i luurv pedants
Old Smokey! G'day!!
I love pedants, being one of those damned pedantic captains!
But I have never understood chart making and makers.
If the object of their exercise is to determine the circumference of an ellipse then
C = pi (a + b) [ 1 + 3 h / (10 + (4 - 3 h)^1/2 ) ]
where h = (a - b)^2 / (a + b)^2 .
Assuming that a = 6378137 metres and b = 6356752.314 metres
Circumference = 40007862.92 metres. So if a sphere had the same circumference the nautical mile might be 1852.216 metres or 6076.824 feet… but it isn’t.
If on the other hand their object of the exercise is to determine the surface area of a spheroid
Then
S = 2 pi a^2 + (pi / e) b^2 ln (1+ e)/(1 - e) where e = eccentricity = (1 - b^2 / a^2)^1/2
S = 5.1066E+14 square metres and a sphere of the same surface area would have radius 6371007.181 metres which gives us a possible nautical mile of 1853.251 metres or 6080.22 feet which it used to be, ish, and probably still is to Jeppesen and the US DoD who happily tell us in inches to the nautical mile.
Now wise men will tell you that the spheroid “radius” at latitude +/- 45 degrees is as near as dammit 1852 metres or 6076.1155 feet. So be it. We obviously fly further now for the same amount of fuel which will please the accountants.
But if you want the nearest possible conformal projection of a spheroid onto a sphere, 6080 feet it is for a nautical mile and a radius of 20901500 feet. But as you rightly point out, I am by International Definition, out of step.
Oh the heresy of it all, Old Smokey!!! I am wrong and everbody else is right!!!!
[They've taken the laces out of my shoes and I'm not allowed anything sharp you know. But the room is nicely carpeted... on the floor, the walls, the ceiling... ha ha!!!!!!]
You'll be pleased to know retirement beckons.
Best Rgds in all good humour
enicalyth