Blade profile calculation

The blades of the turbine, and the hub they are attached to

Blade profile calculation

Postby windgat on Tue Jun 16, 2009 10:16 am

Hi Greystoke, here is a calculation for your blades. Last two columns are what you are after: blade setting and chord length (linearised for easy construction). Near the root shapes is not important, so just ignore that and make the root in any way you can.

Code: Select all
r      l        f (rads)   f°        b°        C        b         C
                                 (IDEAL)   (IDEAL)   (LINEAR)   (LINEAR)
1980   6.00   0.1107   6.3402   0.3402   152.8800   -0.3348   137.4759
1881   5.70   0.1164   6.6710   0.6710   160.7673   0.3516   153.4893
1782   5.40   0.1228   7.0379   1.0379   169.5027   1.0379   169.5027
1683   5.10   0.1300   7.4474   1.4474   179.2288   1.7243   185.5161
1584   4.80   0.1380   7.9072   1.9072   190.1214   2.4107   201.5295
1485   4.50   0.1471   8.4270   2.4270   202.3998   3.0970   217.5429
1386   4.20   0.1574   9.0193   3.0193   216.3405   3.7834   233.5563
1287   3.90   0.1693   9.7004   3.7004   232.2969   4.4697   249.5697
1188   3.60   0.1831   10.4915   4.4915   250.7262   5.1561   265.5831
1089   3.30   0.1993   11.4212   5.4212   272.2298   5.8424   281.5965
990   3.00   0.2187   12.5288   6.5288   297.6099   6.5288   297.6099
891   2.70   0.2421   13.8697   7.8697   327.9541   7.2152   313.6233
792   2.40   0.2709   15.5241   9.5241   364.7573   7.9015   329.6367
693   2.10   0.3074   17.6126   11.6126   410.0912   8.5879   345.6501
594   1.80   0.3547   20.3231   14.3231   466.8029   9.2742   361.6635
495   1.50   0.4182   23.9625   17.9625   538.5840   9.9606   377.6769
396   1.20   0.5071   29.0546   23.0546   629.1040   10.6470   393.6903
297   0.90   0.6375   36.5289   30.5289   736.5322   11.3333   409.7037
198   0.60   0.8380   48.0128   42.0128   827.4440   12.0197   425.7171
99   0.30   1.1479   65.7723   59.7723   736.9157   12.7060   441.7304
0   0.00   0.0000   0.0000   0.0000   0.0000   0.0000   0.00


For example, at radius of 990mm from the axis of rotations, the setting angle should be 6.5288 degrees, and the chord length 297.6mm. This is based on the NACA 4412 profile, so you would scale that profile at each station to get the specified chord (chord = distance from front-most to back-most point). The setting angle is the angle between the chord and the plane of rotation.

If you are after perfection at the cost of construction complexity, then you should use the previous two columns, the ideal figures.
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Re: Blade profile calculation

Postby Greystoke on Fri Jun 19, 2009 7:23 am

Thanks windgat. I'm going to need your help soon.

BTW: I can't get out of a pulley system to get to the voltages I need (minimum ±90V), so I'm considering to go for a 4-blade propellor instead, in order to increase the starting torque.

Is that a good idea :?:
Regards
Cor
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Re: Blade profile calculation

Postby windgat on Fri Jun 19, 2009 11:29 am

Starting torque is useful when there is a lot of cogging resistance. In the air core generators, there is no cogging.

Four blades is 1/3rd more work, I am not sure if it is worth it.

Once you give me figures, I can calculate for 3 and 4 blades.
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Re: Blade profile calculation

Postby Greystoke on Fri Jun 19, 2009 12:47 pm

OK,
This is what I came-up with sofar:

Image
Regards
Cor
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Re: Blade profile calculation

Postby nikolakis on Fri May 14, 2010 8:13 pm

Hi,

My English level isn't high so forgive me for any mistake.

Im a college student from Greece and i make a project about the blades of wind turbines. I try to calculate the chord line and angle beta of each station of naca4412.Does any know the formulas for the calculations?

