### The Case for Large-Scale Electric Multicopters

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.

#### Replies

• @ George Kelly - Part 103 is a beautiful thing indeed. Keep it under 254 pounds empty, don't fly it like an idiot, and all is OK with the g-men regulators. That's subject to change, of course, at the first incident caused by a sufficiently talented idiot.

George Kelly said:

"Google's Larry Page claims this will be in production within the year (and is already 'legal to fly')"
• Rob!

Thanks for your kind words. I've been focusing on my day job for a while to continue my self-funding. In this thread I have tried to stay in the theoretical realm. Talking about what I am (or anyone else is) planning to do would just spur a heated, unproductive debate.

You did make a number of points about which I'd like to offer an opinion.

You're right; Olaeris seems less real today than it was before. They did have some flight videos up but they're obviously gone now.

http://web.archive.org/web/20140503035958/http://www.olaeris.com/vi...

"...Anyway, the machine can hardly deal with 5 m/s lateral airspeed without flipping over.  I have a helicopter UAV, with similar specifications.  Only it's smaller, lighter, uses the same exact batteries, and it can fly for the same period of time.  But it can fly at 30 m/s in complete control..."

A fixed pitch angle optimized for hover will have an effective angle of attack with inflow of around 5 degrees or so (integrated across the disk, yada yada). The instant you start flying forward, that AoA will drop, and 5 degrees isn't a lot of room before the airfoil becomes useless. With these skinny foils common in model airplane propellers (for reasons previously discussed), you can't begin with a higher pitch or you'll start out with a partial blade stall in hover which will obviously ruin efficiency.

A single large blade copter - by necessity - will have a fatter ~12 t/c (like the ubiquitous NACA 0012) because the AoA and pitch will be changing constantly. At a head speed of 1500 RPM this translates into a torsional frequency of 25Hz, which is decidedly non-trivial considering flapping/teetering, unbalanced load mitigation, resultant vibration, and all the other mechanical variables with cyclic pitch. If you have a mechanical control system flexing a blade that fast with all the other stresses, the aerodynamic loads (like pitching moment) start to matter a great deal, making airfoil selection much more limited.

"I agree with Gary, that there's a limit beyond which multirotors using fixed pitch propellers, begin to have serious difficulties with control.  Only, IMO, its around 18" where it starts happening."

I agree with Gary too. Rotational inertia is 1/2 mass times radius squared, adding commensurate delay to your control system. That's why Dr. Pounds went to exotic ducts; if he made the blades any longer, control purchase would be compromised. One of the major points from his first paper 15 years ago was that placing the CG under the lifting plane reduces stability even more. That's why you see so many "people mower" designs lately; they're struggling to maintain control, with an obvious compromise to safety and ergonomics.

"There's something else that I think is not talked about often.  I haven't figured it out the theoretical reason yet, just observed it in practice.  And that is the incredible amount of power increase required for multirotors to fly with lateral speed.  My helicopter hovers on about 50A, but that drops to 40A by 15 m/s due to the benefits of translational lift."

Transitional lift is definitely a thing, and in forward speed the induced power at the disk should be about 30% LESS according to Leishman (and Stepniewski and every pilot I've ever talked to). Why do fixed-pitch multicopters fail to show this effect? See "fixed-pitch skinny foils" above.

"My Octocopter however, hovers on 35A, but it's pulling 80A if I hold it on the 30 degree pitch limit, and it's only doing 13 m/s.  Why?  I don't think it can be attributed purely to the increased airframe drag.  I think it is probably due to the airflow through the rotors."

Absolutely. See "fixed-pitch skinny".

"We know that with helicopters at high flight speeds, some of the retreating blade is actually subject to reverse flow.  The airflow is going over the blade the wrong way, and it's destroying lift.  I suspect this effect is even greater for multirotors.  Particularly those designed for long duration, with very large, slow turning propellers."

Retreating blade stall is an issue everywhere. With a single rotor helicopter, it is usually akin to having your left wing fall off in a fixed-wing ship. Theoretically, I believe it would be less of an issue in a multicopter because of some maintenance of thrust symmetry across all the rotors. In the metaphor, it would be like losing only part of your wing.

It's nice to see that people are still interested in this stuff.

• This thread that Brad started in 2012 remains very interesting! I notice that over the years I have come back various times.

I have build a "large scale electric multicopter" for personal flight and together with a small group of people are in the process of building a much more  capable one. A link to our first manned flight can be found here: https://youtu.be/Omv_WdryGRc

For our next prototype we're using a modular setup that will enable us to try out various motor/propeller combinations. One of the things we haven't decided on is the exact motor/propeller combination. Our optional designs still include a hexacopter with 56" props to a more cluttered design with 24 drives in stacked formation.

