Blades, Length, TSR

[valterra]

I did some TSR and Length measurements based upon what I figure my approximate cut-in should be. But here's the major snag, as far as I can tell. According to Warlock's blade calculator (unable to

check others at the current time), most TSR and Length combinations

result in blades that are impossibly wide at the Root.

Warlock's calc says not to worry, use a more reasonable number based upon your lumber.

But here's what I've discovered.

Plugging in different TSRs, with all other items being equal, as TSR

increases:

• the theoretical Root becomes wider
  
• the theoretical Root angle becomes shallower
  
• the Tip becomes wider
  
• the Tip angle becomes shallower, even going negative in the calculator.
  
  

All of the root widths are unreasonable, meaning noneof the numbers are relevent.  No matter what the calculated width should be, it'll always REALLY be 5.5 inches.

The resulting effect is that the typical angle of attack (4 degrees)

point of each blade moves closer to the Root as the TSR increases. The

negative angles are worrisome. Surely we don't want the blades to twist so much as to start cutting into the wind. I think that's the problem

with theoretical things like calculator programs.

Since I don't have lumber that is,say, 47.1 inches wide, I have to

limit the root to 5.5 inches for 2x6 wood. That means I don't have much control over the actual TSR of the final blade, except to change the location of the 4-degree point along its length. With a specific piece of lumber, the only factor I really have control over would be the length itself.

So here's my idea. I will build a set of blades with a constant angle

from the tip through approximately 75% of the length. At that point, I

plan to start a twist up to something steeper at the root. That's just to try to get a little extra kick in low winds and have SOME twist.

Blades with a 4-foot radius (an easy number for standard lumber sizes), would have about three feet at a four degree angle. My thought is that if the blades end up being too long (slow), I can easily cut the ends off without changing the angles for each calculated length.

Because of the limitations of the source material, I don't think I'll be able to make a blade-set that accurately conforms to a specific calculated TSR anyway (can anyone?). The only thing I think I can really control is the length (have I mentioned that? (wink)). That is why I decided to try this approach.

Plugging numbers into other calculators (Ed Lenz's and Alton Moore's) may result in totally different numbers, and therefore another theoretical approach.

Another reason for trying the mostly solid angle was for ease of construction.

Right? Wrong? Post a comment and let me know!

(Sorry if the formatting is off.  My mobile device is a bear to edit text with.)

[Flux]

Yes all those calculators give this crazy situation at the root. I find it undesirable to take the root to these extremes, it wastes wood and seems to make the thing very critical to maintaining exact tsr. Something that our crude loading methods will not tolerate.

If you take the calculator figures for the outer 2/3 of the circumference and just keep the things at constant angle and constant width for the inner 1/3 it will work better and you can get it out of a sensible sized bit of wood.

Making the blades with no taper or twist based on the calculator figures at .7 radius works just about as well.

Even using a cube law loading circuit I still don't see any virtue in using the stupid width and angle predicted by the calculators and with all the blades I have made the optimum tsr still seems to fall with increasing wind speed, so the best speed needs to fall with increasing wind speed instead of tracking it exactly.

For someone going into large scale manufacture it would be worth spending time measuring performance of various shapes and profile perhaps more so before deciding on something for final manufacture.

Home builders will not have the facility to measure performance with any degree of certainty, it takes weeks for one blade even if you can do it, so you might just as well do what seems to work for everyone else.

What DanB does with 3 deg angle at the tip, 6 deg at half radius and just take it linear to the root seems very effective. Similarly for chord width if you find the calculator chord at .7 radius, use a board twice as wide and make a linear width from the tip to the board width at the root and pick up the width at .7 R  You will again get very close to what Dan does.

Also you do get negative angles at the tip with high tsr figures from the calculators.

For high tsr values things become critical and the things are not suitable for hand carving. Whatever you do the high tsr blades will be noisy, something associated with a lot of commercial machines and something I can do without. Stick to tsr 5 to 7 based at .7R, forget the inner 1/3 and you will be ok.

Flux

[valterra]

Thanks Flux!

I really appreciate your help.  The only thing I don't understand is:

 Similarly for chord width if you find the calculator chord at .7 radius, use a board twice as wide and make a linear width from the tip to the board width at the root and pick up the width at .7 R  

I read that about 10 times, and I just don't get it.

[scorman]

I am in total agreement with Flux.

Even Hugh Piggot makes this claim ( bottom left side):

http://users.aber.ac.uk/iri/WIND/TECH/WPcourse/page7.html

Too many people get bent out of shape on twist and taper, while Bergey and Jacobs have been selling  units with constant 6" cord with no twist, up to 30 ft diameter. Even The similar Wincharger blades that DaveB is using are made by Dave Moller and have more than adequate performance and have been used since the 30's.

http://royalfabrication.com/performance.htm

If you want to see more numbers, I have a xls that calculates lift for tapered vs non-tapered, twist vs non-twist ..it is NOT for the faint of heart!

It shows why the above blades really work.

email me for a copy as it is too large to be embedded here.

Stew Corman from sunny Endicott

[Flux]

Think of it this way. If the calculator predicts a width ( chord) of 4" at .7R, start with a board 8" wide. Leave the leading edge as it is and mark the trailing edge from 8" at the root, let it pass through 4" at the .7R and you will have a width less than this at the tip. I could work out the actual tip width but it seems too much effort at the moment and it only takes a few seconds to draw the line.

Hope that helps.

Flux

[valterra]

Flux, that explanation made perfect sense.  Thank you!

[Ungrounded Lightning Rod]

If you took the calculations all the way to the center the angle would limit at running parallel to the axis and the chord length would become infinite.

The available power is proportional to the swept area, which goes with the square of the radius.  So the inner quarter of the blade potentially collects only 1/16th of the power, the inner 8th only 1/64th, etc.  The inner 10% of the blade only has the potential to collect 1% of the power.  So being non-ideal near the middle wastes you negligible power and saves a lot of wood and weight.

Thus when you get near the hub and the sizes and angles are getting silly, it's fine to stop following the computation and go with the size of a convenient piece of wood.  You can truncate it into a flat-faced hub, stop extending the chord, etc. with essentially no loss of power.  (You'll have less wind loading if you continue to streamline it and follow the prescribed twist angle.  But again it's a small fraction of the swept area and thus also a small fraction of the load, so it's not a big deal if you don't.)

That said, there are two good things about going moderately long and steep near the center:

 1) Due to leverage the stress goes up with the inverse of the radius.  So widening the blade near the base and twisting it to a more fore-aft angle helps support the rest of the blade against wind loading.  (This is also an argument for going with the flat-faced hub over a streamlined profile that cuts away some of the strength.)

 2) When the blade is stopped and the wind picks up, there's virtually no torque from a high TSR design.  A steep and long section near the axis acts as a drag turbine to provide some starting torque to get the blade up to speed.  (This argues for some sort of streamlining or other blade-shape, at least at the outer part of the section where you're deviating from the ideal.)

So even though it provides little power when flying, it's good to do SOME continuation of the twist and chord widening near the hub.