Dive Drive

Dive-Drive Assemblies are the key piece of arcane technology which enable relatively quick and efficient interplanetary travel across Tau Elpis. A Dive-Drive generates a nullfield bubble which effectively 'sinks' into lower dimensions. A ship burning on conventional thrusters at speed can turn on its drive to drastically reduce the net distance it needs to travel - all without ever truly breaching the speed of light or general relativity.

Physics

It was discovered very long ago that lower dimensions exist and, using thaumic energy, can be breached. The metadimensional continuum is best represented as a conical reflection of realspace where distances correlate but are scaled down by an increasing factor the deeper the dive. Using this property, ships can sink into hyperspace and only require to travel a fraction of the realspace distance without bending the space-time continuum or causing time dilation.
Dive-Drives are made possible through the application of huge amounts of energy through a precisely refined Thaumium crystal. The required amount of energy increases with the 'depth' of a dive as well as the mass the ship needs to move. It is the piezothaumic vibrations of the crystal which generate the nullfield bubble required for a successful dive. This damages the crystal over time, meaning that ships must not only refuel but also frequently perform maintenance on the dive-drive assembly.

Navigation

Homebrew gameplay article : Navigation & Charting a Course
Dive-drives simply shorten the distance a ship needs to travel and do not provide motive force on their own - thus conventional thrusters are necessary. A diving route is made up of three steps : acceleration, diving, and deceleration.
Once a course is plotted, the ship will first burn on thrusters in realspace and spend hours to reach its desired speed, sometimes also using gravity wells to aid the process. A compromise has to be made on how much energy is spent on thrust vs on the dive itself, given a required speed.
Once the required speed is reached, thursters come offline and moments later, the dive-drive comes online. The nullfield bubble 'dives' the drifting ship into a lower dimension, where its momentum carries it in a straight, dimensionally shrunken line. At the other end of the dive, the ship must prepare to emerge and slow down in realspace by aiming its thrusters against the direction of travel. The dive-drive comes offline and nearly instantly, thrusters are applied to allow for slowing down. The transition from realspace to hyperspace is generally smooth with no sudden g-forces.
Much of the nav process is fairly painless on any trained pilot. Most vessels will have an onboard Astrometrics module which calculates and routes the best possible paths. Better pilots will also consult documentation. Of particular importance are local and sector rutters, which detail typical local graviometric conditions and space weather.

Physical Properties

Nullfield bubbles have a fixed polarity - anything not attached to the dive-drive will want to fall away from the positive 'top' end and towards the negative 'bottom' end of the bubble. This can be used as a pseudo-gravity field. Larger ships will exploit this peculiarity by orienting their dive-drive so that the 'top' and 'bottom' end matches the thrusters' axis, with the thrusters on the 'bottom', and decks on these vessels tend to be arranged vertically alongside.
Nullfield bubbles are susceptible to outside graviometric anomalies. Ships diving too close to a gravity well may cause the drive to fail - a disaster which almost always leads to a metadimensional incursion and the loss of all matter within the bubble.
Whilst in hyperspace, little can meaningfully interact with the ship (beyond extreme radiation or gravometric anomalies). This means that most comms stop working for the duration of the trip, and a ship's transponder or primary drive signature will not show up on radars. Nevertheless, simple predictive algorythms can deduce a ship's heading and location.
Some scientists believe that proximity to working dive-drives may lead unborn and younger children to be at higher risk of developing Psionic Metadisease in puberty or early adulthood. This theory is under a considerable deal of debate, given that more powerful dive-drives were routinely used for thousands of years prior to the Great Jump with no adverse effects ever recorded.

Engineering

In ages past, wider availability of advanced fusion and antimatter power and extreme abundance of Thaumium in the Pyxis Globula enabled dives past Factor Five - the apparent realspace speed of light, achieving FTL travel. In the Elpis System, on the other hand, fusion power is not readily available for most commercial applications and most worlds only have trace amounts of Thaumium for refining. At such, most dive-drives can only dive up to Factor One (1 V_f / 0.004c) - which is enough to enable travel within reasonable distance of Elpis, including the Nyx and Hepera sub-systems, but would require generation ships to reach any further stars.
Most ships are powered by miniature fission power plants. At such, ready availability of plutonium or uranium, as well as waste disposal facilities, are an essential part of the interplanetary travel infrastructure and industrial complex. Large, capital ships boast extensive fusion power plants instead, which lets a dive-drive help displace far more mass over deeper depths - but the extreme rarity of materials needed for fusion plants ensures that such technology is only available to the largest of military vessels.
The thaumium that makes up the core of a dive-drive assembly loses attunement over a period of time (several years, typically) until, eventually, it becomes inert and useless. A few crews keep a trained spellcaster called Alchemist to re-attune their drive, though many simply choose to visit a shipyard when required.

Appearance

Ships generally appear refracted whilst travelling at sublight speeds within nullfield bubbles. As the ship gains speed relative to realspace coordinates, it appears to blueshift (whilst objects outside the bubble will appear to redshift). Ships travelling towards or beyond FTL speeds would also emit gamma rays and X-rays - though this is not a concern now, given the limited technology available to the colonists of the Elpis system.

