Altitude compensation attachments for standard rocket engines, and applications, Page 4: the double aerospike.

Copyright 2016 Robert Clark

(patent pending)

 On the blog page "Altitude compensation attachments for standard rocket engines, and applications", I suggested various methods to accomplish altitude compensation with already existing engines. One method was a sort-of "inverted aerospike". It consisted of a movable spike pointed inward, rather than pointing outward as with the standard aerospike:

 There are two disadvantages to this method. First the spike has to be movable so that adds mechanical complexity. Secondly, the size of the outer, fixed nozzle in order to achieve high Isp at high altitude has to be large. But this nozzle will be used all the way from the ground, so this will induce high drag at low altitude.

 The reason why this nozzle has to be large is because you are not really using the altitude compensating capacity of a shaped spike on exit from the nozzle. The only purpose of the movable spike is to vary the size of the exit plane of the nozzle, to provide a variable area ratio.

 But could we use a fixed nozzle and the usual outward-pointing aerospike? This would have the advantages that we could use the altitude compensating capacity of the usual aerospike, so we could use a shorter nozzle, and also have a fixed spike, reducing mechanical complexity. 

 The problem with this with a usual engine is you would need to change to a toroidal combustion chamber, an expensive change to an engine. So instead of this, we will also use an inward pointing spike so that the exit of the nozzle has a toroidal shape:

  This now has two advantages. We will be using this as an attachment to a usual ground-firing engine and nozzle. Since these already expand the exit gases to a certain extent, you would need a much shorter, slimmer and lighter outward-pointing spike to accomplish the rest of the expansion at high altitudes. The usual aerospike has to accomplish the full expansion from ca. 100 bar combustion chamber pressures to near vacuum pressures at high altitude, requiring a large and heavy spike.

  Another advantage is that nozzles for sea-level-firing engines actually overexpand the exit gases at sea level. This is because you want a longer nozzle to achieve at least moderate performance also at high altitude. But now, with the addition of the inward-pointing spike you can reduce the pressure at exit of the nozzle to that of sea level by reduction of the exit plane area. This will also improve the performance at sea level.

   Bob Clark

  

A smaller, faster version of the SpaceX Interplanetary Transport System to Mars, UPDATED, 10/15/2016.

Copyright 2016 Robert Clark

 In the blog post "A SpaceX Heavy Lift Methane Rocket, Page 2", I proposed some architectures for a Mars transport rocket. This was based on a quite large 1,800,000 lb. vacuum thrust of the methane-powered Raptor.

 However, recently Elon Musk discussed the current version of the SpaceX Mars transport model called the Interplanetary Transport System (ITS). Here they are going back to a smaller version of the Raptor, at ca. 660,000 lb. vacuum thrust. In this version however, their booster will be quite large at ca. 7,000 metric tons (mT) gross weight.

 Because of the reduced size of the Raptor this will require 42 engines on the booster. However, interestingly the size of the upper stage will be similar to the size of the booster I discussed in "A SpaceX Heavy Lift Methane Rocket, Page 2". So you could get a Mars launch booster by using this upper stage instead as a booster.

But because of the smaller engines in the SpaceX formulation they will use nine of the Raptors on the upper stage. I stated in the earlier blog post I wanted to use at most 5 of the larger Raptor engines to emulate the safety record of the 5 large engines on the Saturn V booster. However, SpaceX seems to have gotten the 9 engines on the Falcon 9 to work, and in any case you could just use the booster to send the cargo and habitats to space and use high safety rockets to launch the crew to meet up with the transport craft in space.

 The objection could be made however, that this is supposed to be just an upper stage, not a booster stage. However, at his IAC presentation of this Mars transport system he stated that the upper stage in both the spaceship and tanker form could be SSTO. Furthermore, the tanker he said could be used a fast intercontinental transport craft. This means necessarily they would have to be able to launch from the ground. So it is not too much of stretch to assume they could be used as a first stage.

An advantage of making this smaller upper stage the actual booster is that Elon has said they will have a development craft within 4 years. So if we make now a smaller upper stage to go with it, we could have a valid Mars transport craft at that early date. If we made this new upper stage correspondingly 1/3rd size, then we would be able to get 1/3rd the crew size to Mars, so a crew of ca. 35 to Mars.

