Handout: McMahon (1979)

12 Pages·2003·1.12 MB·English

0021-9290 79 11Ol4893 5033.~0
THE INFLUENCE OF TRACK COMPLIANCE
ON RUNNING
T~ou.x .sA MCMXHON dna RETEP .R GREENE
noisiviD fo deilppA ,secneicS ecreiP .llaH dravraH ,ytisrevinU ,egdirbmaC AM 02138, .A.S.U
Abstract - A ledom fo gninnur si desoporp ni hcihw eht gel si detneserper sa a noinip-dna-kcar tnemele ni
seires htiw a depmad .gnirps ehT noinip-dna-kcar tnemele sezisahpme eht elor fo gnidnecsed ,sdnammoc
elihw eht depmad gnirps stneserper eht cimanyd seitreporp fo selcsum dna eht noitisop dna eht etar
ytivitisnes fo .sexelfer sihT ledom si desu ot tciderp yletarapes eht tceffe fo track ecnailpmoc no pets htgnel
dna dnuorg tcatnoc .emit ehT snoitciderp era derapmoc htiw stnemirepxe ni hcihw setelhta nar revo skcart fo
dellortnoc gnirps .ssenffits A prahs ekips ni toof ecrof up ot 5 semit ydob thgiew saw dnuof no drah ,secafrus
tub siht ekips deraeppasid sa eht setelhta nar no tfos latnemirepxe .skcart htoB dnuorg tcatnoc emit dna pets
htgnel desaercni no yrev tnailpmoc ,secafrus gnidael ot yletaredom decuder gninnur ,sdeeps tub a egnar fo
track ssenffits saw derevocsid hcihw yllautca secnahne .deeps
NOIl-CCDORTSI lortnoc dnammocfo slangis morf rehgih rotom sretnec
gnirud siht .emit nI the retal noitrop of the ecnats
gninnuR si yllaitnesse a seires of snoisilloc htiw the phase, ,revewoh the stretch xelfer nac eb expected ot
.dnuorg sA the lamina sekirts the ,ecafrus sti selcsum
ekam tnatropmi snoitacifidom of the tnereffe ytivitca
tcartnoc dna yletamitlu esrever the drawnwod yticolev
of .snoruenrotom-* kuoH (1976) has deugra that
of the .ydob noitiutnI seugra that a ecafrus of ylbatius
elcsum ,ssenffits rather naht elcsum ,htgnel si the
egral ecnailpmoc si dnuob ot egnahc gninnur -rofrep
ytreporp hcihw si detaluger yb the stretch .xelfer He
.ecnam gninnuR no a gnivid draobgnirps swols a nam
stniop tuo that a noititepmoc neewteb detaler-htgnel
nwod ,ylbaredisnoc elihw gninnur no a enilopmart si lla
noitaticxe detubirtnoc yb elcsum eldnips receptors dna
tub .elbissopmi ruO laog ni siht paper lliw eb ot dnif na
detaler-ecrof noitibihni detubirtnoc yb igloG nodnet
citylana noisserpxe for the egnahc ni the s’rennur
speed, step htgnel dna foot tcatnoc emit as a noitcnuf of
the track ,ssenffits dna ot erapmoc these snoitciderp
htiw .tnemirepxe
ehT noitacifilpmis that the selcsum of noitomocol
dna rieht sexelfer act yllaitnesse as sgnirps si tnel
troppus yb tnecer stnempoleved ni the yduts of laruen
rotom .lortnoc ,sexelfeR ,revewoh eriuqer emos emit ot
enoyna-tca who has yldetcepxenu stepped off a bruc
lliw llacer the sharp tloj hcihw stluser nehw the
ytivargitna selcsum of the gel are ton prepared for the
.tcapmi ellivleM senoJ dna ttaW (1971) evah nwohs
that yletamixorppa 102 cesm are deriuqer for xelfer
ytivitca morf the htiloto sutarappa ot etavitca the
ytivargitna selcsum ni ,nam so that detcepxenu sllaf of
ssel naht tuoba mc0.5 are deinapmoccanu yb xelfer
.noitadommocca nevE the elpmis stretch xelfer -er
seriuq a laitnatsbus noitrop of the gninnur step .elcyc
ehT ycnetal of GME segnahc detaicossa htiw -otua
citam sesnopser ot a egnahc ni bmil daol are dnuof ot
eb ni the egnar of 79 cesm for woble noixelf ni nam
(Crag0 er ,.la 1976) dna raen 25 cesm for suelos selcsum
ni etarbereced cats slohciN( dna ,kuoH 1976). ecniS
the detroppus doirep ni namuh gninnur si yllacipyt
,cesmOOI rehtien sexelfer of ralubitsev ron stretch .giF 1. citamehcS gnitneserper eht etarapes elor fo -dnecsed
nigiro nac detcepxeeb ot etapicitrap ni the tsrif retrauq gni sdnammoc )noinip-dna-kcar( dna elcsum seitreporp sulp
of the ecnats phase, dna therefore the ytivargitna lacol sexelfer depmad( .)gnirps ehT noitom fo eht rack dna
noinip tnemele senimreted eht ecneulfni fo track ssenffits no
selcsum of the gel tsum eb yllapicnirp rednu the
pets .htgnel ehT s’rennur ssam dna eht depmad gnirps
