I have a control sheet template for a client with a blank for "mapping angle". What is this, who uses it, and how do I determine it?
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State plane grid coordinates have a mapping angle from grid north to geodetic north.
Mapping angle is also known as "convergence angle". In a grid projection system, such as state plane, it is the difference between a bearing on the grid, and a geodetic bearing of the same line. For most purposes the term "Geodetic bearing" can be considered equivalent to "astronomic bearing".?ÿ ?ÿ
Every position in a grid projection system has it own convergence angle (and scale factors). But in practice an average convergence angle for a project area is selected to use for all the points.?ÿ ?ÿ
In TM speak it's sine of latitude times (central meridian minus longitude).
You could look at Chapter 4 of the Caltrans Surveys Manual, everything you ever wanted to know about the California State Plane projections but were afraid to ask:
http://www.dot.ca.gov/landsurveys/docs/surveys-manual/04_Surveys.pdf
And the Caltrans LS/LSIT Exam Preparation Workbook Chapter 11 (see Page 11-11 for mapping angle diagram):
?ÿTypically an OPUS report will give you the scale factor and mapping angle to go from your geographic lat/long coordinate to a State Plane projection. Another quick and easy way to determine the SF and mapping angle I'll use Corpscon6, a free conversion program put out the Corp of Engineers. Think of it as the fudge angle on your plane project to get you back to geodetic bearings, that angle growing larger the farther you depart from the central meridian of the SP projection.?ÿ
I disagree that Astro and geodetic azimuths are equivalent. See below.
http://geodesyattamucc.pbworks.com/w/file/fetch/63366627/Lec5_2013_SPCS_lecture.pdf
-?ÿSome useful graphics
http://www2.unb.ca/gge/Pubs/LN49.pdf - Text extract regarding Astro and geodetic azimuth from Univ of New Brunswick Lecture Notes of Geodetic Astronomy
As I was never a land surveyor, I never quite appreciated bearings preferring azimuths. Of course azimuths can be considered bearings with respect to north (or south).?ÿ
As for using one convergence angle for a project, in a Lambert zone with large E-W extent I wouldn??t do it.?ÿ
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I disagree that Astro and geodetic azimuths are equivalent.?ÿ
You are correct, of course. But the difference is typically less, much less, than the 3 second precision of my instrument. My comment about geodetic and astronomic being nearly that same was intended for an audience that didn't know what "mapping angle" meant.?ÿ
As I was never a land surveyor, I never quite appreciated bearings preferring azimuths. Of course azimuths can be considered bearings with respect to north (or south).?ÿ
As for using one convergence angle for a project, in a Lambert zone with large E-W extent I wouldn??t do it.?ÿ
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Azimuths are used in Canada, where I began my career. And everywhere else besides the US, I think. I agree that they make a lot of sense.
A project would have to be a few miles in extent before a single convergence angle, or a single scale factor, wouldn't work. That's small potatoes for the NGS, but few of us unwashed get to work on project that large. Even most DOT projects are generally small enough to bear an average convergence and CSF.?ÿ ?ÿ
I can't imagine what they will use a mapping angle for on the control point. It is a bit of an anachronism these days, it can be very helpful to know when you are retracing older "true north" deeds. A long east-west highway or railroad was probably surveyed using astronomic north as the basis so it can be nice to have it at the control points. This is an example of two control points, the grid is an LDP, the mapping angle at 3 is different than at 2 because they are mostly east-west of each other, it's just shy of 2' at 3 and 41" at 2.
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It's not possible to represent a mapping angle for an area, only for a point, unless you round to the nearest minute for a small area. If you have a program like this you can calculate the mapping angle. If your Autocad file is correctly set up you can inverse geodetically, other programs have routines to do that. We were required to show it for state easements until a few years ago and the reviewers quit caring about it.
