Author Topic: TSR and angles (Read 4334 times)

scoraigwind · « **on:** February 10, 2005, 02:32:45 PM »

In answer to John's question in http://www.fieldlines.com/story/2005/2/8/171831/1959 (off topic)I'd like to explain a bit about blade angle.

The wind that hits the blade is made up of two parts. One part is the real wind coming through the rotor, but this is already slowed down to about 2/3 of its normal speed by the time it enters the rotor plane. The other part is the headwind of the blade's own motion. These combine in a triangle to make a resultant wind direction hitting the blade at an angle that is less than what you would imagine from just using the tip speed ratio as a guide.

Ok that's only half the story because you don't want this wind to blow straight down the chord line. You want an angle of attack so the blade can generate lift. so the blade has to be about 5 degrees flatter than the angle of wind coming in. In some cases it gets totally flat or even goes into negative pitch but only at very high tip speed ratios.

scoraigwind · « **Reply #1 on:** February 10, 2005, 07:45:16 AM »

OOps I have just noticed that this thread has alredy been chewed quite a bit elsewhere. I hope my comments are still useful though.

As for tip speed ratio this will vary under load, as has been mentioned. With the rotor tied up it is zero. Running free it will be fast and noisy with no useful power output. Between the two will be the best tip speed ratio and that is what we usually mean when we say that a blade is designed for a particular tip speed ratio.

The way I set about designing for a tip speed ratio is this. I work out the angle of incidence of wind on the rotor plane assuming that is being slowed down to 2/3 of its upstream velocity. I use this with the headwind to calculate the angle the wind is making with the rotor plane at the blade tip (seen from the blade as it spins). I then set the blade angle 5 degrees off the angle of the wind so as to get the best lift/drag ratio from the blade. I do the same thing at the other stations along the blade span.

OK so there are all sorts of airfoils, and all sorts of reynolds numbers and stuff, but it reality this approach does work quite well.

johnlm · « **Reply #2 on:** February 10, 2005, 10:21:22 AM »

Hugh, and all

I appreciate the information and explaination of the apparent wind and your approach. I think the variables involved in trying to determine the speed of the apparent wind, from the combination of the real wind and the wind seen by the rotation of the blade for various angles of attack and blade pitch is somewhat complicated, and sounds as if differential equations (finite element analysis as you suggest in your material) are needed to fully solve that. But a best estimate approach will get one in the ballpark.

I am mulling over the comments contained in the several posts that have been generated since my first comment posted on Dan B's story about his new 17 ft mill. I was attempting to offer a suggestion (from my understanding) as to why his mill was apparently stalling, and it led to several comments with a diversity of inputs from other peoples knowledge of the subject, perspectives and experiences. I guess Im hoping to better understand what is really going on with props. Now a few observations as to what I think I've learned.

My simplistic approach to the way I have approached cutting the angle on the blades to attempt to achieve a certain TSR is not the most precise (obviously not the best) approach. Although I have made maybe 10 props using this approach, and most actually run in the ball park of correct RPM verses windspeed and they seem to be able to produce power up to a rate that follows the P=0.0012 X D^2 X mph^3, (1/2 the therotical limit including inefficiencies of the alternator) its likely that using a design with additional factors taken into account would result in a more effecient prop.
Ive come to the conclusion, based on my experiences, and reading this board that one can get some amount, and even reasonable performance out of just about any approach. I cite as examples props that range from something as sophisticated as the pure engineering approach of airfoil design as might be obtained using Ron's (wdyasq) technique to such props as those obtained from cutting sections out of PVC pipe. No insult of any kind intended here as I admire peoples ingenuity and willingness to experiment and the results they achieve.
I better understand why some of the more novice readers on this board seem to be totally mystified, uncertain and turned off as to how to approach building a prop from scratch; yet I hate to see them give up before they try after reading a post of how technically involved it may be by following the ultra-sophisticated methods. As stated in the threads of the several posts on this topic over the past few days, I started carving my own about 25 yrs ago after reading the articles mentioned in those threads. One article (the N Dakota Ag College publication) was apparently aimed at giving 1930's American rural people (likely very little formal engineering education) the information to make their own props without going into the theory of airfoil design. The other article also referenced the LeJay manual as a source of information.
In most of the posts there is an apparent lack of actual data that gives one insight into just how well ( or not well) someones design is actually working. There are usually somewhat vague statements such as - "I got 20 amps at 30 mph" but usually not much detailed information given in tabular format of RPM, Open Circuit output Voltage , Amps into a battery, or Amps into a specified load at various wind speeds. Possibly, some do not have the means to adequately measure all these parameters and others just want to be brief in stating performance, and others just don't want to give many details. I (possibly a data freak) would like to see more detail. I have seen a ( usually justifiable) eagerness by readers to quicky discount or question somebodys or some companies apparently exagerated claims (usually someone trying to sell something) yet I do not see too many posts of readers / members giving enough details of their own system's performance. Just an observation. This is actually more the case regarding props and total system performance than stand-alone tests on alternator / generator performance. I think folks like The Dan's and other folks too numerous to mention on PMG's and others on motor conversions have done an admireable job documenting and sharing with others the details of alternator / conversion design and construction; but there has not been much published on the details of prop design. Maybe Ive just not looked hard enough.

