What is the minimum strength that my forcefield needs to have to keep various atmospheres with a difference of 13% in total pressure?

Question

I’m designing an alien world, which functions as a nature preserve for some extremely powerful aliens. I haven’t worked out the specific size, distance from the sun etc. yet, but I have already determined that I want an extreme amount of diversity of life. This is made possible by humongous towers which project a forcefield between them, and which keeps the drastically different atmospheres and water bodies separate.

However, I’m not sure about the strength needed. There’s no need to answer about the plausibility of it, but I do want to know the strength necessary. Here are some things that you can assume:

• The radius of the planet is 1.8x that of earth.

• The gravity is that of earth

• The air pressure can vary between 0.9x and 2.4x that of earth

• It should be capable of separating lakes and the atmosphere (no need to worry about water)

• If there are any other things you need to know, assume Earthlike conditions.

• Oh, and the atmospherical composition always has at least 21% to as much as 40% oxygen, with the remainder being nitrogen, carbon dioxide, water, and other stuff. But you can assume the earth’s composition if you want, since that’ll also exist.

• I’ve read in this article that clouds can form at a bit above 6km above sea level, so the barrier will be 8km high.

• The length of the barrier (the distance between towers) is 1700km.

• The thickness of the barrier is half a meter.

I think that the difference in airpressure will seriously complicate it, since air flows from dense to less dense places (I think), so we’ll place the climates so that the difference in airpressure between them will be no more than 13% at a time.

• The forcefield has no friction.

• Power is not a problem.

• Light can travel through it, although any matter can’t.

So I’ll reiterate the question: What is the minimum strength that my forcefield needs to have to keep various atmospheres with a difference of 13% in total pressure?

I calculated that the surface area of the atmospheres is 3.57e12 meters. Not kilometers, meters. I did this by making a polygon the size of France and scaling it to an area corresponding to a radius of 1.8x the size of earth.

This is my first question on this forum, so if this doesn’t follow guidelines (which I think it does) or needs clarification, please say so. I’ll edit it if necessary.

I am aware that the gravity will affect the atmosphere, but I don’t know how to calculate the density in that case, so let’s go earthlike for now.

Edit: I’ve just found out that atmospherical pressure relies on the amount of gas, not only size. No idea how to use this info other than raising the height to 17km. That should cover it, right?

Edit 2: As pointed out in the comments, I need to clarify the parameters and the type of forcefield. You can treat it as a solid wall, and the strength I’m talking about is compressive strength. Force in Newtons. Thanks to AlexP and Jiminy Cricket for pointing this out.

Answer 1

Force fields are pretty much fictional constructs, so you have quite a bit of latitude as to how you want to make them work, but it looks like you want to have a science-based answer. So, you can try to do some simple calculations, but probably need to make some assumptions.

1. What is the strength of the force field? That could mean different things to different people? For this I choose to it to be difference in pressure the force field can withstand. But you could choose some other way of thinking about it like how much energy it takes to move an object from one side of the force field to the other.

2. What is the thickness of the force field? That is up to you, and whatever imaginary technology you want to have. For the assumptions I am choosing, I think it would be kind of neat for it be thick and perhaps lightly glowing some so people could see it. I think having some thickness could be useful since the harder something compresses it the more it might push back. But it is up to you to have as thin as a soap bubble or since your idea has a very large scale you could have it be kilometers thick.

3. How tall is the force field? is it open or closed at the top? If we assume the atmosphere is a fluid, if we have the top open then there could be spillover from the high-pressure side of the barrier to the other. If it is very tall then eventually the rate at which it would spill over would decrease. If it is closed or dome like then that might prevent the spillover problem, but then you might want to have some way of controlling the weather inside the dome. If you want to keep the top open, then you could and some function to your force field and have pump some atmosphere from one side to the other. All of that can be up to you.

To plug into some numbers, atmospheric pressure is about 14.7 pounds per square inch at sea level. If you want to have a 13% difference in pressure you would have a force of about 1.1 pounds for every square inch. This would add up very quickly, for every square foot (144 square inches) you would have almost 160 pounds of force. So if you have something like an airlock to go from one side to another, unless you equalize the pressure it will be very hard to open or close doors etc.

Atmospheric Pressure as a function of height in millibar is shown below. (1 atmosphere or 14.7 psi is about 1011 millibar)

One example of a real force field (or at least proposed) are plasma valves or plasma window In this technology a plasma is used to separate atmosphere on one side and have a vacuum on the other. It has only been demonstrated for very small areas, but apparently uses about 20kW per square inch of window.