The Outigge: A Pehistoic Feeback Mechanism Daniel Abamovitch Agilent Laboatoies Communications an Optics Reseach Lab 3500 Dee Ceek Roa, M/S: 25U-9 Palo Alto, CA 94304 Phone: (650) 485-3806 FAX: (650) 485-4080 E-mail: anny@labs.agilent.com Abstact How oes that wok? aske DJ, my 3 yea ol son. We wee staning on the beach at Waikiki, looking at an outigge canoe. He was pointing to the outigge. Like any utiful fathe, I state tying to explain the use of the outigge. Halfway though my explanation, I ealize that I was escibing a feeback mechanism. A cusoy knowlege of Polynesian histoy inicate that this was an ancient mechanism, quite possibly the fist feeback mechanism ceate by humanity, peating the float valve by at least a millennium. This pape is my attempt to chonicle the histoy of this emakable bit of Stone Age contol engineeing. Fig. 1. I. INTRODUCTION The outigge canoe on the beach. Thee ae two types of floating watecaft: those that owe thei buoyancy to the mateial fom which they ae mae, an those that owe thei buoyancy to the amount of wate that they isplace. While the ee boats of Ancient Egypt an the balsa afts of Peu ae in the fome class [1], the ugout canoe so pevalent in Polynesia belongs to the latte class [2]. The ugout canoe suffes fom a tenency to capsize, as compae to plank-built vessels (vessels built of planks attache to some fame). Unlike the latte, thee is limite ability to incease a ugout s esistance to capsizing (i.e. to incease its oll stability) by wiening o changing the shape of the keel. Thus, the ugout canoe begs fo a iffeent solution to the oll stability poblem. At its most basic level, an outigge consists of some sot of a float, attache via one o moe booms to the gunwales (top ege) of a boat. While moen outigges can be mae fom a vaiety of stuy, buoyant mateials, the outigge float has taitionally been some piece of light woo, an the type of boat that it is most often associate with is a ugout canoe. Howeve, outigges ae also foun on plank-built boats, although the necessity is lessene fo these vessels. uiles of plank boats have moe ability to impove oll stability by changing the hull shape than makes of ugout canoes. The action of an outigge is twofol. Fist, it as buoyancy to the vessel, since outigges ae mae of mateials that float iespective of thei shapes. Moe impotantly, the aition of a float at the en of the boom amatically inceases the oll stability of the small canoes to which outigges ae typically attache. Until the publication of Otto May s The Oigins of Feeback Contol [3], [4], the consensus among contol enginees was that the oiginal feeback mechanism built by human beings was Watt s flyball goveno [5]. Howeve, May s wok establishe convincing evience that the wate clock of Ktesibios who live in Alexania in the fist half of the thi centuy.c. was the fist ecoe feeback mechanism [3]. This peate the flyball goveno by two millenia. A seies of othe evices base on the float valve, followe in the succeeing centuies, most of these appeaing in the Mile East. Otto May s book also establishe a set of citeia to etemine if a evice was in fact a feeback mechanism [3]. The thee citeia we have now obtaine contain a sufficiently complete efinition of the concept. iefly epeate, they ae: 1) The pupose of a feeback contol system is to cay out commans; the system maintains the contolle vaiable equal to the comman signal in spite of extenal istubances.
