Mi t t . Mus . Nat . kd . Ber l . , Geowi ss. Rei he 2 ( 1999) 63- 73 19 . 10. 1999
Post ur e and Mec hani c s of t he For el i mbs of Br ac hi os aur us br ancai
( Di nosaur i a : Saur opoda)
Andr eas Chr i st i an' , Wol f - Di et er Hei nr i ch' & Wer ner Gol der2
Wi t h 5 f i gur es
Abst r act
The post ur e and mechani cs of t he f or el i mbs of Br achi osaur us br ancai wer e anal ysed wi t h t he hel p of bi omechani cal model s . Peak f or ces i n t he j oi nt s due t o accel er at i on of t he f r act i on of body wei ght car r i ed on t he shoul der j oi nt s ar e cr i t i cal i n model s wi t h compl et el y st r ai ght , col umn- l i ke l i mbs and a r i gi d shoul der gi r dl e. Dur i ng f ast wal ki ng, ei t her t he f or el i mbs wer e f l exed at t he el bows dur i ng t he mi ddl e of t he suppor t phase or t he appar ent l y r i gi d shoul der gi r dl e al l owed mov ement s of t he shoul der j oi nt s r el at i ve t o t he t r unk . The over al l const r uct i on of Br achi osaur us was r el at ed t o an ext r eme t ask, br owsi ng hi gh above t he gr ound . Consequent l y, ver sat i l i t y was ver y r est r i ct ed.
Key wor ds: Di nosaur s, saur opods, Br achi osaur us, l ocomot i on, l i mbs, l i mb post ur e, f unct i onal mor phol ogy, bi omechani cs .
Zusammenf assung
Di e St el l ung und di e Mechani k der Vor der bei ne von Br achi osaur us br ancai wur den mi t Hi l f e v on bi omechani schen Model l en unt er sucht . Kr af t spi t zen auf gr und v on Beschl euni gungen des von den Schul t er n get r agenen Ant ei l s der Kör per masse er schei -nen i n Model l en mi t völ l i g ger aden, säul enf ör mi gen Vor der bei nen und ei nem unbewegl i chen Schul t er gür t el pr obl emat i sch . Währ end des schnel l en Gehens war en ent weder di e Vor der bei ne i n der Mi t t e der St üt zphase i n den El l enbogengel enken gebeugt oder der schei nbar r i gi de Schul t er gür t el er l aubt e Bewegungen der Schul t er gel enke r el at i v z um Br ust kor b . Di e Ge-samt konst r ukt i on von Br achi osaur us war auf di e Aus übung ei ner ext r emen Tät i gkei t , di e Nahr ungsauf nahme i n gr oßer Höhe, ausger i cht et . Di e Konsequenz war ei ne ger i nge Vi el sei t i gkei t .
Schhi ssel wör t er : Di nosaur i er , Saur opoden, Br achi osaur us, For t bewegung, Ext r emi t ät en, Ext r emi t ät enst el l ung, Funkt i onel l e Mor phol ogi e, Bi omechani k .
I nt r oduct i on
Br achi osaur us br ancai f r om t he Lat e Jur assi c of East Af r i ca i s one of t he most f asci nat i ng di no-saur s. Ev en t hough many det ai l s of t he skel et on ar e wel l - known ( e . g . , Janensch 1935, 1950, 1961) , t he post ur e and t he l i f e- st yl e of t hi s cr eat ur e has been di sput ed f or many year s. I n s ome ear l y r econst r uct i ons, Br achi osaur us i s s hown wi t h semi -ext ended f or el i mbs ( Janensch 1950 ; Fi gs 1, 2, 3A) and even s ome moder n popul ar books on di nosaur s s how Br achi osaur us wi t h t he el bows pr ot r udi ng t o t he si des . However , among most r ecent wor ker s t her e i s l i t t l e doubt about a f ul l y ext ended f or e- and hi ndl i mb post ur e i n Br achi o-saur us and ot her o-saur opods ( Char i g 1979, Al ex-ander 1985a, 1989, Bakker 1986, Paul 1987,
Wei shampel et al . 1990, Fast ovsky & Wei sham-pel 1996 ; Fi g . 3B) .
One i mpor t ant ar gument i n f avour of t hi s i dea i s t he hi gh body wei ght of saur opods . I n geomet r i -cal l y si mi l ar shaped ani mal s of di f f er ent si ze, body wei ght i ncr eases t o t he t hi r d power of l i near di -mensi ons ( e. g . body l engt h) wher eas max i mum muscl e f or ces and st r engt h of bones, t endons and l i gament s i ncr ease onl y wi t h t he squar e of l i near di mensi ons . Ther ef or e, l ar ger ani mal s t end t o be l ess f or cef ul wi t h r espect t o t hei r body wei ght t han smal l er ani mal s . Thi s i mpl i es t hat ver t ebr at es of di f f er ent si zes may have a di f f er ent l i mb post ur e . Gener al l y, t he l i mbs t end t o be mor e ext ended i n l ar ger ver t ebr at es, so t hat t he l ever ar ms of ext er -nal f or ces ar e r educed ( Mc Mahon & Bonner 1983, Schmi dt - Ni el sen 1984, Al exander 1985a, b, 1989,
1 Mus eum f ür Nat ur kunde, I nst i t ut f ür Pal äont ol ogi e, I nval i denst r . 43, 10115 Ber l i n, Ger many .
2 Fr ei e Uni ver si t ät Ber l i n, Uni ver si t ät skl i ni kum Benj ami n Fr ankl i n, Fachber ei ch Humanmedi zi n, Radi ol ogi sche Kl i ni k und Pol i kl i ni k, Hi ndenbur gdamm 30, 12200 Ber l i n, Ger many .
