# Best type of map (projection) for measuring distances?

## Summary:

Trying to do a project, not sure which is the best to use
(**I'm super sorry I didn't realize what this forum was for!)

## Main Question or Discussion Point

Hi! Sorry if this isn't the best question, but I've been trying to do a project where I thought it would be interesting to talk about coastlines.

I downloaded a GIS (QGIS) to try and see if I could roughly measure all the continents for myself, but I haven't really done this before, so I wasn't sure what the best type of map would be better to use? I found a table that gave some advice on which is best for what purpose, but I didn't really understand and also didn't really know which would be the most helpful?

I thought the world extent and maybe equal area (since I don't need the coasts to me that accurate) would be good, but I'm not really sure.

Really sorry if this isn't a good question! Thanks!

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In my view, that's some nice thinking on your part -- I think that, when we're looking at measurement of lengths of coastlines, it's important to be cognizant of resolution -- if resolution is to be maximized, coastline length could become close to infinite --

In my view, that's some nice thinking on your part -- I think that, when we're looking at measurement of lengths of coastlines, it's important to be cognizant of resolution -- if resolution is to be maximized, coastline length could become close to infinite --
:( yeah I wanted to try to do some calculations but thought it would be too much to try and incorporate all the little details and stuff from the more accurate stuff online, so I wanted to measure in like 1000km or something?? But now if I use the map I have I'm worried it'll be really really off

Perhaps you could reduce the resolution so as to not have to be confronted as directly by the problems of real analysis and Chaos theory? -- putting it perhaps a little crudely -- maybe you could reconstruct your problem category as sets of dot-to-dot summations instead of as irresoluble contintnua?

Tom.G
Best type of map (projection) for measuring distances?

A globe and a string!

Which suggests a software implementation may be available that allows tracing a route on a rotatable image and adding the lengths of each route segment.

Unfortunately I don't know of any such program! Maybe others here have run across such an animal.

Best type of map (projection) for measuring distances?

A globe and a string!

Which suggests a software implementation may be available that allows tracing a route on a rotatable image and adding the lengths of each route segment.

Unfortunately I don't know of any such program! Maybe others here have run across such an animal.
Neato -- that reminds of something I here present fondly as an an anecdote -- when I was a kid ('70s) for a few days I tried many times to wrap a wide-woven multicolored string-thread around a cueball thereby marking it into 8 parts, and repeatedly failed miserably -- the Provost at the University, who was biologically the brother of an older-than-I-was adopted sister, opined that it was impossible, but 'our' sister had mercy on me and next-to-impossible patience, and she did it perfectly -- I from the ceiling in my bedroom hung a globe of planet Earth and the well-strung cueball a reasonable distance away to represent the Moon. and my (our) sister was pleased.

BillTre
Gold Member
2018 Award
Unfortunately I don't know of any such program!

Baluncore
No flat map projection will work since the continents are large compared with the size of the spherical globe with slight flattening.

However, the fundamental problem will be that the coastline is the classic example of a fractal line with infinite length. The closer you look the longer it will become until you are measuring half the circumference of all wet sand grains.
To measure the coastline length you will need to define centroids separated by a fixed distance, say 1 km, and counting the number needed to bound the continent. As the chosen centroid separation is decreased the length will increase as expected for a fractal.

Baluncore
While the boundary length and the 3D surface area of a landmass are fractal, and so are not measurable, the plan area on the spheroid is measurable. As resolution of boundary points increases the accuracy of an estimate of the plan area converges to a fixed value.

The problem then is what height of tide marks the boundary. What about the area of mudflats that are just above or just below that level. When does a flowing river stop being land area, how far up a river do you call the sea? How far up the Amazon River does any sea water flow, during which season?

Easy enough (that somebody else can quantify) to calculate distance along an arc between sets of longitude/latitude coordinates.

Bit mind-numbing manually, but inputting say the coordinates of coastal cities into a little C or spreadsheet program should produce the required result.

Or use this

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Baluncore
Easy enough (that somebody else can quantify; it's late and I'm lazy) to calculate distance along an arc between sets of longitude/latitude coordinates.
Nothing can be gained by doing that computation, even on a WGS84 ellipsoid, which is practical. If you had followed the wiki coastline paradox, (ref in post #9), you would realise that the process is futile as the coast is fractal, no matter what size coastal cities or how many points you use. There are data files with coordinates of coastal points available, but unfortunately not applicable to this fractal problem.

