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In a world I'm constructing the sun, the moon, and the stars are not visible but there are tower that stretch from the ground to, roughly, low earth orbit. Each one is around 200 meters in diameter with a unique design (colors, materials, decorations, etc). Over an area the size of Europe there are maybe 12 or so of these towers spread out randomly so they are quite sparse. The people of my world did not build these and are actually at roughly the late middle ages in terms of technology (basically your standard fantasy technology level).

I want to figure out how people in my world navigate across large distances over both sea and land. My idea was that the towers would be used as guides instead of the sun and stars but I don't think people would be able to see them at large distances. Maybe making them glow would work but since people live near them I'd rather not blind anyone who looks at one up close.

Question: How do I modify my very very very tall towers so that people of a standard fantasy world can use them for navigation? Bonus points if your solution makes the towers look cool(er).

Solutions may use any form of technology or magic as long as it is a property of the towers not the inhabitants of the world, who are normal humans.

Edit: To address how the planet is actually lit up, the thing that blocks the sun and the stars is pretty much a Dyson sphere. The entire inside of it glows uniformly during the day and it turns of at night.

Note: All other problems caused by there being no sun or how the towers stay together have been solved through generous applications of sufficiently advanced technology and are out of scope of this question

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    $\begingroup$ The Sun is not visible. So there is perpetual darkness? How do plants get their energy, and how does the planet not freeze? Or does sunlight get through, just so diffused that the position of the Sun is not easily identifiable (like in a permanent very dense fog)? $\endgroup$ – vsz Nov 23 '18 at 5:17
  • $\begingroup$ @vsz Thank you for asking, forgot to include that. Will edit it in. $\endgroup$ – Diasiare Nov 23 '18 at 8:05
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The function of the towers is easily solved by turning them into lighthouses where the light is emitted at or within the cloud line. Perhaps the towers were intelligently designed to accomodate the cloud cover such that the illumination is always 200 meters or so below the cloudline.

Your real problem is visibility. Assuming nothing else is impeding your view, Mt. Everest (~9 km above sea level) could be seen from approximately 370 Km away. If you're standing on a beach, the horizon is only 5 Km away. Now, your towers go up a long, long away, but you can't see them from just anywhere, meaning your count of towers might be very low to make this practical — especially if there are things like mountain ranges in the way.

Here's the equation for an unobstructed (that's really important) view to an object on the horizon on Earth (that's somewhat important) from Wikipedia

$$d \approx 3.57\sqrt{h}$$

where d is in kilometres and h is height above ground level in metres. The constant 3.57 has units of km/m½.

You do not identify the height of the cloud cover. The height of the towers from the perspective of this question is irrelevant. They need only be as tall as the bottom of the cloud cover. Clouds can be, generally, 2 Km to 6 Km above sea level (Source). But, to make it easy, let's assume the bottom of the clouds is really high, almost the height of Everest, such that your maximum sighting is 200 Km away.

  • If your people have no better navigation than to look at the towers, they need to average 400 Km apart.

  • If your people have better navigation, perhaps they could average 1,000 Km apart. The U.S. is about 4,300 Km in width. So you'd have 4 towers across that distance and the need to use a good compass and potentially a clock.

but what about the cool factor?

My vote is to have the towers emit a regular pulse just beneath the cloud line, so that the light travels outward from the tower in an expanding ring, illuminating the clouds. That pulse could travel, say, 400–500 Km (the distance really depends on how easy you want navigation to be in your story) and the pulse can be a specific color or pattern, distinguishing each tower.

The regularity of the pulse would be useful, too, since the pulses from two towers would only meet at the same moment when you are exactly half-way between the two towers. Thus, by measuring the difference in time between the two pulses, you can reasonably estimate where you are between the two towers (or three, or ten, depending on the maximum range you set for the pulses in your story. A simple ground-based GPS system.)

Of course, that previous paragraph assumes the towers are evenly spaced. But even if they are not, it's just a bit of math to achieve the very same effect. This would lend to the idea of a navigator's guild where the secrets of that math are closely protected.

