
Longest Lines of Sight on Earth - pilom
https://beyondhorizons.eu/lines-of-sight/
======
btilly
You can actually work out roughly how far away the horizon should be
surprisingly easily. Just use the fact that if R is the radius of the Earth
and you are at height h, then from you to the horizon to the center of the
Earth back to you is a right angled triangle with one side of length R and the
hypotenuse of length R+h. Therefore the distance to the horizon is
sqrt(2Rh+h^2) which is roughly sqrt(2Rh).

The Earth is roughly 6370 km which is not far from 6400, so if your eyes are
2m = 0.002 km up then the horizon is about sqrt(2 _6400_ 0.002) = sqrt(25.8)
km away, which is roughly 5 km or a bit over 3 miles.

If you apply this to a 6 km tall mountain, the horizon is about sqrt(2 _6370_
6) km away which is about 276.5 km. So something of the same height at the
opposite end of the horizon would be 553 km away. So the top distance of 538
km is pretty close to the maximum that we would expect.

What about an airplane? An airplane flies about 11 km up. So it can see around
375 km. If you work it out, that puts the horizon about 3.37 degrees below
horizontal. This isn't much, but if you take a plumb line and a right angle on
an commercial flight, it is enough to actually see that the horizon is below
horizontal.

~~~
kovek
I had this question worded differently asked to me when I interviewed to do an
undergrad at Cambridge. If you have a rope that is wrapped around earth and
you lift it off the ground as much as possible, and you see that it is 10km
above the ground, then how long is the rope?

I was not able to answer that question right away, and their hint to draw it
helped a lot. I did not end up getting accepted.

~~~
seanmcdirmid
It seems like one of those stupid brain teasers tech companies used to ask
that are not very correlated with success but act as arbitrary filters.

~~~
anyfoo
In this case the "arbitrary filter" was filtering applicants to a university
for very basic math knowledge, so I think assuming that it's correlated with
success at that university is not very far fetched.

~~~
BurningFrog
Sure, but it also filters for people like me, who have seen this problem at
least a dozen times.

~~~
pm215
When I did my university entrance interview (for maths, at Cambridge) the
interviewers were clear that they expected that some subset of candidates
would have seen the problem before, and some wouldn't -- for those in the
first set they'd get them to quickly go through the problem and move onto the
later parts which would be new to them; for those in the second set they'd
provide sufficient guidance to let the candidate walk through the problem. The
point was to get any particular candidate to a point in the problem sequence
where this was something new to them, and then see how they tackled things.
The idea that some applicants (usually from public schools) would have been
very highly prepped for interview and others (usually from state schools)
would not was clearly something they were well aware of and setting their
interview design up to handle.

~~~
erispoe
But how do you know it's a new problem? You can always fake a little struggle
and thinking your way to the solution for a problem that you know the answer
already.

------
yread
The link in the "done" column doesn't work - it should point to

[https://beyondhorizons.eu/2016/08/03/pic-de-finestrelles-
pic...](https://beyondhorizons.eu/2016/08/03/pic-de-finestrelles-pic-gaspard-
ecrins-443-km/)

It's a report how they made an actual photograph of a sunrise over 443km far.
Quite amazing!

BTW if you ever get the chance to go up Mt. Canigou, go for it. Since it's the
first big mountain in Pyrenees from the east you have really spectacular views
and it's not that difficult to hike up there. Plus they brew great beer (from
iceberg water they say) in the refuge just under it.

~~~
KozmoNau7
There's something utterly awe-inspiring about huge distances, especially if
you're simply not used to viewing objects at those scales.

I live in a country where the highest point above sea level is ~171m. Walking
in the Scottish highlands was a transcendental experience for me.

~~~
codfrantic
You must be Danish, I though us Dutch had it bad (320 max) I guess we do go
below sea level more which also makes this calculation more difficult :)

I do agree on the utter amazement of visiting less flat places :)

------
kbenson
_Mt. McKinley (6.194 m.)_

What country uses '.' as the thousands separator but speaks English? Or is
this someone mixing their native language thousands separator with English? Or
is there some weird interaction between country and language that makes this
the preferred, or at minimum an acceptable standard form? I'm actually hoping
it's one of the latter options, that would be something new to me.

~~~
burkaman
.eu suggests this website was not created by native English speakers.

