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.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. W. Emerson, Nature: Addresses, and Lectures, new and revised ed. (Houghton, Mifflin, 1884), p. 22..
  2. Piccard is widely believed to be the first. There are many references to his achievement on the Internet, most of them certainly derivative. I contacted the Piccard family and they were aware of the claim but had no hard evidence or literature citation backing it up.
  3. S. W. Bilsing and O. W. Caldwell “Scientific events,” Science 82586-587(1935).
    [CrossRef]
  4. A brass plaque placed at the Lamont Odett vista point in Palmdale, Calif., by E. Vitus Clampus claims that X-1A pilot Arthur “Kitt” Murray was the first person to see the curvature of the Earth. The plaque does not cite the year or altitude, but, according to the NASA archives, it was probably on 26 August 1954 when Murray took the X-1A to a record-breaking altitude of 90,440 ft (27,566 m).
  5. Entering “curvature of the earth” into the image search using any search engine will find thousands of images. Most photographers place the horizon near the top of the frame in order to capture the scene of interest below the horizon. The resulting barrel distortion produces a pronounced upward (anticlinal) curvature of the horizon that most people incorrectly interpret as the curvature of the Earth.
  6. D. Gutierrez, djgutierrez1@verizon.net (personal communication, 2007).
  7. C. F. Bohren and A. B. Fraser, “At what altitude does the horizon cease to be visible?” Am. J. Phys. 54, 222-227(1986).
    [CrossRef]
  8. A. P. French, “How far away is the horizon?” Am. J. Phys. Vol. 50, 795-799 (1982).
    [CrossRef]
  9. E. J. McCartney, Optics of the Atmosphere (Wiley, 1976), Fig, 4.8, p 205.

1986 (1)

C. F. Bohren and A. B. Fraser, “At what altitude does the horizon cease to be visible?” Am. J. Phys. 54, 222-227(1986).
[CrossRef]

1982 (1)

A. P. French, “How far away is the horizon?” Am. J. Phys. Vol. 50, 795-799 (1982).
[CrossRef]

1935 (1)

S. W. Bilsing and O. W. Caldwell “Scientific events,” Science 82586-587(1935).
[CrossRef]

Bilsing, S. W.

S. W. Bilsing and O. W. Caldwell “Scientific events,” Science 82586-587(1935).
[CrossRef]

Bohren, C. F.

C. F. Bohren and A. B. Fraser, “At what altitude does the horizon cease to be visible?” Am. J. Phys. 54, 222-227(1986).
[CrossRef]

Caldwell, O. W.

S. W. Bilsing and O. W. Caldwell “Scientific events,” Science 82586-587(1935).
[CrossRef]

Emerson, R. W.

R. W. Emerson, Nature: Addresses, and Lectures, new and revised ed. (Houghton, Mifflin, 1884), p. 22..

Fraser, A. B.

C. F. Bohren and A. B. Fraser, “At what altitude does the horizon cease to be visible?” Am. J. Phys. 54, 222-227(1986).
[CrossRef]

French, A. P.

A. P. French, “How far away is the horizon?” Am. J. Phys. Vol. 50, 795-799 (1982).
[CrossRef]

Gutierrez, D.

D. Gutierrez, djgutierrez1@verizon.net (personal communication, 2007).

McCartney, E. J.

E. J. McCartney, Optics of the Atmosphere (Wiley, 1976), Fig, 4.8, p 205.

Am. J. Phys. (2)

C. F. Bohren and A. B. Fraser, “At what altitude does the horizon cease to be visible?” Am. J. Phys. 54, 222-227(1986).
[CrossRef]

A. P. French, “How far away is the horizon?” Am. J. Phys. Vol. 50, 795-799 (1982).
[CrossRef]

Science (1)

S. W. Bilsing and O. W. Caldwell “Scientific events,” Science 82586-587(1935).
[CrossRef]

Other (6)

A brass plaque placed at the Lamont Odett vista point in Palmdale, Calif., by E. Vitus Clampus claims that X-1A pilot Arthur “Kitt” Murray was the first person to see the curvature of the Earth. The plaque does not cite the year or altitude, but, according to the NASA archives, it was probably on 26 August 1954 when Murray took the X-1A to a record-breaking altitude of 90,440 ft (27,566 m).

