Suzy B Software 2/Suzy B Software CD-ROM 2 (1994).iso/nasa/to_orbit/to_orbit.txt

Text File | 1995-05-02 | 35.0 KB | 603 lines

                   Low Cost Launch to Low Earth Orbit (LEO)
                    by Jim Chestek, retired space engineer


ABSTRACT.

    The energy content of a satellite in LEO is of the close order of 30 MJ per
kilogram.  A barrel of oil costs $20-40 (August '90 to October '90) and
contains over 6000 MJ.  Thus, the energy cost of a kilogram satellite is around
1/200th of a barrel of oil or 0.10-0.20 cents per kilogram.  Current launch
costs are in the neighborhood of $3000-10,000 per kilogram.  (Bad
neighborhood).  This article explains some of the reasons for this discrepancy,
and what (maybe) could be done about it in the reasonably near future.


SUMMARY.

    The first section of this article discusses the terms and units used in the
discussion.  If you are already familiar with the technical use of SI (metric)
units, you can skip this.

    The second section describes how to calculate the energy content of a
satellite.  Then the third section shows that this energy content has a trivial
cost.

    The fourth section describes why rockets are so dreadfully inefficient.  It
then introduces some of the concepts which have at least the theoretical
prospect of being vastly more efficient than rockets.

    The fifth and final section introduces the subject of engineering
economics.  Transportation systems, like cars and airplanes, have to be paid
for, and that cost usually far exceeds the fuel costs.  Further there are other
operating costs, like pilots, mechanics, and ticket agents that must be paid.


Definition OF TERMS/UNITS.

    First, let us be clear about the units we will use in this discussion.
Rather than get tangled up in mass pounds (lbm) and force pounds (lbf), which
are NOT the same thing, this paper will use only the Systeme International
d'Unites (abbreviated SI in all languages) units. (1)  Not only does this
eliminate the confusion between weight and mass, it makes the arithmetic easy
since we do not need to be concerned about the relationship of the length of
some English kings forefinger to the length of his foot.  (Twelve inches in a
foot;  what a ridiculous conversion factor!)

    Since this system in unfamiliar to many, lets make sure that the
fundamental terms are clear.  "Mass" is how much stuff something contains.  Two
kilograms (kg) of hydrogen (2.016, to be picky) contains
602,300,000,000,000,000,000,000,000 molecules of hydrogen, (hope I counted the
zeros correctly !) each with two atoms.  This would usually be written as 6.023
E26 molecules of H2, the E26 denoting that the decimal point is to be moved to
the right 26 places.  (This is 1000 times Avogadro's Number, which is the
number of molecules in one gram-mole.)  The number of molecules is the same,
whether the hydrogen is a liquid or a gas.  Of course, the gas takes up more
room.  This is a two kg mass.

    Some old guy named Newton promulgated several laws that are pertinent here.
He observed that force equal mass times equals acceleration.  From this they
have defined the unit of force such that one unit of force will cause one unit
of stuff (mass) to be accelerated by a velocity increment of one meter per
second, each and every second.  This acceleration is written by technical types
as one m/sec 2, read as one meter per second squared.  For making this
observation, the inventors of the SI named the unit of force after this guy; so
force, in SI units is measured in newtons, abbreviated N.  Remember, the
fundamental units of newtons are kg-m/sec 2.

    The same old guy also noticed that apples fall to the ground, and wrote an
equation for how fast.  The acceleration we call gravity is, near the surface
of the earth, about 9.8 m/sec 2.  (Varies a little, since the earth is not a
sphere, but a lumpy oblate spheroid.  This weird shape causes earth satellites
to do so weird things, but that is a subject for another discussion.)  The
consequence of this is that to support a one kilogram mass takes 9.8 newtons of
force to overcome the acceleration of earth's gravity.  (On the moon the force
required to support the same kilogram mass is only about a sixth as much, which
is why space engineer types don't use the term weight very often.)

    The unit of length in SI is a meter.  One thousand meters (a kilometer) was
intended to be a hundredth of a grad arc of the earth circumference.  There are
400 grads in a complete circle.  (Don't ask me where they got the 400!)
Anyway, there were supposed to be 40,000 kilometers in the circumference of the
earth.  They missed a bit when they defined the meter a couple of centuries
ago, so that there are really 40,075 kilometers in a nominal equator.  In
familiar terms, a meter is a yard plus ten percent, approximately.

