Everything Old is new again - Flettner Rotor Ship is launched

I've been digging around some more into the effectiveness, or otherwise, of Magnus effect rotors and have found a few interesting snippets that might be worth noting. My research was prompted by getting some rather odd-looking results from the NASA Foilsim programme. To be fair, NASA do have a very prominent warning about the accuracy of this simulator and it looks like it really runs out of usefulness when looking at the range of rotor sizes, wind speeds and therefore Reynolds numbers that a small boat or ship rotor might be working at.

Prandtl's paper has some data that not only makes sense (inasmuch as it ties up fairly well with theory) but which also seems to have been the source data used by Flettner when designing his rotors. I need to do some experiments, but I've knocked up a spreadsheet that uses Prandtl's wind tunnel data and which can be used to predict lift and drag for a modest size rotor over a range of wind and rpm conditions.

One fairly obvious thing to come out of today's work has been the near-linear relationship, over a fairly large range, of the lift coefficient, Cl to u/V, the ratio of rotor peripheral velocity to free stream (wind) velocity. This makes it possible to approximate Cl for any reasonable value of u/V by a simple calculation. If you want to do it, then Cl ~= (3.4185 x u/V) - 2.2 . This is reasonably valid from u/V = 1 to u/V = 3. Outside this range the value of Cl will be in error to some degree, particularly at the lower end. Knowing Cl it's easy to work out lift from 1/2.rho.Cl.A.V².

Unfortunately working out Cd, the drag coefficient, is much harder. I tried the conventional approach of determining the profile drag (from the known Reynolds number, Re, velocity and dimensions) and then calculating the induced drag (from the known lift coefficient, velocity and dimensions), but the answers were way out. Clearly the standard approach used for non-rotating bodies doesn't hold good in this case, probably because the range of Reynolds number is over the critical value where flow becomes fully turbulent. The only way that I can see to work out Cd at the moment is to fall back on Prandtl's wind tunnel data and look it up from the drag polar. It seems that I'm not alone in finding drag of a rotating cylinder to be hard to model, the web seems littered with papers, often contradictory, from people who've tried to do the same thing. Many of the papers only deal with ideal flow, which means, because of the D'Alembert Paradox, they are useless for determining drag. The other main difficulty I've found is that few seem to have modelled drag in the range of Re from around 100,000 to 2,000,000, which tends to be the operating point for a small boat-sized rotor in normal strength winds.

What is surprising is how small a rotor is needed to derive enough thrust to power a small boat to hull speed. Stephen Thorpe has demonstrated this with his tapered rotor, but it seems that a smaller rotor with end plates might actually work as well. For example, a canoe that needs a thrust of around 30N to achieve 4kts could get this in a 10mph beam-on wind from a 2m high rotor, 0.4m in diameter, fitted with 0.8m diameter end plates and spinning at 350rpm. The rotor area needed is just 0.8m², perhaps a quarter of the size of a typical canoe sail.

Jeremy

 

I think were are missing a trick here. We try to apply technology, but I am confident there are still free Athenians in Athenian galleys. We should look for a better way of oaring, n'est pas

http://www.google.co.uk/images?q=at...&source=og&sa=N&hl=en&tab=wi&biw=1024&bih=593

 

There was Charlton Heston rowing one so it has to be a Roman galley

 

No, it's a Whoa Man galley. Good grief, take me away!!!

 

wrong boat - thats not a rotor ship - thats Mr Leshes 'spinning surboards' concept, with even worse vibration problems

 

I've been doing more work on modelling rotors in an attempt to put together a simple to use performance/size/rpm tool for rotors for small boats. One of the archived NACA Technical Notes, No.209, has some tables of wind tunnel measurements made on what were effectively infinitely long cylinders rotating in a free stream.

I transcribed the drag and lift data, relative to the peripheral velocity/free stream velocity ratio, from this old paper into a spreadsheet and managed to get a reasonably good fit for both Cl and Cd to third order polynomial functions. The result is that I now have a fairly simple way to enter rotor length and diameter, plus wind speed, and get a range of values for lift and drag for a range of rotor rpm from 100 to around 1000 (the upper end is limited depending on wind speed and rotor diameter). The results seem to be within around 10 to 15% of the actual wind tunnel data and are probably good enough for choosing rotor dimensions for a small boat.

