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Thread: Surprised by prop efficiency analysis

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    bwilson4web's Avatar
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    Surprised by prop efficiency analysis

    Hi,

    Re-engine of N19WT replaces a 60 hp VW, 3,200 rpm, with a 60 hp, Hirth 3502, geared to 2,400 rpm. I've found a flight controllable IVOprop whose moment of inertia fits within the Hirth 3502 specs. But I wondered, 'What about prop diameter?'

    My first though was to keep the same pressure differential through the prop disk. The slower turning prop needs a larger diameter to move the same mass at the same pressure differential. It turns out this is the square-root of the ratio of the two rpm and moves the propeller diameter from 52" to 60". The landing gear would have to be 8"/2 or 4" taller. But is that enough?

    So I looked at propeller efficiency and this led to "advance ratio." There are multiple Google references but it all comes down to a non-dimensional formula:

    J = V / (n*d)

    J - advance ratio
    V - velocity feet/sec
    n - revs/sec
    d - propeller diameter in feet

    So I put together a quick spreadsheet and calculated propeller efficiency at three speeds and three diameters:

    • 60 mph - minimum flight speed
    • 80 mph - maximum rate of climb
    • 140 mph - maximum level speed
    • 48" - smallest diameter available
    • 52" - current prop diameter
    • 60" - calculated, constant pressure differential


    I also calculated the prop tip speeds to avoid high mach numbers.

    The prop efficiency surprised me at 60, 80, 140 mph:
    • Original 52" prop @3200 rpm, efficiency range: 27%, 38%, 68%
    • Alt 48" prop @2400 rpm, efficiency range: 46%, 55%, 79%
    • Alt 52" prop @2400 rpm, efficiency range: 38%, 55%, 79%
    • Alt 60" prop @2400 rpm, efficiency range: 38%, 46%, 72%


    I had expected the slower turning, 52" prop to be less efficient because of the higher pressure differential. Instead, it turned out to be more efficient across all speed ranges compared to the original 52" prop turning much faster. But even more surprising, the longer 60" prop was less efficient than the 52" and 48" props.

    The original, fixed pitch, wooden prop would limit the VW power at low speeds and let it generate more power at higher speeds. Due to the characteristics of the Hirth 3502, the replacement prop has to be flight adjustable to stay within a narrow rpm range. But finding that the prop efficiency decreased with larger diameter has me scratching my head. I would have thought that increasing the pressure differential across the smaller propeller disk would have reduced efficiency.

    The only thing that might make sense is the increased tip speed of the larger diameter prop may have a greater impact on efficiency than I originally thought:
    • 48" @2400: 504, 506, 512 ft/s tip speeds at 60, 80, 140 mph
    • 52" @2400: 546, 547, 553
    • 60" @2400: 630, 631, 636


    But these tip velocities are relatively narrow and I don't see enough, even raised to a power, to explain the lost efficiency of the larger diameter prop.

    Have I missed something?

    Bob Wilson
    Last edited by bwilson4web; 02-24-2013 at 01:10 PM. Reason: formatting

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    I'm not an engineer, but I have a few guesses!

    First, the props aren't pitched the same. You may be comparing apples to oranges (speed vs. climb props), as the variable pitch prop changes the dynamic across RPM. I wonder if the fixed prop were pitched to the same as the variable at 2400 RPM that they wouldn't match up more closely. Of course one would have to have three fixed props to match the variable one for more rigorous testing.

    Second, we're missing the thrust. Effectiveness beats efficiency! While the efficiency of the larger prop might be seven percent less than the smaller one, it may have ten or twelve percent more thrust....and that's all that really matters.

    Third, I'm betting that the long prop is vibrating more than the shorter one, which would make it less efficient...or not.

    I'm betting the change in pitch due to RPMs is the efficiency solution.
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    bwilson4web's Avatar
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    Thanks Frank,

    I'm still researching propeller sizing and dynamics. The pitch changes are absolutely necessary, especially at these lower rpms. Also, no problem finding efficiency and other analysis. But I'm running short of practical design rules on the size and number of blades as a function of HP.

