bicycle motorcycle dynamics bicycle motorcycle dynamics science motion components forces acting dynamics branch classical mechanics turn branch physics bike motions interest include balancing steering braking accelerating suspension activation vibration study motions began late 19th century continues today single track vehicles motions fundamental attributes common fundamentally different difficult study wheeled vehicles lack lateral stability stationary circumstances remain upright moving forward experimentation mathematical analysis shown bike stays upright steered center mass wheels steering usually supplied rider certain circumstances bike factors including geometry mass distribution effect contribute varying degrees self stability long standing claims single effect trail solely responsible force remaining upright primary goal beginning riders bike lean order maintain balance turn higher speed smaller turn radius lean required roll wheel contact patches generated force turn force lean usually produced steering opposite direction called skill usually acquired motor learning executed procedural memory conscious thought unlike wheeled vehicles primary control input steering position stable stationary high center mass short lift wheel ground sufficient acceleration braking depending location combined center mass bike rider respect point wheel contacts ground wheel flip bike rider wheel similar situation possible accelerating respect rear wheel history history study bike dynamics nearly old bicycle includes contributions famous scientists early 19th century credited wheeled vehicle variously called horse showed rider balance device steering wheel published article engineer repeating von assertion balance maintained steering direction lean understanding bicycle dynamics goal prix competition end 19th century showed rigid body dynamics safety actually balance moving right speed won prix clear credit steering axis vertical helps possible published article showing effects necessary balance bicycle identified named modes written regularly behavior london worked early 1970s later buffalo usa sponsored study simulate bicycle motorcycle dynamics portions work released public detailed reports posted bicycle dynamics site 1990s researching motorcycle dynamics research experimental numerical covered vehicle modelling tire modelling handling minimum lap time maneuvering published canonical motion proceedings different methods assumed tires roll slip point rider attached rear frame bicycle published article science showing effects called effects trail necessary bike balance designed mass bicycle motion predict self stable negative trail wheel contacts ground steering axis counter rotating wheels cancel effects constructed physical model prediction require details provided steering geometry stability evaluated bicycle dynamics named discover stories cycles awarded examine bicycle stability forces bike rider considered single system forces act system components roughly divided groups internal external external forces gravity contact ground contact atmosphere internal forces caused rider interaction components external forces masses gravity pulls rider bike components earth tire contact patch ground reaction forces horizontal vertical components vertical components counteract force gravity vary braking accelerating details section longitudinal stability horizontal components friction wheels ground including rolling resistance response forces braking forces turning forces aerodynamic forces atmosphere form drag normal speeds level ground aerodynamic drag largest force resisting forward motion faster speed aerodynamic drag overwhelmingly largest force resisting forward motion turning forces generated maneuvers balancing addition changing direction travel interpreted forces accelerating reference frame bike rider simply stationary reference frame forces forces acting rotating parts wheels engine transmission etc rotating parts discussed section effects internal forces internal forces components bike rider system caused rider friction addition rider apply steering mechanism fork wheel etc rear frame rider rear frame friction exists parts drive train steering mechanism rear frame etc addition brakes create friction rotating wheels non rotating frame parts rear steering dissipate undesirable energy spring connecting fork frame provide progressive tends steer bicycle straight ahead rear feedback drive train suspension issue designers attempt handle configurations motions motions bike roughly grouped central plane symmetry lateral central plane symmetry longitudinal vertical lateral motions include balancing leaning steering turning motions central plane symmetry include rolling forward course brake diving suspension activation motions groups interact order bike unstable stationary self stable moving right conditions controlled rider conversely bike stable stationary unstable undergoing sufficient acceleration lateral dynamics lateral dynamics proven complicated requiring dimensional dynamic analysis coordinates analyze minimum coupled second order differential required capture principal motions exact solutions possible numerical methods instead competing theories balance found print online hand shown later sections longitudinal dynamic analysis accomplished simply coordinate balance discussing bike balance necessary distinguish carefully stability self stability recent research suggests rider controlled stability related self stability bike remains upright steered ground reaction forces exactly balance internal external forces experiences leaning turn steered aerodynamic steering supplied rider certain circumstances bike