Talk:Scale (map)

One-inch, quarter-inch, etc.

What is the meaning of "a one-inch map", "a quarter-inch map" etc.? I presume this somehow refers to scale but am uncertain as to what, precisely, it means. -- pne (talk) 15:52, 12 November 2007 (UTC)

One-inch, quarter-inch, etc.- explanation

The meaning here - typically used in the U.S. - refers to the approximate distance on the map to 1 mile on the ground. Thus a representative fraction map with a scale of 1:63,360 is a "one-inch map" in common parlance (in practice this also includes the later scale of 1:62,500 used by the USGS in their older 15' topo series maps). I suppose that makes a quarter-inch map one of the 1:250,000 quadrangles produced by the Defense Mapping Agency.

In general this page could be more clearly written, particularly the first bit.

Patrick McHaffie —Preceding unsigned comment added by 140.192.166.146 (talk) 14:59, 14 April 2008 (UTC)

add common scales

It would be helpful to add common scales for maps and what they are used for; for instance, the 1:24,000 (7.5') USGS topographic maps that are common in the U.S. If there are other scales that are commonly used in other countries that would be interesting. -- phoebe / (talk to me) 23:21, 9 January 2009 (UTC)

I added some hints for scales, because they can be somewhat counterintuitive, but the addition needs some editing, and maybe a citation. RETheUgly (talk) 20:44, 16 December 2013 (UTC)

I deleted the addition. Encyclopædia articles don’t use didactic idioms like “it should be noted” and they do not presuppose or speculate on a reader’s ignorance or confusion. The description of large- and small-scale is quite explicit. (I know this article has a lot of didactic idioms, but we should be paring them down, not increasing them.) Thanks. Strebe (talk) 04:41, 17 December 2013 (UTC)

Suggested modifications

I would like to suggest some modifications for this page.

1 Clarify the discussion of map scale by introducing the idea of point scale using the Mercator projections as examples.

2 Contrast map point scale and RF, the representative fraction for the map. The former is a function of position. The latter is constant over the whole map.

3 Remove some of the trivial examples.

4 Remove all the the non-map stuff. (Areal and volume scaling, de Brito etc)

Peter Mercator (talk) 14:36, 5 April 2009 (UTC)

• Changes well on the way. Should be done soon. Need section on RF and a Mercator example. Does anyone know how to trim the first figure? The original eps was clipped but the svg seems to have picked up white space at the left. Thanks. -- Peter Mercator (talk) 22:29, 7 April 2009 (UTC)
• Two new sections. One further to come on how modified (secant) projections affect scale. Also need to add cross links, references and one or two more figures. Still need help with the white space problem arising in the svg figures. -- Peter Mercator (talk) 16:15, 10 April 2009 (UTC)

Revision

I have at last got around to revising this page. Grateful if any watchers could look through for typos and infelicities. I am also hoping for comments and criticisms. My plans for the future include examples from other classes of projection. More general theory on scales might go into a revision of the Tissot's Indicatrix page. My main self-criticism is that this page is pedagogic rather than encyclopaedic. This is disapproved of in Wiki. What do you think? Peter Mercator (talk) 21:11, 11 November 2009 (UTC)

Earth to globe to map

Currently this article describes the map projection process as: first project the Earth to an (entirely imaginary) paper map wrapped around the entire Earth. Then reduce the 2d image.

I propose we change this article to describe it in a different and (in my opinion) more realistic and easier to understand way: first reduce the entire Earth down to a 3d model globe -- perhaps with a bar scale attached to it. Then project that globe to a paper map wrapped around it.

Using the "globe" approach lets us say things like the following in a more natural way: Often that globe is a perfectly spherical approximation to the nearly-spherical Earth. Any "lines of true scale" on the actual, physical, paper map will have the same length as the corresponding path on that actual, physical globe. If a line of true scale happens to be a straight line on that paper map, and correspond to a great circle on that globe, then that paper can be wrapped around that globe such that the endpoints and every intermediate point along that "line of true scale" on the map simultaneously touch the corresponding points on that globe. Different paper maps projected from the same globe will line up almost exactly in areas of low distortion, although they may look very different in other regions of the map.