enimreted eht ecneulfni fo track ssenffits no dnuorg tcatnoc
l Receiced 17 July 1978. .emit
893
498 SWOHT .A SOHA.MCM dna RES!P .R T~EERG
snagro dluoc tluser ni the oitar of elcsum force ot SDOHTEl>
htgnel gnieb ,detaluger rather naht rehtie eno -xe
.ylevisulc troppuS for siht weiv semoc morf pmar Experiments
stretches of the suelos elcsum ni etarbereced cats E.qw%nental board track. A enal-elgnis gninnur
slohciN( dna ,kuoH 1976). esehT seiduts show how ecafrus 26.25 m ni htgnel was detcurtsnoc of 1.9 mc
xelfer noitca nac etasnepmoc for decudni-hcterts doowylp .sdraob Each draob was 40.6 mc gnol ni the
snoitcuder ni elcsum force, suht gnivreserp a raenil gninnur noitcerid yb 121.9 mc .ediw ehT sdraob were
htgnel-ecrof noitaler ni a stretched elcsum hcihw screwed ot 4.4 x 8.9 mc sliar hcihw devres as ,stroppus
dluow esiwrehto show etuca .ytiraenilnon kuoH -gus as nwohs ni .giF 2. ehT gnirps ssenffits of the track
gests that the noitca of a elcsum (or a riap of )selcsum dluoc eb deretla yb gnivom the gnitroppus sliar resolc
tuoba a tnioj thgim ylbanosaer eb detneserper as ‘a or farther apart. A lacipyt noitcelfed-daol ,noitarbilac
rack dna noinip ni seires htiw a .gnirps deniatbo yb gniylppa 0.22 kN sthgiew ot a mc7.21
A noitacifidom of siht emehcs si nwohs ni .giF 1. ralucric munimula etalp gnitneserper the foot, si osla
tnemevoM sdnammoc dluow knarc the -dna-kcar nwohs ni .giF .)b(2 ehT emit deriuqer for the rennur ot
noinip ot a wen set tniop for the tnioj ,elgna tub force pass neewteb two esrevsnart thgil smaeb 8.20 m apart
secnabrutsid morf the edistuo dluow tcelfed the bmil dedivorp a erusaem of the s’rennur speed. ehT force
yb na tnuoma detatcid yb the depmad .gnirps ehT deilppa ot the track yb the s’rennur foot was derusaem
dashpot ni lellarap htiw the gnirps si ton yllacificeps yb a telssiK A1629 force ,etalp hcihw was raenil
denoitnem ni s’kuoH ,ledom tub si yrassecen ot 50.5% revo a force egnar of 0.2-O kN, dna had a
edulcni the rate ytivitisnes of the stretch receptors dna larutan ycneuqerf nehw dedaol htiw a 70 kg nam
other kcabdeef stnemele nehw htob elcsum force dna evoba 200 Hz. A llams 60.9 mc erauqs lenap of0.95 mc
htgnel are gnignahc .yldipar cilonehp niser draob detroppus at rehtie dne yb
noitatneserpeR of the gel dna sti erutalucsum as a 2.54 mc erauqs enip sliar rested nopu the force ,etalp as
raenil depmad gnirps has ydaerla devorp lufsseccus ni .nwohs ehT noitarapes of the 2.54 mc sliar was -tsujda
gnibircsed na esicrexe ni hcihw the tcejbus spmuj otno ed litnu the noitcelfed-daol evruc of the cilonehp
a force ,mroftalp gnillaf no the sllab of the feet tuohtiw draob dehctam that of the track ot nihtiw 2.0%. nI siht
gnixelf the ,seenk dna htiw the selkna yllufecrof ,yaw the rennur was detneserp htiw a level track
dednetxe ,angavaC( 1970). morF the tnatluser depmad ecafrus of mrofinu ,ecnailpmoc dna the lacitrev foot
noitallicso ni lacitrev force ycneuqerf( tuoba 3.5 Hz), force dluoc eb derusaem as he kcurts the cilonehp
angavaC (1970) detaluclac the evitceffe gnirps ssenffits .draob Each tcejbus nar nwod the retnec of the track,
dna gnipmad tnatsnoc of the srosnetxe of the .elkna ot erusne that he decneirepxe the ecnailpmoc -saem
ehT snoitallicso were syawla ,depmadrednu htiw a deru yb the noitcelfed-daol .noitarbilac A 16 mm enit
gnipmad oitar of tuoba 0.2. ,aremac gnitarepo at yletamixorppa 60 semarf per set,
nI tneuqesbus ,snoitces the noitcnuf of the depmad dedivorp a cihpargotohp record. A kcolc ni the dleif of
gnirps ni .giF 1 si separated morf the noitcnuf of the weiv of the aremac was desu ot etarbilac the aremac
.noinip-dna-kcar ,tsriF rednu the noitpmussa that the speed.
noinip-dna-kcar si ,dekcol we treat the lacitrev noitom A latot of S ,stcejbus lla selam neewteb the ages of 21
of the rennur as na depmadrednu gnirps-ssam ,metsys dna 34 ,ry detapicitrap ni the stnemirepxe elbaT( 1).
