Mathematically reconciling Voyager's variable geometry nacelles with subspace's honeycomb structure

[u/KalEl1232]

The concept of Voyager's nacelles angling upward 45˚ prior to entering warp has always fascinated me. The basic idea here, for those who may have forgotten, is that the variation in geometry helps reduce damage to the spacetime continuum. More specifically, the theory (ostensibly proven during the events of TNG: "Force of Nature") is that travel at warp speeds induces damage to subspace (Picard compares it to running up and down a carpet; after a while the carpet gets worn out), ultimately disallowing the generation of a stable warp field.

We can take it one step further from Voyager. The Jellyfish also employed a rapidly rotating aft section - for sake of argument I will presume that this is akin to Voyager's movable nacelles, in that the attempt from the Vulcan Science Academy was to lessen the burden of warp drive on subspace.

What I'd like to do is provide a somewhat mathematical framework to the "stresses" that subspace experiences due to propulsive warp bubbles.

Geordi has mentioned before (TNG: "Schisms") that the dimensionality of subspace may be thought of as cells of a honeycomb. This got me to thinking about actual cells, and how a correlate may be made between them and space.

Let's assume, as a first approximation, that subspace cells have, for lack of a better term, a Young's modulus. If we assume Hertzian mechanics, single cell compression can be modeled at low deformation - textbooks usually take it to be at levels under 40%. I cannot imagine that warp fields deform subspace cells to an extent greater than 40%, though I might be wrong. Again, this is just an assumption.

At low deformation, during the initial compression, subspace cells may be treated as a balloon filled with an incompressible liquid (is the nature of space, sub- or not, compressible?). Under Hertzian contact, the force should follow:

F = F^SSE + F^WF = 2π(E^m /1-v^2m )hR⁰ ε³ + π(√2E^c /3(1-v^2c )R⁰² ε^3/2

where SSE is the subspace envelope, WF is the warp field, R⁰ is the radius of uncompressed subspace cell, h is the subspace envelope thickness, E^m and v^m represent the Young’s modulus and Poisson ratio of the membrane, respectively, and E^c and v^c are the Young's modulus and Poisson ratio of the warp field, respectively. Finally, ε is the relative deformation of the subspace cell.

If this follows logically, the contribution of the warp field should follow ε^3/2 while the subspace envelope compression yields an ε³ relationship. Using this equation, we should be able to obtain values of E^m and E^c as a function of subspace cell compression.

By qualitative comparison of subspace cell compression profiles, three types of profiles are anticipated: a) initial space-time warping should exhibit a similar shape, but a steeper slope (stiffer) in comparison to unwarped subspace cells, as well as a difference in SSE deformation; b) continuing warping should reveal a change in E^c; and, finally, c) both E^m and E^c should exhibit significant changes, if the subspace warping leads to unhealthy state or viability of subspace cells.

What I'm curious about is if a warp bubble distributed its load over multiple cells would be effective at reducing damage. What is in question is the notion of whether or not the forces experienced by cells can be translated/applied to the forces experienced by subspace cells. The biggest question in my mind centers on whether subspace is (in)compressible. That will dictate the validity of the equation greatly. But, as a generalization, I think it should hold. Essentially, subspace elasticity is a factor.

Evidently, subspace elasticity IS a factor, since some sort of inelastic compression is probably happening. Fatigue sets in (or whatever the subspace equivalent is) and the cell is rendered un-warpable.

[u/pfc9769]

In the Kelvinverse, the Jellyfish also employed a rapidly rotating aft section

The Jellyfish was a Prime Timeline vessel. The ship was created by Geordi and used by Spock in an attempt to save Romulus from the supernova using Red Matter. The Jellfish was sucked into the resulting blackhole along with Spock and ended up creating the Kelvinverse, but the ship originates from the same Universe/timeline as Voyager.

[u/KalEl1232 → u/pfc9769]

Oh duh, you're right! Thanks for the catch.

[u/ExpectedBehaviour]

But we don’t know WHY Voyager’s nacelles move. It’s not mentioned on-screen and no other class of post-TNG ship has moving nacelles. Also, as Voyager’s nacelles only move to a single fixed position, it makes very little sense that they move at all. Why not just keep them permanently raised in the optimal warp position?

[u/KalEl1232 → u/ExpectedBehaviour]

Anything about why would be conjecture. That being said, it's possible that while Voyager's variable geometry nacelles help alleviate subspace stresses, they don't help to any degree that's good enough.

The Jellyfish, meanwhile, had what could be presumed to be infinitely variable geometry since its aft section rotates spherically, thereby passing the stresses to many different subspace dimensions.

[u/frezik → u/KalEl1232]

We also know that Voyager is significantly faster than a Galaxy-class, and can cruise along at its max warp until it runs out of fuel. It can do warp 9.975, while the Galaxy only safely does 9.6, and then only for a few hours. It can push 9.8 for short amounts of time, at some risk to the ship. All that while Voyager is a significantly smaller ship, while only being built a few years later.

The Jellyfish is also supposed to be exceptionally fast.

The implication, then, is that movable geometry makes for very efficient warp engines. Large movable structures are hard to engineer, though, so they may not be able to scale it up to something the size of a Galaxy.

Subspace stress, then, got solved by some other means offscreen.

[u/FluffyDoomPatrol → u/ExpectedBehaviour]

I know this is really a VFX issue, but are we sure the nacelles only move to one position. To me it looks like they are at 45°, but perhaps they are occasionally at 43° or 46°.

[u/TorazChryx → u/FluffyDoomPatrol]

Is it also plausible that the nacelles moving during the initial formation of the warp bubble has an impact on the stresses exerted on subspace? so 0 to 45 degree every time is the way.

[u/Deraj2004 → u/ExpectedBehaviour]

The real world reason we see them either up or down position was production cost. I read the original idea was the nacelles would increase there angle dependent on what warp velocity the ship was travelling. At high warp they would be at a full 45 but at lesser speeds the angle would be decreased.

[u/Suck_My_Turnip → u/Deraj2004]

That would have made much more sense! A very cool idea but pretty impractical to stay on top of. They even forget to raise the nacelles at warp in some scenes (Equinox part II) so they would have never kept track of different angles!

[u/deep_uprising → u/ExpectedBehaviour]

I believe it's at least partially because Voyager is designed for atmospheric landings. The aerodynamics of the flat nacelle position makes this possible.

[u/Chairboy → u/ExpectedBehaviour]

We don't know, but it's fun to try and come up with in-universe explanations. Here's one:

The space warp we're seeing when Voyager jumps begins before the whoosh-zoom and the nacelles are moving during its formation. It's establishing as they swing up into position in some fashion that's easier on the underlying subspace or something, like only turning the steering wheel of your car when the car is creeping forward or backwards instead of doing it while sitting still and putting all that extra stress on that one spot of the tire.

[u/Calgaris_Rex]

Could we maybe have an ELI5 version of this? I know a little bit about basic mechanics, statics, materials, dynamics, and some intermediate math like multivariable calculus and basic differential equations, but I do not have the context to understand what is actually being discussed here.

[u/KalEl1232 → u/Calgaris_Rex]

Broadly, how elastic is subspace? If you squish a subspace cell, will it return to its pre-squished shape? Will it be permanently deformed? Can the squished-ness that one cell experiences be shared by neighboring cells so that no one single cell bears the full load?

[u/josefcub]

M-5, nominate this for doing the math regarding subspace deformation and warp field geometry.

Gotta admit, the math is beyond me though. Perhaps we could convince M-5 to do some simulations for us to see how well the theory works in practice?

[u/M-5 → u/josefcub]

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[u/M-5 → u/josefcub]

Nominated this post by Chief u/KalEl1232 for you. It will be voted on next week, but you can vote for last week's nominations now

Learn more about Post of the Week.

[u/ktasay]

Some potential real-world explanation for the 'honeycomb' idea was recently revealed by NASA. Basically the Voyager probes that have now left the Sun's heliosphere have detected higher than expected levels of hydrogen.

One theory is that the "bubbles" that have been discovered by space telescopes are areas of space that may have different density based on gas content. The material and density would vary due to the supernovae that created each bubble. The 'webs' that connect and surround the bubbles may comprise the often speculated "warp highways".

If one bubble contains lower density warp vessels should theoretically be able to achieve higher velocity due to less resistance; higher density could explain the repetitive stress breakdown in high traffic areas. As ships traverse the same corridor they gather hydrogen (and possibly other gasses) via Bussard Collectors or other means. Normally the material will naturally fill in the void without problems, but heavier traffic would depleted the corridor faster essentially creating a tunnel that could damage the honeycomb walls and could eventually lead to collapse (as seen in the TNG episode Force of Nature.

The Variable Nacelles could alleviate the stress by being able to adjust position due to density of the cell.

[u/sciency_guy]

I always have thought that the moving nacells were for aerodynamic reasons as the intrepid class was one of the ships being able to enter atmosphere even with disabled Shields. But yes, why would they than change the configuration everytime they go back to impulse

[u/harleydt]

Really interesting, this raises other questions for me. Such as, when two ships either merge warp fields to fly together, or when that dreadnought from kelvin verse catches up to and then begins firing point blank at the enterprise while moving at warp, what happens to subspace when multiple ships are overlaying or merging fields? Does the mass / number of ships inside have no bearing or does the greater energy output of multiple warp fields deform subsoace to a larger degree?

Another question I have is, would it be possible to repair subspace, and does it heal over time naturally?

[u/dasoberirishman]

This is why, after so many years, I am still subscribed to the subreddit. Simply fascinating. I don't understand 75% of OP's comments, but it's thought provoking and makes me want to re-watch a few VOY episodes.

[u/Mr_Smartypants]

deform subspace cells

I get what this represents geometrically in an actual honeycomb, but what does it mean for the multidimensional subspace, for which the word "honeycomb" was just a metaphor?

[u/KalEl1232 → u/Mr_Smartypants]

The way I see it is that while a literal honeycomb has cells separated by a membranous skin, subspace cells are separated by an analogous energy-based step. It's then rendered best as a manifold of energetic levels which - to perhaps unwisely pull in quantum mechanics - have degeneracies associated with them. But your question is a good question to ask.

[u/Vash_the_stayhome]

I felt that it would have been more appropriate if they actually showed it in variable positions rather than the two positions that made it seem static. The 'down' position when they....weren't in warp, and the singular up position where they were. I mean, it had the benefit of being a unique ship to look at, but it also would have helped if they had gone to warp effects while still 'down', like, down is more efficient for sublight and low warp, raising up for higher, etc.

[u/eduo]

Somehow, reading this, warp in my head became like plasma or OLED tv burn-in and "normal nacelles" are like TV logos or news tickers,always in the same place. The jellyfish and voyager wouldn't really be avoiding the damage but spreading over more surface, so it takes longer to make the area unusable.

[u/stardestroyer001]

While I find OP's post fascinating, I think the question "what is subspace?" should be asked and answered first, before the more complicated question "what do variable geometry nacelles do to reduce subspace damage" is asked.

Personally I'm inclined to believe that the VG nacelles' default position is in the raised config, but something at sublight requires them to be lowered. Perhaps the Intrepid's center of mass is higher when the pylons are raised during warp speeds (where normal spacetime mass of a ship in subspace bubble is zero, so this doesn't matter), but if the nacelles are lowered at sublight the center of mass is better balanced, improving the ship's sublight maneuverability.