How Can We Improve the Efficiency and Affordability of Flywheel Energy Storage?

[Enthalpy]

Storing energy in flywheels is old. But at a cost competitive with the power grid is uncommon. And low losses over half a day storage, using affordable technology, hasn't been done, I believe. Links to my enabling technologies (drawings need to be logged in, sorry):

A cheap flywheel material storing much energy, and how to produce the wheel
saposjoint.net/Forum/viewtopic.php?f=66&t=1974#p22398
saposjoint.net/Forum/viewtopic.php?f=66&t=1974#p31298

Here a low-loss hydrostatic axial bearing:
saposjoint.net/Forum/viewtopic.php?f=66&t=1974&p=33472#p33178
saposjoint.net/Forum/viewtopic.php?f=66&t=1974&p=33472#p33201

There a low-loss roller bearing for horizontal axis:
saposjoint.net/Forum/viewtopic.php?f=66&t=1974&p=33472#p33263
saposjoint.net/Forum/viewtopic.php?f=66&t=1974&p=33472#p33273

And this shall achieve low loss in normal air:
saposjoint.net/Forum/viewtopic.php?f=66&t=1974&p=33472#p33461

From the cost I evaluated, it would be cheaper to build power plants to produce the mean daily electricity consumption only, and provide the peak consumption over such flywheels.

Also nice if a country lacks electricity production capability, like Japan now. Or if a country wants to close some plants in the future, like Germany.

The designs are to operate immediately after an earthquake with 2G upwards acceleration and 3G sidewards. Useful as an emergency supply, when power plants shut off and lines break. Few units can supply a hospital or a factory.

Cheap storage capability for half a day means that Solar electricity (I mean: Solar thermal electricity) becomes available all the day and dependable in favourable places like California, Neguev, Atacama and many more.

Affordable storage over a few days - as it now seems - makes wind energy dependable in places like Scotland, Brittany, Galicia, Patagonia and more.

Marc Schaefer, aka Enthalpy

 

[Enthalpy]

Well then, as the other site limits images to members logged in, here are the sketches of the hydrostatic axial bearings. You may have to click on the images to enlarge them.

 

[Enthalpy]

And the roller bearings:

 

[Enthalpy]

And the airflow calmer:

 

[Mech_Engineer]

The problem with flywheels is the speed needed to store an appreciable amount of energy; how much energy are you looking to store and using what size disc?

 

[Enthalpy]

Thanks for your interest!

Good steel, for instance spring steel, is cheap and can rotate fast. I compute with 390m/s for a torus used at 1200MPa, near the mean fibre. Other alloys like X35NiCr6 can harden by quenching through the thickness of such a torus and offer margin over this stress if tempered around 300°C.

Wheels weighing 80t for OD=5m can still be transported by road, though requiring a special transport. The stored energy is then 6.1GJ, supplying 850kW*2h during daily peak consumption hours.

80t low-alloyed steel cost around 120k€ from a forge. Two wheels with bearings, airflow calmer, a motor-alternator, a pit, transport, assembly may sum to estimated 570k€ to provide 1.7MW*2h and this is far cheaper than providing the peak power by the power plant's oversize - nuclear plants cost presently 3G€+ for 1.4GW.

More about steel there http://saposjoint.net/Forum/viewtopic.php?f=66&t=1974#p22398
and about cost estimates http://saposjoint.net/Forum/viewtopic.php?f=66&t=1974#p31668

One wheel pair has the adequate size for a small factory. A hospital or a bigger factory would need several of them.
At a power plant, one would assemble many wheels in line to share the pit, the motor-alternator... and would probably produce the flywheel at the site, so they can be bigger.
But even these 80t wheels make sense for 1.4GW: it takes 100 pairs of them, which fit under the car park for the power plant's workers.

 

[Mech_Engineer]

Yikes you're talking about some seriously monster units... You're wanting to spin an 80T flywheel faster than the speed of sound! Are you going to do this in a vacuum bunker with 2m thick reinforced concrete walls?

