Pressure Measurements

Dynamic Pressure vs Impact Pressure

The dynamic pressure and the impact pressure are the same at low speed, and equal to P_{total} - P_{static}. However, at higher speeds, the air density around the airplane is affected by compressibility, and the term P_{total} - P_{static} is called the impact pressure. The dynamic pressure is always equal to

(1)   \begin{equation*}P_{dynamic} = \frac{1}{2} \rho_{static} V_{true}^2 = \frac{1}{2} \rho_0 V_{equivalent}^2\end{equation*}

Dynamic Pressure

(2)   \begin{equation*}P_{dynamic} = q = \frac{1}{2} \rho_{air} V_{true}^2 = 1481.3 \delta M^2 ~ \left[ \frac{lb}{ft^2} \right] = \frac{V_{equivalent} ~ \left[ knots \right]}{295.37} ~ \left[ \frac{lb}{ft^2} \right]\end{equation*}

Impact Pressure

(3)   \begin{equation*}P_{impact} = P_{total} - P_{static} = q_c = P_0 \left[ \left( 1 + \frac{\gamma - 1}{2} \left( \frac{V_{calibrated}}{a_0} \right)^2 \right)^{\frac{\gamma}{\gamma - 1}} - 1 \right] = P_{static} \left[ \left( 1 + \frac{\gamma - 1}{2} M^2 \right)^{\frac{\gamma}{\gamma - 1}} - 1 \right]\end{equation*}

Indicated Impact Pressure

(4)   \begin{equation*}P_{indicated~impact} = P_{total}^{local} - P_{static}^{local} = q_{ic} = P_0 \left[ \left( 1 + \frac{\gamma - 1}{2} \left( \frac{V_{indicated}}{a_0} \right)^2 \right)^{\frac{\gamma}{\gamma - 1}} - 1 \right] = \frac{q_c}{1+C_p}\end{equation*}

Pressure Coefficient

(5)   \begin{equation*}C_p = \frac{ P_{static}^{local} - P_{static}^{free~stream}}{ P_{total}^{local} - P_{static}^{local}} = \frac{ P_{static}^{local} - P_{static}^{free~stream}}{q_{ic}}\end{equation*}


(6)   \begin{equation*}C_{p,total} = \frac{ P_{total}^{local} - P_{total}^{free~stream}}{ P_{total}^{local} - P_{static}^{local}} = \frac{ P_{total}^{local} - P_{total}^{free~stream}}{q_{ic}}\end{equation*}