    That leaves one more important unit we will need to define.  That is
energy.  In any system of units, energy (to an engineer) is a force applied
through a distance.  To make life simple, the SI unit of energy is defined as a
force of one Newton acting through a distance of one meter.  (See how easy the
arithmetic is in SI units.)  This was named the joule, after a very early
electrician.  (It is abbreviated J.)  He got the honor because a watt is the
energy rate of one joule per second.  The joule is a very small unit of energy,
so it is easier to speak of megajoules (MJ), as in million joules.  For
comparison, a kilowatt-hour is 1000 watts for 3600 seconds, or 3.6 megajoules.
Now we can go into orbit.


ORBITAL POTENTIAL AND KINETIC ENERGY.

    There are two ways a brick can hurt you.  It can be dropped upon you, or
thrown at you.  The farther it is dropped, or the faster it is thrown, the more
it will hurt.  This is because, in both cases, it has more energy.  The two
kinds of energy are called potential and kinetic energy.  Note that in the case
of the dropped brick, the acceleration of gravity quickly converts the
potential energy of the brick (what height it was dropped from) into kinetic
energy (how fast it is moving).  Note that this conversion is 100% efficient,
one of few natural processes where this is true.  The reverse conversion is
also 100% efficient, although I can think of no way to attain this without
being already in orbit.  A trampoline bounce would allow most of the kinetic
energy to be converted back into potential energy, but there would be losses in
the trampoline rebound, and of course, air drag on both down and up legs of any
flight in air.

    Both kinds of energy are defined in joules, and both are needed to get an
object from the earth surface into orbit.  Potential energy is just the force
used to raise an object to a higher elevation.  To hold a one kg brick off the
floor takes a force of 9.8 N, as we have discussed.  Now to raise that brick
one meter higher, we must apply that force through a distance of one meter.  So
we have to apply a 9.8 N force times one meter or add 9.8 joules of energy to
the brick.  If we want to raise the brick to 300 kilometers, so it will be in
space, we have to add 300,000 meters times 9.8 N or 2,940,000 joules.  Right?
Well, not quite, because at 300 km altitude, the acceleration of gravity is
very slightly reduced.  So, using the calculus (which is definitely another
subject), we can calculate that the energy needed to raise the brick from the
earth surface to 300 km is only 2,807,560 joules, instead of 2.94 million
joules. (2)

    What keeps a satellite from falling back to earth?  The answer is its
velocity.  This same old codger (Newton--he must have been a smart guy) gave us
yet another law.  He said that an object in motion would continue in a straight
line (forever) unless acted upon by a force.  It you tie a rock to a string and
swing it around your head, there is a definite force on the string.  We call
that centrifugal force.  It is that force that makes the rock travel in a
curved path, rather than continue in a straight line.  (Have you ever seen said
string break?)

    If we want the satellite to fly at constant altitude around the earth, then
it must travel at a given velocity, so that the acceleration of gravity at the
satellite altitude is EXACTLY offset by the centrifugal force of the satellite.
(This NEVER happens.  But we can get the velocity close enough to stay at
nearly the same altitude.)  This orbit velocity can be readily calculated.  For
a circular orbit altitude of 300 km, this velocity is 7725.846827 meters per
second, approximately.

    This represents a LOT of kinetic energy.  Kinetic energy is given by the
formula:

                 KE = one half of mass times velocity squared

Trust me.  (The half comes from the constant of integration, but lets not get
into that.)  The units are thus kg-meter 2/sec 2;  which can also be written as
meter times (kg-meter/sec 2).  That LOOKS like meter (distance) times N
(force).  And it IS.  So the units of kinetic energy (KE) are joules, just like
the units of potential energy (PE).  Numerically, at that velocity a kilogram
mass has an energy of 29.8 million joules.  (7725 x 7725 */2)

    It should be noted in passing that there is a trivial amount of kinetic
energy in the satellite while it is still on the launch pad.  This is
occasioned by the rotation of the earth.  For example, at Cape Caneveral, this
earth velocity is 408 m/sec.  This corresponds to a kinetic energy of about
0.083 MJ per kilogram, about a quarter of one per cent of the orbital energy.
This is not much to fret about, but NASA and other rocket enthusiasts always
make a really big deal out of it; i.e they always launch east instead of north
or west.  This is because rockets are so awful that they need all the help they
can get.


