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Re: Betz limit [was: Re: [AWECS] Re: Makani M1]
 To Dave Lang,It would help to explain why the Betz Limit based on a rotor soliddisc assumption does not apply in a loose general sense to other shapes like a hollow ring or frontal rectangle. I have seen the Betz Limit principle used in this general sense by leading authors struggling to characterize the limits of nondisc windfarm geometries & it makes considerable sense in those contexts. No one proposed a triple penalty, but you could opine as to whether a small turbine disc on a wing inscribing a larger disc is in fact a Betz "double hit".Betz efficiency is a rough indication of the far more meaningful AWE limitation of Surface Sprawl. The Makani M1 will be severely limited in economic efficiency by the excessive requirement for ground interconnect infrastructure (roads, fences, buried cables, nogo zones, etc.). Despite a big sky, highest airspace utilization is very desirable,daveS
Re: Betz limit [was: Re: [AWECS] Re: Makani M1] I was only alluding to two things....1. The (conceptually and quantitatively) shaky ground associated with "shooting from the hip" as regards to efficiency of AWE schemes, and the implications thereof.2. That ROI and COP trumps ALL the details and implications that might be thrown in the mix, such as efficient use of airspace, etc, etc....all of which will show up in the ROI and COP if done rigorously (could one even design an AWE farm without addressing this issue?). These conjectures will ALL "washout to fact" when you do your solid simulations/testing and begin to approach a final design of something that actually works and has potential attraction to investors!Makani's M1 may have an efficiency of 1% for all I know, but who knows (although Makani may well) until one does the simulations and testing and evaluates TOTAL COST (to determine ROI and COP). I would not sell any AWE scheme short based on a "halfbaked assessment of how many Betz limits" they are suffering from...what I am driving at is do the math folks (right).....do the sims....do the tests.DaveLAt 11:27 AM 0700 4/8/11, dave santos wrote:To Dave Lang,
It would help to explain why the Betz Limit based on a rotor soliddisc assumption does not apply in a loose general sense to other shapes like a hollow ring or frontal rectangle. I have seen the Betz Limit principle used in this general sense by leading authors struggling to characterize the limits of nondisc windfarm geometries & it makes considerable sense in those contexts. No one proposed a triple penalty, but you could opine as to whether a small turbine disc on a wing inscribing a larger disc is in fact a Betz "double hit".
Betz efficiency is a rough indication of the far more meaningful AWE limitation of Surface Sprawl. The Makani M1 will be severely limited in economic efficiency by the excessive requirement for ground interconnect infrastructure (roads, fences, buried cables, nogo zones, etc.). Despite a big sky, highest airspace utilization is very desirable,
daveS
 Correction:"18133.5 m²"; a little less because of vertical projection
of the wing.
Note:you put a small turbine with a generator at the tip of each blade
of a conventional wind turbine.Betz limit concerns the whole
conventional wind turbine,but also concerns each small turbine in
rapport to apparent wind:Betz limit within Betz limit.
It is the same thing for AWECS of type flygen (another thing:it is
interesting that a rotor aloft with a low output produces also a low
drag (it is a point for examen)).Losses due to the rotor aloft (which
Betz limit of the rotor aloft) are the price of the conversion,a little
like losses due to reelin phase for an AWECS of type reelinout.
Other example:an existing huge wind turbine sweeps about 12000 m²:%
output within Betz limit gives a main data for the global power. KiteGen
carousel sweeps about 2 km² and more: % output within Betz limit
gives a main data for the global power.
PierreB
 In AirborneWindEnergy@yahoogroups.com, "Pierre Benhaiem"
<pierre.benhaiem@...> wrote:>
a
>
> It is told on Makani website that M1 operates between 200 m and 400 m
> altitude.Span is 35 m;so the swept area could be 18133.5 m².So with
> wind speed of 9 m/s (to obtain the theoretical 1 MW) the power at 100
%
> Betz limit could be 4700203.2 W. If we do not take into account the
volume).
> (big) other losses the obtained power is about 21 % Betz limit.
