Another plus side: with ribbon strength increasing with temperature, the climbers might be able to go faster than 200km/hr. They would still have to reach the 0.1g point before the next climber could begin it's ascent, but this would increase the number of payloads per year.

R^3 = [G*M/(4*pi^2)]T^2

This is the basis for a very ugly equation.

Possible factors affecting orbital mechanics:

• Sun/Moon Induced Oscillation [Ribbon has a characteristic frequency of 7.1hrs]
  
• Coriolis Effect [Counterweight tension varies with ribbons size, but there will usually be two climbers between Earth and GEO and as many as 7 climbers during build-up for a 144,000km ribbon. It is possible to angle the ribbon eastward for some alleviation.]
  
• Ascending/Descending Climber Mass [Climbers are 5-10% of total ribbon mass, but their vertical force will decrease as they approach GEO.]
  
• Varying Counterweight Mass [mostly during ribbon buildup]
  
• Climber-Induced Stretch [I don't have numbers for this yet]
  
• Heat-Induced Stretch: [380% length at 3600 degrees F, nonlinear?]
  --Atmospheric temperature [The bottom 1% of the ribbon is in a 24hr heat cycle]
  --Bidaily temperature [Occuring at 6:00am and 6:00pm local, the ribbon will be at maximum absorbsion. Earth's shadow will also come into play.]
  --Wheel temperature [The climber's wheels will produce different temperatures at different speeds]
  --Laser temperature [This will vary with altitude]
  --Current-induced temperature [local geomagnetics/CMEs/rad belts/ionosphere]
  
• Heat-Induced Tension [280% strength at 3600 degrees F, nonlinear? This will impact the coriolis effect.]
  
• Ribbon Build-Up
  
• Ribbon Damage
  
• Ribbon Repairs
  

I think that's all of them. Needless to say, it's complicated. Keep in mind, actual results will vary depending on the taper. As far as ribbon mass, taper, and stretchability are concerned: your guess is a good as mine. I suppose we could just make up some numbers and see what it might look like. Hopefully, most of these factors will be negligable. What we might end up with is a very complicated computer system that monitors the ribbon with lasers. Even with response times at the speed of light, there will be a 1 second delay time to the end of a 144,000km ribbon and back. It would be nice if someone built a simulator...

You raise a good point. The numbers I am quoting are from the Edward's Report which is available here and here. Some of these numbers (such as the length, taper and mass of the ribbon) are based on his specific design and guesses about the strength of CNT at the time the paper was written. The University of California, Berkeley supplies a 200 kW free-electron laser for $120M, which is the one quoted in the paper. Combining these into a complete power system is the aim of a private company, Compower. The paper does not state whether a complete system is currently being built, or just proposed. My guess is that we wont build the power until we are sure we can build the ribbon. Some of the other numbers, such as the height at GEO and the thermal velocity of atomic oxygen, we can be certain of. The ribbon proposed by the Edwards group is the first reasonable design (meaning one that didn't require the capture of a carbonaceous asteroid). As such, I am quoting numbers for this design as it is the basis for our discussion. There are many variations of this design, which would require different mass, launch costs, etc. so keep this in mind.

The part I said about speeds is incorrect, as Neil pointed out to me. My apologies. However, the SE does differ from a GEO satellite, in that centripetal force is present.

I suppose we should say that the mass/acceleration ratio above GEO is nearly canceled out by the mass/acceleration ratio below GEO, as there is actually a net upward force of 20 tons to compensate for payload mass.

Of course I'm talking about weight! I said a passenger's weight in the upward direction will equal his weight in the downward direction. Mass does not have direction. While this is true for a person in orbit, it will not always be true for a person riding the SE - you only become weightless at GEO. I hope I'm making sense...

My bad - I'm getting rotational speed mixed up with linear speed.

How can this be the case if the end of the ribbon at 14,000km has to be rotating with a 24 hour rotational period? Wouldn't every point on the ribbon closer to earth than the tip have to go slower than that?

The elevator has a natural upward force of 20 tons. The maximum climber weight is 15 tons, meaning that even at the start of ascent, there is an upward force of 5 tons on the ribbon.
Ignore the aspect of elongation for the time being. An ascending climber would stretch the ribbon towards earth. A descending climber will stretch the ribbon in the opposite direction. If a climber went to GEO and back, the stretch would cancel out - except that the payload mass gets unloaded at GEO. This would result in more downward stretch than upward stretch. We could possibly counteract this by moving some of the mass of the sation above the center of force, providing more upward force.

That sounds about right.

By the way, the ribbon's taper has no bearing on the problem of balancing the mass. Remember that the ribbon above GEO is tapered the other way (but not as much). All the taper does is equalize stress along the ribbon.

I should have stated this better, since I knew it would be a point of some confusion. Basically - any satellite that is in geostationary orbit will not be moving any closer or further from earth. This is because earth 'drops away' due to the satellite's rotation just as fast as gravity pulls the satellite closer. The result for the satellite is zero net acceleration in the vertical direction. The same is true for the SE, with the only difference being that there is a centripetal force present. This will require the portion of ribbon that is at GEO to be rotating slower than a GEO satellite would be in order to compensate for centripetal force. The net vertical acceleration is zero in both cases.

