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Date: 5 Jun 91 19:22:17 GMT
From: ssc-vax!bcsaic!hsvaic!  (Dani Eder)
Subject: Re: Beanstalk analysis reprise

In article <>
(Walter Dnes ) writes:

>wreck@fmsrl7.UUCP (Ron Carter) writes:
>     I get to play the devil's advocate again. I don't like to
>destroy people's dreams, but a reality check is in order here.
>Your calculations seem to be based on an airless earth, i.e a
>good vacuum. Don't forget that we have an atmosphere. I briefly
>considered cross-posting this followup to sci.geo.meteorology,
>but decided not to since it's all in support of a theoretical
>space discussion. Some questions to consider...
>     1) You've allowed for longitudinal forces. What about
>perpendicular forces ? What happens when the beanstalk gets hit
>by a 100 km/h (60 mph) wind ? How about a 250 km/h (150 mph)
>jetstream somewhere in the stratosphere ? Can you supply some
>typical "Asurf" values along with the taper as a function of
>height. I work in the Atmospheric Environment Service, (Canada's
>weather service) in a unit that calculates meteorological
>parameters for construction. Just down the hall from me, our
>industrial meteorologist does recommendations for CSA-S37, the
>design standard for antenna towers in Canada. I'd like to ask
>her to calculate the wind loading on the lowest (and thinnest)
>portion of the beanstalk.

To minimize the cost of a beanstalk, you would not design it
to hang all the way down to the ground.  There is a compromise
design which builds up from the ground using compressive structures
and down from GEO using tensile structures, having their tips
connected but not transmitting large forces across the connection.

I have done a conceptual design for a 10 km tower using existing
graphite/epoxy, with standard structural allowables and allowing
for a Mach 1 peak wind at 10km altitude (at jet stream altitude),
tapering down to 150 mph peak wind at ground level.  The numbers
come out not too bad.  Above 10 km, the lower pressure dominates
any conceivable wind speed (I assume no upper atmosphere winds
exceed Mach 1), and the 'scale height', the height over which
the cross sectional area of the structure changes by a factor
of e, increases towards the limit of the material, which is
10's of km for graphite/epoxy.  If we limit the area ratio of
the tower portion to 300, then we end up with a tower on the
order of 60 km tall (this may be off by as much as a factor of
2, since I have not gone and done a detailed structural analysis)

>     3) Surface temperatures at the equator can hit 40C to 50C.
>You can expect -40C to -50C up in the atmosphere, and some
>utterly farcical values (both hot and cold) in the vacuum of
>space. How will your materials react to this gradient ? How will
>the outer-space portion of the beanstalk react to extreme diurnal
>cycles (day/night) in a vacuum ?

The CTE of graphite is -0.5E-6/K.  So if the fiber goes from
200K (on the night side of the Earth you are still illuminated by
the IR of the Earth itself, to 350K (a blackbody will get to
390K maximum in space at 1 AU, use a coating that make it not
black), then you will expect a contraction of 75ppm, over a
distance of 35000 km, or 2.6 km contraction.  I suggest you
install a reel meachanism at the bottom end to take up the slack.

Note that the upper portion of the tether is thick enough to
carry multi-layer insulation, and would have thermal mass, and
that the entire tether does not go into shadow except at the
equinoxes, and even then, the tether will emerge from shadow over
a period of 45 minutes for the upper half (where the emergence
is fastest).  This means the typical excursions will be less than
a few km, and the peak contraction rates will be on the order
of 1 km/hr.

>     5) What about charged particles in the van Allen belts
>"doping" the crystalline structure of the beanstalk ?
>     Questions 4 an 5 are important because you need the great
>strength of a pure "whisker". Chemical impurities and crystal
>irregularities will decrease the strength to the breaking point.

A structure that large will absorb the van Allen belts.  There
is only on the order of 1 kg of stuff in the Van allen belts.

A beanstalk has enough cross section that the material in the
van-allen belts will be absorbed.  Because of meteoroid and
debris hazards, you will design the beanstalk with multiple
strands crosslinked periodically, so that if a particular
strand is cut for any reason you can stand the loss, then go
in and replace the section of missing strand.  A recommended
cross-link interval is 10 km, and a minimal design should have
6 strands spaced more than the width of the largest piece of
orbital hardware, so that in the worst case (for a hexagonal
arrangement of strands) , no more than 2 strands get cut.  If
a 100 m space station is the largets object, then space the
strands at least that far apart.

