ECL 2-2-2 motor run

[Dennis Toth]

Guys,
I've been flying ECL for several years and been using the tried and true 5" & 6" pitch props with satisfactory results. Seeing some of the IC's running the 2-2-2, which seems to pull through the wind a little stronger, made me wonder how many guys fly this in ECL? Things change slowly in stunt and we tend to use what works cause most of us don't have the time we had back in high school to build ten ships a year and try different things. I did a few test block runs and it seems that higher rpm pulls more amps. This makes it hard to keep the weight down cause of the limited sizes of our battery packs. If you have gotten a high rpm - low pitch combination to work with enough juice to do the pattern please post your components.

Best,    DennisT

[Howard Rush]

Electric stuff is amenable to calculation, so you can save some experimenting.  Most of the online prop calculators are bogus, however.  JavaProp is a good resource. 

[Dean Pappas]

Hi Dennis,
I am not sure I understand your question. Are you asking if it is practical to run with lower pitches and higher RPM?
Sure it is, and within limits prop efficiency will suffer if you do.
On top of that, prop efficiency suffers even more dramatically once you start to hear tip-howl as the prop tip velocities exceed maybe Mach 0.6 or 0.7.
take care,
  Dean P.

[Motorman]

The APC 13x4.5 F2B cut down to 12" is the lowest pitch I've heard of. Not sure of the rpm used but, on the bigger 660+ ships, 6 cell battery weight doesn't seem to be a problem. We now have the lighter nanotech batteries. Just make sure your motor has the right Kv and let it rev.


MM

[Dennis Toth]

Guys,
What I was looking to explore was running say a 4" pitch on whatever diameter works for a particular size ship to get a specific lap time. In the IC world this needs an rpm near 11 - 12,000. In ECL we are running rpms 8000 - 9700 ish with pitch of 4.5 - 6. The IC guys use a 2-2-2 run and assume that since it is in "low" gear it will pull the ship at a constant speed, it also has the engine kinda maxed out so there is not much room for the engine to speed up when pushed by the wind. In ECL we don't have the motor speed up problem cause the speed controller will just back off the current and keep the set rpm. The question is would we benefit from the lower pitch as far as constant drive through the maneuvers or is this something that only matters for the IC flyers?

Best,        DennisT

[Tim Wescott]

Hey Dennis:

I think Dean answered your question as well as can be done without someone (maybe someone named Dennis?) going out and experimenting.

Give it a whirl!  You'll probably need more cells, and if Dean is right about efficiency (Dean is right about a lot of stuff, so he's probably right there, too) then you'll probably not be able to scale the battery capacity down as much as you'd like.

What's your motor Kv?  We'll give you a starting number for how many cells you need.

[Dennis Toth]

Tim,
I guess you are right. Since no one on this forum has tried the low pitch/high rpm route in ECL I guess I will put the 4" pitch on the old Stuka and windup the rpm. I am using a 4S 1P 2100 pack with a 1000Kv motor. My spreadsheet give a starting rpm of 11,500 ish. I fully expect to use more amps and but will cut back the time to half (about 2:30) and see what it draws. The objective is to see if the low pitch pulls better than the normal 5 -6", as the IC guys claim. The main reason for pursuing this is to get better drive in higher winds, if it works the pack capacity can then be adjusted to get the full pattern in.

Seems our contests down here in FL always wind up with "stunt hell" winds by second round and having punch at a reasonable lap time would really help. I will do some flights and post results.

Best,     DennisT

[Fred Underwood]

I use Cobra 3520-14 700kv on 6s pack and 67' lines.  With the 13 x 4.5 F2B cut to 12" I turn approximately 10,200 rpm.  It maths out about like a 5.5 pitch.  I also tried a 13 x 4.5 (not F2B), also cut to 12" and used about 11,400 rpm.  I am using a KR timer/governor and IIRC, it is topped at about 11,700 rpm.  The plane flew ok and I did not notice gain, so I guess 2-2-2 or close.  With shorter lines and less rpm I would still likely get some noticeable gain. 

I have flown the same plane on a 12 x 6 F2B which rpm maths out to about a 6.7" pitch.  8900 rpm for 64' lines. I then used a 5s pack with the same airplane and power train.

I prefer the 13 x 4.5 F2B.  The plane seems at a more consistent speed running a fair rpm and still having gain.

I see people using gain, especially with the Igor system where you can have gain on climb/load and slowing with unload. The Igor system is the only one I see that will increase and decrease rpm rapidly enough to work well.  I have not used one yet.

