Tower foreaft modes shapes
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 Posts: 55
 Joined: Tue Jul 28, 2009 1:36 am
 Location: Germany
Tower foreaft modes shapes
Hello everyone,
Tower foreaft and sideside modes shapes are needed in FAST Tower input file. I used ModesV2.22 to calculate the modes shapes. The frequencies of the five shapes are increasing. Are the first two foreaft modes and the second two sideside modes? In Blade calculation it was clearly expained.
If the tower has also point mass at different height position, like flange, how could we consider the point mass for Distributed Tower Properties Section in the Modes or BModes input file?
Thanks a lot!
Tower foreaft and sideside modes shapes are needed in FAST Tower input file. I used ModesV2.22 to calculate the modes shapes. The frequencies of the five shapes are increasing. Are the first two foreaft modes and the second two sideside modes? In Blade calculation it was clearly expained.
If the tower has also point mass at different height position, like flange, how could we consider the point mass for Distributed Tower Properties Section in the Modes or BModes input file?
Thanks a lot!
Last edited by Yinping.Yang on Tue Sep 22, 2009 7:14 am, edited 2 times in total.

 Posts: 6
 Joined: Wed Jul 22, 2009 2:11 pm
 Location: LUBBOCK, TX

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RE: Tower foreaft modes shapes
Dear Yinping Yang,
Kuangmin Gong is correct: The Modes code treats the tower foreaft and sidetoside modes the same way (becuase it only considers a point mass; it doesn't consider offsets or rotational inertia), so, it only outputs one set of mode shapes (the five shapes are the first five modes).
Neither the Modes or BModes codes allow for the placement of point masses along the flexible beam. You must simply use the mass distribution input to define the mass as best as possible.
Best regards,
Kuangmin Gong is correct: The Modes code treats the tower foreaft and sidetoside modes the same way (becuase it only considers a point mass; it doesn't consider offsets or rotational inertia), so, it only outputs one set of mode shapes (the five shapes are the first five modes).
Neither the Modes or BModes codes allow for the placement of point masses along the flexible beam. You must simply use the mass distribution input to define the mass as best as possible.
Best regards,
Jason Jonkman, Ph.D.
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

 Posts: 55
 Joined: Tue Jul 28, 2009 1:36 am
 Location: Germany
Re: Tower foreaft modes shapes
Hi,
As suggested, I converted the point mass to mass distribution, for example, at one of the stations of flange, the point mass is 3000kg, the length 10cm, mass distribution should be 30000kg/m. In the input file, I add these point mass distributions to the tower tube mass distributions, 30000kg/m+2800kg/m, like:
....
0.1 3000 1.000e10
0.2 2800 9.800e9
0.21 32800 9.800e9
0.3 2600 9.600e9
....
I ran Modes and compared the tower modes results with the GHBladed tower modes results. The frequencies are close. The only difference is the magnitude at tower's biggest deflection position. For example,
the biggest deflection of foreaft second mode
GHBladed: 7
Modes: 2
the biggest deflection of sideside second mode
GHBladed: 12
Modes: 2
I did not change the stiffness for the point mass positon. If I change to big values, the frequencies will be very high, it seems not correct. I use Bladed modes shapes for FAST model at the moment.
Thanks for suggestions and help in advance.
Yinping Yang
As suggested, I converted the point mass to mass distribution, for example, at one of the stations of flange, the point mass is 3000kg, the length 10cm, mass distribution should be 30000kg/m. In the input file, I add these point mass distributions to the tower tube mass distributions, 30000kg/m+2800kg/m, like:
....
0.1 3000 1.000e10
0.2 2800 9.800e9
0.21 32800 9.800e9
0.3 2600 9.600e9
....
I ran Modes and compared the tower modes results with the GHBladed tower modes results. The frequencies are close. The only difference is the magnitude at tower's biggest deflection position. For example,
the biggest deflection of foreaft second mode
GHBladed: 7
Modes: 2
the biggest deflection of sideside second mode
GHBladed: 12
Modes: 2
I did not change the stiffness for the point mass positon. If I change to big values, the frequencies will be very high, it seems not correct. I use Bladed modes shapes for FAST model at the moment.
Thanks for suggestions and help in advance.
Yinping Yang

