# 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

Hi Brad, very interesting conversation. Just wondering how you got to that NACA 63-1211 foil and if you could point me to the coordinate file so I can do some real world testing on it. I'm at about 300.000 on the Re numbers so that should fit in well.

Kind regards, joe

Thanks, Joe.  I contribute sporadically when the spirit moves me.  You can find a treasure trove of airfoil data at this site:

Love this stuff, please keep it up!

Woow Reynolds number jumped out from deep in my school memories.. yes love it and seriously following !  yes please keep it up  Brad!

of course, viscosity and friends!

Wow!  How serendipitous to see this thread posted on DIYdrones this morning!

I have been recently paper-studying the effects of low-reynolds number flight for my high-altitude glider project and, ironically enough, the problems that I face there and the problem of multicopter lift share some interesting simirlarities.

The Reynolds and Mach numbers for both cases are very similar, where at high altitude, the low air densities and high true airspeeds make for low Reynolds and high Mach numbers simultaneously.  Indeed NASA proposed and began a venture (APEX) to study this flow regime, but it was sadly postponed and then abandoned.

In a multicopter, we again have low chord Reynolds numbers due to the generally narrow chord of the propellors that are available, but the Mach numbers tend to be high, especially at the blade tips, where the chord and thus the Reynolds numbers drop dramatically.

The fundamental lessons I have learned from my reading is that aerodynamics at low Reynolds numbers is inherently draggy and not very lifty.  On top of that, compressibility factors of high Mach numbers seem to be always deleterious.  Actually, it makes me wonder how insects can fly!

There is a very interesting PhD dissertation by a Mr, presumably now Dr Peter Kunz where he looks specifically at ultra-low Reynolds number flight and winds up in the end building three quadcopters of varying scales, from 15g flying mass to 150g.  Ï'm guessing he may be famous in aerodynamics circles these days and maybe he even lurks here, but I don't know for sure.

My current views of multicopter propellors then is to reduce the speed and diameter (lower Mach numbers) and increase the chord substantially (higher Reynolds numbers) to avoid the worst of the draggy effects the small scale.  A quad-copter made from toilet ventilation fans may work surprisingly well, at least from an aerodynamic perspective...

Awesome thread!  Being an engineer working on UAV propulsion systems, I have been really wanting to dive into the multirotor propeller issue more thoroughly. I don't get to often, but I will definitely be following this thread.  keep up the good work!

Hi Brad - loving this - keep it up. On the ducted fan issue I can't speak for others but my interest in ducted fans for large scale multi-rotors is primarilly safety. I want to build a "moller skycar." :) Obviously it's not working for him though...

What is working for him is the patience of his investors.  :-)

I wonder (have wondered for a long time) if switching Moller's designs over to gigantic outrunner motors and generating the power with gas turbine generators could result in a controllable/practical solution for this sort of design. Hopefully that's one of the possible solution cases you'll be discussing eventually...

It seems like his Wankels don't respond fast enough for good multi-rotor control and are also gas hogs.

A very interesting thread indeed, hopefully would translate to a new platform ;)

I always thought that helicopter blades were long and thin because that is the most efficient wing profile, similar to the way sailplane airfoils are long and thin.  I thought the reason for that was that longer wings tend to be more efficient because there is less... what's the term... when the airflow wraps around the tip of the wing from the bottom back to the top.  Wing-tip vortex?

Ah yes, here it is:

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

Wingtip vortices affect only the portion of the wing closest to the tip. Thus, the longer the wing the smaller the affected fraction of it will be. As well, the shorter the chord of the wing the less opportunity air will have to form vortices. This means that, for an aircraft to be most efficient, it should have a very high aspect ratio. This is evident in the design of gliders. It is also evident in long-range airliners, where fuel efficiency is of critical importance. However, increasing thewingspan reduces the maneuverability of the aircraft, which is why combat and aerobatic planes usually feature short, stubby wings despite the efficiency losses.

If what you say about the importance of Re is true, then why don't gliders all have delta wings or some other long chord wing design?  Doesn't skin drag across a wide chord propeller eventually come into the efficiency equation?

These are all questions for discussion, not challenges or statements of fact.

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