Author Topic: I'm not sure Betz was right (Read 6100 times)

Gunboss · « **on:** May 20, 2009, 08:26:12 PM »

I think that a lot of wind power discussion here and elsewhere miss some of the factors that should be addressed. I feel that too much of the aerodyamics comes from airplanes and thus gets hung up on drag which is of little to no importance to a wind generator. Also a lot of the math tends to obscure what's really happening out in the swept area. I'm limiting my discussion to HAWTs since they are so popular. I have posed these ideas to experts elsewhere, but they say nothing or "You're wrong, but I don't have time to tell you why."

Here are my thoughts. Please point me at the source that has enough detail to refute what I am saying.

I think Betz may have missed an important source of pressure by not altering the underside of his infinite number of blades, but then they would be finite.
I think we should put a series of longitudinal steps (ridges) on the bottom of the blades so that the air gets dammed up, the pressure increases, and the air gets turned so that it flows radially outward along the steps toward the blade tip. This will increase the drag horribly in the direction of the wind, but we don't care because this is not an airplane. It costs nothing in terms of energy (or any other way) since the tower is already there. This will result in (more of) a vortex, but I disagree that a vortex reduces the torque because we're doing work on the wind. The wind is also doing opposite work on the blade. Also we must keep the separation between the blades just far enough apart so that the high pressure on the bottom of one blade does not bleed over into the low pressure on the top of its neighbor. Otherwise the steps on each "upper" blade would more or less follow the curve of the airfoil on the "lower" blade, but still maintaining the necessary gap.
We don't care about drag. We should be designing airfoils for the lowest pressure on "top" while maintaining laminar flow without regard to induced drag.
If your blades have gaps between them, you are letting air escape, you're not slowing it down and you're not getting all the energy out of it.
Blades should get broader as the radius increases so that there is a minimum of gap between the blades. (see 4.) But we need a little gap to keep the high and low pressure apart. (see 2.)
Where they are using more blades (e.g. Windflowers in Denmark -12 blades) they have good things to say, but especially low noise, low running speed and high starting torque.

The odds are that I am wrong, but I would really like to know why and I would like to see some wind tunnel results with my blade / turbine design. Is it possible to make this happen somewhere or do I have to build a wind tunnel and the turbine and do it myself?

DamonHD · « **Reply #1 on:** May 20, 2009, 02:35:03 PM »

Arguing against Betz is not quite as silly as perpertual motion (OverUnity) ideas or disputing the laws of thermodynamics, and I'm no expert myself, but if what you were suggesting was possible why wouldn't Vestas et al be doing it? I know that's not a disproof, but your extraordinary claim needs some extraordinary evidence...

Rgds

Damon

zeusmorg · « **Reply #2 on:** May 20, 2009, 02:44:17 PM »

For anyone to believe your theories, you'll have to prove them yourself. Arguing with a known theory that has been used for years is hard to disprove, although it has been done in the past.

I've yet to see Betz's limits exceeded.

And yes we do care about drag, it leads to lower rpms.

You also are not taking into consideration several factors that Betz did.

Yes, a lower RPM machine can benefit from wider (and more) blades, but will a high rpm machine benefit?

In a nutshell, build it, if it works, they will come.

Flux · « **Reply #3 on:** May 20, 2009, 03:05:15 PM »

There may be arguments to suggest that Betz figure of .593 may not be exact. It is based on momentum theory and if you look at it from other points of view you may get a different figure.

What is not in question is that the Betz figure has not been exceed or even approached with any practical blade that I have heard of. The Windflower you refer to claims something approaching .45. If that is accurate it is pretty good and about as good as you are going to get. It does have to be used with speed increasing drives or an incredibly slow alternator so you will not be much better than a good conventional 3 blade prop. How accurately these figures have been measured is questionable, it is a difficult field.

If you want to devote your life to proving Betz wrong that is fine with me. I don't expect wonders from blades but there is more to be gained from matching over a significant speed range than from worrying about the perfect blade. When you have dealt with the matching problem and sorted that then it may be worth turning attention to blades.

