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I think it would be more efficient for a vertical wind turbine to have a covered funnel about half of it

Something like this figure

enter image description here

It would protected the turbine from opposite wind and also redirect another half wind to the correct side. It should increase overall efficiency

Are there any problem of this model so it not being used?

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I think you may be confusing vertical axis wind turbine based on lift mechanism as in an airplane wing, with the low efficiency models that are used to show the wind speed on rooftops as part of weather vane.

For example in a sail ship as opposed to intuition, the best wind is not the back wind which pushes the ship forward. it at best will push the ship with the speed of the wind minus frictions.

It is side wind at 90 degrees to the direction of the ship, because it gives lift to the sails, then the ship will go forward up to 8 times the speed of the wind.

These vertical axis wind turbines are designed to work based on the lift and they are designed not to create too much drag on the back swing. They are designed to turn in a way that they face the wind deploying in best angle of attack to gain lift and turn around and feather out to make the least drag, basically this aeronautic bias makes them embrace the wind regardless its direction.

Also any vertical shield would be an engineering headache to build and keep solid against 80-100 miles/hr winds.

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    $\begingroup$ While true, shields have been explored at some length. One advantage of them is that they can obviate the need for a prerotator motor to get the tip speed ratio up past 1. They can be designed to weather-vane and also provide speed control and overspeed protection. People don't seem to understand the loads on these things. A friend of mine had one come apart in a wind tunnel. Parts of it were pulling over 200g when it cut loose. Made one heck of a mess. $\endgroup$ – Phil Sweet Feb 19 '19 at 21:15
  • $\begingroup$ @PhilSweet, I didn't know that. I have been flying as a private pilot for43 yrs. as a private pilot. I know how unpredictable the weather can be. It can become turbulent when least expected. and it becomes scary. $\endgroup$ – kamran Feb 20 '19 at 1:05
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That "shield" would create a rotational force that needs to be countered - given vertical turbines use an aerofoil section the "counter" force produced by the aerofoil is probably much less.

Also consider that keeping all that mass of "funnel" pointing into the wind as well will need to be considered.

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    $\begingroup$ One advantage of VAWTs is that you need anything to track the direction of the wind and change the orientation of the turbine. If you lose that advantage, you might as well build a HAWT instead. $\endgroup$ – alephzero Feb 19 '19 at 18:25
  • $\begingroup$ @alephzero I was thinking that the shield is just additional part that track wind. The main turbine is not. That that reduce almost all the moving parts from the horizontal model while boosting the efficiency $\endgroup$ – Thaina Feb 20 '19 at 3:29
  • $\begingroup$ @solar-mike The shield funnel itself would be lightweight material, can be normal plastic or aluminium. And it would be loosely attach to the turbine axis. In the figure above the near section is the funnel shield that redirect the left side wind to the right part of turbine while the far section is the tail that track wind $\endgroup$ – Thaina Feb 20 '19 at 3:34

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