thedrag on a at plateoriented perpendicular whilethe phugoid remains. That is the case for the 1903 Wright tothe owin an air conditioningduct. Flyer. ¶¶Proportionalto the drag of asquare at plateoriented perpendicular to Toagood rstapproximation, the phugoid oscillation is aslowly the wind. decayingoscillation having period equal to 2 ¼p.u=g/, where u is N N 996 CULICK theaverage forward translational velocity. It is a relativelyslow un- dulatingmotion involving periodic exchange of kinetic and potential (gravitational)energy. The angle of attackremains nearly constant. Duringa phugoidoscillation, the aircraft normally undergoes no- ticeableoscillations of altitudeand speed. Incontrast, a stableshort-period motion usually takes place with onlysmall changes of altitudeand speed and is independent of the phugoidmotion. During a short-periodmotion, the nose bobs up anddown, and the change of pitch angle relative to the horizon approximatelyequals the change of angle of attack. The aircraft isbehavingmuch like a weathervanein pitch,the mass being the momentof inertia and the spring or restoringforce is providedby staticstability, that is, a negativeslope of thepitching moment curve. Probablythe most common event causing the phugoid oscillation toappearis a changeof altitude.The slow oscillation may be excited andcause some dif culty in trimming to the new altitude, partic- ularlyif the new altitude is higher than the initial altitude. Unless a) Young (byT .Wright,1978 ) abruptchanges of theelevator are made, a stableshort-period oscil- lationis notlikely to beapparent.On the other hand, ightthrough choppyair will easily excite the short-period oscillation. However,the pilot will always notice an unstable short-period oscillation,which occurs when the aircraft is statically unstable in pitch.The growth of theunstable exponential part requires active control.If alsothe phugoid happens to beexcited,then the aircraft willexecute oscillations superposed on thegrowing exponential; the resultcould be interpretedas anunstableoscillation. That became acharacteristicof all of theWright Flyers.

B.Wrights’Experience withLongitudinal Dynamics: 1900 –1903 Duringtheir yingseasons of 1900–1903, the Wrights rsten- counteredsome symptoms of longitudinal dynamics of theirunsta- blegliders and powered aircraft, but not until 1904 did they mention b) Engler (2001)26 thepresence of oscillations or “undulations.”In1900, the kite/ glider Fig.13 Photographs of recent recreations ofthe 1901Wright glider . was ownmostly as akite,and so the general behavior just described inSec.IX.A isnot relevant. Their total free- ying time was of the orderof 10sorso,andthe Wrights recorded only general observa- the1901 glider have found the machine to have reasonably good tions.There is inadequate information to determine whether or not yingqualities. theyhad any direct experience with the longitudinal modes of mo- Thoseresults suggest that with their modi cation of theirairfoil tion.It does seem that the glider was probably unstable, requiring (Fig.10) the Wrights had movedtheir design in theright direction, thepilot’ s constantattention even for such short yingtimes. The namely,they made the zero-lift pitching moment, or Cm ac , less nega- Wrights’two main conclusions from their tests in 1900—that their tive.However, because they did not have the theoretical framework designof pitchand roll controls worked well and that the lift and tounderstandthe implications of whatthey had done, they were un- dragthey measured were less than the values they had predicted preparedto takeadvantage of theimprovement. They knew that they withLilienthal’ s dataand formulas— were not related to dynamic hadsuccessfully altered the motion of thecenter of pressureand had behavior. improvedthe controllability of theglider. However, they could not Itwas of course a differentstory in 1901.Wilbur’ s difculties with understandthat more signi cantly in thatprocess they had modi ed pitchcontrol necessarily brought problems of dynamics,mainly stall thepitching moment curve substantially, likely making the glider andrecovery.His idea to reducethe camber of theairfoil to smooth nearlystable in pitch.That was probably the one lesson presented themotion of the center of pressureseems to have done much more. totheWrights that they did not learn well enough to applyto their Themodi cation (Fig. 10) not only reduced the camber but also poweredaircraft. causedthe prole tohave roughly a reexed shape, the trailing edge Figure7 makesthe point, showing the airfoil sections for curlingup. Both of those changes reduced the size of thenegative the1900– 1902 gliders and the 1903 Flyer,littlechanged in the zero-liftpitching moment, that is, the moment about the a.c. 1904–1909 Flyers.Onlyapproximations can be sketched for the Atailessaircraft can be made trimmable and stable in pitch if 1900–1902 airfoils for which no accuratedrawings exist. In partic- theairfoil is sufciently re exed that the zero-lift pitching moment ular,the 1902 glider had an airfoil possessing relatively low maxi- ispositiveand the slope of themoment curve is negative (Fig. 6a). mumcamber, 1 =24–1=30,whenconstructed. Because of structural TheWrights of coursehad no ideaabout those characteristics, but exibility,the camber varied along the spans of thegliders, so that Wilburdid ndthemodi ed versionof theglider very yable.In nouniquevalues can be assigned. 1978,R. Youngbuilt a replica(Fig. 13a, photograph by T.Wright, Allevidence suggests that the 1902 glider did not present seri- 1978)of the 1901 glider ownin thetelevision lm“ Windsof Kitty ousproblems of longitudinalstability and control. The lightweight Hawk.”Engler 26 andhis colleagues built and ewa replicaof the structureand the relatively forward position of thepilot favored a po- 1901glider at Kitty Hawk in October 2001, the centenary of Wilbur’ s sitionof the c.g.that, with the airfoil used, probably gave a machine signicant ights.Both report that their versions (Figs. 13), 26 which thatwas only mildly unstable in pitch, possibly even stable. Several alsocontained the king posts and added truss wires to reduce the replicashave been made and successfully ownrepeatedly during camber, ewvery successfully even in windslighter than those the thepast 25 years or so: Y oung(private communication explaining Wrightshad. earliergliding experience, 2002), Engler (private communication, Kochersbergeret al. 42 havereported results of wind-tunneltests 2002),V alentine(private communication, 2000), and Kochersberger ofafull-scalereplica of the1901 glider, carried out inthe30 60 ft (privatecommunication, 2002). Y ounghas reported in privatecon- opensection tunnel at NASA LangleyResearch Center. Their £ data versationthat, so far as thepitch instability is concerned, yingthe showthat the aircraft could be stablytrimmed over a rangeof useful 1902glider was “ notmuchdifferent from riding a bicycle.” speedand lift coef cient. That result is direct explanation of the Onthe contrary, when the Wrights scaled up their1902 design and relativeease with which the Wrights and more recent builders of addeda propulsionsystem, the behavior in ightwas quite different. CULICK 997

