Torque Measurements

Wow, cool, sounds like you know what you're talking about, can you tell me what all that means. I make artificial limbs...legs and arms, Im good with carbon fiber, but don't know a lot about electricity, (and yet Im trying to make it out of thin air). We got mixed up in this wind turbine and now we are at the point of proof of concept. CR4 has helped greatly in the past, please forgive my ignoance on this last final detail, (which wire goes where?). GA though.

Ok, let me expand a little on my test procedure. The goal that you asked was improvement of the power transfer from the wind into mechanical motion. The DC generator attached to the windmill shaft will produce a voltage proportional to rotational velocity of the windmill not the available power. When the only electric load the generator "sees" is your voltmeter, the only mechanical load the wind mill will give to the wind will be unusable losses of various frictions in the mill, any gearing and the generator. By consistently adding a measurable mechanical load that slows the windmill velocity by 5% you can find out which of your mechanical designs transfers the most amount of wind power to mechanical power. A 5% drop you may find will not be your most efficient transfer from mechanical to electrical, but it will make your calculations accurate for the mechanical to electrical conversion will be consistent.

Now, I did make an assumption and didn't tell anyone about it. I assumed you would be prototyping your designs first with a miniature model in a home built laminar flow wind tunnel. The most elegant simple design for quickly making the tubing for the laminar flow comes from the Mythbusters. Find a restaurant supply store near you. Buy several boxes of drinking straws, preferably non-wrapped straws. Leave the straws in the box but remove the top and bottom of the boxes or whichever box ends that the straw tips touch. Blow the turbulent erratic wind from a fan through this stack of straws and bingo you have laminar flow on the other side. By varying the speed of the fan, you can now also change the velocity of your air flow for more measurements.

Have Fun

The goal is actually to measure the the different amounts of torque/power that the blades produce. We are using a modified shipping container as a wind tunnel, this will work for a "slow wind" tunnel. An airplane engine and prop for wind production, so we can accurately reproduce "wind". All things being equal, different blade designs should produce different torque, short of grabbing hold of it with my hand I find I am at a loss for how to measure it. I could use the old ways - rope thru a pulley attached to a mass, measure speed of movement. I know there is a better way and I think redfred has it, I just dont understand everything he said, FORGIVE ME I'M MEDICAL PROFESIONAL, a poor one or I would have hired an engineer.

Well if you identify what you don't understand, I'll gladly explain.

Redfred, so you are saying that just hooking up the blades to the generator and measuring the electricty produced by the generator is not effective - an incremental load on the generator (power usage) must be applied in order to effectivly measure power output. And instead of a generator I could use any steady load that can be manually varied? is this right.

Yes, you must load the generator to measure your net power conversion. The change in output voltage between an unloaded and a loaded generator will relate the converted wind power available. (Later work can be done to optimize your generator but this won't be useful until turbine efficiencies are known.) I choose a 95% drop to ease calculations and to minimize generator loss effects but technically a fixed load will do. Think of it this way; unloaded your windmill will be just an anemometer measuring the wind speed in your tunnel, loaded the generator will now be required to draw power out of that same wind. By doing your blade modifications with the same wind speed and getting different net power outs for each configuration you'll be able to determine at which speed which windmill geometry works better. I suspect you will find different wind speeds will have slightly different maximum efficiency geometries.

Redfred, thx, do you think altitude would significantly affect efficiency, would it require different designs at different altitudes?

Any suggestions as to modulating the load on the generator?

and is there a mathimatical formula for converting the voltage output changes on the generator to torque or horsepower?

Redfred whats your speciality of study?

