The linked "Horizon" article mentions how far you can see, out to the horizon, if you know your altitude above sea level. That is for reference only; the goal here involves imagining "straight" lines on the surface of the Earth.

Since the planet is mostly spherical the task is of course actually impossible, but what IS possible involves the "Great Circle Route" (linked) between any points A and B on the Earth's Surface. Airlines routinely fly such routes (GCRs).

It could be (occasionally!) convenient to be able to mark a GCR with a row of towers. And the taller the towers, the fewer are needed. Well, you don't want to make them too tall, or the airlines will complain. I'm arbitrarily picking 8 kilometers for this Idea; commercial airliners typically fly at 10 kilometers or so, which should give us a comfortable safety margin.

Before I get to describing how to erect an 8-kilometer tower, here's how you use them to mark a GCR. You simply/always need 3-in-a-row. The first and the last of the 3 are nearly as far apart as the curvature of the Earth will allow; the 2nd is placed halfway between them.

You use a laser beam to be certain that the 3 towers are exactly in a row.

Now you can use the 2nd and 3rd tower (and a laser beam, of course) to erect a 4th tower, exactly in line with that 2nd-and-3rd, and sort-of still exactly in line with the 1st (discounting Earth's curvature). Then you use the 3rd and 4th to erect a 5th, and so on.

You can now construct the world's longest AND straightest highway, or railroad track, as an example use for this Idea.

Now, about erecting those 8-kilometer towers... In general, we won't need them to be permanent, if we are only using them to mark various places on the surface of the Earth with high precision.

All we really need is a special large hydrogen-filled balloon that supports a heavy gondola and three "aramid fiber" (trademark name: Kevlar) "guy wires" down to the ground. Aramid fibers are strong enough for such lengths to be very possible.

The gondola is not for carrying people, it is for carrying a bunch of tilt-sensors and servomechanisms and a laser, so that it can shine a bright straight beam exactly vertical down to the ground. (And another laser system, for both detecting and sending, is needed for those "horizontal" links previously described.) Having some significant mass should also help stabilize the gondola, although the gondola should also be designed for as minimal wind-resistance as possible.

We can employ a system I mentioned in another Idea, involving compressed-gas cylinders and pumps. The gondola could contain enough cylinders so that if the hydrogen in them was all released into the balloon, the balloon would rise to 8 kilometers, carrying the load. This is eminately achievable, considering that freed balloons have reached several times that altitude. Later, the gas can be pumped back into the cylinders, brining the balloon back down to the ground.

We can use the Global Positioning System to approximate in advance the locations where the guy wires need to be attached to the ground. We actually just unspool the cables from three huge trucks, first for 6 kilometers toward the balloon-launch location, and then into the air as the balloon rises.

When the balloon is at 8 kilometers of altitude, we stop unspooling the cables, and allow the balloon to pul on the cables until they become very taut. Per Pythagorus, the unspooled cable lengths should be about 10 kilometers (the classic 3-4-5 right-angle triangle, doubled).

We now tweak the position of the balloon by adjusting the guy-wire lengths (spooling and unspooling), until the gondola is exactly in position with respect to the "horizontal" laser-detection system. The vertical laser system now gives us a precise mark on the ground, and our "Tower" is ready to be used for the next stage, of the process of marking GCR points on the ground. (After the next two marks are made, this Tower can be moved to another location in the sequence.)

I suppose if you wanted to use a Tower Balloon for something else, like long-term broadcasting of propaganda into enemy territory, you could just have it loft a hose through which you constantly pump hydrogen, to make up for the inevitable leaks. And the power cables, of course, to run the broadcast equipment. But others have already had ideas like that, which is why this one focuses on something else.
-- Vernon, Jan 08 2012

Horizon http://en.wikipedia.org/wiki/Horizon
As mentioned in the main text [Vernon, Jan 08 2012]

Great Circle Routes http://en.wikipedia...t-circle_navigation
As mentioned in the main text. [Vernon, Jan 08 2012]

Aramid fibers http://en.wikipedia.org/wiki/Aramid
Some info on that subject. [Vernon, Jan 08 2012]

Vertigible Vertigible
As mentioned in the main text; this is where I first talked about recompressing the gas from a balloon. [Vernon, Jan 08 2012]

// tilt-sensors and servomechanisms and a laser, so that it can shine a bright straight beam exactly vertical down to the ground. //

Do you intend the laser to be shone at a point on the surface in line with the centre of mass of your planet, or at the gravitational rotational centre (barycentre) of the Earth-Moon system, which is not the same, and moves continuously ?

These small details are important.
-- 8th of 7, Jan 08 2012


[8th of 7], the Earth has 81 times the mass of its moon, and the inverse-square law applies most notice-ably, such that I'm fairly sure any tiltmeter near the Earth is going to refer to the Earth's gravitational center only. I'd expect any local "mascons" to have more effect on them than the Moon.
-- Vernon, Jan 09 2012


But why? Why would you want to mark out Great Circle Routes at ground level? And why would you want to use towers and laser beams to work out these paths as opposed to the simpler, cheaper, more accurate and less environmentally damaging option of using a map and some maths - or even a globe and a bit of string?
-- hippo, Jan 09 2012


[hippo], why not? Note that one thing you can do, after defining a Great Circle Route, and measuring its length, is calculate a straight-line "chord" distance between two surface points. Such a through-the-Earth straight line is the path that, say, a beam of neutrinos would take.
-- Vernon, Jan 09 2012


//commercial airliners typically fly at 10 kilometers or so//

Airliners typically fly above 10 000 ft, not 10 000 meters, so you're going to have to get quite a bit shorter.
-- MechE, Jan 09 2012


[MechE], please provide a reference? In my experience the airlines prefer to fly their jets at about 35,000 feet. Perhaps you are thinking of the shorter-range hops, and the commuter/propeller planes? I don't know enough about those to say anything about their preferred altitude.
-- Vernon, Jan 10 2012


[Vernon] Yes, and you can do this more accurately on a map, without spending millions of dollars on a series of 8km towers.
-- hippo, Jan 10 2012


I'm wondering about stratospheric GPS-positioned robot blimps with lasers.
-- nineteenthly, Jan 10 2012


350 000 is a common altitude for long distance flights, but yes, shorter range flights frequently cruise in the upper teens/low twenties. 10 000 feet would be a little low, admittedly. The point where reporting transfers from altitude to flight level varies, but can be as low as 3 000 ft (it's 18 000 in the US), strongly implying that some flights spend significant time at that altitude.

This completely ignores general and civil aviation, helicopters, very large exclusionary zones around airports, and similar problems.

And no, I'm afraid I can't provide a specific reference, since there doesn't appear to be a list of flight levels in common use.
-- MechE, Jan 10 2012


Well, in any case, regarding airliners, it plainly says that these Towers are supposed to be temporary structures, for making certain measurements --and it also says that because they are so tall, they need not be common. They should therefore be a relatively minor inconvenience to air traffic.
-- Vernon, Jan 10 2012


// there doesn't appear to be a list of flight levels in common use. //

They're marked on all the standard half-million-scale ICAO charts.
-- 8th of 7, Jan 10 2012


[8th] Including which flights typically use which levels? That's the bit I couldn't find.
-- MechE, Jan 10 2012


Curvature in the guy wires, determined by a complex interaction among wind, tension, and gravity, will be an enormous, and uncontrollable, source of error.

Could this not be done using lasers on the ground, pointing up? Couldn't the third laser be aligned with the first two using ground-based observations? Am I missing something?
-- spidermother, Jan 12 2012


God Dammit! False advertising.
-- Zimmy, Jan 15 2012



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