{"id":5978,"date":"2011-02-09T17:00:03","date_gmt":"2011-02-09T16:00:03","guid":{"rendered":"https:\/\/medianbox.fr\/wordpress\/?p=5978"},"modified":"2014-08-13T22:52:53","modified_gmt":"2014-08-13T20:52:53","slug":"cyclisme-les-frottements-a-velo","status":"publish","type":"post","link":"https:\/\/medianbox.fr\/wordpress\/?p=5978","title":{"rendered":"MeDiaN@Sports &#8211; \u00ab Les Frottements \u00e0 v\u00e9lo \u00bb"},"content":{"rendered":"<h3>Pr\u00e9sentation g\u00e9n\u00e9rale<\/h3>\n<p>Dans ce pr\u00e9c\u00e9dent <a title=\"Cyclisme : &quot;La r\u00e9sistance au roulement du v\u00e9lo&quot;\" href=\"https:\/\/medianbox.fr\/wordpress\/?p=1841\" target=\"_blank\">article<\/a>, nous avons vu que l&rsquo;\u00e9quation g\u00e9rant le mouvement d&rsquo;un cycliste peut s&rsquo;\u00e9crire sous la forme suivante :<\/p>\n<p style=\"text-align: center;\"><img src='https:\/\/s0.wp.com\/latex.php?latex=C_%7Bm%7D+%3D+K%5Cddot%7B%5Ctheta_%7Bp%7D+%7D+%2B+%5Cleft+%28+%5Clambda_%7B1%7D%2B2.+%5Clambda_%7B2%7Dt+%5Cright+%29+%5Cdot%7B%5Ctheta_%7Bp%7D%7D+%2B+%5Cleft+%28M_%7Btot%7D+%5Cright+%29+.g.a.t.sin%28%5Calpha%29+%2B+k_%7Bcorr%7D.C_%7Baero_%7Bp%7D%7D+%2B+C_%7Br_%7Bp%7D%7D&#038;bg=121315&#038;fg=ffffff&#038;s=0' alt='C_{m} = K\\ddot{\\theta_{p} } + \\left ( \\lambda_{1}+2. \\lambda_{2}t \\right ) \\dot{\\theta_{p}} + \\left (M_{tot} \\right ) .g.a.t.sin(\\alpha) + k_{corr}.C_{aero_{p}} + C_{r_{p}}' title='C_{m} = K\\ddot{\\theta_{p} } + \\left ( \\lambda_{1}+2. \\lambda_{2}t \\right ) \\dot{\\theta_{p}} + \\left (M_{tot} \\right ) .g.a.t.sin(\\alpha) + k_{corr}.C_{aero_{p}} + C_{r_{p}}' class='latex' \/><\/p>\n<p style=\"text-align: left;\">Avec <img src='https:\/\/s0.wp.com\/latex.php?latex=K%3Da%5E%7B2%7D.t%5E%7B2%7D+%5Cleft+%28+M%2B2.+%5Cleft+%28M_%7B1%7D%2BM_%7B2%7D+%5Cright%29+%2B+m_%7BP%7D+%2B+2.+m_%7Bp%7D%2BM_%7BCycliste%7D+%5Cright%29%2B0%2C13%5E%7B2%7D+%5Cleft+%28m_%7BP%7D+%2B+2.+m_%7Bp%7D+%5Cright%29+&#038;bg=121315&#038;fg=ffffff&#038;s=0' alt='K=a^{2}.t^{2} \\left ( M+2. \\left (M_{1}+M_{2} \\right) + m_{P} + 2. m_{p}+M_{Cycliste} \\right)+0,13^{2} \\left (m_{P} + 2. m_{p} \\right) ' title='K=a^{2}.t^{2} \\left ( M+2. \\left (M_{1}+M_{2} \\right) + m_{P} + 2. m_{p}+M_{Cycliste} \\right)+0,13^{2} \\left (m_{P} + 2. m_{p} \\right) ' class='latex' \/><br \/>\n<img src='https:\/\/s0.wp.com\/latex.php?latex=M_%7Btot%7D+%3D+%5Cleft+%28M%2BM_%7B1%7D%2BM_%7B2%7D%2Bm_%7BP%7D%2B2m_%7Bp%7D%2BM_%7BCycliste%7D+%5Cright+%29+&#038;bg=121315&#038;fg=ffffff&#038;s=0' alt='M_{tot} = \\left (M+M_{1}+M_{2}+m_{P}+2m_{p}+M_{Cycliste} \\right ) ' title='M_{tot} = \\left (M+M_{1}+M_{2}+m_{P}+2m_{p}+M_{Cycliste} \\right ) ' class='latex' \/><\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Calpha+%3D+Arctan+%28%5Cfrac%7BDenivele%7D%7B100%7D%29&#038;bg=121315&#038;fg=ffffff&#038;s=0' alt='\\alpha = Arctan (\\frac{Denivele}{100})' title='\\alpha = Arctan (\\frac{Denivele}{100})' class='latex' \/> ou <img src='https:\/\/s0.wp.com\/latex.php?latex=sin%28%5Calpha%29+%3D+%5Cfrac%7BDenivele_%7Btot%7D%7D%7BDistance_%7Btot%7D%7D&#038;bg=121315&#038;fg=ffffff&#038;s=0' alt='sin(\\alpha) = \\frac{Denivele_{tot}}{Distance_{tot}}' title='sin(\\alpha) = \\frac{Denivele_{tot}}{Distance_{tot}}' class='latex' \/><br \/>\n<img src='https:\/\/s0.wp.com\/latex.php?latex=t%3D%5Cfrac%7BNdents_%7Bplateau%7D+%7D%7BNdents_%7Bpignon%7D%7D&#038;bg=121315&#038;fg=ffffff&#038;s=0' alt='t=\\frac{Ndents_{plateau} }{Ndents_{pignon}}' title='t=\\frac{Ndents_{plateau} }{Ndents_{pignon}}' class='latex' \/><\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=k_%7Bcorr%7D+%3D+1-%5Cfrac%7Bt_%7Babrite%7D%7D%7B100%7D%2A0.3&#038;bg=121315&#038;fg=ffffff&#038;s=0' alt='k_{corr} = 1-\\frac{t_{abrite}}{100}*0.3' title='k_{corr} = 1-\\frac{t_{abrite}}{100}*0.3' class='latex' \/><br \/>\n<img src='https:\/\/s0.wp.com\/latex.php?latex=C_%7Baero_%7Bp%7D%7D%3Dt.C_%7Baero_%7Broues%7D%7D%3Da.t.R_%7Baero%7D&#038;bg=121315&#038;fg=ffffff&#038;s=0' alt='C_{aero_{p}}=t.C_{aero_{roues}}=a.t.R_{aero}' title='C_{aero_{p}}=t.C_{aero_{roues}}=a.t.R_{aero}' class='latex' \/><br \/>\n<img src='https:\/\/s0.wp.com\/latex.php?latex=R_%7Baero%7D%3DR_%7BC_%7Bx%7D%7D%2BR_%7Bfriction_%7Bair%7D%7D%3D%28%5Cfrac%7B1%7D%7B2%7D%5Crho.S.C_%7Bx%7D%2BC_%7Bf%7D%29.%28V_%7BVent%7D.cos%28i%29%2Ba.t.%5Cdot%7B%5Ctheta_%7Bp%7D%7D%29%5E%7B2%7D&#038;bg=121315&#038;fg=ffffff&#038;s=0' alt='R_{aero}=R_{C_{x}}+R_{friction_{air}}=(\\frac{1}{2}\\rho.S.C_{x}+C_{f}).(V_{Vent}.cos(i)+a.t.\\dot{\\theta_{p}})^{2}' title='R_{aero}=R_{C_{x}}+R_{friction_{air}}=(\\frac{1}{2}\\rho.S.C_{x}+C_{f}).(V_{Vent}.cos(i)+a.t.\\dot{\\theta_{p}})^{2}' class='latex' \/><\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=C_%7Br_%7Bp%7D%7D%3Dt.C_%7Br_%7Broues%7D%7D%3Da.t.R_%7Br%7D&#038;bg=121315&#038;fg=ffffff&#038;s=0' alt='C_{r_{p}}=t.C_{r_{roues}}=a.t.R_{r}' title='C_{r_{p}}=t.C_{r_{roues}}=a.t.R_{r}' class='latex' \/><br \/>\n<img src='https:\/\/s0.wp.com\/latex.php?latex=R_%7Br%7D%3DCrr.M_%7Btot%7D.g.cos%28%5Calpha%29&#038;bg=121315&#038;fg=ffffff&#038;s=0' alt='R_{r}=Crr.M_{tot}.g.cos(\\alpha)' title='R_{r}=Crr.M_{tot}.g.cos(\\alpha)' class='latex' \/> Avec <img src='https:\/\/s0.wp.com\/latex.php?latex=Crr+%3D+Coeff_%7Broute%7D%2ACoef_%7Bpneu%7D%2Ap%5E%7B-0.426%7D&#038;bg=121315&#038;fg=ffffff&#038;s=0' alt='Crr = Coeff_{route}*Coef_{pneu}*p^{-0.426}' title='Crr = Coeff_{route}*Coef_{pneu}*p^{-0.426}' class='latex' \/><br \/>\navec <img src='https:\/\/s0.wp.com\/latex.php?latex=cos%28%5Calpha%29%5E%7B2%7D%2Bsin%28%5Calpha%29%5E%7B2%7D%3D1&#038;bg=121315&#038;fg=ffffff&#038;s=0' alt='cos(\\alpha)^{2}+sin(\\alpha)^{2}=1' title='cos(\\alpha)^{2}+sin(\\alpha)^{2}=1' class='latex' \/> d&rsquo;o\u00f9 <img src='https:\/\/s0.wp.com\/latex.php?latex=cos%28%5Calpha%29%3D%5Csqrt%7B1-sin%28%5Calpha%29%5E%7B2%7D%7D&#038;bg=121315&#038;fg=ffffff&#038;s=0' alt='cos(\\alpha)=\\sqrt{1-sin(\\alpha)^{2}}' title='cos(\\alpha)=\\sqrt{1-sin(\\alpha)^{2}}' class='latex' \/><\/p>\n<p style=\"text-align: justify;\">Cette \u00e9quation nous donne la valeur du couple que le cycliste doit fournir pour rouler \u00e0 une vitesse donn\u00e9, et ce en prenant en compte les diff\u00e9rentes masses en mouvement, les pertes dans les liaisons, le profil de la route, l&rsquo;a\u00e9rodynamisme globale du syst\u00e8me et la r\u00e9sistance au roulement cr\u00e9\u00e9e par les pneus. Un v\u00e9lo n&rsquo;\u00e9tant pas un syst\u00e8me m\u00e9canique parfait, les liaisons entre pi\u00e8ces en mouvement sont le si\u00e8ge de frottements qui conduisent \u00e0 une perte d&rsquo;\u00e9nergie sous la forme de chaleur.