 However, interestingly we might be able to use already existing upper stages on existing rockets for the upper stage, for instance possibly the famous Centaur upper stage used on the Atlas V or the Ariane 5 core itself used here as an upper stage.

 We can estimate how much we could get to LEO using the ITS tanker as the booster and the Ariane 5 core as the upper stage. The required delta-v to LEO is 30,000 ft/sec about 9,100 m/s:

Modern Engineering for Design of Liquid-Propellant Rocket Engines, p.12

 Since we can get a high 465 s vacuum Isp for a hydrolox engine just by using a nozzle extension we'll assume that value for the Ariane 5 engine. Also we'll assume we can get a vacuum 382 s Isp for the ITS tanker by using altitude compensation.

 Then for the propellant and dry mass values for the ITS tanker and Ariane 5 core we could get 225 metric tons to LEO:

382*9.81ln(1 + 2500/(90 + 170 + 225)) + 465*9.81ln(1 + 158/(12 + 225)) = 9,140 m/s.

 This makes clear another key advantage of this architecture: whereas the original SpaceX ITS would require five flights of the ITS to refuel the upper stage spaceship, with this smaller version a single flight would be able to carry the spaceship to orbit as well as its fuel for its flight towards Mars.

 But what would be the crew size for this smaller upper stage? We can estimate it by making a comparison to the delta-v possible in accordance with the stats of the ITS spaceship:

382*9.81ln(1 + 1950/(150 + 450)) = 5,400 m/s.

 So we want the Ariane 5 case to be able to reach a delta-v of 5,400 m/s when fully refueled and firing in space headed towards Mars:

465*9.81ln(1 +158/(12 +55)) = 5,500 m/s.

 So this is a payload of about 55 metric tons. This is about 1/8th the mass for the ITS case, so we can estimate the crew size to be 1/8th also, so to a crew of 12.

  Elon in his IAC presentation says the ITS carrying its 100 member crew might be able to reach Mars in 80 days at a particular close Mars opposition. This is dependent on the departure delta-v however. In the blog post "Propellant depots for interplanetary flight". I noted that at a higher departure delta-v possible by using a smaller 6 metric ton habitat for only a crew of 3, the Ariane 5 used as the in space propulsion stage might be able to make it to Mars in only 35 days, when leaving at such a particularly close Mars opposition.


  Bob Clark

UPDATE, 10/15/2016:

 Dr. John Schilling's launch performance calculator is back up. This allows us to produce a more accurate payload estimate. The vacuum thrust for the 382 Isp Raptor is 3.5 meganewtons, 3,500 kN. So 9 would be 31,500 kN. We'll also increase the vacuum thrust of the Vulcain engine on the Ariane 5 to 1,450 kN in accordance with the increased vacuum Isp of 465 s. Inputting these and the other specs in the calculator results in:

Mission Performance:

Launch Vehicle:	User-Defined Launch Vehicle
Launch Site:	Cape Canaveral / KSC
Destination Orbit:	185 x 185 km, 28 deg
Estimated Payload:	177767 kg
95% Confidence Interval:	150063 - 210818 kg

"Payload" refers to complete payload system weight, including any necessary payload attachment fittings or multiple payload adapters

This is an estimate based on the best publicly-available engineering and performance data, and should not be used for detailed mission planning. Operational constraints may reduce performance or preclude this mission.


 So the calculator estimates 178 metric tons. This is less than the 225 metric ton estimate using just the rocket equation, but it still means a single flight could carry enough payload to fully refuel an Ariane 5 core upper stage for a flight to Mars.

  Bob Clark

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.

REFERENCES.

