How do I calculate CoD of a propeller?

"Theory of Airfoils" is a good reference book to read.

Haven't looked at a NACA airfoil profile document in over a decade but I seem to remember the drag coefficient of popular airfoils being in there.

L. J.

Your formula suggests that the blade angle is a constant.

I've never, ever seen a prop that had a constant blade angle. It is invariably a course angle near the hub and gets progressively shallower towards the tip, no doubt to compensate for the differences in linear speed at each station along the blade.

How does your formula address this?

Thanks

L. J.

The pitch of the propellor is constant but the angle of the blade varies:

This pich is constant from the hub to the outside dia so that the angle of the blade times the radius at the point gives you the same distance.

p= pi * r * tan a where a = angle of the blade ( at radius r).

As r varies so does a

tan a = p/(pi * r )

Hope this clarifies you question.

You wrote: "linear speed at each station"

Shouldn't it read "Linear lift"?

Wangito.

Shouldn't it read "Linear lift"?

No. The difference in linear speed is exactly I meant.

While the angular velocity is obviously the same anywhere along the blade, the speed of air over the leading edge varies from relatively slow by the hub, to much faster at the tip where the radius is largest.

The limiting factor on most aircraft props is the tip speed which can approach but not transition to supersonic without negative consequences.

This may not be a consideration in a wind driven turbine which turns slowly. Without knowing their exact disk size it's hard to say if tip speed is a factor.

It's easy enough to figure out: simply multiply the linear speed at the tip, by the RPM's of the prop and compare it to the speed of sound at that elevation.

I questioned the use of a constant blade angle in the formula because the slower linear velocity of stations closer to the hub mandates a higher angle of attack in order to optimize the thrust being generated.

Just take a look at one. You'll see it immediately.

L. J.

Not trying to be too academic or picky, but the end product of which we are interested in, is lift and not propeller linear speed. As you rightfully say, angular velocity is the same along the propeller stations. (God forbid if not...) You are changing the AOC along the blade to produce equal LIFT in every station, hence linear thrust. Isn't it so?

As far as air turbines are concerned, they usually change AOC along the blade to increase efficiency and in order to avoid undue stress by producing unequal thrust (or lift ) at high velocity winds. I didn't see them all, but never saw a constant angle of attack prop.

Wangito

A small clarification/extension is in order I suppose...

I will need this information and direction and it is perfect for my app, but I want to add another angle...if the "prop" is stationary, how do I get the "resistance" to spin from the prop moving through the air? The loss of energy from the wind that is due to the prop and it's spin...they are for different areas of the same project.

Thank you very much for the details to point, it helps a lot.

Glenn

"My calculations I sent you are purely based on momentum and not on aerodynamic principles."

Heaven forbid we should "want to be difficult" and discuss propellers as aerodynamic devices!

If not in the context of wind driven, fluid dynamic devices, what context would you suggest we use Johan?

L. J.

On the basis that the wind will in due course be driving the turbine, there need not be net drag during the initial spin-up phase. In practice, there will be some drag initially, particularly if the angular acceleration you apply is great, but this should will be well compensated by input energy from the wind as the turbine approaches the operational speed.

That means that J v N's preliminary estimate is likely to be good enough for most practical purposes. If you need to model it with substantially better accuracy you would need to have detail of the design of the blade, which will depend on the mechanics of the blade itself as well as on the wind-speed range over which it is optimised. The more sensible alternative would be to observe the self-acceleration of the unloaded propellor under the range of wind conditions at which you might wish to operate it, and estimate the additional power you might require to spin it up within your required time based on J v N's data.

We use free wheel propeller, with acceleration clutch to avoid initial drag load. it will start spinning even at the slightest breeze, and will not engage before a pre determined rpm. The clutch will disengaged upon reaching low predetermined load. Thus, the turbine is almost always slow spinning having the effect of flywheel.

Wangito

I think i should update the "question"...

I started to tackle the idea on my own, but I can see that good help is NOT hard to find...at least in this instance...lol

I want to calculate the forces that are at work againsty my prop or fan on my wind generator as the wind blows on it. I understand that friction in the bearings and generator/alternator will be there and I can estimate/calculate that from manufacturer data, it's the aero and momentum as said here that I was looking for help on.

Would breaking it down into 2 basic "states" like standing and rotating be enough? I want to assume that once it's rotating there should be ittle change to affect the situation, but again am willing to defer to better exercised cerebrum than mine....

Thanks aagain.

Glenn

I don't understand - why would you wish to spin it up at all if it isn't going to take power from the wind once it is up to speed? And, for that case, I wouldn't anticipate net air drag at any speed that is less than the operational speed. (It may be a paradox, but the prop is designed to slow the air by the maximum amount when it reaches the proper operating speed)

Or maybe what you are really asking is how much the minimum useful wind would help with the start-up of the prop?

Yes, and no....

I do indeed want to figure the start up "losses" but also those that are there after the start up...

That sounds like the full running design of a wind turbine propeller. As these things run turbulent, you will either need to have data provided by the propeller manufacturer, or full details of the format of the propeller and an aerodynamics analysis package. Either way, that's way beyond the sort of assistance that is feasible here.

Thank you...this has been great.