~~~
dwightgunning
Since when does the TLD imply the native language of the website creator?

Also the .eu TLD, which is a country-TLD for the European Union, consider that
the UK (still in the EU), along with Ireland and Malta have English as an
official language [1].

1\.
[http://www.nationsonline.org/oneworld/european_languages.htm](http://www.nationsonline.org/oneworld/european_languages.htm)

~~~
pimlottc
I think it's quite reasonable; the tld suggests the location/nationality,
which suggests the language. It's not ironclad, but it's implied.

Those three english-speaking countries (UK, Ireland and Malta) make up roughly
13.7% of the total population of the EU; when the UK leaves, it will drop down
to around 1.1%.

------
xxxxxxxx
This is very cool. I'm told you can see Mt Fuji from Tokyo on a clear day, but
I never managed to see it. I did manage to see Mont Blanc from my Kitchen in
Lausanne, Switzerland a few times - such a beautiful sight.

~~~
nandemo
Mt Fuji is only about 100km away from Tokyo. Main problem is there are tons of
buildings blocking your view, but if you're at a high enough floor you can see
the it even when it's a bit cloudy. For example, see the last pic here:

[http://traveljapanblog.com/wordpress/tag/mt-
fuji/page/3/](http://traveljapanblog.com/wordpress/tag/mt-fuji/page/3/)

------
11thEarlOfMar
I can't resist... Reminds me of the Beacons of Minas Tirith from Return of the
King, probably my favorite sequence in the entire trilogy:

[https://www.youtube.com/watch?v=GWz51CiG2nA](https://www.youtube.com/watch?v=GWz51CiG2nA)

------
newman8r
very cool - I'd never even given this concept a second thought. I'd like to
graph these and see how they overlap - would be cool to implement networks via
something like
[https://en.wikipedia.org/wiki/Pseudolite](https://en.wikipedia.org/wiki/Pseudolite)

I'd also be curious to see how this would look if you could include manmade
structures like towers or skyscrapers

~~~
moxious
If you included skyscrapers I bet you'd have the same list no changes. Most of
these mountains are > 2km tall.

~~~
newman8r
you'd still probably have one of those coordinates (of the tall mountain)
remain the same, then find a tower that goes even further than the second
point - although I never assume my logic is correct in geodesy/astronomy,
especially when I'm tired

edit* - in practice you're probably right

~~~
jdironman
Laser powered ISPs anyone?

I kid, but is this a possibility?

~~~
URSpider94
This exists already, from some pretty serious telecom companies, for distances
of a few miles. The problem is that, in optical wavelengths, there's too much
absorption and scattering in the atmosphere - fog, rain, storms, smog, smoke -
that can disrupt the signal.

But, in radio frequencies, this is how the microwave tower communications
network works -- it's line-of-sight from tower to tower.
[https://www.wired.com/2015/03/spencer-harding-the-long-
lines...](https://www.wired.com/2015/03/spencer-harding-the-long-lines/)

~~~
kbart
Microwave LoS is still widely used to connect cell towers for example. Look at
these circular dishes in this picture[1].

1\. [https://ssl.c.photoshelter.com/img-
get2/I0000JUzapOxgCs0/fit...](https://ssl.c.photoshelter.com/img-
get2/I0000JUzapOxgCs0/fit=1000x750/1127D-cellular-microwave-communications-
tower-antenna-array.jpg)

~~~
URSpider94
The microwave network is being resurrected between Chicago and NYC as a way to
shorten the communications time for high frequency traders. Even after
successively purchasing straighter and straighter rights of way for fiber, the
microwave path is still shorter.

------
my_first_acct
According to the local paper [1], from the top of Mount Diablo (east of SF
Bay) it is possible to see Mount Lassen (approx 260 km away). "Although you
can’t see Mount Shasta directly, you might be able to see part of the peak,
refracted by the atmosphere." (That would be 380 km).

