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.

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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I've been thinking about this all weekend and I'm not sure I'll proceed with the tandem-motor-T6 idea.  I really can't come up with a great physical construction method that won't weigh an excessive amount, and therefore negate the thrust benefit of not having the extra 3 arms.

Errr.... that's probably confusing.  Try this again:

Traditional hexa design has 6 motors on the end of 6 arms.  So the airframe weight is higher than a Y6 which allows two motors to share an arm, thus reducing weight, but due to the coaxial inefficiency, they also lose thrust.  

So I was thinking of a T6, but with tandem motors on the end of each arm.  So basically, the frame would be a T, but each arm would also be a T.  So it would sort of look like the biohazard symbol.  The problem is, the cross-piece at the end of every arm adds weight.  But furthermore, the base arm would be required to be stronger than a classic hex or Y6 because they will be required to resist the twisting moment created when one or the other of the paired motors is generating more thrust than the other.

Overall, I think I'll just stick with a classic hexa or coax T6.

Is this thread going to die? :(

Well, I guess that depends on your definition of "dead".  I think I laid out the basic, well-supported case that electric multicopters have the ability to reach much higher FMs with their propellers than conventional helicopters.  I can see easily 90 or better being attainable.  Where the disk loading is equal, the multi's have a clear theoretical and potential efficiency advantage over cyclic-pitch-controlled helicopters where both are powered electrically.

Admittedly, if both are powered by fossil-fuel engines, the FM improvement of the multi is going to be more than eaten up by the conversion process, which I covered thoroughly in another thread:

Dr. John's Energy Density Device

But by how much?  That is the question.  There will be a trade-off in efficiency for far, far less mechanical complexity.  Naturally, I'm thinking of MUCH LARGER electric multicopters which can (and undoubtedly will) compete in the full-scale arena with conventional helicopters.

At the risk of disingenuous self-promotion, I see a not-too-distant future where a single or two-passenger electric multicopter, even powered by an engine/generator set with a battery backup, could get to within 80% of the efficiency of, say, a Robinson R-22, for about 10% of the latter's acquisition and operating costs.  Not only that, but a big multi can have a fault-tolerant autopilot platform not at all unlike the venerable APM in functionality, meaning that there's no huge learning curve of piloting skill required.

I am convinced that's where we're headed - convinced to the point of making a very heavy personal and financial investment in it.  The revolution awaits.  This is "disruptive technology" potential in the most classic Clayton Christensen (The Innovator's Dilemma) sense of the phrase.

Here's to punctuating this thread with a new video of a successful prototype flight as soon as the weather permits.

I can agree that if one considers a given rotor diameter, and a given disk loading, that a fixed pitch prop can have better FM.  No question.

But I do question those initial conditions.  How can a multi-copter get anywhere near the weight of a traditional heli for a given rotor area?  

Consider a typical 600.  The rotor disk is about 1.3m2, and they weigh about 6lbs without batteries.  To get the same disk area out of a quad requires 25" props!  That's going to be a very large machine.  Even an Octo would require 18" props.

Then consider that if you're not doing any aerobatics, you can easily fit 800mm blades in the 600, giving a disk of 2.2m2 disk area. To compete with that, a quad would have to have 33" props.

Just as a point of comparison, something like a Droidworx Skyjib 8, I think ends up around 10-11 lbs without batteries.  But it only has 15" props, totalling only 0.9m2.  A 600 class heli can have 40-80% more blade area, with less weight.

Can FM really make up for that?

hey ive only just got here!

been meaning to read it for a week or two now, and have finally done so now.

right at this moment im not really ready to comment, but ive certainly got two or three themes that havent shown up much so far and definitely should.  need to digest it all and see if can put some thoughts together in a comprehensible reply :)


Awesome Brad. I was hoping that's where you were headed. What do you think is the optimum number of rotors for the best trade-off between redundancy and efficiency? I'm thinking a hex.

Here's another thought: since a multirotor can rotate toward horizontal and travel at very high speeds, I wonder if there is value to some kind of stubby vertically oriented "wings" that only provide lift when the aircraft is rotated. VTOL with tilt-aircraft instead of tilt-rotor/wing.

