Wind Force and Power Calculation

[Alkemi]

Let's assume we have swept area of 3 meter diameter for turbine and use profile blades with blade area as 0.092 meter square each.

We can calculate the total power available in 3 meter diameter swept area as [P = 0.5 * rho * A * V * V * V* Cp ]

If I use 3 blades, how can I calculate the force or power generated at 10 m/s speed?
If I use 6 blades, how can I calculate the force or power generated at 10 m/s speed?
If I use 12 blades, how can I calculate the force or power generated at 10 m/s speed?

My intention to ask this question is, how blade numbers / or blade surface area affects power generated or is calculated?

I know Cp is max 0.59, but how it is related to number of blades or area, so I can get results if I change number of blades.

Thank you.

[bigrockcandymountain]

The short answer is the power output will be the same no matter the number of blades.  Same calculation.  Same formula.
 Swept area is the thing that determines power.  More blades are generally less efficient except in purely theoretical cases.  I would put the Cp at .3 if you use a tapered, airfoil blade.  You won't get .59 ever with a 3m diameter.  The large machines can come close because the larger reynolds numbers of their wider chords make them more efficient.

I built a very normal looking 3 blade that is almost 4m diameter.  Would i go to 6 blades or 12 blades? No.  The only problem with 3 blades is they are boring and look like you didn't try at all to be creative. 

The starting torque will be higher with a larger chord or more blades or both.  That only matters if you have a hard to start generator.  I used a wider than optimal chord because my generator does have some sticking torque to overcome.

[SparWeb]

Hi Alkemi,

The Cp varies a lot, running at different wind speeds.  The loading from the generator also affects the Cp (the load profile of the generator should match the power profile of the blades, but this is difficult to achieve).  Gusts in the wind also matter, because if the blades are constantly speeding up and slowing down to adjust to the varying wind speed, then they aren't at any optimal power balance.  And the TSR varies, too, for mostly the same reasons.

So what to do if you want to estimate Cp?  You can use results that others have worked out for similar wind turbines.
Here's some info about my machine:  https://www.fieldlines.com/index.php/topic,147962.0.html
And results I'm getting from the data log:  https://www.fieldlines.com/index.php/topic,149585.0.html

The question of number of blades has a certain effect, but not a very strong one.  Economics is stronger.  More blades cost more to make.


BRCM,

The only problem with 3 blades is they are boring and look like you didn't try at all to be creative.

Then paint them pink!

[Alkemi]

Thank you for valuable inputs. So in a nutshell what I understood is, there is no specific formula, in which we can consider the area of blades itself vs swept area. Increasing number of blades or air contact area doesn't improve the power output of the Windmill is what I understood from your statements.

The reason I'm asking these questions is I'm arguing with one inventor, who is claiming more output from his 12 blade, fully overlapping swept area Windmill than regular 3 blade windmills. I'm having hard time to convince him about his efficiency can only go up to .59 factor but not beyond that. Which means over 3 blades, he may get only up to 20%-30% more efficiency, if at all he gets it. But he doesn't seem to listen. He has built a windmill with 12 blades, the blades if we look from front looks like fully closed, but they have angle, so air can pass through it.
It has 6 ft diameter swept area and can generate 1000 watt at 30 MPH.
I have asked him to verify it with same sized 3 blade turbines, but then I realized we all have tried it and can get results from you without building it in reality.
Today we are testing 1.2 meter diameter mill to compare results. But we don't have 6 or 8 ft diameter windmill, so if anyone have their Mills tested at different speeds, it will be easy for us to compare each other's claims.

For his 6 ft diameter windmill, he get 200 volt output at 35 mph at no load condition. If loaded with 1500 watt Hairdryer, it gets about 56 volts.

[bigrockcandymountain]

If he is only getting 56 volts on a hair dryer he is not getting 1000w. 

Say the hairdryer is 120v 1500w. That means resistance is 9.6 ohms.

At 56 volts a 9.6 ohm resistor will draw 327w. 

If it is a 220v hair dryer it gets even less. 98w or so. 

He may have tested the power output differently and confirmed 1000w.  It is possible at 30mph.  I am just stating what the hair dryer experiment means. 

   

[Alkemi]

What is the best way to measure the power output of the windmill?
For now we drive it around on trolley and measure voltage. We also lit 5 bulbs each of 300 watt simultaneously. I know they could lit by using 100 watts too.
My point is, how we can calculate maximum watt it is generating at 25 MPH? What load should we use to verify the power output?

[bigrockcandymountain]

Run your output through an ammeter.  Measure voltage also and multiply volts x amps.  You will need a battery to charge or a resistive load like light bulbs or a heating element. 

What is the goal with this turbine? Will it be charging batteries or making heat? It is probably best to test it with whatever load you need attached to it.  Efficiency will change depending on the voltage it is running at on the output. 

[Alkemi]

The purpose is eventually build larger windmills and sell them in 1 mw, 2 mw, 3 mw and higher configurations, only if economics makes sense.
They seem to be 20 - 30% more efficient than 3 blade windmills but costs more to build.

[MagnetJuice]

The best thing to use to measure power output will be a drained battery. If you use a battery, you will need two multimeters, one to measure Volts and one to measure Amps. That's because you don't know the resistance of the battery for a certainty.

