How much does convergence affect jobs with network controls of about 1kilometre squared? I can see how it would affect bigger jobs.
It depends on how far E or W of C/M Central Meridian, that you are
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Do you mean for a TM projection or Lambert grid convergence angle, or true geodetic convergence of meridians?
The grid angle changes with east-west distance from TM central but the distortion of a 1 km figure doesnt change much with E-W position.
Distortion is greater at higher latitude. At mid latitudes the E and W sides of a 1 km "square" by distances will be geodetically out of parallel by 10 or 15 arc seconds.
If you ignore it at high latitudes like Bill says, you will have problems even at a 1km square.?ÿ ?ÿTry north of 65 degrees by computing convergence angles from a State Plane projection in a 1 km square even on the CM.?ÿ North of 70 even more so.?ÿ?ÿ
Convergence is about 50" per mile at my typical latitude. That doesn't affect anything much because I do all my jobs in a projection. I will try to use a projection that has the Central Meridian near my jobsite. The last new projection I worked with had 19'00" of convergence on the west section line and 19'53" on the east line.
I wanted to know it because there were surveys surrounding mine that were not using a formal projection but were true northish.?ÿ
It's important to understand how convergence works with your surveys, mainly to follow footsteps.?ÿ
All paper mills, and most every other prefab construction site, have a set baseline in the middle of the project where they have a line that is North and South and then they decide upon a point on that line that is a turned 90 to make an East and West baseline and everything on the project is square to those baselines.
Convergence on a sphere is (Delta longitude) X sin (latitude). The units are whatever the delta longitude values are in (i.e. seconds, minutes, degrees, etc). This approximation is valid for the 1 km extent mentioned in the original question.?ÿ
The formula for an ellipsoid is more complicated
where the m subscript denotes the average latitude between the two endpoints.?ÿ
A few weeks ago I had some spare time and created this free online coordinate calculator tool that would make this type of determination fairly easy, just pick your projection and enter the location coordinates to calculate