Monday, June 27, 2016

Altitude compensation attachments for standard rocket engines, and applications, Page 3: stretchable metal nozzles.

Copyright 2016 Robert Clark
(patents pending)

 Some calculations show a surprising increase in the amount of payload that can be carried by a single-stage-to-orbit rocket (SSTO) by using altitude compensation [1], such as the aerospike, even multiple times more than possible without it. Indeed, the calculations revealed that for an already high propellant fraction stage such as the Falcon 9, alt. comp. gives the SSTO a better cost per kilo ratio than the two stage rocket (!) 

 This was a surprising result since during much of the era of orbital rockets it was received wisdom that SSTO's were not technically feasible. Then, it gradually became accepted it could be done, but it was then felt it would not be worthwhile because of the small payload. Therefore it is quite remarkable that the exact opposite of this is true, the SSTO is more cost effective than the TSTO (two-stage-to-orbit) when using altitude compensation [1]. 

 But the usefulness of altitude compensation is not just for SSTO's. The payload for a two-stage to orbit launcher can be increased 25% by using it [2]. And triple-cored rockets such as the Delta IV Heavy, and Falcon Heavy can have their payload doubled when using altitude compensation in concert with cross-feed fueling [2]. Moreover, by using alt. comp., simple pressure-fed stages that are within the technical means of most university engineering departments can be made to make suborbital [3] and orbital launchers [4].

 However, an argument has been made that transforming already existing engines to altitude compensation such as the aerospike would be expensive since it would require changing the combustion chamber to a toroidal shape. Then I investigated other means of achieving altitude compensation other than the aerospike [5].

 One of these methods was to use high temperature carbon nanotube "rubber" [6] as a nozzle extension. This could be attached to the nozzle of already existing engine nozzles and be variably extended as the rocket gained altitude.

 But could we use metals for this purpose? The metal would have to be stretchable as is rubber to become twice as long or more as the nozzle is extended. Normally though metal can only be stretched by a fraction of its original length before fracturing and even then it takes quite a large amount of force to do the stretching.

 There is a scenario though where metals can be stretched for a longer length and at a small amount of required force, that is at elevated temperatures. This is through forging. This takes place while the metal is still solid. The forging temperature [7] is where the metal is more malleable but below the melting temperature. It is commonly in the range of 60% of the melting temperature. Then the idea would be as the nozzle becomes heated as the engine is firing it would become more and more easily extended further out. 

 For how to extend, that is stretch, the nozzle, one possibility would be to use high pressure inert gas such as helium injected within the hollow walls of the nozzle to stretch it you as would for blowing up a a hollow balloon. Another would be actuators attached to the end to stretch it out.

 For either method you would want the nozzle to maintain the usual bell nozzle shape. You could have the wall thickness vary along the nozzle's length so that as it is stretched out the required shape is maintained. You might also have ribs along the vertical length of the nozzle to help encourage the stretching to proceed in the desired direction.

 Another consideration is that you don't want the nozzle to reach a degree of heating so that it reaches the melting point. An interesting fact about rocket nozzles and combustion chambers is that they actually operate at temperatures above the melting point of the metal composing them. The reason why they don't melt is that for a material to undergo the phase change from solid to liquid, not only does the temperature have to be at the melting point, but a sufficient quantity of heat dependent on the material has to be supplied to the material, the enthalpy of fusion [8].

 Then rocket engines have cooling mechanisms applied to the chamber and nozzle walls to draw away the heat supplied by the combustion products so that this amount of heat is never applied to chamber and nozzle. One key method that is used for high performance engines is regenerative cooling. This is where the fuel is circulated through channels in the walls of the engine to draw away the heat.

 Another factor to limit the temperature and heat applied to the nozzle is that this is envisioned as an attachment to a usual, static nozzle. However, as the engine exhaust is expanded out by a bell nozzle the temperature drops. So for the attachment at the bottom of the usual nozzle, the temperatures it would have to withstand would be reduced.

 A diagram showing the stress-strain curve at elevated temperatures for titanium alloys is here [9]:

  The strain at room temperature is commonly only a fraction of a percent, ca. 0.2%, or 0.002. But here at elevated temperatures in the range of 800C to 1,050C, we see the strain can reach .7, and likely above with continued pressure applied.


1.)Thursday, November 7, 2013
The Coming SSTO's: Falcon 9 v1.1 first stage as SSTO, Page 2.

2.)Monday, January 11, 2016
Altitude Compensation Improves Payload for All Launchers.

3.)Thursday, January 15, 2015
NASA Technology Transfer for suborbital and air-launched orbital launchers.

4.)Thursday, August 13, 2015
Orbital rockets are now easy.

5.)Saturday, October 25, 2014
Altitude compensation attachments for standard rocket engines, and applications.