Just keep those navigators away from the spice.

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    $\begingroup$ Fantastic idea to use pulses, both practical and visual. $\endgroup$ – Diasiare Nov 23 '18 at 10:41
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    $\begingroup$ “Thus, by measuring the difference in time between the two pulses, you can reasonably estimate where you are between the two towers” Requires a detector+clock with nanosecond accuracy. Maybe if both towers emit at precisely the same frequency and are perfectly phase-aligned you could use interference. $\endgroup$ – Michael Nov 23 '18 at 11:27
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    $\begingroup$ +1: I Love this! For Rule of cool Have the pulse go from bottom to top, (you could have the pulse take one hour to reach the top, it might sound like a long time but it's really tall so pulse the is traveling quite fast), then it starts again from the bottom. Each tower now becomes an hour clock. With regular cloud cover the pulse will pass pretty quickly, but you get people reminiscing that "The sky was so clear we could see the pulse all night long". $\endgroup$ – Binary Worrier Nov 23 '18 at 13:30
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    $\begingroup$ Actually, irregular towers would make the navigator's guild even more necessary. You'd need an accurate map of the towers and their patterns for maths to even start being useful. $\endgroup$ – Matthieu M. Nov 23 '18 at 14:13
  • $\begingroup$ If this is the solution, you might take into account just how bright the towers are and the effect on the immediate vicinity. If a pulse is bright enough to show a significant lighting on the underside of clouds... that's very bright. Also, while you could use the towers for dead reckoning, without an accurate clock that's all they can really provide you at that level of technology - pulse or not. $\endgroup$ – Nathaniel Ford Nov 23 '18 at 22:12
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The towers are like a benevolent Eye of Sauron.

  1. Some humans have a palantir compass. These artefacts are incredibly valuable and hard to come by. When you look into them there is a pointer pointing to the nearest Eye.

  2. As above but each Eye has a name. You speak the name into the palantir as you peer into it.

  3. Using mind-waves an Eye detects when a human is searching it out. It projects a pulsing multi-coloured narrow beam of light directly towards the person making sure that the intensity is adjusted to the distance and the visibility to make it safe. If the person is nearby the light comes from low down. If they are over the horizon, the light comes from further up. If they are very far away the light may come from the top of the tower and appear like a bright star in the sky but flashing different colours.

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I remember looking into something similar with landmarks when I was working on my Thesis Topic. This is a simple localisation problem. As long as you can see Two landmarks and know your previous position, you can estimate where you are (assuming the landmarks aren't right next to each other).

I can't put any equations or diagrams in as I'm at work, but here is the basic gist of it.

Firstly you need to know the height or size of each tower. Depending on how high the tower appears to you, you can determine how far away you are from a single tower (or landmark).

This creates a circle around the landmark where you can be. If you can see two circles (draw two intersecting circles on a piece of paper) then you can pin your location down to two different points. In the best case scenario, the circles only meet once and you know where you are. In a normal scenario, the circles meet twice. Using your previous location, you can then determine where this is (as long as the landmarks are far apart so the intersections are clearly identifiable). The worst case, is that you have incorrectly Identified a tower and the circles don't intersect at all (or the landmarks are right next to each other and they intersect the whole time).

With 3 or more landmarks you will always be able to locate yourself. This is similar to the way GPS works, where you will need roughly 3 satellites. The more landmarks, the more accurately you can determine your position (Due to uncertainty, its not like a nicely drawn circle, but more like a blurry circle drawn with a sharpie).

Now the biggest issue in this case is if you only have 1 or no landmarks, but since your towers are so tall, I dont think this will be an issue. You can many different forms of landmarks as well. Unique coastal formations, Villages or islands. Ships which only operate in a certain area.

