diy solar

diy solar

The Magnus Effect

svetz

Works in theory! Practice? That's something else
Joined
Sep 20, 2019
Messages
7,201
Location
Key Largo
Wind power, in general, is awful... details: see: www.solacity.com/small-wind-turbine-truth/

Basically, the problem is most areas have low wind average speeds near ground level. The power formula for the maximum theoretical power from wind using a turbine blade is: P = π/2 r² v³ * ρ; usual efficiency is around 40% of the max. Where P is power, r the radius, v the wind speed, and ρ the air density. The two biggest factors are the wind speed (a cube) and the radius (a square). So for sea level:

wind, mph
wind m/s​
power, W, radius of 1m
1
0.44704​
0.2​
2
0.89408​
1.4​
3
1.34112​
4.6​
5
2.2352​
21.5​
10
4.4704​
171.9​
25
11.176​
2,686.0​

So, as you can see, those gentle 3 mph breezes most people have on average don't generate any power. Most wind turbines don't even show power until you're over 8 mph. It's the cube that kills you at low speeds, and does wonders at high speed.


Magnus Effect
But there is another force that can make use of low wind speeds (or slow tidal currents); that's the Magnus effect. Basically a rotating body in a stream creates a force. It's how golf balls get lift and follows F/L = ρv 2πr²ω, where r is the radius of the cylinder and ω is the cylinder rotational speed. Everything here is linear except the radius (which is independent of wind speed).

Magnus-anim-canette.gif


It's been used in a variety of ways over the years, here's an example a "Flettner ship", basically those cylinders rotate and create thrust as the breeze flows across the ship.

Postbilag.jpeg


So, if the cylinders had a 1.5' radius, then for 1m cylinder length at sea level the power is:

Code:
                        power W, cylinder revolutions per second

wind, mph   wind m/s    1    2     3     4     5     6      7      8

   1        0.44704    49   98   147   197   246   295    344    393

   2        0.89408    98  197   295   393   491   590    688    786

   3        1.34112   147  295   442   590   737   884   1032   1179

   5        2.2352    246  491   737   983  1228  1474   1719   1965

   7        3.12928   344  688  1032  1376  1719  2063   2407   2751

  10        4.4704    491  983  1474  1965  2456  2948   3439   3930

So, four cylinders rotating 1 per second in a 3 mph breeze should have a maximum of 588 W. Or, assuming the same 40% efficiency, ~5 kWhr per day (assuming a constant 3 mph breeze). Think of this as a conventional wind turbine with the blades replaced with 4 spinning cylinders and re-geared so the whole assembly spins slowly.

Conventional bladed air turbines with their cube to the wind speed win hands down in fast winds. But most places don't have fast winds 24 hrs a day and conventional wind turbines have problems in high winds (but with the Magnus effect you can just slow the cylinder RPM to decrease the force. Or, you could adjust the RPM to get the power output you want, great for handling peak loads).

Conventional wind turbine blades require high precision and strength; if they get dirty they're less efficient. A cylinder for the Magnus effect is relatively cheap, and the rougher the better; They should be a lot cheaper to produce; but they do have more moving parts.

It's been tried a few times, but even though the theory is valid I haven't heard of a successful device. Hopefully someone will crack this one day. The US Navy did a report on it here: apps.dtic.mil/dtic/tr/fulltext/u2/a165902.pdf.

See also: https://diysolarforum.com/threads/tidal-power-the-magnus-effect.27/
 
Last edited:
Possibly a VAWT configuration would be best?

It's been tried (ref), but AFAIK there's no successful commercial models out there. I think the problem with a vertical configuration is there's no directionality to the lift surface on a cylinder as there is with a blade:

38EBE21400000578-0-image-m-4_1475767776332.jpg



Same thing for other types, they've been built and tested... but no commercial models (note the flat plate end caps)

Magnus-effect.png
fQ3TGBE.gif%3Fnoredirect%3D

People have even tried to replace airplane wings:

1343519273665556627.jpg



What I haven't seen is one that takes advantage of the math. For example, more power as diameter increases so a turbine "blade" ought to be conical. Maybe a "band" around the outside to control vibration? The navy document suggests a plate at the end too, something about the laminar flow not sliding off.

CgjXZmpZolrUXHpurjSi.png


It's a pity not more has been done with them. The promise of useful power at low wind speed is pretty compelling.
robaroni Avatar

Sep 12, 2019 at 8:43pm robaroni said:
...This project was tough and I built my own house, my own PV poles and mounts, two PV systems at my house and a couple of windmills ...


