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.
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.
i hope you are still following this thread because I'd like you to answer this apparently simple question:
-For a multicopter which characteristics remain the same, do i get more lifting power (thrust) with proppellers having a higher pitch (prop diameter remains the same) . For example , everything else remaining the same - and not caring about efficiency nor power consumtpion changes, do i get more thrust with 14x6 props in comparison with 14x5 props ?
I'm still around, despite going back to my IT industry "day job" for funding. My full-scale multicopter exploits shall begin anew in the spring of 2014.
Your question is simple, but the answer really isn't. A basic rule of thumb is that the lower pitch will be better for static thrust than a higher one. However, if you want to know what a blade section is doing aerodynamically, you have to look at the angle of attack to determine the coefficients of lift and drag (the latter also varies with Re). The AoA will depend on the airspeed velocity of the blade at given radius point, the induced inflow velocity, and the pitch angle. However, at lower rotational speeds, the lateral velocity and the inflow will be low enough to induce stall in a great percentage of the inner blade span. In other words, trying to account for all the potential variables will drive you nuts.
That's why you just have to test the darn things. One manufacturer's 14X6 - by virtue of superior airfoil selection and quality control - might just blow the doors off of some other's 14X5. Or you might find that for a given disk loading (carrying your camera vs. not, etc.) the Re paradox might yield a 13X4 at a higher RPM as a better choice.
thx for answering. Not sure I understand all of your details. It is apparently common knowledge, in the multicopters world, that a bigger pitch number produces more lift (all the rest being equal, except higher current draw of course). This is also what I have experimented on the field. I have only found one guy convinced of the opposite on Rcgroups which advised me to lower my pitch to get more thrust ! He made me doubt a minute but the logic should be simple:
-A bigger pitch means that, if the quadcopter remains at the same place which is the case at hovering, a larger volume of air per unit of time shall be pushed down by the prop. F=MA, thus as the volume of pushed air increases, the mass increases also and therefor the action-reaction force increases = more thrust.
This logic applies of course as long as the motors and batteries can follow the increasing power draw goign along with increasing pitch.
Do you agree with that logic ?
If you have the power, a larger pitch will mean a greater coefficient of lift. Think of pitch like gearing; the higher the pitch, the taller the gear. So yes, you'll produce more thrust if you have the available torque to twist the blade. You didn't say you cared about efficiency and there's the rub - the drag coefficient will increase faster than the Cl. IF you go too high in pitch, though, you'll reach an area where the inboard blade sections will start to stall and this phenomenon will envelop the entire blade radius if you try to produce too little thrust (hover without payload) or encounter ground effect (IOW, balls-to-the-wall or nothing at all non linearity). Also, the risk of vortex ring state or "setting with power" is magnified greatly. Descending straight down is just a bad idea anyway, regardless.
Yes, friends, variable pitch props DO have their advantages. It is up to you to determine if its worth the additional complexity.
Ducted fans are definitely a must on any personal vtol aircraft for sure. Imagine the F/DWI incidents if everyone was whizzing around with exposed rotating blades protruding from every possible point of impact! lol With the massive power to weight ratios of the new brushless motors going through the roof, replacing his insane idea of lashing 8 rotary outboard boat motors to 4 ducted fans is certainly why his Moller car still sits in his garage 20 years later. With the current state of electrical storage densities and cost an all electric unit seems to be far off for any respectable range personal craft. His design retrofitted with brushless motors in the ducts powered by either turbine generators seems like the route to go. Either 2 small turbines for safety through redundancy or a backup battery pack good for 5 minutes margin of safety in the event of a turbine failure. Toss in a 0 - 0 parachute for those white knuckle SNAFU occasions and a viable craft could easily be produced. When the manufacturing costs of carbon fiber eventually drops to near affordable it will be a whole new ball game. The amount of energy required to carbonize the fibers seems like that issue could also be solved with solar concentrators and molten salt heat storage for 24x7 operation off solar energy cutting the major cost out of the calculus. Ammonia should be the next fuel source as well. It has nearly 7 times the stored energy per liter of hydrogen(AKA THE PIPE DREAM SOLUTION) and it can be made from water, air and energy alone and as it is lacking carbon it does not produce any "green house"(Al Gore and his co-conspirator Cabals latest financial profit scam) gases. Add in the fact that it can easily be stored at 150PSI opposed to 10,000PSI it will come to pass as the new defacto fuel source once the filthy oil barrens wring out the last dollar from their present man made ecological disaster or they all get crucified during the revolution(We can dream...lol). The ammonia infrastructure is already largely in place for agricultural use as well. Fuel cell technology is finally passing its birthing pains so that is something to look forward to. Link solar power produced ammonia, fuel cells, economically produced carbon fiber composite materials and brushless motors and you will have a comparatively ecologically friendly mode of transportation that will also allow life on planet earth to continue a little longer then the present paradigm that is dead piloting us all into a catastrophic tail spin of biblical proportion.
