I work on vehicle routing. I've seen mysterious detours that ended up being cause by using an imprecise segment length equation.
Because the earth isn't a sphere, the common length-on-a-sphere great circle distance equation isn't perfect for the earth. However, it's a lot faster to calculate than the haversine length, which takes into account the squashed sphere that we live on.
We were calculating driving routes at high latitudes. The difference in the length calculation meant that east-west road lengths were being calculated as slightly longer than they really were.
Amortized across a long-distance route, this led to the mysterious tendency of the shortest-path algorithm to prefer north-south oriented roads a lot more often than you'd expect.
While we knew we were using the less precise great-circle distance, the deviation is not all that big, so we didn't really expect the difference to manifest in the output.
I bet there's a number of grid corrections due to historical subdivision, not cartography.
The first land developers like George Calvert and William Penn and more going westward had large tracts of land to subdivide into smaller and smaller units but they didn't all make the same choices. Eventually roads within needed to meet and corrections made.
In the East, almost every town has a "County Line Road" and more times than not, it's crooked and met with a number of dogleg corrections.
It should be easy to identify those that are due to curvature, though. My understanding is that states parceled according to the PLSS have fairly consistent township and section divisions, made using a system that takes the earth's curvature into account in a systematic way. This method introduces "corrections" like those in the article at regular, predictable intervals.
Growing up in rural Ontario, I've seen plenty of these, but I was always given a different explanation for it: chains stretching.
The idea was that these concessions were laid out via teams with two sets of horses pulling a chain directly west, then when the chain was fully stretched, putting down a post to mark the point at which the concession ended, tying the chain to it, and pulling the other end ahead until it ran out again.
This worked, but if team A has the old chain, and team B has the new chain, team A will keep being a few inches and then feet ahead of team B, who are working a few miles to the south, because the chain started to stretch over time.
In hindsight, I realize now that I have no idea if any of this is even remotely true, but it was a plausible explanation that I'd heard from a couple of sources.
Isn't using the right projection for a certain geography a solved problem in cartography? This article seems like it's saying: "Here's a common problem for mapmakers that you didn't know!"
It is a known problem, but not a solved problem, in that there does not appear to be 1 best way to map a 3d surface onto a 2d map and vice-versa. There are numerous approximations, but which one to use is an art and not a science.
They are effectively establishing a local grid system within each township. The adjustments allow them to place the grids side by side. The brilliance of the system is it is simple to implement.
Couldn't this also be solved by simply making the plots of land without right angled corners? I'm guessing there is a simple tiling solution that would solve the problem without requiring detours.
Not while satisfying the requirement that each piece of land be six miles square, with the boundaries running north-south and east-west. In fact that's impossible to do for a single piece of land that does not straddle the equator.
One solution would have been to make each parcel of land 36 square miles, with the parcels getting taller and narrower further north.
If the boundaries are running magnetic north-south, then there is no way to make the property square. I'm sure there is a good reason to survey the lands as squares, rather than as trapezoids with the north/south borders running along the lines of longitude - just not sure what it is right now.
The farmer wouldn't care - they would simply survey their property based on the property stakes - and, at 6 miles, their property corners would be close enough to right-angles they probably wouldn't notice, and certainly wouldn't care.
And roads could then run all the way to the north pole, or from coast to coast, without having to detour (mountains, lakes, cities, rivers and other obstacles excepted).
Because the earth isn't a sphere, the common length-on-a-sphere great circle distance equation isn't perfect for the earth. However, it's a lot faster to calculate than the haversine length, which takes into account the squashed sphere that we live on.
We were calculating driving routes at high latitudes. The difference in the length calculation meant that east-west road lengths were being calculated as slightly longer than they really were.
Amortized across a long-distance route, this led to the mysterious tendency of the shortest-path algorithm to prefer north-south oriented roads a lot more often than you'd expect.
While we knew we were using the less precise great-circle distance, the deviation is not all that big, so we didn't really expect the difference to manifest in the output.
Those were some mysterious detours.