# The Geographic Calculator

The Geographic Calculator' title='The Geographic Calculator' />On average, 10 gallons per day of your water footprint or 14 of your indoor use is lost to leaks. Short of installing new waterefficient fixtures, one of the. Publishes street, wall, and reference maps, plus atlases. Also sells globes by other publishers. Compare the cost of living in two cities using the CNNMoney Cost of Living calculator. Determine if you could maintain your current standard of living in a different. The Geographic Calculator' title='The Geographic Calculator' />Geographic Midpoint Calculation Methods. This page shows how to calculate the geographic midpoint also known as the geographic center, or center of gravity for two or more points on the earths surface. A second method is given showing how to calculate the center of minimum distance and finally a third method calculates the average latitudelongitude. The Geographic Calculator' title='The Geographic Calculator' />There are reasons for choosing one method over another. The first two methods assume that the earth is a perfect sphere, which yields sufficiently accurate results for most purposes. In contrast, the third method uses a flat earth model. The National Geographic Society is a global nonprofit organization committed to exploring and protecting our planet. Use this free mortgage calculator to save money on your home loan today. Our calculator includes amoritization tables, biweekly savings estimates, refinance info. We will assume that the latitude and longitude data for the calculations comes from a list called Your places. Each location may be weighted in one of three ways. Weight by time. Use this to specify the amount of time you have lived in each location in order to find the geographic average location for all of the places you have lived in. The time for each location is converted into days, for example w. Simple weighting factor, such as population for each location can be stored in w. Equal weight. If no location is to be weighted more than another then set w. A. Geographic midpoint. Note See this example showing step by step numerical calculations using real latitude and longitude data. The formulas below show how to weight by time. The geographic midpoint is calculated by finding the center of gravity for the locations in the Your Places list. The latitude and longitude for each location is converted into Cartesian x,y,z coordinates. The x,y, and z coordinates are then multiplied by the weighting factor and added together. A line can be drawn from the center of the earth out to this new x, y, z coordinate, and the point where the line intersects the surface of the earth is the geographic midpoint. This surface point is converted into the latitude and longitude for the midpoint. Details. Given the values for the first location in the list Lat. Convert Lat. 1 and Lon. PI1. 80lon. 1 lon. PI1. 80. Convert latlon to Cartesian coordinates for first location. X1 coslat. 1 coslon. Y1 coslat. 1 sinlon. Z1 sinlat. 1. Compute weight by time for first location. If locations are to be weighted equally, set w. Repeat steps 1 3 for all remaining locations in the list. Compute combined total weight for all locations. Totweight w. 1 w. Compute weighted average x, y and z coordinates. Convert average x, y, z coordinate to latitude and longitude. Note that in Excel and possibly some other applications, the parameters need to be reversed in the atan. X,Y instead of atan. Y,X. Lon atan. Hyp sqrtx x y yLat atan. Convert lat and lon to degrees. PIlon lon 1. 80PI. Special case If absx lt 1. Notes for method A. The x,y,z coordinate system is based on the xy plane lying within the equatorial plane, with its origin at the center of the earth. Looking down onto the North Pole, the positive x axis passes through the Greenwich meridian 0E, the positive y axis passes through the 9. E meridian, and the positive z axis extends from the center of the earth through the North Pole. The calculations use a unit radius radius 1 for the earth. Absolute cartesian coordinates in miles or km can be obtained by multiplying x, y and z by the radius of the earth. Most computer applications require that latitude and longitude data be converted to radians before using them in the trig functions. B. Center of minimum distance. This method uses a mathematical algorithm to find the exact point that minimizes the total travel distance from all locations in Your Places. The mathematical implementation of this algorithm is fairly complex, but the general steps are described below. All distances are calculated using the spherical law of cosines given below. Let Current. Point be the geographic midpoint found in Method A. Let Minimum. Distance be the sum total of all distances from the current point to all locations in Your Places. Find the total distance between each location in Your Places and all other locations in Your Places. If any one of these locations has a new smallest distance then that location becomes the new Current. Point and Minimum. Adobe Flash Cs3 Crack Serial Number. Distance. Let Test. Distance be PI2 radians 6. Find the total distance between each of 8 test points and all locations in Your Places. The test points are arranged in a circular pattern around the Current. Point at a distance of Test. Distance to the north, northeast, east, southeast, south, southwest, west and northwest. If any of these 8 points has a new smallest distance then that point becomes the new Current. Point and Minimum. Distance and go back to step 5 using that point. If none of the 8 test points has a new smallest distance then divide Test. Distance by 2 and go back to step 5 using the same point. Repeat steps 5 to 7 until no new smallest distance can be found or until Test. Distance is less than 0. Spherical law of cosines. C. Average latitudelongitude. This method finds a simple average latitude and longitude for the locations in Your Places. This is equivalent to finding a midpoint on a flat rectangular projection map. When the distance between locations is less than 2. Method A. Use the values calculated in Method A for each location lat. All longitudes in Your Places are adjusted so as to be relative to the geographic midpoint longitude calculated in Method A. This helps eliminate the problems associated with locations on both sides of the International Date Line. For example lon. Geographic. Midpointthen if the resulting lon. Calculate the weighted latitude and longitude. Add the longitude of the geographic midpoint to return the calculated longitude to its original reference lon lon lon. Geographic. Midpoint. Add or subtract 3. The center of minimum distance concept and algorithm developed by Geo. Midpoint. Geographic Midpoint Calculator. Simple Serial Wedge. See how the midpoint calculations can work in real life with this free online application. With the Geographic Midpoint Calculator you can find the midpoint of an airline flight between two cities. You can also find your personal center of gravity by selecting all of the locations that you have lived in, then view all of those locations displayed on a map along with a marker pointing at the location of your exact personal center of gravity. Random Point Generator With Maps. The Random Point Generator generates points at random locations on the surface of the earth. You can throw one or more virtual darts at a Google map and see where they land at. Random point generator calculation methods. Lets meet in the middle. This free tool finds the ideal restaurant or other point of interest halfway between two or more addresses. Meet your friend or business acquaintance for lunch. Next. Distance calculator. National Geographic Society National Geographic Society. Explorer Paul Salopek is walking across the planet, following the pathways of the first humans who migrated out of Africa in the Stone Age. Along the way, hes covering some of the major stories of our time by giving voice to the people who inhabit them every day.