Perhaps you want flatter pitch with high rpm + gain, not just flat pitch and 2-2-2, easily done with electric. 

[Tim Wescott]

Hey Dennis:

You should have -- barely -- enough voltage overhead with your setup and 11,500 RPM.  If you find yourself bogging down in the overhead eights or clover, switch to a 5S pack (make sure your ESC is rated for it).  You do want to use a governing setup, either a "helicopter" ESC with a Hubin timer, or a correctly set up KR timer.

The relevant math, if you care to sling some numbers, is that the motor's peak RPM with no load is kV * voltage.  Stick a prop on and it'll get slower.  Batteries will put out around 3.7V/cell when fully charged, but more like 3V/cell under load, and the motor will be bogging down because of that danged prop.  So the rule of thumb is to set a top speed equal to (cells)(3.7V/cell)(kV)(0.75).  Work this backwards and you get
cells = (top speed) / ((3.7V/cell)(kV)(0.75)) -- my numbers pencil out to you needing 4.1 cells in series for 11,500 RPM, which means that you'll maybe get by with four cells, and you'll have lots of overhead if you use 5.

I see people using gain, especially with the Igor system where you can have gain on climb/load and slowing with unload. The Igor system is the only one I see that will increase and decrease rpm rapidly enough to work well.  I have not used one yet.

A bit of nit-pickery:  "gain" in an Igor system is different from "gain" in an ESC governor or KR system.  In the case of a governor (inside the ESC or with KR's help), the system is trying to keep the RPM rock-steady and the "gain" is from the RPM error to the throttle setting.  In the case of an Igor system the timer is trying to keep the plane flying at the same speed and the "gain" is from the speed error (actually, as far as I know, the outward acceleration error) and the speed command to the ESC -- all complicated by the fact that this demands a very fast-responding, RPM-governing ESC, of which only one specific Jeti product is known to work (Igor may see this and contradict me -- if he does, he's right.  Further, other ESC's may work -- but AFAIK there's only one that's known to work).

[Howard Rush]

It maths out about like a 5.5 pitch.

Using a formula having nothing to do with reality.

[Howard Rush]

On top of that, prop efficiency suffers even more dramatically once you start to hear tip-howl as the prop tip velocities exceed maybe Mach 0.6 or 0.7.

Here's a prop tip Mach number calculator.  You guys check my ciphering.  Looks like you won't have any Mach trouble until you get to 13K RPM or so.

Mind you, IC engines accelerate about 1500 RPM between ground and air.  Regulated motors don't. 

[Howard Rush]

The main reason for pursuing this is to get better drive in higher winds...

What's "drive", maintaining constant speed relative to the air?  to the ground?  I reckon that you want to be able to get up to the top of the hourglass in the wind.  If you have a regulated motor that holds RPM well, I would guess that you would want a prop that becomes more efficient when airspeed falls below the level-flight airspeed, and you figure that a low-pitch prop would have a steeper slope of efficiency thrust vs. airspeed than a higher-pitch prop would.  First, you'd want to see if this is true.  A real propeller analysis program--maybe Javaprop--could tell you.  But even if it does, would it give you what you want?  It would get you to the top of the hourglass better on a calm day, but when it hits the headwind, it would slow down.  To get what you want may take more than you can do by propeller alone.

Modified to make more sense.  I hope it does, anyhow.

[Motorman]

Using a formula having nothing to do with reality.

What he means is the props have under camber or something that gives you more air speed at a given rpm than the labeled pitch should give.

MM

[Fred Underwood]

Hey Dennis:

You should have -- barely -- enough voltage overhead with your setup and 11,500 RPM.  If you find yourself bogging down in the overhead eights or clover, switch to a 5S pack (make sure your ESC is rated for it).  You do want to use a governing setup, either a "helicopter" ESC with a Hubin timer, or a correctly set up KR timer.

The relevant math, if you care to sling some numbers, is that the motor's peak RPM with no load is kV * voltage.  Stick a prop on and it'll get slower.  Batteries will put out around 3.7V/cell when fully charged, but more like 3V/cell under load, and the motor will be bogging down because of that danged prop.  So the rule of thumb is to set a top speed equal to (cells)(3.7V/cell)(kV)(0.75).  Work this backwards and you get
cells = (top speed) / ((3.7V/cell)(kV)(0.75)) -- my numbers pencil out to you needing 4.1 cells in series for 11,500 RPM, which means that you'll maybe get by with four cells, and you'll have lots of overhead if you use 5.

