Development of the Energy Method and Study of Algorithms for Predicting the Takeoff Trajectory of Aircraft

Abstract

The article is devoted to the development and research of the method of predicting the events on the trajectory of takeoff, climb and overcome highrise obstacles on the course. The prediction method is based on the energy approach to flight control, created by us in previous works. The mathematical formulation of the method is the energy balance equation describing the mutual influence of all acting forces in the aircraft-engine-environment" system. In this article, the equation is extended to ground modes of movement along the runway. For this, a term is added to the equation that takes into account the action of braking forces from the chassis. The balance equation allows us to directly obtain an algorithm for calculating the length of the forward trajectory required for the accumulation of the required amount of terminal energy. Takeoff trajectory includes ground and air segments. Therefore, the possibility of overcoming the obstacle is fixed by the algorithm at the point of a possible decision to takeoff, taking into account the next air segment. This point is reached before the decision-making airspeed prescribed by the flight manual is reached. This advance warning of the possibility of takeoff improves situational awareness of the pilot, which reduces stress and reduces the risk of erroneous actions. A computer stand was developed for the research. Single launches and series of statistical tests are possible. Takeoff scenarios are generated in the stand operator window, as well as initial runway conditions, atmospheric disturbances, aircraft configuration, and obstacle coordinates are specified. The parameters of random errors in the takeoff weight and centering are assigned, as well as the noise of longitudinal overload measurements are set. A large volume of deterministic and statistical tests of algorithms for predicting events on the takeoff trajectory was performed at the stand. Using the statistical analysis module, the characteristics of the range prediction errors to the take-off decision point and the nose wheel separation point were calculated. Probability densities and histograms of error distribution over five characteristic zones of deviations from the mean are constructed. The confidence intervals for calculating the mathematical expectation are obtained. A prototype of an electronic indicator of the takeoff trajectory with marks of predictive characteristic coordinates has been developed.