deection of the canard. This motion may be interpreted equiva- lentlyas the response to a verticalgust striking the canard. The doublingtime of roughly 0.5 s, slightly longer than the average person’s reactiontime, can be controlledby a skilledpilot, as the Wrightsdemonstrated in 1903 and 1904. As an approximationto feedback(closed-loop) control, suppose that to maintain level ight thepilot exerts corrective de ection of thecanard proportional to thedifference between the observed pitch angle of theaircraft, for example,the orientation of the canard, and the horizon. For a gain of4 deg(of canard de ection for 1 degof error) the closed-loop rootsare identi ed inFig.14. The response in pitch and the pilot’ s controlinput are shown in Fig. 16 fora commandedstep change in pitchangle of theaircraft. Notein Fig. 16 theoscillations of both canard de ection and pitch angleof the aircraft. The behavior of theangle ±c ofthecanard is due tothepilot’ s attemptto reachthe command angle of climb. Then controlactivity is re ected in the oscillation of pitch angle itself, representinga dampedpilot-involved oscillation (PIO). Given the lightlydamped oscillatory roots shown in Fig. 14 for K 4, the presenceof the PIO isnot surprising. Even though the DFlyer is severelyunstable in pitch, it can be controlled by a skilledpilot. Themotion is described further by Culcik and Jex 41 and Jex and Fig.14 Locus of dynamic roots for longitudinal motion of the 1903 Culick.43 Itcan be seenin lmsof theWrights yingin 1909–1910. Wright Flyer;pilotcontrol law: canard de ection proportional to pitch angleerror ,gaincoef cient K. X.TheWrights Discover Lateral Dynamics Amajorreason for the problems of pitchmotions with their powered Thethree lateral degrees of freedom are translation along the axis aircraftwas their choice of airfoil based on best lift-to-drag ratio perpendicularto the plane of symmetry, rotation in roll, and rotation withno attentionto pitching moment. That is a seriousfundamental inyaw.Itisthe presence of tworotations that makes lateral motions differencebetween the aerodynamics of the1902 glider and the 1903 seemsomewhat more complicated than the longitudinal motions. Flyer.The1903 airfoil had maximum camber greater than that of Thetranslational velocity is v,andthe two rates are p and r in roll the1902 airfoil and signi cantly greater curvature over the aft half andyaw, respectively. ofthechord. Those properties cause the Flyer—indeedall Wright poweredaircraft to 1910— to havea relativelylarge negative zero- A.NormalModes for Lateral Motions liftpitching moment, which, with an aftc.g., produces the problems Fora rigidaircraft there are usuallythree distinct normal modes: discussedin Sec. VII. theroll subsidence, the spiral mode, and the lateral or Dutch roll Thelarge zero-lift pitching moment and the aft location of the oscillation.All three generally have components of motionsin the c.g.dominated the longitudinal dynamics of the1903 Flyer. Anal- threelateral degrees of freedom,but some simpli cations are pos- ysesand numerical simulations provide the best evidence we have sibleand often give acceptably accurate results. forthe sorts of dynamics the Wrights must have encountered with Theroll subsidence is nearlya purerolling motion that can be their 1903 Flyer.Culickand Jex 41 andJex and Culick 43 reported excitedby astepchange of aileronsetting. Small yaw and lateral the rstresults. With the use of wind-tunnel data acquired in sub- translationalmotions may be generated due to the action of lat- scalewind-tunnel tests 39;44 bothlongitudinal and lateral dynamics eralcross derivatives. In any event, the roll subsidence is heavily of the Flyer,open-loopand closed-loop with a pilotexercising pro- attenuateddue to thelarge damping-in-roll provided by the wings. portionalcontrol were calculated. Since that work, a testprogram Asecondmode, the spiral mode, also usually has behavior expo- withthe AIAA full-scalereplica 45 hascon rmed and extended the nentialin time. It is either lightly damped or weaklyunstable. The subscaleresults. Nearly all data required are available for carrying spiralmode for the 1903 Flyer wasseriously unstable due to the realisticanalysis of the Flyer’s dynamicbehavior using well-known negativedihedral, causing the Wrights so much trouble that they methods.46 Quantitiesnot measured, notably the rotary derivatives eventuallymade the modi cations necessary to stabilizethe mode. anddampingforces, are estimated with the simple formulas of aero- Thethird lateral mode is thelateral oscillation, which always in- dynamicstrip theory. A thoroughreport of themore recent analysis volvescontributions from the three degrees of freedom.It is most hasbeen prepared by Papachristodoulouand Culick. 47 One detail obviouslya coupledyaw/ rolloscillation but also involves oscilla- isworthnoting: For all of theWright gliders and powered aircraft, torytranslational or slippingmotions perpendicular to theforward 1900–1912, the virtual or apparentmasses associated with acceler- motion.Usually the frequency of thelateral oscillation lies in the ationof theair are signi cant for all rotational motions and isabout rangewhere it is easily excited during ightthrough turbulent air 28%oftheactualmass in heaving accelerations for the1903 Flyer. orbyappropriateperiodic manipulation of thecontrols. Otherwise Figure14 isa rootlocus plot for the pitch angle dynamics of the itishardlynoticeable in normal ightof conventionalaircraft. Flyer.Asthe preceding discussion has established, the open-loop (zero-gain)roots represent a lightlydamped phugoid having a ¤¤¤ B.The Wrights’Experience withLateral Dynamics: 1901 –1902 periodabout 5 sanda degenerateshort-period oscillation and a Itwas Wilbur’ s observationof adverse yaw in 1901 that rst stableand a divergentexponential, the latter having doubling time causedthe Brothers to pay attention to motions in yaw .Even- ofapproximately 0.6 s. The locations of the open-loop zeros are tuallythey also noticed a slippingmotion subsequent to rolling dominatedby thevalues of thestatic margin ( T ,thehigh-frequency µ2 theiraircraft, an observationcon rming that they encountered the factor)and the damping forces and pitching moment due to changes spiralmode. intheforward speed ( T ,thelow-frequency factor). µ1 Whenthey returned for ighttests at Kitty Hawk in 1902,their Theinstability in pitch is illustrated by the simulation in Fig. 15 newglider (Fig. 17a 24 and Fig. 17b26)waslarger and heavier than showingthe exponential increase of pitchangle following a brief the1901 machine but had the same wing loading (0.84 psf). More signicantly, it sported a xeddouble vertical tail intended to com- pensateadverse yaw when the aircraft was rolled to turn. ¤¤¤Because theaircraft is unstable,this is notatruephugoid, and its period isnotaccurately estimated withthe formula 2 ¼p.u=g/. Etkin37 refers to Duringthe rstpart of their yingseason in 1902, the Broth- thismotion as thethird mode of longitudinaldynamics. N The Appendix is a ersconcentrated on learninghow to turn. Because they were ying briefexplanation of this important characterization ofan aircraft unstablein closeto the slopes of the hills— they probably rarely reached al- pitch. titudesgreater than a wingspanor two—they never completed, or 998 CULICK

a) Pitchattitude angle

b) Angleof canard de ection Fig.15 Open-loop time response ofthe 1903 Flyer toa triangulardisturbance of the canardsetting.