A bit of nit-pickery:  "gain" in an Igor system is different from "gain" in an ESC governor or KR system.  In the case of a governor (inside the ESC or with KR's help), the system is trying to keep the RPM rock-steady and the "gain" is from the RPM error to the throttle setting.  In the case of an Igor system the timer is trying to keep the plane flying at the same speed and the "gain" is from the speed error (actually, as far as I know, the outward acceleration error) and the speed command to the ESC -- all complicated by the fact that this demands a very fast-responding, RPM-governing ESC, of which only one specific Jeti product is known to work (Igor may see this and contradict me -- if he does, he's right.  Further, other ESC's may work -- but AFAIK there's only one that's known to work).

Tim, a little nit back at you :-)  I did not attempt to define gain other than to note that Igor's system will add and subtract rpm at a user controllable amount.  You mention "You should have -- barely -- enough voltage overhead with your setup and 11,500 RPM.  If you find yourself bogging down in the overhead eights or clover, switch to a 5S pack (make sure your ESC is rated for it)." and that overhead voltage, and corresponding RPM allowance, is to be able to gain rpm if I understand Keith correctly.  I have corresponded with him about that gain in trying to determine what adding to the gain setting will do, add more rpm or increase the sensitivity of response.  My working knowledge of adding/gaining rpm is obviously not based on what is going on in the control loops.  But, perhaps this is beyond the original question as well as my understanding.

[Howard Rush]

Our people use "gain" to mean a number by which a parameter is multiplied.  Igor's system appears to have at least two sensors.  The signal from each is probably multiplied by some gain before they are combined in an output.  The user only gets access to one number, "sensitivity", which we have been calling a gain, but only Igor knows what it really is.   

[Tim Wescott]

Tim, a little nit back at you :-)  I did not attempt to define gain other than to note that Igor's system will add and subtract rpm at a user controllable amount.

I wasn't trying to diminish anything you said -- just to make sure that any newbies reading the thread don't mistake Igor's gain for Keith's.  They're related things (see Howard's comment), but not the same.

You mention "You should have -- barely -- enough voltage overhead with your setup and 11,500 RPM.  If you find yourself bogging down in the overhead eights or clover, switch to a 5S pack (make sure your ESC is rated for it)." and that overhead voltage, and corresponding RPM allowance, is to be able to gain rpm if I understand Keith correctly. 

You're bringing in something different here -- the pack voltage limits the maximum attainable RPM under load, but it doesn't affect the same things that the gain in the RPM loop does.

I have corresponded with him about that gain in trying to determine what adding to the gain setting will do, add more rpm or increase the sensitivity of response.  My working knowledge of adding/gaining rpm is obviously not based on what is going on in the control loops.  But, perhaps this is beyond the original question as well as my understanding.

If I understand Keith's system correctly, increasing gain will first increase the crispness of corrections to deviations from the set RPM.  Then it will cause the RPM to hunt, possibly violently, around the set RPM.  Finally, if you haven't lost courage and if Keith's system and the ESC allows it, it'll make your ESC burn up.  This last event is generally assiduously avoided by control systems engineers, even while we'll happily talk about it over beer when the boss isn't around.

[Howard Rush]

What he means is the props have under camber or something that gives you more air speed at a given rpm than the labeled pitch should give.

What he means is those formulas and calculators one sees on the Web calculate something, but not anything related to the physics of the prop.  The idea that the angle of the back side of a prop tells you how fast it will go is equivalent to the bottom surface of the wing determining the climb angle of the airplane.   

[Fred Underwood]

I hesitate to respond, and probably wouldn't, but I may need to explain what I meant.  There is a  pitch stated by the maker and then "Effective Pitch - The forward distance the prop actually moves on each revolution when operated in air."

The effective or mathematical pitch uses lap time, rpm, and distance traveled and then the effective pitch is calculated.  Distance traveled would assume level flight and radius of handle to fuse center.  It helps me estimate what rpm I might start at for a given line length or for changing line length, of when starting a setup.  I have used that information for years before running across the term effective pitch and thought of it as calculated pitch.  Using others data in "List your setup" will calculate fairly close to correct rpm and lap time, though in the end it is still trial and adjustment.

The effective/mathematical pitch of the 13 x 4.5 and the 13 x 4.5 F2B are different and I don't have to understand all of why to calculate motor rpm settings.  The calculated or effective pitch of the F2B is closer to 5.5 than 4.5. 

