Formal Variation in Australian Spear and Spearthrower Technology 9780860546931, 9781407348414

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Formal Variation in Australian Spear and Spearthrower Technology

B. J. Cundy

BAR International Series 546

1989

B.A.R. 5, Centremead, Osney Mead, Oxford OX2 ODQ, England.

GENERAL EDITORS A.R. Hands, B.Sc., M.A., D.Phil. D.R. Walker, M.A.

BAR -8546, 1989: 'Formal Variation in Australian Spear and Spearthrower Technology' @ B. J. Cundy, 19U9

The author’s moral rights under the 1988 UK Copyright, Designs and Patents Act are hereby expressly asserted. All rights reserved. No part of this work may be copied, reproduced, stored, sold, distributed, scanned, saved in any form of digital format or transmitted in any form digitally, without the written permission of the Publisher. ISBN 9780860546931 paperback ISBN 9781407348414 e-book DOI https://doi.org/10.30861/9780860546931 A catalogue record for this book is available from the British Library This book is available at www.barpublishing.com

FORMAL VARI ATION AUSTRALIAN

SPEAR AND

B . J.

IN

SPEARTHROWER

CUNDY

1

TECHNOLOGY

TABLE OF CONTENTS page Acknowledgements

iii

One 1 .1 1 .2 1 .3 1 .4

-T echnology and Artifact Variations I ntroduction Artifact Variation Historical Perspective Sources of Technological Variation

1

Two 2 .1 2 .2 2 .3 2 .4 2 .5 2 .6

-T echnological Comparison a nd P erformance Technological comparison Hand Thrown Spears on the Mainland The Tasmanians and s ome other e xamples The Spearthrower Accuracy Spearthrower Advantage: a hypothesis

9

Three 3 .1 3 .2 3 .3 3 .4

-A erodynamic Factors Vacuum Ballistics Projectile Aerodynamics Construction and S tability Australian Spear Construction a nd Aerodynamic S tability

1 2 7

1 0 1 1 1 2 1 3 1 6 21 2 2 2 4 2 7 3 1

Four -W ounded Ballistics 4 .1 Momentum, Energy and P ower 4 .2 Shape and S ize 4 .3 Wound Energy 4 .4 Barbing

3 3

Five 5 .1 5 .2

3 8

5 .3 5 .4

Six 6 .1 6 .2 6 .3 6 .4 6 .5 6 .6

-P ropulsion The Dynamics o f Throwing Models of Spearthrower Operation ( A) Impulse and the L inkage Models ( B) The Lever Model Kinesiological Analysis Spearthrower Rotational Dynamics ( A) Static l oading ( B) Rotation dynamics ( C) Dynamic l oading -S pear and Spearthrower Articulation Static Models Dynamic Models Spear Spine Spear Mass and Spearthrower Length and Mass Performance L imitation and Construction Variation Evidence f or the S tructural R elationships

i i

3 4 3 5 3 6

4 1 4 5 4 8 5 4 5 5 5 8 61 6 2 6 4 6 9 7 1 7 3

Seven 7 .1 7 .2 7 .3 7 .4 7 .5 7 .6

-S tructural Relationships Expected G eneral R elationships The Samples Spear and Spearthrower Masses Spearthrower Length and Mass Spearthrower Moments o f I nertia Spear Energy

75

Eight 8 .1 8 .2 8 .3 8 .4 8 .5 8 .6 8 .7 8 .8 8 .9 8 .10 8 .11

-S pear a nd Spearthrower Forms Central A ustralian Spearthrowers Central A ustralian Spears North Australian ( NA) Cylindrical Spearthrowers North Australian Notched Lath Spearthrowers E ast Arnhem Land Spearthrowers E ast Arnhem Land Spears North-western Northern Territory Spearthrowers North-western Northern Territory Spears Goose Spearthrowers Goose Spears Sabre Spearthrower

8 7

Nine

-C onclusion: With Some Implications f or the S tudy of Hunter-Gatherer Technology

Bibliography

7 6 7 8 8 1 8 4

9 5 1 04 1 07 1 07 1 09 13 1 15 1 16 1 19 1 1 20

1 24 1 27

ii i

ACKNOWLEDGEMENTS

This monograph i s based on an MA t hesis completed i n 1 980 at the Australian National University and refers principally to works published before t hat date. Many people have been i nvolved i n the production o f both the thesis and this monograph over t he past t en years. F irstly, my original s upervisors, P rofessor I sabel McBryde, Andree Rosenfeld and Wilfred S hawcross who bore the bulk of the proofreading. A s f ilm r ecords p layed an important role i n this work the f ilm d epartment of the Australian I nstitute o f Aboriginal S tudies must a lso b e thanked f or the u se o f their editing m achine and f ilm s tock. Thanks are a lso due to the curators and s taff o f the Australian Museum, National Museum and what i s now the National Museum o f Australia, e specially Ron Lampert, Alan West and Mrs Keith f or permission to u se their collections. The National Museum a lso g ave a ccess to the Donald Thomson collection. Time and expertise was a lso contributed by Bill Atyeo ( Forestry -A NU) Kari B arz, Marjorie S ullivan, P eter Lauer and Betty Meehan. The Australian Museum a lso provided a grant to cover the cost o f photographic equiment. Chris Haigh o f the Northern Territory Museum o f Arts and S ciences a lso patiently c orrected drafts and r etrieved the work f rom a computer l imbo. F inally, B rian Cotterell and Johan Kamminga provided encouragement.

i v

ONE TECHNOLOGY

1 .1:

AND ARTIFACT VARIATION

Introduction

S pear a nd spearthrower t echnology was once f amiliar t o a wide r ange o f h unter-gatherer s ocieties ( see Garrod, 1 955; K ellar, 1 955; Krause, 1 902; von Luschan, 1 896), yet, t o the prehistorian the performance characteristics and t he mechanical p rinciples which g overned the operation o f t his t echnology r emain l argely unknown. The a im o f this w ork i s t o p rovide a n i ncreased understanding o f one o f m an's s implest and possibly o ldest t echnologies, by d efining these principles a nd r elating them t o the s tructural variation extant i n a r egional s ample oof A ustralian s pear and s pearthrower f orms. The combination o f both s pears a nd s pearthrowers a s a s ingle unit o f analysis i s a d eparture f rom c onventional m aterial culture methodology which h as i solated each a s an i ndividual e lement. Knowledge o f t he operation o f t echnological s ystems i s e ssential t o t he prehistorian's a ppreciation o f the s tructural variation which can o ccur w ithin the a rtifacts a ssociated w ith a g iven t echnology. I n this r egard, Australian s pears a nd s pearthrowers i ncorporate a w ide variety o f f orms which h ave g enerally b een l inked w ith ' cultural' or ' adaptive' variation. B efore s uch a ssessments c an b e made, t he t echnological b asis f or this v ariation must b e more c learly defined. The r ange o f s pear a nd s pearthrower f orms will be r epresented by a s ample drawn principally f rom Central A ustralia a nd t he n orthern h alf o f the N orthern Territory. T he sample c overs a wide variety o f s pearthrowers r anging f rom s imple cylindrical t o h ighly d eveloped l ath f orms and a comparable r ange o f s pear types. I t a lso encompasses an e nvironmental r ange f rom a rid t o t ropical and a llows an a ssessment o f the way i n which material availability a ffected f orm. The s pearthrower was n ot universally adopted t hroughout Aboriginal s ociety b eing a bsent i n Tasmania, M elville a nd B athurst I slands, p art o f t he Queensland c oast a nd possibly p arts o f s outhern Q ueensland, n orthern N ew South Wales a nd e astern S outh Australia ( Davidson 1 936:453). T his r aises the q uestion o f what, i f a ny, p ractical a dvantage t he a doption o f t he s pearthrower c onfirmed upon i ts u sers. The problem i s e ssentially one o f a ssessing t he p erformance c apacities o f t echnologies w hich, i t i s a rgued, may n ot b e d irectly c omparable. A lthough an e xamination o f t he e thnographic a ccounts o f b oth h and thrown a nd s pearthrower t echnologies s hows this t o be t he c ase on t he mainland t he T asmanians appear t o 1

have a chieved h and t hrown p erformances c omparable t o that o f the s pearthrower u sing groups. This c omparability derives f rom t he c omplex manner i n which Aboriginal s ociety appears t o h ave u tilized t his c hange i n extractive t echnology.

1 .2:

Artifact Variation

A s s pears and s pearthrowers a re e lements o f m aterial culture, an a nalysis o f t heir morphological variation must be conducted w ithin a f ramework which d efines the o rigins o f variation f or e lements o f material c ulture. U sing a systematic model, c ulture i s s een a s " a complex o f i nteracting e lements" or s ub-systems ( Layton, 1 973:499). Although there i s d ifficulty i n defining the n ature o f the system ( Wood a nd Watson, 1 973:673-674) a nd the e lements or s ub-systems which c ompose i t, t he m odel h as a d efinite advantage f or material c ulture s tudy. The s ub-systems, r egardless o f t heir s tructure or h ierarchical r elationship, must operate i n two major f unctional f ields. These were d efined by White ( 1959:8) a s, " relating man t o h is environment" a nd regulating i nteraction w ithin t he s ociety. W hite ( 1959:10) a lso argued that t he t hree s ub-systems o f c ulture are: i deological, s ociological and t echnological. B inford ( 1962) l ater a dapted t hese i nto categories o f m aterial culture objects: t echnomic, s ocio-technic and i deotechnic. He originally proposed that these represented categories o f a rtifacts which operated t otally w ithin s ingle s ub-systems. The a rgument t hat v ariation could not be viewed a s b eing d ependent on a ny s ingle source was directed a t t he v iew h eld by t he i deational or normative approaches o f a nthropology, which r educed a ll variation t o differences i n i deas, a llowing e xplanation v ia a s ingle s et o f i nterpretive principles. B inford ( 1972:17) l ater a cknowledged t hat t he problem w ith h is i nitial c lassification was t hat i t proved p ractically impossible t o define an object which operated t otally within a s ingle s ub-system. Artifacts d o n ot operate i n s ingle s ub-systems, t heir morphological variations a r esult o f i nputs f rom the various s ub-systems o f the entire culture. I t i s a ssumed that the n umber o f morphological e lements s temming f rom a s ub-system, manifest i n a ny a rtifact, will be d irectly proportional t o t he magnitude o f the a rtifact's operation i n that s ub-system. The d esign o f a c rown, f or e xample, may be more a dequately explained b y r eference t o i ts f unction i n t he s ocial a nd i deological s ub-systems a s a symbol o f p ower, t han i ts r ole i n t he t echnological, a s h ead protection. The problem which a rises f rom t his view i s t hat o f i dentifying which s tructural e lements a re a product of a g iven s ub-system. T o overcome t his t he analysis o f 2

v ariation i n a rtefacts i n g eneral, a nd s pears and s pearthrowers i n p articular, s hould be c arried out via a d etailed analysis o f t heir f unction i n t he t echnological s ub-system. I n t his s ystem t he a rtifact's variation can b e most e asily r elated t o t he operational and e nvironmental f actors which may a ffect i ts f orm ( Binford, 1 962). Once t hese h ave b een i solated, those e lements which a re s ignificant i n t heir operation i n o ther s ubs ystems can b e more easily r ecognized. This approach d epends on a f ormal c lassification o f traits, and n ot a s i nitially proposed by B inford ( 1962), o f a rtifacts, being r elated t o a g iven s ub-system. As s pears and s pearthrowers i n Aboriginal s ociety f unctioned m ainly i n a rticulating man with the e nvironment, a s a n extractive t echnology, much o f their v ariation i s e xplicable i n t erms o f t echnological f actors. T his c onclusion h as, h owever, n ot been s upported by p revious analyses, which h ave g enerally c oncluded quite t he opposite.

1 .3:

Historical P erspective

Although t here h ave been f ew s tudies d irected a t a s pecific analysis o f Australian s pear a nd s pearthrower v ariation, c omments a bout t he s pearthrower i n Australia a re a s o ld a s a ny a ccounts o f the Australian Aborigine. A s new f orms were s till b eing d escribed ( Etheridge, 1 982), i t was n ot u ntil l ate i n t he n ineteenth century, that e nough i nformation was a vailable f or t he variation i n s pear and s pearthrower f orm t o b e f ully a ppreciated. Most d iscussions o f v ariation were i ncorporated i n e thnographies ( eg. Smyth, 1 878). These works were mainly d escriptive, r elying h eavily on E uropean i nformants or a lready published s ources. The f irst w ork t o d eal s pecifically w ith Australian s pear throwers was von L uschan's D as Wurholz i n NeuH olland and i n O ceanien p ublished i n 1 896. Von L uschan's w ork i s mainly d escriptive b ut f ollows many o f t he other s pecialist writers o f t he d ay i n o ffering hypotheses about t he origins o f u nusual f orms. There w as a t t his t ime a n extensive i nterest i n m aterial culture s tudies t hroughout t he world, e specially i n artifacts l ike t he s pearthrower ( see B ahnson, 1 889; K rause, 1 902; M ason, 1 884, 1 893; Murdoch, 1 890; S eller, 1 890; S tolpe, 1 890). The b elief t hat c ontemporary h unterg atherer s ocieties w ere " palaeolithic r eflections" and t hat a s tudy o f t heir material c ulture c ould n ot only s upplement t he a rchaeological r ecord, s uch a s i t was, but a lso b e u sed t o d evelop a nd d ocument evolutionary s equences themselves, s eems t o h ave b een t he r ationale b ehind much o f t his r esearch ( see Myres, 1 906); t he more i nformation t hat w as a vailable t he more d etailed the k nowledge o f a g iven e volutionary s equence. This approach 3

i s evident i n works l ike Mason's The O rigins o f ( 1895), i n which Mason s ets o ut d evelopmental and c ites e thnographic examples a ppropriate evolutionary phase ( see Mason, 1 895:376-382 development o f ballistic t echnology).

Invention s equences to e ach f or the

The i ncreasing i nfluence o f t he B oasian p articularist s chool o f anthropology s eemed t o l imit t his f orm of research, l eaving many r esearchers d isinterested and unfamiliar with the s tudy o f material c ulture f rom a technological or evolutionary s tand p oint. The m ainly American b ased s chool o f t he h istorical d istributional approach ( Binford, 1 972:213) c ontinued, h owever, to s tudy artifact variation a t a g eneral l evel. This s chool, a s exemplified by the work o f Wissler ( 1926), was centred on the belief that r ecorded g eographic d istributions of material culture e lements or b ehaviour a ssociated w ith them could be u sed t o d emonstrate d iachronic historical relationships a nd therefore r econstruct prehistoric change. A s this methodology underlies o ne o f the m ost i nfluential s tudies o f s pear a nd s pearthrower variation a ttempted i n Australia, t he problems a ssociated with the approach will be o utlined i n d etail. F irstly, i t m ust a ssume that a ll e lements c an b e t reated, r egardless of their f unction, a s equal. S econdly, t hat e lements w ill move out f rom their s ource a t a u niform v elocity, and t hat they will be a dopted equally by a ll p eople who a re in contact with them. Thirdly, t hat t here a re two s ources of e lement variation: external ( transmitted by d iffusion f rom o ther cultures) a nd i ndependent i nnovation. The r easons f or the d evelopment o f a g iven i nnovation a re not emphasised, a nd a ppear t o b e p art o f a n a ssumed unilinear evolutionary cultural d evelopment. D ue t o the a ssumption o f u niform r ates o f diffusion the origins o f a t rait may b e d iscovered by s tudying i ts d istribution. F or example, a s et o f concentric d istributions i ndicates a s table s ource o f i nnovation a s the o ldest traits a re f urthest away f rom t heir c ommon point o f origin. The method d epends o n t he existence o f a s table s ource o f i nnovation, a lthough n o a ttempt i s m ade t o explain i ts s tability. E xternally d erived traits can be i dentified by their proximity t o a n e xternal s ource. This a pproach i s a lso d ependent o n a typology of traits. A s t he g eographical d istributions a re of t raits or g roups o f t raits f orming types, varying t he types w ill a lso change the d istributions. The r esult i s a different s et o f apparent h istorical r elationships. The dependence on t he a ssumption, that a ll t raits a re a nalytically e qual i s a lso a weakness with t he a pproach. A s t he variation within a rtifact g roups w as u sed a s t he b asic unit o f the analysis, n ot i ts s ubject, t he o rigin o f variation h ad to be a scribed t otally t o v ariation i n i deas; unaffected by i nteraction w ith t he environment o r p roblems of 4

a daptation. A s t he t raits c an n ot r epresent equivalent h istorical entities, the r esult o f a s eries o f s uch s tudies f or a g iven area, i s a l ist o f externally and i nternally d erived traits, whose s pecific synchronic and d iachronic r elationship i s n ot explained. Davidson ( 1934, 1 936), f ollowing this methodology, a ttempted t o d efine the h istorical r elationship o f a n umber o f Australian c ultural traits. H is s tudy o f s pears a nd spearthrowers i s the most extensive d ealing with the v ariation i n t hese a rtefacts. A lthough Davidson was i nterested i n t he " derivation o f the varieties", the problem a s h e s aw i t, was primarily one o f a scribing variation t o e ither i nternal d evelopment or external i nfluence. D avidson was f ully aware that the analysis o f t rait d istribution r equired the t raits t o be equivalent a nd unencumbered by a daptive considerations. F or example, i n his conclusion t o " Australian S pear Traits and their D istributions" t he s tated: There i s n othing t o s how that even the variations are t he results o f a ttempts t o meet certain n eeds, r eal or f ancied. ( 1934:160). T he o f:

origin

o f

v ariation

was

i n

Davidson's

view

the

r esult

. ..accidental combination or experimentation which, t o t he mind o f, or i n t he experience o f the n ative, d emonstrated c ertain s uperiorities. ( 1934:160)

Although t his s tatement s eems c ontradictory i n the l ight o f h is c onclusion, D avidson a rgued that Aborigines w ere s o i nconsistent what t hey s aw a s an advantageous t rait, that a t rait's distribution bore l ittle r elationship t o any problem s olving r eality which i s n ot " culturally" d ependent. D avidson c oncluded: For h istorical problems i t would a ppear, t herefore, that f unction may be o f s econdary importance and that the l ocal f unction o f a ny t rait may b e the r esult o f h istorical f actors, s uch a s t he c ultural background o f t he t ribe which a cquires t he n ew t rait, t he cultural b ackground o f t he tribe f rom which i t was obtained, a nd t he f orces r esponsible f or i ts diffusion a t a ny particular t ime. ( 1934:160)

Davidson, f or example, q uite c orrectly argued that the u se of s pearhead f orms varied f rom t ribe t o t ribe and t here a ppeared t o h ave been l ittle c onsistency i n u se o f a g iven f orm. I t i s a rgued, h owever, that he was u njustified i n a ssuming that a ll t raits exhibited s imilar i nconsistency.

5

Davidson ( 1934) produced a chronology o f t raits w hich divided i nto both external ( from N ew G uinea) and i ndigenous f orms. I n r ough chronological order they a re a s f ollows: ( A ) External - 1) p lain o ne-piece spears, 2 ) " death" s pears ( spears with s tone chips a long the h ead), 3 ) barbs c ut i n t he s olid, 4 ) t he s pearthrower, 5 ) r eed s pears, 6 ) d etachable barbs, a nd 7 ) m iscellaneous ( eg. s tingray spine h eads); B ) I nternal - 1) composite wood s pears, 2 ) three p iece c omposite s pears, 3 ) r ound w ooden detachable barbs, 4 ) f lat wooden d etachable barbs, 5 ) quartzite s pearheads and 6 ) K imberley s pearheads ( finely chipped bifacial p oints). The validity o f this chronology i s s econdary t o t he argument f orwarded i n this work, t hat the origins o f t raits i s o f s ubsidiary i nterest u ntil their operation i n the t echnological s ub-system i s examined. The l ist d oes s erve, h owever, t o i llustrate the traits which were u sed i n D avidson's s tudy. A lthough t hey a ll r elate t o construction, they a re f ar f rom equivalent i n terms o f their operation i n the t echnological s ubsystem. I n 1 936 D avidson p ublished The S pearthrower i n Australia. L ike h is 1 934 a rticle, i t i s a d etailed and comprehensive s tudy. A lthough n ot explicitly s tated, he was again i nterested i n p roducing c hronological r elationships b etween s pearthrower a nd s pear f orms. Unlike the s pear, h owever, t he s pearthrower was n ot universally d istributed among t he A borigines, and was extremely varied i n f orm. The d istribution o f s pearthrower f orms did n ot r epresent " ideal" d istributions, and D avidson was unable t o d evelop a r elative chronology o f f orms, a lthough h e d id l ink s pecific s pear f orms with the arrival o f the s pearthrower f rom N ew G uinea. The extensive variation i n Australian s pearthrowers i s s hown by h is extensive t ypology w ith i ts t hree c lasses, thirteen types and e ight varieties. The origin o f this variation Davidson ( 1936:445) again a scribed t o t he a lteration by the Aborigines o f t he primary New G uniea type " to s uit their own i deas". The primary type i s n ot described. The h istorical-distributional a pproach i n g eneral a nd D avidson's work i n particular, c ame under s ubstantial criticism f rom R adcliffe-Brown ( 1930). Mulvaney ( 1975:121) p oints o ut that i t i s p ossibly a s a result o f R adcliffe-Brown's i nfluence t hat t he u se o f material culture s tudies h ave t ended t o l anguish i n Australia s ince the 1 930's. F ollowing D avidson, M cCarthy ( 1940, 1 957, 1 963) i n considering the s ources o f material c ulture variation, concluded that most o f t he major f eatures were t he products o f d iffusion f rom external s ources. He a rgued more s pecifically, h owever ,that variation i n spearthrowers e specially t he Central A ustralian f orms, was due t o adaptive pressure f or the n eed t o c onvert the s pear thrower i nto a multi-purpose i mplement. M cCarthy concluded: 6

Thus, a s a s ubstitute f or a nother domestic article which would h ave t o be c arried, the s pearthrower s erves many u seful purposes w ithout i mpairing i ts e fficiency, and h as been modified l ocally ( 1940:249). M cCarthy d id n ot extend s pearthrower varieties.

this

approach

t o

o ther

The s econd major s tudy o f Australian s pearthrowers was c arried out i n 1 970 by K elly. Her s tudy i s an excellent s urvey o f t he l iterature v irtually exhausting the e thnographic a nd e thno-historical s ources f or any g iven s pearthrower f orm. The a im o f h er s tudy was t o explain t he variety o f s pearthrowers by examining how they were u sed. Kelly ( 1970:139) concluded, h owever, that " historical" f actors were more important t han those r elated t o s econdary f unction or t echnical e fficiency i n i nfluencing t he spearthrowers f orm. This c onclusion was e ssentially a n affirmation o f D avidson's a rguments. The major methodological problem o f Kelly's analysis w as her t otal r eliance on t he e thnographic l iterature. T his l iterature, a lthough extensive, i s o f l imited value f or the testing o f complex theories o f e fficiency, s imply b ecause i t does n ot contain t he r elevant i nformation. Palter's ( 1977) s tudy o f variation i n Australian s pears t ook a d ifferent a pproach. I n t esting D avidson's s tatement that h and thrown s pears were h eavier than s pears t hrown by the s pearthrower, h e c oncluded that much o f the c onstructional variation would b e d irectly related t o the a erodynamics o f i n-flight s tability. This a rgument will be d iscussed i n more detail i n Chapter 3 . Past s tudies h ave, t herefore, n ot f orwarded any c onsistent view o f variation w ithin Australian s pears and s pearthrowers. The r easons f or t his a re c losely l inked w ith changes i n a im, c onceptual b asis and methodology i n m aterial culture s tudy over t he l ast h undred years. One o f the major problems c ommon t o a ll these s tudies h as been t he d ivision o f s pears a nd s pearthrowers i nto s eparate a nalytic units. A f urther problem which b eset many o f the l atter a ttempts, was t hat variation i n f orm could n ot b e a dequately c orrelated w ith variation i n the a rtifact's o peration i n t he t echnological s ub-system.

