Chart Projections

In 1849, Dr. Samuel Birley Rowbotham published the pamphlet “Zetetic Astronomy: Earth Flat_earthNot a Globe”  in which he asserted that the Earth is an enclosed plane, surrounded by the ice of Antarctica and (somehow) suspended over which are the stars, the Sun, the Moon and the planets.  Nearly three hundred years later, the astrophysicist Neil DeGrasse Tyson found himself in a smackdown with Rowbotham soul-mate and rapper B.o.B., arguing that the latter’s tweet “Once you go flat, you never go back,” defies not only common sense but gravity.

Cartography is based on the assumption that the world is not flat but an oblate spheroid.  The challenge for the mapmaker is how to project that sphere onto a flat surface.  In every case, projection involves distortion.  It is not possible to peel an orange and reassemble its rind into a seamless flat surface.  The inevitable twisting and stretching distorts the original shape.  And so it goes with the Earth.

Mercator, Gnomonic and Lambert Conformal (Ney’s)

The maritime world relies primarily on three types of distortion (chart projection) in flattening out the Earth.  The first and most common is the Mercator projection which girds the Earth in a cylinder and then rolls the cylinder flat.  Areas nearest to the points of tangency of the cylinder, the points at which the cylinder “touches” the sphere, will be most accurately depicted.  Areas not snug with the cylinder will be stretched to approximate their relative positions.  On the Mercator projection, rhumb lines (lines which do not change direction) are straight lines and great circles, with the exception of meridians and the Equator, are curved.

The second commonly used projection is the gnomonic projection, primarily used for Great Circle charts.  Imagine an enormous plane tangent to the Earth.  Points on the Earth are projected onto the plane from a powerful (metaphorical) light source at the center of the Earth.   On the gnomonic projection, all great circles (the shortest distance between two points on a sphere) are straight lines.  All small circles are curved.

A third projection, used primarily for polar charts, is the Modified Lambert Conformal (also known as Ney’s Projection).  As on the Lambert Conformal projection on which it is based,  the Earth is developed by means of a conic projection; a secant cone intersects the Earth at two parallels.  Great circles plot as straight lines on the Lambert Conformal projection; rhumb lines plot as curves.

Here are some typical examination questions on chart projections.

A Mercator chart is a __________________________.
A.   cylindrical projection
B.   simple conic projection
C.   polyconic projection
D.  rectangular projection
(Answer: A)

What is NOT an advantage of the rhumb line track over a great circle track?
A.   Easily plotted on a Mercator chart.
B.   Negligible increase in distance on east-west courses near the Equator
C.   Does not require constant course changes.
D.  Plots as a straight line on Lambert Conformal charts.
(Answer: D)

Which statement about a gnomonic chart is correct?
A.   A rhumb line appears as a straight line.
B.   Distance is measured at the mid-latitude of the track line.
C.   Meridians appear as curved lines converging toward the nearer pole.
D.  Parallels, except the Equator, appear as curved lines.
(Answer: D)

Which statement is true concerning a Mercator projection?
A.   Degrees of longitude decrease as latitude increases.
B.   The length of the meridians is increased to provide for equal expansion in all directions.
C.   The mileage between the meridians is increased as the latitudes increase.
D.   All of the above
(Answer: B)

All straight lines represent great circle tracks on a chart based on a _________________.
A.   Mercator projection
B.   polyconic projection
C.   orthographic projection
D.  gnomonic projection
(Answer: D)]

Here is a close analysis of a complex map projection:

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