Mi t t . Mus . Nat . kd . Ber l . , Geowi ss. Rei he 2 ( 1999)
Fi g . 2 . Mount ed skel et on of Br achi osaur us br ancai f r om t he Lat e Jur assi c of Tendagur u ( Tanzani a) i n t he Mus eum of Nat ur al Hi st or y of t he Humbol dt Uni ver si t y, Ber l i n . Ant er ol at er al vi ew, showi ng det ai l s of t he shoul der gi r dl e and ant er i or l i mbs
Pr euschof t & Demes 1985, Bi ewener 1989a, b, 1990, St eudel & Beat t i e 1993, Pr euschof t et al . 1994, 1998, Chr i st i an & Gar l and 1996) . These bi o-mechani cal ar gument s suggest a f ul l y ext ended l i mb post ur e i n ani mal s as l ar ge as saur opods . I n saur opods and ot her di nosaur s, t he usual l y nar r ow t r ackways ( Lockl ey 1991, Thul bor n 1990, Lockl ey & Hunt 1995) i ndi cat e t hat l i mb mov ement s i ndeed wer e r est r i ct ed t o par asagi t t al pl anes . Addi -t i onal l y, f or mos -t di nosaur s, a mammal - l i ke l i mb post ur e can be model l ed f r om skel et al f eat ur es ( Char i g 1979, Bakker 1986, Paul 1987, 1988, Wei shampel et al . 1990, Fast ovsky & Wei shampel 1996) . Compl et el y st r ai ght l i mbs, however , ar e not sui t abl e f or accel er at i on, as wi l l be demonst r at ed bel ow. Ther ef or e, a f ul l y ext ended l i mb post ur e wi t h ver y l i t t l e f l exi on i n t he el bow and knee j oi nt s can be expect ed onl y i n heavy, gr avi por t al ani mal s
65
( Coombs 1978) . The heavi est r ecent t er r est r i al ver t ebr at es ar e el ephant s . I n wal ki ng el ephant s, under l oad ( dur i ng t he suppor t phase) , t he l ong l i mb bones r emai n mor e or l ess i n l i ne ( Gam-bar yan 1974, Chr i st i ansen 1997) . Because of t he evi dence l i st ed above, t he i dea of f ul l y ext ended l i mbs i n Br achi osaur us i s ver y at t r act i ve .
Mi t t . Mus . Nat . kd . Ber l . , Geowi ss. Rei he 2 ( 1999)
I n mammal s , dur i ng l ocomot i on, t he ef f ect i ve l i mb l engt h i s changed by f l exi on and ext ensi on i n t he l i mb j oi nt s . I n t he f or el i mbs, peak l oads ar e r educed by mov ement s of t he shoul der bl ades r el at i ve t o t he chest , so t hat t he t r aj ect or y of t he cent r e of gr avi t y of t he mass car r i ed by t he f or e-l i mbs i s smoot her t han t he t r aj ect or y of t he shoul der j oi nt s. Li ke saur opods, t he bi ggest l i v-i ng t er r est r v-i al ani mal s, el ephant s, do not ut i l i se t r ue r unni ng gai t s. Ther ef or e, l ess mobi l i t y i s ne-cessar y i n t he shoul der gi r dl e of el ephant s com-par ed t o ot her mammal s ( Gambar y an 1974, Haynes 1991) . However , t he scapul a i s st i l l sui t ed f or moder at e movement s r el at i ve t o t he under -l yi ng r i bs, so t hat t he shoul der j oi nt s can shi f t r el at i ve t o t he t r unk dur i ng l i mb mov ement s . Addi t i onal l y, pads of sof t t i ssue under t he f eet hel p t o cushi on i mpact s due t o t hei r compl i ance . These pads ar e compr essed when t he f oot i s pl aced on t he gr ound and t hey ext end at t he end of t he suppor t phase . I n addi t i on, t he l ong bones of t he f or el i mbs ( i ncl udi ng t he met acar pal s) ar e not per f ect l y i n l i ne so t hat some changes i n t he j oi nt angl es ar e possi bl e under l oad . These f ea-t ur es hel p ea-t o cushi on i mpacea-t s ea-t her eby r educi ng peak f or ces act i ng on t he l i mbs dur i ng l ocomo-t i on .