Rob's pretty clever at building things and has built a lot of stuff, he might have some insight into what the issues are.



Attachments:

 
Hate to make it sound like these things never worked. They were very successful on the Flettner ships, but I suspect they failed economically because people didn't understand how it could work. Here's an excerpt from the navy document:

In many instances a revolving cylinder can be used in place of "an airfoil shaped wing or blade and with greater efficiency. As a substitute for a conventional sail or rudder, it is the compactness of a Magnus effect unit that makes it attractive. Flettner's sails had about one-ninth the area of the old rig they replaced. A rotor can change its lift by varying its rpm rather than changing its angle of attack...

The document shows some astounding test results replace rudders as the cylinder can be retracted into the hull and unlike a conventional rudder it can't stall at low speeds.

There are also a number of interesting capabilities:
In addition to its inability to stall, a Magnus effect rotor possesses another useful characteristic, its ability to become "invisible" or at least tend to fade away under certain conditions. The "Barkley Phenomenon" was named for the gentleman who pointed out the characteristic to the author during model basin tests of rotary rudders. It had been noted by earlier investigators, but lacked an identifying name. It manifests itself as a distinct drop in drag acting against the rotor just prior to reaching a surface-to-flow velocity ratio of one. This means that the resistance of the cylinder tends to disappear at that point in a way not yet fully explained. One suggestion is that the eddy normally located behind a static cylinder is displaced to the pressure side and becomes part of the lift component.

Flettner made use of the Barkley phenomenon in hurricane conditions. His rotor sails had a maximum surface velocity of about 80 miles per hour so that in winds of 20 miles per hour they would have a surface to flow velocity ratio of 4 and an ideal lift coefficient of more than 9. When he encountered winds in excess of 80 miles - per hour the velocity ratio dropped to less than one and consequently the wind resistance diminished dramatically. The stability of the ship was actually greater than a full rigged vessel under bare poles.


Ironically, shortly after the successful sea trials the ship was sold, the rotary sails removed and replaced with a traditional rig, and promptly sank due to a hurricane.
 
Did you catch that bit where at the right speed drag disappears? That would make it very convenient/safe for a roof since in a hurricane winds it could become transparent to the wind. Eliminate towers and such and a lot of wind power complexity/cost goes away.

3 mph wind use case
Governing EquationBlade configNumber BladesMax Power (W)
MagnusF/L = ρv 2πr²ω1m tall, 1m diameter, 3 revolutions/s31,325
VAWTP = π/2 r² v³ * ρ1m tall320

Wind speed (v) is a cube for traditional aerodynamic blades, so when less than 1 it greatly decreases the power. But in the Magnus effect wind speed is linear, so low wind speed in't such a detriment.

Considering the amount of power is so considerable I'm sure someone would have built one if there wasn't some huge problem with them. If it's not a vibration issue it's probably drag on the rotors causing a net power loss (that is, you have to subtract from that 1.3 kW the amount of power it takes to spin the rotors). I don't know that the rotors have to have a lot of mass, as long as Styrofoam held together at the spin rate it ought to work.

According to the data in the navy document, a somewhat rough surface enhances the effect, so it wouldn't take precision milling like a turbine blade would. You'd just have to figure out how to get variable speed on the rotors while the assembly was spinning too.

Anyone have a high-school age student that needs a science fair project and can report back to us?
::)
 
Very nice and thorough writeup. It's almost hard to believe that wind speeds that low can be captured and utilized. I have this overactive imagination perhaps, but I think it would be interesting to attach hydraulic arms to trees and convert the swaying motion into fluid power. No pesky blades, the infrastructure (forest) is already in place, and hydraulic cylinders are some of the most simple and reliable devices. Cables would work too.
 
Small question: what is the required power for the rotation of the cylinder?
 
Small question: what is the required power for the rotation of the cylinder?
Probably excessive....
...Considering the amount of power is so considerable I'm sure someone would have built one if there wasn't some huge problem with them. If it's not a vibration issue it's probably drag on the rotors causing a net power loss (that is, you have to subtract from that 1.3 kW the amount of power it takes to spin the rotors). I don't know that the rotors have to have a lot of mass, as long as Styrofoam held together at the spin rate it ought to work...
 
