Most manufacturers design propellers in the same way and they read the old books and reports and the prop gets no more than 80-85% efficiency at best. It is written in books that propeller efficiency will be about that at best and it is left often open how low it can be at worst.

Here is an interesting article about a guy that made a prop that was 90 percent efficient by not abiding the "old truths" but thinking out of the box:

http://www.eaa.org/experimenter/articles/2020-02_elippse.asp

Having a strong taper certainly makes sense since the propeller tip travels very much faster than the root through the air. Also the old saying that single blade prop is most efficient does not make sense if you think it in detail: the air that enters in the next blade is not the same air that went through the previous blade because of the forward movement of the aircraft. This could be extrapolated in a such way, that the faster the aircraft travels, the more blades the propeller can have without sacrificing the propeller efficiency. This should not actually require very high mathematics, but I am quite sure that it could be estimated with simple calculations where the downwash of the previous blade goes in relation to the next blade on the speed range intended for the aircraft being designed.

High altitude propeller will require some additional thinking for the tip chord because the Reynolds number will become low if the chord is this short. The TAS is much higher at high altitude, therefore the air travels faster through the prop, that would mean that the prop could have more blades. The high altitude propeller does not require full efficiency at low altitude because to be able to operate at high altitude, there needs to be a lots of excess thrust available regardless.

I have been ranting about that personal aviation is starving and struggling at best to stay alive. But there is no such reason it has to stay that way. If nothing is done, ever increasing regulation and bureaucracy and the increasing expenses will make personal aviation extinct sooner rather than later. And in my opinion, sportplanes/LSA are not the right answer. They are substitute for something else that would be really needed instead - airplanes are most useful when they are used to get somewhere - with fun and with style. Let's face it, flying traffic pattern is such hardcore fun that only dedicated pilots like me and maybe the readers of this blog will enjoy about. And to get somewhere, there is the blocker, which is weather. And I think there is a solution for that:

What is missing in general currently in current general aviation market is simply:
- affordable mass produced aircraft that are so simple to fly that much greater portion of population can do that, and with less training than currently is required for pilot's license.

Lets address this simple to fly thing: mechanically controlled aircraft can be easy to fly to an extent. For example Diamond DA40 is very easy airplane to fly. However, it still requires a lot of training to fly one. To make airplanes more accessible to people, controls should be extremely simple to learn, should not be any harder to get it than learn to ride a motorcycle, or ideally, it should be easier. So what would be the cure then?

In my opinion the answer is in fly-by-wire. No control rods, cables and the like, but instead a (doubled for redundancy) computer that controls all control surfaces and specially purpose built brushless DC servo motors which are directly connected to control surfaces. User uses a fully electronic stick that only gives input to the computer which then decides what control surfaces to move and how much to respond to the input the way user wanted. Pushrod assemblies are very complicated, have many parts, of which many are expensive. To make the plane less expensive, all expensive parts should be designed out of it. Servo motors can be made in large quantities quite inexpensive and the control system will not be super expensive either as it would use off-the-shelf hardware. Doubling that for redundancy would not be very expensive as the hardware in question is similar than what controls all quadro copters and toys like that.

Second enabler will be avionics which displays only important information to the user. E.g. user does not need to know oil pressure, oil temperature, EGT, CHT etc. values if they are all well and optimal, ECU is controlling the engine without bothering you about mixture controls or other obsolete things, and trend analysis done by the computer concludes that trends are not alarming and user does not need to worry about engine failure. Only when something would fail, or something suspicious would be found from analysed trends, the computer would inform the user about the problem. If things are ok and green, why to bother user with 100 gauge displays on a cluttered control panel. User would be left with much less workload and he or she could concentrate on looking for other traffic and flying the plane rather than trying to watch all the engine monitoring etc. values.

The system could communicate automatically with ATC and would display the pilot a very easy path to follow to make a IFR approach without needing any of the workload that is the burden for IFR-pilots. The plane would do things automatically, a bit like a copilot that would be helping you on the right seat. You would not need to worry about what is ILS alpha approach as all the necessary information would be presented you automatically and the display would show you in very clear way which way to turn your plane. You would still be able to control the plane to not lose the fun of flying, but the hard and messy parts would be handled by automation. And for pilot going to weather he or she is not able to fly through, there could be a panic button that would direct the plane to the next airport and land automatically if the pilot so wishes.

And one more enabler would be nice to have. It takes awful lot of time to pre-flight a modern high performance aircraft such as Cirrus SR22. You open the checklist and start checking this and that and that and that and there are zillion items to check before you can even start the engine. What if there would be a computer with sophisticated sensors wired everywhere in the plane and it could do the pre-flight automatically without user needing to care about it unless he or she wants. Sometimes, in case of a short trip, due to the long time spent to pre-flighting the plane, one could reach the destination by car faster by driving rather than getting to airport, pre-flighting plane, filing flight plan etc. There surely should be a faster way to do it with some technology.