Travel Speeds

Realspace travel speed

Out in space, the unit of choice for realspace travel is the Kilo-Knot (KKn) (also known as Klik or Klunk). The conversion is thus :
1000 KKn = 0.0017c
(for reference, 1 KKn = 0.514 km/s = 1150 mph)
Most ships have maximum orbital realspace speeds of about 20 KKn or 23000 mph. Nothing but a ship's energy reserves and the condition of its thrusters can stop it accelerating beyond that, but ship crews tend to slip into hyperdrive the moment their ships exits the nearby gravity exclusion zone, for the ship will also need to decelerate upon arrival.

Hyperspace travel speed

Due to the faster apparent speeds achieved in hyperspace, the favoured unit becomes the Warp Factor or Dive Factor - which represents how far the ship dives, and thus how fast it appears to go in realspace terms. Hyperspeed is expressed as a ratio of V_f, the speed of a ship travelling at Dive Factor One (or 2550 KKn)

As a rule of thumb (if you must forget everything else) :
A ship at Dive Factor 1 will take one sideral day to cross one Astronomical Unit.
A ship at Dive Factor 0.5 will take twice longer.

This factor is quite handy, as most vessels travel at speeds approximating Warp Factor 0.5. A light ship, barely laden, with a fresh drive and the best technology available in Elpis will travel at a speed just slightly below Warp Factor 1.

Type of Ship	Dive Factor achievable
Skybarge	0.1 Vf (10x slower)
Heavily-laden cargo vessel	0.25 Vf (4x slower)
Frigate or heavier armoured vessel	0.4 Vf
Lightly-laden cargo vessel	0.5 Vf (2x slower)
Cruiser or lighter armoured vessel	0.75 Vf
Fast courier vessel - reference speed	1 Vf

Travel Times

Thus here are some example trips and the time it would take different ships - without any heroics, such as slingshot manouvers, gravometric anomalies and the like :

Journey	Distance (AU)	Travel time at Factor 0.5	Travel time at Factor 1.0
Elpis - Nevael	0.7	~ 33 hours	~ 16 hours
Elpis - Nufano	0.87	~ 40 hours	~ 20 hours
Elpis - Hakaria	0.92	~ 2 days	~ 23 hours
Elpis - Embassy	1	~ 2 days	~ 24 hours
Elpis - Aistanar	1	~ 2 days	~ 24 hours
Elpis - Planetfall	1.32	~ 2 days 12 hours	~ 31 hours
Elpis - Hestia	6.3	~ 2 weeks	~ 6 days
Elpis - Zindra	11.2	~ 3 weeks	~11 days
Elpis - Nyx	31.1	~ 2 months	~1 month
Elpis - Hepera	37.2	~ 2 months, 2 weeks	~1 month, 1 week
Embassy - Aistanar	2	~ 4 days	~2 days
Hakaria - Aistanar	0.1 to 1.92*	~ 4 hours to 4 days	~2 hours to 2 days
Nufano - Aistanar	0.13 to 1.87*	~ 4 hours to 4 days	~2 hours to 2 days
Aistanar - Hestia	5.3 to 7.3*	~ 10 days to 2 weeks	~5 to 8 days
Aistanar - Zindra	10.2 to 12.2*	~ 3 to 4 weeks	~10 to 13 days

* - As bodies shift throughout their orbital cycle, the distance between planets can change dramatically, which has impacts on local economies, astrometrics, etc.

Maths for rough estimates

For the more formula minded, this is what the math looks like :
An ideal ship will travel at a Warp Factor of 1 and thus achieve this apparent realspace speed :
1V_f = 2550 KKn = 0.0044c (0.44% of the speed of light)
Many ships will travel at a Warp Factor of 0.5 - twice slower. Thus we can estimate their realspace apparent speed to be :
0.5V_f = 1275 KKn = 0.0022c
And a handy formula that roughly estimates the time required to cross from two points of the Elpis system, negating any external gravometric effects and assuming ideal momentum at the point of diving is :
Δ_t = AD * wV_f
where Δ_t is the travel time in days, AD is the realspace distance in astronomical units, and w is the Warp/Dive Factor, with 1V_f the Dive Constant, equivalent to 0.0044c or 2550 KKn.
In addition, the estimated distance between two points in space can be roughly calculated using Elpis as a reference star (so long as somebody knows the average, or even better true distance between Elpis and both points, it can be triangulated)
AD_min(A→B) ~ | AD_avg(Elpis→A) - AD_avg(Elpis→B) | _ADmax(A→B) ~ | AD_avg(Elpis→A) - AD_avg(Elpis→B) |
Thus resulting in this rough calculation :
Δt(A→B) = | AD_avg(E→A) ± AD_avg(E→B) | * wV_f
...or you can consult astrometrics tables and local astrometric condition , then simply have your onboard computer do it all for you as you plot your course and file your flight plan, with proper up-to-date data and all variables accounted for beyond the scope of this quick article.