# What would a 1.5 km wide, 20 km tall spire look like?

In the middle of the North Atlantic is a black, hexagonal spire. It's 1.5 kilometers wide at the base, tapering to a mere 100 meters wide at the top. It rises 20 kilometers above sea level, and an unknown distance down (anchoring it to the crust). It's made of a magically strong material, is perfectly rigid, and does not sway in the breeze. It extends perfectly perpendicular to the surface.

I'm having trouble comprehending what this would look like to an observer on the ground, and so I have three main questions:

• Would you be able to see the top on a clear day?
• How far away would the structure be visible, and would it first stop being visible due to the horizon, or due to the atmosphere obscuring it?
• Are there any other interesting, readily-apparent effects caused by this tower? I imagine that, if it's in the Northern hemisphere, it'll act like an enormous sundial, but that's all I can think of.

Bonus question, but not required: Is there any known material that could even come close to withstanding the forces acting against a construction this large?

• "is perfectly rigid, and does not sway in the breeze" I'm afraid that would mean all this forces will be transmitted to the ground, cracking the rock and eventually dislodging your spire and making it fall. Jul 29 '20 at 9:32
• @DiegoSánchez More likely the tower just snaps Rigid means stiff, but not necessarily strong. Jul 29 '20 at 13:23
• why wouldn't it act as a sundial on the southern hemisphere?
– ths
Jul 29 '20 at 13:31
• @DiegoSánchez But OP only magically strong but perfectly rigid. Not that it was magically, perfectly strong. I think perfectly rigid beats out magically, but imperfectly, strong. Jul 29 '20 at 18:54
• Tourists would have cricked necks from looking at it. Jul 30 '20 at 2:53

If you were at sea level (e.g. on a boat), the tower would disappear over the horizon at approximately 505km away.

Horizon calculations are generally dealt with as simple right-angle triangles; a tower meets the horizon at $$d = \sqrt{t^2 + 2rt}$$, where $$t$$ is the tower height and $$r$$ is the radius of the earth.

According to this site, the visual acuity of the human eye is about 1/60 of a degree. That means at a distance of 500km you could distinguish something about 150m tall/wide or bigger. So you likely won't see the top of the tower (at 100m) at this distance.
Working backwards, if the tower were a constant 100m wide it seems you would cease to be able to make it out at $$d = x/(2\tan (1/120))$$, which is 344km. The tower is actually tapered so it would likely be a bit further than that, but the maths gets more complicated.

Let's say for now that ignoring the atmosphere, the distance you could see the tower with the naked eye would be somewhere between 350km and 400km. This also answers question one: yes, if you were underneath the tower you could see the top (20km away) if there was no atmospheric scattering.

It's hard to find hard data, but various sources suggest the best-case distance when considering atmospheric scattering is perhaps about 160km. This is sufficiently far that the difference between looking at the top of the tower and the part touching the horizon is negligible. At a distance of 160km, the bottom 2km of the tower would be below the horizon.

At 20km, the top of the tower is in the mid-stratosphere, above cloud layer and in amongst the ozone layer. It definitely could be obscured by clouds, but if the sky was clear I don't think the atmosphere itself would be a problem. I'm struggling to find much data on that. It would possibly depend on the time of day and how well-lit the tower was.
One thing that occurs to me though is that there may be permanent cloud cover (see next paragraph) which could mean the top of the tower is never visible from the ground.

I imagine the temperature differential between the top and bottom of the tower might make for some interesting effects (condensation? Permanent cloud cover? Perhaps it could be used as some kind of heat engine?). Similarly, it might provide a useful nesting surface for sea birds, shade for fish etc.

• For visibility, there will be a real world effect (reproduced in Minecraft, by the way). Just before the sunrise or after sunset, top of the tower will be illuminated by the Sun and stand out against the sky, visible from great distance - possibly even beyond 400 km. Jul 27 '20 at 18:20
• I can see mountains much more than 30 km distant, even though they're lower in the atmosphere. For instance, Mount Rainier is only seldom fully obscured by atmospheric haze as seen from Seattle, despite being close to 160 km away and less than 4 km tall. Jul 27 '20 at 19:22
• On a truly clear day you can see about 296 km en.wikipedia.org/wiki/…. Though practical averages are often less due to pollution and humidity. Jul 27 '20 at 20:18
• This also depends on contrast. I can see the ISS at a distance of 200km, but I have difficulties seeing a nearby chameleon Jul 28 '20 at 21:41
• I specified the longest photographed one as 443km for a reason: beyond-horizons.org/2016/08/03/… Jul 30 '20 at 8:38

Interesting side effect:

Astronomers would kill for a tower like this.