    Bob Wilson

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    I'm guessing it's all about torque with more blades.

    Let's say we have high RPM's and plenty of torque. The length of the blade is limited by the RPM's (darned mach numbers!), but we have loads of power. Solution - add another blade! Three blades won't interfere with each other aerodynamically, and I get a third more thrust in the same disk.

    With lower torque it doesn't matter what the RPM potentials are; we just won't have the power to drive it through the air to keep the RPMs up. That's the "unloading" of the prop and rise in RPM's a lot of planes have after they leave ground effect.

    Looking back at WWI Dh4's and SE5a's we start seeing four blades. RPM's are lower, but they had monstrous torque available to them to overcome the resistance of the blades through the air.

    Working backwards, we see four bladed props on wind-driven generators for the same reason, but now resistance is what we want to drive the shaft as quickly as we can.

    The Kansas City Dawn Patrol guys did some back of the envelope stuff with props and then put pull testers behind their planes to validate differences. They were more interested in finding out minimum thrust numbers for safe flight than the science behind it, but they worked out min/max for prop pitch and length for their Nieuport 11's. Of course anything but a wooden two blade prop on a WWI replica would be heresy, so they had that constraint to work with.

    Again, I'm woefully ignorant on the science of this other than the basics - I'm hoping to spark an idea to help you out.
    Last edited by Frank Giger; 02-26-2013 at 08:31 AM. Reason: formatting
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    Dang ol' double post!
    Last edited by Frank Giger; 02-26-2013 at 08:29 AM.
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    bwilson4web's Avatar
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    Thanks Frank,

    Somehow sleeping on the problem made things a lot clearer:

    1) blade area and profile defines the lift/drag per blade - this is the fundamental force the engine has to overcome.
    2) integrating the drag per slide of the prop times the radius - this gives the 'anti-torque' or the moment the engine torque has to overcome
    3) maximum static pitch is the angle that leads to blade stall - in effect the boundary between a prop and a club

    Now I was concerned that the 52", two-bladed prop might not have enough blade area to avoid prop-stall at 60 hp, take-off power, at 2,300 rpm. But with a better understanding of the physics, I should be able to work up a credible model.

    BTW, I did speak with Ivoprop yesterday and they think this is going to work based upon another customer's experience. But I also have the option of adding another blade later if testing reveals a problem.

    I'm fairly confident this this going to work but I will be thinking about how to test for torsional vibration . . . just to make sure.

    Bob Wilson

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    I don't know much about prop formulas, but I have read that the Wright Bros prop with no help from computer design was about 70 percent efficient and the best our most modern props can do is about 90% so not that much above them.

    Howard Pardue raced his Fury at Reno many years, top speed around 420 or so. One year some computer wizard boffin came up with a fabulous new prop design, and convinced Howard to buy it .
    He then went about 15 mph Slower with the new prop!

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    Quote Originally Posted by Bill Greenwood View Post
    I don't know much about prop formulas, but I have read that the Wright Bros prop with no help from computer design was about 70 percent efficient and the best our most modern props can do is about 90% so not that much above them.Howard Pardue raced his Fury at Reno many years, top speed around 420 or so. One year some computer wizard boffin came up with a fabulous new prop design, and convinced Howard to buy it . He then went about 15 mph Slower with the new prop!
    Well, the Wright Brothers might not have had computers but they were pretty good scientists! They spent A LOT of time testing different airfoils both for the wings and the props until they settled on both.Apart from the whole crazy sue-everyone-breathing affliction they had, they'd fit pretty well with any group of homebuilders - their testing platform was a circular deal set on the handlebars of a bike with the airfoil to be checked bolted upright against it.That and they begged for every bit of research available at the time (and got it) before they started building their first gliders.
    The opinions and statements of this poster are largely based on facts and portray a possible version of the actual events.

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    bwilson4web's Avatar
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    I'm pretty confident in the prop selection although I will have to call Ivoprop on Wednesday and get the moment of inertia for both the two-blade and three-blade configuration. "Back of the envelope" indicates it will work with a two-blade but having the ability to make it into a three-blade provides an extra margin.