>
> Four remarks:
>
> 1) The center of the loop is not swept.
>
> 2) Knowledge of the output in rapport to Betz limit is yet useful for
> the knowledge of swept area then space occupation (surface and
>
high
> 3) It is not sure that here the swept area is optimal (perhaps too
> for M1 potential,that could explain the low value of % Betz limit, or
account
> for other considerations like a necessary high value of radius of loop
> because of high kite speed ).Diehl's formula does not take into
> Betz limit because it does not take into account the swept area,but it
because
> would be possible to make a translation to obtain a rapport between
> (kite area and kite ratio CL/CD)/(swept area).I think KiteGen already
> made this calculation.
>
> 4) With a less performant flygen (per m² of kite area) like
> FlygenKite <http://flygenkite.com/> the swept area will be very
> different than for M1. FlygenKite <http://flygenkite.com/> flying
> slower the radius can be reduced:it could be a good point to reduce
> space occupation (this point should be clarified).
>
> Doug,DaveS and me are right about the necessary limits of speed
> of the too high tip speed of the rotor.
of
>
> PierreB,
>
> http://flygenkite.com <http://flygenkite.com/>
>
>  In AirborneWindEnergy@yahoogroups.com, Pierre BENHAIEM
> pierre.benhaiem@ wrote:
> >
> > Correction of the precedent message:"To obtain 1000 000 W with 70 %
> losses".It is 30% of losses,and 70% of the initial value.
35
> >
> > PierreB
> > http://flygenkite.com
> >
> >
> >
> >
> >
> > > Message du 04/04/11 20:19
> > > De : "Pierre Benhaiem"
> > > A : AirborneWindEnergy@yahoogroups.com
> > > Copie Ã :
> > > Objet : [AWECS] Makani M1
> > >
> > >
> > >
> > > On Makani website datas for the expected prototype M1 are;span =
> m,and nominal power of 1 MW is reached with wind velocity = 9
=
> m/s.Illustrations show a very thin design:the width of the wing should
> be about 3 m,maybe 5 m,but not more.So with an area of 175 mÂ² the
> power could be formalized as following:
> > > 4/81 aD A w3 CL(CL/CD)Â² with aD = air density;A = kite area;w
> wind speed;CL = lift coefficient;cD = drag coefficient;4/81 is the
Betz
> transformation of 2/27 (see Diehl's formula and the link below) after
> conversion from a reelout system towards a flygen system,including
> limit and drag of an ideal rotor (8/9);
93
> > > So 4/81 1.2 175 93 1.2 = 9072; complete formula is: 4/81 1.2 175
> 1.2 (1.2/CD)Â²
m/s
> > > To obtain 1000 000 W with 70 % of losses (comprising Betz limit):
> 1000 000/6350.4 = about 157.47 ; square root of 157.47 is about 12.549
> > > So (CL/CD) should be the value of 12.549 which is also the ratio
> kite speed/wind speed.
> > > So kite speed should be (12.549) 9 2/3 =75.294 m/s. 2/3 is the
> optimal kite speed after slowing down because of turbines.
> > > So the tip speed of turbines aloft should be some value like 300
> .
http://www.energykitesystems.net/OrthoKiteBunch/OptimizationOfAManualFly\
> > > Thank you for corrections and comments.
> > > PierreB
> > > http://flygenkite.com
> >
>
\> gen.pdf
> > >
> > >
> >
> I agree with Dave Lang. The Betz limit sort of loses its relevance with most AWE configurations (flygen or groundgen). Betz developed this law to describe the theoretical maximum amount of energy that could be extracted from a full stream tube of fluid passing within the outer tip diameter of a turbine relative to the total energy passing through it.
I suppose you could look at each turbine on a flygen separately and try to estimate the energy in the complex, helical stream tube that passes through each turbine on the flygen, but it seems like it would be very difficult (although not impossible) to model. Using the Betz limit calc with knockdown factors, or “double Betz” is probably an oversimplification of the problem.