a) Pitchattitude angle

b) Angleof canardde ection Fig.16 Closed-loop (piloted) timeresponse ofthe 1903 Flyer toa step commandinput of pitchangle. evenattempted, full circles. Rather, it seems clear that they were wingis rotated downward. That was troublesome to the Wrights for tryingto gureout the basic mechanics of theturn partly to learn thefollowing reason. howto maintain straight ightin the presence of wind gusts. They TheWrights were gliding down a slopeinto the wind.Most gusts encounteredtwo problems that demanded small changes of their de- occurredin thedirection of the wind,that is, up thehill. When they sign.Or perhaps they were two manifestations of the same problem, attemptedto turn, or for some other reason they were not ying causedpartly by adverse yaw. directlyinto the wind, a gustwould cause the uphill wing to drop Duringthe early gliding tests, both Brothers encountered an an- (positivedihedral effect), occasionally striking the slope. That hap- noyingform of the response to gusts. Up to this time, all of the penedsuf ciently often that the Brothers decided to trussthe wings glidershad positive dihedral effect, following Cayley’ s ideato pro- fornegative dihedral (also called “ anhedral”), withthe tips being videintrinsic stability to disturbances in roll. If one wing drops lowerthan the center. or—what is thesame aerodynamically— the aircraft is exposedto Withor withoutanhedral, the glider having xedtail also several asidegust, then positive dihedral causes the airplane to right itself timesexhibited a secondproblem associated with adverse yaw. As inthesense indicated in Fig. 18. In particular, for example, a gust agentleturn, having relatively small roll angle, was being corrected fromthe right causes the airplane to roll to theleft, that is, the left tolevel ight,the outer wing of the turn dropped and struck the CULICK 999

sothat any attempted turn would lead to a crashunless corrected veryquickly. Thoseunsatisfactory results with the glider having xedtail con- vincedthe Brothers of the need to modify their design. It was Orvillewho suggested that the vertical tail be made controllable. Intheinterest of simplifyingthe pilot’ s workload,Wilbur proposed connectingthe rudder control to thewarp control. From then until September1905, the Wrights ewtheir aircraft with roll and yaw controlsinterconnected. They were the last designers to connect rolland yaw controls until Fred W eickinvented the Ercoupe in the late 1930s. Notfully recognizing the consequences of giving an unstable spiralmode, the Wrights retained the negative dihedral until November 1904.They nallyrealized that it wascausing problems when they attemptedturns and removed the anhedral in early November. Fig.17a First versionof the Wrights’1902 glider (McFarland,24 Plate Afterinstalling anhedral and a movablevertical tail, the Brothers 41). spentthe remainder of the 1902 season learning how to ytheir glider.At most,they seem to have attempted only gentle turns. They continuedthat kind of practicing for two months in 1903 while theyprepared the powered aircraft. It seems a fairassessment to characterizethis period of their yingas aprocessof learning how toymore-or-lessstraight and level in thepresenceof disturbances orgusts.They did not exposeany new problems of ightdynamics. Inthat context, the rstpowered ightswere really powered and sustainedlevel gliding ightsfollowing takeoffs. The 1903 Flyer waslarger than the 1902 glider (span 40 ft4in.compared with 32 ft 1in.)and heavier(750 lb compared with 257 lb) and had wingload- ingincreased from 0.84 to 1.47 psf. Moreover, the 1903 airplane wasmuch more unstable than the 1902glider. Hence, the 1903 air- planesurely offered more dif cult handling qualities, but with only fourstraight ights,the Brothers did not report new dynamic problems.If unexpected dynamics did appear, they were likely not easily identied, being obscured by theBrothers’ vigorous efforts to keep Fig.17b Recreation ofthe 1902glider (Engler 2001).26 theairplane in the air under very dif cult windy conditions. Surely thesheer excitement of executing the rstpowered ightsmust also haveblunted the observational powers even of the Wright Brothers.

C.LateralDynamics of the 1903 Flyer Thatthe 1903 Flyer hada seriousinstability in pitch has been widelydiscussed and argued about. Little attention has been paid tothe lateral dynamics, the chief exceptions being the analyses byCulick and Jex, 41 byJex and Culick, 43 andmost recently by Papachristodoulouand Culick. 47 Mainlybecause of the negative dihedraleffect and low directional stability (a consequenceof the smallvertical tail volume), the spiral mode had a relativelyshort doublingtime, approximately 2 s,anda weaklydamped Dutch roll Fig.18 Dihedral effect. oscillation. Combinationof the lateral instability with the pitch instability ground.The Brothers called this event “ well-digging.”W ald 48 has makes yingthe 1903 Flyer anorderof difculty greater than rid- bestexplained the cause of the problem. Suppose the glider is turning inga bicycle.The level of pilothandling qualities is not apparent totheleft, for example, and tocorrectthe turn the wings are warped, fromthe analyses described here; it isa characteristicthat can be withthe trailing edge of theleftwing warped downward to increase understoodonly with three-dimensional simulations. That was ac- itslift and stop the turn. Because of adverseyaw ,thewing is slowed, complishedas part of a projectcarried out two years ago by six thelift is initiallyreduced, and the wing actually drops. If the glider studentsat the Air Force T estPilot School 49;thesoftware was pre- issufciently close to theground, the tip of the wing would strike paredby engineers at Veridian,Inc., for a groundsimulation and for thesand and serve as apivotpoint for the glider to swingto rest. theLearjet-24 V ariable-StabilityIn-Flight Simulator T estAircraft. In1902, the new vertical tail, because it provided directional Thepilots found that yingthe aircraft was made more dif cult due stability,did help the aircraft turn. However, also because it was tothe attention demanded by the two instabilities having signi - xed,it hada seriousshortcoming: It was effective only if the aircraft cantlydifferent doubling times (0.6 s inpitch and 2.0 s laterally). hadtranslationalmotion laterally, that is, slipping. When a turnwas Thus,for example, concentration on controllingthe pitch instability, initiated,adverse yaw swung the aircraft such that the lift (to the whichrequires constant attention, may lead to losingcontrol of the side)generated by thetail would correctly compensate the swinging spiralmode. motion.However, apparently the correction was too large under Understandingthe natural lateral motions and controlled response somecircumstances, causing the glider’s noseto swing too far into of the Flyer is,therefore, particularly helpful if one intends to ya theturn, which is the beginning of motion that we now know as recreationof theairplane. Performance in a turnis a goodway to thespiral mode. Whatever the cases may have been, the absence of assessthe problem. The Wrights were rstto understand the correct anycontrol of theyaw moment generated by the vertical tail had methodfor turning an airplane:de ection of wingwarp (or ailerons) unacceptableconsequences. fora shorttime to givea niteroll angle, use of rudder to provide Orville(McFarland, 24 p.470)later testi ed ina depositionthat therequired yaw rate in bodyaxes, and, if necessary, application of theirglider having “ cathedralangle [anhedral] with xedrear verti- poweror changeof pitchattitude to maintainsafe airspeed above caltail and adjustable wing type was the most dangerous : : : :” The stall.Here we ignore the last and assumeconstant speed. Figure 19 negativedihedral caused the spiral mode to be seriously unstable showsthe uncontrolled response of the Flyer to10 deg of wing warp 1000 CULICK