You are right that most of the wind tunnel testing has been for aeroplane wings for obvious reasons. I haven't seem much complete windmill testing results that I would trust. It takes a monster tunnel to test a windmill of any reasonable size and then you can't be sure that real wind behaves in the same way.

Flux

Gunboss · « **Reply #4 on:** May 21, 2009, 08:52:14 AM »

I see I put too much info in one posting and I should not have put Betz in the title. But as usual no one has said why I am wrong. And no one points to any reference that addresses my two major issues.

1. Why not get some power out of the lost wind that blows between the blades?

Are you saying that putting extra blades in the spaces of a typical turbine would not produce more torque? Even Betz filled the disk with an infinite number of blades. He did not waste a single molecule of wind.

2. What happens if we put steps or ridges on the underside of the blades?

Of course this would create intolerable drag in the direction of the wind on an airplane wing, but we don't care about drag in the direction of the wind on a turbine blade because we have a tower. The increased pressure on the underside of the blade would mean a higher pressure differential between the top and the bottom which means more torque. The parasitic drag does not work against the torque, it works against the tower.

Surely someone has tried these ideas? Where are the results that disprove what I am suggesting?

clflyguy · « **Reply #5 on:** May 21, 2009, 09:17:11 AM »

GB-

Just out of curiosity, which way do these steps or ridges run?

ghurd · « **Reply #6 on:** May 21, 2009, 10:30:38 AM »

You seem to think clearance between the blades is a waste.

When the solidity is too high or the blades run past their TSR, each blade is running in the earlier blade's wake.

It looks to me like you are getting closer and closer to a drag blade, something like an American water pumper.

It is easy to test. Make a dozen lift-based blades and mount them on a free-wheeling hub (in safe winds) and measure the RPM. Remove half and test 6. Remove half and test 3.

I expect you don't see the point in that, but the 3 or 6 blades will turn faster.

The torque is just what it takes to turn itself, so the operating in its own wake shows up.

At least that's how I see it. I can hear it with PVC blades.

Could test it with a high solidity 3 blade fan blade. Check the torque and RPMs.

Cut some solidity out and retest. The again.

That's what I did. The factory blade did not start the PMA turning in as low wind as the modified blade. I figure the wind had to fight so hard to go 'through' the blades, most of the wind went 'around' the diameter. Maybe not.

But try it and see what kind of numbers you come up with.

G-

TomW · « **Reply #7 on:** May 21, 2009, 11:20:42 AM »

GB;

Surely someone has tried these ideas? Where are the results that disprove what I am suggesting?

Uh, how did it become "our" responsibility to satisfy you on your misguided suggestion?

Extraordinary claims require extraordinary proof. Wheres yours?

I think anyone who claims to "know better" must bear the burden of the proof.

Where is your proof it is wrong?

Where are your test results.

Betz and his limit suck but, like Ohm and the limits he puts on power production we are simply stuck with the facts.

Simple as that.

Don't get me wrong, I disbelieved Betz in the beginning, too, but it seems to be born out in real world situations that he is either right or very close to right on the numbers.

Awaiting your testing and results.

The ball is in your court now.

Unless, of course, this post is simply the troll I think it is. Without more than you have posted it is tough to believe it is not just a fishing expedition by you to stir things up here.

Tom

TheCasualTraveler · « **Reply #8 on:** May 21, 2009, 11:57:19 AM »

Gee Tom, what's wrong with stirring things up? I didn't get the impression Gunboss wanted trouble, just an interesting debate. I thought a little discussion on Beltz was a nice break from some of the more mundane topics. I was enjoying the thread and learning more from the way folks here explain things than I would if I tried to learn it from a book.

His last paragraph says he assumes he is wrong but just wants to know why, sorta like playing devils advocate to learn better. Really Tom, I think it's just good clean educational fun, no harm. Wadda ya think?

Bruce S · « **Reply #9 on:** May 21, 2009, 01:23:27 PM »

Traveler;

Actually, I am leaning towards TomW's post. The original post was a request. The 2nd was a statement.

Some very intelligent people have explained a few items and he came back with a statement of not being proven wrong. NO person here gets paid for their time to prove a known tests wrong.

As TomW put it, balls in his court.

