# Is it possible to perceive the curvature of the Earth from the surface? **URL:** \ **Category:** Factual Questions\ **Created:** [July 27, 2007, 1:31pm UTC](https://boards.straightdope.com/t/is-it-possible-to-perceive-the-curvature-of-the-earth-from-the-surface/413362 "2007-07-27T13:31:13Z")\ **Posts on this page:** 10\ **Page:** 1
**Author:** ![Whiteknight](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whiteknight/32/4962_2.png) [@Whiteknight](https://boards.straightdope.com/u/Whiteknight)\ **Post date:** [July 27, 2007, 1:31pm UTC](https://boards.straightdope.com/t/is-it-possible-to-perceive-the-curvature-of-the-earth-from-the-surface/413362/1 "2007-07-27T13:31:13Z")
A search turns up to previous threads on this subject but neither seemed to offer a definitive conclusion either way and both were more general than my case. I have a long running debate with my father-in-law regarding the curvature of the horizon. Please note that I am not referring to the curvature in the medial plane (as one is facing the ocean), but rather in the frontal plane. The debate is as follows. At his Miami Beach apartment building on the 8th floor, one can see the ocean. The view is partially obscured by the building itself, as well as the adjacent building, so it is not possible to see all the way down the beach. You can see the building [here](http://maps.google.com/maps?f=q&hl=en&geocode=&q=100+lincoln+road,+miami+beach,+fl&sll=25.790072,-80.128747&sspn=0.003579,0.007167&ie=UTF8&ll=25.790207,-80.128731&spn=0.00179,0.003583&t=h&z=19&om=1). The apartment is located in the section of the building directly to the left of the larger of the two pools, across the large patio section. He argues that he can see curvature at the horizon while I maintain that while he may _think_ he does, it is impossible for the human eye to actually perceive the minimal curvature. Based on my rough calculations, the horizon is approximately 12.4 miles away at that height (~100ft). Estimating the amount of visible horizon (due to the blocking buildings) at that distance as a generous 20 mi, I believe that the difference in “height” between the midpoint of the visible arc and the side points is ~16 ft. I do not believe that it is possible to detect a difference in height of 16 ft at a distance of 12.4 miles. To put it another way, if we were to approximate the horizon as a short, wide triangle, the “slope” of horizon would be 1.6 ft rise for every mile of horizontal distance. Is it really possible for a human to perceive such a minimal slope at a distance of 12.4 miles? I contend that it is not. ---
**Author:** ![Freddy\_the\_Pig](https://avatars.discourse-cdn.com/v4/letter/f/a587f6/32.png) [@Freddy\_the\_Pig](https://boards.straightdope.com/u/Freddy_the_Pig)\ **Post date:** [July 27, 2007, 2:04pm UTC](https://boards.straightdope.com/t/is-it-possible-to-perceive-the-curvature-of-the-earth-from-the-surface/413362/2 "2007-07-27T14:04:02Z")
I’m afraid I don’t understand your comment about “the midpoint of the visible arc and the side points”. Every point on the horizon is equidistant from an observer. People ask from time to time about perceiving the “curvature of the Earth”, and the only meaning I can ascribe to this is perceiving the dip of the horizon, as I explain in Post # 12 of [Is it possible to see the curvature of the Earth, from the Earth?"](http://boards.straightdope.com/sdmb/showthread.php?t=367982&highlight=horizon+curvature) ---
**Author:** ![Whiteknight](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whiteknight/32/4962_2.png) [@Whiteknight](https://boards.straightdope.com/u/Whiteknight)\ **Post date:** [July 27, 2007, 2:09pm UTC](https://boards.straightdope.com/t/is-it-possible-to-perceive-the-curvature-of-the-earth-from-the-surface/413362/3 "2007-07-27T14:09:54Z")
[QUOTE=Freddy the Pig] I’m afraid I don’t understand your comment about “the midpoint of the visible arc and the side points”. Every point on the horizon is equidistant from an observer. People ask from time to time about perceiving the “curvature of the Earth”, and the only meaning I can ascribe to this is perceiving the dip of the horizon, as I explain in Post # 12 of [Is it possible to see the curvature of the Earth, from the Earth?"](http://boards.straightdope.com/sdmb/showthread.php?t=367982&highlight=horizon+curvature) [/QUOTE] Giving him the benefit of the doubt regarding the curvature and the various ways that he might perceive it, I’m estimating the curvature for the given arc where the horizon is the chord between the “side points”. I realize that this isn’t really what is seen, but I’m just trying to give a rough approximation of what he is seeing _if_ it were visible at all. ---