ORBITAL ENERGY COST

    Now we can determine the energy cost for a mass in orbit.  The total energy
of a kilogram satellite at 300 km altitude is the sum of the potential and
kinetic energy, as just seen in the previous section is 29.8 plus 2.8 = 32.6
million joules.  In more familiar terms, this is a little less than 10
kilowatt-hours.  (9.06 kw-hr.).  You know what you pay your electric company
for a kilowatt hour, so now you know that launch costs are not so high because
of any energy requirement.

     According to the Standard Handbook for Mechanical Engineers, (Baumeister &
Marks, Seventh Edition, McGraw Hill page 7-22) Texas crude has a higher heating
value (HHV) of 19,460 Btu/lbm, 7.286 lbm/gal, 42 gal/bbl.  (old book, so they
gave it in English king units.)  This gives 5.95 million Btu/bbl.  This
translates into 6.3 thousand million Joules/barrel, or 6300 MJ per barrel in
the notation we are using.

    This one barrel of oil has as much energy as 6300/32.6 or 193.25 kilograms
in a 300 km orbit.  If oil cost $20 per barrel, and ALL of the energy in the
oil could be converted into orbital energy, then the energy cost for one
kilogram would be $20./193.25 or 10.35 cents.  If oil costs $40 a barrel.....
(This is left to the student.)

    This "ALL the energy" is the first catch in why launch costs are so much
more than pennies per kilogram.  There is no known process that will convert
the chemical energy in petroleum (or anything else) into orbital energy at 100%
efficiency.  A modern steam power station will convert something like 30 to 40
per cent of the chemical energy into electricity.  This can in turn be
converted into many other forms of energy, such as velocity (kinetic energy),
elevation (potential energy is increased by elevators) heat, etc.  This can
usually be done with rather high efficiency, which is why electricity is so
popular.  Most large motors convert electricity into either of these forms of
mechanical energy with efficiencies that range between 80 and 90%.  Hence if
you could take an elevator to our 300 km orbit, and then use a linear motor to
increase the speed to orbital values, the energy cost of a kilogram in orbit
could be kept to something under a dollar per kilogram.  One problem is the
lack of sky hooks to support this elevator and linear motor.  So we must seek
other solutions.


ROCKET PERFORMANCE AND FUTURE SOLUTIONS.

     Rockets are a lousy way to get to space.  Unfortunately, they are the only
means developed to the point we can routinely use to get there.  They work of
the principle (Newton AGAIN !) that action equal reaction.  So rockets throw a
lot of stuff (mass) out the back as fast as they can.  This produces a force to
propel the rocket in the other direction.  But, they have to throw a LOT of
stuff away to get much of a result.  And they don't throw it away very fast.

     There is no point in belaboring this unhappy truth very much.  Current
rockets use the chemical energy of propellants to provide the energy needed to
throw stuff out the back of the rocket.  They usually react a "fuel" with an
"oxidizer" to liberate this energy.  Then, they have to use this energy to hurl
something out the back.  Since they are through with the chemicals they used to
liberate the energy, they (rather sensibly) use the depleted chemicals as the
"working fluid" to throw out the back.  NOTE that this is NOT a given.  They
could keep the depleted chemicals and throw away something else.  The point is
that the energy source and the working fluid DO NOT have to be the same.

     For example, a nuclear reactor is a marvelous energy source.  It contains
vastly more energy per pound than any chemical system.  It could be used to
provide the energy to throw rocks out the back to provide thrust.  In fact,
this very system has been seriously proposed to move asteroids around the solar
system.  It is a good scheme.  It could have a very high performance; much
better than the space shuttle engines.  (3).

     In the 1960's there was a major program conducted by the Atomic Energy
Commission to develop nuclear rockets as a space launch system.  Their
particular notion was to use high temperature reactors to heat hydrogen working
fluid to high temperature.  They advanced to the point that they were operating
such rockets, with more than enough thrust to lift the reactor, and with
specific impulse much better than todays space shuttle engines.

     This scheme does have problems, however.  Would you want a nuclear reactor
to crash near your house?  In your state?  On planet Earth?  Recent thinking
has been that reactor powered space machines may only be used after they are in
such high orbit that they will not fall to earth while they are still
radioactive.  Many centuries, in other words.  So these will not help us into
orbit.

