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Cours 12: Application: A class America’s cup |
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1.3 Vitesse apparente vue du safran
Vitesse apparente vue du safran
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Les angles $\beta $ et $\gamma $ |
![\includegraphics[width=3.3cm,height=3.7cm]{aeroimages/image12-51.png}](images/img-0008.png) |
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Vitesse du point $S$ |
($z$ est le pilonnement en $O$) \[ V_ s=(\dot z-\dot\gamma (h\cos (\gamma )-d_ s\sin (\gamma ))e_ z-\dot\gamma (h\sin (\gamma )+d_ s\cos (\gamma ))e_ x \] Vitesse apparente vue de $S$ \[ V_{as}\hskip-1.42263779528pt=\hskip-1.42263779528pt(V\hskip-1.42263779528pt+\hskip-1.42263779528pt\dot\gamma (h\sin (\gamma )\hskip-1.42263779528pt+\hskip-1.42263779528ptd_ s\cos (\gamma )))e_ x\hskip-1.42263779528pt-\hskip-1.42263779528pt(\dot z\hskip-1.42263779528pt-\hskip-1.42263779528pt\dot\gamma (h\cos (\gamma )\hskip-1.42263779528pt-\hskip-1.42263779528ptd_ s\sin (\gamma )))e_ z \] Module de la vitesse apparente en $S$ \[ \vert V_{as}\vert ^2\hskip-1.42263779528pt=\hskip-1.42263779528pt(V\hskip-1.42263779528pt+\hskip-1.42263779528pt\dot\gamma (h\sin (\gamma )\hskip-1.42263779528pt+\hskip-1.42263779528ptd_ s\cos (\gamma )))^2\hskip-1.42263779528pt+\hskip-1.42263779528pt(\dot z\hskip-1.42263779528pt-\hskip-1.42263779528pt\dot\gamma (h\cos (\gamma )\hskip-1.42263779528pt-\hskip-1.42263779528ptd_ s\sin (\gamma )))^2 \] Incidence apparente du pied du safran \[ (\beta +\gamma )_ a= \hbox{arcsin}( \frac{[V_{as}\wedge (\cos (\beta +\gamma )e_ x-\sin (\beta +\gamma )e_ z].e_ y}{\vert V_{as}\vert }) \] |
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\[ \boxed {OS=(h\cos (\gamma )-d_ s\sin (\gamma ))e_ x-(h\sin (\gamma )+d_ s\cos (\gamma ))e_ z} \] NB: On suppose que la poussée hydrodynamique est en $S$.
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Cours 12: Application: A class America’s cup |
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