A lot of people get confused because they are thinking of stabalizing the elevator in a frictionless environment with no outside forces present. Once you compensate for gravitation, etc. - you end up with more mass above GEO than below.

The Center of Weight is really the point where a passenger's weight in the upward direction is equal to his weight in the downward direction. Maybe CW isn't the best term - especially since it might be confused with Counter Weight. We could say CoW (as in: CoW station  ;-) ) or Center of Force.

0.8 nanometers is truely amazing. It reminds me of those Chinese finger traps. Perhaps there is a medium temperature that would work well. Consider that a stronger ribbon material would require less binder (and therefore less mass). A good application of LiftPort would be to research extreme-temperature binders.

I found a more in-depth article about the same study. http://www.llnl.gov/pao/news/news_releases/2006/NR-06-01-06p.html

:-? !
The journalist made an error in this paragraph. Going from 24 to 91 is a 280% increase, or 380% of the original length.

Sounds like good news and bad news. I saw in another thread where you describe the problems with transcients that stretch introduces to the ribbon.
To further complicate matters, there is the coriolis effect:
Because of Earth's rotation, an otherwise straight ribbon will have a westward bough in the middle. The extent of the bough depends on the length of the ribbon. The bough would oscillate slightly assuming a ribbon with 1% stretch. With a 280% stretch, the oscillation would likely become much more pronounced before the counterweight gains the neccessary altitude to compensate. A possible result would be that the center-of-weight would be shifted too close to Earth and the ribbon would drag itself down.

Looking at the graph inset in the picture, it appears that stretch vs. temp is non-linear. Unfortunately, the quality of the picture makes the graph indecipherable. The research was done by Boston College, but I was unable to find any papers on their website. They did place an article in Nature, which might have a better picture, but I do not have a subscription to Nature. I will keep trying to locate the Nature article. If someone has a copy of that article, could you please post the picture?

Are you sure about this? Intuition tells me that a breaking climber would pull the ribbon upward. Wouldn't sending the climber to GEO and back largely cancel out the transient? (excepting for the transfer of payload mass)


-------------------------------------------------
Bob - In Neil's second post, I believe that he is critiquing some other dude's post. Not sure whose. Neil's words are enclosed in tildes.

I think he's talking about a geostationary ribbon which has, by definition, a 24 hour revolutionary period. The morning stretch I believe would be lesser since part of the ribbon will be coming out of earth's shadow, as opposed to being in the sun all day. Incedentally, it would take the ribbon 7 days to unroll, so with bidaily expansion you have a minimum of 14 expansions during deployment.


I don't think an SE should even have an LEO station. Unless you're talking about assembling the ribbon in LEO before sending the roll and counterweight to GEO for deployment.

The proper term we should be using is CW: Center of Weight. This is the point at which Gravitational Acceleration+Rotational Acceleration+ Centripetal Acceleration = 0. (in the upward direction or z-axis)

Hmm. Lesse- 91,000km ribbon. GEO at 36,000km. Yet still providing an upward force of 20 tons. I'd say that Neil is patently correct!  :wink:

That's 2000+ degrees celsius. The binder may also cancel out a lot of the stretch. Also, I don't know if stretch vs. temp is linear or if there is a threshhold. I suspect it would be linear.

I've compiled a list of statistics about the SE. These are mostly from the Edwards report, but some have been gleaned from the forums and various other sources. I understand that the LiftPort concept differs slightly from the Edwards and space.com SE, so you might see some that are a bit odd. Feel free to repute, disagree or add to this list and I can change it for you. If you want to discuss the implications of specific statistics, please do so in another thread as this is for reference only.

91,000 km - length of ribbon with counterweight
144,000 km - length of ribbon without counterweight
36,000 km - height at GEO
200-1200 km - height at LEO
500km-1700km - area of significant meteor impact (ribbon width is doubled here)
60-800 km - region where atomic oxygen is present (highest density at 100km)
10 km - height above 72% of atmosphere (cruising altitude)

1.5 - aproximate ribbon taper ratio
1 micron - average ribbon thickness
8mm/2.5cm - ribbon curvature displacement over width
0.87 - cable mass to counterweight mass ratio
2%-10% - approximate percentage binder mass (epoxy)
64% - percentage mass increase for an optional Hoytether ribbon design

130GPa - theoretical tensile strength of CNT
1300 kg/m^3 - density of CNT
1.31nm-2.25nm - diameters of CNT
10^-4milliohms - conductivity of CNT
50kiloohms - approximate ribbon resistance
3300 degrees C - approximate melting point of ribbon

19,800 kg - initial ribbon mass
5 cm - initial ribbon width at base
11.5 cm - initial ribbon width at GEO
1,238 kg - initial ribbon tension(capacity) before breaking
288 kg - initial ribbon maximum payload

1500 tons - final ribbon mass
30 cm - final ribbon average width
250.7 cm - final ribbon width at GEO
20,000 kg - final ribbon tension(capacity)
13,000 kg - final maximum payload

