# 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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As something related to T-Motor, I bought six of their 80A ESC's for \$70 each. They left the factory receipt in the box with each ESC costing \$6 each to manufacture. Funny how amazingly cheap these electronics are to make.

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