Entering “curvature of the earth” into the image search using any search engine will find thousands of images. Most photographers place the horizon near the top of the frame in order to capture the scene of interest below the horizon. The resulting barrel distortion produces a pronounced upward (anticlinal) curvature of the horizon that most people incorrectly interpret as the curvature of the Earth.

D. Gutierrez, djgutierrez1@verizon.net (personal communication, 2007).

E. J. McCartney, Optics of the Atmosphere (Wiley, 1976), Fig, 4.8, p 205.

R. W. Emerson, Nature: Addresses, and Lectures, new and revised ed. (Houghton, Mifflin, 1884), p. 22..

Piccard is widely believed to be the first. There are many references to his achievement on the Internet, most of them certainly derivative. I contacted the Piccard family and they were aware of the claim but had no hard evidence or literature citation backing it up.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

The horizon from sea level (left) and from an elevation of 35,000   ft (right). Note the sharpness of the sea-level horizon and how indistinct the horizon from high elevation is. Also, note the overall contrast reversal between the two images. From sea level the sky is bright and the water is dark. But from high elevation the sky is dark and the sea and clouds are bright.

Fig. 2
Fig. 2

Vertical scans through the two images from Fig. 1. Also shown is a small strip from each image placed to match the scans. The sea-level horizon is sharp and has a high contrast. The transition from sea to sky is only about two pixels wide, corresponding to about 2   arc   min . The angular resolution of the perfect eye is about 1 arc   min , so virtually every naked-eye observer will see the horizon as absolutely sharp. The high-elevation horizon is almost as sharp, but its contrast is low, less than 10% of the sea-level horizon. The sharpness of the high-elevation horizon is a surprise in view of the fact that it is formed entirely within the atmosphere and is not a hard edge like the sea level horizon. The scans were made from JPEG images, and such images contain some compression. The signal level is only relative and, though not of photometric quality, is nonetheless monotonic and nearly linear with scene brightness.

Fig. 3
Fig. 3

Apparent curvature of the horizon. Top, horizon placed near the top of the frame; middle, horizon placed in the center of the frame; bottom, horizon placed near the bottom of the frame. The apparent curvature is due to barrel distortion. These three images are horizontally compressed in Fig. 4 to enhance the visibility of the barrel distortion.

Fig. 4
Fig. 4

Apparent curvature of the horizon. On the left, the full frames are shown. On the right are the horizon photos cropped and compressed 10 : 1 horizontally to enhance the barrel distortion.

Fig. 5
Fig. 5

This picture shows a photograph of the horizon from an elevation of 35,000   ft and with a horizontal FOV of 62.7 ° . Also shown are the three reference points defining the horizon, a horizontal line connect the left- and right-hand points, and the measured amount of sagitta (see inset for a closeup of the sagitta measurement).

Fig. 6
Fig. 6

Model of the horizon and the Earth’s curvature as seen by an observer from an arbitrary elevation h above the surface. The amount S (sagitta) by which the apparent Earth limb falls below the horizon is easily calculable: S = R ( R 2 X 2 ) 1 / 2 . To convert this linear dimension to an angular dimension, we need only divide each quantity by the distance to the horizon D ( 2 R h + h 2 ) 1 / 2 ).

Fig. 7
Fig. 7

Model calculations of the curvature of the Earth from various elevations. The curve for an elevation of 35,000   ft is the thick line, and the asterisk shows the measurement from Fig. 5.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

S = R ( R 2 x 2 ) 1 / 2 .
D ( 2 R h + h 2 ) 1 / 2 .
9.88 exp ( E / ho ) = 1.0 ,

Metrics