topic Re: Calculated locations differ from plotted locations in Transportation Questions

Calculated locations differ from plotted locations

MattStevens1 — Tue, 20 Nov 2018 17:12:55 GMT

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.

Re: Calculated locations differ from plotted locations

DanPatterson_Retired — Tue, 20 Nov 2018 22:42:09 GMT

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?

Re: Calculated locations differ from plotted locations

MattStevens1 — Wed, 21 Nov 2018 09:32:43 GMT

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.

Re: Calculated locations differ from plotted locations

DanPatterson_Retired — Wed, 21 Nov 2018 13:44:15 GMT

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

Re: Calculated locations differ from plotted locations

MattStevens1 — Tue, 27 Nov 2018 16:46:09 GMT

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.

Re: Calculated locations differ from plotted locations

DanPatterson_Retired — Wed, 28 Nov 2018 02:45:42 GMT

Matt

Trying to figure out this example location are the angular units in mils? or did they do a quick twirl around to go past 360 degrees?

Re: Calculated locations differ from plotted locations

MattStevens1 — Wed, 28 Nov 2018 08:10:08 GMT

Dan

Sorry, you've managed to find one of the two errors in the dataset that I forgot to correct before sending:

OID7 - Distance and Bearing are transposed - they should be the other way round - Distance = 650, Bearing 289

OID22 (in c2016SprCON_Project) - Typo. Distance should be 336 and not 3360

Re: Calculated locations differ from plotted locations

DanPatterson_Retired — Wed, 28 Nov 2018 14:42:59 GMT

Not in the first case

Perhaps for 7, 8 and 9 , the lines in the first image, can you show what you got for those locations close to the blue line.

Re: Calculated locations differ from plotted locations

MattStevens1 — Wed, 28 Nov 2018 19:48:08 GMT

Re: Calculated locations differ from plotted locations

DanPatterson_Retired — Wed, 28 Nov 2018 20:00:56 GMT

Matt, I will check those two examples... I just got stuck on the one on the left, where the distance was 288 (measured and in table) but the bearing was 640.

I will check D and E later

Re: Calculated locations differ from plotted locations

DanPatterson_Retired — Thu, 29 Nov 2018 00:11:04 GMT

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.

Re: Calculated locations differ from plotted locations

MattStevens1 — Thu, 29 Nov 2018 08:35:19 GMT

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?

Re: Calculated locations differ from plotted locations

MattStevens1 — Thu, 29 Nov 2018 08:37:04 GMT

Edit:

The calculated v mapped values are D - 103.6m v 76.9m and E - 67m v 64.7m

Re: Calculated locations differ from plotted locations

DanPatterson_Retired — Thu, 29 Nov 2018 10:39:00 GMT

everything is relative to that blue baseline

here are some manual measurements off the file.

If the blue line is wrong, then the angles are wrong and the hypotenuse is wrong.

That is one of the problems with one length-one angle calculations.

All triangles were formed from the blue line, the intersection points of blue/green and the observation points C13G and C13H

Re: Calculated locations differ from plotted locations

MattStevens1 — Thu, 29 Nov 2018 16:36:58 GMT

In order for those figures to work using trigonometry i.e. for point C13G, Adjacent = 211.9m, Opposite = 64.7m, Hypotenuse = 222m, ϴ (the angle at the intersect between blue/green lines) has to be 24.35^o (since ϴ = cos^-1 (adjacent²/hypotenuse²)).

But, because of their relative locations, ϴ must be the same as (Transect Bearing - Observation Bearing), yet this = 82.4^o – 61^o = 21.4^o!

Similarly, for the figures to work for C13H, ϴ has to be 82.58^o but it should be 73.4^o based on the transect route and bearing to the observation (82.4^o – 9^o).

I understand what you are saying re. the potential for the blue (transect) line being wrong but, given that it was plotted in ArcMap from lat/lon points (with the bearing determined by Arc), and the points being determined by Arc from empirical distance and bearing measurements, I don’t see where the error can be.

Re: Calculated locations differ from plotted locations

DanPatterson_Retired — Thu, 29 Nov 2018 17:08:11 GMT

blue line... 21.4 degrees relative to x-axis (?!?)... I will check when I get a chance.

Re: Calculated locations differ from plotted locations

MattStevens1 — Thu, 29 Nov 2018 18:21:18 GMT

No...treating these as trig problems, the internal angles of the triangles formed by the intersection of the green and blue lines (see below - ϴ1 & ϴ2).