Bok ship simulation

Inspired by C.J. Cherryh's various SF stories regarding Bok/Knnn drives.

For discussion about in-system (non-hyper-drive) engines in the CJC universe,  read this.

The ship is assumed to adopt a wave-like trajectory between the normal-space interface and the next hyper-level (ultra-space?), oscillating between the two at 20-200 times light speed until a large mass coincides with the ship's proximity to the lower interface. Look at the diagram below. In other words, in order to make a hyper-space journey a ship must:

1) have enough generator power (high enough Power/Mass ratio) to boost past the interface;

2) reach the proximity of a sufficiently large mass at the correct phase in the ship's wave trajectory.

The methods below make a LOT of assumptions about the way this all works; I'll explain the assumptions as I go:

Variables:

M.cargo = cargo mass in metric tons (1000s of kg)
M.ship = total ship mass
M.fuel = fuel mass
M.ls = life support system mass
M.gen = mass of field generator

C.pm = power-to-mass ratio (kW / ton)

n.crew = number of crew (cargo mass can be used for passengers)

r.field = range of generated field in meters
-- Range of the field in which EVERYTHING will be boosted into hyperspace

r.safe = range of safety in kilomenters
-- Range at which field can be said to be 'negligeable'.

r.t = range at time t from departure point

lambda.Bok = the Bok 'wavelength' of the ship's traveling mass
-- ALWAYS slightly longer than the trip distance because the phase at boost is 'advanced' in order to keep the ship in hyperspace near the mass it is leaving.
theta0.Bok = initial phase at boost
-- Phase will be advanced slightly to keep proximate masses from bouncing back into normal space.
theta.Bok = intantaneous phase under drive

r.Bok = approximate target range in parsecs (1 pc = 3.26 ly = 206265 AUs)

v.ps = 'pseudo velocity' in parsecs/week ~ typically 20-200 times light speed
-- 1 pc/week = 170.07 * c

t.Bok = elapsed time in jump ~ (distance/pseudo velocity)

z.Bok = 'amplitude' of Bok wave; always positive in hyperspace
-- depends on phase of wave + gravitational effects + 'damping' (energy loss); when this is negative ship will spontaneously drop out into normal space

F.g = field due to gravity from near masses
-- must be > 0.826 steller masses per AU^2 for safe drive operation
-- typical safe ranges to turn on drive:
-- .45 AU from SUN
-- 105,000 km from Earth
-- 11,500 km from Moon

Mass.a, Mass.b etc. = mass of large proximate objects in units of the mass of the sun
dist.a, dist.b etc. = distance to above masses in AU

D.x = max v-dump factor = amount of kinetic energy that can bled off in a v-dump

beta.d = velocity at drop out
-- usually somewhere between 53% - 95% light speed

K = kinetic energy of ship in joules

K.d = kinetic energy after a dump

gamma = Einsteinian relativistic dilation factor

beta = velocity in % light speed

rho.f = % chance of drive failure per v-dump

Equations:

You can go ahead and look at my Perl code here.   Cut and paste it into a text editor, save it as 'boktk.pl' and run it; download Perl  here  if you are a Windows user and don't have it.
NOTE: many of my constants are purely arbitrary, but here are the basic assumptions:

1) I use the 'boxcar' analogy for designing space-ships, i.e. the smallest possible ship of ANY kind (Bok drive or not) has about the same size and cargo capacity as a railroad boxcar: empty ~ 65 tons, gross wt. ~ 150 tons. The Space Shuttle, by these standards, is a pretty rotten cargo platform, but we can hope for improvement in the future...

2) Fuel weight at full capacity, due to the inefficiency of in-system propulsion systems, can be as much as 50% of total ship weight. If we assume the basic engine is based on high-temperature plasma or photon (i.e. fusion) principles rather than something exotic, we just have to carry lots of fuel. No problem as long as we can use the Bok drive for V-damping, though.

3) I have quite capriciously chosen 32.5 km as the safe distance to be from a 26 MW Bok field-generator when it turns on. Likewise anything within 100 meters of such a generator is going to (attempt to) head for hyperspace also, whether it be the ship, a rock, or a big chunk of the hull of the station you are docked at. Note that the mass of such things needs to be taken into consideration when turning on the drive.

4) Equally capriciously (but based on close reading of the texts) I have assumed a Bok drive of this general configuration can be operated safely at the distances (from large masses) talked about above; i.e. about 0.45 AU (42 million miles) from a star the mass of our Sun. This allows one to theoretically orbit a station around Mercury and still be able to reach a low-g realm (and thus be able to turn on the drive) in a reasonable interval. Under full in-system drive power it should take no more than a day to get outside this minimum distance; so I gather from the texts.

5) The 'damping factor' is something I intend to add at a later date in order to simulate energy loss due to Bok drive inefficiency; the ultimate effect is that trips to a target at that cooincide with a more distant harmonic of the Bok wave would be less likely to be successful; I will have to think of consequences of coming out of drive TOO close to a large mass, also. For now, assume damping to be near zero and higher harmonics of the wave to be difficult or impossible.