2) The system opeates as a close loop with negative feeback. 3) The system inclues a sensing element an a compaato, at least one of which can be istinguishe as a physically sepaate element. Using these citeia, this pape will ague that the outigge on an outigge canoe, the evice that Heyeahl efee to as the most esiable of the Asiatic navigational inventions ([1],pp. 160 161), is in fact a feeback mechanism. Futhemoe, this evice peates the float valve by at least a thousan yeas, making it the ealiest feeback mechanism built by humans to be ocumente thus fa. The oganization of this pape is as follows. Section II gives a cusoy explanation of the ynamics of boat stability. Section III, iscusses the use of an outigge in poviing oll stability fo a ugout canoe. Section IV gives a qualitative esciption of the opeation of an outigge, specifically how it satisfies the May citeia of a feeback mechanism. Section V elves into the oigins of the outigge an taces its pogession aoun the wol. II. ASIC ROLL STAILITY M R M R,MAX 0 o 45 o 90 o Fig. 3. A typical ighting moment cuve. The ighting moment inceases with inceasing angle until some maximum value, M R,MAX. a a A C D F G a F G a Fig. 4. A cylinical hull has no oll stability, because the cente of buoyancy is always une the cente of gavity. Aing ballast at the bottom as stability. An unballaste hull, mae fom a section of a cyline, has geneally poo oll stability. F F A C Fig. 2. Righting moment fo a typical plank boat hull. (Repouce fom [6], p. 252.) A key component of any watecaft is its oll stability. Put simply, a watecaft with poo oll stability will capsize easily. If the caft is mae of heavie-than-wate mateials, then it elies on the isplacement of wate to achieve buoyancy. In such a situation, capsizing leas to the watelogging of the vessel, which in tun leas to it sinking. Even fo watecaft mae of buoyant mateials, capsizing puts people an cago in the wate. Resistance to capsizing, o oll stability comes fom having a ighting moment that esists angula istubances. Consie the typical plank-built boat coss section in Figue 2. The boat floats because it isplaces wate equivalent to its weight. As long as the boat can isplace moe wate than its weight, it will be buoyant. Fo most boats with bilateal symmety about the cente line, this means that the cente of gavity is above the cente of buoyancy (Figue 2A). When the boat otates aoun its cente of gavity (Figue 2), the cente of buoyancy moves out fom une the cente of gavity, esulting in a moment opposing the otation equal to [F G + F ] a. As long as the cente of buoyancy moves away fom the cente of gavity, the ighting moment inceases. At some point it eaches its maximum, an the moment am an the ighting moment stat eceasing (Figue 2C). As the angle gets lage, the cente of buoyancy gets close to the cente of gavity, loweing the effective ighting moment. A typical shape of a ighting moment cuve is shown schematically in Figue 3. The shape of the hull has a amatic effect on the shape of the ighting moment cuve. In paticula, a pefectly cylinical hull with a cicula coss section, as shown in Figue 4A, has no ighting moment, since fo an angula isplacement, the cente of buoyancy is still ight une the cente of gavity (Figue 4). Aing ballast at the bottom of the hull lowes the cente of gavity (Figue 4C), an allows fo a ighting moment (Figue 4D). Single Outigge Fig. 5. Double Outigge Double Hull Aing outigging to stabilize a ugout hull.
One possibility fo aing a ighting moment to a cylinical hull is to attach it to a secon cylinical hull. The fathe apat the two hulls, the easie it is to geneate a ighting moment (at least fo small angles). This can be one in one of seveal ways. Hee we will concentate on the thee methos most closely associate with outigge technology: a single outigge, a ouble outigge, an a ouble hull canoe, shown in Figue 5. We will see that all thee ae pesent in the sailing technology of the Austonesian peoples 1. They all wok on simila pinciples. The tae-offs in choosing one type of watecaft ove anothe seem to have moe to o with ease of manufactue, stuctual safety, an cew equiements fo each type of caft. Qualitatively, the opeation of the outigge is athe simple. When the canoe otates so as to aise the boom fom the wate, its weight at the en of a moment am povies toque to otate the boom back to the suface. When the otation of the canoe acts to push the boom into the wate, the buoyancy of the boom acts to estoe the boom to the suface of the wate. In othe wos, it senses an esists angula istubances tuly a negative feeback mechanism. III. THE DUGOUT CANOE (a) (b) buoyant foces fo vaious simple shapes of outigge floats as a function of change in ept will be pesente to show the evelopment of ighting moments. A pictoial compaision of plank built an outigge canoes can be seen in Figue 6. Unlike a plank-built boat, a ugout canoe is hollowe out of a single tee tunk. This limits the shape of the coss section to something that closely follows a potion of a cyline. This has a vey small inheent ighting moment, as shown in Figue 7A. In othe wos, the oll stability is poo. Howeve, the aition of an outigge (Figue 7) impoves this situation consieably. Fom a feeback pespective, the outigge as a ighting moment. In Figue 7, the float has a nominal epth of at which the buoyant foce exactly cancels the foce of gavity, i.e. F () =. Fo a istubance that moves the epth away fom the nominal by, M R ( ) = [F ( + ) ] a (1) = [F ( + ) F ()] a. (2) Computing the ighting moment fo iffeent configuations essentially consists of