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


which with the small perturbation theory is


in stability axes, \(W_0=0\)


and since \(w\) is small


the perturbational forward speed is much smaller than the trim forward speed and the linear angle of attack is:



Sideslip is defined as


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