self stability generated combination effects depend geometry mass distribution forward speed bike tires suspension steering frame influence especially staying relatively rider balance bike principle performing track stand rider line contact patches combined center mass steering wheel moving forward backward slightly contact patch necessary forward motion generated simply backwards motion generated way fixed gear bicycle rider advantage slope pavement upper body backwards brakes momentarily engaged steering bike locked virtually impossible balance riding hand effect rotating bike wheels cancelled adding counter rotating wheels easy balance riding way bike balanced locked steering applying appropriate bike rider similar way swing hanging straight uneven parallel bars person start swinging swing rest pumping legs double inverted controlled elbow forward speed rider applies order turn wheel control lean maintain balance high speeds small steering angles quickly ground contact points low speeds larger steering angles required achieve results time usually easier maintain balance high speeds self stability usually occurs speeds minimum going faster increases chances bike contributing stability center mass location farther forward closer wheel center mass combined bike rider wheel order maintain balance conversely closer rear wheel center mass located wheel lateral movement bike forward motion required regain balance noticeable long issue touring heavy load gear rear wheel mass rear wheel easily controlled lower mass wheel bike example inverted easier balance pencil tall bike high center mass easier balance ridden low lean rate slower rider opposite impression bike stationary heavy bike require effort upright stopped traffic example bike tall lower center mass example vertical second class small force end seat bike easily moves large mass mass closer tires touch ground touring advised carry loads low bike hang rear racks trail factor influences easy difficult bike ride trail distance wheel ground contact point trails steering axis ground contact point steering axis axis entire steering mechanism fork wheel etc traditional bike designs steering axis vertical positive trail tends steer wheel direction lean independent forward speed simulated pushing stationary bike wheel usually steer lean gravity provides force dynamics moving bike complicated factors contribute effect trail function head angle fork offset wheel size relationship described formula formula formula wheel radius formula head angle measured clock wise horizontal formula fork offset trail increased increasing wheel size decreasing head angle decreasing fork trail traditional bike stable feels trail bike feel difficult steer negative trail contact patch steering axis intersects ground reported feel unstable normally road racing trail touring mountain mountain designed reduced head angles road improve stability greater trail touring built small trail allow rider control bike weighed baggage consequence touring bike feel unstable fork curve fork blades forward steering axis diminish trail negative trail exist experimental bike negative trail shown self stable refers head angle instead offset created triple tree diminish trail small survey wilson found touring head angles trail racing head angles trail track head angles trail ranges hard fast example offers offset size wheels course designed road racing head angle varies depending frame size trail varies designed track head angle varies depending frame size trail varies trail particular bike vary time reasons suspension especially suspension heavy braking example steering axis angle reduce trail trail varies lean angle steering angle usually decreasing maximum bike straight upright steered straight ahead trail decrease zero sufficiently large lean steer angles alter stable bike feels finally profile tire influence trail varies bike steered measurement similar trail called mechanical trail normal trail true trail perpendicular distance steering axis wheel contact patch factor influences directional stability bike horizontal distance ground contact points rear wheels given displacement wheel disturbance angle resulting path original proportional radius given steer angle lean angle proportional finally increases bike steered extreme lean angle bike steered direction lean increased radius rear wheels steering mechanism mass distribution factor contribute self stability traditional bike designs distribution mass steering mechanism includes wheel fork center mass steering mechanism steering axis pull gravity cause wheel steer direction lean seen leaning stationary bike wheel usually steer independent interaction ground additional parameters fore aft position center mass elevation center mass contribute dynamic behavior bike effects role effect bike designs help steer wheel direction lean phenomenon called rate object proportional rate spin slower wheel spins faster bike vice versa rear wheel prevented wheel friction tires ground continues lean spinning forces provide resistance low forward speeds wheel quick contributing bike tendency start lean way eventually fall high forward speeds usually slow contributing bike tendency eventually fall having reached upright position instability slow order seconds easy riders counteract fast bike feel stable actually self stable fall contribution effects roll moment generated wheel example steering left causes moment right moment small compared moment generated tracking wheel begins soon rider applies helpful motorcycle racing detail section article self stability unstable regimes mentioned previous section influenced factors described contribute balance trail