Definitely makes me want to experiment with a wind power generation model to see what the net watts are. This flight looks cool, the landing is definitely honest ;-)

 
Last edited:
From the calculations/tables in the OP the theoretical power is:

Wind Speed mphWatts TurbineWatts Magnus Effect
10.249
21.498
34.6147
521.5246
10171.9491

Not included in the comparison above is the energy required to spin the cylinders to generate the lift from the magnus effect or losses due to drag. It could well be there's a conservation of energy, that is the energy required to overcome the drag is equal to the force of the lift.

So how to calculate that? Fluid-flow calculations are pretty well understood. So from this ref:

Power = 0.5πρΩ^3 a^4 LCmc, where a is the radius, L is the length, Cmc is the moment coefficient, Ω is the angular velocity, and ρ is the fluid density.​

1614546647750.png
The power required to overcome frictional drag for a 1m cylinder diameter of 500 mm rotating at 60 rpm in air with a density and viscosity of 4 kg/m3 and 3x10^5 Pa. ω = r × v / |r|² = 6.28 r/s

Re = ρΩb^2/μ = 4 x 6.28 x 0.5^2 / 3x10^-5 = 209,000 so Cmc ~= 0.02,

iterate to solve Cmc=> Cmc = (1 / (−0.8572 + 1.25 ln(209,000 Cmc^0.5))^2 = 0.0069301
= 0.00776​
= 0.007669​
= 0.007679​
= 0.007678​


Power 0.5π x 4 x 6.28^3 x 0.25^4 x 1 x 0.007678 ≈ 0.04 watts from atmospheric drag? So, that's not a big impactor.

Update: There's a flaw in this, it assumes no cross-flow of air such that would create the magnus effect.
 
Last edited:
From the same reference, this was interesting:

Salter, Sortino, and Latham (2008) have proposed the use of rotor ships to propel a fleet of
1500 ships for the purpose of spraying a fine mist of seawater spray worldwide to alter the
Earth’s albedo and as a result affect the energy balance due to insolation and radiation to
space. The concept is to offset the effects of the presumed 3.7 W/m2 heating rise
apportioned to worldwide industrial activity. A concept design for a spray vessel
is shown in Figure 6.41. For the vessel shown, the wind would be blowing from
the right-hand side of the image, the rotor angular velocity would be clockwise
as viewed from above, and the resulting rotor thrust would be to the left.
1614552484298.png

Energy is needed to make the spray. The proposed scheme will draw all the energy from the wind. Numbers of remotely controlled spray vessels will sail back and forth, perpendicular to the local prevailing wind. The motion through the water will drive underwater ‘propellers’ acting in reverse as turbines to generate electrical energy needed for spray production.
 
Ran across this interesting chart, looks like the 2003 data has a technique to maximize lift and minimize drag. Have to dig into this paper...

1614603140374.png

Considering how high the CL:CD's are getting this to work must be a tough nut to crack (or someone would have done it long ago).
 
Saw an interesting post that the Magnus effect couldn't work at low wind speeds, because the energy contained in the wind is too small small (a cube from the earlier math, that is P = π/2 r² v³ * ρ). This makes sense for an airfoil:

400px-Aerofoil1.jpg


The amount of lift is literally limited by the fluid speed over the surfaces, or solely the energy of the wind. Lift occurs because the air pressure becomes lower on the top of the airfoil.

But, I'm still unsure about the net power from the Magnus effect at low wind speeds.
Magnus-anim-canette.gif


Air pressure difference is also what creates the magnus effect, but the difference is the spin in combination with the air-flow causes the pressure difference. At a constant wind velocity, the force can be altered by changing the rpm up to where the cylinder becomes invisible to the wind ("Barkley Phenomenon")). The force per length is F/L = ρv 2πr²ω, here wind velocity v is a scalar. The practical upper limit is most likely governed by the Coandă effect (that is the bigger the cylinder diameter the greater the fluid will "stick" to the surface). But, the faster the rpm the more net energy you're losing.

So, that boils it all back down to the power loss from the resistance to the rotating the cylinder with a cross-flow and probably drag as the cylinder moves. That's going to have a lot to due with the smoothness of the cylinder, rougher being better for the magnus effect - but also probably more resistance. Need to look more into those papers....
 
Lift occurs because the air pressure becomes lower on the top of the airfoil.

