Author Topic: Furling Calculations (Read 8260 times)

ChrisOlson · « **on:** February 24, 2010, 12:13:42 PM »

Rotor Thrust = diameter squared * wind speed squared / 24

Where the diameter is in meters and the wind speed is expressed in m/sec. The result is the axial thrust of the turbine rotor in kg.

So, for us English speaking people, let's say we have an 8 foot (2.44 m) rotor and the wind is blowing slightly over 24 mph (11 m/sec). This formula would give a rotor thrust of 30 kg or 66 lbs.

However, wind pressure in lbs/square foot is given by:

PSF = .00256 * wind speed squared

Wind speed is in mph in that formula so with this same 8' diameter circle, instead of a turbine rotor we're going to hold a 8' diameter piece of solid plywood into the wind at 24.6 mph (11 m/sec). The wind pressure at 24.6 mph is 1.55 lb/square foot, or on our 8 foot diameter piece of plywood a total force (thrust) of 77.8 lbs.

So a turbine rotor can convert 85% of the wind's total amount of force into direct axial thrust? I don't think so. At the most a real efficient rotor might slow the wind 40% and convert some of what it captured to shaft power and the remainder (due to drag) to direct axial thrust. It's no wonder people's turbines only furl correctly after some trial and error, or by following a set of plans that have been debugged in the past with trial and error, as far as furling.

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Chris

Beaufort · « **Reply #1 on:** February 24, 2010, 01:54:23 PM »

What is the electrical power at 24.6 mph? And what is the TSR? I've been using IEC 61400-2 formulas for these calculations and the amount of thrust depends in part on how much power is extracted (makes sense). I can try to run your numbers through what IEC says to use.

Flux · « **Reply #2 on:** February 24, 2010, 02:10:22 PM »

I have come to the conclusion that a prop has a thrust loading that is virtually Cp times the disc thrust loading. It is probably higher than this due to inevitable losses but from guy wire loading that I have measured the thrust of a normally loaded prop is typically half the disc loading.

Even if you allow for all this the sums still go wrong because there is a seeking force defeating the thrust component. You may be able to fairly accurately calculate the thrust but the seeking force depends on so many factors that I see no hope of dealing with it.

I think one case where things go wrong is with machines running well stalled, the thrust will be way below the disc loading but if the thing pulls through stall the thrust loading will go up very considerably. This would imply that it ought to continue furling and be very safe. In real life this condition almost always seems to end up with a large increase in seeking force and the thing increases output to the burn out point before furling kicks in ( if it ever does).

At best the equations will only give you a starting point so start with a much lighter tail than predicted to be on the safe side and beware that if you choose an offset that is too small it will never furl at all no matter ho light you make the tail.

Flux

fabricator · « **Reply #3 on:** February 24, 2010, 03:18:25 PM »

That 77lbs sure seems low, an eight foot disc in held perpendicular to a 24 mph wind only has 77 lbs of thrust on it? I find that very hard to believe.

ChrisOlson · « **Reply #4 on:** February 24, 2010, 04:06:04 PM »

That's taken from the standard building code and calculations for figuring direct-on wind load on structures, and the constant assumes air density at sea level. It goes up pretty fast as the wind speed increases. For instance, at 50 mph wind speed in a thunderstorm, or whatever, that same 8 ft (50.24 sq ft) circle would have 6.4 lbs/sq ft, or over 320 lbs of total force exerted on the 8 ft circle.

If you think about a 4 x 8 sheet of plywood in a 24 mph wind, 32 sq ft, the formula says there would be 47 lbs of force on that sheet. I can find that believable. I've handled plywood sheets like that in 20-25 mph wind before.

Try this if you don't believe it. Put the bathroom scale on the wall and push on it until it says 47 lbs. It takes more effort than you would think when you're dealing with a horizontal force like that. I'm not any little dude by any means, and the most I could push on it, with a steady push and hold it there, was around 80 lbs. The reason I tried that today is to have no doubt in my mind that there's no way a 8 foot turbine rotor can make 66 lbs of axial thrust @ 25 wind speed.

