This discussion thread is a follow-on to several conversations I've had with people in the forums who are particularly interested in the aerodynamics of vertical take off and landing (VTOL) aircraft.  Much of the dialog in these forums appropriately surrounds the mechanisms for robotic automation of VTOL aircraft, and in those contexts, I am much more a listener than a contributor.  There are some brilliant engineers, code smiths, and experimenters who frequent these hallowed pages.  The group effort to yield such a marvel as the APM platform is nothing short of astounding.

However, I think we can all agree that the primary functionality of anything that flies is related to how it generates forces to oppose gravity.  Much of the focus here has been on the control system, for a myriad of reasons.  Seemingly ignored is the aerodynamics of propeller thrust, but fairly speaking, it is unromantic as having been largely figured out 90 years ago.  In fact, here's a link to the NACA (forerunner to NASA) original paper entitled "The Problem of the Helicopter", dated 1920.  It is of interest to note that we widely applaud Sikorsky for inventing the modern helicopter, but his contribution was one of a control scheme; he gave us cyclic pitch variation for thrust vectoring coupled with a variable pitch tail rotor to counterbalance torque.

http://naca.central.cranfield.ac.uk/reports/1920/naca-tn-4.pdf

If technical papers like that make your eyes glaze over, perhaps an essential basic treatise is in order.

We go back to Newton's basic laws here, and one in particular: Force=Mass X Acceleration, or F=MA.  In order for our craft to fly, we need it to generate a force equal to and directly opposing the force of gravity.  To produce this force, we normally take the air around our craft as our readily available mass, (except in the case of the rocket and to some degree, the jet engine, where the mass is a product of combustion), and accelerate it (add to its velocity) toward the ground.  Yes, rotors, wings, and propellers all do this, and they all rely on the same principles.

However, there is another factor to consider.  While this particular law is not attributable to Newton, it is still a primary expression: energy is equal to half the mass times the velocity squared, or E= 1/2M X V^2.  So while the lifting force is linearly proportional to mass and acceleration, the energy required to perform the acceleration increases exponentially with the change in velocity.  It naturally follows, then, that taking a lot of air and accelerating it a little takes a lot less energy than taking a little air and accelerating it a lot.  This is why heavy-lift helicopters have such large rotor spans, and their technically analogous cousins, sailplanes, have long wings.  (I drive some people in the pseudo religion of ducted fan technology crazy by pointing out that all their purported efficiency gains can be had by merely making the propeller blade longer...ah, but I digress...) 

In the final analysis we must be concerned about lifting efficiency.  The basic expression for us in comparing efficiencies of different designs can be simplified to merely the number of watts (power) it takes to produce a pound of thrust (mass).  Of course, we cannot simply make our rotors infinitely large and fly with no power expended at all.  There are therefore some engineering compromises which must be made in a VTOL aircraft design.  I hope you can see now why aerodynamic designers first examine the ratio of lifting surface area to the weight lifted as an indicator of potential efficiency.  In the rotary wing world, this ratio is called disk loading, and it is expressed as so many pounds per square foot of total rotor swept area.

Disk loading is a basic predictor of hovering efficiency, but it is by no means the only one.  In my next message, I'll get into evaluating basic rotor (or propeller) blade design criteria.

I hope you've enjoyed this little introduction, and yes, I do plan to eventually show that electric multicopters can be a very viable solution for large payloads compared with conventional helicopters.  However, we need to "level set" on the concepts.  Let the discussions begin.

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Just to throw a little fuel on the fire.  Brad, have you seen these?

http://shop.spinblades.com/en/spinblades-onlineshop/asymmetrical-ro...

The AP heli guys really like them.

No fire, just sharing information.  :-)

There's not much to see there - they look like every other RC gasser copter blades I've seen.  Did you get the impression somehow that I denied the existence of asymmetrical helicopter blades?  I have a pair of 720mm "semi-sym" blades in my lab (as well as a few differing pairs of sym blades).  Frankly, I would have rather used off-the-shelf blades than learn how to do carbon-fiber layups myself.  Suffices to say, equivalent radius and solidity ratio (span to chord) Clark-Y blades kick the pants off of any model heli blade I've ever tested, and that's without any taper or twist.  All I did was offer a plausible technical explanation for my own experimental experiences.

To be fair, taper and twist will get you efficiency improvements in the 2-5% range.  Airfoil section selection is the key, as is getting the pitch right (assuming fixed pitch) for your total "mission profile" (i.e. how much time hovering vs. forward speed performance).  I have made my own blades, but I'm probably in the minority.

The critical thing here is to get the leading edge and upper surface geometry correct, which is mightily difficult with hand fabrication.  Make sure the surface is smooth and the trailing edge is as sharp as you can get it (to minimize drag).

I just meant it would be better to stick new material at the back of this thread, not the first page. ;)

I don't think this answered my question, or at least, not in simple enough terms that I understood it.

The pitching moment is created by a seperation between the pitch-axis, and the center of lift, yes?

The center of lift is fixed, yes?

Can't a heli blade designer simply match the pitch axis to the center of lift, resulting in zero pitch moment?  I'm just not sure why this is an issue.

I didn't mean fire in a bad way.  Maybe I should have said stoke the discussion a bit.

