Prediction of Jump Phenomena in Roll-Coupled Maneuvers of Airplanes

An easily computerized analytical method is developed for identifying critical airplane maneuvers in which nonlinear rotational coupling effects may cause sudden jumps in the response to pilot's control inputs. Fifth- and ninth-degree polynomials for predicting multiple pseudosteady states of roll-coupled maneuvers are derived. The program calculates the pseudosteady solutions and their stability. The occurrence of jump-like responses for several airplanes and a variety of maneuvers is shown to correlate well with the appearance of multiple stable solutions for critical control combinations. The analysis is extended to include aerodynamics nonlinear in angle of attack. HILLIPS'! original analysis of the roll-coupling problem considered the rotational coupling effects of constant roll rate on the stability of the short-period longitudinal and lateral oscillations. Although the constant rolling constraint is artificial, it is physically realistic for well-behaved airplanes with good damping in roll. Phillips' analysis predicted that divergence-like motions would be expected at certain critical roll rates, when the usual linearized stability analysis predicted perfectly acceptable behavior. This dangerous coupling effect of rapid rolling, leading to large deviations in incidence angles and tail loads, was confirmed in many nonlinear computerized simulations and in flight. In con- nection with these simulation studies, there were many at- tempts to extend Phillips' analysis. The main objective of these studies was to obtain a simplified method for predicting the peak motions in roll-coupled maneuvers. Pinsker2 and Rhoads and Schuler3 showed that Phillips' critical roll rates also could be obtained as steady-state (autorotational) solutions of the approximate equations of motion used by Phillips. This method has the advantages that it also predicts steady-state solutions for the other variables, is more readily generalized, and permits the use of control input values as independent parameters, instead of roll rate. However, attempts to use this method to predict peak disturbances reliably in coupled maneuver were not suc- cessful. In the present study we have returned to this method of calculating the steady states of the approximate equations of motion, which we shall call the pseudosteady-state (PSS) method, because it neglects the effects of varying weight components in body axes. However, instead of trying to predict the magnitudes of response peaks, the method will be used to predict those control input combinations that may cause sudden "jumps" in the response as the motion is "attracted" to a new stable pseudosteady-state.