Modular beanstalk design also allows incremental upgrading
as better materials become available.  With today's materials,
about half a beanstalk could be built with a tolerable taper
factor.  As stronger materials get developed, or simply for
scheduled replacement if aging is a worry, you go through and
replace one strand section at a time.

Date: 20 Jun 91 13:52:04 GMT
From: ssc-vax!bcsaic!hsvaic!  (Dani Eder)
Subject: Re: Beanstalk analysis reprise

In article <> writes:

>There was a science fact article in ANALOG Science Fiction/Science Fact a
>couple of years ago that concluded that, given our understanding of chemical
>bonds, there was no material theoretically strong enough to build a beanstalk
>on Earth (on Mars or the Moon, yes; on Earth, no), but that pinwheels would be
>feasible.  Anybody out there who can point us to the appropriate issue of

I don't know about Analog, but take a look at the current issue of
'Science'.  There is a paper on observation of transparency changes
in graphite being subjected to 18 GPa (2.61 million psi) in a diamond
anvil cell.

Therefore pure diamond has a demonstrated compressive strength of
at least this much.  The specific gravity of diamond is 3.513 g/cc,
or 0.127 lb/cubic inch.  Thus the scale height in compression is
20.56 million inches, or 324 miles.

Graphite fiber has a commercial tensile strength of 1 million psi
and a density of 1.84 g/cc.  This gives a scale length in
tension of 15.04 million inches, or 237 miles.  

In theory, if we allow an area ratio of 100 for each of a 'tower
of babel' from the ground and a 'jacob's ladder' from orbit, we 
can build to 4.6 scale lengths with an optimal exponential taper.
This means that the combined structures can be built to 2583 miles
in 1 g.  Since the Earth's gravity well is equivalent to 3963 miles
at 1 g, we can build 65% of a beanstalk.  This is with no factor
of safety in design, but is intended to show that we are within a
factor of 2 of being able to build a beanstalk.

Dani Eder

Date: 13 Dec 91 20:13:41 GMT
From: ssc-vax!bcsaic!hsvaic!  (Dani Eder)
Subject: Re: Tubular fullerine / Space elevator (Doug Caldwell) writes:

>However, the beanstalk is still unprotected from all the pre-existing,
>uncontrollable space junk.  As destruction of incoming space junk 
>would simply create more junk, this does not seem to be be a 
>viable alternative.  Thus, IMHO the only workable solution is that the
>beanstalk must get out of the way.  As it may potentially have to avoid

I don't think this is correct.  Two objects in LEO colliding tends
to breed more space debris via fragmentation, and much of the new
debris remains in orbit.  This is because both colliding objects
had orbital speed to begin with.  In the case of the classical
beanstalk that goes through GEO, the part at Low Earth Orbit altitude
is moving about 500 meters/second in inertial space.  This is
the equatorial rotation velocity of the earth (462 m/s) plus a little
for the added radius from the Earth's center.

Therefore a piece of debris that struck part of a beanstalk would
see a deceleration.  If it was in circular orbit, the fragments
would tend to come off with less than orbital speed.  In effect,
the mass/km of height of the beanstalk adds to the mass density
of the natural atmosphere at that altitude, and increases the
effective drag on things in low orbit.  The fact that the \
beanstalk is concentrated at one point rather than spread evenly
over the globe is irrelevant, since as was pointed out earlier,
things in orbit eventually sweep out all the area of their 
orbital altitude, so the distribution of the retarding mass
is averaged out.

Even if all the man-made space debris were eliminated, there would
still be natural meteoroids to contend with, and these would not
generally be observable before they hit you.  Therefore, when I think
about tether-type structures, I assume that they would be
multi-stranded, with the strands separated by tens of meters, and
with cross-strapping to redistribute loads around a cut section
of tether.  Then you have to have some robotic 'spider' that can
go to the cut, and play out a replacement strand.  Think of it
as maintenance, like the painting that goes on for suspension

Dani Eder/Boeing/Advanced Civil Space/(205)464-2697(w)/232-7467(h)/
Rt.1, Box 188-2, Athens AL 35611/Member: Space Studies Institute
Physical Location: 34deg 37' N 86deg 43' W +100m alt.