**Author:** ![Freddy\_the\_Pig](https://avatars.discourse-cdn.com/v4/letter/f/a587f6/32.png) [@Freddy\_the\_Pig](https://boards.straightdope.com/u/Freddy_the_Pig)\ **Post date:** [July 27, 2007, 2:43pm UTC](https://boards.straightdope.com/t/is-it-possible-to-perceive-the-curvature-of-the-earth-from-the-surface/413362/4 "2007-07-27T14:43:13Z")
I _think_ I understand what your asking . . . but what your father-in-law is perceiving _is_ curvature in the medial plane, and would look exactly the same on a flat Earth. As I write this I’m looking out the window of the office behind my cube, about fifty feet away. The office window has a divider in the middle. The horizon “bulges” in the middle in the sense that it clips the divider at a higher point then it clips the sides of the window. But that has squat-all to due with the curvature of the Earth. It’s a consequence of the _foreground_: I’m superimposing a flat, vertical, two-dimensional window in front of a three-dimensional background. If my office building were round, I wouldn’t see that effect. ---
**Author:** ![Whiteknight](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whiteknight/32/4962_2.png) [@Whiteknight](https://boards.straightdope.com/u/Whiteknight)\ **Post date:** [July 27, 2007, 3:45pm UTC](https://boards.straightdope.com/t/is-it-possible-to-perceive-the-curvature-of-the-earth-from-the-surface/413362/5 "2007-07-27T15:45:04Z")
[QUOTE=Freddy the Pig] I _think_ I understand what your asking . . . but what your father-in-law is perceiving _is_ curvature in the medial plane, and would look exactly the same on a flat Earth. As I write this I’m looking out the window of the office behind my cube, about fifty feet away. The office window has a divider in the middle. The horizon “bulges” in the middle in the sense that it clips the divider at a higher point then it clips the sides of the window. But that has squat-all to due with the curvature of the Earth. It’s a consequence of the _foreground_: I’m superimposing a flat, vertical, two-dimensional window in front of a three-dimensional background. If my office building were round, I wouldn’t see that effect. [/QUOTE] I agree, I think that whatever curvature he thinks he’s seeing is due to that. To make matters worse, my ex-Navy uncle also insists that you can see the curvature when at sea. He also says that the horizon is 11 miles distant for a 6 ft observer, which is clearly false. So much for Navy training. 🙂 ---
**Author:** ![John\_DiFool](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/john_difool/32/19543_2.png) [@John\_DiFool](https://boards.straightdope.com/u/John_DiFool)\ **Post date:** [July 27, 2007, 3:53pm UTC](https://boards.straightdope.com/t/is-it-possible-to-perceive-the-curvature-of-the-earth-from-the-surface/413362/6 "2007-07-27T15:53:11Z")
I had a photographer friend. He went crazy trying to take a closeup of the horizon. ---
**Author:** ![Whiteknight](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whiteknight/32/4962_2.png) [@Whiteknight](https://boards.straightdope.com/u/Whiteknight)\ **Post date:** [July 27, 2007, 3:56pm UTC](https://boards.straightdope.com/t/is-it-possible-to-perceive-the-curvature-of-the-earth-from-the-surface/413362/7 "2007-07-27T15:56:56Z")
[QUOTE=John DiFool] I had a photographer friend. He went crazy trying to take a closeup of the horizon. [/QUOTE] What was the problem? Was he trying to minimize the distortion due to the lens? ---