First my background, I have a degree in Electrical Engineering. Many years back I pursued a Physics degree but found building tangible things more to my liking. (I also had a unexpected urge to eat and support family members.) I now work at a premiere scientific research facility on Long Island building precise "toys" for Physicists, Chemists, Biologists, Geologists and a whole batch of other "-ists". To be able to build these "toys" to measure or move arcane things, I've had to learn a little bit of many fields outside my realm of Electrical Engineering. _{(I'm never comfortable about seemingly bragging. But you did ask.)}

Now onto your technical questions. I'm not sure if the efficiency of a pitched blade to convert wind power to mechanical power will change with altitude. But with less total mass per unit volume in the air I would expect less energy in and out of the process. The pilots and Aeronautical Engineers here should have a better idea on this.

As far as the generator output and relationships one must understand what the units actually measure. Torque (τ) is the measurement of rotational force. The angular acceleration (α) and torque relate by the rotational inertia (I) in the formula τ=I*α. The angular velocity (ω) determines the kinetic energy of a rotating body by K_rot=1/2*I*ω². Calculating I requires some complicated three dimensional calculus, depending on the shape and density of the object to be spun. Most of the time I is empirically measured instead. Now with a generator with a fixed rotor magnetic field the voltage output will be proportional to the angular velocity of the rotor's motion. The energy out of a DC generator is calculated by W=V*i (using a small i for current to not confuse with rotational inertia). So by measuring the generator voltage you will be indirectly measuring the rotational velocity only. To measure the torque you must either change the torque and see how quickly the angular velocity changes or change the rotational inertia. By loading the generator with an external load, you will have effectively changed the rotational inertia of the windmill.

So, if I haven't totally baffled you by now, you should see that a series of initial calibrating tests will have to be done measuring voltages that will change in time as different loads and energy sources get applied, along with your blade measurements.

Redfred, Wow that was fascinating, yea I got, well explained, GA.

Once the patent goes thru I would like to share, more of whats being done,...and get your opinion - got an email address or do you want to be contacted thru CR4?

I added the adjective "effectively" as a quick CYA. You are correct that it will not have the same effect in energy storage that rotational inertia does. Thinking this though a little more carefully, the resistive electric load will actually act as a drag proportional to rotational velocity of the windmill. I believe a combination of inductors and capacitors to store the energy could achieve the same dynamics as rotational inertia. But including the bidirectional energy transformation losses required through the motor/generator will require a bit more thought on my part to be sure.

Good catch Nick.

Due to your study you are familiar with transfer functions.

Let us make a simple model of the windmill+generator and assume a resistive load on the last.

The windmill will be actuated by a "wind torque" and mechanically bond to the generator so that the two inertias will be connected (mechanical inertia). The generator will give a tension proportional to the rotational speed and the resistant torque will be proportional to the current in the loop build up by the load and the internal resistance of the generator windings. This torque will thus be: Kt*Kn*n/Rg. The rotational speed "n" is the integral of the angular acceleration or we can consider that the acceleration is the time derivative of speed. So that writing the Equation for the system we get:

(J1+J2)*[dn/dt]+Kt*Kn/R*n= Tw where

J1+J2= sum of the 2 inertia

n= rotational speed of system windmill+generator

Tw= wind generated torque.

As one sees a resistive load is a "damper". If the load is more complex then the equation will be of a higher degree which leads under circumstances to oscillations and even instability.

But in any case the inertia will not be changed by the load.

It is a simple model but good enough to make effects clear.

Comments?

niak name, you lost me.

Why?

In fact it is a simple torque balance equation considering the "wind torque " as the active one and the load as the resistive one.

The general equation based on the Newtons law says that acceleration is due to the resulting sum of all active and resistive torques acting on the inertia and divided by value of last. It is for rotational movements of the well known M* X" = Σ(F-R) where M is the mass, F the active forces on the mass and R the resistive forces on same mass.

For the generator -provided it is one with a permanent magnets rotor - the resistive torque depends on the speed which is the integral of the acceleration or the other way around the acceleration is the derivative of the speed if this one is taken as reference parameter.

For your research the effect of the resistive load as a damper is positive since it will make your test system quieter and the measurements will be more reliable since with less ripple.