computing F ( + ) F (). Fo a otation of the main hull though an angle θ, the change in epth,, is foun by = L sin θ, (3) while the moment am of the buoyant foce, a, is given by a = L cos θ. (4) This lineaizes fo small θ to = Lθ an a = L. (5) Fig. 6. Compaison of plank built (a) vesus outigge (b) canoe. Note the naow hull of the outigge as compae with the plank built hull. Rectangula Tiangula Cicula L Fig. 8. Diffeent float shapes yiel iffeent eo equations. A Fig. 7. An unballaste hull, mae fom a section of a cyline, has geneally poo oll stability. This is the case fo the ugout canoe on the left. Aing an outigge, on the ight, ceates a ighting moment. This section will pesent a simplifie static analysis of a ugout canoe, showing the effect of aing an outigge. The 1 The tem Austonesian is use by Doan [7] an othes to escibe the geneal set of people that move out of Asia to Austalia an into the Pacific. The name enotes a supeset of the inigenous peoples of Austalia, Inonesia, Malaysia, an Polynesia It is athe staightfowa, albeit teious to compute the buoyant foces fo iffeent float coss sections. This is one in etail in the Appenix, while esults ae pesente hee. Fo all of these coss sections, the equations geneate ae in tems of the nominal epth of the float,, the change in epth,, an the float geomety. In these esults, l is the length of the float, ρ is the ensity of the isplace wate, an g is the acceleation ue to gavity. The fist shape is the ectangula float, shown on the left sie of Figue 8. This is the simplest to compute an is the one that gives a linea eo equation, that is the esultant buoyant foce as a esult of the vetical isplacement,, is F = ρg. (6)
A moe likely pai of shapes fo a float is one with a tiangula coss section o a cicula coss section, at the cente an ight of Figue 8, espectively. Fo the coss section in the shape of an isosceles tiangle, we woul like to calculate the buoyancy as a function of the epth of the section,. In this case the iffeence in foces is given by ( + ) () = [V imm ( + ) V imm ()] ρg (7) = l [A + A ] ρg (8) = l(2 +( ) 2 ) tan θ ρg, (9) 2 whee θ is the angle of the tiangle cone in the wate. Now, the feeback tem is epenent upon the nominal epth,, an has a quaatic component. If we epeat the same set of calculations fo the cicula coss sectional float, we must calculate the aea of the submege segment as a function of the aius,, an the epth,. This esults in a iffeence in foces equal to (, + ) (, ) [( = l 2 Cos 1 ( + ) ( ( + )) ) 2( + ) ( + ) 2 ( 2 Cos 1 ( ) )] 2 2 ρg. (10) Fo small, Equations 9 an 10 both become linea in, which matches physical intuition. IV. THE OUTRIGGER AS A FEEDACK MECHANISM The outigge may have evolve fom the custom of lashing two canoes togethe to povie geate oll stability. Howeve, at fist blush the ouble hulle canoe oes not seem to qualify as a feeback mechanism since the secon hull oes moe than just povie oll stability. Fist of all, unlike the outigge, it is ha to istinguish which hull is the feeback mechanism an which hull is the main pat of the boat. The secon hull also inceases the cago capacity of the ship, an gives it moe length in the wate which eceases the wake an impoves the spee [6],pp: 255 257. The outigge itself povies no such exta capacity an thus its chief pupose is that of oll stability. Fom the pespective of the May citeia, the outigge satisfies all thee: 1) The outigge povies oll stability fo the canoe. That is, it keeps the canoe fom capsizing. In this espect, the contolle vaiable is the angle between the bottom of the canoe an the suface of the wate. 2) The outigge povies negative feeback. Fom a nominal position on the wate, the buoyancy esists otations that woul futhe submege the outigge an the weight esists otations that woul aise it out of the wate. 3) The outigge itself is a sepaate element fom the canoe. It is the sensing element an the actuato fo etecting an coecting otations. Its only pupose is to povie oll stability. The ouble outigge makes the stabilization poblem symmetic by putting a buoyant float on eithe sie of the hull. The ouble hulle canoe also makes the poblem symmetic, by aing a secon hull in paallel to the fist. Retuning to a stict intepetation of the Otto May citeia, the secon hull might not be consiee a feeback mechanism. Howeve, the ouble hull canoe is an obvious membe of the outigge family, spinging fom the same cultue an use in paallel with the outigge canoes. Viewe in the context of othe outigges the ouble hull shoul be seen as a stabilization evice. Thus, we consie all thee foms to be instances of outigge technology. As such, the age of one ove anothe is not citical to unestaning the age of outigge technology, but is useful to stuy. V. THE ORIGINS AND HISTORY OF OUTRIGGER CANOES Fig. 9. Mual epicting ancient Polynesian voyaging canoe in the lobby of the Outigge Waikiki Hotel. Debates about the oigins of outigge technology ae intimately connecte to ebates about who oiginally populate the South Seas, an when an how they i it. Cental to both ebates ae questions about the seawothiness of Polynesian canoes an the skills of Polynesian sailos. The absence of witten ecos an scacity of mateial emains of canoes fuele the ebates 2. The taitional view of Polynesian migation, islan hopping acoss the Pacific in elibeate exploation, was coifie by Pete uck in his classic book, Vikings of Sunise, late 2 The ancient Polynesians ha no witten language. Futhemoe, thee wee no taces of the ancient canoes as they wee mae of soft woos which woul swiftly ecompose in the wam wates of the South Pacific an Inian Oceans.