Ducted fans are not efficient for multirotors, I do not see any differences if blades are exposed or not when something fall in to your head from above.
As anyone ever thought to put any protection on blades of a small airplane ?
The other stuff is just biblical and here we are not talking about saving the world, please stay on the topic.
Hi, and a huge thanks for all the great detail here! Still planning to put your machine together this spring?
Key question (if you care to disclose): what are you planning to use for rotors/props? Have you had time to run any of the existing asym big blades through javafoil? I found some nice Clark-Y props, 75 inch diameter, ground adjustable pitch, from Powerfin at Aircraft Spruce & Specialty. But, they're designed for 50hp+ engines so they're heavy (6.5# each) and a bit expensive: ~$1K each.
For power, there are various range extender products coming on the market. Here's one: http://www.metisdesign.com/multidisciplinary-systems/propulsion-sys... (probably not yet a real product).
And, NYJYL R, for airspace just stay below 500 feet AGL and away from airports. Regular fixed-wing traffic is prohibited there, but rotorcraft just have to stay far enough from people & property to avoid endangering them. (Also, if you're ultralight, you can't fly over congested areas, i.e. the bright yellow areas on an aviation chart.)
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
I see you recently responded to another blog and I was just wondering if you had been doing any more development on your (large) multicopter.
One of the things I have observed is that as our large fixed pitch multicopter propellers get bigger and slower, it appears that we have increasing instability.
Possibly this is due to asymmetric relative blade position actually producing angular torques on the motor shafts causing occasional wobble or large amplitude low frequency oscillation or vibration.
The bigger (and slower) the props the bigger the effect (also the fewer the props).
Presumably helis do not have as pronounced a problem because they actually correct during each rotation of the prop blades.
My suspicion is that this is actually based on the fact that air is a fixed physical medium and you can't simply scale things up or down willy - nilly and expect the results to remain the same. (Lilliputian effect, possibly).
I have noticed that really large Quadcopters with 26" - 29" props have not taken off so to speak as it earlier might have been predicted that they might have.
I have noticed on some of my own quadcopters with only 14" blades that accelerating rapidly up or rapidly stopping a descent can result in high vibration amplitudes, loud noise and even wobble and instability whereas reducing just 1" in prop diameter greatly improves the situation.
I am wondering if the effect that I have observed and taken an intuitive shot at describing above, might be partly the reason why.
Basically I am wondering if you think this idea has any validity at all, or is what I am observing due to other factors.
From the other direction I have definitely observed that although tiny little quadcopters suck at efficiency their vibrations are all really high frequency and low amplitude meaning that they can often be effective camera platforms whereas large ones can need considerably more vibration isolation.
I'd really appreciate your feedback on this, when it comes to props and basic multicopter design you really do know more than the rest of us.
Best Regards and I hope all is well with you,
Thank you for your kind words. I have not been very active the last two years due to budget and personal considerations, like the logistics of moving from Illinois to Texas. But I have far from given up. In fact, I am more convinced that the future of transportation belongs to electric multicopter technology than ever before.
It is probably true that I have bloated more LiPoly packs, smoked more motors into oblivion, smashed more blades to smithereens, and destroyed more FlameEmittingTransistors than the next 100 DIYDrones users combined.
You're absolutely correct that large electric multicopters are a new, uncharted frontier for exploration and development. The sheer number of variables one must consider simultaneously is daunting to say the least.
Let me address your points one at a time.