dna etaluclac the emit deriuqer ot dnuober morf the ehT stcejbus were dlot ot nur at a mrofinu speed. yehT
track as a noitcnuf of track .ecnailpmoc ehT -pmussa detanretla snur no the track htiw snur no the etercnoc
noit that the noinip-dna-kcar si dekcol sezisahpme ecafrus ediseb the track. Each tcejbus nar at a yteirav of
the lacol lortnoc of elcsum ssenffits at the latnemges speeds, gnidulcni sih top speed. llA srennur wore
level gnirud the elddim dna etal snoitrop of the ecnats lanoitnevnoc gninnur shoes htiw ,niht talf .selos
phase of bmil .noitom Later, we emussa that the wolliP track. nI order ot enimreted the effect of a
depmad gnirps si ,dekcol dna cirtemoeg -edisnoc yrev soft ,ecafrus the draob track was decalper yb a
snoitar are deilppa ot the noinip-dna-kcar tnemele ot 10.9 m gnol ecneuqes of rebbur-maof ,swollip each
etaluclac the effect of the track ecnailpmoc no the gnirusaem 1.22 m ediw yb 0.9 1 m hgih yb 2.74 m .gnol
s’nam step .htgnel sihT noitpmussa sezisahpme the ehT s’rennur speed, step htgnel dna dnuorg tcatnoc
,demmargorp-erp xelfer-non lortnoc of bmil noitisop emit no each edirts were denimreted yb mlif .sisylana
gnirud the ylrae noisnetxe phase, erofeb dna tsuj after ehT noitcelfed-daol evruc for the wollip track si
the foot sehcuot the .dnuorg yllaniF we niatbo a nwohs ni .giF 2(c). erehT was a egral ,siseretsyh
noitciderp for the top gninnur speed as a noitcnuf of gnitluser ni a tnereffid ssenffits for gnidaol dna
track .ecnailpmoc snoitavresbO of stcejbus gninnur no gnidaolnu at a ralucitrap force .level
latnemirepxe tracks of suoirav ssenffits are detneserp roF the esoprup of tneuqesbus ,snoitaluclac the
for .nosirapmoc hguohtlA the snoitaluclac show that gnirps ssenffits of the swollip was detaulave at two
the nam si ylereves dewols nwod nehw the track tnereffid force .slevel sihT was enod yb gniniatbo the
ssenffits si ssel naht sih nwo gnirps ,ssenffits there stsixe lacol epols of the noitcelfed-ecrof evruc at the 0.8 kN
na etaidemretni egnar of track sessenffits where sih level ,)gO.l( gnidnopserroc ot foot forces of the order of
speed si rehtie detceffanu yb the track or tahwemos the s’rennur ydob ,thgiew dna at the 1.34 kN level
.decnahne (1.67g), gnidnopserroc ot the naem foot forces ot eb
ehT ecneulfni fo track ecnailpmoc no gninnur 895
END EDIS
.giF 2. (a) eerhT sweiv fo eht latnemirepxe nedoow .kcart doowylp-A gninnur ,ecafrus ecurps-D,B
gnitroppus ,sliar etercnoc-C ,roolf cilonehp-E niser ,draob ecrof-F ,mroftalp munimula-G etalp
gnitneserper eht .toof ,sthgiew-H tnemecalpsid-l .eguag
kN
fbI
0 2.0 4.0 6.0 0.0 0.1 2.1 ni
I I ,
0 1 2 3 cm
NOITCELFED
.giF 2. )b( noitcelfed-ecroF sevruc rof owt snoitarugifnoc fo eht latnemirepxe nedoow .kcart stnegnaT tif ot
eht 2.3g level evig k, = 13,333 tf/fbI (195 )m/Nk dna 6857 tf/fbI (100 .)m/Nk
1 I
-0x
250-
-OOZ
IW-
, 8
0 1.0 2.0 I 3.0 4.0 1 m
NOITCELFED
.giF 2. )c( noitcelfed-ecroF sevruc rof eht maof rebbur wollip ,kcart gniwohs gO.l dna 1.67g ,stnegnat hcihw
evig k, = 320 tfjfbl (4.67 )m/Nk dna 985 tf/fbI (14.4 .)m/Nk
896 THOUS A. MCMUJON dna PETER R. REERG
expected gnirud the foot tcatnoc emit no siht -moc
tnailp .ecafrus ehT 1.09 dna 1.67g wollip sessenffits
were 4.67 kN m dna 11.38 I\rk ,m‘ .ylevitcepser
Each tcejbus yllareneg was tested at neewteb 5 dna 8
tnereffid gninnur speeds no each of the ruof track
secafrus ,etercnoc( draob track at 195 ,mi,Nk draob
track at m!NkOOl dna wollip track). erehT were
,snoitpecxe as ni the case of the wollip track, where
ylno 3 stcejbus .detapicitrap sA denialpxe ni the txen
,snoitces foot tcatnoc emit ,t was dedulcni ni the
snoitalubat (for .giF 8) ylno at the tsehgih gninnur
speed of each rennur no each ecafrus (27 .)stniop yB
;tsartnoc each step htgnel noitanimreted deriuqer a
enil-thgiarts gnittif process ekil that nwohs ni .giF 6.
eroferehT each of the 27 step htgnel stniop .giF( 7)
stneserper 5 or erom laudividni .snur
Theoretical snoitaredisnoc
foot rcacnoc time. sA a lareneg ,elpicnirp gninoihsuc
works ot decrease the forces neewteb gnidilloc seidob
yb gnisaercni the emit of the .noisilloc Joggers wonk
that yeht are ssel enorp ot tnemagil seirujni dna
stilpsnihs nehw yeht nur no tahwemos tnailpmoc
secafrus hcus as ,frut as opposed ot ytic .stnemevap
lacipyT sessenffits of emos gninnur secafrus are nwohs
ni elbaT 2.
nI .giF 3, a lanoisnemid-eno ledom of the rennur dna
the track si nwohs hcihw serongi noitom ni the forward
noitcerid dna sredisnoc ylno the lacitrev .tnenopmoc
nI siht ,ledom we evah dexif the -noinip-dna-kcar
tnemele morf .giF 1 ni a elgnis ,noitisop suht -zisahpme
gni the elor of elcsum xelfer .ssenffits ehT ssam ,m si the
s’nam ,ssam dna k, si the depmul gnirps ssenffits of the
selcsum dna sexelfer gnitca ot dnetxe sih ,pih eenk dna
.elkna ehT evitceffe ssam of the track ecafrus (the
edutingam of na tnelaviuqe ssam detartnecnoc at a
)tniop si m,, dna the gnirps ssenffits of the track (the
esrevni of sti )ecnailpmoc si nwohs as k,. nI the ,erugif
lla the sessam dna sgnirps are attached, so that ylno
that elcyc-flah of the noitom for evitisop drawnwod
stnemecalpsid of the nam (x,) dna track (x,) has yna
ecnednopserroc htiw lacisyhp .ytilaer nehW x,,, dna Ir.
