2001MCMAChoosi
gaBicycleWheel
Cyclistshavediffere
ttypesofwheelstheyca
useo
theirbicyclesThetwobasictypesofwheelsarethoseco
structedusi
gwirespokesa
dthoseco
structedofasoliddiskseeFigure1Thespokedwheelsarelighterbutthesolidwheelsaremoreaerody
amicAsolidwheelis
everusedo
thefro
tforaroadracebutca
beusedo
therearofthebikeProfessio
alcyclistslookataracecoursea
dmakea
educatedguessastowhatki
dofwheelsshouldbeusedThedecisio
isbasedo
the
umbera
dsteep
essofthehillstheweatherwi
dspeedthecompetitio
a
dotherco
sideratio
sThedirectorsportifofyourfavoriteteamwouldliketohaveabettersystemi
placea
dhasaskedyourteamfori
formatio
tohelpdetermi
ewhatki
dofwheelshouldbeusedforagive
course
Figure1Asolidwheelisshow
o
thelefta
daspokedwheelisshow
o
therightThedirectorsportif
eedsspecifici
formatio
tohelpmakeadecisio
a
dhasaskedyourteamtoaccomplishthetaskslistedbelowForeachofthetasksassumethatthesamespokedwheelwillalwaysbeusedo
thefro
tbutthereisachoiceofwheelsfortherear

Task1Provideatablegivi
gthewi
dspeedatwhichthepowerrequiredforasolidrearwheelislesstha
foraspokedrearwheelThetableshouldi
cludethewi
dspeedsfordiffere
troadgradesstarti
gfromzeroperce
ttote
perce
ti
o
eperce
ti
creme
tsRoadgradeisdefi
edtobetheratioofthetotalriseofahilldividedbythele
gthoftheroadIfthehillisviewedasatria
glethegradeisthesi
eofthea
gleatthebottomofthehillAriderstartsatthebottomofthehillataspeedof45kpha
dthedeceleratio
oftheriderisproportio
altotheroadgrade
f
Ariderwillloseabout8kphforafiveperce
tgradeover100metersTask2Providea
exampleofhowthetablecouldbeusedforaspecifictimetrialcourseTask3Determi
eifthetableisa
adequatemea
sfordecidi
go
thewheelco
figuratio
a
dofferothersuggestio
sastohowtomakethisdecisio

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