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.
Highlights
The application of the principles of classical physics to mechanical systems marked the beginning of what is currently understood as modern engineering, dating back to the the scientific revolution on the 16th and 17th centuries
To demonstrate the wide range of aircraft to which the proposed results applies, the takeoff distance was calculated for the Cessna 172 Skyhawk models S and N, and for four unmanned aerial vehicle (UAV) used in the AeroDesign competitions of 2014, 2017, 2018 and 2019
We believe that Aircraft Performance Toolbox (APT) met all the requirements stipulated, including the didactic ones
Summary
The application of the principles of classical physics to mechanical systems marked the beginning of what is currently understood as modern engineering, dating back to the the scientific revolution on the 16th and 17th centuries. In the field of aeronautical engineering the use of classical mechanics can be traced back to the aviation pioneers, around the start of the 20th century, when machines heavier than the air, capable of flying by its own means with fixed wings started to be studied. After all, flying is an activity that leaves very little space for trial and error, as so many early accidents demonstrated. Two crucial phases of the flight were carefully considered: the takeoff and the landing. It is not to say that the other phases were not important, but most accidents happen around or during takeoff and landing. According to a statistical survey by the Boeing company, 49% of all fatal accidents happen during the final descent and landing, while 14% of all fatal accidents happen during the takeoff and the initial climb
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