Water Cooled Gravity Tubes

 The standard idea presented on this blog includes some of these following points, relevant to the argument I want to make here:

• A very large outer pressure vessel holds in air, and the space inside is micro-gravity as the outer pressure vessel does not rotate
• Tubes inside rotate to provide gravity
• The tubes are surrounded by nested flow dividers to make fluid forces workable
• People, cargo, and many utilities go in and out via 2 openings at either side of the tubes

On that last point, the movement of air removes the heat produced in the tube and the excess CO2. I wrote about the thermal limit that this imposes here:

https://gravitationalballoon.blogspot.com/2014/12/natural-circulation-heat-removal-from.html

Here, I will revisit that, and add a new idea that breaks the upper limit. For the numbers, I'm using this script:

https://github.com/AlanCoding/gravitational-balloon-mathematics/blob/master/thermal/gravity_tube_scaling_sweep.py

(I am using AI for many of my scripts and data generation now, but not having it write for me)

In all cases, that script assumes a heat production of 20 W/m^2 on the inner surface of the rotating tube. This is much lower than the 400 W/m^2 number for Earth equator, but still probably a dramatic under-estimate because it is not thought that people will grow food inside of these tubes (low-g tubes specifically for farming are more likely). Given that, a rough reproduction of the prior result would be this:

Air velocity through the access opening, acting as inlet/outlet

A couple of numbers and assumptions here:

• L/R, length over radius for cylinder, is 2.0
• q'', mentioned above, 20 W/m^2
• Air Delta T is 5 degrees F for comfort, 2.77 Kelvin
• 6 m/s is allowable speed for the tip of the access tunnel and air flow in/out

We don't really need to discuss population density as a real metric. Depending on the density you're interested in, you update that 20 W/m^2 number. It would obviously increase if you have people packed in living on 10 levels. Lower population levels might not _necessarily_ decrease it by much if you still expect the inside to be brightly illuminated.

So for these numbers, natural circulation is effective until about 2 km. And above, I used a lazy free jet condition. Natural circulation might only get you to 1km before it starts to heat up. This is very large. Keep in mind you have to increase the number of dividers almost linearly. So if R=250m requires 16 dividers, and R=500m requires 32 dividers, then R=1km requires 64 dividers, and R=2km requires 124 dividers. Knowing that these will require some form of stabilization, that seems like a tall order. But we don't know for sure! It could be active control by valve modulation, which scales very well, or it could even be the negative pressure design with some form of fully passive stabilization! No one really knows.

I came here to answer the absurd question of "can we go bigger?"

Let me start by rejecting forced air flow. This is probably a bad idea. Even if it allowed you to make things a little bigger (disrupting traffic a lot) that solution won't work for very long before the velocities get too big.

To go bigger, let's review the parameters that are holding us back. The 5 F temperature change is very stifling. That requires large volumes, plus the very low density of air. What could do better in both respects? Just do water cooling. For this, I'll invoke a prior post about water supply:

https://gravitationalballoon.blogspot.com/2016/03/water-sewage-service-between-space.html

You could have continuous water supply. So scale that up to supply a LOT more water, and use that water for cooling. And because people aren't in direct contact with the water, you can accept a much larger temperature difference.

Water-specific assumptions:

• water velocity 2 m/s (probably conservative)
• water temperature drop 20 K = 36 F

Now I'm going to give a very boring graph to ballpark the pipe size of a water pipe for different gravity tube sizes.

It's fully linear. And qualitatively, we have very large water pipes in real cities on Earth. About 0.5 meters is normal for water supply. But stormwater and other things will go to extreme sizes, I would ballpark at 5 meters which is a more relevant number here.

But how would this affect the rotating transfer joint for water? Well, we might sacrifice some of the center space to make this more viable because for the quantities involved it might get splashy. This might be an unnecessary change, I'm not sure.

Now for the conclusions. If a 5 meter diameter pipe is reasonable, where does that put the maximum radius under this scheme? Around 4km, which is substantially larger. Almost unthinkable. You could make it even bigger, you would just need a larger pipe. I have basically rejected the natural circulation outcome because it would make the water flow too fast. This, itself, would become a problem.

But to sanity check some things about a R=4km tube:

• population ~60,000 people
• L=8.6 km
• CO2 rise under stated assumptions, 0.97 ppm if 1 acre per person, 2 ppm for more reasonable 500 m^2/person

Even all other things being workable, the simple transit in and out of this starts to look absurd and/or impractical. The entire point of the shared atmosphere from a superstructure is to make transit fast, but you would wind up spending a lot of time in the shuttle just in and around the tube itself. That said, these sizes might still be physically plausible. Water cooling might, in general, be a good idea for all sizes. And because it is so viable, I have to change my position somewhat from 800m being an upper limit for a tube, to, I don't know what the size limit would be.