I thought navigation was traditionally done using flat maps that as far as I know cannot accurately map either a sphere or the very nearly a sphere.
Only on long distance navigation could I imagine it making any difference and then only fractionally. Maybe the America’s cup yacht race teans account for the earth being non spherical but I doubt it. The earth also bulges out towards the sun and moon but again only imperceptibly.
The earth is 100% a sphere because it is approximately 99.65% a perfect sphere. Picturing the earth as a squashed ball or lumpy potato shape is wrong. The earth is a fractal that changes with scale and time cannot be exactly represented by any geometric construct. The one that comes closest is a sphere.
Straight line navigation is done over short distances, like crossing the Gulf of Mexico. The longer one travels, the more error is going to be introduced. Also, there is increased waste of distance and time, which can be expensive. the shortest distance between two points on a sphere is drawn on a Mercator as a curve. Also in the efficiency equation is the safe distance at which one passes hazards to navigation, which can be underwater and invisible. If one assumes that the earth is a perfect sphere, small errors begin to be introduced, and become large errors during a long transit.
We currently use WGS84 standard, which is that the earth’s surface is an oblate spheroid (ellipsoid) with major (equatorial) radius a = 6378137 m at the equator and flattening f = 1/298.257223563.[6] The polar semi-minor axis b then equals a times (1 − f), or 6356752.3142 m.
it seems obsessive, but when you are navigating a ship costing hundreds of millions of dollars, on voyages of thousands of miles scheduled down to the minute and the meter, every advantage matters.