From: (Jordin Kare)
Subject: Re: Space Elevator
Date: 25 May 1994 18:47:03 GMT

In article <2rul6e$> (George Herbert) writes:

>You missed it, Marcus.  You take Phobos, break it in two... and make a gravity
>stabilized tether by unwinding your beanstalk between them.  

I have to admit, the first image this brought to mind was of the two
halves of Phobos separated by a few meters, with a large post 
holding them apart and umpteen thousand km of tether wound around the
post... and presumably a large "WHAM-O" label on the side.  Or 
maybe "Yoyodyne"

It would lend a whole new meaning to "'Round the world" as a yoyo trick....

[As a friend once said, when giving me a yoyo as a birthday gift, 
"It's good to have a yoyo in a high-stress job..."]

	Jordin (I prefer Slinkys) Kare

From: (Dani Eder)
Subject: Re: Space elevator danger?
Date: Jun 01 1995
Newsgroups: (Joseph Hertzlinger) writes:

>If a space elevator fell, how much damage would it do?

>How far away from the equator would you have to be
>to be safe?

The earth environment is cluttered with natural meteoroids and man-made
debris.  For safety, you would design a space elevator with multiple strands
of cable to support the load.  That way if one strand is cut, the remainder
can support the load until the broken strand is replaced.  You can on
purpose choose a strand size that if it falls to the ground will do no
damage.  For example, have someone throw 1/4 inch nylon rope at you,
it doesn't hurt very much, does it?.  Drop it from a high building, it
still doesn't hurt much (actually not at all).  A big length of strand
rolled up on a spool dropped on you would hurt, but the strands are
stretched out in use, so if they fall, they should land pretty spread

A bigger worry is payloads climbing the elevator.  If you drop one of
them it could go splat pretty hard.  

Dani Eder

From: (Dani Eder)
Subject: Re: Space Elevator II. The story continues.
Date: Jun 01 1995

"Geoffrey A. Landis" <> writes:

>Bob Zubrin may discuss it, but he is analyzing concepts originated
>elsewhere.  (His analysis is, however, very good).  You ought to credit
>Hans Moravec with inventing and publishing the idea of rotating skyhooks.
> BTW, they are *vastly* superior to stationary geosynchronous skyhooks in
>terms of the amount of taper ratio (i.e., *mass*) required.

And also credit Dr. Brian Tillotson here at Boeing for coming up with
the multi-stage tether.  This is where you hang a rotating structure at
the end of a hanging skyhook.  Since rotating skyhook's masses go as
an exponential of the tip velocity, if you do it in 2 stages you lower
the overall mass since (exp(0.5v))^2 < exp(v).  I say rotating structure
rather than rotating tether because the dynamics of two strings coupled
gets very messy.  If you build a spindle as the rotating structure it
gets more manageable.  This is where the tension members are still cables,
but you have some compression struts in the center to spread the
cables apart and give the structure some depth to make it more stable.

Another advantage of a 2 stage tether is the flexibility in operations
it gives you.  If the hanging 1st stage has a bottom end that is moving
v less than orbit velocity, and the rotating stage has a tip velocity
of v, then you can get on at v(orbit)-2v, and jump off half a rotation
later at orbit velocity.  This eliminates a tedious elevator ride (and
the elevator).

If you have two rotating stages, one on the tip of the other, with their
rotation periods not in resonance, you can get picked up near earth, and
then get released with whatever velocity vector you want from v(orbit)-2v
to v(orbit)+2v, simply by choosing when to let go.  If, for example,
v = 0.25v(orbit), which can be acheived with current materials, you
can let go at a maximum of 1.5v(orbit), which is more than escape
velocity (1.414v(orbit)).

Dani Eder

From: (Dani Eder)
Subject: Re: Space elevator danger?
Date: Jul 14 1995
Newsgroups: (Henry Spencer) writes:
>(Dani Eder) writes:
>>...I say 'when' a cable gets broken because in the current space
>>environment, a 1 cm diameter cable will be cut on average once per
>>1000 kilometer-years.  Since a GEO elevator is 35,000 km long, you
>>would expect breaks every 10 days or so.

