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Forum Index : Windmills : Calculating wind mill power

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VK4AYQ
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Joined: 02/12/2009
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Posted: 11:13am 28 Apr 2010
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Question from Gordon re method of testing power.


I quote from your own testing :-

"A rotor 3 meters in diameter and 4 meters high with six airfoil blades gave on a test 600+ ft pounds torque at 125 rpm gave maximum horsepower reading of 14.25 hp and at 75 rpm 3.6 hp this was at about 5 mph wind or at around 2.6 mtr sec."

Perhaps you could explain how you obtained the 3.6hp output power, from a rotor 3m dia and 4m high in winds of 2.5m/s.

BTW the total energy in the wind at a velocity of 2.6m/s and a cross sectional area of 12m^2 is only, approx 170W.

Perhaps, supplying the formulae you used for calculating the power can shed some light on this difference.

Gordon.
Edited by VK4AYQ 2010-04-29
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VK4AYQ
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Posted: 11:19am 28 Apr 2010
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Previous entry is an entry from Gordon on our discussion for calculating power output of windmills.

Gordon has suggested this new thread to save obfuscation on Gizmos new wind mill site so please add your comments on and suggestions for calculating power both horsepower and watts out of different blade combinations in both HWT and VWT.

All the best

Bob
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VK4AYQ
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Posted: 11:23am 28 Apr 2010
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Reply to Gordon


  VK4AYQ said   Hi Gordon

The 3.6 hp was a typo error by late night brain death I have recalculated it to be 2.4 hp compared to nearly nothing from my design.



Also we didn't have an accurate wind speed reading at such low wind speed it was estimated from a vain that frank designed for low speed.

The windmill we tested was a experimental machine designed by an aeronautical engineer friend of mine unfortunately now deceased.

The blade design was a six blade rotor with special aerofoil blades 12 inch cord with vortex generators on upper and lower surfaces of the aerofoil this nearly doubled the torque from the ones that I was building at the time.

The horsepower was calculated by a 12 inch arm connected to a disk brake on the mill shaft to get foot pounds of torque. this was monitored by a shaft rev counter to monitor rpm with loading on the brake monitored so there was no constant reduction in rpm during the test the free running blades where faster than the test rpm, it was difficult to load the blades evenly at such slow rpm but it was done many times to get some meaningful average.

The power formula used to calculate horsepower was; rpm x ftlb torque divided by 5252
At the time we did so many calculations that the formula has stuck in my head ever since.

The mill produced nearly double the torque at low rpm to my design but as the rpm increased the the power increase dropped off but was still there, The significant factor I believe was the increase of power at low revs, I believe that the constant airspeed over the entire length of the blade is like having a constant TSR on a HAWT optimized by the vortex generators both sides of the blade this I believe gives twice the energy into the blade by extending the degrees of the arc that the blade is flying and creating lift.
In a HAWT the working section of the blade is only 25 to 30 percent at ideal loading and TSR so the inner section is only there to hold the outer section to the hub in a non twisted blade it does however work to get the blade started and produces some power at low rpm. The fact that it does work as well as we know is the cube rule in wind velocity and the power transmitted therefrom

His design for vortex generators is now used extensively on aircraft to reduce drag and increase lift, I believe it increases the effective cord of the aerofoil and increases the stall angle significantly hence a lot more lift energy from the aerofoil.

I know from sad experience that the torque of the VAWWT is enormous even at relatively low revs and the stored energy in the rotor due to flywheel effect evens out the power produced by the rotor.

Hope this clears things up a bit

All the best

Bob

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GWatPE

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Posted: 12:06pm 28 Apr 2010
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Hi Bob,

I still have a problem with 2.4hp.

The Kinetic Energy of a cross section of wind [moving air] of 12 square meters is known.

Here are some wind energy figs. for this sectional area at different wind velocity.

3m/s gives 210W
4m/s gives 490W
5m/s gives 970W
6m/s gives 1.67kW
7m/s gives 2.65kW
8m/s gives 3.95kW

etc

Even if the VAWT was the same efficiency as a HAWT, then say at a generous 40% rotor efficiency, then the windspeed would have to have been above 8m/s to give a shaft power of 2.4hp [approx 1.7kW]

Is it possible the windspeed measurement was this far out. Can you indicate how the ftlb was measured.

I would imagine that if the power was as much as you have quoted, then you would not be on this forum but swanning about on the proceeds from sales of rights to build these windmills, and we would see them everywhere.

Gordon.


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oztules

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Posted: 12:33pm 28 Apr 2010
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Power AVAILABLE in the wind = .5 x air density x swept area x (wind velocity cubed)

Air density = 1.23 kg per cubic meter at sea level. Swept area = pi x r squared (hawt)or width X height (Vawt) (meters).