I do appreciate all the inputs as I am constantly attempting to learn more.

Thanks

Johnlm

bob golding · « **Reply #3 on:** February 10, 2005, 03:32:08 PM »

hi hugh, glad to see you didnt get blown to norway. :-)how did your mills survive the recent gales up there?

bob golding

rotornuts · « **Reply #4 on:** February 10, 2005, 04:55:47 PM »

I'm with ya john. I'm a relative newcomer to all this really. I just happen to be a bit obsessive and I have been obsessing for about a year now after a couple years dabbling. I'm as the name implies a bit obsessed with the rotors and like you would like to see some more discourse with regards to blade design and more so aerodynamics so we can all really understand what's going on. We can all build blades by simply copying someone else's work but I tend to trot down a different path than some folks so I've been taking myself to school on this stuff. Fortunately I've been Interested in aircraft for ever(my father was a pilot and did time with several aerobatics teams) so I have some prior knowledge of aerodynamics and have seen many examples of how aircraft designers have solved problems.

I think part of the problem though is the fact that beyond creating simple rotors, that do indeed perform very well, things start to get a bit complex, not to say it's really difficult there's just so many things to consider and I see alot of them ignored or not talked about here.

Part of the reason I decided to do the single blade was to get people talking. As far as I know it hasn't been done here before so really we're all on the same learning curve.

Fliud dynamics is an entire disipline of science, there should be a few ideas we can hack about some without drawing too many quick conclusions

Keep at it.

Tippy · « **Reply #5 on:** February 10, 2005, 09:32:44 PM »

Here are some numbers on my 9' turbine, perhaps not as exact as you would like but i dont really have the equipment to measure exerything properly. It is a 9' prop with a TSR of 8(carved for the mountains in central mexico 6900' elevation). Testing in the last norther (live in Texas) the wind speed (weather report) was 28 and my rig did 59 volts and pegged the inline automotive amp meter at 30+ (multiple sealed beams for load) but hooked to a 24 volt battery bank it did about 28 volts @12 amps and would furl right before it got to 31 volts. Thats the scoop on mine. Hope to do better, building 3 more soon.

How do i post pictures on here people? Also i deliver the 9 footer to mexico in March and want to teach them how to build turbines for themselves. Does anybody have plans or tips for using car alternators or something readily available even in Mexico? Availability over efficentcy they have tons of wind up there in the mountains. Also are there load diverters or regulators that can be homemade? I have no access to those things down there. Advice please.

thanks

tip

ghurd · « **Reply #6 on:** February 11, 2005, 08:19:10 AM »

To me, it looks like the effort and magnet cost to convert a car alternator is quite high compared to the output.

Induction conversions (like furnace motors) using the stock wire, like Jerry and others here do, are cheap, easy and get decent output.

Look under 'controls' at the top of this page for regulator designs.

G-

johnlm · « **Reply #7 on:** February 11, 2005, 09:39:10 AM »

My experience with car alternators is that they are actually just as easy as motor conversions IF one is going to rewind the motors. The reason I say this is that car alternators more or less have to be rewound to lower the rpm at which you can start getting 12 V out of them. The other option if you use the stock windings on a car alt is you have to gear them up (about 6:1) quite a bit more, as they will not get into the 12V output area until around 800 to 1000 RPM (depends on the brand, model etc). As for the magnets, I have just ground off a little over 1/8 inch (about 3.5 mm)of the face of the pole finger and then mounted 1 X 1/2 X 1/8 thick neos to the pole faces with the mags tilted at about a 30 degree angle to get rid of most of the cogging problem. But I have found that they work reasonably well with this mag setup and being rewound, although you still may have to gear them up in the range of 2:1 or so.

