Revision as of 17:07, 15 September 2024

Up: Energy transmission

Historical image of mechanical energy transmission rotative via axles and translative belts of a spinning mill factory in Germany (~1925). – Systems of the future made with gemstone metamaterial technology will look quite a bit different, possibly in flexible cables, be completely silent and suffer only minor degradation over time. Degradation mostly from cosmic rays which occurs no matter whether the system runs or not. – All scales are imaginable from home utility cables all the way to cross continental and undersea cables. – (wiki-TODO: Add a sketch of a cross section of a possible future cable design.)

Mechanical energy transmission cables

Scaling laws predict that very high energy energy densities
should be handleable in future gemstone metamaterial nanosystems.
Both for mechanical systems and for electrostatical systems. (Less so for magnetostatical systems.)
See e.g. page Electromechanical converters

Hypothesis:
Due to the availability of FAPP wearless very low friction bearing technologies
including infinitesimal bearings, nano- to microscale atomically precise gearbearings and other methods (See: Levitation)
energy could potentially be transmitted purely mechanically instead of electrically as it is today.

Replacing:

• ohmic losses and losses from radiated stray fields (grid hum) by
• friction losses and losses from radiated (infra)sound respectively

Transmission cable medium (meta)material

Bundles of nanotubes may be a good option due to their high tensile strength.
Maybe such bundles with finite strand length could be made into incrementally repairable metamaterials?
Anisotropically elastic metamaterials might be a good choice to get aground tight corners.
See: Elasticity emulation

Transmission cable geometry – depending on type (translative and/or rotative)

Energy could be transmitted via translative or rotative or combined movement of macroscale diamondoid ropes/rods/tubes.
For continuous pulling flexible belts ropes or chains could maybe be considered.
For a flex-axle type rotative power transmission a tubular axle core seems a good geometry
since the center contributes little torsional stiffness.

• Rotation has higher stiffness but also higher speed dependent power dissipation [to verify].
• Translation has lower stiffness and lower speed dependent power dissipation [to verify].

Limits to transmittable power density – determined by tensile strength

Power is force times speed (corresponding to voltage times current).

• The force is limited by the tensile strength of the used rods.
• The speed is limited by the turn radius and thus indirectly by the tensile strength of the housing structure.

Quantitative numbers – surface power density limits

Conservative (safe side wrong & intentionally underestimating) estimates for the maximal power density per cable cross section area.

Assumptions:

• E = 50GPa ... approximate tensile strength of natural diamond
  almost defect free mechanosynthetisized diamond will be notably stronger
  metamaterial nanostructuring will make those levels of strength accessible at the macroscale by stopping cracks from propagating
• v = 3km/s ... the Unsupported rotating ring speed limit
  with structural support one can go higher
  with c_sound ~ 18km/s ... being the longitudinal speed of sound in diamond
  3km/s = ~16% of c_sound:

Result:

• P/A = 150MW/mm² ... Power density at the tensile stength limit and Unsupported rotating ring speed limit

Surface power densities for various speeds at tensile strength limit: Power densities for reasonable speeds:

• 1000th c_sound: 50GPa * 18m/s = 900GW/m² = 9GW/dm² = 90MW/cm² = 900kW/mm²
• 100th c_sound: 50GPa * 180m/s = 9TW/m² = 90GW/dm² = 900MW/cm² = 9MW/mm²
• 10th c_sound: 50GPa * 1.8km/s = 90TW/m² = 900GW/dm² = 9GW/cm² = 90MW/mm²

Power densities for insane speeds (if possible then only in linear DC systems):

• 1x c_sound: 900MW/mm²
• 10x c_sound: 9GW/mm²

Present losses or necessary infinitesimal bearing thicknesses may become intolerably high.

Surface power density of a perhaps practical system:

• P/A = 10GPa * 180m/s = 1.8TW/m² = 18GW/dm² = 180MW/cm² = 1.8MW/mm²

Compare that to surface power densities of overhead power lines:

• Overhead power line: ~1MW/mm²

(wiki-TODO: estimate losses and centrifugal forces for some curve radii)
(wiki-TODO: estimate kinetic energies per cross section and cable length)

(TODO: How do the numbers fit together with the ones for Electromechanical converters as presented in Nanosystems? Note that they are related to volume not area like here.)

(TODO: Also analyze the case where kinetic energy is used for power transmission (m·v²)/2 & compare with chemical. Where is the crossover?)

Related: areal power density:

Method of bearing

To maximize power density in mechanical energy transmission both the force and the speed needs to me maximized.
This can lead to significant centrifugal forces at places where mechanical power transmission lines curve.

There are methods for ultra low friction levitaion but these typically can provide much less supporting force.
Thus these methods of bearing motion may more suitable for:

• rotative/torsional power transmission
• low speed chemical and entropic power transmission (beyond the scope of this page)

Infinitesimal bearings seem like the only non-macroscopic bearing technology that can take very high loads.
Thus the feasibility of translative/reciprocative mechanical energy transmission depends on the effectiveness of infinitesimal bearings.

