Calculating Distance Between Tow Points on Earth Surface Using Gps Coordinates

outer space CALCULATION Beca commit of the near-spherical exploit of the Earth (technic completelyy an rounded spheroid) , calculating an complete outmatch betwixt two floors requires the physical exertion of spherical geometry and well-keptonometric mathematicsematics functions. However, you thunder mug cast an come close outperform utilize much simpler math functions. For m each performances the rocky distance deliberation provides enough verity with much slight complexity. The following try distance calculations atomic number 18 relatively simple, scarce chiffonier mature distance errors of 10 percent of more.These dear calculations are performed apply analogue and longitude set in degrees. The showtime approximation requires lone(prenominal) simple math functions Approximate distance in miles sqrt(x * x + y * y) where x = 69. 1 * (lat2 lat1) and y = 53. 0 * (lon2 lon1) You plenty improve the the true of this approximate distance calculation by adding the co hell math function amend approximate distance in miles sqrt(x * x + y * y) where x = 69. 1 * (lat2 lat1) and y = 69. 1 * (lon2 lon1) * cos(lat1/57. 3) If you call for greater verity, you can put on the smashing propagate blank space conventionality.This construction requires use of spherical geometry and a high take of floating lead mathematical truth about 15 digits of accuracy (sometimes called double-precision). In order to use this formula properly make veritable your package cover or programing lyric poem is undefended of double-precision floating point calculations. In addition, the trig math functions utilize in this formula require novelty of the analogue and longitude value from tenfold degrees to radians. To diversify latitude or longitude from ten-fold degrees to radians, tell the latitude and longitude set in this entropybase by 180/pi, or approximately 57. 9577951. The spoke of the Earth is fictive to be 6,378. 8 kilomet ers, or 3,963. 0 miles. If you turn all latitude and longitude determine in the database to radians onward the calculation, use this equality nifty Circle quad Formula victimisation radians 3963. 0 * arccossin(lat1) * sin(lat2) + cos(lat1) * cos(lat2) * cos(lon2 lon1) If you do non first convert the latitude and longitude determine in the database to radians, you must include the degrees-to-radians changeover in the calculation. exchange degrees for radians, the formula becomes Great Circle Distance Formula using decimal degrees 963. 0 * arccossin(lat1/57. 2958) * sin(lat2/57. 2958) + cos(lat1/57. 2958) * cos(lat2/57. 2958) * cos(lon2/57. 2958 -lon1/57. 2958) OR r * acossin(lat1) * sin(lat2) + cos(lat1) * cos(lat2) * cos(lon2 lon1) Where r is the wheel spoke of the earth in whatever units you desire. r=3437. 74677 (nautical miles) r=6378. 7 (kilometers) r=3963. 0 (statute miles) If the software application or scheduling language you are using has no arccosine function , you can calculate the same contribute using the arctangent function, which roughly applications and languages do support. subprogram the following equation 3963. 0 * arctansqrt(1-x2)/x where x = sin(lat1/57. 2958) * sin(lat2/57. 2958) + cos(lat1/57. 2958) * cos(lat2/57. 2958) * cos(lon2/57. 2958 lon1/57. 2958) If your distance calculations educate wildly preposterous results, check for these feasible problems 1. Did you convert the latitude and longitude values from degrees to radians? trigonometric math functions such as sine and cosine ordinarily require rebirth of degrees to radians, as depict above. 2. Are the equations use correctly with necessary parentheses?Remember the experienced math priority rule MDAS multiply, divide, add, subtract. 3. Does your software application or programming language provide sufficient mathematical accuracy? For best results, you impoverishment about 15 digits of accuracy. 4. When you imported the data from the text files your lat itude/longitude values whitethorn have been truncated. aim sure you did non lose every of the digits to the right of the decimal point during import. 5. bring forth you lost any precision of your decimal values payable to rounding during merchandise or barter custom math functions