As a Note: The position of the sun can also serve as a landmark. While its not good for measuring distances, it does allow you to use it as extra information with a tower, Aka you could figure out the relative positioning and your logical position as a result, and it will help you identify the orientation of the tower which further lets you narrow down your position. (E.g. if there is a door on the front of the tower, and I can see the door, I must be infront of the tower). This can be combined with the land around the tower (the coast) and should also lets you pinpoint your location based on the distance from the tower and the orientation of the landscape that you can see.

So ideally, with just 1 tower in sight, you should be able to determine your rough location (assuming the towers are different from each other in either shape, height or surrounding terrain)

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    $\begingroup$ "The position of the sun can also serve as a landmark" yeah but the question says the sun is not visible. $\endgroup$ – Renan Nov 23 '18 at 10:19
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People were navigating before GPS, by using mountains as directional beacons, or following coasts, rivers and mountain ranges.

If people in your world can climb a tower, they can plan their journey, e.g. by realizing that they can get to the next tower by following that one river, and then going left at river's fork.

Alternatively, if the benevolent ancients have anticipated this problem, they could have put a powerful laser on top of the tower, to shine a concentric grid on the clouds around the tower. Or just to have a light spot moving through the clouds towards the tower.

Finally, if the beacon (or the sun) is above the clouds, you can use a certain natural stone that acts as a polarizing filter to find direction to actual light source, and thus navigate: https://en.wikipedia.org/wiki/Sunstone_(medieval)

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Each tower is a pole of a giant magnet, as strong as the dipole within the Earth's core.

Compasses will point to (or away from) the nearest tower. A little triangulation tells you where the towers are. Couple it with known landmarks and you have a quite descent positioning system that peopoe in mefieval ages can use.

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Part of the answer to this has to be determined by what you define as 'large distances' but Low Earth Orbit is pretty high; anything between 160 - 2000km. Your original idea of using triangulation on the towers would probably work in the Mediterranean at least. But, unless there are even more towers interspersed around the globe, they're unlikely to help you around the Cape of Good Hope, for example.

That said, there is actually a research paper on the coverage of low earth orbit satellites that looks at the problem from the opposite direction, but could be useful. My advice? Read the paper in detail, reverse engineer the coverage angles to show where on the earth you should still be able to see the top of the tower, then subtract 50% for atmospheric visibility, potential cloud cover, need to see at least 2 towers, etc. then distribute your towers on the surface of your planet accordingly.

It's actually a pretty neat idea - an optical, low tech version of GPS. The other advantage is that your fantasy world inhabitants may get to space earlier than we did because they learn to use the towers as space elevators, eliminating the need for 1, possibly 2 stages of your regular Saturn V rocket in order to get to the moon, just from launching from the top of one of these towers.

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I can think of one clever solution. Breed lots of ravens (e.g. Game of Thrones) in the easternmost tower and wrap a silver wire around one leg, so that they can only get food from that one tower. If they fly to one of the 11 other towers they get no food. Then caravan leaders and ship captains can purchase some of those ravens for their journeys and watch which direction they fly when released. Most likely that would be the eastern tower. Repeat the process for Southern Tower ravens with gold wires on their legs. Once you have two vectors you can figure out where you are on the global map. Some super smart but expensive ravens can be trained to selectively fly to any of the 12 towers but then return to the caravan after one hour if they haven't been fed enough to make that journey, so this way the caravan navigator can watch one raven's flight direction back and forth towards selective towers for a few hours to make sure the caravan is heading in the right direction.

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Make them some kind of lighthouses, but instead of just emitting light they start some kind of energy pulse in regular intervals, causing something like aurora polaris.

Those energy pulses could travel much slower than light, so you could actually see the rings getting bigger and bigger. Over the distance the light would change color/intensity so you could estimate the distance to the next tower and you will clearly see where the pulse is coming from.

Also this solves the issue with clouds/mountains obstructing view, as you only need some free sky above you to navigate and there is no issue of the signals traveling below the clouds.

Maybe you want mountains slowing down the signal, creating a nice effect of not perfectly round signals - creating additional information for navigation.

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