So the cost of conversion between motors and car alternators is pretty similar if both are rewound, obviously less for the motor if you use stock windings.

John

windstuffnow · « **Reply #8 on:** February 11, 2005, 09:48:34 AM »

At one point I used to obsess over blade efficiencies, trying to carve the perfect blade and matching them with the alternators as precice as possible. I consider myself a "recovering" perfectionist. Also, spending way to many hours carving the "perfect" blades. I've found from making blades in various forms that you can "fudge" quite a bit and still come out with a very efficient blade, obviously not perfect but one that works very well for a given application.

Now, I have a question, reguarding the D^2 part of the formula... maybe this is some perfectionism still lingering... Isn't this misleading for finding the actual area of a given circle area? You would actually come out with greater expectations of the power output by using this. Isn't Pi r^2 or D^2 x .7854 more appropriate? As an example... a 6 ft prop

D^2 = 36 sq ft

D^2 x .7854 = 28.27 sq ft

Pi r^2 = 28.27 sq ft

If your trying to calculate power from sq footage and wind speed you'd end up with an exaderated end result by using D^2.

Just an observation from seeing formulas in books laid out this way... its always bothered me...

Have Fun

Windstuff Ed

finnsawyer · « **Reply #9 on:** February 11, 2005, 09:59:25 AM »

You make a number of good points. My own view is that for an air foil to act efficiently it must operate in "clear" air similarly to an air plane wing. This means that each blade of a windmill must be free of the wake of the previous blade. The leading edge of the blade at a radius R then has a pitch angle determined by it's velocity V(R) combined vectorialy with that of the incident wind Vi. One also takes into account the angle of attack. The incident wind must sweep away the wake of the blade before the following one encounters it. However, there's a catch. When air passes over an air plane wing the air flow off of the trailing edge has a downward component. For the windmill this effect Vo (a wake effect) shows up as a velocity component opposite to the incident wind. The faster the blade turns the stronger this effect. At the trailing edge we have Vi - Vo for this component. Ideally Vo is small enough so that the wake disappears behind the windmill before the next blade would encounter it. If it doesn't performance suffers.

As far as making accurate measurements I think that's a job for those with deep pockets. To begin with, how do you measure wind speed to better than a tenth of a mile per hour? If you increase the wind speed by 10% you have available 33% more power. Where do you measure the wind speed? So, it's not likely you're going to get really accurate data from most back yard set-ups.

You are right about just about anything working. That's due to that good old velocity cubed factor. So people should not be afraid to try.

wdyasq · « **Reply #10 on:** February 11, 2005, 10:16:42 AM »

The formulas I remember are PI x R^2 or PI x D^2/4, resulting in the same number.

Ron

johnlm · « **Reply #11 on:** February 11, 2005, 10:35:55 AM »

After reading something that Dan B said, that maybe Im only looking at the prop TSR as a screw (and I add here, - with variable pitch, meaning high pitch at the root and shallow pitch at the tip ; twist as its commonly refered to) and he sees the TSR as a function of the Chord width (blade width), I went back and studied Hughs information and realized that Hugh more or less defines TSR as a function of blade width with his equation C=4D/(TSR^2 X B) with C=blade width, D= prop diameter and B= number of blades. Then (as he said above also) he sets the pitch (angle of attack) at about 5 degrees relative to the apparent wind as a good operating point on the Lift verses Angle of attack curve. And he really does not speak of how to go about tapering pitch (twist) to carve into the blade.

In my approach I usually just arbitrarily picked a raw piece of wood that seemed correct for a given blade size (maybe a 1 X 4 inch) for 3 to 5 ft diameter blades, a 2 X 6 in for 6 ft, and a 2 X 8 for 8 ft dia blades) then cut a taper in it making it about 1/2 the width at the tip as it was at the root. Then ( and this is apparently where my idea of putting in the TSR came in) I would set the pitch at the tip at the angle that corresponded slope of angle = 1/TSR; for example; if it was to be a TSR of 6 then the slope would be rise/run=1/6 which would give me a pitch at the tip of arc tan 1/6 = 9.5 degrees. I would then cut each station at a corresponding increasing pitch for example at the 1/2 radius point the slope would be 1/3 or 18.4 degrees etc.