6.)Carbon Nanotube Rubber Stays Rubbery in Extreme Temperatures.
Liming Dai
Angew. Chem. Int. Ed. 2011, 50, 4744 – 4746

7.)Forging temperature.

8.)Enthalpy of Fusion.

Z. Guo, N. Saunders, J.P. Schillé, A.P. Miodownik
Sente Software Ltd, Surrey Technology Centre, Guildford, GU2 7YG, U.K

Tuesday, April 12, 2016

Combined amateur telescopes for asteroid detection.

Copyright 2016 Robert Clark

 NASA is conducting an interesting program to get the public involved in the upcoming ORISIS-REx mission to retrieve a sample from an asteroid. It is asking amateur astronomers to make observations of known asteroids using their telescopes:

Target Asteroids!

 However, a slight modification of this program should allow it to also to discover unknown asteroids. This article discusses that even an 8-inch scope equipped with a CCD camera can discover new asteroids:

Hunting Asteroids From Your Backyard
By: Dennis Di Cicco | July 28, 2006
There are no hard and fast rules regarding the telescope or CCD camera needed for asteroid work. To be effective, the system should record stars as faint as 18th magnitude with a single, 4-minute exposure. Almost any CCD camera on an 8-inch telescope can do this under a clear, dark sky.

 The article discusses down to magnitude 18. But combining the observations of many of these scopes acting in concert should allow the discovery of asteroids of weaker magnitude and therefore smaller size.

 As discussed in the article, CCD's can have imaging artifacts where a pixel will show as lit but it's not really corresponding to a light photon hitting the device. Moreover, the weaker the imaging source, the more difficult it is distinguish these imaging artifacts from a real light source.

 However, since these imaging artifacts are occurring at random, the idea would be to have several of the amateur scopes from different parts of the world focused on the same spot in the sky. Then several of the scopes' CCD's registering a hit on a pixel corresponding to the same point in the sky at the same time would be taken as indicating a real light source.

 The scopes would have to have a high degree of sky location specificity and timing synchronization for this to work.
 Another aspect of the imaging artifacts of the CCD's is that at low imaging illumination the CCD might correctly register a lit pixel but at a later time not register it. For individual scopes used to detect asteroids, it's done by noticing the light source moving between exposures. But if the imaging light source is too weak the CCD for the scope might not register the light source the second time to detect the motion. Then in this proposal of using multiple scopes, you also need to be able to correlate a second detection by another scope as indicating the light source moved, even if this scope did not detect the light source the first time. All the information would need to be correlated at a central site for this to work.

 Then after sufficient numbers of scopes give a high level of confidence the asteroid is indeed there, larger professional telescopes could be used to confirm the detection.

 This would have importance also for planetary protection purposes since it would allow the detection of smaller asteroids.

Credit and Financial Rewards for the Discovery?
 Certainly the amateur astronomers whose scopes detected the asteroid should get credit for the discovery. But an intriguing question of financial rewards arises because of the companies such as Planetary Resources, Inc. and Deep Space Industries that are working towards returning valuable minerals from asteroids. According to this article an asteroid potentially worth $5 trillion in platinum passed nearby to Earth last year:

‘Platinum’ asteroid potentially worth $5.4 trillion to pass Earth on Sunday.
Published time: 18 Jul, 2015 11:21

 There are very many near Earth asteroids still to be discovered. Then one can imagine these coordinated amateur scopes detecting one of these highly valuable asteroids. If one of them is eventually used to recover valuable minerals should the amateur astronomers who discovered it take part in the financial rewards?

 Not an easy question but it is notable that it would increase the interest and participation of amateur astronomers in the program. In view of its potential importance for planetary defense purposes this participation should be encouraged.

   Bob Clark

Monday, February 15, 2016

Carbon nanotubes for "ionic wind" craft or "ionocraft".

Copyright 2016 Robert Clark
(patents pending)
Note: this is the technical background to an announced crowdfunding campaign now live, as of February 5, 2016:


 Long has it been dreamed about a personal "aircar" or "flying car" that could be privately owned and takeoff from the family garage. Carbon nanotubes now make that possible.

 About the last decade or so there was much research among amateur experimenters about "ionocraft", commonly called "lifters":


 They work on the principle of 
electrohydrodynamic (EHD) propulsion: electrical power is used to ionize the air which is then directed by electric fields.

 The problem with the lifters has been though the power requirements are so high they could not produce enough thrust to lift their own independent power supply. The lifters that have been produced work by having a power supply on the ground and connecting the power supply to the lifter through cables.

 BUT there is an interesting aspect of the equations describing the thrust produced by the lifters. The thrust increases as the diameter of the wires producing the ionization, called the "corona wires", decreases. The wires used for the lifters so far have been a few hundred microns wide, a few widths of a human hair.

