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Among the six pseudo-rectangular Eckert projections, three are equal area and three have equally spaced latitudes. The equal area maps have parallels spaced to preserve area, I wonder if the same can be achieved by changing the shape of the meridians.

Is it possible for an equal area pseudo-rectangular map projection to be both equal area and have equally spaced latitudes?

If yes, what are some examples of projections that share all three properties (equal area, pseudo-rectangular, equally spaced parallels)?

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    Sinusoidal is close to what you want I think, except maybe no cylindrical enough. – mkennedy Nov 14 '18 at 17:26
  • @mkennedy It's pseudocylindrical as long as all lines of latitude are straight parallel horizontal lines. – gerrit Nov 14 '18 at 17:31
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    Yes, the sinusoidal projection is pseudocylindrical, equal area and the parallels are equally spaced, so it fits with your description. – FSimardGIS Nov 15 '18 at 0:12
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The sinusoidal projection satisfies your criteria of

  • equal area – areas are true to scale
  • pseudo-rectangular – aka pseudo-cylindrical
  • equally spaced latitudes

It also is equidistant in that scale along the equator and along all parallels of latitude are true to scale.

enter image description here

Note, however, that the equal-spacing of the parallels is not what makes it an equidistant projection (it is their lengths). The wording in your question suggests you may have conflated these.

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