Betz, did tons of true testing and to this day no where on the Net or anywhere else, Sandia? has anyone been able to prove him incorrect, or gone over.

Best way now is to go build it and be the hero of the world.

Places like GE, Pristine Power ect will beat a path to his door.

My 1/2 cent worth, no stimulis has arrived in my mailbox yet .

Bruce S

ghurd · « **Reply #10 on:** May 21, 2009, 01:47:35 PM »

Wondering now if you are looking for pure torque.

Then thick wide fat blades at a very tiny angle of attach should be dandy.

And bigger as the radius increases.

Counter productive for remotely cost effective power generation.

Speed makes cheap power.

G-

Stonebrain · « **Reply #11 on:** May 21, 2009, 02:29:11 PM »

Hey,gunboss(what's in a name)

You got it the wrong way.

It's not up to us to prove that you're wrong,

but it's up to you prove you're right.

You really want someone to build your design to prove it's wrong?You're just not serious.

cheers,

stonebrain

electrondady1 · « **Reply #12 on:** May 21, 2009, 10:13:09 PM »

this post reminds me of finnsawer.

i wonder why he hasn't posted for a year.

TheCasualTraveler · « **Reply #13 on:** May 21, 2009, 10:32:34 PM »

I was looking at his user info today and wondering the same thing

Gunboss · « **Reply #14 on:** May 22, 2009, 01:28:29 PM »

I appreciate the responses from ghurd, clflyguy and TheCasualTraveler and the others who jumped in constructively. OK I was stirring things up, but I did not ask for YOU to prove me wrong or educate me. I asked for someone to point me at the existing research or results or findings that would prove me wrong. I have done enough research on the internet to know that there are lots of assumptions (i.e. airplane thinking) thrown in here and there that leave me unsatisfied when they extend the assumptions to wind turbines. That's the exceptional part that needs to be researched more. Wind turbines are not airplanes. I don't feel bad about asking you folks who have more experience to point me at the results or findings that address my issues. If nobody knows where those issues have already been tried and written about then maybe they have not been tried yet.

All that being said, ghurd did try and educate me, which I appreciate. He mentioned the "American water pumper" and I admit that if the blades had an airfoil top and a honeycomb bottom I would like them a lot. He understands my concern about developing more torque and comes out with a nugget "Speed makes cheap power." He is correcting my stand that might be summarized something like "High torque and proper gearing makes cheap power." I would like to know where the comparisons are that I can go and research. This sounds physically / mathematically unsupportable so it must have been addressed somewhere.

Nobody (that I have found) addresses the idea of ridges or steps (radial or crossing) or open honeycomb that would increase the "bottom" pressure. The increased pressure and turbulence would add to the torque and, of course, push harder on the tower. Has anyone tried this and written some results that can be researched?

Since ghurd mentioned the leading blade's wake interfering with the following blade, why not advance the trailing blade out of the way. Put it out on a plane or "disk" in front of the leading blade's plane? You could then move the trailing blade closer to the leading blade looking from the front, but ahead of it looking from the side. This would make a "staggered" two-blade set. Then put three or four (or more) sets around the hub spaced so that the trailing blade of set 1 does not affect the leading blade of set 2 etc. and you have doubled your power. Has anyone tried this and written results that can be researched?

I apologize for stirring things up and I'm not asking you to build anything, but I can't imagine that these simple ideas have not been tried already and that the findings are not available. But if these ideas have not been tried and if there is any merit to even one of them, I would love to see somebody edge past that 59.3.

wooferhound · « **Reply #15 on:** May 22, 2009, 06:24:06 PM »

OK , I'm not the most knowledgeable on this subject but I think I have a general idea how to explain it.

If you extract all of the power out of the wind, then you have stopped it from blowing and new air can't blow through to replace it. So you need to let at some of it get past the turbine or the airflow cannot continue. if you let 40% of the air past without extracting that power, then you will be left with the 60% betz limit that is available to use.