Though the hexacopter should be the most efficient (at least in theory), I'm worried about the agility of such a set up. You can also read it in some of the posts in this thread but whith props over 50", inertia becomes a real topic.

I would be interested to hear what the people of this forum think what would be the best motor/prop combinations for a small person carrying multicopter with a take off weight of ±210 kg?

Regards,

Peter

• I do not have the same experience with the quite efficient  hexas (11,5 gr/watt ) with 16" props.

I notice that in no wind conditions the energy used to move at 5 m/s was only 5-7% more that the energy used for hovering , and increase the speed to 10 m/s request only  another 5% - 8 % .

I think that the reason is that the largest amount of used energy is to keep the multirotor in the air without any aerodynamic help while when it flies or more correctly it translate  , there is just the friction of the air and the  propellers might play a role.

I agree about propellers size, their weight is crucial and large propellers weights a lot  I think also because of a commercial choice.
Over 17" there are only few manufacturers and the propeller is a "quality" product with a high price so it must meet different needs as an high load and that means a robust design and a high weight to catch the maximum numbers of clients.

Some companies made multirotors with 22-35 kg AUW , for heavy load , IMO these multirotors are an hymn to inefficiency , intrinsically unsafe devices;  a heli is much better for heavy payloads I totally agree with Rob Lefevre.

My best selling  multirotors are a light quad with 45' fly time , 250 grams payload , 12,1 gr / watt  and a hexa with 30' fly time and 1100 grams of payload , 11,3 grams / watt, both with 16" props.

Rob_Lefebvre said:

CUT...

There's something else that I think is not talked about often.  I haven't figured it out the theoretical reason yet, just observed it in practice.  And that is the incredible amount of power increase required for multirotors to fly with lateral speed.  My helicopter hovers on about 50A, but that drops to 40A by 15 m/s due to the benefits of translational lift.

My Octocopter however, hovers on 35A, but it's pulling 80A if I hold it on the 30 degree pitch limit, and it's only doing 13 m/s.  Why?  I don't think it can be attributed purely to the increased airframe drag.  I think it is probably due to the airflow through the rotors.

We know that with helicopters at high flight speeds, some of the retreating blade is actually subject to reverse flow.  The airflow is going over the blade the wrong way, and it's destroying lift.  I suspect this effect is even greater for multirotors.  Particularly those designed for long duration, with very large, slow turning propellers.

• Here's another in the news recently:

Google's Larry Page claims this will be in production within the year (and is already 'legal to fly')

• Hi George,

At least in conventional helicopters versus multicopters it is truly no contest, for a given size - weight capacity the Helis single larger rotor is always more efficient than an equivalent multicopters multiple props, it is a simple fact that prop/rotor diameter has an overwhelming effect of efficiency versus all other characteristics.

It is true that a heli blade is less efficient than a fixed pitch prop blade of the same diameter, but if you are stuffing 4 or more smaller diameter prop blades into the same are covered by the single heli blade, the heli rotor is way more efficient period even with it's assorted losses.

So 8" multicopter propeller versus 8" helicopter rotor advantage multicopter, but 4 - 8" multicopter propellers versus one roughly equivalent say 16" helicopter rotor, no contest heli wins by a huge margin. Even with the tail rotor.

As for coaxial helicopter, there seems to be an unavoidable 10 to 20 percent loss going with the stacked rotors, but they do counteract torque and varying speed can even be used to yaw copter.

That said a conventional heli tail rotor is considerably more efficient than a coaxial setup.

Diameter is king.

BTW there was a University attempt with Coaxial center rotors and conventional multicopter prop units around it, but it did not seem to work out for them, I suspect efficiency was crap.

There have also been quite a few attempts with variable pitch single motor driven multicopters and some of those have been remarkably successful especially Curtis Youngblood's, but the mechanism is tricky and they are somewhat fragile so they tend to break a lot, but they are really cool while they work.,\

They hover perfectly well upside down and have phenomenal performance.

The simple fact is a lot of this stuff has already been tried and even analysed.

This thread is really about large (man carrying capable) multicopters and those seem unlikely to get made with truly fixed pitch propellers, the mass of the prop (and the air it is displacing) is so large that the propeller simply can't speed up or slow down fast enough to provide necessary control response times.

There are various strategies for providing an intrinsic automatic pitch control with a mechanism simpler than that found in helicopters.

Where those lead will be interesting, without it man carrying fixed pitch multicopters are just an accident waiting to happen.

Best,

Gary

• I do get the superiority of traditional helis, and of gas power.

I think Brad's point was that fixed-pitch is not only mechanically simpler, but potentially more efficient because the airfoil can be optimised for a single pitch, which isn't possible for a rotor that has to pitch up and down so much, so rapidly. Maybe this isn't significant enough to be important (?)