• Middle of the ocean is where you find lowest light pollution levels on Earth
• 20km up the atmosphere is rather thin further making telescopes work better
• The tower is absolutely rigid so long exposures can be done and stabilization is easy
• But how would astronomers get on top of such tower? For example, one had to be superhumanly fit to climb Korin Tower Jul 27 '20 at 18:24
• @Alexander Internal elevator? Staircase? Crane on the top? Even if it is indestructible, you can glue things to it, otherwise use suction cups. If that doesn't work, simply wrap a cable around the spire: since it's tapered, you can then use multiple cable wraps to attach an elevator to the exterior. Also, telescopes don't need to be permanently manned, and at 20k up, you probably need less maintaining because there's no birds, rain, or weather really. Jul 27 '20 at 18:33
• This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - From Review Jul 28 '20 at 0:42
• @sphennings it's a partial answer to: "Are there any other interesting, readily-apparent effects caused by this tower?" Jul 28 '20 at 5:10
• If you can get a rocket to the top, space missions would get a lot cheaper. Jul 29 '20 at 5:13

There would be a lot of local climate effects caused by the tower. One of the most visually dramatic would be clouds. It would likely have a cloud wake, the most dramatic of which are Von Kármán Vortices.

Cloud wakes are caused in real life by islands, and your tower is comparable to an island at the base.

• A likely side effect of this is that pilots will really not want to fly downwind of the tower, due to the turbulence it would cause. Jul 30 '20 at 22:11

Clearly it's going to be visible from extreme distances. You can see the Shard in London, or the Burj Kalifa in Dubai long, long before you can see anything at ground level around them, and from some places you can see the tower appearing to rise out of nothingness.

Obviously whenever there is a cloud base the top will disappear, as happens with many skyscrapers (eg the Shard) on a regular basis.

Depending on the smoothness if its sides, it will become a habitat for assorted wildlife from weeds and shellfish upwards. It may acquire it's own ecosystem.

Condensation from clouds etc running down the side might be a useful source of fresh water for birds or seafarers. It is unlikely to remain its original color for long and unless it si perfectly smooth plant life will get hold, birds will cling to it etc. It's a pretty decent-sized island, it just lacks horizontal surfaces until it has some growth.

EDIT: At with some skyscrapers, you will get an interesting situation at sunset and dawn where the base of the tower is still it darkness but the upper section is illuminated by the sun. This tower will be an extreme case: depending on how well it reflects, it may look like a bright red star or second sun well above the horizon.

• "Obviously whenever there is a cloud base the top will disappear" .. I did not think of that at all !! Jul 28 '20 at 12:48
• Considering the base, I wouldn't be surprised if material started to accrue near the base, leading to the rising of the sea floor, maybe enough to create shallows or an island. Considering that this place is far from anything else this ecosystem would likely be unique. Jul 28 '20 at 16:25

One thing that no one has yet picked up on is the requirement that the tower be perfectly rigid. Such a material is fantastical indeed because it has a very important property - it violates the theory of relativity.

A perfectly rigid material must have an infinite speed of sound. If it did not, then it would take some time for the sound of a bird hitting the bottom to reach the top. In fact quite a bit of time, since it's 20km tall. Physically this would manifest as a compression of only part of the structure, which is by definition a violation of it being rigid - you cannot compress part of the structure and not others.

So this thing would be very, very strange indeed. For one thing, any vibration of the object is automatically felt throughout the entire structure, immediately. You aren't allowed to say that it doesn't vibrate, because it's attached to the crust and the crust most definitely does, so it would act as a microphone to the insides of the Earth.

There is another issue, though. I didn't say that the speed of sound was "very fast", I said it was infinite. This is beyond "faster than light" to literally "there is no finite number to describe it". As one consequence you could use it for time travel experiments, since objects further from the earth's surface experience different time dilation compare to objects at the top, albeit on the order of nanoseconds.

• This is one reason that a completely rigid substance cannot physically exist: it violates the speed of light. Jul 30 '20 at 2:55

Would you be able to see the top on a clear day?

Sure. On a clear night we can see the ISS.

How far away would the structure be visible, and would it first stop being visible due to the horizon, or due to the atmosphere obscuring it?

K. Morgan already mathed this out.

Are there any other interesting, readily-apparent effects caused by this tower? I imagine that, if it's in the Northern hemisphere, it'll act like an enormous sundial, but that's all I can think of.

