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
Is this thread going to die? :(
On a slightly different note, Brad, could you comment on your findings related to using propellers in coaxial counter-rotating placement, rather than forming a ring.... so X8 vs. traditional Octo.
I originally thought that coaxial propellers are more efficient, because the bottom prop benefits from extra thrust derived due to the fact the air column entering it is rotating counter to it's own direction. But I recently read this isn't true at all, and that coaxials a substantially less efficient than the typical arrangement in a ring.
I've been thinking about building a smallish hexa, only to lift a small P&S camera, but I want some redundancy which is why I don't want a quad. But I want to make sure the booms are not in the field of view because I don't want a large hanging gimbal. So a traditional hexa is out of the question. Then considering Y6 may be less efficient...
I've been thinking about making a T6, but instead of coaxials, use two motors close-coupled at the ends of each boom, and just fly using the Y6 code. Does that make any sense?
Just to throw a little fuel on the fire. Brad, have you seen these?
http://shop.spinblades.com/en/spinblades-onlineshop/asymmetrical-ro...
The AP heli guys really like them.
Does anyone here make their own propellers or rotors?
I made a prop from a piece of oak, and it seems pretty nice, but I haven't flown with it yet. I wonder how much efficiency there is to be had with a fancy plastic design. My prop is kind of like those wooden hand spinner toys, the ones you rub your palms together and they take off.
It's airfoil shaped with the leading tips rounded out, but doesn't have the twist and kind of "S" shape.
Speculate now and I'll post back when I get a chance to try it.
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?!
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)
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 )
Great thread Brad.
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
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.
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...
-
4
-
5
-
6
-
7
-
8
of 8 Next