So again, I agree with Dave L. Build the simulations as best you can (hand calcs all the way up to CFD). Build the test articles. Get data. Recalibrate models (or throw them out and use empirical performance curves from the data). Rinse and repeat.
Efficiency does matter (e.g. high L/D, low drag tethers, super efficient turbines/generators, light weight/strong materials, etc.) but In the end ROI (which involves much more than efficiency) will probably be the only figure of merit that matters. The teams that can field marketable systems with decent ROI (better than fossil fuels) will be successful and profit. This is why I was musing before about the really low efficiency Chinese drag system before (don’t slam me Doug S. !). I’m not a big fan of these low efficiency drag systems, but their R&D, DDT&E and materials costs are probably much lower than everybody else’s. And they’ve certainly got low labor costs for sewing enormous square meters of low cost fabric drag buckets.
I think the winning AWE solution may be somewhere in the middle between the hightech (high cost, high efficiency, high performance, composite construction, complex electronic autonomous controls) and the lowtech (low cost ,fabric construction, low L/D, , large(r) surface area, simple (semipassive?) controls). Kind of hard to visualize something in between the two that combines the best features of both.
Kind of got off track from the Betz discussion! But anyhow.
Dave North
Disclaimer:
The views and opinions expressed herein are my own and do not necessarily state or reflect those of NASA or the United States Government, nor do they represent the official position of NASA.Re: Betz limit [was: Re: [AWECS] Re: Makani M1] Thanks for the comments DaveN.Even the Betz limit for the highly idealized streamtube model has been revisited with more sophisticated analyses and realistic CFD models and it has been conjectured that for the assumed Betzmodel, a more accurate power conversion limit could be as low as 30% efficiency (rather that the oftquoted 60%)....this is due to flow escaping/diverting around the (idealized streamtube) rotor geometry (not included in Betz' very elegant but somewhat oversimplified model) and thus avoiding getting robbed of its kinetic energy (thus the loss of efficiency).If one wants a challenge to stretch their AWE analytical wings, a good exercise is to try to figure out what an equivalent Betz limit would be for a closehauled sail boat (a sailboat on a full downwind leg is pretty simple to do)....many surprises await, even to the point of having to examine what one means by (the blurry definition of) efficiency  it is the prime baseline ingredient if one wants to express power conversion as a ratio of two quantities :)?DaveLAt 2:54 PM 0500 4/8/11, North, David D. (LARCE402) wrote:I agree with Dave Lang. The Betz limit sort of loses its relevance with most AWE configurations (flygen or groundgen). Betz developed this law to describe the theoretical maximum amount of energy that could be extracted from a full stream tube of fluid passing within the outer tip diameter of a turbine relative to the total energy passing through it.
I suppose you could look at each turbine on a flygen separately and try to estimate the energy in the complex, helical stream tube that passes through each turbine on the flygen, but it seems like it would be very difficult (although not impossible) to model. Using the Betz limit calc with knockdown factors, or ³double Betz² is probably an oversimplification of the problem.
So again, I agree with Dave L. Build the simulations as best you can (hand calcs all the way up to CFD). Build the test articles. Get data. Recalibrate models (or throw them out and use empirical performance curves from the data). Rinse and repeat.
Efficiency does matter (e.g. high L/D, low drag tethers, super efficient turbines/generators, light weight/strong materials, etc.) but In the end ROI (which involves much more than efficiency) will probably be the only figure of merit that matters. The teams that can field marketable systems with decent ROI (better than fossil fuels) will be successful and profit. This is why I was musing before about the really low efficiency Chinese drag system before (don¹t slam me Doug S. !). I¹m not a big fan of these low efficiency drag systems, but their R&D, DDT&E and materials costs are probably much lower than everybody else¹s. And they¹ve certainly got low labor costs for sewing enormous square meters of low cost fabric drag buckets.
I think the winning AWE solution may be somewhere in the middle between the hightech (high cost, high efficiency, high performance, composite construction, complex electronic autonomous controls) and the lowtech (low cost ,fabric construction, low L/D, , large(r) surface area, simple (semipassive?) controls). Kind of hard to visualize something in between the two that combines the best features of both.
