Also regarding big, you can debate how "practical" these numbers are, but they are empirical (tested).
Motor: 24V DeWalt Brushed Hammerdrill Motor (obviously not a recommended application) geared down 8:1
Prop: 46 X 36 Custom Carbon Fiber/Balsa Composite, Clark-Y Section @ 14 degree pitch, 2.25" chord, no twist.
(ESC is also custom, 10S LiPo)
Result: 1320W, 17 lbs static thrust at 1875 RPM (78 watts/lb vs. John's example of 168 w/lb)
The motor at that operating point is about 60% efficient, so that makes the rotor FM almost exactly .50. (hey, my CF layup skills are minimal)
The ideal power for John's example is: square root of (37 pounds/2 * 0.00238 * 3.14sqft.) = 49.8 feet/second ^-1 and times our thrust is 1,842.6 pound feet/sec ^-1. Dividing by 550 yields an ideal power of 3.35 horsepower or * 746 = 2,499 watts. Wow, that's what I call disk loading. Figure his motor is about 70%, and the prop FM comes out to .58. Not bad at all.
I worked this example to show that disk loading is important. Even though my prop is less "efficient" than John's, the fact that it's twice as big nets me less than half the induced power per pound. And if we can get somebody to make props with a FM around 75 or so (yes, it is proven possible), then this community's efficiency will really "take off".
Since we are talking about making big custom propellers. What about vary-pitch?
This is easy.
You'll need to use something like this as a gearbox:
Well! That's the $20 Billion question, isn't it? I've spent man-years playing with airfoils, pitch settings, rotational mass, and ground-effects trying to find the "sweet spot". Going to variable pitch would have solved all those problems almost instantly. There is no doubt that the highest efficiency and performance would result from implementing variable pitch. There is equally no doubt that the mechanical complexity of such a solution, the concomitant failure risks, and the resulting costs, would increase 10-fold.
That's exactly what I'm trying to avoid. I think I've learned enough to make an educated compromise. But it is possible that I'm wrong.
In the end, it might very well be that heavy electric multicopter payloads will require variable pitch for control authority if there is to be any hope of reasonable flight times. The requirements of low rotational inertia and low disk loading are diametrically opposed to each other. Yah canna violate the laws of physics, Jim.
Brad I'm sure you must have considered 4 large rotors with a low disc loading and high inertia for the bulk of the lifting and 4 smaller ones with lower inertia for the stabilization control. All fixed pitch. I'm curious what you may have concluded about that configuration. I really enjoy and benefit from your posts.
Thank you for your kind words, Chris. Yes, I have thought about this.
Control authority is all about how much of the total thrust you can change and how fast. Consider the case of a conventional cyclic-pitch-controlled helicopter as an example.
A typical production helicopter has a rotor speed of 500 RPM. That translates into about 8 "control modification cycles per second", so to speak. A helicopter rotor's pitch angle, and therefore the blade section coefficient of lift and thrust, can be varied over its entire range from zero (or even negative) to maximum in only one quarter of a rotational cycle. It can do this 32 times per second, yielding a theoretical control response time of 31 milliseconds. Actually doing that in a flying, full-scale helicopter would produce a very violent control reaction, but the fact is: it CAN be done. When you see those crazy-agile R/C helicopter videos, remember their head speeds are about 1500 RPM, so the on-ship control response is three times faster than at full scale. They can and do vary the whole thrust vector in about 10 milliseconds (not counting obvious control system delays).
If you push the cyclic stick forward in a regular full-size helicopter, it will be changing the pitch of the blades from about 3 degrees in the front to 6 degrees in the back every 62 milliseconds. To match that, a typical electric quadcopter would have to have fixed-pitch blades that go from roughly half speed or 1/8th of total thrust to full speed or 1/4 total thrust in that same 1/16th of a second. And that's for a quad, where one blade is changing 25% of the total thrust that fast. The Dr. Jonathan How/Mark Cutler team at MIT was reporting responses in the 270 millisecond range for 9-inch diameter fixed-pitch blades. My own testing of various propeller and motor combinations at this scale has generally confirmed a very wide thrust transient performance gap.
In light of this, it's amazing that small quads actually fly as well as they do. This is due in no small part to the fact that the control dynamics of a typical quad are quite different than an overhead-rotor helicopter. Having a center of mass near, or even slightly above, the lifting plane makes for a much more stable craft.
Smaller propellers would certainly be able to change thrust faster than longer ones, but their percentage of the total would also be proportionally smaller.