 Posts: 5882
 Joined: Thu Nov 03, 2005 4:38 pm
 Location: Boulder, CO
 Contact:
Re: Tower foreaft modes shapes
Dear Yinping Yang,
I agree with how you incorporated the point masses into the mass distribution and I agree that you should not change the stiffness distribution.
From my experience, the frequencies that the Modes code calculates are far more accurate than the mode shapes that the Modes code calculates. This is one reason why we developed the BModes code as a replacement for Modes.
In your situation, I expect that the lack of towertop rotational inertia in the Modes code is what is causing the large difference in the mode shape predictions between Modes and Bladed. I suggest you recalculate your modes using BModes and compare again to Bladed. If the results agree better, than you can be more comfortable that the mode shapes you've input into FAST are correct.
Best regards,
I agree with how you incorporated the point masses into the mass distribution and I agree that you should not change the stiffness distribution.
From my experience, the frequencies that the Modes code calculates are far more accurate than the mode shapes that the Modes code calculates. This is one reason why we developed the BModes code as a replacement for Modes.
In your situation, I expect that the lack of towertop rotational inertia in the Modes code is what is causing the large difference in the mode shape predictions between Modes and Bladed. I suggest you recalculate your modes using BModes and compare again to Bladed. If the results agree better, than you can be more comfortable that the mode shapes you've input into FAST are correct.
Best regards,
Jason Jonkman, Ph.D.
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

 Posts: 55
 Joined: Tue Jul 28, 2009 1:36 am
 Location: Germany
Re: Tower foreaft modes shapes
Hi,
I have calculated all the tower section properties for BModes input file. I understand tipmass as: Tipmass=rotor mass(hub+3 blades)+nacelle mass
Several parameters are difficult to calculate in the main input file for BModes. cm_loc is overhang ? I looked at the example input file of Winpac 1.5MW. This cm_loc is just the overhang 3.3 m. Is cm_axial tipmass c.m. offset from the tower top measured along zt axis? This parameter can not be found in the user mannul. Is it specified only for the tower case?
I do not know how to calculate these mass of inertia: ixx_tip, iyy_tip, izz_tip, ixy_tip, izx_tip,iyz_tip The body shape is irregular for the whole tip mass.
Is tip mass simply assumed as a point mass? I=m*r^2 I checked the values used in the Bmodes certtest for Winpac 1.5MW. It seems not right. Or these values are just measured from experiment instead of calculated?
Thanks
Best regards
I have calculated all the tower section properties for BModes input file. I understand tipmass as: Tipmass=rotor mass(hub+3 blades)+nacelle mass
Several parameters are difficult to calculate in the main input file for BModes. cm_loc is overhang ? I looked at the example input file of Winpac 1.5MW. This cm_loc is just the overhang 3.3 m. Is cm_axial tipmass c.m. offset from the tower top measured along zt axis? This parameter can not be found in the user mannul. Is it specified only for the tower case?
I do not know how to calculate these mass of inertia: ixx_tip, iyy_tip, izz_tip, ixy_tip, izx_tip,iyz_tip The body shape is irregular for the whole tip mass.
Is tip mass simply assumed as a point mass? I=m*r^2 I checked the values used in the Bmodes certtest for Winpac 1.5MW. It seems not right. Or these values are just measured from experiment instead of calculated?
Thanks
Best regards

 Posts: 5882
 Joined: Thu Nov 03, 2005 4:38 pm
 Location: Boulder, CO
 Contact:
Re: Tower foreaft modes shapes
Dear Yinping Yang,
Your understanding of tip_mass in BModes is correct. cm_loc in BModes is the horizontal offset along the xtaxis from the tower centerline to the center of mass of tip_mass. cm_axial is the vertical offset along the ztaxis from the tower top/yaw bearing to the center of mass of tip_mass. cm_axial was added to the code after the last update to the BModes User's Guide, which is why it is not listed in the guide. (You'll notice that the current BModes User's Guide is only in draft form. Gunjit Bir has plans to add a few more features to BModes, and when he does this, he will update the guide accordingly.) The towertop mass moments of inertia, ixx_tip, iyy_tip, izz_tip, ixy_tip, izx_tip, and iyz_tip, are not trivial to calculate. Altough I can't find this explicitly stated in the draft BModes User's Guide, they are defined about the towertop center of mass (not the tower top / yaw bearing). So, if all the mass were lumped at a point, these inputs would be zero even if the offsets were nonzero. It is easiest to calculate the towertop mass moments of inertia using a 3D model within a CAD program or the like (we often use the "Aggregate Mass" tool in MSC.ADAMS for this). All of these tip mass inputs are available for both towers and blades. For blades, the inputs are related to the blade reference axes, not the tower axes.
I do not know how the towertop mass input data were derived for the sample tower model in the BModes CertTest (Test03_tower.bmi). If these data are for the WindPACT 1.5MW turbine model, I cannot reproduce the data from the mass specifications defined in the FAST model. I will ask Gunjit Bir about this.
Best regards,
Your understanding of tip_mass in BModes is correct. cm_loc in BModes is the horizontal offset along the xtaxis from the tower centerline to the center of mass of tip_mass. cm_axial is the vertical offset along the ztaxis from the tower top/yaw bearing to the center of mass of tip_mass. cm_axial was added to the code after the last update to the BModes User's Guide, which is why it is not listed in the guide. (You'll notice that the current BModes User's Guide is only in draft form. Gunjit Bir has plans to add a few more features to BModes, and when he does this, he will update the guide accordingly.) The towertop mass moments of inertia, ixx_tip, iyy_tip, izz_tip, ixy_tip, izx_tip, and iyz_tip, are not trivial to calculate. Altough I can't find this explicitly stated in the draft BModes User's Guide, they are defined about the towertop center of mass (not the tower top / yaw bearing). So, if all the mass were lumped at a point, these inputs would be zero even if the offsets were nonzero. It is easiest to calculate the towertop mass moments of inertia using a 3D model within a CAD program or the like (we often use the "Aggregate Mass" tool in MSC.ADAMS for this). All of these tip mass inputs are available for both towers and blades. For blades, the inputs are related to the blade reference axes, not the tower axes.
I do not know how the towertop mass input data were derived for the sample tower model in the BModes CertTest (Test03_tower.bmi). If these data are for the WindPACT 1.5MW turbine model, I cannot reproduce the data from the mass specifications defined in the FAST model. I will ask Gunjit Bir about this.
Best regards,
Jason Jonkman, Ph.D.
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