Fig. 10. Dawing of ouble hull Polynesian voyaging canoe. Fig. 12. The istibution of outigge canoes acoss the wol. Note the boae istibution of single outigges to ouble outigges. Data summaize fom maps in Honell [2] an Doan [7]. Fig. 11. Dawing of Hawaiian style single outigge canoe. eissue as Vikings of the Pacific [8]. This theoy came une attack fom two souces: Tho Heyeahl an Anew Shap. Heyeahl claime that the Polynesian canoes wee too pimitive to sail against the pevailing cuent an win (which blows fom East to West most of the yea in the South Pacific). ase on this ismissal of the Polynesian caft, he popose that Southen Polynesia was settle fom South Ameica while Hawaii was settle by Nothwest Pacific Coast Native Ameicans, who ha oiginally aive at the Vancouve Achipelago in ouble canoes fom Asia by way of the Humbolt cuent [9]. These Nothwest Native Ameicans ha followe the cuents that lea Oegon pines that fall into the ocean to ift to Hawaii. Heyeahl s theoy was populaize by the expeimental voyage of the Kon Tiki, a balsa woo aft which Heyeahl an his cew saile fom South Ameican to Polynesia, mainly by ifting on the pevailing cuents. As the achaeological evience suppote migation fom Asia, Heyeahl s theoies foun little scientific suppot [10]. Anew Shap launche a iffeent attack on the taitional theoies. While he accepte Polynesian migation fom Asia, he claime that the Polynesian caft an sailing methos wee too cue fo anything but acciental migation. He ismisse theoies an stoies of intentional Polynesian exploation as omantic nonsense [11]. Howeve, simulation stuies showe that the pobability of success with acciental migation was infinitesimally small [12]. To counte Shap s an Heyeahl s theoies, a team le by en Finney at the Univesity of Califonia in Santa abaa began a poject to buil a taitional Polynesian ouble hull canoe (shown in a mual in Figue 9 an in a simple awing in Figue 10) an sail it between Hawaii an Tahiti by taitional Polynesian seafaing methos. The voyages of the Hokule`a [13], [10] pove that taitionally built an navigate Polynesian ouble hulle canoes wee capable of voyaging long istances against the win an fining emote islans. The boats pove extemely seawothy, both in thei ability to sail close to the win, thei stability, an thei spee. Thus, the unelying pemise of Shap s an Heyeahl s theoies wee invaliate. Finney also points out that such Kamikaze migation was not vey logical. If one exploes by sailing with the pevailing win an cuent, then etuning home is a eal poblem. Howeve, if one sails against the win an cuent to o exploation, then it is elatively easy to tun aoun an hea home. The latte metho seems much moe likely to ensue the suvival of the exploe. Toay, thee is little ebate that Polynesians ae eive fom the Austonesian peoples. The achaeological evience suggests that the Austonesian peoples migate fom Southeast Asia somewhee between 40,000 an 30,000 yeas ago. Even with the lowe ocean levels of the Pleistocene Ea, this still meant cossing 100 miles of open ocean to get to Austalia [14]. The Austonesians state moving out into the Pacific islans 3500 yeas ago. The lack of seawothiness of ugout canoes, ue to thei stability poblems, implies that one of the outigge mechanisms must have been in use to
make this possible. This pins the minimum age of outigge technology at 3500 yeas. It is quite possibly associate with the migation to Austalia, which woul make it consieably ole [14]. Anothe piece of evience is in the migation fom Asia to Polynesia. The Polynesians use both outigge canoes (Figue 11) an ouble canoes, with the the latte being the pimay vessel fo long ange exploation [13]. Finney points out [13] that the Polynesian cultue itself is necessaily a seafaing cultue: Polynesian cultue evelope not in any Asian o Ameican homelan, but in Polynesia itself. Seafaes ancestal to the Polynesians move fom easten Melanesia to the uninhabite islans of Tonga an Samoa between 1500 an 100.C. They settle thee, an ove the centuies the basic Polynesian cultual patten evelope. Stating about the time of Chist, seafaes, full-flege Polynesians now, move fom these westen Polynesia centes to the east to settle fist pobably the Maquesas Islans an then the Society Islans (the most impotant of which is Tahiti). Stanley also places the oigins of Polynesian migation at aoun 1500-1600.C: Sometime afte about 1600.C., boa-nose, light-skinne Austonesian peoples entee the Pacific fom Inonesia o the Philippines.... Thee thousan five hune yeas ago, the ealy Polynesians set out fom Southeast Asia on a migatoy tek that woul lea them to make the many islans of Polynesia thei home. Geat voyages, they saile thei huge ouble-hulle canoes fa an wie, steeing with huge pales an pananus sails. To navigate they ea the sun, stas, cuents, swells, wins, clous, an bis. Sailing puposefully, against the pevailing wins an cuents, the Lapita peoples eache the ismack Achipelago by 1500.C., Tonga (via Fiji) by 1300.C., an Samoa by 1000.C. Aoun the time of Chist they pushe out fom this pimeval aea, emembee as Havaiki, into the easten half of the Pacific [15]. Given the pobable oigins of the outigge in Southeast Asia an the timing of the migations into the Pacific, we can establish that the outigge likely ates to at least 1500.C., 1200 yeas befoe the the wate clock of Ktesibios. Note that the use of the outigge spanne most of the Pacific an Inian Oceans, fom Easte Islan an Hawaii in the east, to Maagasca in the west. Maagasca itself was fist settle by Inonesians who cosse the Inian ocean in outigge canoes appoximately 2000 yeas ago [2]. To the east, the pimay Polynesian exploation vessel was the ouble hulle canoe, ancesto to the moen catamaan [13]. The single outigge canoe was a technology that they bought with them fo thei smalle caft. One of the main ifficulties with making ouble hulle canoes was fining two matching logs of sufficient size. Among the most pize logs fo canoe builing wee Oegon pines that fell into the ocean an ifte to Hawaii. They wee so value that logs woul be kept fo yeas until a matching one ifte ashoe [2], [9]. The outigge povie equivalent oll stability fo a canoe mae of only one lage log. Heyeahl also points out iffeences between iffeent types of outigge canoes: All though Inonesia, fom Sumata an the Philippines to the neaest tip of New Guinea, the Malays an Inonesians have since ealy times use the ouble outigge to stabilize thei caft, i.e., a buoyant boom fastene to cossbas on each sie of the vessel. The Miconesians an the Melanesians use a single outigge, that is on one sie only, an fo this eason the Miconesians built thei canoes lateally asymmetical. When the Polynesians aopte the single outigge on thei bilateally symmetical canoes they i not follow the Miconesian moel but followe that of neighboing Fiji. In shot, neithe the Inonesian no the Miconesian type of outigge canoe eache the East Pacific [1] (pp. 160 161). Whee each style of outigge fist appeae is a matte of some ebate. Much of the souce mateial on outigge canoes comes fom wok by James Honell, an official who woke in itish Inia in the ealy pat of the twentieth centuy. Honell s joint wok with A. C. Haon [16] emains the efinitive souce book fo most eseach in this aea. Many of the boats ocumente in the thee volumes of Canoes of Oceania have passe fom existence since the book was witten in the 1940s. Afte his etiement, Honell tavele the wol to ocument the evelopment of watecaft [2]. Although thee has been moe ecent wok on the subject, the souce mateial often inclues Honell an Haon s wok, since the isappeaance of many of these watecaft in the past hune yeas have mae thei books the main ocumentation on the vessels. One of the moe ecent stuies was one by Ewin Doan. Doan looke at this same souce evience with moe moen methos an came to opposite conclusions about the elative ages of iffeent outigges in his book, Wangka: Austonesian Canoe Oigins [7]. Section V-A will iscuss Honell s view while Section V- will pesent Doan s. A. Honell s View Outigge canoes ae closely associate with Inonesia. Honell lists Inonesia as the cente of ispesal of the outigge ([2], pp. 263 269). Howeve, Honell goes on to point out that vitually all watecaft technology oiginate in ives an mashes, athe than in the ocean ([2], pp. 264 265). Inonesia, lacking any significant lakes o ives, is then a poo caniate fo the oigins of the outigge canoe. Evience is that the settles of Inonesia migate own fom Southeast Asia, an it is this egion, with its wie ives that is the most likely cale of the outigge canoe. Honell suggests that the Iaway, Salween, an Mekong ives, which have been fom time immemoial the only highways of migation available to the peoples pessing southwas
Fig. 13. Dawing of ouble outigge canoe of style foun in Inonesia. fom the col an eay mountain lans of the noth to the fetile lowe plains, as the likely locations. Nowhee else can the evelopment of the ugout canoe into sailing ships of lage size be so clealy taceable, step by step, as on the geat umese ive. The ugout in geneal use by the ive people, scattee in innumeable villages along its banks, is the most beautiful of its class. Hewn by men possesse of unconscious skill an inbon atistic feeling, the huge teak baulk is fashione into a long an elatively naow caft sheeing upwas in a gaceful cuve towa each en, whee it ises well above the wate line like the hons of a gigantic cescent ([2], p. 265). Honell goes on to place the oiginal outigge caft at ouble outigge with bamboo tunks fo floats [2],(p. 266). Fom these ives, the migation to Inonesia was mae necessaily by watecaft. Thus, fo the outigge to appea in Inonesia, it must have been use in the migation fom Southeast Asia. Heyeahl inicates that outigges [wee] use on local poas 3 in Southeast Asia since the secon millennium.c. ([9], p. 64). The outigges of Inonesia typically have ouble outigges, that is, they have an outigge on each sie of the canoe [2]. This is iagamme in Figue 13, which is base on images in Aian Hoige s book [17]. Honell attibutes 3 A type of Asian boat. this to the elatively sheltee wates of the Inonesian achipelago. As outigges move into moe open wate, the single outigge was stuctually safe. y compaison, the ouble outigge stans a goo chance of suspening the main hull fom the outigges in heavy seas.. Doan s View Doan s wok [7] ebates the theoy of the seawothiness of the ouble outigge an the notion that it is the ealie vesion of the technology. Doan bases his analysis on ispesal pattens centee on Inonesia. He claims that the ouble canoe pecee the single outigge, which in tun pecee the ouble outigge. He claims that Honell s aguments of ouble outigges being less seawothy than single outigges ae pooly suppote by any actual evience. Instea, the evience points to the seawothiness of ouble outigges, as they spea into aeas that aleay ha single outigges. He makes the case that the geogaphic extent of ouble outigge canoes, being a subset of the the geogaphic extent of single outigge canoes, inicates that it is a late technology, emanating fom the cente of invention. (See Figue 12.) Likewise, Doan notes that the pactice of shunting athe than tacking use in Miconesian single outigge canoes une sail is a late evelopment. C. Double Hull vesus Outigge The issue of using a ouble hulle canoe vesus a single hulle canoe with outigge can be seen as an issue of ease of manufactue, human inteface, an capacity. Double canoes equie two vey simila tee tunks to be pesent. Most pize fo canoe making in Hawaii wee Oegon pines that ha fallen into the Pacific an ifte to the islans. In fact, it was common fo a log to be stoe fo yeas until a matching one aive at the Hawaiian shoes [2], [9]. Outigge canoes have no such manufactuing issues, since the outigge will not have any nee to match the main hull. Double hull canoes wee lage evices, equiing seveal men to hanle popely. Thus, such canoes wee inappopiate fo iniviual use. Outigges wee geneally small enough fo a single peson to hanle. Finally, it shoul be note that the mateials use to stap the two hulls of a ouble canoe togethe limite the istance between the hulls. These canoes ha a much naowe aspect atio than thei escenants, the moen catamaan an timaan. Geneally speaking, the weight an buoyant foces on the secon hull of a ouble hull canoe wee lage enough to pouce moments to snap the connecting beams if they wee too long. The smalle outigge booms ha much less weight an buoyant foce, an thus coul allow fo longe booms. D. Shunting Vesus Tacking Among the moe inteesting featues of outigge canoes ae the iffeent ways that these canoes wee saile into the win. While a sailboat cannot sail into the win iectly,