When discussed by email with APC a couple of year ago, there was some agreement with the concept and I excerpt the following reply. That reply may not be the definitive answer, but I was mostly using their props so asked them my questions.


"The pitch quoted on our propellers is in terms of the classic definition, forward travel per revolution.
In practice, the forward travel can be higher or lower than this number. It can be higher, because the airfoil produces lift and helps advance the propeller forward beyond the theoretical cork-screw value, even when slip is accounted for.

The pitch, flight rpm, and distance covered cannot be used to calculate flight speed for the above reason.

The 'effective' pitch (which will include slip, airfoil lift, airframe drag, etc.) can be calculated as you describe below.

The 12x6EP and 12x6EP(F2B) use different airfoils. The F2B prop is a thinner version of the 12x6EP. When the blade thickness was reduced the camber of the airfoil increased. Although the pitch has not changed, the F2B prop will produce more lift at the same rpm, this will result in a higher airspeed."


The formula is based on simple math not from the web or from calculators.  I have tried the numbers of effective pitch is calculators instead of stated pitch for my interest and it seems to bring the simple calculators, such as E-Calc, closer to real life. I don't depend on them.

The calculation involves observed/measured data and math and does not try to explain the observation or how propellers move through air, nor does the effective pitch suggest which propeller would fly an airplane most desirably.

Dennis, sorry that my replies have turned to a hijack of the thread; didn't or don't mean to start a controversy.

[Tim Wescott]

I think that, by and large, the whole propeller behavior thing is voodoo black magic, and the number we use for "pitch" gives us two things: one, a number which, when all else is equal, we more or less know what to do with (mo pitch = mo speed), and two, it gives us a nice comforting illusion of competence which allows us to do what we need to do anyway, which is go try a bunch of props to see which ones actually work right.

[Keith Renecle]

Hi Tim,
My KR Governor timer system does not use the gain in both directions and only works when the system is loaded, as in a hard corner. The gain multiplication factor then sets how much gain or boost it will add to the feedback loop. It will hunt a little if you set the gain too high, but it does not hunt like overall gain in both directions, and I do limit this gain factor so that it does not get violent. It does however fly a little better than a straight, constant rpm governor which tends to lose a bit in the hard corners. It has no active elements like the accelerometer in Igor's system, so it cannot back off on the downhills, but it really is nice to fly this way with the extra kick when you hit those hard corners.

Keith R

[Tim Wescott]

... and I do limit this gain factor so that it does not get violent. ...

Oh how boring.

Whatever you're doing it's well away from a regular ol' speed governor -- and it seems to work well.  I'll have to remember not to pontificate too much upon it.  (From a strictly control engineering perspective it's either weird, or perhaps a candidate for a detailed 20 page monograph on the interaction of your control rule with a pilot's desired behavior.  So there's something for you to do if you decide to get a PhD in controls.)

[Howard Rush]

I think that, by and large, the whole propeller behavior thing is voodoo black magic, and the number we use for "pitch" gives us two things: one, a number which, when all else is equal, we more or less know what to do with (mo pitch = mo speed), and two, it gives us a nice comforting illusion of competence which allows us to do what we need to do anyway, which is go try a bunch of props to see which ones actually work right.

It's not magic.  I think Glauert's 1926 book explains it.  "Pitch" as most modelers define it is merely something you can easily measure, at least for places on the back side of a prop that are flat or concave such that a pitch gauge gives an unambiguous reading.  That wouldn't give you pitch by the standard definition, which is relative to the chord line, the line that runs between the LE and TE, but we don't care.  The "pitch" that we measure is useful for comparing props of the same type, e.g. APC 13-4.5.  Typically, we measure "pitch" at various places along each blade, then adjust them until they come out to the "pitch" distribution of a reference prop of that type.  It would be a peculiar coincidence if the "pitch" number comes out the same for all stations along the blade.  

"Effective pitch" does have an actual aeronautical definition.  It is not "The forward distance the prop actually moves on each revolution when operated in air."  It is defined as the pitch of a constant-pitch prop with infinitesimally thin blades producing zero thrust.  Aero people tend to use the term "advance ratio" instead, which is this effective pitch normalized by dividing it by prop diameter.  It's not a "theoretical cork-screw value", as the APC guy put it, nor does "slip" have any physical meaning, even if you can calculate it.  As Chris Machin, the Rev-Up guy, said, "A propeller is not a screw going through cheese."