 Posts: 55
 Joined: Tue Jul 28, 2009 1:36 am
 Location: Germany
Re: Tower foreaft modes shapes
Hi,
If cm_loc and cm_axial are xT and zT coordinates of tipmass, how to calculate them? Also using the Aggregate mass Tool or using formular for different components of tipmass like:
xT=Sum(m1*x1+m2*x2+...)/(m1+m2+...) zT=Sum(m1*z1+m2*z2+...)/(m1+m2+...)
In the example of Winpact 1.5MW model, xT is just the overhang.
For the preparation of using Aggregate mass Tool, the adams datasets of FAST model should also be generated. That means the ADAMSPrep is chosen 2 or 3. I tested the Winpact 1.5MW model by Aggregate mass Tool. The parts should be all the components consisting of tower tipmass selected. How to choose the reference frame, the available frame has no tower top center of mass frame, could we define the frame ourselves?
Thanks for your kindly reply and help
Best regards
Yinping Yang
If cm_loc and cm_axial are xT and zT coordinates of tipmass, how to calculate them? Also using the Aggregate mass Tool or using formular for different components of tipmass like:
xT=Sum(m1*x1+m2*x2+...)/(m1+m2+...) zT=Sum(m1*z1+m2*z2+...)/(m1+m2+...)
In the example of Winpact 1.5MW model, xT is just the overhang.
For the preparation of using Aggregate mass Tool, the adams datasets of FAST model should also be generated. That means the ADAMSPrep is chosen 2 or 3. I tested the Winpact 1.5MW model by Aggregate mass Tool. The parts should be all the components consisting of tower tipmass selected. How to choose the reference frame, the available frame has no tower top center of mass frame, could we define the frame ourselves?
Thanks for your kindly reply and help
Best regards
Yinping Yang

 Posts: 5882
 Joined: Thu Nov 03, 2005 4:38 pm
 Location: Boulder, CO
 Contact:
Re: Tower foreaft modes shapes
Dear Yinping Yang,
The equations you stated for cm_loc and cm_axial are correct. As I said in my prior post, I do not believe that the towertop mass input data are specified correctly for the WindPACT 1.5MW turbine in Test03_tower.bmi of the BModes CertTest. I need to ask Gunjit Bir about this.
You are correct that setting ADAMSPrep equal to 2 or 3 will cause FAST to generate the ADAMS dataset. In order to find the cm_loc and cm_axial, you should select all of the towertop PARTs and choose NacelleCS_M as the reference marker. Since there is no marker at the towertop CM, you will have to use the Parrallel Axis Theorem to shift the inertias found about the NacelleCS_M marker to the inertias found about the towertop CM. I calculate:
 ADAMS Output 
Aggregate mass for objects:
.Test13_ADAMS.Nacalle_P
.Test13_ADAMS.TailBoom_P
[lines removed]
.Test13_ADAMS.TipBrake3_P
The aggregate mass relative to .Test13_ADAMS.Nacalle_P.NacelleCS_M is:
Mass : 7.8055827759E+004 kg
Center of Mass :
Location : 1.2221466805, 5.0666880962E008, 1.5637349496 (meter, meter, meter)
Orientation : 359.9999724196, 90.000347689, 355.2981476095 (deg)
Mass Inertia Tensor :
IXX : 3.5622774377E+006 kgmeter**2
IYY : 1.9539222007E+006 kgmeter**2
IZZ : 1.821096074E+006 kgmeter**2
IXY : 1.212354417E002 kgmeter**2
IZX : 1.1141296293E+004 kgmeter**2
IYZ : 0.2919524772 kgmeter**2

