Motorized Watercraft on a Hyperdimensional Planet

[Hornbein]

Consider a ship with a propeller. A propeller has to be perpendicular to the way you want the ship to move. It has to be perpendicular to the forward direction. In 3D that means that the propeller rotates in the right-up plane.

In 4D we have other choices. The ana-right plane is also perpendicular to the forward direction. The propeller could rotate in that plane. That means a horizontal propeller. Such a ship would be able to operate in shallower water, so it seems like the clear choice.

(In 4D the dimensions are up, forward, right, and ana. Only up is vertical, all others are horizontal. So the right-ana plane is horizontal.)

 

[Drakkith]

My limited understanding: For a 3D ship, the axis of rotation of the propeller has to point in the direction you want to go. If you simply rotate the propeller so the axis of rotation is along the 4th dimension then you'll just apply a torque to the ship and rotate it, just like rotating the propeller so it points to the right instead of forward.

 

[Hornbein]

In 4D the "axis of rotation" concept applies only in special cases. A freely rotating body has no axis of rotation, instead it has two planes of rotation. In the case of a drive shaft for a propeller you fashion and constrain it so that it has only one possible plane of rotation. But then it doesn't have a unique axis. There is a whole plane of directions in which you have prevented it from rotating.

4D propellers confused me for a long time. The thrust has to go in a direction perpendicular to the plane of rotation, but there are a full 360 degrees of perpendicular directions. Which one? Is it stable? I thought it would be necessary to use ducted propellers. Then someone came along and pointed out it was possible to shape the blades of the propeller to push the water in one particular direction. Oh.

In this case, the propeller can be shaped so that the thrust goes any direction or directions in the forward-up plane. Forward only is the direction you want.

 

[Drakkith]

Is the ship and propeller 3D or 4D?

 

[TeethWhitener]

A propeller has to be perpendicular to the way you want the ship to move.

Depends on how you define a propeller:
https://en.wikipedia.org/wiki/Paddle_steamer

 

[Hornbein]

Is the ship and propeller 3D or 4D?

We are in the 4D Universe so every object is 4D.

 

[Drakkith]

We are in the 4D Universe so every object is 4D.

Ah, my mistake. Got any good references for this topic?

 

[Hornbein]

Ah, my mistake. Got any good references for this topic?

You bet.
https://www.researchgate.net/publication/359213812_Elsewhere_Everyday_Life_On_A_Hypergeometric_Earth.