[Howard Rush]

I've been flying ECL for several years and been using the tried and true 5" & 6" pitch props with satisfactory results. Seeing some of the IC's running the 2-2-2, which seems to pull through the wind a little stronger, made me wonder how many guys fly this in ECL? Things change slowly in stunt and we tend to use what works cause most of us don't have the time we had back in high school to build ten ships a year and try different things. I did a few test block runs and it seems that higher rpm pulls more amps. This makes it hard to keep the weight down cause of the limited sizes of our battery packs. If you have gotten a high rpm - low pitch combination to work with enough juice to do the pattern please post your components.

I looked at your question again after going off on tangents.  I sorta did what you have in mind, as did my homeboys.  I started with APCs, then went to some carbon quadcopter props Leonard Neumann put me onto that looked like copies of APCs.  Then I switched to Cox-Resinger (CA) 3-blade 11" diameter props.  The CA required more RPM, so I had to use a motor with more KV.  The CA also used more electricity.  I eventually went from 5s to 6s batteries to get enough Joules. The CA may not solve your problem, but we found that it makes planes score better.  Here are pitch distributions for two examples.  Prop 20 is a quadcopter prop.  Prop 8 is a CA prop.

[Tim Wescott]

It's not magic.  I think Glauert's 1926 book explains it.

But I don't understand it, and it works.  Therefor, to me, it is magic.

[Peter Germann]

The CA may not solve your problem, but we found that it makes planes score better. 

"makes planes score better" This of course rings a bell and I wonder whether you could detail this a bit more?

Thanks, Peter Germann

[Howard Rush]

"makes planes score better" This of course rings a bell and I wonder whether you could detail this a bit more?

Corners were nicer and the noise during corners went away.  I don't remember any difference in performance in wind.   More proficient pilots like Mr. Walker, whose equipment I copy, could give you better detail.  Igor uses a similar prop.  His is magically (using Tim's definition of magic) hollow.  We have been using Igor's props recently. 

[Dennis Toth]

Howard,
If I read the data correctly the CA 3blade prop is slightly lower pitch, pulls more amps but has better "drive" through maneuvers. This seems to go along the idea that the pipe guys use and would tend to suggest that the lower pitch is a benefit even if in theory it is less "efficient". My feeling is that for Stunt we are flying in several flight regimes that change as we fly through maneuvers so "ideal" conditions never exists for very long and we compromise and try to gain were we need it most. It would be interesting if you could try to lower the pitch of the two blade to say 4" and see how that compares to the 3 blade.

On the pitch calculation I to use a simple calc of advance per revolution times a correction factor. From flight data of rpm, line length and lap time I back calculated the pitch need to match those conditions with the zero correction factor then forced the calculation with the "stamped" pitch to get the correction factor that matches the flight data. This factor can be used to make pitch adjustments for a particular prop and its fairly close. It also gives a starting point for rpm needed on other prop designs. You then get the actual flight data for the new prop and adjust the C factor.  In general on my electrics it is around -14% for 11" diameter. This corrects for airfoil lift and slip all in one.

Best,    DennisT

[Howard Rush]

If I read the data correctly the CA 3blade prop is slightly lower pitch, pulls more amps but has better "drive" through maneuvers.

It seems to be easier to turn accurate corners.  Is that what you mean by "drive"?

This seems to go along the idea that the pipe guys use and would tend to suggest that the lower pitch is a benefit even if in theory it is less "efficient".

The CA prop is a benefit and in practice is less efficient: it uses more electricity that the APC or carbon clone. Nobody has looked at theory (well, no doubt Igor has), even though Javaprop is free and available.

It would be interesting if you could try to lower the pitch of the two blade to say 4" and see how that compares to the 3 blade.

Me?  I'm too lazy even to look at it theoretically, although I'm kinda curious.  I suspect the benefits of the CA and Igor props over the two-bladers come mostly from diameter and number of blades.

On the pitch calculation I to use a simple calc of advance per revolution times a correction factor. From flight data of rpm, line length and lap time I back calculated the pitch need to match those conditions with the zero correction factor then forced the calculation with the "stamped" pitch to get the correction factor that matches the flight data. This factor can be used to make pitch adjustments for a particular prop and its fairly close. It also gives a starting point for rpm needed on other prop designs. You then get the actual flight data for the new prop and adjust the C factor.  In general on my electrics it is around -14% for 11" diameter. This corrects for airfoil lift and slip all in one.

