# Cylindrical Projections

## I. What is a cylindrical projection?

• A cylindrical projection can be imagined in its simplest form as a cylinder that has been wrapped around a globe at the equator. If the graticule of latitude and longitude are projected onto the cylinder and the cylinder unwrapped, then a grid-like pattern of straight lines of latitude and longitude would result. The meridians of longitude would be equally spaced and the parallels of latitude would remain parallel but may not appear equally spaced anymore. In reality cylindrical map projections are not so simply constructed.
The three aspects of the cylindrical projections:
• Tangent or secant to equator is termed regular, or normal.
• Tangent or secant to a meridian is the transverse aspect.
• Tangent or secant to another point on the globe is called oblique.

### Sources

Text: Originally prepared for the Seminar in Map Projections and is currently being adjusted to a common format with the other Map Projection Pages.

Graphics: Come from two sources: 1. Paul S. Anderson, these are graphics containing the graticule shorelines and 2. Shaded maps by Peter H. Dana, The Geographers Craft Project. Department of Geography, The University of Texas at Austin. http://www.utexas.edu/depts/grg/gcraft/notes /mapproj/mapproj.html

## II. Regular cylindrical projections

### Characteristics

• Lines of latitude and longitude are parallel intersecting at 90 degrees.
• Meridians are equidistant.
• Forms a rectangular map.
• Scale along the equator or standard parallels is true.
• Simple construction.
• Can have the properites of equidistance, conformality or equal area.

### Equirectangular Projection

• Among the oldest projections and simplest.
• Parallels are equally spaced.
• Plate Carree-square grid.
• History
• Invented by Marinus of Tyre at about 100 A.D.
• Popular during Renaissance.
• Declined in popularity in 18th century.
• Used for regional maps.

### Mercator Projection

• Conformal.
• Meridians unequally spaced, distance increases away from equator directly proportional to increasing scale.
• Loxodromes or rhumb lines are straight.
• Used for navigation and regions near equator.
• History
• Invented in 1569 by Gerardus Mercator (Flanders) graphically.
• Standard for maritime mapping in the 17th and 18th centuries.
• Used for mapping the world/oceans/equatorial regions in 19th century.
• Used for mapping the world/U.S. Coastal and Geodetic Survey/other planets in 20th century.
• Much criticism recently.

### Lambert's Cylindrical Equal Area

• Meridians are equally spaced
• Parallels get closer near poles.
• Parallels are sines.
• True scale at equator.
• History
• Invented in 1772 by Johann Heinrich Lambert with along with 6 other projections.
• Prototype for Behrmann and other modified cylindrical equal-area projections.

### Gall's Sterographic Cylindrical

• Neither equal area or conformal.
• Projected geometrically from a point on the equator opposite meridian being projected
• History
• Invented by James Gall in 1855
• Modified in 20th century by changing standard parallels

### Miller Cylindrical Projection

• America's compromise projection
• 4 proposals with different lat. spacing
• Perspective compromise
• Modified Mercator A
• Modified Mercator B-.8 spacing of Mercator
• Modified Gall's
• History
• Invented by Osborn Maitland Miller (Scot) in 1942
• Hired by U.S. Dept. of State

## III. Transverse Cylindrical Projections

### Cassini Projection

• Equirectangular rotated 90 degrees-applied to ellipsoid
• Scale true along central meridian, meridians 90 degrees to central meridian, and equator
• History
• Invented by Giovanni Cassini
• Used for topo maps in France until 1803
• Modified in 1810 by Soldner and used for topo maps in U.K. and German States
• Declined use in 20th century

### Transverse Mercator

• Mercator rotated 90 degrees
• Applied to sphere
• Conformal
• History
• Invented by Lambert in 1772
• Modified for ellipse by Gauss in 1822, Kruger in 1912
• Used for regions with a N/S expanse
• Used for topo mapping
• Basis for State Plane Coordinate System, UTM

### Transverse Cylindrical Equal Area Projection

• Transverse of Lambert's Cylindrical Equal Area-for N/S expanse
• Used sparingly

### Modified Transverse Mercator

• 2 standard meridians-Guozco Li (1981)

## IV. Oblique Cylindrical Projections

### Oblique Mercator

• 45 degree tilt of regular cylinder
• Introduced by Charles Peirce in 1894 with little fan fare
• Used by Debes's Atlas for S.E. Asia and Central America