# Optical telegraph that can be seen as far as 90 km. How?

You see, I have this world that has the same planetary characteristics as Earth, and the people of the Snoopish Empire are building an optical telegraph net. The only problem they have is that their Empire is made of tens of islands separated by distances ranging from 30 km to 90 km.

So the problem is: I need some type of optical telegraph design that can be seen at a distance of 90 km.

(Yeah, I know that the curvature of the planet would occlude the towers if they were at sea level. However, I've done my maths, and if each tower is at a height of 250 m over sea level, they would have direct vision of each other at a distance of 90 km. And for this specific reason [and plot convenience] there are mountains of that height at the appropriate places.)

So the only problem is about designing a system of optical telegraph towers that (with good weather and amateur telescopes) can be deciphered at that distance.

-There's no problem with building an extra or 2 more towers, but not 3 more (in the same place), our budget is limited and the Emperor may decide that ships, while slower, are cheaper to rent.

-We need to use technology that would be available to any civilization of the 1500s, for when we share the method with our allies in the younger continents.

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– L.Dutch
Commented Apr 21, 2022 at 15:22

If you have your heart set on using movable semaphore towers with 1500s tech, they're going to have to be quite large. But if you allow for simple telescopes, it's probably feasible.

To distinguish the size, shape, orientation, etc. of an object like a semaphore tower, it needs to subtend a certain angular size. Features of an object whose angular size is smaller than this will just blur together and be indistinguishable. At a distance of 90 km, an object of size 1 meter subtends an angle of about 2.3 arcseconds. (There are 60 arcseconds in 1 arcminute, and 60 arcminutes in 1 degree.) This scales basically linearly; so an object 10 meters across would have an angular size of 23 arcseconds, 100 meters across would have an angular size of 230 arcseconds ≈ 3.8 arcminutes, etc.

If you literally mean the technology level of the 1500s, then that precludes having telescopes at all (the first known telescopes were invented in the early 1600s), and you're limited to the resolution of the unaided human eye. This is around one arcminute; so at a distance of 90 km, the unaided human eye could only distinguish features about 25 meters across. The whole flag assembly might need to approach 100 meters in diameter. This is comparable to the diameter of a typical modern wind-farm turbine.

However, if you'll allow for your world's version of Galileo to construct a 25x telescope in the late 1500s, then it becomes much easier. (Our world's Galileo constructed a 23x telescope in 1609.) With this magnification, it would be possible to discern features 1 meter across at a distance of 90 km. I would expect that a flag assembly of 4–6 meters in diameter would be able to transmit information. Galilean telescopes do have fairly small fields of view, which makes them awkward for astronomical purposes; but this is not nearly as much of a problem for your purpose, since they can be permanently mounted to point at the nearest towers in the network.

• Thank you very much. This is the type of answer I was looking for. Commented Apr 20, 2022 at 20:29
• If we are taking about distances like 90 km and nearly sea level atmosphere, resolution power will be weaker by at least one order of magnitude. Atmospheric effects such as haze and turbulence are taking their toll here. If you try to use strong binoculars from the top of a mountain or tall skyscraper, you'll find that you can see nearby peaks or buildings in stunning detail, while those in the distance remain stubbornly hazy. Commented Apr 20, 2022 at 21:16

Use a heliograph.

A 6 inch mirror will do you well.

https://royal-signals.org.uk/Datasheets/THE_HELIOGRAPH.php

Range of the Heliograph

The rough distance in miles at which the heliograph can be used, is obtained by multiplying the diameter of the mirror in inches by a factor of 10 miles. This range is governed by the angles at which the rays strike and leave the mirror and the state of the atmosphere.

The total lateral range (divergence) at which the heliograph can be read, is obtained by dividing the distance between the instrument and the receiving station by 107. The lateral range on either side of receiving station will be (approximately) half the total lateral range.

A 6 inch mirror will easily allow communication over 90 kms. You don't really need a telescope. You can put filters over the heliograph to change the colour to communicate a wider array of messages.

The telescope could be for emergency communication where you build a big fire and use that when it's night or gloomy.

# Use a 3 colour system for a small alphabet.

Using common filters for red, green, and blue, you can send faster messages. Each message can be a short sequence of three colours. Red Red Red might be the symbol for stop say. You can either have an apprentice lift up colored cough, or design a small machine to move it automatically.

The person on the other end can write down each sequence, and get a message.

For shorter messages you can signal any messages to a receiver in a city or town below the mountain. For longer messages you can send a runner up or down the mountain with the message.

# The outposts are self funding.

The sender and receiver would basically be a farm where someone was moderately educated. They'd get their primary income from farming, but have a secondary income sending messages to other islands. The state may need to subsidize this initially, but soon local merchants and others will likely fund this to ensure their own advantages and speedy communication.