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Chris

ChrisOlson · « **Reply #5 on:** February 24, 2010, 04:22:37 PM »

Well, here's what happened to me. I replaced the blades on my 7.6 footer with these new PowerMax blades I got (It's now an 8 footer). It used to furl at 24 mph. It doesn't even try to furl at 24 mph anymore, with a bigger set of blades on it that should make more thrust than the old ones, and we got the wind yesterday to try it. I haven't determined the furling point on that thing yet with these new blades on it. And the blades was the only thing I changed.

I can monitor that turbine really close because the controls are right in my shop office. At 24 mph yesterday on my little anemometer it was putting out 55 amps and the batteries were right at 14.5 volts. The loaded TSR on those blades is supposed to be 6. As I mentioned in another post on another topic here, I need to tighten the air gap on the generator a bit on that turbine after putting those blades on, because they're actually running at around 7 TSR in the 18-20 mph range and they fall off a bit as the wind speed picks up. Unfortunately I didn't have my AC frequency meter hooked up to it yesterday to figure out how many rpm it was turning to precisely calculate the TSR. But I know it's more than 6 with the way the generator is set right now. My rough guess, at the point where I wrote down the data in my chart, is that they were probably at around a 6.5 TSR.

And at that 24 mph wind speed that I recorded the 55 amps at, it's pretty much identical to my old blades. I looked back thru my chart and I got three different times that I recorded 52-55 amps at 24 mph in the last two months.

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Chris

ChrisOlson · « **Reply #6 on:** February 24, 2010, 04:48:54 PM »

Even if you allow for all this the sums still go wrong because there is a seeking force defeating the thrust component. You may be able to fairly accurately calculate the thrust but the seeking force depends on so many factors that I see no hope of dealing with it.

Exactly. I'm building my 21 foot turbine in the shop right now - got the head built and waiting for the generator rotors to get waterjet cut. I think the furling tail is very reliable if you're dealing with known factors, and following a specific set of plans from somebody who has built one before. But when I changed blades on two of my machines in the last week and get completely different furling results, just with a blade change, it's impossible to arrive at any sort of concrete conclusions as far as tail weight, tail boom length, etc., and have it furl where it's supposed to.

I started building an electric yaw drive for this machine, then scrapped that idea as being too complicated from a reliability standpoint. So I'm back to a tail. But I think I'm going to take a cue from Jacobs on this one and use a spring loaded tail on a double vertical hinge - just because it's easy to set it at low spring pressure and let it furl early. Then crank the spring up a bit at at time until it furls at 22 mph, which is where I'm going to limit this one.

This is the biggest machine I've ever built, and I don't feel comfortable using the "standard" calculations for furling on it with an inclined tail hinge and using tail weight to set it. I want to use a long enough tail to have good steering control in gusty winds. But getting the tail light enough when you add 4 feet in length is a challenge. So I concluded that hinging the tail horizontally and using a spring to replace gravity and tail weight is probably safer. Jacobs has done it for years and it works for them.

Having a little 8 footer runaway is exciting. Having a 21 footer runaway could be disastrous.

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Chris

fabricator · « **Reply #7 on:** February 24, 2010, 05:38:52 PM »

Chris I hate to admit it but I forgot the name of the guy who carves those custom blades, could you remind me? Anyway what do you think about those blades?

ChrisOlson · « **Reply #8 on:** February 24, 2010, 06:46:07 PM »

His name is Dave Moller at Royal Welding and Fabrication, and he's got a website here:

http://www.royalfabrication.com/

Those blades are what I'm using on my 21 when it get it done. DaveB runs them on his machine and they got torque up to yin yang. He can probably tell about burning up his genny with Dave M's 18's and de-rating to 16's to keep the smoke inside the generator where it belongs.