Of course you can't get up to the betz limit either unless you use

Frictionless bearings

Superconducting wire

Nonturbulent wind

and perfect Batteries

TheCasualTraveler · « **Reply #16 on:** May 22, 2009, 06:35:53 PM »

""OK , I'm not the most knowledgeable on this subject""

Neither am I, that's one reason I found the discussion interesting. From reading the comments I did a search on "windflower" which took me to a site with an interview by Marcellus Jacobs. It's a story I read before and believe many on this site have also.

http://www.windmission.dk/workshop/Marcellus%20Jacobs.htm

In reply to your comment about letting some of the air through the blades, in the interview he talks about the blades throwing nearly all the wind out so that you could stand behind an efficient blade and the wind getting through would not blow out a match. Fascinating stuff. Anyone who hasn't read the article, might want to give it a look.

wdyasq · « **Reply #17 on:** May 22, 2009, 09:31:16 PM »

Sometimes posts are just not worth answering. As others are curious, I'll throw out a few things one might research IF they are serious about windpower. Of course, GB will need to crack a book and actually DO some research.

Paul Gipe, Danish windpower association, Marcellus Jacobs, Michael Selig, Sandia Labs and NACA/NASA are good places to start. Again, it will requite READING ... possibly taking notes and maybe even a bit of math.

Well GB - banquet is in that last paragraph. I'll be damned if I'm going to spoon feed those too lazy to research.

Ron

Stonebrain · « **Reply #18 on:** May 23, 2009, 05:07:55 AM »

Topgun,

Of course you have to do some research yourself,but I'll try to help you with some of my reflexions on the subject,ifever they can be of any help.

NO!You'll never beat the betz limit.

But betz law is defined for some special conditions:rotor is a disk,perpendicular to the wind direction,with no obstruction around the rotor.

So if you choose conditions that don't correspond to the conditions of betz law you can get other results.

One way to achieve it is using helping structures,for exemple you can place the rotor in a hole in a wall that's perp to the wind or in a tube that's parralel to the wind.It's easy to imagine that the rotor can have a bigger rendement at the same wind speed.betz limit is not beaten,but conditions are diffferent than betz law was difined for.

Another way is to change the geometry of the rotor itself.

For exemple vawts are basicly a cilinder,with the axis perp to the wind.

But you can imagine some allongated form or a cilinder with the axe paralel to the wind too,that eventually 'catch all of the wind' (lol).Without beating the betz limit.

So that leaves room for dreaming about having more than 59% rendement per swept area,allthough for the moment the results for a simple disk rotor is better than any other fancy design.

Were just waiting for a matematical genious that can extend betz law to those more complex conditions.

But then there is the reality that windmill builders don't care a damn about yield per swept area.What counts is yield per $ that you put in your mill.And that's where allmost surely any genious,but complicated design will be beaten by a simple disk-form rotor.

cheers,

stonebrain

erne · « **Reply #19 on:** May 24, 2009, 07:21:10 AM »

I lurk more than write. Often because of my unconventional ways seem to bring ire.

Many years ago, I was told that there were 1760 ways to do something right but only one way to do it wrong. So when told this is the only way!!!! I will leave it there.

When I was younger, I had a Jacobs wind generator, and it provided my electricity along with a gas generator. I have also had several other wind chargers. I live in an area that the rural electrification act never reached to date. (n/w CO.) I now live in an area that does not have enough wind to use the Jacobs or that type of charger. But, a 12-foot, multi blade windmill supplies my water without problems. I have solar panels and a large multi-blade mill to provide my electric needs. My winds are in the 4 to 10 mph range I get between 8 and 12 hrs of these low winds a few times a week, the rest of the time it is still. I have never had an over-speed problem, even in rare high winds. Multi blade turbines disrupt the air to the following blades (solidity) and keep them from over-speeding, as does the off set for the tail vain. It also increases the surface area inducing power. Water mills have ran for years without problems and many are never turned off. I produce between 700 and 1200-watt hours per windy day. I often get one or so hours of wind in morning and evening wind due to the temperature change between the mountain above and the valley below. These usually produce 1 to 2 amps per leg (110 volt Jacobs alternator regulated to 24 volt). If my batteries are full I have a dump load to heat water. I use this water to heat the ground in my greenhouse. I built this type of mill for what I believed were my conditions and am satisfied I did the right thing for my wind climate. Others say It Won't Work. "BUT" they have never built one or tried to generate electricity in very low wind conditions. A 24 ft. mill is very large, but smaller would not have had the power I needed. (See photo in my photo section.) Know what you need and build accordingly. In a 30 mph wind according to Aero-motor charts my machine produces 38 horsepower. I have a 12-foot aero-motor and doubled the dimensions for my electric mill. Also back in the 60's an engineer wrote an article on a mill with offset blades in popular mechanics or popular science. He did wind tunnel work for ford or one of those before he retired. He built a tunnel in his basement to research it after he retired. You might want to research their archives. erne

