Windmill or Wind Turbine- powered boats: how many are out there, and are they viable?

[Demiurg]

A short comment on wind turbines. They are all sub-servient to one annoying little law or two...
1. Betz law clearly proves that no wind turbine of any configuration can exceed an efficiency of 59 percent. Just had to clear that since I've seen quite a few references to peoples 90 percent effective turbines. (Actually the jurors are still out debating cyclone wind plants, but no one has discussed that one).
2. Everyone seems to miss this little point... 1 meter squared effective surface gives one watt at one meter per second windspeed.
3. A propeller can only give the inverse of Betz law in power. Bizarre cyclone effects not withstanding.

So now for some simple math, Lets say we have a meter squared of effective surface on our turbine, a high yield generator (if electric, but you get more losses with mechanics...) of 85% effectiveness and an 85% percent effective engine. Notabene, the generator and engine are normally not that effective. But here we are talking theoretical maximum aren't we?
Energy in wind = 1 watt
Energy captured in turbine = 0,59 watt
Energy after generetor = 0,5 watt
Energy after electric motor = 0,425 watt
Energy expended via prop into water (thrust forward obtained) = 0,252 watt.

So we will be able to use 1/4 of the windpower for propulsion in an absolute maximum situation.

[Demiurg]

Delete me... Double post:-(

[Guest625101138]

Originally Posted by Demiurg

A short comment on wind turbines. They are all sub-servient to one annoying little law or two...
1. Betz law clearly proves that no wind turbine of any configuration can exceed an efficiency of 59 percent. Just had to clear that since I've seen quite a few references to peoples 90 percent effective turbines. (Actually the jurors are still out debating cyclone wind plants, but no one has discussed that one).
2. Everyone seems to miss this little point... 1 meter squared effective surface gives one watt at one meter per second windspeed.
3. A propeller can only give the inverse of Betz law in power. Bizarre cyclone effects not withstanding.

So now for some simple math, Lets say we have a meter squared of effective surface on our turbine, a high yield generator (if electric, but you get more losses with mechanics...) of 85% effectiveness and an 85% percent effective engine. Notabene, the generator and engine are normally not that effective. But here we are talking theoretical maximum aren't we?
Energy in wind = 1 watt
Energy captured in turbine = 0,59 watt
Energy after generetor = 0,5 watt
Energy after electric motor = 0,425 watt
Energy expended via prop into water (thrust forward obtained) = 0,252 watt.

So we will be able to use 1/4 of the windpower for propulsion in an absolute maximum situation.

Using the term efficiency in relation to Betz limit is not accurate. It is a limit of the power recovery not efficiency in the sense that the remaing energy has done work in the system. This is an important distinction when considering the application to a moving turbine rather than being fixed.

Also the Betz limit does not apply to ducted turbines. You can extract more than 59% of the energy in the air stream if you use ducting.

Now why restrict the swept area to 1sq.m. Two thin blades 2m long will sweep and area of 24sq.m. And why coose 1m/s. Most sailing boats will not move in wind of this strength. Speeds of 3 to 5m/s would be more common in most locations. Power is a function of velocity squared so power rises rapidly with wind speed.

Your prop efficieny is much lower than what is practically possible. Possible to get better than 85% prop efficiency. The air turbine can achieve efficiencies up around 90%. When going windward the apparent velocity on the prop increase giving it much improved operating conditions for high efficiency.

The real value of an electrical system is that it can be combined with storage so you can store excess power in strong wind and release in low or negligible wind to maintain a high average speed. This is a very important feature when you consider any boat application as power required goes up with the cube of the speed. So you waste a lot of energy to go a little faster in strong wind.

Rick W

[Tcubed]

The Betz limit refers to the efficiency expressed in these terms: energy delivered by turbine/energy of stream tube intercepted by turbine. Maximum is 0.59. No reference is made as to force on pylon.

In the case talked about here betz limit is mostly irrelevant, ass we are measuring efficiency in terms of energy delivered by turbine/energy required to move the turbine. Very different.

And the Betz limit still applies to ducted turbines. The important measurement is the intercepted flow, not the turbine's diameter.

[Guest625101138]

Originally Posted by Tcubed

..