  However, the nanotubes have widths at the nanoscale. Calculations show the thrust then produced should be enough to lift the lifters AND their power supply. Theoretical discussion of the inverse dependence of the thrust on the corona wire radius by Evgenij Barsoukov here:
Lifter theory
Force/Power optimization
by Evgenij Barsoukov
Courtesy of Evgenij Barsoukov

Created on April 30, 2002 - JLN Labs - Updated on April 30, 2002
Thrust/current :
Here :
And values of parameter used in calculation are :
1.   Voltage optimization
Voltage was calculated for 100 points from minimal corona initiation voltage (6.9kV) calculated by Peek's equation for given distance, until voltage 100kV.

3.    Corona wire radius optimization

Radius was changed from gauge 50 (0.015 mm) to gauge 20 (1.5mm). Resulting thrust/power relation is given below :

It is great to see, that efficiency does not change, but thrust does! See below absolute thrust/radius dependence :

With decreasing radius thrust increases a lot, without losing efficiency!


  • Increasing the wire/collector distance by simultaneous increase of wire/collector lenght can allow to achieve thrust/power ratios up to 40g/W.
  • Decreasing wire radius increases thrust without degrading thrust/power ratio.

(credit to calculations and graphs above to Evgenij Barsoukov.)

 Note that using nanotubes for the wires would be trebly more efficient. First, their extremely small diameters should significantly increase the thrust. Second, their small weight compared to metal wires should greatly reduce the weight. And third, their increased conductivity, i.e., reduced resistance, means less power would be required to achieved the same results which means a smaller, lighter power supply, further reducing the weight of the craft.

 Putting these factors together means there's a very good chance we can finally get an independently flying lifter able to carry its own power supply. Note this would also work to get a real hoverboard (Back to the Future would only have been off by 1 year) and personal jetpacks. Note also it makes the U.S. Army's billion dollar V-22 Osprey obsolete before being fully deployed.

Producing long nanotubes.
 So the question becomes can we make nanotubes of arbitrarily long lengths? Note it has already been proven by Rice University researchers the nanotubes when tied together can conduct electricity better than the metal wires now in use.

Nanotube Cables Hit a Milestone: As Good as Copper.
Researchers achieve a goal they've been after since the 1980s—the advance
could make cars and airplanes lighter, and renewable energy more practical.
Monday, September 19, 2011 By Katherine Bourzac

  The article describes research by scientists at Rice University who created
lightweight electrical cables by mechanically tying together nanotubes. In their research the Rice scientists also tested the strength of these tied together nanotubes and found them to be of comparable strength to the aluminum or copper wires now used but at lighter weight.

 Then the only thing needed now is to confirm the validity of the modeled thrust of the lifters that nanoscale wires can produce EHD thrust sufficient to lift the craft and its power supply.

 The Nanomanipulator™ that can manipulate objects at the nanoscale will be used to produce an ionocraft with wires consisting of nanotubes tied together.  

The Nanomanipulator™:

 Note though that the equations show the higher thrust should arise for any wires at the nanoscale not just for carbon nanotubes, though the carbon nanotubes may be able to carry more current. Then this patent should be interpreted to cover the use of nanowires of any type to increase the thrust produced by ionocraft or ionic wind flow devices, such as proposed for use on aircraft to improve laminar air flow.

Increased air pressure increases thrust.

 The equations for the ionic wind thrust also show that the thrust should be higher at higher pressures, which has been confirmed experimentally. However, not only that but in fact the thrust to power efficiency also increases at higher pressures. This should not be surprising since that is also the case for example with jet engine propulsion, which is why compressors are used after the intakes of jet engines. In fact typically 2/3rds of the power generated by a jet engine goes just to run the compressors:

What is a Gas Turbine Engine and How Does it Work?
The turbine drives the compressor via a fixed shaft, and the cycle is complete, and self sustaining. The cycle that governs the operation of a gas turbine engine is referred to as the Brayton constant pressure cycle. The engine compressor typically requires about 2/3 of the usable heat energy produced in the burner to turn at maximum speed; the remaining energy can then be used to produce thrust or mechanical power, or a combination of the two.

 Remarkably a recent analysis found that actually the thrust to power ratio for the ionocraft is higher than for jet engines(!) This is surprising considering the low thrust of the ionocraft:

 MIT researchers study electro-hydrodynamic thrust.
 David Szondy
 April 8, 2013
In the ‘60s, the ionocraft seemed like a revolution in aviation. There was talk about them being used in all sorts of small aircraft, and the military were interested because ionocraft give off no heat, so there’s no infrared signature. Ionocraft were seen as replacing helicopters, as silent commuter ferries, as craft capable of operating at the edge of space, as traffic monitors or anti-missile platforms.
The problem was, the technology didn't scale very well. What worked for a small model that was built like a kite didn't do at all well as the ionocraft got bigger. It couldn't even carry its own power supply, so it wasn't long before ionic thrusters became the denizens of science fairs and the obsession of anti-gravity cultists.
Where MIT came in was at the point that the researchers realized that very few rigorous studies of ionic wind as a viable propulsion system had ever been carried out, and exactly what the ionic thruster is capable of hadn't been measured. So, they devised a test where an ionocraft was hung under a digital scale and tens of thousands of volts with enough amperage to run a light bulb were run through the craft.
The results were surprising. The team discovered that the ionic thruster turned out to be remarkably efficient compared to, for example, jet engines. Where a jet produces two newtons of thrust per kilowatt, the ionic thruster punched out 110 newtons per kilowatt. Furthermore, the thruster was most efficient at low thrust, which meant that power wasn't being wasted. 

On the performance of electrohydrodynamic propulsion.
Kento Masuyama, Steven R. H. Barrett
Published 3 April 2013.DOI: 10.1098/rspa.2012.0623 

 Then increasing the pressure of the air before applying the ionic wind thruster should improve this thrust/power even further. However, the calculations that say thrust to power for the lifters should improve at high pressure are simply taking the air as already pressurized when presented to the lifter. That is, none of the power is being used to drive compressors. More careful analysis that considers the power requirements needed to pressurize the air needs to be made before it can be said this offers an improvement on the performance. Still, because the lifters are 50 times better than jet engines without even being pressurized, it is likely pressurization will help to provide sufficient thrust for liftoff while still remaining better than jet engines in thrust to power ratio.

 So additionally the patent will cover methods suggested here of producing high pressures with the ionic wind propulsion. A problem with the jet engine compressors is their high weight which severely reduces a jet engines thrust/weight ratio, compared to rocket engines for example. But the weight issue is an even more important problem for ionic wind devices. One suggested method to get the compression at lightweight would be to use for example carbon fiber piston within a carbon fiber cylinder. Other possibilities in keeping with nanotechnology would be to use recently discovered carbon nanotube "rubber". This is stretchable yet has high strength and temperature resistance.

 Still another possibility would also be in keeping with the nanotechnology theme. The compression due to centrifugal compressors is due to air being forced against the wall due to the acceleration measured by a = v2/r. Normally, the high acceleration comes from high velocity. But it can also come from the radius r being at the microscale or nanoscale even using low velocities, v.

 Then another proposal here would be use multiple microscale or nanoscale cylinders with the air being circulated within them by the ionic wind  devices. This creates high pressure on exit. Then use ionic wind devices again on this high pressure air, resulting in increased speed, once more. Then this process can be repeated in stages at each time increasing the pressure and therefore the speed and thrust.

Single Electrode Operation.
The classical lifter design uses an emitter wire and a collector plate. However, it has been known for many years you can get thrust using an emitter only known as a "corona wheel" or "corona pinwheel":

Lifter - High voltage plasma levitation device
(Lifter - Dispositivo que levita sob alta tensão)
M. Cattani1  , A. Vannucci 1   , V. G. Souza
1Instituto de Física, Universidade de São Paulo, São Paulo, SP, Brasil
Rev. Bras. Ensino Fís. vol.37 no.3 São Paulo July/Sept. 2015

5B30.50: Electrostatic pinwheel.

 It is also known you can get an intense corona discharge around sharp points. This report compared the thrust between the single electrode approach using sharp pins as the emitter and the dual electrode approach and found for low voltages the thrust is comparable, at least for AC, though the dual electrode approach has the significant advantage for high voltage:

Journal of ELECTRICAL ENGINEERING, VOL. 66, NO. 2, 2015, 117–120
Tom´aˇs Ilit’, Michal V´ary, Pavol Valko

 The idea of using sharp points for the emitter might be especially useful for carbon nanotubes used as the emitter.

 Also since the flat collector plate makes up the majority of the weight for the lifter, removing that and using the emitter only would save significantly on the weight. This becomes especially important with the nanotubes used as the emitters because of their ultra low weight.

 Another report was able to increase the thrust using solid plates rather than aluminum for the collector:

High efficiency Lifter based on the Biefeld-Brown effect.
Moshe Einat and Roy Kalderon
AIP Advances 4, 077120 (2014);

­ The researchers noticed there was vibration with the aluminum foil collectors on the lifters. They reasoned this may detract from the thrust since some of the energy of the moving air molecules would go to causing the collector vibration rather providing thrust.

 They were able to get higher thrust using the solid plates. However, the plates were so heavy the lifter could not then liftoff. To get lightweight but stiff plates perhaps we could use graphene as the collector material. Presumably as with nanotubes there would be versions of the graphene that are conducting.

Space applications.
 A non-propellant method of satellite station-keeping being investigated now is the "electrodynamic tether". One version uses a conducting tether and produces thrust by acting against the planets magnetic field.

