From: throopw@sheol.UUCP (Wayne Throop)
Newsgroups: rec.arts.sf.science
Subject: Re: Donaldson's _Gap Cycle_: does this add up?
Summary: nope, Donaldson hasn't a clue
Date: 29 Aug 92 02:20:20 GMT

> From: alberti@mudhoney.micro.umn.edu (Albatross)
> My first question is, does Donaldson have a clue?

Nope.

> My second question is simpler:  [...] is there
> a table which might demonstrate whether these descriptions were credible?
> In other words, something which would show...
>      [.. acceleration time with resulting velocity ..]

As far as I know there isn't a table as such, but such things can be
computed "easily enough".  (Note: the example table Albert gave didn't
seem to have accurate numbers even for the newtonian case, so I may be
missing something here...)

I used the brute force and massive ignorance method of numerical
solution to this instead of trying to remember the analytical solution. 
Essentially, I simply sumed up velocities as seen from a stationary
observer over an interval of time while an accelerating observer holds a
constant acceleration (in the accelerating "frame").  Errors creep into
such a crude method of course, but I assured myself that I was getting 3
or more digits of more-or-less accurate numbers in the range I was
interested in, and then ignored the remaining error.  That error becomes
overwhelming as lightspeed approaches, however, so I stay away from that. 

Ok, now that I've overexplained what I went and did, what are the results?

First, my results bear out the rule of thumb that lightspeed is
reached in about a year of 1G.  In particular, 365 rest-frame days
of 1g gives .85 or so lightspeed, consuming 304 or so accelrating-"frame"
days.  Something like 600 rest-frame days gives .999... lightspeed,
and more-or-less a year of acclerating-"frame" time.  (Note that
this was pushing IEEE floating point limits as mentioned above, so
I didn't really look into that range in detail, not trusting it.)

Next, if you want to get to .5 lightspeed in 10 hours, be prepared
to endure 450g (yes, that's four-hundred and fifty times earth gravity)
acceleration.  Can you say "strawberry jam"?  I knew you could.  (That
would be about 9.5 hours time in the accelerating-"frame".)  Here's a
table giving ballpark figures for a range of methods of getting to .5c.

           accel        rest          accel      
            in g    time in days   time in days  
           -----    ------------   ------------  
               1        185           177        
               4         46.2          44.3      
              16         11.5          11.0      
              64          2.9           2.7      
             256           .72           .69     

( Somebody should check my arithmetic from this table... I'm not 
  really *totally* sure it's right, given the quick and dirty 
  numerical methods I used... )

Note that at .5 lightspeed, tau is still only .87, so you can get a good
general feel for times and accelerations up to this velocity by just
dividing up terminal velocity by acceleration times time, newton-like. 
Donaldson didn't even do *that*. 

Also, in my review of _The_Gap_Into_Vision_ on sf.reviews, I already
noted that Donaldson doesn't know about relativistic velocity addition,
and gives .9c - .4c = .5c, where it really should be about .78c instead. 
And that's not even conSIDering how much energy and reaction mass his
antics would be throwing around...  not at all consistent with the level
of technology portrayed. 

Interestingly enough, two cases where relativistic treatments of
accelerations are featured in stories and are gotten right leap to my
mind...  and both of them are Heinlein stories.  I'm thinking about
_Citizen_of_the_Galaxy_, which features warships ad 400-ish g and
merchant ships at 100-200-ish g getting to lightspeed in hours or days. 
And I'm thinking of _Time_for_the_Stars_, where the 1g
year-to-lightspeed scenario is treated pretty well.  (Not that I think
Heinlein really understood special relativity all that well, as passages
from TftS and _Farmer_in_the_Sky_ hint at, but at least he doesn't blow
it big-time as Donaldson does.  Further, let me say that IMHO Heinlein
isn't pointed out as a "hard SF author" nearly as often as he deserves...  
his controversial reputation overshadows this aspect of his career.)

Busby also does fairly well with such scenarios.  Heinlein and Busby
at least can do their relativistic arithmetic, more or less.  Neither
one of them go into details of energy budget, but they both at least
handwave plausibly at it, Heinlein with the total-conversion Torch
and other such, and Busby with the "magic" alien drive components.

> I'm curious as to how bad the science is going to be 
> in the rest of these [.. Gap ..] books...

Probably pretty bad, sad to say.


> From: pepke@ds1.scri.fsu.edu (Eric Pepke)
> From my high school physics class, I seem to remember that relativistic 
> momentum is p = gamma m0 v, where gamma is 1/(sqrt(1 - (v^2/c^2))), 
> [.. calculations omitted ..]  To get [.. to .5 lightspeed at 10g ..]
> you would need to run the engines for 1.7e6 seconds, or about 20 days.

Eric's simple analytic solution agrees with my clumsy numerical one
pretty closely.  The 20 days (actually I get 19-and-something) is in the
rest-frame...  it's about 18 days in the accelerating-"frame". 

Not that I'd like to endure 10g for 20(ish) days.  Consider the
portrayal of (if I'm remembering right) 8g for a week or so in
_Have_Space_Suit_Will_Travel_.  And the poor gung-ho torch pilot 
taking the vaccine to pluto in that short story whatsitsname?

Anyway, it only reinforces the point: Bo may know SR, but
Donaldson definitely does NOT.
--
Wayne Throop  ...!mcnc!dg-rtp!sheol!throopw