It would not be the thing how fast the plane would be. That would be secondary after the plane would be fast enough. How economic the plane would be has greater importance. But how easy it is has greatest importance. Not everybody is skilled enough to ever become IFR-pilots and let's face it, single pilot IFR is a quite dangerous thing to do in hard IMC to the minimums alone without second pilot as helper. The second pilot would need to be replaced with very intelligent computer system that would take off the workload from the pilot so the pilot could concentrate on flying a perfect approach.

Since the plane would be fly-by-wire, it could be made more stable and the ride could be augmented to be less bumpy by automation. So that the plane would be always rock solid, in perfect trim etc. in all flight conditions that would make flying the IFR-approaches very easy and safe. This would enable really this pre-requisite of getting somewhere. Who would want to drive 1000 km with a car slowly averaging 80 km/h at best if there was a way to do it with airplane with no more expense, as easily as with the car, and much more conveniently and certainly with a lot more style. That would make airplanes desirable again to general public, that they currently are not. Only hardcore pilots (like myself) have a desire for the current selection of airplanes.

None of these things I presented here are technically impossible to do and neither they would or should cost much. Everything presented above is doable with even a less sophisticated hardware than a typical smartphone that costs no more than 400 euros. The authorities with ancient rules, regulations and bureaucracy is a thing that makes everything expensive, and I could imagine that some certification process could kill this idea for starters even before it began and this kind of installed system would cost due to certification costs, millions per one single unit. But lets assume that this would not happen and things would go the right way for a change.

To get somewhere, regulation should be largely reinvented in order to not kill personal aviation. Well it is already killed by certification requirements and regulations, it is more like a zombie now, but I would be really happy the GA to be reanimated and to be a real business again, and this time reinvented to be better than ever before. This is a market that would exist if it was not overregulated and that would employ a lot of people and would revolutionize how people travel from point A to B - instead of sitting in Boeing or Airbus and licking their knees in tourist class, they could enjoy similar freedom as driving a family car and getting to the destination with their own schedule without queues, waiting, walking kilometers in huge terminals of huge airports, and without associated anxiety etc. Instead of a large jumbo-jet now and then, there would be demand for hundreds of thousands to millions of small inexpensive and easy to fly aircraft that would be designed for serious transportation and not to be toys like LSAs. Current airplane market is more like a joke. To make it a real market, it would need to be completely reinvented and revolutionized, otherwise it is a dead end that leads to nowhere else than the gradually reduced amount of pilots and the remaining pilots facing more and more ridiculous expenses which will further reduce their interest and numbers which is no good for the individuals nor businesses.

In addition to the RC batteries from http://www.hobbyking.com, you can also get more robust packaged batteries from for example here:

http://www.ev-power.eu/

They also have high power motor controllers which are at or exceeding power class of a big hybrid aircraft.

XFLR5 is the most sophisticated easy to use free tool currently for modelling aircraft. I found some interesting articles about how to use it. They are covering old versions, but you may find them helpful.

Resources for getting started with XFLR5:

1. Get XFLR5 here (for Mac): http://sourceforge.net/projects/xflr5/files/v6.09.06/XFLR5-6.09.06-MacOSX.dmg/download

Read some instructions (covers old version of XFLR5 though):

http://www.v0id.at/downloads/XFLR5-tut-v1.pdf

https://engineering.purdue.edu/~aerodyn/AAE333/FALL10/HOMEWORKS/HW13/XFLR5_v6.01_Beta_Win32(2)/Release/Guidelines.pdf

Then something from this magazine (covers old version of XFLR5 though):

http://www.rcsoaringdigest.com/pdfs/RCSD-2020/RCSD-2020-02.pdf

The moment curve especially in wing analysis is great tool for making your plane stable.

The Reynolds number at very high altitude is very low. Here is an article about airfoil study for 60000 ft altitude flight. My previous airfoils are not very suitable in a small aircraft at 60000 ft, they require longer chord to be efficient. I made series of new airfoils for short chord and high altitude and ended up with the KS415/14.3.

Example:
altitude = 20000 m
velocity = 80 m/s
wing chord = 0.8 m (80 cm)
=>
Re = 396331.94
M = 0.2711

Therefore it is beneficial that the airfoil used in this kind of aircraft is such that provides maximum L/D at low Re, here around 400000.

Here are some simulations:

Then some airfoils that I created:
http://www.katix.org/karoliina/airfoils/KS414.dat
http://www.katix.org/karoliina/airfoils/KS415%2014.3.dat
http://www.katix.org/karoliina/airfoils/KS416%2014.20.dat

KS416:

More simulation at low Re, two conditions: 80 m/s at 600000 ft and 111 m/s (400 km/h) at 60000 ft:

Added case 154 m/2 (300 kts) at 60000 ft:

Of these, the KS415 exhibits the lowest drag. Here is the geometry of the KS415:

Here is a smoothed version of KS415/14.3:
http://www.katix.org/karoliina/airfoils/KS415_14_3sm.dat

And simulation for a Reynolds number range: