Projections

Objectives:

  1. Hands-on construction
    1. Cylindrical
    2. Conic
  2. Debate on projection choice (world maps)

Construct a projection

Why? Doing it by hand shows you the geometric relationships, allows you to remember critical relationships that you might just let the computer do for you...

Equipment needed: ruler, protractor, compass (some substitutes can work)

Demonstrated in class, take home and finish, turn in by Friday reveiw session.

Cylindrical

  1. Lay out a straight line, this will be your Equator, mark equal increments along this for the meridians.
  2. Construct parallel lines at right angles to the Equator at those marks (your meridians). Projection is halfway done, looks easy?)
  3. Off to side, construct circle to represent the earth, aligned with center on Equator line (continued). Mark latitudes required (every 10 degrees?) on the circle.
  4. Construct a line tangent to the circle at Equator, parallel to the polar axis (and the meridians)
  5. Project marks on circle (parallels) to the tangent line (the cylinder):
    1. From center : Mercator
    2. Parallel to Equator: orthographic
    3. From opposite side of circle: gnomonic
    4. etc.
  6. Use these intersection points to construct the parallels as lines parallel to the Equator.

This graticule defines your projection. Now you would have to draw all the continents, rivers, international boundaries, cities, etc.) into place (Good luck!)

Conic (secant projection with two standard parallels)

Procedure for Nothern hemisphere, for southern, flip everything over...

Part I: lay out the cone (to get spacing of parallels)
  1. Lay out a straight line, this will be your Polar axis from Center of Earth.
  2. Trace quarter circle (Northern hemisphere) with protractor centered on Center of Earth. Mark your two standard parallels, and other parallels required. (For practice use 20 degrees and 60 degrees?)
  3. Construct straight line through the two standard parallels, this is your cone (viewed in cross-section).
  4. Project parallels from circle to the cone (use lines from Center of Earth, other procedures for other conics...)

Now cone is marked with spacing of parallels.

Part II: Construct the graticule
  1. Lay out straight line from polar apex of cone. This is Central Meridian.
  2. Use protractor to mark off even spacing of angles from Central Meridian, draw meridians from apex through these marks
  3. Set compass to each distance along the cone, draw arc for parallel

Debate

What projections of the whole Earth are useful for what purposes? There is a persistent debate, and not much resolution.

  • Mercator Projection is traditional in nautical charting (for really practical reasons in that it preserves compass courses), but reading distances requires special care and knowledge. Areas are badly distorted, but mariners have little interest in area. See NY Times review of book on Mercator - have to register...)
  • Arno Peters revived Gall's equal area cyclindric projection under his own name with some bold claims. most directly evident at a German church web site.
  • Some anti-colonialists (like Rachel Naba) take up Peter's claims;
  • London Times obituary 2002;
  • Matt Rosenberg (about.com) argues that Mercator was already passe;
  • Excerpt from Snyder's book (1993)
  • lots of vendors sell the map though the discussion at this site is less unbalanced than New Internationalist. another vendor. Hammond has a real pitch.
  • the writers for West Wing ran out of material and did a show about the projection controversy.
  • John Krygier's lecture on this subject (Ohio Weslyan University).
  • Professional cartographers have said things against "rectangular" projections (see statement from 1989 in textbook). They also got inordinately peeved at Peters (for running press conferences? for making a splash? for actually unseating the projection establishment?)
  • Snyder's rebuttal of Peters
  • ACSM publication Matching the Map Projection to the Need copyright 1997, but many of the authors died before then.
  • National Geographic has hopped from projection to projection, adopting Robinson's compromise projection for ten years, then moving on to another one..
  • US Geological Survey project on world projections (powerpoint and .pdf) Usery and Cheong

    • Discuss with your neighbors and come to a position on some questions:

    1. Are Peter's claims justified? Are map projections an instrument of colonialist hegemony?
    2. Are the professional cartographers claims justified? Should a world projection appear to be "circular" or non-rectangular?
    3. What projection should be used for a world map?

    Record your vote to submit with the construction diagrams, and we will also take votes interactively in the last 5 minutes of class