P =F\cdot |v| =( \underbrace{c_1 cos(\alpha)(|v_w|^2 + |v_b|^2)}_{lift}-\underbrace{c_2sin(\alpha)(|v_w|^2 + |v_b|^2)}_{drag})|v_b|
with c_1 = c_l\frac{\rho_{air}}{2}A and c_2 = c_d\frac{\rho_{air}}{2}A
The question is now how to optimize v_b and \alpha.
julia> h(w,b;c_l=1.4,c_d=0.4,c=1,α=atan(b/w)) = (c_l*cos(α)-c_d*sin(α))*c*(w^2+b^2)*b
h (generic function with 1 method)
julia> [h(10,n;c=1.3/2*5*50) for n in 20:25].*8
11-element Array{Float64,1}:
3.488266044899673e6
3.5558980961776716e6
3.593981194385971e6
-> 3.599463287991695e6
3.5692799999999944e6
3.500357124637429e6
julia> [h(15,n;c=1.3/2*5*50) for n in 31:37].*8
7-element Array{Float64,1}:
1.1935643590958968e7
1.2055588129394608e7
1.2129686531052653e7
-> 1.215488427581274e7
1.2128118671088275e7
1.2046319999999981e7
1.190641249199773e7
So with my basic calculation I get about 3.5MW with 10\frac{m}{s} wind speed and 12MW with 15\frac{m}{s} wind speed. Wings are 50m\times5m.
How do you like the idea. Does that have any potential?
Hi there,
first of all: looking pretty cool what you tried there, and it’s guaranteed to be an interesting exercise for you. By all means, go on!
On the other hand, it looks almost too simple, so you would imagine that somebody already tried that. Turn out it’s kinda true, see:
http://www.heiner-doerner-windenergie.de/windcuriosity2.html
(German site (very old German professor, thus the horrible site, but still a good read), horrible resolution and pretty old, but it shows similar concepts from the 80s that didn’t work out)
There are some issues that come to my mind right away:
friction and inertia, especially at low winds and for initiation of movement
terrible material to capture area ratio, may or may not be offset by cheaper materials
assumes perpendicular and kinda non-turbulent flow to work efficiently, hard to guarantee. For perpendicularity you probably need a yaw mechanism, which puts heavy stress on the middle tower. You may drop this but that’d make it only applicable in places with a fixed wind direction
blades need cutouts and some kind of suspension to be able to turn around the wheels, may induce wear there. Relatively many moving parts, may or may not be offset by cheaper materials
I don’t want to spoil your fun, just some things to consider. Good luck to you and sorry that I can’t help with your optimization problem
Thank you for the new input. I’m German so no worries^^
The projects you send me are very similar, but not the same. The key difference is the orientation of the rotation. In my case the rotation is up, turn, down turn. As far as I can see the movement in older ideas is side wise. So the whole thing isn’t that stable and there is only one perfect angle of attack for the wind.
Because in my case the movement is up and down the steal cable can easily cope with the forces. And secondly the whole thing is able to turn around the z axis to face perfectly the wind.
I have a few thoughts - it’s been a few years since I got my B.S. in aeronautical & mechanical engineering, and I’ve not touched the aero side since.
How are you going to manage aeroelasticity / flutter concerns with only cables holding the blades?
e.g. As the wind changes directions it will increase lift on one side of the blades
As the rear blades pass through the wake of the front blades they will experience dynamic loads. Also, due to the downwash, I wouldn’t be surprised if the rear blades experience stall – thus massive drag increases.
You mention that “because it’s rectangular it covers more area” - I presume that you’re comparing to the circular profile of traditional wind turbines. But don’t forget that finite wings don’t have a uniform lift distribution.
It’s not clear to me that your rectangular profile is more “efficient” than a traditional turbine with the same “width”
You’ll need to be able to “feather” the wings if the wind-speed is above allowable conditions. This means you’ll need to have a mechanism in the blades to accomplish this, but it will need to be a powerful motor if it can only apply torque to the cable running through the blades. You’ll then also need a braking mechanism to hold an AOA
This is a dynamic system - it’s going to vibrate and it’s going to deform. You’re going to have uneven load distributions. Your structural members are minimal (draw a FBD for the outermost pulleys). You need a lot more structural members. Those will disrupt flow and increase drag… you’re going to have a lot of lateral force on your single strut… I fail to see how this will be able to “use less material”.
You have multiple moving parts… those are all regions of potential failure.
Where will the turbine be located? Will you have multiple turbines?
The max theoretical efficiency of wind turbines is 59% (Bentz limit) – essentially, you can’t extract all the energy from wind, because that would require stopping the wind, which means no more wind can enter. Currently, wind turbines are able to extract ~50% of the energy from the wind that passes through the rotor area. Thus it will be very difficult to supplant traditional wind-turbines.
I don’t mean to dissuade you, but you asked “does the idea have any potential”? In its current state I don’t see much potential from a commercial viability standpoint. But that doesn’t mean it can’t be a fun project!
The link I provided above references this document for that statement:
See page 62 where it states:
Modern utility-scale wind turbines generally extract about 50% of the available power in the wind at wind speeds below the rated wind speed, while the maximum power that a device can theoretically extract is 59% of the available power (the “Betz Limit”). Typically, a modern turbine will begin to produce power at a wind speed of 3–5 m/s and reach its rated power at 11–14 m/s. Around 25 m/s, the control system pitches the blades to stop rotation, feathering the blades to prevent overloads and protect turbine components from possible damage due to high winds.
Chapter 2 of that paper is actually quite an interesting read on the technologies that go into wind turbines – I’d highly recommend reading it.
Anyways, that statement references this other report (see page 31):
This report has similar information, plus a pretty graph:
The Betz Limit
Not all of the energy present in a stream of moving air can be extracted; some air must remain in motion after extraction. Otherwise, no new, more energetic air can enter the device. Building a wall would stop the air at the wall, but the free stream of energetic air would just flow around the wall. On the other end of the spectrum, a device that does not slow the air is not extracting any energy, either. The maximum energy that can be extracted from a fluid stream by a device with the same working area as the stream cross section is 59% of the energy in the stream. Because it was first derived by wind turbine pioneer Albert Betz, this maximum is known as the Betz Limit.
My recollection is the energy in wind in proportional to the velocity cubed. Usint this relationship the power at 12 m/s should be 6 MW if the power is 3.5 MW at 10 m/s.
I did not try to check your calculations from first principles, just providing a sanity check. I would echo GregVernon’s concerns. It is interesting to view galloping wires in ice storms and traffic signs that vibrate rotationally at certain wind speeds due to vortex shedding frequencies being coincident with the torsional resonant frequencies. You may also note that many chimneys have strakes on them to prevent vortex shedding damage.