a) Bank angle

b) Sideslipangle

c) Warp angle Fig.19 Open-loop time response ofbank angle and sideslip following an impulseof wing warp (1.0 deg s). ¢

a) Fixedrudder b) Linkedwarp and rudder Fig.20 Root loci for lateral motions of the Wright1903 Flyer,pilotcontrol; warp de ection proportional to roll angle error ,gaincoef cient K.

1 appliedfor 2 s.T oexecutea turn,the pilot must actively compensate Figure21 showsthe time responses for the two cases of xedand thelateral instability. linkedrudder. The results are very different. If therudder is de ected, Whenthe Wrights added their vertical tail to their1902 glider, theaircraft quite smoothly enters the steady turn, albeit with error theychose rstto xthesurface, but soon linked its de ection to the inbankangle on the timescale shown. The corresponding root locus wingwarping. The 1903 Flyer hadthe warping and rudder de ection (Fig.20b) shows the reason. Loop closure causes the roll subsidence linked.W eexaminethe two cases of xedand linked with the root andspiral mode to coalesce, forming a lightlydamped pure roll locusshown in Fig. 20, prepared with aerodynamic data collected oscillationhaving very long period, roughly 6 s.Simultaneously the intheLos Angeles AIAA Project.For both cases, we assume that frequencyof the Dutch roll oscillation is slightly increased but has thepilot exercises control, that is, warp de ection, proportional to muchgreater damping. theerror observed between commanded, that is, desired, and actual Incontrast, if therudder is xed,the spiral mode combines with bank angle. partof theDutch roll to forma rolloscillation similar to that arising Executionof aturnis analyzedby specifyingthe desired angle whenthe rudder is xed.The remainder of theDutch roll combines ofbank(here 10 deg),the input being a rampfollowed by astep. withthe roll subsidence to forma newmode, a sortof wallowing CULICK 1001

a) Bank angle

b) Sideslipangle

c) Warp angle

d) Rudderangle Fig.21 Closed-loop (piloted) timeresponses ofthe 1903 Flyer fora 10-degbanked steady turn. motioncomposed of relatively large oscillations of bankangle and sideslip,due to the anhedral and uncompensated adverse yaw. It isdif cult to control and, paired with the PIO inpitch, produces unacceptablepilot handling qualities. Thepilots in the project with the Air Force T estPilot School foundthis behavior just described and concluded that the Flyer is nearlyun yable if the rudder is xed.An alternative scheme is to useconventional three-axis control, the pilot operating the canard, wing-warp,and rudder independently. However, Wilbur made a wise choiceto link the roll and yaw controls. His reasoning, supported by thetest pilots’ experience, is that the pilot’ s workloadis unaccept- ablyhigh when the lateral controls require independent operation. Fig.22 Wrights’ catapult launching apparatus at Hoffman Prairie, 24 XI. MoreTrouble with Dynamics:1904 August 1904 (McFarland ). TheWrights’ program became a differentstory in 1904. They beganwith a newairplane having the same design as the 1903 Flyer theyknew they had tomaintain some minimum speed, in thevicin- butwith a largerengine producing about 20– 25 hp comparedwith ityof 27– 28 mph,the fact that they really did not understand the the12– 16 hp of the earlier aircraft. From the beginning of the 1904 phenomenonof stallingand why it occurred probably hindered their tests,the Brothershad trouble. In the light or calmwinds and higher progress.They seem not to have been aware that the canard could densityaltitude 19 takeoffswere dif cult and often failed, even with stallas well, with consequent loss of controlpower in pitch. alongertakeoff rail. Orville stalled the machine shortly after one of Thus,with an airplanethey knew to beunstable but controllable his rst ights,and Wilbur soon imitated him. They rstused the inpitch, always plagued with the familiar pitch undulations, the termstall in their report of those ights. Wrightspressed on to learn how to ycircles.Wilbur ewtheir rst Moredistressingly, they continually fought the pitching undula- completecircle on 20September 1904, a grandachievement with tionsthat, though unreported, were likely present also in the1903 the1903 design. As they continued practicing turns, both Broth- ights.In aneffort to correct the problem, they moved the engine, ersencountered a newserious problem that they characterized as itswater tank, and the pilot aft, exactly the wrong direction. The “unableto stop turning” (McFarland, 24 p.457), identifying those recordsare not complete, but according to the ightlog compiled ightssometimes terminated by crashes. Evidently the cause was byRenstrom, 50 theWrights made only two ightswith the aft c.g. onenow familiar: stalling of theinner wing of the turn due to its Wilburnoted in a letterto Chanuteon 17July that “ theresult was not slowerspeed and higher angle of attack. The Wrights sensed the satisfactory,”andthe Brothers restored the original con guration. causeand correctlyeased the problem by adding seventy pounds of Theymade no furtherchanges to theairplane in 1904, but they steelballast to thecanard, a movethat reduced the amplitude of the diddevise their catapult apparatus to ease their takeoff problem pitchundulations and also caused them to yfaster. (Fig. 22).24 Theywere continually forced to cope with the dynam- Moreover,they also correctly concluded that the anhedral was icsof takingoff. Many trials ended in minorcrashes before ying causingthem dif culties. Nowhere do theyspeci cally mention any speedwas reached. Even when takeoff was successful, it seems that feelingthat the airplane seemed to have a tendencyto tighten turns, theywere always yingvery close to thestalled condition. Although butthat was surely a factor.In aturn,the presence of theirunstable 1002 CULICK