are ,evitagen the s’nam foot ,dluow ni the lautca
,noitautis eb separated morf the track ecafrus dna
dluow therefore ton tcaretni htiw .ti hguohtlA the
tnenamrep noitcennoc of the nam ot the track si
,suoititcif ti sekam the scitamehtam tneinevnoc dna
sdnopserroc yletamixorppa ot the laer noitautis -rud
gni the tcatnoc noitrop of the gnippets .elcyc
kcarT .ssam Let su erongi the s’nam gnipmad for the
,tnemom dna redisnoc the depmadnu noitarbiv of the
nam dna the track. ehT larutan ycneuqerf w,(rad/sec)
of the tsewol edom of ,noitarbiv ni hcihw the two
sessam evom drawnwod ni phase, si nevig yb neD
Hartog :)6591(
1U = ,&m+,m( k,
n
,m% ,mz‘
_ ,/[mrkm + m,(k, -t k,)]’ - 4m,m,k,k,
. (1)
2m,m,
ehT ecneulfni fo track ecnailpmoc no gninnur 897
/” OI i KCART SSAM
LOW KCART SSENFFITS ETOTPMYSA
tk mk/
.giF 3. dezilamroN natural ycneuqerf sv dezilamron track .ssenffits ehT tesni swohs eht depmad ,ssam-owt
gnirps-owt .metsys yvaeH enil swohs orez ,gnipmad orez track .ssam
elbaT 2. ssenffitS fo gninnur secafrus I?$uence of the man’s damping. ecniS the track ssam
deretnuocne ni ecitcarp has so elttil effect no cc”, we
ssenffitS redisnoc ti on .rehtruf gnikaT m, = 0, we etagitsevni
lairetaM )tf/fbI( )m/Nk( the denibmoc effect ofthe yticolev-ecrof noitaler ni the
s’nam selcsum dna the yticolev kcabdeef ni the s’nam
,etercnoc tlahpsa ooo,003 + 4376
stretch ,sexelfer detneserper here yb the dashpot
dekcap srednic 200.000 2918
draob skcart Ooo.O6 875 ,tnemele b, nwohs ni the citamehcs gniward ni .giF 3.
latnemirepxe nedoow track 13,333 195 morF the noitulos detneserp ni xidneppA ,A the
latnemirepxe nedoow track 6857 100
dezilamron ycneuqerf o,,/w, si dettolp as a noitcnuf of
kcart-wollip at 1.67g 985 14.4
sselnoisnemid track ssenffits kdk,,, for 4 seciohc of the
gnipmad oitar [ = b/(2-). ecitoN that the
nI the kcart-digir ,timil k,/k,-t co, m,/m,+ ;c, dna depmad sevruc eit evoba the depmadnu ,seno a -noc
the evoba noisserpxe semoceb & = k&n,,,. In the ecneuqes of the fact that the dashpot tnemele sdnet ot
redniamer of the paper, the tpircsbus o lliw etoned the neffits the s’nam ecnadepmi ni siht dezilamron -moc
kcart-digir .timil nI the timil as the track semoceb yrev .nosirap ehT retemarap k, deriuqer for siht noitaluclac
soft, iw = k,/(m, + m,). ehT noitcesretni of these two was denimreted for each [ morf k, = 1(/!&m ,)2C-
citotpmysa sroivaheb srucco at a track ssenffits where m, dna co = z/w, are the ssam dna hard ecafrus
:k = ,m(,k + ,,m/),m where the larutan ycneuqerf wf, tcatnoc emit etairporppa for tcejbus .F.M esehT sevruc
si nevig yb lliw retal eb derapmoc htiw latnemirepxe .stluser
+ 2 Step length. owT secneuqes of kcits ,serugif deniatbo
W- ” _ tm + mm JZ t21 yb sisylana of the tnit ,smlif are nwohs ni .giF 4. Each
0 % 4 lm erugif was nward yb gnitcennoc stniop gnitacol the
A nekorb enil gniwohs the ecneulfni of track ssam no rojam bmil .stnioj ehT tsompot tniop setacol the
ycneuqerf si nwohs ni .giF 3. gnimussA a lanoitnevnoc noitisop of the ear. A elbakramer noitavresbo si that
nedoow track noitcurtsnoc ni hcihw a 1.9 mc x 1.22 m the yrotcejart of the ear, dna therefore of the htiloto
x 2.44 m doowylp lenap decrofnier yb 4.4 x 8.9 mc sutarappa gnisnes head ,noitarelecca si ylevitaler ,level
sregnirts si the gninnur ,ecafrus the evitceffe ssam ofthe whether the tcejbus snur no the swollip or no the hard
track si 21.0 kg, hcihw sekam mdm, = 0.25 for na .ecafrus htoB rewol seitimertxe dna a elgnis reppu
87 kg .rennur nI siht ,noitaluclac the evitceffe ssam of ytimertxe are nwohs ni the kcits .serugif nehW the
the track si deniatbo yb s’hgielyaR ,dohtem gnimussa a tcejbus snur no the ,swollip as nwohs at the ,mottob sih
ladiosunis lanoisnemid-owt edom shape -miT( ecnats foot sknis otni the maof ,rebbur tub the gniws
,oknehso 1937). rednU these ,secnatsmucric the tluser foot syawla sniamer evoba the detcelfednu wollip
si that the evitceffe ssam si hatf the latot ssam of the .ecafrus ehT dednetxe gel sretnuocne the wollip ecafrus
.lenap ni a noitisop nehw pih noixelf si greater naht si the case
ehT noitulos nwohs ni .giF 3 gnidulcni the track for gninnur no a hard .ecafrus ehT step htgnet no the
ssam si nees ot eb ton yrev tnereffid morf the noitulos wollip ecafrus si yltneuqesnoc greater.