The evi dence put f or war d by Chr i st i ansen ( 1999) i ndi cat es ver y r est r i ct ed mov ement s i n t he f or el i mbs and l i t t l e ver t i cal di spl acement s i n t he pect or al gi r dl e under l oad i n a wal ki ng Br a-chi osaur us ( see al so bel ow) . Thi s concept , how-ever , i s cr i t i cal wi t h r espect t o t he peak f or ces t hat occur i n t he l ocomot or appar at us, especi al l y i n t he j oi nt car t i l age, as wi l l demonst r at ed her e . I n or der t o r educe peak f or ces dur i ng f ast wal k-i ng ek-i t her s ome f l exk-i on k-i n t he el bows of Br achk-i o-saur us was necessar y or t he pect or al gi r dl e must have al l owed s ome mobi l i t y, so t hat ver t i cal shi f t s of t he shoul der j oi nt s r el at i ve t o t he chest wer e possi bl e. Thi s r esul t conf i nes t he possi bl e r econst r uct i ons of Br achi osaur us.
Met hods
For t he bi omechani cal anal ysi s, body di mensi ons of Br achi osaur us wer e der i ved f r omt he exhi bi t ed r econst r uct i on i n t he Humbol dt Mus eum of Nat -ur al Hi st or y, Ber l i n, Ger many ( Fi gs 1, 2) . Despi t e i t s composi t e nat ur e, t hi s skel et on al l ows a r ea-sonabl e r econst r uct i on of t he body pr opor t i ons t hat ar e r el evant f or t hi s st udy because suf f i ci ent bone mat er i al bel ongs t o a si ngl e i ndi vi dual ( SI I ) ( Chr i st i an & Hei nr i ch 1998) . Est i mat es of t he
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f r act i on of body mass t hat was car r i ed on t he shoul der j oi nt s ar e based on est i mat es of t he mass di st r i but i on i n t he body of Br achi osaur us by Gunga et al . ( 1995) . Accor di ng t o Gunga et al . ( 1995) t he t ot al vol ume of t he body of t he Ber l i n speci men of Br achi osaur us br ancai was about 74 . 4
M
Z.
Gunga et al . ( 1995) assumed ci r cul ar cr oss sect i ons i n neck and t ai l t her eby over est i -mat i ng segment vol umes by about 20% or 30%. Ther ef or e, i n t hi s st udy, t he vol ume of neck and t ai l was r educed by a f act or of 0 . 8 . The l ungs and pneumat i c cavi t i es i n t he neck wer e al so t aken i nt o account by assumi ng a mean densi t y of t he body of 900 kg/ m3 i nst ead of ar ound 1000 kg/ m3 as usual f or many moder n ver t ebr at es ( Al exan-der 1989) . These r educt i ons i n est i mat ed body mass most l y af f ect t he f r act i on of mass car r i ed on t he shoul der j oi nt s . For compar i son, t he di st r i bu-t i on of body mass was al so der i ved f r om t he scal ed r ubber model of Br achi osaur us pr oduced by t he Br i t i sh Mus eum of Nat ur al Hi st or y. I f l ung cavi t i es wer e added t o t he r ubber model , bot h est i mat es of mass di st r i but i on yi el ded essent i al l y t he s ame r esul t s wi t h r espect t o t he l oad on t he f or el i mbs . The neck was model l ed i n ver t i cal pos-t ur e accor di ng pos-t o pos-t he f i ndi ngs of Chr i st i an & Hei nr i ch ( 1998) . Wi t h t hese assumpt i ons a t ot al body mass of about 63, 000 kg was est i mat ed . Of t hi s mass a f r act i on mof appr oxi mat el y 20, 000 kg was car r i ed on t he shoul der j oi nt s . To cal cul at e t he mass m, most of t he mass of t he l i mbs was subt r act ed f r om t he t ot al body mass because i t was not car r i ed on t he shoul der and hi p j oi nt s . Assumi ng t hat t he l ungs wer e l ocat ed i n t he f r on-t al par on-t of on-t he on-t r unk, on-t he cenon-t r e of gr avi on-t y of on-t he r est of t he body was l ocat ed cl oser t o t he hi p j oi nt s t han t o t he shoul der j oi nt s. Ther ef or e con-si der abl y l ess t han hal f t he t ot al body wei ght was car r i ed on t he shoul der j oi nt s .Dur i ng l ocomot i on, Br achi osaur us was as-s umed t o be conf i ned t o wal ki ng gai t as-s ( Thul bor n
1990, Chr i st i an et al . 1999) . I n accor dance wi t h moder n speed est i mat es i n t he l i t er at ur e ( Al ex-ander 1976, 1989, Thul bor n 1990, Chr i st i an et al . 1999) , a max i mum wal ki ng speed of 4 . 5 m/ s ( 16 . 2 km/ h) was est i mat ed f or a Br achi osaur us t he si ze of t he Ber l i n speci men . At t hi s speed, st r i de l engt h s was est i mat ed t o be t wi ce t he hei ght of t he hi ps h above t he gr ound ( Al exan-der 1976, Thul bor n 1990) . The f oot f al l pat t er n i n a wal ki ng Br achi osaur us was assumed t o be si mi -l ar t o el ephant s dur i ng wal ki ng ( Gambar yan 1974, own obser vat i ons) .