 However, another version acts in an analogous process to the ionic wind devices. The advantage of the space version though is that it is operating through already ionized air. So the amount of power that is needed to ionized the air is eliminated. For this version as well using carbon nanotubes for the tether can significantly improve the thrust.

  Ion drive and plasma drives such as the Hall effect thrusters also work on a similar principle to the ionic wind devices. Then they also should have improved thrust using carbon nanotubes for their ion inducing wires. Then this could improve the thrust/weight ratio for these thrusters given better performance both for unmanned and manned space drives.

  Bob Clark

Wednesday, February 3, 2016

From nanoscale to macroscale: applications of nanotechnology to production of bulk ultra-strong materials.

Copyright 2016 Robert Clark
(patents pending)


Note: this is the technical background to an announced crowdfunding campaign now live, as of February 5, 2016:


 For the twenty years since their discovery, the "Holy Grail" of nanotube research has been to produce them in arbitrarily long lengths. They initially were only produced at micron-scale lengths. After intense research, so far they have still only been made in millimeter to centimeter lengths.
 Still, in the micron-scale samples tested, their tensile strength has been measured to be a maximum of 150 gigapascals (GPa) at a density of only 1.6 g/cm3, 200 times stronger than steel at only 1/5th the weight, for an improvement of 1,000 times in strength-to-weight ratio.

 The big question is can we make or combine the nanotubes to macroscale sizes while maintaining the strength of the individual nanotubes? Individual carbon nanotubes and the 2-dimensional form monolayer graphene have been measured at micron-scale lengths to have tensile strengths in the range of 100 to 150 GPa, [1], [2], [3]. Carbon nanotubes have been combined, intermingled into bundles and threads for awhile now. These always have significantly lower strength than the individual nanotubes, [4]. However, this is because there were many single nanotubes connected together by weaker van der Waals forces rather than the stronger carbon-carbon molecular bonds that prevail in individual nanotubes. In these cases, with separate nanotubes weakly connected end-to-end, they can just peal apart under tensile load. This is explained here, [5].

  However, some tests of aligned, arrays of nanotubes at millimeter length scales also showed significantly lower strength than individual micro-scale nanotubes, [6], [7], [8]. This may be because of the predicted effect of longer nanotubes having more defects and therefore becoming weaker. If this is the case, then rather than pursuing arbitrarily long nanotubes it may be better to pursue methods of bonding the micro-scale nanotubes at their ends so that their ultra high strength is maintained.  Some possibilities will be suggested in the following pages.

 Joining nanotubes to arbitrary lengths.
 Tying ropes together has been known to create longer ropes whose strength can be 80% to 90% as strong as the component ropes, [9], [10]. Quite key then is that the capability exists to manipulate individual nanotubes at the nanoscale:

The stress test: One experiment repeatedly bent a nanotube through contortions to see if it would break. All these modifications were performed by the NanoManipulator, with the user guiding the AFM tip by moving the Phantom force-feedback pen. [11], [12], [13]

  See also, [14], [15], [16]. Then the suggestion is to tie the nanotubes together using some of the knots known to maintain near the strength of the original ropes. (patent pending.)

 To prevent slipping of the nanotubes under high tensile load we might use them with “nanobuds” along their lengths, [17].

 Also, since the nanotubes are quite thin they might be expected to cut into each other when knotted thus weakening the strength of the knot. One possibility might be to fill the portion of nanotube that is to be knotted with water or other fluid to make the nanotube more spongy there, [18].

This method of tying nanotubes together to produce greater lengths has already been proven to work to preserve at least one characteristic of nanotubes, high conductivity:

Nanotube Cables Hit a Milestone: As Good as Copper.
Researchers achieve a goal they've been after since the 1980s—the advance could make cars and airplanes lighter, and renewable energy more practical.
Monday, September 19, 2011 By Katherine Bourzac

 The article describes research by scientists at Rice University who created lightweight electrical cables by mechanically tying together nanotubes.

 An alternative method for linking the nanotubes together would be to connect them with nanotube rings:

Ring Closure of Carbon Nanotubes.
Science, Vol. 293, No. 5533, p. 1299-1301, 17 August 2001
Lightly etched single-walled carbon nanotubes are chemically reacted to form rings. The rings appear to be fully closed as opposed to open coils, as ring-opening reactions did not change the structure of the observed rings. The average diameter of the rings was 540 nanometers with a narrow size distribution. [19]

 These are closed rings formed from one or more nanotubes. They are about 540 nm across so several of the aligned nanotubes would have to be fitted into the rings. One question would be how to tighten the rings around the nanotubes once they were fitted into the rings. One possibility might be to apply heating to the rings so that they lengthen then insert the nanotubes inside. Then as the rings cooled they would shrink back to their normal size forming a tight stricture around the nanotubes. As before with the knotting we may have to fill the rings with a fluid so that they are spongy and don’t cut into the nanotubes.

