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fix typo
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peterdsharpe committed Dec 10, 2023
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\label{eq:laitone} \text{Laitone \cite{laitone_new_1951}:}\qquad & \Cp = \frac{\Cpo}{\beta + \Mi^2 / \beta \cdot \Cpo / 2 \cdot \left( 1 + \frac{\gamma - 1}{2} \Mi^2 \right)}
\end{align}

\noindent where $\beta = \sqrt{1- \Mi^2}$, and $\gamma$ is the ratio of specific heats (1.4 for air near standard conditions). In theory, these compressibility corrections should apply only to the pressure-derived forces on the airfoil, while the shear forces are relatively unaffected. In practice, NeuralFoil does not have access to the breakdown ofpressure and shear forces, so this is not possible. Instead, NeuralFoil applies the compressibility correction to the lift force and pitching moment (which are pressure-dominated) but does not apply the correction to the drag force (which is often shear-dominated). This assumption, while relatively simple, proves to match compressible airfoil drag data computed with other methods quite closely, as shown in Section \ref{sec:validation_transonic}.
\noindent where $\beta = \sqrt{1- \Mi^2}$, and $\gamma$ is the ratio of specific heats (1.4 for air near standard conditions). In theory, these compressibility corrections should apply only to the pressure-derived forces on the airfoil, while the shear forces are relatively unaffected. In practice, NeuralFoil does not have access to the breakdown of pressure and shear forces, so this is not possible. Instead, NeuralFoil applies the compressibility correction to the lift force and pitching moment (which are pressure-dominated) but does not apply the correction to the drag force (which is often shear-dominated). This assumption, while relatively simple, proves to match compressible airfoil drag data computed with other methods quite closely, as shown in Section \ref{sec:validation_transonic}.

Another useful definition is that of the sonic pressure coefficient $\Cpcr$, which is the pressure coefficient below which flow goes supersonic. This is derived from the isentropic relations, yielding:

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