>Dani, is that 1000km-yr number for the LEO environment, or an average
>over the full length of a GEO elevator?  Only about 2000km of the GEO
>elevator is exposed to the LEO space-debris environment; most of its
>length is at altitudes where there is little or no debris.
>-- i

I gave that figure as a simplification so that people can get a 
rough idea of the situation.  It is correct for LEO, a specific
diamter cable, and mid-1990s.  In general, as you go up in altitude,
the man-made flux decreases, with most of the man-made stuff in the
first few thousand km.  Smaller cables can be cut by smaller pieces
of debris, and there is more small debris than large debris.  
Space debris is 'breeding' as dead satellites and stages occasionally
get fragmented by impact with debris, making more debris.  There
is a worry that if somehting is not done about controlling debris,
there will eventually be a 'debris catastrophe'.  This happens
because if you double the number of objects, the collision rate
quadruples (twice as many impactors and twice as many impactees).

At some point the impact rate rises exponentially and all the
stuff in orbit gets ground into dust, which eventually settles into
a ring system.  The limiter on this scenario is that stuff in
low orbit gets removed by air drag, and the smaller particles get
removed quicker.  The worry is that in 30 years or so the debris
count might overwhelm the removal process.

The Space Station meteroid/debris shield has already been thickened
once because the program has taken so long that the debris problem
has gotten that much worse in the interim.

Dani Eder

From: (Dani Eder)
Subject: Re: Space elevators
Date: Dec 18 1995

Jason Goodman <> writes:

>Got some disagreements here.

>In article <> Dani Eder,
> writes:

>>Now, how fast is your hoist?

>continuous chain of elevator cars running up and down.  You can also be
>clever with the hoist design: I've seen suggestions for using linear
>induction motors to move donut-shaped cars up along the cable...
>presuming you've got the power, you can go as fast as you like.  (and

Unfortunately, you cant neglect the power supply for the hoist
(it still takes 31 MJ to raise a kg to GEO), and the power line
running up the space elevator represents a parasitic mass.  

>>Of course, if you had materials 10 times stronger than what is
>>available today, you presumably could build much better rockets

>Perhaps not: there are fundamental limits on the temperature of chemical
>reactions, and therefore on the efficiency of chemical rocket engines. 
>Again, sources on request.

I did not mean you can get the combustion to get hotter, I meant you
can get the rocket structure to be lighter, allowing more payload, or
increase the service life of the structure, or increase the factor or
of safety of the structure, or some combination of the above.

>>A better answer, which lowers the required material strength by 30%,
>>is to build a tower up from the ground and have it meet a cable
>>coming down from GEO.

>Are you taking into account the fact that materials are generally much
>stronger in tension than compression?  A tower will have to be built in
>compression, and our strongest compressional materials are orders of
>magnitude weaker than our strongest tensional ones.  In any case, the
>mass requirements will be vastly huger.  I agree that if you have a
>montaintop handy, you should use it, but beyond that...

The specific figures are: Carbon Fiber in tension (Amoco Performance
Products T-1000 fiber) 1,000,000 psi.  Carbon fiber/epoxy in compression
(same fiber, ERL-1916 epoxy resin) 280,000 psi.  The minimum mass
total structure is found when the tower up from the ground and the
cable down from GEO have the same area ratio from base (ground or GEO)
to tip (where they meet).  If the area ratio is e^n for both, the mass
is 2e^n times the payload mass.  If the cable hangs all the way down
to the ground, it will have a mass of e^(1.28n), which is generally
a larger mass.

>>aN EVen better answer is to have a partial space elevator in Earth
>>orbit, extending from 400 km upwards 1-2000 km.  The bottom of the
>>cable will orbit slower than earth orbit velocity at that altitude.

>Now, that's an idea I like.  But I'll go you one better (not my own
>idea).  Spin it end for end at the same speed as the orbit, so the
>earthward tip comes to rest in the upper atmosphere, a high-flying plane
>attaches to it, then the tip flicks out again.  The kinetic energy loss
>is balanced by an equal number of planes coming back in for landing. 
>Tidal effects will be a pain, though.

