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Brief setting notes: it's a "basically earth" type situation, a spinning ball of rock in space with the same size and gravity and atmosphere and magnetic fields and everything else.

The main difference is that there is also a HUGE dungeon-cave system across the continent. No one knows how deep it goes, or how extensive it is. People have been exploring it for hundreds of years, using it for travel and trade, towns have been built around the entrances, and decent amounts of society and industry are built around it. But because of how large it is, and how inherently difficult it is to navigate in caves, only tiny fractions of it have been mapped, and what lies in the deepest depths is largely unknown.

Things are about at a 1890s level of technology, and many people are all trying to solve the problem of underground navigation. When you're travelling underground for weeks and months at a time, knowing where you are can get almost impossible. Compasses help, but they only do so much, and there's no sun or stars to help determine latitude, to say nothing of longitude or altitude (which is often what people really want to know, no use in bragging about how you've been deeper than any other explorer if you don't know how deep you actually are.)

So, given the technology that would realistically exist at about this time, is there some sort of surveying method or mechanism, portable and handy enough to be carried with the average explorer, which lets them know exactly where they are in terms of longitude, latitude, and altitude?

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    $\begingroup$ Does anything prevent inferring altitude from air pressure? $\endgroup$ – Patricia Shanahan Mar 21 at 3:45
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    $\begingroup$ You can't do it WITH modern electronics, if by that you mean GPS &c. You might be able to build a sufficiently accurate inertial navigation system with modern solid-state accelerometer chips: analog.com/en/analog-dialogue/articles/… $\endgroup$ – jamesqf Mar 21 at 4:13
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    $\begingroup$ After thinking about it... Why would they want to know these things? This subterranean civilization would live in a network of connected tunnels. They would navigate the topology of that network, not the topology of a spherical surface. Depth might still have some relevance if not for navigation but latitude and longitude would be fairly irrelevant. The concepts might even be familiar to only few mathematicians. $\endgroup$ – Ville Niemi Mar 21 at 4:43
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    $\begingroup$ @VilleNiemi they don't live in them, they just travel through them a lot, like how there's shipping routes on the ocean but very few people actually live permanently at sea $\endgroup$ – possiblySerious Mar 21 at 14:18
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    $\begingroup$ People have been exploring for hundreds of years and haven't put up any road signs down there? $\endgroup$ – DSKekaha Mar 23 at 16:30

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Altitude (or depth) can be measured with a barometer.

Latitude is doable, but tricky. Two methods come to mind, but they require staying on one spot for rather a long time to make accurate measurements.

The first option is to use a Foucault pendulum. The rate of precession of such a pendulum is directly related to latitude; the pendulum conveniently serves as its own timekeeping device, so you don't even need a pocket watch to go with it. A protractor and a single-sheet conversion table would be sufficient. You just have to hang around in one spot long enough to get an accurate measure of the precession rate, which would take several hours at least, and while it could be packed down quite compactly for transport, the device would be rather tricky to set up.

The second option is to use a gyroscope. This would be slightly past the level of technology that gave us pocket watches for measuring longitude on Earth, to be able to use spring-driven clockwork to keep the thing spinning long enough, and on sufficiently free bearings. The basic idea is to start the gyroscope spinning, and then observe its apparent axis of precession over a significant portion of a day; the gyroscope will maintain a constant orientation in space while it is transported along by the rotation of the planet. The precession axis is parallel to the axis of the planet, and the angle it makes with the direction of gravity tells you your latitude. It is a good idea to run at least two gyroscopes in parallel, at ninety degrees to each other, to get a better reading, although with sufficient development it is possible to build damped gyroscopes which will naturally align themselves with the precession axis, making taking a reading much easier. Unlike a Foucault pendulum, a gyroscopic device will also indicate north and south--hence the name gyrocompass.

Longitude is much harder. Pocket watches don't do anything for you if you can't measure local solar time. Odometers could be used to assist with dead reckoning. Compasses might actually be useful in this regard as well; if you can establish a depth, latitude, and orientation to true north with a barometer and gyrocompass, and have a detailed magnetic declination map developed on the surface, you could simply consult the table of magnetic declinations along your line of latitude to narrow down options that match your magnetic compass reading.