mass distribution effects etc range forward speeds given bike design effects steer bike upright proven effects positive trail sufficient necessary self stability certainly enhance hands free control self stability bike ridden steering wheels note effects mentioned combine produce self stability overwhelmed additional factors friction stiff control cables video shows bicycle exhibiting self stability longitudinal acceleration longitudinal acceleration shown large complex effect lateral dynamics study positive acceleration self stability negative acceleration changes speeds self stability turning order bike turn change direction forward travel wheel aim approximately desired direction wheel steered vehicle friction wheels ground generates acceleration necessary alter course straight ahead combination force thrust radius turn upright leaning bike roughly small steering angles formula formula approximate radius formula formula steer angle formula angle steering axis leaning unlike wheeled vehicles lean turn balance relevant forces ground support angle lean easily calculated laws circular motion formula forward speed radius turn acceleration gravity case slight increase lean angle required compensate width modern tires forward speed turn radius example bike radius steady state turn mph angle rider lean respect bike order bike upright desired angle matters horizontal plane plane defined tire contacts location center mass bike rider lean bike decreases actual radius turn lean angle resulting radius roughly exact value formula approximate radius lean angle steer angle angle steering axis bike tires contact patches farther causing wear portions edge motorcycle tire remain leaning turns referred chicken strips finite width tires actual lean angle rear frame ideal lean angle described actual lean angle frame vertical increase tire width decrease center mass height fat tires low center mass lean tires higher centers mass negotiate turn speed increase lean angle tire thickness calculated formula ideal lean angle height center mass example motorcycle inch wide rear tire inches combined bike rider center mass height inches lean increased nearly increase tires inches wide lean angle increase half shown couple created gravity ground reaction forces necessary bicycle turn custom built bicycle spring loaded exactly cancel couple bicycle rider assume lean angle traveling straight line riders find impossible turn soon wheels straight path bicycle rider begin lean opposite direction way right steer straight path order initiate turn necessary lean direction turn bike momentarily steer opposite direction referred wheel finite angle direction motion lateral force developed contact patch tire force creates longitudinal roll axis bike causes bike lean away initially steered direction direction desired turn external influence wind create force necessary lean bike necessary initiate rapid turn initial steer steer angle opposite desired turn direction case maintain steady state turn sustained steer angle usually direction turn remain opposite direction turn especially high speeds sustained steer required maintain steer angle usually opposite turn direction actual magnitude orientation sustained steer angle sustained steer particular bike particular turn depend forward speed bike geometry tire properties combined bike rider mass distribution turn radius changed appropriate change lean angle accomplished additional turn increase lean decrease radius turn decrease lean increase radius exit turn bike momentarily steering turn order decrease radius increasing forces decreasing angle lean steady state turning turn established applied steering mechanism order maintain constant radius constant forward speed depends forward speed geometry mass distribution bike speeds speed described section called speed self stability bike cause tend steer turn exiting turn applied opposite direction turn speeds speed instability cause tend steer turn increasing lean applied direction turn speed input steering necessary maintain steady state turn steering angle effects influence steering angle angle assembly rotated steering axis necessary maintain steady state turn unique single track vehicles experienced automobiles mentioned article repeated necessarily order importance found place actual steering angle angle projected road plane assembly rotated function steering angle steering axis angle formula formula steering angle formula steering angle formula angle steering axis second lean bike decreases actual radius turn lean angle resulting radius roughly exact value formula formula approximate radius formula formula lean angle formula steering angle formula angle steering axis rear tires different slip angles weight distribution tire properties etc experience steering angle greater steering angle slip angles equal maintain given turn radius authors use term counter steering refer need conditions steer opposite direction turn negative steering angle maintain control response significant rear wheel fourth thrust contributes force necessary cause bike straight path force slip angle largest contributor thrust contributes ability negotiate turn radius automobiles smaller steering angle bike steered direction angle tire greater rear generate thrust equal hands usually initiated applying directly lighter vehicles accomplished shifting rider weight rider right relative bike bike left conserve angular momentum combined center mass remains nearly vertical plane lean bike called counter lean authors cause steer left initiate right hand turn rider left applying directly technique complicated additional factors friction stiff control cables combined center mass