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Chris

Beaufort · « **Reply #9 on:** February 24, 2010, 06:51:10 PM »

OK, so we're looking at about 800W at 24.6 mph, 8 ft dia, 6.5 TSR. The thrust loading on the shaft in the direction of the wind according to IEC is about 60 lbs (Delta Fx-shaft). They also give formulas to use for the maximum design force assuming a Class 4 site (for example), in this case it's 124 lbs (Fx-shaft). That's the maximum force to be expected for all wind speeds over a 50-year span (from what I understand).

ChrisOlson · « **Reply #10 on:** February 24, 2010, 06:54:12 PM »

Where do they have the calculator, or formulas to figure this out?

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Chris

ChrisOlson · « **Reply #11 on:** February 24, 2010, 07:00:23 PM »

And by the way, that blade profile those custom blades have has flown on Winchargers for over 70 years. It's very similar in shape to the PowerMax S809's that I got recently. Note I said similar - it's not the same. Dave M's blades use a Gottingen 222 profile. But it has many of the same characteristics of the S809, which is mainly that they put out more power and torque at lower wind speeds.

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Chris

fabricator · « **Reply #12 on:** February 24, 2010, 07:00:41 PM »

Thanks Chris, that is the way I'm going on my next machine, I'll be following your progress as I plan on a twenty something next, it is almost double the output of a 17' from just another 3' in diameter.

Beaufort · « **Reply #13 on:** February 24, 2010, 07:15:32 PM »

They make you buy the specification to get the formulas (about $250 or so). 61400-2 is a great one to have, and worth the money for what I'm doing. They pulled together the great minds in wind turbine theory and came up with these formulas and many include empirical corrections so they work in the real world. I've got them all loaded into a spreadsheet to play around with the variables to see what changes have the most effect on blade and machine loading. One of the more useful numbers is related to gyroscopic forces as a turbine yaws..as we know this can cause many problems with furling and bearings, gaps, etc.

But...prop-seeking force doesn't seem to concern IEC as it's not in there that I can tell.

Perry1 · « **Reply #14 on:** February 24, 2010, 07:45:43 PM »

Hi Chris,

Here is how I calculate thrust forces.

The formula is defined as;

Ft = 2 x rho x V^2 x a(1-a)x Area

Ft = thrust force

rho = air density

V = velocity

a = axial induction factor

Area = well, um, area of your rotor

The key to incorporating the amount of power your turbine is capturing from the wind and differentiate away from the piece of plywood analogy is the axial induction factor. For a rotor operating at the Betz limit a value of 1/3 is used for 'a'. This is usually done to include a factor of safety, assuming you are pulling the max energy out of the wind. When trying to determine furling forces you are looking for an actual value as opposed to a conservative one. For this situation an axial ind factor of .091 represents a rotor CoP of .30, which I think you will be working at. There are further formulas to calc the AIF so knowing the term, you can Google it now.

As stated by Flux I believe, there are times of nuance where this breaks down such as stall conditions or overspeed conditions.

Perry

Perry1 · « **Reply #15 on:** February 24, 2010, 07:54:13 PM »

I'm usually not a big fan of wikipedia but they do have a pretty good page on the axial momentum theory as well as the blade element method

http://en.wikipedia.org/wiki/Wind_turbine_aerodynamics

Perry

ChrisOlson · « **Reply #16 on:** February 24, 2010, 09:14:09 PM »

Thanks Perry. That was some interesting reading.

As I said, I'm using a furling tail system on my 21 but I'm going to use a apring loaded tail as apposed to using gravity against the weight of the tail on an inclined hinge. I still need to come up with a close estimate of rotor thrust on this beast so I can decide how big of a spring to use.

I just built the tail boom and hinge tonight. The tail boom is 14' from the hinge to the end of the boom and it will be 16' from the hinge to the end of the tail fin.