That's actually incomplete. Part of the lift (probably the biggest part in most cases actually) is also because air gets redirected toward the ground (that's also why things like flaps works, if lift was only because of Bernoulli's principle then they wouldn't), for more info check that video:

Note that if magnus effect would be the highest efficiency solution then all commercial planes would use it. I didn't run the numbers on that one but I have the feeling that not only it's not the highest but it's probably far far lower than any classic NACA airfoil profiles. But who knows, you might have a good surprise, I'm very curious to see your conclusion on that project ;)
 
Thanks for the educational video!

I'm very curious to see your conclusion on that project ;)
Me too, but fair warning I might not be smart enough to get there and my skills with calculators aren't exactly renown ... so readers might wade through a bunch of calculations that ultimately go nowhere. As a journey of understanding, it's about a year old and I haven't made much progress really. Of course, it's more of a curiosity too, so much to explore and too little time. I think it would be fun to build one, but lots of people have tried already and I'm fairly dubious.

The Baden Baden and air-plane video show the force exists and provide lift, the basic mathematics provide the magnitude of the forces, the experimental data suggests the lift to drag is better than the best airfoils currently in production, the anecdotal evidence suggests the efficiencies are there.

So, it has been successful at propulsion...but never for generation AFAIK. But, the successful cases weren't rotating in two dimensions like the attempts in post #2. Or it could be for wind generation the net energy after subtracting out the rotational energy isn't positive except at high wind speeds.

...lift (probably the biggest part in most cases actually) is also because air gets redirected toward the ground ...
Quibble: poor word choice.... if it had something to do with the ground (ignoring ground-effect that is), the airfoil of a wind turbine blade perpendicular to the ground wouldn't work. :)

What you mean is that air has mass, so redirecting it in one direction by the angle of attack causes an equal and opposite force in the other direction (or again, air pressure difference in that you're creating higher pressure on one side).

It's exactly that reasoning that makes me think the Magnus effect might work at low wind speeds. Power from an airfoil depends on the airmass moving past it with a cube in regards to velocity. The magnus effect only depends on it as a scalar.

... if magnus effect would be the highest efficiency solution then all commercial planes would use it.
Not necessarily, all solutions have Pros & Cons. For example, from the Navy document tested it and found good applications (e.g., rudders) - but to my very limited knowledge they were never applied. Politics? Passive forms were deemed safer than powered?

In the event of engine failure airfoils allow airplanes to glide and helicopters to autogyrate to provide some lift. With the magnus effect an engine failure would stop producing lift altogether. Compared to a wing it adds complexity, it adds weight, removes space for fuel, all bad for airplanes.

Here are some tidbits from A review of the Magnus effect in aeronautics:

4.1. Comparison between wing and rotating cylinder
A rotating cylinder in cross-flow produces aerodynamic forces similar to a wing. However, the characteristics of both lifting devices are different. First of all, the magnitude of the cylinder lift is controlled by the velocity ratio and not by the angle of attack. ... the lift-to-drag-ratio is a good measurement for comparing the aerodynamic efficiency of both devices.

The maximum efficiency measured for a wing with an aspect ratio A=8 is given by L/D=24 at an angle of attack AoA=10°. For example, a Flettner-rotor with a little higher aspect ratio A=12.5 provides a L/D=12, at a velocity ratio a=2.

But....
Taking the power requirement for spinning a rotor into account, the overall efficiency of a Magnus rotor will probably always be below that of a wing.
That at least supports the net-loss theory...

Of interest to aviators:
4.1.1. Stall characteristics
The stall characteristics of a rotating cylinder differ from airfoil stall. The lift breaks down when the rotation of the cylinder stops. ...The lift of a symmetrical airfoil typically breaks down if the angle of attack is increased above approximately 15°. The lift force of a rotating cylinder is insensitive to angle of attack. The lift vector remains perpendicular to the free stream without changing its magnitude. However, the lift coefficient is dependent on the velocity ratio and is therefore dependent on the airspeed.

The major advantages of a Magnus effect device are high-lift forces or rather high wing-loading and stall resistance. The disadvantages are the need for an additional driving mechanism with additional weight and complexity compared to a conventional wing

Who cares about airplanes? Back to Power Generation!
Airplanes and wind generators are different, for example weight isn't all that important for a wind generator and wind speeds are a lot lower. The two big advantages of a magnus effect generator would be if it can have a net positive power at lower wind speeds (low speed winds being far more common) and be safer at high wind speeds. The latter has been proven, but the former is still unclear.
 
