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.

Tags: Electric, control, cyclic, helicopter, multicopter, quadcopter, quadrotor

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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.

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 :)

james

Brad,

Have you posted any pictures of you machine?

thanks,

Mike

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

If by "stability" you mean an aerodynamic tendency to self-level, then pointing the thrust axes inward to a common point above the craft would be one simple method of accomplishing this.  The analogy would be fixed-wing dihedral, except in both pitch and roll.  The no-free-lunch cost would be a reduction in efficiency and less control headroom on the APM (slower response). 

Articulating thrust units would just add mechanical complexity and points of failure.

To be honest, I can't see any possible stability advantage to this compared to a simple well built frame, good motors, fast ESC's, and good PID tuning.

Not disagreeing with the theory.  You're right.  But I'm just saying to anybody reading that I think this is a lot of effort with little reward over what is currently possible with a standard setup.

Well, then, amigo, let's just say we're both right.  The best thing in the vast majority of use-cases is to point the rotors straight up and rely on the APM for stability. 

Also, servo-tilting anything is a bad idea. 

Yep.  Because then you might as well be using them to tilt a swashplate controlling one really big rotor. ;)

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

well, since i'm a kid in this regard... and have a very less idea on APM,

i thought controlling all the four rotors in a single function input would be less complex, with consequences like heavy battery-drain and overall design weight increase..

and, since we are controlling all the four rotors with a single input, what i felt is, distinct thrust values may not be created

I was actually dreaming of automated ambulance sort of multicopters, which might be able to carry payload with stability.. So I started thinking of different possibilities. :)

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