     There have been other suggestions to decouple the energy source from the
working fluid.  One such notion is to use a laser beam on the ground to heat a
working fluid in the flying machine to give a high specific impulse propulsion
system.  Speaking for one man, I do not care for such a scheme.  One slip of
the laser beam and you have fried rocket.  Further, any thing that comes into
the beam is instantly destroyed.  Plus clouds, etc.  Moreover, it is not
necessary, in my opinion, in order to develop low cost launch.

    There are at least four schemes that offer some prospects for low cost
launch into orbit.  They are, in my view:

    1.  Air breathing boosters, one or two stages.
    2.  Ground based catapults
    3.  Launch loops, or space fountains.
    4.  The space elevator to geosynchronous orbit.

In addition, there are several non-rocket schemes that can be used to move
about in space, once low earth orbit has been attained, plus more very high
performance jet propulsion schemes that may be useful in that regard.  Several
of these involve tethers.  There is a whole body of literature on this, so I
will not treat the subject here.  One useful starting point is the report of
the National Commission on Space.  (4)


CONCEPT 1.  AIRBREATHING BOOSTERS

    The SR-71 airplane, recently retired by the USAF, takes off horizontally
under its own power, and is capable of sustained flight (many thousands of
kilometers) at Mach 3+ at about 25 km altitude.  By the time our "best" rocket,
the infamous space shuttle, achieves that energy state it has burned something
like a million kg of propellant (about half of its initial load).  Then it
struggles on up from there.  It should be noted that the SR-71 is twenty-five
year old technology.

    If we gave it just a bit of attention we could devise a first stage booster
that could get into "space" by getting high and fast enough to zoom into
vacuum, trading kinetic for potential energy. (I suggest Mach 4+ at an altitude
of 30-35 km before starting the zoom.)  At this point rockets could take over,
operating all of the time at their best performance; i.e. vacuum Isp.  After
the rocket separates,  the airplane "re-enters", which is quite easy from such
"low" speeds, and lands.  It could be reused many times with very little
"refurbishment."  The second stage goes into orbit.  The engines and
electronics could be recovered and reused, but it would be better to sell the
whole thing for scrap to the space colonists.

    I did enough calculations on this concept to make a presentation at the
Chicago Space Development conference in July 1989.  That exercise convinced me
that there is a lot of potential in this approach.  However, the existing space
flight organizations are sufficiently enamored of rockets that this kind of
thinking does not get much attention.

     A much more well known approach is that of the National Aerospace Plane,
or NASP or "Orient Express."  A prototype, sometimes known as the X-30, has
been funded by the US government (NASA and DoD combined) for several years now.
This is, at present (August '90), only a technology development effort.  Funds,
and DC politics permitting, it MAY be funded as a flight project "soon."  It is
expected, if the development succeeds as well as hoped, that an "airplane" will
be able to take off from a (long) runway, and "fly" into orbit and return, just
like an airliner.  This is a long stretch of current technology, so it will
take awhile, and cost a lot of money to make this come true.  There is a paper
in LIB14 (NASP.TXT) that discusses this approach in considerable more detail.

    The biggest apparent problem with this approach may be cost.  At the
Chicago Space Development Conference there was a presentation on this subject.
The presenter, in answer to a question, "guessed" ( and you KNOW it had to be a
wild guess) that, after the development was done, each vehicle might cost $1
billion!  You can buy ten 747's for that.  This will be discussed in the
section on engineering economics.


CONCEPT 2.  CATAPULTS

    The second concept, ground based catapults, is finally getting a little
attention.  Several years ago when working on some far future space weapon
concepts I discovered that, contrary to my expectations, atmospheric drag DID
NOT prevent a "bullet" from exiting the earth atmosphere.  Mach 25 at earth
surface does lead to a SERIOUS aerodynamic heating problem, but there are well
established technical approaches that can solve that problem.  Last year I
answered a question in the "letter to editor" column of Ad Astra with this
finding.  Just recently (July 23, 1990) AvWeek described a Lawrence Livermore
National Laboratory concept for a light gas gun concept for accomplishing space
launch from a gun tube on a small mountain.  They projected the cost to be
$600/kg, which a small fraction of rocket costs.  I was very glad to see that
proposal.  Livermore gets a lot more respect than a lone retired engineer.

    This concept is not yet ready to fly.  It will take substantial R&D on
several aspects, not the least of which is thermal protection of a projectile
moving at Mach 18 or so in dense atmosphere.  This scheme WILL NOT be suitable
for people.  Livermore projects 5000 gee acceleration.  An electric gun would
let you control that to lower values, but not low enough for people, until we
build an evacuated "tunnel" many hundreds of kilometers long.  Of course, on
the moon we don't need to provide our own vacuum ...