Time dilation. Time will pass differently on the top and the bottom of the tower, due to relativity (the top has greater linear velocity than the bottom, considering Earth's rotation). This actually happens to everything, even our bodies, but on a structure that tall the effect would be easily measurable with modern clocks.

Bonus question, but not required: Is there any known material that could even come close to withstanding the forces acting against a construction this large?

No. That's why mountains won't go higher than the Everest on Earth. Not even them withstand such forces easily.

• The last point seems to assume that there is no stronger material than what mountains are made of, I doubt that's true.
– Mark
Jul 28 '20 at 10:26
• (Still it's a big step from '<9000m mountain with wide base' to '20.000 in a narrow spike' so the answer is still no)
– Mark
Jul 28 '20 at 10:28
• "Sure. On a clear night we can see the ISS." - But since we look upwards, the atmospheric reduction or distortion is reduced. Even if you look at something just 10° over the horizon, the light have to traverse a much less dense layer of atmoshere from something that it 500 km away in the horizon. Jul 28 '20 at 14:20
• Just a note: time dilation in a 20 km tall tower is completely negligible for practically any purpose. Sure, it's measurable, but only because modern clocks are ridiculously precise. In fact it's already measurable even on much smaller differences in altitude, such as 33 cm in this 10-year old article. Jul 28 '20 at 20:19
• "the effect would be easily measurable with modern clocks." For broad very definitions of "easily measurable" and "modern clocks". Jul 29 '20 at 5:15

Bonus question, but not required: Is there any known material that could even come close to withstanding the forces acting against a construction this large?

One important property here is breaking length (see https://en.wikipedia.org/wiki/Specific_strength), the distance after which a material will break under its own force of gravity. For steel this is under 7km, so it is unsuited for building such a tower. But there are a number of metal alloys (mostly aluminium and titanium) that have breaking length beyond 20km and many carbon composite materials have breaking lengths in the dozens of kilometers. You could build your spire out of these and they would at least withstand gravity.

Harder to answer is how they'd have to be built to withstand the forces of wind and whether the continental plate below the tower can withstand its enormous weight. I fear that the mass of the spire will crush the rock its built on and cause it to start sinking. This is one of the factors that limits the height of mountains here on Earth, see this answer on earthscience.stackexchange: https://earthscience.stackexchange.com/questions/9745/how-high-can-a-mountain-possibly-get, which reasons that the maximal height of a mountain on Earth is roughly 10km.

To counteract this, you'd need a gigantic base that spreads out under the spire's foot and distributes the force to the point the pressure is below the compressive strength of rock.

• "you'd need a gigantic base" - and/or a mostly hollow tower, I suspect Jul 29 '20 at 0:18
• its towers all the way down
– Ewan
Jul 29 '20 at 15:51
• Your explanation of breaking length isn't quite correct. That applies to structures loaded in tension, which is computationally straightforward, basically just distributing force over a cross-section. That would only apply to a “tower” that's not standing on the ground but hanging from the top somehow. A actual tower is instead loaded under compression. Most materials are in principle stronger under compression than under tension, but unfortunately you get a whole bunch of buckling problems that the tensile situation doesn't have to deal with. Jul 30 '20 at 11:00

From even modest distances, it would appear to be slightly leaning away from the viewer.

The difference in the directions of "vertical" at largish distances apart on the globe would be noticable to the unaided eye.

• The top would be a 100 m object at 20,000 m distance. That should make it difficult to observe many details from a ship near the base, or even to judge if there is a top or if that is a distorted perception. Take a broomstick and peer along the length, can you really tell if the other end is round or flat?
• The horizon distance, as mentioned by James in his comment, is 500 km away. Take that broomstick again, glue a cent on top, and then observe it from 50 m away. Can you make the cent out?
• Concerning haze, the Rafale fighter has an optical sensor with 40 km identification range against other aircraft. So an instrument like that should be able to identify a fighter-sized object standing near the rim of the top, some 30-40 km from the base. At that angle, objects standing near the rim are visible.
• These points are valid, but to clarify: A 100m object from 20km appears roughly half as large (0.28°) as the moon (~0.5°). In general this is well observable by eye, let alone a telescope. With the tower being black and obscured by clouds the discussion is different, but in general 100m from 20km is not tiny. Jul 28 '20 at 14:08

Would you be able to see the top on a clear day?

The air pressure at a height of 20km is about 60mBar. Air pressure is proportional to the amount of air above it (because it's the weight of the air above that produces the pressure).

An observer at sea level will need to look through the air below to the top of the spire, and see it behind a background of the air above the spire. This is a 94% to 6% ratio. There is roughly 16 times more air between the top of the spire and the observer than there is behind the spire top.

