Good morning
Wind is a tricky beast. I am reading a lot on how much tweaking of PIDs make a difference and compromise between best wind handling and maintaining straight lines.
But my question now is about size for wind.
My gut feeling is that a larger scale copter (something like the Steadidrone) is going to be best for wind. There is however a nagging feeling that a smaller copter has quicker response and may be better.
Short question - which is better: Larger motor, larger propeller copter; or smaller motor (maybe more, Y6 or X8) copter for both high winds and high gusts?
Thanks
Scott
Replies
If I may proffer an opinion...
Size doesn't matter. Lifting surface loading in pounds per square foot (wing or disk) DOES. As does control response time and thrust headroom. (unless you want to start discussing relative Reynolds Number scale effects in transient aerodynamics, which would be a mildly interesting if somewhat esoteric discourse)
In the case of a typical quad rotor, think of a wind pertubation effect in the context of a percentage of induced velocity at the rotor disk. A small lifting area vs. mass ratio means two things: the downwash velocity must be higher, and a smaller prop will have less rotational inertia. With higher disk loading, the wind is proportionally less of a factor and the control system can change the thrust more quickly to compensate. Of course, the price to be paid for higher loading is lower efficiency.
It also follows that collective pitch control choppers can get away with the higher efficiency of lower disk loading because they can compensate for attitude anomalies ~100X faster. Ah, the subtleties of engineering compromises.
Hi Brad,
You certainly may...
From my point of view wind causes a problem in two ways - unwanted changes to location and to orientation. It seems to me that you can prioritise one or the other but not both. A multicopter has to be able to alter its orientation in order to maintain position, alternatively it can maintain its orientation at the expense of its position. In designing a copter for use in high wind the first priority should be minimising the effect of the wind by reducing the copters profile as much as possible. With a more 'dense' copter (total weight relative to profile) inertia is going to assist in reducing the effect of the wind on attitude even before we have had a chance to try and counter it.
In my case I am more concerned with the copters ability to maintain its attitude - absolute positional accuracy is not as important. Luckily most of my flights are in a smooth laminar flow of air out over open water. Gusts and turbulence are what affect me most.
I am not sure if I agree with the relevance of wind perturbation in the context of percentage of induced velocity at the rotor disk. Typically these are orthogonal (or at least close to it - unless things have gone really wrong...)
On the topic of smaller props=better response, I am also unsure as to the validity of this premise. I realise that this seems to be the prevailing wisdom of the community but it just doesn't sit right with me. Strictly speaking, manoeuvrability relates to how fast thrust can be changed, not rpm. When comparing two props of different diameter, the amount of additional thrust available from a given rpm increase is not the same. Sure the mass of a smaller diameter prop may require less force to accelerate, but is the resulting change in thrust with respect to time greater than what is achievable with a larger diameter prop using a similar output motor? If you do not have to accelerate the larger prop as much to achieve the same thrust increase then perhaps not.
When a prop accelerates, it not only has to put power into accelerating the mass of the prop itself, but it in order to do the job it is designed for, it has to further accelerate the mass of air flowing through it. My gut feeling is that the amount of work the prop is doing on the air is an order of magnitude larger than the work it is doing just accelerating itself in which case the effect of the lower mass of a smaller diameter prop would be less significant.
In practice it is not such an easy thing to compare as an optimal setup with different diameter props requires different spec motors. I have never seen anyone do a proper comparison. It would require two motors of the same size/power output but different kv rating and matched props. You could then time how long each motor takes to accelerate between two set thrust levels. I would really like to see some actual data on this as my hunch is that bigger slower props can provide just as much 'manoeuvrability' but with better efficiency...
@James: You're correct in that there is no direct physical causal relationship between lateral air movement rates and downwash speeds relative to positional or attitudinal stability. I was trying to craft a simple metaphor for what you undoubtedly know is a complex set of aerodynamic and electromechanical variables. With a larger prop, disk loading is directly proportional to blade length while rotational inertia increases exponentially. You're also correct in observing that for nominal operation, a typical quad motor is "working" mostly to produce hover thrust. However, what we're talking about here is the transient response of the system - the greater the instantaneous power available for speed changes, the quicker the system can respond. Less lifting area also means less surface for the lateral wind to push against. More power equals more weight, and less rotational inertia means higher disk loading. This is the proverbial Achilles heel of fixed-pitch rotary thrusting systems.
Given your "the copters ability to maintain its attitude - absolute positional accuracy is not as important" mission profile, then you absolutely should be using a cyclic pitch single rotor helicopter, which can vector its thrust much faster and without necessarily changing the absolute attitude or position of the fuselage. If you really do want the advantages of lower mechanical complexity and potential fault-tolerance of an electric multicopter, then the best advice would be to go with a greater number of smaller thrust units.
