This is a first for me in 35 years of surveying. I have never seen this before.
In doing research for a 100+ acre survey in Pontotoc County, MS, I obtained a copy of the powerline easement crossing the parcel. In reading the description, it said, "....S 49°17' W, 1910.5 feet to survey station 510+00 where there is an equation in bearing on the center line survey, the bearing of S 49°17' W on the line back of said survey station being equal to the bearing of S 49°23' W on the line ahead; thence S 49°23' W 627 feet to point...."
With a BS degree in Civil Engineering, Highway Option, and spending years doing State Aid road construction design work, I am familiar with station equations for distances, usually correcting for curve/tangent lengths or matching up station numbers for different projects.
But this is a first for me to see a bearing equation. In retrospect, the power transmission line runs Northeast-Southwest over a long distance, and realizing that the direction of "East" follows a latitudinal arc (and always being perpendicular to "North"), it stands to reason that there would be a change in "direction" of a straight line over a long distance. Therefore, a correction would be necessary every so often (in this case, six minutes) to apply a correction to the direction of a straight line. I would reason that doing this would cause a better match with local property line directions for the purpose of writing easement descriptions.
I am originally from the "flat earth" society with very few years in geodetic surveying. Everything used to be small, flat, astronomic, and simple geometry and trigonometry. Most of my surveys are small, and fall completely within one section of land. All of the road projects I have worked on were small, meandering county roads. I know that some of you guys that have worked on corridor projects over long distances have encountered this or even perhaps created this.
I am just thinking out loud. Have any of you ever encountered or created a bearing equation? What are your thoughts on this? :-S
That is interesting. I've never seen it. I guess I could see it where your out setting a "straight" line for miles and miles, and occasionally take a solar observation and create a station equation to correct yourself.
It's called a bearing equation.
I've seen them in Forest Service logging road surveys and in State and County Highway surveys.
A [very] few times, some more logical than others.
Elevation Equations are more common in my experience.
eg. BM-12 Station 45+12.5, 65 ft. Right, Elevation = 9510.12 Ah 9511.12 Bk
A couple of times- always at the connection to the adjoining project.
They are all to common in old ITD right of way plans. When I first encountered them years ago I was baffled by them, not so much anymore. Typically it means its the break point in the alignment, one stops another starts....but with the new CL bearing.
T've ran across them on several older highway drawings.
Are they correcting to north?
The old railroad plans in particular that I have are true north, but of course with long east-west tangents and flat curves it becomes harder to apply curve data.
Maybe they ran grid (not state plane) bearings for a while then corrected at that station.
Many center lines were run in from both directions.
That information may have exposed their closing angle.
Equation stations for bearings would be necessary if one worked a LARGE project across zone lines like a power line or something.
That being said, that is insane in your example. They could have corrected up at a property line and rolled on.
Interestingly enough, I just discovered that one of tomorrow's tasks involves a situation where I need to write a description of a parcel where one line is an Interstate Highway boundary that has a point of non-tangent compound curvature, so there are two radial bearings through the same point! This would seem to involve a bearing equation...
It would be a handy and simple way to combine legacy data, especially prior to going digital...