for the wol track ssam ,timil 0. = k,k,,Jm,(k,+k,), sihT noitavresbo yam eb desu ot tcurtsnoc a ledom
dettolp as a yvaeh dilos enil tsuj evoba .ti roF for the ecneulfni of track ecnailpmoc no step .htgnel
,nosirapmoc the noitulos nehw the track ssam si nI the citamehcs margaid of .giF 5(a), the ,gel
desaercni yb a factor of 10 si osla .nwohs htgnel 1, si nwohs htiw the eenk ylluf dednetxe at the
898 THOMASA . MCMAHON dna PETER .R X>EERG
c
.giF 4. kcitS serugif fo tcejbus .F.M ,gninnur morf .smlif :poT drah ;ecafrus :mottob wollip .kcart diloS enil
swohs detcelfednu ecafrus fo wollip track ; nekorb enil swohs naem noitcelfed fo swollip revo na eritne pets
.elcyc ylnO esoht serugif rof hcihw eht toof saw ni tcatnoc htiw eht ecafrus era .nward ehT gnimarf deeps saw
59 .tes/semarf
(a) )b(
.giF 5. citamehcS fo a pets no (a) drah ecafrus dna )b( wollip .kcart diloS enil swohs eht ecnats ,gel nekorb enil
swohs eht gniws gel gnivom .drawrof esuaceB eht toof sdnecsed a ecnatsid 6 otni eht ,swollip eht pets htgnel
no eht wollip track si ylirassecen .retaerg
ehT ecneulfni fo track ecnailpmoc no gninnur 899
tnednepedni of gninnur speed, deveihca yb the -kcar“
”noinip-dna rehgih larutsop srellortnoc for the -rup
pose of gniniatniam the ydob dna( therefore the ear) no
na yletamixorppa level .yrotcejart ecitoN that siht
noitpmussa ylevitceffe sexit the htgnel of the depmad
gnirps ni .giF 1 as fi the gnirps ssenffits k, were won
nekat ot eb .etinifni ecniS 6, = 9.6 mc for tcejbus .F.M
gninnur no the hard ,ecafrus tub the mumixam
noitcelfed of sih ”gnirps“ dluow eb expected ot eb ylno
1.86 ,mc siht noitpmussa appears ot eb .deifitsuj ehT
tnatropmi tniop si that the esab of the elgnairt nwohs
Q
ni the rewol part of the erugif si ,regnol dna suht the
step htgnel L si regnol no the wollip ecafrus .giF( .)b5
ehT ecnatsid 6 si the naem noitcelfed of the wollip
ecafrus tuohguorht a etelpmoc ,edirts gnidulcni the
lairea phases. fI the nam were ton gninnur at ,lla tub
ylerem gnidnats ylteiuq no the ,swollip he dluow eb
gnidnats ni a llew of depth 6 = where k, ni siht
m,g//c,,
ecnatsni si the wollip ssenffits derusaem at the gO.l
force .level ehT nekorb enil ni .giF ,)b(5 gnitneserper
the naem noitcelfed of the wollip track, syalp the emas
elor as the dilos enil ni .giF 5(a) : lla sliated of the step
,
0 05 .I0 !5 20 .25 Xsch are ylirartibra demuserp ot eb the ,emas gnidulcni the
ii ecnatsid morf the nekorb enil ot the ,pih .,6-I ylnO
.giF 6. dnuorG tcatnoc emit ,I sv esrevni gninnur deeps ,u/l the pih noixelf elgna at hcihw the leeh stcatnoc the
rof rennur .F.M ehT thgiarts senil hguorht eht nigiro wohs
track si tnereffid no the ,swollip gnidael ot the regnol
taht na s’laudividni pets htgnel si ,tnatsnoc tnednepedni fo eht
gninnur ,deeps no a ralucitrap .ecafrus petS htgnel si retaerg step .htgnel gniylppA the naerogahtyP meroeht ot the
no eht wollip track naht no eht drah .ecafrus rorrE srab wohs elgnairt ni .giF ,)b(5
mumixam ytniatrecnu eud ot mlif .gnidaer
L = 2Jl’ - (1 - 6, - 6)2. (3)
tnemom fo tcatnoc htiw eht drah .ecafrus tI si osla
nwohs ni ,ecnats-dim nehw eht eenk si ,dexelf dna at ehT tnatsnoc 6, yam eb nettirw ni smret of the step
the dne of the ecnats phase, tsuj erofeb the toe si .detfil htgnel no the hard ,ecafrus L,,
nI ,ecnats-dim the htgnel of the gel si ylno ,,,6-I where
the gninetrohs ,b si demussa ot eb a tnatsnoc ,htgnel .77J-i=,6 (4)
.giF 7. petS htgnel sv track .ssenffits ehT dilos enil shows the laciteroeht .noitciderp (a) tcejbuS .F.M ,enola
)b( sselnoisnemiD tolp gniwohs all 8 .stcejbus
B .V 12 12-B
009 THOMASA . MCMAHON and PETER .R GREEY.X
gninibmoC snoitailqe (4) dna (3), htiw d = ,,k/g,m Foot contact rime cs track srifliess