All what Redfred wrote is correct.

Even the comment with respect to the "inertia" is correct according to a check I made after my comment. If the load is partly capacitive the system behaves as the inertia would be increased. This can happen if you load a battery since it has same behaviour as a capacitance with respect to the generator. As long as you only want to compare power harvesting capability it would be better to work with resistive loads -power resistors- and take care to cool them the right way.

Nick,

I avoided doing precisely the simple transfer function you listed because of my realized fear of baffling people here. (Don't you just hate it when Mathematics declares something as simple or elementary. There is nothing elementary about elementary differential equations. This must be an extension of Newton's arrogance. But I digress.) There's also the rotational inertia of the rotor, friction effects from the bearings and any dampening transmission losses that should be added to your equation for accuracy. Let's not forget that this assumes the simplest model for the DC motor; no brush commutation, changing magnetic fields, eddy current losses, source impedance or core saturation effects. But I do realize that that's why you labeled your equation as simple.

But now that I've piled on more apparently baffling characteristics, let me simplify this by focusing on the measurement approach. By doing a time based measurement of the initially unloaded output voltage with a constant, non swirling airflow past the wind mill blades and seeing how much and quickly the voltage drops when the known resistive load gets applied, accurate quantitative measurements of variations in windmill design can still be accomplished.

Redfred, ok, I understand the second paragraph, thx GA

Hi,

first of first you should have a calculation of safe maximum speed or a concrete/steel encapsulation to capture the fragments.

Then calculate by angle of attack of blades to wind-direction the maximum theoretical velocity that will never be reached.

Then do your test at half this velocity, this will be near the amximum available power.

Full speed: no power,

zero speed: no power.

Half way to full speed: near optimum.

See if safe at this speed!

Have success.

RHABE

I have been trying to find a way to do a CFD analysis, but can't find anyone I can afford. any suggestions.

There was a time when Scaled Composites (Burt Rutan's company) might have been willing to partner with you, and help get this going. His company is close to you. I think that time may be long gone, but it might be worth contacting them for suggestions.

The easiest and cheapest way is to offer it as a project for aeronautical engineering students. It would be excellent experience. Solid Works and Flomerics together are something like $30,000 per seat, but universities get a huge discount. I think Georgia Tech has many seats, and lots of students who would bid for this kind of project. Stanford has a good program in aeronautics, and that department could probably send you in the right direction -- possibly to a university closer to you. You might try giving Desktop Aeronautics a call.

Blink, thks for the CFD info, GA.

There are simple rpm-meters which could be put on the other end of the DC generator.

You need a DYNOmite dynamometer. They will have all the answers for you.

www.land-and-sea.com

You need to know how well the blades works. Torque is one measurement.

Power generated is another. You can put the blade on a generator and just measure power output. You can vary your "wind" speed and see how the blade works in different conditions.

In a small scale, you can use a DC motor. When you spin the rotor it'll generator electricity which you can measure in Volt and Amp.

In a larger scale you'll use AC generator and measure in kW.

Redfred, let me get back to you on exacetly what I need defined, thank you for your help and understanding. I've learned a lot from CR4 and thank everyone for their help.

From what I understand, it is power you want to measure.

P (kW) = T (Nm) * n (rpm) / 9550

To find power you need to measure both, torque and rpm.

To measure torque I would suggest to make yourself a simple Prony brake which lends itself to low speeds. In this case two wood blocks at 180 degrees spaced and pressed together with variable force (a screw with a spring) and mounted on a lever at which end you put a "load cell" of sorts. Torque = force x length of lever arm.

The simplest would be a spring scale which is not too accurate, the best is an actual load cell the instrumentation fellows use. To measure rpm is also not too difficult. There are many ways even a hand held Infrared sensor you can buy.

That is essentially it.

What was said before by Rhabe with half speed between maximum wind speed and zero speed may need some explanation. It is the same principle that applies to a turbo in any car for example.