1.)Thursday, November 7, 2013

The Coming SSTO's: Falcon 9 v1.1 first stage as SSTO, Page 2.

http://exoscientist.blogspot.com/2013/11/the-coming-sstos-falcon-9-v11-first.html

2.)Monday, January 11, 2016

Altitude Compensation Improves Payload for All Launchers.

http://exoscientist.blogspot.com/2016/01/altitude-compensation-improves-payload.html

3.)Thursday, January 15, 2015

NASA Technology Transfer for suborbital and air-launched orbital launchers.

http://exoscientist.blogspot.com/2015/01/nasa-technology-transfer-for-suborbital.html

4.)Thursday, August 13, 2015

Orbital rockets are now easy.
http://exoscientist.blogspot.com/2015/08/orbital-rockets-are-now-easy.html

5.)Saturday, October 25, 2014
Altitude compensation attachments for standard rocket engines, and applications.
http://exoscientist.blogspot.com/2014/10/altitude-compensation-attachments-for.html

6.)Carbon Nanotube Rubber Stays Rubbery in Extreme Temperatures.
Liming Dai
Angew. Chem. Int. Ed. 2011, 50, 4744 – 4746
http://case.edu/cse/eche/daigroup/Journal%20Articles/2011/Dai-2011-Carbon%20Nanotube%20Rubb.pdf

7.)Forging temperature.
https://en.wikipedia.org/wiki/Forging_temperature

8.)Enthalpy of Fusion.
https://en.wikipedia.org/wiki/Enthalpy_of_fusion

9.)MODELLING HIGH TEMPERATURE FLOW STRESS CURVES OF
TITANIUM ALLOYS
Z. Guo, N. Saunders, J.P. Schillé, A.P. Miodownik
Sente Software Ltd, Surrey Technology Centre, Guildford, GU2 7YG, U.K
http://www.sentesoftware.co.uk/media/2524/flow_stress_curve.pdf

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!

http://www.asteroidmission.org/get-involved/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.

http://www.skyandtelescope.com/observing/celestial-objects-to-watch/hunting-asteroids-from-your-backyard/

 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
https://www.rt.com/news/310170-platinum-asteroid-2011-uw-158/

 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

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

Copyright 2016 Robert Clark

(Patents Pending) 

 

 Nanotechnology makes possible an "ion drive" for air vehicles analogous to the famous ion drive of NASA's deep space probes:

Carbon nanotubes for "Ionic Wind" Craft or "Ionocraft".
Clark R*
Department of Mathematics, Widener University, USA
Review Article
Volume 1 Issue 2 / Received Date: September 26, 2016 / Published Date: October 20, 2016
Abstract

  Peter Thiel of the Founders Fund once famously said, "We wanted flying cars, and we got 140 characters."But nanotechnology now does make possible the long desired flying cars. It's a different propulsion method though than propellers or jets however. It's propulsion by electric fields known as electrohydrodynamic propulsion (EHD). It works by ionizing air then using electric fields to propel the charged air molecules rearward, thus producing thrust. It's quite analogous to the famous space ion drive of NASA. EHD has been known at least since the sixties. Its problem is, as with ion drive, the thrust is so low. So far the EHD craft have not been able to lift both themselves and their power supplies. The ones made so far leave the power supply on the ground and connect to the craft through power cables. But the equations of EHD suggest the thrust for the power required gets larger for thinner ionizing wires. In fact if the wires are at the nanoscale then this important thrust-to-power ratio can be a hundred times higher than for the craft constructed so far. This would be enough to lift the craft and the power supply. This research is to prove what the mathematics suggests. Note that if it works then all propeller and rotor driven craft become obsolete. Also, intermediate range automobile travel would be taken over by the EHD craft, so a large proportion of carbon-emissions would be eliminated, replaced by this zero-emission travel method. In regards to space propulsion, since EHD is so similar to ion drive, using components at the nanoscale may also work to improve the thrust of ion drive. This would be important to shortening the flight times of spacecraft using such drives. This is important not just for robotic spacecraft but also satellites that use such ion drives to reach their final GEO destinations. As it is now, the ion drives used have such low thrust it takes months for such satellites to reach GEO, resulting in millions of dollars of lost revenue to the satellite companies. Being able to increase the thrust of these drives would reduce the flight time, and therefore reduce this lost revenue.

Keywords: Electrohydrodynamic propulsion; Carbon nanotubes; Nanowires; Ionic wind; Ionocraft; Plasma drive

https://medwinpublishers.com/NNOA/NNOA16000108.pdf

 

     Bob Clark

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:

Nanotech: from air to space.
https://www.indiegogo.com/projects/nanotech-from-air-to-space/x/13319568

_________________________________________________

 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:

Energy

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

http://www.technologyreview.com/energy/38615/

 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]

NEWS & VIEWS

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

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