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Cours 12: Application: A class America’s cup |
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1.4 Vitesse apparente vue du foil
Vitesse apparente vue du foil
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Vitesse et angles du foil |
![\includegraphics[width=3.1cm]{aeroimages/image12-60.png}](images/img-0009.png) |
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$h=a+b=\vert O’O\vert $ |
Vitesse du point $F$ |
($z$ est le pilonnement en $O$) \[ V_ f=(\dot z+\dot\gamma d_ f \sin (\gamma +\alpha ))e_ z- \dot\gamma d_ f \cos (\gamma +\alpha )e_ x \] Vitesse apparente vue de $F$ \[ V_{af}\hskip-1.42263779528pt=\hskip-1.42263779528pt(V\hskip-1.42263779528pt+\hskip-1.42263779528pt\dot\gamma d_ f\cos (\gamma \hskip-1.42263779528pt+\hskip-1.42263779528pt\alpha )))e_ x\hskip-1.42263779528pt-\hskip-1.42263779528pt(\dot z\hskip-1.42263779528pt+\hskip-1.42263779528pt\dot\gamma (d_ f\sin (\gamma \hskip-1.42263779528pt+\hskip-1.42263779528pt\alpha )))e_ z \] Module de la vitesse apparente en $F$ \[ \vert V_{af}\vert ^2\hskip-1.42263779528pt=\hskip-1.42263779528pt(V\hskip-1.42263779528pt+\hskip-1.42263779528pt\dot\gamma d_ f\cos (\gamma \hskip-1.42263779528pt+\hskip-1.42263779528pt\alpha ))^2\hskip-1.42263779528pt+\hskip-1.42263779528pt(\dot z\hskip-1.42263779528pt+\hskip-1.42263779528pt\dot\gamma d_ f\sin (\gamma \hskip-1.42263779528pt+\hskip-1.42263779528pt\alpha ))^2 \] Incidence apparente du socle du foil \[ \begin{array}{c} (\alpha +\gamma )_ a= \hbox{arcsin}(\displaystyle {\frac{ [V_{af}\wedge (\cos (\alpha +\gamma )e_ x-\sin (\alpha +\gamma )e_ z].e_ y}{\vert V_{af}\vert }}) \end{array} \] |
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\[ \boxed {OF=-d_ f\sin (\alpha +\gamma )e_ x-d_ f\cos (\alpha +\gamma )e_ z} \]NB: On suppose que la poussée hydrodynamique est en $F$.
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Cours 12: Application: A class America’s cup |
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