Your 12sqm turbine=.5 x 1.23 x 12 x2.5 m/s ^3

or .5 x 1.23 x 12 x 15.625 = 115.3 watts

From that I would expect well less than 25W for a big vawt.... barely enough to overcome the bearing loss on a big machine.

Now to get a few HP at the shaft with everything going well would be probably .2 X power in the wind for a Vawt... or 1800 x 5 = 9000W For 12sq meters, that would be nearly 11m/s winds. You'd notice the difference from 6mph ~(2.5m/s)

If you ignore Betz (59% with a perfect airfoil) and had a 100% rotor (not possible in this universe) then ~6 to 7m/s

Your aeronautical man should have questioned the results immediately. Nothing is for nothing in the energy stakes. [quote] I have recalculated it to be 2.4 hp compared to nearly nothing from my design.[/quote] your design was probably closer to the truth

...........oztules.

Edit... I can't seem to even agree with Gordon's figures I make 3m/s= .5x1.23x27x12=199 watts and so on Edited by oztules 2010-04-29
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GWatPE

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Posted: 02:54pm 28 Apr 2010
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Hi Oztules,

I was a bit lazy and just punched the m/s numbers into a wind energy calculator provided a while ago on the forum. I had assumed the calculator was pretty close. I would normally multiply it out as well. I suspect there may be a problem with the calculation for the torque. Bob should be able to clarify the test data.

Gordon.
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VK4AYQ
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Posted: 03:58pm 28 Apr 2010
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Hi Gordon And OZ

I have looked at my notes on the testing again and the only thing I can see in the testing that could be the variable is the wind speed indication Frank used was calibrated in error as at low wind speed it is very difficult to be accurate with a wind vane ASI.

The foot pound device I made to measure torque was a disk brake on the main shaft that is used to stop the mill for service and high winds, it was demounted and connected to a 12 inch moment arm that was connected to a 1 to 1 bell-crank which acted on a set of 1000 lb platform scales, I tested this and it was quite accurate. it was activated by a hand operated master cylinder.

My original blades where Clark Y airfoil section with a 10% thickness ratio and in testing on the same frame they started in a slight breeze but didn't produce any useful power until the wind sock was at 45deg around 5 to 6 knots I would estimate and increased from there. The brake system wasn't powerful enough to measure high speed wind as the brake smoked up to quickly.

When we fitted Franks blades I modified the brake into a twin rotor and caliper system for torque measurement.

The rpm measurement was with a shaft rpm meter that went onto the pinion and then divided by the step up ratio.

Franks blades where a semi symmetrical section that he designed with a 20% thickness ratio.

The effect of these blades was dramatic at low speed but decreased as wind speed increased, His explanation to me was that my blades where only lifting on one surface, the outer one over a 16 degree angle of the rotation of the blade and the rest of the time acted as wind resistance blades adding only a very small amount of power if any.
His blades worked over twenty five degrees due to the vortex generators and worked on both side of the blades so as the blade rotated into the apparent wind the outer section of the blade started working at a angle of attack around 20 degrees while the back of the blade worked as a deflection plate, as the blade rotated the outer surface generated lift until it was at negative angle to the relative airflow by this time the inner side of the blade was gaining lift and maintained lift until it stalled at around 25 degrees The two downwind blades I believe didn't contribute any power as they where going faster than the apparent airspeed for 180 degrees. Allowing for the apparent wind being deflected as it went through the rotor there where three blades out of the six producing positive power at all times.

On top of this whole contraption there was a small savonius rotor to get the machine spinning it was six foot dia by four foot high It may have contributed a small amount of power at low speed but I never measured it.

I had a small scale mill that we built as a prototype on the roof of my workshop for years it produced around 200 watts in a breeze, I took it down to keep when I sold the workshop but it got destroyed in the move to QLD.

We where going into manufacturing these machines but the farmer market was taken over by the roll out of rural SWER line power so they took the cheap option, and if they needed a small mill they would cut some drums in half and make their own. Also at the time I got involved in the assembly and commissioning of a paper pulp and saw mill so never did any more with wind at the time, its only since retirement that I have taken an interest in wind mills again, in the past energy was so cheap there wasn't any point playing with mills, now it is a point of interest again. More a hobby really as wind is scarce where I am.

All the best

Bob

Edit
I forgot to mention that the wind vane was mounted six feet above the ground only and the center of the blades was 20 foot above the ground so the wind speed would have been a bit more at that height so that may make a difference.Edited by VK4AYQ 2010-04-30
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MacGyver

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Posted: 03:29pm 29 Apr 2010
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Just curious:

Why were vortex generators installed on these blades? Were the blades set at a stall angle? Can't for the life of me figure out why this would help a wind-driven rotor; seems to me it would just add drag.