nI .giF 8, foot tcatnoc emit Qt,, si dettolp tsniaga
L = 2Jlr - ’I([ - Lf/4)‘,’ - .‘],k/g,m (5)
track ssenffits kJk,. ehT laciteroeht enil stneserper a
noitauqE (5) si dettolp ni .giF 7(a), gnimussa a gnipmad oitar for the nam of < = 0.55. sihT gnipmad
0.8 kN nam htiw a gel htgnel I = 1.09 m dna a -drah oitar was nesohc gnoma the ruof nwohs ni .giF 3, no
ecafrus step htgnel L, = 0.896 m etairporppa( for the sisab of sti yrotcafsitas tif ot the latnemirepxe
tcejbus .).F.M nehW the noisserpxe ni the erauqs stniop nwohs ni .giF 8. ehT deziraenil gnirps ssenffits of
tekcarb si zero, the step htgnel has reached sti the swollip was nekat as the 1.67g ,ssenffits t-.41 ,m/Nk
,mumixam yleman eciwt the gel .htgnel suhT gninnur ecnis the swollip acted htiw siht ssenffits gnirud tsom of
no secafrus whose ssenffits si ssel naht the emit the rennur ni tcatnoc htiw the track, nehw
was
k: = m,g/Jm dluow ton eb ,elbissop -drocca foot forces were ni the egnar of 1.67 semit ydob .thgiew
gni ot siht ,ledom ecnis the spih dluow evah dednecsed eW llahs nruter ot siht tniop ,retal htiw na noitanalpxe
woleb the ecafrus of the .swollip of how the erugif 1.67g was .denimreted
ehT error srab for each tniop show the detamitse
mumixam ytniatrecnu ni gnidaer the smlif dna force
RESULTS records, hcihw was yllareneg ssel naht &/“0.7? ehT
Dimensionless piotting dotted senil no rehtie edis of the laciteroeht enil are
ecniS the stluser are detneserp no sselnoisnemid decalpsid yb eno dradnats noitaived 0, where (r si
axes, we evah dedulcni a short noitacifitsuj for the detamitse morf the root of the naem of derauqs
ytidilav of siht erudecorp ni xidneppA .B ,yllacisaB the slaudiser :
dohtem si deriuqer esuaceb we hsiw ot erapmoc the
secnamrofrep of lareves srennur no the emas .erugif fI
the lanoisnemid axes were ,deniater the ecnamrofrep of
a elgnis rennur dluoc eb derapmoc ot a elgnis enil Here )x(,y si the derusaem eulav dna J(X) si the
yllaicepse detupmoc for that rennur (for ,elpmaxe .giF detupmoc eulav of a retemarap at a nevig .‘c ,reyeM(
7a for tcejbus ,).F.M tub a etelpmoc noitatneserp of the 1975). .
stluser dluow eriuqer as ynam serugif as there were
.srennur Step length independent of running speed on a gicen
surface
Man’s spring determined by foot contact time nI rieht evisneherpmoc yduts of namuh ,tiag -vaC
nI gnittolp each data tniop no a lacipyt -noisnemid anga et al. (1976) deciton that the step ,htgnel the
ssel graph (e.g. .giF ,)b7 ti was tsrif yrassecen ot wonk ecnatsid a nam slevart elihw eno foot si ni tcatnoc htiw
the s’nam gnirps ssenffits k,. ,sihT ni ,lareneg si a the ,dnuorg si a tnatsnoc eulav for a nevig laudividni
noitcnuf of the s’nam effort, dna sesaercni as he snur rennur no a hard ,ecafrus tnednepedni of sih gninnur
faster. nI .sgiF 3, 7, 8 dna 9, we erapmoc ylno the speed. eW were elba ot etaroborroc siht ,gnidnif as
mumixam gninnur ecnamrofrep as a noitcnuf of track nwohs ni .giF 6 for tcejbus .F.M ehT emit ni tcatnoc
ssenffits dna therefore k, = m,wz/(l - )zi where htiw the ,dnuorg t,, si lanoitroporp ot the esrevni of
0” = ,,t/n r, si the emit the foot si ni tcatnoc htiw the .yticolev ehT epols of siht enil senifed the step htgnel L,
dnuorg elihw gninnur at mumixam effort no the hcihw si tnednepedni of the speed tub yrev hcum regral
hardest ,ecafrus dna c si the gnipmad oitar demussa( ot no the swollip naht no the hard .ecafrus nehW L/L, si
eb 0.55 for each ,rennur as denialpxe .)woleb dettolp tsniaga kdk, ni .giF 7, a yrev good tnemeerga si
.giF 8. dezilamroN toof tcatnoc emit ,.tJt sv dezilamron track ,ssenffits gnimussa gnipmad oitar C = 0.55.
