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Date submitted2016-09-18
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Date accepted2016-11-04
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Date published2017-02-22
Development of methods of analytical geometry of a sphere for solving geodesy and navigation tasks
- Authors:
- G. I. Khudyakov
The article develops ideas and formulas of analytical geometry for spherical surface of the Earth globe in relation to main tasks of global geodesy and navigation. It examines peculiarities of sphere inner geometry and properties of its primary, secondary and higher-order curves. It was proved that spherical hyperbola and parabola are spherical ellipses with specific parameters. The Cartesian ordinates were introduced into the sphere and the relation between them and polar spherical coordinates was established. With the help of central projection of sphere points on tangential plane the corresponding elliptical plane with beltrami ordinates was introduced. The article describes main formulas of analytical geometry for projected elliptical plane, which correspond to geometry of projected sphere. It also introduces several formulas for primary, secondary and higher-order curves for this sphere.
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Date submitted2015-10-18
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Date accepted2015-12-01
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Date published2016-08-22
Effect of surface geometry and insolation on temperature profile of green roof in Saint-Petersburg environment
- Authors:
- S. A. Ignatev
- D. S. Kessel
The paper addresses an issue of creating an environment favorable for the life in megacities by planting vegetation on the rooftops. It also provides information about rooftop greening practices adopted in other countries. The issues of ‘green roof’ building in climatic conditions of Saint Petersburg and roof vegetation impact on the urban ecosystem are examined. Vegetation composition quality- and quantity-wise has been proposed for the roof under research and a 3D model of this roof reflecting its geometric properties has been developed. A structure of roof covering and substrate qualitative composition is presented. An effect of rooftop geometry on the substrate temperature is explored. The annual substrate temperature and moisture content in different parts of the roof have been analyzed. Results of thermal imaging monitoring and insolation modelling for different parts of green roof surface are presented.