    "Back of the envelope" means the published specs claim it can handle 100 hp which would make sense for a three-bladed prop. A two-bladed prop then should handle 2/3 or ~66 hp. But "back of the envelope" are notoriously imprecise. If that 100 hp is for their 74" diameter, three-bladed prop, then a three-blade 52" prop should handle up to 83 hp and a two-blade only 56 hp. But these are "back of the envelope" and the real test will be at engine run-up. <grins>

    The best news is there is a second supplier for electrically adjustable props, Airmaster, and they have an active, USA distributor. I called him on Tuesday just to make sure he got my e-mail and dang it . . . we probably could have spent the rest of the afternoon discussing the technology. I'm impressed with Bud Yerly who runs "Custom Flight Creations" in Florida.

    At this point I'm very confident the Hirth 3502 is going to work out great. I have some weight and balance and a whole, firewall forward design to work out but it really looks like it going to work. Friday I'll go visit Matt at Recreational Power and we'll work out the fine details.

    Bob Wilson

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    David J. Gall's Avatar
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    Bob,

    First of all, you don't say how you arrived at your effficiency numbers. J = V / (n*d) is only one of the formulae needed for propeller calculations. Further, the test for efficiency is not uniformity of the pressure differential across the propeller disk. As Betz stated in 1919, the criterion for efficiency is the uniformity of delta-V along the length of a blade (delta-V in the airplane's longitudinal direction). In 1929, Goldstein calculated the distribution of circulation required along the blade at various advance ratios for various numbers of blades. This is the "gold standard" for propeller design absent specialized computer software. Still, its application is beyond the scope of a forum post.

    But why are we even looking at efficiency? You've already established your constraints: You're using 60 hp, and you're limited to 52" diameter because of ground clearance issues. You previously had 60 hp at 3200 prop rpm (at Vh - maximum full-power level flight speed), and your "only" change is that now you'll be making that power at 2400 prop rpm at Vh. Simple enough. Let's look at some rules-of-thumb that can get you in range of what you should be looking for in a prop for your new engine. These rules are from Al Schubert's book "How I Make Wood Propellers," but the underlying formulas are available in numerous scholarly works on propeller design.

    Power required to turn a propeller varies in proportion to the cube of the rpm. 2400/3200 = 0.75, therefore the power absorbed by your 52" prop turning at 2400 rpm will be 0.75 ^ 3 = .422 = 42.2%, assuming that same prop absorbed 100% power at 3200 rpm. Naturally, the prop would need to be re-pitched for the new (lower) Vh at this rpm, and the throttle would be near idle, even though the engine would be near red-line rpm.... Not good so far.

    Power required to turn a propeller varies in proportion to the fifth power of the diameter. But you're restricted to not changing the diameter.

    Just for fun, let's see what change in diameter would be needed to get the power absorbed back up to 100%. We want the prop to absorb 100 / 42.2 = 2.37 times as much power, so we need the prop diameter to increase by a factor of 2.37 ^ (1/5) = 1.19 or a 19% increase in diameter. So you'd need a 52 x 1.19 = 61.9 inch diameter. But that's unacceptable, so we need to find another way to absorb that power while still generating thrust efficiently.

    Another good rule of thumb is that the rpm will increase by about 100 rpm if the blade width is decreased by 1/6. Turning that to our advantage, we'll increase the blade width to absorb more power. 3200 - 2400 = 800 rpm, so it looks like you might try increasing the total blade width by about 8/6 = 4/3 = 1.33. You could do that by increasing the width of each blade by 1/9 and then adding a third blade, or by decreasing the width of each blade by 1/6 and then doubling the blade count to 4 blades.

    You are at a definite advantage at this stage since you already know the expected Vh of your plane with the 60hp VW, and you're (supposed to be) getting the same hp from the Hirth, so you can figure the prop pitch from the simple rule of thumb that pitch in feet = MPH x 100 / RPM. So using 140 mph as Vh, you prop pitch should be 140 x 100 / 2400 = 5.83 feet = 70 inches.

