MANAGING MISCONCEPTIONS
Seafarers, great circles, and a tad of
rhumb: Understanding the Mercator
misconception
by Michael A. DiSpezio
H
ow does the landmass area of Africa roughly compare to that of Greenland?
a. the same size
b. twice as large
c. 7 times as large
d. 14 times as large
How taken aback might you be to learn that Africa’s
landmass area is about 14 times greater than that of
Greenland? Would you return to the Mercator maps
that hung in your elementary classroom, or perhaps to
the distorted game boards on which you first engaged
in global conflicts?
Being flat, maps inherently misrepresent some
aspects of Earth’s geography. That’s because there
is absolutely no way to simultaneously conser ve
all of the elements of three-dimensional space in a
two-dimensional model. Even the best maps contain
embedded inaccuracies that arise from distilling three
dimensions into two.
The transformation from a spherical surface to a
flat model is called a map projection. As you have encountered, there are all sorts of map projections, each
offering a unique flattened interpretation of the world.
Every projection has advantages and disadvantages.
Faced with choices, map readers select the projection
that best meets their needs.
One of the most familiar translations is called the
Mercator projection (see Figure 1). Presented by the
Flemish cartographer and mathematician Gerardus
Mercator (1512–94) in 1569, this map was the first
projection developed to meet the needs of navigators. However, to realize its advantages in navigation,
Mercator’s mapping equations produced distortions
in landmass size and shape.
Unlike a globe’s converging lines of longitude, the
Mercator projection artificially maintains all meridians
as parallel throughout their length. Because these lines
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SCIENCE SCOPE
Gerardus Mercator
of longitude don’t converge at the poles, the Mercator
introduces a contrived stretching of Earth’s surface,
which is most exaggerated approaching the poles.
A consequence of this projection is the exaggerated
size of polar landmasses, while equatorial geography
appears smaller. Hence, the all-too-familiar confusion
when it comes to estimating the relative landmass size
of Africa and Greenland.
With the potential for significant error in area comparison, how did the Mercator projection become so
popular? Could Eurocentrism be at the root of its favor?
Although this map certainly inflates the footprint of
MANAGING MISCONCEPTIONS
Typical Mercator projection of
the world
nasa
FIGURE 1
Europe, its attractiveness was driven by its maritime
value. As Mercator so eloquently put it, his new map
“was corrected for use of navigation.”
Navigation? Surely, you’ve got to be kidding? How
can a map that produces a landmass distortion the
scale of the Africa–Greenland misconception be useful
in navigation? No doubt your students will raise this
same question, and what better way to construct an
answer than by actually modeling how vessels used
the Mercator projection?
To plot a transatlantic voyage, roll out the appropriate Mercator map and identify the two ports between
which you wish to travel. Connect these points with a
straight line. Next, measure the compass bearing of
this line. This angle measure is your constant degree
heading that puts you on a fixed course to your destination port. Communicate this angle measurement to
the ship’s helmsman and away you go—sailing across
an entire ocean on a single compass bearing.
The straight line you plotted on the Mercator projection is called a rhumb line. Derived from the French
word rhombe, the term refers to angles or points on
a compass. A rhumb line will intersect every line of
longitude it crosses at the exact same angle. It is this
conservation of compass heading that made navigation by rhumb line the preferred means of charting
a course. Select one degree heading and follow it to
your final destination.
Although practical for navigating, the rhumb line
is most often not the shortest distance between two
ports—especially when it comes to voyages of great distance or those spanning polar latitudes. Seafarers (and
aviators) know that the most direct paths are identified
by great-circle routes—not rhumb lines. On Mercator
and related projections, great-circle routes appear as
arcs that are longer in length than the corresponding rhumb lines. How can that be? Isn’t the shortest
distance between two points a straight line? Yes, it is,
but the distorted geometry of the Mercator projection
throws in a proverbial curveball: Straight lines drawn
on a globe may appear curved on a Mercator projection. Likewise, curved lines on a globe may appear
straight on a Mercator projection. In order to obtain a
valid comparison of distance, you need to go back to
the globe and put the Mercator projection away.
Although seafarers had for centuries been aware of
the shorter courses identified by great-circle routes,
they opted to follow the longer rhumb lines. The simplicity of rhumb-line navigation far outweighed any
extra time at sea: Supply the helmsman a single bearing and without ever changing course, you ultimately
reach your destination. Following a great-circle course,
instead, requires ongoing and continual course adjustment—an extra procedure that was easily abandoned
for the simplicity of rhumb-line navigation.
Today, with the availability of electronic navigation
systems, the choice between rhumb-line and greatcircle routes usually depends on the length of the
voyage and proximity to the poles. One of the betterknown examples is found in air travel between New
York City and Hong Kong (see Figure 2). The rhumb
line between these two cities is about 18,000 km. In
contrast, the great-circle route is 13,000 km. That’s a
difference of 5,000 km, or about 5½ hours of flying time.
With considerable savings in fuel and time, this “into
the Arctic” great-circle route becomes the preferred
course.
In your classroom, a most effective strategy for
dealing with any misconception involves identifying
and tackling the false foundation on which it was
constructed. In the Mercator example, we have a rich
landscape of misdirection that lies at the essence of
every map —inaccuracies based on the limits of spatial
projection. To appreciate the pervasive and insidious
nature of this misconception, challenge students to
draw a world map from memory. You’ll no doubt uncover distortions founded in the Mercator projection.
