User:Tim Zukas/lat-lon

Say you set up your Wild T4 next to the water tank north of the airport at Hilo, Hawaii, intending to determine its latitude and longitude by the stars. NGS predicts you will find the tank to be at 19.7323 deg North, 155.0412 deg West.

You cross the island and set the T4 next to the Keahole Point lighthouse; NGS estimates that by the stars the lighthouse will turn out to be 19.7244 N 156.0787 W. Calculating the distance from the water tank to the lighthouse using those lat-lons we get about 108.8 km, but if we measure the actual distance it turns out to be 105.5 km. What went wrong?

Hawaii is an extreme case of a problem that exists everywhere: when trying to measure latitude and longitude by the stars we can only orient our measuring device by gravity. We'd like the T4's axis to point to the center of the Earth, but the T4's level vials don't know where that is &mdash; all they know is the direction of gravity, which is much affected by that 4000-meter mountain 50 km away. So when we measure the lat-lons for two points the relationship between those two points can be distorted, which renders their lat-lons fairly useless for most people. When we measure the lat-lons of two points we want to be able to use those lat-lons to calculate the distance and direction from one to the other; we want to be able to draw a scale map and plot points on it by their lat-lons, and the distance between any pair of points on the map is supposed to closely match the actual distance we would measure on the ground.

So we need a different plan &mdash; a different definition of latitude and longitude. What they did in Hawaii circa 1930 was call the marker "Oahu West Base" 21 deg 18 min 13.889 sec North, 157 deg 50 min 55.796 West, and define the lat-lon of every other point by its distance and direction from there. NGS now says that in 1993 that point was 21-18-02.54891 N 157-50-45.90280 W in the present NAD83 system. Was the old lat-lon off by 300+ meters? Well, yes, but the relationships between points in the islands were much more accurate than that. C&GS triangulated from island to island, calculating each successive point's lat-lon by its distance and direction from the previous points in the chain. Eventually they deemed the Hilo water tank to be at 19-43-54.526 N 155-03-26.463 W, which would make it 339191.7 meters from Oahu West Base on the Clarke 1866 spheroid. NGS now figures those two points are 339192.8 meters apart.

Similarly in North America. If in 1980 you had asked NGS for the lat-lons for the Empire State Building and a certain water tank in Anchorage, the NAD27 lat-lons they would have given you would be different from the current ones, but the distance you would have calculated then is 8.2 meters different from now&mdash; and triangulation cannot do better than that.