    Let's back up a moment and do that same calculation for your old engine/prop: 140 x 100 / 3200 = 4.375 feet = 52.5 inches. Is your original 52" diameter VW prop a 52" or 53" pitch? If not, you might want to adjust your new prop's pitch from 70" proportionately to the difference in your current prop's pitch from 52.5 inches. I'll leave that to you and continue as though your current prop is a 52D x 52P.

    So, we've narrowed it down to a 52D x 70P three-blader with slightly wider blades, or a four-blader with slightly narrower blades (same pitch and diameter).

    What about that efficiency?

    Some people have said that the pitch/diameter ratio is the primary influence on efficiency, and that the ratio should be kept near 85%. Efficiency supposedly drops in either direction of variance from 85%, and 50% or less will give poor efficiency. Your original prop was ~100% P/D, and we're calculating a 70/52 = 135% P/D ratio for your new prop. Hmmm. You might be looking at reduced efficiency.

    Personally, I do not subscribe to this particular rule of thumb. If you do, you might want to re-think the diameter. (Pitch is a function of rpm and airspeed only, so will be 70" no matter what -- unless you decide you want a slower Vh!) An added inch of diameter will cost about 100 rpm, so you'll want to re-figure your blade widths again if you choose to change the diameter. However, this is EXPERIMENTAL avaiation at its best, and it seems that you probably have ample margins in your airplane's flight envelope to accomodate some judicious testing. You might be surprised to find that the efficiency doesn't drop off all that much with higher P/D ratios. Consider: a Reno Unlimited racer might be going 500 mph turning 1300 prop rpm. That would require a 45 foot diameter prop to keep the P/D ratio at 85%. A Formula I racer might be going 270 mph on the straights turning 4400 rpm. That would require an 86" prop, but those planes usually run 54 to 56 inch props. That's a 130+% P/D ratio....

    There is some consideration needed for the Reynolds number of your new prop. The lower rpm definitely means that you'll want to lean toward the wider blades of the three bladed prop, although small four bladed props have been successful on some VW powered planes (higher rpm).

    Due to its construction, I question the ability of the IVOprop electric prop to achieve the high pitch you need, especially near the inboard ends of the blades (don't discount the importance here, as so many people do). The prop blade angles need to increase from tip to hub, not decrease as the flat mounting structure of the IVOprop hub forces its blades to do at the inboard ends. [see the Ellippse(TM) racing props for contrast.] Regardless of manufacturer, the blade angle "schedule" from hub to tip needs to be appropriate for your airplane, speed, and prop rpm. Granted, a controllable pitch or constant speed prop, by varying its pitch, can be made to allow the engine to rev up to rated max-power rpm at almost any airspeed, but at what cost in lost efficiency because the "twist" is wrong, and then the thrust just isn't there to keep the plane moving at that airspeed.

    Finally, the power curve of a two-sroke engine can be difficult to match to an airframe and propeller, especially a fixed-pitch propeller. In the low-airspeed range particularly, a fixed-pitch propeller's power absorption curve can be parallel to the engine's power available curve. If the prop is pitched a bit too much, has a bit too much blade width, or just a shade too much diameter, the engine may never be able to exceed the propeller's power absorption curve to spin it up to rated engine rpm. In other words, the engine can't rev up to its operating rpm unless you can get the airplane going downhill and "unload" it for a moment. But then it sags when you start climbing and you're back in a pickle. I've seen a two-stroke airplane takeoff under these conditions -- thankfully the next airport was nearby! The ground-adjustable prop had just had the pitch increased by 1/2 degree. It went from delightful to unflyable. Naturally, it got changed back right away.

    Those are my thoughts on your prop design/selection problem. Use them at your own risk. They are rules of thumb only and are a possible starting point from which further refinement will undoubtably be required. There are, of course, some excellent prop carvers around who can give you just about exactly what you need in a fixed-pitch prop, besides the two electric adjustable props you're already considering.

    Then again, wouldn't it be easier to just get a smaller output pulley for the Hirth so that the prop rpm is 3200? No need for a new prop at all....


    David J. Gall

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