# Curvature of the Earth as viewed at altitude **URL:** \ **Category:** Factual Questions\ **Created:** [December 5, 2008, 1:43pm UTC](https://boards.straightdope.com/t/curvature-of-the-earth-as-viewed-at-altitude/475840 "2008-12-05T13:43:10Z")\ **Posts on this page:** 13\ **Page:** 2
**Author:** ![GuanoLad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/guanolad/32/42_2.png) [@GuanoLad](https://boards.straightdope.com/u/GuanoLad)\ **Post date:** [December 6, 2008, 11:02am UTC](https://boards.straightdope.com/t/curvature-of-the-earth-as-viewed-at-altitude/475840/21 "2008-12-06T11:02:09Z")
Surely seeing the horizon as an uninterrupted circle, something most people don’t get to see when on the ground, would be evidence of the curvature of the earth. It’s a circular horizon, not an infinite plane. Just seeing something like that, from a height, would appear different to the flat line of horizon we’re used to, even when in the middle of the ocean. ---
**Author:** ![hamishritchie](https://avatars.discourse-cdn.com/v4/letter/h/f4b2a3/32.png) [@hamishritchie](https://boards.straightdope.com/u/hamishritchie)\ **Post date:** [December 6, 2008, 1:56pm UTC](https://boards.straightdope.com/t/curvature-of-the-earth-as-viewed-at-altitude/475840/22 "2008-12-06T13:56:07Z")
An ant standing on the surface of a bastetball would look around and see the horizon as a line which circles around his head, 360 degrees. This is Joe Average, who is standing in the middle of that field in Kansas. From the perspective of another ant sitting a few feet away, the same ball would be percieved as a small circle formed by the outline of the ball. Imagine Laika the dog, looking at the Earth from his rocket window, mourning the borsch he’ll never taste again. Joe’s horizon actually \*would \*appear to curve - If he was to take a photo of his view, and he was to hold a straight edge against the picture, he would be able see that the horizon does actually curve downwards at the edges of his photo, if only by an almost inperceivable amount. This curve should be present for every observer with an unobstructed view of the horizon, (except perhaps for someone resting their eyeballs exactly at sea level), but it would become more obvious at greater altitudes, to the point where some pilots (and perhaps the occational stuntman or space pooch) may begin to notice it with the naked eye. ---
**Author:** ![sailor](https://avatars.discourse-cdn.com/v4/letter/s/a587f6/32.png) [@sailor](https://boards.straightdope.com/u/sailor)\ **Post date:** [December 6, 2008, 2:08pm UTC](https://boards.straightdope.com/t/curvature-of-the-earth-as-viewed-at-altitude/475840/23 "2008-12-06T14:08:28Z")
> [@GuanoLad](#): > > Surely seeing the horizon as an uninterrupted circle, something most people don’t get to see when on the ground, would be evidence of the curvature of the earth. > > It’s a circular horizon, not an infinite plane. > > Just seeing something like that, from a height, would appear different to the flat line of horizon we’re used to, even when in the middle of the ocean. The only difference is that from very high up you can see it all simultaneously while lower down you need to turn your sight. The view is basically the same. The difference is more psycological than actual. As an exercise I have calculated the distance to the horizon as an angle from the earth’s center and the height of the horizon above vertical both as functions of observer height above the surface. I have used the radius of the earth = 6371 Km. The first column is the height of the observer above the surface expressed in Km. The second column is the angle (in degrees) formed by the lines drawn from the observer and from the horizon, both to the center of the earth. The third column is the height of the horizon from horizontal also expressed in degrees. The complement of this quantity to 90º is called in navigation the “depression of the horizon” (from the horizontal, defined as perpendicular to vertical). - - - - Height Km - - - - angle aº - - - - height of horizon º ```auto 000000.002 00.045 89.955 000000.003 00.052 89.948 000000.004 00.060 89.940 000000.005 00.070 89.930 000000.006 00.080 89.920 000000.008 00.092 89.908 000000.011 00.107 89.893 000000.015 00.123 89.877 000000.019 00.142 89.858 000000.026 00.163 89.837 000000.034 00.188 89.812 000000.046 00.217 89.783 000000.061 00.250 89.750 000000.081 00.288 89.712 000000.107 00.332 89.668 000000.143 00.383 89.617 000000.189 00.442 89.558 000000.252 00.509 89.491 000000.335 00.587 89.413 000000.445 00.677 89.323 000000.591 00.780 89.220 000000.785 00.900 89.100 000001.044 01.037 88.963 000001.387 01.195 88.805 000001.843 01.378 88.622 000002.449 01.589 88.411 000003.255 01.831 88.169 000004.326 02.111 87.889 000005.750 02.433 87.567 000007.641 02.805 