## 4D fluid propulsion

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

### 4D fluid propulsion

I found this place via "Elsewhere: Everyday Life on a Hypergeometric Earth" (which I in turns found while searching for resources on how to do celestial navigation on a 4D world).

I was particularly interested in this quote:
There also is a problem in that rotors are by their nature two dimensional. This leaves two dimensions to which they would move the air. Only one of those two dimensions is up. The power used to thrust that air into the extra 4th dimension is wasted. It seems it would be necessary to enclose the rotor in a cylinder in order to favor the up- down direction.

Supposing that it is true that a rotor/propeller will indeed naturally expel fluid in a plane rather than confined to a line, there seem to be several ways to either exploit or avoid that.

In any case, propellers produce thrust perpendicular to their plane, and parallel to their axis. Thus, for an airplane, we want the propeller to spin in some plane perpendicular to the forward direction, and for a helicopter we want the rotor to spin in a plane perpendicular to the down direction. In 4 dimensions, we can do both of those things at the same time! Suppose that a propeller is spinning in the left-ana plane. it would then expel air in the forward-down plane--which means that, rather than fully enclosing the propeller in a duct to linearize the output, one could leave it open and obtain helicopter-like lifting force and plane-like propulsive force from a single propeller!

Alternately, one could more fully embrace the planar nature of the output, and replace the propeller with an impeller, which is designed specifically to expel fluid in its own plane of rotation, and would presumably be much more efficient at that than a propeller is. An impeller creates high pressure at its outer edges inside a casing, and tubes could be connect to that casing to direct pressurized air in desired directions. This a specific case of the more general idea of fluid jet propulsion, where the pump can be replaced with any other kind of pump in principle.

Finally, a variation on a cyclorotor should also work to produce one-dimensional thrust. A cyclorotor has blades mounted parallel to its axis of rotation, with continuously variable pitch (just like helicopter blades). To generate directional thrust, one simply ensures that the blades turn so that they are oriented flat-on to push against the air (or water, or whatever fluid you are traveling in) like an oar when at the point in their rotation that is tangent to the desired direction of thrust. And by altering the blade phase, one can get thrust in any direction in the plane of rotation. So, again, it would be possible to use a single rotor for both lift and thrust--but with more control than a partially-ducted propeller would have
loganrk
Mononian

Posts: 4
Joined: Mon May 02, 2022 7:31 pm

### Re: 4D fluid propulsion

I think the quote is somewhat wrong.
Because metaphorically speaking, the propeller decides to engage the fluid, deflect it, depending on the tilt of its propeller blades. No tilted blades, the rotor will just cut through the water. If for some axis (perpendicular to the planar propeller), the propeller blade is not tilted in a plane parallel to that axis, the propeller will produce NO force along that axis.

Depending on the tilt of its blades, a 3d propeller will propel the boat along the single axis that is orthogonal to the planar propeller.

In 4d, depending on the tilt of its blades, a planar 4d propeller will propel the 4d boat along a direction that lies perpendicular to the circle which the propeller inscribes. The blades, e.g. flat cubes, could be tilted in two rotation planes, each one is spanned by the tangent of the circle (that the propeller inscribes) and a vector that is perpendicular to said circle.

A 4d boat could have multiple propellers, lying in different planes, and they could still produce thrust in the direction (but differently tilted blades). As long as no planar propeller lies parallel to the forward direction of the boat.
DonSoreno
Mononian

Posts: 11
Joined: Fri Jun 17, 2022 4:46 pm

### Re: 4D fluid propulsion

loganrk wrote:I found this place via "Elsewhere: Everyday Life on a Hypergeometric Earth" (which I in turns found while searching for resources on how to do celestial navigation on a 4D world).

I was particularly interested in this quote:
There also is a problem in that rotors are by their nature two dimensional. This leaves two dimensions to which they would move the air. Only one of those two dimensions is up. The power used to thrust that air into the extra 4th dimension is wasted. It seems it would be necessary to enclose the rotor in a cylinder in order to favor the up- down direction.

Supposing that it is true that a rotor/propeller will indeed naturally expel fluid in a plane rather than confined to a line, there seem to be several ways to either exploit or avoid that.

I'm fairly certain that in 4D the thrust of a propeller would be random and highly unstable. The reason is that it can go anywhere that is in a plane. In that plane there is likely to be one direction that has the least resistance. It will get more air or fluid than the other directions. This will decrease the resistance, causing more air or fluid to go that way, which will decrease the resistance even more, and so forth. I think the way out is to have a tube or nozzle to direct the flow, such as on jet engines or many drones.

I'll also mention that the concept of an axis of rotation is useful only in odd-dimensional situations. In even dimensions you must work in terms of planes of rotation. This will also work in odd dimensions, so once you get used to it it is tempting to use planes of rotation here in 3D.
PatrickPowers
Tetronian

Posts: 387
Joined: Wed Dec 02, 2015 1:36 am

### Re: 4D fluid propulsion

loganrk wrote:I found this place via "Elsewhere: Everyday Life on a Hypergeometric Earth" (which I in turns found while searching for resources on how to do celestial navigation on a 4D world).

I've worked on celestial navigation in a 4D world. It was too advanced for the book posted here. I'm getting inspired to write another book about the more advanced topics. If you want to debate this I'm all ears, uh, eyes.
PatrickPowers
Tetronian

Posts: 387
Joined: Wed Dec 02, 2015 1:36 am

### Re: 4D fluid propulsion

PatrickPowers wrote:I'm fairly certain that in 4D the thrust of a propeller would be random and highly unstable. T

Now I think DonSoreno is right. Just shape the blades so they have thrust in one dimension but not the other. Ducts unnecessary. Duh.

He is also correct in that a propeller could lie in the sideways plane and still provide forward thrust. That would allow the boat to operate in shallower water so it seems like the way to go.
PatrickPowers
Tetronian

Posts: 387
Joined: Wed Dec 02, 2015 1:36 am