Using trapezoid integration of coastal coordinates to compute the surface area of a continent on a sphere would be possible and converge to a result. But how do you tell where Asia and Europe meet? Is Panama in North or South America? Where or what is the boundary of Antarctica? Is India a continent?

"Engineering is the art of approximation" - R.D. Middlebrook

As others have said; there is no projection without errors, and there is also the resolution (fractal) problem. What I think you need to do is include the errors present in whatever method or tools you use as a fundamental guide to your approach. It's all about the error bars...

What sort of accuracy do you want, and what methods are sufficient to get that?

Agreed. Too many times we find ourselves measuring with a micrometer, marking with a crayon, and cutting with an axe. You're probably best off using a geographic coordinate system (WGS 84), with some kind of world spherical projection but keep in mind that in the U.S., the horizontal and vertical datums are changing to a fixed-plate "geo-potential" datum by 2022. Considering that, if accuracy is paramount, I would recommend using plate-specific datums as well as a geographic coordinate systems for measurements, and if you plan on going this deep with it, you might want to consider an optimum timestamp for sea level measurements as well. The datum is a integral part of the projection, as projected coordinated systems are based on geographic coordinates, which are in turn referenced to a datum and ellipsoid. As you can see this can be a real can of worms if you're not keen with crayons. Best of luck!

New Datums:
• North American Terrestrial Reference Frame of 2022 (NATRF2022)
• Pacific Terrestrial Reference Frame of 2022 (PATRF 2022)
• Mariana Terrestrial Reference Frame of 2022 (MATRF 2022)
• Caribbean Terrestrial Reference Frame of 2022 (CATRF 2022).

Filip Larsen
Gold Member
To measure the coastline length you will need to define centroids separated by a fixed distance, say 1 km, and counting the number needed to bound the continent. As the chosen centroid separation is decreased the length will increase as expected for a fractal.
Also, if the process is repeated for a set of different scales then one can make an estimate of the fractal dimension of the coastline in question for the scale range in question, like for example for Ireland's coastline. If the correlation is good you can then estimate the length at any scale in-between.

Using a specific map data source there will of course be a lower limit to the scale, below which the fractal dimension will drop to 1 (e.g. if you start making linear interpolation between data points). This scale limit (resolution) may, for some data sets, also be higher than the lowest linear distance you find if the set already contains interpolated points, so make sure to check what the source resolution and accuracy is.

Regarding correcting local length when using planar map projection data you should be able to find a correction equation for the specific projections you use. If you really plan on going world wide in the same "run" then, like others here, I would certainly recommend you stay in WGS84 coordinates with a data set where the coastline positions has been corrected to match local mean sea level. However, a global data set probably also mean a fairly high upper limit on the lowest scale you can expect to use.

A Lambert conformal conic projection (LCC) is a conic map projection used for aeronautical charts
Its benefits are:
-Meridians of longitude converse towards the pole
-Parallels of latitude are curves which concave towards the pole
- Scale is almost perfectly uniform
-A straight line draw on this map is a great circle.

Every pilot knows this and all of the E charts used in Foreflight, Garmin Pilot and other programs also use this projection. After all, what could possibly be better than using a ruler, a straight line, and getting a great circle route?

Baluncore
The best map projection is not a map projection, it is the WGS84 ellipsoid used by GPS.
The data set is here;
https://www.ngdc.noaa.gov/mgg/shorelines/

Given WGS84 lat, lon and h=height .
Compute the x, y, z position of the point relative to the centre of the Earth as follows.
a = 6378137. ' WGS84 constant semi-major axis, metres
bars = .9933056200098587 ' WGS84 constant, bb/aa
ee = 6.694379990141316D-03 ' WGS84 constant, square of first eccentricity f(2-f)
SinLat = Sin( lat )
RofC = a / Sqr( 1 - ee * SinLat * SinLat) ' radius of curvature
term = ( RofC + h ) * Cos( lat )
x = term * Cos( lon ) ' x-axis is Atlantic Ocean positive
y = term * Sin( lon ) ' y-axis is Indian Ocean positive
z = (h + (RofC * bars)) * SinLat ' z-axis is North Pole positive

Where the straight line distance between two points is used, the arc length is under-estimated by 1mm at 10km range, and by 1 metre at 100km range.