With a combination of pocket watch and really good gyrocompass, however, you can do better. To make this work, you will need an extremely accurate gyrocompass set rotating at a known position (say, when you enter the dungeon system) exactly perpendicular to the planetary axis. If you were to stay in one place, it would appear to rotate at a known rate as the planet spins, making one full rotation every day, so you can compare its actual rotation with that predicted by your pocket watch. If you stay in one spot, they will match exactly--but if you move east or west, they won't. The difference in the actual position of your gyrocompass at any point from that predicted by the pocket watch will indicate transport around the planet's axis farther or lesser than would be accomplished by the planet's own rotation--and thus, indicates how far you have traveled across the planet yourself. Essentially, the gyrocompass replaces the sun as your indicator of local time, to compare with time at your starting point as indicated by the pocket watch--with slight differences in time-interval-to-longitude conversions since the position of the sun tracks, well, solar time, while a gyrocompass tracks sidereal time.

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    $\begingroup$ A dipping needle combined with a plumb bob is a better choice than a Foucault s pendulum. Much lighter, more portable and no setup or configuration (en.wikipedia.org/wiki/Magnetic_dip) $\endgroup$ – RBarryYoung Mar 21 at 16:54
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    $\begingroup$ @LoganR.Kearsley the OP says compasses are available. $\endgroup$ – Ryan_L Mar 21 at 17:39
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    $\begingroup$ Measuring depth with a barometer won't be accurate over time, as the atmospheric pressure varies. That's why airports broadcast the current pressure, and aircraft altimeters have an adjustment so pilots can set them correctly - the small window pointing to 29.9 in the first picture here: en.wikipedia.org/wiki/Altimeter $\endgroup$ – jamesqf Mar 21 at 17:48
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    $\begingroup$ @jamesqf Like the pendulum or gyrocompass, measuring depth with a barometer will work over time. Yes, atmospheric pressure varies, but over time those variations will average out. Aircraft altimeters have an adjustment, but they adjust for current conditions, not long-term trends. Barographs (recording barometers) have been available since the 1840's, with the earliest design from the 1760's. Put one next to the Foucault pendulum, and let it record for a few months. $\endgroup$ – Buddha Buck Mar 21 at 22:05
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    $\begingroup$ @Buddha Buck: That should work ok for measurement at a particular point, but I thought the idea was for the explorers to have something they could carry with them as they travel. Also, it doesn't consider pressure changes due to the caves themselves. The few I've looked at often have wind blowing in/out due to pressure differences. $\endgroup$ – jamesqf Mar 22 at 2:48
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People on the surface or at established underground settlements could set up "thumpers" which are massive weights that are raised and then dropped great heights according to a predetermined time schedule. With an exact enough seismograph (paper and pen), cave explorers could triangulate with a good clock and regular "thumps" happening around them.

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    $\begingroup$ Also, keeps away ant-lions... $\endgroup$ – Harper - Reinstate Monica Mar 22 at 22:53
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    $\begingroup$ @Harper-ReinstateMonica Attracts thresher maws though $\endgroup$ – DKNguyen Mar 23 at 1:29
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    $\begingroup$ I don't think it is a good idea because it can put nearby caves under a danger of collapse. I would rather think about something similar instead like infrasonic signals or other source of seismic signals that are not any powerful thrust into the ground $\endgroup$ – mpasko256 Mar 23 at 15:18
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    $\begingroup$ @mpasko256 any caves that haven't collapsed a long time ago wouldn't be collapsed by some man-made thumping, but true, it still is a risk $\endgroup$ – Dragongeek Mar 23 at 15:23
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    $\begingroup$ @Dragongeek Yes, you are right, especially in places where earthquakes are very common. But in a places where they are rare, the thumping generated regularly for a long period a time can cause risk even if it is only man made. I'm not only talking about total collapse. Simply falling large pieces of rock can put random travelers into danger. $\endgroup$ – mpasko256 Mar 23 at 16:25
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is there some sort of surveying method or mechanism, portable and handy enough to be carried with the average explorer, which lets them know exactly where they are in terms of longitude, latitude, and altitude?

I am afraid that, if you can't rely on stars to determine your position and you really want/need to know it, you will be forced to constantly use a theodolite to triangulate your position with respect to some known location.

Your entrance point will be the one having coordinates measured with respect to the stars, and from that on you will proceed by marking and measuring successive points.

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For quick and easy reference? No. For slow and methodical surveying? Yes.

