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Subject: SPACE Digest V11 #206

SPACE Digest                                     Volume 11 : Issue 206

Today's Topics:
          Space-tech excerpt:  Launch Loops
----------------------------------------------------------------------

Date: Mon, 2 Apr 1990 20:18-EDT
From: [e-mail]
Subject: Space-tech excerpt:  Launch Loops

This is some condensed discussion from the space-tech mailing list, about the
Launch Loop concept championed by Keith Lofstrom, and a variation of it we
called the Hula Hoop.  Beware, it's 660 lines long!

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 \\\ Marc Ringuette \\\ Carnegie Mellon University, Comp. Sci. Dept. \\\
  \\\ [e-mail] \\\ Pittsburgh, PA 15213.  Phone [phone](w) \\\
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Space-tech excerpt:  Launch Loops   [660 lines, Feb. '90]

------------------------------

From: [e-mail]

I'm sure many of you have heard of Keith Lofstrom's concept of the Launch
Loop.  I think it's incredibly cool, and I'll take a crack at describing
what the principle of it is.


1. Kinetic Structures
=====================
The physical basis of the concept is something which I call a kinetic
structure.  I'll explain it by example.

Shoot a stream of water from a garden hose up in the air.  It forms an arc.
There is no need for material strength in the water:  there's no tension or
compression going on, but rather just the water's free-fall motion along the
path prescribed by gravity.

Imagine shooting a stream of water into a very high arc: it could go higher
than you could build the tallest skyscraper, since it's not limited by
the strengths of construction materials.  Now imagine balancing a pie plate
on top of the arc of water, so that it is supported by deflecting the water
downwards slightly.  The plate is suspended there, higher than you might
have thought possible, by the force from the continuing deflection of the
stream of water.


2. The Launch Loop
==================
If you replace the stream of water with a segmented ribbon of iron, achieve
the deflection of the stream by using magnets, and have two 'stations'
suspended by the ribbon rather than a single pie plate, you have Lofstrom's
launch loop.  It is a structure about 2000km long and 80km high.  The loop of
iron runs along the earth's surface in one direction, is deflected upwards
by magnets at an earth station, back parallel to the earth's surface by a
station 80km high, downwards by another station, and back along the earth's
surface.


         A --------->------------->------------->--------------- B
          /                                                     \
         /                                                       \
        /                                                         \
      C ---------<----------<------------<--------------<---------- D
===============================Earth====================================

   The Launch Loop.  A and B are stations, 80 km high.  C and D are
   deflector stations, 2000 km apart, on the ground.  The segmented
   iron ribbon moves at 14 km/s.  The horizontal sections, and the
   earth, are actually convex, not straight as shown.

The whole loop of iron segments whizzes along at 14 km/s inside a vacuum
sheath.  The stations at A and B are held up by the force generated by
magnetically deflecting the ribbon downwards; they are anchored to the
ground by cables, which are needed for stability and to counteract the
horizontal forces.


3. Say What?
============
I should head off your initial skepticism.  This is no joke.  The guy has
worked out details of how you deflect the ribbon, what materials are
required, how to anchor the stations, and all the other details.  The idea
has been reviewed by a lot of people, so if you think you see a glaring flaw,
it's probably because I haven't conveyed the idea properly.  The paper I
have, AIAA-85-1368 (from an AIAA conference in 1985), has lots of numbers
for everything.

Some details that I should mention:

  - the iron ribbon consists of 200cm x 5cm x 1cm segments, which are
    slotted to fit into each other.

  - the ribbon undergoes no stress whatsoever; it is just a passive holder
    of kinetic energy.

  - starting up the launch loop is a difficult task, involving spinning
    up the ribbon while it is floating on the surface of the ocean.


4. Using the Launch Loop
========================
Once you have spun up this thing, what do you do with it?  The stations
themselves are useful things: they're outside the atmosphere, yet they
are anchored to the surface by cables.  You could put an observatory on
one of them, and commute to it up and down the 80km cable.

But the main use of the loop is to launch vehicles, weighing about 5 tons,
including passenger vehicles.  The idea is that the vehicle sits on the top
section of track, and uses magnetic coupling with the moving ribbon to
accelerate along the 2000km top portion until the desired velocity is
reached (which could be orbital velocity or escape velocity).  So to get
into orbit, you winch yourself up a cable to station A, hop in a car, get
accelerated up to orbital velocity on the cable, and let go.