1 .4:

S ources o f T echnological Variation

I t h as b een s uggested t hat s pears and s pearthrowers, a s artifacts which a rticulate man w ith the environment, v ia the t echnological s ub-system, exhibit s tructural v ariation which i s r elated t o t his f unction. Artifact v ariation s temming f rom o peration i n the t echnological 7

s ub-system will d erive f rom variation i n t he control of energy expenditure i n t he s ub-system. A s White ( 1959:545 ) points o ut, there a re two b asic m eans o f controlling this expenditure. The f irst i s t hrough modification of t ask performance, a nd s econd t hrough t he c ontrol o f the energy n eeded f or t he p roduction a nd u se o f the t echnology. Taking the f ormer o f t hese a spects i t i s argued that i n the case o f s pear a nd s pearthrower t echnology t he task p erformance i s n ot a s s elf-evident a s may i nitially be a ssumed. Optimizations f or d ifferent performance characteristics h ave h ad very s ubstantial e ffects o n the s tructure o f both s pears a nd s pearthrowers. The s econd a spect, the control o f p roduction a nd u se c ost, i s an extremely complex s tructure which may b e d ivided i nto: u se cost, ( which this i s equivalent t o the s kill n ecessary f or the manipulation o f t he t echnology a nd t he e ffort e xpended i n i ts u se), and materials, manufacture, and maintenance costs. Control o f these cost e lements m ay b e optimized to minimise the cost o f e ach or f or t he production o f a s pecific p erformance c haracteristic r egardless of production or u se c osts. T he i nter-relationships b etween p erformance a nd p roduction optimizations i s f undamental to both ' adaptive' a nd ' cultural' i nterpretations o f a rtifact variation. These r elationships must b e explored b efore the s ignificance o f a rtifact variation c an b e a ssessed. I t i s n ecessary i n t his a pproach t o provide a f ramework i n which s tructural variation c an be l inked with d ifferent p erformance characteristics. A fter examining t he p erformance o f s pears t hrown by t he s pearthrower, the f irst part o f t his work w ill c oncentrate on the mechanical f actors a ffecting s pear a nd s pearthrower operation: s pear f light, penetration a nd wound production, propulsion, ( including a n a nalysis o f s pearthrower operation) and s pear and s pearthrower a rticulation. The s econd part uses s amples o f s pear a nd s pearthrower types f rom Central and N orthern Australia t o s how t he p resence o f these performance a nd production o ptimizations i n the s amples.

8

TWO

TECHNOLOGICAL COMPARISON AND P ERFORMANCE

Before analysing the performance optimizations and s tructural r elationships f ound i n Australian spears and s pearthrowers, the performance details o f hand thrown s pears will be compared with those thrown with the s pearthrower. The possession o f s uch a l ong distance weapon enormously i ncreased the e ffectiveness o f hunters who had t o k ill swiftly moving g ame i n country where good cover was s canty. ( Hawkes and Wooley, 1 963:145) I t enables a man t o throw a spear with much f orce and i ts perfect adaption to the u ses f or which i t designed, s trengthens one's belief i n the natural genius o f this people. ( Smyth, 1 878:310)

i s

These two quotations, s eparated by n early a century a re typical o f many s imilar general s tatements made about the advantages o f the spearthrower. The weapon i s s een to be capable of i ncreasing the f orce, velocity, a ccuracy and d istance of the s pear. None o f these a ssumptions can, h owever, be s upported a s completely a ccurate g eneralisations.

2 .1:

Technological

Comparison

The proposition that one t echnology i s s uperior to another i s d ifficult to test, because i t requires some a ssessment o f t he t echnology's e fficiency i n a specific t ask performance. As outlined i n a previous s ection, there are i n theory an extremely l arge number of optimizations which could improve efficiency. Therefore, one technology can only be c laimed to be more efficient than another i f the optimization i s specified. A t echnology designed and u sed f or one purpose when compared w ith another i n t erms o f the l atter's optimization, may a ppear inefficient. I t may be questioned, however, whether this i nefficiency i s meaningful i n arguments which r equire the u se o f very general s tatements o f e fficiency; evolutionary arguments, f or example. The f ailure t o r ealise the need f or optimization equivalence i n performance a ssessment could l ead t o the u se of i nappropriate ethnographic comparisons t o s upport i nvalid hypotheses. Generalised s tatements o f the e fficiency or a dvantage o f the s pearthrower over the hand t hrown spear h ave n o empirical basis. The a ssumption of 9

advantages i s n ot s upported by the e thnography, which has not been extensively r eferred t o i n s upport of s uch s tatements.

2 .2:

Hand Thrown

Spears

on the Mainland

For mainland Australia there a re v ery f ew references to the d istance and a ccuracy to which hand spears were thrown. Eyre ( 1845:306) described f our types, mainly f rom the Adelaide tribe, which h e c laimed c ould be thrown with " force and a ccuracy" s ome 3 0-40 f eet ( 9-12m). Cawthorne ( 1844:51) a lso n oted a maximum r ange o f 1 2-15 yards ( 111 4m) f or a s pear f rom the Adelaide t ribe. Giles ( 1889:10) c laims an a ccuracy o f 4 0-50 yards ( 36-46m) f or Central Australian hand thrown s pears. Horne a nd Aiston ( 1924:79) observed that the h and s pear o f the D ieri and Wongkonguru f rom the Lake Eyre r egion was n ot a ccurate beyond 2 0 y ards ( 18m), and Spencer and G illen ( 1928:690) r ecorded the r ange o f maximum d istances t o which n ine Melville I slanders threw spears a s b eing f rom 3 1.8-43.7m w ith a mean o f 3 7m. None o f the s pears t hrown i n t hese examples c ould, however, be a ccurately compared w ith a ny d istance f or a s pear thrown by a s pearthrower because they are f ar f rom being t echnologically equivalent i n u se or design. For example, Horne and Aiston ( 1924:79) s tate that the D ieri and the Wongkonguru s eldom threw t he s pear, preferring to u se i t a s a l ance. A s they were n ot g enerally u sed f or throwing, the weapon appears n ot h ave been designed f or either d istance or a ccuracy ( see B rowne, 1 898 f or a more detailed description o f i ts u se). Cawthorne ( 1844:51) c laimed that t he weapon h e described was u sed exclusively f or warfare. H is observation that the s pears were h eld in the middle may i ndicate t hat the p osition o f the centre of gravity would h ave made them unsuitable f or l ong distance f light ( see Chapter 3 ). Spencer a nd G illen ( 1928:690) a lso n ote that the Melville I slanders could possibly h ave thrown f urther i f their s pears were l ighter. At 4 lbs ( 1.8kg) the s pear u sed f or the t est i s over twice the weight o f an O lympic j avelin a nd i n the order o f t hree t imes h eavier than the mean mass f or h and thrown spears in g eneral ( cf. Oakley et. a l., 1 977:24-6; P alter, 1 977). G iles' ( 1889:10) observation may, b e exaggerated i n the l ight o f Gould's ( 1970:2) comment t hat G iles over s tated the range a nd a ccuracy o f Central Australian s pears t hrown by the s pearthrower, and t hat the h and s pear in C entral Australia i s u sed a s a f ighting l ance. The continental evidence comes f rom people who made l ittle u se o f the h and thrown s pear f or basic s ubsistence. The D ieri a nd Wongkonguru u sed the b oomerang and throwing s tick a s the major e lement i n their b allistic technology ( Horne and Aiston, 1 924). The Adelaide tribe described by Cawthorne ( 1844) u sed the r eed s pear a nd s pearthrower f or h unting and t he h and s pear exclusively f or f ighting. The 1 0

s tatus o f the s pear on M elville I sland i s d ifficult t o a ssess. D avidson ( 1936:456) c onsiders that t he h and s pear was m aintained i n i ts extremely h eavy f orm f or a n umber o f " cultural" r easons. A lthough, Graebner ( 1913:7, p late 2 ) i llustrates a s pearthrower f rom t he i sland u sed a s a child's t oy, S pencer a nd G illen ( 1928:670) maintain t hat they were n ot present. I n a ny c ase, the I slanders s eem t o have been a iming f or s ome p erformance characteristic o ther than l ong d istances. N one o f t hese examples c ould, therefore, b e s uccessfully u sed a s a c omparison with spears thrown by t he s pearthrower on the mainland.

2 .3:

The Tasmanians

a nd s ome o ther e xamples

The only Aboriginal g roup which c ould b e u sed t o s upply an a ccurate c omparison f or t he h and t hrown s pear with the s pearthrower a re t he Tasmanians. A s t hey a ppear to h ave been unfamiliar w ith t he s pearthrower a nd boomerang, t heir h and s pear was u sed f or b oth h unting a nd f ighting ( Jones, 1 977:197). The d istances r ecorded i n t he e thno-historical l iterature f or T asmanian s pears r ange f rom 4 0 t o 7 0 yards ( see Roth, 1 899:71). J ones ( 1977:197) s uggests t hat ranges of 1 00m w ere a lso p ossible. A lthough there i s s ome variation, these r anges a re c onsistently f urther than those recorded f or t he mainland. Tasmanian s pears were made f rom a s ingle s tem o f t he t ea t ree ( Leptospermum s p.), s harpened t o a c onical point. Noetling ( 1911) r ecorded t he l ast s even r emaining examples of t hese s pears i n t he T asmanian Museum. Their a verage l ength was j ust under 4m w ith a r ange o f maximum thicknessess f rom . 23-.13mm, a nd a mean mass o f . 614kg. Noetling ( 1911) a lso n oted t hat t he c entre o f g ravity varied between . 27-.29/. A r e-analysis o f t hese d ata, however, s howed t he c entre o f g ravity t o b etween . 33-.361. The spears would, i n theory, s till h ave g reater h igh trajectory s tability than many s pears t hrown by t he s pearthrower ( at l east 8 0% o f t he s pears thrown by t he spearthrower measured by P alter [ 1977] h ave c entres o f gravity . 361) ( see Chapter 3 ). I t h as b een s tated t hat t he T asmanians were c apable o f i mparting l ongitudinal s pin t o t he s pear, apparently t o i ncrease the i n-flight s tability ( Noetling, 1 911:82; Jones, 1 977:196). The evidence f or t his i s b ased on a s ingle ethno-historical s ource. Mrs P rinseps s tates that: " they poise i t f or a f ew s econds i n t he h and t ill i t a lmost spins" ( Roth, 1 899:71), which c ould equally mean that i t was h eld a t i ts c entre o f g ravity. A lthough modern j avelin t hrowers impart s pin t o t he s haft which c an be a s g reat a s 3 0 r evolutions p er s econd t here i s disagreement a s t o t he magnitude a nd r elative value o f i ts s tabilising e ffect ( Dyson, 1 962). A lthough i t c ould b e effective i f t he T asmanian s pear h ad a f orm s imilar t o 1 1

t hat o f t he j avelin, t he s pin c ould a lso t end t o s tabilise t he i n-flight b ehaviours ( see chapter 3 ).

over-

There d oes n ot a ppear t o h ave b een a ny other e thnographically r ecorded c ulture w hich u sed t he hand s pear a s extensively a s t he T asmanians. Mason ( 1895:379) c laims that the h and t hrown s pear r eaches i ts h ighest development i n t he a ssagai a nd q uotes B aker's ( 1874:135) observation t hat t he B an s were a ccurate up to 3 0 yards with a maximum r ange o f 5 0 yards, b oth d istances being c omparable w ith t hose o f the Tasmanians. The P ersian j arid q uoted by Chardin ( Blackmore, 1 971:102) a s being t hrown up t o 7 00 p aces. A lthough t his d istance must be a n exaggeration, these weapons a ppear t o h ave b een very s ophisticated t hrowing d arts with f lattened t ail s ections f or a erodynamic s tability ( see S tone, [ 1934:320] f or a n i llustration). Unfortunately, l ittle w as n oted a bout the weapon or h ow i t was t hrown.

2 .4:

The S pearthrower

Krause ( 1902) c laimed t hat t he s pearthrower could throw a s pear t hree t imes f urther t han one t hrown b y hand. This s tatement a nd o ther g eneralisations h ave l ong r einforced prehistorians' b asic a ssumptions a bout the t echnology a nd the n ature o f i ts a dvantage. I n c omparison w ith h and-thrown s pears there i s more i nformation a bout t he a ccuracy a nd r ange o f spears thrown by t he s pearthrower f or mainland Australia. I n t erms o f maximum r anges t he s ituation a ppears t o h ave been a ccurately s ummed u p by b oth Eyre a nd M cGillivray: ..each s pear a verages f rom s ix t o e ight f eet in . l ength, and i s thrown w ith f acility a nd precision t o d istances, varying f rom t hirty t o one h undred yards, a ccording t o t he k ind made u se o f, a nd the s kill of t he n ative u sing i t. ( Eyre, 1 845, 1 1:306) ..a s pear c an b e t hrown t o a d istance varying . a ccording t o i ts w eight f rom 3 0 t o 8 0 yards.... ( McGillivray, 1 852, 1 1:19)

A lthough there a re m any r eferences i n the e thnographic a nd e thno-historical l iterature t o the d istances t o which s pears c ould b e t hrown ( see Kelly, 1 970) very f ew r efer s pecifically t o measured d istances, thus making i t d ifficult t o i solate t he p ossibility o f exaggeration. F or t his r eason r eference w ill be m ade only t o d istances which h ave b een measured. Maximum measured d istances a re m eaningless i n terms o f t he t echnology's everyday f unction a nd s erves o nly a s a method o f expressing t he r elative p erformance o f two t echnologies w ith a s ingle variable. The l ongest m aximum 1 2

d istances r ecorded f or a s pear t hrown f rom a s pearthrower w ere taken by F alkenberg ( 1968:34) f rom t he P ort K eats a rea of t he Northern T erritory, where f orty t hrows by f our m en consistently a chieved d istances o f b etween 9 0 and 1 25 m etres. F aulkenberg ( ibid) a lso r ecorded a n exceptional t hrow o f 1 80 m etres f rom a previous t est. These d istances w ere, a s w ill b e argued l ater, ( Chapter 7 ) a chieved by a s pear and s pearthrower c ombination e specially d esigned f or h igh velocity a nd i s f ar f rom r epresentative o f the t echnology a s a w hole. I n 1 942 T homson ( 1935/45) r ecorded t he maximum d istances a chieved by d ifferent s pear f orms f rom n ortheast A rnhem Land. T he d istances r anged f rom 4 9-105m, with a m ean of 7 4m. T he s pears r epresent a ll the major f orms u sed i n Arnhem Land, r anging f rom l arge i ron h eaded " shovel-nosed" s pears t o the s mall r eed s pears l ike those u sed f or F aulkenberg's t est. Thomson's observations g ive t he most r epresentative s ample o f t he r anges a ssociated w ith the t echnology. A s eries o f t ests c arried o ut by Mountford ( 1940) a t E rnabella(Central Australia) g ives t he most c omprehensive p icture o f the r ange o f i ndividual v ariation, a s t he s ame s pear f orm w as u sed by a ll o f t he s even throwers. M ountford ( ibid) r ecorded both t he maximum d istance t hrown a nd the d istance t o t he s pear's f irst contact w ith the g round. F or maximum d istance t he r ange varied f rom 5 0-91m w ith a mean o f 7 1m . Comparable variation was a lso r ecorded f or t he f irst c ontact d istances. The variation b etween i ndividuals was q uite extensive e ven when the s cores o f one m an, who M ountford d escribed a s b eing unable t o use t he s pearthrower s uccessfully, w ere excluded. B oth T homson's and M ountford's t ests provide c omparable r esults a nd indicate t hat 7 0m may b e u sed a s a g eneral " rule o f t humb" maximum d istance. I t c annot b e a ssumed h owever, to a pply ' a priori' t o a ny s pecific s pear and s pearthrower c ombination even though many e arlier writers g ive s imilar f igures ( eg. B assett-Smith, 1 894:328; B eaglehole, 1 962:58, 9 5; B ennett, 1 843:62; B radley, 1 969:47; B reton, 1 833:236; Collins, 1 804:584; Hunter, 1 793:53). I n c omparison therefore w ith the f igures f or the h and-thrown t echnology, t he d ifferences i n maximum r ange, b oth i n a bsolute a nd m ean values, a re n ot a s s ignificantly g reater f or the s pearthrower t echnology a s m ight h ave been a ssumed.

2 .5:

Accuracy

Maximum r anges a re more a n i ndication o f a s pear's v elocity a nd a erodynamic capabilities t han i ts performance i n the f ield. L ong r anges a re unimportant i f a ccuracy c annot b e maintained. A ccuracy i s therefore a b etter m easure o f a s pear's o perational e ffectiveness t han the m aximum d istance t o which i t c an be t hrown.

1 3

There a re many s tatements i n t he e thnographic and e thno-historical l iterature which c laim that the s pearthrower was a ccurate up t o a s pecific d istance. The problem w ith u sing s uch s tatements i s t hat a ccuracy i s e ssentially a s tatement o f t he probability o f h itting a g iven t arget a t a g iven r ange. A very ' inaccurate' w eapon c an be d efined a s a ccurate i f the t arget universe i s s uitably expanded. T he a ccuracy r equired f or a h unting weapons i s dependent u pon t he s ize o f t he g ame which will present a smaller t arget a t g reater d istances, t herefore r equiring i ncreased a ccuracy f or e ffective operation. D espite s ome c laims that a ccuracy may b e maintained a t r anges o f up t o 1 00 yards ( eg. G iles, 1 889:114) most f igures quoted vary f rom 2 0-60 yards. Thomson ( 1935/43) p laces t he r ange o f a ccuracy a t h alf t he maximum range r ecorded f or a g iven s pear f orm ( 30-50m). Spencer and G illen ( 1899:20) s tate t hat: " Different men vary m uch i n their s kill i n s pear-throwing, b ut i t takes an exceptionally g ood man t o k ill or d isable a t more than twenty yards". This f igure, a lthough d erived specifically f rom C entral Australian observations, i s s upported by Chauncy's ( Smyth, 1 879, 1:251) f rom Western Australia 1 t hat: " They d o n ot throw with p recision more t han 2 0 or 3 0 yards; b ut when n ot f lurried, t heir a im i s very a ccurate". A ccuracy a lso d epends u pon t he t echnology's basic optimization. A s h igh velocity projectiles h ave a f latter trajectory over a l onger r ange o f d istances they s hould a fford e asier a im. T his m ay a ccount f or most o f the observations f rom S E Australia b eing l onger than those f rom t he central part o f t he c ontinent where a h eavier t echnology was i n u se ( Bradely, 1 969:74; Breton, 1 833:236; C ollins, 1 804, 1 :584; C urr, 1 886, 1 :252). A n umber o f f ield t rials i n which groups o f Aborigines were a sked t o t hrow a t a g iven t arget h ave been c arried o ut ( Falkenberg, 1 968:34; G ill, 1 968:27; G ould, 1 970:18; Haddon, 1 912:196; M ountford 1 940:205; T indale, 1 925/6:94). A s t arget s ize, r ange a nd n umber of t hrows varied i n each c ase, a n i ndex o f t arget d ifficulty was d evised t o a llow c omparison. By d ividing t he target area by the r ange a nd multiplying by a s uitable c onstant, the r elative d ifficulty o f h itting t he t arget could be expressed a s a n umerical i ndex, e nabling t he d ifferent t ests t o be r anked a ccording t o t heir d ifficulty. This r anking, when c ompared w ith t he p ercentage h its f or each t est, g ives a more u sable p icture o f t he f unctional l imits o f s pear/spearthrower a ccuracy. Unfortunately only f our o f the above t ests provide enough i nformation f or c omparison ( Table 1 ). The r esults s hown i n T able 1 c an, h owever, o nly be u sed a s a g uide t o t he a ccuracy o f s pears t hrown b y the s pearthrower f or two r easons. F irstly, two o f the t ests ( Gill, 1 968:127 a nd H addon, 1 912:196) w ere c oncluded when a h it was made. E ven t hough t he probability o f h itting a 1 4

target i s very l ow i t may b e s truck by chance w ithin a f ew throws, i f the t est i s c oncluded a t this p oint the percentage n umber o f h its i s exaggeratedly h igh. S econdly the index a ssumes t hat t he d ifficulty o f h itting a small target a t c lose r ange i s equivalent t o h itting a l arge t arget a t l ong r ange. This would b e true i f the projectile velocity i ncreased w ith g reater d istances. F or projectiles ( with l imited velocity), h owever, l onger d istances c an only b e a chieved by r aising the projection a ngles. Apart f rom t he problem o f s tabilising a s pear with a h igh t rajectory, t he t arget presentation a rea i s r educed because the m issile i s c losing f rom a ngles a bove the h orizontal. Therefore, d espite i ncreases i n t arget s ize, l onger r anges w ill p resent a dded d ifficulties, d epending upon the missile's velocity. F or t his r eason F alkenberg's ( 1968:34) t ests c arried o ut a t 2 0m and 3 0m r espectively p robably r epresent a more a ccurate t echnology t han the i ndex would o utwardly s uggest. I n comparison w ith o ther b allistic t echnologies, h owever, these s cores a re n ot l ow ( Table 1 ). Certainly, i n c omparison w ith . 22 t arget s hooting where 1 00% a ccuracy c an be a chieved on t argets o f . 02 d ifficulty, the a dvantage o f r ifles i s evident. Against b ows, h owever, t he gap n arrows. The O lympic a rcher's expectation o f h itting a target o f . 47 d ifficulty w ith 1 00% a ccuracy, i s p robably the h ighest l evel o f b ow t echnology's a ccuracy. C ontrolled t ests o f h unter/gatherer b owmanship a re c omparatively r are. The r esults o f P ope's ( 1918:121) t ests on I shi ( the l ast o f t he Y ahi I ndians o f C alifornia) s howed that, a lthough c omparable a ccuracy was a chieved on t argets o f m oderate d ifficulty t he s pearthrower's p erformance s eemed t o d ecline more r apidly with i ncreasing d ifficulty. Such f ormalised t ests, h owever, may bear l ittle r elationship t o i n-use a ccuracies, a s Mountford's ( 1940:209) f inal s et o f t ests i ndicate. Against a moving t arget o f the s ame s ize a nd r ange a s u sed f or t he s tanding t est the percentage n umber o f h its f ell f rom 8 8% t o 2 0%. Absolute a ccuracies a re a lso m isleading i n t erms o f a t echnology's o peration b ecause t hey exclude the o bservation that a s a g eneral r ule h unters try t o g et a s c lose t o animals a s p ossible before t hrowing i n order to i ncrease the p robability o f a n a ccurate s hot ( van B uren, 1 974: 1 5-16; Woodburn, 1 970:14). R eferences t o Aboriginal h unting b ehaviour c ertainly c onfirms this p icture ( Table 2 ). Even a t t he c lose r anges s hown i n t he t able t here i s n ot a 1 00% c ertainty o f a n a ccurate s trike.