If I know the amount of rotor thrust it will make I figure I can set the furling point in the shop by bracing the tail against the wall with the turbine on my test stand, pull on the rotor axis with a spring scale to simulate the thrust and adjust the spring so the tail starts to "break away" and furl at the right amount of pull on the scale. Then back the spring off a few turns for a safety cushion to fly it the first time.

The longer the tail is, the more smoothly it will furl with a spring loaded tail. But it's still going to take a pretty stout spring. A few minutes ago, before I came in my office for a cup of coffee, I was swinging the tail with the turbine head on the test stand and where I plan to weld on the spring anchors it looks like I'm going to need a spring with about 12" of travel.

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Chris

Perry1 · « **Reply #17 on:** February 24, 2010, 09:28:10 PM »

Yes Chris, I am aware of what you are trying to do as I follow your posts. Using the formula I provided you can calculate your your thrust forces well enough. As with all things such as this there will be a fair amount of building and testing to bring it from an outer ring to a bulls eye.

Perry

ChrisOlson · « **Reply #18 on:** February 24, 2010, 09:57:41 PM »

Thanks for that. I'll use that to figure the thrust and go from there.

I went and did some more figuring on this deal and I came up with another idea. If I use a compression spring I can build a cylinder with the spring in it and put an adjusting screw in the end of the cylinder. If any of you guys have ever raced stock cars it's called a "weight jack". Just turn the screws on the springs to set the wedge for the track. The more you crank the weight jacks, the stiffer the spring rate. Same principle.

If I do it that way I can go from fully flying to fully furled with only 8" of spring travel. And it will also be a built-in tail stop so the boom can't fly around and hit the blades.

I think I came up with a way to figure the starting point for the spring rate. Let's say you have 12" of rotor offset and you have a 100 lb thrust force. I'm using round numbers for easy figuring. That's 100 lb-ft of torque at the yaw shaft being applied by the rotor. Let's say, for sake of argument, that this is the calculated furling point. The spring loaded tail has to apply that same amount of torque in the opposite direction to keep it flying.

The tail hinge is now the yaw shaft because the hinge has a zero degree angle and the tail hinges directly on the yaw tube. If I attach one end of my compression cylinder on the offset bracket at 12" from the yaw shaft, and the other end to the tail boom, the spring has to have 100 lbs of push to balance the rotor thrust. If the rotor thrust exceeds the 100 lbs it will overcome the 100 lbs of counteracting push on the same point by the spring cylinder, and it will furl.

Feel free to tell me why it won't work :-)

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Chris

Flux · « **Reply #19 on:** February 25, 2010, 12:19:12 AM »

Perry

"Hi Chris,

Here is how I calculate thrust forces.

The formula is defined as;

Ft = 2 x rho x V^2 x a(1-a)x Area "

The thrust on a disc is 1/2 x rho x A x v^2. If you use 2 then your figures are 4 times too big. Apart from that it looks fine.

Flux

Perry1 · « **Reply #20 on:** February 25, 2010, 12:43:43 AM »

I would be a brilliant man if it were not for typo's............ :-)

The axial induction factor is what integrates the Cp relationship that you spoke of above.

Perry

dlenox · « **Reply #21 on:** February 25, 2010, 04:59:17 AM »

Me TOO!

I'm so glad that my 17'er is down for this wild winter, and that others are really charging ahead to work out some of the design stuff to get these large machines to furl.

Gosh I never would have believed that changing blades could affect furling. With that impact I don't see how any body can build a large machine from known design specs and have it properly furl....

I'm waiting till spring till I get mine back up. Maybe by the time Dale (fabricator) has his up I will learn some more about this condition.

Dan Lenox

ChrisOlson · « **Reply #22 on:** February 25, 2010, 08:40:20 AM »

I've been reading this thread:

http://www.fieldlines.com/story/2009/1/29/71849/8735

And looked at Steven Fahey's very excellent tabular data here:

http://www.sparweb.ca/Wind_Turbine_Comparison.htm

I'm arriving at some more useful figures after studying this a bit and punching the calculator keys. I've typically used my 8 (formerly 7.6) footer as a test bed for new things. I'm going to pull it off the tower this afternoon because I need to set up the generator air gap anyway, and it doesn't furl properly with the new blades.