Infinitesimal bearings can be arranged as concentrically cylindrical shells along the whole length of the cable.
Infinitesimal bearing layer-number reduces the relative speeds per layer linearly.

Doubling the thickness of an infinitesimal bearing cuts the total friction by half.
While internal bearing area doubles interface speeds half and dynamc friction quaters.
Overall total speed dependent dynamic friction halves. (See: Superlubrication)

Quantitative numbers – friction power losses

(TODO: Do the math here.)

Note: In case this does not work out favorably there is still the option of
much slower speed (and thus much lower friction) chemical and/or entropic power transmission.
Half speed means quarter the dynamic friction.

Related: Friction in gem-gum technology

• [math] v_{bearing} = 180m/s[/math]
• [math] r_{cable} = 5cm[/math]
• [math] l_{cable} = unspecified[/math]
• [math] t_{bearing} = 1cm [/math]
• [math] t_{layer} = 100nm [/math]

• [math] n_{layers} = t_{bearing}/t_{layer} = 100000 [/math]
• [math] v_{layer} = v_{bearing}/n_{layers} = 1.8mm/s[/math]

• [math] A_{bearing} / l_{cable} = 2 \pi ~ r_{cable} ~ n_{layers} = 31400 m^2/m [/math] - disregarding t_bearing
• [math] \rho_{dynfric} = (P_{loss}/(A_{bearing} ~ v_{layer}^2)) = \{23\|1000\} W/(m^2(m/s)^2)[/math] - dynamic friction coefficients - two cases (see: Friction in gem-gum technology)
• [math] P_{loss} / l_{cable} = A_{bearing} / l_{cable} ~ v_{layer}^2 ~ \rho_{dynfric} = \{2.34mW\|102W\}/m[/math]

• [math] \tau_{powdens} = (P_{trans}/A_{cross}) = 1.8MW/mm^2 [/math]
• [math] P_{trans} = r_{cable}^2 \pi ~ \tau_{powdens} = 14.1GW [/math]

• [math] P_{loss} / P_{trans} = \{0.16\%\|7.2\%\}/1000km [/math]

Dropping speeds to 1/10th that is dropping speeds to a perhaps more reasonable 18m/s

• drops power transmission by 1/10th to 1.41GW and
  
• drops losses by 1/100th to {0.0016%|0.072%}/1000km
  

If true then these are superb results.
(TODO: Compare that with the specs of overhead and underground power lines of today)
(TODO: Investigate reachable efficiencies with AP roller gearbearings)

Note that the final numbers here assume a continuous sheath of atomically precise slide bearings (as infinitesimal bearing metamaterial)
Instead going to an (at some scale) intermittent support by atomically precise roller gearbearings should drop the friction losses further by a huge factor. Or Allow notably higher speeds without exceedingly high losses.

Sharp turns – slow speeds

For lower power densities and lower speeds very sharp bends can still be problematic as the transmission medium needs to bend. Anisotropic elasticity metamaterials may be a good option. See: Elasticity emulation One may want to use metamaterials anyway for

• stopping cracks from propagating
• doing easy incremental repair (perhaps even live on hot on running systems?!)

But adding anisotropic elasticity is additional design effort and may lead to a bit of a trade-off.

For torsional/rotational transmission lines specially designed 90° turning elements may be usable.

Sharp turns – high speeds

With rising speeds in translational transmission cables centrifugal forces become exceedingly high making beefy supporting structures necessary.
Power densities beyond the already very high limit imposed by by diamondoid systems withstandable centriugal forces are then accessible. See: Unsupported rotating ring speed limit.

Note that for a mechanically unsupported (or weakly supported) transmission cable going around a circular arc there is a scale invariant speed limit of about 3km/s. Above this limit even a nanotube ring ruptures due to centrifugal force. See: Unsupported rotating ring speed limit.

The Unsupported rotating ring speed limit thus poses a limit to areal power density. See further down in quantitative numbers section.
Especially on smaller scales where there is insufficient for low friction support.

Rate limitations on startup and power surges

For medium long to very long distances one can meet the limit of specific strength that is the rods can't turn/pull their own inertial weight anymore.
This limits the power-up rate (unit: watts per second). To mitigate that one could put energy storage cells and interfacial drives continuously alongside the power line. This can kick-start powerlines or compensate for too sudden power surges.

Speed of sound as limit for (uncached) energy transmission

The energy transfer speed (propagation of the rising flank after power-up) is equal to
the (very high) transversal or longitudinal speed of sound of the chosen diamondoid material but
still significantly slower than electrical impulse propagation.
The maximum speed of continuous axial movement is not limited by the speed of sound though.
For most practical purposes this limit is likely so high that it won't matter much.

Violating the the speed of sound limit

There are

• AC alternating rotative
• DC continuous rotative
• AC alternating translational (aka reciprocative)
• DC continuous translational

Note that for the last one translational energy transmission cables
the speed of sound of the energy transmission medium (meta)material is not a limit.
Cables carrying speeds exceeding that significantly exceed the speed of sound c_sound in diamond may be possible possible.
Consequences:

• Energy can be transmitted faster than the speed of sound (without caching)
• Limits on areal power-density are set only by against centrifugal force supportable turning radii and tolerable friction losses

Note that when going to the multi km/s speed range even with bending radii the size of planets
there is already notable (albeit not brutal) centrifugal force.

