It may be quite possible to get ten times the wind power we currently get, based on research and development using new methods. As a starting point, let's consider the obvious fact that the single most important factor is wind velocity, especially since the amount of energy in a wind flow is proportional to its velocity cubed. Thus, as the wind velocity doubles, it has eight times the amount of energy! (2³ = 8)
Next, consider the wind gradient (see Image 1), which says that the wind velocity increases as we go up above the ground; the rate of increase depends on terrain and surface features. Thus we see that there is a huge benefit to harvesting wind power high above ground. Since the Towerdome system is primarily concerned with vertical structures, it is a natural candidate for this type of application.
Some very interesting research has been done by Prof. John Dabiri, MacArthur Fellow at Stanford, showing that a distributed 2D array of smaller turbines can collectively produce much more power (10x) than a fewer number of large turbines. His research has investigated the effect of different 2D arrays, especially using vertical axis wind turbines (see Image 2). By changing the spacing and arrangement of turbines, and alternating their spin direction, he shows how turbines can be kept out of the turbulence region produced by up-wind turbines, and also take advantage of a drafting effect that speeds up (at least partially) an air flow which had been slowed down by going through a turbine, before it goes through another turbine in the array.
We believe that it is possible to take Dabiri's work further with a 3-dimensional array of turbines that may produce an additional exponential increase in power output, and also take advantage of higher wind speeds for the turbines higher up in the 3D array.
We propose using the Towerdome component system, which is based on icosahedral geometry, to construct turbine modules that have an icosahedral shape (see Image 3). The icosahedron is triangulated (making it strong), has polar vertexes to hold the turbine axis, and it is well-suited to accomodate a cylindrical spin volume. The human figures shown give a sense of the recommended size of the turbine housing for industrial power production. The blue strut components and the brown horizontal beams are both 10 ft. long, a size easily managed by a construction worker.
The basic icosahedron housing is strong, but it is also somewhat "squashable". Because of this, we suggest that ten extra struts (five at the top and five on the bottom) form a pair of tetrahedronal trusses that not only brace the icosahedron extremely well, but also provide extra stability for the turbine axis, shorten the spin axis length (also increasing stability), and create internal mounting areas for the turbine bearings and electrical parts.
One very interesting question to explore is how lightweight can a windfarm be, that is elevated high above the ground? Lightweight is good because it reduces the resources needed to manufacture it, and it also requires less support. For more discussion of this see the Towerdome Component System page.
Our claim is that there is nothing inherently heavy about wind energy production; perhaps only the generator has a limit to how lightweight it can be, even with advanced technology. There are already lightweight turbines on the market; we propose that the support structure be also lightweight.
Image 5 shows the turbine housing with a mock-up of a 3-bladed, vertical-axis turbine mounted in it. The turbine shown is about 8 ft. high and 13 ft. in diameter; it is not supposed to refer to any product currently on the market; there are many kinds of turbines available, and this design only requires that the spin volume fits neatly inside the housing and makes efficient use of the space.
Vertical-axis wind turbines are good because they are more human-sized and therefore manageable, they can produce power at lower wind velocities and from any wind direction, are more silent in operation, and are much less likely to kill birds.
Image 6 shows how two turbine modules form a shallow array by sharing a horizontal beam component and two hubs. To stabilize against rotation around this axis, two extra struts (shown in red) connect the two modules with two interstitial tetrahedrons, forming a rigid linear icosahedral truss.
To help stabilize the structure, four cable components connect the two modules (see Image 7). They are shown thinner than the struts, also red. Thus the module array is completely surrounded by six tension paths that route powerful wind forces down to the ground anchor points. Four of the paths are purely tension (no compression), and the other two function in either tension or compression. To help show these six paths clearly, the image extends them out from both ends.
Image 8 shows five shallow turbine arrays, each with 11 turbine modules, arranged around a central module. This alone is a stable structure, but to reduce stress on the central module we support it with a vertical turbine array.