While I got it off the tower I'm going to cut the tail hinge off it, build a new zero angle hinge like I got on my 21 foot head, use this new data that you guys have pointed out and see how close I come to getting it to furl at 24 mph with a spring loaded tail.

If I can work out what I need for a starting point for spring pressure on the smaller one, hopefully I can scale it up to the big one. The key here is knowing EXACTLY what the rotor thrust is, fully loaded at the point where it's supposed to furl. As flux pointed out in the previous thread:

It's nice to be able to reduce these things to formulae but unless you can account for all the factors the answer will not be very exact. Fluid dynamics is a tricky subject and seems to contain more constants and fiddle factors than most other branches of science.

If Steven Fahey is listening in, is there anyway you could email me that interactive spreadsheet so I could play with it directly in Excel without having to go thru my web browser?

Thanks, guys.

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Chris

fabricator · « **Reply #23 on:** February 25, 2010, 08:56:00 AM »

One question I have is what about partial furling? Are you calculating your spring to start furling like 25% below full furl? I guess what I mean is so it's not an all or nothing situation.

ChrisOlson · « **Reply #24 on:** February 25, 2010, 10:23:14 AM »

I'm going to use a constant rate spring so the pressure doesn't change from full extension to full compression of the spring. What I want to do on the 21 is set it so it starts limiting power at 22 mph wind speed, running partially furled. By 25-26 mph, and above, rotor thrust increases quite a bit even running partially furled and it should fully furl and stay furled. In fact, I've thought about incorporating a latch in the spring cylinder so if it fully furls it just stays latched like cranking the tail on a Bergey. And to make it fly again I'd have to pull a cable hanging down the tower to release the latch and let the tail steer it again.

I've pulled on the tails with a spring scale on my other machines that have an angled hinge and the pull rate from flying to fully furled is pretty constant on the scale. So I don't think I'm re-inventing the wheel here - just using a different, and what I think is a more adjustable method, to control the point where the tail starts folding up.

Like I said, Jacobs has been using these spring loaded furling tails for quite a few years and they work really well for them. They use the spring loaded tail with an offset rotor axis to govern power in moderately high winds, then their governing variable pitch hub kicks in in really high winds to feather the blades and stall it. Plus they have a mechanical disc brake to keep it parked, which my 21 is also going to have. But I think I may copy your brake design, which looks to me like a very simple, powerful and effective turbine brake.

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Chris

fabricator · « **Reply #25 on:** February 25, 2010, 11:00:44 AM »

Copy away, but make sure you take lots of pics of your spring design, I'm liking this idea a lot.

Flux · « **Reply #26 on:** February 25, 2010, 11:03:23 AM »

Perhaps I can offer one little bit of advice that I have found the hard way over a lot of years. Don't assume that because the tail moves from its stop you are starting to furl.

There is negligible drop in power up to about 30 deg to the wind so you won't see any effect until the tail is at about 45 deg.If things are working you will then find power tailing off or falling. If it still keeps rising you can bet you are not furling.

If it seeks the wind rather than turn the blades at an angle of 45 deg or more then it will not reduce power. Don't ask me to explain why but I can assure you it is possible to have a tail at 90 deg to the normal position and still have the blades pointing sufficiently directly into the wind to produce power well beyond what the alternator can handle.

Base your observations on the angle between the alternator shaft axis and the true wind direction observed from some other device and you will be ok.

I suspect that at some critical angle to the wind one side of the blades go into stall and from this point onwards the seeking force starts to disappear. if you don't somehow reach this point it will seek the wind harder than the thrust against offset moment can turn it away.

Keep us updated on progress.

Flux

ChrisOlson · « **Reply #27 on:** February 25, 2010, 11:08:52 AM »

Will do. I'm pulling my 10 footer down this afternoon now that it got above zero degrees here. As soon as I get it in the shop I'm going to cut the tail hinge off and build the same tail I got on the 21 on a smaller scale.

