美赛优秀论文.docx
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美赛优秀论文.docx
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美赛优秀论文
TheDesignofSnowboardHalfpipe
Abstract:
Basedonthesnowboardmovementtheory,theflightheightdependsontheout-velocity.Wetakethetechnicalparametersoffoursitesandfiveexcellentsnowboardersforstatisticalanalysis.Asresultsshowthatthesizeofhalfpipe(length,widthanddepth,halfpipeslope)influencethein-velocityandout-velocity.Helpramp,theanglebetweenthesnowboard’sdirectionandspeedaffectvelocity’sloss.
Forthehalfpipe,weestablishedthedifferentialequationmodel,basedonweight,friction,airdensity,resistancecoefficient,theareaofresistance,andotherfactorsandthelawofenergyconservation.themodel’sresultsshowthatthesnowboarders’energylosefromfouraspects
(1)theanglebetweenthedirectionofsnowboardandthespeed,whichformedbecauseoftheexistinghalfpipe
(2)Thefrictionbetweensnowboardandthesurface
(3)theairbarrier
(4)thecollisionwiththewallforgettingverticalspeedbeforeslipingoutofhalfpipe.
Therefore,weputforwardanimprovingmodelcalledL-halfpipe,soastoeliminateorreducetheanglebetweenthesnowboardandthespeed.Smallerradiuscanalsoreducetheenergyabsorptionbythewall.
Atlast,weputforwardsomeconceptiontooptimizethedesignofthehalfpipeintheperspectiveofsafetyandproducingtorsion.
Keywords:
snowboard;halfpipe;differentialequationmodel;L-halfpipe
Contents
1.Introduction.............................................................................................................3
简介
1.1theoriginofthesnowboardcourseproblems......................................................3
滑雪课程的起源问题。
1.2thebackground....................................................................................................3
背景
2.TheDescriptionofProblem....................................................................................3
问题的描述
2.1Practicalhalfpipe’srequirements.........................................................................3
实用halfpipe的需求
2.1.1themaximumverticalandthelargestbodytwist...........................................3
最大垂直和最大的身体扭曲
2.1.2Speedanalysis....................................................................................................3
速度分析
2.2Halfpipe’sownconditions...................................................................................4
Halfpipe自身的条件
2.2.1Friction............................................................................................................4
摩擦
2.2.2thesizeofhalfpipe..........................................................................................4
halfpipe的大小
3.Model.........................................................................................................................4
模型
3.1DefinitionsandSymbols......................................................................................4
定义和符号
3.2Assumptions.........................................................................................................5
假设
3.3thesimpleanalysisofgravityandfrictionwhenslidinginthehalfpipe.............5
简单的分析重力和摩擦力的halfpipe时滑动
3.4in-velocityoffactors............................................................................................6
速度的因素
3.4.1thesnowboarder’anglewheninandthespeedloss.......................................6
滑雪在角和速度上的损失
3.5out-velocityoffactors..........................................................................................8
初速度的因素
3.5.1Helpramp........................................................................................................8
帮助坡道
3.5.2theforcepointandtheplateanglewhenout...................................................9
力的点和板角
3.5.3thesnowboarder’anglewhenoutandthespeedloss......................................9
滑雪在角和速度上的损失
3.5.4Halfpipe’sRadius..........................................................................................11
Halfpipe的半径
3.6thein-velocitycomparisonwiththeout-velocity..............................................14
速度与速率的对比
3.7Snowboarder’spositionimpactonthespeed.....................................................14
滑雪的位置影响速度
3.8theentiremovementoftheenergychangeinthehalfpipe..................................15
在halfpipe中整个运动的能量变化
3.9thebalanceofspeedafterconsideringtheairresistance....................................18
后速度的平衡考虑空气阻力
3.10L-halfpipe.........................................................................................................19
左halfpipe
3.11SolutionandResult..........................................................................................20
解决方案和结果
4.Conclusions.............................................................................................................21
总结
4.1Conclusionsoftheproblem…………………………………………...………21
结论的问题
5.FutureWork...........................................................................................................21
工作展望
5.1othermodels………………………………………………………….....……..21
其他模型
5.1.1Halfpipe’slocationoutdoor………………………………………………..22
Halfpipe位置的户外
5.1.2Halfpipe’smaterial………………………………………….....…………...22
Halfpipe的材料
6.References...............................................................................................................22
参考文献
1.Introduction
Inordertoindicatetheoriginofthesnowboardcourseproblems,thefollowingbackgroundisworthmentioning.