And the Betz limit still applies to ducted turbines. The important measurement is the intercepted flow, not the turbine's diameter.

If you use a duct you can extract more than 59% of the free air stream. So the Betz limit does NOT apply for a ducted prop.

Rick W

[Tcubed]

From wiki;

Points of Interest

Note that the preceding analysis has no dependence on the geometry, therefore S may take any form provided that the flow travels axially from the entrance to the control volume to the exit, and the the control volume has uniform entry and exit velocities. Note that any extraneous effects can only decrease the performance of the turbine since this analysis was idealized to disregard friction. Any non-ideal effects would detract from the energy available in the incoming fluid, lowering the overall efficiencies.
There have been several arguments made about this limit and the effects of nozzles, and there is a distinct difficulty when considering power devices that use more captured area than the area of the rotor. Some manufacturers and inventors have made claims of exceeding the Betz' limit by doing just this, in reality, their initial assumptions are wrong, since they are using a substantially larger A1 than the size of their rotor, and this skews their efficiency number. In reality, the rotor is just as efficient as it would be without the nozzle or capture device, but by adding such a device you make more power available in the upstream wind from the rotor.




Source http://en.wikipedia.org/wiki/Betz_limit

[Guest625101138]

Originally Posted by Tcubed

From wiki;

Points of Interest

Note that the preceding analysis has no dependence on the geometry, therefore S may take any form provided that the flow travels axially from the entrance to the control volume to the exit, and the the control volume has uniform entry and exit velocities. Note that any extraneous effects can only decrease the performance of the turbine since this analysis was idealized to disregard friction. Any non-ideal effects would detract from the energy available in the incoming fluid, lowering the overall efficiencies.
There have been several arguments made about this limit and the effects of nozzles, and there is a distinct difficulty when considering power devices that use more captured area than the area of the rotor. Some manufacturers and inventors have made claims of exceeding the Betz' limit by doing just this, in reality, their initial assumptions are wrong, since they are using a substantially larger A1 than the size of their rotor, and this skews their efficiency number. In reality, the rotor is just as efficient as it would be without the nozzle or capture device, but by adding such a device you make more power available in the upstream wind from the rotor.




Source http://en.wikipedia.org/wiki/Betz_limit

You should not believe everything you read. Do the analysis and you will find the wiki is wrong:
http://www.ibpsa.org/proceedings/BS2...3_0407_414.pdf

Rick W

[Tcubed]

Thanks for that informative paper. I will read it in depth later. At first glance though it seems to me it is referring to apertures in large obstructions rather than a 'cowl' to try and 'concentrate' flow. There is a qualitative difference here that makes me think that yes indeed it may be possible , although i don't think that is what wiki had in mind nor me.. i look forward to understanding the writ.

[Demiurg]

Originally Posted by Rick Willoughby

Using the term efficiency in relation to Betz limit is not accurate. It is a limit of the power recovery not efficiency in the sense that the remaing energy has done work in the system. This is an important distinction when considering the application to a moving turbine rather than being fixed.

Also the Betz limit does not apply to ducted turbines. You can extract more than 59% of the energy in the air stream if you use ducting.

Now why restrict the swept area to 1sq.m. Two thin blades 2m long will sweep and area of 24sq.m. And why coose 1m/s. Most sailing boats will not move in wind of this strength. Speeds of 3 to 5m/s would be more common in most locations. Power is a function of velocity squared so power rises rapidly with wind speed.

Your prop efficieny is much lower than what is practically possible. Possible to get better than 85% prop efficiency. The air turbine can achieve efficiencies up around 90%. When going windward the apparent velocity on the prop increase giving it much improved operating conditions for high efficiency.

The real value of an electrical system is that it can be combined with storage so you can store excess power in strong wind and release in low or negligible wind to maintain a high average speed. This is a very important feature when you consider any boat application as power required goes up with the cube of the speed. So you waste a lot of energy to go a little faster in strong wind.

Rick W

Hello Rick!

You are quite right, I was a wee bit sloppy in my vocabulary, probably out of not being a native english speaker. I shouldn't have used efficiency.