1 5

TABLE

T echnology

1 :

ACCURACY

T arget Area A t(m 2 )

S ource

T arget R ange R ( m)

10 2 At x R

% hits

1 .4

6 3,88

Spearthrower

Mountford

Haddon

( 1940:205)

( 1912:196)

. 13

9

. 2

2 8

. 7

1 0

Falkenberg

( 1968:34)

. 07

2 0

. 4

1 8

F alkenberg

( 1968:34)

. 07

3 0

. 2

1 0

. 06

4 0

. 2

G ill

( 1968:127)

E thnographic Archery

( Californian

P ope

( 1918:121)

2 .6:

Spearthrower Advantage:

1 .2 1 .2 1 .2 . 005

3

I ndian) 3 7 4 6 5 5 9

3 .2 2 .6 2 .1 . 05

7,64 7 5 7,67 4 3,33 2 0,40

a h ypothesis

G iven t he observation t hat s pears thrown b y the s pearthrower d o n ot operate a t d istances which are o ut o f the r ange o f h and t hrown t echnologies a nd a re not s ignificantly more e ffective i n a bsolute range, the question a s t o what a dvantages l ie i n t he u se o f the s pearthrower r emains o pen. There h ave b een s everal a lternative hypotheses f orwarded. Kelly ( 1970:74) h as a rgued t hat t he s pearthrower i s most valued f or i ts " powerful t hrust" i ncreasing penetration a nd a ccuracy. This a rgument i s e ssentially a confirmation o f t he c onventional v iew h eld b y many prehistorians, a nd makes a ssumptions a bout t he performance characteristics o f t he p rojectile w hich h ave n ot been d emonstrated. I n a ccordance w ith t he model t o b e presented ( see Chapter 6 ) t he t echnology i s i ncapable o f a chieving b oth h igh p enetration a nd h igh a ccuracy over l ong r anges. T his i s b ecause b oth performance characteristics a re d ependent upon variables which a re not positively c orrelated. H igh p enetration e fficiency i s s hown i n Chapter 4 t o b e d ependent upon a m issile's 1 6

k inetic e nergy a nd i ts r esistance t o r etardation by the target. The v ariable o f p ositive a dvantage t o both f actors i s mass. A lthough k inetic energy i s a f unction o f velocity, s o i s t he missile's r etardation. On the o ther hand, h igh a ccuracy i s a p roduct o f t rajectory f latness, which i s a f unction o f t he velocity. A projectile's velocity, when t hrown by t he s pearthrower i s i nversely r elated t o i ts mass ( see Chapter 6 ). H igh velocity projectiles s hould t herefore, h ave improved a ccuracy but n ot necessarily h igh e nergy or p enetration. The s ame f actors a lso g overn h and t hrown p rojectiles. In a rguing t hat h igh p enetration energies or r anges were not n ecessary f or t he k illing o f small t hin s kinned Australian marsupials, F alkenberg ( 1968:36) c onsidered t hat the s pearthrower's main a dvantage l ay i n the f act t hat i t r equired n o r un-up, which ensured t hat the t arget a nimal was l ess d isturbed a nd t herefore l ess l ikely to e scape. This explanation c ontinues t o d epend on an i mplicit a ssumption t hat t he s pearthrower imparts h igher velocities a nd t hat r un-ups a re n ot u sed w ith s pearthrowers. I n c ontrast, F lood ( 1983:223-224) a rgues t hat the s pearthrower was r etained i n Australia b ecause o f t he necessity o f maintaining a t echnology c apable o f p enetrating t he t ough h ides o f Australian marsupials.

TABLE

T arget

2 :

APPROACH

D istance ( m)

s leeping K angaroo s leeping K angaroo s tationary k angaroo s tationary k angaroo moving k angaroo moving k angaroo emu a pprox emu s mall s eal a pprox man a pprox

DISTANCE

S uccess

R eference

( *) T indale ( 1974:plate 4 7) M cCarthy & M cArthur ( 1960:163) i bid.(153) i bid.(153) i bid.(156) i bid.(163) C lement ( 1903:3) Gould ( 1969:10) K ing ( 1827,11:126) Collins ( 1804,1:143)

7 4 9 5 1 8 1 8 1 5 9 1 0 1 0

The problem l ies n ot only i n a misunderstanding o f t he performance c haracteristics o f the t echnology but a lso o f how h unters will u tilize b allistic i mprovement. A ssuming the s pearthrower a ffords s ome advantage, the e vidence d iscussed a bove s uggests t hat this a dvantage i s n ot explicit i n a c omparison o f p erformances o f h andt hrown a nd t he s pearthrower t echnologies when t hey a re b oth used f or s imilar a ctivities. Any a dvantage which t he s pearthrower o ffers i s n ot b eing s hown i n o utright p erformance i mprovement. T he hypothesis f orwarded t o c over this i s t hat t he s pearthrower h as b een u sed t o r educe t he n ecessity o f a cquiring throwing s kills. Skill 1 7

i s u sed i n t his c ase t o c over b oth t he r equired t o perform a g iven operation r equired t o properly d irect i t.

physical a nd the

effort e ffort

Hand throwing b oth l ight a nd h eavy o bjects r equire s ome practice i f o ptimum p erformance i s t o be a chieved, depending upon s kill a cquisition a nd physique ( see Chapter 5 ). I f a p eople h ighly s killed a t throwing by h and a re compared with those who u se t he s pearthrower only within a s et r ange o f expected p erformance l imits, then the two t echnologies may a ppear very s imilar i n performance. I t may be a rgued t hat t he comparative material u sed h ere c ould b e h eavily b iased i n f avour o f the h and-thrown t echnologies, a s s ocieties which m aintain h and thrown t echnologies i n t he f ace o f t he spearthrower and the bow may h ave a s ocio-ideological i nvestment in the t echnology a s they s ee i t a nd a re m ore l ikely to t ake a n i nterest i n the maintenance o f h igh s kill l evels. The problem o f the r eplacement o f one b allistic t echnology with a nother which i s n ot d istinguishably better, i n p erformance t erms, i s p arallelled i n the replacement o f t he l ongbow by t he arquebus i n the Esper ( 1965) came to the s ixteenth c entury E nglish a rmy. conclusion that a r eduction i n t he s ociety's interest i n maintaining h igh l evels o f s kill u ltimately c ontributed t o the r eplacement o f l ongbow ( see a lso H ardy, 1 976). A cherson ( 1975:134) h as a lso n oted t hat t echnology c hanges i n s ubsistence a ctivity would b e i nitially a imed a t l evelling the d iscrepancy i n i ndividual skills, but eventually a d ifference i n s kill l evels would r eturn. Hypotheses which emphasise t he i mportance of s kill i n contributing t o t he u tilisation a nd r eplacement o f technologies, are a lso more c onsistent with the behavioural a spects o f h unting. Laughlin ( 1968:309) h as s uggested that hunters, a s part o f a g eneral s ubsistence s trategy, prefer t o invest hunting s kill i n g etting c lose t o a nimals, necessitating the a cquisition o f d etailed i nformation of animal behaviour. H e a rgued t hat t he o rientation o f early hunters was that: Children were t aught t o c lose t he d istance b etween t hemselves a nd t heir q uarry by s ophisticated s talking methods t hat d epended m ore upon c omprehensive observation, d etailed e thological k nowledge a nd an equally d etailed s ystem o f i nterpretation and a ction, than upon the improvement o f t heir equipment a nd the a ddition o f t en t o twenty yards t o i ts e ffective r ange. I n f act, one may p ass f rom t his g eneralisation t o a nother a nd s uggest t hat the very s low improvement i n t echnology, c lubs, s pears, t hrowing b oards, b ows a nd a rrows, a s i ndicated by the a rchaeological r ecord, w as c ontingent upon s uccess i n l earning a nimal b ehaviour. I t w as e asier or m ore e ffective t o i nstruct c hildren i n e thology, t o t ake 1 8

up the s lack by minimizing their d istance f rom the animal p rey, than t o i nvest h eavily i n equipment improvement. ( Laughlin, 1 968:306) A lthough Laughlin o ffers n o d etailed s upporting analysis, h is argument d oes point t o t he c lose l ink between h unting b ehaviour and t he e ffectiveness o f t he weapon u sed. The art o f s talking a ppears t o h ave been h ighly d eveloped among s ome Aboriginal g roups. M cCarthy and M cArthur ( 1960:153) r ecorded a s uccessful throw o f 1 0 y ards ( 9m) a fter a s talk o f 3 00 yards. Alternative m ethods which were a lso widely u sed, i ncluding drives t owards h ides a nd t raps, or h ides a round prime r esources a ll contributed t o a r educed r eliance on l ong d istance a ccuracy and t hrowing s kill ( see Anell, 1 960; Gould, 1 970). McCarthy a nd M cArthur ( 1960:192), i n a d iscussion o f s ubsistence c hoices made by t he Aboriginal groups s tudied i n North Australia r ated h unting s kill a s important: I ndividual s kill, particularly w ith the men, was probably a n important f actor; a nd i t may have b een the r eason f or the p reference f or f ishing a s against hunting i n the H empel B ay c amp ( Groote Eylandt), a lthough t hese p eople a re t raditionally f ishing people. The f our men i n t his c amp, were k een f ishermen, whose a ttitude t o h unting was well expressed by Kumbiala when h e s aid " Bush tucker ( food) t oo h ard t o g et". They made n o a ttempt t o spear t he s crub wallabies t hat l ived i n the n arrow s trip o f m onsoon f orest b etween t he beach and t he l ake. One m an h owever, who was i n this camp the week before t he s urvey b egan, went o ut every day, b ecause he preferred h unting t o f ishing even though h e was not very s uccessful. ( Ibid.) P resumably i nland g roups were l imited i n the t erms o f this c hoice a lthough i ndividual s kill s till appears important a nd varied. F or example, o f t he s ix m en i n t he F ish Creek g roup s urveyed by M cCarthy a nd M cArthur ( 1960:147-180), o ne individual s upplied over 5 7% o f t he g ame k illed i n a t hirteen day p eriod, a t r anges a nd t argets which o ther m embers o f t he g roup s eemed unable t o equal. To c onclude this s ection i t i s s uggested that the s election f or m ore c omplex i tems o f b allistic t echnology w ith the i ntent o f r educing t he s kill or e ffort n eeded o f u se would h ave t he a dvantage o f f reeing t he h unter t o c ontinue t o i nvest i n o ther a reas, s uch a s ' ethological' k nowledge and s talking s kill. I n s ocieties where h igh s talking and t hrowing s kill i s well d eveloped, the s kill r eduction a fforded by t he i mprovement i n ballistic t echnology m ay b e u tilized i n a ny o ther a spect o f b ehaviour, s uch a s t he manufacture o f the more c omplex t echnology. T his h as t he e ffect o f r educing t he n ecessity 1 9

f or s ocieties r elying o n h igh physical s kills which are h eavily dependent on i ndividual a ptitude a nd a llows a broader r ange o f i ndividuals, w ith l ess potential s kill d evelopment, t o b ecome more e ffective h unters. For example, an i nvention which r educes t he physical e ffort r equired i n h unting would enable b oth younger and o lder h unters t o be p otentially more e ffective, even i f their r espective s kill l evels w ere n ot optimal. This optimization r equires, h owever, t hat i ncreased efforts be made i n the production o f t he more c omplex a nd expensive t echnologies. This d emands a n i ncreasing i nvestment i n production skills, a gain emphasizing t he i mportance o f the s killed i ndividual. T his r e-orientation a nd c oncentration o f physical s kills away f rom o peration and into production, i s one o f t he major themes o f t echnological change.

2 0

THREE

AERODYNAMIC

FACTORS

A s their f light t hrough the a ir i s a prime performance characteristic o f s pears, i t h as been s uggested that much o f t he variation s een i n Australian s pears i s a r esult o f a ttempts by Aborigines t o obtain the most a erodynamic f orms p ossible ( Palter, 1 977). B efore considering t his p oint f urther, i t i s n ecessary t o examine the f actors a ffecting l ow velocity projectiles and determine what a spects o f t heir c onstruction control their i n-flight behaviour. There h as, a s English ( 1930:805) pointed out, been very l ittle a ttention p aid t o t he a erodynamics o f l ow velocity projectiles, e specially s pears. A lthough i t i s n ot possible t o a ccurately predict the i n-flight behaviour o f i ndividual p rojectiles, i t i s possible t o determine g eneral principles which can b e u sed t o i nterpret construction v ariation and i ts r elation t o s pear performance. N ewton's

f irst

axiom o f

motion

s tates

that

an

object

will: ..continue i n i ts s tate o f r est or uniform motion i n a s traight l ine, except i n s o f ar a s i t i s compelled by i mpressed f orces t o change t hat s tate. ( Hannah a nd H illier, 1 971:83) This a xiom s tates t hat o nce l aunched, a projectile will t ravel i n a s traight l ine unless i t i s a cted upon by an external f orce. I f i t i s a cted upon by s uch a f orce i ts d irection may c hange a nd i ts motion w ill n o l onger be uniform. The f act t hat objects thrown on the earth's s urface d o n ot t ravel i n a n i nfinite s traight l ine i ndicates that t hey a re s ubject t o external f orces. There a re two m ajor f orces which a ffect t he motion of projectiles n ear t he e arth's s urface. The f irst i s g enerally t ermed t he f orce o f g ravity, t he s econd, are the f rictional f orces produced by t he projectile's motion through the a ir. A s t he a cceleration o f g ravity i s c onstant throughout f light, a nd i ndependent o f the object's s hape, velocity a nd mass, i t h as b een u sed t o c onstruct a t heoretical model which predicts the c urvilinear motion characteristic o f projectiles, f orming a s imple f irst a pproximation t o projectile motion. Most unspecialized d iscussions o f b allistics i gnore t he e ffects o f a erodynamic f actors a nd concentrate on what i s t ermed " vacuum ballistics", c onsidering g ravitational and p rojecting f orces a s t he only two operating on the p rojectile. 2 1

3 .1:

Vacuum Ballistics

I f an object i s projected a t a n a ngle t o t he h orizon, gravity will c ause t he projectile t o f ollow a parabolic f light path ( fig.1). This i s b ecause a ny object g iven a d iagonally upward motion w ill h ave two c omponents t o i ts l inear projected velocity ( V0 ) : one o f these i s i n the vertical d irection ( V v ) the o ther i n t he h orizontal ( Vs ) . Gravity r educes the vertical c omponent p rogressively until i t i s equal t o z ero. At t his p oint t he object h as n o vertical velocity, only t he h orizontal c omponent which i s equal t o Vo . This i s the h ighest p oint o f the f light p ath, which becomes progressively more c urved t owards the e arth because g ravity decreases Vv a t a n i ncreasing r ate. Once s n eutralised the body ' falls t o e arth i n exactly the Vv i 5 äme t ime a s i t t ook t o r each t he h ighest p oint b ecause under gravitational a cceleration t he b ody obtains a n ew Vv d irected downwards. The b ody t hen s trikes t he earth a t the s ame angle a s i t was projected, w ith equal but opposite Vy and an unchanged Vx component. The f orce o f g ravity a nd the projecting f orce c an be considered t o a ct through t he c entre o f g ravity. I n the vacuum model the f light p ath i s t raced by the objects centre o f gravity only. The a xes o f t he projectile r emain i n the s ame p lanes i n which t hey were i nitially projected ( fig. 2 ). From this model various e lements o f t he f light p ath can easily b e c omputed. F or example, the d istance f rom the ground t o the h ighest p oint o f t he f light, the l ine o f f light and most i mportantly f or t his a nalysis, the r ange o f the f light ( see Abbott, 1 971; B roer, 1 973:113-121 f or details). The equation f or r ange i s: R = V2 s in 2 6 g where v i s t he projectile v elocity v0 , g t he a cceleration due to g ravity ( 9.8 m/sec') a nd 0 t he a ngle o f projection. This equation can a lso b e u sed t o a pproximate projectile velocity: V = 1

R g s in 2 6

B oth these equations a re d erived f rom R = Vx t , where V, i s the h orizontal component a nd t i s t he t ime o f f light; s peed travelled by t he t ime t aken equalling the d istance travelled ( see B eiser,1962:51 f or a d escription o f the derivation o f t he a bove equations).

basic

From the f actors

equation a bove i t c an b e s een t hat a ffecting projectile r ange a re i ts 2 2

t he t hree velocity,

X

F igure

F igure

1 :

2 :

Trajectory and ballistics.

velocity

Projectile orientation vacuum ballistics.

2 3

components

and

i n

vacuum

trajectory

in

projection a ngle a nd the a cceleration d ue t o gravity. equation g ives the optimum a ngle o f projection a s ( sin2[45] = s in 9 0 = 1 ).

The 4 5°

Although vacuum b allistic c an b e u sed t o derive the basic f actors a ffecting t he i n-flight b ehaviour, i t c annot be the only a pproximation u sed, b ecause the m odel's a bility t o predict the i n-flight b ehaviour o f objects more complex than h eavy n on-revolving s pheres i s very l imited. F or example, the model maintains that once a n object, l ike a s pear, h as b een l aunched, i ts l ong a xis r emains i n the s ame p lane, maintaining t he s ame a ngle with the g round throughout f light, l anding b utt f irst ( fig. 2 ).

3 .2:

Projectile Aerodynamics

The a ction o f a ir on t he object m ust be considered to g ain a more a ccurate p icture o f t he i n-flight behaviour o f projectiles. The i nteraction b etween the projectile and the a tmosphere, h owever, l acks the theoretical elegance o f vacuum ballistics. , Although a ir h as a c omparatively l ow density ( 1.3 kg/m' compared t o water's 9 98 k g/m') i t, l ike any l iquid ( or g as), will h ave a r etarding e ffect on any o bject passing t hrough i t. When a projectile i s moving s uch that i ts l ong a xis i s i n l ine w ith t he " relative w ind" p roduced by i ts motion, t he r etarding f orce o f t he a tmosphere ( F) a cts through the object's c entre o f g ravity. I n this case a ll the F i s a cting a s d rag ( D). The drag o n any projectile i s proportional t o t he o bjects velocity ( V), s ectional a rea ( s) a nd t he d ensity o f t he a ir ( p): D a

pV 2 s ( Clancey,1975:49)

The g eneral r elationship:

f ormula

f or

d rag

i s

d erived

f rom

this

et.

a l.,

D = CdpV 2 s 2 ( Butler,1973:90; 1 953:164)

C lancy,1975:49;

C i s the drag c oefficient which object's s hape a nd R eynolds n umber.

