Ideal Semispatial Mechanics

In Exophysics, **Ideal Semispatial mechanics**, **Corralyn Exospace mechanics**, or simply **Corralynian mechanics** (sometimes abbreviated to **CEM**) refers to several laws and concepts under the Superstrata Interpretation of Exospace Node Theory which can be roughly described as a precursor to the related *Sakko-T'pahl Exopsace mechanics* (STEM). When comparing the two, Corralynian mechanics is often described as being to STEM what Newtonian mechanics is to relativity― highly simplified, but much easier to use and still accurate enough in the majority of cases. Thus, Corralynian mechanics is the more generally-preferred method, being the first to which most students are introduced while acting as a useful set of tools for estimation in more technical circles.

The main application for Corralynian mechanics is in modeling of ships, communications signals, and other objects that employ exospace to achieve apparent Faster-Than-Light travel― the original intent of ENT. Because the relevant aspects of the theory were relatively new when CEM was first conceived, it is tied much more closely with engineering and practical applications in comparison to similar realspace theories― to the point where much of its terminology has been scavenged directly from the pertinent fields of astronavigation and superluminal engineering.

## History

### Early Divergence

By the late 2500s, the galaxy's scientific was divided― while almost everyone agreed on the now-ancient exospace Node Theory as a fundamental aspect of the universe's inner workings, scientists bickered on the exact details. Many of the old empires, championed by the venerated Federation, insisted on the *Substrata Interpretation*, which posited the existence of over a dozen *subspace* layers "below" realspace. The Substrata interpretation indeed worked very well in describing the motion of vessels using warp drives, as well as explaining several anomalies which previous ENT iterations had struggled with.

As proficient as it was with ENT's traditional issues, however, the Substrata interpretation quickly broke down when trying to explain the more exotic propulsion systems favored by the newer empires, such as the MSI. In response, these factions quickly forwarded several interpretations of their own, including the *Point-Chasm interpretation* and controversial *Null Space* *Interpretation*― each with their own advantages and failings. The result was a scientific firestorm, a massive back-and-forth battle between experts across the galaxy on the nature of the universe's most ethereal aspects responsible for FTL travel. By all accounts, the scientific community was deadlocked for years.

### Superstrata Interpretation and Rise of CEM

Enter Starfleet-petty-officer-turned-exospace-major Jay Tsanu-Baalak Corralyn. Corralyn, in an attempt to find a subject for her doctorate dissertation, scoured the scientific literature― and hit the jackpot. Buried in a forgotten university archive, Corralyn discovered a little-known paper dating from soon after the introduction of the Substrata Interpretation― a new take on the theory we now call the *Superstrata Interpretation*. A byproduct of an attempt to simplify some of ENT's underlying equations, the Superstrata interpretation differed wildly from most existing interpretations― proposing the existence of 24 *hyperspace* layers "above" realspace alongside the 24 subspace layers "below" it.

Corralyn's final paper, *An Analysis of the Movements of Exospace Objects Within Ideal Settings*, assimilated several unexplored applications of this Superstrata interpretation into an existing fabric of laws and rules to create a unified set of dynamics that successfully explained the behaviors of both standard and nonstandard propulsion systems. Corralyn called this set of rules *Ideal Semispatial mechanics*, in reference which is still technically its proper name. The media buzz, however, quickly redubbed it "Corralyn Exospace mechanics", after an off-handed joke by a notable researcher on the subject; this has become the name by which it is most widely known.

Despite this ability to correctly predict the movements of most FTL drives, Corralynian mechanics was not immediately adopted by most groups. Aside from some lingering hostility between the various factions, many scientists disliked the new theory for its lack of accuracy and failure to explain some of the stranger subspace phenomenon, such as tachyon storms. It was not until 2611, after years of iteration and modification, that the modern version of Corralynian and Sakko-T'pahl mechanics gained the wide acceptance they enjoy today.

## Common Units

Different ships and drive types are capable of entering different exospace layers; the absolute value of the se'Poi number for the strata a ship is currently in is called its *warp factor*, Ж― for example, a vessel at subspace level 3 would be said to have a warp factor of Ж = 3, as would one at hyperspace level 3. Entering an exospace layer requires the application of a *warp field*, which stresses ("warps") the fabric of space time to allow a vessel passage; the strength of this stress field is measured in *Cochranes* (Д), where 1 Д = the amount of stress required to enter the first exospace plane.

The amount of power required to maintain a stress field for a given energy layer is given in *Asrics* (Я), as defined by *Asric's First Law*: Я = P / Д. In essence, it defines the amount of power required to maintain the current level of stress on local exospace (see below).

### Pertrandian Mechanics

A sub-group of Corralynian mechanics, Pertrandian mechanics is named for an early Federation Exospace physisict, Alfred Pertrand, who explored the efficiency of watts-Asrics conversions. This watt-Asric conversion ratio is known as the *Pertrand value* (sometimes also called a *Pertrand ratio*), given by *Pertrand's law*: S = (Я \* Y) / P, where:

* S = Pertrand value
* Я = output Asrics
* Y = Pertrand's constant (Approx. .81)
* P = input power in megawatts

The effective Pertrand value varies widely based on a host of parameters, including local realspace and exospace conditions, FTL drive type, model of ship, proximity to local gravity wells, etc. Thus, measuring a vessel's "average" Pertrand value is rather pointless, as the value tends to depend much more heavily on a vessel's location and activities than make or model; instead, engineers and shipwrights use a measure called the *maximum ideal Pertrand value* (symbolized SMax) to compare vessels, which is essentially a measure of what the ship's Pertrand value *would* be given perfect ("ideal") conditions.