a-chi osaur us and ot her Tendagur u- saur opods was anal ysed wi t h t he hel p of Comput ed Tomogr a-phy scan r econst r uct i ons . The pr ocedur e and t he basi c r esul t s of t hi s CTst udy ar e descr i bed by Gol der & Chr i st i an ( 1999) . I n t he Ber l i n speci -men of Br achi osaur us, t he mi ni mal cr oss- sect i on i n t he mi ddl e f r act i on of t he humer us ( of t he speci men SI I ) i s ar ound 29, 000 mm2 ( at a di s-t ance 970 mmabove i s-t s di ss-t al end) . Accor di ng s-t o CT scan r econst r uct i ons, t he di aphysi s of t he hu-mer us of Br achi osaur us i s near l y sol i d, wi t h dense bone f or mi ng bet ween 80% and 90% of t he cr oss- sect i on ( Gol der & Chr i st i an 1999) , so t hat compr essi ve f or ces coul d be di st r i but ed over
appr oxi mat el y 25, 000 mm2 of dense bone . Com-pr essi ve f or ces al so act ed i n t he j oi nt car t i l age. For ces act i ng i n t he car t i l age of t he shoul der j oi nt s can be used t o est i mat e t he max i mum accel er at i on of t he f r act i on of mass car r i ed on t he shoul der j oi nt s, as wi l l be demonst r at ed bel ow. Wi t h t he hel p of t he CTdat a pr esent ed by Gol der & Chr i st i an ( 1999) and t he di mensi ons of t he shoul der j oi nt s of t he Ber l i n speci -men of Br achi osaur us, i t can be est i mat ed t hat t he f or ces exchanged bet ween scapul ocor acoi d and humer us had t o pass t hr ough an ar ea of about 50, 000 mm2 or l ess ( ` sur f ace ar ea' of t he shoul der j oi nt ) .
The anal ysi s i s based on t he f ol l owi ng as-sumpt i ons about a Br achi osaur us t he si ze of t he Ber l i n speci men wal ki ng at i t s max i mum speed . Some of t he dat a pr esent ed bel ow cannot be mor e t han r ough est i mat es. Er r or s of 10% or even 20% ar e possi bl e, except i n t he f or el i mb l engt hs, but do not af f ect t he gener al concl usi ons r egar di ng f or el i mb post ur e and mechani cs pr e-sent ed bel ow. I nsi de t he er r or r age, t hose val ues wer e chosen t hat gave t he l east suppor t f or t he ar gument at i on bel ow.
For el i mb l engt h ( f r om gr ound t o shoul der j oi nt ) : 4 . 1 m ( upper ar m - 2 . 15 m; f or ear m - 1 . 30 m;
f oot - 0 . 65 m)
Hei ght h of t he hi ps above t he gr ound: 3 . 5 m Max i mum st r i de l engt h s ( = 2 - h) : 7 . 0 m Max i mum speed of l ocomot i on v : 4 . 5 m/ s
Tot al body mass : 63, 000 kg
Fr act i on m of t he body mass car r i ed
on t he shoul der s : 20, 000 kg
Mi ni mum cr oss- sect i on of dense bone
i n t he humer us : 25, 000 mm2
` Sur f ace ar ea' of t he shoul der j oi nt
( as def i ned above) : 50, 000 mm2
Wal k i ng wi t h f ul l y ex t ended l i mbs
Wal ki ng wi t h f ul l y ext ended l i mbs can be de-scr i bed wi t h t he hel p of t he model of an " i
n-ver t ed pendul um" ( Moc hon & Mc Mahon 1980a, b, Al exander 1980, 1982, Fi g . 4) . To appl y t hi s model t o a quadr uped, t he body of Br achi o-saur us i s model l ed as t wo uni t s, f r ont and hi nd, each of whi ch i s car r i ed by a si ngl e pai r of l i mbs. Wi t h l i mbs t hat r emai n st r ai ght t hr oughout t he suppor t phase, hi p or shoul der j oi nt s mov e al ong ar cs wi t h t he convex si des f aci ng upwar ds t her
e-A
B
C
di r ect i on of mov ement
- - - - t r aj ect or y wi t h st i f f l i mbs
t r aj ect or y wi t h changes i n l i mb l engt h
t r aj ect or y of t he shoul der j oi nt s
A
FZ=CO
=F=F g +F, =w
Mi t t . Mus . Nat . kd . Ber l . , Geowi ss . Rei he 2 ( 1999)
by f or ci ng t he f r act i ons of mass car r i ed on t he shoul der or hi p j oi nt s, r espect i vel y, t o per f or m t he s ame ki nd of mov ement s .
To cal cul at e t he t ot al l oad on a l i mb, f or ces due t o accel er at i on have t o be t aken i nt o ac-count ( Al exander 1982) . The l oadi ng f or ce F on a pai r of l i mbs i s gi ven by :
F=m. g+m- a=m- ( g+a) ,
wher e m = t he f r act i on of body mass car r i ed on t he pr oxi mal l i mb j oi nt s, g = accel er at i on due t o gr avi t y, and a = accel er at i on t hat r esul t s f r om movement s of t he mass m on i t s t r aj ect or y ( Fi gs 413, 4C) .
