Hi DaveS,

“You statement below seems to conflate high lift with high stability here, when stability features are understood to reduce "ideal" lift. Inverse dihedral design, of the same degree as normal dihedral, has greater lift, but less stability, and dihedral is more clearly taught with conventional wings than your overall level rotor with both positive and negative angles to confuse the issue. Note also that unstable WECS can be easily stabilized by suspending them from a pilot-lifter unit or array.”

I’ll try to clarify to clear up the confusion. I’m not talking about positive and negative dihedral in general as applied to wings in general. I’m talking about them in the context of my rotor. I’m saying that the higher lift of the top of the rotor (than the bottom of the rotor) is what produces the increased stability. So let me explain that.

When my Donaldson rotor with dihedral is looked at from the front, the top of the rotor has positive dihedral and the bottom of the rotor has negative dihedral. The top of the rotor, with its positive dihedral, gives the rotor increased stability. The bottom of the rotor, with its negative dihedral, gives the rotor decreased stability.

However, the top of the rotor produces about twice as much lift as the bottom of the rotor. (That is roughly the case for wings in general.) So the negative stability cancels out only about half of the positive stability. That leaves a net positive stability. It’s not a lot, but it’s noticeably more stability than a Donaldson rotor has. Is there a reduction in lift due to using dihedral? Probably. But it’s not significant.

It’s difficult to fly a Donaldson rotor outside due to normal air turbulence. But my rotor with dihedral can be flown outside when the air is fairly calm. One fun thing to do is to briefly fly it above my head while I walk along under it into a slight breeze. I launch it into the breeze, and it does a back loop, and then begins to glide. If it could be made very light, it could ride on the updraft created by my body moving forward through the air.

I hope those comments served to clear up the confusion.

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Additional information:

The end discs on the Donaldson rotor with dihedral can cause a problem if there is too much instability due to the roll angle of the launch or due to a wind gust. If the rotor rolls too much due to those factors, the rotor will experience too much side slip for the dihedral to correct it. Then the end disc on the lower end of the rotor will block air from reaching that side of the rotor. That will reduce the lift on that side and increase the sideslip. The rotor will not be able to recover and it will crash.

So the hourglass dihedral of the rotor works well only as long as the rotor stays reasonably level. The stability is not nearly as good as for a glider, but the stability is noticeably better than for a Donaldson rotor in free flight, which has only a little bit of pendulum stability and almost no gyroscopic stability.

Pendulum stability does not contribute much to the stability of my rotor with dihedral because there is not much of it. A Donaldson rotor in free-flight has only about the same small amount of pendulum stability, so it must be launched level, and it can’t handle minor turbulence. It’s best flown indoors.

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A Sharp Rotor in free-flight has noticeably more pendulum stability than a Donaldson rotor. That is because the Sharp Rotor has a greater distance between its center of mass and the top surface of the rotor. If I recall correctly, a Sharp Rotor in free-flight has about the same stability as a Donaldson rotor with dihedral.

Unfortunately, a Sharp Rotor can’t use dihedral to further increase its stability. It loses a lot of lift if the three wing surfaces are given dihedral to create an hour-glass profile. That is because the mid-span of the rotor has a smaller diameter and a lower spin ratio than the tips of the rotor. The tips of the rotor produce more torque because they have a larger radius than the mid-span of the rotor, so the rotor spins at about the spin ratio of the tips of the rotor. The mid-span of the rotor spins too slowly and produces much less lift than normal.

There is also only a little gyroscopic stability produced by two-sided Donaldson rotors, and the Sharp Rotor, because they fly slowly and spin slowly in free-flight; the spin ratio is only one.

In free-flight, a Flettner rotor has a significant amount of gyroscopic stability because it spins much faster.

Flettner rotor stability in free-flight can be further increased by using an hour-glass shape because that produces both positive and negative dihedral, and the effect of the positive dihedral is stronger than that of the negative dihedral. The mid-span and the tips of the Flettner rotor can operate at different spin ratios while both produce considerable lift. The tips produce more lift because they have a higher spin ratio than the mid-span of the rotor.