Robert, you're stuck comparing current embodiments which exist due to some commercial success without really looking at what's possible.  Perhaps I've been quoting Dr. Leishman's rotor overlap paper with an ulterior motive?  Are you assuming that there are some reasons why a quad can't have larger rotors? 

Did you see the pictures of the eCopter(tm) prototype?  Using the design fully disclosed in USP 7,699,260, I can squeeze more disk area into a smaller physical footprint than a conventional helicopter, using precisely the overlap technique pioneered by Frank Piasecki in 1944 (the XHRP-X "Flying Banana"), only with many rotors instead of just two (the lifting capabilities of Piasecki's craft and its derivatives, such as the CH-47, are legendary).  In fact, here's a drawing from the March, 1959 issue of Popular Mechanics depicting four Flying Bananas used in concert for heavy lifting.  Vertol Aircraft, the owners' of Piasecki's intellectual property at the time, in conjunction with the US Army, decided that the idea wasn't viable due to the lack of control coordination between the ships - a problem now solved on a daily basis.

All that's left is the power-to-weight ratio of the electric motors, which keeps dropping by the week.  I never bothered to experiment with smaller models; there was nothing to prove, as small-scale electric multicopters have been around since about 1997.

The majority of the electric multicopter enthusiasts, both hobbyists and vendors, are focused on the power and control aspects of the art, resigning themselves to the errant paradigm that model airplane propellers are "as good as it gets".  This was my main point from the beginning.

All the math you need is here, in this thread.  The "sweet spot" for overlap was determined through rigorous analysis by Dr. Leishman and his team at about 27% or so.

Yes, FM can make up for some increase in disk loading, but it doesn't necessarily have to.

What's optimum?  That depends on how much lift or pitch/roll control you're willing to lose in the event of a failure.  Also, rotational inertia has to be weighed (pun mildly intended) against disk loading for control response.  The greater the number of thrust units (single rotor/motor combo), the more rotational inertial issues are mitigated (by using shorter blades), but airframe inertia (the weight of the motors) comes into play.

A hex would be a minimum, with perhaps 12 as a good number.  That way, less than 10% of total lift and 25% of pitch or roll axis control would be lost.  The number is certainly less than 36 (!), which is the count in my current PoC prototype (the airframe was designed in 2004 when motors with great P/W ratio north of 1 HP were very uneconomical).  There's some research to do yet.

The trouble with the whole "wing" idea is that the drag becomes a significant factor at attitudes other than full cruise.  The Osprey's dubious honor of introducing "fountain effect" into the aerodynamics lexicon comes to mind.  As you suggest, you could articulate them, but then, I'm not a fan of adding mechanical complexity. 

Actually what I was suggesting is fixed wings (non-articulated) in which they only generate lift when the whole vehicle tilts on its side at full speed.

Also - I like 12 - a 12 would have the benefit that you could have side-by-side fully redundant systems powering 2 interleaved hexes which would mean you could lose half the system and still be able to do a controlled landing.

Also if each system had redundant controllers/sensors you could have 4 parallel controllers doing parity/sanity of each other so if one controller went down or began doing things "wrong" the other 3 could vote it out of the loop and take over.

Another note - IBM's recently publicized Lithium Air battery project could make a fully electric large scale multirotor practical as well although that is probably around 10 years out. But they are saying the potential power to weight ratio for lithium air (in the long run after solving a lot of problems) is up to 15x of lithium ion. In the next 10 years the target is about 4X for electric cars. They plan to have a prototype to show the world in the next year or so. Lots of stuff is trending in the right direction for large scale multirotors to be a reality within the next decade in my opinion.

I'm planning on one in 12-18 months, actually.  The initial production unit will be a FAA Part 103-compliant 12-thruster with a M/G powered by a Rotax-582-style-on-steroids 2-stroke as the primary power source (200H MTBOs are acceptable in the ATV market).  On the other hand, I'm not opposed to a 4-stroke if we can keep the weight and the cost down.  It will be a bit of a challenge to keep the dry weight under 254 pounds so the Feds are happy.  I'm figuring a range based of the FAA-allowed maximum of 63 MPH at 42 miles on the requisite 5 gallons of fuel.

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