  Another method for fitting the carbon nanotubes into the rings would be by using ring-shaped nanotubes of materials that are piezoelectric. Carbon nanotubes are not piezoelectric but nanotubes of many different types of materials have been made, such as boron nitride nanotubes and zinc oxide nanotubes. Nanotubes of both these types are piezoelectric, and they can also be made in the form of nanorings, [20], [21]. Then we could apply electric current to these nanorings to get them to expand, insert the carbon nanotubes, then remove the current to get the nanorings to shrink back to their regular size.

  Note that using the rings as a means of binding the ropes together means you are using frictional effects to get the nanotubes to hold together. Then is this any better than the van der Waals forces holding just intermingled nanotubes together? I believe it can be as long as you make the rings stricture tight enough. But if it is made too tight, this would cut into the nanotube ropes reducing their strength. Then the optimal degree of tightening would have to be found to maintain the greatest strength.
 Interestingly, the method of knotting the nanotubes together or binding them by rings might also be applied to the intermingled bundles, that is, to the case where the nanotubes are of different lengths held together by van der Waals forces. You would note the shortest length of the nanotubes composing a bundle and tie knots around the bundle or bind it with rings at short enough intervals to insure that every nanotube is held tightly with a tie or knot at least once all along the length of the bundle.

  Another question that would need to be answered is how binding together a group of equally long nanotubes effects the strength of the nanotubes when the binding is only going around the outer nanotubes. That is, suppose you created a string made from single nanotubes bound end-to-end and measured the string’s strength.

 Then you composed a string by using aligned nanotube arrays that all contained the same number of nanotubes, say 100, and bound these ropes end-to-end with the rings. Would the string composed of the aligned ropes be able to hold 100 times as much as the string composed of individual nanotubes? This is asking a somewhat different question than how knotting weakens the nanotubes. It's asking how strong a composed string will be when a binding can only go around the outer nanotubes composing the string.

  Yet another mechanical method for joining the ends together might be to use some nanotubes bent into shapes as clamps. Since nanotubes have such high stiffness they should as clamps be able to hold the ends of aligned arrays of nanotubes together. Again so the clamps don’t cut into the nanotubes you might want to have the clamping nanotubes and/or the nanotubes that are being tied to be fluid filled.
 A different method of joining individual nanotubes or aligned nanotube arrays end-to-end is suggested by the recent research that created diamond-nanotube composites, [22], [23]. To form the strongest bonds for our purposes, I suggest that the method of creating the strongest nanotubes be used first to create the nanotubes, the arc-discharge method by which the 150 GPa tensile strength nanotubes were made, as in [1]. Then the ends of separate nanotubes or nanotube arrays should be placed on the same diamond seed particle and the high strength microwave CVD method of [4] be used to grow diamond around the ends of both, encasing the tips of each of them inside the diamond thus grown. In order to keep the weight low, you only use a small seed particle and you only grow the diamond large enough to maintain the strong bonds that prevail in individual nanotubes.

 Another highly promising method for joining the nanotube ends arises from the surprising effects found by irradiating nanotubes by electron beam:

Reinforcement of single-walled carbon nanotube bundles by intertube bridging.
Nature Materials, 3, p. 153 – 157, March 2004
During their production, single-walled carbon nanotubes form bundles. Owing to the weak van der Waals interaction that holds them together in the bundle, the tubes can easily slide on each other, resulting in a shear modulus comparable to that of graphite. This low shear modulus is also a major obstacle in the fabrication of macroscopic fibres composed of carbon nanotubes. Here, we have introduced stable links between neighbouring carbon nanotubes within bundles, using moderate electron-beam irradiation inside a transmission electron microscope. [24]

Strong bundles.
Nature Materials, 3, 135-136, March 2004.
The mechanical properties of nanotube bundles are limited by the sliding of individual nanotubes across each other.
Introducing crosslinks between the nanotubes by electron irradiation prevents sliding, and leads to dramatic improvements in strength. [25]

 The researchers noted as had others that intermingled bundles of nanotubes were relatively weak compared to the strength of individual tubes, in this case their measurements being of bending strength. However, after electron beam irradiation the bundles achieved almost 70% of the bending modulus strength of individual nanotubes. A similar effect was seen in  [26], [27], [28]. The irradiation produced interconnections between the nanotubes that prevented slipping. Then quite likely this can also be used to combine nanotubes at their ends.

  Electron beam irradiation has also been used to attach nanotubes to sensors in scanning electron microscopes for strength testing. One method used was to direct a small amount of hydrocarbons by focused e-beam to weld the nanotubes to the SEM sensor tip. Then this may also work to weld nanotube ends together, [29]. Note that e-beam irradiation can also be used in concert with the tying or ring binding methods to insure no slipping of the nanotubes.