A Sharp Rotor, when spun at a spin ratio higher than one, begins to benefit from gyroscopic stability in free-flight. But that greater stability is fairly brief because the rotor’s spin ratio reduces more quickly than for a Flettner rotor. (That is why a little more power is required to spin a Sharp Rotor at a spin ratio greater than one than is required to spin a Flettner rotor at the same spin ratio.)

A Sharp Rotor in free-flight flies faster than a Donaldson rotor or a Donaldson rotor with dihedral. That is partially because it is heavier due to the extra wing surface. It has the same L/D ratio as a Donaldson rotor because they have the same glide ratio, but both the lift and the drag of the Sharp Rotor may be lower. That is probable because the lifting wing surface of a Sharp Rotor – the top wing surface – is rotating aft with the passing air at the same time that its angle of attack is increasing. In contrast, the top wing surface of a Donaldson rotor moves aft only a little bit while it increases its angle of attack. Only the center of lift moves aft as it rotates, while the trailing edge rotates forward.

When I launch both rotors straight up using an underhand launch, and spinning them with my fingertips, the Donaldson rotor flies a much smaller-diameter forward-loop.

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Hi DaveS,

“The confusion-question to me is why a conventional wing is not less-confusing to a student first learning about wing dihedral. The Sharp Rotor seems to me more suited to introduce more complex interactions, like gyroscopic effects and the Magnus effect itself. That's my deep confusion, about how the Sharp Rotor is a better dihedral-concept  training aid than a simple wing (?)”

Are you by any chance thinking of those two different rotors (my Donaldson rotor with dihedral and my Sharp Rotor) as being the same rotor?

I would expect a teacher of aerodynamics to begin the discussion of dihedral with respect to conventional wings. Only later might my two-sided Donaldson rotor with dihedral be used as a way to demonstrate that the top of a wing produces more lift than the bottom of a wing. A teacher could compare it to a Donaldson rotor with the opposite profile (thickest at mid-span -- which is entirely unstable) so as to further confirm that the top of the wing produces more lift than the bottom of the wing.

The three-sided Sharp Rotor has no dihedral. So there would be no reason to use it to teach about dihedral. It could be used to teach about pendulum stability by comparing it to a Donaldson rotor (with no dihedral) that has very little pendulum stability.

The similarity between those two different rotors is that they could both be used to illustrate the Kramer effect.

Then the Sharp Rotor could be used to illustrate the difference between the Kramer effect and the Magnus effect (which can be subtle because they overlap).

So I would certainly agree with you that these rotors should not be used to introduce the most basic concepts in aerodynamics, and that discussing them should be reserved for students who are already familiar with the basics and who are ready for more advanced topics.

Since these rotors could be flown in a classroom by students, they would make interesting teaching tools. Most people find them to be fascinating. I do. I hope to post some YouTube videos.

I hope that helps to clarify.

I have another rotor that is a very simple but fun toy – sort of a party favor. It’s called a “Zinger”. It’s just an ice cream stick with notches at mid-span. It’s launched using string wrapped around the notches and a rubber band attached to the string. The other end of the rubber band attaches to notches on the end of another ice cream stick so as to protect the launcher’s hand. The Zinger spins at a high rpm and makes a loud, high pitched “zing” sound when launched. It’s basically a miniature, free-flight bull-roarer. It illustrates the high lift of the Magnus effect primarily.

“The best way to learn physics is by playing with toys.” – Professor of Physics, Richard Muller, UC Berkeley

Hi DaveS,

"Its a workable rig, similar, but not identical to schemes like AWElab and KiteLab, especially by the use of the Sharp Rotors. How great to someday see these flying, as surely they will, and to eventually learn what exact design finally emerges from all the thicket of open choices, like just how best to rig, and what kind of wing; and rigging arrays as well. Everyone who can muster a flyable prototype deserves their chance, as Dave Lang opined."

I’m glad to hear that the kite might actually work as intended. I hope to build a small, single kite to see if I can control it. Thanks for your encouragement. Could you please refer me to the similar kites you have in mind? I haven’t yet seen anything similar and I would like to make comparisons. All I can recall is the V-tether system using two kites that fly apart, and the Savonius rotor kite for short stroke pumping.

"For baseline kite pair comparison in future testing, there is the looping-foil under a pilot-kite shown to fly stably while pumping effectively, where the kite pair is not  mirrored identical twins; but asymmetrically rigged non-identical staggered kites."