1:40 - ratio of initial cross-section to final cross-section
1.5% - increase in ribbon strength after each strand is added
207 - number of strands added
2.3 years - time to add 207 strands on initial ribbon
170 days - time to produce the second SE or double the ribbon capacity
2.8 years - time to expand the capacity by factor of 50 (large enough to lift a shuttle)

200 km/hr - ribbon deployment speed
20-40 kW - power generated during ribbon deployment
0.46m/s - angular velocity of low end mass during ribbon deployment

619 kg - initial climber mass
0.87 - climber mass to payload mass ratio
200 km/hr - climber speed
97hours(4days) - time between climber launches (time it takes to reach the 0.1 G point)
7.5 days - time for climber to reach GEO
81W/kg - power to mass ratio of climbers
50kW - power required for initial climber motors
90-96% - energy effeciency of motors
30% - approximate energy effeciency of rollers
100 degrees C - approximate maximum heating of climber due to air friction
200 degrees C - approximate heating of ribbon due to rollers
1-4kW - heat generation from entire locomotion system

3m - diameter of photovoltaic array
12m - diameter of transmitter
25cm at 100km - resolution of beam
2.4MW - total laser output for 20,000kg capacity
120MW - total laser output for 1x10^6kg capacity
3-30% - wallplug to laser energy efficiency (depends on individual laser wattage)
54W/cm^2 - beam power density
0.84 microns - beam wavelength
59% - photovoltaic conversion efficiency
2% - overall laser efficiency
50,000 km - approximate laser maximum effective distance
20% - percentage laser energy converted to heat (17kW for initial climber)

7 km - maximum altitude where wind is a problem
1cmx7.5microns - ribbon cross-section where wind is a problem
116km/hr - wind speed required to break initial ribbon

100-400kV/m - potential differences produced in thunderstorms with 20-40C of charge
10^14milliohms - conductivity of air

1km/s - thermal velocity of atomic oxygen
1micrometer/month - rate of atomic oxygen etching on unprotected cable

2000-6000 q/cm^3/s - charge rate of the ionosphere
5megaohms - ionospheric discharge resistance of ribbon (for 20-ton ribbon with 10^-4 milliohm resistance and 2mm^2 cross section)
3x10^11V - approximate current voltage difference required between ionosphere and earth to produce current
2X10^9V - maximum static voltage potential during thunderstorm

<3 Mrad/yr - radiation rate for exposed cable
10^4 Mrad - radiation hardness of epoxy/carbon fiber composites
>1000 yrs - lifespan of irradiated fiber

0.00068 V per m - maximum electromagnetic voltage at far end
0.4ohm-meters - minimum ribbon resistance
0.0064 W per m - maximum electromagnetic heat generation at far end

8,000 - number of objects being tracked by U.S. Space Command
100,000 - number of objects 1-10cm in diameter currently too small to be tracked
250 days - average time between debri impacts on ribbon

170,915 kg - initial spacecraft total mass
enormous kg - maximum sustainable mass at GEO
7.1hrs - characteristic frequency of ribbon
0.002 G - gravity at end of ribbon (144,000 km)
-0.08 G - centripetal acceleration at end of ribbon (144,000 km)

US$40B - estimated cost of first SE
US$14.3B - estimated cost of second SE
US$220 per kg - estimated operating cost of SE

24,000 km - altitude on the SE where a dropped object will orbit with a perigee just above the atmosphere
47,000 km - altitude above which an object released from the SE is at or above Earth escape velocity, trajectory is hyperbolic

If we had a strong enough material today and enough of it today, we could build 1 SE for $40B in 2 years, or 2 SEs for $60B in 3 years. We are looking at about 150 years or more for the SE to pay for itself when you factor in repair costs. The biggest limiting factor is the cost of ribbon production which is estimated at $3B for a 1500 ton ribbon. If that cost could be reduced to $1B, you could scale up the payload by 2 orders of magnitude and pay for everything in 10 years. The cost ratio would drop even further after that, and also the payloads might generate their own revenue...

MACchine:
First of all, be careful when you use the phrase "beyond gravity" since even the outer reaches of the universe are under the influence of gravity. The atmosphere at 3km is about 0 degrees C. Air freezes at a little less than -200 degrees C and you wouldn't be able to get a balloon high enough for that to happen without it being virtually weightless. Temperature is dependant on the time of year, time of day, latitude, solar flux and other variables. Your line of thought reminds me of a idea of Buckminster Fuller. Mr. Fuller had devised what he called a 'cloud 9 structure': very light weight geodesic spheres, about 1 1/2 miles in diameter, with an interior concave surface that would heat the air inside. The structure would then become self-lifting in the daytime. The air could be vented to lower it at night and platforms could be built on the sides and top. If such a structure could be a stable base station for an SE, it would lower the taper and strength requirements of the ribbon. However, these structures were never built, and I do not believe that a structure that size and density would be able to weather a storm. Sorry, this post is very off-topic. I think beamed power is a good idea.