M cShane

i s

d ependent

o n

the

H iggins ( 1933:93) f orwarded t he f ollowing expression f or the drag on l ow velocity projectiles l ike a rrows: D = K Cdp rd/V 2 r 2

2 4

K i s a f actor a llowing f or a dditional ( if any) and n dl i s a more complex a llows f or s urface f riction.

t he

The a bove f orm:

e xpression

f or

d rag

a rea f or s tabilisers expression o f which

i s

g enerally

g iven

i n

D = kV 2 where k i s c alled the ballistic m issile. A s drag r etards t he motion r esultant n egative a cceleration ( -a) f ollowing: a

c oefficient o f o f a projectile, i s g iven by

the the the

= kV 2 ( Higgins

, 1933;

Pratt,1976)

Objects w ith small s urface a reas, s treamline s hapes, l ow velocities a nd l arge masses w ill t herefore be l ess a ffected by drag than l arge, l ight objects t ravelling a t h igh speed. B utler ( 1973:92) h as s hown that f or a n a rrow l aunched h orizontally the drag was s ufficient t o r educe t he horizontal v elocity f rom 1 76'/sec t o 1 08'/sec ( 39%) i n f our s econds o f f light. F or projectiles l aunched a t a ngles ( 0) g reater than t he h orizontal, the e ffects are e ven more pronounced. B utler ( 1973:82-4) observed that a rrows l aunched a t 4 5 d egrees t ravelled only 5 5% o f the r ange calculated by vacuum b allistics. The d iscrepancy b etween t he observed and t heoretical d istances was quite m arked t hrough o ut a ll r anges o f 0 , b ecoming g reater a s 0 i ncreased. E ven t hough t his e ffect was observed f or a rrows, t he p rinciple a pplies equally well t o s pears and u nfletched a rrows. Although t he i nclusion o f a ir r esistance a llows c omplex f ormulae which predict t rajectory, r ange and m aximum h eight t o b e d eveloped, t hey a re n ot r eadily a pplicable t o s pears, b ecause o f t he a ssumptions which h ave t o be made a bout t he i n-flight behaviour o f the p rojectile. B oth English ( 1930) a nd H iggins ( 1933) a ssumed that t he l ong a xis o f t he projectile w ill be t angential t o t he f light p ath t hroughout f light. This i s q uite d ifferent t o the vacuum b allistic model i n which the a ngle b etween t he l ong a xis o f t he m issile and the d irection o f i ts c entre o f g ravity i ncrease throughout f light. The angle b etween t he l ong a xis a nd the f light path i s the a ngle o f i ncidence or yaw o f a p rojectile ( fig. 3 ). The a ir r esistance experienced by a projectile i s p roportional t o t he a ngle o f i ncidence. A s the a ngle i ncreases t he s hape o f t he object changes r elative t o i ts d irection s o t he drag c oefficient a nd s ectional a rea b ecome l arger, i ncreasing t he Fr.

2 5

F igure

3 :

The c entre projectile.

F igure

4 :

The c entre projectile.

o f

pressure

o f

2 6

on

pressure

an

on

unspecialized

a

f letched

The presence o f yaw i s n ot n ecessarily detrimental t o range. L ift, t he s econd c omponent o f F operates a t 9 0 degrees t o drag a nd t ends t o k eep t he object i n the a ir. At s mall a ngles o f i ncidence, t he l ift may b e s ufficient to m aintain l onger f light t imes. At h igher i ncidences, however, t he l ift c omponent b ecomes progressively l ess. For projectiles l ike s pears a nd a rrows, l ift i s n ot a major f actor, unless, l ike t he prohibited g liding j avelin, they are e specially designed a nd t hrown t o make maximum u se o f i t. an b e c onsidered, l ike The r etarding f orce ( Fr ) c gravity, t o operate t hrough a s ingle p oint t ermed t he centre o f pressure. The p osition o f t he c entre o f pressure a long t he l ong a xis o f t he projectile i s dependent upon t he a ngle o f i ncidence a nd t he s hape. When t he projectile i s i n t he s ame p lane a s t he r elative w ind, t hat i s, t angential t o t he f light path, the c entre o f pressure operates t hrough t he c entre o f g ravity. I f the yaw angle i ncreases the c entre o f pressure moves up t he s haft toward the p oint i f t he a ngle i s p ositive, a nd t owards the butt i f t he a ngle i s n egative. I f t he yaw i s f urther i ncreased, t he c entre o f pressure t hen moves b ack t oward the c entre o f g ravity until a t a n i ncidence a ngle o f 9 0 degrees t hey a gain c orrespond. I t i s the i nteraction b etween t he c entre o f pressure a nd the c entre o f g ravity which l argely d etermines t he i nf light behaviour o f p rojectiles l ike s pears a nd a rrows. The Fr a cting t hrough t he c entre o f p ressure exerts a t urning e ffect o r t orque on t he p rojectile. The magnitude o f this t orque a bout a ny g iven p oint on the s pear i s he d istance d etermined by t he f orce ( F r ) multiplied by t ( r) to t hat point f rom t he c entre o f p ressure. This i s c alled t he moment o f a f orce a bout t he point ( see K aufmann,1963:313). W ith many s tructures, e specially t hose with symmetrical p rofiles, t he centre o f pressure i s i nvariably positioned a t t he q uarter l ength p osition even a t very l ow a ngles o f i ncidence ( fig.3) ( see G ordon,1978:266-7; K aufman,1963:314). I f the t orque i s s ufficient t o o vercome t he s pear's moment o f i nertia ( resistance t o t urning), t he a ngle o f i ncidence or yaw w ill increase a s t he s pear t urns i n t he d irection o f t he t orque. A s the a ngle i ncreases, s o d oes t he Fr a nd the t orque, until t he projectile s talls. This o ccurs when i ts l ong axis i s p erpendicular t o t he f light p ath producing m aximum drag. E ven i f t he t orque i s i nsufficient t o t urn t he projectile i n t he e arly s tages o f f light, i t may well s tall a t s ome f urther p oint, f or a s s hown i n vacuum b allistics the a ngle o f i ncidence i ncreases t hroughout f light r egardless o f t he e ffects o f a ir r esistance.

3 .3:

Construction a nd S tability

d egree

Most objects w ill exhibit s talling behaviour t o s ome when t ravelling t hrough a ir. The c ontrol o f 2 7

s talling i s the major p roblem t o b e overcome i n maintaining a u seful f light p atten f or a p rojectile. I n this d iscussion i t i s a ssumed t hat t he d esired b ehaviour o f a s pear i s t hat i t maintains i ts l ong a xis t angential t o t he f light p ath l anding t ip f irst. There a re two methods o f c ontrolling s talling b ehaviour i n projectiles: t he f irst i s t o produce what Cranz and B ecker ( 1921:319) t erm a n over s tabilized projectile. This i s e asily obtained by i ncreasing the mass i n p articular o r t he moment o f i nertia in g eneral. A s a lready s hown, t he e ffect o f drag i s i nversely proportional t o the object's mass. I f i t i s sufficiently h eavy and i ts velocity i s l ow, t he projectile may s uccessfully r esist t he e ffect o f t he t urning moment about the c entre o f g ravity. T his s olution i s g enerally not a cceptable b ecause t he s pear will b ehave a s the vacuum model predicts a nd maintain a c onstant angle between i ts l ong axis a nd the g round t hroughout the f light. This method certainly c ontrols t he s tall problem, b ut does n othing t o a chieve t he i n-flight b ehaviour d efined a bove. o t hat i t The s econd a pproach i s t o make t he Fr work s c ontinually h olds t he l ong a xis t angential t o the f light p ath. This i s a chieved by ensuring that the c entre o f pressure i s b ehind t he c entre o f g ravity, producing a t orque which c ontinually f orces t he projectile b ack into a lignment. This may b e a chieved i n two ways: a . The c entre o f g ravity c an b e moved sufficiently f orward t o ensure t he c entre o f pressure i s b ehind i t. b . The s hape o f t he p rojectile c an be changed so t hat the centre o f p ressure i s drawn toward the r ear, b ehind t he c entre o f g ravity ( fig.4). The f irst o f t hese m ethods ( a) h as proved t he more d ifficult t o a chieve f or p ractical r easons. Firstly, i t i s d ifficult t o p lace t he c entre o f gravity f ar e nough f orward t o ensure a s ufficient n egative moment to p rovide s tability. I f the c entre o f pressure i s a bout t he . 25/ point on a s haft, a s g enerally o bserved, a d ifficult d esign problem i s presented. T o a chieve a centre o f g ravity o f . 25/ d emands t hat the p rojectile have three q uarters o f i ts mass i n one q uarter o f i ts l ength. S uch a projectile would n ot only b e d ifficult t o c onstruct, but a lso d ifficult t o u se w ith a p ropulsion d evices l ike the s pearthrower ( see chapter 6 ). The s econd a pproach, o f changing t he shape, i s u sually a chieved by a dding l arge a nd r elatively l ight s urfaces t o t he r ear o f t he s haft, f orcing t he centre of pressure b ehind t he c entre o f g ravity. This i s most r eadily s een i n a rrows, which when f letched, have l arge proximal s urface a reas w ith l ittle w eight addition. The l ightness o f t hese a dditions i s i mportant a s t he c entre of 2 8

g ravity c annot b e drawn t oo f ar t o t he r ear before the p urpose i s d efeated. Arrows a re t herefore w ell d esigned t o u tilise a erodynamic f orces s uccessfully. H iggins ( 1933:91) c omments t hat t hey a re p ossibly over d esigned f or the p urpose. S ome t hrowing d arts a lso make u se o f t his m ethod, e ither by f letching, o r f lattening the proximal p ortion. Another method, u sed by m odern j avelins i s t o p roduce a r elatively h igh s urface a rea i n t he m id r egion o f the s haft. Cranz and B ecker ( 1921:321) proposed that a s a g eneral principle t he c entre o f g ravity s hould b e b etween . 25 and . 35 o f t he l ength t o ensure a dequate i n-flight s tability ( or i nstability). A lthough t here h as n ot b een a ny systematic r esearch i nto t his matter, t here i s s ome e vidence t o s upport t his principle. Evans ( 1957:83) i n c arrying o ut t ests on unfletched a rrows f ound t hat a ccuracy c ould only b e a chieved w ith the c entre o f g ravity a t . 3 o f t he l ength. F or unfletched t ournament a rrows h e f ound t he c entre o f g ravity t o be b etween . 33 a nd . 25 o f t he l ength, very c lose t o the f igure g iven by C ranz a nd B ecker ( 1921). Mau ( 1963) c arried e xperiments a nd f ound t hat:

o ut

a n

e xtensive

s eries

o f

The unfletched j avelins u sed by t he writer a ttained maximum r anges only when t hey balanced..., a t a point b etween 2 8 a nd 3 5 p er c ent ( .28-.35) o f t he d istance f rom t he f ront e nd o f t he p oint... B est performance was obtained f rom t hose which were i n equilibrium when h eld c lose t o t he 3 1 p er c ent ( .31) position. ( Mau, 1 963:6) A lthough Mau's r ange i s s lightly o utside t hat a nd i s more r estricted, h is o ptimum p oint i s t he. 3 3-.25/ r ange.

o f the a bove s till w ithin

An exception t o the a bove r ule i s t he modern O lympic j avelin. The j avelin must h ave i ts c entre o f g ravity a t a f ixed d istance f rom t he t ip, r egardless o f t he l ength. T he construction r ules were d eveloped by a n O lympic c ommittee with a view t o s tandardisation, n ot a erodynamic s tability. W ith a m inimum a llowable j avelin l ength the c entre o f g ravity i s b etween . 35-.42 o f t he l ength, w ith l onger l engths t he c entre o f g ravity would m ove t oward the t ip. The r equirement t hat t he j avelin t ravel a s f ar a s p ossible yet p itch on i ts p oint p laces d ivergent d emands o n i ts c onstruction. I t must m aintain a ngles o f i ncidence s ufficient t o g ain l ift f or m inimum d rag, y et i t must l and p oint f irst. The modern j avelin's l ight t ubular c onstruction e nsures h igh s urface a rea f or m inimum mass a llowing i ncreased s ensitivity t o a erodynamic f orces. The t apering a t both ends a lso ensures t he c entre o f p ressure w ill n ot 2 9

move t oo f ar t o t he r ear s tabilising e ffects.

producing

r apid

a nd

extreme

over

The c omplex mechanics o f t he j avelin throw are described by Dyson ( 1962). The j avelin must b e t hrown s uch t hat the c entre o f g ravity a nd c entre o f pressure are c lose throughout t he f irst p hase o f t he throw ( the angle o f i ncidence b eing a bout 10 d egrees). A t the h ighest phase o f t he t hrow , t he a ngle o f i ncidence s hould b e l arge enough t o a llow a l arge l ift t o drag r atio s o that extra d istance c an b e obtained by g liding. A s energy i s e xpended and the j avelin b egins t o f all t o t he g round, a nd the a ngle o f i ncidence i ncreases. The o bject's mass a llows i t t o counter the a ir r esistance which i s s till helping t o maintain f light w ithout overturning. F inally the c entre o f pressure moves s ufficiently f ar b ehind the centre o f g ravity t o move t he j avelin's p oint b ack t oward the f light path a nd s o l and p oint f irst. The f inal p itching s hould be delayed a s l ong a s p ossible t o a llow the m aximum g liding e ffect. The O lympic j avelin h as b een i ncluded i n this d iscussion a s a n example o f t he c onstruction modifications which must b e m ade t o e nsure t hat t his h ighly s tandardised projectile a chieves i ts c omplex i n-flight b ehaviour. The modern j avelin i s very much a product of m odern t echnology; i ts p erformance c ould n ot b e equalled i n prehistoric a nd e thnographic h unter-gatherer s ocieties g iven t he s ame d esign l imitations. The f act t hat its performance i n t erms o f r ange, t hough n ot i n-flight behaviour was equalled by a n umber o f s ocieties, i ndicates the h ighly s pecialised n ature o f t he projectile which s hould only b e u sed w ith c aution i n c omparison with preindustrial t echnologies. A lthough the proper p ositioning c entre of g ravity will h elp t o ensure f light s tability t he s ituation i s not n ecessarily s imple. E vans ( 1957:83) c omments that a lthough a ccuracy was r easonable a t l ow trajectories unfletched projectiles t ended t o b ecome unstable a t h igher t rajectories. Van B uren ( 1974:30) a lso r ecorded difficulty i n s tability o f s hafts w ith c entre o f g ravity positions f rom . 25-.33/. The s tability o f a m issile w ill be proportional t o t he d istance o f t he c entre o f gravity f rom the p oint; t he c loser i t i s t o t he t ip t he more s table the projectile w ill b e. E vans' ( 1957) o bservation t hat the a ccuracy i ncreased a s t he c entre o f g ravity a pproached the t ip c onfirms t hat t his i s a p rogressive r elationship not n ecessarily c onfined t o t he r ange n oted by Cranz and B ecker ( 1921). A projectile w ith a c entre o f gravity at . 25/ will b e more s table t han one w ith a c entre of g ravity a t . 35/, which i n t urn w ill b e more s table than one w ith a c entre o f g ravity a t a . 45/ p osition. T he i ncrease m ay not b e l inear. I t c ould n ot b e a rgued, f or example, t hat a missile w ith a c entre o f g ravity a t . 251 i s twice a s s table a s one w ith a c entre o f g ravity a t . 5/, w ithout f urther r esearch ( see C otterell a nd K amminga, i n press). 3 0

Stability a s i t i s u sed h ere i s a measure o f a projectile's a bility t o r emain t angential t o a g iven f light path. T he f urther t he p ath d eparts f rom t he h orizontal, t he more p arabolic i t b ecomes, the more d ifficult a s table f light w ill b e t o a chieve. A ll projectiles can t herefore b e considered a s p otentially s table i n f lat t rajectories. O nly m issiles w ith h igh centre o f g ravity p lacement will, h owever, maintain s tability a t h igh projection a ngles and be c apable o f h igher e ffective r anges.

3 .4:

Australian S pear Construction a nd Aerodynamic Stability

Palter ( 1977) h as a rgued t hat t he variation i n c onstruction s een i n A ustralian s pears t hrown by the s pearthrower i s a r esult o f a ttempts t o obtain t he c orrect p oint of b alance f or t he projectile. A preliminary i nvestigation o f the r ange o f b alance o f s pear-thrower projectiles s uggests that t he optimum d istribution o f weight d iffers a ccording t o the type o f projectile. ( 1977:172) P alter's r eason f or employing t his a rgument a ppears t o s tem f rom the e xtreme variation i n the c entre o f g ravity o bserved i n Australian s pears. Palter's measurements o f 2 93 s pears t hrown with t he s pearthrower produced a r ange o f centre o f g ravity p ositions f rom . 25-.48/. L ess t han 9 % o f t he s ample were w ithin the . 25-.33 r ange, a nd over 5 0% h ad p ositions g reater than . 401. A ssuming t he s ample i s r epresentative, i t must b e concluded t hat a h igh p roportion o f t he s pears i n Australia a re n ot well b alanced f or h igh angle p rojections, a nd would, i f t hrown f or maximum d istances, e xhibit s ome s talling b ehaviour. Palter ( 1977) a lso s howed t hat various f orms, ( reed c omposite and g eneral c omposite s pears) s howed very l ow c oefficients o f variation f or t he c entre o f g ravity l ocation. D ifferent c onstruction methods t herefore p roduce d ifferent c entre o f g ravity l ocations w ith h igh c onsistency. H e a rgues t hat t here i s enough variation i n A ustralian s pears t o ensure that a ll s pears would h ave b een aerodynamically s table. W ith the f indings o f t he p revious s ections i n mind i t s eems, that unless many o f t he spears were f letched or c onstructed on s imilar l ines t o an O lympic j avelin ( which t hey a re n ot), t here i s n o p ossibility that Australian s pears a s a g roup, exhibit enough v ariation i n c onstruction t o ensure a erodynamic s tability t hroughout t he r ange. I t i s m ore r easonable t o predict 3 1

that the variation e xhibits s tability r anging f rom s table h igh projection angles.

a t o

s pread o f aerodynamic u nstable projectiles a t

The a ssumption, n ecessary t o P alter's a rgument, that h igh projection s tability was e ssential t o the e ffective operation o f s pearthrower t echnology, i s n ot supported by t he e thnographic evidence. I t may b e a ssumed, t herefore, that a s econd s et o f f actors was operating o n spear construction, which s tandardized t he production o f s pecific f orms a nd made t he s uitable p lacement o f the centre o f g ravity o f s econdary i mportance. These f actors will be d iscussed i n t he f ollowing c hapters.

3 2

FOUR

WOUND BALLISTICS

Prehistorians h ave u sed two d ealing w ith projectile p enetration: 1 . to

b asic

principles

i n

That t he depth o f p enetration i s proportional s ome q uality o f motion o f t he projectile.

2 . That t he d epth o f p enetration i s proportional to the s hape o f t he projectile i n g eneral a nd the point i n p articular. For example, D avidson ( 1934:61) u sed b oth i n a rguing that some Australian s pears r elied on t he s harpness o f t heir point f or p enetration r ather t han t heir weight. C lark ( 1963:60) u sed t he s econd i n s uggesting t hat t he i nnovation o f s tone projectile h eads m eant a n i ncrease i n e ffectiveness. U ntil these principles h ave b een made more e xplicit i n t erms o f t he q uality o f motion most i mportant f or penetration, t he s hapes which a re most e fficient and t he amount o f e nergy r equired f or p enetration, i t i s n ot p ossible t o make a nything but i ntuitive o r ' common s ense' a ssessments o f v ariation.

4 .1:

Momentum,

E nergy a nd P ower

There h as b een s ome debate over which q uality o f m otion b est e xpresses t he wounding c apability o f a p rojectile. M ost modern a uthorities f avour t he u se i g f k inetic energy ( mV`/2) over momentum ( mV) a nd p ower ( mV') ( see French a nd C allender, 1 962:359). P ope ( 1923:359) d emonstrated t hat t here was a n ear p erfect l inear r elationship b etween the k inetic energy o f a r od ( diameter 7 .9mm) a nd i ts p enetration o f a p araffin b lock ( see a lso K lopsteg, 1 943:190). S everal r esearchers h ave, h owever, m aintained that m ass a nd velocity a re o f equal i mportance. T he argument t hat momentum i s t he most i mportant quality s tem either f rom a n o versimplification o f t he f actors i nvolved ( see D avenport, 1 943:33; J osselyn, 1 961:51) or t heir misapplication ( Cole, 1 972:2). Accepting f or t he moment t hat a projectile's p enetration i s p roportional t o i ts energy, t he f actors a ffecting penetration a re mass a nd t he s quare o f the v elocity. Variation i n e ither f actor w ill n ot, h owever, p roduce equivalent changes i n p enetration. F or example, g iven a s et a mount o f energy a nd e quivalent s hape, a m issile which h as h alf a unit o f mass t ravelling a t f our u nits/sec will n ot h ave t he s ame p enetration a s a p rojectile o f two units mass a nd a velocity o f two u nits/second. T he r eason f or t his i s t hat the p enetrated b ody h as density a nd exerts a r etarding f orce on the 3 3

projectile. This r etarding f orce i s a s pecial example o f drag on moving b odies. The d rag on a missile ( as s een i n chapter t hree) i s proportional t o i ts s ectional area, velocity s quared, s hape a nd the d ensity o f the medium through which i t i s t ravelling. T he d eceleration d ue t o drag h as b een s hown t o b e i nversely proportional t o the object's mass. This i s why, when a ll other f actors are h eld constant, h eavier projectiles w ill penetrate f urther than l ighter objects a t h igher v elocity. A lthough high velocity i ncreases t he k inetic energy by a s quared f actor i t a lso i ncreases drag by a n equivalent amount. The e ffect o f t his r elationship c an be s een i n P ope's ( 1923) experiment. By u sing a t en p ound weight d ropped f rom varying h eights t o s upply t he energy Pope e nsured ( possibly by a ccident) t hat t he h igh m ass c omponent would r esist drag enough produce a l inear r elationship. The importance o f mass i n r educing the e ffect o f drag r elative t o the importance o f velocity i n p roducing energy has possibly been the f oundation o f t he momentum energy debate.

