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The Earth and Its Coordinate System
Published in Terry A. Slocum, Robert B. McMaster, Fritz C. Kessler, Hugh H. Howard, Thematic Cartography and Geovisualization, 2022
Terry A. Slocum, Robert B. McMaster, Fritz C. Kessler, Hugh H. Howard
The shortest distance between any two points is a straight line. On Earth's curved surface, however, the shortest distance between two points is an arc of a great circle. A great circle results from the trace of the intersection of any plane and Earth's surface as long as the plane passes through Earth's center. Because lines of longitude are traces of planes that intersect Earth's surface and its center, all meridians are great circles. It is important to note, however, that not all great circles coincide with meridians. The Equator is also a great circle because its plane intersects Earth's center, but no other parallels intersect Earth's center. Rather, all other parallels form circles on Earth's surface called small circles. However, not all small circles coincide with a parallel. A small circle results when a plane passes through Earth's curved surface but does not intersect Earth's center. Figure 7.4 illustrates great and small circles on Earth's surface.
Mapping Applications
Published in Pearson Frederick, Map Projections:, 2018
We consider two points on the spherical model of the Earth. The shortest distance between these points on the surface of the sphere is along the great circle. However, as one moves along the great circle, the angle formed by the tangent to the great circle and the tangent to the local meridian is constantly changing. This angle is the instantaneous bearing. The loxodrome is a line which has the characteristic that the angle between the tangent to the loxodrome and the tangent to the local meridian is constant. Thus, the bearing is constant. Since in navigation it is relatively easy to maintain a constant bearing, the loxodrome is the curve of choice. However, a loxodrome is of greater length than the great circle distance, unless along the equator or a meridian.
The Earth–Sun Relationship
Published in Matt Fajkus, Dason Whitsett, Architectural Science and the Sun, 2018
This grid aligns with the axis on which the Earth rotates. The North and South Poles are those points on the surface of the Earth pierced by the imaginary line of the rotational axis. The plane perpendicular to the rotational axis through the center of the Earth is known as the equatorial plane. The circle formed where this plane intersects the surface of the Earth is the equator. The equator is a great circle, which is a circle on a sphere whose plane intersects the sphere’s center point. As such, a great circle traces the full circumference of the sphere. This is in contrast to minor circles, which are circles on a sphere that do not lie in planes intersecting the sphere’s center and have a diameter smaller than the full diameter of the sphere.
Ship voyage optimisation considering environmental forces using the iterative Dijkstra's algorithm
Published in Ships and Offshore Structures, 2023
Navid Bahrami, Seyed Mostafa Siadatmousavi
The Haversine formula determines the distance of a great circle between two points on a sphere according to their longitude and latitude coordinates (Prasetya et al. 2020). As mentioned in section 3.5, after assuming the great circle arc, its segments and vertices, several alternatives for each vertex were produced (except for the start and destination points). To do it, a distance , perpendicular to the great circle arc was assumed and two alternative points with a length of below and above the considered vertex were assumed. The same process was repeated for , 2, etc. to produce new waypoints, as shown in Figure 4 (Lu et al. 2015).
Learning electric vehicle driver range anxiety with an initial state of charge-oriented gradient boosting approach
Published in Journal of Intelligent Transportation Systems, 2023
The distance between charging eventand the home location of driver It is suspected that, when EV drivers drive further away from home, the range anxiety may become more intense, as the battery level becomes lower and the distance to home is longer. The Haversine formula (shown below) is used to calculate the great circle distance between two points on the Earth. The latitude and longitude of the charging event () are directly available in the dataset, while those of the driver ’s home () is approximated with the centroid of the zip code. is the radius of the Earth.
Deep learning– just data or domain related knowledge adds value?: bus travel time prediction as a case study
Published in Transportation Letters, 2022
M.A. Nithishwer, B. Anil Kumar, Lelitha Vanajakshi
Data from GPS devices were received at every 5 or 10 seconds, round the clock (data-collection interval was configurable and can be set to 5 seconds or 10 seconds). Raw information received from GPS devices contains the GPS ID for the unit, latitude, and longitude, and the corresponding time stamp. The data were transmitted in real-time using general packet radio service (GPRS). During the processing, the first step was to calculate the distance between any two consecutive entries. This was done using the Haversine formula, which gives the great circle distances between two points on a sphere from their latitudes and longitudes (Chamberlain 2012). After this process, the data consisted of the travel times and the corresponding distance between consecutive locations for all the buses. In the next stage, the entire section was divided into smaller sections and the time taken to cover each subsection was calculated using linear interpolation. The acquired data were further divided into two sets: (i) training dataset and (ii) testing dataset. The training dataset was analyzed further to identify patterns in travel time and to determine the optimum number of input groups and the same has been used to train the deep learning model. In the test stage, identified inferences were incorporated as features to predict bus travel times of the trips.