scholarly journals Calculation of Charts on an Oblique Gnomonic Projection by Electronic Computer

1960 ◽  
Vol 13 (3) ◽  
pp. 345-347
Author(s):  
P. B. Sarson
Keyword(s):  
Electronic Computer ◽  
Great Accuracy ◽  
Lightning Flash ◽  
Projection Plane ◽  
Mercator Projection ◽  
Straight Lines

IN the Meteorological Office, great accuracy is not usually attainable in determining or forecasting the position of significant weather features. Special projections of charts are therefore not often required; the normal conic projection with two standard parallels or (near the equator) the mercator projection is quite adequate. However, in the radiolocation of thunderstorms a chart drawn on a gnomonic projection is required. The bearings of each lightning flash within one or two thousand miles are recorded from a small number of special stations (SFERICS stations). When these bearings are plotted on a gnomonic chart by straight lines drawn from the appropriate observing station the coordinates of the source of the lightning can be quickly determined and reported through normal meteorological channels. Speed is essential and therefore the charts on which the bearings are drawn are specially designed with the SFERICS stations grouped more or less evenly about the tangential point of the projection plane of the gnomonic chart.

scholarly journals The Determination of Jupiter's Mass from Large Perturbations on Cometary Orbits in Jupiter's Sphere of Action

1972 ◽  
Vol 45 ◽  
pp. 227-232 ◽  
Author(s):  
E. I. Kazimirchak-Polonskaya
Keyword(s):  
Electronic Computer ◽  
Sufficient Conditions ◽  
Great Accuracy ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient

Necessary and sufficient conditions are formulated for determining the mass of Jupiter from large perturbations induced in cometary orbits in the sphere of action of Jupiter. A procedure for the investigation has been developed and programmed for an electronic computer. Comparison of heliocentric and jovicentric computations shows that the perturbations on P/Wolf could be determined with great accuracy when this comet passed through Jupiter's sphere of action in 1922. The first attempt has been made to determine the mass of Jupiter using this passage and the observations of the comet in 1925. The resulting value for the reciprocal mass is 1047.345.

Approximation of a Great Circle by using a Circular Arc on a Mercator Chart

2017 ◽  
Vol 71 (2) ◽  
pp. 497-508
Author(s):  
Miljenko Lapaine ◽  
Tomislav Jogun
Keyword(s):  
Stereographic Projection ◽  
Great Circle ◽  
Actual Length ◽  
Circular Arc ◽  
Projection Plane ◽  
Mercator Projection

This paper describes George Biddell Airy's almost completely unknown method of approximating an orthodromic arc (great circle arc) using a circular arc in the normal aspect Mercator projection of a sphere. In addition, it is demonstrated that the centre of the circle can be defined in at least two different ways, which yields slightly different results. Airy's approach is built upon in this paper. The method of computing coordinates of Airy's circle arc centre is described. The formulae derived in the paper can be used to calculate the length of Airy's approximation of the orthodromic arc connecting two points on the sphere and on the Mercator chart. Moreover, the actual length of the orthodromic arc on the sphere and on the Mercator chart can be computed using the formulae derived in this paper. The purpose of the paper is not to suggest an application of Airy's method in navigation, but to analyse Airy's proposal and to show that a great circle arc on a Mercator chart is close to a circular arc for distances which are not too great. This property can be useful in education, having in mind that the stereographic projection is the only one that maps any circle on a sphere onto a circle in the projection plane.

scholarly journals Interference Identification for Time-Varying Polyhedra

2021 ◽  
Author(s):  
Adam Bienkowski
Keyword(s):  
Traffic Control ◽  
Potential Conflict ◽  
Linear Projection ◽  
The Earth ◽  
Large Numbers ◽  
Mercator Projection ◽  
Maritime Operations ◽  
Conflict Identification ◽  
Polygon Intersection ◽  
Straight Lines

Identification of when and where moving areas intersect is an important problem in maritime operations and air traffic control. This problem can become particularly complicated when considering large numbers of objects, and when taking into account the curvature of the earth. In this paper, we present an approach to conflict identification as a series of stages where the earlier stages are fast, but may result in a false detection of a conflict. These early stages are used to reduce the number of potential conflict pairs for the later stages, which are slower, but more precise. The stages use R-trees, polygon intersection, linear projection and nonlinear programming. Our approach is generally applicable to objects moving in piece-wise straight lines on a 2D plane, and we present a specific case where the Mercator Projection is used to transform objects moving along rhumb lines on the earth into straight lines to fit in our approach. We present several examples to demonstrate our methods, as well as to quantify the empirical time complexity by using randomly generated areas.

scholarly journals Interference Identification for Time-Varying Polyhedra

2021 ◽  
Author(s):  
Adam Bienkowski
Keyword(s):  
Traffic Control ◽  
Potential Conflict ◽  
Linear Projection ◽  
The Earth ◽  
Large Numbers ◽  
Mercator Projection ◽  
Maritime Operations ◽  
Conflict Identification ◽  
Polygon Intersection ◽  
Straight Lines