So, cm_loc = 1.222 meter, cm_axial = 1.564 meter, and tip_mass = 7.806E4 kg. Here are the inertias translated to the towertop CM:
ixx_tip = ( 3.5622774377E+006 kgmeter**2 )  ( 7.8055827759E+004 kg )*( 1.5637349496 meter )**2 = 3.371E6 kgmeter**2
iyy_tip = ( 1.9539222007E+006 kgmeter**2 )  ( 7.8055827759E+004 kg )*( ( 1.2221466805 meter )**2 + ( 1.5637349496 meter )**2 ) =1.646E6 kgmeter**2
izz_tip = ( 1.821096074E+006 kgmeter**2 )  ( 7.8055827759E+004 kg )*( 1.2221466805 meter )**2 = 1.705E6 kgmeter**2
ixy_tip = 0
izx_tip = ( 1.1141296293E+004 kgmeter**2 ) + ( 7.8055827759E+004 kg )*( 1.2221466805 meter )*( 1.5637349496 meter ) = 1.603E5 kgmeter**2
iyx_tip = 0
Best regards,
The equations you stated for cm_loc and cm_axial are correct. As I said in my prior post, I do not believe that the towertop mass input data are specified correctly for the WindPACT 1.5MW turbine in Test03_tower.bmi of the BModes CertTest. I need to ask Gunjit Bir about this.
You are correct that setting ADAMSPrep equal to 2 or 3 will cause FAST to generate the ADAMS dataset. In order to find the cm_loc and cm_axial, you should select all of the towertop PARTs and choose NacelleCS_M as the reference marker. Since there is no marker at the towertop CM, you will have to use the Parrallel Axis Theorem to shift the inertias found about the NacelleCS_M marker to the inertias found about the towertop CM. I calculate:
 ADAMS Output 
Aggregate mass for objects:
.Test13_ADAMS.Nacalle_P
.Test13_ADAMS.TailBoom_P
[lines removed]
.Test13_ADAMS.TipBrake3_P
The aggregate mass relative to .Test13_ADAMS.Nacalle_P.NacelleCS_M is:
Mass : 7.8055827759E+004 kg
Center of Mass :
Location : 1.2221466805, 5.0666880962E008, 1.5637349496 (meter, meter, meter)
Orientation : 359.9999724196, 90.000347689, 355.2981476095 (deg)
Mass Inertia Tensor :
IXX : 3.5622774377E+006 kgmeter**2
IYY : 1.9539222007E+006 kgmeter**2
IZZ : 1.821096074E+006 kgmeter**2
IXY : 1.212354417E002 kgmeter**2
IZX : 1.1141296293E+004 kgmeter**2
IYZ : 0.2919524772 kgmeter**2

So, cm_loc = 1.222 meter, cm_axial = 1.564 meter, and tip_mass = 7.806E4 kg. Here are the inertias translated to the towertop CM:
ixx_tip = ( 3.5622774377E+006 kgmeter**2 )  ( 7.8055827759E+004 kg )*( 1.5637349496 meter )**2 = 3.371E6 kgmeter**2
iyy_tip = ( 1.9539222007E+006 kgmeter**2 )  ( 7.8055827759E+004 kg )*( ( 1.2221466805 meter )**2 + ( 1.5637349496 meter )**2 ) =1.646E6 kgmeter**2
izz_tip = ( 1.821096074E+006 kgmeter**2 )  ( 7.8055827759E+004 kg )*( 1.2221466805 meter )**2 = 1.705E6 kgmeter**2
ixy_tip = 0
izx_tip = ( 1.1141296293E+004 kgmeter**2 ) + ( 7.8055827759E+004 kg )*( 1.2221466805 meter )*( 1.5637349496 meter ) = 1.603E5 kgmeter**2
iyx_tip = 0
Best regards,
Jason Jonkman, Ph.D.
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

