QUESTION:

I am doing a study on propeller design and have some questions to which I have been unable to answer.

1. I have read and article that claims to have had success with higher efficiencies of propellers at high activity factors. Please could you give me the definition of activity factor? Is this similar to solidarity?

2. I note that some newer propellers use a scimitar shape. What is the reason for using this shape?

ANSWER from Brent Wellman on October 27, 1999:

Good question. This is one that doesn't come up a lot due to the nature of helicopter rotors versus propellers.

Activity factor is a measure of how much power any given propeller can absorb. It is roughly equal to solidity times a constant for any particular prop.

Here are the details:

Solidity is simply the ratio of the total blade area of the propeller to the disk swept out when the prop turns. The blade area is roughly the length (called the radius) times the width (called the chord). That works well for untwisted rectangular blades, but there are few serious props like that, so engineers use integral calculus to figure the area of the blades. They integrate the chord (width) over the radius (length). For reasons known only to them, propeller engineers tend to integrate from 15% of the radius outward while helicopter engineers like to start at 0% (propeller hubs tend to be much larger than helicopter hubs in relation to prop size...).


It is useful to know solidity, because the pressure difference across the prop disk moves the slip stream (propelling the aircraft). The pressure differences between blade surfaces maintain this overall pressure gradient (they *are* wings, after all). The blades though, as rotating wings, will only maintain so much thrust per unit blade area, so knowing the ratio of areas gives you an idea of how fast you can make the slip stream motivate...sorta.

In props, some blade area is better than other blade area.

It turns out that low solidity yields high efficiency. Therefore, low-speed, low-power props tend to have few blades and they are skinny (we say short chord, or high aspect ratio). The Cessna 172 has a two-bladed McCauley prop, and it does just fine with it, thank you.

It turns out that if you really want to drive a prop to high speeds and pump a load of power into it, you need higher solidity. The engineers who worked on this problem in the 1930's developed a prop measure called activity factor. It appears to have been defined to yield a nice number "around" 100, than for any other purpose, but it *does* give an apples-to-apples comparison of propeller designs with respect to their ability to absorb power efficiently.

As I said above, all blade area is not created equal in props. Bits near the tip tend to spin faster, encounter higher dynamic pressures, generate more lift (thrust), sweep over a larger portion of the propeller disk, and so on as compared to bits closer to the spinner. So engineers developed a "power weighted" solidity measurement called "activity factor." It is measured per blade and doesn't account for the number of blades as solidity does.

It is defined as follows (and words are not as good as mathematical notation for this): Activity factor equals (100,000 divided by prop diameter to the fifth power) times the integral, from 15% radius to the tip, of the radius cubed times the chord at that radius, with respect *to* the radius. If you don't have the math, don't sweat it.

Activity factor was important as high speed became important to the sacrifice of efficiency. Prop blades designed for high speed put more area near the tip to put more lifting area where it would do the most good. They also tend to have more blades (4 or 5) for the same reason. Look at the prop on a P-51 Mustang, for instance.

Such paddle-shaped blades are really quite good at high speeds, and are still in use. The C-130 Hercules transport uses the Hamilton Standard Hydramatic constant speed prop. Its activity factor is 162 per blade.

The Cessna 172 prop mentioned above has an activity factor of 103 per blade.

You have described props with a scimitar shape. This was the result of some prop research done at NASA Lewis (now *Glenn*) Research Center in the 70's and 80's in an attempt to design an efficient prop designed to operate at Mach .8 or so (nearly jet transport speeds).


At extremely high power settings, the pressure difference is enough to stall out prop tips. Blade area is moved inboard and the tip is tapered to allow more of the blade area to continue to operate efficiently. Also, if high Mach numbers are seen at the tip, it is useful to sweep back the tips, like the wings of a high-speed transport, and for the same reasons. A swept blade, however, would tend to break off at the base if spun at great speed, therefore, the inner portion is swept *forward* to balance things out (at least overall). The result is a blade the shape of a scimitar.

Such experimental props have been reported to have activity factors of 203 per blade. See NASA-TM-X-73612, Mikkelson, et al, "Design and Performance of Energy Efficient Propellers for Mach 0.8 Cruise." It is available from the Society of Automotive Engineers as paper #770458.