Because the loop is so massive, accelerating a vehicle doesn't decrease its
velocity much; the velocity is added back in by the ground-based magnets.
The result is that ground-based electrical power has been used to send a
payload into orbit.


5. Practical Objections
=======================
Lofstrom talks of the project as if it might be real, and even gives some
guesses as to construction costs ($2 billion total).  My evaluation of this
whole thing is:  incredibly cool physical concept, incredibly impractical
engineering problem.  Particularly, the ocean-based leg of the system is a
2000-km-long vacuum sheath which must be flawless.  Spinning up the thing
involves getting the entire 4000-km-long loop going perfectly on the first
try, dealing with weather and all sorts of unpleasantness, and gradually
lifting the stations up to their correct positions.


6. My preferred version: the hula hoop
======================================
I think the ground-based section of this thing is the worst part.  So I
propose having the loop go all the way around the earth, in low orbit.
The ribbon will be moving faster than orbital velocity, so that it can be
deflected by the stations to hold them up.  I'd say there should be about
60 stations spaced around the equator, each of them fastened by cables to
the ground.  The ribbon moves in a shape somewhere between a 60-sided
polygon and a circle.  In between stations, it flies in free fall.  It's
still a really complex device, but at least it isn't in the weather.

To spin up this structure, you could start with the stations in low orbit,
and gradually decelerate them to a standstill as the ribbon is spun up and
starts to support them.

I notice that Lofstrom references some articles in the L-5 news and JBIS
which discuss this idea.

------------------------------

From: Tom Neff <[e-mail]>

I thought the point of the Launch Loop was that it could be powered from,
and launch payloads from, the ground.  The Hula Hoop might be easier to
construct, but how do you power it and how does it get anything launched?

------------------------------

From: [e-mail]

This isn't a problem:  the ~60 stations are all _stationary_ with respect
to the ground, approximately 100km up, and are anchored by cables.  You can
run power lines and elevators up the cables.

------------------------------

From: [e-mail] (Paul Dietz)

One of my complaints with the launch loop is what happens when it
fails.  Should the loop break anywhere, or should the airtight jacket
spring a leak, all the levitated sections fall back to earth,
spread over thousands of kilometers.

IMHO, the launch loop idea is more feasible on the moon.
The levitation magnets can be anchored to the lunar surface, and
can be externally powered.  The loop provides a nice way to
store energy over the lunar night.  And, the required loop
velocity is lower, if all you want to do is get to lunar orbit.

Some work at Argonne National Labs has been inspired by the
launch loop.  A fellow there named Hull and some coworkers have
looked into magnetically levitated rings for energy storage here
on earth.  The concept is nice, since (for fixed centripetal
acceleration) the energy stored scales as R^2, and the energy
stored per ring + magnet mass scales as R.

Hull found a nifty *passively* stable attractive magnetic
levitation scheme (Lofstrom used active stabilization).  The
idea works like this.  Let o and + denote cables carrying currents
into and out of the page, and let - represent the iron loop.
Then, there are two positions where the magnetic field of the
currents support the loop against gravity:

    +     o        +     o
       -
               -

In the first position, the loop is stable against vertical perturbations
but unstable against lateral perturbations.  In the second, the opposite
is the case.

Hull noticed that if you alternate sections of the two types, then
the net effect, if the loop is moving in the right range of speeds,
is to make it stable in *both* directions.  This is the principle of
Strong Focusing, which is vital to the operation of modern particle
accelerators (where alternating gradient quadrupole magnets focus
particle beams).

------------------------------

From: [e-mail]

I guess I'd be more interested in launch loops on the moon if I actually
cared about being able to launch things from the moon.  But it seems like
a tidy little mass driver would be a better bet there in any case.
==
Paul correctly points out a really big drawback of the design, namely the
fact that the thing has to work flawlessly, all the time, or the whole thing
falls down.  Any system which must be in continuous operation is far, far
less practical than a system which just goes BANG and is done.