To me, these blades seemed "special" because they are very rare these days since everybody is fixated on "3D", a style I just don't really get.  Even pilots just learning, spending all their time hovering, use symmetrical blades because that is all that's available on the market.  It's really kind of a stupid situation.

I don't bring this all up to suggest that these blades are better than what you're proposing for multi-rotors.  I am just discussing it here because it's a relevant thread.

I will probably pick up some of these and give them a test, report the numbers back to you so we can compare.

I was planning on building a tandem heli soon, but I think I'm going to back-burner it for now unless I can find a source of left AND right hand rotation semi-syms.  Because my guess is that a single rotor with semis will outperform a tandem with sym's.  

I tracked down another prop that has claimed greater efficiency...

http://z8rc.blogspot.com/2011/02/introducing-z8-3d-scissor-prop.html

http://www.youtube.com/watch?v=KHoe69ol4XM

23% efficiency increase is a pretty bold claim, but I suppose anything's possible.

From the video page...

My radical new prop design yields most of the benefit of a 4-blade while retaining most of the efficiency of a 2-blade propeller.

The angular alignment, relative pitch, and asymmetric diameters of the interior and primary prop blades extract new efficiencies from Vortex Aero design. The Z83D interior prop tip vortices swirl up and over the primary, trailing blades, energizing the air flow and increasing primary blade lift at high AoAs (slow airspeed; high RPM). By recycling energy otherwise lost to cumulative, superimposed tip vortex swirl, the Z83D prop substantially boosts zero to low airspeed efficiency.

The design principle is the same as an Eagle's wing tip, where interior wiglets roll high energy vortices over successively wider span trailing winglets. The mechanism is also similar to a fighter strake design, which roll a high energy leading vortex over the primary wing, allowing high energy airflow to stay attached during high-alpha flight. For the same reasons, the Z8-3D prop is the optimum design for static airspeed and slow speed flight regimes.

Using a Z83D Scissor Prop properly will result in more thrust per amp/fuel. Initial tests indicate a 23% increase in Thrust/Amp over a slow flight prop design of the same diameter and pitch as the Z83D primary blades.

Based on Leishman's overlap paper, there might be a slight advantage with a CH-47-style layout, or it might be a wash.  If the disk loading is the same, give a 5% advantage to the tandem for recovery of the tail rotor waste (as in not much).  I would concur with your guess if the rotors were a different 'foil.

To your question about center of lift versus pitch axis, of course an airfoil designer can place the CoL within quite a wide range.  However, all the high L/D ratio airfoils I've ever seen have that bent teardrop look to them, which undoubtedly torques the leading edge down.  Center of lift is certainly influenced by the same airfoil attributes which produce a pitching moment, but they are not the same thing.  Perhaps this article might make things a bit clearer:

http://en.wikipedia.org/wiki/Pitching_moment

Yeah, I've seen guys claim twice the the flight time out of those Asym blades, so it really kills the tandem idea.  Not worth the effort unless I find RH and LH Asym blades.

Still, it was a cool idea, and I might make one out of a pair of small helis just for fun.

On a slightly different note, Brad, could you comment on your findings related to using propellers in coaxial counter-rotating placement, rather than forming a ring.... so X8 vs. traditional Octo.

I originally thought that coaxial propellers are more efficient, because the bottom prop benefits from extra thrust derived due to the fact the air column entering it is rotating counter to it's own direction.  But I recently read this isn't true at all, and that coaxials a substantially less efficient than the typical arrangement in a ring.

I've been thinking about building a smallish hexa, only to lift a small P&S camera, but I want some redundancy which is why I don't want a quad.  But I want to make sure the booms are not in the field of view because I don't want a large hanging gimbal.  So a traditional hexa is out of the question.  Then considering Y6 may be less efficient...

I've been thinking about making a T6, but instead of coaxials, use two motors close-coupled at the ends of each boom, and just fly using the Y6 code.  Does that make any sense?

I am a big believer in redundancy, but coaxials cost power efficiency.

According to a compilation of empirical data and simulation at the University of Maryland, rotor overlap starts to degrade hover efficiency at anything closer than 70% of diameter, or roughly the overlap of the CH-47 (some say 0%, but there is expert disagreement on this matter).  The actual reduction is a function of vertical separation, which gets better as the distance increases, but never approaches more than 80% of unity (in other words, 20% less thrust than the two rotors would produce with the same induced power and aerodynamically isolated from each other).  The paper to which I refer is here:

http://terpconnect.umd.edu/~leishman/Aero/AHS2002_Griffiths.pdf

You may have a use case for a T6 configuration in which the benefits outweigh a modest reduction in efficiency.

Just in case it wasn't clear (probably wasn't) what I'm talking about is a T6, but instead of coax, put the motors close, side by side, and just run it on a Y6 code, hoping that the small physical difference don't actually cause a problem.

I'm running the eCopter(tm) PoC prototype on the APM quad (+) code with the four zones laid out electrically.  On the overlap issue, do know if you get enough of them in close proximity, your ground-effect issues are magnified tremendously.  I doubt you'd encounter anything close to what I've seen, but take care to watch for weird blade stalling issues from the ground effect pressure bubble cutting off the disk inflow.

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