6) Mass calculations for the ship assume that superstructure and life system have a minimum amount of dead weight; ditto for the field generator. I also make some assumptions about the practical minimum power of a field generator. If you do the math on the 'boxcar' analogy you find that smaller field generators (and smaller ships) are pretty impractical; you end up mostly carrying dead weight. Example 1 below (The Pride of Chanur) is about the smallest practical cargo ship.

7) Velocity dumps involve a huge number of assumptions. I reason that there is a certain amount of 'friction' at the interface, and turning on the field generator with the polarity reversed (deep BS here) bleeds real-space velocity off by a factor roughly preportional to 'pseudo-velocity' and the local g-field. In all my v-dump calculation I used the average of 3-5 dumps as typically for a normal system entry. Below 500 km/sec the insystem drive can be used.

8) Also, since v-dumps involve running a Bok-drive 'backward', this should have a particular chance of failure depending on how much power is used to do the v-dumps; at some maximum (about 150% of the dump factor) failure is certain.
----

Constants:

PI =~ 3.1415926535
c =~ 300,000 km/sec (speed of light)
1 day = 86400 seconds
1000 kg = 1 metric ton
1 AU = 149,600,000 km = 93,000,000 miles
1 pc = 206265 AU = 3.26 light years
1 pc/week = 170.07 * c

Formulas:

M.ship (tons) = (3/2) * (500 + (3/2) * M.cargo + 20 * n.crew) / ( 1 - 3 * C.pm / 200)

P.gen (kW) = C.pm * M.ship

M.gen (tons) = 400 + P.gen / 100

M.ls (tons) = 100 + n.crew * 20

M.fuel (tons) = (M.gen + M.ls + M.cargo) / 2

r.field (meters) = P.gen / 260

r.safe (km) = P.gen / 800

theta0.Bok (radians) = PI * C.pm / 80 + PI / 8

lambda.Bok (AU) = (1 + theta0.Bok / (2 * PI)) * 206265 * C.pm / 5

theta.Bok (radians) = 2 * PI * r.t / lambda.Bok + theta0.Bok - PI / 2

r.Bok (parsecs) = C.pm / 5

v.p (parsecs/week) = C.pm ^ 1.1 / 1700
v.p ( c's) = C.pm ^ 1.1 * 17.007

t.Bok (days) = r.Bok * 7 / v.p

z.Bok = sin(theta.Bok) - sum of all F.g / 2 + 1.01 + damping factor
-- NOTE: always >0 in hyperspace

F.g (stellar masses per AU^2) = Mass.a /(7 * dist.a^2)
+ Mass.b /(7 * dist.b^2) + ....
-- or --
F.g (Earth masses per km^2) = (9.6 * 10^9) * Mass.a / dist.a^2 + ...
-- or --
F.g (kg per m^2) = (1.6 * 10^-7) * Mass.a / dist.a^2 + ...

D = (2/5) * c.pm^2

v.D (%c) = (F.g * v.p / 10000) ^ (1/3) + 0.53

beta (%c) = v / c = sqrt(1 - 1 / ((2 * K) / (M.ship * c^2) + 1))

gamma = 1 / (1 - v^2/c^2) = 1 / (1 - beta^2)

K (joules) = (1/2) * (gamma - 1) * M.ship * c^2

rho.f (% per event) = (D / D.x)^4 / 10

K.d = K / D

Example 1: Pride of Chanur (old drive)

r.0 = 1.1 AU from hani Sun (Mass = 1), 'far enough' from station
C.pw = 10
M.cargo = 600 tons (5-6 boxcars)
n.crew = 5

Target: Jupiter size mass at 1.88 parsecs;
course accurate to .1 AU at target or .05 arcseconds

Results:
M.ship = 2647.1 tons
M.gen = 664.7 tons
M.ls = 200 tons
M.fuel = 732.4 tons
M.cargo = 600 tons

P.gen = 26470.6 kW
r.safe = 33.1 km
r.field = 101.8 m

lambda.Bok = 464,096.25 AU = 2.25 pc
r.Bok = 2 parsecs
v.p = 0.577 pc/week = 98.13 times light speed

dropout =~ 0.05 AU from target ~ 7.5 million km ~ 25 light-seconds
actual travel time 22 days 19 hours

max dump factor = 40

Example 2: Norway

r.0 = 1.1 AU from hani Sun (Mass = 1), 'far enough' from station
C.pw = 17
M.cargo = 20000 tons - 4 riders, 5 tons food etc. per crew, ammo
n.crew = 1000

Target: Sol to Pell (61 Cygni, M=0.6, dist=3.49 pc), one jump
course accurate to 1 AU at target or .5 arcseconds

Results:
M.ship = 101578 tons
M.gen = 17685 tons
M.ls = 20100 tons
M.fuel = 28893 tons
M.cargo = 20000 tons

P.gen = 1,728,523 kW
r.safe = 2161 km
r.field = 6650 m

lambda.Bok = 819645.5 AU = 3.97 pc
r.Bok = 3.4 parsecs
v.p = 0.981 pc/week = 289.12 times light speed

dropout =~ 2 AU from target ~ 300 million km ~ 17 light-minutes
actual travel time 24 days 21 hours

max dump factor = 115.6

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