------------------------------

From: Jordin Kare <[e-mail]>

    The "full orbit" launch loop has been proposed several
times.  I (re)invented it in about 1980, but later found a
fairly detailed analysis, I think by Hans Moravec.
It is simpler than the Lofstrom loop, but takes much more material,
and would be much more subject to cutting by LEO debris/meteorites.
Stabilizing it is also nontrivial, although not necessarily more
difficult than for the Lofstrom loop.  There are serious problems
starting the thing up.  However, the big problem is getting
the mass up there in orbit to begin with -- at least the
Lofstrom Loop gets built on the ground.

    Jordin Kare

------------------------------

From: Lou Adornato <[e-mail]>

I think a surface based loop would be a better plan for lunar colonization
because of the lower materials and construction demands.  Keep in mind that the
size and speed of a lunar loop would be a lot lower than for a terrestrial
loop.  Also, for a lunar loop you wouldn't need a vacuum sheath, and there
wouldn't be any concerns about weather.

There are several advantages of the loop over a mass driver.  According to
Lofstrom, the accelerations of a terrestrial (and possibly a lunar) mass driver
would be so high that it could only be used for inanimate payloads.  Also,
there would be a lot of problems providing the required peak energy demands.  A
loop would have a fairly constant energy demand, and the peak acceleration to
escape velocity (at least to get to an L point or the moon) would be 3g's, and
(if my understanding of the the math is correct), about 0.5g for a lunar loop.
From what I understand of the design of this monster, if higher acclerations
are allowed, the loop can be made smaller.

------------------------------

From: "Edward V. Wright" <[e-mail]>

The Kevlar slingshot promises to be cheaper than the
mass driver for launching lunar payloads.

The Kevlar slingshot is just what it sounds like -- a Kevlar sling attached
to a mechanical arm.  Attach a payload to the end of the sling.  Spin the
sling until the tip reaches orbital velocity, then release the payload.

The idea is almost absurdly simple, but apparently will work on the Moon.
The idea was developed by Dr. Jerry Pournelle and Dr. Marvin Minsky and was
mentioned by Pournelle in one of his columns.  I think they gave a paper on
this somewhere, but I don't have exact references.

------------------------------

From: Bob Munck <[e-mail]>

The Hula Hoop (loop entirely around the earth, I assume moving faster
than orbital velocity) has the obvious drawback of weighing on the order
of 150,000 tons (for a 1x5 cm loop) and needing to be in orbit before
it's usable.  If we could put that much up, we probably wouldn't really
need it.  How about a 2.7 cm diameter Kevlar cable with a 1 cm iron
core, breaking strength about the same as the Launch Loop (about 300T?)?
That's down to a "mere" 50,000T in LEO.  Does it really need that kind
of strength?  Would 50T be enough (cable weighs 8,000T)?  That's down
under 100 shuttle missions, a distinct possibility.  The iron core could
be discontinuous, say 1 cm pellets at 2 cm intervals.

OK, where have I wandered?  A 40,000 km Kevlar hoop (i cm diameter) with
a (possibly discontinuous) iron core (j cm diameter) around the earth at
k km altitude, traveling at x m/s.  Stations at y km intervals capable
of accelerating the hoop by magnetic coupling to the iron with power
coming up a (superconducting) cable from the ground.  Some of the
stations would have an elevator capable of lifting an z ton payload and
hanging it on the hoop, which would accelerate it up to orbital (or
more) velocity.

I like it.  Possible values: i=1.5, j=0.6, k=75, x=15, y=2000, z=5.
Starting up is fairly easy (but k might be low) and the broken cable
mode flings cable outwards and drops stations straight down, relatively
safe.  What factors have I missed?  How stable is it with wind and
random payloads on the spokes?

                                    -- Bob Munck

------------------------------

From: Bob Munck <[e-mail]>

Come on, folks, help me out.  In a previous message I rambled on about
a Kevlar/iron hoop around the Equator in LEO (or lower) spinning faster
than orbital velocity.  Stationary facilities would "ride" it
magnetically (hence the iron component) with Kevlar tethers down to
ground level bringing up electricity to keep the hoop spinning and
payloads on the order of 5T.  The payloads would couple (also
magnetically) to the Hoop and, letting go of the station, be accelerated
to orbital velocity and beyond.

The Hoop and tethers are all on the order of 5 sq cm: the Hoop must
withstand whatever strain is generated by its higher-than-orbital speed,
its mass, and the weight of the stations; the tethers must support their
own weight and the payloads.  I *think* that the total is within reason
for us to boost into orbit -- a hundred or so Shuttle launches or a lot
of little mass driver shots.

