Finding the coefficient of lift of a propeller blade?

[theBEAST]

Homework Statement

I need to approximate the thrust given by a propeller blade that are plastic and around 10-15cm in diameter but I am not sure what the coefficient of lift (or coefficient of thrust because they are the same thing?) is.

For example, a propeller blade may look like this:

From non-dimensionalization we know that:

d_Thrust = 0.5ρC_Lω²r²c dr
where c = chord​

Thus we can integrate that given the value of omega (which can be found from the torque curve) and also given C_L which is unknown and dependent on the propeller blades.

To find the thrust, my professor recommended that I look into the following article.

It gives graphs of C_D and C_L versus the angle of attack of both flat and cambered propeller blades I think? Also what are cambered propeller blades? How can I find the angle of attack of a propeller blade as it spins? Can we assume the coefficient is constant?

All in all, could anyone help me with finding the coefficient of lift.

Thanks

 

[haruspex]

According to http://en.wikipedia.org/wiki/Propeller_(marine), "The camber line is the line through the mid-thickness of a single blade. The camber is the maximum difference between the camber line and the chord joining the trailing and leading edges. The camber is expressed as a percentage of the chord."
I.e., if you look at a cross-section of the blade tangential to the rotation, it's roughly lens-shaped. If you draw a line from leading edge to trailing edge, staying about half way between the two sides, it may be curved. Its max deviation from a straight line joining the two end points is the camber.

 

[rcgldr]

To find the thrust, my professor recommended that I look into the following article.

A propeller doesn't quite behave like a wing. The lift from a wing is perpendicular to it's direction of travel, while the thrust from a propeller is in the same direction as the air flow relative to the propeller. A propeller operates in it's own induced wash (the air drawn into the propeller from in front of the propeller).

You can do a web search for "static thrust calculators", which approximate the thrust of a prop assuming a reasonable amount of pitch. Most of these calculators don't even have pitch as an input parameter, since it doesn't make a lot of difference in a static situation as long as the pitch is reasonable.

 

[haruspex]

A propeller doesn't quite behave like a wing. The lift from a wing is perpendicular to it's direction of travel, while the thrust from a propeller is in the same direction as the air flow relative to the propeller.

Surely the primary component of the velocity of the air relative to the blade is orthogonal to the direction of travel of the aircraft. It's not that different from a wing.

 

[CWatters]

How can I find the angle of attack of a propeller blade as it spins?

Thats not very easy. Not possible without knowing more information about the set up. eg what velocity is the aircraft/air is doing. I would look at the data for the section and see what angle of attack gives reasonably lift - say 75% of max Cl - or something like that.

I've seen model aircraft use a large spinning propellor as an air brake and I don't mean reverse thrust. It was a folding blade design eg the blades folded to reduce drag. To increase drag and steepen the descent the motor was switched on slowly. Enough to spin the blades but not to provide any thrust (eg the pitch speed was slower than the actual speed). In this condition the blade AOA is negative even though the blade pitch is +ve.

 

[CWatters]

Looking at that paper on page 829 there are charts showing typical Cl vs AOA for cambered sections. it would appear reasonable to use a value for Cl of about 0.5 to 0.7 at say 5 to 8 degrees. You might push it up a bit higher but that would be close to stalling.

 

[rcgldr]

A propeller doesn't quite behave like a wing. The lift from a wing is perpendicular to it's direction of travel, while the thrust from a propeller is in the same direction as the air flow relative to the propeller. A propeller operates in it's own induced wash (the air drawn into the propeller from in front of the propeller).

Surely the primary component of the velocity of the air relative to the blade is orthogonal to the direction of travel of the aircraft. It's not that different from a wing.

Having to operate in it's own induced wash reduces the efficiency of a propeller. As an example of this, it takes signficantly more power for a helicopter to hover in it's own induced wash than for the helicopter to travel forwards just fast enough to avoid most of the induced wash effect. The tangental speed of a rotor blade increases with distance from the axis, but the induced wash speed is nearly constant and also has a angular component that spins in the same direction of the propeller. The result is a component of "lift" from a propeller blade is in the direction of rotation, reducing efficiency. Most propellers are around 80% efficient. Wiki article:

http://en.wikipedia.org/wiki/Propeller_(aircraft)

In a static (zero ground speed) situation, increasing pitch (average AOA) beyond some practical minimum doesn't make that much difference in thrust versus rpm, due to a combination of issues like turbulence and/or blade stalling. The increased pitch is needed to operate at higher forward speeds though.

Link to one of many articles on propellers. Note the variation in chord angle and the airfoil used for a propeller blade from inner blade to outer tip. Thrust and drag calculations are complex. The outer portion of the propeller has more effect than the inner portion, the direction and magnitude of lift and drag changes as you go from the outer tip of a propeller to the center of a propeller, the induced wash affects the direction and speed of the relative flow.

propeller aerodynamics.htm

Getting back to the orignal question, do a web search for static thrust calculator. Some of these will include data for specific models of propellers used on radio control aircraft. There are also some calculators that calculate a recommended engine / motor and propeller combination given parameters for a model aircraft (would include drag and weight for a model) and desired speed.