Whilethose repairs and modi cations were being made, the Brothersmade some measurements of thecenter of pressure on their airfoil,the rstsuch data they (or any others) had taken (Fig. 12). Apparentlythose tests were done in direct response to the July crash. However,there is noevidencein theirdiaries (McFarland 24) about theirinterpretation of theirresults or whatin uence the tests may havehad on theirdesign changes. Their decisions about changes in thegeometry affecting behavior in ight,and their interpretations oftheconsequences, continued to berestrictedby theirinattention tothedetails of momentsacting on theaircraft. Whenthey modi ed the canard, they also enlarged the verti- Fig. 23 Flyer on16 November1904: 1903 design with a largerengine caltail. They had nallyconcluded that the tail was too small andno anhedral (McFarland24 ). togive the control they required. From 1903 to the naldesign in1905, the tail area and the distance between the wing and the tailwere increased. The increase of dimensionless tail volume spiralmode was bound to be feltbecause of its short ( 0.8 s) dou- gavecomparable increases in the directional stability and control blingtime. In lateOctober, the Brothers nallyremoved »the anhedral power. (Fig. 23).24 Thatwas the airplane for their last tests of 1904. Installationof thelarger vertical tail initially caused a handling problem.Wilbur commented that Orville’ s rst ightwith the new XII. 1905:Flight T ests Leadto the FinalDesign 24 ofaPracticalAirplane tailwas “ averycomical performance” (McFarland, p.507).Possi- blythe dif culty arose because the hinge line was too far aft, behind Ina courtdeposition (Wrights vs Herring– Curtiss), Wilbur 24 thecenter of pressurewhich for a atsurface is approximatelyat the (McFarland, p.469) explained clearly that, while they had pro- quarterchord. No change was made at that time, but in the1907– gressedconsiderably in 1904, the Brothers were still left with a 1909machines ownpublicly, the vertical tail was hinged at the puzzle:“ onafewoccasions, the machine did not respondpromptly leadingedge. (toaction taken to restorelateral balance) and the machine came to Forthe remainder of the1905 season, all of Septemberand for theground in a somewhattilted position.” That is, the pilot could the rsttwo weeks of October, only minor structural changes were notcause the transition from a turnto level ightand the aircraft made;the Brothers concentrated mainly on learningto turn. On 7 crashed.The airplane was unreliable and certainlynot yet a practical SeptemberWilbur ewfour circles consecutively, but then two days machine. later,with larger propellers installed, he stalledthe airplane twice. TheWrights eventually solved the puzzle when they discovered Againon 12September, he stalledwhile turning, and on15Septem- thecorrect yingtechnique, in the last days of September 1905. berhe was“ unableto stopturning” (McFarland, 24 p.511). A week Beforethey reached that point, they made some important mod- laterthey removed the anhedral they had been keeping since the ications in their design, relating to both lateral and longitudinal beginningof the season, an indicationthat they were bothered by dynamics. slippingin turns. Whenthey began yingagain in June 1905, the Brothers still On26 September, Orville executed 16 circles in one ight,re- hadessentially the 1903 design, but with some detailed structural mainingaloft 18 min until his fuel supply was exhausted. The changesfor improved strength and a largerengine, now producing Brothers’performance remained erratic, however. On the follow- morethan 30 hp.Forsome reason, not documented, they reinstalled ingday, Wilbur noted that the “ machineat lowspeed could not be asmallamount of anhedral.They also added small vertical vanes to stoppedfrom turning.” On the 29 September,Wilbur made 14 cir- thecanard that came to be called“ blinkers.”Those surfaces mainly cuitsin 19 min,but on 3 Octoberhe was“ unableto stop turning” reducedthe directional stability and in the absence of explanation (McFarland, 24 p.513).The last was a mistakehe understood,be- itisnot clear why the Wrights thought they would help ease their causeon 28 September he nallyisolated the source of theproblems steeringproblems; evidently they believed they would reduce the bothhe andOrville had been having: failure to maintain suf cient problemof slippingwhen the aircraft has alateraltranslational ve- speedwhile turning, causing the inner wing to stall.They had been locity.That in turnreduces a rollmotion, in a sensedepending on ghtingwhat remains, even a centurylater, a causeof manyacci- thedihedral effect (positive or negative).Perhaps the most impor- dents:stall/ spinout of aturn.Wilbur explained the matter as well tantconsequence was that the blinkers increased the damping in asanyonecould today (McFarland, 24 pp.520– 521): yawand, hence, helped pilot control in yaw . On14 July, Wilbur noted that at a higher ightspeed he had : : : Whenit was noticedthat the machine was tiltingup andsliding troubleonce again with the undulations in pitchand crashed, causing towardthe tree, theoperator then responded promptly to the lateral considerabledamage to the canard. When they made repairs, the control.The remedy was foundto consist in the more skillful Brothersincreased the area of thecanard by about73% and moved operationof the machine andnot in adifferentconstruction. The 1 1 troublewas reallydue to thefact thatin circling, the machine has itshinge line forward from about 6 4 to 1 10 4 ft.That is an interestingmodi cation, which re ects again ¡the Wrights’ lack of tocarry theload resulting from centrifugal force, in additionto understandingof stability and, probably, their central concern for itsown weight, since theactual pressure thatthe air mustsustain control.The larger volume of thecanard causes the NP tolie farther isthat due to the resultant of the two forces. Themachine in questionhad but a slightsurplus of powerabove what was required forward,a destabilizingeffect. forstraight ight,and as theadditional load, caused bycircling, Onthe other hand, the larger canard volume increases the damp- increased rapidlyas thecircle became smaller, alimitwas nally ingin pitch, which gives substantial improvement in controllability reached beyondwhich the machine was nolonger able tomaintain byreducingthe frequency and amplitude of theoscillations. Also, sufcient speed to sustain itself intheair. And as thelifting effect themore forward placement of the canard reduces a destabiliz- ofthe inner wing, owing to its reduced speed, counterbalanced ingin uence of upwash from the wing. Recent tests with ground alarge partof the increased liftresulting from the greater angle simulations 49 havecon rmed the advantage of increased damping ofincidence on that wing, the response to lateral controlwas so inpitch. T echnically,it causes the maneuver point to move aft, a slowthat the machine sankto the ground, usually before it had favorableresult for controlling accelerated motions, including un- beenbrought back to the level again. : : : Whenwe haddiscovered thereal natureof the trouble, and knew that it could always be dulations.The Wrights clearly found that to be agoodmodi cation, remedied bytiltingthe machine forwarda little,so that its ying althoughin their 1907– 1909 models the canard was made smaller speedwould be restored,we felt thatwe were readyto place ying andmovedfarther forward, a 3.8%decrease in tail volume from the machines onthemarket. valuein 1905. Nothing in their diaries gives explicit reasons for the detailsof those changes, but it isa reasonableguess that they expe- Withtheir identi cation of the stall/ spinproblem and Wilbur’ s riencedimproved controllability in pitchdue to theslight reduction discoveryof itssolution, the Wrights announced they had a practi- oftheinstability. calairplane. They ceased yingto turn all of theirefforts to selling CULICK 1003