I'll also assume now from the examples given that any central rotor would almost have to be co-axial - as this would negate the Dissymmetry of Lift problem, as well as the problem of the perimeter rotors having to fight the torque of the central rotor instead of mainly just stabilising horizontal attitude

I don't doubt that other configurations have not necessarily gone well, but I do wonder how many similarly bad outcomes accompanied the first attempts at conventional electric multicopters before the control issues were worked out.

Anyway, I'll remain a little curious.

George

Gary McCray said:

There was actually an Indian gentleman 5 years ago (eternity) that built a man lift capable gas powered Septo copter with one large gas powered non-variable pitch, non-cyclic control central rotor (small aircraft prop I think).

He had it chained in the middle of his patio area, I don't think he ever tried it with a person in it, but the videos I saw were not promising and looked a lot like that old movie of the guy with the 2 cone shaped umbrella things that reciprocated up and down.

There was another later smaller electric multicopter that was built using a single central rotor with 6 conventional prop motors around it that was successful.

Possibly successful is too strong a word, it did fly, but control was very marginal and the surrounding motors had to be installed at a considerable angle off of vertical to counter the torque direction of the central prop unit.

Basically it was a complete pig (apologies to pig).

Single rotor helicopters for a given size weight are almost certainly higher performance and more efficient than an equivalent multicopter.

The cost is in complexity of variable and cyclic pitch control of the rotor.

It seems like the efficiency larger equivalent rotor diameter more than makes up for the inefficiencies from pitch control in comparison to a bunch of smaller props on a multicopter.

Also because of the pitch and cyclic control it appears that helis can totally outperform multicopters in every possible way.

Multicopters main  advantage really seems to be simplicity and, with a microcontroller, ease of piloting, maybe sometimes at least safety, big heli blades can be and have been literally killers at times.

It is also possible that at some sizes / rotor diameters multis may at least sometimes have superior handling or safety in ground effect.

That helis have been so minimized in the emergence of multis as THE drone, is not based on performance or even reality.

It is based on the faddish popularity of multi's and their emergence simultaneous with decent computer automatic pilot systems.

When things settle down and the new wears off, I am very confident that helis will be back in a very significant way.

Certainly and foremost in the serious and commercial end of things.

Best,

Gary

• There was actually an Indian gentleman 5 years ago (eternity) that built a man lift capable gas powered Septo copter with one large gas powered non-variable pitch, non-cyclic control central rotor (small aircraft prop I think).

He had it chained in the middle of his patio area, I don't think he ever tried it with a person in it, but the videos I saw were not promising and looked a lot like that old movie of the guy with the 2 cone shaped umbrella things that reciprocated up and down.

There was another later smaller electric multicopter that was built using a single central rotor with 6 conventional prop motors around it that was successful.

Possibly successful is too strong a word, it did fly, but control was very marginal and the surrounding motors had to be installed at a considerable angle off of vertical to counter the torque direction of the central prop unit.

Basically it was a complete pig (apologies to pig).

Single rotor helicopters for a given size weight are almost certainly higher performance and more efficient than an equivalent multicopter.

The cost is in complexity of variable and cyclic pitch control of the rotor.

It seems like the efficiency larger equivalent rotor diameter more than makes up for the inefficiencies from pitch control in comparison to a bunch of smaller props on a multicopter.

Also because of the pitch and cyclic control it appears that helis can totally outperform multicopters in every possible way.

Multicopters main  advantage really seems to be simplicity and, with a microcontroller, ease of piloting, maybe sometimes at least safety, big heli blades can be and have been literally killers at times.

It is also possible that at some sizes / rotor diameters multis may at least sometimes have superior handling or safety in ground effect.

That helis have been so minimized in the emergence of multis as THE drone, is not based on performance or even reality.

It is based on the faddish popularity of multi's and their emergence simultaneous with decent computer automatic pilot systems.

When things settle down and the new wears off, I am very confident that helis will be back in a very significant way.

Certainly and foremost in the serious and commercial end of things.

Best,

Gary

• Cool thread! Missed it first time around. Thanks for explaining these things in a way that I could understand them. Very interesting indeed!

• @ Rob Lefebvre - It is good to see an octocopter that has made the leap from paper to a real aircraft that flies.

The performance stats for this octocopter that you have mentioned here bring me to ask:

Why did you use motors that do not have higher capacity for work that would allow the octocopter to be more controllable?

What made you choose 18" rotors over any other size?

What 13lb (or any weight) payload would you want to lift and fly with this craft? And based on that payload, why do you want it to fly so fast that it requires a 30 degree pitch?

Why did you choose 8 rotors rather than 6? (Are these 8 rotors in 4 stacked counter-rotating pair?)

Thanks.