<\/p>\n<h3>Le si\u00e8ge des frottements<\/h3>\n<p style=\"text-align: justify;\">Dans l&rsquo;\u00e9quation ci-dessus, les pertes au niveau du bo\u00eetier de p\u00e9dalier (<img src='https:\/\/s0.wp.com\/latex.php?latex=%5Clambda_%7B1%7D&#038;bg=121315&#038;fg=ffffff&#038;s=0' alt='\\lambda_{1}' title='\\lambda_{1}' class='latex' \/>) et les roulements de roues (<img src='https:\/\/s0.wp.com\/latex.php?latex=%5Clambda_%7B2%7D&#038;bg=121315&#038;fg=ffffff&#038;s=0' alt='\\lambda_{2}' title='\\lambda_{2}' class='latex' \/>) apparaissait dans le terme <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cleft+%28+%5Clambda_%7B1%7D%2B2.+%5Clambda_%7B2%7Dt+%5Cright+%29+%5Cdot%7B%5Ctheta_%7Bp%7D%7D&#038;bg=121315&#038;fg=ffffff&#038;s=0' alt='\\left ( \\lambda_{1}+2. \\lambda_{2}t \\right ) \\dot{\\theta_{p}}' title='\\left ( \\lambda_{1}+2. \\lambda_{2}t \\right ) \\dot{\\theta_{p}}' class='latex' \/> qui suppose des pertes proportionnelles \u00e0 la vitesse du cycliste (hypoth\u00e8se de d\u00e9part).<\/p>\n<p style=\"text-align: justify;\">Ce calcul n&rsquo;est cependant pas repr\u00e9sentatif de la r\u00e9alit\u00e9, puisque pour tout v\u00e9lo en bon \u00e9tat, les pertes dans les roulements sont n\u00e9gligeables devant celles g\u00e9n\u00e9r\u00e9es par la transmission. De plus, la d\u00e9termination des coeff <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Clambda_%7B1%7D&#038;bg=121315&#038;fg=ffffff&#038;s=0' alt='\\lambda_{1}' title='\\lambda_{1}' class='latex' \/> et <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Clambda_%7B2%7D&#038;bg=121315&#038;fg=ffffff&#038;s=0' alt='\\lambda_{2}' title='\\lambda_{2}' class='latex' \/> est compliqu\u00e9e (pas de donn\u00e9es constructeur, caract\u00e9ristiques \u00e9voluant dans le temps,&#8230;).<\/p>\n<p style=\"text-align: justify;\">Ci-dessous une petite listes des endroits susceptible de dissiper de l&rsquo;\u00e9nergie par frottement :<\/p>\n<div id=\"attachment_5993\" style=\"width: 257px\" class=\"wp-caption alignright\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-5993\" class=\"size-full wp-image-5993\" src=\"https:\/\/medianbox.fr\/wordpress\/wp-content\/uploads\/2014\/08\/frottements.jpg\" alt=\"La source principale des frottements\" width=\"247\" height=\"215\" \/><p id=\"caption-attachment-5993\" class=\"wp-caption-text\">La source principale des frottements<\/p><\/div>\n<p style=\"text-align: left;\">&#8211; Frottements de la cha\u00eene sur le plateau;<br \/>\n&#8211; Frottements de la cha\u00eene sur les pignons;<br \/>\n&#8211; Frottement de la cha\u00eene sur les 2 galets du d\u00e9railleur;<br \/>\n&#8211; Frottement de la cha\u00eene contre la fourchette du d\u00e9railleur;<br \/>\n&#8211; Frottements internes \u00e0 la cha\u00eene : entre maillons&#8230;;<br \/>\n&#8211; Les roulements de roues et de p\u00e9dalier mais aussi ceux des p\u00e9dales;<br \/>\n&#8211; Des freins mal centr\u00e9s amen\u00e9 \u00e0 frotter la roue, voire une roue voil\u00e9e;<br \/>\n&#8211; La roue libre de la cassette en descente par exemple.<br \/>\n&#8211; La d\u00e9formation des pi\u00e8ces qui g\u00e9n\u00e8re des frottements internes \u00e0 la mati\u00e8res&#8230;.<\/p>\n<h3 style=\"text-align: left;\">Estimation de ces pertes<\/h3>\n<p style=\"text-align: justify;\">Comme on le constate ci-dessus, de nombreuses sources de frottements existent sur un v\u00e9lo et peuvent conduire \u00e0 la diminution du rendement globale de la machine. Bien que ces pertes soient fortement variables (qui n&rsquo;a pas d\u00e9j\u00e0 maudit un v\u00e9lo \u00e0 la transmission rouill\u00e9e?), nous pouvons am\u00e9liorer la pr\u00e9cision de l&rsquo;\u00e9quation en int\u00e9grant un facteur suppl\u00e9mentaire repr\u00e9sentant ce rendement globale.<\/p>\n<p style=\"text-align: justify;\">L&rsquo;estimation de ce facteur a \u00e9t\u00e9 r\u00e9alis\u00e9 d&rsquo;apr\u00e8s de nombreux site ou livre qui font \u00e9tat un rendement de 97% pour une transmission par cha\u00eene. Ceci signifie que le couple exerc\u00e9 par le cycliste pour rouler \u00e0 vitesse constante sur une portion de route \u00e0 d\u00e9nivel\u00e9 constant devra \u00eatre dans le meilleur des cas 1,03 fois plus important que si celui-ci disposait d&rsquo;un v\u00e9lo parfait (rendement de 100%, rigidit\u00e9 infinie&#8230;.)<\/p>\n<h3 style=\"text-align: left;\">Conclusion<\/h3>\n<p style=\"text-align: justify;\">La prise en compte des frottements nous permet d\u2019accro\u00eetre encore la pr\u00e9cision de l\u2019\u00e9quation du mouvement \u00e9tablie pr\u00e9c\u00e9demment. L&rsquo;ajout d&rsquo;un\u00a0 facteur de rendement nous donne l&rsquo;expression suivante :<\/p>\n<p style=\"text-align: center;\"><img src='https:\/\/s0.wp.com\/latex.php?latex=C_%7Bm%7D+%3D+1%2C03.%28K.%5Cddot%7B%5Ctheta_%7Bp%7D%7D+%2B+%28M_%7Btot%7D%29+.g.a.t.sin%28%5Calpha%29+%2B+k_%7Bcorr%7D.C_%7Baero_%7Bp%7D%7D+%2B+C_%7Br_%7Bp%7D%7D%29&#038;bg=121315&#038;fg=ffffff&#038;s=0' alt='C_{m} = 1,03.(K.\\ddot{\\theta_{p}} + (M_{tot}) .g.a.t.sin(\\alpha) + k_{corr}.C_{aero_{p}} + C_{r_{p}})' title='C_{m} = 1,03.(K.\\ddot{\\theta_{p}} + (M_{tot}) .g.a.t.sin(\\alpha) + k_{corr}.C_{aero_{p}} + C_{r_{p}})' class='latex' \/><\/p>\n<p style=\"text-align: justify;\">Le terme <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cleft+%28+%5Clambda_%7B1%7D%2B2.+%5Clambda_%7B2%7Dt+%5Cright+%29+%5Cdot%7B%5Ctheta_%7Bp%7D%7D&#038;bg=121315&#038;fg=ffffff&#038;s=0' alt='\\left ( \\lambda_{1}+2. \\lambda_{2}t \\right ) \\dot{\\theta_{p}}' title='\\left ( \\lambda_{1}+2. \\lambda_{2}t \\right ) \\dot{\\theta_{p}}' class='latex' \/> a bien s\u00fbr \u00e9t\u00e9 supprim\u00e9 puisqu&rsquo;il est d\u00e9sormais int\u00e9gr\u00e9 au facteur 1,03.<\/p>\n<p style=\"text-align: left;\">Cette \u00e9quation nous permet d\u2019\u00e9crire quelques remarques int\u00e9ressantes :<\/p>\n<p style=\"text-align: left;\">L&rsquo;entretien r\u00e9gulier d&rsquo;un v\u00e9lo est primordial pour conserver un niveau \u00e9lev\u00e9 de performances. Ceci passe par une bonne lubrification de la transmission et des roulements, mais aussi par un parfait r\u00e9glage des d\u00e9railleurs afin d&rsquo;\u00e9viter les frottements dans ces derniers.