Basic aerodynamic equations
I collect here some basic equatin wich we need e.g. for airfoil dimensioning.
Total lift force
with
\(F_{L}\): lift force (N)
\(\rho\): denisty of air (we typ. use 1.1673 kg/m³ at 500m)
\(v\): velocity (of the plane, m/s)
\(c_{L}\): total lift coefficient
\(S\): projected surface (m²)
We use large letters as indices, e.g. \(F_{L}\) and \(c_{L}\) to indicate total (integrated over the whole wing) values in contrast to local values (e.g. given for a wing section).
Stall velocity
We regularly need to determine the lowest velocity, a plane can be flown without loosing height. Therefore, we resolve \(\eqref{eq:liftForce1}\) for \(v\):
Reynolds number
with
\(\mu\): dynamic viscosity
\(\nu\): kinematic viscosity of air (we typ. use 1.52 E-05 m²/s at 500m)
ResqrtCl
Solving \(\eqref{eq:reynolds}\) for \(v\), insertion in \(\eqref{eq:liftForce1}\) and grouping the terms gives:
First, we note that, in horicontal flight, the lift force needs to be constant (\(const_1\)). For higher velocities \(v\) we require less \(C_l\) and vice versa. All the values aggregated as \(const!\) are definitely constant. From this follows that \(Re^2\cdot C_{L}\) needs to be constant, too. Hence:
Note: at a given wing section we have local values (small indices)