From: MLINDROOS@FINABO.ABO.FI (Marcus Lindroos INF)
Subject: More warp/s'date babble...
Organization: Abo Akademi University, Finland
Date: Sun, 13 Dec 1992 15:15:41 GMT
X-News-Reader: VMS NEWS 1.24

Yet another stab at the never-ending subject of warp velocities and stardates.
First, has it occurred to anyone that warp factors might translate into
different velocities for different starships?! R.a.s. warp guru Leon Myerson
came up with the idea that the warp scale measures power rather than speed and
I have to agree.

According to Sternbach's/Okuda's technical manual, warp factors work like this:

Warp factor 1 = 1     x the speed of light
            2 = 10
            3 = 39
            4 = 102
            5 = 214
            6 = 392
            7 = 656 
            8 = 1024
            9 = 1516
          9.2 = 2000 (estimate from graph. on page 55)
          9.6 = 2500 (              "                )

The main problems with this scale:
1) In "Where No Man Has Gone Before," Geordi tells Picard the Enterprise will
   need 300 years to travel 2,7 million light-years "at maximum velocity" 
   which is supposed to be warp 9.6. This translates into a maximum velocity of
   9000c.

2) If one "stardate" equals one day (more of that later), the Enterprise needed
   about 600 days to travel back to Earth ("Conspiracy") from Deneb IV
   ("Encounter at Farpoint"), which is 1800 light-years away. After Q tossed
   the ship 7000ly. in "Q Who", Geordi estimates that it will take five years
   to get back. The time-difference between TNG 3rd season episodes "Who
   Watches the Watchers" [on Mintaka, some 2500ly. from the Sun] and "Best
   of both Worlds" [on Earth] is also about two Earth-years. This means the
   warp factors are somewhat to small, or that the (in my opinion false) 
   theory that 1000 stardates = 1 year is wrong. In any case, it seems like
   warp 6 (the maximum cruising speed) is about 1000c.

THE SOLUTION(?): Sternbach/Okuda's warp scale only represents THEORETICAL
values! The correct formula is:

     Warp Factor = theoretical Sternbach/Okuda velocity ^ correction factor

For the NCC-1701-D, the correction factor is about 1.16372 (i.e. 
2500^1.16372 = 9000c).The older Enterprise's corresponding figure is 0.9 - 
warp 6 is about the same as the theoretical value for warp 5 on an average 
24th century starship.
---
This makes sense, there is no reason why starfleet should have modified the
warp scale - especially because the difference between "old" and "new" is so
small (OK, English miles [1.5km] versus metric miles [10km] but still). No,
a 2000hp engine is more effective on a propeller-driven boat than on a
paddle-steamer (or whatever it is in English) and so is an engine working at
warp 6 on a modern starship compared to older designs. 
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Finally, the stardates. Last night, "Best of both Worlds" was on Finnish 
television, enabling me to scribble down this timeline:

STARDATE:    EVENT:
43996        Enterprise arrives at the New Providence colony
43998        Enterprise departs, encounters a Borg vessel - Picard is kidnapped
44000        After a 12-hour pursuit at warp 9.6, the E.crew manage to slow
             down the Borg for a few hours. Extensive repairs necessary
44002        The Battle of Wolf 359 [7ly.from Sun] occurred shortly before 
             this date. Enterprise entered the system at 44002.
44002-3?     The Borg are defeated in Earth orbit [no stardate, but it appears
             as if the E. continued towards Earth directly from Wolf 359]
---
The problem with this is that the whole episode took place in only 4-5 days (if
1 stardate=1 day) or even less (if 1000 stardates=365.25 days). Assuming
Sternbach/Okuda's warp scale *AND* the latter stardate theory holds, New
Providence has to be within eight light-years or so of the Solar system. Note
that the "12-hours-maximum-at-warp-9.6" limitation works really well if 1
stardate=8.766 hours, a point in its favor. However, if we assume that "my"
invented warp scale is correct and that stardates correspond to Earth days,
everything makes more sense - New Providence is now at a distance of about 100
light-years from the Sun. Does this mean that the Enterprise-D's "continuing
mission" of six years in fact has taken place over 18 years? Yes, but only in
Earth time. The biological clocks aboard the ship still show that the crew and
ship have aged only six years. Other good points:

1) One would expect that days (apparently using the 24-hour Earth format as
   an arbitrary standard) would make a lot more sense than Earth years in
   an interstellar society. Face it, humans (=the predominant race of the
   Federation) live according to their built-in 24-hour clocks and other
   species are more likely to follow the same pattern, too. If the day is
   much longer than 25 hours, the nights will be too cold and the days to
   hot for most lifeforms on class M worlds. A significantly shorter rotational
   period than 20 hours must be very rare among small, rocky planets orbiting
   close to their central star because of tidal effects.

2) Even if there are no relativistic effects to speak of, and one stardate
   = 8.766 hours, there are going to be problems with leap years, right? 
   One would have to "add" a stardate here and there to the calendar to
   make it work.

3) Finding the number of days that have elapsed is generally very useful 
   in fields such as astronomy and astrophysics - which is why astronomers
   use the Julian calendar for calculating the position of a body on a certain
   day. Most likely, all astronavigation computers and the like have built-in
   tables containing the positions of stars and planets on stardate 0.0 -
   estimating their current position 41000 days later is a simple problem if
   you know the orbit and velocities of the object in question. By contrast,
   using the Gregorian (=western) calendar disguised as stardates is virtually
   useless to anybody expect Earth residents spending their entire lives on
   the planet. Even spacefaring Earthpeople won't need it.

4) Worf's birthday problem? Well, assuming he was born stardate 28xxx, he'll
   soon be fifty!! But don't forget most of those fifty years have been spent
   on various starships, so his "physical" age is actually closer to thirty. 

MARCU$

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. . . Fififinlandssvensk
     
Marcus Lindroos                             Internet:     mlindroos@abo.fi
Computer Science
Abo Akademi University
Finland