A real rotor, with end plates, will probably perform slightly less well than these calculations predict, due to the limited effectiveness of the end plates in preventing tip vortex formation. Nevertheless, I now think I have a way of quickly looking at a range of rotor sizes to see what the effect of varying diameter, height or rpm will be in a given wind.

The spreadsheet needs some tidying up, but when it's finished I'd be happy to post it as a tool that might be of use to anyone else who wants to look more closely at Magnus rotor performance.

Jeremy

 

Hi Jeremy - I would be interested to look at the calcs. Did you do any comparisons with the formulae posted earlier on this thread ?

 

I haven't done a complete comparison yet, but I can say with certainty that the drag formulae earlier in this thread don't give an answer that seems to match reality (or at least, the reality of wind tunnel test data). The data do match reasonably well to that measured by Prandtl, allowing for the fact that Prandtl used a smaller cylinder with 2D end plates in a smaller wind tunnel (as with a lot of things, size matters when it comes to wind tunnels).

The author of TN 209 made many more measurements than Prandtl and tabulated them (Prandtl just presented curves with a few imprecise data points). All I've done is taken the Cd, Cl and u/V data, filtered out the low u/V data that is irrelevant because it gives lower than unity L/D and used the remainder to derive approximate functions that describe Cd and Cl in terms of u/V. This side-steps the purely mathematical approach of using the Kutta-Joukowski theorem and uses instead measured data to predict performance by simulation. Given that the Kutta-Joukowski theorem gives a value for lift in ideal flow (i.e. a non-viscous incompressible fluid) and cannot give a figure for drag (because of the D'Alembert paradox drag = 0 in ideal flow), I believe that this approximation method should yield results that are closer to reality. Certainly the estimates of lift and drag for a rotor of around the size and spin rate of that used by Stephen Thorpe on his Rotorboat look to be in the right ball park, which is encouraging, as Foilsim won't give an answer in this range at all.

What I can't easily predict is the rotor power requirement, but I suspect that it will be dominated by friction in the motor, bearings and drive system. TN 209 does include power data, but they are probably unreliable given the state of electric motor technology at that time - it's likely that the motor and bearing losses exceeded the rotor drive power, in my view.

I'm not sure if TN 209 has been linked earlier in this thread or not, but in case it hasn't I've attached a copy. The key data is that obtained for wind speeds of 5m/S to 10m/S, where a realistic range of L/D ratios were measured. Note that this paper refers to lift as crossways force, so the lift coefficient is denoted Ccw. This is due to the orientation of the tunnel, where drag was along the tunnel major axis, with the cylinder running vertically from floor to ceiling.

I've attached the Excel spreadsheet, hopefully it should be fairly self-explanatory to use.

Jeremy

 

Firstly, Please let me apologise to everyone for dragging up an old thread, but I have an excuse.


I am currently studying Marine Engineering at Warsash Maritime Academy. As part of my studies I have to complete a project, which is to design and evaluate a wind assisted propulsion system for an Oil Tanker.

My studies have led me to the Flettner Rotor, and through that subject to this forum and this thread.

I am contacting Jeremy specifically, and the board as a whole, as the files Jeremy has provided above contain some extremely useful information, I am contacting to ensure that Jeremy is okay with me referencing his material in the project.

I will only be using a small part of the information provided (specifically relating to Drag and Lift Coefficients) but I would hate for anyone to think that I was taking credit for work that is not mine.

Many thanks for your time.

Derek.

 

Derek, feel free to use whatever you wish, with the caveat that it's largely based on experimental data from tests conducted a long time ago. I intend to build a small rotor powered sailing boat to test out some ideas I have on control of rotor speed and direction, following a useful email exchange with Stephen Thorpe. Unfortunately I don't have time to build the system just yet, as I'm finishing off a boat for another project and am starting a house self-build project.