Last edited:
Quibble: poor word choice.... if it had something to do with the ground (ignoring ground-effect that is), the airfoil of a wind turbine blade perpendicular to the ground wouldn't work. :)

What you mean is that air has mass, so redirecting it in one direction by the angle of attack causes an equal and opposite force in the other direction (or again, air pressure difference in that you're creating higher pressure on one side).

Yep, I was simplifying a bit too much... you're correct ;)


In the event of engine failure airfoils allow airplanes to glide and helicopters to autogyrate to provide some lift. With the magnus effect an engine failure would stop producing lift altogether. Compared to a wing it adds complexity, it adds weight, removes space for fuel, all bad for airplanes.

Yes, good points.


Not necessarily, all solutions have Pros & Cons. For example, from the Navy document tested it and found good applications (e.g., rudders) - but to my very limited knowledge they were never applied. Politics? Passive forms were deemed safer than powered?

My guess is too much power needed to rotate the cylinder and/or too much drag. But it's only an educated guess.


Airplanes and wind generators are different, for example weight isn't all that important for a wind generator and wind speeds are a lot lower. The two big advantages of a magnus effect generator would be if it can have a net positive power at lower wind speeds (low speed winds being far more common) and be safer at high wind speeds. The latter has been proven, but the former is still unclear.

Actually most wind generator also use classic airfoils, very similar to those on airplanes, so what I said about airplanes wings still applies.

But, as said I'm very curious to see the conclusion, because for now it's very hard to tell which one is best (and in which context of course).
 
....My guess is too much power needed to rotate the cylinder and/or too much drag. But it's only an educated guess.
The CL to CD at high alpha is great, but lower it drops to a ratio of 3 ... so systems like those shown in post #2 might lose 30% of the energy to drag. Fortuantely, no reason to follow that model, you could put a chain drive on something like this where the cyliders moved at slow speed with high torque.
1614709382992.png

(hmmm, wonder if in the system above you could have a top/bottom plate not attached to the cylinder to eliminate vortex's and increase CL?)
Actually most wind generator also use classic airfoils, very similar to those on airplanes, so what I said about airplanes wings still applies.
Agreed, but what doesn't apply are what the one paper described as disadvantages to magnus effect (e.g., weight) as they were talking airplanes.

There's also this bit from that reference:
The initial euphoria accompanied by the technical success of Flettner’s rotor ship stimulated the creation of a new concept for the propulsion of an airplane, the so called rotor propeller [11]. Such a propeller is based on rotating cylinders, which replace the conventional propeller blades of a propulsion system or wind turbines, respectively. For some reason such a concept has not been developed past the experimental stage. Models have been constructed that work well, proving that the principle is valid. Calculations indicated that the thrust that can be developed by a rotor propeller is 59% higher than that of a screw propeller of similar diameter [24].
Thrust isn't everything... but far easier to create a well-balanced cylinder than a propeller.

But, as said I'm very curious to see the conclusion, because for now it's very hard to tell which one is best (and in which context of course).
There are a ton of papers out there carefully duplicating experiments and doing deviations, but so far not one I've seen has listed their experimental energy consumption for the rotors. The equations for no crossflow (a few posts up) showed the resistance as negligible, but doubtful that's true in crossflow.

There are tantalizing bits:
  • Flettner powered his toy model with a severous rotor
  • Modi’s tests... power required to rotate the cylinders was always below 50 W [ref ... says the rotational energy is negligible at low speeds]
  • The Bauckau had two 15 hp electric motors to drive the cylinders, but no rotor data
  • The barbara had three 35 hp motors, rotors 204 square meters, 4m diameter 150 rpm max... but no mass and that hp was probably to get them spinning rather than to keep them spinning.
  • NASA's Modified YOV-10A prototype used 30 hp and The power required to rotate the cylinders was nearly proportional to the cube of rpm. For a flap deflection of 60° at 40 kts, approximately 0.7 hp per foot of cylinder (ref)
 
Last edited:
These guys say their experimental Pnet > 0 experimental was 4.5 m/s (~10 mph).
 
What about an upright spinning cylinder that can alter its shape somehow? Maybe not large scale surface deviations but like a ring of vertical aero foils running the length of the cylinder. Perhaps having a control loop to determine best orientation based on heading of wind?

I haven’t thoroughly reviewed all the links yet (very content rich thread! :)) so please excuse if it’s too much like the other turbines.
 
Back
Top