<\/p>\n<p style=\"text-align: left;\">Le rendement de 97% (97.5% pris un v\u00e9lo de pro r\u00e9gler au petit oignon) prit comme hypoth\u00e8se correspond \u00e0 un v\u00e9lo parfaitement entretenu et avec des composants proches du neuf (hypoth\u00e8se optimiste). Il pourra \u00eatre beaucoup plus faible si les pi\u00e8ces sont us\u00e9es ou corrod\u00e9es par exemple.<\/p>\n<p style=\"text-align: left;\">Le choix des braquets est \u00e9galement important et il faudra veiller \u00e0 limiter le plus possible les croisements de cha\u00eenes qui, outre une projection g\u00e9om\u00e9trique d\u00e9favorable des efforts, entra\u00eenent une augmentation des frottements.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pr\u00e9sentation g\u00e9n\u00e9rale Dans ce pr\u00e9c\u00e9dent article, nous avons vu que l&rsquo;\u00e9quation g\u00e9rant le mouvement d&rsquo;un cycliste peut s&rsquo;\u00e9crire sous la forme suivante : Avec ou Avec avec d&rsquo;o\u00f9 Cette \u00e9quation nous donne la valeur du couple que le cycliste doit fournir pour rouler \u00e0 une vitesse donn\u00e9, et ce en prenant en compte les diff\u00e9rentes [&hellip;]<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"ngg_post_thumbnail":0,"footnotes":""},"categories":[60],"tags":[],"class_list":["post-5978","post","type-post","status-publish","format-standard","hentry","category-mediansports"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>MeDiaN@Sports - \u00ab Les Frottements \u00e0 v\u00e9lo \u00bb - MeDiaN@Tour<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/medianbox.fr\/wordpress\/?p=5978\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"MeDiaN@Sports - \u00ab Les Frottements \u00e0 v\u00e9lo \u00bb - MeDiaN@Tour\" \/>\n<meta property=\"og:description\" content=\"Pr\u00e9sentation g\u00e9n\u00e9rale Dans ce pr\u00e9c\u00e9dent article, nous avons vu que l&rsquo;\u00e9quation g\u00e9rant le mouvement d&rsquo;un cycliste peut s&rsquo;\u00e9crire sous la forme suivante : Avec ou Avec avec d&rsquo;o\u00f9 Cette \u00e9quation nous donne la valeur du couple que le cycliste doit fournir pour rouler \u00e0 une vitesse donn\u00e9, et ce en prenant en compte les diff\u00e9rentes [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/medianbox.fr\/wordpress\/?p=5978\" \/>\n<meta property=\"og:site_name\" content=\"MeDiaN@Tour\" \/>\n<meta property=\"article:published_time\" content=\"2011-02-09T16:00:03+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2014-08-13T20:52:53+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/medianbox.fr\/wordpress\/wp-content\/uploads\/2014\/08\/frottements.jpg\" \/>\n<meta name=\"author\" content=\"MeDiaN\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u00c9crit par\" \/>\n\t<meta name=\"twitter:data1\" content=\"MeDiaN\" \/>\n\t<meta name=\"twitter:label2\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/medianbox.fr\\\/wordpress\\\/?p=5978#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/medianbox.fr\\\/wordpress\\\/?p=5978\"},\"author\":{\"name\":\"MeDiaN\",\"@id\":\"https:\\\/\\\/medianbox.fr\\\/wordpress\\\/#\\\/schema\\\/person\\\/e1cba8e776ddbc5e91ef69e134732c6d\"},\"headline\":\"MeDiaN@Sports &#8211; 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