Dur i ng wal ki ng at const ant speed, at bot h t he hi ghest and t he l owest posi t i ons al ong t he t r aj ec-t or y, ec-t he hor i zonec-t al accel er at i on of t he mass m can be negl ect ed . I n or der t o cal cul at e t he t ot al l oad on a l i mb, however , at t he t ops of t he ar cs t he cent r i f ugal f or ce FZ has t o be subt r act ed f r om t he wei ght f or ce ( Al exander 1982) wher eas a cent r i f ugal f or ce has t o be added at t he t r ansi -t i on poi n-t s of -t wo consecu-t i ve ar cs ( Fi gs 413, 4C) . The cent r i f ugal f or ce Fz i s gi ven by t he squar e of t he speed v di vi ded by t he r adi us of cur vat ur e r of t he t r aj ect or y :
FZ = v 2 / r . ( 2)
Wi t h st i f f l i mbs, t he r adi us of cur vat ur e r i s zer o at t he t r ansi t i on poi nt s of consecut i ve ar cs ( Fi g . 413) , so t hat t he t ot al l oad on t he l i mbs i s i nf i ni t e at t hese poi nt s . Ther ef or e, wal ki ng wi t h a f r act i on m of t he body mass f i xed t o t he pr oxi -mal j oi nt s of absol ut el y st i f f l i mbs i s i mpossi bl e . Thus, i n t he f or el i mbs of Br achi osaur us, even un-der axi al l oadi ng condi t i ons, ei t her consi der abl e f l exi on i n t he el bow j oi nt s or mov ement s of t he shoul der j oi nt s r el at i ve t o t he chest wer e neces-sar y t o r educe peak f or ces dur i ng t he suppor t phase, as wi l l be demonst r at ed i n mor e det ai l i n t he f ol l owi ng.
The wei ght l oaded on a l i mb r esul t s i n f or ces act i ng i n t he l i mb bones . A mi ni mum ( compr es-si ve) f or ce occur s under axi al l oadi ng condi t i ons and a homogeneous di st r i but i on of t he f or ce over t he cr oss- sect i ons of t he bones . I n t he humer us of Br achi osaur us ( SI I ) , t he mi ni mum cr oss- sect i on of dense bone i s about 25, 000 mm2 ( see met hods) . Assumi ng a max i mum st r ess ( yi el d st r ess, st r ess = f or ce/ cr oss- sect i on) of about 200 MPa ( Mega- Pascal , 1 MPa =1 N/ mm2 ) bef or e br eaki ng ( Bi ewener 1982) , each humer us was capabl e of sust ai ni ng a max i mum axi al compr essi ve f or ce of about 200 N/ mm2 t i mes 25, 000 mm2 = 5, 000 k N ( equi val ent t o about
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500, 000 kg) whi ch i s 25 t i mes t he est i mat ed t ot al wei ght car r i ed on t he shoul der j oi nt s ( see above) or appr oxi mat el y ei ght t i mes t he t ot al body wei ght . I n t he f or ear m ( r adi us pl us ul na) , t he mi ni mum cr oss- sect i on of dense bone i s not ver y di f f er ent f r om t he upper ar m ( humer us) , so t hat t he max i mum sust ai nabl e compr essi ve f or ce i s si mi l ar t o t he humer us . These r esul t s ar e onl y moder at el y af f ect ed by t he l i mb mass . The l i mb mass i s negl ect ed her e ( see met hods) , but mod-er at el y i ncr eases t he st r ess i n t he hummod-er us and t he st r ess i n t he bones of t he l ower l i mb .
I n ext ant ver t ebr at es, dur i ng r egul ar l y occur -r i ng act i vi t i es, t he max i mum st -r ess i n bones, t en-dons and l i gament s, i s muc h l ower t han t he yi el d st r ess. The r at i o bet ween t he yi el d st r ess and t he max i mum occur r i ng st r ess i s cal l ed saf et y f act or . I ndependent of body si ze, t he saf et y f act or i s ar ound t hr ee ( bet ween t wo and f our ) i n bones ( Al exander 1985, Bi ewener 1989a, b, 1990) . As-sumi ng a saf et y- f act or of about 3 i n t he humer us of Br achi osaur us, as wel l , t he max i mum com-pr essi ve st r ess t hat i s l i kel y t o have occur r ed dur i ng r egul ar mov ement s was appr oxi mat el y 70 MPa ( i n accor dance wi t h Al exander et al . 1990) , so t hat t he max i mum compr essi ve f or ce on each humer us was about 70 N/ mm2 t i mes 25, 000 mm2 = 1, 750 k N. Wi t h an angl e of about 51° f or med by bot h f or el i mbs at t he t r ansi t i on poi nt s of consecut i ve ar cs of t he t r aj ect or y of t he mass m car r i ed on t he shoul der j oi nt s ( Fi g . 4) , t he t ot al ver t i cal f or ce exer t ed on t he shoul der j oi nt s coul d have been as hi gh as 3, 500 k N or bet ween 17 and 18 t i mes t he wei ght of t he mass m. Then, t he accel er at i on a of t he mass m coul d have been bet ween 16 and 17 t i mes t he accel er at i on due t o gr avi t y g ( equat i on ( 1) ) wi t h-out evoki ng undue st r esses i n t he humer i . Ther e-f or e, t he mi ni mum r adi us oe-f cur vat ur e r oe-f t he t r aj ect or y of t he mass m coul d have been as shor t as 13 c m ( equat i on ( 2) , Fi g . 4) .
mass m car r i ed on t he shoul der s, t he t ot al f or ce act i ng on bot h f or el i mbs coul d not have been muc h hi gher t han about 600 kN, whi ch i s j ust t hr ee t i mes t he wei ght f or ce of t he mass m. The cor r espondi ng mi ni mal r adi us r of cur vat ur e of t he t r aj ect or y of t he mass m i s about one met r e or appr oxi mat el y a quar t er of f or el i mb l engt h ( equat i on ( 2) ) .
