05-20-2016, 04:31 PM
The distance per degree of latitude varies only slightly with latitude, by less than 01% from the equator to either pole, so we on the level at which we're working it's probably effectively okay to treat it as a constant figure.
If we go with the range of [basically] 20 to 55 degrees north for latitude that's already been mentioned then, on an Earth-sized planet (with the same oblateness as Earth) that's around 2413.94statute miles (not sure whether that's UK statute or US statute: over that distance the difference between them would be a little bit under 1 mile), 2097.66 nautical miles, or 3884.85 kilometres. That gives us the scale for the map's North-South axis.
If we say that the projection being used is most accurate for one specific latitude then comparing the width of the map to its 'height' (in terms of either pixels or just size on the monitor's screen) gives us the east-west distance, and thus the scale, for the map at that latitude.
The east-west scale for the map at any other latitude can then be found by comparing the ratio of longitudinal degree-length at that 'most accurate' line to longitudinal degree-length at the latitude about which one was wondering, and applying that ratio to the scale for that 'most accurate' line.
And there's a useful calculator for finding degree lengths at http://stevemorse.org/nearest/distance.php.
:Bear:
If we go with the range of [basically] 20 to 55 degrees north for latitude that's already been mentioned then, on an Earth-sized planet (with the same oblateness as Earth) that's around 2413.94statute miles (not sure whether that's UK statute or US statute: over that distance the difference between them would be a little bit under 1 mile), 2097.66 nautical miles, or 3884.85 kilometres. That gives us the scale for the map's North-South axis.
If we say that the projection being used is most accurate for one specific latitude then comparing the width of the map to its 'height' (in terms of either pixels or just size on the monitor's screen) gives us the east-west distance, and thus the scale, for the map at that latitude.
The east-west scale for the map at any other latitude can then be found by comparing the ratio of longitudinal degree-length at that 'most accurate' line to longitudinal degree-length at the latitude about which one was wondering, and applying that ratio to the scale for that 'most accurate' line.
And there's a useful calculator for finding degree lengths at http://stevemorse.org/nearest/distance.php.
:Bear: