Linear Aerodynamic Terms#
In addition to the terms expressed previously, linear expressions are required for the aerodynamic angles and the total flightspeed.
Angle of Attack#
Angle of attack is defined as
\alpha\triangleq\arctan\frac{W}{U}
which with the small perturbation theory is
\alpha=\arctan\frac{W_0+w}{U_0+u}
in stability axes, W_0=0
\alpha=\arctan\frac{w}{U_0+u}
and since w is small
\alpha\simeq\frac{w}{U_0+u}
the perturbational forward speed is much smaller than the trim forward speed and the linear angle of attack is:
(83)#\alpha=\frac{w}{U_0}
Sideslip#
Sideslip is defined as
\beta\triangleq\arcsin\frac{V}{V_f}
where V_f=\sqrt{U^2+V^2+W^2}. Looking at a linear expression for the total flightspeed:
\begin{split}\begin{align}V_f&=\sqrt{\left(U_0+u\right)^2+\left(V_0+v\right)^2+\left(W_0+w\right)^2}\\
&= \sqrt{\left(U_0+u\right)^2+v^2+w^2}\end{align}\end{split}
the trim U_0 is \gg all the perturbational terms so
V_f\simeq U_0
giving the linear sideslip, subject to small v as
\beta=\frac{v}{U_0}