 Additionally laser irradiation has been used to connect double-walled nanotubes strands together, [30]. This resulted in longer nanotube strands as strong as the original ones. However, the starting strength of these was low at 335.6 MPa. It needs to be tested if this method can maintain the strength of the original nanotubes at the highest measured strengths of 150 GPa.

 Note that these e-beam or laser irradiation methods may also work to produce graphene sheets of large size as well. Currently the 2-dimensional graphene has only been produced in micron-scale sizes, though its strength has been shown to be comparable to that of the highest measured strengths of the nanotubes at 130 GPa, [3]. However, irradiating overlapping graphene sheets on their edges may also allow these to be bonded together.

Friction-stir welding of nanotube arrays.
Another method for joining the aligned arrays of nanotubes might be the method friction-stir welding. This method is used to weld metals while maintaining relatively low temperatures. This reduces the damage to the metals and helps to maintain strength. Since this uses relatively low temperatures it may also work to combine the ends of the aligned arrays of nanotubes.

 The Space Elevator.
 Such high strengths in the 100 to 150 GPa range if they can be maintained in the bonded nanotubes are within the range to make the “space elevator” possible.
 However, even at such high strengths it is expected the space elevator ribbon would require tapering. Then you would need a means of connecting nanotubes ropes to each other of ever increasing diameter. One possibility for accomplishing this might be by using the “y-shaped” nanotubes, [31]. These are nanotubes that branch off into a Y-shape. If each branch is as strong as the base column then we could attach a base column of one to a branch of another, thereby creating larger and larger diameters.

  Using “y-shaped” nanotubes might also be a way to maintain the high strength across connections in general, assuming each branch is as strong as the base, if multiple branches of one are attached to multiple branches of another. To continue this indefinitely, you would need the y-branches to be on both ends of each nanotube.

  If in general, the connections weakened the strength by some factor we would just use enough branches so that the total strength would be the same as the individual nanotubes. Then if the branches are quite short compared to the base column, the total mass would be just a small fraction larger than that of just the base columns alone, so the strength to weight ratio would be about the same.

 In regards to the space elevator, NASA and the SpaceWard Foundation had sponsored a competition with a $1 million prize for a team that can produce a cable material at about double the strength to weight ratio of the strongest commonly used materials now:

Tether Strength Competition.
By the numbers:
Tether Length: 2 m (closed loop)
Tether Weight: 2 g
Breaking Force: 1 ton, 1.5 ton (approx)
Prize Purse: $900k, $1.1M
Best performance to date: 0.72 Ton
Number of Teams: None Yet
Competition Date: February-March, 2009. [32]

 I believe both a carbon nanotube cable joined by one the methods described above and a cable made of the new synthetic diamond could each win this competition.

  Bob Clark

1.) Direct mechanical measurement of the tensile strength and elastic modulus of multiwalled carbon nanotubes.
B.G. Demczyk, Y.M. Wang, J. Cumings, M. Hetman, W. Han, A. Zettl, R.O. Ritchie
Materials Science and Engineering, A334 (2002) p. 173–178.

2.) Measurements of near-ultimate strength for multiwalled carbon nanotubes and irradiation-induced crosslinking improvements.
Bei Peng, Mark Locascio, Peter Zapol, Shuyou Li, Steven L. Mielke, George C. Schatz &  Horacio D. Espinosa
Nature Nanotechnology 3, 626 - 631 (2008)

3.) Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene.
Changgu Lee, Xiaoding Wei, Jeffrey W. Kysar, James Hone
Science, vol. 321, 18 July 2008, p. 385-388

4.) Direct Synthesis of Long Single-Walled Carbon Nanotube Strands.
H.W. Zhu,  . L. Xu, D. H. Wu, B. Q. Wei, R. Vajtai, P.M. Ajayan
Science, Vol 296, Issue 5569, 884-886 , 3 May 2002

5.) Pulling nanotubes makes thread.
October 30/November 6, 2002

6.) Tensile tests of ropes of very long aligned multiwall carbon nanotubes.
Z. W. Pan, S. S. Xie, L. Lu, B. H. Chang, L. F. Sun, W. Y. Zhou, G. Wang, and D. L. Zhang
Appl. Phys. Lett. 74, 3152 (1999) 24 May 1999.

7.) Tensile strength of single-walled carbon nanotubes directly measured from their macroscopic ropes.
F. Li, H. M. Cheng, S. Bai, G. Su, M. S. Dresselhaus
Applied Physics Letters, 77, p. 3161 (2000)

8.) Strong Carbon-Nanotube Fibers Spun from Long Carbon-Nanotube Arrays.
Xiefei Zhang, Qingwen Li, Yi Tu, Yuan Li, James Y. Coulter, Lianxi Zheng, Yonghao Zhao, Qianxi Jia, Dean E. Peterson, and Yuntian Zhu
Small, 2007, 3, No. 2, 244 – 248.

