Auriga said:
How do I find the distance between these two lat/long points in feet, where the coordinates are presented in decimal format?
Point 1: Lat 42.984665, Long -87.831505
Point 2: Lat 42.98461957, Long -87.83139252
I’ve seen the Great Circle formulary web site but I’m not sure what units their formula is in. I need to know the distance in feet. Also, I’m dealing with short distances so I don’t need to factor in the curving of the earth (I know the lines converge at the poles but I don’t need to worry about that for this example). I can’t use a separate converter program….I need to know the formula so that I can put it into Excel.
Thanks, Christine
First, here's a good explanation of converting Latitude and Longitude to feet:
Latitude-Longitude Conversion to feet
A degree of latitude is 60 nautical miles, or 69.04 statute miles. A minute of latitude is equal to one nautical mile, or 6076 feet; thus, a second of latitude (6076 divided by 60) is 101 feet, 3 inches. Conceptually and practically, latitude is the same no matter where you go on earth; however, in reality it varies from 69.41 statute miles per minute at the poles to 68.70 statute miles per minute at the equator due to the earth bulging slightly from its rotational spin.
Longitude, of course, varies in length according to degree of latitude. The following is a sampling of longitude lengths for selected latitudes, beginning in the southern US and working north.
30 degrees North, (approximately Houston, Texas) a degree of longitude is 59.96 statute miles, 5274 feet per minute (almost equal to a statute mile), 88 feet per second.
35 degrees North, (approximately Albuquerque, New Mexico) a degree of longitude is 56.73 statute miles, 4992 feet per minute, 83.2 feet per second.
40 degrees North, (Kansas/Nebraska border), a degree of longitude is 53.06 statute miles, 4669 feet per minute, 77.8 feet per second.
45 degrees North, (Montana/Wyoming border), a degree of longitude is 49.00 statute miles, 4312 feet per minute, 71.87 feet per second.
49 degrees North (US/Canada national boundary), a degree of longitude is 45.40 statute miles, 3995 feet per minute, 66.59 feet per second.
50 degrees North (approximately Powell River, BC, Medicine Hat, Alberta, and Winnipeg, Manitoba), a minute of longitude is 44.55 statue miles, 3920 feet (1195 meters) per minute, 65.34 feet (19.9 meters) per second.
55 degrees North (approximately Ketchikan, Alaska and Dawson Creek, BC) a degree of longitude is 39.77 statute miles, 3500 feet (1066.8 meters) per minute, 58.33 (17.78 meters) per second. Finally, 60 degrees North (southern border of the Northwest Territories), a degree of longitude is 34.67 statute miles, 3051 feet (930 meters) per minute, 50.85 feet (15.5 meters) per second.
So, let's assume for your example, we'll say 1 degree of latitude is 60 nautical miles (we'll disregard the bulging earth). For the longitude, we'll interpolate the values for 40N and 45N. (40N - 280,140 feet, 45N - 258,720 feet, 43N - 267,288 feet)
SO... Latitude is 364,560 feet per degree
and... Longitude is 267,288 feet per degree
Now for the High School geometry (remember Pythagorus and the distance formula?) ...
Think of Latitude and Longitude as X and Y coordinates, and recall that the square of the distance between 2 points is equal to the sum of the squares of the differences between the Y-coordinates and the X-coordinates.
Your formula:
Distance between points = SQUARE ROOT [(LAT2 - LAT1)squared + (LON2-LON1)squared]
LAT2 - LAT1 = 42.98461957 - 42.984665 = -0.00004543 degrees
(apply the degrees to feet conversion for Latitude -> 364,560 feet/degree)
-0.00004543 degrees * 364,560 feet/degree = -16.5619608 feet
... (don't worry about a negative number, that'll be ironed out when we square it)
LON2 - LON1 = -87.83139252 - (-)87.831505 = 0.00011248 degrees
(apply the degrees to feet conversion for 43N Longitude -> 267,288 feet per degree)
0.00011248 degrees * 267,288 feet/degree = 30.06455424 feet
Square 'em, add the squares, take the square root of the sum, and we're done.
Distance = SQUARE ROOT [ (-16.5619608 feet)squared + (30.06455424 feet)squared ]
Distance = SQUARE ROOT [ 274.2985 ft^2 + 903.8774 ft^2 ]
Distance = SQUARE ROOT [ 1,178.175967 ft^2 ]
Distance = 34.3246 feet
Now, I've done about everything except put it into the spreadsheet for you.
Remember, there are assumptions made that make this value inaccurate. The earth bulges. The relationship between degrees of longitude and feet is NOT linear, so simple interpolation is just an estimation. And don't hammer me on significant digits. I brought you this far, you have to do something for yourself.