Fig.24 Transition from canard to afttail. theirinvention, another interesting story quite apart from technical a P´enaudaft tail. That is the origin of thecon guration having both matters. canardand aft tails used by severalpioneers in France and adopted alsoby Curtiss in the United States. Aftertheir two-year ight-testprogram, the Wrights had nally XIII. TheWrights’ Transition from Canard to Aft Tail gottenrid of their lateral instability. Their observations demonstrated Wilburinitially settled on his canard con guration to avoid(he repeatedlythat the unstable spiral mode interfered with circling— so expected)the inadequate pitch control that Lilienthal had with his theyremoved the anhedralinitially installed to solvea problempe- afttail. Combined with the concentration of weight in the biplane culiarto theirglide tests close to theground. Their tests also showed cell,the canard presents a verydif cult problem of designing for thatby carrying ballast to movethe c.g. forward the intensity of the trimand stability. It was dif cult to shift the c.g. far enough to give pitchinstability was reduced. Geometrical restrictions raised seri- apositivestatic margin. The choice of airfoilfor the wing then be- ousobstaclesto making their canard stable, and they were satis ed comesa crucialmatter nearly as important as the location of the withan aircraftunstable in pitch, but controllable. c.g.An airfoil having a largenegative zero-lift moment may give an Followingthe Wrights’ rstpublic ightsin 1908, when their aircraftthat has a stablemoment curve but cannot be trimmed,or contemporaries nallygrasped the signi cance of control, advan- canbe trimmed but has an unstable moment curve. Moreover, in the tagesof conventionalcon gurations became increasingly apparent. secondcase, the trim condition may require lift from the canard that TheWright aircraft were undoubtedly more dif cult to learn to cannotbe reachedbecause the surface already stalls at a lowerangle y,a distinctshortcoming at thetime when the new businesses of ofattack.In practice, there are really only two certain ways out of yingschools and aircraft manufacturing were growing rapidly in thissituation: Use a substantiallydifferent airfoil, even one having manycountries of Europe. Conventional aircraft slowly gained a areexed camber line or change the con guration from canard to reputationfor being safer. The Wrights were effectively pressured aft tail. torelax their commitment to their canard design. Possibly at the TheWrights learned from ighttests in 1904some of thenasty suggestionof a Germancustomer, they relented. Their rststep consequencesof their 1903 design. They were severely handicapped wassimply to add a xedhorizontal tail to their existing design, inunderstandingthe problems they discovered because they were in1910. The improvement in handling qualities must have been notaware of methodsbased on analyzing the moments acting on immediatelyevident. Few picturesof the airplane exist (Fig. 24), 24 theaircraft in ight.Moreover, neither experimental nor theoretical andwithin a yearthe Wrights removed their canard surfaces. That investigationshad progressed to the stage where anybody could endedtheir use of the con guration that had been their invention understandthe dependence of aerodynamicpitching moment on the andhad served them well for a decade.Despite their commitment shapeof thecamber line. All in all, then, the state of theart(which tothatform of theairplane, original with them, the Wrights did not infact had been developed by the Wrights themselves) was such tryto patent it. ††† Thebasis for their patent, granted in 1906 and thatit was dif cult for them to understand any technical reasons to neverbroken, was their two-axis control of lateral motion, in gen- justifychanging their canard design. eral,not for their particular aircraft design, and not including pitch Noother designers contemporary with the Wrights suffered the control. samecommitments to the canard. The French in particular were Itis certainly true that if not the Wrights, somebody else would notso concerned with control as the Wrights were, and so they haveinvented the airplane in the early years of the 20th century. didnot share the same fear of the aft tail. In fact, because it was Bleriotwas closest to having all of the practical pieces in place P´enaud’s tail,the French for the most part were biased, if noteven by1908—except for three-axis control, which he learnedfrom the prejudiced,to that con guration. As a result,the Wrights sought a Wrights.In fact,Bleriot (see Crouch 52 andGibbs-Smith 17) owes an controllableairplane, even if unstable,and they got it; the French earlierdebt to theBrothers, for their achievements motivated Fer- soughtan intrinsically stable airplane design, and got it, but at the berto initiate the “ rebirthof aviation in Europe” (Gibbs-Smith 17), expenseof payingtoo little attention to the fundamental problem of control.Ferber 51 generatedFrench interest beginning in 1902 with crudecopies of the1901 glider. While he continuedto use the canard †††Subsequentto theWrights it became accepted practice, stillcontinued, surface,problems with his rstpowered aircraft caused him to add topatent an aircraft conguration (external geometry). 1004 CULICK

attemptedabout 150 takeoffs, of which 115– 120 were completed butonly 100 led to successfullandings. In toto they had less than 6hexperiencewith their powered aircraft, giving them a totalof about12 hyingexperience between them when they nishedtheir researchand development program. What a testamentto their ability toobserveand act accordingly to improvetheir design. Amodernstudent pilot has perhaps 8– 12 h ofdual yingex- periencebefore soloing. The Wrights both learned how to yand inventedtheir airplane with combined yingtime not much longer thana goodnight’ s sleep.