4 .2:

Shape a nd S ize

The s econd major f actor a ffecting p enetration i s the s hape a nd s ize o f a m issile. A s d rag i s proportional to the s ectional a rea, the e ffect o f s hape i s g enerally s imulated by t he a ddition o f a s hape c onstant in t he drag equation, a nd i s e specially n ecessary f or p ointed projectiles ( see F rench and C allender, 1 962:120). A s the overall s hape o f t he l ow velocity m issiles s tudied i n this thesis i s s imilar, t he e lement which w ill h ave i nitially the most e ffect on p enetration i s " the character o f the h ead". A lthough s everal r esearchers h ave conducted t ests on the p enetration e fficiency o f d ifferent types o f p oint, P ope's ( 1923) r emains the most s ystematic ( see also Browne, 1 940:212; F rison, 1 978:331-333; van B uren, 1 974:33). P ope t ested point f orms r anging f rom blunt through conical t o b road a rrow a nd s pear p oints. The e fficiency was measured by t heir p enetration o f a p araffin b lock ( a s tandard t est f or p enetration). O f the f ifteen points t ested o nly f our a re d irectly c omparable, h owever, due t o t he d ifferences between t he m asses o f the p oints. Two s eries o f t ests were c arried o ut, w ith consistent r esults. The broad a rrow f orm g ave i n t he order o f a 1 25% i ncrease i n p enetration over a b lunt s haft, and c onical points g ave o ver a 7 5% i ncrease. T he g eneral i ntuitive impression o f p oint s hape a nd e fficiency was therefore confirmed. I t i s n ot d ifficult t o s ee why t his w ould be the c ase. A fter i nitial p enetration t he d rag will r ise r apidly a s a f unction o f the s ectional a rea presented. R etardation i s a lso produced by c ontact between the 3 4

m issile a nd the s ides o f the wound. I n this r egard the p oints with a cutting edge or a c onsistently small s ectional area m ust h ave a n a dvantage over s impler conical f orms which h as t o physically p ush t issue a side t o create a w ound. The broad h ead, on t he o ther h and, makes u se o f i ts converging c utting edges t o cut the t issue. These c utting edges, e xtending w ider than the s haft ensure the a ccommodation o f the s haft, s o r educing the e ffects o f the i ncreased s ectional a rea a nd s urface f riction. Frison ( 1978:337) f ound t hat the binding o f the s pear p oint t o the s haft extensively i ncreased the drag on the m issile. H is e xperiments on c ows a nd buffalo i ndicated t hat the way a p oint was h afted h ad more r etarding e ffect t han the variation i n the points t ested.

4 .3:

Wound Energy

The third m ajor q uestion which must be dealt with i n a d iscussion o f t erminal b allistics i s h ow much energy i s r equired t o penetrate a nimal t issue. This question h as a b earing on t he u se o f evidence f or the performance d ifferences b etween projectiles. An example o f how p rehistorians h ave a pproached the matter, i s K elly's ( 1970) a ssumption that t he a nimal b ody i s a n exceptionally s olid object a nd that f or a s pear t o t ransfix i t was e vidence f or t he possession o f g reat f orce. I n r eality most a nimal t issue i s easily penetrated by s harp objects. The variation i n t he r etardation 2m) o f a p articular object c an b e u sed c oefficient ( pAC d / t o develop a r elative s caling o f various t issues' r esistance t o p enetration. F or example, a 1 /8 i nch s phere h as a c oefficient f or muscle ( .136) very c lose t o that o f a gelatin s olution ( .106) a nd water ( .091). A s imilar o rder o f f igures r esult f rom the variation i n drag c oefficients f or the s ame m issile ( see Harvey e t. a l. 1 962:225). N ext t o b one, s kin i s the most r esistant t issue t o penetration w ith a drag c oefficient o f . 528 ( human), compared with t hat o f muscle o f . 448. I t t akeg , v ery l ittle energy t o p enetrate the s kin. A 1 /16 i nch ( d = 2 .52mm') s phere r equires only . 1 j oule 9 f e nergy t o penetrate. A s phere o f 1 /4 i nch ( d' = 4 0.3mm') r equires 2 .6 j oules. These f igures a re n ot a l arge a mounts o f energy -a mass o f . 1kg f alling one metre h as a k inetic energy o f a pproximately 1 j oule. The s ectional a rea o f a p oint would r equire s ubstantially l ess energy t han the 1 /16 i nch s phere f or i nitial penetration. The i ncrease i n s ectional a rea will, h owever, r equire e xponential i ncrements i n energy f or t he process t o c ontinue. The amount o f energy r equired t o ensure wounding i s d ifficult t o a ssess. I t was g enerally c onsidered t hat 5 8 f t-lbs ( 92.8 j oules) was n ecessary, but this f igure i s n ow 3 5

r egarded a s i naccurate ( Beyer, 1 962:94). H arvey e t. a l ( 1962:233) g ive a f igure o f 1 5 f t-lbs ( 20 j oules) a s an average f igure f or small d iameter s teel s pheres. With pointed projectiles t he f igure i s p robably s ubstantially smaller. Knight ( 1975) c arried o ut e xperiments d esigned t o a ssess that the f orce r equired ( by pointed and s harpened objects) t o p enetrate. S harpness was f ound to be very i mportant i n d etermining the f orce r equired which varied f rom 5 t o g reater t han 4 9 N ewtons. A lthough, Knight d id n ot present h is r esults i n t erms of e nergy their magnitude may b e a pproximated. A ssuming t hat the t est knives were entered t o t en c entimetres ( .1m ) the energy u sed was between . 49 a nd > 5 j oules. These f igures a re probably t oo l ow t o b e a g eneral g uide t o penetration energies because they a ssume uniform r esistance. K night's observations on t issue r esistance were, h owever, s imilar t o the f igure a lready q uoted: Skin was by f ar t he most r esistant t issue. Once a knife penetrated t he s kin n o f urther f orce need be a pplied t o cause r apid p enetration o f the s ubcutaneous t issues a nd underlying organs except f or b one and calciferous c artilage. ( 1975:253)

I nitial b allistic p enetration o f animals does not therefore, r equire very h igh energy l evels, a lthough m issiles with r apid r ises i n s ectional a rea would r apidly expend the energy a vailable. P enetration i n many s pear f orms would, a s a r esult, b e l ittle f urther than the l ength o f the h ead. An example o f h ow the e ffectiveness o f a projectile's energy i n f orming w ounds i s d ependent on i ts s hape i s g iven by t he h unting a rrow . A lthough h unting a rrows h ave a r elatively small energy ( 60 j oules) in c omparison with s ome s pears ( 200 j oules) t hey are q uite capable o f k illing l arge g ame a nimals ( see B rowne, 1 940; H ardy, 1 976; K lopsteg, 1 943; P ope, 1 923).

4 .4:

Barbing

A major f eature o f many s pears i s the presence of b arbs d esigned o stensibly t o r etain t he s pear i n the wound. Unless b arbs a re i ncorporated behind a c utting e dge a s i n a broad a rrow t heir p resence w ill i ncrease the s ectional a rea o f t he h ead a nd l imit p enetration. A s the e ffectiveness o f b arbs m ust b e p roportional t o the a mount o f t issue which c an b e c aught b ehind t hem, there are t hree f actors which would a ppear t o g overn t he e fficiency o f any b arb: 1 . The h eight o f l ong a xis o f t he h ead. 2 .

I ts

t he

b arb p erpendicular

proximity t o t he n ext b arb.

3 6

t o

the

3 .

I ts

overall

s hape.

T he height o f t he b arb d etermines t he amount o f t issue which the barb i s a ble t o make c ontact with. This i s a lso d ependent on t he d istance t o t he n ext barb, a s the t issue w ill tend t o c lose a bout t he projectile this d istance will a ffect the amount o f enclosed t issue which i s available t o t he proceeding b arb. H igh, well s paced barbing will t herefore b e m ore e ffective than s hort t ightly grouped f orms. Shape i s p ossibly o f s econdary e ffect, a s l ong a s i t i s capable o f r etaining t issue. The c losely s paced m ultiple barbing s een on s ome Australian s pears i s p robably more e ffective i n i ts p sychological impact than i ts immediate f unction.

3 7

FIVE

PROPULSION

5 .1:

The Dynamics o f Throwing

A s Toyoshima a nd Miyashita ( 1973) h ave p oint o ut, the " essential mechanism" o f throwing i s t hat energy i s transferred f rom t he body t o t he object t hrown. A lthough this mechanism i s b asic t o a wide r ange o f h uman a ctions, the overhand throw pattern i s most c ommonly resorted t o when throwing r elatively l ight objects ( ie., b aseball pitch) or i n overhand s triking m otions ( ie., t ennis s ervice) ( see Cooper a nd G lassow , 1 968). T o obtain high projectile velocities the motion o f v arious body s egments must be t imed i n a definite s equence t o obtain m aximum energy transfer. I n a s ummation o f t hrowing f orces, therefore, t he l evers o f the b ody s hould operate s o that each can make a maximum, or very n ear maximum, c ontribution to the s peed. H ence t he u se o f s lower b ut more powerful muscles a nd l evers f irst ( ie. o f the trunk and thighs); while t he f aster b ut r elatively w eaker j oints ( ie. o f t he a rms, h ands, l ower l egs and f eet) exert t heir f orces a fter t he m issile h as developed considerable s peed. ( Dyson, 1 962:189)

Much o f the i nitial motion a ssociated with t hrowing s erves a s a base u pon which t he h igher velocity s egments can c ontribute t o t he projectile's v elocity ( O'Connell and Gardner, 1 972:64). When t he a ngular v elocities o f v arious body s egments a re p lotted a gainst t ime, there i s a s uccession o f velocity p eaks f rom t he h eavy segments to the l ighter f aster moving s egments ( see Ariel, 1 974; O 'Connell a nd Gardner, 1 972:64). I n a g iven muscle or g roup o f m uscles, the s peed a t which they c ontract ( or s horten) d epends on t he load against which they a re a cting; t he l arger the l oad the s low the s hortening a nd v ice versa. Muscles d evelop maximum f orce a t z ero s hortening s peed, which occurs when the l oad i s t oo g reat f or t he muscles t o d o any w ork on i t. On the o ther h and, maximum s peed i s d eveloped a gainst z ero l oad. The r elationship i s n ot l inear a s the s hortening s peed i ncreases r apidly a gainst l oads t hat are l ess t han 3 0% o f t he maximum. I t i s t he s peed of m uscular s hortening which d etermines t he f inal velocity o f the projectile. The muscles o f the l arger b ody s egments c ontract s lowly against the l arger l oads a nd m ust b e o perated early i n the throw . The c ontribution o f t hese s egments i s

3 8

n ecessary i n a maximum throwing v elocities are c umulative.

e ffort

because

s egment

The mechanical power o f muscles a lso depends on the s peed and l oading. The p ower or r ate o f d oing work i s z ero at b oth maximum l oad a nd z ero l oad a s i n both cases n o work i s done. Maximum power i s developed a round 3 0% o f t he maximum velocity ( see H ill, 1 950; Margaria, 1 976:79; R ash and B urke, 1 974:178). These l aws o f muscular dynamics a re f undamental to a ll animal motion. From t hese we may predict that h umans w ill be c apable o f propelling l ighter objects a t h igher v elocities than h eavier ones, a nd t hat there will b e a r ange o f l oads w ithin t he peak p ower r ange o f the group o f m uscles i nvolved, which exhibit h igher energies. I n examining the a pplicability o f the a bove r elationships ( which were d eveloped f rom the observation o f individual m uscles) t o a ctions r equiring the whole b ody, T oyoshima and M iyashita ( 1973) measured the v elocities o f b alls o f varying masses thrown by a s ample o f Japanese males. The r ecorded velocities d ecreased with i ncreasing ball mass i n l inear f ashion. F or example, f or t he . 1kg ball t he mean velocity was 2 7.1 m/sec. f or the . 5kg i t was only 1 8.2 m/sec, ( ibid.: t able I a nd f ig. 3 ). When the k inetic energy ( m 1 /'/2) o f the balls was measured t o indicate t he amount o f work d one by the thrower the r elationship was r eversed: t he . 1kg ball possesses only 3 7 j oules whereas the . 5kg possesses 8 3 j oules. I t c an be s een f rom f igure 5 that t he r elationship may be e ssentially p arabolic w ith t he h ighest energy b eing p ossessed by t he . 45kg b all. T he energy t ransferred f rom t he thrower t o the projectile becomes more e fficient a s t he l oad i ncreases, b ut only u p t o a p oint f rom which the e fficiency begins t o d ecline a gain. The r esults f rom T oyoshima's and Miyashita's work t oo l imited t o be u sed a s a nything more than a t est s pecific performance r elationships. The magnitude t hese p erformance characteristics ( ie., energy v elocity) will vary f rom i ndividual t o i ndividual a ppear d ependent on b oth t he s kill a nd physique o f t hrower. Toyoshima and M iyashita ( 1973) conclude that:

are o f o f and and the

..physical r esources ( muscular s trength) are a prevailing f actor i n d etermining performance i n t hrowing t he h eavier ball while s kill i s important i n the c ase o f t he l ighter ball. ( 1973:93) F or example, b aseball p itchers c an t hrow a . 15kg b all a t m ean velocities r anging f rom 2 9-44 m/sec.. These v elocities a re h igher t han t hose f or a n average i ndividual b ecause p itchers h ave more s kill i n co-ordinating the a cceleration o f body s egments which enables more work t o b e done on the b all. J avelin t hrowers, on t he other h and, r epresent the opposite end o f the s pectrum. A s the 3 9

J ou les

1 00-

-

8 0-

_

E ne rgy

6 0-

_

4 0-

-

f

I . 1

1 2

1 • 3

1 . 4

I • 5

1 -6 K gs

Mass

F igure

5 :

Mass by energy o f h and t hrown projectile Toyoshima and Myashita ( 1973).

4 0

f rom

j avelin, a t . 8kg, i s a r elatively h eavy mass t o throw s uccessfully u sing a n overhand pattern the amount o f work w hich can be d one i s much more c losely r elated t o the t otal power which c an b e d eveloped. This i s i n turn d ependent on t he amount o f muscle which can be brought i nto a ction ( Wilkie, 1 960). This i s c onfirmed by Tanner's ( 1964) observation t hat j avelin throwers t ended t o have m ore muscular physiques t han most o ther O lympic a thletes. As s pears g ain energy f rom h uman e ffort their p erformance characteristics must r eflect the capacities of t he machine which p owers t hem. H uman throwing performance i s l argely g overned by t he l oad/velocity r elationship o f m uscular dynamics. The f act that t he velocity which can b e imparted t o a n object i s i nversely proportional t o the o bjects l oad ( or mass) i s i mportant n ot only i n analysing t otal body motions ( ie., t hrowing), but a lso t o s pecific m ovements l ike t he r otation o f i ndividual body s egments. O f equal importance i s t he d evelopment o f maximum muscular p ower and e fficiency only w ithin a l imited r ange o f the l oad/velocity r elationship. This n egates the concept that h igh missile v elocity n ecessarily i ndicated h igh energy, w hich 4 though p erfectly valid i n a p ure Newtonian s ense ( E = mv'/2) c annot b e a ssumed t o be a ccurate when d ealing w ith human mechanics.

5 .2: ( A)

Models o f S pearthrower Operation Impulse a nd t he L inkage Models

T he use o f i mpulse t o explain the f unction o f the s pearthrower w as f irst f orwarded by Mason ( 1884;1895) who d escribed the a dvantages o f s pearthrower i n t he f ollowing w ay: I ts greatest a dvantages, h owever, a re the f irm g rip which i t g ives i n h andling t he h arpoon or dart, and the l onger t ime which i t p ermits t he h unter t o apply t he f orce o f h is a rm t o t he propulsion o f h is weapon. ( 1884:280) A lthough t alking i n t his c ase s pecifically a bout E skimo s pearthrowers h e l ater extended t he explanation t o a ll s pearthrowers ( Mason, 1 895:377). Mason's a rgument g ained l ittle a cceptance b ecause, a s Howard ( 1974) points o ut, he g ave n o i nformation on h ow t he s pearthrower i ncreased c ontact t ime, n or h ow t his i ncreased t ime improved p erformance. Howard ( 1974) d eveloped Mason's explanation i nto a m odel which v isualised t he s pearthrower a s a l ink which c onverted the p ost r elease d ownward motion o f t he arm s een i n a n ormal t hrow ( see Ariel, 1 974: f ig. 2 ; Muybridge, 1 955) i nto l inear motion which c ontinued t o a ccelerate the s pear. H e s tates that:

4 1

A s the h and and the f orward end o f the a tlatl b egin the downward curve, the a ft end, w ith s pur s till in contact with the s pear, c ontinues on a s traight thrust l ine. The a tlatl i s therefore c onverting downward c urving t hrust t o s traight f orward t hrust, thereby prolonging c ontact b etween s pear and t hrust. ( Howard, 1 974:103) Howard, h owever, a lso n eglects t o s tate why, in t heory, this s hould i ncrease s pear p erformance, or what e lements o f performance will be i ncreased. Both writers make i mplicit u se o f t he concept of impulse, which i s d efined a s the p roduct o f a f orce b y the t ime o f i ts a pplication, a nd i s o ften equated with the change i n an object's momentum ( ie., F t = mv where m u, the i nitial momentum i s z ero) ( Hannah a nd H illier, 1 971:221). I f the f orce a nd t he mass a re h eld c onstant any i ncrease i n t must t herefore r esult i n a n i ncrease i n the projectile's velocity. This f ormula a lso serves to i llustrate the d ifferent p erformance c haracteristics w hich may be optimized i n a ny mechanical s ystem. F or e xample, i n t erms o f the a bove r elationship i t i s equally r ealistic t o s acrifice velocity i ncrease f or a dded mass to a id in penetration, or t o h old momentum c onstant a nd reduce the applied f orce s aving on h uman e ffort. The performance characteristics which t he s pearthrower i s a ssumed to a fford d o n ot n ecessarily f ollow f rom t he u se of i mpulse a s an explanation. L inkage models h ave b een u sed i n the analysis of h uman motion f or s ome t ime, e specially i n conjunction with anthropometric a pproaches t o motion s tudies ( Demster, 1 955). H oward ( 1974), h owever, d oes n ot g ive any e xact i nformation on h ow h e v isualises the s ystem i n which the s pearthrower operates a s a l ink. I t i s a ssumed f rom his explanation o f t he a ction t hat a j oint ( elbow) f orms a c entre a bout which a l ink ( forearm) r otates. The e nd of this l ink i n t urn f orms a p ivot ( wrist) a bout which a f urther l ink ( spearthrower) operates. T he f ree end o f this f inal s ection i s i n t urn f ree t o move i n a s traight l ine maintaining c ontact with t he s pear. A ssuming t hat b oth l inks a re o f t he s ame l ength ( r), f or each i ncrement o f r otation a bout t he s tationary p oint ( A ) there will b e a c orresponding movement o f the f ree end o f the l inkage ABC a long t he p ath o f t he i ntended s pear f light D F ( fig. 6 ). The e fficiency o f t his l inkage c an be determined by t aking t he r atio o f t he d isplacement o f C by t he d isplacement o f B . F or example, i f p oint B moves a t a r ate o f 1 0 units a nd C moves a t only 5 units the r atio VC /V, D g ives a n e fficiency o f . 5 b ecause C moves a t only h alf the r ate o f B . A d etailed velocity o f t he r educed r elative

a nalysis o f t his m odel f ound that the f ree end o f t he l inkage C was i nitially t o B , b ecoming equal w ith i t only a t 0 = 4 2

00 ( 0

00

a ) 01

00

e •

i 01

i 01

00

1 D I

4 3

0 t o c 0

6 0o a fter which i t r apidly i ncreased the velocity o f B ( Cundy 1 980:54-57).

t o

o ver

s even

times

The i nitial r eduction i n velocity presents t he f irst d ifficulty with t he m odel, b ecause, a s points C a nd B a re i nitially i n t ranslation t he s pear would l eave t he s pearthrower when B b egins t o r otate i f t he l inear velocity o f B r emained c onstant. I n order to m ake t he model operational t here w ould h ave t o be a n a cceleration o f B i n t he r egions o f 0° -6 0 ° i n o rder t o compensate f or the r eduction i n e fficiency. The model a lso predicts that there will be a marked i ncrease i n a cceleration o f C j ust before r elease r egardless o f B 's a cceleration. The analysis a lso s howed t hat i f B C i s s een a s t he l ength o f the s pearthrower, variation i n i ts l ength will h ave n o e ffect on t he f inal velocity o f the s pear. Howard ( 1974:103) confirms t his by s tating t hat: " Because t he a tlatl i s n ot a c atapulting d evice i ncreasing i ts l ength will n ot provide a c orresponding i ncrease i n t he trust energy". H is s tatement i s n ot, h owever, b ased on a s imilar a nalysis but on t he s upposition t hat l ittle d ownward energy would be t ransferred t o t he s pear, a nd t hat a s hort l ink could t ransfer energy a s well a s a l onger unit. Longer s pearthrower's d o, h owever, i n h is opinion, h ave a n advantage b ecause they r educe " hooking" ( see chapter 5 ). The major p roblem w ith this m odel i s t hat i ts r elationship t o t he a ctual mechanics o f t hrowing i s only approximate. A s t he model i s presented t he i ncreasing velocity during t he f inal phase o f t he throw i s a result fter b eing f orced t o o f the angle ABC r eturning t o 9 0° a become a cute d uring t he e arly phase o f t he throw . I n mechanical t erms t here i s n o way i n which t he velocity a t B can be e fficiently t ransferred t o A without a s eparate i nput a t point B . A s t he velocity o f B i s i ncreasingly n ormal t o the d irection o f C t he r esulting amount o f velocity t ransferred b ecomes l ess a nd l ess a s 0 a pproaches 9 0o. I n order t herefore, t o i ncrease t he " thrust" a t the t ip o f the s pearthrower t he a cceleration o f AB m ust b e i ncreased s ubstantially t o c ompensate f or t he reduction a t C . Howard's ( 1974) a rgument t hat t he s pearthrower works a s a l ink which c onverts d ownward t hrust i nto l inear velocity i s n ot o nly m echanically d ifficult to a chieve b ecause i t p laces h igh physiological d emands o n the thrower t o continually i ncrease a cceleration, but i t a lso i ncorrect i n i ts a ssumption t hat t he only a cceleration will come f rom t he d ownward i nput. I n r eality i t i s the a cceleration a bout t he wrist ( B) which makes t he whole model workable. A s w ill b e s een f rom the k inesiologlcal analysis, this i s a n a ccurate p rediction o f t he importance o f the wrist a ction.

