A theoretical investigation of the rolling oscillations of an airplane with ailerons free

An analysis is made of the stability of an airplane with ailerons free, with particular attention to the motions when the ailerons have a tendency to float against the wind. The present analysis supersedes the aileron investigation contained in NACA Technical Report no. 709. The equations of motion are first written to include yawing and sideslipping, and it is demonstrated that the principal effects of freeing the ailerons can be determined without regard to these motions. If the ailerons tend to float against the wind and have a high degree of aerodynamic balance, rolling oscillations, in addition to the normal lateral oscillations, are likely to occur. On the basis of the equations including only the rolling motion and the aileron deflection, formulas derived for the stability and damping of the rolling oscillations in terms of the hinge-moment derivatives are also presented showing the oscillatory regions and stability boundaries for a fictitious airplane of conventional proportion. The effects of friction in the control system are investigated and discussed.