. . . . . Mac
Nothing difficult is ever easy!
Perhaps better stated in the words of Morgan Freeman,
"Where there is no struggle, there is no progress!"
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VK4AYQ
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Posted: 10:20pm 29 Apr 2010
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Hi Mack

The vortex generators give a larger arc of positive lift of the blade from 18 to 28 degrees on the upper surface and from 10 degrees to 28 degrees on the lower surface
This allows the blade to convert wind energy to rotational energy for a larger portion of the rotation of the VAWT This is of course in conjunction with a special aerofoil designed to optimist the effect.

This increase on the six blades makes a significant increase in the low speed torque of the mill.

The effect would be less pronounced in a HSWT as the blades are in a lift situation for all of the rotation of the blade the vortex generators on the lift surface of the blade, they would lower stalled speed of the blade making the blade unstall at a lower rpm, the vortex generator on the lower surface would only contribute blade drag, mind you this could be useful to help control runaway in high winds. This I theorize as I have never tested it.

Yes they do increase drag at higher speeds but there is enough energy to spare at these revs to make up for the extra drag the quote below is from Gordon to show energy increase as the wind speed increases.

As I said before it may be useful to control blade speed to some extent.

Here are some wind energy figs. for this sectional area at different wind velocity.

3m/s gives 210W
4m/s gives 490W
5m/s gives 970W
6m/s gives 1.67kW
7m/s gives 2.65kW
8m/s gives 3.95kW

The energy in wind speed is increased by the cube rule.

Hope this has cleared it up a bit

All the best

Bob
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GWatPE

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Posted: 01:39am 30 Apr 2010
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Hi Bob,

You seem to be quoting me, suggesting that I am supporting your data. This is not the case.

I still see no way that your data can be backed up by physics. There just isn't enough energy in 2.6m/s wind to produce 2.4hp for the rotor size you quoted.

As I implied before, If this VAWT was able to do what you have stated, all windmills would be built this way. They aren't, as we can see.

You are talking about over an order of magnitude more power than that available. Vortex generators/inhibiters may provive a percent change.

I think the makers of the A380 have reduced the wingspan by several meters. in about 80, by the addition of vortex eliminators, to increase lift [the wing tip mods]. A vortex generator, to increase drag may have a similar effect the other way.

I do think there is some problem with the measurements, or formulae you have used, but you will only be able to confirm this.

Gordon.

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VK4AYQ
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Posted: 03:04am 30 Apr 2010
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Hi Gordon

If you read the entry as intended you will find that I was referring to the increase in wind speed giving extra power at the cube of the speed not saying that you sanction my HP output.

The previous post gave a reason for the apparent problem with wind speed measurement and its relation to the torque would be magnified by small inaccuracies in the measuring thereof.

If you feel there is a problem with the torque measurements please let me know as I would appreciate your input.

On the airspeed measurement I can see problems with the way it was done as I said in the previous entry.

A vortex eliminator has the opposite effect to a vortex generator it decreases the drag on the blade while a vortex generator increases the drag but increases the lift by increasing the angle of attack before stall sets in, as a large HSVT operates at near constant TSR the effect of vortex generators would detrimental.

A vortex eliminator on our type of mills would also encourage speed runaway not good.

All the best

Bob

PS" the effect you quoted on the vortex eliminators reduces drag not increases the lift of the aerofoil allowing it to produce more power per span therefore to produce the same power the span can be reduced as you noted.Edited by VK4AYQ 2010-05-01
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GWatPE

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Posted: 06:38am 30 Apr 2010
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Hi Bob,

I would hope the data was increasing at the cube rule, as this was how it was calculated.

I do think you would know if the windspeed during the measurements was close to that indicated by the measuring device.

If you look at the numbers, your test windspeed would need to be closer to 8m/s than 2.6m/s, for the machine you describe to produce 2.4hp.

I think you would notice this difference.

Speed runaway is more related to loading mismatch.

I would like to see a report that is supported by physics and objective experimentation. As you have the windmill, this should not be difficult to replicate.

Gordon.


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VK4AYQ
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Posted: 07:58am 30 Apr 2010
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Hi Gordon

The wind speed is the point that I am not sure of now as the height difference between the wind vane and the blades would have made some difference but not the amount in question, as it happened around 35 years ago all I can be sure of was the notes Frank and I made on the tests and weather he recorded the speeds in mph or knots isn't stated, I don't think it would be in mps as I never remember him using metric.

Unfortunately the windmill was left in Victoria when I moved to QLD I am now building one for myself but don't have the specs for his blades so cant duplicate it exactly.

I am using a naca non critical laminar symmetrical airfoil 10 inch cord, 25% thickness ratio will do a test, with and without the vortex generators and now I have a wizz bang airspeed indicator to check it with. I hope to have it finished to grab the august windy weather we get here, but the F&P has to go up first.I have ordered a radio link weather station that records everything onto the laptop so should have some hard data recorded on that only have to work out how to synchronize the torque readings with it to get graphs.

All the best

Bob
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