Nick
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Re: Blade profile calculation

Postby windgat on Sat May 15, 2010 12:45 pm

Hello Nick. Have you looked at this?
http://windpower.org.za/bladecalcs/blades.php
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Re: Blade profile calculation

Postby nikolakis on Sun May 16, 2010 11:22 am

Yes, I have seen this!! Very useful calculator but I need the equations that uses the calculator.

For example the equation for the chord width of each station e.t.c.

Because I have to write in my project HOW I designed and calculated the blades.. I can't say that only used a calqulator.. :(
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Re: Blade profile calculation

Postby windgat on Sun May 16, 2010 3:24 pm

Try this:
BladeFormulas.png
BladeFormulas.png (8.38 KB) Viewed 6544 times
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Re: Blade profile calculation

Postby nikolakis on Sun May 16, 2010 3:40 pm

Thank you very much!! :) :)

I have some more questions

1) Im not sure but i think that lift coefficient cl changes along the blade. I have read that a good choice of cl is 0.6 at the wing tip with a gradual increase to 1.3 at the wing root. Do you have to suggest something?

2) ?? is the tip speed ratio. In my calculations does it change?

3) I found some charts from NASA about cl,cd and angle of attack for Re=3.110.000. This number of Re is ok? or I should find charts for higher Re number?
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Re: Blade profile calculation

Postby windgat on Sun May 16, 2010 3:51 pm

The angle of attack and therefore coefficients stay constant along the blade.

The TSR ?? is fixed - its at the tip by definition. ?r changes depending on r - the radius as a fraction.

Re is complicated! I think you will find for that profile the optimal angle of attack is pretty much the same across a wide range of Re.

I have been told that the best way is to do the calculation, and then verify that the Re is in an acceptable range all along the blade afterwards.
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Re: Blade profile calculation

Postby nikolakis on Sun May 16, 2010 3:58 pm

ok, thank you for the details!!
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Re: Blade profile calculation

Postby nikolakis on Sun May 16, 2010 5:43 pm

Do you know how is calculated cos?? I think 3/2*?r but Im not sure. :(
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Re: Blade profile calculation

Postby windgat on Sun May 16, 2010 5:59 pm

As I recall, ? = atan(2 / 3?r) Then take the cos of that.
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Re: Blade profile calculation

Postby nikolakis on Sun May 16, 2010 8:06 pm

I made tha calculations but something is going wrong. The calculated chord length is wrong. Could I send you the excel file to check it?
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Re: Blade profile calculation

Postby windgat on Sun May 16, 2010 9:42 pm

Sure. Perhaps you can just post the formulas you used here?
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Re: Blade profile calculation

Postby nikolakis on Mon May 17, 2010 6:21 pm

well,

All the calculations are done in excel. First of all is calculated ?r=(r/R)*??

After is calculated angle ? by the equation : =DEGREES(ATAN(2/3*?r)) and cos? by =cos(radians(?))

Final the chord length by c=((8*3,14*r)/(B*cl)*(1-cos?)

These equations are written in excel and the next tables are the results :


R (mm) r (mm) ? ?r ? cos?
850 150 5 0,882352941 30,46554492 0,861934215
850 200 5 1,176470588 38,10757688 0,786853417
850 250 5 1,470588235 44,43273359 0,714072839
850 300 5 1,764705882 49,63546343 0,64764842
850 350 5 2,058823529 53,92398844 0,588858019
850 400 5 2,352941176 57,48248938 0,537557339
850 450 5 2,647058824 60,46121774 0,493012572
850 500 5 2,941176471 62,97841841 0,454326083
850 550 5 3,235294118 65,12584609 0,420626604
850 600 5 3,529411765 66,97450799 0,39114064
850 650 5 3,823529412 68,57954088 0,365209222
850 700 5 4,117647059 69,9840404 0,342281879
850 750 5 4,411764706 71,22196678 0,321902733
850 800 5 4,705882353 72,32031902 0,303695196
850 850 5 5,000000000 73,30075577 0,287347886




r (mm) cl cos? ?(blades) c(chord) (mm)
150 1,188 0,861934215 3 145,9685402
200 1,188 0,786853417 3 300,4625228
250 1,188 0,714072839 3 503,82227
300 1,188 0,64764842 3 745,0397043
350 1,188 0,588858019 3 1014,242508
400 1,188 0,537557339 3 1303,766515
450 1,188 0,493012572 3 1608,020731
500 1,188 0,454326083 3 1923,025926
550 1,188 0,420626604 3 2245,966006
600 1,188 0,39114064 3 2574,839582
650 1,188 0,365209222 3 2908,210951
700 1,188 0,342281879 3 3245,038001
750 1,188 0,321902733 3 3584,554575
800 1,188 0,303695196 3 3926,190052
850 1,188 0,287347886 3 4269,514014