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Modern Surveying assumes a plane since the late 19th century (?).?ÿ Since all lines pointing to the geodetic north pole are not parallel this creates a situation where only one line is actually oriented to geodetic north (assuming the survey was started with a determination of north such as a sun observation).?ÿ Lines parallel to the east and west of the central meridian (E to F on the diagram below) are not oriented to geodetic north but they are oriented to grid north although the direction of geodetic north for each point of the survey can be determined.?ÿ For points E and F geodetic north equals grid north.?ÿ For points A, B, C and D grid north is not the same as geodetic north:
The difference in the mapping angle from point to point results in the concept of "Forward Azimuth" and "Back Azimuth" when inversing between points. The grid azimuth/bearing is the same whether inversing from A to B or B to A, but the geodetic azimuth is different depending on which way you inverse.
Dave,
Modern 'private' surveying generally assumes the plane.
Anyone performing surveys for the BLM is still reporting true mean bearings. On new work I compute the bearings using current geodetic understanding. In retracements I still use table 11 as the GLO budgets did not allow deputy surveyors the luxury of carrying an hp11c. I understand batteries were an issue then too... ????
Dave,
Modern 'private' surveying generally assumes the plane.
Anyone performing surveys for the BLM is still reporting true mean bearings. On new work I compute the bearings using current geodetic understanding. In retracements I still use table 11 as the GLO budgets did not allow deputy surveyors the luxury of carrying an hp11c. I understand batteries were an issue then too... ????
One of my projects involves a Dependent Resurvey from 1970.?ÿ I entered it into Cogo although I know that the bearings aren't referenced to a plane.?ÿ Then I rotated all the bearings to State Plane because I've located enough monuments to know the mean mapping angle on every line then rotated them to state plane grid.?ÿ The closure got worse, much worse.?ÿ So that has me confused.?ÿ The notes do say the survey was conducted by "continuous angulation" so maybe it is plane, not sure.
One thing I was told was circa 1970 BLM would run lines so each line would sort of be an independent measurement if I understand it correctly.?ÿ I assume they manually intersected the centerlines to set the center quarter, for example, then the notes are their actual measurements.?ÿ They didn't traverse everything then calculate it back at the office then go out and set monuments as we see commonly done by our Surveyors from that era.
At another project in the mountains several counties away I did some calculations on a early 2000s Dependent resurvey to get search lat/long more or less using a similar procedure, convert to state plane, calculate coordinates via cogo then convert back to lat/long.?ÿ That one worked out very close in reality, the monument is pretty close to where they say it is (sub-foot which is what I expect up there).?ÿ So I think it really is a spherical geodetic system via mean bearings.
Things usually go sideways in one of two ways. Most commonly, the surveyor does not draw a cartoon or visualize the problem well and applies the correction backwards. The second most common is forgetting the plat is true MEAN bearing and doubling the correction. Of course you sometimes get real lucky and both are done...
Your post is also a good reminder that every group in every office had (and has) its own quirks.?ÿ
Fun times, Tom
MightyMoe,
There are two reasons most have dropped the requirement. Reason 1 is they don't know what it is. Reason 2 is they don't use it.
One of my duties the last 20 years was unscrewing coordinate data with incorrect or missing metadata. Having a convergence angle on one of the points made backing in the central meridian of the projection easy. You can literally do it with a sine table and scratch paper. That piece of the puzzle solved more problems than you can imagine..
MightyMoe,
There are two reasons most have dropped the requirement. Reason 1 is they don't know what it is. Reason 2 is they don't use it.
One of my duties the last 20 years was unscrewing coordinate data with incorrect or missing metadata. Having a convergence angle on one of the points made backing in the central meridian of the projection easy. You can literally do it with a sine table and scratch paper. That piece of the puzzle solved more problems than you can imagine..
I totally agree, one real mapping angle on a set of plans can give you the entire basis of bearings even if they don't state the basis. And it can be used as a check against the stated basis if something looks weird. Yeah, they don't know what it means or how to use it, it's just a check in a box that they need to comply with.?ÿ
I learned mapping angles, by multiple sunshot, on a job.
If I used "true north", it had to be accounted for. If I used grid brngs, then it was accounted for.
True north, ain't true, after you move e or w.
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