Practically though with the speed of sound already being very high in diamondoid systems
supersonic speeds will likely not be present in widespread infrastructure systems.
Rather only experimental systems and maybe (highly speculative) launch loops.

Some form of nanoscale levitation method may be needed to get acceptable friction losses.
But than turns are no longer an option. Further analysis needed.

Safety

While

• AC components may reflect at a high impedance end of a transmission line (no load connected infinite resistance)
• DC components may easily destructive

For not well designed translational energy transmission cables damage from mechanical impact can becomes a very serious hazard.
Concentrated release of the transitionally in the system stored energy at the damage point could result in a serious detonation.
It should be not too difficult to design systems such that horrendous accidents pretty much are impossible though.

Insertion and extraction of mechanical power

• electromechanical Interfacial drives?
• Some form of nanomechanical incoupling??

(TODO: Further analysis needed in insertion and extraction of mechanical power)

AC losses

• Radiated (infra)sound: In case of AC transmission in order to reduce acoustic losses towards the environment using several litzes/strands operated in different phases could perhaps be a viable strategy. This is likely a tradeoff with an increase in bearing surface.
• Reactive power induced losses: Just like in electrical systems reactive power in the consumer side leads to real power losses along the transmission line.
  In more comprehensible words: Energy in mechanical waves tat are reflected back rather than used up travels back to the producer thereby experiencing the friction through the transmission line once again.
• Elastic losses: Capacitive dielectric losses in electric systems correspond to nonplastic inelasticities in elastic deformations.
  In more comprehensible words: Heating from deformations that are structurally reversible but energetically not fully reversible.

Transporting chemical energy

The idea is to pack some energy storage cells on the energy transport track.
Not static on the outside for boosting a startup or buffering a power surge as described before,
but moving transported with the rope/rod.

It's probably very useful for low speed systems - including almost all the stuff of everyday use.
For high speed systems at some point the kinetic energy will outgrow the chemical energy since it grows quadratically instead of linear with speed.
Objects moving around with orbital speeds can easily carry more energy than if they were made out of explosives.
Also chemomechanical converters are slower than mechanomechanical transmissions and may lose efficiency when operated to fast.

Mechanical energy transmission cables vs electrical superconductors

• Non mechanical technology path

It's still unclear whether superconductors will some day meet widespread use.
It doesn't seem too unlikely though.

• With advanced thermal isolation even today's superconductors may be usable.
  These YBCO superconductors contain not the most abundant but also not exceedingly rare elements.
• The discovery of a practically usable room temperature superconductors is (as of 2017 to the knowledge of the author) still an unpredictable scientific discovery.
  Superconducting topological insulators may be a promising field.
• With advanced mechanosynthesis a giant space of strongly metastable non-equilibrium structures becomes accessible that
  is not accessible via conventional thermodynamic production methods (mixing,melting,annealing,...).
  The neo polymorphs. This allows for much more powerful random and systematic search.

Measuring the remnant resistance of superconductors has (to the knowledge of the author) never been archived (physics usually does not like true infinities / true zeros). So the energy transmission efficiency should be even higher than the one of mechanical energy transmission cables.

The downsides of superconducting energy transport in comparison are:

• involvement of not so extremely abundant elements
• susceptibility to electromagnetic interference (solar storms / EMPs)
• associated strong magnetic stray fields
• achievable efficiencies for mechanical energy transmission cables should be near 100% anyway.
• power density limitation by critical fields

On a highly speculative note:
Has anyone thought about bearing things by floating them on superfluids?
May not provide any supporting force ...

Alternate uses

Warning! you are moving into more speculative areas.

Beside energy transport continuous linear movement cables could be used for the forces they develop.
When curvature and speed produces forces exceeding gravitational acceleration (note that there is no need for escape velocity)
the cable could (very speculatively) lift by itself and build a launch loop.
When such a cable is cut a big scale explosion may follow depositing lots of material at the explosion site.

A better approach may be J. Storr Halls static Space Pier.
If you want some discussion of the widely known space elevator concept in light of advanced APM capabilities go here.

See: Launch loop

Related

• up: energy transmission
• superlube tubes
• global scale energy management
• power density
• upgraded street infrastructure
• unsupported rotating ring speed limit
• global microcomponent redistribution system
• Pages with math
• Large scale construction
• The challenge of high speeds near nanoscale

External links (wikipedia)

• Category:Mechanical_power_transmission
• Category:Mechanical_power_control

Historical:

• Flatrod system
• Line shaft – Images: Category:Line_shafts
• Belt (mechanical)
• (Lineshaft roller conveyor)

Exploiting inertial mass for lift:

• Small scale existing: Lariat chain
• Large scale hypothetical: Launch_loop