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Thousands of years ago, a wizard created a "downroad." This is an area of invisible magic in the shape of a cylinder 3m in diameter, 100km long, laid down east to west just above the surface of a flat land area. Inside the downroad, gravity is altered 90 degrees so that it pulls straight west instead of towards the ground. So, if someone steps into the downroad at the east end, they will free fall for 100km until they exit at the west end (and hopefully have something to slow them down there safely).

The downroad naturally pulls air as well as people. So, there will be strong winds blowing down the road. The wind speeds will be limited by friction with surrounding air outside the downroad. Due to friction they will pull this surrounding air along with them, so that there might arise a large weather pattern around the road.

The friction of the air in the downroad with the air outside it would also cause heating.

My question is this. Roughly how fast will the winds in the downroad be? Are we talking 10 m/s, 100 m/s, 1000 m/s? And, to follow up, how much global effect would these winds have - nothing? Ecological destruction of a continent? Destruction of the whole planet's ecosystem?

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    $\begingroup$ "Due to friction they will pull this surrounding air along": Uh, no. The real picture is vastly more complicated than "a cylinder". Air at the western end of the cylinder will be at the pressure which would be achieved at the bottom of a 100 km deep well, which is an awful lot. (Maybe about 180 atmospheres, but I have no confidence in that.) On the other hand, the air is not confined in the cylinder, and will bleed out radially at high speed over all the length of the cylinder. So what you have is air enters at the eastern end at supersonic speed and blows out over most of the 100 km. $\endgroup$
    – AlexP
    Sep 19, 2021 at 19:28
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    $\begingroup$ Given that the walls of the cylinder are permeable to air, working out the problem fully and correctly is likely to be hideously difficult, FYI. How is momentum conserved, by the way? if I shoot a gun through the cylinder wall, will the bullet shoot out of the other side of the cylinder, slightly displaced by the altered gravity? $\endgroup$ Sep 19, 2021 at 19:28
  • $\begingroup$ @StarfishPrime Yes, the bullet will pass straight through with barely any change to its trajectory (except that the winds would deflect it) - momentum is not altered, only gravity. $\endgroup$
    – causative
    Sep 19, 2021 at 20:47
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    $\begingroup$ @AlexP The pressure at the bottom would be less than the pressure at the bottom of a 100km deep well, because the air is not confined inside the cylinder. Areas of extreme high pressure would result in the air expanding out of the downroad towards areas of lower pressure, relieving the pressure. I don't know if the air would be supersonic. It might be - but there's a lot of drag along the way. $\endgroup$
    – causative
    Sep 19, 2021 at 20:52
  • $\begingroup$ Accelerating at 1g over such a long distance is likely to end badly. Probably talking multiple 1000m/s and horrendous frictional heating issues $\endgroup$
    – Slarty
    Sep 20, 2021 at 12:46

1 Answer 1

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TL;DR:

Destruction of the whole planet's ecosystem?

Ayup.


100km long, laid down east to west just above the surface of a flat land area

FYI, if the world you're building this on is like Earth, the ends of the tube will be about 200m above ground level due to the curvature of the planet's surface.

Or at least, it'll be this way to start with. I expect that the place where the tube just touches the surface will be subject to winds of terrifying speed and power that will generate massive dust storms that will rapidly excavate a deep trough, so most of the tube will end up being well above local ground level.

free fall for 100km until they exit at the west end

In a vacuum, the trip would take about 140 seconds, and you'd reach a terminal velocity of about 1.4km/s.

Because you're in an atmosphere, and the walls of the tube are entirely permeable, the actual speed of the wind through the tube is exceptionally difficult to calculate, as will be mass flow rates and pressures. So much so, I'm not even going to try.

And, to follow up, how much global effect would these winds have

As a parcel of air accelerates in the tube, the pressure behind it (towards the entrance of the tube) decreases, and the pressure ahead of it increases. This might not necessarily lead to catastrophically high pressures at the exit end and a vaccuum at the input end, because wherever the internal tube pressure is greater than ambient, air will move across the boundary of the tube.

Clearly though, the pressure at the exit will end up being higher than the pressure further upstream, and that pressure differential will generate winds.

Now, problem two: you've created a perpetual motion machine. Lets imagine you put a wheel at the boundary of the tube, with a portion of the rim inside the tube, and the wheel is mounted on a vertical axis.