But that is with the ducting. The turbine and of itself will still be below Betz. But as you noticed I hedged my bet and noted that there is one turbine type that is able to go postbetz... www.energytower.se

Rick, the reason I used one metre squared and one metre per second is quite simple for the sake of the example. Of course you can use any size and windspeed you feel like. But the general idea will still be the same.
And no... Two wings with a length of 2 meters each will never have the surface area of 24 metres squared. It will just sweap over that area. It will though only take up the power of the actual surface area facing the wind at the instant of wind impact.

A wind turbine working at 90 percent efficiency? I am stumped. I've seen one in the entire world able of producing more then 59. Or do you mean 90 out of 59? Regarding the props (water) you are correct, I had a momentary laps of reason. 85 is quite doable.

Carl

[Guest625101138]

Originally Posted by Demiurg

.... Two wings with a length of 2 meters each will never have the surface area of 24 metres squared. It will just sweap over that area. It will though only take up the power of the actual surface area facing the wind at the instant of wind impact.

A wind turbine working at 90 percent efficiency? I am stumped. I've seen one in the entire world able of producing more then 59. Or do you mean 90 out of 59? Regarding the props (water) you are correct, I had a momentary laps of reason. 85 is quite doable.

Carl

The important feature of a wind turbine on a moving vehilce is its mechanical efficiency. Efficiency rather than energy recovery is the important parameter.

For example a 4m diameter turbine operating in a 9m/s air stream can generate 1400W at the shaft at 89% efficiency. The drag on the turbine blades is 200N. The energy taken from the air stream is 1620W or 28% of actual airstream enenrgy. Blades in this case have a maximum chord of 100mm.

Rick W

[Demiurg]

Originally Posted by Rick Willoughby

The important feature of a wind turbine on a moving vehilce is its mechanical efficiency. Efficiency rather than energy recovery is the important parameter.

For example a 4m diameter turbine operating in a 9m/s air stream can generate 1400W at the shaft at 89% efficiency. The drag on the turbine blades is 200N. The energy taken from the air stream is 1620W or 28% of actual airstream enenrgy. Blades in this case have a maximum chord of 100mm.

Rick W

Since you are not stating the actual surface area of the wings I cannot calculate it correctly. But, let's say that the surface area for two wings of that wingspan are the normal 1 sqm. Sweaparea of the wings might be nice for something, but it has absolutely nothing to do with power-generation.
And with one sqm and to into the bin with betz and everything else you are getting 256 watts per square metre.
The currently most efficient turbine generates 1440W per sqm at 17 metres per second. And that is from a real and existing powerplant that anybody can order. If you can get that much watt per sqm I just have one thing to say... I want 4000 of your plants, can you deliver them by the end of the month?

Seriously, I have a wee bit of doubt. But if you will allow me to hook up some testgear and you can deliver 1400 watts...

Regards!
Carl

[Guest625101138]

Originally Posted by Demiurg

........ Sweaparea of the wings might be nice for something, but it has absolutely nothing to do with power-generation.
...Carl

Carl
Take a look at large commercial turbines. The manufacturers go to a lot of effort to produce long slender blades to maximise swept area. You need to inform them of your theory so they stop wasting all this effort on blade design and just avoid the bending issues by using short wide blades to achieve the same blade area.

Rick W

[Demiurg]

Originally Posted by Rick Willoughby

Carl
Take a look at large commercial turbines. The manufacturers go to a lot of effort to produce long slender blades to maximise swept area. You need to inform them of your theory so they stop wasting all this effort on blade design and just avoid the bending issues by using short wide blades to achieve the same blade area.

Rick W

Weird... I thought I worked with those... Ever heard of Vestas?
Now you are talking an entirely different principle here.

Long and slender blades have a quite a few advantages over short and stumpy. The one you are thinking about I suspect is the simple fact that a long wing has a higher tip speed than a short thusly producing more power. The normal reason for long and slender is that they cut the air better than the "stumpies". And if you have a lot of stumpies as in a classic windmill you will after a while offset the gain in sqm by the increasing wind resistance.
When you design a wing you want one with a high area towards the wind, that passes easily through the air it "cuts" and a high energy potential in the tips giving a wholesome inertia if the wind is uneven. There are few other principles too, but the fact is that a modern wing is a compromise between the relevant factors. As soon as you try to be funky and go all out in one direction you are normally in for it at some other place.