You could have markers in the form of rods painted with alternating bands of colors and use something similar to a theodolite to measure compass bearing, angle of inclination from point to point.

With a stadiametric rangefinder integrated into the theodolite scope, you could calculate the distance to the rod marker based on what size its image appears compared to the etched lines on the scope.

This way, you could map out the cave painstakingly point to point, calculating position with trigonometry. Marking paths with markers, etc.

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While I don't think this is the best explanation for how to determine position, I think it's a worthwhile idea and I'm putting it out as a suggestion.

If it's really important that your explorers be able to work out their location underground for the plot of the story, you could build in some regular-period known seismic wave sources that let you triangulate your location.

These could be set up by governments or explorers' associations or whatever – large beacons that emit a regular pulse of low-frequency seismic compression through the Earth. That way, you can triangulate your position by looking at a sensitive seismograph. Here's how it works:

  1. You set up the seismograph and watch the path traced by the needle
  2. The needle swings up and down in regular seismic waves. You record the time interval between two consecutive waves and the height of each wave: enter image description here

    Above, there are two waves visible, one with period T1 and one with period T2.

  3. You look up the time period of each wave in an index table. The table contains data specifying the intensity of each wave at its source, as well as the geographical position of the sources.
  4. You compare the intensity of each wave with its source intensity. From the amount by which the intensity of the wave has decreased, you can calculate how far it has traveled. Once you know how far you are from 4 or more sources, you can calculate your exact position in 3 dimensions relative to the sources.
  5. Using the known locations of the sources, you can then calculate your coordinates using trigonometry.

Yes, this requires a lot of setup. But since this technology would be difficult to acquire in the far distant past, it could be a useful way of explaining why it is only recently that explorers are able to navigate very deep below the surface. This means that there's a lot of unexplored, but explorable, territory.

Essentially, humans were unable to navigate the cave systems for a long time until these beacons were set up. Now, caving is much safer and more profitable, and explorers are able to go to depths previously thought to be unreachable, because the beacons allow precise navigation.

Also, the signals get weaker farther away from the surface. So beneath a certain depth you have to keep coming back up to get a reliable signal. As long as the cave systems are connected by the same body of air, you should be able to work out depth using a barometer, so that would be possible.

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    $\begingroup$ Basically how GPS works if I'm not mistaken. But instead of having satellites send signals, you send signals with seismic activity. Not sure how technically viable this is but it seems like a very usable solution if it works. $\endgroup$ – Deruijter Mar 23 at 9:27
  • $\begingroup$ Except that the speed of EM waves from GPS are only slightly affected by the medium they traverse (mostly air at increasing pressure from space to earth surface). The compensation for these speed variations is well known. Sonic waves on the other hands can have speed varying from several order of magnitude when it crosses different medium. You would need to know the exact composition of all the rocks above your tunnels to be able to position yourself accurately. $\endgroup$ – Hoki Mar 24 at 12:29
  • $\begingroup$ @Hoki absolutely there is a source of inaccuracy there, but with more than one source you can get probably the same amount of precision and any handheld gyroscopic precession method. And of course, the speed of EM waves is significantly reduced when they try to pass through kilometers of rock. $\endgroup$ – Adrian Hall Mar 25 at 7:10
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All of those would be affected by limited precision, but still workable:

  • Latitude - by the direction of the magnetic vertical component of Earth's magnetic field. That would require some well balanced magnetic needle and knowledge about the magnetic ore deposits (one may map them on the surface).

  • Altitude by air pressure. First order correction based on the latitude, to account for the varying thickness of the atmosphere due to Earth's rotation

  • Longitude - that IS hard. Other than the dead reckoning method... ummm... since you supposedly already mapped the magnetic ore deposits for the surface, can their position be used as "passive beacons" or "magnetic geo map"? Maybe some infrasonic beacons on the surface and some "time-of-flight" triangulation?

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In 1890 there WAS some kind of radio. Directional antenas are not much of a high technology and they could be invented and developed then if there were demand.

So, for low enough frequencies (in order for the waves to enter underground) and away from large iron ore deposits, you can get a rough estimate of a direction to a known radio station(s). See "ham radio fox hunting" or just abuse them as a "radio-stars" to navigate by.

The deeper you go, the better your receiver has to be. If you allow some 20-30 years of development after 1890, it can be quite good.

