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Calculated locations differ from plotted locations

MattStevens1

Hello

Please accept my apologies in advance if this proves to be the result of an elementary mistake.

I have a set of observations made from given points. For each of these I have an observer location (coordinates) and a distance (metres) and bearing (degrees) to an observation target. I want to determine the perpendicular distance of this observation target from a specific route(line). When mapped (Projected Coordinate System = British National Grid) the perpendicular distances produced (identified using 'Generate Near Table' and checked roughly using the measurement tool) differ markedly (10-40%), and inconsistently, from those obtained if I calculate the distance from the original data using simple trigonometry. Given that the units of the coordinate system are metres and the distances are not geographically large (generally <500m), I'm struggling to understand why this should be. What am I missing?

The attached document perhaps gives a clearer explanation.

Mapped vs Calculated distance differences.pdf

List Zoom Return to Extent.jpg

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DanPatterson_Retired

Is there any chance that your dataframe (arcmap) or map (ArcGIS Pro) has been tainted with a Web Mercator dataset? (it causes errors in distance and area measurements. Your calculation from the numbers is correct,

np.sin(np.deg2rad(40))*180. = 115.70176974357706 , but where did you get those numbers? from the measure tool or from points representing the triangle itself?

MattStevens1

Hi Dan,

Thanks for getting back to me. I have not used, or re-projected anything to, a Web Mercator dataset on the dataframe (I'm using ArcGIS 10.5). The numbers are from empirical measurements taken in the field using a laser rangefinder (Distance) and old-school compass (Bearing) so there should be no issue with any 'electronic interpretation/adjustment'. Nevertheless, this wouldn't make a difference would it? If I plot some randomly-derived pairs of points on the map (in the same format as the pdf example) and then compare the perpendicular distances between the targets and the line with those derived from trig calculations, there are still discrepancies.

DanPatterson_Retired

strange a sample of the data used might help.

when you mention 'old school compass' as in one that references to magnetic north, I remember from student surveying labs them forgetting to adjust for the magnetic declination on the compass or post data collection

MattStevens1

I've attached a package of some data - hopefully I've managed to do this correctly and you can then see what I mean.

To clarify, the idea is to determine the perpendicular distance from each of the 'KESTRSprCON2016_Location' points to the relevant line (layers with 'TITL' in the name) section. The original 'From' locations are given by the 'c2016SprCON_Project' points and I've included a line between these points to aid identification. Please ignore the other points. Lastly, I am aware that some of the 'Location' points extend beyond the length of the relevant line section, these are a special case and should be ignored for now.

With regard to your point re. magnetic declination, this is of limited relevance here since this is ca.1 degree in the section of map shown here. Also, the error in measurement of bearing by fieldworkers is likely to be greater than this anyway.

Error_Map.mpk.zip

DanPatterson_Retired

Ok... have a look

I used Near as Table to see how far those 2 points were from the line.

I then used XY to Line to produce the adjoining line.

MattStevens1

Dan, this is great but reiterates what I've already determined.

The question is: what figures do you get for these two perpendicular distances when you calculate them using basic trigonometry? Are they the same as the mapped distances? Or do they differ from the mapped distances by

by -35% and -3.5%, as I've found? Assuming you find the same difference, this is the crux of my problem. Why do they differ?

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