Understanding the 5km Horizon: How Far Can We See at the Beach?

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Discussion Overview

The discussion centers on the visibility of distant objects, specifically islands and boats, from a beach perspective, exploring the implications of horizon distance calculations based on observer height and object elevation. Participants examine the effects of atmospheric conditions, geometry, and potential discrepancies in mapping data.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants note that the horizon distance for a human is approximately 5 km, increasing with height, suggesting that a 100-meter tall observer could see up to 40 km away.
  • Others argue that the visibility of objects like ships can depend on their height; masts may be visible even when hulls are not, leading to the term "hull down."
  • A participant recounts a personal experience of seeing islands approximately 50 km away, which they claim contradicts mathematical calculations based on horizon distance.
  • Some participants propose that atmospheric refraction could allow for visibility beyond the calculated horizon, with light bending due to temperature gradients.
  • A geometric calculation is presented, suggesting that the horizon for an observer at height h is about ##80 \sqrt{h/500}## km, indicating that additional factors must be at play for the observed distances.
  • Discussions include the potential impact of tidal variations on perceived height and visibility, as well as the accuracy of mapping data.
  • Participants mention the role of temperature gradients in affecting light behavior over water, which could contribute to seeing objects that should be below the horizon.
  • There are references to historical accounts of visibility and range in naval contexts, questioning how long-range visibility is achieved in practice.

Areas of Agreement / Disagreement

Participants express a range of views, with no consensus reached on the visibility of distant objects or the factors influencing it. Multiple competing explanations are presented, including geometric calculations, atmospheric effects, and personal experiences.

Contextual Notes

Participants acknowledge limitations in their calculations and assumptions, including variations in observer height, object elevation, and environmental conditions that could affect visibility. There is also mention of different chart datums that may lead to discrepancies in reported distances.

Who May Find This Useful

This discussion may be of interest to those exploring topics in physics, atmospheric science, geography, and navigation, particularly regarding visibility and horizon calculations in coastal environments.

  • #31
sophiecentaur said:
And how high are your eyes above sea level?
Total distance of 51km.

Water tower is about 80 feet tall. (at least it was. It seems to be missing now.)

On a good day I can see it from the Islington bridge, which is maybe 40 feet high.
On a very good day, I see see it from the shoreline (15 feet).

For a long time I toyed with the idea of going out every few days for a year to the exact same spot and taking a pic of the horizon with some referencible landmarks in view - just to show a montage of the horizon in varying temperatures and seasons. (I may have waited too long.)
 
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  • #32
A.T. said:
This is what happens when the job is given to an artist, who misses the entire point. Most of the ship, especially the chimney for which the light path is shown, are not beyond the horizon anyway.
It gets the point across.

It would be very difficult - and not very informative - to try to render this to-scale.

And, I confess, there is an extreme paucity of such diagrams out there. This is the best I could find.
 

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