So essentially following Hugh's approach I actually (more or less) set the TSR when I arbitrarily cut the taper into the blade and all I was doing by cutting the pitch at various stations was setting the blade angle of attack.

However, I have gone back to an existing blade that I wanted to speed up and recut the pitch angle all along the blade to some lower angle of attack and the result was the prop increased in speed. So Im assuming here that the rpm is affected by TSR (blade width) as well as angle of attack; which makes sense as thats how some props are speed controlled by changing angle of attack? Or does changing angle of attack just change the lift factor thus changing the effectivness of the blade under a given load?

The curious part is that if I wanted a prop to run at a certain RPM at a given wind speed (to match the alternator cutin speed) My approach usually always got me pretty close, and seemed to give power that roughtly followed the P(in watts)=.0012V^3D^2 equation when I loaded it up. Maybe the wind Gods just liked me. lol.

Still learning, thanks for the patience. Maybe some of this is usefull to other folks, who may not fully understand it.

John

johnlm · « **Reply #12 on:** February 11, 2005, 11:06:57 AM »

Ed,

I think the simplified equation has some of the constants factored out. Briefly:

Power (max) = 0.593 X pAV^3/2 where A is swept area, V is wind speed, and p is air density. 0.593 is Betz limit.

assume 0.08 lbs / cubic ft for the air density; Power in Watts; A in square ft; and V in mph; the equation boils down to

Power (max) Watts = 0.0031AV^3

then putting it in terms of swept area being a circle. A= pi D^2/4 (or pi R^2)

3.14/4= 0.785 so A=0.785D^2

Power (max) Watts = 0.0031 X 0.785 X D^2/4 X V^3 = 0.0024D^2V^3

Then assuming due to innefficiencies of you only get 50 % of the max

Power Watts = 0.0012 X D^2 X V^3

as you can see the 0.785 has been multiplied by the 0.031 to get the 0.0024.

johnlm · « **Reply #13 on:** February 11, 2005, 11:45:14 AM »

Fin,

Point well taken regarding the measurements. I cant measure wind speed any better than many folks. I agree that its difficult to to get reasonable accuracys because of where you measure it, what the instantneous value really is etc. And from a couple of comments I think folks misunderstood what I was suggesting. Im not wanting exact measurements but (as an extreame example) when I see something like they got 150 Watts out of a 5 ft prop at 10 mph, I wonder what is really happening.

Even best guesses as to wind speed vs output if presented as such that fit a first pass approximation of is that even possible are much better than information presented as exact that are far from possible.

I think I should have NOT made the statement so stictly as I did about providing data, and as Windstuff Ed suggested (in one of these threads) its not worth being such a perfectionist. Thanks for the comments. Im really not an A..hole but I can see where from some of what Ive said, or maybe the way I said it, it comes across that way. Sorry.

John

Walt · « **Reply #14 on:** February 11, 2005, 05:01:55 PM »

John

Is if possible that: when you changed to a lower angle of attack, that you also created a more efficient air foil? How else would lowering the angle of attack cause you to achieve a higher RPM? The only other thing that could possible be, is that the load on the first set of blades was to low and they were at their maximum RPM for the airfoil and/or angle of attack. Let me know if you think that this is a possibility or not.

Walt

johnlm · « **Reply #15 on:** February 11, 2005, 08:26:39 PM »

Hi Walt,

I am going to answer your question but first I need to correct another error I made several threads up when I said that in the material I had of Hugh's he did not talk about carving the pitch into the prop. After going back and looking at his material - and now understanding it much better- he does address that topic, just not in the way I was expecting to see it before I understood how he was doing his design.

As for your question as to whether I might have altered the prop into a more effecient operating point, Im thinking now that may be what happened. By me changing the face pitch on the prop to a lower pitch angle, thinking I was upping the TSR, in reality I was likely really changing the angle of attack and thus moving the point on the Lift vs angle of attack operating curve. I believe the operating load (at least at light loading) did not change because the problem I had was a rewound / converted to permanent mags car alternator that would not reach cutin voltage until about 520 RPM which was occurring at about 10 mph wind speed with the first cut of the prop. so at the operating area below cutin since no charging current I define it as light load. After I recut the prop with less face pitch angle the cutin was lowered to around 8 mph. So the light load was pretty constant. I didnt take enough data readings of power out and rpm for various wind speeds before, or after I recut the prop to fully understand if the effeciency and output power of the prop at various wind speeds was altered. The prop was soon thereafter destroyed in a windstorm, and what remains of it is now the single blade on my post "single blade madness continued"

