34. Dubay claims that ship captains never use spherical trigonometry

“Ship captains in navigating great distances at sea never need to factor the supposed curvature of the Earth into their calculations. Both Plane Sailing and Great Circle Sailing, the most popular navigation methods, use plane, not spherical trigonometry, making all mathematical calculations on the assumption that the Earth is perfectly flat. If the Earth were in fact a sphere, such an errant assumption would lead to constant glaring inaccuracies. Plane Sailing has worked perfectly fine in both theory and practice for thousands of years, however, and plane trigonometry has time and again proven more accurate than spherical trigonometry in determining distances across the oceans.”

Dubay is just blatantly lying.  He is completely shameless.


Lie 1. “Both Plane Sailing and Great Circle Sailing,…. [make] all mathematical calculations on the assumption that the Earth is perfectly flat”.  


How can Great circle sailing not take the curvature of the earth into account when it is based on the earth being a sphere!  There is a clue in the name. The "Great circle" refers to the circumference of the Earth.  Duh.
"Great-circle navigation or orthodromic navigation (related to orthodromic course; from the Greek ορθóς, right angle, and δρóμος, path) is the practice of navigating a vessel (a ship or aircraft) along a great circle. Such routes yield the shortest distance between two points on the globe."
          See: https://en.wikipedia.org/wiki/Great-circle_navigation



Lie 2. “If the Earth were in fact a sphere, such an errant assumption would lead to constant glaring inaccuracies”.  

The implication being that navigating on the assumption that the Earth is flat does not lead to inaccuracies.  It does.
Plane sailing is an approximate method of navigation over small ranges of latitude and longitude.  This is possible with a spherical earth because the earth is so large.  It does not work over long distances. 
"Plane sailing (also, colloquially and historically, spelled plain sailing) is an approximate method of navigation over small ranges of latitude and longitude."
          See: https://en.wikipedia.org/wiki/Plane_sailing


Lie 3. “Plane Sailing has worked perfectly fine in both theory and practice for thousands of years”.  

Not it has not.

By the time of Captain Cook (1728-1729) navigational techniques and instruments based on the assumption that the Earth is a sphere were well established.


Captain Cook undertook extensive journeys in the southern hemisphere, where he could not have failed to notice the huge discrepancies in distances had they occurred. since on a flat Earth projection map of the world  the distances in the southern hemisphere are many times greater than they are on a globe.

Here is a clue, note in this navigation instruction from 1807.  Latitude and Longitude are measured in degrees.  I.e. measuring the angle on a sphere.  Measuring latitude in degrees makes no sense on a flat Earth.



Great circle navigation actually goes far further back.  Here is an article detailing how Pedro Nunes formalised this method of navigation in 1537, and how it was adopted by the great naval powers of the time.



There would have been no need for Pedro Nunes to work on improving navigation if Plain Sailing was as successful as Dubay claims. 

Lie 4. “ … plane trigonometry has time and again proven more accurate than spherical trigonometry in determining distances across the oceans.”.

If this were true, then ships navigation officers would not be taught Great Circle Navigation.
Here are more modern reference showing that navigation on a spherical Earth is actively taught.


The following link has Great Circle Sailing in the curriculum under "more info"



The fact that Dubay chooses to lie about this most easily verifiable subject tells me that he can't really believe this stuff himself.  Perhaps I am being unfair.  Perhaps he just repeats nonsense spouted by others without investigation or giving it any thought.  Either way, you should take this as a good reason to disbelieve anything he says and check it out yourself.


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