Kind of got off track from the Betz discussion! But anyhow.
Dave North
Disclaimer:
The views and opinions expressed herein are my own and do not necessarily state or reflect those of NASA or the United States Government, nor do they represent the official position of NASA. Thanks for the comments DaveN and DaveL.They open my eyes about CFD models and the probably great difficulties to obtain realistic simulations of AWE.
PierreB> Message du 08/04/11 23:18
> De : "Dave Lang"
> A : AirborneWindEnergy@yahoogroups.com
> Copie à : "North, David D. (LARCE402)"
> Objet : Re: Betz limit [was: Re: [AWECS] Re: Makani M1]
>
>>
Thanks for the comments DaveN.
>Even the Betz limit for the highly idealized streamtube model has been revisited with more sophisticated analyses and realistic CFD models and it has been conjectured that for the assumed Betzmodel, a more accurate power conversion limit could be as low as 30% efficiency (rather that the oftquoted 60%)....this is due to flow escaping/diverting around the (idealized streamtube) rotor geometry (not included in Betz' very elegant but somewhat oversimplified model) and thus avoiding getting robbed of its kinetic energy (thus the loss of efficiency).
>If one wants a challenge to stretch their AWE analytical wings, a good exercise is to try to figure out what an equivalent Betz limit would be for a closehauled sail boat (a sailboat on a full downwind leg is pretty simple to do)....many surprises await, even to the point of having to examine what one means by (the blurry definition of) efficiency  it is the prime baseline ingredient if one wants to express power conversion as a ratio of two quantities :)?
>DaveL
>
>
>At 2:54 PM 0500 4/8/11, North, David D. (LARCE402) wrote:
>I agree with Dave Lang. The Betz limit sort of loses its relevance with most AWE configurations (flygen or groundgen). Betz developed this law to describe the theoretical maximum amount of energy that could be extracted from a full stream tube of fluid passing within the outer tip diameter of a turbine relative to the total energy passing through it.
>
>I suppose you could look at each turbine on a flygen separately and try to estimate the energy in the complex, helical stream tube that passes through each turbine on the flygen, but it seems like it would be very difficult (although not impossible) to model. Using the Betz limit calc with knockdown factors, or ³double Betz² is probably an oversimplification of the problem.
>
>So again, I agree with Dave L. Build the simulations as best you can (hand calcs all the way up to CFD). Build the test articles. Get data. Recalibrate models (or throw them out and use empirical performance curves from the data). Rinse and repeat.
>
>Efficiency does matter (e.g. high L/D, low drag tethers, super efficient turbines/generators, light weight/strong materials, etc.) but In the end ROI (which involves much more than efficiency) will probably be the only figure of merit that matters. The teams that can field marketable systems with decent ROI (better than fossil fuels) will be successful and profit. This is why I was musing before about the really low efficiency Chinese drag system before (don¹t slam me Doug S. !). I¹m not a big fan of these low efficiency drag systems, but their R&D, DDT&E and materials costs are probably much lower than everybody else¹s. And they¹ve certainly got low labor costs for sewing enormous square meters of low cost fabric drag buckets.
>
>I think the winning AWE solution may be somewhere in the middle between the hightech (high cost, high efficiency, high performance, composite construction, complex electronic autonomous controls) and the lowtech (low cost ,fabric construction, low L/D, , large(r) surface area, simple (semipassive?) controls). Kind of hard to visualize something in between the two that combines the best features of both.
>
>Kind of got off track from the Betz discussion! But anyhow.
>
>Dave North
>
>Disclaimer:
> The views and opinions expressed herein are my own and do not necessarily state or reflect those of NASA or the United States Government, nor do they represent the official position of NASA.
>
>
>  I also agree with DaveL that ROI rules but there are so many critical dimensions to a real AWE system that elevating any isolated factor (like Betz performance) above the rest is a distortion. The doubleBetzhit conjecture is still an interesting question, but in the abstract.A personal beef is how often someone gushes about wind power increasing at the cube of velocity, which is true, but then they presume that they will effectively harvest all this increased power, which is not true. For a variety of reasons, including the runaway capital cost of chasing top performance, its far safer to estimate one can harvest the increase at the square of velocity. This ruleofthumb, while incorrect textbook physics, is a properly pessimistic design assumption.DaveN is probably right that the winning early AWE formula will be the sum of many middleoftheroad tradeoffs, a balance of performance & cost. Still, the solution may also involve some very clever inventive leaps unforseeable by any conservative design strategy.
 I've read comments elsewhere by guys who feel challenged by the Betz limit and want to beat it. This misses the point on two counts. One, is that there are seldom any hard physical limits on the section of air available. The other, more fundamental misunderstanding is that this is not like the problem of increasing efficiency in heat engines, where the limits are not fixed, but subject to improvements in design and materials. Betz simply warns us about being too greedy, and reducing the flow through our device below the optimum level.Bob StuartOn 8Apr11, at 5:45 PM, dave santos wrote:I also agree with DaveL that ROI rules but there are so many critical dimensions to a real AWE system that elevating any isolated factor (like Betz performance) above the rest is a distortion. The doubleBetzhit conjecture is still an interesting question, but in the abstract.A personal beef is how often someone gushes about wind power increasing at the cube of velocity, which is true, but then they presume that they will effectively harvest all this increased power, which is not true. For a variety of reasons, including the runaway capital cost of chasing top performance, its far safer to estimate one can harvest the increase at the square of velocity. This ruleofthumb, while incorrect textbook physics, is a properly pessimistic design assumption.DaveN is probably right that the winning early AWE formula will be the sum of many middleoftheroad tradeoffs, a balance of performance & cost. Still, the solution may also involve some very clever inventive leaps unforseeable by any conservative design strategy.
 Interesting paper:reading p.6 and 7 about tether3 wires:"
Consider a realistic example of what one might try to build, a 100 kW wind generator with
a tether length of 1500 feet (circa 450 metres) running 3phase output at one of 380, 480, or 600
VAC. The corresponding phase currents at full power and full voltage into a resistive load are
88.6, 70.2, and 56.1 amperes respectively. In turn, the minimum required cable gauges are 3, 4,
and 6 AWG respectively, and greater if the reactance of the load cannot be guaranteed to stay
low. Even with a threewire delta with no additional grounding lead, the weight of the copper
alone is 325, 257, or 162 kg for the 1500 ft run. The ohmic losses in the tether at full current are 7
kW, 5.5 kW, and 5.6 kW respectively, or 5.5 to 7 percent of total production over 1500 ft."
So for 1MW the weight of the copper alone (waiting for nanotube?) is from 1620 to 3250 kg with a tether length of 450 m.In static use M1 (hypothetical 175 m² and wind = 9 m/s) could lift only 850 kg,FlygenKite (700 m²) could lift 3400 kg (it is not yet enough).What are the repercussions about safety and reliability if lifting tether is only possible during dynamic use?
After discussions about "to Betz or not to Betz" limit(s),to consider that rough calculations I take is for a very (too) favorable hypothesis,and already requirements seem to be very difficult to satisfy.
PierreB
http://flygenkite.com> Message du 04/04/11 20:59
> De : "Pierre BENHAIEM"
> A : AirborneWindEnergy@yahoogroups.com
> Copie à :
> Objet : re: [AWECS] Makani M1
>
>> Correction of the precedent message:"To obtain 1000 000 W with 70 % of losses".It is 30% of losses,and 70% of the initial value.