Both approaches are mathematically identical and produce the same paper map. Any comments before we make sweeping changes throughout the article on something that is, after all, a matter of opinion rather than fact? --DavidCary (talk) 05:40, 21 July 2010 (UTC)

I agree with the approach you outline. The present description seems strained. Strebe (talk) 08:03, 21 July 2010 (UTC)

• Greetings. As you say, it is a matter of opinion. I mulled over this topic for some time but in the end I decided to keep clear of the idea of a representative sphere. Basically I thought I was in fairly good company (Snyder in the Working Manual and Flattening and others) in including an explicit factor of radius (or semi-major axis) in the equations. The coordinates so defined must then be reduced by the RF for actual maps. Perhaps the error is to talk about big sheets of paper wrapping the Earth.

Without the explicit radius factor you are working on the unit sphere (or equivalently in units of the radius). It is still non-trivial to discuss the variable scale from map to model and the constant rf (reduction factor) between model and reality.

Didn't understand "Often that globe is a perfectly spherical approximation to the nearly-spherical Earth." Does this imply modelling the ellipsoid by a sphere? What happens to the projections of the ellipsoid? Will you have model ellipsoids too?

My version isn't brilliant, even a little strained :-), but this is Wiki, after all, so feel free to edit (but perhaps you could make a draft for a new version in your own user space before removing the current version). Peter Mercator (talk) 22:06, 23 July 2010 (UTC)

Hello, Peter Mercator. Thanks for the comments. Here are my thoughts about how to present the topic:

• We choose an abstract solid for the earth; that is, normally a sphere or ellipsoid. The abstraction closely approximates the actual earth in scale, as is usual for geodetic datums. This gives the link between physical reality and the abstraction of the datum. It avoids the practical problem of wrapping a gigantic sheet of paper around the earth (infeasible) and the conceptual problem of projecting from infinitely complex surface of the physical earth directly to a sheet of paper. It emphasizes that metric properties preserved by the projection are properties of the abstract solid, not those the physical earth.
• Next we choose a nominal scale (= representative fraction). This is the ratio between the dimensions of the model globe to be used for projection, and the datum. The model globe is what the sheet of paper gets wrapped around.
• Next we project. W do not project to the unit sphere or ellipsoid; we project to the solid as scaled from the original by a or R, directly related to the nominal scale.

Snyder’s usage on spherical projections does not suggest that R includes or excludes the representative fraction, but merely that it is the radius of the model globe. ("R = radius of the sphere, either actual or that corresponding to the scale of the map", from the table of symbols in Map Projections— A Working Manual.) That is also how I read the literature at large. So, for example, he switches between unit radius and real datum radii in his worked examples in Appendix A of that volume. Meanwhile his examples on ellipsoidal datums always use a and b unscaled, presumably because geodetic work uses real or stylized real (false eastings &c.) distances in communicating information, regardless of the map’s nominal scale.

Having said all that, I don’t think the entire discussion in the article is strained or that it all needs to be reworked. It’s excellent in general. I just think the section on representative fraction should be reworked. The phrase intrinsic projection scaling is used but not explained in that section. (I infer it to mean the datum’s radius.) I recommend R be used instead of a throughout, since there is no discussion of ellipsoidal development. R should be understood to mean the radius of the developing globe, and not the datum’s radius. I recommend changes to the discussion at large be limited to whatever is necessary to clarify that the text refers to the (scaled) model globe rather than the datum. Strebe (talk) 00:54, 24 July 2010 (UTC)

• The more I look at the article the more I become dissatisfied! The easiest point is to accept 'R' for 'a', as long as you don't suggest transformation equations on the unit sphere. I was amused to be caught out on the small print of the 'Working Manual' but I had never looked at the glossary or Appendix A.

The very first sentence defines scale=map/ground but I later define it in terms of transformation coordinates to a full sized datum. These definitions are incompatible since they differ by the RF. The typical map user uses the first and assumes that, say, 2cm anywhere on the map is 1km on the ground (at 1/50000). But scale varies so the 1/50000 is only a nominal scale and the map scale is only approximately 1/50000, varying over the map. On the other hand we wish to discuss scale varying close to unity. How do we decouple these two for the 'man in the street'? I had hoped to mention RF very briefly and move on. So both intro and RF section need attention. I'm not sure how to proceed. (Your queue for a rewrite David Cary?)