Stephen Thorpe pointed out that there are some critical operating points for a rotor powered vessel. The major issue is making sure that the vessel doesn't suddenly find itself head or stern to the wind with the rotor turning. If it does, then the lift vector that normally provides propulsive thrust instead provides a strong overturning moment!

My thinking is to incorporate solar cells in the end plate to provide the power required to operate the motor, with storage batteries at the rotor base to cover times when the solar cells can't provide enough power (excess solar power would be used to charge the batteries). I also intend to fit a wind direction sensor to the top of the rotor and use this to provide feedback to the rotor speed and direction control system. This should eliminate the sudden overturning moment should the vessel encounter a sudden apparent wind shift and allow a simplified interface for controlling desired speed and direction. It may even be possible to couple the control system to the rudder, so that best speed over the ground in the desired direction can be obtained automatically, by changing course and rotor speed as required.

For the purposes of an initial experiment I was looking at making a removable self-contained rotor unit that could fairly quickly and easily be fitted to a boat. This would also allow land based testing on a load balance, so that lift and drag vectors could be measured at various wind and rotor speeds.

Good luck with the project, it sounds like fun!

Jeremy

 

Another potential source of torque on the rotor are the shear stresses at the surface. They are not symmetric so the result when intergrated around the cylinder should be a net torque. In principal a boundary layer calculation based on velocities from the potential flow solution for lifting flow around a two dimensional cylinder along with the speed of the cylinder surface could provide an estimate of the surface skin friction which could then be integrated for the torque. The potential flow solution for a two dimensional cylinder is a uniform stream plus a doublet plus a vortex. Doublet strength depends on the radius of the cylinder and free stream velocity; vortex strength depends on the circulation and thus the lift, and it also determines the stagnation point locations. I'm sure this has been done before.

 

It's an easy calculation, but as the relative velocities and rotor surface area are modest the rotor total power demand is still likely to be dominated by the frictional losses in the bearings and drive system, plus the motor resistive losses. The relationship between rotor drive power and rpm in TN209 shows that it doesn't follow the cube law relationship that might be expected if viscous/shear drag was significant, hence my view that bearing and transmission losses are likely to be the dominant cause of power loss. In fact, it looks to be fairly linear, which very strongly suggests that frictional loss is the primary cause of power loss in the rotor drive system.

 

"Another potential source of torque on the rotor are the shear stresses at the surface." This was a source of discussion for many years.

A scottish engineer (whose name eludes me now) had calculated that the drag was too significant to make the system workable, but other engineers have identified problems with those calculations, and actual practice seems to confirm the error.

Derek - you may find it usefull to contact the "Windship" Enercon engineers, or even their PR people. They may be pleased to supply some useful research info.

 

Enercon don't seem to be too willing to talk to me unfortunately, I sent them some requests for information a few months ago, but never received a reply.

Jeremy, I understand that the test data is from a while ago, however it's all I have to go on, whilst I am investigating the use of the Flettner rotor, I do not have access to a towing tank or other test facilities.

This is a two fold problem, firstly it means relying on other people's data (typically from studies carried out in the 1920s) secondly it means that I am "guessing" at hull form coefficients and resistances in order to determine thrust requirements and so forth as, not surprisingly, the current shape of Oil tankers does not really represent the most streamlined or efficient of hull designs.

The project itself may serve me as a starting block for further study, but in and of itself, I feel that there are going to be some fairly serious omissions.


I appreciate the help that I have received here however, it has lead me to think about a few things that I had previously not even considered.

 

Nice to see this thread is still current - I have been away for a bit. It seems that Jeremy and I have very similar ideas regarding a small rotor for inland waterways use. Since he is a doer and I am a dreamer (and stuck in San Diego for a bit before I can return to Blighty) I can't wait to see what he comes up with!

A small drop-in rotor with integrated batteries and solar panel sounds just the thing for a low-energy river launch that is easy to handle and elegant to maneuver. With human power as well (probably pedal) it would be a lovely way to cover river miles.