I can’t quite picture the kite system that you are referring to. It sounds interesting. I would like to study it. Do you recall what it’s called, who invented it, or where to find an image of it? All I can recall is the single, soft, looping kite suspended from a pilot kite, and used for short-stroke pumping. But that obviously isn’t what you are referring to.

"Sadly, while I am sure that opposed kite toys would work, I do not know of actual working versions. My feeling is that they would be overly fussy and tend to interfere too much to be popular toys."

I definitely agree with you that toy Twin Stretch Kites would be problematic. Way too complex for a toy. What I said was that I want to test a single kite at toy scale to see how well I can control it.

I’ve flown rotor kites at that small scale, but they weren’t designed to be sufficiently stable. (They used a single tether, plus an extra-large central disc.) I think that a single kite like the Stretch Kite Twin in the sketch might make a good toy if it proves to be very stable and if it can be easily controlled with almost no learning curve.

The minimum size for a toy would depend upon the necessary minimum wind speed (the lower the better), and maybe also the size of the protective packaging required for retail sale.

I think that the three surfaces for the Sharp Rotors could be vacuum formed using thin sheet plastic because I made some small Donaldson rotors with dihedral that way and they worked even better than paper rotors (due to the aerodynamic smoothness of the plastic). I made the rotor in two halves, and then used a bit of clear tape to join the halves. Additional ridges can be molded in chord-wise to make the surfaces stiff, yet still very thin and light. (The curves of the wing surfaces make the rotor stiff span-wise.) I did that, and I also used internal foam ribs to prevent crushing. The foam ribs lock in place using the molded ridges to contain the edges of the ribs – plus a bit of glue. So the process is sort of the reverse of making a model airplane wing where the connected ribs provide most of the rigidity and the skin is just a covering. With these rotors, the skin can be molded to provide most of the rigidity based on compound curves. So I guess that would be called a monocoque design, analogous to an egg shell.

Hi JoeF,

The approximate glide ratio of the Sharp Rotor is 2 for paper models made from business card stock with an aspect ratio of a little less than 6. That glide ratio should increase as the Reynolds number increases, as it does for free-flight Flettner rotors, to something closer to 3. The glide ratio should increase as the aspect ratio of the rotor increases, but the limit still might be around 3. The glide ratio equals the L/D. It is a bit tricky to measure the glide ratio precisely because that would require moving the rotor through the air at its normal glide speed and glide angle before releasing it, so that the spin ratio was also normal. When I launch them free-hand, I use my fingers to impart spin, and I push the rotor forward faster than its glide speed. It does a brief climb and almost stops in mid-air, or it even does a back loop, and then starts to fall a short distance while it picks up enough speed to begin its normal glide. So videoing the rotor and noting where its normal glide path begins and ends might be the simplest way to get a reasonably accurate measurement. The background could have a calibrated grid pattern, and the camera could be placed as close to the expected beginning of the normal glide path. Or, a second person could just note that beginning point and hold their finger at that spot and then measure the distance to the floor and the distance to where the rotor landed.

The profile of the Sharp Rotor has not been optimized. I use what "looks right". What looks right is a rotor with smooth curves and balanced proportions. The human brain can sometimes make unconscious calculations that the conscious brain cannot do without great difficulty. But of course that it not a reliable guideline. I've made and flown a lot of Sharp Rotors, so the profile I use is just the one that "seems" to work best. But the differences are subtle, so again, that is not a reliable guideline.

The diameter should probably be assumed to be based on the longest radius. And that depends upon the specific profile of the three surfaces. I tend to measure the size of the rotor by measuring the dimensions of the strips that form the three surfaces -- before rolling them to create the curves. Another way to measure the size of the rotor is by measuring the chord length of each of the three surfaces. The chords form an equilateral triangle. When comparing different Sharp Rotor profiles, that triangle size (based on the chord length of each surface) should be kept the same for all of them. So the size of that triangle might be the best way to measure the size of the rotor, regardless of the maximum diameter of the rotor. The size of that triangle will be different than the method you proposed – the biggest circle that could be contained within the profile. The circle method will be inconsistent because it will change with the profile of the threes surfaces. For example, the circle will be bigger if there is no reverse camber at the trailing edges of wing surfaces. Since the triangle is based on the chord length of each surface, it seems like the most consistent method, and closest to the way conventional wings are measured. When I draw a Sharp Rotor profile on my CAD program, I begin by first drawing an equilateral triangle, and then I draw the wing-surface profile on one of the sides of that triangle. Then I place the same profile on the other two sides. So the rotor is constructed around that imaginary triangle created by the three chord lines.

The way I classify the Sharp Rotor is to start with a category of “cross-flow, cylinder-like rotors”. Then I divide that category into 4 main groups. Group one includes the predominantly torque producing rotors of Savonius, Benesh, Rahai, and roof ventilation rotors with many small blades around the circumference. Category 3 includes the predominantly lift-producing rotors: a flat rectangle like the Zinger toy, the Lesh rotor (thin oval shape profile), the Donaldson rotor, the Sharp Rotor, and the Flettner rotor. Category 2 includes a 3-sided Magenn rotor which is intended to combine both torque and lift. So it’s a blend of a 3-sided Savonius rotor (category 1) and a Sharp Rotor (category 3). Category 4 includes cylinder-like rotors used primarily for propulsion, such as the FanWing, which can also glide (glide ratio about 3 due to the extra wing parts) when not powered. Any additional rotors, such as the Thom rotor, and the my Donaldson rotor with dihedral, can fitted within those four basic categories. I would classify driven, variable pitch rotors used for lift/propulsion in a different category altogether (they look like VAWT), along with helicopter rotors and gyrocopter rotors.

Banesh rotor:  https://www.youtube.com/watch?v=ybfFOcBeYzs  ;   http://www.google.com/patents/US5494407 

Rahai rotor:  http://www.energy.ca.gov/2005publications/CEC-500-2005-084/CEC-500-2005-084.PDF  See Fig. 4 and Fig 14. Confusing as to exactly what the final configuration is.

Lesh rotor:   http://blog.modernmechanix.com/new-rotor-ship-sails-in-lightest-wind/   Sometimes the edges are rounded to create an oval profile.

FanWing rotor:   http://www.fanwing.com/ 

Additional sub-divisions could be added to the 4 main sub-categories based on: increasing lift, increasing lift to increase torque, amount of torque vs. lift, using external power to spin the rotor,  whether the rotor uses predominantly the Kramer effect or the Magnus effect, the use of end-discs and their size, and types of stability for gliding and/or for operating as a kite or as the wing of an airplane.

An interesting possible way to compare various Sharp Rotor profiles so as to test their lift is to swirl the rotor around in a horizontal circle on the end of a string which is attached to a horizontal, rotating arm that is motorized. The arm length and the string length need to be standardized, such as making them both 1 meter. The rotor will need to be weighted at its outer end to create enough centrifugal force. And the string will require a small, ball-bearing fishing swivel so that it does not become twisted. Then measure the rpm at which the rotor achieves level flight. Use the weight of the rotor, the size of the rotor’s triangle, and the speed of the rotor to calculate the coefficient of lift during level flight. Then speed up the horizontal arm to a given rpm and measure the upward angle of the string, which can be used to calculate the increase in lift and to see if the coefficient of lift remains about constant. The angle of the string can be used to move a pointer next to the string so as to record the angle of the string.

I define the Sharp Rotor as: A cross-flow, cylinder-like rotor with three equal sides, each of which is like the top surface of a wing which has very high camber near the leading edge and a moderate reverse camber near the trailing edge, plus the addition of end-discs. It produces high lift and low torque at a spin ratio of 1, while relying primarily on the Kramer effect. When using external power to increase the spin ratio, it can produce very high lift using the Magnus effect, but a little more power is required than is required to spin a cylinder (although this will depend upon how the radius of the Sharp Rotor is measured).

Hi RodR,

Thanks much for your detailed response. It’s good to hear that running a business appeals to you.

"One paragraph you wrote struck me as curious. I'd like to ask you about it.

'How high can the kite fly before the torque-tether becomes prohibitively

heavy? Why do you want to use a high torque, low rpm design when that makes

the torque-tether much heavier, and requires the generator's transmission to

be more expensive?'

" I'd like to know your reasoning or see diagrams as to why you think low rpm = heavy tethering."

My assumption is that, for a given rotor kite power, the higher the torque, the larger in diameter the tether rings must be, or the closer the rings must be spaced. So to transmit a given amount of power, higher torque means higher weight. Power equals torque times rpm.

Compared to the weight of a kite, those rings will be relatively heavy, and also expensive if they are carbon fiber. So, for a given amount of power transmitted, a higher torque/lower rpm adds to the weight of the tether (per meter) that is transmitting the torque. If the rotor spins at a higher rpm, then the same power can be transmitted using a lower torque and a lighter tether (small diameter rings or larger spacing between rings). So, other things being equal, it would be preferable for the rotary kites to spin as fast as possible. But they do not appear to be designed to spin especially fast (TSR). Also, how do you know that your kind of torque-tether is the lightest? What comparisons have you done?

My guess is that your rotors spin at a tip speed ratio of about 2 or less, as compared to a conventional HAWT rotor which spins at a TSR of 5 to 6, or more if desired. For example, counterweighted, single-blade HAWT rotors can operate at a TSR over 12. They use a very low solidity ratio. They produce high efficiency and high power, but low torque. Your Daisy kites seem to use a relatively high solidity ratio, and so they must operate at a relatively low TSR, and therefore – for a given amount of power – they must produce a relatively high amount of torque (but still much less than drag-type rotors such as Savonius rotors which have a TSR of roughly 0.5).

It would seem that a high rpm, low torque rotor would be most appropriate when coupled to a tether that must transmit that torque to the ground.

However, spinning your type of torque tether at a high rpm would create a lot of aerodynamic drag due to the multiple strings between rings. A general guideline is that a cylindrical object creates about 10 times as much drag as a streamlined wing with the same thickness. And drag is proportional to the square of the apparent wind speed seen by the string. There will be a sweet spot where the tether spins fast enough to be light, but not so fast as to be inefficient due to creating aerodynamic drag due to its rotation.

A conventional, thin tether tends to be quite light relative to the weight of the kite. But a torque-transmitting-tether will be quite heavy by comparison. So assuming a given size and number of Daisy kites, lifting a torque-tether requires a larger lifting kite (pilot kite). The longer the tether, the bigger the lifting kite must be because the torque tether is probably the heaviest part of the system aloft. Also, your type of torque tether has a lot of wind-induced aerodynamic drag, and that will require a larger pilot kite for a given size and number of Daisy kites. The drag of the torque tether is equivalent to it being heavier.

For a given number and size of Daisy kites aloft on one torque tether, there is probably a sweet spot for the length of the torque tether. That is because the cost of the pilot kite and the cost of the torque tether (which is far more expensive than a conventional tether) will increase substantially as the kite elevation increases.  At some point, those costs will become too high for the amount of power the Daisy kites can produce, meaning that the payback period for the kite to earn back its cost becomes too long, and may exceed the projected life of the kite. If and when that happens, the kite loses money for the owner rather than saving money. Payback times should be a short as possible. For small scale wind turbines to save any money at all, they usually require an especially high average wind speed, or they are used where normal electrical lines are not available or too expensive to install.

Some of Doug Selsam’s torque tethers, if I remember correctly, use 3-bladed HAWT rotors instead of rings. The advantage to doing that is that the rotors contribute a significant amount of lift to support their own weight, and counter their own downward drag, so the weight of the torque-tether is less of an issue. They also spin quite fast (TSR) so they can be small and light. Why bother with a rotary kite if the torque-tether can do all of the work by itself, while being lighter, spinning faster, being more efficient, and not needing a transmission?

As I mentioned, most modern, small-scale HAWT use direct-drive, low-speed alternators because most kinds of transmissions add to the cost and reduce the reliability of the turbine. Using any sort of transmission places your system at a disadvantage relative to modern, small-scale HAWT. Multi-blade farm windmills are almost never used to produce electricity because the rotor spins too slowly (typically the TSR is around 2 or less), and would require a transmission.

Placing your generator at ground level avoids the necessity for a tower, but it is a disadvantage with respect to accidents, vandalism and theft (especially in developing countries), and will require additional security/safety features that will add to the cost.