nepO selcric wohs data decudorp yb mlif ;sisylana desolc selcric wohs ecrof mroftalp .atad rorrE srab wohs
stimil fo ytniatrecnu eud ot mlif dna epocsollicso ;gnidaer dettod senil era eno dradnats noitaived evoba dna
woleb eht laciteroeht .enil
ehT ecneulfni fo track ecnailpmoc no gninnur 901
dnuof htiw eht laciteroeht ,enil htiw a dradnats erusaem foot force gnirud the wollip gninnur -irepxe
noitaived of 0.045. ,stnem tub the noitciderp dluow eb that egareva force
Note that the gnirps ssenffits desu for the swollip si was derewol ot 0.71 semit sti ecafrus-drah ,eulav or
won the gO.l ,ssenffits 4.67 ,m/Nk esuaceb the -ed tuoba 1.67 semit ydob .thgiew
noitcelf 6 ni noitauqe (3) tsum. dnopserroc ot the evitatneserpeR force ,serutangis traced morf the
ecnatsid a nam dluow knis nwod fi he were ylerem epocsollicso photographs for tcejbus J.C., are nwohs ni
gnidnats at rest no the )deziraenil( .swollip llaceR that the rewol noitrop of .giF 9. nO the hard ,ecafrus the
the step htgnel yroeht was devired yleritne no the sisab laitini tcatnoc of the foot htiw the dnuorg decudorp a
of lacirtemoeg ,snoitaredisnoc dna did ton evlovni the ekips ni foot force hcihw netfo exceeded 5 semit ydob
s’nam gnirps .ssenffits tI si tnetsisnocerofereht htiw the .thgiew sihT ekips was rehtie tnesba or yrev hcum
devresbo fact that the step htgnel no a ralucitrap detaunetta nehw the emas tcejbus nar no a tnailpmoc
ecafrus si tnednepedni of gninnur speed. track. eW tcepsus siht citamard noitcuder of foot force
at laitini tcatnoc si the nosaer that lla stcejbus reported
Foot force a evitcejbus noisserpmi of desaercni gninnur trofmoc
ehT egareva lacitrev force deilppa ot the dnuorg yb no the tnailpmoc secafrus evitaler ot the hard .secafrus
the foot gnirud a step si lauqe ot the s’rennur ssam
semit sih naem lacitrev ,noitarelecca Running speed
gnivaH deniatbo snoitciderp for the dnuorg tcatnoc
F = g,m + 2m,p/t,, (7) emit ,t dna step htgnel L, we yam tup these together ot
where u si the drawnwod lacitrev yticolev at the niatbo the gninnur speed, u = L/t,. A ecneuqesnoc of
tnemom .tcatnocfo nI ruo ,stnemirepxe we derusaem u the fact that L dna ,C are ylraen tnatsnoc ni the
yb gnitargetni the force revo the noitarud of t,, dna etaidemretni egnar of track ssenffits si that gninnur
dnuof on tnacifingis ecnereffid ni u for a nevig tcejbus speed dluohs ton eb yltnacifingis affected litnu k,/k,
no a hard, as opposed ot a ,tnailpmoc .ecafrus suhT u si drops woleb 1.0. tA wol track ,ssenffits foot tcatnoc
nekat ot eb a ,tnatsnoc dnuof for a ralucitrap rennur emit rc ,sesaercni tub so does step ,htgnel so the rennur
morf the area rednu the emit-ecrof ,evruc si ton dewols nwod as hcum as tcatnoc emit enola
dluow .tciderp roF ,elpmaxe gninnur no the swollip
” (F - m,gVt desaercni ,t yb na egareva factor of2.3, tub the s’rennur
s speed was ton .devlah ,daetsnI ecnis step htgnel
c= * )36
2m, ’ desaercni yb a factor of 1.6, the s’rennur speed was
devreserp at 70% of sti ecafrus-drah .eulav
gnikaT a evitatneserper v = 0.732 tes/m for a 0.8 kN
,tcejbus dna gnisu seulav for ,t deniatbo morf .giF 8 ni
the case where the gnipmad oitar C = 0.55, a -nemid NOISSUCSID
sselnois ,FISF/F sv kJk, evruc yam eb dettolp .giF( 9).
sihT laciteroeht enil agrees ylbanosaer llew htiw the Limitations of the analysis
etalp-ecrof data ,stniop dna shows that on elbaicerppa tI si tnatropmi ot weiver the snoitpmussa edam at
egnahc ni the naem slevel of foot force nac eb expected suoirav stniop tuohguorht siht paper, dna ot -rednu
litnu the track ssenffits si yltnacifingis ssel naht the dnats how yeht timil the .sisylana eW nageb yb
ssenffits of the .nam Note that ti was ton elbissop ot gnitneserper the ytivargitna selcsum dna rieht sexelfer
.giF 9. dezilamroN egareva toof ecrof sv dezilamron track .ssenffits diloS enil swohs ,yroeht dilos stniop
wohs egareva ecrof mroftalp stluser rof hcae fo ruof .stcejbus stesnI wohs woh eht laitini ecrof tneisnart
decneirepxe no drah secafrus si dehsiloba no eht latnemirepxe nedoow .kcart
902 .A dna .R ENEERG
THOMAS MCMAHOH PETER
yb the elpmis lacinahcem metsys nwohs ni .giF 1, dna was citsilaer dedneped no the gnittif-evruc erudecorp
desu the cimanyd scitsiretcarahc of the gnirps dna nwohs ni .giF 3. ecniS the evruc gnitneserper a
dashpot ot etaluclac the ecneulfni of track ssenffits no gnipmad oitar <fo = 0.55 dedivorp the tseb tif hguorht
dnuorg tcatnoc .emit Later, we desu the lautpecnoc the yllatnemirepxe denimreted stniop for ,,,r:dt we took
ledom of the noinip-dna-kcar ,tnemele gnirongi the that eulav of < for tneuqesbus snoitaluclac of foot force
depmad ,gnirps ot etaluclac the ecneulfni of track dna gninnur speed.