That idea was proposed by Hans Moravec.  An improvement over the
simple rotating tether was invented by Brian Tillotson, here at Boeing,
where a small tensile structure rotates at the tip of a larger cable,
which is either hanging vertically under gravity gradient  forces
or rotating itself.  Then I came up with the '3 stage tether', where
a tower sticks up to the top of the atmosphere and has a rotating
tether on top, with rocket attached to the tip.  The rocket is slowly
brung up to speed, then released, to fly up and rendezvous with the
two stage tether described before.  This sufficiently lowers the required 
materials strengths that existing materials are adequate to mostly
eliminate the rocket propulsion requirement.

Dani Eder

From: (Dani Eder)
Subject: Re: space elevator
Date: Jan 04 1996

Julian Treadwell <> writes:

>This is the 'Skyhook' idea that's been around for a long time, and should 
>work theoretically but we haven't yet devised a material strong enough to 
>make the cable out of.

>I think what you do is extend another cable in the opposite direction, 
>i.e. away from the Earth, to keep the space station balanced in 
>geosynchronous orbit.  As you lift the load from the ground, you 
>simultaneously wind in the other cable as well.

Space Elevator (aka Beanstalk, Space Bridge, Orbital Tether, Skyhook)

This concept has a number of forms and has goneunder a number of names.
You can categorize them according to:

(1) Length of cable
(2) Location of Center of Mass
(3) Rotation Rate
(4) Number of Parts
(5) Tension or compression

The most common form the idea gets re-invented in is: 35,000 km long,
center of mass at GEO, non-rotating, single part in tension.  This version
is both naive and incorrect.  In order to get zero velocity at the ground,
the center of attraction (not center of mass) must be at GEO.  The
difference is that a large object like a space elevator spans large
differences in g forces due to the variation in distance from the Earth.
Thus you need a lot of stuff out beyond GEO to balance the stronger pull
of gravity below GEO.  This can be a big counterweight, or by extending
the cable out several times GEO distance.  

The naive aspect is thinking that the simple space elevator is the 'best'.
Depending on what you want to do, more complicated configurations usually
serve better.

Some examples:

If you are trying to just get to orbit cheaply, a space elevator a few
thousand km long is better.  With existing materials, or even with better
materials expected in the next 10-15 years, a full GEO elevator is 
impractical.  The materials are not strong enough, so the structure must
have an enormous taper from top to bottom, and thus mass an enormous number
of times the payload mass.  You can't carry enough payloads up the thing
for it to make economic sense.  For example, let us assume that you want
to build a space elevator and make a modest 10% return on your investment.
For simplicity's sake, assume that the only thing you have to pay for 
is launching the cable.  The materials are free and operating costs are
zero.  Assume also that yor elevator can winch up a payload in one hour,
and that you can charge customers as much for your lifting payloads as
unassisted rockets do.  So to make 10% return, you need to hoist 10%
of the space elevator's weight in payloads each year.  Therefore the
cable can mass at most 87,600 times the payload.  Using 1 million psi carbon
fiber (the best material I am aware of) at a realistic stress level
(60% of ultimate strength), you canafford to make a space elevator
about 2,600 km long before it gets to this mass.  These are unrealistic,
simplified calculations, but if you attempt to do them realistically, 
you find that a full space elevator does not make sense.

Useful length can range from 20 km (for experiments, like the Shuttle
flight due next month), to 40 km (for de-orbiting stuff from the 
Space Station), and on up.

The center of mass/attraction can be anywhere from LEO on up for orbiting
cables.  For ground-based tower structures that are part of a 'space
elevator', the center of mass can be lower still.

They can be 'gravity stabilized', which means they hang vertically, 
swinging, or fully rotating.

You can put one rotating unit on the end of another, and get any vector
sum of their tip velocities by suitable choice.  Thus you can have a 
'space elevator' that you don't climb at all.  It is more of a
'space sling'  that can pick you up at the ground and then fling you
off at high speed a half turn later.

You can build towers up from the ground to meet cables from space.

Dani Eder

From: (Dani Eder)
Subject: Re: beanstalk cable
Date: Jan 14 1997
Newsgroups: (Beth and Richard Treitel) writes:

>My guess is that the likeliest place for breaks would be the 1000 km
>nearest Earth (more and faster orbital junk, more ionised gas, etc.),
>so the part that fell to Earth would be short and quite thin.  Also,
>this part *would* fall almost vertically.  A quick BotEC suggests that
>a break at 1000 km would result in the broken end arriving at ground
>level some eight minutes later, at a speed of up to 4 km/sec, about 25
>km east of the anchor point.

