http://www.islandone.org/LEOBiblio/SPBI1SI.HTM

There must be something wrong in all of this, or else why would us
High Frontier types maintain our love affair with the mass driver.
This sounds like it might be another case of 'proving' that bumble
bees can't fly. My math isn't good enough to show this right or
wrong, but there must be *something* wrong with this argument. $4
billion dollars just for the silicon?!?

Xenophile (couldn't think of anything to put in these parentheses)

First off, the author of that post is referring to a mass driver for
an earth launch system. He rightly points out the complexity of such
a system by using plausible numbers, such as escape velocity of
10,000 m/s, cargo mass of 1,000 kg and 1 meter length.

Now we High Frontier types don't usually advocate mass drivers as
earth launch systems, rather we think they make a lot of sense for
lunar material launch systems. Note, most people don't even advocate
using a lunar mass driver for human capsule launches.

So, our relevent numbers become a lunar escape velocity of 3,000
m/s, a cargo mass of a fraction of a kilo to a hundred kilos, and a
bucket length (into which our lunar material is placed) of at most
50 centimeters (this becomes the limiting factor in the switching
circuitry.)

So let's run through some numbers. Here's my scenario. A launch
bucket in the shape of a semi-sphere with a radius of 25 cm. This
corresponds to a volume of 32,738 c.c. Filled with lunar regolith to
a capacity of 86.5%, the volume of material is 28,318.45 c.c. with a
mass of 78,8856 Kg. For those who think in English units, this is 1
cubic foot of material with a mass of 173.91 pounds. You can
substitute in your own optimum cargo package.

Now at an acceleration of 322 gravities, a track length of 1,425
meters and a period of acceleration of .95 seconds, an escape
velocity of 3,000 m/s can be achieved. This allows one launch per
second with a bit of fudge factor included. Of course, theoretical
mass driver designs should be able to handle higher accelerations
with shorter track lengths, but we've got to use some numbers, so I
chose these.

If we take our 25 cm radius bucket, and want it to fit into one
track section with no overlap, let's use a 30 cm track section.

So using the author's reasoning but substituting our lunar example
in place of his earth launch system, we would need an acceleration
of 3,157.85 m/s^2, and 4,750 track sections.

Our time pulse would be 100 microseconds (1/10,000th of a second)
and our power at the last section of track would be 747,042,469
watts.

The 100 ms time pulse allows us to dissipate 10,000 watts for a
dollar, just as the author points out in his post.

So, using the last formula in his post, the cost of the silicon
would be . . . M * 2^(1/4) * A^(5/4) * LS^(3/4) * NT^(5/4) / 1250

so plugging in

78.8856 Kg * 2^(1/4) * (3,157.85 m/s^2)^(5/4) * .3m^(3/4) * 4,750^
(5/4) / 1250

we get a cost of $28,398,313.11.

What our the differences in the two proposals. Our moon mass driver
accelerates at 3,157.85 m/s^2, compared to the Earth system at 500
m/s^2, our track section is .3 meters compared to 1 meter, our
escape velecoity is 3,000 m/s compared to 10,000 m/s, our track
length is 1,425 meters compared to 100,000 meters, our projectile
mass is 78.8856 kg compared to 1,000 kg, our mass driver has 4,750
sections compared to 100,000 sections.

So, the earth mass driver hs to be very robust compared to the lunar
mass driver and needs $4,000,000,000 of silicon for switching
purposes compared to our $28,398,313.

Now, our system on the moon will have different operating
constraints, i.e. operating in vacuum so no heat diffusion into the
atmosphere; lunar day temperatures of 250 C, lunar night
temperatures of -250 C, (if the mass driver is shaded during the day
then the environmental temperature will drop.) How this affects the
system, I still don't know.

Also, another interesting fact is that the 750 MW we would need to
power the system could be produced by a surface area of 2,225,000
m^2 of solar cells operating at 25% efficiency; 2.225 km^2 of
surface area. Using solar thermal power should decrease the area to
1.59 km^2 operating at 35% efficiency.

Once that power is available, especially if in the form of a SPS at
L2, thus available without interuption, we'd be able to launch 6,815
metric tonnes per day into our mass catcher. That's just shy of
2,500,000 metric tonnes per year. That'll go a long way to building
our habitat.

Now one thing that I still need to figure out is why this author's
calculations show a power requirement of 747,042,469 watts for the
variables I've input, but my earlier calculations of using KE=1/2(m
* v^2) 1/2(78.8856 * 3,000^2) = 354,985,200 watts and:

V/A = 3,000 m/s / 3,157.85m/s^2 = .95 sec; thus

354,985,200/.95 = 373,668,631 watts

This result is exactly half of the 747 MW the author calculated.
It's very late for me and I'm not sure why there is this discrepency
of power requirements. Anyone care to find out and post an answer.
Obviously, if we need only half the power so much the better for our
infrastructure requirements.

So, in conclusion, it looks to me like his math is OK, it's just
that his conclusion doesn't apply to a lunar mass driver scenario.

--- In spacesettlers@y..., "xenophile2002"
> http://www.islandone.org/LEOBiblio/SPBI1SI.HTM
>
> There must be something wrong in all of this, or else why would us
> High Frontier types maintain our love affair with the mass
driver.

In a message dated 8/28/02 12:04:00 AM, xenophile2002@... writes:

<< There must be something wrong in all of this, or else why would us
High Frontier types maintain our love affair with the mass driver.
This sounds like it might be another case of 'proving' that bumble
bees can't fly. My math isn't good enough to show this right or
wrong, but there must be *something* wrong with this argument. $4
billion dollars just for the silicon?!? >>

You are right, silicon is too cheap for that kind of price. I can see 4
millions for the cost of launchs and so forth but not that much.

Carl E. Mullin
visionary artist and entrepreneur
homo asteralis
ravenart@...
www.ravenartstudio.com

The more you love, the more you can love-and the more intensely you love.
Nor is there any limit on how many you can love.
If a person had time enough, he could love all of the majority who are
decent and just.
-Robert A. Heinlein (Time Enough For Love)

I'm not enough of a engineer to answer in detail, but there are mag-lev
trains operating today on the same principles, experimental mass-drivers
for small payloads have been constructed, the same principle has been
used for experimental high-velocity weapons, and there is a project at
NASA's Marshall Space Flight Center to develop electromagnetic
propulsion as the 'first stage' of a launch vehicle.

On Tuesday, August 27, 2002, at 09:03 PM, xenophile2002 wrote:

> http://www.islandone.org/LEOBiblio/SPBI1SI.HTM
>
> There must be something wrong in all of this, or else why would us
> High Frontier types maintain our love affair with the mass driver.
> This sounds like it might be another case of 'proving' that bumble
> bees can't fly. My math isn't good enough to show this right or
> wrong, but there must be *something* wrong with this argument. $4
> billion dollars just for the silicon?!?
>
> Xenophile (couldn't think of anything to put in these parentheses)
>
The International Space Station (ISS) most important legacy may be
jump-starting space tourism. Consider: the first space tourist, Dennis
Tito, was supposed to go to the Soviet era Mir space station. Under
pressure from NASA, Russia de-orbited the Mir which resulted in Mr. Tito
going to the ISS instead. Now the Mir was old, smelly, crowded and
probably not all that nice. The ISS was brand new, shinny, much more
roomy, etc. Mr. Tito came back to Earth with glowing accounts of how
great space is. Would his experience have been as good on Mir?

Al Globus
CSC at NASA Ames Research Center
http://www.nas.nasa.gov/~globus/home.html