>
> PierreB
> http://flygenkite.com
>
>
>
>
>> Message du 04/04/11 20:19
> > De : "Pierre Benhaiem"
> > A : AirborneWindEnergy@yahoogroups.com
> > Copie à :
> > Objet : [AWECS] Makani M1
> >
> >> >
> > On Makani website datas for the expected prototype M1 are;span = 35 m,and nominal power of 1 MW is reached with wind velocity = 9 m/s.Illustrations show a very thin design:the width of the wing should be about 3 m,maybe 5 m,but not more.So with an area of 175 m² the power could be formalized as following:
> > 4/81 aD A w^{3 }CL(CL/CD)² with aD = air density;A = kite area;w = wind speed;CL = lift coefficient;cD = drag coefficient;4/81 is the transformation of 2/27 (see Diehl's formula and the link below) after conversion from a reelout system towards a flygen system,including Betz limit and drag of an ideal rotor (8/9);
> > So 4/81 1.2 175 9^{3 }1.2 = 9072; complete formula is: 4/81 1.2 175 9^{3 }1.2 (1.2/CD)²
> > To obtain 1000 000 W with 70 % of losses (comprising Betz limit): 1000 000/6350.4 = about 157.47 ; square root of ^{ }157.47 is about 12.549
> > So (CL/CD) should be the value of 12.549 which is also the ratio kite speed/wind speed.
> > So kite speed should be (12.549) 9 2/3 =75.294 m/s. 2/3 is the optimal kite speed after slowing down because of turbines.
> > So the tip speed of turbines aloft should be some value like 300 m/s .
> > Thank you for corrections and comments.
> > PierreB
http://www.energykitesystems.net/OrthoKiteBunch/OptimizationOfAManualFlygen.pdf
> > ^{ }
> >
>  Pierre BENHAIEM schrieb:
...> Consider a realistic example of what one might try to build, a 100 kW
...
> wind generator with a tether length of 1500 feet (circa 450 metres) running 3phase output
> at one of 380, 480, or 600 VAC.
> So for 1MW the weight of the copper alone (waiting for nanotube?) is
...
> from 1620 to 3250 kg with a tether length of 450 m.
I would think that this much copper or whatever is suboptimal. Using
highvoltage DC might be better if the inverter aloft doesn't weigh too much.
Then one could use two wires and many kilovolts, saving a lot of material and
weight in the lines. Of course one also needs a sure method of shorting this out
in case of accidents. And remember that insulation weighs, too. An interesting
optimisation problem which I'm sure has been done.
Theo Schmidt  On 10Apr11, at 1:58 AM, Theo Schmidt wrote:
Pierre BENHAIEM schrieb:
...
> Consider a realistic example of what one might try to build, a 100 kW
> wind generator with a tether length of 1500 feet (circa 450 metres) running 3phase output
> at one of 380, 480, or 600 VAC.
...
> So for 1MW the weight of the copper alone (waiting for nanotube?) is
> from 1620 to 3250 kg with a tether length of 450 m.
...
I would think that this much copper or whatever is suboptimal. Using
highvoltage DC might be better if the inverter aloft doesn't weigh too much.
Then one could use two wires and many kilovolts, saving a lot of material and
weight in the lines. Of course one also needs a sure method of shorting this out
in case of accidents. And remember that insulation weighs, too. An interesting
optimisation problem which I'm sure has been done.
Theo SchmidtI wondered about using aluminum conductors, but was recently informed on this list that for a combination of conductivity and tether strength, steel is better. If necessary, considerable line losses can be tolerated. It may be possible to use a capacitor to use highfrequency AC with only a single conductor, saving the weight of insulation.Bob  On Sun, 20110410 at 07:26 0600, Bob Stuart wrote:
>
Yes, that was me. The spreadsheet showing the calculations is still
>
> On 10Apr11, at 1:58 AM, Theo Schmidt wrote:
>
> > Pierre BENHAIEM schrieb:
> > ...
> > > Consider a realistic example of what one might try to build, a 100
> > kW
> > > wind generator with a tether length of 1500 feet (circa 450
> > metres) running 3phase output
> > > at one of 380, 480, or 600 VAC.
> > ...
> > > So for 1MW the weight of the copper alone (waiting for nanotube?)
> > is
> > > from 1620 to 3250 kg with a tether length of 450 m.
> > ...
> >
> > I would think that this much copper or whatever is suboptimal.