 

[Enthalpy]

This will happen in normal air, because my airflow calmer reduces losses efficiently (at least according to my computations!). The sketch is in the present thread, in the third message that has drawings. Computations are on the other forum, there
http://saposjoint.net/Forum/viewtopic.php?f=66&t=1974&start=20#p33461
with a sort of post-scriptum there
http://saposjoint.net/Forum/viewtopic.php?f=66&t=1974&start=20#p33472

To catch the pieces in case of a mishap, I consider only burying the flywheels. 2m concrete wouldn't stop 20t at 390m/s. For that sake, a vertical axis could be better.

Seriously monster unit... The rotor of a turbo-alternator for 1300MW is about D=2m L=8m of steel, hence roughly 200t, and it rotates at 150m/s.
http://en.wikipedia.org/wiki/Turbo_generator
http://de.wikipedia.org/wiki/Turbogenerator (nicer pictures)

 

[russ_watters]

...this is far cheaper than providing the peak power by the power plant's oversize - nuclear plants cost presently 3G€+ for 1.4GW.

Nuclear plants are not typically oversized for peaks, they are run at 100% and the peaks are served by cheaper souces such as natural gas turbine.

 

[Enthalpy]

Sure! In reasonable countries that don't produce 75% of their electricity by nuclear plants...

With the flywheel costing about 1/3 €/W if I'm not too wrong, it's still significantly cheaper than a combustion power plant.

 

[redargon]

You're talking about energy storage, but where does the energy come from to get the wheels spinning? Are you talking about storing energy that is produced during low requirement periods and then having that available during peak requirements?

 

[Unrest]

Can you explain how your bearing concepts could lead to products will lower losses than existing hydrostatic and roller bearings? I'm deeply suspicious that adding some rollers can somehow reduce losses. How about fatigue life, misalignment, etc?

As for the air calmer, the air will still have the same average velocity gradient either with or without the disks, so there's still going to be high viscous losses. How did you calculate it?

 

[AlephZero]

Judging from the pictures (I haven't gone to your own website) you don't have any idea what is involved in making a safe and reliable device at this scale. For example the cross section of your rotor could be politely described as fanciful, if you actually try doing some stress and rotordynamics analysis on it. There is no way you can make this successfuly out of "standard quality" forged steel. And the only sort of "airflow calmer" that will work is to put the whole thing in a low vacuum.

The company I work for has a rig that can spin a rotor weighing about 1T with rim speeds of about 300 - 350 m/s (and a lot of smaller spinning rigs as well) Based on that experience, I think your cost estimates are out by a factor of 100, or more likely 1000.

 

[Enthalpy]

...I haven't gone to your own website...

It's not my website. But the thread there does contain answers to some of your interrogations.

There is no way..."standard quality" forged steel.

I don't write "standard quality", quite the opposite. Why do you, if you know it's impossible?

The company I work for has...a rotor

So did my last company, and we developed them by ourselves.

...you don't have any idea...only in a low vacuum..your cost estimates are out...

Do I perceive here a desire to denigrate instead of discuss? I've put figures about flow losses and references to computation methods, so I don't feel a need to answer unjustified assertions. And as the inventor of several successful new technologies, I'm not naturally inclined to believe existing ones impose the solutions, feasibility or cost of new ones.

If you're worried by the shaft's diameter on the sketches, it's certainly not to scale nor even computed. The necessary shaft is feasible, so I concentrated on wheel material and on losses.

 

[Enthalpy]

...Are you talking about storing energy that is produced during low requirement periods and then having that available during peak requirements?

Yes, that's it.

This is an easier task for energy storage, as only the difference between peak and mean power must be given back and during a limited time, so a limited energy is to be stored for few hours.

Storing Solar-only-produced electricity for instance would mean the complete consumption during the whole night, and this translates into more energy and bigger wheels - more difficult. Or worse, in a location where Sunlight during daytime isn't certain, one would have to store for several days the full consumed power times several days - a completely different task!

-----------

Unrest, your interrogations about the rollers and the air calmer need and deserve detailed answers, but I'll first go to bed.