First of all, rotary wing vehicles are inherently unstable. A fixed wing plane can be trimmed to fly straight and level and will tend to remain in this condition without pilot control input - even in turbulent air. Not so with helicopters. They require constant control correction from some source, hence the need for a very busy human pilot or active electronics. The corollary here is that small electric multicopters owe their very existence to low-powered microcontrollers and MEMS-based inertial sensors. However, the only force the IMU can use to modify the attitude of the copter is the torque applied to the propellers. In this situation we're stuck with the realities of rotational inertia when using fixed-pitch blades, which is equal to half the mass times the radius SQUARED. Adding that extra inch or two of blade radius may not seem like much, but the system's instantaneous torque requirements to maintain the same reaction time go up tremendously.
For example, Master Airscrew makes a 12 X 6 and a 14 X 6 electric prop. The first weighs 27g and the latter, 58g. The difference in rotational inertial moment is 486 vs. 1421 - a staggering nearly 3-fold increase! Unless the new torque requirements are satisfied with a much larger motor, no, the system will never be able to cope, and I surmise that's the source of any observed instability.
Vibration is the bane of all things which rotate. Nowhere is this more true than in the art of rotary wing aircraft. It is well known fact that I'm an airfoil snob, so I ended up hand-making all of my rotor blades either with carbon-fiber layups or molded polystyrene over aluminum. They're also rotational inertia MONSTERS at 300g and 46" in diameter (responsible for just a few of the aforementioned smoked motors). Even after careful examination and meticulous balancing, some of them are as smooth as silk and some of them shake like a paint mixer. And I can't tell just by looking at them which is which. I just have to throw the shakers in the garbage. Some vibration triggers a resonance somewhere.
I do concur with your observation that smaller quads require less vibration mitigation for photography than larger ones. I believe this is mainly due to the operating RPMs involved. A 10 inch blade is happy twisting away at 6K RPM, whereas a 14 incher would normally be operated at half that pace. Given two blade passes per rotation, that yields 200 perturbations per second (Hz) for the smaller one and a more bass-like 100 Hz for the larger. I twist my prototype blades at about 1800 RPM, which gives me a 60 Hz hum to get rid of. Lower frequencies are harder to dampen, and if they incite a resonance, the whole system can quake out of control very quickly.
There are two basic approaches to mitigate resonance - move the natural frequency of the dynamic system up or down. Basic one-piece molded props are so rigid that I have to believe their resonant frequency is in the stratosphere. If they're balanced properly, there should not be a problem, although the RPM-based excitement cannot be ignored. APC had an issue with structural resonance in one of their props, but that is a very rare occurrence. Their solution was basically to change something - anything - to get rid of it. If you're seeing a vibration problem in hover, then something rotating is out of balance (run your motors without props to see if they're the problem) or there is something loose in the airframe. There is a phenomenon called ground resonance that can affect full-size helicopters, but it too is highly uncommon (and you have to be IN ground effect for it to occur).
Regular cyclic pitch helicopters have the opposite problem; due to their intrinsic nature, making the rotating system rigid is not an option. They have to go the other direction, lowering the resonance fundamental and then damping any vibrations that occur. They do this with both horizontal and vertical hinges (although the vertical hinge has more to do with mitigating lift dissymmetry) and otherwise loosely coupling the blades to the rotor mast.
In my opinion, the scale issues are related to rotational inertia and the natural inertial moments of something large. The aerodynamic scalability is well described by the inclusion of Reynold's Number (Re) in the various equations (unless I'm missing something).
Starting and stopping performance can also related to this inertial moment issue, although there IS a phenomenon in virtually all rotary wing aircraft called the Vortex Ring State. VRS is a well-documented reduction of flight integrity primarily caused by rapid vertical descents. The pressure differential above and below the rotor disk becomes so great that the air flow stream is highly compromised. Vortex “rings” form under the disk, flow around to the top, and disrupt the aerodynamic lifting effect. Helicopter pilots are consequently warned that vertical descents must be done slowly, if at all. I have heard stories of quads of all sizes being affected by this.
Ultimately, it remains to be seen if the rotational inertia issues can be overcome, and this will largely depend upon the reasonable availability of even more powerful and lighter motors. That's the next upgrade project for my prototype. It may be that full-scale electric multicopters cannot be done with off-the-shelf technology and fixed-pitch blades. Even with variable pitch factored in, there is still a compelling value proposition for a fault-tolerant lifting system. A variable-pitch multicopter control system, while representing an unfortunate increase in mechanical complexity, is still much simpler and potentially more cost-effective than cyclic thrust vectoring.
There have been a few examples of large man carrying multi-rotors in the media:
Here is another example of a man carrying multi-rotor I just found: