### 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

• Hi Gary,

Thank you for your kind words. I have not been very active the last two years due to budget and personal considerations, like the logistics of moving from Illinois to Texas. But I have far from given up. In fact, I am more convinced that the future of transportation belongs to electric multicopter technology than ever before.

It is probably true that I have bloated more LiPoly packs, smoked more motors into oblivion, smashed more blades to smithereens, and destroyed more FlameEmittingTransistors than the next 100 DIYDrones users combined.

You're absolutely correct that large electric multicopters are a new, uncharted frontier for exploration and development. The sheer number of variables one must consider simultaneously is daunting to say the least.

Let me address your points one at a time.

First of all, rotary wing vehicles are inherently unstable. A fixed wing plane can be trimmed to fly straight and level and will tend to remain in this condition without pilot control input - even in turbulent air. Not so with helicopters. They require constant control correction from some source, hence the need for a very busy human pilot or active electronics. The corollary here is that small electric multicopters owe their very existence to low-powered microcontrollers and MEMS-based inertial sensors. However, the only force the IMU can use to modify the attitude of the copter is the torque applied to the propellers. In this situation we're stuck with the realities of rotational inertia when using fixed-pitch blades, which is equal to half the mass times the radius SQUARED. Adding that extra inch or two of blade radius may not seem like much, but the system's instantaneous torque requirements to maintain the same reaction time go up tremendously.

For example, Master Airscrew makes a 12 X 6 and a 14 X 6 electric prop. The first weighs 27g and the latter, 58g. The difference in rotational inertial moment is 486 vs. 1421 - a staggering nearly 3-fold increase! Unless the new torque requirements are satisfied with a much larger motor, no, the system will never be able to cope, and I surmise that's the source of any observed instability.

Vibration is the bane of all things which rotate. Nowhere is this more true than in the art of rotary wing aircraft. It is well known fact that I'm an airfoil snob, so I ended up hand-making all of my rotor blades either with carbon-fiber layups or molded polystyrene over aluminum. They're also rotational inertia MONSTERS at 300g and 46" in diameter (responsible for just a few of the aforementioned smoked motors). Even after careful examination and meticulous balancing, some of them are as smooth as silk and some of them shake like a paint mixer. And I can't tell just by looking at them which is which. I just have to throw the shakers in the garbage. Some vibration triggers a resonance somewhere.

I do concur with your observation that smaller quads require less vibration mitigation for photography than larger ones. I believe this is mainly due to the operating RPMs involved. A 10 inch blade is happy twisting away at 6K RPM, whereas a 14 incher would normally be operated at half that pace. Given two blade passes per rotation, that yields 200 perturbations per second (Hz) for the smaller one and a more bass-like 100 Hz for the larger. I twist my prototype blades at about 1800 RPM, which gives me a 60 Hz hum to get rid of. Lower frequencies are harder to dampen, and if they incite a resonance, the whole system can quake out of control very quickly.

There are two basic approaches to mitigate resonance - move the natural frequency of the dynamic system up or down. Basic one-piece molded props are so rigid that I have to believe their resonant frequency is in the stratosphere. If they're balanced properly, there should not be a problem, although the RPM-based excitement cannot be ignored. APC had an issue with structural resonance in one of their props, but that is a very rare occurrence. Their solution was basically to change something - anything - to get rid of it. If you're seeing a vibration problem in hover, then something rotating is out of balance (run your motors without props to see if they're the problem) or there is something loose in the airframe. There is a phenomenon called ground resonance that can affect full-size helicopters, but it too is highly uncommon (and you have to be IN ground effect for it to occur).

Regular cyclic pitch helicopters have the opposite problem; due to their intrinsic nature, making the rotating system rigid is not an option. They have to go the other direction, lowering the resonance fundamental and then damping any vibrations that occur. They do this with both horizontal and vertical hinges (although the vertical hinge has more to do with mitigating lift dissymmetry) and otherwise loosely coupling the blades to the rotor mast.

In my opinion, the scale issues are related to rotational inertia and the natural inertial moments of something large. The aerodynamic scalability is well described by the inclusion of Reynold's Number (Re) in the various equations (unless I'm missing something).

Starting and stopping performance can also related to this inertial moment issue, although there IS a phenomenon in virtually all rotary wing aircraft called the Vortex Ring State. VRS is a well-documented reduction of flight integrity primarily caused by rapid vertical descents. The pressure differential above and below the rotor disk becomes so great that the air flow stream is highly compromised. Vortex “rings” form under the disk, flow around to the top, and disrupt the aerodynamic lifting effect. Helicopter pilots are consequently warned that vertical descents must be done slowly, if at all. I have heard stories of quads of all sizes being affected by this.

Ultimately, it remains to be seen if the rotational inertia issues can be overcome, and this will largely depend upon the reasonable availability of even more powerful and lighter motors. That's the next upgrade project for my prototype. It may be that full-scale electric multicopters cannot be done with off-the-shelf technology and fixed-pitch blades. Even with variable pitch factored in, there is still a compelling value proposition for a fault-tolerant lifting system. A variable-pitch multicopter control system, while representing an unfortunate increase in mechanical complexity, is still much simpler and potentially more cost-effective than cyclic thrust vectoring.