The torque of the propeller or turbo is maximum with maximum differential speed of air flow to propeller speed.

If the propeller turns as fast as the wind there is not differential velocity and torque is zero, If the propeller turns very slow or near zero there is maximum differential wind speed and maximum torque. However, as Power is the product of both, torque and speed you also need speed. Going somewhere close to half speed of the propeller between zero and maximum, you have about half the torque and also half the speed. Multiplying both gives you the maximum power.

To illustrate that you can also compare that with the area of a square to the area of a rectangle. If the total length of the circumference is given, (adding all four sides) the maximum area is achieved by a square, meaning each of the sides are of same length. (4x4 = 16, 2x6 = 12, where 2 could be power and 6 to be speed, or vice versa).

If the propeller turns very slow or near zero there is maximum differential wind speed and maximum torque.

That is not generally true. If the propeller is turning very slow or stopped, the angle of attack of the wind with the blades goes beyond the stall angle of attack, and lift (therefore torque) falls off dramatically.

Hi Blink

I was concerned with the principle of near half speed providing the optimum power as the product of torque and rpm is at its maximum.

Comparing the rotating propeller with a fixed wing of that of an aircraft, I am not so sure if you are correct.

At near zero propeller speed we have maximum relative speed between wind and blade. This would correspond to maximum aircraft speed. Aircraft stall at low speed when the velocity is insufficient and angle of attack too great for the air to flow over the wing. The air separates and the wing stalls. A wing never stalls at too high velocity, staying sub-sonic in our example. (That should apply at super-sonic speeds too. I have never heard of a wing stalling at super-sonic speed either).

If you could explain your theory a bit more and what you mean "beyond" the angel of attack, too high or too low? would be appreciated. I don't think the angle of attack can ever be too low. Being too high yes, but that occurs at low relative speed or at high propeller rpm not at low propeller speed and high differential velocity between blade and wind.

You comments?

Thank you Blink,

That was a very good explanation. Deserves a GA.

It is the angle of attack that is dominant.

The answer would be to have windmills with variable propellers as well. However, just like in planes, the cost will go up, likely sufficiently for it not to be justifiable.

I agree that my statement was incorrect at the "outer edges". It is valid though in concept and may be valid between 20% and 80% of wind speed and blade rpm. The speed of the windmill should be adjusted according to the mean wind speed as higher wind speed would require a higher blade rpm for the same angle of attack.

Nicely done again Blink. One added extrapolation I'd like to add here. One of the advantages of a windmill stalling at higher airspeeds is that with the considerable higher energy available with higher wind speeds one doesn't want to over stress the blades or more easily the supporting mast. Let's not forget the mast must provide a sufficient opposing torque to produce power at the hub. So having the blades stall and lose efficiency in a gale or hurricane wind speed can be a good thing.

It is a difference to be made between small and big wind mills. For the small the blades are mostly straight and have same angle all along with respect to wind direction. This is done for cost reasons for an easier manufacturing.

For big turbines the ratio between outer radius and smallest effective radius is so big that the tangential speed is very different and the apparent wind speed cannot be assumed to be the mean value. It is thus necessary to use a torded profile which changes its angle along the radius. This is to compensate at least partly the variation of the attack angle.

Those turbines have also a controller which reduces automatically the angle is thresholds are reached in order to reduce the rotational speed via reduction of the wind generated torque.

In some designs even the torsional stiffness of the blades was used to compensate a too strong wind effect.

In order to optimize designers try to obtain the highest "portance" and the lowest drag since portance is the productive part of load on the profile and drag leads -via the bending- only to a stronger structure and a higher weight, inertia and cost.

A calibrated voltmeter and a calibrated ammeter connected to the alternator would do fine.

Alternatively, how about a Joule Calorimeter?

Remember the maximum power transfer theorem? Match the impedance of the alternator to the combined impedance of the cable and load, and "Robert is your mother's brother", as some might say......