However, even this measurement tends to be class-specific; to compare FTL drives as a whole, one must use the further-abstracted *absolute maximum Pertrand value* (symbolized SAbs or SA), which is the maximum possible Pertrand value a drive could produce; although far higher than any real-life Pertrand value could realistically reach with current technology, is does allow for comparisons of efficiency between radically-different propulsion methods.

## FTL Applications

### The Asric Curve

According to CEM, the number of Cochranes (and, by extension, Asrics) required to reach a certain position in subspace does not follow a linear path, as supported by empirical measurements. Indeed, graphing the warp factor against the Asrics needed to maintain it results in a sawtooth curve: the required Asrics increases exponentially, followed by a dramatic drop, and then increases again. The lowest point for a given "cycle" of the curve, called the *trough*, is usually taken as the dividing line between two strata― for instance, the second trough in hyperspace is where the first energy plane A ends and energy plane B begins. The highest point, meanwhile, is called the *crest*; the areas of the curve with proportionately-high slopes compared to surrounding areas are called *warp barriers*. Every successive strata has a higher trough and crest than the last, as well as a larger difference between the two.

This unusual pattern, stemming from complex interactions between stress fields and exospace's energy strata, has several important implications for FTL travel. Because of the wear and energy requirements induced by this extreme "hump-trough" plane-crossing style of movement, most FTL drives will either limit themselves to shallower strata (such as Warp drives) or attempt to "burn" straight through to the desired level and bypass the intervening layers altogether (such as in Tachyon Waveform Hyperdrives); the the finer points of these differences are discussed in greater detail in the appropriate documents.

### Warp Fields

As stated earlier, entering or exiting exospace requires the use of a warp field, whose role is given away by its more technical "proper" name: *exospace stress field*. By stressing realspace through a process called *Galleki warping*, a "hole" is opened in the local space-time continuum, allowing a vessel to "fall" into the desired energy plane; moving between planes requires the processes described above.

A symmetrical warp field's strength is measured in Cochranes, and has two components: *magnitude* (how "big" the number is) corresponding to the "depth" the field allows the ship to go; and *sign (*sometimes called its *polarity*, especially in older texts), with positive fields entering hyperspace and negative fields entering subspace. At integer warp factors, magnitude can be estimated at ±10Ж-1, dipping immediately afterward before rapidly climbing again due to the curve described earlier.

#### Arcite-Summins Effect (Eccentricity)

The vast majority of vessels do not employ symmetrical warp fields, however, due to the *Arcite-Summins Effect*, which states that all asymmetrical warp fields are innately propulsive ―naturally propelling the generating object through exospace― according to *Arcite's law*: v = Д \* c / Y \* (1 − e)3. This is due to an unpredicted but fortunate effect of exospace: whenever a symmetrical warp field is created, the four dimensions of both hyper- and subspace "press" down on it equally― equivalently to how fluids apply pressure to objects within them. When a field is asymmetric, however, it tends to reside in some hyper/subspace dimensions more than others; due to Netwon's third law, this dimension pushes back. If the field is in the correct direction, this force will be propulsive, and thus help the given ship along.

This tendency for asymmetrical fields to exist in some exospace dimensions more than others ―behavior known as eccentricity― is critical for modern spaceflight. Like realspace eccentricity, warp field eccentricity ranges in value from one to negative one, noninclusive; what is important, however, is that eccentricity has a cubic relationship with velocity, due to the previously-mentioned Arcite-Summins Effect, meaning increasing a vessel's warp eccentricity is a far more efficient method of increasing a vessel's apparent FTL speed than increasing its Cochrane output.

Warp fields, however, are fragile things; for the vast majority of ships, warp fields will only remain stable within a very small range of eccentricities― usually ± .0001, though this varies widely. Destabilized warp fields are exceedingly dangerous for the generating vessel― with effects range from simply depositing the ship in realspace, to reverting its entire mass into neutrinos instantaneously. Furthermore, higher-eccentricity fields tend to be more difficult to control, whereas increasing the Cochrane output has no real negative effects and much more flexibility (not to mention is often easier overall).

## See Also

* List of FTL Drives (WIP)
* Exospace Node Theory
* FTL Drive infobox
* This Ex Astric Scientia article, which served as the foundation for much of what you see here

## Notes

1. ↑ ENT predicts that stress requirements are perfectly mirrored for both hyperspace and subspace layers; that is, it requires the same amount of stress to enter level A as level α, to enter level B as level β, etc. This proposition holds true in every tried experiment, and is now well-accepted as fact; thus, it doesn't matter whether one is discussing entering hyperspace or subspace layers, as the required stress is the same.
2. ↑ P = power, usually in megawatts
3. ↑ Alternatively: S = Y / Д
4. ↑ Y uses the Cochrane as a unit, in order to make S a unitless value
5. ↑ Technically, SMax can only be calculated on a ship-by-ship basis, as tiny differences between each vessel means the chance they share an SMax value is virtually nil― even if they are members of the same class. However, these differences are so small, the SMax value can often be generalized to a whole class regardless.
6. ↑ Where v = effective realspace velocity, Д = number of Cochranes, c = the speed of light, Y = Pertrand's constant, and e = ecentricity
7. ↑ As some readers may have guessed, the dimension itself does not actually "push" against anything; rather, it is a complex series of structures and particles that restrict themselves to individuals exospace dimensions, not layers. However, the true nature of these objects are well out of the scope of this document; thus, it uses the convenient simplification that it is the dimension itself pushes against a warp field.