[1] [http://www.mercurynews.com/2015/11/24/bay-area-facts-what-
ca...](http://www.mercurynews.com/2015/11/24/bay-area-facts-what-can-you-see-
from-the-top-of-mount-diablo/)

------
marceldegraaf
Vsauce had a video about this recently:
[https://www.youtube.com/watch?v=mxhxL1LzKww](https://www.youtube.com/watch?v=mxhxL1LzKww)

------
prawn
K2 incorrectly listed as being in New Zealand?

~~~
knz
Looks like it. Aoraki is ~3,700m and this website lists "K2" in NZ as 8,611m
(same altitude as the real K2 on Wikipedia -
[https://en.m.wikipedia.org/wiki/K2](https://en.m.wikipedia.org/wiki/K2)).

The Southern Alps _are_ growing rapidly but not that fast!

------
jmcqk6
There are places in oregon where you can look North and see Mount Adams in
washington, and look south and see Mount Shasta in california. So basically
the entire heigth of oregon. I've personally done this on Paulina Peak on
several occasions.

------
kovrik
Does this mean that there is no known place (point) on Earth from which you
can see some other point that is more than 538km away?

~~~
tristanj
Under certain atmospheric conditions it may be possible to see further

[https://en.wikipedia.org/wiki/Mirage#Superior_mirage](https://en.wikipedia.org/wiki/Mirage#Superior_mirage)

~~~
Nition
I wonder what the maximum you can ever see is due to atmosphereic fog. I
suspect it's less than 538km.

The site has photos listed for up to 381km, although the link for that one is
broken.

~~~
KozmoNau7
This one is the longest: [https://beyondhorizons.eu/2016/08/03/pic-de-
finestrelles-pic...](https://beyondhorizons.eu/2016/08/03/pic-de-finestrelles-
pic-gaspard-ecrins-443-km/)

Fog is definitely a factor.

------
a12jun
Surely the longest distance would be, from the top of the highest point on
Earth (top of Everest), to the horizon?

~~~
kazagistar
A mountain might be past the "natural" horizon but emerge from beyond it.
Thus, two mountains at the right distance and line of sight could easily have
a longer horizion distance.

~~~
tzs
And this is indeed the case for the ones at the top of the list. The longest
possible distance to horizon is a little over 330 km, but almost 40 of the
items on the list have longer line of site.

In fact, it looks like every item on the list is between two points that are
each farther away than the other's horizon.

That raises the question of among all places on Earth where the longest line
of sight is to the horizon, which has the longest line of sight?

~~~
jameshart
Hawaii would be where I'd start looking for that.

~~~
jcranmer
Mauna Kea is 4,207m above sea level and can definitely see the oceanic
horizon. Mount Wilhelm (4509m) and Puncak Jaya (4884m) are the highest peaks
in the central mountain range on the island of New Guinea, which makes the
ocean horizon probably visible from those peaks.

Western peaks in the Andes are perhaps 150-200km from the sea. A tall peak in
that portion could probably see the ocean. Chimborazo (6263m) is ~215km from
the sea as the crow flies, although there is a large valley ~100m above sea
level in the way.

I don't think Hawaii is the best bet.

------
vmarsy
Interesting, I'm not sure how the list was created, it seems to be missing
entries such as the one mentioned in that March 2015 comment at the end of the
post.

------
zeristor
So are there pictures of what a distant mountain actually looks like over
500km across the Earth; that is the point after all?

Or is there already a YouTube video of this?

~~~
newman8r
looks like someone posted this pic from the same site
[https://beyondhorizons.eu/2016/08/03/pic-de-finestrelles-
pic...](https://beyondhorizons.eu/2016/08/03/pic-de-finestrelles-pic-gaspard-
ecrins-443-km/)

------
amacbride
The Mount Hamilton to Half Dome in Yosemite (168 miles) is the view that blew
my mind when I first saw it.

[http://astronomy.snjr.net/blog/?p=416](http://astronomy.snjr.net/blog/?p=416)

------
amacbride
The Mount Hamilton to Yosemite view (168 miles), is the one that blew my mind
when I first saw it:

[http://astronomy.snjr.net/blog/?p=416](http://astronomy.snjr.net/blog/?p=416)

~~~
hodgesrm
Another good one is Mt. Diablo to Mt. Lassen, which is around 180 miles.
That's the longest one I have seen in California. Tom Stienstra claimed it's
180 miles, which is a long way. [1] Other sources claim somewhat shorter
distances.

