Mathematical Problems in Engineering
Volume 8 (2002), Issue 1, Pages 43-67
Modified guidance laws to escape microbursts with turbulence
Department of Aerospace Engineering, University of Michigan, 1320 Beal, Ann Arbor 48109-2140, MI, USA
Received 7 September 2001
Copyright © 2002 Atilla Dogan and Pierre T. Kabamba. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper introduces Modified Altitude- and Dive-Guidance laws for escaping a microburst with turbulence. The goal is to develop a procedure to estimate the highest altitude at which an aircraft can fly through a microburst without running into stall. First, a new metric is constructed that quantifies the aircraft upward force capability in a microburst encounter. In the absence of turbulence, the metric is shown to be a decreasing function of altitude. This suggests that descending to a low altitude may improve safety in the sense that the aircraft will have more upward force capability to maintain its altitude. In the presence of stochastic turbulence, the metric is treated as a random variable and its probability distribution function is analytically approximated as a function of altitude. This approximation allows us to determine the highest safe altitude at which the aircraft may descend, hence avoiding to descend too low. This highest safe altitude is used as the commanded altitude in Modified Altitude- and Dive-Guidance. Monte Carlo simulations show that these Modified Altitude- and Dive-Guidance strategies can decrease the probability of minimum altitude being lower than a given value without significantly increasing the probability of crash.