Theory and measurements of kites or sails

No theory seems to exist regarding wind forces arising at standard kites.

We engaged to develope it for kites in general. It says that the produced power of the kite in the soaring phase is proportional to the surface and the power of 3 of the wind speed. The maximum power is extracted when it flies with one-third of the wind speed. For the overall performance the loss is to be deducted for the sinking and retrieval phase. This is further to be optimized, particularly the folding to a minimal resistance. We expect that one can reduce that power loss to less than 20%. But since it is not expensive to increase the kite’s surface easily to almost any size, that is not a crucial problem.

We measured the forces on the rope of two sled types by loading the base station into a car, driven with the desired speed , Table 1.

 

      Powersled of 1,81m² face Flowform with 3,6m²
wind velocity                   rope force with
blocked kite            		 soaring power     

               

rope force per m² kite face        

 power      
per m²          		 rope          force      soaring      power     rope        force per m² kite face        power
per m²           
Beaufort m/s km/h           N       W

    

    N

        

     W     N      W      N      W   
1,0 0,9 3,2 0,40 0,03 2,2         0,0 1,04 0,09 2,9         0,0
2,0 2,5 8,8 2,93 0,68 16,2         0,4 7,69 1,88 21,4         0,5
3,0 4,4 15,8 9,46 3,92 52,3         2,2 24,81 10,90 68,9         3,0
4,0 7,2 25,9 25,33 17,17 140,0         9,5 66,44 47,78 184,6       13,3
5,0 10,0 36,0 48,87 46,00 270,0       25,4 128,16 128,00 356,0       35,6
6,0 12,5 44,8 75,75 88,77 418,5       49,0 198,65 247,01 551,8       68,6
7,0 15,5 55,8 117,41 171,30 648,7       94,6 307,90 476,66 855,3     132,4

 

Table 1 Measured wind forces and calculated power on two types of free flying sleds

 

Other measurements were performed with Rokkaku kites and sleds in the open air with real wind

on a hill, because we did not have access to large enough wind tunnels.

For example, with the sled Flowform on a rope length of 100m, flying at about 60m high, at wind speed of 4-5 bft (measured at 2m height) we registered a power of 150W.

The indicated wind velocities are the mean values in the Beaufort's scale. A well feasible small  kite of 20m² would produce an output of at least 1 kW at 6 bft.

For the aerodynes, running on a rope to a lifter kite or balloon or on a mast up and down, the calculated power is outlined in table 2.

 

 

 

Table 2  Large kites or sails running on a rope or mast up and down, type ferries

                                                                                                                                                                                              

On several versions of concept 3 (mast with sail) many tests were accomplished and much knowledge accumulated.  

 

Summary, conclusions for wind generators

Each of the three concepts outlined  have pro and cons and are suited differently well for regions with little technical and economic potential and such with high-tech. With all, the essential difference to the wind wheels is that the effective flow area for the wind, which is the width of the aerodyne (kite, sail) times the movement stroke, can without great expenditure be realized much larger than the rotor area of a wind wheel. And this area is the decisive parameter for the power of a wind generator. Therefore it is to be expected for all the mentioned concepts that they will be substantially more economical than conventional windmills. In particular regarding the concept 3 it is obvious that a mast braced with ropes to the ground is clearly cheaper than a heavy tower, embodied tilt proven at the soil in a solid concrete patten. Just as a sail can be fixed more cheaply in a frame than rotor blades on just one side to the wheel shaft, exposed to strong bending air resistance and centrifugal forces. Further, because of automatic reaction to change of the wind direction and speed and why masts can easily  be built into higher wind-stronger air layers, the wind energy is substantially better exploited, birds not being chopped etc. With the highest-tech solution it would be advantageous to transform the kinetic energy into electricity by a linear generator in the mast, instead of using bobbins and ropes. See the patent applications mentioned above!
According to our results we do not recommend concept 3 for developing countries being too complex and going beyond a cost limit of a few hundred Euros, we would prefer the most simple concept 1, a freely flying kite watched over by men.

There where the technology and resources are available, concept 3 is an interesting alternative to the wind mills for small and larger installations.
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Ingenieurbüro Franetzki