 

[Mech_Engineer]

You haven't really answered the problem of spinning this flywheel so fast. Have you ruled out storing it in a low-grade vacuum for a specific reason?

 

[AlephZero]

If you're worried by the shaft's diameter on the sketches, it's certainly not to scale nor even computed. The necessary shaft is feasible, so I concentrated on wheel material and on losses.

So, you don't like my "unjustified assertions", but you say something is "feasible" and admit you haven't computed anything about the shaft design. Yeah, right.

So let's do an elementary calculation for you:

You have a 2.5m radius rotor with a rim speed of 390 m/s and mass 80t concentrated around the rim.

That gives an angular velocity of 390/2.5 = 156 rad/sec = about 1500 RPM

The acceleration at the rim is about 2.5 x 156² m/s² = about 6000 G.

Fine, those numbers are in a sensible ballpark compared with existing real machines.

But - the diaphragm of your disk needs to withstand about 80 x 6000 = 480,000 tons force of radial load.

And if you have a disk burst, your bearings needs to withstand a similar sized load, unless you are confident that your design will never ever fail..

Sure, you can quibble about factors of 2 or 3 in my numbers, depending on the exact shape of your rotor, but that won't get you out of jail.

Sorry, but it's your call to draw something that looks like "real engineering" if you want me to take any of this seriously - not a big square section ring stuck on the outside of a thin plate and the whole thing supported on wimpy little bearings.

 

[Enthalpy]

...The diaphragm of your disk needs to withstand about 80 x 6000 = 480,000 tons force of radial load.

Certainly NOT. The tore itself resists the centrifugal force, thanks to its tangential strength, and does not rely on the diaphragm for that, of course.

This is a computation I of course did because it tells how much energy the tore stores. You can reasonably suppose I'm able to do it.

 

[Enthalpy]

And if you have a disk burst, your bearings needs to withstand a similar sized load...
If you want me to take any of this seriously...

If a disks bursts, I don't care a bit that the bearings resist! No single flywheel has bearings designed for that. Installing the flywheel in a pit shall give protection.

Want you to take this seriously? Well, I didn't mean you in particular, no.

 

[Enthalpy]

...Have you ruled out storing [the flywheel] in a low-grade vacuum for a specific reason?

Vacuum would be possible but has serious drawbacks: it needs a huge vacuum vessel that resists big forces and is hermetic - this is costly, it adds significant failure modes, and makes operations more complicated.

So as I found flow loss can be small in air, I clearly prefer it, and try to explain it now.

As for the air calmer, the air will still have the same average velocity gradient either with or without the disks, so there's still going to be high viscous losses. How did you calculate it?

For a wheel of OD=5m ID=3.8m L=1.11m that rotates at 28Hz = 1680/min = 177rd/s, or 440m/s at the external radius, I add per side 70 disks spaced by 5mm air. That's many disks, but composite material makes them for cheap - we're talking about a storage unit costing half a million.

Now, speed drop across the 5mm is 6.3m/s only. Air viscosity of 15mm²/s and 18.6µPa*s gives a Reynolds number Re = 2100, meaning a laminar flow. Shear constraint is then 23mPa at R=2.5m; combine with 19.6m² and an integral coefficient of 0.5 to get a torque of 0.57N*m only. Tripling it for the other side and for the cylindrical face, the power loss is 305W, or over 10h 0.2% of the stored energy, nice. 70*5mm are in fact an exaggeration.

Why add the many disks, as they don't reduce the speed shear?
- They prevent radial eddy flows. Air with a high tangential speed near the wheel feels a centrifugal force which makes it flow outwards there and inwards farther from the wheel. Losses would be 1000 times bigger.
- A bigger speed drop over more distance would enable turbulence, with the usual losses depending on V² instead of V, again much bigger.

Quite a few, err, engineering details remain open... I suppose the cylinders (which must be necessary) and disks composing a layer can be tied together around the wheel using a thread of high-performance fibre. 5mm spacing over thin parts of 5m diameter may require additional measures, maybe some flexible skis between the layers, that would fly by ground effect.

