A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2017 Nov 19, 13:32 -0800
Bob, You wrote:
"the link gave me half of the root answer I was looking for but did explicitly spell out which was why was the haversine formula developed in the first place and does it still have an advantage"
The author of that web page is a guy named Chris Veness. He is neither a mathematician nor a historian of science or navigation. What you have picked up from that website is useful information, but it's only a rough outline of the history and the math.
I'll expand a bit on my comments on the modern history in my earlier post. The haversine technique was still useful in 1984 when Roger Sinnott first wrote about it in that brief note for Sky & Telescope (Greetings, Roger, by the way! I notice you signed up for NavList emails last night). At that point in time, common desktop PCs had very limited chip-level math computation capabilities. If you bought a typical inexpensive PC, like the infamous "Trash 80", or more correctly, the TRS-80 (known at that time as a "PC clone", as many of you may recall), you could do scientific calculations including trigonometric calculations like the great circle calculation, but users were sometimes shocked to discover that a common scientific calculator could produce more accurate results. This is why such antiquated arithmetic as the haversine had a short window of opportunity. It allowed those early desktop computers to perform as well as common calculators. Most of the math on early PCs was done in software libraries, and it was limited to what was known as "single precision" in most cases. In those days, you had to pay up if you wanted better math and buy a special plug-in piece of hardware called a "math coprocessor". This enabled so-called "double precision" math and also much faster single precision math, and if that coprocessor was available, it wiped out the benefit that came from using the haversine algorithm. It was obvious that this math capability deserved to be on every computer, and as quickly as the economics of the market permitted, math or "floating point" coprocessors disappeared. As soon as Intel's 486 chips became widespread, which was by 1993 roughly, the game was done. The special instructions that were formerly found in the expensive coprocessor chip were moved onto the main CPU. And for the vast majority of computer users, that was the end of it --except for specialty applications on devices which did not have chip-level floating point math, like some early cell phones. Enter Chris Veness...
You believe me, right? ;)
The history of "the" haversine in celestial navigation in the 19th and early 20th centuries is also burdened by confusion, and I'll try to get into that in a later post.