XIV.ConcludingRemarks Aspart of the international celebrations accompanying the cen- tenaryof the Wrights’ rstpowered ights,several groups in theUnited States are constructing yingrecreations of the 1903 Flyer.Thebest known at this time are those led by Engler in Dayton,Ohio (www. rst-to- y.com); Hyde in W arrenton,Virginia (www.wrightexperience.com);Y oungworking with the Science and SpaceMuseum in Richmond,Virginia; and the AIAA, LosAngeles Section,Wright Flyer Project(www.wright yer.org). The rstthree aircraftare intended to be accuratereplicas of the original Flyer as bestas can be determined from the available information. Only Hyde,under sponsorship of theExperimental Aircraft Association andwith generous private funding, plans to yatKitty Hawk on theanniversary day, 17 December 2003. His aircraft is a meticu- louslyaccurate replica, including engine and possibly fuel. Follow- ing ightsof a replicaof the1902 glider, current plans apparently includeone takeoff from a replicaof theoriginal 60-ft rail, placed accuratelyin the sand at KittyHawk. Success will require close repli- cationof the original ightconditions, steady winds of 25– 27 mph. Fig.25 Summary of Wrightaircraft, 1903 –1912(drawingsreproduced Itis an extremely dif cult and ambitious goal. How difcult has fromMcFarland, 24 pp. 1188–1200). beendemonstrated by Kellett(reported in AOPA Magazine53), who seemsto have had only partial successes getting his accurate replica theactivity in France that attracted Bleriot to the problem of offthe ground, the only known attempts. The aircraft is seriouslyun- mechanical ight. derpowered,and totake off in windsroughly 75% ofcruisespeed is Bleriot’s approachof largely uninformed trial and error contrasts rarelyattempted with any airplane. In a statementto theAssociated stunninglywith the Wrights’ systematic research and development Pressin January1904, the Wrights themselves remarked: programcentered on the evolution of one design. (His successful monoplanethat was his rstreal success, later crossing the English Onlythose acquainted with practical aeronauticscan appreci- Channel,was his 11th design.) Everybody began with the same his- ate thedif culties of attempting the rst trials ofayingmachine toryand known results at theend of the19th century, but the Wrights ina twenty-ve mile gale.As winterwas alreadywell set in,we broughtwith them the revolutionary idea of rollcontrol; willingness shouldhave postponed our trials toamore favorableseason, but forthe fact thatwe were determined,before returning home, to gainedfrom their experiences with bicycles, to acceptan unstable, knowwhether the machine possessedsuf cient power to y,suf- butcontrollable, machine; and especially their own original style, cientstrength to withstand the shocks of landings,and suf cient nowrecognized as amodernresearch and development program. capacity ofcontrolto make ightsafe inboisterous winds, as well Thatstyle was central to the ability of the Wrights to develop as incalm air. theirairplane in such a relativelyshort time without bene t ofthe understandingand guidance later provided by theories of aerody- The AIAA Flyer Projecthas different goals. Formed 25 years namicsand ightmechanics. Had those theories been developed agowith $20,000, an insuranceaward for loss of apreviousreplica, earlier,it seems certain that the Wrights would have avoided the theproject has hadtwo primary goals: 1) build a full-scaleaccurate problemscaused by theirhighly cambered airfoil and their canard replicaof the 1903 Flyer tobe tested in the 40 80 wind tun- conguration. Their systematic progress to solutions to thoseprob- nelat NASA AmesResearch Center and 2) build£and yarecre- lemsis clearly shown by the sequence of sideviews of theiraircraft ationof the1903 Flyer capableof repeated ights,by several pi- (Fig. 25).24 lots,to give publicly an accurate impression of the Wrights’ rst Thesummary given in Fig. 25 (McFarland 24)isreally a pictorial ights.Throughout the project, the participants have prepared pub- progressreport of asuccessful ight-testprogram. While the biplane liclyavailable documentation and have been actively engaged in cell,notably the airfoil, remains practically unchanged, and mostof educationalactivities. The rstgoal has been achieved; the aircraft theweight is concentrated between the wings, the change of thesize wason displayin thebuilding housing the W esternRegion Head- andlocation of thesecondary horizontal surface nallyproduced a quartersof the Federal A viationAdministration, until September stableaircraft in 1911. The forward displacement of the c.g. from 2002,when it began an 18-month nationwide tour sponsored by 1903to 1905 was important but insuf cient to providelongitudinal the AIAA. staticstability. Toachievethe second goal requires an aircraft slightly modi- At thebeginning of their program, the Wrights estimated that edfromthe original design, but it mustmeet the vague require- inallhis gliding tests, Lilienthal had been in the air perhaps 5 h, mentof stand-off scale such that from a distanceof a coupleof toolittle, they felt, to reach his goal of having a powered ying wingspans,even an expert will be hardpressed to detect the mod- machine.They set out to dobetter, the chief reason they selected ications. That constraint has been part of the motivation for the KittyHawk, a placeknown to have steady strong winds during most twosubscale wind-tunnel test series and the full-scale tests, as ofthetimes they planned to bethere.In fact, the Brothers themselves wellas for the investigations of ightmechanics reported in this accumulatedbetween them less than 6 hglidingexperience from paper.The comprehensive analysis reported by Jex and Culick 43 1900to 1903. andPapachristodoulou and Culick 47 serveas thebasis for making Whatis trulysurprising is that by thetime in October 1905 they minimalchanges of design to give an aircraft less unstable than weresatis ed theyhad their practical aircraft, the two together had the 1903 Flyer andwith improved yingqualities. Understanding CULICK 1005