The flow calmer looks odd? Sure! Because it's new. Being useful to alternators, pumps, turbines beyond the flywheel, it can become as natural in two decades as laminations are now in transformers cores.

-----

Unrest, I'll answer later about the big rollers at the bearings.

-----

Marc Schaefer, aka Enthalpy

 

[Unrest]

Quite a few, err, engineering details remain open... I suppose the cylinders (which must be necessary) and disks composing a layer can be tied together

It really needs all these important details nailed down. Without that you just have an idea no better than the millions of other ideas that never quite worked because of some seemingly small detail.

turbines beyond the flywheel, it can become as natural in two decades as laminations are now in transformers cores.

I think your focus on having invented something useful, and your confidence that it would be cheap enough, or even work at all, is off-putting to people. It's easy to come up with ideas, and easy to imagine uses for them. But it's not easy to carry them through! That's what will make or break it.

If this air calmer really worked then it would surely have many other applications. Why not focus on that, since it seems to be the key feature.

The bearings too - if you've invented a better kind of bearing, it would have many other applications. You're doing yourself a disservice by combining several speculative ideas together. Anybody can conclude they could be useful for a flywheel, you don't have to mention that.

 

[AlephZero]

Certainly NOT. The tore itself resists the centrifugal force, thanks to its tangential strength, and does not rely on the diaphragm for that, of course.

You only half understand the situation. What you say would be true if there were no diaphragm at all.

But the tensile hoop strain in the rim produces an increase in diameter, which creates a radial strain in the diaphragm. Something's got to give, unless you make the diaphragm strong enough to take its share of the stress distribution. If you have a thin diaphram with a small inner radius "shaft", the rim will just tear the diaphragm apart when you spin up the disk.

That's why the "shaft" in high speed rotating machines is often a large diameter hollow drum rather than a small diameter shaft, with conical sections at the ends to reduce the diameter down to the bearings. The cones can change their angle of slope to accommodate the strain distribution..

You might want to look at some of the issues in designing computer disk drives, regarding the aerodynamic stability of a stack of closely spaced thin rotating plates.

You might also want to think about what temperature rise your 305W (or whatever the correct number turns out to be) of windage heating is going to create in 10 hours, in a more or less sealed system.

 

[Enthalpy]

...The tensile hoop strain in the rim produces an increase in diameter, which creates a radial strain in the diaphragm. Something's got to give, unless you make the diaphragm strong enough to take its share of the stress distribution. If you have a thin diaphram with a small inner radius "shaft", the rim will just tear the diaphragm apart when you spin up the disk.

Tell me if you expect the acceptable strain in steel to differ in the peripheral and radial direction.

That's why the "shaft" in high speed rotating machines is often a large diameter hollow drum rather than a small diameter shaft, with conical sections at the ends.

False. It's because of dynamic stability. Strictly a matter of stiffness, not resistance.

 

[Unrest]

But the tensile hoop strain in the rim produces an increase in diameter, which creates a radial strain in the diaphragm. Something's got to give, unless you make the diaphragm strong enough to take its share of the stress distribution.

Technically I think you're right, but you somehow presented it to appear opposite. The circumferential strain in the rim should be proportional to the radial strain in the diaphragm. If the rim can survive that strain, then so can the diaphragm. So there's no problem having a thin diaphragm, from the point of view of steady centrifugal loading.

 

[Enthalpy]

...millions of other ideas that never quite worked because of some seemingly small detail...It's easy to come up with ideas, and easy to imagine uses for them. But it's not easy to carry them through!

200% agreed!

But I have a reason to cite uses early: that no one gets a patent for obvious uses of my invention.

You see, at a symposium about micro-satellites in Arcachon around 1992, I explained one could put in low-Earth orbit a satellite, profiled to reduce its drag, and stabilize its orientation by fins working in the residual atmosphere, even at 300km. Then people said "how could this possibly work". Now Goce has such fins. And about a year after the symposium, someone at the French space agency wrote "fixed fins to stabilize satellites are well-known, but I have invented tiltable fins" and a clerk granted him a patent for that.