valterra · « **Reply #20 on:** May 25, 2009, 09:59:30 PM »

While working for the Twentieth Century Motor Company, I designed a generator that took static electricity from the atmosphere.

GE and Pristine Power and the like didn't come beat down MY door! Instead my company went socialist, so I gathered up my buddies and moved into the Rockies.

- John G.

Bruce S · « **Reply #21 on:** May 26, 2009, 08:19:23 AM »

Perhaps because this is taught in 4th grade science classes? Think Leyden jar?

Nothing new. There's even a working circuit that uses a simple Cap and airborne wire to do the same thing.

Try again

Bruce S

dbcollen · « **Reply #22 on:** May 28, 2009, 09:34:17 AM »

Gearing by nature is not "cheap" in more ways than one. there is the cost of the gears, good low friction gears are not cheap, "V" belts that everyone thinks about using are incredibly inefficient. When you multiply RPM you divide torque, and

MULTIPLY LOSSES, so the net power out will be a fraction of the power in. It is ALWAYS more efficient to not use speed reduction or multiplication if you have the option of direct drive.

Dustin

valterra · « **Reply #23 on:** May 29, 2009, 05:49:17 PM »

(Atlas Shrugged reference) :-P

stop4stuff · « **Reply #24 on:** May 31, 2009, 03:42:25 PM »

dunno where GB went...

anyways, since viewing this 'story', i've been researching this whole betz thing and below is what (if i got it right) happens...

in a nutshell...

air molecules behind a wind turbine are moving slower and occupy more space than the same amount of air molecules moving faster in front of the turbine when extracting power from the wind... at some point there is a limit as to how many air molecules will move behind the turbine, so as the blade efficiency increases, there comes a point when more power cannot be extracted from the moving air because the air molecules behind the turbine are moving too slow to get out of the way of the air trying to pass through the turbine... as air cannot get through the turbine, it spills out around the sides... so, the betz limit is when the turbine blades cannot extract anymore energy and wind (moving air) spills out around the turbine.

For Reference:

http://www.windpower.org/en/tour/wres/tube.htm

explains how a wind turbine deflects the wind and that there must be the same amount of air behind as in front of a turbine... the air behind the turbine is going slower and occupies a greater volume

http://www.windpower.org/en/tour/wres/betz.htm

explains betz law

http://www.windpower.org/en/stat/betzpro.htm

mathematically prooves betz law

http://www.flapturbine.com/betz_limit.html

has a great interactive flash animation using an analogy of cars going through a toll booth to explain why there is a limit

Bruce S · « **Reply #25 on:** June 02, 2009, 11:35:36 AM »

tieole · « **Reply #26 on:** June 02, 2009, 04:44:39 PM »

A simple explanation of Betz law is the wind hits the swept area of the blades, 1/3 of the wind is deflected by the blades turning and 2/27 of the wind is need to get past the blades to keep the blades in motion. So we are left with 16/27 or 59.3% of the wind left to extract power from.

This being said, I'm seeing a maximum of 23% of the energy in the wind getting down my tower and past the rectifier. So I have the choice, either to try to refine my genie, reducing the airgap, improving the blades, reducing the resistance in the windings, or just building a bigger one. If I build a 4m machine instead of a 3m machine (with the appropriate generator) I should be able to get 33% more power. Probably the easiest way to get more power next to building a taller tower.

Jay

tieole · « **Reply #27 on:** June 03, 2009, 03:58:50 PM »

Sorry that should be 77% more power when going from 3m to 4m.

Jay

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Author Topic: I'm not sure Betz was right (Read 6100 times)