[1] [http://www.sfgate.com/outdoors/article/Clear-viewing-from-
Mo...](http://www.sfgate.com/outdoors/article/Clear-viewing-from-Mount-
Diablo-5988343.php)

(Oops somebody already pointed it out!)

~~~
jackfoxy
Mt. Lassen, ha. If the atmospheric conditions are good enough you can see Mt.
Shasta from Mt.Diablo. I know, I have seen it. That has to be around 250 miles
(I don't have the exact figure). That would be 402 kilometers and worth a
mention on this list.

------
js8
OT: Is there an application that can generate panoramic view from some point
of Earth based on map and altitude data (e.g. OpenStreetMaps)?

~~~
rmc
FYI OSM doesn't (really) store elevation data. Individual mountain peaks are
often mapped, and tagged with the elevation. But OSM doesn't store land
contours like that.

There are some free, open, datasources for that, like SRTM[1], ASTER[2] (and
maybe OpenDEM[3], but I don't know what that's like)

[1]
[https://wiki.openstreetmap.org/wiki/SRTM](https://wiki.openstreetmap.org/wiki/SRTM)
[2]
[https://wiki.openstreetmap.org/wiki/ASTER](https://wiki.openstreetmap.org/wiki/ASTER)
[3] [http://www.opendem.info/](http://www.opendem.info/)

~~~
4ad
So how are these contour lines being generated?

My hike of a few months ago:

[https://www.gaiagps.com/datasummary/route/67dcc2001bea9e9e39...](https://www.gaiagps.com/datasummary/route/67dcc2001bea9e9e394fa45ca935ff9f/?layer=openhikingmapHD)

Also, if OSM doesn't store elevation data, then why do you need a GPS tracker
with a barometric sensor in order to map for OSM?

~~~
rmc
> So how are these contour lines being generated?

It depends on the people make the map.

That map uses Thunderforest's Outdoor style[1]. The person running that
company is a long time OSM contributor, but that isn't "from the OpenStreetMap
project". I suspect they are using SRTM data to generate countour lines _in
addition to_ OSM to create the map

> why do you need a GPS tracker with a barometric sensor in order to map for
> OSM?

You don't? You can map for OSM without needed a GPS tracker. You can just
trace things from the aerial imagery, or add local features from memory
("There's a post office at that road junction", "the speed limit of this road
is 40 kmph").

[1]
[https://www.thunderforest.com/maps/outdoors/](https://www.thunderforest.com/maps/outdoors/)

------
utoku
Reminds me of a habit I have which made me end up on tops of mountains
occasionally. I guess the algorithm can be called "observable ascent":

1\. Look around 2\. Find a relatively close high spot that is visible 3\. Plan
and climb on top of it 4\. From the peak, find the next highest spot visible
5\. Repeat

Also works for other topologies.

~~~
Scarblac
This fails in countries that are simply too flat (the Netherlands).

------
nprecup
You can see the sisters from Mt Adams, which is ~230 km away. I'm guessing
there are several more of these that the site didn't catch. You can probably
easily see Mt Rainier from 300 km+ standing at the right place. How were these
determined? It would cool to see a write up on how it was done.

~~~
jmcqk6
I know you can see Mount Rainier from Mary's Peak outside of Corvalais, which
is 295km away. And I mentioned it in another comment here, but standing on
paulina peak on a clear day, you can see both Mount Adams and Mount Shasta,
more than the entire height of Oregon.