ssenffits no step .htgnel eW degdelwonkca the cisnirtni ruO noitpmussa that the gnipmad tnemele si raenil
ytiraenilnon of the htgnel-ecrof citsiretcarahc of -hcterts si ylniatrec a great .noitacifilpmisrevo ztaK (1939)
ed ,elcsum tub ,demialc gniwollof ,kuoH that xelfer showed 40 sraey ago that the gnipmad retemarap b
noitasnepmoc acts ot restore .ytiraenil nI rehtona .giF( 3) si tuoba 6 semit greater for wols gninehtgnel as
paper eneerG( dna ,nohaMcM 1979), we evah -aem opposed ot wols gninetrohs ni detalosi .selcsum ehT
derus the egnar-trohs gnirps ssenffits of the ralucsum tnetxe ot hcihw siht effect si deifidom yb xelfer
sexelfer of the ,gel as a noitcnuf of htob eenk elgna dna anemonehp si .nwonknu
latot force, dna dnif that the evitceffe gnirps ssenffits of dluoC na tnednepedni set of ,stnemirepxe ton
the gel seirav yb a factor of 2 revo the eenk selgna gnivlovni ,gninnur eb proposed ot erusaem the eulav of
deretnuocne ni ,gninnur tub tsom of the noitairav i etairporppa for ?gninnur angavaC (1970) was elba ot
srucco ni the tsrif 15 degrees of eenk .noixelf -eR erusaem i yb gniwolla sih stcejbus ot go hguorht
,ylbakram the gnirps ssenffits at a tnatsnoc eenk elgna lareves depmad selcyc gnignir,fo elihw the selcsum of
si dnuof ot eb on erom naht 25% greater as the tcejbus the flac deniamer ni deniatsus .noitcartnoc nI ,gninnur
seirrac sdaol pu ot eciwt ydob thgiew no sih .sredluohs on hcus gnignir snoitallicso dluoc reve eb devresbo
,suhT as gnol as the eenk elgna 6 si kept nihtiw the esuaceb the foot sniamer ni tcatnoc htiw the dnuorg for
egnar 15” 2 0 < 45”, as ti ylnommoc si gnirud -nur ylno flah a gnignir ,elcyc dna the latot lacinahcem
,gnin ruo noitpmussa of eno elgnis gnirps ssenffits for ygrene si the emas at the gninnigeb dna the dne of each
the gel tuohguorht the step elcyc si ylbanosaer .dilav detroppus .doirep nI fact, siht si a ytreporp of lla
rehtonA noitacifilpmis sevlovni the :swollip we evah raenilnon ,snoitallicso that the ygrene tsol ni the
demussa that rieht noitcelfed-daol evruc si ,raenil evitapissid msinahcem sehctam the ygrene added per
whereas .giF 2 shows that ti si tsom yltcnitsid -non elcyc yb the evitagen“ ”ecnatsiser .nonemonehp ,suhT
.raenil eW evah osla detcelgen gnipmad ni the ,swollip ylno tceridni seuqinhcet hcihw egnahc the gnitarepo
hcihw si ylbaborp ton yleritne .deifitsuj nI ,noitidda we scitsiretcarahc of the rotallicso yb gnignahc eno of sti
evah detcelgen the latnoziroh ecnailpmoc of the tnenopmoc parts (here we desu the track) nac evres ot
.swollip ezylana the gniniamer .stnenopmoc
eW tlaed htiw the seitiraenilnon of the swollip yb sA a lanif kramer ti si worth gniton that the ledom of
gningissa the gO.l ssenffits sti proper elor ni -nimreted the lacitrev noitom of the rennur nwohs ni .giF 3 nac
gni step ,htgnel elihw we demussa that the 1.67g ylisae eb edam otni a raenilnon .rotallicso esoppuS
ssenffits senimreted foot tcatnoc .emit ecniS we dnuof that nehw htob the nam dna the track are ,gnidnecsed
that tsom of the stcejbus deilppa a deniatsus lacitrev dna therefore nehw the gel si gnieb dexelf yb the s’nam
force of tuoba 2.4 semit ydob thgiew ot the -drah drawnwod ,mutnemom the gnipmad tnatsnoc of the
ecafrus track, gnidrocca ot .giF 9, F no the swollip dashpot, b, si ,evitisop as was demussa ni the ydob of
dluohs eb tuoba 0.7 semit siht ,eulav or tuoba 1.67 the paper. sA na lanoitidda ,erutaef esoppus that nehw
semit ydob .thgiew suhT ruo stnemerusaem dna the yrotcejart of the retnec ssamfo x,,, reaches sti tsewol
snoitciderp are tnetsisnoc htiw ruo cisab snoitpmussa ,tniop b ylneddus sehctiws ,ngis dna sedivorp evitagen
tuoba foot force no the .swollip gnipmad for the txen .elcyc-flah ehT neddus egnahc ni
the ngis of b seriuqer a neddus ecnavda ni the phase of
,X-,X. htiw respect ot x,, dna siht seriuqer a step
ehT tpecnoc of the s’nam gnirps ssenffits si -moc egnahc ni the htgnel of x,. ehT laitnesse tluser si that,
detacilp yb the fact that ti sdneped no sih effort. rednU yb gnitalutsop a gnipmad hcihw sehctiws ngis at -dim
the snoitpmussa of noitauqe ,)l( nehw the nam snur edirts (as fi ti were denimreted yb tnioj receptors), we
eciwt as fast, sih gnirps ssenffits sesaercni yb a factor of yam etareneg na yrotallicso noitom whose edutilpma
4. eW evah detpmetta ot etanimile the effort -ed does ton yaced htiw ,emit dna tey whose doirep si the
ecnednep of the s’nam ssenffits ni siht paper yb gnikam emas as the elpmis metsys htiw raenil gnipmad
snosirapmoc of ecnamrofrep no tnereffid track dessucsid ni the ydob of the paper.
sessenffits ylno nehw the nam si gninnur at lamixam
effort.
SUMMARY AXD COSCLUSIOES
Man’s damping gninnigeB htiw a ledom of the ytivargitna selcsum
eW deyolpme gnipmada tnemele ni lellarap htiw the dna sexelfer hcihw semussa that yeht evah na -otua
s’nam gnirps esuaceb we wenk that (1) detalosi selcsum ,citam or ,evitcaer tnenopmoc hcihw sekam meht
yebo a lliH yticolev-ecrof evruc ,lliH( 1938), dna (2) evaheb ekil a depmad raenil ,gnirps dna siht si ni seires
the elcsum seldnips nruter yticolev noitamrofni ot the htiw a lufesoprup tnenopmoc hcihw sevaheb ekil na
lanips cord. ruO noisiced tuoba how hcum gnipmad yllanretxe dellortnoc ,noinip-dna-kcar we evah devired