User:Arthurv~enwiki/aeroformulas

From Anderson, for inviscid flows,

$C_{n}={\frac {1}{c}}\left[\int _{0}^{c}(C_{p,l}-C_{p,u})dx\right]$

$C_{a}={\frac {1}{c}}\left[\int _{0}^{c}\left(C_{p,u}{\dfrac {dy_{u}}{dx}}-C_{p,l}{\dfrac {dy_{l}}{dx}}\right)dx\right]$

$C_{m}={\frac {1}{c^{2}}}\left[\int _{0}^{c}(C_{p,u}-C_{p,l})xdx+\int _{0}^{c}\left(C_{p,u}{\dfrac {dy_{u}}{dx}}\right)y_{u}dx+\int _{0}^{c}-C_{p,l}{\dfrac {dy_{l}}{dx}}y_{l}dx\right]$

$C_{L}=c_{n}\cos \alpha -c_{a}\sin \alpha$

$C_{D}=c_{n}\sin \alpha +c_{a}\cos \alpha$

$x_{C_{p}}={\dfrac {-M_{LE}}{L}}$

$C_{L_{landing}}={\frac {M_{L}\times g}{{\frac {1}{2}}\rho _{SL}V_{L}^{2}S}}$

$V_{TO}={\sqrt {\frac {M_{TO}\times g}{{\frac {1}{2}}\rho _{SL}SC_{L_{TO}}}}}$

$acc={\frac {V_{TO}^{2}}{2\times d_{TO}}}$

$Th_{TO}=m_{TO}\times acc$

Full Potential Equation

<math>

\left [ \left ( \frac{\partial \phi}{\partial x} \right ) ^2 - a^2 \right] \frac{\partial ^2 \phi}{\partial x^2} + \left [ \left ( \frac{\partial \phi}{\partial y} \right ) ^2 - a^2 \right] \frac{\partial ^2 \phi}{\partial y^2} + \left [ \left ( \frac{\partial \phi}{\partial z} \right ) ^2 - a^2 \right] \frac{\partial ^2 \phi}{\partial z^2} + 2\frac{\partial \phi}{\partial x}\frac{\partial \phi}{\partial y} \frac{\partial ^2 \phi}{\partial x \partial y} + 2\frac{\partial \phi}{\partial x}\frac{\partial \phi}{\partial z} \frac{\partial ^2 \phi}{\partial x \partial z} + 2\frac{\partial \phi}{\partial y}\frac{\partial \phi}{\partial z} \frac{\partial ^2 \phi}{\partial y \partial z}=0