4 4

The model a s H oward proposed i t d id n ot, h owever, provided many p redictions a bout t he important variables i n spear and s pearthrower c onstruction. I t h as only one principal p rediction; t hat s pearthrower l ength i s o f l ittle importance.

( B)

The L ever Model

The s econd, a nd most w idely u sed g roup o f explanations o f s pearthrower mechanics h ave u tilised the concept o f t he s pearthrower a s a l ever or part o f a l everage s ystem. The e arliest observers o f t he s pearthrower i n Australia, a lthough i mpressed by i ts u se, were c ontent t o r ecord the f orms, a nd c omment on t he a ccuracy and d istance t o w hich i t c ould p ropel a s pear ( e.g. C ollins, 1 804:5567 ; H unter, 1 793:53,55). I t i s n ot until t he middle o f the n ineteenth c entury t hat e thnohistorical writers made f irst u se o f the l ever a s a n explanation f or t he s pearthrower's operation. H enderson ( 1851:145), f or example, calls the s pearthrower " a p erfect l ever" a nd M cGillivray ( 1852,11:19) r efers t o " the powerful l everage" which the s pearthrower brings t o b ear on t he s pear. P ossibly the most influential w riters i n t he s pread o f this v iew were t he l ater e thnographers l ike Spencer a nd G illen ( 1904:668) a nd Smyth ( 1878,1:310), who both r efer t o the s pearthrower a s a l ever o r t o i ts l everage. I n c onjunction with t hese e xplanations t here were n umerous writers who p referred d escribing s pearthrower mechanics i n t erms o f i ts l engthening o f t he a rm or i ncreasing t he a rm's l everage. F or example, M itchell ( 1839,11:348) n otes: " the womera a ffords a g reat a dditional i mpulse f rom i ts most i ngenious l engthening o f t he arm" ( see a lso D ahl, 1 926:13; Montague, 1 921:13; O ldfield, 1 865:262). The s econd g roup, i s exemplified by B lackman's ( 1903:42) c omment that t he s pearthrower was " a d evice f or i ncreasing velocity a nd r ange by l engthening t he arm l everage o n t he s ame principle a s t he s ling" ( see a lso Davidson, 1 936:445; Thomas, 1 906:81). I t c an b e s een f rom B lackman's s tatement t hat t he c oncept o f what exactly t he spearthrower d oes a nd what p rinciples i t operates on b ecome quite b lurred. The l ever i s a machine d evice by which t he p oint a nd/or d irection o f a f orce a re changed t o g ain practical T here are t hree c omponents o f 1 .

The f ulcrum rotates.

( F)

o r

which by d efinition i s, " a o f a pplication, magnitude, ( or f orces) p erforming work a dvantage" ( Tuma, 1 976:82). a l ever ( fig. 7 ):

p ivot

4 5

a bout

which

the

system

2 .

3 .

The r esistance a rm ( Rr ) o r t he d istance point o f a pplication o f t he l oad ( L) f ulcrum.

f rom a nd

the the

The e ffort a rm ( R e ) or d istance f rom the p oint o f application o f the r otating f orce a nd the f ulcrum.

These e lements system:

may b e

combined

i nto

1 .

The f ulcrum i s between ( E-F-R) ( fig.7).

the

2 .

The r esistance or f ulcrum ( E-R-F).

i s

3 .

The e ffort ( F-E-R)

l oad

i s b etween

t he

t hree

c lasses

e ffort

a nd

the

b etween

the

e ffort

f ulcrum a nd

the

o f

l ever

r esistance

a nd

the

r esistance

The advantage o f a l ever system i s t hat i t c onverts a small e ffort f orce a pplied over a l arge d istance ( s) into a l arge f orce a pplied over a s hort d istance or vice versa, thereby changing b oth the m agnitude a nd t he direction o f the f orce performing work. The w ork d one on the e ffort arm i s equivalent t o t hat d one o n t he l oad, j e. work output equals work i nput. A s the l ength o f the e ffort arm fig. 8 ) the i s proportional t o t he l ength o f t he a rc Se ( l onger the e ffort a rm i n r elation t o the r esistance arm the l arger t he l oad t hat c an b e d isplaced f or a given e ffort f orce because F Se = F Sr . This a llows the mechanical a dvantage o f t he s ystem t o b e expressed a s the ratio o f the l ength o f t he r esistance a nd e ffort a rms, j e. d efinition o f the mechanical advantage = Rr /R e . This advantage, b eing a p roduct o f a n e ngineering convention, i s n ot absolute. By considering the d efinitions o f t he three l ever c lasses i t c an b e s een t hat t he s pearthrower i s not a l ever a s i t d oes n ot possess a f ulcrum or r esistance and e ffort arms. I t c an, h owever, b e u sed a s part of a l everage s ystem t o p erform work. O nly when a body i s i n s uch a system c an i t be d efined a s a l ever. I t i s therefore the l everage s ystem i n w hich t he spearthrower operates and n ot t he s pearthrower i tself which determines the n ature o f t he l ever explanation. The body c an b e s een a s a l everage system with muscles s upplying t he e ffort, j oints t he f ulcrums and s keletal s egments a s l ever a rms. T his method o f a nalysing h uman mechanics h as b een r ecognised s ince t he s eventeenth century ( Harvey, 1 627) a nd f orms t hat a nalytic b asis o f present day k inesiology. The l ever s ystems o f t he b ody a re mainly 3 rd c lass ( F-E-R) with a small n umber o f i st c lass ( E-F-R) and a debatable n umber ( possibly n o) 2 nd c lass ( F-R-E) l evers. B ody l evers d iffer f rom t he c onventional f orms d escribed 4 6

F igure

7 :

F irst c lass

l ever.

sr F igure

Se

8 :

R elative d istances g iven r otation.

of

a rm

movement

F F igure

9 :

I nefficient

f irst c lass

4 7

l ever.

f or

a

above, a s the e ffort arm i s much shorter than the a ccompanying r esistance arm. This produces a mechanically disadvantageous system, where muscles produce much g reater f orce to move a g iven resistance t han i n a " efficient" system ( fig. 9 ). Although i t may be a t a mechanical disadvantage the system has the advantage o f speed. For example, a disadvantageous i st c lass l ever with an e ffort arm f ive units l ong and a r esistance a rm o f f ifteen units when rotated 9 0 ° will make two arcs e ight and twenty-four units r espectively. A s the t ip o f the r esistance arm travels a greater distance than the t ip of the effort arm i n the s ame t ime i ts s peed must be greater. I f the spearthrower i s considered part o f this s ystem i ts f unction i s to add extra l ength t o the r esistance arm o f any existing body p ivot about which i t operates. The added l ength i ncreases the system's r esistance a rm and therefore the l inear velocity a t the end o f the spearthrower. I n disadvantageous l ever systems, h owever, the f orce being applied a t the end o f the lengthened resistance arm i s i nversely proportional to i ts l ength, r educing the system's ability t o move l arge l oads. This model predicts t hat t he l ength o f the spearthrower will have a direct r elationship t o the a mount o f velocity which i s a vailable to t he spear. This, i t will be remembered i s directly opposite to H oward's l inkage model, i n which the velocity i s related o nly to the speed of the body s egments. The major problem a ssociated with the l ever model in the above f orm i s, that l ike the l inkage model, the s ystem i n which i t operates h as been defined only at a very g eneral l evel. For example, a lthough the spearthrower may improve the l ength o f body r esistance arms the s pecific e lements of the system ( ie., f ulcrums, r esistance and e ffort arms) have not been i dentified. The throw p attern a ssociated with the s pearthrower, a lthough a g eneral overhand motion, i s n ot explicit i n the l evel model.

5 .3:

Kinesiological Analysis

The two models discussed above a re l imited, b ecause they are not based on an examination o f h ow the s pearthrower i s u sed t o cast a spear. The problem i s s imilar t o trying to analyse the mechanics o f a golf club i f the correct swing i s n ot understood ( at l east in principle). The operation o f the s pearthrower i s not s elfevident. This i s demonstrated by reference t o some o f the American experimenters. Browne ( 1940:211-212) described the motion of throwing a s a " fast o verhand sweep which l ifts the spear t o a h eight above the head equal t o the l ength o f both the arm and t he a tlatl" - p resumably much l ike a cricket bowl. Howard ( 1974:102), on the other h and, 4 8

c laims that the s pearthrower does n ot r ise above the l ine o f i ts original position and the throwing motion i s exactly the s ame a s f or a g eneral overhand throw, ( see a lso Davenport 1 943:37). Many o f the Australian observers would presumably have had the advantage o f s eeing the spearthrower u sed at f irst hand, yet t o the writer's knowledge, the motion has n ot been described i n any detail. The r eason f or this appears t o be t hat the a ction takes place over s uch a short t ime that i t i s impossible t o visually appreciate the motion i n any detail. A number o f f ilms o f Aborigines throwing s pears with a s pearthrower have been u sed to overcome this problem. By examining the f ilm f rame by f rame n ot only could the rapid and complex series of motions be more easily appreciated, but the a cceleration and velocity o f b ody s egments could a lso be determined. The f ollowing analysis i s based on an examination of two s equences f rom Howard Hughes' Spearthrower ( 1970) produced by the Australian Museum. The f ilm contains three s equences o f Mick Edwards o f the Edwards River ( Cape York) throwing a spear with a s pearthrower. This was the only f ilm f ound s uitable because the s equences were shot a t near 9 0 ° to t he a ction and contains the only recorded s equence shot f rom behind the thrower in l ine with the d irection o f s pear f light. F igure 1 0 s hows that the throw pattern i s not a bowling motion, b ut i s s imilar to a conventional overhand throw pattern. The d istances between the outlines of the s ame body s egment can be u sed a s a rough g uide to their r elative velocity. D uring the early phase o f the throw the whole body i s moved f orward i n the direction of throwing ( frames 1 -5). This i s f ollowed by a rotation about the spine producing s houlder r otation, which begins a t f rame 3 and c ontinues throughout the throw. At f rame 4 the l ateral r otation o f the humerus begins. This i s f ollowed by one o f the most characteristic f eatures of the overhand throw: t he humerus and the f orearm rotate about a c entre passing t hrough the l ong axis o f the humerus. The e ffect o f this rotation, which i s initially i n the opposite direction t o the i ntended throw i s to a llow the thrower t o medially r otate the f orearm, beginning f rom f rame 6 , f or a much l onger distance l ater in the throw. Cooper and G lassow ( 1968:18) point out that this medial r otation, which c ontinues up t o f rame 1 2 i s, next to wrist f lexion, " the f astest j oint a ction o f the upper l imb", and that i ts i nclusion i s vital to the s uccess o f any overhand throw . The f inal s egment t o be rotated i s the wrist which i s adducted f rom f rame 9 . This s equence o f j oint rotations n ot only equates with the general p icture o f the throw, which entails s equential s egment motion s tarting f rom the movement of h eavy body s egments t o the l ighter and more rapid, but

4 9

5 0 Spearthrower

a lso compares i n detail w ith t he overhand d escribed by C ooper a nd G lassow ( 1968).

throw pattern

a s

Examination o f o ther f ilms o f Aborigines throwing w ith the s pearthrower ( Balfour, 1 933; Campbell, 1 958; C ampbell, 1 963) a ll s howed a s imilar pattern. The only o bservable variation between t hrowers was the angle ( to t he horizontal) o f the p lane i n which the s pearthrower was r otated. Mick E dwards' t hrow t ends ( fig. 1 6) t o be f latter i n the f inal phase than those r ecorded by Campbell ( 1958) i n which the s pearthrower f ollows a more vertical p lane. A lthough t his variation i n s tyle does n ot a ffect t he overall operation o f t he s pearthrower i t does a ffect t he contribution o f s ome o f the body s egments t o the f inal v elocity. The s pearthrower m ay i ncrease t he r esistance arm o f a ny body l ever i n t he s ame p lane. F or example, i f the s pearthrower i s h eld o ut ( horizontally) f rom the body and a r otation i s a pplied f rom t he s houlder the added l ength o f the s pearthrower i ncreases the e ffective l ength o f the s houlder's r esistance a rm a nd s o i ncreases the e ffective l inear velocity o f t he r otation. I n the s ame p lane i t can a lso i ncrease t he e ffective velocity o f pelvic and wrist r otations but n ot h umeral. Variation i n the s pearthrowers r otational p lane c an b e s een a s an adjustment by the t hrower t o t he r elative s trengths and weaknesses o f h is b ody. A f latter t hrow w ill emphasise the contribution of b ody s egments a bout t he vertical a xis ( ie. pelvic and s houlder). The more overhand t hrow pattern t ends to emphasise the c ontribution o f t he " humeral twist". These p atterns s eem t o b e s pontaneous a nd depend t o s ome extent o n physique. A g roup o f t he writer's f riends t hrew spears w ith a s pearthrower i n a very i nformal experiment ( all w ere equally i nexperienced) a nd s howed the s ame variation i n s tyle, with t he most h eavily built i ndividuals t ending t owards more vertical s tyles. The visual a nalysis o f E dwards' t hrow s howed that the s pearthrower g ained much o f i ts r otational velocity f rom a w rist r otation i n t he f inal phases o f the throw . By f ollowing methods o utlined by Smith ( 1975) and O 'Connell a nd Gardner ( 1972) t he a ngular velocity a nd a cceleration o f the f orearm a nd wrist were c alculated f or Edwards' t hrow . The a ngular velocity o f t he f orearm a nd s pearthrower i n the vertical p lane by t ime i s s hown i n f igure 1 1. The f igure s hows t hat t he p eak velocity o f the f orearm i s s mall a nd precedes t he m uch h igher velocity c urve o f the s pearthrower which c ompleted i ts r otation i n l ittle more t han . 1 o f a s econd. A t t he p oint o f r elease ( between 1 f rame 1 and 1 2) t he f orearm r otation i s s ubstantially sec t o r educed f rom i ts maximum o f a pproximately 9 00 ° / b elow 4 00 ° / sec. The r esults o f two o f t he writer's throws w hich correlate w ith E dwards' n ot only i n g eneral

5 1

2 0

•

A

0 4

0 8

1 2

0

1 6

2 2

2 6 s ec .

t ime

Figure

1 1:

Forearm Edwards

and wrist • f orearm

0 A wrist.

5 2

angular velocity by time: 0 wrist; Cundy , Aforearm

c onfiguration but i n range i ncluded i n f igure 1 1.

of

s pecific

values

are

a lso

Kinesiological s tudies have analysed the velocities and contributions o f various body s egments in the overhand throw. Cooper and G lassow ( 1968:122) recorded the wrist a s contributing greater than 5 0% o f the f inal velocity, f ollowed by h ip, spinal and shoulder rotation. The a ngular velocity o f the wrist was over 8 ,500 ° /sec which a ppears to be very h igh. The velocities recorded f or the wrist rotation of M ick Edwards and myself r anged f rom 1 900 to 1 700 ° /sec., which compare well with the above. Although the s pearthrower's overall contribution relative to other body s egments could n ot be calculated, i t was a ssumed that the wrist rotation provides much o f the spear's f inal velocity. This analysis a lso provides an opportunity f or t esting Mason's ( 1884, 1 895) argument that the s pearthrower i ncreased the time i n which the thrower was i n contact with the spear, by comparing the t imes f or a h and throw with those o f a spearthrower. Table 3 , compiled f rom various s ources, i ndicates that the s pearthrower i ncreased the time i n which the thrower was i n contact with the spear, f rom between 1 5-30%.

TABLE

3 :

THROWING T IMES

H and Throw R eference

Time/Sec.

Projectile

Ariel

. 203

j avelin

. 15

baseball

( 1974)

Muybridge

( 1955)

Spearthrower Rotation Time C ampbell C undy H ughes

( 1958)

( 1980) ( 1970)

Total Time %

. 41

. 125

3 0

. 52

. 08

1 5

. 5

. 125

2 5

Although i mpulse i s u seful i n demonstrating that a n umber o f variables may be changed t o produce practical a dvantage without changing i n-flight performance o f the s pear i t i s d ifficult t o apply a t any greater depth. A lternatively t he l ever explanation, which emphasises the i ncrease i n l inear velocity which the s pearthrower a ffords t o the rotating body s egments, i s more s uccessful in 5 3

analysing h ow t he s pearthrower operates w ithin the c ontext o f the throw pattern, a nd i n d efining t he basic mechanical r elationships b etween the b ody a nd t he thrower. I t i s, h owever, a lso l imited i n d ealing w ith more c omplex problems o f s pearthrower mechanics.

5 .4:

Spearthrower Rotational Dynamics

Regardless o f which c oncepts a re u sed i n analysing the mechanics o f the s pearthrower t he implement m ust be g iven a r otational velocity a nd a cceleration by the thrower t o be e ffective. The amount o f r esistance which the i nertia o f the s pearthrower, exerts against the thrower i s, u sing the l oad/velocity r elationship, d irectly r elated t o t he body's a bility t o do work o n the s pearthrower and u ltimately on t he s pear. I f the s pearthrower's l oad i s t oo g reat, velocity and a cceleration will b e r educed; i f i t i s t oo small, h igh a ccelerations w ill b e a chieved a t t he expense o f power development. The f actors which a ffect t his l oading m ay be determined by r educing the s pearthrower's operation t o a s imple mechanical s ystem. A ssuming t hat most o f i ts a cceleration i s g ained f rom t he wrist r otation, i t may s imply be modelled a s a l ever a rm which extends the operation o f the p re-existing l everage s ystem o f the wrist. This i n t urn may b e s implified t o a rigid b ody r otating about a p ivot l ocated a t a p oint c lose t o one end, r educing the l oad producing variables t o a problem o f r igid body dynamics. A lthough t his i s n ot e ntirely a ccurate, a s o ther b ody s egments would a lso contribute t o the s pearthrower's a cceleration, t he m athematics i nvolved i n what i s t ermed a " multiple s egment" problem i s q uite extensive and adds l ittle t o t he b asic understanding o f the important variables ( see P lagenhoef, 1 971:51). A s the methods a nd units u sed i n r igid body dynamics will be unfamiliar t o most p rehistorians, t he f ollowing i s a brief i ntroduction t o the f orces i nvolved i n r igid b ody rotation. The s pearthrower, h owever, a s a lready s how, i s n ot r otated until the f inal phase o f t he throwing m otion. For t his, and r easons o f s implicity, t he f orces i nvolved i n the i nitial s tatic s ituation w ill b e c onsidered f irst.

( A)

S tatic

l oading

The product o f a f orce a nd a d istance i s c alled a moment. Moments produce a t orque a bout a g iven p oint, i n this c ase t he wrist ( fig. 1 2). Dyson ( 1962) i llustrates the e ffect o f moments a nd t heir i mportance w ith the example o f a j avelin. When h eld a t i ts c entre o f g ravity the l oad exerted by the j avelin i s equal t o i ts weight only -a s by d efinition t he c entre o f g ravity i s t he p oint where the s um o f a ll t he c lockwise a nd a nti-clockwise 5 4

m oments i s equal t o z ero ( see Abbott, 1 971:60). I f the j avelin i s h eld a t one o f i ts ends, h owever, the h older e xperiences a twisting f orce ( torque) about t he wrist w hich i s much m ore s ubstantial than t he l oad exerted by t he weight a long, making the j avelin much more d ifficult t o hold s teady. T o h old t he j avelin or s pearthrower and s teady the h older must exert a t orque ( Tb ) equal o pposite t o that exerted by the object ( Ta ) . Ta = Tb

= mgr

W here m i s t he mass o f t he s pearthrower, g the a cceleration d ue t o g ravity, and r i s the d istance f rom t he centre o f g ravity p erpendicular t o the d irection o f t he gravitational a cceleration.

( B)

Rotation d ynamics

g roups

I n o f

r otation f orces:

a s pearthrower

i s

s ubject

t o

two

major

I .

External f orces -t hese i nclude: t he f orce producing the r otation, t he c onstraining f orce o f the p ivot, gravitational f orces a nd f rictional f orces ( incorporating both s urface and f luid f riction).

2 .

I nertial body's

F orces -t hese f orces a re r esistance t o r otation.

a product

o f

the

I n t he f ollowing a nalysis both constraining and f rictional f orces were a ssumed a s c onstants. I nitially, t he rotating f orce i s d iscussed primarily i n t erms o f the f orces i t produces on t he r otating body o f the s pearthrower. These f orces a re d escribed a s an i ntroduction t o t he i nertial f orces. Any point o n a r igid b ody r otating a bout a f ixed axis w ill have an a ngular velocity ( w ) a nd a ngular a cceleration ( a). I t h as a lready been s hown t hat a ny point on a l ever a rm will h ave a n i nstantaneous l inear velocity which i s a p roduct o f the a ngular v elocity a nd t he d istance ( r) f rom t he pivot t o t he point. This velocity i s tangential to t he rotation o f t he a rm . S imilarly, a s the body i s a lso u nder a cceleration ( a) t he point w ill a lso h ave a l inear a cceleration ( a t ) which i s a lso t angential t o body's path. T his t angential a cceleration i s a product o f the angular a cceleration a nd t he d istance r . at = a r

The point a lso h as a r adial a cceleration ( ar) which i s a product o f the d istance r a nd t he angular velocity s quared ( see B arham, 1 978:327-9) ar = rw 2 5 5

)

M

Figure

1 2:

Figure

1 3:

o

= mgr

Static

Free body

f orces

on a thrower's wrist.

body d iagram o f the f orces i n dynamic equilibium .

5 6

on

a r igid

The radial a cceleration a cceleration, a nd i s r otation. Using Newton's f orces can be e asily f orce of a rotating r adial a cceleration, Fr

i s perpendicular to the tangential directed toward the centre of

s econd l aw the tangential and radial expressed. The radial or centripetal body i s a product of i ts mass and i ts a cting through the centre of gravity.