CONCEPT 3.  SPACE FOUNTAINS

    The third concept absolutely fascinates me.  I first ran across it in a
book by Robert Forward called "Future Magic." (4)  This scheme is anything but
magic!  It appears most practical, given a very large investment to develop and
operate the system.  Basically it uses a "mass driver" to accelerate mass up
into space.  To avoid aerodynamic losses, the lower part of the system is
enclosed in a vacuum tube (or tower), open to space at the upper end.

    At the space terminus, the mass is "caught", turned around and hurled back
to earth.  This can support the space terminus against gravity, for just the
energy loss in the mass driver motors (and a bit of residual aero drag.)  Now
once in space, you can build a LONG catapult to launch things, including
people, into orbit.  That is a quick description.  Better, buy Forward's book
and read it for yourself.

     At the Chicago Space Development Conference, Forward gave a presentation
which enlarged somewhat on the material in his book.  In particular, he
suggested that tiny prototypes "only a few miles high" could be built as
attractions for Worlds Fair type exhibitions.  This would provide some of the
initial technology, and create a climate such that the full fledged space tower
could be undertaken.


CONCEPT 4.  SPACE ELEVATOR

    The "space elevator to geosynchronous" concept has been around a long time.
The notion is very simple.  You hang a rope down from a geosynchronous
satellite and just climb up it.  Better, use an elevator.

    I think I first heard of this idea in the late 60's or maybe early 70's.
The problem is that the "rope" requires materials that are not yet even nearly
available.  When I first heard of the concept it was being suggested that a
single crystal diamond 36,000 km long might cut it.  Of course, nobody then had
any idea how to make such a thing.  We might come closer today with vapor
deposition techniques.  The development of Kevlar by DuPont brought us a step
closer, but still no cigar.

    The same book by Forward also discuss this concept in more detail than
this.  There are some clever ideas involving tapered ropes, and "twanging" to
avoid low flying satellites described there.  Arthur Clarke also mentions this
concept in his book "Profiles of the Future." (5)  In the same book Clarke also
describes a trolley/elevator concept for getting into orbit. (page 208,9)
Either I don't understand what he is getting at, or it won't work as
described.


ENGINEERING ECONOMICS

    This subject is simply a formal treatment of Robert Heinlein's TANSTAAFL
(there ain't no such thing as a free lunch), so don't be put off by the title.
Simple put, it treats the cost of engineering projects in a way that B School
types can deal with.  For our present purposes, it can be reduced to a few
simple calculations.

    First, there is amortization.  Consider a simple mortgage of $100,000,
payable over twenty years.  At an interest rate of ten percent, the payments
would be $11,746 calculated on an annual basis.  This is a simple calculation
that you can verify by looking at any amortization table.  If the payments are
calculated on a monthly basis they are $965 a month, a bit less.  The easiest
way for a computer user to do these calculations is to use your favorite spread
sheet.  (If your favorite spread sheet can't do this, it is time to upgrade!)

    Now suppose that an aerospace plane (ASP) actually does cost
$1,000,000,000.  (I do not seriously consider that any serious space
transportation system will result from efforts by the US government--0r any
other government, but only from a commercial enterprise.  Hence I eschew the
term NATIONAL ASP.)  If the cost of money is 10%, and you want to use it for
twenty years, the monthly "mortgage" payment on the airplane is $9.65 million.
If each plane can make a flight per week (call it 50 per year) then the
"mortgage payment" per flight is $2.3 million.

    There are some good reasons to expect that the flight frequency to orbit
will be less than current airplane flight frequency..  First, orbit mechanics
limit flight opportunities.  It is hard to expect that you will get more than
one launch opportunity per day to reach any given space destination.  Once in
orbit, it will take some time to rendezvous with the "space station", more time
to unload passengers and cargo. Then you must wait until a suitable entry
window to return.  It is very hard to imagine a time much shorter than a day or
two from lift-off to touchdown.  Take a day to "turn-around" the airplane, and
you are limited to two or maybe three flights per week, and that seems to
pushing things.  Maybe after some years of operation that will happen, but not
at first.