This calculation is a waste of your time.  Just go fly, adjust RPM or pitch to get what you want, and see what happens. 

[Dennis Toth]

Howard,
Kinda yes. What I mean buy "drive" is that as the ship goes through a maneuver you feel that you have positive control without any additional effort and that the wind doesn't disrupt the flight path. It is a solid feel that you can fly without fear of getting pushed around in the hemisphere.

This higher rpm lower pitch kinda came out of the pipe guys going to this set up (Howard didn't you fly piped ships with this?) and someone tried it on a non-piped mufflered engine and it was pretty close to the pipe set ups. For the pipe set up they use 3.5 - 4" pitch ish. The question is does using the low pitch give better maneuver performance, better wind performance on any set up or is it just that it allows the IC engines to run more consistent and the prop would be better at the higher pitch if they could run it? In other words is it an engine thing or will any ship benefit from it.

Best,    DennisT

[Howard Rush]

Howard didn't you fly piped ships with this?

Yes, and you showed me how to start my .40VF at the Nats. 

I regret that I don't know what effect a lower pitch prop would have, but we could probably get some insight with Javaprop.  We have the drive with the 3-bladers, but they are augmented by Igor's autothrottle. 

[Dennis Toth]

I'm not sure that doing an engineering analysis on the prop efficiency will give us useful information. It seems to me that we would find out that the prop is not at the optimum pitch and rpm. But for Stunt this doesn't really mean much.

It really will take just putting the 4" pitch prop on an ECL ship and fly in light winds, no winds, high winds and see how it pulls the ship. I expect that for ECL we will find that it might work but the amp draw will be significantly higher than we can stand with the current battery technology and would require a battery pack 30% larger and the weight would likely be more than 30% higher then the low rpm set up we use now.

Having said that I still want to try it and see how it works.

Best,  DennisT

[Keith Renecle]

Hi Dennis,
It will be good to see the results of your testing with 4" pitch. I have never tried below that APC 4.5" pitch props myself and I did not have any success besides the 13 x 4.5 thin blade. It also had to spin too fast and used more power, so I went back to 5.5 to 6.0" pitch. I also prefer less noise these days, and running high rpm means more noise as well. A 4" pitch prop is going to spin really fast so it will make quite a bit more noise.

The 13 x 5.5 worked well for me because I enjoyed the power/drive thing a lot but then it slowed down the nice sharp turns I had and used too much power. Cutting it down to 12" was o.k. as far as using less power was concerned but then the thin blade 12 x 6 F2B APC props feel better. I like turning a prop at around 9000 rpm on 4 cells with a 900~950 Kv motor, so I guess that I'm stuck with 5.5 to 6" of pitch. There could also be a good reason why Igor sticks to this sort of pitch with his props as well. He seems to do o.k. with them.  I look forward to seeing the results of your testing with the 4" of pitch. This is a great thread!

Keith R

[Igor Burger]

I'm not sure that doing an engineering analysis on the prop efficiency will give us useful information. It seems to me that we would find out that the prop is not at the optimum pitch and rpm. But for Stunt this doesn't really mean much.

I see I missed something here :- P

Well nothin to add too much, but regarding that analyse - may be efficiency is not very important for IC engines, but it makes sense for electric. If your battery can handle only 11" prop and your improved 12" prop will need the same amount of energy, it makes little bit sense :- )))

However it is not only efficiency what should be analised and optimised. Important is how much the prop pulls regarding its speed in air. We have some limited over or underspeeding during usual flight. Optimal prop is somewhere close to "square" prop (pitch = diameter or P/D = 1) but that prop loses thrust slowed down. While P/D=0.5 works much better. That happens because roots of blades at some slippage work at higher then critical AoA. If you do such analyse with known (measured) speeds you can estimate what is the pitch which will not load motor and loose thrust too much when slowed. Looks like the pitch 5' on 11" and 12" props works well. That is answer for Keith why all our props have 5" pitch.

The same is with blade airfoils, well selected airfoil will load or unload shaft when necessary. Props for well controlled motors can work at its good gliding ratio, while props for IC engines or motors with no so well self regulation benefit from undercambered airfoils which have lower drag (means also shaft load) when they pull, while they go to bad gliding ratio unloaded, so they do not allow prop overspeeding (engine tends to overspeed because of low induced drag on prop tips when prop does not pull), means that airfoil drag at low AoA compensates missing induced drag. May be you remember that "pffffff" prop spoken some months ago :- )))