slightly left rider right relative bike bike left response action space tires right prevented friction tires ground pushes combined center mass left small effect evidenced difficulty people balancing bike method effects mentioned section balance effect turning wheel roll moment caused magnitude moment proportional moment wheel spin rate forward motion rate rider turns wheel applying angle steering axis vertical sample motorcycle moving mph wheel moment turning wheel degree half second generates roll moment comparison lateral force tire tracks motorcycle reaches maximum acting height center mass generates roll moment moment forces play significant begins act soon rider applies instead building slowly wheel tracks especially helpful motorcycle racing wheel steering theoretical benefits turning radius low speed attempts construct wheel steering working prototype australia reported work issues design include provide active control rear wheel let swing freely case active control control needs decide steering opposite direction wheel implementation wheel steering sideways bike lets rider control steering wheels directly second steering axis seat controlled built long low wheel steering bicycle called steering mechanisms control wheels independently steering motions included balance wheels steer tire contacts center mass true circle wheels steer equally opposite directions steering bicycle substantially changing lateral position tire contacts relative center mass able wheels parallel line frame instance wheel near roadway center line rear wheel near curb balance steering allowed easy balancing despite long low center mass self balancing hands configuration discovered true circle expected essentially impossible balance steering correct tire patch center mass cycling angles tested tendency fall braking mentioned passing wilson science 2nd edition rear wheel steering theoretical benefits especially simplified wheel drive mechanism attempts construct rear wheel steering bike built rear wheel steering bicycle commissioned construction rear wheel steering motorcycle proved illinois offered person successfully ride rear steered bicycle documented example successfully riding rear wheel steering bicycle specially designed bike difficulty turning left accomplished turning rear wheel right initially moves center mass right vice versa task induced environment examination common mass shows moving reverse rear wheel steering inherently unstable purpose built designs published suffer problem center steering extremes classical wheel steering strictly rear wheel steering class pivot point referred center steering similar articulated steering early implementation concept phantom bicycle early 1870s promoted safer alternative penny design allows simple wheel drive current appear stable hands photographs illustrate designs usually head angles positive negative trail builder bike negative trail states steering bike straight ahead forces seat rider rise slightly effect negative trail reverse steering constructed investigation demonstration purposes steering reversed turning left causes wheel turn right versa possible ride bicycle found riders experienced normal find difficult learn manage effect effect expression describe extend far steering axis head tube act like boat moves bars right order turn wheel left vice versa situation commonly found cruiser troublesome limits ability steer interference limits arm reach tires tires large influence bike handling especially tires influence bike dynamics distinct ways finite crown radius force generation increase crown radius tire shown decrease size eliminate self stability increasing crown radius rear tire opposite effect lesser degree tires generate lateral forces necessary steering balance combination force thrust tire inflation pressures found important behavior motorcycle high speeds rear tires different slip angles weight distribution tire properties etc experience wheel rear wheel dangerous wheel steering critical maintaining balance real tires finite contact patch road surface generate turn experience slipping roll generate axis normal plane contact patch generated tire called self caused slip length contact patch resultant force slip occurs geometric center contact patch distance described trail creates tire direction slip outside turn force tire center turn tends turn wheel direction slip away direction turn tends increase radius turn produced finite width contact patch lean tire turn portion contact patch outside turn actually moving respect wheel hub faster rest contact patch greater radius hub reasoning inner portion moving slowly outer inner portions contact patch slip pavement opposite directions generating tends turn wheel direction turn tends decrease turn radius combination opposite creates resulting wheel direction function slip angle tire angle actual path tire direction pointing angle tire angle tire vertical result suppression speed predicted rigid wheel models described section steady state turning high high type bike motion caused rear wheel gaining traction facing direction travel usually slipping sideways curve occur heavy braking acceleration varying road surface suspension activation especially interaction drive train form single slip flip series violent handling bike handling difficult reasons geometry bike especially steering axis angle makes analysis complicated conditions inherently unstable rider control finally rider skill large influence bike performance maneuver bike designs tend consist trade stability rider control primary control input rider apply directly steering mechanism bike dynamics steering geometry effects direct position control steering