Report KD 684 about the cone angle epsilon, available

[Adriaan Kragten]

Report KD 684 can be copied for free from my website: www.kdwindturbines.nl at the menu KD-reports. The tittle of this report is: "Derivation of the formula for the cone angle epsilon for a constant chord blade which is connected to the hub by a hinge". The formula for the cone angle epsilon was already derived in report R 409 D from 1980 but as this report is in Dutch and no longer available, the derivation is now given in this public report KD 684. The formula is used to calculate the bending stress at the blade root of for instance the VIRYA-3B3 rotor as described in chapter 8 of report KD 484.

[SparWeb]

Cone angle - as in the furling mechanism of the Proven turbines?

[Adriaan Kragten]

Cone angle - as in the furling mechanism of the Proven turbines?

Not exactly. For my calculations of the cone angle, the hinge axis is perpendicular to the blade axis. So moving backwards of the blade doesn't change the blade angle. For the Proven turbines, the hinge axis makes an angle of about 45 degrees with the blade axis and moving backwards therefore results in change of the blade angle.

I don't use a real hinge in the rotor of the wind turbine. What is really used is an elastic connection in between a blade and the hub. The hinge is only introduced to find a formula for the cone angle if the elastic blade connection has no bending stiffness. 

[SparWeb]

...an elastic connection in between a blade and the hub

Got it.  Even the flexibility of the blade materials and hub components are a factor.

And on a wind-facing turbine (not the wind-following type such as the Proven in the photo above) the cone angle brings the tips closer to the tower.  A significant hazard to wind turbines when exposed to extreme winds.
Thank you Adriaan.

[Adriaan Kragten]

The formula which I have found gives the cone angle for stable conditions if the rotor is running at the design tip speed ratio. The angle is only some degrees for a massive wooden blade and for a rotor with a design tip speed ratio of about 6. However, the angle can become much larger during strong wind gusts. So the distance in between the blade tip and the tower should be made rather large for a rotor which has blades with an elastic connection in between the blade and the hub. For my VIRYA-4.2 rotor this was done by giving the rotor shaft a tilt angle of 5 degrees.

Certain big modern wind turbines have a cone angle frontwards in stead of backwards but they have no elastic blade connection at the blade root. This negative cone angle results in an extra bending moment at the blade root but the blade can have this because it is very strong at that point. These very big blades are rather elastic themselves and at strong wind gusts they bend backwards at the tip over a distance of some metres. Without this negative cone angle, they would touch the tower.