# 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.

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### Replies to This Discussion

Robert,

Full-scale gliders still have reasonably large Reynolds numbers. Long wings are still required to reduce induced drag, but if it forces your chord to be very short, like a rotor blade, or a propellor blade, or even a model glider, then the Reynolds number becomes more significant.

When you are above a million or two, which is where most full-size aircraft are, things are pretty predictable.  When you stray below the 1 million, or into the hundred-thousand range, things seem to become very difficult indeed.  Whereas an aerofoil section might get you a max Cl of 1.5 or more in full-scale, at miniature sizes, you're lucky to breach 1 in a predictable fashion.

I am beginning to wonder what a fully Re-optimised model glider might actually look like.  A lot less like a scaled down ASH26 than they currently do.  I suspect aspect ratios would drop significantly.

Is anyone tried props like this yet?

http://www.theengineer.co.uk/1011588.article?cmpid=TE01

http://www.whalepower.com/drupal/

Whale power might make quads the underwater platform of the future.

That's an interesting technology Jake - thanks for posting about it.

Here's a CFD video I've found about it.  I believe what it's doing is suppressing the formation of the laminar separation bubble that forms at low Reynolds numbers at very low AoA's and which creates much of the extra drag compared with megaRe flow.

you can do CFD on a desktop PC these days Monroe, if you drink enough coffee between runs...

A year or so ago I built a PC with the idea that i wanted it to last, therefore, I built it to go as quick as I could.

It's got a bog standard i7 920, but i got lucky. With some pricey dominator RAM and full board water cooling I can run it at almost 100% overclock (it will run prime95 for hours at 4.85ghz!!) - and then theres the 35% clocked crossfire ATI5890's. When i first put it together the highest score in the world for the 3d mark benchtest was 29800 using a i7 920. My first run was 36400! Needless to say i was quite chuffed with that, given that it was mainly down to getting 'lucky' silicon in my i7.

Anyway, to my point, I'm very busy with work at the moment but if you'd like to make use of my hardware I'd be happy to do runs for you, the PC is on 24 hours as it also runs my security system, it flies through anything I throw at it, for example arduino can compile the Arducopter code in about a fifth of the time my new i3 laptop can :)

Yup count me in! Work is very hectic atm but from May 1st I will have time on my hands.

@ Robert: Thanks for your sentiments.  Sailplane wings were perhaps an inappropriate metaphor for me to use earlier, particularly because they don't rotate.  :-)

It's not about having a high Re, but rather the best Re and AoA for the chosen airfoil section.  The airspeed changes with radius too, as does the inflow velocity (lift being the ^2 of speed).  Tip vortexes (vortices?) themselves are the stuff of PhD dissertations and ducted fan acolyte sermons.

Speaking of PhD's, Paul Pounds does an excellent job of making the mathematical case for blade taper and twist in his X-4 paper.  It really is worth a read.

Very interesting discussion.

Do you know about any measurements made on multicopters (tri, quad, hexa, etc.) regarding hover lift efficiency?

Where can be positioned   multicopters  on this diagram.

(the diagram can be found  here )

Way over in the upper left.  Typical disk loading is in the 1 to 3 pounds/square foot and hovering efficiencies are directly related - 5 to 15 pounds per horsepower.

quick one to add to the mix, was wondering if anyone had done some simulation around ducted vs non ducted for similar set of props ( i.e. i am thinking of adding protection to arducopter thus reducing risk of injuries and understanding impact on perfomance)

Most of the claims I've seen average around a 3% performance improvement if done correctly.  However, they'll likely add significant parasitic drag in forward flight.  I've seen shrouds that are basically just barrier rings around the circumference of the propeller disks, which should reduce the risk of accidental strikes.

Brad, so do I understand correctly, based on a summary of the information presented so far, that for a given (model) aircraft such as a helicopter or multi-rotor, the lift duration decreases rapidly as payload increases?  ie: it's not a 1:1 ratio.  For example, the first pound of payload requires X power to lift.  Reducing flight time a certain amount.  But then for every extra pound added, the power required would be something like (Y^2)X, where Y is some number, probably between 1 and 2.

So theoretically, if one tried to extend the range or hover duration of an aircraft by adding more and more batteries, at first you would observe that each additional unit of battery capacity you added, will not increase the flight time as much as the unit before.  And eventually, you could even cross a point where adding more batteries REDUCES flight time?!

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Season Two of the Trust Time Trial (T3) Contest has now begun. The fourth round is an accuracy round for multicopters, which requires contestants to fly a cube. The deadline is April 14th.

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