**Author:** ![Freddy\_the\_Pig](https://avatars.discourse-cdn.com/v4/letter/f/a587f6/32.png) [@Freddy\_the\_Pig](https://boards.straightdope.com/u/Freddy_the_Pig)\ **Post date:** [July 27, 2007, 4:00pm UTC](https://boards.straightdope.com/t/is-it-possible-to-perceive-the-curvature-of-the-earth-from-the-surface/413362/8 "2007-07-27T16:00:43Z")
> [@Whiteknight](#): > > I agree, I think that whatever curvature he thinks he’s seeing is due to that. To make matters worse, my ex-Navy uncle also insists that you can see the curvature when at sea. The problem is, people confuse the curvature of the horizon with the curvature of the earth. The horizon is a circle, because (without obstructions) you see an equal distance in all directions, and the locus of points equally distant from an observer is a circle. **It would be a circle even if the earth were flat**. The difference between the flat-earth circular horizon, and our round-earth circular horizon–the **only** difference–is that the flat-earth horizon encloses _exactly_ 180 degrees of your field of vision, whereas the round-earth horizon encloses a tiny bit less than that, with the “tiny bit” slowly growing as you gain height. Can you perceive this from the deck of a ship? Sure, if you happen to be watching another ship disappear hull-first over the horizon–which is why the ancient Greeks recognized this as evidence for the sphericity of the earth. Otherwise, no chance. But people see what they want to see. You get out on a ship and see that big circle of a horizon all around you, and you’re an educated Twenty-First Century Citizen of the World who knows that the world is round, and you blurt out, “Wow, I’m seeing the curvature of the earth!” But you’re not. ---
**Author:** ![Whiteknight](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whiteknight/32/4962_2.png) [@Whiteknight](https://boards.straightdope.com/u/Whiteknight)\ **Post date:** [July 27, 2007, 4:08pm UTC](https://boards.straightdope.com/t/is-it-possible-to-perceive-the-curvature-of-the-earth-from-the-surface/413362/9 "2007-07-27T16:08:16Z")
[QUOTE=Freddy the Pig] The problem is, people confuse the curvature of the horizon with the curvature of the earth. The horizon is a circle, because (without obstructions) you see an equal distance in all directions, and the locus of points equally distant from an observer is a circle. **It would be a circle even if the earth were flat**. The difference between the flat-earth circular horizon, and our round-earth circular horizon–the **only** difference–is that the flat-earth horizon encloses _exactly_ 180 degrees of your field of vision, whereas the round-earth horizon encloses a tiny bit less than that, with the “tiny bit” slowly growing as you gain height. Can you perceive this from the deck of a ship? Sure, if you happen to be watching another ship disappear hull-first over the horizon–which is why the ancient Greeks recognized this as evidence for the sphericity of the earth. Otherwise, no chance. But people see what they want to see. You get out on a ship and see that big circle of a horizon all around you, and you’re an educated Twenty-First Century Citizen of the World who knows that the world is round, and you blurt out, “Wow, I’m seeing the curvature of the earth!” But you’re not. [/QUOTE] Exactly, you can see the the curvature of the earth from a ship if you see things disappearing over the horizon (medial plane), but you certainly cannot see curvature in the frontal plane. I’ve spent a good deal of time on ships myself and I cannot for the life of me figure out what my uncle is talking about. Anyway, I believe that what my father-in-law see as curvature in the frontal plane is, just as you describe, actually curvature in the horizontal plane since the limits of vision in that plane are, logically, a circle, assuming no obstructions. ---
**Author:** ![Myself](https://avatars.discourse-cdn.com/v4/letter/m/8491ac/32.png) [@Myself](https://boards.straightdope.com/u/Myself)\ **Post date:** [July 28, 2007, 7:23pm UTC](https://boards.straightdope.com/t/is-it-possible-to-perceive-the-curvature-of-the-earth-from-the-surface/413362/10 "2007-07-28T19:23:57Z")
I found this exchange which may contribute. In short, 60,000 feet is when you can see the curvature of the earth. [http://www.stratofox.org/twiki/bin/view/Stratofox/ViewingCurvatureOfTheEarth](http://www.stratofox.org/twiki/bin/view/Stratofox/ViewingCurvatureOfTheEarth)