Hopefully, by later tonight sometime, I should have a spring cylinder designed and built for it to test as a "prototype". I'll take some pictures of it and upload them so you can look at it and see what you think.

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Chris

ChrisOlson · « **Reply #28 on:** February 25, 2010, 11:22:52 AM »

Thanks for that tidbit, flux. That's why I'm going to try this on one of my smaller machines first. I have a good idea of what they put out for power and how they've acted in the past.

One thing I think I have going for me is that I build a lot of "lead" into the rotor hub. In other words the rotor is quite a ways forward of the yaw axis. It's 14.1" ahead on the machine I'm going to experiment on. This helps with furling quite a bit. If it steers about 10-15° out of the wind the effective offset increases because of the "lead" and aids it in continuing to yaw to a point where it reduces the power. It also makes it harder to steer it back into the wind, which I don't consider to be a bad thing. If the wind is blowing that hard I don't really want it getting snapped around back into the wind and spooling the rotor back up anyway.

At any rate, since I've started doing that, my machines furl much more smoothly than they did with the rotor set back more. On one of the first machines I built it would come out of furl so fast sometimes in gusty conditions it would just about break the tail off it.

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Chris

ChrisOlson · « **Reply #29 on:** February 25, 2010, 11:40:22 AM »

That was a typo. I'm pulling my 8 down, not the 10. I would be ashamed to show you guys how I'm flying my 10 footer right now. I got it on a 21 foot piece of Schedule 40 pipe that's bolted and guyed to a hay wagon (thrower rack) and parked out in the field where the full wind blast can get at it.

It's kind of crude, but it works in a pinch until I can set a decent tower in the spring.

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Chris

scoraigwind · « **Reply #30 on:** February 25, 2010, 02:36:59 PM »

Chris,

"Rotor Thrust = diameter squared * wind speed squared / 24.....

So a turbine rotor can convert 85% of the wind's total amount of force into direct axial thrust? I don't think so. "

I derived this simple equation from the Betz analysis of what happens and so it's only a very idealised simplification. But this thrust is correct to extract the maximum energy from the swept area of the rotor (by slowing the wind down the correct amount). It's a very different situation from wind pushing on a flat surface. The real world is actually much messier and less predictable than Betz's analysis, but it's a good starting point for applying rules of thumb.

Finding the exact thrust is probably an endless task since it will depends heavily on the tip speed ratio etc and it not fixed. And even if you do manage to get a handle on it, the job is not nearly done, because a large part of what influences furling is the movement of the centre of thrust away from the centre of the rotor when it runs in yaw. I have seen a machine with a small offset pull itself into the wind and run briskly with no tail at all.

Most people used to start off with a spring on the furling tail and then realised that gravity is more reliable and also has a constant rate. You seem to be going in the opposite direction so maybe you know something the rest of us have missed.

It's good to have a fresh mind and a vigorous experimenter on the job. Have fun.

ChrisOlson · « **Reply #31 on:** February 25, 2010, 06:18:38 PM »

Well here it is - a prototype furling control cylinder on my 8 foot machine.

Here's a photo of the cylinder disassembled on the bench:

Here's a photo of the cylinder assembled on the bench:

And here's a photo of it installed on my test 8 foot machine:

And finally, you can watch this little video of me demonstrating and explaining the thing:

http://www.youtube.com/user/OlsonFarms

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Chris

ChrisOlson · « **Reply #32 on:** February 25, 2010, 07:00:11 PM »

Hugh, I'm not trying to re-invent the wheel. I just want something that's easily adjustable right from the yaw shaft. With my experimental spring cylinder all I have to do is climb the tower with a 3/4" wrench and make a few turns on the adjusting screw. Hanging out there on a sky hook to change tail weights is a pain.

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Chris

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Author Topic: Furling Calculations (Read 8260 times)