There is another reason for this that is not as obvious at this scale; I call it the "Reynolds Number Paradox". Everyone is taught that lifting force increases with the square of the relative wind velocity, and drag, the cube. Of course slower is more efficient, right? This is true if Re is ignored, and as a practical matter it can be at large scales. However, when you get blade sections operating below a Re of 500K, the drag coefficient goes up very quickly while the lift coefficient stays the same (depending on the airfoil shape). There are other effects, too, like having a larger amount of the inboard blade radius operating in a stall condition at lower thrusts. Consequently, buying an off-the-shelf model airplane propeller and twisting it more slowly than it's design RPM virtually guarantees an inefficient result.
http://diydrones.com/forum/topics/propeller-selection?commentId=705...
The actual data says, admittedly counter-intuitively, that bigger and slower just sucks.
One more thing that I forgot to address:
"Less lifting area also means less surface for the lateral wind to push against."
By "lifting area" are you referring to the props? Surely the lateral component of the air flowing through the props due to the wind never reaches the point where the AOA goes negative and creates a force on the craft down wind? With a positive AOA the pressure of the air hitting the prop is always on the underside creating a force into the air flow. I agree that as the craft pitches over more, the effect of wind will increasingly reduce the total available thrust.
First off, let me apologize to Scott for thoroughly hijacking his topic into a classical mechanics physics discussion. I will attempt to make a note relative to his original point of responsiveness and ask James to continue this elsewhere if he likes, perhaps even starting another thread.
For a thrusting efficiency treatise, I believe I beat that proverbial dead horse into glue fodder here:
http://diydrones.com/forum/topics/the-case-for-large-scale-electric...
If my ramblings sparks further conversation, feel free to comment there or start another topic.
My favorite classical mechanics law is F=MA, or force equals mass times the rate of change in velocity of an object. It explains how wings produce lift (Kutta-Jou is just a very elegant flow circulation analysis of this basic expression), why hollowpoint bullets are (theoretically) more lethal than fully-jacketed ones, and how airbags save lives. In the present matter, it relates to responsiveness; we're not concerned with static energy values here, but rather, how much force it will take to make changes in a TIMELY fashion. Given a particular puff of wind, our copter only has a few hundred milliseconds to respond at most.
James' specific prop examples shows approximate design point use of both. Given that the thrust output is the same, and assuming all other things are substantially equal, I would expect the 16" prop to require less power. Considering the energy the thrusting system is imparting to the airflow (joules = watt-seconds), the energy capacitance of the rotating mass is not significant.
What IS significant in terms of control response is the added inertial mass of the 16" prop. Assuming that the two props are the same mass (they obviously are not), then it follows that because inertial mass is equal to static mass times the radius squared, then it will take 78% more (almost twice as much) applied force to accelerate the larger prop the same proportional amount in the same time period, i.e. to provide the same response time versus the 12" one.
Here is an excellent summary of the issues involved:
http://www.forbes.com/sites/quora/2013/12/23/what-makes-the-quadcop...
I assert that for responsiveness benefits, two thrust units with the same combined lifting area will be better than a single one. Ultimately, the two in aggregate won't be more efficient for the simple fact that appropriately sized hardware (motor, shaft, wiring, ESC, etc.) will be more than twice the weight of the single, larger unit. But they WILL be more responsive and more able to compensate for undesirable air perturbations precisely because they will be able to effect changes rotational velocity more quickly.
If you are interested in further study, almost nobody articulates all the parameters of electric multicopter control better than Dr. Paul Pounds. Specifically, the equations for control starting on page 99 of this paper should prove quite informative. I think he makes a bigger deal out of lift asymmetry (blade flapping) that he ought to, but that, like all the forgoing, is just my opinion.
http://www.eng.yale.edu/pep5/P_Pounds_Thesis_2008.pdf
Finally, please accept my apologies for an earlier misstatement. When I typed, "With a larger prop, disk loading is directly proportional to blade length while rotational inertia increases exponentially." I meant to say "swept area" instead of "length". Of course area increases with length exponentially as well, considering pi times radius squared is the formula for the area of a circle.
So, Scott, the next time your up in that sailplane getting bounced around by the wind, remember that wing loading is why your uncle's Cessna 210 cuts through the thermals with far less excitement. ;-)
Brad, since my specific concern still relates to Scotts topic, and since he seems to be OK with our discourse (though it is probably at a level of detail greater than he intended) hopefully you do not mind if I continue here.
I have skimmed the reference material you have linked to and though I have found it interesting, it still does not seem to directly address my point.
I presume that we agree that by 'responsive' we are referring to the systems ability to react and counter unwanted forces due to wind. So when we are comparing smaller vs larger props, all other parameters being substantially equivalent, it is the ability to change thrust and not RPM with respect to time that counts.
