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# Determining the optimal angle of attack for a propeller

## Determining the optimal angle of attack for a propeller

(OP)
Hey everyone I looking for a way to determine the optimal angle of attack so at the cruise speed the efficiency of my propeller is as high as possible.

The exact amount of thrust it need to deliver and the outer dimensions are given.

What the teachers/professors said to us is that we should just find it with iterating the angle in a program we got from them that shows the values, like thrust, torque, power and efficiency.

But still I gives me no foundation in how I find the values and I just can't be satisfied by iterating(a freaking chimpansee could do that).

So I tried find a way to calculate it, you can see what I tried in the attachment "Uitwerking_bepalen_alpha".
This way I devised isn't a exact way either, since I make a few assumptions, the program uses 5 different shape models, so I decided to divide the blade in 5 parts where I take the center of every part as the radius of that part. This way I can calculate the radius of every part by r= r_min + r_percentage * (r_max - r_min), where r-min is the edge of the hub, r_max the outer of the propeller and r_percentage is the percentage at which the center of the blade type is placed on the propeller blade.
(r1 0% r2 25% r3 50% r4 75% r5 95%)

Since it's quite a lot of work to calculate the angles this way I asked a professor first if it was correct, he said that it was not.
We have 2 values for alpha and phi, the target values (theoreticall values) and effective values (the real values).

Now the target phi is completely indepent of the target alpha but for the effective values he said this wasn't the case.

In the other attachment, you can see the sheets of our class, in there there're several formula's in the end you can see they use 2 coefficients a and b, these are calculated by the program through algorithms they told me.
He said it had something to do with these coefficients, but he also said he didn't have the time to completely look through it.

My question does anyone know a good way to calculate these angles of attacks or if my way is correct/incorrect or can be made correct.

http://files.engineering.com/getfile.aspx?folder=d...
http://files.engineering.com/getfile.aspx?folder=0...

### RE: Determining the optimal angle of attack for a propeller

i applaud your attempts to get more out of your project than just going through the motions, completing the lab, and going onto the next assignment.

i'm not really seeing your efficiency calc (1) ... V*T is produced power, w*Q ? i'd've thought Q was more the engine supplied torque (and not a function of propeller properties) ?

there are also many things to optimise ... maybe the program you're trying to understand isn't optimising speed by maximising propeller power efficiency ?
you can minisise drag, maximise thrust, maximise power ...

and we'll probably both get into trouble with student posting ...

### RE: Determining the optimal angle of attack for a propeller

Best alpha to use an airfoil at is where Cl/Cd is maximum. Hugh Piggot's books
http://www.scoraigwind.com/
on wind turbine design have the tip speed ratio (R*omega / wind velocity along the axis of rotation) as a design parameter. If you think about it, this is 1/tan alpha.

Tip alpha, and RPM would be likely starting place to optimize. Use vector diagram and airfol data to get a starting point.

### RE: Determining the optimal angle of attack for a propeller

i would separate airplane propellers from wind turbine propellers, airplane propellers are designed to maximise thrust, and wind turbine propellers (which don't want thrust) are designed for torque (no?).

### RE: Determining the optimal angle of attack for a propeller

I initially thought it might be a boat propeller posted in the wrong forum as shaft angle in boats is a critical aspect of both propeller and hull efficiency and it changes constantly with speed.

I am only guessing it is aeroplane propellers as that is not mentioned in the OP, but other details seem to suggest it.

Aeroplane propellers is certainly not my area, so my comments are straight from the hip. I have had a bit to do with high speed boat propellers and I think a little might transpose over.

I presume the efficient shaft angle is related to wing lift and angle of attack and to airspeed of the aircraft. I am still not clear if the question is about shaft angle or pitch angle, but I presume pitch angle which of course changes from the hub to the tip. The aerofoil shape of the blade cross section obviously also comes into play.

Regards
Pat
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### RE: Determining the optimal angle of attack for a propeller

I think you'll run into trouble because working out the efficiency of even a 2D airfoil at a given AoA is way beyond where you are in your course. But that's no reason not to read ahead.