So: the flow calmer is also useful at electric motors, and at compressors.

 

[Unrest]

But I have a reason to cite uses early: that no one gets a patent for obvious uses of my invention.

OK so you can just document it somewhere, and focus on the engineering details in this forum. But really I think too many people are worried about patents. Even if someone does patent it, is that so bad? Patents have a purpose - to promote technology development. Are you trying to stifle it? I also thought of this same different-speed-disks idea myself years ago. So it's probably a very common idea that has been investigated by many people and either found to be useless or maybe actually used for something.

Anyway, I have a feeling this thread might get locked soon. Why not start a separate thread about some specific aspect of the flow calmer that you're not sure of. Like what other factors might influence losses, or the structural requirements. As soon as you talk about saving the world people aren't going to take you seriously, that's why you're getting dismissive replies.

 

[Dmytry]

What's the problem with magnetic bearings again? Patents too expensive? edit: ahh, you're speaking of a very giant wheel, which is easier to suspend with conventional bearings and more expensive to suspend with magnetic bearings. I see. When i think of energy storage I primarily think of applications such as electric cars, not the day-night grid storage.

I recall reading of a stupidly simple magnetic bearing. Something like a copper pipe inside an axial ring magnet with two steel washers on it's ends. When the pipe is centred there is no current in the copper, when the pipe is off-centre it develops force pushing it towards centre (as the pieces of copper go in and out of stronger magnetic field).

For the active designs - with clever enough electronics (AKA writing a good microcontroller program) you can make the motor-generator also function as the bearing.

Of course in practice, the hard part is not making it, but making it cheaper than e.g. gas turbine.

 

[Dmytry]

I like the airflow calmer idea, seems feasible to me. The bearings, how are you centring the axis in the vertical axis configuration? Did you estimate the losses for the hydrostatic bearing?
Did you estimate the bearing losses, in particular the rolling friction (from deformation of the rollers) ?
edit: on the magnetic bearings... the power wasted in coil (for same magnetic field) grow proportionally to size, but the field energy proportional to size cubed. The force is equal to dE/dx where E is the energy of the system, and that will be proportional to size squared. Meaning that 2x larger electromagnet has 4x the force for 2x the power requirement, so for sufficiently big system you'll be able to suspend the thing under electromagnet, not sure though for energy requirements for the control circuit that is to keep it stable. The motor-generator and bearing could perhaps be combined. I imagine a conical shaped diaphragm with torus-shaped flywheel at the rim, motor/generator/magnetic bearing on the top of the hat, emergency bearing under the top of the hat. Perhaps some permanent magnets and coils along rim to compensate for precession due to Earth's rotation, but i'd think that won't be needed if the hat is always tilted slightly from the vertical. In low grade vacuum because it is going to be inside an underground concrete pit anyway so you could as well add a stainless steel lining on outside of the pit (so that concrete is holding the air pressure) and pump the air out.

 

[Enthalpy]

Hi Dmytry, thanks for jumping in here!

Magnetic bearings are an option, sure. I know only pulling ones, hence active, to offer low-loss with cheap materials.

Let's check the magnetic energy:
- 1.3T makes 672kJ/m³
- The gap is e=5mm OD=2.4m dR=0.1+0.1m or 6.6dm³
or 4.4kJ just to lift the wheel.
Now, I believe retroaction can be slower than one wheel turn. I took an earthquake as the defining case, if the flywheels are to provide night-to-day storage in Japan. I take a huge 1+1G vertical acceleration, needing to add 4.4kJ within maybe 1/4s, so the regulation electronics must be able to supply around 20kW but be power-efficient at mean 1.3kW, making the design interesting.

Yes, the motor-generator can be (and sometimes is) combined with the magnetic bearings. As multi-function hardware is too often bad at all functions, I have no clear opinion here.

And yes again, if you add the failure modes of the control electronics (...and software), the need for a rest-and-emergency bearing, possibly the aerodynamic losses at the thin magnetic gap, the core losses imposing a vertical axis that limits access and flywheel grouping possibility, clearly I prefer a roller bearing now.