Win [13]. VI. CONCLUSIONS (a) (b) (c) Fig. 14. Sailing into the win: tacking fo a sloop (a), weaing fo a squae igge (b), an shunting fo an outigge canoe (c). (Fom [6], p. 254.) iffeent sailboats can sail close to the win that is at a iagonal angle into the win. The issue then becomes one of how to tun the boat to go on the opposite iagonal as one woks against the win. On a moen sailboat, such as a sloop, the boat pogesses against the win by tacking (Figue 14a). In this case, the bow of the boat always is angle into the win. When the boat tuns, the sail goes slack as the boom swings to the othe sie an the win fills the sail again. This oes not wok fo a squae igge which at some point in a tack woul en up with its sails being pushe backwa by the iect win. Instea, squae igges ae tune by a looping metho known as weaing (Figue 14b). Although most of the outigge canoe sailing against the win is one by tacking, thee is a subset of the outigge canoes that employ what is known as shunting (Figue 14c). In oe to keep the outigge on the winwa sie, the Miconesians sail in one iection an then pull to a stop. Since they on t want to have the outigge on the leewa (away fom the win) sie, they change the position of the sail so that the sten is now the bow (longituinally symmetic boat) an then they zag back that way. Having the outigge on the leewa sie coul cause it to plow into the ocean an capsize the boat. Thus, a bias foce can push the system out of its stable zone an into a positive feeback situation. They o the shunting to stay in the negative feeback egion [6]. This is in contast to tacking. The font of the boat is still the font of the boat. In tacking, the winwa sie an leewa sie change with evey iection change. In the case of shunting, the bow becomes the sten an the sten becomes the bow. To o this, they physically move the mast. Thus, the winwa sie an the leewa sie neve change. Shunting is a elatively ecent aition to the sailing techniques. In fact, Doan points out that shunting is one by Miconesians [7], but not by Polynesians, even though both use a single outigge configuation. Malaysians use ouble outigges, which makes shunting useless. Likewise, ouble canoes (fobeaes of moen catamaans) simply tack [7], Fig. 15. Moen outigge canoe iing a wave. When fully consiee, the outigge technology, whethe use as a single outigge, ouble outigge, o a ouble hulle canoe, is tuly emakable. y solving the poblem of oll stability fo ugout canoes, it amatically incease the seawothiness of these caft, allowing the Austonesian people to coss the vast eaches of the Pacific an Inian Oceans. This was one by a Stone Age cultue with no witten language, no metal woking, an no plank-built boats. As a best estimate, this feeback mechanism peates the wate clock by at least 1000 yeas. Futhemoe, while the wate clock was an inteesting execise, it i not achieve a boa penetation into society as a timekeeping evice. That task woul be pefome by the mechanical clock. The outigge, howeve, by amatically inceasing the sea wothiness of the Austonesian canoes, beas at least pat of the esponsibility fo the boa colonization of islans fom Maagasca to Polynesia, an by that espect, to the vey existence of the Polynesian people. ACKNOWLEDGMENTS This pape woul not have happene without the mechanical inquisitiveness of my son, D.J. Fo putting me on this path, an fo many othe things, I owe him my gatitue an paental amazement. In eseaching the pape, I once again got a huge amount of help fom the eseach libaians at Agilent Labs. In paticula, Ron Roiguez was tieless in fining exta efeences an souces fo mateial on these ancient evices. I also got a lot of encouagement an assistance in making this pape moe legible fom Calene Stephens of the National Museum of Ameican Histoy (NMAH). I also appeciate the assistance of Calene s colleague, D. Paul F. Johnson, Cuato of Maitime Histoy at the NMAH, who gave me some excellent pointes to efeence mateials an Polynesian migation theoies. D. Richa augh, of Hewlett-Packa Laboatoies, who actually buils stone age
tools in his gaage, an his wife Macia also povie some highly useful efeences. Teil Hust, of Hewlett-Packa Laboatoies, mae his usual stong attempt to impove my witing style. Finally, I vey much appeciate the suppot of my management at Agilent Laboatoies fo allowing me to epesent the Labs with this wok. Rectangula Tiangula Cicula VII. REFERENCES Fig. 16. Diffeent float shapes yiel iffeent eo equations. [1] T. Heyeahl, Ealy Man an the Ocean: A Seach fo the eginnings of Navigation an Seabone Civilizations. Gaen City, NY: Doubleay & Company, 1979. [2] J. Honell, Wate Tanspot: Oigins & Ealy Evolution. Lonon: Davi & Chales, 1970. [3] O. May, The Oigins of Feeback Contol. Cambige, MA: MIT Pess, 1970. [4] O. May, The oigins of feeback contol, Scientific Ameican, vol. 223, no. 4, pp. 110 118, 1970. [5] N. Wiene, Cybenetics, Secon Eition: o the Contol an Communication in the Animal an the Machine. Cambige, MA: MIT Pess, 2n e., Mach 15 1965. [6]. Cotteell an J. Kamminga, Mechanics