A Theoretical Investigation of the Rolling Oscillations of an Airplane with Ailerons Free
NATIONAL AERONAUTICS AND SPACE ADMIN LANGLEY RESEARCH CENTER HAMPTON VA
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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 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 are derived for the stability and damping of the rolling oscillations in terms of the hinge moment derivatives and other characteristics of the ailerons and airplane. Charts are also presented showing the oscillatory regions and stability boundaries for a fictitious airplane of conventional proportions. The effects of friction in the control system are investigated and discussed. If the ailerons tend to trail with the wind, the condition for stable variation of stick force with aileron deflection is found to determine the amount of aerodynamic balance that may be used. If the ailerons tend to float against the wind, the period and damping of the rolling oscillations are found to be satisfactory in a mass-balanced system so long as the restoring moment is not completely balanced out. Unbalanced mass behind the hinge, however, has an unfavorable effect on the damping of the oscillations and so shifts the boundary that close aerodynamic balance may not be attainable.