angle found problematic secondary control input rider lean upper relative bike mentioned effectiveness rider lean varies mass bike heavy rider lean ground clearance requirements turn improves view road improves bike system dynamics low frequency passive manner motorcycle racing leaning moving body projecting knee inside turn relative bike cause aerodynamic moment entering rounding turn differences automobiles need bike upright avoid injury rider damage vehicle limits type testing commonly performed example automobile publications perform quote results motorcycle publications need set turn lean bike appropriate angle means rider ahead necessary typical car speed need increases proportion speed rating schemes schemes devised rate handling particularly roll index ratio steering roll lean angle acceleration index ratio steering lateral acceleration steering ratio ratio theoretical turning radius based ideal tire behavior actual turning radius values wheel slip greater rear wheel slip described steering equal neutral steering greater steering values zero wheel turned opposite direction curve greater rear wheel slip wheel described counter steering riders tend prefer neutral slight steering car drivers tend prefer steering index ratio peak steering product peak lean rate forward speed large touring tend high index sport tend medium index tend low index easier maneuver light heavy lateral motion theory motion bike system variable solved written linear sum independent components behavior sum behaviors generally systems difficult solve linear systems case friction ignored bike conservative system demonstrated right circumstances decrease time energy added sideways bike running straight upright demonstrating self stability converted increased forward speed lost die bike system outcome path dependent order know exact configuration especially location necessary know configuration parts histories moved time mathematical analysis finally language control theory bike exhibits non minimum phase behavior turns direction opposite initially steered described section degrees freedom number degrees freedom bike depends particular model simplest model captures key dynamic features called model developed rigid bodies knife edge wheels rolling slip flat smooth surface degrees freedom configuration required completely describe location orientation bodies coordinate rear wheel contact point coordinate rear wheel contact point orientation angle rear frame rotation angle rear wheel rotation angle wheel lean angle rear frame roll steering angle rear frame end adding complexity model rider movement suspension movement tire compliance frame adds degrees freedom rear frame pitch leaning steering pitch angle completely constrained requirement wheels remain ground calculated seven location bike rotation wheels ignored degrees freedom ignored bike described lean angle steer angle motion motion bike consisting rigid frame rigid fork knife edged rigid wheels connected rolling friction slip smooth horizontal surface operating near upright straight ahead unstable represented single fourth order ordinary differential equation coupled second order differential lean equation formula steer equation formula formula lean angle rear assembly formula steer angle assembly relative rear assembly formula formula moments applied rear assembly steering axis respectively analysis bike taken zero represented matrix form formula formula symmetrical mass matrix contains terms include mass geometry bike formula called matrix bike dissipation contains terms include forward speed formula formula called matrix contains terms include constant formula formula formula formula formula lean angle steer angle formula external forces moments mentioned model geometric parameters head angle mass body wheel radius etc significant lean angle lean rate steer angle steer rate verified comparison multiple models derived completely independently bicycle like inverted lateral position support controlled terms representing roll acceleration roll velocity roll displacement steering feedback roll acceleration term normally wrong sign self expected important mainly respect roll velocity feedback correct sign nature proportional speed dominated wheel contribution roll displacement term important mainly controlled trail steering offset frame mass center steering axis terms involve complex combinations bicycle design parameters speed limitations bicycle considered extensions treatments tires frames riders implications included optimal rider controls path following control discussed possible state lean angle lean rate steer angle steer rate order analyze normal modes self stability particular bike design plot right particular bicycle calculated forward speeds mph real parts shown dark blue negative bike self stable imaginary parts shown non zero bike exhibits point origin bike design self stable region forward speeds self stable going backwards speed forward speeds identified plot right motion bike changes forward speed begin mph example called double root speed repeated root characteristic exactly value speed bike simply falls inverted forward speed increase mode switch positive negative mph example called speed speed increase bike falls speed eventually die forward speed non leaning increases mode switch negative positive pitchfork mph example called speed speed non lean eventually causes bike fall speeds exist range forward speeds particular bike design self stable case bike shown self stable range mph fourth usually stable negative represents behavior wheel tends turn direction bike traveling note model exhibit rear described seen models incorporate tire interaction ground