User:Arthurv/aeroformulas

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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})x dx + \int_0^c \left( C_{p,u} \dfrac{dy_u}{dx}\right) y_udx+\int_0^c -C_{p,l} \dfrac{dy_l}{dx} y_l dx \right]
CL = cncosα − casinα
CD = cnsinα + cacosα
x_{C_p}=\dfrac{-M_{LE}}{L}
C_{L_{landing}}=\frac{M_L \times g}{\frac{1}{2}\rho _{SL}V_L^2S}
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

\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