I have made a design for creating artificial gravity on low gravity worlds for my world, does it work?

Question

So I have been thinking about making a building on the moon that would create a 1g environment for the people inside without making the structure too inconvenient to attempt to get into. This is my design. Note, it has no airlocks because it would be in an enclosed dome or structure with an artificial Earth-like atmosphere and a good temperature.

So the structure itself is a spinning cylinder and the point of this structure is to provide a section within that cylinder which will experience a constant force of 1g. So the vast majority of the cylinder houses nobody but the small part that does is the "hab", each Hab has 2 bunkbeds on either side, a small kitchen and a table for four people, they can cram. So how it works is that, depending on the position of the "hab", the cylinder will slow down or speed up to create the artificial gravity, when the hab is closer to the bottom of the cylinder then the top it will be adding gravity to what the planet is already providing within the given direction while when it is closer to the top then the bottom it is spinning to create the same amount of G-force as the planet is producing plus 1g to get a total of 1g.

Now as for getting in, there is a ring on both ends of the cylinders which is totally separate from the cylinders themselves, this ring has a small box which anybody who wants to enter in will have to go through. So a person who wants to get in will enter the box, then they will press the button that begins the process, a hook will then protrude from the box at the right time and at the moment of contact with a receiving hook that is part of the cylinder it will speed up to 1g to where the box is parallel to the door, after this a semi "draw-bridge" will go between the box and the door which allows the person (or people) in the box to enter.

Now my question is if this is something that can be made within this century with current tech or tech we are likely to gain, and another thing I want to know is if there is a better design that you can think of, I will take an alternative design into consideration but I don't require that you give me one to answer. Now if I spoke albeit confusingly and you don't exactly understand what it is then tell me. Now final thing, if you have an alternative design and can draw well it would be appreciated if you have an illustration.

Answer 1

If the only point is to have 1G somewhere, don't vary the speed. Make a circular disc about a hundred yards across and a maybe five yards high; and spin it horizontally. You then have two vectors to consider, a 0.3G planetary vector pointing down, and a centrifugal force vector pointing out. The addition of these two vectors can be 1G pointing somewhere in-between straight out and straight down. Angle the floor inside this disk to be perpendicular to that 1G vector. There should be plenty of room for bedding, cooking, etc.

As for getting in and getting out: Leave the center of the top of the disk open; the gravity there will be 0.3G. Have a structure build over the top, it lowers an elevator into this opening. You have a fancy hydraulic tilting floor that slowly moves to track whatever the apparent gravity vector is, as it spins up, so people can walk out when the speed is matched and the door lined up. That goes into another traditional elevator that brings them to the edge of the disk. Same ideas apply to exiting the disk.

I haven't done the math, but I think this might work.

Edit: Here is a physics lesson on adding force vectors. If I did that correctly, then for a 0.3G gravity planet you need 0.954G of centrifugal force and your floor would be set at a 17.5 degree angle to the disk wall.

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Edit: To OP: As to your design, it will not work. I agree with Shadowzee. To simplify that answer, you are only considering the person positioned at the bottom or top of your cylinder, at those poles the answer is yes, they feel one G pulling down, and the cylinder must generate 0.7G and 1.3G at those points, respectively.

But consider the person positioned halfway between those points: Say standing horizontally, or parallel to the planet surface. If you accelerate smoothly between 0.7G to 1.3G, the cylinder at this point will be generating 1G.

But the planetary gravity vector will still be pulling down with 0.3G.

Thus the net vector (see vector addition link above) will be of magnitude $\sqrt{1^2+.3^2}=1.044G$ and $\arctan\left(\frac{.3}{1}\right)=-16.7^{\circ}$ (degrees) down from horizontal.

The same thing applies everywhere except the top and bottom, because the 0.3G down vector is always present. But your design can be proven defeated just by this one point at $0^{\circ}$, the horizontal:

At this particular point, the horizontal vector from centrifugal force and the vertical vector from gravity always form a right triangle. There is no length (=magnitude) of a horizontal vector that counteracts the $-90^{\circ}$ vector of planetary gravity. The hypotenuse of that right triangle will never itself be horizontal. (If you made it 17.2G, it would come within a degree and nobody would notice the 0.3G.)

But you need a magnitude of just 1G. To have a magnitude of 1G, the vector must be $\sqrt{x^2 + .3^2}=1 \rightarrow x=0.954$, but then the angle=$\arctan\left({\frac{0.3}{0.954}}\right)=17.46^{\circ}$.

In your design, that angle changes throughout the trip from bottom to top, and top to bottom, swaying the passengers back and forth dramatically. It will make the passengers dizzy and sick.

So the answer is no, your design won't work. My design is effectively what ColonelPanic was trying to convey, we thought of the same thing; but I made a short cylinder (a disc) and the floor does not have to be movable or stabilized; the angle is a constant. Always $17.46^{\circ}$ for 0.3G, because all we need consider is that same horizontal vector, and the velocity of the disc is constant.

Answer 2

As Shadowzee pointed out, what (we believe to be your) design is lacking is a constant vector for the moon's own gravitational pull. (Although maybe something like this could assist in at least reducing some of the effects.

But I do believe a similar design CAN work for you. Instead of a cylinder laying on its side, why not put it vertically? For simplicity sake, imagine a simple centrifuge with a pod hanging off of it. The hab module can have a floor which will be 'gyroscopically' (or perhaps even digitally since we know all of the requisite variables) stabilized to account for the constant ~0.16G from the moon itself. Maybe someone else with a calculator handy could give the approximate angle.

What this would look like, simplified, would be the pod's floor mostly parallel to your cylinder's axis but slightly tilted up and 'away' from the moon's surface to nullify the Moons gravitational vector.

Your transfer modules would behave similarly to what you envision with basically an exact replica being placed above or below, and then RPM matched and docked, likely with a transfer joint which also can slide/tilt with the pods and their floors. Climb down or up the ladder at approximately 1G as you would on earth.

To answer your question on whether this can be achieved with current tech, I can't see why not. Getting it all to the moon would be incredibly expensive, but I see no reason from an engineering standpoint why it couldn't be accomplished. Here is a neat little calculator which may assist you some. You don't need a full 1G because we are 'stealing' some of the moon's gravitational component, so with a radius of about 100m, you're only looking at a couple RPM. Make that 30m and still only ~5RPM (but probably a bit uncomfortable for the people in the pod).

Answer 3

I don't think this will work the way you described. As I see it your design won't be able to generate 1g in only a single direction all the time.

First let's address the main point, Let's say that the gravity on the moon is 0.3 G. If I want 1G at all times, it will need to be accelerating upwards at 0.7G at the bottom and accelerating 1.3G downwards at the top. At the top of the cylinder, my person needs to be flipped around because centrifugal force will act outwards. The problem is that are you rotate upwards, the moon's gravity will always be acting downwards towards the centre of the moon. So at 45 degrees I need to be accelerating upwards an extra 0.3G so that the total forces will be 1G (it's 45, both acceleration vectors are going to be the same from centrifugal force). Basically I'm going to feel something other than the 1G you want me to.

Creating gravity in only 1 direction on the ground is going to be basically impossible because you have a constant acceleration you need to apply in one direction to cancel out gravity. You can try all the rotational tricks you want, but they will vary in a sine wave shape which you will feel. The only place it kind of works is if you were to be free falling, then I could spin you sideways to create artificial gravity because you can't feel the gravity from falling because everything falls with you and our body measures forces by forces acting on us. So basically if you want 1G, it's going to need to be off the ground.

Answer 4

If you want to augment existing gravity with centrifugation, it is best to place the centrifuge so that it rotates orthogonally with the existing lunar/planetary gravity. The combined net force direction inside the centrifuge then defines a stable "water level" that is always a paraboloid. (This shape can also be shown experimentally, as seen in the wikipedia page for absolute rotation )

The slope of the parabola and the perpendicular curve depends on the radius of the centrifuge, and the ratio of centrifugal and gravitational force magnitudes. For a 10 m radius centrifuge, rotating to add up to 1 g centrifugal acceleration to 1/6 g lunar gravity, the "water level" curve looks like this:

The net force vector direction also defines another curve, what I call "plumb line", which is always perpendicular to the "water level" paraboloid:

As indefinite integrals, these curves can be offset vertically by any amount, and they always intersect at a right angle:

These curves are named so because they follow the local net force vector direction. Real pendulums would point according to the plumb line, and water surface in a container would follow the paraboloid:

Pieces of these curves can be picked as generatrices for surfaces of revolution, to create toroid interiors where floors and other "horizontal" surfaces are always perpendicular to the net force direction:

The example radius of 10 m, corresponding to 9.5 RPM constant rotation, is at the lower end or slightly below the typically stated comfort zones for artificial gravity, but anecdotally is possible to adapt to with some training (the "slow rotating rooms" used by US and Soviet scientists in the last century were smaller than that, and the tilted floor in "Jupiter-2" seems to have helped in the adaptation). In addition to the curvature of the floors and the walls, there will be quite noticeable Coriolis effects for dropped or thrown objects, which of course would also be affected by lunar gravity to make ballistic trajectories more interesting.

The entries and exits into the constantly rotating rooms would have to be near the central axis, where the tangential speed difference between rotating and stationary parts is comparable to stepping onto a moving escalator. Some safety system is probably still needed for the transition, since unlike an escalator the rotation cannot be stopped by emergency button. (There is too much flywheel energy in the rotation to stop it fast, and trying to do so would harm the people living inside the toroids, as they would be thrown sideways in their reference frame.)

There are of course major engineering challenges in the design, such as keeping the center of mass from shifting when people walk around inside. More info can be found in my recent blog post.