8Chanute,O., Progressin Flying Machines ,1894,reprint, Lorenz and Herweg, LongBeach, CA,1976. 9Spearman,A. D., JohnJoseph Montgomery ,1858 –1911:Father of Basic Flying,Univ.of Santa Clara, SantaClara, CA,1967. 10Anderson,J. D., AHistory ofAerodynamics ,CambridgeUniv. Press, Cambridge,England, U.K, 1997. 11Combs, H., KillDevil Hill ,HoughtonMif in, Boston, 1979. 12Crouch, T., ADream ofWings: Americans and theAirplane 1875 –1905, W.W.Norton,New York,1981. 13Crouch, T., TheBishop’ s Boys ,W.W.Norton,New York,1989. 14Culick,F. E. C.,“Originsof theFirstPowered, Man-Carrying Airplane,” Scientic American ,Vol.241, No. 1, 1979, p. 86. 15Culick,F. E. C.,andDunmore, S., OnGreat WhiteWings , Hyperion, New York,2001. 16Gibbs-Smith,C. H., TheWright Brothers ,Science Museum,Her Majesty’s StationeryOf ce, London,1963. 17Gibbs-Smith,C. H., Aviation:An Historical Survey fromIts Origins tothe End of World War II ,Her Majesty’s StationeryOf ce, London, 1970. Fig.A1 Locus of rootsas the staticmargin is variedfrom the initial 18Hooven,F., “ TheWright Brothers’ Flight Control System,” Scienti c stablecondition toan unstablecondition corresponding to that of the American,Vol.240, No. 1, 1978. 1903 Flyer. 19Howard, F., Wilburand Orville ,AlfredA. Knopf,New York,1987. 20Jakab,P .L., Visionsof a FlyingMachine ,SmithsonianInst. Press, Wash- ington,DC, 1990. the ightcharacteristics of theWright Flyers providesthe context 21 withinwhich minimal modi cations of the original geometry are Kelly,F. C., TheWright Brothers ,Ballantine,New York,1943. 22Walsh,J. E., One Day atKitty Hawk: TheUntold Story of the Wright accomplished. Brothersand the Airplane ,Crowell,New York,1975. 23Wolko, H., TheWright Flyer— An Engineering P erspective , Smithso- Appendix: Migrationof Rootsfor Decreasing nianInst. Press, Washington,DC, 1987. StaticMargin 24McFarland,M. W,(ed.), TheP apersof Wilbur and Orville Wright , Itseems that only Etkin 37 (pp.352 ff) has previously examined McGraw–Hill, New York,1953, pp. 38, 469, 470, 503, 520, 521, 721. 25 quantitativelythe in uence of negative static margin on the longi- Engler,N., “ Resurrectingthe 1899 Wright Kite,” WorldW arIAero. , 1999. tudinaldynamics of arigidaircraft. The locus of rootscan be con- 26 structedusing available software for feedback control by takingthe Engler,N., “ TheWrights 1902 Glider— Its Construction,Design and FlightCharacteristics,” AIAA Paper2001-3384, Aug. 2001. gainequal to the static margin. Figure A1 illustrates the migration 27Wright,W .,“SomeAeronautical Experiments,” Journalof the W estern oftheroots representing the phugoid and short-period oscillations Societyof Engineers ,”V ol.1, Dec. 1901,pp. 99–118. ofa stableaircraft (identi ed by )tothe roots for the degener- 28Chanute,O., “ Articial Flight,”Pocket-Bookof Aeronautics ,Whittaker, ateshort-period motion and the low-frequency “ thirdlongitudinal London,1907. modeas the static margin increases.” The nallocations of theroots 29Moedebeck,H. W., Pocket-Bookof Aeronautics ,Whittaker,London, indicatedby correspondto theopen-loop roots for the root locus 1907. plotin Fig. 16. £ 30“AerodynamicCharacteristics ofAirfoils”NACA TR93,1920. 31Jacobs,E. N.,Ward, E. K.,and Pinkerton, R. M.,“TheCharacteristics of Acknowledgments 78Related AirfoilSections from Tests inthe V ariable DensityWind Tunnel,” NACA Rept.460, 1932. Iamespeciallyindebted to Henry Jex for all he hastaught me 32“EngineeringSciences Data,” AeronauticalSeries ,AeronauticalSub- aboutaerodynamics, ightmechanics, and controlduring our asso- Series, Item 70015,Royal Aeronautical Society, 1970. ciationfor more than 20 years in theAIAA Wright Flyer Project. 33vonMises, R., “ FurTheories des Tragachenauftriebes”¨ ZAMM, Onlythe extraordinary efforts of themembers of theproject, partic- Vol.11, No.5, 1920,pp. 68– 73, 87– 89. ularlyChairman Jack Cherne and Deputy Chairman Howard Marx, 34Tchaplygin,S. A.,“Ona General Theoryof the Monoplane Wing,” madepossible the construction and wind-tunnel tests of the full- MemorandumSuperior War Councilfor Publications, 1922; translated by scaleWright Flyer inMarch 1999. The test results, and those ob- Garbell,M. A., Selected Works ,Garbell Research Foundation,San Francisco, 1956. tainedfrom tests of the subscale models, form the basis for analyz- 35Bryan,G. H.,andWilliams, W .E.,“TheLongitudinal Stability of Glid- ingthe special ightmechanics of the1903 Flyer.Ihavebene ted ers,” Proceedingsof theRoyal Society of London ,Vol.73, 1904, pp. 100– greatlyfrom many private discussions and from exchanges of e-mail 116. messageswith correspondents otherwise unknown to me. Figures 36Bryan,G. H., Stabilityin Aviation ,Macmillan,London, 1911. 13–15 and 18– 20 were prepared by Antonis Papachristodoulou. 37Etkin, B., Dynamics ofAtmosphericFlight ,Wiley,1972. Portionsof this paper appeared in the Proceedings of the Forty- 38Perkins,C. D.,and Hage, R.E., AirplanePerformance Stability and FifthAnnual Symposium of the Society of ExperimentalT estPilots Control,Wiley,New York,1949. (September2001). I thankMelinda Kirk for her enormous efforts 39Bettes, W.H.,andCulick, F. E. C.,“ Reporton Wind Tunnel Tests of preparingthe naltyped and formatted version of the manuscript. a1/6-Scale Modelof the1903 Wright Flyer,”Guggenheim Aeronautical Lab.,GALCIT Rept.1034, California Inst. of Technology,Pasadena, CA, 1982. References 40Turnbull,W .R.,“Researches onthe Forms and Stability of Aeroplanes,” 1Gibbs-Smith,C. H., SirGeorge Cayley’s Aeronautics1796 –1855, His PhysicalReview ,Vol.24, No.3, 1907,pp. 133– 135. Majesty’s StationeryOf ce, London,1962. 41Culick,F. E. C.,andJex, H., “AerodynamicsStability and Control of the 2Cayley,G. G.,“ OnAerial Navigation,” Nickolson’s Journal , Vol. 24, 1903 Wright Flyer,” Proceedingsof theSymposium on the 80th Anniversary Pt.1, 1810, pp. 164– 174. oftheWright Flyer ,SmithsonianInst. Press, Washington,DC, Dec. 1987, 3Cayley,G. G.,“ OnAerial Navigation,” Nickolson’s Journal , Vol. 25, 1983. Pt.2, 1810, pp. 81– 87. 42Kochersberger,K., Ash, R., Sandusky, R., andHyde, K., “AnEvaluation 4Cayley,G. 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46McRuer,D., Ashkenas, I., and Graham, D., AircraftDynamics and oratingthe Hundredth Anniversary of theBirth of Orville Wright , Library AutomaticControl ,PrincetonUniv. Press, Princeton,NJ, 1973. ofCongress,Washington, DC, 1975. 47Papachristodoulou,A. N.,and Culick, F. E. C.,“ FlightMechanics of 51Ferber, F., L’Aviation: Ses D ebuts—´ Son Development´ ,Berger–Levrault, theWright Aircraft, 1903–1912,” AIAA Paper2003-0097, 2003. Paris,1908. 48Wald, Q., TheWright Brothers as Engineers,an Appraisal , published 52Crouch, T., Bleriot´ XI: TheStory of a ClassicAircraft ,Smithsonian bytheauthor, 1999. Inst.Press, Washington,DC, 1982. 49“ALimitedHandling Qualities Evaluation of anIn-Flight Simulation of 53“Pilots:Ken Kellett,” AOPA Magazine,Feb.1989, p. 124. the2003 Wright Flyer,”Air ForceFlight Test Center,Rept. AFFTC-TIM- 01-07,U.S. Air ForceTest PilotSchool, Edwards AFB, CA, April 2001. G. M. Faeth 50Renstrom,A. G., Wilburand Orville Wright—AChronology Commem- FormerEditor-in-Chief

The Wright Brothers Absorbed Nt =Dimensionlesstail Volume, ´T `T0 T = V =Ightspeed Allthat Was Known in Aeronauticsbefore Them, Then Added Their Own 1

The Wright Brothers Absorbed Nt =Dimensionlesstail Volume, ´T `T0 T = V =Ightspeed Allthat Was Known in Aeronauticsbefore Them, Then Added Their Own 1