9.) The Study of Knot Performance

10.) Knot Break Strength vs Rope Break Strength.

11.) Carbon nanotubes.

12.) Bending and buckling of carbon nanotubes under large strain.
M. R. Falvo, G.J. Clary, R.M. Taylor II, V. Chi, F.P. Brooks Jr., S. Washburn and R. Superfine
Nature, 389, p. 582-584. (1997)

13.) Nanomanipulation experiments exploring frictional and mechanical properties of carbon nanotubes.
M. R. Falvo, G. Clary, A. Helser, S. Paulson, R. M. Taylor II, V. Chi, F. P. Brooks Jr, S. Washburn, R. Superfine Microscopy and Microanalysis, 4, p. 504-512. (1998)

14.) Nanotube Nanotweezers.
Science, Vol. 286, No. 5447, p. 2148-2150, 10 December 1999

15.) Fabrication and actuation of customized nanotweezers with a 25 nm gap.
Nanotechnology, 12, p. 331-335, 2001

16.) Three-dimensional manipulation of carbon nanotubes under a scanning electron microscope.
Nanotechnology, 10, p. 244-252, 1999

17.) New Nanomaterial, 'NanoBuds,' Combines Fullerenes and Nanotubes.
March 30th, 2007 By Laura Mgrdichian in Nanotechnology / Materials

18.) Water-filled single-wall carbon nanotubes as molecular nanovalves.
Yutaka Maniwa, Kazuyuki Matsuda, Haruka Kyakuno, Syunsuke Ogasawara, Toshihide Hibi, Hiroaki Kadowaki, Shinzo Suzuki, Yohji Achiba & Hiromichi Kataura.
Nature Materials 6, 135 - 141 (2007)

19.) Ring Closure of Carbon Nanotubes.
Masahito Sano,  Ayumi Kamino,  Junko Okamura,  Seiji Shinkai
Science, Vol. 293, No. 5533, p. 1299-1301, 17 August 2001

20.) A facile sulfur vapor assisted reaction method to grow boron nitride nanorings at relative low temperature.
The Journal of Physical Chemistry. B, 2005, vol. 109, no. 41, pp. 19188-19190.

21.) Nanorings: Seamless Circular Nanostructures Could be Sensors, Resonators and Transducers for Nanoelectronic and Biotechnology Applications.
February 26, 2004

22.) Synthesis of a Self-Assembled Hybrid of Ultrananocrystalline Diamond and Carbon Nanotubes.
X. Xiao, J. W. Elam , S. Trasobares , O. Auciello, J. A. Carlisle
Advanced Materials, Volume 17, Issue 12, Pages 1496 – 1500

23.) Growth of nanodiamond/carbon-nanotube composites with hot filament chemical vapor deposition.
Nagraj Shankar, Nick G. Glumac, Min-Feng Yu, S.P. Vanka
Diamond & Related Materials 17 (2008) 79–83

24.) Reinforcement of single-walled carbon nanotube bundles by intertube bridging.
A.Kis, G. Csányi, J.-P. Salvetat, Thien-Nga Lee, E. Couteau, A. J. Kulik, W. Benoit, J. Brugger & L. Forró
Nature Materials, 3, p. 153 - 157 (2004)

25.) Strong Bundles.
P.M. Ajayan, F. Banhart
Nature Materials, vol. 3, p. 135-136, March 2004.

26.) Modeling of carbon nanotube clamping in tensile tests.
Chunyu Li, Rodney S. Ruoff, Tsu-Wei Chou .
Composites Science and Technology 65 (2005) 2407–2415

27.) Measured properties of carbon nanotubes match theoretical predictions.
August 14, 2008

28.) Electron beam welds nanotubes.
By Ted Smalley Bowen, Technology Research News
August 1/8, 2001.

29.) Tensile Test of Carbon Nanotube using Manipulator in Scanning Electron Microscope.
Seung Hoon Nahm
April 3-4, 2006

The 3rd Korea-U.S. NanoForum.

30.) Connection of macro-sized double-walled carbon nanotube strands by current-assisted laser irradiation.
Tao Gong, Yong Zhang, Wenjin Liu, Jinquan Wei, Kunlin Wang, Dehai Wu, and Minlin Zhong
Journal of Laser Applications -- May 2008 -- Volume 20, Issue 2, pp. 122-126.

31.) Controlled fabrication of hierarchically branched nanopores, nanotubes, and nanowires.
Guowen Meng, Yung Joon Jung, Anyuan Cao, Robert Vajtai,, and Pulickel M. Ajayan
PNAS  May 17, 2005  vol. 102, no. 20,  p. 7074-7078.

32.) Tether Strength Competition.