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Commit 6aac3835 authored by Thomas Lambert's avatar Thomas Lambert :helicopter:
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Fix lambda_infty notation

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......@@ -488,11 +488,11 @@ Assume
The Blade Element Theory gave us previously
$$dC_T = \dfrac{1}{2}\sigma c_l r^2 dr = \dfrac{\sigma c_{l_\alpha}}{2}(\theta r^2-\lambda r)dr$$
Combining the two results gives a quadratic equation
$$\lambda^2 + \left(\dfrac{\sigma c_{l_\alpha}}{8}-\lambda_c\right)\lambda - \dfrac{\sigma c_{l_\alpha}}{8}\theta r = 0$$
$$\lambda^2 + \left(\dfrac{\sigma c_{l_\alpha}}{8}-\lambda_\infty\right)\lambda - \dfrac{\sigma c_{l_\alpha}}{8}\theta r = 0$$
and solving for $\lambda$ leads to
$$ \lambda(r,\lambda_c) = \sqrt{\left(\dfrac{\sigma c_{l_\alpha}}{16} -
\dfrac{\lambda_c}{2}\right)^2 + \dfrac{\sigma c_{l_\alpha}}{8}\theta r} -
\left(\dfrac{\sigma c_{l_\alpha}}{16} - \dfrac{\lambda_c}{2}\right)$$
$$ \lambda(r,\lambda_\infty) = \sqrt{\left(\dfrac{\sigma c_{l_\alpha}}{16} -
\dfrac{\lambda_\infty}{2}\right)^2 + \dfrac{\sigma c_{l_\alpha}}{8}\theta r} -
\left(\dfrac{\sigma c_{l_\alpha}}{16} - \dfrac{\lambda_\infty}{2}\right)$$
\end{frame}
......@@ -610,14 +610,14 @@ Assume
\textbf{Prandtl's tip-loss function}
\begin{itemize}
\item The correction factor can be incorporated in the BEMT\\[0.2cm]
$dC_T = 4 \textcolor{mLightBrown}{F} \lambda(\lambda-\lambda_c)rdr$
$dC_T = 4 \textcolor{mLightBrown}{F} \lambda(\lambda-\lambda_\infty)rdr$
\vspace{0.35cm}
\item In this case, the inflow velocity becomes\\[0.2cm]
$\lambda(r,\lambda_c) = \sqrt{\left(\dfrac{\sigma c_{l_\alpha}}{16
\textcolor{mLightBrown}{F}} - \dfrac{\lambda_c}{2}\right)^2 +
$\lambda(r,\lambda_\infty) = \sqrt{\left(\dfrac{\sigma c_{l_\alpha}}{16
\textcolor{mLightBrown}{F}} - \dfrac{\lambda_\infty}{2}\right)^2 +
\dfrac{\sigma c_{l_\alpha}}{8 \textcolor{mLightBrown}{F}}\theta r} -
\left(\dfrac{\sigma c_{l_\alpha}}{16 \textcolor{mLightBrown}{F}} -
\dfrac{\lambda_c}{2}\right)$
\dfrac{\lambda_\infty}{2}\right)$
\vspace{0.35cm}
\item Iterative process as $F = f(\phi) = f(\lambda)$!
\end{itemize}
......
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