Several comments:

- Rational space elevator design given the earth orbit debris 
environment is a damage tolerant one.  This means a minimum of
six cables in a hexagon pattern, spaced a least a couple of
hundred meters apart (i.e. several times the width of the
Space Station - the largest piece of 'debris' that is in Earth
orbit).  The hexagon pattern ensures that no single object can
take out more than two cables at once.  Of course you design to
take the loads with only four out of six cables left, and
cross-connect the cables every so often (say every 10 km) to
distribute loads around a break.  That way you can take several
hits at different locations along it's length.  You also have
a 'spider' that can crawl up and down the structure removing
broken strands and replacing them with new ones.

- Minimum weight design has a tower going up from the ground
meeting a cable hanging from orbit, with the same taper ratio
from ground to top of the tower as from GEO (if that's where
you reach to) to the bottom of the cable.  If you cut the 
structure where the tower and cable meet what happens is -
nothing.  The present strength of carbon fiber composite is
about 40% in compression compared to pure fiber in tension.
So the strength required for a 'GEO elevator' is reduced by
about 29%.

- For a structure that makes economic sense, you have to
transport enough cargo to pay back your investment.  For example,
if you need to earn 10% return to pay off your construction loan,
and you can lift one cargo an hour, you can make some estimates
on the maximum mass of the structure.  At 10% return, you have
10 years to earn back your cost.  There are 87,660 hours in that
time, so you can lift 87,660 cargoes.  Assume that your structure
cost $100/kg, and you also charge $100/kg to deliver cargoes.
Then your structure may mass at most 87660 times the cargo weight.

If we divide the structure into a tower and cable, each may mass
43,830 times the cargo.  Taking the natural logarithm, we get a
figure of 10.7 scale lengths for each.  The Earth's gravity well
is equivalent to 1 gee x 6375 km.  This, given the 40% factor
for compressive structures, means that 6375/1.4=10.7 scale lengths.

Therefore the required scale length is 425 km.  Existing carbon
fiber has a theoretical scale length of 382 km.  Allowing for a
maximum of 60% of theoretical strength as allowable stress, 25%
overhead structures, and the 4 out of 6 cable damage tolerant
design, we get a useable scale length of 122 km.  Therefore we
need a factor of 3.5 increase over current materials (3.5 million
psi vs 1 million psi).

- Finally, a full space elevator is not required.  You can build 
a structure in Earth orbit that is vertical, but shorter than GEO.
The bottom end will move slower than orbital velocity, reaching
zero velocity as the length gets to the full GEO size.  Any reduction
in the job a launch vehicle has to do is very useful, and a partial
elevator can be built with today's materials.

Dani Eder

From: Hans Moravec <>
Subject: Re: The Problem with Space Elevators
Date: Mon, 04 Dec 2000 22:47:43 -0500

Jason Goodman <>:
> Which brings up my other point.  Having a cable much longer than
> geosynch is *useful*.  You can launch a spacecraft toward any
> planet in the solar system by simply climbing up to the right
> height, and letting go at the right moment.  No rockets, no
> fuel(*), just push the right button on the elevator.  "Second
> floor: Mars, the Asteroids.... Third floor: Jupiter, the Trojan
> Colonies... Fourth Floor: Saturn..."
> (*) It's not a free ride to the planets.  The energy to accelerate
> the spacecraft comes from slowing down the cable.  You have to put
> energy back into the cable somehow, and rockets mounted to the
> cable might be the best way to do so.  But they can be *good*
> rockets...

No rockets necessary.  The cable "leans" a little from coriolis
force as the spacecraft rides up it.  The lean puts a torque
on the earth through the anchor.  Momentum and energy is
transferred from the earth to the spacecraft through the sideways
component of the leaning cable force vector acting on the
upriding spacecraft.  Some sway remains after launch, but there
are damping effects, eg electromagnetic.

If you feel guilty about stealing earth's rotational energy to
launch you to Saturn, assuage your guilt by returning the same
way.  As you grapple your way down the cable to synchronous
altitude against the centrifugal force, and then coast down with
gravity below synchronous, the cable leans the other way and
your energy and momentum are returned to mother earth.

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