Start-up is easy: assemble in LEO at orbital velocity, spin it up a bit
with strap-on rockets, fly up a couple of stations and reel down their
tethers.  If the Hoop snaps, it throws itself all over the Solar System
and drops the stations straight down. (Humm.  It might shotgun all our
comsats.)

WHAT'S WRONG WITH THIS IDEA?  Does the Hoop have to be spinning so fast
that it can't possibly hold together?  (I haven't the foggiest how to
calculate the strain on such a Hoop for a given velocity.)  Is it
unstable?  Are the tethers beyond our current strength-of-materials
capabilities?  Am I orders of magnitude off on the launch mass
requirement?  Is the whole idea of holding up the stationary facilities
crazy? (But isn't that what a Lofstrom Loop does?).  HELP!!

                                  -- Bob Munck, MITRE McLean

ps. I'm struck by the thought of standing on the Hoop in a 1g field with
my head toward Earth, going around every 45 minutes.  Hence the
"Ringworld."

------------------------------

From: [e-mail]

Bob - At first, I thought you were misguided -- the Launch Loop as proposed
was meant not to require any tension in the loop at all -- but now I'm
starting to like this!  I think we're looking at a new form for the hula
hoop: use tension to hold the structure together, rather than deflector
stations.  Magnetic deflection is only used to hold up the launch station,
and magnetic coupling is still used to launch payloads and re-accelerate the
ribbon.  It requires much smaller deflectors than the original scheme, and
may have better reliability, since the loop can 'idle' with no deflectors
operating and there's the prospect of passive or mostly-passive operation.

To sum up the idea: put a Kevlar ring in low orbit, then spin it to create
tension.  Float a station on it as for the Lofstrom Loop, and launch vehicles
using magnetic coupling with iron pellets in the cable.

The tensile strength works out OK -- even with standard Kevlar like you'd use
to anchor an oil rig, you can spin it to 1 km/s above orbital velocity, which
is probably enough.  We still need to work out the dynamic properties of the
system, even if roughly, to see if we can hold up a station and succeed in
launching vehicles, while staying within tension bounds and remaining
dynamically stable.


Here are my calculations for the tensile strength question:

The tension on a spinning loop (disregarding gravity) is

                2
                 M v
       F    =  --------
        t       2 pi r

=================

What's the maximum spin velocity (in excess of orbital velocity) of a loop
with these parameters? ....

       X = tensile strength of cable
       Y = density of cable
       c = cross-sectional area of cable
       r = radius of loop
       M = total mass of cable                           2
       G(r) = gravitational acceleration at radius r = Vo / r
       Vo = orbital velocity at radius r

              2                           2    2
               M   | v         |     2 pi r c Y (v - Vo )         2    2
       F    = ---- |--- - G(r) |  = --------------------- = c Y (v - Vo )
        t     2 pi | r         |     2 pi r

                              2       2
       F     =  X c  =  c Y (v    - Vo )
    t              max
     max

                      2
       V     =  SQRT( X / Y  + V  )
        max                     o

=================

For Kevlar 29 as used for oil rigs,

    tensile strength = X = 2.76E9 N/m/m
             density = Y = 1.44E3 kg/m/m/m

    V    = 120 m/s  (in excess of orbital velocity of ~ 8.3 km/s for LEO)
     max

This isn't too useful, but with 10-50x stronger materials, this increases
to 1-3 km/s, which should be enough to hold up a deflector station and
accelerate vehicles.

==============

This design has the advantage that we need only one station, plus some
guy cables spaced around the equator.

------------------------------

From: John Sahr <[e-mail]>

Some commentary on the calculations by Marc.

Summary: the Kevlar Hula hoop is likely to be very unstable if it is
"anchored" and the loop travels at "reasonable" speeds.  The loop must
spin at "unreasonable" speed in order to become stable.

For a lineal density of 1 kg/m and tension of 100T, we can calculate the
speed of the transverse waves along the loop, namely

v = sqrt(T/rho),  ( rho = M/(2 pi r) )
  = 1 km/sec.

