Re: starship-design: Genuine STR question

[Steve VanDevender <stevev@efn.org>]

Johnny Thunderbird writes:

 > Thank for the backup on the relativistic mass enhancement of the jet.
 > If this holds up, it implies that every feasible star drive system must use
 > linacs to throw their jet, for every gram of reaction mass that leaves the
 > ship at less than relativistic velocity is "wasted" by not going through the
 > linac to get its mass boosted. The linac would make that gram into a
 > dozen grams, or a hundred grams, or a kilo. If it flies back at 0.7 C or
 > 0.8 C it's just a gram, so to us it means a leak, but if it flies at 0.99 C
 > it's a bunch of grams, and saves us from having to carry that much
 > reaction mass.

To a certain extent this is right; I would say this as a higher
exhaust velocity means a higher momentum-to-energy ratio, meaning 
you're getting more velocity for the amount of energy expended.

Unfortunately you can't get a momentum-to-energy ratio greater
than 1 if you're counting both the energy obtained from burning
fuel and the energy equivalent of the reaction mass.  Only if you 
can convert your fuel completely to photons can you get the ideal 
maximum momentum-to-energy ratio of 1, and consequently get the
most velocity for a given amount of beamed power.

Some of this was discussed a long time ago in the LIT
starship-design newsletter; Timothy van der Linden has archived
a posting where I derived this result at:

http://www.xs4all.nl/~jvdl/sdnewsletters/39-62/engineer-1.txt

Search for the subject header "What's the best reaction mass?"

Note that my derivation was based on the idea of a self-fueled
ship.  If you beam power to the ship things can be quite
different; Timothy managed to convince me that if you beam power
to the ship and use it to accelerate reaction mass it can be
better to carry lots of reaction mass that you expel at lower
velocity, and thereby use less beamed power to get the payload to 
the same velocity.

Overall I found your discussion to have some possibly problematic
confusion regarding the notion of "relativistic mass increase",
which turns up over and over in physics texts but which I was
taught is something of a misnomer.  Older physics texts go a
little too far with the notion of mass-energy equivalence, and
give the false impression that accelerating something makes it
heavier, while more modern texts define mass as a
relativistically invariant quantity, so that the proper
distinction is made that accelerating an object preserves its
mass, but increases its momentum and energy in the relation

m^2 = E^2 - p^2

(m = mass, E = energy, p = magnitude of momentum).

Or, approximately, older texts called E "relativistic mass" and
tried to preserve the Newtonian p = mv by claiming that m
increased with v.

I suppose I should plug Taylor and Wheeler's _Spacetime Physics_
again, but I already have within the past month or so.  I can
send you the detailed bibliographic information if you want.