Work in Progress
This page will describe the warp drive as it is purported to exist in the UNSEO universe.
The warp drive is strictly slower than light at any point where the acceleration due to gravity is greater than about 1/10,000 of Earth’s surface gravity. The radius within which gravity is too high for faster than light travel will be referred to as the Breakout Zone for reasons which should become clear.
RBreakout = 637,653,737.123 * (M/MEarth)1/2 meters
RBreakout = 100 * (M/MEarth)1/2 * R_Earth
RBreakout = 2.12698391873 * (M/MEarth)1/2 light seconds
RBreakout = 367,887,634,962 * (M/MSol)1/2 meters
RBreakout = 2.45917646546 * (M/MSol)1/2 a.u.
RBreakout = 1227.14106091 * (M/MSol)1/2 light seconds
At the moment the sig-figs are insanely excessive. Please bear with me…
This fails to take into account the intrinsic velocity of the vehicle. In order to make life harder for people trying to make the warp drive into a WMD on a grand scale, I’ve decided to add a fudge factor to this based upon the relative intrinsic velocity of the vehicle:
RBreakout,v = RBreakout*(1 + (v/c)1/2)2
RBreakout,v is the radius of the Breakout Zone taking into account the vehicle’s relative velocity.
v is the intrinsic velocity of the vehicle relative to the body into whose gravitational Breakout Zone the vehicle is entering.
c is the speed of light, 299,792,458 meters per second.
Within the Breakout Zone the vessel’s pseudovelocity is also reduced based on its intrinsic velocity relative to the body in whose gravity well it is.
VEff,sublight = 0.48 * τ * VEff,FTL
VEff,sublight is the pseudovelocity of the warp drive within the Breakout Zone, measured in astronomical units(a.u.) per day.
VEff,FTL is the normal pseudovelocity of the warp drive outside of the Breakout Zone, measured in light years per day.
τ is the relativistic time dilation factor expressed as a multiplier of time rate(also spatial length):
τ = sqrt(1 – v2/c2)
At reasonable velocities both RBreakout,v/RBreakout and τ can be treated as essentially unity. These only make a real difference at intrinsic velocities exceeding several hundred kilometers per second. Especially τ.