As you notice the value of chord is huge!! :( :(
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Re: Blade profile calculation

Postby nikolakis on Mon May 17, 2010 6:29 pm

    R r ? ?r ? cos?
    850 150 5 0,88 30,47 0,86
    850 200 5 1,18 38,11 0,79
    850 250 5 1,47 44,43 0,71
    850 300 5 1,76 49,64 0,65
    850 350 5 2,06 53,92 0,59
    850 400 5 2,35 57,48 0,54
    850 450 5 2,65 60,46 0,49
    850 500 5 2,94 62,98 0,45
    850 550 5 3,24 65,13 0,42
    850 600 5 3,53 66,97 0,39
    850 650 5 3,82 68,58 0,37
    850 700 5 4,12 69,98 0,34
    850 750 5 4,41 71,22 0,32
    850 800 5 4,71 72,32 0,30
    850 850 5 5,00 73,30 0,29


    r cl cos? ? c
    150 1,188 0,86 3 146,0
    200 1,188 0,79 3 300,5
    250 1,188 0,71 3 503,8
    300 1,188 0,65 3 745,0
    350 1,188 0,59 3 1014,2
    400 1,188 0,54 3 1303,8
    450 1,188 0,49 3 1608,0
    500 1,188 0,45 3 1923,0
    550 1,188 0,42 3 2246,0
    600 1,188 0,39 3 2574,8
    650 1,188 0,37 3 2908,2
    700 1,188 0,34 3 3245,0
    750 1,188 0,32 3 3584,6
    800 1,188 0,30 3 3926,2
    850 1,188 0,29 3 4269,5
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Re: Blade profile calculation

Postby nikolakis on Mon May 17, 2010 6:30 pm

Im sorry for the mess. I can't copy-paste properly the tables.. :(
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Re: Blade profile calculation

Postby nikolakis on Thu May 20, 2010 2:41 pm

Something more, do you know where can I find lift and drag coefficients data over a range of Re numbers for naca 4412 airfoil? Do you have any charts?

Thanks
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Re: Blade profile calculation

Postby windgat on Thu May 20, 2010 6:05 pm

I have found that information very hard to find. Either you use empirical tests, or something like XFoil which calculates theoretical results.

About your formulas, I think there may be a problem with brackets. It is sloppy to write DEGREES(ATAN(2/3*?r))

Rather make it clear which you mean: DEGREES(ATAN(?r*2/3)), or DEGREES(ATAN(2/(3*?r)))
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Re: Blade profile calculation

Postby nikolakis on Thu May 20, 2010 10:33 pm

finally I calculated the chord and angle ?. Thank you very much fro your time !! Also I have found this site http://www.worldofkrauss.com/foils/793
has very usefull information for anyone who is interested to design a blade (but Im sure that no one is going to use equations and charts :) :) ) An other one is http://easyultralightdesign.com/airfoils/index.php

Do you know If Xfoil software is free?
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Re: Blade profile calculation

Postby windgat on Fri May 21, 2010 9:54 am

Well done for getting it all correct! Was it a brackets problem?

I had seen the Krauss website - its great. Thanks for the other link. Still, I haven't found a good source of all the airfoil data, across a range of Re numbers. If you ever find one, please let me know!
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Re: Blade profile calculation

Postby nikolakis on Fri May 21, 2010 3:02 pm

Yes, it was brackets problem. Ok, If I find something more Im going to inform you!!
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Re: Blade profile calculation

Postby nikolakis on Sat May 22, 2010 7:34 pm

Hi again,

This is the wind turbine that I have constructed.

HowImage

Does anyone know how can I mesure the mechanical (shaft) power for a range of wind speed?

Thank you
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Re: Blade profile calculation

Postby nikolakis on Sat May 22, 2010 7:49 pm

This is the wind rotor

Image
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