In my example, I have compared a 16" vs 12" prop and determined the performance parameters at specific thrust levels. I calculate the increase in kinetic energy required to accelerate the mass of both blades such that the thrust increases from 1.5Kg to 1.7Kg. The result is that the smaller prop takes more energy to accelerate compared the larger one in order to achieve this same increase in thrust . Even though the smaller prop has less mass, it is spinning significantly faster and thus, in this example, has more energy (which increases with velocity^2)
What you refer to as "energy capacitance of the rotating mass " I believe is in fact significant as it is directly related to rotational inertia. I calculate the amount of energy required to accelerate the mass of the prop from one level of thrust to another (the energy difference of the two states). Regardless of the amount of time you might take to do this, with the same power input, these figures show the smaller prop in this example is always going to take longer to get there.
"I assert that for responsiveness benefits, two thrust units with the same combined lifting area will be better than a single one." After this statement you then go on to say that such a drive system will be less efficient and weigh more than twice as much. Not withstanding that my example contradicts that "a small prop responds faster", does the additional responsiveness of your two thrust unit setup overcome the additional weight of its drive system to provide a net benefit? If the additional weight allowance was applied to increase the power of the drive of the larger prop, which system is more responsive now?
@James: Your position is based on your measurements of your own props. There are a myriad of aerodynamics variables (not to mention potential for measurement errors) to consider when looking at a real-world application. I know that Dr. Pounds arrived at a disk loading of approximately 3 lbs/sq. ft. because longer length blades took too long to provide thrust changes. The math is all in the paper.
I have tried to keep the discourse at the theoretical level. It could very well be that you have a wonderfully performing 16" prop and a rotten 12". It is certainly true that the thrust response of a propeller is non-linear over its RPM range. Perhaps you should look to see if the U of I has professionally collected wind-tunnel data on the exact make and model of your propeller(s) and work from there. You may have the last word.
Brad, with so many variables and room for error, I understand you reluctance to deal with my results. The argument I see most often is along the lines 'smaller props weigh less so are easier to accelerate and respond better' My calculations were simplified and ignored aerodynamic efficiencies altogether. I was comparing the kinetic energies of the rotating mass at specific thrust points (calculated using your favorite F=MA). It may well be that factoring in the aerodynamic losses alters the results.
Basically, all I was hoping to demonstrate was that a larger prop spinning at lower RPM can have less energy in its mass compared to a smaller prop spinning at higher RPM and relate this to specific thrust levels.
I am unsure of your reference to Dr Pounds. In the paper of his that you referenced in your earlier post, he uses the largest props he can given the constraints of the geometry of his craft (165.1mm). His disc loading ends up at 2.59lb/ft^2 but this does not seem to be specifically optimised.
If I wanted to directly test a large vs small prop to determine which was more 'responsive', what setup would you recommend? When designing my quad I built a test stand for my motors/props to determine their performance characteristics. It is micro processor controlled and includes RPM, voltage, current and thrust measurements. The load cell I use is accurate to 0.1N and can measure at 100Hz. What prop/motor combinations would you consider appropriate to best test the subject of our debate?
Brad, I agree that there has been very little debate. My posts seem to have stimulated some prolific responses from yourself, however it is most unfortunate that I have not managed to provide you with sufficient incentive to address the issues I have raised directly. I will keep pursuing this subject regardless.
As for the physical size of the copter, considering your F=MA or A=F/M, if we are to increase the dimensions of a given copter by factor X then in general, the mass will increase proportonal to x^3 where the frontal area will only increase proportional to X^2. This is known as the square-cube law. Doesn't it then follow that the acceleration imparted by a given gust of wind, in general, gets smaller for larger craft?
There is no debate about response; your position is that longer, heavier blades are easier to accelerate than short, light ones. We are at an impasse.
There is no debate about efficiency; it is well understood that (all other things being even approximately equal) a 10" prop producing X thrust will require more power than a 16" prop providing the same.
The main point of Paul's paper is that responsiveness of the entire system must be considered, including the airframe moments of inertia. The location of the CG away from the lifting plane is the most important attribute. He is far better than I at working the math and I haven't the time or inclination to provide a derivation here.
For the original issue about size vs. the wind, I give you Bernoulli's famous equation:
For our subject multicopter, a lateral wind gust will apply a force proportional to 1/2 the air density times the surface area times the aerodynamic coefficient times the velocity of the wind squared. What is the aerodynamic coefficient of a quadrotor aircraft at 170 degrees incident to the relative wind direction with all the variables that go along with it? That's the stuff of which mighty good PhD theses are made - I haven't a clue. But the effective frontal area IS something, and it is at least proportional to the the total propeller area plus whatever the fuselage provides. So we're back to F=MA, or rather, A=F/M - the acceleration is equal to the force applied (which is proportional to area) and inversely proportional to the total mass.
Now I'm seriously DONE with this thread.
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