I’m still not clear on how your system will self-launch and operate independently for months at a time. If it can’t, then you may have a low capacity factor and a high cost of energy. I’m also not clear on who will want to buy it instead of a conventional, small-scale HAWT. The cost of your system is likely to be higher than for a comparable HAWT due to the complexity of construction. Why is your system superior to a conventional small-scale HAWT? High altitude winds can be a huge advantage, but they are only one of a number of considerations that contribute to the cost of the energy produced.

Please be sure that you can confidently answer all of the questions that I raised initially. Please understand that these are just normal questions that should be asked of any WECS. I’m not trying to discourage you. I’m only trying to make sure you understand some of the important issues associated with commercial, small-scale WECS.

Well, I hope that I answered your questions adequately. If I am mistaken about anything, please let me know.

Hi DaveS,

Thank you for your advice on how to give business advice. But why not just give Rob your advice?

"We are only seeing your reply to Rod, but not the text that you are responding to.”

I quoted what I was responding to. Please ask Rod to post his Email, if he wishes to do so, and address it to the group.

“Please keep in mind most questions you pose here as "normal questions" were in fact duly addressed in past years, pro and con.”

Then why has Rod not already addressed those issues, and why have you not already encouraged him to do so?

“For example, no one expert in kite technology believes in kite-based or other aviation systems that "operate independently for months at a time".  Real airplanes require pilots and close maintenance. The informed presumption is a lot fine active outdoor kite labor, much like sailing the seas has involved since time immemorial, but in the sky in our time.

I am sorry to see that you have given up on making small-scale energy kites competitive. I disagree with your pessimism. I think that they can be competitive if they can be made to operate independently for months at a time. If they require human labor to be available around the clock to re-launch them after wind lulls, in most cases the cost of that labor will enormously exceed the value of the energy produced by the kite system, and the kite system will be remarkably uncompetitive. For small-scale energy kite systems to be competitive, they must be fully automatic. And my guess is that most large-scale energy kites will have to meet that requirement too. Most energy kite companies seem to assume that to be true and are building accordingly, which contradicts your claim above.

The small-scale Bird Windmill is a step toward automatic operation of a small-scale, tethered kite. It does sacrifice high elevation, so it is far from an ideal energy kite, but it should at least be able to operate independently for months at a time, and it can sweep a large area of wind for a very low cost. A major focus should be directed toward low-cost launching systems for small-scale energy kites.

“Let it be a grand adventure rather than a banal process, if thats how we must do it to ace RAD.”

As for your grandiose and romantic vision of the future of kite energy, I share it. Please recall that I have already proposed a system for supplying a major portion of the world’s energy by using piloted (at first), twin, mutually-tethered, flying-wing dirigibles flying back and forth across the jet streams to produce vast quantities of hydrogen, and how to distribute that energy. (In my original paper I also mentioned how to replenish the ozone depleted by hydrogen leaks.) So I am definitely in favor of thinking big about kite energy. But large-scale systems and small-scale systems have different requirements. Doing research and doing business have different requirements. Let’s not blur those differences. Instead, let’s highlight them.

“Rod's star role is not to defend the Daisy architecture in writing on demand, but to do his best with the architecture, hands-on, in actual flight testing. Its Oliver, the PhD candidate,  who will be the accountable party for formal theoretic conclusions, and he has hardly begun his study. We all agree about low-RPM and high-mass as trade-offs, just not on many other uncertain factors, and on the patience required and value delivered to actually test theory by practice, if only to silence those unable to accept the correct theory analytically. Just so, prepare for your own ideas to be flight-tested as well, without just resting on the arguments for and against that anyone may demand,"

I’m sorry to see that you are not in favor of asking the questions that could be critical to the success of a small-scale, wind energy business. In my opinion, it is far too soon for Rod to try to convert his experiments into a business product because there is still so much to learn about his system, and so many potential ways to improve upon his system. If further research were his primary goal, instead of selling a wind energy product in the near future, I would consider that continued research to be appropriate and desirable at this stage of his kite’s development. I strongly agree with you when you state that “he has hardly begun his study”. That is my point. I definitely would like to see Rod do further field research, just as you recommend. I agree with you that hands-on field testing is where we learn the most. And I’m delighted to see that Rod has enlisted a PhD student to focus on the theoretical issues of his system. If Rod focuses on continued research to maximize his system, I have confidence in his ability to succeed. I admire his research, and he is open to feedback. Many people are not.