By the way I think that all I meant to convey by 'intrinsic scale' was the varying scale as against the constant RF. Nothing deep.

Plans to extend the article to non-equatorial CP, ellipsoidal, azimuthal etc have fallen by the wayside but I hope any changes won't make for difficulties later on. Peter Mercator (talk) 17:41, 24 July 2010 (UTC)

The scale resulting from projection distortion is the "scale factor" at a point (and in some particular direction if the projection is not conformal) and can be discussed as "scale variance". I think that suffices to distinguish it from plain ol’ "scale"?

Definitely let’s keep aware of ellipsoidal, azimuthal &c. in any rewriting! David Cary: Does this give you enough to go on? Strebe (talk) 03:05, 25 July 2010 (UTC)

The recent edits (29 Dec 2013) by an anonymous editor show that we must try and sort out the point-scale/RF confusion. I shall try to make good my promise to rewrite the intro and the RF section along the lines suggested in the above comments.  Peter Mercator (talk) 20:10, 29 December 2013 (UTC)

merge ?

Linear_scale article looks to have a good chunk of stuff that could/should merge in here I think. EdwardLane (talk) 11:35, 27 February 2012 (UTC)

As its creator, I have a bias in favor of the separate article. With that said, I argue that maps are simply one kind of scale drawing so that merging Linear_scale here would make it harder to use it in articles on architectural and mechanical drawings. Note also that of the approximately 200 links into the two articles, only three are shared. That is a very good indication that they have very separate uses. . . Jim - Jameslwoodward (talk to me • contribs) 14:43, 27 February 2012 (UTC)

OK then perhaps just a bunch of images from Linear scale could be used here too. Or some links from one article to the other and back should be included. EdwardLane (talk) 15:05, 27 February 2012 (UTC)

The purposes of two articles differ nearly completely. Linear scale refers to the stated scale and especially its iconography. It is mentioned and linked to in Scale (map)#Terminology of scales. The Scale (map) article is detailed discussion of the concept of scale as it pertains to maps, where the actual scale varies continuously over the map, regardless of what its stated (fictitious) scale might be. This article is specifically NOT about the bar scale graphic and not much about the stated scale. Possibly the top of the article should link to Linear scale as a convenience for those who actually want to know about that. Strebe (talk) 21:12, 27 February 2012 (UTC)

Thanks for the clarification Strebe, I missed the 'about' stuff at the top - my error. EdwardLane (talk) 09:50, 28 February 2012 (UTC)

No, no; I just added that. Thanks for tipping me off to its need. Strebe (talk) 18:31, 28 February 2012 (UTC)

Actually a can not understand the reasons said about not to merge. Why would the merge "make it harder to use it in articles on architectural and mechanical drawings"? And off course this article is not about the bar scale graphic (its' topic is very broader), but a section can deal it. --109.53.229.124 (talk) 10:30, 27 July 2014 (UTC)

If you read the two articles proposed for merging, you will see they don’t have much to do with each other. Strebe (talk) 01:04, 28 July 2014 (UTC)

Even more merge: Scale (ratio)

I wondering why not merge with Scale (ratio) (or not to change the titles). This is not a disambiguation, Scale (ratio) is about every kind of models, so it's a broader topic. See Wikipedia:Disambiguation#Broad-concept articles. --109.53.229.124 (talk) 10:35, 27 July 2014 (UTC)

On the contrary, scale ratio is restricted to scales which are constant whereas scale (map) has to address the fact that the scales of maps are varying (except for maps of small regions). This is a subtle concept which would be out of place in the discussion of ratios.  Peter Mercator (talk) 18:01, 28 July 2014 (UTC)

map projection issues

I intend to split this article in two: Map point scale and Map scale, where the former is more concerned with map projection issues and the latter is more concerned with map symbology and map generalization (e.g., level of detail, resolution, etc). Fgnievinski (talk) 20:16, 16 August 2014 (UTC)

Don’t. The two are too closely intertwined; nor does that separation exist in the literature. When scale factor varies largely across a map, then it’s also a problem for symbology, generalization, level of detail, and resolution. Strebe (talk) 21:22, 16 August 2014 (UTC)

