# Height of the Hywind

Hi all,

I’m doing a project on the Hywind concerning the reduction of the tower top oscillation. Of course I need the height of the tower, but I found some different values.
For the total displacement of the tower top I’m using:

z_tot=TTDspFA+Hsin(PtfmPitchpi/180)

In the “Definition of 5 MW reference wind turbine of offshore system development” and “Definition of the floating system for phase IV of OC3” I found as tower top height H=87.6m.
I’ve computed also the height starting from the TTDspFA and TTDspPitch, following the equation:

H=TTDspaFA / { sin(TTDspPitch*pi/180) }

But with this computation I found a value of H=40.2657.
The questions are then:

• Is the first equation correct? As H I should consider also the elevation of the platform top above SWL? Around which point is defined the platform Pitch? The center of mass of the platform or the point where the mooring lines are connected to the platform?
• Why with the second equation I found such a different value? Is it because the TTDspPitch is defined around the CM of the tower?

Thank you,
Have a nice day you all!
Giuseppe

Dear Giuseppe,

The first equation is not correct (and thus the second is not either). FAST output TTDspFA is the relative tower-top displacement due to elastic deflection of the tower only; it does not reflect the rigid-body platform motion. The proper equation in 2D would involve TTDspFA, PtfmSurge, and PtfmPitch TowerHt; in 3D it would more complicated. FAST output PtfmPitch is defined relative to the platform reference point (not a center of mass), which for a floating wind turbine is at the intersection of the still water level and undeflected tower centerline.

Best regards,

Dear Jason,

thank you for your answer. I’m sorry I didn’t explain precisely my purposes. I’m just considering the platform pitch and the tower deflection in the model that I’m developing, considering the tower as rigid. Without considering the PtfmSurge I think that the equation should be correct. The first part is the deflection contribute, and the second part is the contribute of the platform rotation (where as H there is the distance of the tower top from the rotational point reference of the platform). If it’s not correct could you explain me where the problem is please? Or could you write the equation for the total displacement of the tower top?

Also, as TowerHt for the Hywind I have 87.6 m, but should I consider also the 10 meters of platform that are above the SWL? Or maybe for the Hywind the rotation point reference is at the connection between platform and tower?

Thank you in advance, and sorry for maybe the obvious questions,
Regards,
Giuseppe

Dear Giuseppe,

With only 2 DOFs (platform pitch and bending of the 1st tower mode), the equations would be:

TotalHorizontalDisplacementOfTheTowerTop = TTDspFACOS(PtfmPitchpi/180) + TowerHtSIN(PtfmPitchpi/180)

and

TowerHt = ( TotalHorizontalDisplacementOfTheTowerTop - TTDspFACOS(PtfmPitchpi/180) )/SIN(PtfmPitch*pi/180)

You missed the cosine term in the first equation (due to the rigid-body rotation of the tower) and dropped some terms in the second equation.

The TowerHt for the OC3-Hywind spar system of 87.6 m already includes the 10 m of the platform above the still water level.

I hope that helps.

Best regards,

Dear Jason,

now I’ve understood the problems. I totally forgot the cosine…
I will consider as tower height the 87.6 m.

Thank you a lot for your kind help,
Best wishes
Giuseppe