Identification of when and where moving areas intersect is an important problem in maritime operations and air traffic control. This problem can become particularly complicated when considering large numbers of objects, and when taking into account the curvature of the earth. In this paper, we present an approach to conflict identification as a series of stages where the earlier stages are fast, but may result in a false detection of a conflict. These early stages are used to reduce the number of potential conflict pairs for the later stages, which are slower, but more precise. The stages use R-trees, polygon intersection, linear projection and nonlinear programming. Our approach is generally applicable to objects moving in piece-wise straight lines on a 2D plane, and we present a specific case where the Mercator Projection is used to transform objects moving along rhumb lines on the earth into straight lines to fit in our approach. We present several examples to demonstrate our methods, as well as to quantify the empirical time complexity by using randomly generated areas.

Domain Formation in Synthetic Quartz

1971 ◽  
Vol 29 ◽  
pp. 156-157
Author(s):  
Joseph J. Comer
Keyword(s):  
Electron Beam ◽  
Room Temperature ◽  
Domain Formation ◽  
Synthetic Quartz ◽  
Transmission Electron ◽  
Black Spots ◽  
Diffraction Mode ◽  
Domain Boundaries ◽  
Kikuchi Lines ◽  
Straight Lines

Domains visible by transmission electron microscopy, believed to be Dauphiné inversion twins, were found in some specimens of synthetic quartz heated to 680°C and cooled to room temperature. With the electron beam close to parallel to the [0001] direction the domain boundaries appeared as straight lines normal to <100> and <410> or <510> directions. In the selected area diffraction mode, a shift of the Kikuchi lines was observed when the electron beam was made to traverse the specimen across a boundary. This shift indicates a change in orientation which accounts for the visibility of the domain by diffraction contrast when the specimen is tilted. Upon exposure to a 100 KV electron beam with a flux of 5x 1018 electrons/cm2sec the boundaries are rapidly decorated by radiation damage centers appearing as black spots. Similar crystallographio boundaries were sometimes found in unannealed (0001) quartz damaged by electrons.

Automatic Tread Gaging Machine

1979 ◽  
Vol 7 (1) ◽  
pp. 31-39
Author(s):  
G. S. Ludwig ◽  
F. C. Brenner
Keyword(s):  
Experimental Tests ◽  
Automatic Machine ◽  
Wear Rates ◽  
Handling Device ◽  
Straight Line ◽  
Component Systems ◽  
Before And After ◽  
Good Repeatability ◽  
The Difference ◽  
Straight Lines

Abstract An automatic tread gaging machine has been developed. It consists of three component systems: (1) a laser gaging head, (2) a tire handling device, and (3) a computer that controls the movement of the tire handling machine, processes the data, and computes the least-squares straight line from which a wear rate may be estimated. Experimental tests show that the machine has good repeatability. In comparisons with measurements obtained by a hand gage, the automatic machine gives smaller average groove depths. The difference before and after a period of wear for both methods of measurement are the same. Wear rates estimated from the slopes of straight lines fitted to both sets of data are not significantly different.

Investigation of Zero Crossing Detection for First Return Stroke in Negative Cloud-to-Ground Lightning Flash

2019 ◽  
Vol 11 (3) ◽  
Author(s):  
Ahmad Idil Abd Rahman ◽  
◽  
Muhammad Akmal Bahari ◽  
Zikri Abadi Baharudin ◽  
◽  
...  
Keyword(s):  
Lightning Flash ◽  
Return Stroke ◽  
Zero Crossing ◽  
Cloud To Ground Lightning

The characteristics of transforming coordinates from the geocentric system WGS-84 for the Mercator projection under low latitudes conditions

2018 ◽  
Vol 940 (10) ◽  
pp. 2-6
Author(s):  
J.A. Younes ◽  
M.G. Mustafin
Keyword(s):  
Coordinate System ◽  
Satellite System ◽  
Programming Algorithm ◽  
Low Latitude ◽  
Model Calculations ◽  
Mercator Projection ◽  
Low Latitudes ◽  
Rectangular Coordinates ◽  
Global Navigation Satellite ◽  
Coordination Methods

The issue of calculating the plane rectangular coordinates using the data obtained by the satellite observations during the creation of the geodetic networks is discussed in the article. The peculiarity of these works is in conversion of the coordinates into the Mercator projection, while the plane coordinate system on the base of Gauss-Kruger projection is used in Russia. When using the technology of global navigation satellite system, this task is relevant for any point (area) of the Earth due to a fundamentally different approach in determining the coordinates. The fact is that satellite determinations are much more precise than the ground coordination methods (triangulation and others). In addition, the conversion to the zonal coordinate system is associated with errors; the value at present can prove to be completely critical. The expediency of using the Mercator projection in the topographic and geodetic works production at low latitudes is shown numerically on the basis of model calculations. To convert the coordinates from the geocentric system with the Mercator projection, a programming algorithm which is widely used in Russia was chosen. For its application under low-latitude conditions, the modification of known formulas to be used in Saudi Arabia is implemented.

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