degrees freedom experimentation real far confirmed mode predicted found tire slip frame important lateral dynamics bicycle speed range bike model shown incorporate real tires generate tire interaction pavement prevent mode unstable high speeds wilson suggest happens real world modes complex mechanisms variety modes fundamental ways modes stable unstable depending bike parameters forward speed context stable means bike continue rolling forward falling long forward speed maintained conversely unstable means bike eventually fall forward speed maintained modes differentiated speed switch stability relative phases leaning steering bike experiences mode bike motion consists combination amounts possible modes main modes bike experience lesser known mode rear usually stable word describe bike falling wheel usually direction lean stop increasing lean high lean angle reached point steering turn opposite direction happen slowly bike moving forward rapidly instability slow order seconds easy rider control actually rider initiate lean necessary turn depending geometry mass distribution stable low speeds stable speed increases longer stable tire interaction pavement sufficient prevent unstable high speeds word describe slow leaning left steering right vice versa entire bike affected significant changes steering angle lean angle roll heading angle steering phase heading phase leaning movie shows depending geometry mass distribution unstable low speeds pronounced speed increases longer unstable decrease frequency actually increases speed tank speed death words phrases describe rapid primarily end wheel fork involved rear frame contribute flexible instability occurs high speed similar experienced shopping cart wheels airplane landing gear automobile wheels easily adjusting speed position grip fatal left begins minor fork wheel restoring force applied phase progress wheel turns process repeated insufficient steering increase system failure occurs frequency changed changing forward speed making bike lighter increasing steering rider main component rear term rear describe mode lean angle roll heading angle phase phase steer angle rate moderate maximum rear heavily falls quickly bike speed increases design criteria effect design parameters bike modes investigated examining motion details motion section motion general conclusions drawn described lateral rear frame wheel affects mode substantially long trail flat steering head angle found increase mode lateral distortion countered locating fork axis low possible tendencies degraded rear suspension length rear tire largest contribution parameters tire lesser effect rear loading tendencies rear load assemblies appropriate successful study shown theoretically bike turn road mode high speed mode low speed frequencies match vehicle speed parameters mode effective steering mode worse light riders heavy riders riding riding theoretically identical riding stationary pavement physical testing confirmed developed specifically indoor bicycle training riding investigation appear simple mechanisms major moving parts frame fork wheels parts arranged way makes complicated analyze fact ridden effects wheels canceled hypothesis effects wheels bike upright common print online examples print angular momentum motorcycle counter steering discussion demonstration motorcycle hill new_york new_york longitudinal dynamics experience variety longitudinal forces motions wheel turned entire rear frame pitches forward slightly depending steering axis angle trail rear trim describe geometric configuration bike especially response forces braking accelerating turning drive train aerodynamic drag load borne wheels varies center mass location turn varies location passengers acceleration phenomenon known load transfer weight transfer depending author provides challenges opportunities riders designers example motorcycle use increase friction available tire attempts reduce suspension compression heavy braking spawned motorcycle fork designs net aerodynamic drag forces considered act single point called center pressure high speeds create net moment rear driving wheel result net transfer load wheel rear wheel depending shape bike shape installed aerodynamic lift present increases reduces load wheel stability stable stationary bike unstable sufficient acceleration second law analyze ground reaction forces generated example normal vertical ground reaction forces wheels bike formula center mass height formula distance formula rear wheel hub simplicity wheels locked expressed formula rear wheel formula wheel horizontal forces simply formula rear wheel formula wheel formula friction formula total mass bike rider formula acceleration gravity formula occurs center mass line extending wheel contact patch inclined angle formula horizontal normal force rear wheel zero point equation longer applies bike begin flip loop forward wheel hand center mass height line tandem long wheel base cars likely wheel generate braking force flip bike means nearly limit tires road reach friction upright bicycle best conditions science author points puts upright particular risk causing rear end collision cars similarly powerful generate rear wheel lift wheel ground maneuver called line similar described analyze braking performance drawn rear wheel contact patch predict possible given available friction center mass location sufficient power happen power available center mass far rider applying power course angle terrain influence calculations remaining equal risk pitching end reduced riding hill increased riding hill possibility performing increases riding hill major factor motorcycle competitions braking according ground conditions braking