of Pe- Inustial Technology. Cambige: Cambige Univesity Pess, 1990. [7] E. Doan, Wangka: Austonesian canoe oigins. College Station: Texas A & M Univesity Pess, 1981. [8] P. H. uck, Vikings of the Pacific. Chicago, IL: The Univesity of Chicago Pess, 1959. [9] T. Heyeahl, Ameican Inians in the Pacific: The Theoy ehin the Kon-Tiki Expeition. Lonon: Geoge Allen & Unwin. Lt., 1952. [10]. R. Finney, Voyage of Reiscovey: A Cultual Oyssey Though Polynesia. ekeley, CA: Univesity of Califonia Pess, Mach 1995. [11] A. Shap, Ancient Voyages in the Pacific. Hammonswoth, Milesex, Geat itain: Pengin, 2n e., 1957. [12] G. Iwin, The Pehistoic Exploation an Colinization of the Pacific. Cambige, UK: Cambige Univesity Pess, 1992. [13]. R. Finney, Voyaging canoes an the settlement of Polynesia, Science, vol. 196, pp. 1277 1285, 1977. [14]. Fagan, Outigges to the outback, Achaeology, vol. 43, pp. 16 18, July-August 1990. [15] D. Stanley, Moon Hanbooks Tahiti - Incluing Easte Islan an the Cooks. Chico, CA: Moon Publications Inc., fouth e., May 15 1999. [16] A. C. Haon an J. Honell, Canoes of Oceania. Honolulu, HI: ishop Museum Pess, 1975. [17] A. Hoige, Outigge Canoes of ali an Maua, Inonesia. Honolulu, HI: ishop Museum Pess, 1987. APPENDIX: CALCULATION OF UOYANT FORCES FOR VARIOUS FLOAT SHAPES Qualitatively, the opeation of the outigge is athe simple. When the canoe otates so as to aise the boom fom the wate, it s weight at the en of a moment am povies toque to otate the boom back to the suface. When the otation of the canoe acts to push the boom into the wate, the buoyancy of the boom acts to estoe the boom to the suface of the wate. The buoyancy of the float is easy enough to calculate fo seveal of the typical shapes. The fist of these, the ectangula float, on the left sie of Figue 16 is the simplest to compute an is the one that gives a linea eo equation. ΣF y = W =0. (11) Fo a float with a ectangula coss section an aea, a, the weight of the float, equals the weight of the isplace wate: = = V imm ρg, (12) whee V imm is the volume of the immese potion of the float, i.e. V imm = A b, (13) whee A b is the aea of the boat bottom, is the epth of immesion, ρ is the ensity of wate, an g is the acceleation ue to gavity. Now, let s assume that the epth of the float is istube away fom the nominal,, by : ΣF y = W = F (14) = ρg( + )A b (15) = ρga b + ρg (16) Since the fist two tems cancel in equilibium, we aive at the esultant buoyant foce as a esult of the vetical isplacement is F = ρg. (17) In othe wos, the float esists any change away fom equilibium as expecte. A ectangula coss section on a float is convenient fo calculation as it leas to a linea eo equation (Equation 17). Howeve, it is less likely that a tiangula coss section o a cicula coss section, at the cente an ight of Figue 16, espectively.
Fo the coss section in the shape of an isosceles tiangle, we woul like to calculate the buoyancy as a function of the epth of the section,. Applying Equation 12 again, we have V imm = A l, (18) whee l is the length of the float into the page an A is the aea of the submege tiangula coss section as a function of. A = 1 b, (19) 2 whee b is the base of the tiangle. We can calculate this fom the angle of the submege cone, θ, an the epth,, by tan θ b 2 = 2 (20) so b =2tan θ 2, (21) an A = 1 2 (2 tan θ ) 2 (22) = 2 tan θ 2. (23) Again, we change the epth away fom nominal by so that Finally, A + =( + ) 2 tan θ 2, (24) A + A =(2 +( ) 2 ) tan θ 2. (25) ( + ) () = [V imm ( + ) V imm ()] ρg (26) = l [A + A ] ρg (27) = l(2 +( ) 2 ) tan θ ρg, (28) 2 whee l is the length of the float, θ is the angle of the submege coe, ρ is the ensity of wate, an g is the acceleation ue to gavity. Now, the feeback tem is epenent upon the nominal epth,, an has a quaatic component. If we epeat the same set of calculations fo the cicula coss sectional float, we must calculate the aea of the submege segment as a function of the aius,, an the epth,. A segment (, ) = 2 Cos 1 ( ) 2 2. (29) when the float ises out of the wate, we see that as 0, both the fist an secon tems ten to 0. The buoyant foce is thus [ (, ) =l 2 Cos 1 ( ) ] 2 2 ρg. (30) If we consie to be the equilibium epth fo a given float mateial an aius, then the foce opposing any isplacement,, is (, + ) (, ) [( = l 2 Cos 1 ( + ) ( ( + )) ) 2( + ) ( + ) 2 ( 2 Cos 1 ( ) )] 2 2 ρg. (31) Fo small, Equations 28 an 31 both become linea in, which matches physical intuition.