Due t o t he act i on of muscl es spanni ng over t he shoul der j oi nt , t he compr essi ve f or ce i n t he car t i l age must have been consi der abl y gr eat er t han i n t he si mpl e model pr esent ed above ( see e . g. , Pr euschof t 1989, Bi ewener 1989a) , so t hat t he t r aj ect or y of t he mass m car r i ed on t he shoul der s must have been even mor e l evel .
So f ar , t he f r ont par t of t he body has been r egar ded as an i sol at ed uni t . For ces, however ,
coul d have been t r ansmi t t ed t o t he hi ndl i mbs vi a t he t r unk, t her eby r educi ng peak f or ces on t he shoul der s and i ncr easi ng t he l oad on t he hi ps . Dur i ng t he cr i t i cal phase of t he st r i de di scussed her e, when t he l oad on t he shoul der s i s shi f t ed f r om one l i mb t o t he ot her , however , onl y one hi ndl i mb was pl aced on t he gr ound . I n t he Ber -l i n speci men of Br achi osaur us, compar ed t o t he shoul der j oi nt , t he sur f ace ar ea of t he hi p j oi nt appear s s omewhat l ar ger ( by a f act or of r oughl y 1 . 5) . Gi ven t he hi gher f r act i on of body mass car -r i ed on t he hi p j oi nt s ( see met hods) , howeve-r , a shi f t of f or ce f r om t he shoul der s t o a si ngl e hi p j oi nt appear s unl i kel y.
A second pr obl em wi t h a model of wal ki ng wi t h l i mbs t hat ar e kept at a const ant l engt h dur -i ng t he suppor t phase -i s t he f l uct uat -i on of pot en-t i al ener gy. I n en-t hi s model of a Br achi osaur us at max i mum wal ki ng speed, t he mass m car r i ed on t he shoul der s r i ses appr oxi mat el y 0 . 4 m dur i ng t he f i r st 1 . 75 mof a st ep and dr ops by t he s ame hei ght di f f er ence dur i ng t he second 1 . 75 mof each st ep. Thi s i s equi val ent t o car r yi ng t he mass m uphi l l and t hen downhi l l at an aver age sl ope of about 13° dur i ng each st ep. Al t hough most of t he ext er nal ener gy needed t o accompl i sh t hese changes i n hei ght coul d be r egai ned by shi f t i ng pot ent i al ener gy t o ki net i c ener gy and back, a cer t ai n f r act i on of t hi s ener gy woul d be l ost due t o i nt er nal f r i ct i on ( Tayl or 1977, Al exander 1982) .
I n any case, ani mal s of t he si ze of Br achi o-saur us must have l ar gel y r educed peak f or ces and ener gy f l uct uat i ons dur i ng l ocomot i on ( Al ex-ander 1985a, b, 1989, Bi ewener 1989, Pr euschof t et al . 1994, 1998, Langman et al . 1995) . Ther e-f or e, i t can be assumed t hat t he e-f r act i ons oe-f body mass car r i ed on shoul der s and hi ps, r espect i vel y,
mov ed al ong smoot h t r aj ect or i es wi t h max i mum shi f t s i n hei ght t hat pr obabl y wer e l ess t han 0 . 1 m. Ther ef or e, as i n ext ant ver t ebr at es, Br a-chi osaur us had t o change t he ef f ect i ve l i mb l engt h dur i ng t he suppor t phase. Wi t h over l ap-pi ng suppor t phases of bot h l i mbs of a pai r , one l i mb can shor t en whi l e t he opposi t e l i mb ext ends when t he l oad i s shi f t ed f r om one l i mb t o t he ot her r esul t i ng i n a smoot h t r ansi t i on bet ween t he ar cs al ong whi ch t he shoul der and hi p j oi nt s mov e ( Fi g . 4C) . Al t er nat i vel y, dur i ng t he suppor t phase, t he cent r e of gr avi t y of t he f r act i on of body mass car r i ed by a pai r of l i mbs mi ght have changed i t s posi t i on r el at i ve t o t he hi p or shoul der j oi nt s, r espect i vel y, t her eby r educi ng t he peak f or ces t r ansmi t t ed t o t he l i mbs .