> > Using
> > highvoltage DC might be better if the inverter aloft doesn't weigh
> > too much.
> > Then one could use two wires and many kilovolts, saving a lot of
> > material and
> > weight in the lines. Of course one also needs a sure method of
> > shorting this out
> > in case of accidents. And remember that insulation weighs, too. An
> > interesting
> > optimisation problem which I'm sure has been done.
> >
> > Theo Schmidt
> >
> >
> I wondered about using aluminum conductors, but was recently informed
> on this list that for a combination of conductivity and tether
> strength, steel is better. If necessary, considerable line losses can
> be tolerated. It may be possible to use a capacitor to use
> highfrequency AC with only a single conductor, saving the weight of
> insulation.
>
>
> Bob
>
there. I promised to update it and post an excel version but have been
too busy with other things to get it done yet. Hopefully soon.
HF AC down a single line would be inefficient. The way to go is 2 lines
carrying single phase AC, or preferably DC. Single phase generators tend
to vibrate too much so 3 phase is better. It only needs a simple
rectifier to convert to DC and a multikilovolt version would weigh very
little. Inverters are for going the other way.
Using 2 wires has an important safety benefit because if one breaks the
other can still be used to pull the airborne generator back to a safe
place. There is no need to insulate these lines and in fact the
insulation would just get in the way.
Something that no one else seems to be considering is using a
combination of airborne and groundbased generators. The airborne
generators/motors only need to be powerful enough to get the wing off
the ground and into the wind. Any more powerful than that and their
mass, and the mass of the tethers, start to become a problem. The main
generator will be on the ground driven by the reeling out of the twin
tethers.
Another reason for restricting the power of the airborne electrics is
the tip speed of the blades  as recently discussed by Pierre et al.
Noise from the blade tips rapidly increases as their speed increases
(5th to 6th power) so to be a good neighbour the blade rotation rate
needs to be kept down.
Quadracopters can be controlled very precisely. Putting more than 4
generators on a wing would be extravagant. Less than 4 makes control
difficult.
Robert.  "Consider a realistic example of what one might try to build, a 100 kW
> wind generator with a tether length of 1500 feet (circa 450 metres) running 3phase output
> at one of 380, 480, or 600 VAC.
..."
That is an extract from the attachment (see " " on the precedent message).Note:Makani uses a bruschless DC motor.
PierreB> Message du 10/04/11 15:06
> De : "Theo Schmidt"
> A : AirborneWindEnergy@yahoogroups.com
> Copie à :
> Objet : best voltage [was: Re: [AWECS] Makani M1 [1 Attachment]]
>
>> Pierre BENHAIEM schrieb:
> ...
> > Consider a realistic example of what one might try to build, a 100 kW
> > wind generator with a tether length of 1500 feet (circa 450 metres) running 3phase output
> > at one of 380, 480, or 600 VAC.
> ...
> > So for 1MW the weight of the copper alone (waiting for nanotube?) is
> > from 1620 to 3250 kg with a tether length of 450 m.
> ...
>
> I would think that this much copper or whatever is suboptimal. Using
> highvoltage DC might be better if the inverter aloft doesn't weigh too much.
> Then one could use two wires and many kilovolts, saving a lot of material and
> weight in the lines. Of course one also needs a sure method of shorting this out
> in case of accidents. And remember that insulation weighs, too. An interesting
> optimisation problem which I'm sure has been done.
>
> Theo Schmidt
>  We need to be careful with the rather misleading terminology here.
"Brushless DC" refers to the whole package including the electronics.
The motor/generator itself will be 3 phase AC.
Robert.
On Sun, 20110410 at 20:41 +0200, Pierre BENHAIEM wrote:
>
> "Consider a realistic example of what one might try to build, a 100
> kW
> > wind generator with a tether length of 1500 feet (circa 450 metres)
> running 3phase output
> > at one of 380, 480, or 600 VAC.
> ..."
> That is an extract from the attachment (see " " on the precedent
> message).Note:Makani uses a bruschless DC motor.
>
> PierreB
>
>