Other than that, a piece of thick nichrome wire will be the best to use because you can measure the resistance of the length of wire that you will be using. And you only need one multimeter to measure volts. Then use ohms law to find Amps. But if you have two multimeters, go ahead and measure Amps too. You can buy a dryer heating element like this for $17. That heating element nichrome wire is about 16 Gauge, and is good for about 5000 Watts. Very good to use for high power tests.



A hair dryer heating element is also made of nichrome wire but it is very thin and gets very hot. With the increase in temperature, the resistance goes up a lot. If you start with 10 ohms at room temperature, even with the very low temperature coefficient of .0004 for nichrome wire, the resistance will be 15 ohms at 1300 F, which is barely amber in color at that temperature.

But don't use this dryer element to test your 3 Megawatt turbine. The best thing to test the output of that would be a big city, like Chicago 

Ed

[Adriaan Kragten]

All your questions are answered in my public report KD 35 which can be copied for free from my website: www.kdwindturbines.nl at the menu KD-reports. Chapter 4 gives the reasons why the real Cp is smaller than the Betz coefficient. Chapter 5 gives the design procedure for a rotor and the formulas given in this chapter give the chord c and the blade angle beta as a function of the local radius r if the rotor diameter, the design tip speed ratio, the number of blades and the airfoil are chosen.

[Alkemi]

Thank you all for the guidance. I'll try to find the bigger heating coil to take better measurements.
Adriaan, I saw your website, I think I viewed it earlier in search results, but I overlooked the content.
Maybe on first home page, if you write more about what your website is and what reports are in it. It will be useful for people to go through it. First home page doesn't give much idea and you know people are very lazy now a days.

Anyways. I'll start new thread for the discussion of the windmill I'm talking about (depending on the result we get). It deserves a new thread and surely is new concept in windmills.

[Adriaan Kragten]

Adriaan, I saw your website, I think I viewed it earlier in search results, but I overlooked the content.
Maybe on first home page, if you write more about what your website is and what reports are in it. It will be useful for people to go through it. First home page doesn't give much idea and you know people are very lazy now a days.

In the folder about Kragten Design at the home page of my website it is written that you can find many free public reports and manuals at the menu KD-reports. The menu KD-reports starts with a folder which gives an overview of all public KD-reports. Next there is the folder "Sequence of KD-reports for self-study". I advice to read this folder first as it gives an overview of all areas which you will meet if you want to design a wind turbine and of all relevant KD-reports which I have written about each area.

But thank you for your comment and the folder about Kragten Design which you can find at the menu "Home" has slightly been modified.

[oneirondreamer]

I agree that it sounds like measurement precision is not high enough to get a clear picture of what's going on with your turbine.    If you believe that you are close to having a new commercial product for this market, then it sounds like investing in some better measurement systems would be a good idea.   I'd suggest googling labjack, or vernier for inexpensive data logging devices, then acquiring sensors for measuring volts and current, as well as shaft speed and wind speed.   

I will be publishing an instructable on measuring wind turbine output, oriented toward my new VAWT, but would be applicable to your needs as well.   As I lost access to my old account, oneirondreamer, I'm not allowed to publish links here yet, but you can find me and my new VAWT on the instructables site as drewrt   

[Adriaan Kragten]

They seem to be 20 - 30% more efficient than 3 blade windmills but costs more to build.

This is impossible. The effect of the number of blades is given in figure 4.3 of my public report KD 35. The higher the number of blades, the lesser the tip losses so the higher the theoretical maximum Cp. The higher the optimum tip speed ratio, the higher the maximum Cp. The difference is largest in between a 1-bladed and a 2-bladed rotor. For an optimum tip speed ratio of about 6, the difference is only small in between a 2-bladed and a 3-bladed rotor and even smaller in between a 3-bladed and a 6-bladed rotor. Figure 4.3 is valid if the Cd/Cl value is zero. Figures 4.5 up to 4.11 give the theoretical max Cp value for different Cd/Cl values and for different number of blades depending on the optimum tip speed ratio.

A negative effect of increasing the number of blades for a rotor with a certain diameter and a certain design tip speed ratio is that the chord c decreases with the same ratio as the ratio in between the increase of the number of blades. This results in decrease of the Reynolds number and decrease of the Reynolds number results in increase of the Cd/Cl ratio. The increase of the Cp max by increase of the number of blades can be smaller than the decrease of the Cp max by the increase of the Cd/Cl ratio. This effect is especially important for small rotors as they run a low Reynolds values at low wind speeds. A small 2-bladed rotor can have a higher maximum Cp at low wind speeds than a 3-bladed rotor with the same diameter and design tip speed ratio because of this effect. For bigger rotors, three blades have been proven to be the optimum.

Another negative effect of increasing the number of blades for a certain optimum tip speed ratio is that the blades become very slender and so the bending and torsion stiffness decrease strongly. This makes slender blades much more sensible to flutter. A high number of blades is normally only used for very slow running rotors of water pumping windmills because these rotors must have a high starting torque if they drive a single acting piston pump. However, these rotor have a low maximum Cp because a lot of power is lost in wake rotation (see KD 35 figure 4.2).