You and your companions have been flying this loaded down BC-4-class transport from Barnard's Star and your headed into the Sol system. Destination: Earth. Traveling at 0.48 light-years per day, your 12 day journey between star systems will be over any moment now, right? Not so fast . . .
Once in-system, you've got that old 0.0001g gradient to worry about. In the Sol system, the "Threshold", as you star jockeys call it, forms a sphere 2.45 astronomical units from Sol itself. Naturally, you plotted your course so that you came into the system with earth lying directly between your ship and the sun. That cuts a potential 1 AU off of your trip, but you still have to cross 1.45 AU of threshold space to get to Earth. Traveling at 0.31 AU ( 0.48 x 0.645) per day after crossing the threshold, Miller time ain't for almost another five ( 4.7) days!
Calculating the radius of the threshold sphere is actually very easy. We've boiled down most of the math for you, leaving you with the simplified formula: R = 2.45 x M1/2 = 2.45 x Squareroot ( M).
Where R is the star's threshold radius measured in astronomical units, and M is the mass of the star measured in solar masses ( 1 solar mass = 1.99 x 1027 tons).
So, find the mass of the star measured in solar masses ( GDW's Invasion sourcebook provides this info for many colony worlds on the French Arm. Colonial Atlas also provides this information for a number of colony worlds, but requires some digging to get to). Take the square root of this number and multiply it by 2.45. The result is the star's threshold radius measured in astronomical units.
For interstellar travel, the number of light-years a vessel can travel in a day is equal to the ship's drive efficiency rating. Within a system's threshold boundary, the number of AU a vessel can travel in a day is equal to 0.645 times the ship's warp efficiency.
To determine the total travel time between two star systems you must divide the distance between the two systems ( in light-years) by the ship's drive efficiency. Add to this, the interplanetary travel times.
Interplanetary travel is calculated twice -- once for the departure system, and once for the destination system. In each case, subtract the planet's orbital radius from the star's threshold radius. The result is the distance that must be covered at sub-light velocity. Divide this number by the ship's stutterwarp efficiency factor, then divide the result by 0.645 to get the required travel time in days.
In addition to a system's threshold sphere, there is a second region of space where a drive's warp efficiency drops so much that it cannot overcome the pull of gravity. This region which occurs at the 0.1g gradient is commonly referred to by navigators and pilots as the "Dead Zone." Ships which venture beyond this line can not utilize their stutterwarp drives to pull away without some fancy maneuvering. Such ships can, however, use thrusters if they are so equipped. Note that all ships must travel to the edge of a system's or planet's dead zone to discharge its drives. Stutterwarp drives are sufficiently effective to maneuver a vessel into and out of this orbit.
Calculations Calculating the radius of the dead zone is identical to calculating the threshold sphere except that the formula is now: R = 0.078 x M1/2 = 0.078 x Squareroot ( M)
For those of you who prefer not to go through all the calculations, I've created a table of 34 of the most visited star systems. The most useful feature of this table is a column showing the distance from the system's main outpost I colony to the closest edge of the threshold boundary.
System Name - Thresh - Outer Body - Thresh Travel Sol (1.00) 2.45 y 1.45 Alpha Centauri A (1.05) 2.51 y 1.41 Nyotekundu (0.24) 1.2 y 1.15 Bessieres A (0.33) 1.41 y 0.61 Neubayern (0.55) 1.82 y 1.42 Augereau A (0.46) 1.77 n 1.37 Queen Alice's Star(0.62)1.94 y 1.52 Kimanjano (0.60) 1.91 y 1.24 Beta Canum (1.04) 2.50 y 1.37 Henry's Star (0.47) 1.69 n 1.33 61 Ursae Majoris (0.87) 2.28 y 1.51 DM+36 2219 (0.54) 1.79 y 1.53 Vogelheim (0.70) 2.06 y 1.56 Beta Comae Berenices (1.04) 2.50 y 1.02 DM+36 2393 (0.42) 1.59 n 1.38 Hochbaden (0.72) 2.08 n 1.68 Aurore (1.75) 3.23 y n/a Barnard's Star (0.35) 1.42 n 1.27 Serurier (0.38) 1.51 y n/a Broward (0.32) 1.39 n 1.19 Clarkesstar (0.005: VB-8B) 0.17 y 0.15 King (0.53) 1.82 y 1.58 New Melbourne (0.46) 1.66 n 1.46 Mu Herculis A (2.03) 3.47 y 1.52 Vega (3.20) 4.38 n 4.33 Red Speck (0.41) 1.57 y 0.37 Ellis (0.013) 0.28 n 0.21 Ross 863 (0.34) 1.42 n 0.28 Botany Bay (0.56) 1.83 y 1.49 DM-26 12026 A (0.79) 2.18 y 1.38 Davout (0.33) 1.41 y n/a Delta Pavonis (0.91) 2.34 n 1.44 Beta Hydri (1.82) 3.29 y 1.62 Zeta Tucanae (0.98) 2.42 y 1.32
Notes: mass of star is located in parenthesis next to the system's name and is given in solar masses; Threshold and Dead Zone = radius of each, given in AU's ( astronomical units); Thresh Travel = distance between colony world's orbit and threshold measured in AU's; n/a = not applicable.
A ship can discharge its stutterwarp at a world outside the threshold if one is indicated in the Outer Body column of this able. As a general rule of thumb, until we provide a more accurate means, assume it takes 6 hours to reach the dead zone ( 0.1g discharge zone) of an outer planet. This allows a ship traveling through the system to bypass a colony or outpost on an inner world, thus reducing total travel time. This assumes that a ship has adequate fuel to reach the next star system.
When navigating between star systems, the normal procedure is to maneuver me ship in such a way that the ship spends the least amount of time within the threshold sphere. Since interstellar travel is so efficient, the time added to cover the additional distance is negligible. The benefit is the time saved by minimizing the amount of travel done within the threshold sphere. Also note that in the example illustrated, a direct travel path would also carry the ship within the star's 0.1g "Dead Zone" where stutterwarp efficiency drops so much that it cannot overcome the pull of gravity. This region would have to be avoided by a ship following a direct line course.