Abstract: Aerodromes protection zones are defined by plans that establish the limits that objects can project into airspace without affecting the safety and regularity of air operations. These plans are composed of a set of imaginary three-dimensional surfaces that impose restrictions on the use of properties within the protection zones. Our research problem is how to classify the risk of obstacles in aerodromes protection zones. In this paper, we propose a methodology to obtain an obstacle risk classification model. We defined the risk factors and applied a questionnaire to an expert in civil aviation. The obstacle risk classification model resulted from the specialist analysis and by applying the analytic hierarchy process (AHP) for multi-criteria decision analysis. The advantage of the AHP in studies that use specialists’ empiric knowledge for risk modeling is the treatment of uncertainties, and the use of tangibles and intangibles criteria. The results showed that the most significant influence on the risk of an obstacle is how much that obstacle protrudes the limiting surfaces, followed by the distance between the obstacle and the nearest airport runway threshold, the limiting surface in which the obstacle is, and the nature of the obstacle.

Abstract: Aerodromes protection zones are defined by plans that are determined by three-dimensional (3D) limiting surfaces, which establish the airspace that must remain clear of obstacles, imposing some restrictions on land use. The objective of this paper is to generate 3D models of the surrounding area of Salgado Filho International Airport, considering the constructive altimetric limit established in the Aerodrome Protection Zone Basic Plan (PBZPA), to identify and quantify obstacles related to plots (urban land parcels) and buildings. The adopted methodology includes the analysis and selection of geospatial data, data modeling and performing spatial analysis on the generated 3D models. The results showed that out of a total of 106,838 plots, covering an area of 69.68 km², 4,826 plots (4.52%) exceeded the limiting surface and 1,054 plots (0.99%) represent critical areas where constructions may not be allowed. And, out of a total of 200,573 buildings, 26,418 of them (13.17%) exceeded the limit imposed by PBZPA’s. Also, the methodology is valid for detecting and quantifying critical areas concerning the constructive viability of the plots, affected areas regarding the height of the plots and buildings, and for identifying obstacles to aerodromes according to their respective airspace laws.

Ao se planejar o levantamento de uma rede geodésica, deseja-se que as observações a serem realizadas e as coordenadas dos pontos a serem estimadas atendam critérios de precisão e confiabilidade pré-estabelecidos de acordo com os objetivos do projeto. Na etapa de pré-análise, antes mesmo da coleta das observações, é possível estimar a precisão e confiabilidade da rede, estipulando uma geometria/configuração para a mesma e a precisão esperada para as observações. O objetivo deste artigo é apresentar o planejamento de uma rede geodésica que atenda critérios de precisão e confiabilidade, considerando a possível existência de dois ou mais erros não detectados nas observações, bem como a influência (simultânea) destes erros sobre os parâmetros (coordenadas ajustadas dos vértices). Além da revisão teórica, experimentos foram realizados em uma rede GNSS, onde foram estipulados critérios de precisão e confiabilidade considerando a existência de até duas observações contaminadas por erros (outliers), de maneira simultânea. O planejamento da rede foi feito por meio do método da tentativa e erro. Depois do processamento dos dados e do ajustamento da rede, se verificou que os critérios de precisão e confiabilidade que foram estipulados na etapa de pré-análise foram devidamente obtidos.

When planning a survey of a geodetic network, it is desirable that the observations to be measured and the points coordinates to be estimated follow criteria of precision and reliability preestablished according to the project objectives. In the pre-analysis step, even before the measurement of observations, it is possible to estimate the precision and reliability of the network, by setting a geometry / configuration for it and the expected precision of the observations. The goal of this paper is to present the design of a geodetic network following criteria of precision and reliability, taking into account the possible existence of two or more undetected errors in the observations, as well as their influence (simultaneous) on the parameters (adjusted coordinates of the points). Besides the theoretical review, experiments were performed in a GNSS network, that were established criteria of precision and reliability considering the existence of up to two observations contaminated by errors (outliers), simultaneously. The network design was done by the method of trial and error. After the data processing and the adjustment of the network, it was found that the criteria of accuracy and reliability that have been stipulated in the pre-analysis step were properly obtained.

O Método dos Mínimos Quadrados (MMQ) é um dos critérios mais utilizados para o ajustamento de informações onde o número de observações é superabundante e o sistema de equações, devido à presença de erros no processo experimental de medições, inconsistente. Este método adota como solução única para tais problemas aquela que minimiza a soma do quadrado dos erros aleatórios, e é largamente empregado em aplicações geodésicas. A fundamentação teórica envolvida no MMQ, contendo o desenvolvimento matemático do método, é amplamente difundida na comunidade geodésica. Porém, neste artigo, o objetivo é apresentar uma revisão teórica sobre a interpretação geométrica do MMQ, e uma solução alternativa de cálculo para este, advinda desta interpretação. Dois exemplos também são apresentados, onde a interpretação geométrica foi demonstrada numericamente para problemas envolvendo duas observações e um parâmetro e também quatro observações e dois parâmetros.

The Least Squares Method (LSM) is one of the most useful criteria for the adjustment of data where the number of observations is redundant and the system of equations, due to the presence of errors in experimental measurements, inconsistent. This method takes as a single solution that which minimizes the sum of the squared random errors, and is widely used in geodetic applications. The theoretical foundation involved in the LSM, containing the mathematical development of the method, is widespread in the geodetic community. However, in this paper, the goal is to present a theoretical review of the geometric interpretation of the LSM, and an alternative computation solution, derived from this interpretation. Two examples are also shown, where this geometric interpretation has been demonstrated numerically for problems involving two observations and a parameter, and also four observations and two parameters.