Thus, an observer on a stationary earth would observe perturbations
travelling along the loop at speeds of 9.3 and 7.3 km/sec, both in the
same direction of the loop.  Factoring in the earth's rotation, and
assuming prograde spinning of the loop in the equatorial plane, the
velocities of the waves observed from the earth's surface would be 7.7
and 5.7 km/sec, still in the direction of the loop.

This is a real problem, as any "stationary" perturbations (anchoring
cables, suspended stations, advertising signs, and other whatnot) will
be generating waves along the loop, only downstream, and none
upstream.  This situation is analogous to the operation of certain
microwave tubes which rely upon "fast" and "slow" waves to amplify
perturbations in the electron beam density.  The difference is that
this is a periodic problem (it is a loop, after all), and it is
possible that there is a stable, noncircular, and probably
(mathematically) nonlinear solution involving rather large amplitude
perturbations of the loop (I'll have to think about it).

A way to combat this problem is to find a way to increase the velocity
of waves along the loop, so that one of the waves can travel
"upstream."  This can be done by increasing the T/rho ratio by a
factor of about 35.  From an equation above, T == F_t is proportional
to the mass density, and we can write

T/rho = F_t/(M/(2 pi r)) = v^2/r - G

In other words, the only way to increase the wave speed is to increase
loop speed.  In fact, because of that pesky G, v_wave can never exceed
the speed of the loop.  However, the Earth is spinning with an
equatorial speed of about 1600 km/hour = 450 m/s = V_e.  So, the
slowest loop speed V_s that will satisfy the stability condition
satisfies

V_w + V_e >= V_s;  where V_w^2 = (V_s^2 - rG).

Solving this for the minimum possible loop speed gives

            V_e^2 + rG
V_s(min) = ------------ = 75 km/sec
              2 V_e

The loop must make a complete orbit every 9 minutes or less.  This is
a rather large velocity; it could be reduced substantially by either
letting the stations drift prograde, or by spinning the Earth up so
that its day was shorter, say 4 hours instead of the current 24.

In the absence of a stable nonlinear large amplitude solution, or an
ambitious dynamic active correction of perturbations, or a loop
material which is very good at damping out transverse motions, this
strikes me as a pretty fundamental limitation to this idea.

note:  Someone should double check the statements I have made.

-john

------------------------------

From: [e-mail]

The question remains: how to make the Hula Hoop stable?  John's wave
calculations were very informative, and I will assume that it is necessary
to damp out any waves that occur.  Then the key to achieving stability is to
have a means of damping out the waves downstream of the perturbation.

A factor in our favor is that the main perturbation, the station, is
stationary, so there can be an anchored damping mechanism downstream from
it, which applies a continuous damping force to the cable.

My best idea for dealing with the perturbations caused by the launch vehicle,
which are not stationary, is to use a series of cables to the ground which
actively damp out perturbations by adjusting their downward force.  I have no
idea if this will work.  Can anyone fill in any details, or think of a passive
way to achieve the damping?

=====================

Thinking further about it, I conclude that it's important to distinguish
between two separate issues.  One is how to get the hoop to move in a circle:
the idea of a Kevlar cable was introduced in order to achieve the desired
curvature through tension rather than by using a whole lot of deflector
stations.

The second issue is how to aim the cable precisely where you want it.  In the
original loop proposals, the ribbon must be aimed at its destination with
incredible precision, since there is no internal strength in the ribbon.
This involves very aggressive active control.  However, when we use a Kevlar
cable, it is tempting to use the strength of the cable to help guide it to
its destination, in order to reduce the control problem.  I believe that it
is these transverse guiding forces which introduce waves, and if we can't
deal with the waves, we can always go back to strict active control a la
Lofstrom.

=====================

I'm trying to do some clearer thinking about what the shape of the
hoop would look like.  I've been imagining, in my weaker moments, that
we just hang the station from the hoop, and that the hoop bends down
in a 'U' shape.  This is totally wrong!  A 'U' shape would indicate that
the tension of the cable is holding up the station.  But unless we
totally change the concept of the thing, it's magnetic deflection of the
moving cable that provides the necessary force.

I think a good mental picture to start from is the following.  Imagine that
the earth is a point mass, and that we want to support two stations 180
degrees apart, using only the iron-pellet type loop.  We can do this by
firing the pellets back and forth in curved paths:

       __-------__
     -=__   O   __=-
         -------

The faster the pellets are going, the straighter the path.  If they go too
fast, they run into the Earth (which isn't really a point mass after all).