If you are handwaving a bit, you can add a planet or two that buzz in low frequency (Jupiter and Saturn actually do, so do some quazars, the Sun, etc, but you will need some later technology for that). This way you can have a constellation of radio sources to look for.

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  • $\begingroup$ I like the idea of searching for Jupiter and Saturn. It would require a very long antenna, I think. $\endgroup$ – Willk Mar 24 at 16:23
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    $\begingroup$ Not sure how much large, but it helps to have large antena for sure. I was thinking about ferrite-wound loop antenna as of early fox-hunting receivers. Actually, you turn the antenna in order to find minimum reception and not maximum. $\endgroup$ – fraxinus Mar 24 at 16:27
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The only effective way of navigating is the good, old-fashioned surveying method. Set up a theodolite at a known marker with another known marker behind it. Send someone hiking ahead with a survey's pole to an unknown point. Measure the angle to the unknown point (horizontal and vertical, using the backsight line for the horizontal angle). Measure the distance to the unknown point (assorted ways of doing it, including simply stretching a line). Pack up the surveying gear, head on down to the guy with the pole, and mark that position. Send the guy with the pole off again, and while he's hiking, you set up, backsight, measure the angles to the new unknown position, rinse and repeat.

After that, you'll have a whole bunch of triplets consisting of a horizontal angle, vertical angle, and distance. And now someone has to draw those on a map. Hooray! Now you can use them to calculate where you are horizontally and vertically, based on the place where you started, which is a known location.

And you get to do it in the dark!

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Sir John Ambrose Fleming invented the first thermionic valve or vacuum tube in 1890 and research into radio waves at higher energies got truly started. At first not surprisingly the quest was for distance and it was not long before researchers discovered that longer wavelengths could skip around the planet. However radio waves get quirky below a certain range and instead of bouncing off the ground, mountains and charged atmosphere layers will instead go straight through them more akin to magnetism. For over a century this was just a quirky footnote until the 1970's when a group a cavers got drunk with the electronics geeks and several designs for portable VLF (very low frequency) radios such as the Molephone, Ogophone & Troglaphone appeared. These devices would enable a surface team to track with a moderate accuracy the subterranean explorers & communicate with them.

more info at http://www.scavalon.be/avalonuk/technical/radio1.htm

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Looks like sound waves are the best bet. The governments/kingdoms could mantain a net of sound "Lighthouses" (beacons). Like a example the Egyptians had the Faros (one of the Seven Wonders of the (Ancient) World). Using different frequencies and time of release (sounding) for any of these sound beacons plus a really accurated clock could make navigation possible. But, more importante, it is a matter of mathematics. I think it is possible. Before GPS seamen could loud yell and wait the echo answer. By counting the heart beating they could to estimate how away was the sea shore. Hard to believe, but it is true.

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  • $\begingroup$ Nice first post on Worldbuilding. Please take the tour and read-up the help center to inform yourself of the nitty-gritty of our workings. Welcome to Worldbuilding new_smile_in, you've made a great start. $\endgroup$ – Tantalus' touch. Mar 24 at 4:03
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Since there are known openings, people could measure location underground as a set of vectors from a know opening. For example, "Starting at BookTown, north 50m, east 25m, right at the fork, continue for 35m, etc."

Also, Using this technique, common locations underground would evolve and the directions could change to something like this: "First, get to the BookTown underlibrary, then exit using the east corridor for 35m, right at the fork, continue 35m, etc."

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Just my 10 cent to add to the others[1] answers...

  • Depth The Earth (and so your world) is heated by the Sun from the surface and by radioactivity from the core [2]. Close the surface it is affected by the surface local conditions, with a time delay depending on the depth. Deeper not. So a good thermometer may give you indication about the depth. Remember on the Earth the geothermal gradient is 25-30 degrees per km, but on your own world it can be different. Pressure may work well too.

  • Longitude is hard, but... the world spins always in the same direction. So is the propagation of the heat wave from the surface (a delay that depends from the depth). So enough close to the surface you may create to find special mushrooms, stones, vegetables with an orientation East-West... at least for the direction.

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    $\begingroup$ The method for the longitude is utterly unclear. Can you explain it more? $\endgroup$ – L.Dutch - Reinstate Monica Mar 21 at 13:51
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    $\begingroup$ Daily temperature fluctuations don't penetrate more than a few centimeters into the ground; annual fluctuations barely make it ten meters. $\endgroup$ – Mark Mar 21 at 19:13

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