Visually discerning the curvature of the Earth

Abstract

Reports and photographs claiming that visual observers can detect the curvature of the Earth from high mountains or high-flying commercial aircraft are investigated. Visual daytime observations show that the minimum altitude at which curvature of the horizon can be detected is at or slightly below 35,000 ft , providing that the field of view is wide ( 60 ° ) and nearly cloud free. The high-elevation horizon is almost as sharp as the sea-level horizon, but its contrast is less than 10% that of the sea-level horizon. Photographs purporting to show the curvature of the Earth are always suspect because virtually all camera lenses project an image that suffers from barrel distortion. To accurately assess curvature from a photograph, the horizon must be placed precisely in the center of the image, i.e., on the optical axis.

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Visually discerning the curvature of the Earth
David K. Lynch
Thule Scientific, P.O. Box 953, Topanga, California 90290, USA
(thule@earthlink.net)
Received 9 April 2008; accepted 28 April 2008;
posted 1 May 2008 (Doc. ID 94635); published 25 July 2008
Reports and photographs claiming that visual observers can detect the curvature of the Earth from high
mountains or high-flying commercial aircraft are investigated. Visual daytime observations show that
the minimum altitude at which curvature of the horizon can be detected is at or slightly below 35;000 ft,
providing that the field of view is wide (60°) and nearly cloud free. The high-elevation horizon is almost as
sharp as the sea-level horizon, but its contrast is less than 10% that of the sea-level horizon. Photographs
purporting to show the curvature of the Earth are always suspect because virtually all camera lenses
project an image that suffers from barrel distortion. To accurately assess curvature from a photograph,
the horizon must be placed precisely in the center of the image, i.e., on the optical axis. © 2008 Optical
Society of America
OCIS codes: 010.7295, 000.2060, 000.2700, 010.1290.
1. Introduction
The health of the eye seems to demand a horizon. We
are never tired, so long as we can see far enough.—
Ralph Waldo Emerson [1]
The first direct visual detection of the curvature of
the horizon has been widely attributed to Auguste
Piccard and Paul Kipfer on 27 May 1931 [2]. They
reported seeing it from a hydrogen-filled balloon at
an elevation of 15;787 m(51;783 ft) over Germany
and Austria. On 11 November 1935, Albert W.
Stevens and Orville A. Anderson became the first
people to photograph the curvature [3]. They were
flying in the helium-filled Explorer II balloon during
a record-breaking flight to an altitude of 22;066 m
(72;395 ft) over South Dakota. Other claims have
been made as to being the first to see the curvature
of the Earth, but they seem to have come long after
visual curvature had been established [4].
Since that time, countless people have claimed to
be able to discern the curvature of the Earth as an
upwardly arched horizon from high mountains or
commercial aircraft. Some claim to see it from sea le-
vel or relatively low elevations [5]. We know that if
we get high enough (i.e., from space), the curvature
of the Earth is evident, but commercial aircraft sel-
dom exceed altitudes of 40;000 ft (1ft ¼0:3048 m).
Interviews with pilots and high-elevation travelers
revealed that few if any could detect curvature below
about 50;000 ft. High-altitude physicist and experi-
enced sky observer David Gutierrez [6] reported that
as his B-57 ascends, the curvature of the horizon does
not become readily sensible until about 50;000 ft and
that at 60;000 ft the curvature is obvious. Having
talked to many other high fliers (SR-71, U2, etc.),
Gutierrez confirms that his sense of the curvature
is the same as theirs. Passengers on the Concorde
(60;000 ft) routinely marveled at the curvature of
the Earth. Gutierrez believes that if the field of view
(FOV) is wide enough, it might be possible to detect
curvature from lower altitudes. The author has also
talked to many commercial pilots, and they report
that from elevations around 35;000 ft, they cannot
see the curvature.
When trying to understand the perception of a
curved horizon, two issues must be kept in mind.
First, a large fraction of people wear eye glasses.
Eye glasses produce a variety of distortions when
the observer is not looking through the center part
of the lens. Second, above the altitude of Mt. Everest,
no observer can look directly at the horizon—he
must look through a window or canopy. Plane-
parallel windows like those on most aircraft will
0003-6935/08/340H39-05$15.00/0
© 2008 Optical Society of America
1 December 2008 / Vol. 47, No. 34 / APPLIED OPTICS H39