------
analog31
I wonder if this is computable from a contour map of the earth, assuming
optimal atmospheric conditions.

~~~
dmurray
I think that's what the site is doing already.

------
dzdt
There are many more such pictures at [http://theviewshed.com/views-
list/](http://theviewshed.com/views-list/) including some that boast greater
distances than the original post.

------
mrb
And I thought seeing Mont Blanc from my town Le Creusot, France (a 216 km line
of sight) was very long... not! Apparently it would only rank 6th from the
bottom of this list!

~~~
runarberg
That is very nice. Here from Reykjavík, Iceland, you can see Snæfellsjökull on
a clear day (about 118 km away; featured in Jules Vernes’ “Journey to the
Center of the Earth”), and it seems very far away indeed. I can only imagine
216, or let alone 500+ km distances.

~~~
mrb
It was the silouhette (before sunrise) that I saw. It looked very much like
this: [https://beyondhorizons.eu/2016/08/03/pic-de-finestrelles-
pic...](https://beyondhorizons.eu/2016/08/03/pic-de-finestrelles-pic-gaspard-
ecrins-443-km/)

Edit: this is awesome, I managed to use
[http://www.udeuschle.selfhost.pro](http://www.udeuschle.selfhost.pro) to
simulate the view of Mont Blanc from my city: its exactly 215.2 km away:
[http://www.udeuschle.selfhost.pro/panoramas/panqueryfull.asp...](http://www.udeuschle.selfhost.pro/panoramas/panqueryfull.aspx?mode=newstandard&data=lon%3A4.44706%24%24%24lat%3A46.81081%24%24%24alt%3Aauto%24%24%24altcam%3A10%24%24%24hialt%3Afalse%24%24%24resolution%3A200%24%24%24azimut%3A119%24%24%24sweep%3A4%24%24%24leftbound%3A117%24%24%24rightbound%3A121%24%24%24split%3A6%24%24%24splitnr%3A1%24%24%24tilt%3Aauto%24%24%24tiltsplit%3Afalse%24%24%24elexagg%3A1.2%24%24%24range%3A300%24%24%24colorcoding%3Afalse%24%24%24colorcodinglimit%3A221%24%24%24title%3AZugspitze%24%24%24description%3A%24%24%24email%3A%24%24%24language%3Age%24%24%24screenwidth%3A1920%24%24%24screenheight%3A1080)

And as it turns out this is not the max line of sight, there is the
hypothetically visible Grandes Jorasses slightly to the left (221.5 km away).
You have to use the 10x zoom to see it:
[http://www.udeuschle.selfhost.pro/panoramas/panqueryfull.asp...](http://www.udeuschle.selfhost.pro/panoramas/panqueryfull.aspx?mode=newstandard&data=lon%3A4.44706%24%24%24lat%3A46.81081%24%24%24alt%3Aauto%24%24%24altcam%3A10%24%24%24hialt%3Afalse%24%24%24resolution%3A1600%24%24%24azimut%3A119.5%24%24%24sweep%3A5%24%24%24leftbound%3A116.99375%24%24%24rightbound%3A117.74375%24%24%24split%3A7.5%24%24%24splitnr%3A1%24%24%24tilt%3A0.13697916666666665%24%24%24tiltsplit%3Afalse%24%24%24elexagg%3A1.2%24%24%24range%3A300%24%24%24colorcoding%3Afalse%24%24%24colorcodinglimit%3A221%24%24%24title%3AZugspitze%20%5BFernglas%5D%24%24%24description%3A%24%24%24email%3A%24%24%24language%3Age%24%24%24screenwidth%3A1920%24%24%24screenheight%3A1080)

------
tomxor
And it's only from 5.971 m high... why people use decimals to indicate 3
orders of magnitude I will never understand... either that or they got the
wrong SI unit.

~~~
mauvehaus
Possibly because they're not (natively?) English-speaking Europeans:
[https://en.wikipedia.org/wiki/Decimal_mark#Digit_grouping](https://en.wikipedia.org/wiki/Decimal_mark#Digit_grouping)

------
foota
I'll make a tableau public viz with these when I get home

------
gwbas1c
I clicked on three pictures. Two are dead links.