Regards,

• Although  making a mechanically self stable multirotor  helps the flight controller to perform less corrections, a thing that would ultimately traduce in less load on the motors and a little more flight time.

Thats the case of the s800 of DJI

Hi, and a huge thanks for all the great detail here!  Still planning to put your machine together this spring?

Key question (if you care to disclose): what are you planning to use for rotors/props?  Have you had time to run any of the existing asym big blades through javafoil?  I found some nice Clark-Y props, 75 inch diameter, ground adjustable pitch, from Powerfin at Aircraft Spruce & Specialty.  But, they're designed for 50hp+ engines so they're heavy (6.5# each) and a bit expensive: ~\$1K each.

For power, there are various range extender products coming on the market.  Here's one: http://www.metisdesign.com/multidisciplinary-systems/propulsion-sys...  (probably not yet a real product).

And, NYJYL R, for airspace just stay below 500 feet AGL and away from airports.  Regular fixed-wing traffic is prohibited there, but rotorcraft just have to stay far enough from people & property to avoid endangering them.  (Also, if you're ultralight, you can't fly over congested areas, i.e. the bright yellow areas on an aviation chart.)

• MR60

i hope you are still following this thread because I'd like you to answer this apparently simple question:

-For a multicopter which characteristics remain the same, do i get more lifting power (thrust) with proppellers having a higher pitch (prop diameter remains the same) . For example , everything else remaining the same - and not caring about efficiency nor power consumtpion changes, do i get more thrust with 14x6 props in comparison with 14x5 props ?

• I have been very interested in this idea , using rotomax motors that put out about 20hp a pc ,using a 6 motor setup ,doubling the electronics for safety ,also using mini gas rc engine rated about 11.5hp to turn a generator head instead of using batteries ,using an ac/dc converter of corse.it sounds plausible, but safety will always be concern , just as real airliners use flight paths , airspace must be laid out to accommodate thest types of vehicles.
• Boy I'm really late to this party but I've got a few observations and a few questions.

Thank you Brian for starting and continuing this thread.

You are covering several important issues and propeller efficiency in particular is way under addressed especially as it relates to multicopters.

Your generator powered man carrying multicopter is an amazing undertaking.

While the Rotax can provide adequate power I am sure, you are going to need one really state of the art ultralight and ultra-efficient generator to make it work.

And clearly brushless motor efficiency at hover is going to be really important as well. AC or DC?

However, as you have illustrated the most important thing is going to be propeller efficiency at hover, with a little compromise for actually doing anything else. Pretty much the normal multicopter (or any copter for that matter) conundrum.

The most basic tenet is that for a given set of conditions the biggest propeller diameter you can manage is going to have the highest efficiency within practical structural and weight boundaries.

I am curious that your man carrying copter is going to have a high number of propellers, obviously redundancy can increase safety in the event of failure, but efficiency says that the fewest blades (4) with the largest diameter would be best.

Thomas Shenkel made a short (and very brave) flight in Germany with a whole pile of motors and props, but this was clearly neither efficient enough or safe enough to consider for actual practical use.

Your unit will get around flight longevity  by using the comparative high energy density of gasoline versus LiPo batteries, but it still seems to me that 4 rotors would be a lot less complicated and require less net horsepower than more rotors.

I am sure the rotors would need to be custom made and I don't know if appropriate and appropriately efficient brushless motors are available, but the brushless motor used by the Swiss conventional electric aircraft was at least 15hp and looked like it might work.

There was an extremely complex mechanically balanced man carrying quadcopter made back in the 60's or 70's which certainly had plenty of power, but failed for now obvious reasons of mechanical complexity and inadequate control capability. Of course there was the Piasecki AirJeep dual rotor ducted fan also with plenty of power but very unstable and not really controllable.

Basically just a question why lots of rotors and not a Quad?

Then there is the main issue, propeller efficiency for our multicopter hobby.

Propellers with top efficiency at static thrust in a hover yet still usable above and below that threshhold.

Clearly a multicopter propeller has far more complex requirements that a straight fixed airfoil like a straight wing for a whole bunch of reasons.

What are the best propellers commercially available to us right now for various multicopter sizes?

Ones that actually incorporate the best and most appropriate designs for multicopter use in various sizes, power, weight and motor speeds.

I'm sure you or some of the other followers of this thread have some thoughts on that.

Way too many of the props I see do not seem designed at all for maximum static thrust, have way to short a cord, are too symmetrical, too tapered and while pretty, seem like theyd work much better on a high speed fixed wing aircraft than a multicopter.

Also, possibly, any thoughts on appropriateness of multi-blade or more turbine like designs as in some of the newer full sized unshrouded fan jet designs would be appreciated.

• Does introducing tilting rotor system (using rotating servo mechanism) in the design give better stability?

Have you posted any pictures of you machine?

thanks,

Mike

This reply was deleted.

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