rider motion seeking change speed combined mass rider plus bike negative acceleration line travel acceleration causes forward force mass braking initial speed final speed length time equation implies greater acceleration shorter time needed change speed stopping distance shortest acceleration highest possible value compatible road conditions equation makes low high low braking force apply wheel depends ground conditions balance weight wheels instant time total braking force exceed gravity force rider bike times friction tire ground occurs ratio greater rear wheel having negative impact lateral stability braking force line travel linear tends rotate tendency rotate moment resisted moment taking moments wheel contact point instance time braking mass typically way rear wheels greater constant light braking emergency stop required poor ground conditions prevent heavy braking weight rests rear wheel meaning large contribute braking increases decrease moment increases maximum constant clockwise anti clockwise moments equal point greater factors downhill easier wheel moves line closer try reduce tendency rider stand try far possible braking increasing center mass forward relative wheel rider moves forward relative bike bike suspension wheel load changing bike geometry puts extra load wheel end brake maneuver rider comes halt suspension pushes rider values vary greatly depending number factors material ground road surface ground wet dry ground ground speed vehicle friction reducing mph friction rolling sliding sliding friction peak rolling friction braking braking force standard upright comes wheel analysis shows brakes strong rear wheel easy wheel generate stopping force flip rider bike wheel called rear wheel lifted bike flip abbreviated form end end bike long low cruiser tire instead possibly causing loss balance assuming loss balance possible braking performance depending bike geometry location center gravity bike rider maximum friction case suspension especially fork tubes increase downward force wheel braking cause suspension end lower known brake diving riding technique takes advantage braking increases downward force wheel known trail braking wheel braking limiting factors maximum wheel braking maximum limiting value static friction tire ground rubber dry asphalt friction brake pads rim disk pitching bike rider wheel upright bicycle dry asphalt excellent brakes pitching probably limiting factor combined center mass typical upright bicycle rider wheel contact patch allowing maximum rider brakes properly pitching avoided rider moves weight larger possible brakes inexpensive strong road limiting factor cheap brakes especially power style pull brakes severely restrict stopping force wet conditions effective wheel common road mud water loose stones reduce friction tire trail tires effect grabbing surface irregularities wheel common corners road acceleration adds forces tire ground contact friction force exceeded wheel rear wheel braking rear brake upright bicycle produce best decrease normal force rear wheel described rear braking subject limitation example coaster brake fixed gear braking mechanism situations warrant rear wheel braking slippery surfaces surfaces wheel braking lower friction cause wheel results loss balance flat tire braking wheel flat tire cause tire come rim greatly reduces friction case wheel result loss balance brake failure long require good rear brake near rear wheel braking technique expert opinion varies use equally fastest stop bike normal apply brake hard rear wheel lift ground depending road conditions rider skill level desired fraction maximum possible suspension rear suspension suspension operate primarily central plane symmetry consideration given lateral compliance goals bike suspension reduce vibration experienced rider maintain wheel contact ground maintain vehicle trim primary suspension parameters sprung mass tire characteristics irregularities terrain brake acceleration drive train forces activate suspension described examples include bob pedal feedback shaft effect brake dive vibration study vibrations includes causes engine balance wheel balance ground surface transmission absorption effects bike rider safety important factor vibration analysis comparison natural frequencies system possible driving frequencies vibration sources close match means mechanical resonance result large challenge vibration create compliance certain directions vertically sacrificing frame needed power transmission handling issue vibration bike possibility failure material fatigue effects vibration riders include discomfort loss efficiency secondary form disease body vibration instruments inaccurate difficult read primary cause vibrations properly functioning bicycle surface rolls addition tires traditional bicycle variety techniques developed damp vibrations reach rider include materials carbon fiber frame key components fork tube shapes curved seat stays special specialized addition road surface vibrations motorcycle caused engine wheels manufacturers employ variety technologies reduce damp vibrations engine balance shafts rubber engine mounts tire weights problems vibration causes spawned industry market parts systems designed reduce add include weights isolated foot engine high speeds riders experience aerodynamic changing air flow key parts experimentation variety experiments performed order verify bike dynamics built search configuration built confirm jones findings built bike rocket bike investigate steering effects built motorcycle fixed investigate effects rider motion position steering performed measurements bike moore performed measurements bike
Bicycle and motorcycle dynamics