Cheers

Greg Locock

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### RE: Determining the optimal angle of attack for a propeller

RB, A wing doesn't know or care what it's doing, and BTW, should I serve it up on a platter? For max propeller efficiency, you want to maximize the ratio of thrust to shaft work, a windmill is simply the geometric inverse, but your desired operating point is where the lift/drag ratio is maximum. You can find (l/d)max and alphal/dmax by reading a drag polar.
Ref:
http://en.wikipedia.org/wiki/Drag_Polar

Theory of Wing Sections, Abbot & von Doenhoff, can be found free online. You should be able to find the section properties for the propeller.

This is really cool, because on looking you can see it in many applications.

The concorde used a cruise climb profile by which it flew at (l/d)max during the whole cruise. As fuel is burned and the a/c weight and required lift decrease the plane climbs to a higher altitude. Dynamic pressure and lift decrease as the air thins, so the plane flies at the optimum l/d ratio during the whole cruise.

Optimum glide? The glide angle = atan (l/d)max, and the optimum glide ratio = (l/d)max

Prop twist? You might find that at any station on the prop, Forward velocity/R*omega is the same.

Using the same principal, Paul Macreadie wrote an amateur scientist column in scientific american, mid-late 80's, estimated (l/d)max of soaring condors using just, IIRC diameter of the circle they flew in and how long it took to complete a circle. His other credits include the gossamer albatross, gossamer condor, and aerovironment.

So bug your professor, the above should be a few starting points.

### RE: Determining the optimal angle of attack for a propeller

i agree the wing doesn't care, but the "intelligent" designer does.

a wind turbine blade doesn't want to produce thrust, at least the way i see them mounted rigidly to the ground, and the way i feel the flow downstream of the blade. A wind turbine blade does want to produce torque, to drive the generator. This means the desired lift vector is in a different direction relative to the propeller disc, compared to an airplane propeller. When I first saw modern wind turbine blades i thought they looked really odd (having experience with airplane propellers) until i thought about this difference in design goal. another obvious difference (that'll affect the blade shape) is the very low out-of-disc-plane velocity (for an airplane forward speed is a much higher fraction of tip speed than for a wind turbine.

### RE: Determining the optimal angle of attack for a propeller

RB, A wing doesn't know or care what it's doing, and BTW, should I serve it up on a platter? For max propeller efficiency, you want to maximize the ratio of thrust to shaft work, a windmill is simply the geometric inverse [READ BASS ACKWARDS PROP], but your desired operating point is where the lift/drag ratio is maximum. You can find (l/d)max and alphal/dmax by reading a drag polar.

Wing sections should be appropriate to operating Re as well.

I'm not asking anyone to make a propeller like a wind turbine. I mention 4 or 5 different cases where the same operating point alpha=alphal/dmax applies. I bet if you do the vectors on a prop or wind turbine, you'll find that an airfoil alpha wrt the apparent wind (R*omega x + Vinfinityy) is a good place to start optimization. I'm sure the rest of the real world will figure in.

### RE: Determining the optimal angle of attack for a propeller

While this thread originates from a student post, I think it has been left alone because it was interesting and the OP seemed to be looking to go beyond normal school work levels.

If it becomes obvious that someone answers a homework question for himm rather than helping a real world situation at peer review level, it will certainly evaporate into the ether.

Regards
Pat
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### RE: Determining the optimal angle of attack for a propeller

Correction, wind turbine is not bass ackwards prop. In a wind turbine drag vector is parallel to vinfinity, lift vector is perpendicular. In a prop, lift vector is opposite vinfinity, drag is perpendicular, so 90 degree rotation.

Still the same problem. You want the wing to fly at max Cl/Cd. Use geometry and rotation to put the apparent wind where it needs to be.

### RE: Determining the optimal angle of attack for a propeller

(OP)
I'm still here :D

Looking through the comments, will comment more tommorow.

Sorry it took me so long to respond (but this isn't the only thing I've for school and it's on a lower priority since it's already finished and thus for self intersest).

Just as a small clarification, it's about an airplane propeller (in our case it was for a model airplane, but that should be more or less the same).

Also thanks everybody for the responses :D

### RE: Determining the optimal angle of attack for a propeller

Hi MechIrTue:..

Cheers

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