    The performance of an ASP is altogether uncertain.  Much development and
many questions remain before even any credible preliminary design numbers can
be cited.  So let us speculate a bit.  Most current illustrations, (which are
"only" artists concepts) picture a vehicle about the size of a modern airliner.
The shape looks like a Concorde, but the mass is probable more like that of a
747.  Maybe a 747 with the payload of a Concorde seems reasonable.  Say, a
take-off mass of 300,000 kg, an empty vehicle mass of 50,000 kg and a usable
payload of 20,000 kg.

    Now, assuming that each flight can carry 20,000 kg into orbit, the capital
cost is $116 per kg if you only get one flight per week.  This is vastly better
than present costs, but it still isn't "cheap."  And of course we are just
getting started adding up costs.

    The fuel for the ASP almost certainly has to be liquid hydrogen (LH2).
(Probably no other fuel will burn rapidly enough to support operation of a
ramjet in which combustion is occurring at SUPERSONIC velocity.) It will take
for the assumptions just cited, 230,000 kg of LH2 for each flight.  The current
cost of LH2 is several dollars per pound.  That doesn't mean too much since it
is produced in rather small quantities with very stringent specifications.
Given large scale commercial production, the cost can probably be reduced.  The
energy content of LH2 is about three times that of jet fuel.  Hence on a pure
energy cost basis it will probably never cost less than three times the price
of jet fuel.  Moreover, since it will always be more challenging to produce,
transport and store a cryogen, LH2 can be expected to command a premium above
jet fuel.  Jet fuel is presently about $1 per US gallon.  This translates to
about $0.35 per kg.  Hence LH2 will cost, say, $2 per kg in large production at
some future time.  So add another $0.5 million per flight.

    It should be noted that the ASP will need a tad of liquid oxygen (LO2) for
the last bit of delta-V to get into space.  However, the amount is small, and
the cost of LO2 is low, so we will just lump that into into the half million,
along with the dribs and drabs of rocket propellants needed for maneuvering to
rendezvous with a space station.

    The flight crew has to be paid, but this should not be a big deal.  Say an
annual salary of $200,000 per year to make ten flights.  (I bet we could hire
crews for that.)  For two pilots and one flight attendant we are looking at
$0.06 million in direct salary.  Add 66% for benefits and call it $0.1 million
for flight crew.

    A much bigger item is maintainence.  For commercial airlines this exceeds
the direct operating costs, fuel and salaries.  There is a multiple of many
hours of maintainence for each flight hour for both large commercial airliners
and high performance military aircraft.  For the current NASA shuttle, this
multiple has been taken to ridiculous extremes.  Literally thousands of people
work all year to provide a dozen flights or less.  (Call it 10,000 people
working 2000 hours per year for ten flights per year.  That arithmetic comes
out to two MILLION hours of "maintainence" per 100 hour flight.)  Military
aircraft can do something like 200 hours of maintenance per hour of flight, or
100 times better per hour than the space shuttle.  Commercial aircraft do even
better.  For the ASP, lets call it 500 hours per hour of flight, and figure 20
hours per flight.  This comes to 10,000 hours per flight.  At say, $50 per
hour, labor and overhead, this is another half million dollars.  Add that much
more for parts, and we have $1 million per flight.

    There will also be some cost for the ground-based portion of the system.
In the airline analogy this would be the weather office, the tower controllers,
the passenger agents, and the like.  At present NASA has a staff of hundreds
working around the clock during manned flight operations.  Our future
"spaceline" must do much better than that, so we will consider a bill about the
size of the maintainence bill.

     Now we can add up the bill for each flight of the ASP:

     Capital costs     $2.3  million
     Fuel               0.5
     Crew salary        0.1
     Maintainence       1.0
     Ground Support     1.0
          _______
     TOTAL              4.9 million

Oh heck, these are rough numbers, so lets round it off to $5.0 million per
flight, or $250 per kilogram.  While this is FAR better than the $10,000 per
kilogram of today, it is still far from cheap.  Each passenger, including
accommodations and life support will mass at least 200 kg.  This makes your
fare about $50,000, BEFORE profit and taxes.  This is in 1990 dollars, and just
includes the transportation. (The "hotel bill" will be extra, a LOT extra.)
Evidently, only the rich will be able to afford a week-end in space.

    This is probably our best example of "engineering economics" applied to
future space flight costs.  I would love to be able to do a similar estimate
for Forward's "space fountains", but the concept is still too far from
practical development to feel able to do that.  For example, will a few more
years of development in high temperature superconductors result in inexpensive
and practical supermagnets for mag-lev transportation and/or mass drivers?  If
so, the day of affordable space transportation will be much advanced.  Can we
devise automated construction machinery, so that the building of a "space
fountain" tower 50 miles high will be affordable ?