1.1Theoriginofthesnowboardcourseproblems
Inthepast,asignificantamountofhalfpipeanxietywasduetothelearningcurveofanewsport,andeducatingresortsandpipeconstructionpersonnelsonhowtopreparethebestshapeswithbasicresortequipment.Thismodeofoperationischangingwiththeadventofnewsnowboardspecifictechnologybothinmachineandhandtools.Astechnologyhasmadehalfpipesbetter,thestandardshavealsobeenproved.Mosthalfpiperidershaveavisionofwhatanidealpipeshouldlooklike,butshiftingthatvisionintorealityseemstobeaquantumleap.
1.2Thebackground
Theproblemliesinthefactthattoomanypeoplewhocontrolthedecisionmakingprocessviewofthehalfpipeasafixedandstaticfeature,andthatoncebuilt,apipeislefttotheforcesofnature.Aseverechangeofopinionsneeded,asthehalfpipeneedstobethoughtofasanelasticform(almostlifelike)thatchangesdailyandwhichneedscontinualmaintenance.Anotherhugefactorindevelopingconsistenthalfpipesisasetofstandards.Overtheyears,theNASBA,OP,USASA,USSA,ISF,andFIShavegivendifferingpipedimensionstoresorts.Allthishelpfromvariousorganizationshasleftpipebuildingmoreofanartthanascience.BoththeISFandtheFISarenowpromotingsimilarversionsofhalfpipedimensions.Soweneedtoredesigntheshapeofasnowboardcoursetomaximizetheproductionofverticalairbyaskilledsnowboarder.
2.TheDescriptionoftheProblem
2.1Practicalhalfpipe’srequirements
2.1.1themaximumverticalandthelargestbodytwist
Snowboarders’greatestheight,thenumberofrotations(thelargestbodytwist)andthebeautifulactionwillaffecttheathlete'sscore.thelongerthesparetimeleft,themorerotationstodoforsnowboarders.Thebasicphysicsprincipleatworkhereistheconservationofangularmomentum.Theangularmomentumofthesnowboarderisdeterminedattakeoff,andcannotbechangedoncethesnowboarderisairborne.Sotomaketurnsintheairthesnowboardermustgivehimselfinitialrotationupontakeoff.
Inordertoreachthemaximumheight,themaximumout-velocitywouldberequired.soweanalyzedthein-velocityandtheout-velocity,andtheshapeofspace(length,width,depth,fieldgradient)affectthein-velocityandtheout-velocityobviously.Buttheheightcannotbetoohigh,becausetoohighspeedwouldbeabigthreattothesafetyofsnowboarders.Therefore,inordertocontrolthemaximumspeed,weneedtoredesignthehalfpipe.
2.1.2Speedanalysis
Whethertoreachthemaximumverticalheightortoproducethelargestbodytwistspeedisisareflectionofpracticalindicatorstothehalfpipedesign.Thecompositionofthefactorsintheaction.Includingtheflyheight,difficulty,diversity,qualitycompletionoftheaction,Siteuseandlandingconditionsandsoonbecausetheheighthaveanlimiteffectondifficulty,diversity,qualityofactioncompletement,sotheflyheightisthecoreelementsofmanyfactors.Toconclude,noheight,nonoflighttimeandnoflighttime,nodifficultaction.
Asthefreefallshows:
.Theheightsnowboarderscanreachhaveaverycloserelationshipwiththespeed.
2.2Halfpipe’sownconditions
2.2.1Friction
Friction,includingfrictionbetweentheboardandthesnowaswellasairfriction.ThedynamicfrictioncoefficientbetweenSnowandtheboardchangesfrom0.03to0.2.Take0.2forexample,themaximumfrictioncoefficientandthefulleffectofbodyweighttocalculatetheverticalfriction
thattheaccelerationlessduetofrictionisgeneratedtoacceleratetheroleofbodyweight0.2times,muchsmallerthanresultingintheaccelerationofgravityeffect.Airfriction
inourmodel,wedonotconsidertheinfluenceofairfriction.
2.2.2thesizeofhalfpipe
Undercertaincircumstances,asthelength,depth,tiltangleincreases,thespeedwillbe.Inviewofsnowboardsafety,speedcannotbeinfinite,whichhassomeofthevalueoftheconstraints.
3.Models
3.1DefinitionsandSymbols
Flat:
thebottomgroundofUgroove
Transitions:
thetransitionzonebetweenHorizontalandverticalgroovebottomwall
Verticals:
theverticalpartsofthewallsbetweentheLipandtheTransitions
Platform:
thelevelplatformonthesnowwallsurface
EntryRamp:
theslippery
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