For el i mb post ur e i n a wal ki ng Br achi osaur us
I n t he hi ndl i mbs of Br achi osaur us, dur i ng t he suppor t phase, t he ef f ect i ve l i mb l engt h pr obabl y changed by moder at e f l exi on and ext ensi on of t he ankl e j oi nt s possi bl y t oget her wi t h compr es-si on and ext enes-si on of sof t pads under t he f eet , as i n el ephant s . I n t he f or el i mbs, however , t he met acar pal s wer e near l y ver t i cal and t hi ck pads of sof t t i ssue under t he f eet wer e not pr esent ( Chr i st i ansen 1997) . Consequent l y, wi t hout f l ex-i on and ext ensex-i on at t he el bows, ef f ect i ve l i mb l engt h woul d have r emai ned near l y const ant dur -i ng t he suppor t phase . Assum-i ng a he-i ght change of not mor e t han 0 . 1 m i n t he t r aj ect or y of t he cent r e of gr avi t y of t he mass m car r i ed on t he shoul der j oi nt s ( see above) , f l exi on and ext en-si on at t he el bows must have r esul t ed i n a change i n l i mb l engt h of 0 . 2- 0 . 3 m dur i ng each suppor t phase . To cover t hi s hei ght di f f er ence, t he angl e f or med bet ween t he upper ar m and t he f or ear m woul d have been 145° or l ess at t he mi ddl e of t he suppor t phase i f t he l i mb was f ul l y ext ended at max i mum excur si ons. The change i n ef f ect i ve l i mb l engt h depends on t he cosi ne- f unc-t i on of unc-t he angl e beunc-t ween upper and l ower l i mb
-Mi t t . Mus . Nat . kd. Ber l . , Geowi ss . Rei he 2 ( 1999)
shoul der
j oi nt
F
G-
-
-
f ul l y ext ended l i mb
moder at el y f l exed l i mb
Fi g. 5 . Moder at e f l exi on i n t he el bow j oi nt r esul t s i n l i t t l e change of t he ef f ect i ve l i mb l engt h, but i n consi der abl e i n-cr ease of t he l ever ar ms of t he gr ound r eact i on f or ce. FG, gr ound- r eact i on- f or ce ( f or si mpl i ci t y FG i s assumed t o poi nt exact l y upwar ds so t hat onl y t he l ever ar m at t he el bow j oi nt i s of i mpor t ance) . c, max i mum change i n l i mb l engt h dur i ng ext ensi on
r ect ed t owar d t he shoul der j oi nt , an angl e of 145° bet ween upper ar m and f or ear m woul d have i ncr eased t he l ever ar m of t he gr ound- r eac-t i on- f or ce aeac-t eac-t he el bow by aeac-t l east 0 . 3 m ( de-pendi ng on t he angl e f or med bet ween t he l ower l i mb and t he f oot ) whi ch i s about hal f t he max-i mum l ever ar m of t he ext ensor s of t he el bow. An angl e of 160° bet ween upper ar m and f or e-ar m woul d have r esul t ed i n onl y a smal l i ncr ease i n t he ext er nal t or ques at t he j oi nt s, t he maxi -mum l engt h change of t he f or el i mbs, however , woul d have been l ess t han 0 . 07 m. Ther ef or e, i t i s doubt f ul whet her Br achi osaur us used f l exi on
at t he el bow dur i ng t he mi ddl e of t he suppor t phase i n or der t o accompl i sh t he changes i n l i mb l engt h necessar y t o r educe peak f or ces on t he l i mbs.
The CTanal yses of t he humer i of sever al Tendagur u- saur opods conduct ed by Gol der & Chr i st i an ( 1999) showed t hat i n al l of t hese di no-saur s f or ces wer e t r ansmi t t ed mai nl y t hr ough t he br oadened mi ddl e f r act i ons of t he pr oxi mal epi -physes of t he humer i . The over al l di mensi ons of t he l ong f or el i mb bones ( Chr i st i ansen 1997) and t he t hi ck wal l s of t he shaf t ( see above) i ndi cat e an appr oxi mat el y axi al l oadi ng of t he l ong f or e-l i mb bones . These r esue-l t s ar e i n accor dance t o t he assumpt i on of a f ul l y ext ended l i mb post ur e wi t h t he humer us i n l i ne wi t h ul na and r adi us .
As ar gued above, wi t h l i t t l e compl i ance i n t he f or el i mbs and a st r ai ght al i gnment of t he l ong f or el i mb bones t hr oughout t he suppor t phase, t he shoul der j oi nt s must have changed by a ver -t i cal di s-t ance of 0 . 2- 0 . 3 mr el a-t i ve -t o -t he cen-t r e of gr avi t y of t he f r act i on of body mass mcar r i ed on t he shoul der j oi nt s dur i ng each st ep . I f and how t hi s mi ght have been possi bl e wi l l be t he subj ect of a f ur t her st udy.
Act i vi t i es di f f er ent f r om st r ai ght f or war d l ocomot i on at const ant speed
t hat coul d have count er act ed such neck movment s, as i n many ot her saur opods, and t he f or e-l i mbs di d not have t o exer t gr ound r eact i on f or ces wi t h hi gh hor i zont al component s whi ch occur i f neck and t ai l ar e shi f t ed t o t he si de . I ndeed, compar ed t o saur opods t hat ar e l i kel y t o have had a l ess ver t i cal neck post ur e, t he f or e-l i mbs of Br achi osaur us ar e e-l ess compact ( Chr i s-t i ansen 1997) .