======

Now, let's come back to reality.  If we try this two-node solution using
iron pellets around the Earth, we can't fire them very fast at all or their
paths would pass through the Earth.  But if we use the Kevlar hoop, the
tension of the cable can pull it in a more tightly curved path, so it misses
the Earth even at higher velocities.

At least, I think this works.  If somebody could work it out in more detail,
it would be a good thing.  And is a two-node setup appropriate, or more,
or less?  A 1-node solution is sort of asymmetrical, but perhaps a setup
with 1 big node and a dozen smaller ones (cables to the ground) or something.

But do we agree that any version of this will have the station supported
on a 'peak' of the hoop rather than a 'valley'?  I think this is right.

======

Some general reflections:  I'm starting to think that we haven't really
solved any fundamental problems by making the loop out of Kevlar.  My feeling
is that it should be able to operate in a more passive mode than the original
loop, but it doesn't seem to be working out that way.

------------------------------

From: John Sahr <[e-mail]>

>How about sixteen spokes anchored to the earth, one every 2500 km?
>The mechanism that couples to the Hoop could include some way to pull
>down harder or loosen up on the Hoop over a couple of meters of play
>and with tenth-second response time.  Would that do to damp the
>perturbations?

For a passive support system for this kinetic structure, it is
possible that evenly spaced supports would be about the worst choice.
Because the transverse wave speed is slower than the loop orbit speed,
ordinary standing waves couldn't form; however, since the loop itself
is periodic, the n=8k (n = number of wavelengths, n, k are integers,
for both fast and slow waves) modes would stand between 16 spokes.  A
better solution would be to have aperiodic spacing such that no modes,
or very few, were allowed.  This could be used to filter out the long
wavelength waves.

In a linear world, it would be enough to have two supports, such that
the ratio of the two distances between them is irrational.  However,
this cable is going to stretch, have nonlinear restoring forces at
large amplitudes, and will be excited by the spokes them selves.  With
16 suitably spaced spokes, you might be able to effectively filter out
the waves of wavelength greater than a few hundred kilometers, and one
or two spokes might be able to have damping mechanisms for shorter
wavelengths.

I could never recommend building this structure if it wasn't passively
stable.

I had an idea for stabilizing the loop, though, whose dynamics I have
not yet had time to work out.  It goes like this.  The problem with
the loop is that transverse waves both travel "downstream," a
"negative energy mode" situation.  It seems to be the case that the
loop must spin terribly fast in order to allow the loop tension to be
large enough to have one wave travel upstream in the frame of a
rotating Earth.  Notice that a retrograde loop would have the same
problem, but in the opposite direction.  Therefore, what would be the
dynamic stability properties of two loops mechanically coupled to each
other, one spinning prograde, one retrograde?  To couple the two
loops, they could be put side by side and connected by rungs like a
ladder (probably won't work), connected like a spiralling ladder (like
DNA, and probably most feasible), or connected concentrically (one
inside the other; best mechanical connection, most esthetically
pleasing: how to spin that inside loop, though?).

Each cable separately provides one direction of wave modes; perhaps
the composite structure will have 2 or 4 modes.  I suspect that this
structure might have very good dynamic stiffness.  But it might also
explode into a million tiny pieces.  It may not be necessary for the
retrograde loop to have the same momentum as the prograde loop.  There
are a few other nice properties as well; residual loop-spoke friction
can be canceled (as far as the the spoke is concerned).  It's just an
idea.

Even if this doesn't work for a launch loop, it might provide a nice
frame for space structures.

------------------------------

From: Bob Gray <[e-mail]>

Check out:

"Orbital rings and Jacob's ladders" by Paul Birch.
Vol 36, Journal of the British Interplanetary Society.
pp 115-128 (1983)

The article describes how to bootstrap the system by
starting with a thin cable, and using that to lift the
materials to build the main orbital ring.

Eventual cost to orbit was estimated at $0.05/Kg.

He then describes how more than one ring can be used to
reach any point on the Earth's surface, and how the ring
could be used in conjunction with a Lunar ring to provide a
very high speed shuttle service from the Earth's surface to
the Lunar surface in a few hours.

------------------------------
[ End of excerpt ]


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------------------------------

End of SPACE Digest V11 #206
*******************