Citation

Pellegrini CC, Moreira EDO, Rodrigues MS. Rev. Bras. Ensino Fís. 2022; 44: e20210410.

Copyright

(Copyright © 2022, Sociedade Brasileira de Física)

DOI

10.1590/1806-9126-RBEF-2021-0410

PMID

unavailable

Abstract

Most aeronautical accidents happen during takeoff and landing. The main objective when studying those phases of the flight mission is to answer a seemingly simple questions: can the airplane safely takeoff and land on the stipulated runway dimensions with the intended weight? The main objective of the present paper is to obtain new analytical answer to those questions, for fixed wing airplanes. To our present knowledge such a solution, with the degree of generalisation proposed here, is new in the literature. Regarding previous studies, first a new power unit traction equation is employed to explicitly consider the influence of air density, angular velocity and diameter of the propeller. Then a new method for calculating the maximum weight is proposed. Next, the use of breaks is modeled and analysed and an equation to calculate the static gliding wind velocity is proposed. Finally, a toolbox created to perform the calculations is described. A thorough analysis of the influence of the airplane design parameters on the behavior of the motion equations is made, with special attention to the use of brakes. Numerical results are successfully compared with experimental data from two models of a commercial airplane, the Cessna 172 Skyhawk models N and S, and four UAV prototypes. The methodology employed uses simple laws of classical mechanics allied to basic calculus and is easy to understand by first year students of physics, engineering or mathematics.

Language: en

Keywords

aircraft performance; Flight mechanics; maximum weight; takeoff and landing distances