Image 9 show a close-up of the apex of the pyramid, with the turbines and vertical array removed so that it is easier to see how the cable network of each array joins with cables from the other arrays to form a comprehensive network. This network can efficiently transfer powerful wind forces from one array to another, and from there down to the ground, without crushing the module arrays and turbines embedded in them.
Image 10 shows how two turbine modules form a vertical array, which is like a pillar of stacked turbine modules. In this array, an extra set of 10 strut components connect the two modules, and the pentagonal trusses at the top and bottom interlace to form a sturdy support, that also generates electric power.
A vertical array of 5 turbines is used in Image 8 to help support the pyramid of shallow arrays. Note that the vertical array does not have any tension cables, since it operates only in compression.
Wind turbines are typically mounted on a mast. The problem with this is that the mast acts like a lever arm, and the lateral force of the wind creates a very large bending force, especially at the base (see Image 11). This causes the designs to be massive and require huge foundations.
This design, by contrast, mounts lightweight turbines in a lightweight structure that "holds open" a comprehensive cable network. Since the structure is lightweight, the major forces on the structure are the drag forces induced by the wind torquing the turbine rotors. As these forces are efficiently routed through the structure to the ground, it acts like a type of kite that is held in place by the tension of the kite-string, securely anchored in the ground. The wind does not hold up the kite; rather, it generates power, and the lightweight support structure holds everything up.
Image 12 (below, right) shows how wind forces, transmitted from the turbine axis bearings through the icosahedral truss, has the same effect as a single force applied at the top of the truss, which is balanced by two force vectors, the vertical support vector and the cable tension vector. Because the shallow array has a low angle (31.8°) the support vector is relatively small and the cables take most of the force. Since cable tension is always linear, there is no bending force (torque) at the anchor points; thus the foundation is much more simple and much less impactful to the ground.
Starting with the pentagonal pyramid of turbine arrays (Image 8), we can find a way to support this pyramid higher above ground to take advantage of higher windspeeds (Image 1). One way to do this is to support each leg of the pyramid on a tripod (see Image 13). Using shallow arrays for the tripod legs is good, because two outer legs from adjacent tripods meet at a common (shared) foundation point, efficiently reducing the number of foundation points needed.
The third, inner leg of the tripod could be a shallow array, which would bring it back to the center and share the center foundation. Alternatively, it could be a vertical array; however, the support that is best needed is a steep angle provided by the steep array of turbine modules (see Image 14). The climb angle of this array is 58.2°, the complement of the shallow angle, 31.8°. The steep array is geometrically identical to the shallow array (just a rotation) but in terms of components it is different; two adjacent turbines share a strut instead of a horizontal beam component (see Image 15, below).
Icosahedral geometry provides a number of different kinds of arrays, which function as the building blocks of windfarm support structures. We have already seen the shallow, vertical and steep arrays. In cases where a turbine module is not feasible (e.g. too close to the ground) or where extra strength is needed, the turbine housing can be converted to a structure module (not shown), a tetrahedronal truss that is extremely strong.
This exploration of lightweight windfarm support structures is completely new and shows great promise. We still need to perform extensive computer modeling with engineering stress analyses, wind tunnel testing with aerodynamic analyses, materials and components design and testing, etc. With this approach, windfarms can be:
- upgradable, as new turbine designs or other components become available
- configurable to different locations and different terrain (hills, mountains, sea-shore, etc)
- completely removed from a location much easier than current windfarms
This windfarm design is one of many possible designs that can use the Towerdome system. Icosahedral trusses support 206 vertical-axis wind turbines above ground. Each turbine is approximately 8 ft. high and 13 ft. in diameter. Some industry sources claim that turbines of this size can generate 50 kw; if all 206 could operate at this level, the total would exceed 10 megawatts.
The intent of this design is to 1) get as many turbines as high up as possible, in an arrangement where they don't interfere with each other, 2) provide a stable structure that can withstand all forces on it, and 3) have the structure be sparse enough so that it is not oppressive to the eye or block out sunlight and also allow the wind to flow through it, taking advantage of a drafting effect. We would also like to 4) minimize the impact on the ground, in terms of foundation and anchoring requirements.