I like your suggestion to put the metal liner outside the concrete walls. Steel cost had stopped me from putting a liner inside. Remaining potential difficulties: hermetic lid on a liner deformed by concrete pouring, and concrete outgassing, especially at cracks, when vacuum is re-established after maintenance.

 

[Enthalpy]

More about the hydrostatic bearing depicted in thread #2.

This vertical axis design is centred by two roll bearings, strong enough to hold (actually push) the flywheel during an earthquake, but which operate at very light load usually, hence shall waste little power.

The D=0.12m shaft has only dR=10µm uniform clearance in the cylinder's hole, and oil at 700b lifts the flywheel. No seal adds friction. I suppose simple laminar flows in such a thin gap.

At 174rd/s, 39mPa*s oil produces a shear strain of 41kPa, and over only 5mm fitting height, 800W losses.

700b in 10µm uniform gap produce a maximum leak speed of 4.5m/s and a throughput of 11cm³/s or 800W hydraulic power.

Both added (pump is perfect...) waste over 10h 0.9% of the stored energy.

-----

I don't rely on low-loss roll bearings to centre the shaft in a 10µm gap. In the right sketch of post #2, you see the axial hydrostatic bearing under flexible rods which support the vertical force.

Oil bearings have some self-centring capability, but not necessarily at such a small gap and a small height. Will it?

Height can increase with a lighter oil. I like the small height to give passive stability to the wheel's altitude.

An actuator and a sensor can move the cylinder to follow the shaft if this doesn't occur naturally. Some fitting filled with oil can dampen the cylinder's oscillations then.

The second, external chamber at the sketch minimizes the cylinder's deformation at the fitting.

-----

Some features let me prefer the hydrostatic bearing against the magnetic one. It can be passive, or at least consequences of software failures are more benign. The passive valve in the cylinder gives force for vertical accelerations. If the pump fails, the flywheel touches down gently.

Marc Schaefer, aka Enthalpy

 

[Dmytry]

Well, the functionality of this software is very narrowly defined (keeping the wheel hanging), not at all like a web browser or the like, so it is a lot easier to get the software right and verify it's correctness.
For combining the motor with bearing, that may or may not be feasible but the point is to minimize the switching electronics.
The idea is that the rotor will use permanent neodymium magnets. Need to calculate magnet weight. Quick research indicates that nuke lobby pushed for some BS that 1 ton of neodymium is required for 1MW wind turbine which doesn't make any sense (1KW motor or generator needs far less than 1kg of neodymium magnets, which are far from being 100% neodymium).

 

[Enthalpy]

Magnetic bearings look feasible, it's just that I prefer the big rollers and the hydrostatic bearing. What could ruin them is aerodynamic loss at the magnetic gap: this gap must be thin, have a minimum area, and be empty. The gap alone could require vacuum operation.

A 1MW motor doesn't need 1t of magnets, sure. Far less here, at 300m/s ! An alternator is difficult when a wind turbine rotates it without a gear, but even there, no ton is needed - see Enercon:
http://www.enercon.de/de-de/ringgenerator.htm ("Choose your language" - nice Pdf)
and my electrostatic alternator and motor would use no magnet on wind turbines, hydroelectric dams, boat propeller pods. Topic "electrostatic alternator" at Saposjoint.net, Science > Technology.

Obscure to me, when combining the motor-generator with a magnetic bearing: I estimate an amorphous core material is unaffordable as it needs boron, and iron-silicon looses too much power if the induction varies at the rotation frequency - hence the design with a DC axial induction. As opposed, the motor-alternator needs some induction rotating against an iron core: I suppose this can't be the lifting flux, but a much smaller flux that affords expensive material. Then, sharing the electronics looks difficult.

Atmospheric operation, roller bearings, steel... are all consequences of cheap and big construction. A reaction wheel for spacecraft would make the opposite choices.

 

[HowlerMonkey]

An 80 ton flywheel escaping it's mounting would be a great for inclusion into a movie script.