87.195 000010.155 03.233 86.767 000013.496 03.726 86.274 000017.936 04.294 85.706 000023.837 04.949 85.051 000031.679 05.702 84.298 000042.101 06.569 83.431 000055.952 07.566 82.434 000074.360 08.712 81.288 000098.823 10.027 79.973 000131.335 11.535 78.465 000174.543 13.261 76.739 000231.966 15.232 74.768 000308.281 17.476 72.524 000409.702 20.019 69.981 000544.490 22.888 67.112 000723.623 26.103 63.897 000961.687 29.675 60.325 001278.073 33.601 56.399 001698.547 37.860 52.140 002257.353 42.406 47.594 003000.000 47.167 42.833 003986.971 52.042 37.958 005298.646 56.911 33.089 007041.849 61.641 28.359 009358.550 66.107 23.893 012437.422 70.200 19.800 016529.214 73.847 16.153 021967.166 77.008 12.992 029194.151 79.681 10.319 038798.745 81.892 08.108 051563.158 83.686 06.314 068526.939 85.120 04.880 091071.640 86.251 03.749 121033.330 87.134 02.866 160852.127 87.817 02.183 213770.923 88.342 01.658 284099.492 88.743 01.257 377565.482 89.049 00.951 501780.879 89.282 00.718 666861.943 89.458 00.542 886253.082 89.591 00.409 ``` It can be seen that you have to get upwards of 1000 Km to be able to see the entire horizon simultaneously but even at 100 Km one can see enough of it to appreciate the roundness of the earth. And even at ground level you can see it. It is just a matter of degree and it slowly increases over the entire range of height. There is no definite transition point. By the way, you can easily simulate the view using Google earth if you know the right distance to put your eye from the screen. This depends on the resolution of each display. ---
**Author:** ![Muffin](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/muffin/32/4341_2.png) [@Muffin](https://boards.straightdope.com/u/Muffin)\ **Post date:** [December 6, 2008, 2:15pm UTC](https://boards.straightdope.com/t/curvature-of-the-earth-as-viewed-at-altitude/475840/24 "2008-12-06T14:15:46Z")
It will not look like curvature to you, but you can see the curvature of the earth as you sit on the beach for half an hour on Lake Superior watching a freighter sail away (or for geographically challenged people, as you sit on your stoop in Saskatchewan for a day watching your dog run away). The object eventually sinks below the horizon. What you are seeing, but not perceiving as a curve, is the curvature of the earth. ---
**Author:** ![GusNSpot](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/gusnspot/32/436_2.png) [@GusNSpot](https://boards.straightdope.com/u/GusNSpot)\ **Post date:** [December 6, 2008, 4:40pm UTC](https://boards.straightdope.com/t/curvature-of-the-earth-as-viewed-at-altitude/475840/25 "2008-12-06T16:40:51Z")
Always remember and never forget is that elevation is on earth is relative to the center of the earth and line of sight is not. If you forget this and don’t balance you shot lengths, your level run will not close and you’ll have to go out and do it over. And that sucks on a cold wet day. ---
**Author:** ![\_Undecided\_Adrian](https://avatars.discourse-cdn.com/v4/letter/_/eada6e/32.png) [@\_Undecided\_Adrian](https://boards.straightdope.com/u/_Undecided_Adrian)\ **Post date:** [December 6, 2008, 9:18pm UTC](https://boards.straightdope.com/t/curvature-of-the-earth-as-viewed-at-altitude/475840/26 "2008-12-06T21:18:11Z")
> [@hamishritchie](#): > > Joe’s horizon actually \*would \*appear to curve - If he was to take a photo of his view, and he was to hold a straight edge against the picture, he would be able see that the horizon does actually curve downwards at the edges of his photo, if only by an almost inperceivable amount. > > This curve should be present for every observer with an unobstructed view of the horizon, (except perhaps for someone resting their eyeballs exactly at sea level), but it would become more obvious at greater altitudes, to the point where some pilots (and perhaps the occational stuntman or space pooch) may begin to notice it with the naked eye. I’m convinced that this is the effect. You only start to notice that around cruising altitude of commercial flights, around 10 km altitude. ---
**Author:** ![Musicat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/musicat/32/20189_2.png) [@Musicat](https://boards.straightdope.com/u/Musicat)\ **Post date:** [December 6, 2008, 11:17pm UTC](https://boards.straightdope.com/t/curvature-of-the-earth-as-viewed-at-altitude/475840/27 "2008-12-06T23:17:00Z")
> [@Muffin](#): > > It will not look like curvature to you, but you can see the curvature of the earth as you sit on the beach for half an hour on Lake Superior watching a freighter sail away (or for geographically challenged people, as you sit on your stoop in Saskatchewan for a day watching your dog run away). > > The object eventually sinks below the horizon. What you are seeing, but not perceiving as a curve, is the curvature of the earth. What you are seeing is not the curvature of the earth, but the effects from it or an illustration on how it works. This post has been brought to you by your friendly GQ Pedantic and Nitpicking Department. ---
