Lux Wind Power

The drawing above shows 2 separate turbines, one on top of the other.  The 3 outside frames are cubic shapes and are also stacked on top of each other.  The turbines are slightly smaller than the cubic frame to allow for movement in high winds.  Most straight bladed VAWT have Height/Diameter ratio close to one, so I picked the cube shape for simplicity.  Each cube has 4 vertical beams, 4 horizontal beams and 5 pairs of diagonal beams crossing in the middle of each side.  The diagonal beams are tensioned, which causes the other beams to be in compression, even under extreme wind loads.  Usually, I do not put a turbine in the bottom cube, but one can be added even if it is not the full height of the cube.  The diameter of the lower turbines could be a bit smaller than the top turbine to accommodate wind shear. 

The diagonal beams/cables on the top face of each cube contain a bearing housing and bearing at the intersection.  The bearings and housings are the only places where the outside frame experiences the thrust forces from the wind. 

The weight of all the masts, struts and blades is supported by the bearing at the bottom of the lowest mast.  Therefore, the only major forces acting on the cubed frame are the thrust forces from the wind on each turbine and gravity from the frame above it.  The ends of the horizontal and vertical beams can be considered as pinned, which prevents bending moments, torsion or shear on these beams.  All beams are in compression, so column buckling is the only mode of concern.

About Column Buckling

Column buckling happens when a beam under compression suddenly deforms laterally.  The critical buckling load (Pcr) is the maximum allowable force applied at each end of the beam before buckling occurs.  Euler’s formula is used to predict Pcr on simple beams but cannot predict Pcr on more complicated structures.     

Prestressed Stayed Columns (PSSC), or just Stayed Columns, are beams with cross arms at one or more positions and stays (pretensioned cables or beams) are attached close to the ends of the beam and at the end of each cross as shown in the diagrams below.  

There are many ways to change the maximum allowable force on stayed columns.  If we adjust any of the properties such as the cross section or lengths of the main beam, crosses or stays, the Pcr will change.  Making changes to the PSSC may increase Pcr but it may also increase the weight to the point where the change is not economically feasible.  Clearly, more work needs to be done to optimize the parameters for the stayed columns on the cubic frame we are proposing.   

To analyze the PSSC we use a numerical procedure called the Stiffness Probe Method developed by German Gurfinkel and Sudarshan Krishnan.[1]  I have built and tested stayed columns of various sizes and I found this method corresponds to the prediction of Pcr.  This method works well with almost any structure under compression. 

Gravity becomes a bigger concern when the beams are in a horizontal position.  However, the tension in the stays below the beam can be increased to overcome the gravity force and to keep the beams straight.  These stays typically need to have a larger cross section due to the increased tension.

The crosses and stays on the beams do not interfere with the blades and the parasitic drag from the wind is minimal.  The horizontal diagonals are positioned between the upper and lower turbine blades, which require a clearance to allow for movement within the cubed frame.  The frame is secured in position on the ground by 4 pillars/posts at each corner extending above the ground at a favourable height.

Benefits of this design

Stacking VAWT on top of each other is a simple and economical way to take advantage of the higher winds higher above the ground.  Please go to the ‘Analysis’ section of this website for further information.

This is an excellent way to support a floating wind turbine for offshore energy.  The four corners of the frame are a considerable distance apart, which helps to stabilize any structure floating on the ocean.  The frame could be continued at and below water level, providing a base for the mechanical components while lowering the center of gravity.   

Stacking 2 or more VAWT on top of each other increases the power output without increasing the diameter.  Therefore, the rotational speed remains the same as it is for one turbine, which will decrease the cost of a direct drive generator or the cost of a gearbox.  VAWT are generally slower turning machines than HAWT, so this is an improvement. 

The cubed frames and turbines can be installed in a horizontal position and pulled into place with a gin pole or crane.  A gin pole was used to raise the turbines in the video.

The beams and cross arms can be modular for easy transportation.  The connections between each component are simplified since the beams and cross arms are always in compression.

[1] Gurfinkel, German and Krishnan, Sudarshan. “Analysis and Design of Cable-stayed Steel Columns using the Stiffness-Probe Method,” Engineering Journal, 3rd Quarter, pp. 195-209, American Institute of Steel Construction (AISC), United States, July 2017.

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