Please note here that I am not an winged "propellerlike" turbine friend. They are nowhere near as efficient as the second generation vertical screws. They are also inherently unsafe as it is, and if you than hark it onto a boat, then you are waiting for a disaster. Not to mention that bladed turbines are less forgiving if the wind is turbulent than the verts.

Actually I think you are trying to point out that a blade in motion due to it's motion will be subservient to a larger area of wind since it is moving through the air (wind) faster than the wind is moving. Am I correct in my assumption? If so you are in a way correct, the area will be larger than the physical area, but not so much that it is actually of any greater benefit.

Regards

[Guest625101138]

Originally Posted by Demiurg

.....

Actually I think you are trying to point out that a blade in motion due to it's motion will be subservient to a larger area of wind since it is moving through the air (wind) faster than the wind is moving. Am I correct in my assumption? If so you are in a way correct, the area will be larger than the physical area, but not so much that it is actually of any greater benefit.

Regards

For the 4m prop I gave the data for above has a tip speed ratio of 9 so will extract power from the entire disc it sweeps. This is the basis of modern turbine design.

My design is very concervative on power extraction coefficient because my interest is in overall efficiency.

If you look at small domestic use turbines they will extract 1500W from a 3m turbine in wind speed around 9 to 10m/s.

Rick W

[Demiurg]

Originally Posted by Rick Willoughby

For the 4m prop I gave the data for above has a tip speed ratio of 9 so will extract power from the entire disc it sweeps. This is the basis of modern turbine design.

My design is very concervative on power extraction coefficient because my interest is in overall efficiency.

If you look at small domestic use turbines they will extract 1500W from a 3m turbine in wind speed around 9 to 10m/s.

Rick W

Hello Rick!

I just want to point out that I am not in any way picking on you. I have seen some of your designs and I do think they are innovative.
But, I also wish to point out that I work on a daily basis with a variaty of sizes and types of turbines, although mostly in hybrid systems.
3 meter turbines regularly have the mark effect of 2,2kW, but very rarely actually deliver it at any windspeed... There are two ways to do the calculation. Ol' lazy man style is to count from the generator, very few generators hooked to an optimum blade configuration delivers more than 35 percent of the mark-effect of the generator. So if you are having 2,2kW generator hooked to an optimum blade-set than you will have a practical maximum of 489W.
The way we are doing it goes like this;
Pmax = 0,5 x 1,25 x A x V x V x V
Pmax is the theoretical maximal out-effect given in Watt for a given wind-area at a given wind-speed (and a given medium, in this case air, the average weight of air is 1,25kgs per kubic metre)
A is the Area i sqm that the windplant uses, fir instance the radius r in metres of a free-movers rotor-blades (circular are A = 3,14 x r x r)
V is wind-speed in metre per second.
To the formula you can add the efficiency ratio nVv (1,0 is = 100%) for the construction in and of itself, and for the generator nE. Total efficiency is than nVtot = nVt x nVv (x nE).
För nE it is true that on a general basis 0.85 (85%), depending on type.
For a free mover (classical windplant) is the theoretical maximum nVt 0,59 (Betz), but not even the largest and most efficient plants cream out more than (Vestas VX90 for instance) 0,6 (60%) nVv of the beforementioned 0.59 (over the entire wind-spectrum, can peak at 75% nVvo at optimum range of the plant).
Thereby follows nVtot = nVt x nVv = 059 x 0,6 = 0,35 (35%) The wind is thusly moving around and through the turbine area. So a large wind-plant looses 65%. For a small plant the figures are nVv = 0,35, which gives nVtot = 0,59 x 0,35 = 0,20 (20%). Ie, 80 percent losses.

Let's here compare with the Vestas V-27 plant: 27 metre diameter.
Vestas V-27 developes 225 kW electrical effect at 14,5 m/s
nE = 0,9 (90%, ?) gives mechanical effect = 250 kW.
Diameter of 27 m gives r Pmax = 1091000 W, 1091 kW, 1,091 MW.
nVtot = 20%.
nVv = 23%.

You do the math...
Carl