Linear Aerodynamic Terms

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}