4d control surfaces of planes and boats

[DonSoreno]

In 3d the rudders on boats generally have 1 degree of freedom.
4d Boats will be similar to 3d planes, Except they need two orthogonal (probably equal sized) stabilizers (fins) and at least two rudders, or 1 rudder with two degrees of freedom.

In applications where the we have to steer a moving vehicle left & right, and up & down (i.e.planes, and foiling boats) two orthogonal control surfaces are used in , (plane => elevators and rudder.)

(This could be achieved with a single control surface, but I cant of anything where this is used.)

So 4d planes would most likely have wings that resemble 3d planes, with flaps for forward-upward rotation, and then at the end there would be elevators, and two orthogonal rudders. They would be very similar to 3d planes. There can be a single wing that goes around the entire fuselage, and I think that this might reduces wing tip vortices/losses.

plane_4d_aft_cross_section.jpg

aft section of plane with horizontal stabilizer, and two vertical stabilizers.

(57.67 KiB) Not downloaded yet

And a spherindrical fuselage.

Your thoughts?

a top down view might look this (in 3d):

top-down view, showing the fuselage, the wing, and the horizontal stabilizer.

plane_4d_fuselage_wings_horizontal_stabilizers.jpg (17.94 KiB) Viewed 419 times

[PatrickPowers]

What you are asserting is widely believed but is not correct. I wrote a whole book about this and other things.

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

A simple fin will always work, no matter how many perpendicular dimensions there are. It's profile is small in the forward-back and up-down dimensions and large in all the sideways dimensions. It resists moving sideways. It will still do that, no matter how many sideways dimensions you may have.

Now suppose that fin is a rudder attached to a vertical rod. In 3D that rod can rotate in a single plane. In 4D that rod can rotate in any plane that is inside three dimensions. In N D it can rotate in any plane that is inside N-1 dimensions. No more control surfaces are needed. That rudder setup, simple as can be, can steer in any direction other than up or down.

Similarly with steering vehicles. I started with a tricycle (quadcycle) and worked my way up.

Another thing you often see is that people would need 3 eyes, three legs, etc. Not so. Two suffice no matter how many dimensions you may have.

I dunno about infinite dimensional spaces. That's going too far for me.

[DonSoreno]

You mean we only need a single rudder (tilting 3d plane) for ana-kata & left-right, with 2 DOFs. Right?
I think using 3 orthogonal stabilizers+control surfaces are useful, because each control surface only has 1 DOF.

[PatrickPowers]

You mean we only need a single rudder (tilting 3d plane) for ana-kata & left-right, with 2 DOFs. Right?

Right.

YI think using 3 orthogonal stabilizers+control surfaces are useful, because each control surface only has 1 DOF.

Now we are in the realm of opinion. What would a 4D person who grew up in such an environment do? I prefer going for simple direct things.

[quickfur]

The way to understand how rudders work is to understand that a rudder is a subset of a plane that divides space into two halves. It is this dividing property that gives it its function of resisting lateral motion. We know that in n dimensions, an (n-1)-dimensional plane divides space. Therefore, in 4D, a rudder would simply be a subset of a 3-plane. A (3D) cube-shaped rudder would serve the purpose.

[wxyhly]

A single wing that goes around the entire fuselage may cause significant shear stress, I think it's better to use 3 wings like fan blandes with 120 degrees, it can shrink mass and stress, and also provide enough elevation force. (assume 3 is the most efficient design than 2 or 4 wings, you can think about wind turbine).


The best number of horizontal control surfaces at the tail is also 3, since it can provide controls of exact 3 degree of freedom: left/right, ana/kata, and spin.

spin motion:


I wrote a 4D flight simulator for airplane and also drone. link:https://wxyhly.github.io/tesserxel/examples/?en#aircraft

Here is the aircraft design:https://wxyhly.github.io/archives/aircraft4d/
and a wireframe animation for orthogonal 4 views:

[PatrickPowers]

"A single wing that goes around the entire fuselage may cause significant shear stress,"

That could be but I don't see why. The proportional forward-back distance of the wing could be the same for a tutu wing, so the lift is distributed even more evenly than here on Earth. It's diameter is very small though, like maybe a few inches more than the fuselage. It would make for a very stiff, inexpensive, and low weight wing, which would be great for efficiency. The stiffness might be bad for turbulence though. There could be some clever solution. I don't know any aeronautics.

[steelpillow]

There are assumptions here that we need to be clear about.

A 3D aeroplane has three axes: forwards, lift and sideways.

Might a 4D aeroplane have a second forwards direction of flight, or a second upwards direction against gravity? OK, no, let's assume a second sideways direction, i.e. a sideways plane of complex directions.

A 3D rudder must present a 2D resistance to sideways flow, i.e. it must have extent in the forwards and upwards directions. Any reactive force against that extent must be in the third, sideways direction. But in 4D that force may be in any direction in the plane of the two sideways directions. So for effective control we must have n-2 rudders, each with extent in every direction except one.
Similarly, to direct force upwards, the elevator must extend in every sideways direction, as well as the forwards one.

Ailerons pose a different problem. 3D ailerons create roll around a line. But in 4D you roll around a plane, and there are 3 such 2D roll axes to choose from. So you need 3 sets of 3D ailerons.

It is possible to combine some control surfaces but not others. In 3D we have elevons, V-tails and various other oddities. Some work better than others, for example when using a V-tail as a rudder, you may have to apply opposite aileron.

Designing the control yoke becomes painful.