**Author:** ![sailor](https://avatars.discourse-cdn.com/v4/letter/s/a587f6/32.png) [@sailor](https://boards.straightdope.com/u/sailor)\ **Post date:** [December 6, 2008, 11:17pm UTC](https://boards.straightdope.com/t/curvature-of-the-earth-as-viewed-at-altitude/475840/28 "2008-12-06T23:17:49Z")
never mind ---
**Author:** ![The\_Flying\_Dutchman](https://avatars.discourse-cdn.com/v4/letter/t/9fc348/32.png) [@The\_Flying\_Dutchman](https://boards.straightdope.com/u/The_Flying_Dutchman)\ **Post date:** [December 6, 2008, 11:38pm UTC](https://boards.straightdope.com/t/curvature-of-the-earth-as-viewed-at-altitude/475840/29 "2008-12-06T23:38:23Z")
When I was a boy, I observed the curvature of the earth when on a clear day I looked at the skyline of Toronto from across the lake some 30 miles away. It was obvious that all I could see above the horizon were the tall skyscrapers of down town. ---
**Author:** ![SharkB8](https://avatars.discourse-cdn.com/v4/letter/s/977dab/32.png) [@SharkB8](https://boards.straightdope.com/u/SharkB8)\ **Post date:** [December 7, 2008, 12:36am UTC](https://boards.straightdope.com/t/curvature-of-the-earth-as-viewed-at-altitude/475840/30 "2008-12-07T00:36:40Z")
> [@The\_Flying\_Dutchman](#): > > When I was a boy, I observed the curvature of the earth when on a clear day I looked at the skyline of Toronto from across the lake some 30 miles away. It was obvious that all I could see above the horizon were the tall skyscrapers of down town. Do you mean that if you were to continue to back up, would you then only be able to see the very tops of the buildings in the skyline? Thus, not really being able to “see” the curvature of the earth on the x axis, but proving it’s curvature is perceivable on the y axis? ---
**Author:** ![jackdavinci](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jackdavinci/32/3259_2.png) [@jackdavinci](https://boards.straightdope.com/u/jackdavinci)\ **Post date:** [December 7, 2008, 8:59am UTC](https://boards.straightdope.com/t/curvature-of-the-earth-as-viewed-at-altitude/475840/31 "2008-12-07T08:59:27Z")
Based on image alone, to get a sense or impresion of the curvature of the Earth, all that is required is to see enough of the horizon that you can see that it starts to bend. This is certainly possible from a building or low plane, maybe even from a beach on the ocean. Now to directly sense the curvature, we have to talk about our binocular vision, which gives depth perception. It should be possible to calculate the height from which a flat circle is distinguishable from a spheroid section by nature of paralax alone. ---
**Author:** ![\_Undecided\_Adrian](https://avatars.discourse-cdn.com/v4/letter/_/eada6e/32.png) [@\_Undecided\_Adrian](https://boards.straightdope.com/u/_Undecided_Adrian)\ **Post date:** [December 7, 2008, 11:55am UTC](https://boards.straightdope.com/t/curvature-of-the-earth-as-viewed-at-altitude/475840/32 "2008-12-07T11:55:29Z")
> [@jackdavinci](#): > > Now to directly sense the curvature, we have to talk about our binocular vision, which gives depth perception. It should be possible to calculate the height from which a flat circle is distinguishable from a spheroid section by nature of paralax alone. I agree with your first paragraph, but stereoscopic vision has nothing to do with the horizon. The maximum range for that is around [10 meters](http://astro1.panet.utoledo.edu/~lsa/_color/19_depth.htm), everything above is perspective, motion parallax and so on. ---
**Author:** ![jackdavinci](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jackdavinci/32/3259_2.png) [@jackdavinci](https://boards.straightdope.com/u/jackdavinci)\ **Post date:** [December 8, 2008, 7:24am UTC](https://boards.straightdope.com/t/curvature-of-the-earth-as-viewed-at-altitude/475840/33 "2008-12-08T07:24:04Z")
> [@'\[Undecided](#): > > Adrian;10541089’]I agree with your first paragraph, but stereoscopic vision has nothing to do with the horizon. The maximum range for that is around [10 meters](http://astro1.panet.utoledo.edu/~lsa/_color/19_depth.htm), everything above is perspective, motion parallax and so on. I agree stereoscopic vision has nothing to do with the horizon, just with depth perception. But I didn’t realize that depth perception ends at 10 meters. I guess ignoring the horizon, one would have to depend on perspective cues. If an Earth sized sphere were covered in a grid, at what distance would the fact the the lines are diverging from parallel be noticable? [Previous page](https://boards.straightdope.com/t/curvature-of-the-earth-as-viewed-at-altitude/475840.md?page=1)