 Posts: 5882
 Joined: Thu Nov 03, 2005 4:38 pm
 Location: Boulder, CO
 Contact:
Re: Tower foreaft modes shapes
Dear Yinping Yang,
I asked Gunjit Bir about the towertop properties from Test03_tower.bmi. He told me that the inputs were not chosen to match the true towertop properties of the WindPACT 1.5MW turbine; instead, they were chosen simply as an example. If you want to model the WindPACT 1.5MW turbine properly, you should use the values I stated in my previous post.
Best regards,
I asked Gunjit Bir about the towertop properties from Test03_tower.bmi. He told me that the inputs were not chosen to match the true towertop properties of the WindPACT 1.5MW turbine; instead, they were chosen simply as an example. If you want to model the WindPACT 1.5MW turbine properly, you should use the values I stated in my previous post.
Best regards,
Jason Jonkman, Ph.D.
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

 Posts: 55
 Joined: Tue Jul 28, 2009 1:36 am
 Location: Germany
Re: Tower foreaft modes shapes
Thanks for your information.
Last edited by Yinping.Yang on Wed Jan 20, 2010 8:50 am, edited 2 times in total.

 Posts: 55
 Joined: Tue Jul 28, 2009 1:36 am
 Location: Germany
Re: Tower foreaft modes shapes
Hi,
I want to use BModes to calculate the mode shapes of the tower of my model. The parameters like cm_axial, cm_loc, Ixx, Iyy, Izz, Izx are needed in the input file of BModes. In order to apply the Aggregate mass Tool of MSC.ADAMS, I need to have the ADAMS datasets of my model. The problem is that I do not have the data for GJStiff, EAStiff, Flap Inertia, Edge Inertia, and the Edgcgof. I made some values for these properties of blade and generate the ADAMS datasets. Then I use the method you taught above to get the cm_axial, cm_loc, Ixx, Iyy, Izz, Izx. I do not know if they are correct. I understand they have only relations with mass density. The properties GJStiff, EAStiff, FlpIner, EdgIner, Edgcgof will not affect them. The frequency of first mode agrees well with that of GH Bladed. The frequency of second mode is smaller than that of GH Bladed.
I am not sure if I have done this totally false.
Thanks a lot
Best regards
Yinping Yang
I want to use BModes to calculate the mode shapes of the tower of my model. The parameters like cm_axial, cm_loc, Ixx, Iyy, Izz, Izx are needed in the input file of BModes. In order to apply the Aggregate mass Tool of MSC.ADAMS, I need to have the ADAMS datasets of my model. The problem is that I do not have the data for GJStiff, EAStiff, Flap Inertia, Edge Inertia, and the Edgcgof. I made some values for these properties of blade and generate the ADAMS datasets. Then I use the method you taught above to get the cm_axial, cm_loc, Ixx, Iyy, Izz, Izx. I do not know if they are correct. I understand they have only relations with mass density. The properties GJStiff, EAStiff, FlpIner, EdgIner, Edgcgof will not affect them. The frequency of first mode agrees well with that of GH Bladed. The frequency of second mode is smaller than that of GH Bladed.
I am not sure if I have done this totally false.
Thanks a lot
Best regards
Yinping Yang

 Posts: 5882
 Joined: Thu Nov 03, 2005 4:38 pm
 Location: Boulder, CO
 Contact:
Re: Tower foreaft modes shapes
Dear Yinping Yang,
The blade stiffnesses, such as GJStiff and EAStiff, have no influence on the result of the aggregate mass of the rotornacelle assembly. While the total mass of the rotornacelle assembly is not affected by the blade inertias and mass offsets, the center of mass and inertias of the rotornacelle assembly are, of course, affected by the blade inertias and mass offsets. If you do not want the influence of the blade inertias and mass offsets in the solution, set their values to zero in FAST's blade input file before creating your ADAMS dataset.
When you compared the frequencies to Bladed, did both models have a rigid rotor or a flexible rotor (i.e., were the models consistent in this regard)? The blade flexibility, for example, can have a big impact on the frequencies of the 2nd bending modes of the tower.
Best regards,
The blade stiffnesses, such as GJStiff and EAStiff, have no influence on the result of the aggregate mass of the rotornacelle assembly. While the total mass of the rotornacelle assembly is not affected by the blade inertias and mass offsets, the center of mass and inertias of the rotornacelle assembly are, of course, affected by the blade inertias and mass offsets. If you do not want the influence of the blade inertias and mass offsets in the solution, set their values to zero in FAST's blade input file before creating your ADAMS dataset.
When you compared the frequencies to Bladed, did both models have a rigid rotor or a flexible rotor (i.e., were the models consistent in this regard)? The blade flexibility, for example, can have a big impact on the frequencies of the 2nd bending modes of the tower.
Best regards,
Jason Jonkman, Ph.D.
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov
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