The two are rarely treated together. I just took a look at Robinson, "Elements of Cartography". Issues such as smaller-scale maps (whole country) vs. larger-scale maps (city) take the map projection as a given. In the whole thematic mapping business, point or localized scale is only treated marginally when recommending the adoption of an equal-area projection -- so only areal scale is considered, linear scale is not even mentioned. Again: the nominal scaling of map-projection coordinates is concerned with different problems and neglects the map projection distortions. This article deals with the latter. There's no mention whatsoever about the visualization, representation, generalization, symbology, thematic mapping, level of detail issues. I think the bulk of the present article should be split into Map scale distortion, in close association with Tissot's indicatrix. Portions related to the nominal scaling of a projected map should go into Map scale. The presence of scale distortion issues makes the discussion about nominal scale strained. Fgnievinski (talk) 20:06, 17 August 2014 (UTC)

As the principal author of this article in its present form may I add some comments to the above. I am very aware of the shortcomings of the article and I am currently in the process of drafting a revision. I would maintain that a title of Scale (map) necessitates clear definitions of nominal scale (RF) and true (point) scale and a discussion of the relationship between them: this of course requires some general discussion of projections. I feel that the average map user should be aware that the distinctions are of no importance for town maps, may usually be ignored for national maps but are of great importance for regional and world maps. Sadly, the average map user assumes that the nominal scale printed on most world maps applies throughout the map rather than (usually) on the equator. Consequently I would envisage a clearer discussion of these topics and a great trimming of all the examples that I added in the final sections. The resulting article should be a little leaner.

User Fgnievinski rightly points out that topics such as symbology, level of detail, resolution, etc are not covered here. These matters would be better covered in Maps with links to to this article (and to Map projections) for a more technical coverage. The relation of this article to Tissot's indicatrix and a possible new article on map convergence remains to be explored.

I do not believe that Wikipedia should be constrained by the approach of one textbook.  Peter Mercator (talk) 19:04, 22 August 2014 (UTC)

Thanks for your input and all your effort on this article. I most certainly would agree on general discussion of map projection issues. It's is just that currently there is too much detail about those issues. As these issues have merit, let me insist on splitting the concept of map projection local scale distortion into its own article. It could and should be briefly summarized here, but no more than that. As you admitted, these issues are of no importance if the map projection was well designed for the map purpose and intent. Fgnievinski (talk) 18:20, 24 August 2014 (UTC)

There is at least a third type of map scale worth of mention: the reduction from the terrain altitude to the ellipsoid's surface (see, e.g., [1]). Fgnievinski (talk) 18:20, 24 August 2014 (UTC)

Here's a proposal of outline: Fgnievinski (talk) 18:20, 24 August 2014 (UTC)

• Nominal scale (earth to globe)
• Local scale (spatially variable)
  • Projection distortion (ellipsoid to plane)
    • Linear scale
      • Infinitesimal distances
        • Azimuth dependence
      • Integrated distances (e.g., city-to-city)
    • Areal scale
      • Infinitesimal areas
      • Integrated areas (e.g., whole country)
  • Altitude reduction (terrain to ellipsoid)
    • Horizontal/planimetric
    • Slant/3D

The revisions suggested Fgnievinski cannot be achieved by splitting and renaming articles. I would suggest that he prepares a draft of a new article within his own user space. After discussion we can agree on an amicable restructuring of this area.  Peter Mercator (talk) 19:20, 26 August 2014 (UTC)

I've taken the liberty of creating a stub section about "Altitude reduction" within the present article. Fgnievinski (talk) 20:51, 26 August 2014 (UTC)

I've also enforced hierarchy of subtopics, so that everything that belongs to the projection distortion is self-contained. Fgnievinski (talk) 20:57, 26 August 2014 (UTC)

Map vs. plan

can someone please explain, how can a 1:0.00001 "map" of a virus can be done? Since the representation of a virus is not depending on a projection, the proper term is "plan". Same for tube plans, even if the London Underground company calls it "map". — Preceding unsigned comment added by 193.48.126.37 (talk) 16:52, 17 December 2018 (UTC)

Your definition of “plan” seems suspect. New Oxford American Dictionary:

A detailed map or diagram.

• A drawing or diagram made by projection on a horizontal plane… Strebe (talk) 17:57, 17 December 2018 (UTC)