Ev en wi t h s ome f l exi bi l i t y i n t he pect or al gi r dl e, t he f or el i mbs of Br achi osaur us ar e not sui t ed f or pr oduci ng hi gh i mpul ses si nce t he max i mum change i n l engt h under heavy l oads was shor t . Not onl y f or war d and backwar d ac-cel er at i ons ( Chr i st i ansen 1997) but al so t or ques necessar y t o t ur n t he body t o t he si de must have been pr oduced most l y by t he hi ndl i mbs . Tur ni ng was l ess of a pr obl em t han i n saur opods wi t h a mor e hor i zont al neck post ur e and a ver y l ong t ai l , such as Di pl odocus, because i n Br achi o-saur us t he body mass was concent r at ed cl oser t o t he cent r e of gr avi t y r esul t i ng i n a r educed moment of i ner t i a about t he ver t i cal axi s t hr ough t he cent r e of gr avi t y . Ther ef or e, wi t h one hi ndl i mb pushi ng f or war d and t he ot her hi ndl i mb pushi ng backwar d t he t or que necessar y t o t ur n t he body t o t he si de coul d have been pr oduced, possi bl y wi t h t he addi t i on of si deways mov ement of t he t ai l . The f or el i mbs pr obabl y have been i nvol ved i n t ur ni ng by pr oduci ng s ome si deways f or ces . However , wi t h st r ai ght and r at her r i gi d f or el i mbs and f ul l y ext ended hi ndl i mbs, Br achi osaur us was not capabl e of hi gh accel er at i on or swi f t t ur ns. Ev en l yi ng down wi t h t he t r unk r est i ng on t he subst r at e and r i si ng agai n mus t have pushed Br achi osaur us t o i t s l i m-i t s - i f t hi s was ever done - as wi l l be demon-st r at ed i n t he f ol l owi ng .
Assumi ng a mor e or l ess ver t i cal gr ound r eac-t i on f or ce, dur i ng l yi ng down and st andi ng up, t he out l ever / i nl ever r at i o ( r at i o bet ween t he l e-ver ar m of t he ext er nal f or ce and t he l ee-ver ar m
of t he muscl es) at t he el bow j oi nt s woul d have been at l east 2 . 5 . Thus, t he compr essi ve f or ce act i ng on each el bow j oi nt woul d have been mor e t han 350 k N. I n f l exed post ur e, t he sur f ace of ar t i cul at i on i n t he el bow j oi nt was 50, 000 mm2 or l ess, so t hat t he st r ess i n t he j oi nt car t i l age was at l east 7 MPa whi ch i s r at her hi gh f or car t i -l age ( Yamada 1973, A-l exander 1985, see above) . The ener gy needed t o l i f t t he cent r e of mass over a hei ght di f f er ence of about 3 mi s appr oxi -mat el y 1, 850 kJ Wi t h t he max i mum per f or mance of st r i at ed ver t ebr at e muscl e cont r act i ng sl owl y t hr ough i t s ent i r e r ange bei ng 0 . 22 kJ/ kg muscl e
( Al exander & Bennet - Cl ar k 1977) , at l east 8, 400 kg of muscl e mass or one sevent h of t he t ot al body mass was necessar y t o l i f t t he body of Br achi osaur us f r om a l yi ng t o a st andi ng posi -t i on . The s ame r esul -t , -t he mass of ac-t i ve muscl e bei ng at l east one sevent h of t he t ot al body mass, cal cul at ed f or an aver age si zed human ( 70- 75 kg) woul d be equi val ent t o r i si ng f r om a pr one t o a st andi ng posi t i on car r yi ng a backpack of 150 kg mass. I f Br achi osaur us ever l ay down f ul l y, r i si ng must have been a st r enuous act i vi t y. A speci al t echni que mi ght have been used i n or -der t o r educe peak f or ces. The hi ndl i mbs mi ght have been f l exed f i r st dur i ng l yi ng down and t he f or el i mbs wer e ext ended f i r st dur i ng r i si ng, so t hat t he l oad on t he f l exed f or el i mbs was r e-duced . The t ai l mi ght have ser ved as a f i f t h l i mb . I n t he l i ght of t hese consi der at i ons i t appear s doubt f ul whet her Br achi osaur us ever r ear ed up on i t s hi ndl i mbs .
Concl usi ons
The anal ysi s pr esent ed above i s i nevi t abl y based on many assumpt i ons . However , even wi t h con-si der abl e er r or s i n s ome of t he est i mat es used f or t he cal cul at i ons, t he gener al concl usi ons ar e not si gni f i cant l y af f ect ed .
Mi t t . Mus . Nat . kd. Ber l . , Geowi ss . Rei he 2 ( 1999)
Ac k nowl edgement s
Dr . H. - Chr . Gunga and Dr . A. Wi edemann have suppl i ed or i gi nal dat a of segment masses al ong t he neck of Br achi o-saur us . Mr . J. E Mendau dr ew t he Fi gur es, Mr s . W. Har r e pr oduced t he phot ogr aphs . We al so t hank G. Chr i st i an f or di scussi on of t he t ext . Pr of . Dr . B. Kr ebs, Pr of . Dr . H. Pr eu-schof t , and Dr . D. M. Unwi n have r evi ewed t he manuscr i pt . The st udy was suppor t ed by DFG ( Deut sche For schungs- Ge-mei nschaf t ) pr oj ect SCHU 212/ 16- 1 .
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