= mrw 2

L ike an Fr i s a lso directed towards the centre of r otation. g imilarly, the tangential f orce F i s g iven by the product o f mass and the tangential a cceleration, and i s a lso tangential t o the rotational path. Ft = mar

The inertia o f a r otating body ( or i ts resistance to motion) produces two more f orces which are equal and opposite to the tangential and rotational f orces. The f irst, constitutes the f amiliar centrifugal f orce and i s opposite in direction and magnitude to the radial f orce: F .

= mrw 2

As the spearthrower i s modelled a s a s ingle s egment motion, the centripetal and centrifugal f orces, being n ormal to the r otation, have no e ffect on the dynamic l oading about t he wrist. The tangential i nertial f orce ( F. 4 t ) on the o ther h and, i s o f considerable importance. This force i s derived on the s ame principle a s Ft . F . i t

= mar

This tangential i nertial f orce applies a torque about t he pivot which i s the product of the f orce and the d istance r : = mar

( r)

= mar 2

A third i nertial f actor must be i ntroduced at this p oint. I n rotating about a f ixed point a r igid body a lso r otates about i ts own centre o f gravity. The f orces producing centroidal r otation reduce to a s ingle couple I a a bout the centre o f gravity ( see Beer and Johnston, 1 962:606-7 f or f urther explanation). I n the expression I stands f or the object's moment o f inertia about i ts c entre o f gravity, and a i s the angular a cceleration. The moment o f inertia i s a r otational analogue o f mass. Like t he radial and t angential f orces the couple ( Ia) h as an i nertial reaction called the i nertia couple ( Ia i ) . The 5 7

i nertia I a.

c ouple

i s

opposite

i n

magnitude

and

direction

to

The r eality o f the e ffect o f a n i nertia couple will be a ppreciated by a nyone who h as t ried t o a ccelerate a b icycle wheel r apidly by h and. A lthough the w eight may b e carried wholly by t he b earings an e ffort i s r equired t o s et t he wheel s pinning. An i nertia couple i s o f course r eactive. ( Hannah and H illier, 1 971:183) T o expand on t his example, m ost people will h ave experienced t he problem t hat t he g reater the i nitial e ffort a pplied t o the wheel t he more d ifficult i t i s to r otate.

( C)

Dynamic

l oading

A s " motion i s g overned by t he a ction o f f orces, i t i s e ssential i n a ny motion a nalysis t o i dentify and d escribe the magnitudes, d irections a nd p oints o f a pplication o f these f orces" ( Barham, 1 978:404). T o a id i n this p rocess most a nalyses make u se o f a f ree-body d iagram. These d iagrams i solate the mechanical s ystem and s how a ll the a pplied a nd i nertial f orces a cting on the body. This method i s made possible by t he a pplication o f d ' Alembert's principle which s tates that: " the f orce o f i nertia o f a body i s equal t o and opposite a n a pplied f orce u sed t o move t he body r esulting i n k inetic equilibrium ( Barham, 1 978:405) ( see a lso B eer a nd J ohnston, 1 962:439-441, f or a more c lassical exposition). This p rinciple c onverts problems o f dynamics i nto p roblems i n s tatics, which may b e more e asily r esolved. F igure 1 3 i llustrates t he f ree body d iagram o f a s pearthrower a s d efined by the r igid b ody model ( see P lagenhoef, 1 971:46 a nd B arham, 1 978:404 f or details). The d iagrams s how a ll the applied and i nertial f orces n ecessary f or " kinetic equilibrium". The two a pplied f orces a re weight a nd the r otating t h as a lready b een s tated, produces Fr f orce ( F a ) which, i and Ft . Weight a s we h ave a lready s een i n the s tatic model o perates through t he b ody's c entre o f gravity and a pplies a t orque a bout t he wrist. This t orque i s not c onstant t hroughout r otation a s t he d istance r o f the moment i s measured n ormal t o t he vector ( or d irection) o f t he f orce. A s weight a lways o perates i n a d ownward d irection, r r educes a s t he s pearthrower a pproaches the vertical. The r otating f orce i s s upplied by m uscular c ontraction. A s the n umber o f muscles i nvolved i n any a ction, t he extent o f t heir c ontraction and the d istance o f their a ttachments f rom t he j oint c entres i s n ot k nown, i t i s d ifficult t o d etermine t he d irection o f the a pplied f orce. I t i s, t herefore, r epresented c onventionally by a vector t angential t o t he b ody's l ong a xis, producing the t orque which r otates t he b ody.

5 8

The major i nertial f orce i s g iven by the s ummation o f t he inertia couple a nd the i nertial t angential f orce. The i nertial t orque produced by these f orces i s g iven a s f ollows: mar)r Ti = ( U sing the b ecomes:

parallel

T .

=

a xis

( mr 2 + Ii ) a t heorem

the

above

equation

Io a

a s mr 2 + I .

= Io

In i n this c ase r epresents the moment o f i nertia o f a body when i t i s r otating a bout a p oint o ther than i ts centre o f g ravity. The t otal r eactive t orque ( T r ) or l oad producing t orque i s g iven b y t he a ddition o f the g ravitational ( T ) a nd inertial t orques ( Ti): Tr =

+ T

= Io

+ mg cosO

r

This equation s hows t hat the moment o f i nertia o f a b ody i s a primary f actor i n d etermining i ts r esistance t o r otation. The m oment o f i nertia o f a ny body i s dependent n ot only on i ts m ass, b ut a lso on t he d istribution o f the mass about t he a xis o f r otation. The c loser t he mass i s t o t he axis, t he e asier i t i s t o t urn. A f amiliar example o f t his i s a n i ce s kater's p irouette. When t heir a rms a re s tretched o ut f rom t he b ody t he d istribution o f mass about t he axis i s i ncreased a nd t he s kater r otates s lowly. As t he arms a re b rought c loser t o t he b ody t he moment o f i nertia decreases a nd d ue t o t he c onservation o f angular m omentum t he s peed o f the p irouette i ncreases. The g eneral f ormula f or t he moment o f i nertia i s g iven by I = fdmr` where " I i s t he s ummation o f the q uantities ( mass) t imes ( radius) f or a ll the particles o f t he body" ( Hannah a nd H illier, 1 971:182). The important p oint to d erive f rom t his expression i s t hat the d istance f actor ( r) i s s quared. I f, f or example, t he l ength o f a r od i s doubled y et m aintains t he s ame mass the moment o f i nertia will b e f our t imes g reater. I f t he mass i s a lso a llowed t o d ouble t he r od b ecomes e ight t imes harder t o r otate. This r elationship h as very i mportant i mplications f or s pearthrower mechanics, b ecause a ny a ttempts t o extend the l ength o f t he s pearthrower t o i ncrease l inear velocity w ill rapidly i ncrease t he l oad a bout t he wrist by a s quare f actor. The uncontrolled i ncrease i n l ength will a lso 5 9

increase the mass proportionally a dding a s econd f actor to the l oad. Although the thrower's body must be capable o f compensating f or this i ncrease t o s ome extent, t he range would be l imited. To overcome t his problem and m aintain high velocities and l ow l oads, s teps t o r educe either the mass per unit l ength or concentrate i t about the p oint o f rotation are necessary. To conclude this s ection the approximate magnitude o f the spearthrower's l oading about t he thrower's w rist i s considered. A f igure f or the angular a cceleration o f the spearthrower was calculated f rom the velocity/time curves ( fig. 1). I n the t ime period j ust before release th 1 a cceleration were a s f ollows: M . E eards, 8 23 r ads/sec' the writer, 8 73 and 1 004 rads/sec'. The differences between Edwards' and my own a ccelerations i s probably due to his being taken over a l onger t ime s pan ( .04 c ompared with . 02 s ec.). I f a s pearthrower o f cylindrical construction with a l ength o f one metre and a mass gf . 2 kgs i s g iven an angular a cceleration o f 8 00 rads/sec the inertial torque i s i n the order o f 6 0 newton/metres. This f igure i s very c lose to that f or h eavy tennis racket during a t ennis s erve, which P lagenhoef ( 1971:158) calculated a t 5 3 n ewton/metres. R emembering t hat the wrist velocity i s a lso comparable between the two a ctions the s imilarity i s not unexpected.

6 0

SIX

SPEAR AND

SPEARTHROWER ARTICULATION

The a rticulation o f t he s pear and s pearthrower i s the most mechanically c omplex a rea o f s pear and s pearthrower o peration. A s t he s pear's velocity i n the d irection o f t he target i s e ssentially a l inear motion and the s pearthrower i s a r otating s ystem the transfer o f energy f rom the s pearthrower t o the s pear i s the f undamental p roblem o f s pear a nd s pearthrower mechanics.

6 .1:

Static Models

Previous a pproaches t o s pear and s pearthrower a rticulation h ave d epended on s tatic models. These a pproaches will b e d iscussed b ecause they a re a pplicable t o t he s tage o f t he t hrow b efore the s pearthrower b egins t o r otate. The s pearthrower, j oined t o the base o f t he s pear by a p eg or s ocket i s, prior t o t hrowing, h eld i n a position s uch that i ts l ong a xis i s parallel t o that o f the s pear. T he spearthrower, i n t his position, exerts a t orque a bout t he wrist. By t he s ame principle o f moments the s pear w ill a lso exert a t orque a bout the wrist, equal t o i ts m ass and the d istance ( r) f rom the s pear's centre of g ravity t o the p ivot o f t he wrist. I f the s pear i s o f s ufficient l ength a nd mass t he t orque produced by the s pear will b e opposite t o t hat produced by the s pearthrower a nd o f a g reater m agnitude. The wrist o f the t hrower i s therefore b eing t urned f orward a nd downward. T his imbalance o f moments h as l ead s everal writers to a rgue that s pecific r elationships must o ccur b etween the s pear and t he s pearthrower. The s econd, a nd t he most c ommonly u sed s tatic model, i s b ased on a b iomechanical a rgument which a ssumes that h umans have an o ptimum l oad which t hey may t hrow or h old. A s s een i n chapter f ive t his may b e t he case f or energy p roduction, but i ts unqualified u se h as produced s ome u nsatisfactory p redictions a bout s pear and s pearthrower a rticulation. Davidson ( 1936:451) a rgued t hat h eavy s pears could be t hrown b est w ith a s hort s pearthrower a nd t hat l ight w eight s pears c ould b e t hrown w ith e ither l ong or s hort s pearthrowers. H e r easoned t hat a s a weight h eld i n the h and requires a n e ffort f or t he arm t o h old i t, h eavy s pears combined w ith a l ong h eavy s pearthrower would be t oo heavy t o t hrow . W ith l ight s pears i t d id n ot matter g reatly a bout t he a dded mass s o b oth l ong a nd s hort s pearthrowers c ould b e u sed. D avidson's prediction a bout 6 1

the r elationship b etween h eavy s pears and short s pearthrowers i s c orrect, b ut n ot f or the r easons proposed. H e was, h owever, i ncorrect i n a ssuming that s hort s pearthrowers a re n ecessarily l ighter. P eets ( 1960) i n f orwarding a s olution t o the American b annerstone p roblem a rgued t hat weight c ould b e added t o a s pearthrower t o c ounter the t orque o f the s pear. Long h eavy s pears, t herefore, r equired heavier and possibly l onger s pear t hrowers. P eets' argument h as a lso been u sed by C osgrove ( 1978) t o d efine t he f unction o f the s hell a ttachment t o the p roximal end o f Queensland s pearthrowers. P alter ( 1976), on t he o ther h and, n oted that there a re n o b annerstone l ike d evices f or adding mass t o the s pearthrower i n u se i n Australia d espite t he l engths o f the s pears u sed. H e c oncluded t hat: " ...the l ength o f these weapons s eems t o vary i ndependently w ith r espect t o the l ength a nd weight o f t he s pearthrower projectiles" ( 1976:503). This c onclusion i s n ot b ased o n any theoretical principles, but on a f ew brief references t o the e thnography, which h as very l ittle information r elevant t o this problem. Garrod ( 1955), l ike D avidson ( 1936) i mplicitly u sed a weight compensation model t o c onjecture that heavy s pearthrowers may be o f u se i n throwing l ight spears, she adds: " in e ffect, most modern t hrowers, s uch a s t hose o f the Australians and E skimos, f or e xample are l ight i n themselves, b ut a re u sed w ith h eavy s pears whose weight balances the thrower" ( 1955:52). T his s tatement i mplies that there i s s ome optimum c ondition o f " balance" which t he mass o f t he s pearthrower m ust m ake up i f the s pear i s l ight. Unfortunately Garrod d id n ot expand o n this explanation. The available p icture o f s pear a nd spearthrower a rticulation i s therefore l imited and c ontradictory. D avidson ( 1936) a rgues f or s hort l ight s pearthrowers/heavy s pears; P eets ( 1960) a rgues f or h eavy s pearthrowers/heavy s pears; P alter ( 1976) a rgues f or n o c orrelation and G arrod ( 1955) postulates h eavy s pearthrowers/light s pears.

6 .2:

Dynamic Models

A s a lready s een, t he s pearthrower, f or a t l east 7 5% o f the throw t ime a dds only i ts mass to t he l oad a ccelerated by t he t hrower, i t i s o nly i n t he f inal phase o f the t hrow t hat the s pearthrower t ransfers energy t o the s pear. To d emonstrate t he p roblems a ssociated w ith this t ransfer l et u s r eturn t o t he l inkage model of c hapter f ive. A s f igure 6 s hows, i f t he r atio o f the l ength o f the s pearthrower a nd t he r adius o f t he r otating s egment t o which i t i s l inked i s unity, t he t ransfer o f energy may b e 6 2

d istortion

L i J

0

1

6 3

a ccomplished w ithout d istortion o f t he s pear s haft. To d o this h owever, t here h as t o b e a n egative r otation about the wrist which r educes t he a ngle b etween t he s egment AB a nd the s pearthrower. I n t he l inkage model t he f inal i ncrease i n velocity o f the s pearthrower i s d ue to a r otation about B t o ensure t hat t he p oint C maintains a s traight l ine by r eturning a ngle ABC t o 9 0 degrees. I f the angle b etween t he f orearm a nd t he s pearthrower i s held constant throughout the r otation t he p oint C rises above the l ine FG a nd the s pear s haft must d istort to m aintain contact with the s pearthrower ( fig. 1 4). The distance ( e) a bove D E i s d irectly p roportional t o t he l ength o f the s pearthrower. I n a n ormal overhand t hrow p attern t he motion o f the projectile during t he f inal phase o f t he t hrow i s i n the d irection o f t he i ntended f light, i f t his were n ot the case much o f t he work d one by t he t hrower would not provide i ts maximum c ontribution t o t he velocity o f the projectile i n t he l ine o f f light. T he f inal rotation o f the wrist does n ot a ffect this n ormally a s i ts p rojected moment a rm i s r elatively small. When t he wrist's moment arm i s extended by t he s pearthrower, h owever, i ts r otation will be well o utside t he l ine o f t he n ormal t hrow, f orcing the spear t o bend i n order t o r emain i n c ontact w ith the s pearthrower. T he only way t o a void t his s ituation would be to f ollow t he p attern c onsistent w ith the l inkage model, by l imiting t he l ength o f t he s pearthrower and a llowing a n egative r otation a bout t he wrist.

6 .3:

Spear S pine

To r emain i n c ontact w ith t he s pearthrower t he spear must bend i n a c omplex manner. The s equence c an be s een i n the r ear projection o f M . Edwards' t hrow ( fig. 1 5). A s the s pearthrower b egins t o r otate t he s pear b utt i s progressively f orced o utward b ending t he body o f t he spear i nwards t owards t he t hrower. This b ending reaches i ts maximum when t he s pearthrower i s p erpendicular to t he l ine o f f light a nd d ue t o i ts e ffects the s pearthrower r emains i n contact with t he s pear a s i t c ontinues t o rotate away f rom the l ine o f f light. I n t he v ery f inal p hase o f contact t he s pearthrower moves t he s pear butt i n the opposite d irection, r eversing t he d irection o f the f lexion. This b ending c an a lso b e s een i n the C ampbell ( 1958) s equence. This b ending i s a k ey f actor i n a rticulating the s pear with t he s pearthrower, n ot only i n a llowing c ontact between the two c omponents, b ut a lso a s a v ital l ink i n the e fficient t ransfer o f energy f rom t he s pearthrower t o the s pear. A s t he s pearthrower b egins i ts i nitial r otation f rom a p osition p arallel t o t he s pear shaft, f or t he f irst f ew 1 /100ths o f a s econd m ost o f t he w ork done by the s pearthrower i s d irected n ormal t o t he direction o f f light. D uring t his s tage t he s pearthrower produces a 6 4

F igure

1 5:

S pear a nd s pearthrower projection).

6 5

articulation

( rear

torque about the s pear's c entre o f g ravity which w ill be a product o f the f orce a t the t ip o f t he spearthrower ( F t cose) by the h orizontal d istance ( r) f rom the b utt o f the s pear t o i ts c entre o f g ravity. I f t he spear shaft were perfectly r igid a nd t he t orque were o f s ufficient magnitude, t he s haft would r otate i n t he d irection o f the torque producing, a t b est, a n uncontrolled d irection, a t worst, t he s pear would t umble end o ver end until i t h it the g round. The only a lternative i s f or the s haft t o absorb the work d one by t he s pearthrower i n the d irection, perpendicular t o the l ine o f f light by b ending i n the direction o f the a pplied f orce. This b ending h as two advantages. F irstly, i t r educes t he e ffect o f the t orque by s toring the work done i n t he s pear s haft a s s train energy which would o therwise b e l ost or p roduce uncontrolled s pear behaviour. S econdly, this s tored energy may be converted i nto k inetic energy l ater i n the throw . A s the r otation continues, t he work done b y the s pearthrower becomes more a ligned w ith t he direction o f i ntended f light, h owever, d ue t o t he deflection o f the butt produced by the i nitial bending, t he f orce a pplied by the s pearthrower becomes more and m ore e ccentric, a s i t i s no l onger a pplied d irectly behind t he l ong axis o f the spear but t o the s ide. Energy i s c ontinually being s tored i n the s haft a s the bending c ontinues. This i s evident i n the i ncrease i n s haft f lex up until t he s pearthrower i s normal t o the d irection o f f light. A s t he spearthrower continues t o r otate beyond 9 0 d egrees t he work done i n the d irection o f f light d ecreases and t he b utt o f the s pear i s pushed i n the opposite d irection. D uring this p hase the energy s tored i n t he s haft b egins t o b e released a s k inetic energy, a s t he s haft begins t o s traighten. In a system with perfect energy c onservation a ll the e nergy s tored i n the s haft would be c onverted gradually t o k inetic energy a s t he s pearthrower r otates away a nd the spear l eaves the s pearthrower s moothly. I n r eality, however, s ome o f the energy i s n ot r eleased r apidly enough because the s pearthrower i s s till c ontributing some s train energy to the s haft. The r esidual s train energy r esults, upon the s pear's r elease, i n s haft v ibration a s the energy i s d issipated. This process c an b e s een c learly i n the Edwards s equence i n which t he motion o f the s pear b utt i s p lotted a fter r elease ( fig. 1 5). T he wave l ike p attern s hows that s ome o f the s tored energy was r eleased a s a dampened vibration o f t he r ear p ortion o f t he shaft. The ability o f a s haft t o a bsorb a nd r elease e nergy correctly i s r eferred t o by a rchers a s i ts spine; the s tiffer the s haft t he more s pine i t h as. To determine the f eatures o f s haft design which a re i mportant i n the control o f s pine r eference must b e m ade t o c olumn a nd beam theory. I n the i nitial phase o f the s pearthrower's r otation when the l oad a pplied i s n ormal t o the l ong axis o f the s haft, the s pear i s a nalogous t o a c antilever beam ( fig. 1 6). I n t he s econd phase a s t he spearthrower 6 6

b ecomes more e ccentric t he s haft behaves i n the s ame a s an e ccentrically l oaded column ( fig. 1 6). s eparation o f t hese two concepts i s done primarily c onvenience, a s the s haft b ehaves a s both f orms s tructure throughout the throw .

w hich

Taking the b ending f irst, i s absorbed by the s haft

t he amount o f i s g iven by:

way The f or o f

s train energy

U = F e 2 w here U i s t he s train d eflection ( see Axelrad, a lso g iven by:

energy, F 1 959:451).

t he The

l oad and e the deflection e i s

e = FL 3 3 E1 w here F i s the l oad L the l ength, E i s Young's modulus ( a m easure o f t he material's s tiffness) and I the areal m oment o f i nertia ( a measure o f the cross-sectional s tiffness o f a s tructure) ( see B eer and J ohnston 1 962: G ordon, 1 976:276-277). By c ombining both equations the s train energy a bsorbed becomes: U = F2 L3 6 E1 I n terms o f t he s haft c onstruction this equation s tates t hat t he amount o f energy absorbed i s g oing t o be p roportional t o t he l ength ( or d istance f rom the centre o f g ravity cubed a nd i nversely p roportional t o the s haft's s tiffness. The c ube f actor o f t he l ength makes l ength the m ost critical f actor i n controlling t he amount o f energy a bsorbed. A s imilar equation c an b e T he energy absorbed i s g iven by:

u sed

f or

s haft

b uckling.