Why is this important?

Well, when you look at the sky, the blue stuff, that's the air. And if you look at 94% of air, that's almost the same as if you look at 100% of air. The spire is black, as is the space behind the atmosphere. The only visible contrast that the spire has, is those 6% of air behind it that scatter the sunlight. And you look at it through a layer of air that's about 16 times as bright as the background.

As such, you'll be able to see the spire all right. But the further up you follow its shape with your eyes, the fainter the black becomes until you can hardly make out a slight shadow in the blueness of the sky.

• During the day the sun will illuminate the spire, so it will stand out as lighter than the sky around it. Unless the sun is on the other side of the spire, and assuming it is not magically perfect black such that it doesn't reflect any light. Note that the moon is actually black (it has the reflectivity of charcoal), but the reflected sunlight is still enough for it to be visible during the day. Jul 30 '20 at 13:17
• @JanKanis The spire is supposed to be black. And an imperfect black is even worse for visibility than a perfect black: It's brightness would be even closer to the 6% blue sky. Jul 30 '20 at 14:03
• The moon's surface is also black, but common black materials still reflect a few percent of incoming light. The few percent sunlight that is reflected by the moon still makes it much brighter than the blackness of space. The illuminated part of the top of the spire will show as white. Jul 30 '20 at 14:44
• @JanKanis The moon still reflects 13.6% of the incident light, that's far from black. A dark grey, yes, but nowhere near black. And even the moon is not visible when the sun is high in the sky. Jul 30 '20 at 14:49
• Even a reflectance of 1% of the incident sunlight would be brighter than the sunlight dispersed by 6% of the atmosphere. Jul 30 '20 at 16:54

Viewing distance: on a clear day it might be up to 150km away, especially the top part which is above most of the dirt and haze in the atmosphere.

On normal days it will be rather 30km to 60km.

The detail you can make out is directly depending on the lens size you are using. You cannot, under no circumstances see the Apollo landing sites on the moon with naked eyes. With a rather big telescope, you can. The size of the lens that you need is calculable.

On a boat, with your eyes, you will have difficulties seeing the top. With a handheld telescope, it might still be difficult. At least it is principally possible. If your boat has an installed telescope with an electronic control for all the movement, it will become easy.

You can't see from below if there is a platform or something else, because of your perspective. You can't even see what's on your neighbours flat roof if he has three or four stories.

## It wouldn't look all that tall

Seriously!

If you visit Dubai and wander around and look at the Burj Khalifa building. Since it tapers and you have no frame of reference it looks maybe 2x times bigger than those around it.

It is not until you are way out in the desert and you can see it beside the other 'normal' sized buildings around it that you see it is towers 6-8x times taller than anything else.

Your structure would be similar only there are no other buildings around to gauge it by. So it would just look like a moderately tall spike shaped building in the distance.

Perhaps with a little snow and ice shading near the top half.

You'd only see the top on a very clear day Take a look at where the top (20km) would sit in the stratosphere, in relation to even the tallest clouds:

Its way above the tops of thunder heads! But don't worry, there will be lots of clear days here, because it's safe to say that this thing would act as a giant grounding rod for any storm in the area. It would probably de-ionize the air so much that thunderstorms wouldn't be able to occur anywhere for around 20km from the spire, and depending on the material, it could be so grounded that it literally saps all the particulates out of the air (making the tower very very dusty) and preventing the formation of clouds. So, any clouds that do form within 100km of the tower would eerily drift always to the tower (because of the negative ionic attraction), just to always wisp away and disappear within kilometers of the spire. Would make for a very good "north star" idea, but yknow, "north atlantic spire" instead of a star.

Also look at where it exists in our atmosphere:

More than half of this tower would be -55C ! The cold temperatures would propogate down the tower (assuming it's a good heat conductor) and cause condensation at lower levels (because the atlantic ocean air is very moist), so there would always be water trickling down the sides, starting at around 5km high. It'd be a very cool waterfall in the middle of the atlantic.

Given that the air here would be very clean/pure, that every day was nice and balmy, and that the tower itself was a source of pure water, it probably is a great place to live or even take a vacation.

Can We Build It?

Unfortunately, no, with today's technology there is no way to make a tower that could be this tall. As an engineer, I could show the mathematics as to why we couldn't but I'll simplify it to this: Because the earth rotates, the bottom of the tower moves slower through space than the top of the tower. Thus, this is the same effect as placing a stick in the dirt, then grabbing the top and bending the stick. We don't have any materials in existance that are both strong enough to be built tall and flexible enough to withstand the forces of bending.