 

[Enthalpy]

Sure! Especially if the movie let's the wheel run slower than 390m/s, like: somewhat faster than a car...

And because I prefer this to remain a movie script, I consider burying the wheels in a pit.

What about a turbogenerator escaping its bearings, for your script? Only 150m/s, but 200t, and it runs over the ground.

Because engineers worried about this script, newer power plants with several units orient their generators so that an escaping turbogenerator doesn't smash the other unit's boiler. On older plants the orientation was random, and indeed unfavourable sometimes, including at nukes.

A series-cabled motor jumped from its bearings after running mad in my engineering school. This small one, like 1m long, destroyed the stone wall facing the motor. But hey, it has never happened with a full-sized turbogenerator - up to now.

 

[Enthalpy]

Roller bearings must be oversized to live long, and here's an improved choice, with the usual design first.

Most producers stick to the standard and indicate a dynamic load applicable for 1M turns, but a flywheel at 39Hz makes 25G turns in 20 years. Life shall then vary with the power 10/3 of the load. But SKF observes a faster improvement at light loads and tells "no wear at all under this limit" which I shall use through this applet:
http://www.skf.com/skf/productcatalogue/calculationsFilter?lang=en&newlink=&prodid=&action=Calc5
that computes losses if you choose a bearing and an oil viscosity in the process.

390kN per side is below the fatigue load of the NNCF 5048 CV (shaft d=240mm, bore D=360mm). Maximum 1000rpm impose a wheel of D=8.4m, undesired. With an oil viscosity of 6.6mm²/s, loss is 27N*m or 2.8kW per bearing (screenshot), the pair summing over 10h 3.3% of the stored energy.

Several smaller bearings at each shaft end accept more rmp and reduce the loss torque. This wins the 5m wheel back at identical power loss. It needs added hardware to align the bearings and share the load, like calottes working similarly to bogies.

3.3% energy loss isn't bad. Compare with transformers and high voltage lines working at full load instead of medium load: they must lose nearly that. But the big roller I suggested at saposjoint.net/Forum/viewtopic.php?f=66&t=1974 on Sat Jul 09, 2011 and on pictures 3 and 4 in the present thread shall reduce losses.

-----

How much do the big rollers dissipate? Data exists for railways
http://www.engineeringtoolbox.com/rolling-friction-resistance-d_1303.html
but is pessimistic for hardened steel, and bearings are >10 times better.

First, how wide is the shaft? I keep the material and long-run contact pressure of existing bearings, with 20 rolls (uncritical), of which the 10 lower work. Because force is proportional to deformation in a cylindrical contact, and cos² has 0.5 mean value, 10 rolls bear 5 times the load of the lowest roll. Since the rolls have the shaft's diameter times pi/20, and bearing capacity is proportional to the diameter
http://en.wikipedia.org/wiki/Contact_(mechanics)#Contact_between_two_cylinders_with_parallel_axes
a shaft with a diameter multiplied by pi/4 running on a huge roller bears as much. Or rather, keep the shaft's diameter, and have a roller 3.7 times larger, since 1/R add.

Ho do losses vary with the diameter? Unclear... With the identical stress, contact width increases as sqrt(R) or 2.5 over the previous 20 rolls, and the equivalent length of rolling resistance shall do the same at most. Then, as the big roller is supported by its smaller shaft, this loss occurs once, instead of twice at a roll bearing. The main improvement comes from the radius increased 6.4 times over the rolls. The combination cuts loss by 5.

The roller's shaft must be supported, but at a smaller speed wasting less power - or if you prefer, this rolling force is slashed by the radius ratio. And the roller's shaft itself can run on a big roller.

This shall bring rolling losses over 10h under 1% of the stored energy.

Roll bearings need a long contact line, so the big roller would be longer than a roll bearing, and the shaft accordingly narrower. Fine, as the shaft's diameter has margin, and this reduces loss. Elastic bending at the shaft may become a limit, but the roller can be inclined (already done at turbogenerators' hydrodynamic bearings) and grinded slightly non-cylindrical.

Marc Schaefer, aka Enthalpy