    It should be noted that the transportation costs for a system such as this
will be dominated by the capital costs for the facility and the maintainence
costs.  Energy costs will be pennies per kilogram, and the "crew" may be you
pushing an elevator button.  (I can dream, can't I?)

    In any case, the object of this paper is to show that there are prospects
in sight for much lower costs for a trip to orbit.  There is a "chicken and
egg" problem about the development of these systems however.  Any of these
schemes will cost billions to develop.  Nobody, government or private, will
spend those billions until there is a "market demand" for large amounts of
transportation to low earth orbit.  On the other hand, the demand for such
transportation will not develop until it is much lower in cost.  It may take
quite a while to "ratchet-up" to the level of demand that will warrant spending
the billions on these developments.

    At some point, there may be a development which will can later be
identified as a turning point in this process.  For example, if an AID's
vaccine could be produced only in microgravity, that would produce an immediate
demand for transportation to low earth orbit.  However, such a demand cannot
occur until some such process that demands orbital operations has been
developed.  This has already happened for GEO.  Corporations can buy and launch
comsats, and make large profits from their operation.  We still await for an
analogous profit-making business to be developed for low earth orbit.  I am
personally hopeful that the manufacture of some materials in microgravity will
provide a market driver at LEO.

    If any readers have any suggestions about how to expedite this
"ratcheting-up" process, I would love to hear them.  I would also like to hear
from any readers who have comments or corrections to the material I have
presented here.

                                       Jim Chestek
                                       Retired Space Engineer


FOOTNOTES.

(1)  A good description of this system is given in the "Metric Practice Guide."
This is also known as American National Standard Z210.1.  The version I use was
issued by the American Society for Testing and Materials, as publication
E380-74.  This is a valuable compendium of conversion factors;  hundreds of
them.  About the only one I could not find was the factor to convert furlongs
per fortnight into meters per second.

(2)  This is a bit complicated to explain, since most orbit mechanics texts put
the datum point for calculating potential energy at an "infinite" distance from
the earth, with the result that the potential energy of a satellite is usually
given as a large NEGATIVE number.  However, in this system, the potential
energy of a mass of an object on the surface of the earth is a MORE negative
number.  In case anybody wants to do arithmetic on orbit energy using the
surface of the earth as a datum point the relevant formula is rather simple:

    PE = mass (kg) x (mu/re -mu/ ro)       where

         PE   is the potential energy of a kilogram satellite in joules;
         re   is radius of the earth, 6378.2 km
         ro   is the radius of the satellite orbit in km,
         mu   is 398601.2 (km 3/sec 2);  earth's  gravitational constant.
              Hence, the first term of the equation is numerically equal to
              62.5 million m 2/sec 2  OR 62.5 megajoules per kilogram.)

    In my example, for a 300 km altitude, ro is thus 6678.2, and the fraction
mu/ro is 59.7 million, making the difference 2.8.  When multiplied by one kg
mass, this is 2.8 MJ.

     A good text on Astrodynamics is "Fundamentals of Astrodynamics;" by Roger
R. Bate, Donald D. Mueller, and Jerry E. White.  Dover Publications Inc.,  180
Varick Street, New York, NY  10014.  Library of Congress Catalog 73-157430.  I
recommend this one because it is reasonably priced, and probably can be ordered
by most book stores.  You will need a working knowledge of the calculus to
follow the derivations, but there is some hope of understanding the concepts
without that.

(3)  The first mention of this scheme that I am aware of came from Dandridge
Cole.  In "Islands in Space,"  (Cole & Cox) published by Chilton in 1964  (Lib.
of Cong. 64-7625) there is an illustration by Roy Scarfo of a linear motor on a
planetoid busily launching cargo.  This same device could be used for
propulsion, and I believe that Dan Cole discussed this in other work later.
The idea has been advocated in several other publications since that time.

(4)  "Pioneering the Space Frontier," The report of the National Commission on
Space.  Bantam Books, 1986 (Illustrations Copyrighted), Library of Congress
TL789.8 U5 U565 1986.  ISBN 0-553.34314.9

(5)  "Profiles of the Future," Arthur C. Clarke;  Holt, Rinehart and Winston
(New York).  Library of Congress T20.C54.  ISBN 0-03-069783-2