Although few modern textbooks and atlases use the
Mercator projection when illustrating world maps or
November 2010
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MANAGING MISCONCEPTIONS
Activity Worksheet: Mercator misconceptions
Activity 1
Using World Wind (free for download at http://worldwind.arc.nasa.gov/download.html), have students
observe a more accurate representation of landmass
size. NASA’s World Wind program illustrates a portion of the globe whose vantage shows the actual
size difference between Greenland and Africa.
Activity 2
To further uncover misconceptions based
on the Mercator projection, supply students
with a disposable Mercator map. Instruct
students to cut out Africa and Greenland (or
Alaska and Brazil). Have them compare and
contrast the areas of these landmasses as
represented by this style of map. Then, offer access to a globe constructed on a similar scale. Have students compare and contrast
the sizes of their two-dimensional cutouts to the
areas represented on the globe’s curved surface.
Undoubtedly, students will uncover a discrepancy in
landmass size. Explain that this difference is an artifact of translating the curved surface of a sphere
onto a flat, two-dimensional map that is distorted for
rhumb-line navigation.
Activity 3
Supply students with a globe, a Mercator map of the
world, tape, and yarn. Have students locate New York
City and Hong Kong on the globe. Instruct them to use
the yarn and tape to illustrate the great-circle route between these cities. Using the globe’s distance scale,
students should uncover a journey of about 13,000 km.
Then, supply students with a Mercator projection and
have them plot a rhumb line for this voyage to be used
as a reference. Based on this map plot, have students
use another length of yarn and tape to lay out the rhumb
line between these two cities on the surface of the globe.
Using the globe’s distance scale, students will uncover a
distance of about 18,000 km.
Activity 4
Have students use the internet to research the impact of technology on mapmaking. Then, challenge
16
SCIENCE SCOPE
A more accurate representation of the world’s land masses as
seen at NASA’s World Wind website.
students to assemble a presentation populated by
images that represent a time line of mapmaking. For
each map, students should identify the new technology or discovery that led to the observed improvements or practical application.
Activity 5
Supply student teams with a Mercator map, a ruler, and
a protractor. Students select an assortment of historic
ports on either side of an ocean basin. Then, challenge
the teams to calculate the course heading for backand-forth travel between these ports. Increase the sophistication of the challenge by identifying courses that
require multiple paths (legs) in order to go around obstructions to a single, straight-line path.
MANAGING MISCONCEPTIONS
FIGURE 2
The great-circle route and the corresponding rhumb
line from Hong Kong to New York City on a world
map that places the Pacific Ocean center stage.
Rhumb
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irc
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e
Gr
On this map, which retains inaccuracies of the Mercator projection, you can see
that the plotted rhumb line appears shorter, even though on a spherical globe it
is about 5,000 km longer than the corresponding great-circle route.
polar regions, Mercator and its variants live on. Log
onto Google maps and zoom out to get a world view.
Look familiar? It should. This distorted version of our
planet’s surface is an artifact of the Mercator projection. Note the size disparity of Greenland and Africa.
Then, examine the enormity of Antarctica. Because
the distortion of longitude increases drastically approaching the poles, a landmass located on the pole
has colossal proportions. Antarctica has a distortion
that is as excessive as it can get. However, because this
landmass is mostly unpopulated, its out-of-the-ordinary
proportions were often cropped from traditional Mercator world maps. This clipping of the southern polar
latitudes has also been submitted as further evidence
of a Eurocentric strategy that centers the cropped
projection at the European latitudes.
One of the best-known contemporar y maps of
Earth is a composite of NASA imagery. Ornamenting the walls of many Earth science classrooms, this
iconic map is often referred to as “The Cloudless
Earth.” Like the Mercator projection, this cylindrical projection also has lines of longitude that remain
parallel throughout their length. But unlike Mercator,
the separation between latitude
lines is not as exaggerated, reducing the vertical stretching of
polar landmasses. The trade off
is increased accuracy in relative
landmass size at the expense
of distor ted shapes, with the
resultant loss of rhumb-line
navigation.
With knowledge of students’
misconceived notions, it’s up to
you as the instructor to deconstruct erred understanding as
you replace inaccuracies with
valid scientific concepts. To help
achieve this goal, check out the
Activity Worksheet and the websites in Resources. Along with
your own arsenal of mapping
experiences, these suggested
resources offer a rich and varied
landscape on which to tackle the
Mercator misconception and associated misunderstandings in
map projections. n
Resources
Great circle mapper (a program that draws and analyzes
great-circle routes flown by commercial aircraft)—www.
gcmap.com
Make your own globe— www.gma.org/surfing/imaging/
globe.html
NASA World Wind (an open-source alternative to Google
Earth that offers maps with rich scientific data sets—
http://ti.arc.nasa.gov/projects/worldwind
USGS map projections (a variety of map projections and a
table that summarizes the strengths and weaknesses of
each projection)—http://egsc.usgs.gov/isb/pubs/Map
Projections/projections.html
USGS maps & globes gallery (an assortment of templates
that can be assembled into globes of planets and
moons)—http://astrogeology.usgs.gov/Gallery/Maps
AndGlobes
Michael A. DiSpezio ([email protected]) is an
author and science education specialist in North
Falmouth, Massachusetts.
November 2010
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