• I like the sound of being able to make signals also by night. Commented Apr 19, 2022 at 23:07
• Wiki says the world record distance with an 8-inch mirror is 295km, which is great. (Sorry to mix imperial/metric.)
– Tom
Commented Apr 20, 2022 at 2:12
• I think this is a better solution than a mechanical semaphore tower, but one wrinkle occurs to me. I wouldn't expect that people with 1500s-level technology would be able to grind a mirror as flat as the manufacturers of "real-world" heliographs were able to in the 19th and 20th century. A mirror that wasn't flat would lead to divergence of the beam, which might reduce the feasible range compared to real-world heliographs. But I have no idea by how much. Commented Apr 20, 2022 at 12:51
• They didn't add that requirement till later. Commented Apr 20, 2022 at 15:59
• @NepeneNep Yeah, in my head it was clear but I didn't specify, sorry. It's done now. Commented Apr 20, 2022 at 20:26

The first obstacle is tower height. Factoring in standard refraction and surface curvature you'll need a tower around 150m tall at both ends of the span. On a clear day that will give you around 115m obstructed height, leaving 35m of the top of the towers visible from either side.

At that range you'll need either a good-sized signal panel (flags, shutters, whatever) or a fairly bright light to be visible without a telescope. If you're using signal panels they'll need to be at least 30m across to be barely visible to the naked eye, which has a minimum resolution of about 1 arcminute (1/60th of a degree). If you can build a pair of 150m-tall towers with an array of signal panels on top, you are probably capable of building some fixed telescopes on the towers to allow you to see smaller signal panels.

As an aside, a shutter mechanism that has bright lights behind it is more visible, because we can see a light source that has an angular resolution smaller than our eye resolution. You still need the lights separated enough to resolve which light you are seeing.

Moving on, let's consider the coding.

While you can use a single light to transmit all of the information you need to, but if you're relying on human perception your bandwidth is going to be quite low since each signal has to be long enough to be visible when the observer blinks. Having multiple signal bits is harder, from an engineering perspective, but it greatly increases the bandwidth available... to a point. You need to keep the total number of signal panels down to the point where a human can unambiguously recognize each valid combination of states in a short amount of time. I honestly can't tell you where the break point is, but I expect that you should be able to get upwards of 5 bits of data (32 symbols) into each frame without too many problems.

No, that's not 5 signal panels, that's 32 combinations of 6-7 panels. Yes, that's 50-75% worth of wasted bandwidth, but there are a lot of combinations that are difficult to read accurately because they're too similar.

Consider a 3x2 array of signal panels. Single bit combinations are mostly out since it relies too much on the observer being able to figure out which particular bit is lit, and they need to do so quickly. So that's 6 possible combinations out of the way. Same deal with two adjacent bits - which two are they? There's another 7 bad ones we need to get rid of. And so on.

So how many good combinations are there for a 3x2 array? Not as many as you might think. There are a couple of rules to consider:

1. All combinations must have at least one light on in both rows.
2. No combination may be shifted on the grid, which means:
• No empty left column.
• No empty right column.

Seems pretty simple. We can enumerate those fairly quickly (there's only 6 bits of data here after all). Here's the full list, split by common bottom row values:

☒☐☐  ☒☐☒  ☒☒☐  ☒☒☒
☐☐☒  ☐☐☒  ☐☐☒  ☐☐☒

☒☐☒  ☒☒☒
☐☒☐  ☐☒☐

☒☐☐  ☒☐☒  ☒☒☐  ☒☒☒
☐☒☒  ☐☒☒  ☐☒☒  ☐☒☒

☐☐☒  ☐☒☒  ☒☐☒  ☒☒☒
☒☐☐  ☒☐☐  ☒☐☐  ☒☐☐

☐☐☒  ☐☒☐  ☐☒☒  ☒☐☐  ☒☐☒  ☒☒☐  ☒☒☒
☒☐☒  ☒☐☒  ☒☐☒  ☒☐☒  ☒☐☒  ☒☐☒  ☒☐☒

☐☐☒  ☐☒☒  ☒☐☒  ☒☒☒
☒☒☐  ☒☒☐  ☒☒☐  ☒☒☐

☐☐☒  ☐☒☐  ☐☒☒  ☒☐☐  ☒☐☒  ☒☒☐  ☒☒☒
☒☒☒  ☒☒☒  ☒☒☒  ☒☒☒  ☒☒☒  ☒☒☒  ☒☒☒


With just those two rules we've whittled it down to 32 viable combinations - 50% of the 64 possible combinations of 6 lights. With training I think an average human operator could be trained to recognize 2 of these symbols per second, maybe more if they're using a keyboard of some sort to enter the symbols. That's upwards of 10 bits per second worth of bandwidth... which is slow, but far from useless.

To put this into perspective, highyly skilled amateur enthusiasts can transcribe Morse Code from audio (via keyboard) at about the same rate - 60 words per minute, or approximately 10 bits per second (assuming: 5 characters per word, ~5 symbols per character and factoring for inter-character and inter-word gaps). While there are people who can go higher, first class licencing requirements are much, much lower: 25 WPM (~4 bps) for text.

• I like this answer too. Have you thought about the ability to make an extra encryption/compression to get more speed that way? If you think about it, the things that process the signals are human brains, not computers, so we could make a dictionary of the only useful phrases to be utilized, put them in the dictionary, assign each one with a code and send the code. It's more compressed than plain letters and already encrypted. You just need dictionaries of codes on both ends of the line and a regular (8-12 months) update of the dictionaryWithMoreCodesForNewPhrasesAndPhrasesWithDifferentNumbers. Commented Apr 24, 2022 at 9:14
• Sorry for the camel case up there, I run out of characters for the comment and had to compress the info XD. Commented Apr 24, 2022 at 9:14