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Re: starship-design: Motion of sail driven by constant-power beam -- Excellentwork Rex!

At 6:47 AM 9/12/96, Kevin \"Tex\" Houston wrote:
>DotarSojat@aol.com wrote:
>> Hi all
>> Kevin has written, on 9/4 to the Group,
>> >How about a mission which has a constant beam power, the
>> >acceleration would drop off toward the turnaround point.  In
>> >this case, the crew would start off with earth-like gravity,
>> >and towards the middle of the trip, the gravity would be more
>> >lunar-like. ... The advantage would be simplified beaming
>> >requirements, and the disadvantage would be a slightly longer
>> >flight time.

[aggresive sniping]

>So, let me see if I understand this.  For a trip to Tau Ceti (12 Lt-yrs
>(interpolating from above 6 is almost halfway in between 5.3 and 6.6)
>The ship accelerates for 4.25 years crew time to turnaround.  It
>a final velocity of .933 C and the acceleration felt by the crew is .186
>Earth's transmitters have been on for 1.63 years (as measured by earth)
>and turnaround would be achieved at 7.618 years earth time.
>Doubling these numbers (where appropriate)  gives for a one-way trip:
>15 earth years for travel.
>8.5 crew years for travel.
>3.5 earth years of transmitter time.
>With 10 years for in-system study (and return maser construction),
>This gives a crew time of 27 years for the entire mission.  and an earth
>time of 40 years.  This is not too bad.  The crew would be able to see
>earth again, the time differential upon return is not so horrendous that
>all your family would be dead.  your twin would be "only" 13 years
>older than you.  I think this is even favorable in terms of "political
>return"  A politician who voted for this would expect to see results
>in about 30 years (travel time plus transmission time back to earth)
>Long enough to  be forgetable if it goes bad, short enough to hope to
>be alive to see it if it works.

Nit, politicians generally arn't interested in effects past 4 years.  For
example. Social security is expected to melt down in 20 years, but the
problem was considered 'solved' when that number was upped from 10 years.

On the other hane a 27 year service life is short enough to be reasonable
for realistic ships systems, and the professional lives of the crew.

>> These results seem to confirm Kevin's intuitive estimates regard-
>Can I say "I told you so"?  Aw, come on be a sport.  ;-)
>> ing acceleration levels.  They also substantiate Steve's conclu-
>> sion that the time of emission is limited (even for a constant-
>> output emitter); from the table above, the duration of emission
>> of the radiation accelerating a sail half way to a destination
>> more than 16 lt-yr away (the last entry) is only about a year
>> and three quarters.
>> The deceleration phase (here assumed without justification to
>> be a mirror image of the acceleration phase) needs to be
>> addressed in a separate discussion.  Timothy has already put
>> a lot of thought into it.
>I thought Tim's treatsy on the subject of deceleration with a beamed
>poser source showed that it will work.  That is to say that the ship
>receives ennough power via the antenna to power an ion engine with
>a fairly decent mass ratio.
>=============begin included text =============================
>Calculations for the deceleration phase of the MARS design.
>by Timothy van der Linden (T.L.G.vanderLinden@student.utwente.nl)
>Last modified April 14th, 1996
>[derivation snipped]
>Vstart  Vexh optimal  Fuel:ship-ratio  Energy per kg of ship (in Joules)
> 0.1        0.062          5.36              7.45E14       7.73E14
> 0.2        0.121          5.84              3.25E15       3.50E15
> 0.3        0.180          6.40              8.11E15       9.08E15
> 0.4        0.240          7.06	             1.64E16       1.91E16
> 0.5        0.300          7.87              2.99E16       3.64E16
> 0.6        0.364          8.91              5.23E16       6.69E16
> 0.7        0.433         10.38              9.21E16       1.25E17
> 0.8        0.512         12.72              1.73E17       2.53E17
> 0.9        0.615         17.75              4.04E17       6.62E17
> 0.99       0.803         52.00              3.12E18       7.02E17
> 0.9996     0.906        238.81              2.91E19       9.26E19
>Note that the power of the maser-beam is NOT constant during the
>phase, it is supposed that it decreases while the ship gets lighter
>(because it repulses mass).
>======================End included text==============================
>By repluses mass, I think Tim means the beam tends to accelerate the
>ship more than the engine can compensate.  this was supposed to be a
>minimum energy solution, perhaps a constant energy beam will raise the
>costs.  But turning down a power beam is very easy. (think dimmer
>Also Fuel:ship ratio is Reaction Mass:Dry Mass ratio I think.

This is a key point, and I'm not sure we ever decided one way or the other.
But obviously if you can't stop a MARS configuration, the rest is

>For a top speed of .9333 C, we are looking at a mass ratio of "only"
>30.4 (interpolated).  this seems to me to much better than any other
>mission discussed so far.

Certainly beats the Explorer or Fuel/Sail mass ratios, probably come close
to a anti-matter too.  But of course you have to figure out how to make it
work.  Thats a lot of power to transmit, and a lot for a ship to swallow
and process.

>> (Note: This exercise may turn out to be purely academic because
>> the inverse-square effects, without unforeseeable advances in
>> focusing abilities, would be much larger.)
>I think we can make some advances here using :
>1) Coherent energy (masers instead of microwaves)
>2) Large focusing elements in outer solar system (ala Robert Foreward)
>3) Phased array transmitters to simulate large arperature ~ 400km
>With proper microwave optics (moptics? :) yeah, Moptics!) I think we
>can make the beam nearly non-divergent.  Not totally, but enough to
>make this mission possible.  Remember, Tim's derivation requires a
>diminished beam during deceleration.  Inverse square is too much
>diminished certainly, but at least it's the right direction for a

Agreed.  Acceptable optics should be doable, thou you still would need to
'pad' by boosting the transmisionm power level up a couple orders of
magnitude.  After all, most of the beam (and power) won't hit the sail.

>I think this mission profile is looking more and more doable.  the high
>energy costs were (mostly) due to:
>1) The extremely large ship 1 E 09 Kg when I calculated that number.
>2) The desire to accelerate at 1G the entire time.
>3) The foolish notion of increasing the exhaust velocity to save mass.
>#1 can be changed any time we wish.  We just have to settle on a mass
>that seems reasonable (although in this group, the very word is open to

We really do neeed to get a handel on what the ship would need to carry and
how big it will need to be.  Still I dobt you could scale down the ship by
a factor of 10 from my Explorer numbers (about 500,000 tons) without
seriously cripliing an mission potential.

>#2 has been shown by Rex and others for the folly it is.  A gradual
>decline into lunar gravity, and a gradual climb back out will certainly be
>doable for the astronauts.  no clumsy swiveling sections, no artificial gravity
>generators (although if we had those, we could do this mission easily ;)

I don't follow this?  Low grav is still bad for you, and spending a decade
parked in orbit in zero-g is REAL bad for you.  Given that the centrafuges
don't have a serois weigh problems (well possibly shielding) I think we'ld
have to carry them.

>#3 Was shown by Tim to be foolish.  According to the above chart, the
>optimum Vexh is .685 (interpolated)
>A beamed mission is safer than anti-matter (and easier); it is faster
>and less costly than a fusion fuel mission (excepting perhaps the hybrid
>mission Kelly has proposed).  It only requires one major advance (self
>replicating machines to make the solar collectors.) Other than that,
>the technology is all present day.

We're a very long way from self replicating machines or systems.  So I
wouldn't jump over that so quickly.

It is definatly faster then a fusion system.  Even Fuel/Sail couldn't get
past .4C without rediculus deceleration fuel masses.

>Kevin "Tex" Houston 	http://umn.edu/~hous0042/index.html


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