I + e2 ) U = F2 L ( 2 E A I w here e i s t he d istance f rom t he n eutral axis t o the point o f application o f the l oad a nd A i s t he s haft's s ectional a rea ( Axelrad; 1 959:461). I n t his case t he energy s tored i s not only p roportional t o the l ength b ut a lso t o a s quared f actor o f the d istance e . This d istance will be p roportional t o t he l ength o f t he s pearthrower a s the l onger t he thrower t he g reater t he value o f e and a s e i s a squared f actor the l ength o f the s pearthrower becomes c ritical i n d etermining the amount o f energy absorbed by t he shaft. By s ubstituting r elevant values i n these equations i t b ecomes evident t hat the s haft w ill s tore more energy a s a c olumn t han a s a b eam. I f t he s haft, t herefore, d oes not 6 7

G " C I u ) a ) 0 : 17 : 1 Z 1 4 0 r — i > 1 — 1 > , • — i r c i, — I C D 0 : 1 U C — I l„ C 4 ) 4 ) C D U U 0 ) '

e ( I ) C I C l ) a )(„ 1( x i . _ Q . , •u )z a ) > , i -

w 4 ) 0 : 1 e, 1 -

4 ) •3

1 1 0 : 1 0,U g 4 4

u ) 0 : 1

4

a ) •, -

° I4

• , 1

e

( i ) I a ,4 I 0

( f ) 0

••

V D r i

6 8

0

a bsorb s ufficient energy n ormal t o t he d irection o f f light ( y) i t may t ip t owards the g round, on the o ther h and, i f i t absorbs t oo m uch i n t he d irection o f f light ( x), a s a r esult o f too g reat a d eflection t he s haft i s much more l ikely t o f ail t hrough b ucking. A s a ll s hafts must b e m inimally designed t o absorb the work i n the n ormal or y d irection the e xtra amount s tored d uring the s econd phase w ill place critical l oads on the s haft during the period w hen maximum w ork i s b eing done i n the d irection o f f light. A ssuming t hat t he a pplied f orce i s constant, the s haft i s f ar m ore l ikely t o f ail ( through buckling) i n t his f inal phase than i n a ny o ther p art o f the throw . There a re s everal ways i n which the s haft may b e made m ore capable o f s toring energy. F irstly, the equations p redict that l ong t hin s hafts s ubject t o l ow f orces will b e the best d esign. W ith s hafts o f l imited l ength, h owever, a f urther method i s t o t aper the s haft s o that i t i s capable o f d istributing t he energy more uniformly. A s A xelrad ( 1959, 3 67) s hows the amount energy which can be s tored i s i ncreased by 5 0%. This method would a lso h ave t he added advantage o f w eight r eduction. S econdly, the s haft could a lso b e made f rom c omplete t ree s tems; a s G ordon ( 1978: 2 82) p oints o ut, p lant s tems a re pres tressed s o t hat the c ompression s tress i n bending i s h alved, a llowing f or g reater b ending a nd energy s torage. Spears a nd s pearthrowers must t herefore be correctly m atched. F ailure t o d o t his may r esult i n s pear d eflection, r otation, or s haft f ailure. V irtually every a spect o f s haft d esign i s i mportant i n controlling the s pine o f the s pear. The n umber o f variables i s s o e xtensive, h owever, t hat t he b est s et o f f orms f or any g iven spear/spearthrower s ystem would only b e a rrived a t a fter extensive experimentation a nd experience with d iffering materials, construction, s ize and s hape.

6 .4:

Spear Mass a nd S pearthrower Length a nd Mass

Spear and s pearthrower a rticulation i s a lso d ependent o n the r elationship b etween t he mass or i nertia o f the s pear and the l ength a nd mass o f t he s pearthrower. I n the s pear/spearthrower a rticulation t he s pear's r esistance can b e considered t o operate t hrough t he t ip o f the s pearthrower. T o a chieve maximum p ossible a cceleration o f t he spear t here must b e a n a dequate f orce a t the s pearthrower's t ip t o overcome t he s pear's i nertia. I f t he f orce i s i nsufficient t he s pear will n ot b e g iven a h igh f inal velocity. The f orces d eveloped a t t he t ip o f t he s pearthrower a nd their r elationship w ith t he s pear a re c omplex. There a re two f orce c omponents i n t he x d irection which will c ontribute d irectly t o t he a cceleration o f t he s pear. The f irst i s that s upplied by t he extension o f t he t hrower's a rm and o ther b ody s egments. This f orce ensure the 6 9

continued a cceleration o f the s pear during the e arly phases o f the s pearthrower r otation ( when most of i ts work i s being done i n t he y d irection). The s econd f orce i s the component o f the t angential f orce a t the t ip o f the s pearthrower i n the x d irection. Considering the t angential f orce i n i solation, the magnitude o f i ts c omponent i n t he x d irection i ncreases a s the s pearthrower r otates, until i t i s equal t o the tangential f orce when the s pearthrower i s perpendicular to the s pear's l ine o f f light ( figs. 1 6). The magnitude o f the t angential f orce i s d ependent upon a c omplex r elationship between t he l ength a nd i nertia o f the s pearthrower and t o s ome extent the s pear' s r esistance to r otation. B ecause t he muscles controlling wrist r otation will operate under the s ame l oad/velocity principle a s any other s et i n the body, t he work which the wrist may perform on the s pearthrower v ia r otation w ill be proportional t o t he l oad a gainst t he wrist. With s pearthrowers o f l ow moments o f i nertia the v elocity imparted by the wrist w ill b e h igh b ut l ittle f orce will be g enerated by the thrower a nd s o the f orce a t the t ip o f the s pearthrower will b e correspondingly l ow . With s pearthrowers o f h igh i nertia t he w rist r otation would produce h igher f orce w ith l ower angular velocity. Spearthrowers o f h igh i nertia will t herefore have h igher tangential f orces a nd be c apable o f o vercoming the i nertia o f h eavy s pears. A s the s pearthrower operates a s an " inefficient" f irst c lass l ever the t angential f orce a t the t ip will be i nversely proportional t o the l ength; the l onger the s pearthrower the l ess f orce will be a vailable a t the t ip t o overcome t he s pear's i nertia. To f urther complicate the matter, t he l ength o f t he s pearthrower has a lready been s hown t o b e a s quare f actor o f t he moment o f i nertia s o any i ncrease i n l ength would r apidly r educe any advantage which i t would a fford i n h igher l inear velocity. There must, h owever, b e a n optimum r ange where m aximum f orce and velocity may b e obtained f or a g iven l ength and moment o f i nertia. W ithout f urther i nformation this r ange can only be g auged by examining t hese parameters i n the artifacts. A f urther f actor which l imits t he ability o f l ong s pearthrowers t o propel h eavy s pears i s that the s pear will exert a i nertial t orque a bout t he wrist which i s proportional t o i ts mass, l inear a cceleration a nd the l ength o f the s pearthrower. The a cceleration which the s pear will experience i n t he d irection o f f light ( as a r esult o f the s pearthrower's r otation) i s the x c omponent o f the t angential a cceleration a t the t ip o f the s pearthrower. A s t he magnitude o f t his a cceleration i s dependent on the a ngle o f r otation a nd the l ength o f the s pearthrower the i nertial t orque produced by t he s pear becomes greater a s t he s pearthrower r otates becoming more perpendicular t o t he l ine o f f light.

7 0

I n s ummary, l ong a nd l ight s pearthrowers will have d ifficulty i n p ropelling h igh mass s pears because a s an e xtended r esistance a rm t he f orce a t the t ip o f the s pearthrower c apable o f overcoming the s pear's i nertia b ecomes l ess a s the l ength i ncreases. S econdly, the i nertial moment o f the s pear about the thrower's wrist i s d irectly proportional t o t he l ength o f the s pearthrower a nd i ts a cceleration.

6 .5:

Performance Limitation a nd Construction Variation

The r eader w ill r emember that i t h as been e stablished t hat there was a complex r elationship between the work d one on a p rojectile by the thrower and the body's r esistance t o motion. I n s ummary l ight objects when thrown w ill tend t o h ave h igh velocity but l ow energy, and there w ill be a r ange o f l oads against which h umans will be able t o more e ffectively transfer energy, even though the v elocity o f s uch systems i s n ot n ecessarily h igh. A s this r elationship i s a product o f the p erformance o f i ndividual m uscles i t i s a pplicable t o the r otation o f a ll body s egments. The energy/velocity r elationship predicts that s pear a nd spearthrower t echnology i s e ssentially l imited i n i ts r ange o f performance optimizations f rom h igh energy/low velocity t o h igh velocity/low energy systems. O ptimizations f or h igh velocity will r esult i n a r elatively l ong r ange b allistic t echnology. The a dvantages o f t his a re, h igh e ffective r ange ( if the p rojectile c an b e c orrectly s tabilised), and f latter t rajectories f or s hort r ange t argets, thus f acilitating a iming. On t he o ther h and, t hese l ow energy projectiles l ack penetration a bility and w ill be t oo l ight to s eriously r educe t he g ame's ability t o e scape once s peared. The h igh energy s pear, on t he o ther hand, will p ossess p erformance characteristics c ompletely opposite to t he above, w ith h igh energy p enetration and ' stopping p ower', but r elatively s hort r ange and the n ecessity o f h igh trajectory a ngles. For h igh velocity t echnology, the optimum l oad v elocity r elationship would r equire a r eduction o f a ll i ntertial l oadings provided by t he s pear and s pearthrower. I t w ould a lso i nvolve the l engthening o f the s pearthrower t o i ncrease t he potential velocity o f the system. The f actors l imiting t hese p articular d esign f eatures h ave a lready been mentioned and c an be s ummarised a s f ollows: 1 .

The i nertia o f t he s pearthrower i s a f unction o f the l ength s quared s o d oubling t he l ength t o i ncrease t he p otential velocity o f the system i ncreases t he i nertial l oading by a f actor o f f our. This produces only a n arrow r ange where l ength may be i ncreased w ithout h aving t o r educe the mass t o compensate f or t he r ise t o i nertia. 7 1

2 .

The i nertial moment o f the s pear a bout the w rist of the thrower i s proportional t o t he l ength o f the spearthrower; by doubling t he s pearthrower's l ength the s pear's i nertial moment i s a lso d oubled ( assuming i ts a cceleration i s m aintained).

3 .

The l onger the s haft must bend with the s pear.

s pearthrower t he more a nd buckle t o r emain

the spear i n c ontact

To avoid the e ffects o f t he f irst o f t hese l imiting f actors the s pearthrower would h ave t o b e modified t o l ower i nertia but maintain l ength. T his may be a chieved by making the s pearthrower l ighter f or a g iven l ength. This creates the problem o f ensuring s ufficient r igidity i n the shaft o f the s pearthrower. The s pearthrower s hould be a s r igid a s possible i n the p lane o f r otation a s any energy s tored i n the b ending o f i t's s haft will n ot be r eleased t o the s pear until the very f inal phase o f the throw, when i t will b e r eleased a s l ateral movement o f the s pear shaft. To a chieve r igidity a nd l ightness the spearthrower can be modified b oth by materials choice a nd construction. A s most woods have r oughly t he s ame s tiffness the e asiest construction modification i s t o g ive t he s haft a rectangular cross s ection a nd r otate i t i n the p lane o f f light s uch that the n arrow f aces a re n ormal t o the p lane, i e. edge up. This changes t he a real moment o f the s pearthrower's cross-section s o t hat i t i s the s tiffest possible s hape f or t he l east mass ( see B eer and J ohnston, 1 962:319). The s econd method o f r educing t he inertia of a s pearthrower i s t o modify the s hape o f the s haft, s o that the mass i s more concentrated a bout t he wrist. T he best shapes f or c oncentrating mass a re pyramids a nd c ones, a s each h as a centre o f g ravity a t . 25 o f t he l ength. The construction o f s pears f or a h igh v elocity t echnology a lso r equires t he manipulation of c omplex variables. F or example, t he mass o f t he s pear m ust b e l imited, yet the s pear must b e l ong e nough to c ope with the l ong s pearthrower, a nd s tiff e nough n ot t o buckle excessively during the f inal phases o f the throw . A s a lready mentioned t his c an be a chieved by tapering the s haft and u sing s pecific types o f w ood, but this i s a ll that can be d one. With the h igh energy optimization on t he other hand, the mass o f the whole s ystem h as t o b e maintained at a l evel which ensures t hat the b ody w ill b e a ble t o do the maximum work possible on the s pear. This p resents f ewer t echnological problems, b ecause t he m ajor l imiting f actor i s the mass or i nertia o f t he s ystem, e specially o f the s pear. A lthough t he t echnology a lso h as t he problem o f mass l imitation, the existence o f a r ange over which peak power i s developed, i nsures t hat t he critical f actors 7 2

which l imit the optimization h igh velocity technology.

are

not

a s

pressing

a s

i n

the

The key design f actor of the high energy optimization i s the high mass of the spear. This ensures that the s pearthrower must be s hort i n order to reduce the spear's i nertial moment and ensure that there i s s ufficient f orce a vailable at the peg to overcome the spears greater i nertia. To maintain h igh i nertia with the shortened l engths the mass of the spearthrower would have to be i ncreased. As t he spearthrower i s shorter and heavier i ts s tiffness and mass concentration become l ess important, a nd so apart f rom ensuring s ufficient mass there would be l ittle n ecessity to modify h igh energy spearthrowers in a ny way directly related to the optimization.

6 .6:

Evidence

f or the

Structural

Relationships

There i s l ittle published evidence available on the s tructural relationships present in spear and spearthrower t echnology. The only material available comes f rom the American experimenters who have l ong been puzzled by the p resence of what appear t o be weights ( bannerstones) which w ere added to the a tlatl ( spearthrower). Conclusions a s t o the advantages/disadvantages of these weights have u nfortunately been s o variable, a s to cast doubts on the e xperimenters' b asic understanding of the mechanics and t he procedure o f experiment. Both Palter ( 1976:502) and H oward ( 1974:104) concluded that the extra mass of the s tones d id not improve the spear's distance; Mau ( 1963:11), on the other hand, concluded a 1 5-20% i mprovement; H ill ( 1948:42) postulated a l imited i mprovement f or l ight s pears and Peets ( 1960:109) and H obbs ( 1963:6-7) s aw l ittle variation in the results. B ecause of this variation none of these experimental s ources can, unfortunately, be u sed to test the e ffectiveness o f the i ncrease i n the spearthrower's moment o f i nertia which these weights would have a fforded. The only r eference t o l ong spearthrowers being d ifficult to operate with heavy spears comes f rom D avenport ( 1943:34). Howard's ( 1974:103) comments on an e ffect called " hooking" i n which the shaft i s overturned i f " the thrower f ails t o keep the atlatl l evel during t hrust", are an example o f the effect of i ncorrect spear s pine and i s exactly what would be expected i f the shaft d id not absorb enough s train energy. This e ffect i s a lso p erfectly i llustrated i n Brennan ( 1975:31-3). Other e xperimenters comments on the problem of s tability i n the s horter s hafts when thrown with an a tlatl may a lso be a r esult o f this e ffect ( see Davenport, 1 943:34; van Buren, 1 974:30). There i s t herefore l ittle empirical s upport f or the r elationships f orwarded i n this chapter f rom the available experimental l iterature. This i s not s urprising, a s no 7 3

existing experiments h ave extensive s eries o f t ests n umber o f f actors which performance.

b een d esigned t o c arry o ut the n ecessary t o control the l arge a ffect s pear and s pearthrower

7 4

S EVEN

STRUCTURAL R ELATIONSHIPS

7 .1:

Expected General

R elationships

I n chapter f ive i t was s uggested that the two major p erformance optimizations open t o s pearthrower t echnology were f or energy and velocity r espectively. E ach r epresented d ifferent ends o f a t echnological s pectrum; n either optimizations c an b e f ully r ealised i n any g iven s pear and s pearthrower combination. The model o f s pear a nd s pearthrower dynamics a lso d eveloped i n chapter f ive s howed that the f ollowing i nterr elationships c ould b e expected: 1 .

That there will be a p ositive correlation the mass o f t he s pearthrower and the mass spear.

2 .

That there will be a n i nverse r elationship between the l ength o f t he s pearthrower and t he mass o f the spear; h eavy s pears r equiring s hort and h eavy spearthrowers.

3 .

As a r esult o f predictions I a nd 2 t here will be an inverse r elationship b etween t he l ength a nd the mass of t he s pearthrower.

4 .

I f the h igh velocity optimization i s present there may a lso b e a ttempts t o l ower the s pearthrower's moment o f i nertia by c oncentrating the mass o f the spearthrower a bout t he p ivot o f t he t hrower's wrist. I n this c ase, mass c oncentration w ill b e correlated positively w ith i ncreased l ength.

7 .2:

between o f the

The S amples

To t est t he p redictions made about s pear and s pearthrower c onstruction a s ample o f s pears and s pearthrowers f rom the N orthern Territory o f Australia was examined. This a rea was chosen b ecause t he Northern Territory provides one o f t he widest r anges o f s pearthrower f orms f ound i n a ny part o f Australia, and a c omparatively l arge amount o f e thnological i nformation has been gathered f rom t he Aborigines o f t he area. The major s pear a nd s pearthrower Northern t erritory a nd a re: 1 .

Central Australian

( CA )

s pears

7 5

f orms

present

i n

a nd s pearthrowers

the

2 .

North Australian

( NA)

3 .

Northern spears

4 .

Goose

spearthrowers

5 .

Sabre

spearthrower

Australian

cylindrical notched

and

l ath

s pearthrowers spearthrowers

and

s pears

The Northern Australian notched l ath f orm was d ivided i nto two s ub-groups: east Arnhem Land ( EAL) and n orthwest ( NW). The North Australian cylindrical and t he sabre spearthrower s amples are n ot a ccompanied by a spear s ample because there i s either l ittle or n o i nformation about which f orms were u sed with the spearthrowers ( as i n the sabre case) or there are f ew collected s pecimens a vailable ( as in the NA cylindrical case). A ll f ive f orms are discussed i n more detail i n chapter e ight. The s amples were a ssumed t o be r epresentative o f the general population f or a type and were made as l arge a s practicably possible. Museum collections are by n o means i deal s amples. Their representative nature m ust b e a ssumed, a s the c ircumstances o f c ollection are rarely known. The researcher can take s ome s teps to a void the over representation of a s ingle i ndividual's work, but i n general the f actors a ffecting the collection o f these artifacts can be only minimally controlled. The a im o f the sampling was t o be a s representative a s possible and include, where possible, the o ldest and most varied representatives o f a g iven type. The s ample means, s tandard deviations and confidence l imits o f the population means are g iven f or s pearthrower f unctional l ength, mass, maximum width, minimum width, m aximum thickness, minimum thickness and distance f rom the centre of gravity to the p ivot i n Cundy ( 1980).

7 .3:

Spear and

Spearthrower Masses

I n comparing spear and spearthrower attributes o f populations which f ormed part o f t he s ame technological system, i t i s n o l onger possible t o match i ndividual spears with spearthrowers. I n s uch cases i t i s n ecessary to select the s ample means a s the basic analytic u nit even though the correlation o f means has restricted a nalytic power. The mean values f or the masses o f Central Australian, Northern Australian and goose spear and spearthrower s amples are p lotted i n f igure 1 7. F igures g iven by Gould ( 1970) f rom the Western D esert and B rokensha ( 1975) f or Central Australia s amples are a lso i ncluded. There i s a c lear positive correlation between t he mean masses o f the spears and those o f the s pearthrowers. The 9 5% c onfidence l imits o f the population means f rom which the samples were drawn are s o small that the correlation can not be h eavily 7 6

o

0 o

A

+

4-

-4 -

4. 2 -

V • 1 -

+ I . 3

I

. 1

2

S pea r th rowe r F igure

1 7:

M ass

Spearthrower mass by spear mass: B v Victoria; A NW; . EAL; P Brokensha ( 1975); 0 Gould ( 1970)

7 7

r A

K GS

G oose; • CA;

a ltered by variation i n e ither value. B oth Gould's and Brokensha's f igures c omply very well w ith the trend o f the graph. The f igures f rom s amples o f V ictorian spears and s pearthrowers, a lthough n ot w ithin t he s tudy area, also a gree with the t rend.

7 .4:

Spearthrawer Length a nd Mass

I n this a nd s ubsequent a nalyses which make u se of a s pearthrower's l ength, t he l ength w ill be converted t o what i s t ermed the f unctional l ength (4). A s the s pearthrower i s h eld a long i ts s haft, the l ength which r esists r otation, i s n ot the t otal l ength o f the s haft, but a f raction o f t hat d istance, d epending on the p osition o f t he t hrower's wrist p ivot a long t he s haft. The c loser the p ivot point i s t o the c entre o f g ravity of t he shaft t he easier i t i s t o r otate. The f unctional l ength i s defined a s t he t otal l ength m inus t he point at which the s pearthrower i s g rasped by t he i ndex and m iddle f ingers ( which i s g enerally i ndicated by n otching or r idging), p lus a constant value u sed t o r epresent the distance from the f ingers t o the wrist p ivot ( 6cm), m inus the h orizontal d istance f rom the d istal end o f t he s pearthrower t o the t ip o f the peg. I n c ases s uch a s t he Central Australian and s abre s pearthrowers this only meant the s ubtraction o f the peg l ength because they were b oth h eld very n ear the proximal end. I n o thers, l ike t he g oose spearthrower which were h eld s ome d istance up t he s haft i t w as a n important consideration. F igure 1 8 s hows t he f unctional l engths by mass o f f ive s pearthrower types: C entral A ustralian, Northern A ustralia ( east Arnhem L and a nd NW), NA cylindrical, g oose a nd sabre f orms. I n t he f irst f ive g roups t here i s a n egative trend between the mass and t he l ength c onfirming b oth t he s econd and third predictions. The d istribution s uggests, h owever, that this r elationship i s n ot a s s imple a s the i nitial prediction maintains. The model a llows f or t he existence o f two s trategies f or g aining t he most f avourable l oad/velocity relationship f or a g iven s pearthrower f orm. I nitially, i t was s uggested that t o maintain a c onstant moment o f i nertia w hen the s pearthrower was l engthened t he m ass would have to b e r educed t o maintain a f avourable l oad/velocity r elationship. The r ate a t which t he mass was reduced was an i nverse f unction o f the l ength s quared; a hyperbolic r elationship. The c urve ( A ) i n f igure 1 8 r epresents the mass/length r elationship f or the maintenance of a moment o f i nertia o f . 05 k g/m', a ssuming t he s pearthrower has a constant symmetrical s hape w ith a c entre o f gravity a t . 51 and a uniform d iameter. The c urve p asses close to a n umber o f means a nd t ends t o f ollow t he trend of t he graph i ndicated mainly by t he s abre s pearthrower s ample.

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