Your question is very germain to my thinking I have been doing today, as I went back to an intact 4.3 ft prop I made a few weeks ago using my old approach described in these threads, and using Hughs design approach, I took physical (length, width, face angle etc) measurements on the prop and plugged them into his formulas and worked them backwards to determine rough TSR, apparent wind direction, actual angle of attack etc to she what I had made. Its interesting to compare how my simple approach I had used compares to his approach. Without going into all the calculations here, the bottom line was:

My old simple approach:

planned TSR was 10 on a 4.3 ft prop

actual measured TSR (using RPM at a given wind speed) at light load was 8.75

I didnt even consider angle of attack or apparent wind angle when making it.

Backward engineered numbers using Hughs approach:

Rough calculated TSR (using his formula C=4D/(tsr^2 X B) it came out 6.3

Using this tsr to calculate rotational speed for a given wind speed;

at the 3/4 Radius point; Apparent wind angle = 13.4 degrees and angle of attack (blade angle) = 7.4 degrees

If I run the reverse engineered approach on the prop using its actual measured tsr of 8.75 (light loading)then:

Apparent wind angle = 9.8 degrees and the blade angle = 3.8 degrees.

So it can be seen the prop is operating inside a reasonable operating area, (I learned this part of it just today) and in reality the prop seems to work pretty well under load at low (6mph) and high (20+ MPH) windspeed, although I havent taken alot of data on it yet. It starts at about 4mph (overcomes startup friction and slight cogging) and will continue to run as low as 2-3 mph. The motor conversion (small 1/25 hp fan motor) I have this prop has too high of output inductance to be able to load it to a stall point in winds above maybe 17 or 18 mph, I think.

John

scoraigwind · « **Reply #16 on:** February 12, 2005, 01:15:55 AM »

John wrote

However, I have gone back to an existing blade that I wanted to speed up and recut the pitch angle all along the blade to some lower angle of attack and the result was the prop increased in speed. So Im assuming here that the rpm is affected by TSR (blade width) as well as angle of attack; which makes sense as thats how some props are speed controlled by changing angle of attack? Or does changing angle of attack just change the lift factor thus changing the effectivness of the blade under a given load?

I am getting pretty confused myself by some of this analysis, although the subject is essentially quite simple.

First of all the angles. Please be clear that there is a difference between blade angle (pitch or whatever) and angle of attack. If you reduce the blade angle (make it flatter) then you increase the angle of attack (the angle the wind strikes the blade at) and increase the lift (or stall the blade if you get it wrong and have too much load on it).

Reducing the blade angle will allow the blade to run faster and achieve a higher TSR so long as you load it correctly as well.

Optimium chord also depends on TSR, so it is important to get both the angle and the chord right if you want to fly right. But, as many people have noticed, there is a lot of tolerance as to what you can get away with.

As for taper and twist, you calculate the best angle and chord at each station. I use a spreadsheet to do this. I do not use differential equations, I use my simple rules of thumb. You can find these at http://www.scoraigwind.com/wpNotes/index.htm and http://www.scoraigwind.com/sheets/bladedesign.xls

A simpler shape of blade will also work so long as it is about the right shape in the outer 2/3 of the blade. This part is relatively straight, so you can carve it straight if that's what pleases you. I prefer the more complex shape as it is nicer looking, more efficient (slightly) and stronger too!

We did have 112 mph gusts in January, and there were quite a few repairs to do. Not only to the windmills but also trees falling down and roofs blown off!

johnlm · « **Reply #17 on:** February 12, 2005, 02:46:57 PM »

Hugh,

Thanks for all the help. I already had your design notes and the spreadsheet as I had downloaded them some time back. I just did not quite understand exactly what you were talking about in your notes until the last couple of days. I think I will use your notes, and likely your spreadsheet to design the next prop I build. I can see now how to follow along with your notes and the logic behind them.

Johnlm

finnsawyer · « **Reply #18 on:** February 13, 2005, 09:47:40 AM »

I do wish people would be more thorough about presenting their results, but I also realize they are not trained to do so. They understand very clearly their own situation in their minds, but fail to recognize that some point that is obvious to them may not be to others. I see a number of posts that I don't respond to because the situation is not clear to me. No need to get excited about it, though. Just the way it is.

News:

Author Topic: TSR and angles (Read 4334 times)