The altered gravity inside the tube will pull the rim of the wheel, causing it to rotate. As each slice of the rim enters the tube, it experiences acceleration until it rotates out of the tube, at which point it escapes the magical gravity field and is only subject to air resistance. Until the object reaches its terminal velocity, it will be continuously accelerated by the alternating gravity field it is experiencing. Congratulations: you've invented a perpetual motion machine of the first kind.

Now, lets think about what happens next. Air will flow out of the exit end of the tube, creating a region of high pressure. Air will flow outside of the tube in the upstream direction into a lower pressure region, and diffuse back in to the tube.

This creates a toroidal vortex that is driven by a perpetual motion machine. It meteorology, this sort of situation is probably not considered a good thing.

I think that as the vortex grows and intersects the ground it will split into two contrarotating vertical vortices, like a pair of tornadoes. Its possible these will grow and eventually form a single giant vortex, but I can't say for sure. The whole thing is entirely too complicated to think about.

Quite how big and how powerful the resulting circular storm(s) will be I couldn't tell you. But I can say that they're being driven by a perpetual motion machine that can apparently provide an arbitrary amount of energy... there's probably some practical upper limit to air flow rates here due to weird compressibility factors, but you could develop supersonic wind speeds. Due to the speeds and volume of air involved, and the fixed position of the storm, it would strip up soil from the ground. The resulting dust clouds would be swirled round and sucked back into the tube and accelerated for free, so no energy is actually lost to the storm in lifting and accelerating material.

You'll eventually end up with continuous sand-hurricane at the exit... possibly a pair of contra-rotating ones. I'm not sure how big these could be. The centre of the storm might be 100km across to neatly fit around the source of its power. It will throw vast amounts of material into the sky, mostly dust. As it never tires, the dust might conceivably envelope the world, plunging it into gloom. If the tube was anywhere near an ocean, the ocean would probably generate huge quantities of water vapour which would in turn produce vast rainstorms and maybe even enough high-altitude water vapour to cause problematic greenhouse effects.

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  • $\begingroup$ Good discussion, the problem is how can we convincingly argue that the winds actually will be supersonic or not? Yes, it's a perpetual motion machine, constantly generating some amount of energy per second, but how does that amount of energy compare to total sunlight on the surface of the planet? If it's only 1% of incident sunlight, or less, then I wouldn't expect a fully global catastrophe. $\endgroup$
    – causative
    Sep 26, 2021 at 9:23
  • $\begingroup$ For example, I calculate that if the winds are moving at 1000 m/s then the downroad will generate around 10 GW of power, which is insignificant on a global scale. The power generated is proportional to the speed of the winds. wolframalpha calculation based on Power = work/time = force * distance / time = acceleration * (mass of air in the downroad) * distance / (time air takes to pass through downroad) $\endgroup$
    – causative
    Sep 26, 2021 at 9:30
  • $\begingroup$ Also, this power generation from 1000 m/s winds is tiny compared to the energy in a hurricane, so it wouldn't be enough to sustain a hurricane-sized vortex on either side of the downroad. And we'd need the surrounding air to be going very fast indeed for the winds in the downroad to be 1000 m/s without slowing from friction with surrounding air - and 1000 m/s surrounding air would require something like a hurricane or more. So perhaps 1000 m/s is physically unrealistic and the winds would be more like 100 m/s or less. $\endgroup$
    – causative
    Sep 26, 2021 at 9:36
  • $\begingroup$ @causative the amount of power that is generated is almost arbitrary... it depends on the mass of material being injected into the the tube. It will only start off as air (and the density of the air at the exit point may rise as flow speed increases). As dust and water and other dense materials are entrained, it will rise considerably. The really interesting thing is what happens over longer timescales, and the geology underneath the exit. Lava hurricanes, anyone? $\endgroup$ Sep 26, 2021 at 10:35
  • $\begingroup$ Sure there would be some non-air matter going into the downroad, dust and water and the like, but it's not going to be that much beyond the air itself. Denser objects are less likely to get picked up, and solid objects that do get picked up will get spat out downstream so that they won't enter again. Most of the mass in the downroad would be air (900,000 kg of air). Maybe with compression of the air this could be three or four times greater mass, but 30 or 40GW is still not much compared to a hurricane. $\endgroup$
    – causative
    Sep 26, 2021 at 11:00

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