The wind field creation symbol in the QBlade main tool bar.
The Wind Field Generator in QBlade is essential for defining the atmospheric conditions affecting the turbine during simulations. This section provides an overview of how to generate different types of wind fields, including turbulent, uniform, and hub-height wind fields, each crucial for various simulation scenarios. Below, we describe the options available for each type of wind field and guide you through the settings and parameters necessary to tailor the wind conditions to your specific simulation needs.
A turbulent wind field generated in QBlade.
This section describes the process of generating a three-dimensional, fully turbulent wind field. Turbulent wind fields are essential for simulating real-world atmospheric conditions and assessing turbine performance under variable wind speeds and directions.
This can be either generated through the Wind Input Type button of the turbine simulation dialogue, as shown in :numref:`fig-wind-pane` or by directly generating this within the turbulent wind module, shown in :numref:`fig-wind-module`.
Three different options, to generate a three dimensional, fully turbulent wind field exist in QBlade.
- TurbSim: Generates the wind field using NREL's TurbSim binary (see B. J. Jonkman :footcite:`TurbSimGuide`).
- Mann: Generates the wind field using DTU`s Mann generator (see J. Mann :footcite:`mann1998`).
- Veers: Generates the wind field after the Veers algorithm (see P. S. Veers :footcite:`veers1988`).
When a new TurbSim wind field is created, a range of parameters must be specified as shown by the wind field generator dialogue in :numref:`fig-turb-dia`. After these have been selected, clicking on the Create button automatically passes the information to the TurbSim program :footcite:`TurbSimGuide`. The TurnSim binary is automatically called by QBlade, and after creation the wind field is automatically imported, so that no additional user input is required. The input parameters are described in detail in the following section.
Turb sim wind field dialogue in QBlade.
Main Parameters
These parameters dictate the spatial dimensions of the generated turbulent wind grid. A turbulent box is be generated which is then translated through the field of interest at the average velocity (defined below) as is consistent with Taylor's hypothesis for a turbulent flow :footcite:`BatchelorBook`.
- Name: The name of the wind field object.
- Ref. Wind Speed: The reference wind speed of this wind field.
- Seed: The random seed used to generate the wind field.
- Time: Determines the length of the generated turbulent box.
- Timestep: Specifies the discretisation in free stream (x) direction.
- Grid Width: Specifies box size in lateral (y) direction.
- Grid Height: Specifies box size in vertical (z) direction.
- Grid Y Points: Specifies spatial discretisation in y direction.
- Grid Z Points: Specifies spatial discretisation in z direction.
- Center (Hub) Height: Specifies the vertical position of the box center.
Turbine Class
These determine the turbine class as defined in the IEC 61400 design standard :footcite:`IEC61400-1`.
- Turbine Class: Specifies the design turbine class.
- Turbulence Class: Specifies the design turbulence class.
- I_ref: Specifies the turbulence intensity.
- V_ref: Specifies the reference velocity.
- b: The b parameter, used to calculate the turbulence standard deviation in IEC 61400.
Wind Parameters
These parameters specify the parameters and model inputs required for generation of the turbulent velocity field.
- IEC Standard: Specifies the version of the IEC standard, used to generate the wind field.
- Wind Type: Specifies the wind field type of the generated wind field.
- Spectral Model: Specifies the form of the spectral tensor applied to generate the stochastic velocity fluctuations.
- Wind Profile Type: Specifies the model used to represent the atmospheric shear layer.
- Reference Height: Specifies the reference height of the aforementioned shear layer model.
- Shear Exponent: Specifies the shear exponent of the aforementioned shear layer model (if exponential model chosen).
- Roughness Length: Specifies the reference height of the aforementioned shear layer model (if logarithmic model chosen).
- Jet Height: Specifies the jet height of the aforementioned shear layer model (if jet model chosen).
- ETMC value: Specifies the extreme turbulence model c value (if ETM model chosen).
- Remove TurbSim Files: If checked, the TurbSim files generated and subsequently read by QBlade, are automatically deleted.
- Close Console: If checked, the console which is called to generate the TurbSim file is automatically closed upon completion of TurbSim file generation.
When a new Mann wind field is created, a range of parameters must be specified as shown by the wind field generator dialogue in :numref:`fig-mann-dia`. After these have been selected, clicking on the Create button automatically passes the information to DTU's Mann 64bit Turbulence Generator. The Mann binary is automatically called by QBlade, and after creation the wind field is automatically imported, so that no additional user input is required. Please note that the Mann 64bit generator currently is only available for Windows operating systems. The input parameters are described in detail in the following section.
Mann wind field dialogue in QBlade.
Main Parameters
These parameters dictate the spatial dimensions of the generated turbulent wind grid. A turbulent box is be generated which is then translated through the field of interest at the average velocity (defined below) as is consistent with Taylor's hypothesis for a turbulent flow :footcite:`BatchelorBook`.
- Name: The name of the wind field object.
- Ref. Wind Speed: The reference wind speed of this wind field.
- Seed: The random seed used to generate the wind field.
- Time: Determines the length of the generated turbulent box.
- Timestep: Specifies the discretisation in free stream (x) direction.
- Grid Width: Specifies box size in lateral (y) direction.
- Grid Height: Specifies box size in vertical (z) direction.
- Grid Y Points: Specifies spatial discretisation in y direction (must be power of 2).
- Grid Z Points: Specifies spatial discretisation in z direction (must be power of 2).
- Center (Hub) Height: Specifies the vertical position of the box center.
Turbine Class
These determine the turbine class as defined in the IEC 61400 design standard :footcite:`IEC61400-1`.
- Turbine Class: Specifies the design turbine class.
- Turbulence Class: Specifies the design turbulence class.
- I_ref: Specifies the turbulence intensity.
- V_ref: Specifies the reference velocity.
- b: The b parameter, used to calculate the turbulence standard deviation in IEC 61400.
Wind Parameters
These parameters specify the parameters and model inputs required for generation of the turbulent velocity field.
- IEC Standard: Specifies the version of the IEC standard, used to generate the wind field.
- Wind Type: Specifies the wind field type of the generated wind field.
- Spectral Model: Specifies the form of the spectral tensor applied to generate the stochastic velocity fluctuations.
- Wind Profile Type: Specifies the model used to represent the atmospheric shear layer.
- Reference Height: Specifies the reference height of the aforementioned shear layer model.
- Shear Exponent: Specifies the shear exponent of the aforementioned shear layer model (if exponential model chosen).
- Roughness Length: Specifies the reference height of the aforementioned shear layer model (if logarithmic model chosen).
- ETMC value: Specifies the extreme turbulence model c value (if ETM model chosen).
Mann Box Parameters
- Alpha Epsilon: The Mann model \alpha\epsilon^{\frac{2}{3}} parameter.
- L Mann: The Mann length scale parameter.
- Gamma: The non-dimensional shear distortion parameter.
- High Freq. Compensation: If checked: applies the high frequency compensation, so that point velocities represent local anemometer measurements.
- Scale to Turbulence: If checked: scales the Mann box turbulence to the defined IEC turbulence, multiplied by the parameters described below
- X-Scale Factor: Scales the longitudinal turbulence along the x-axis to the IEC turbulence, mutiplied by this value.
- Y-Scale Factor: Scales the transversal turbulence along the y-axis to the IEC turbulence, mutiplied by this value.
- Z-Scale Factor: Scales the transversal turbulence along the z-axis to the IEC turbulence, mutiplied by this value.
When a new Veers wind field is created, a range of parameters must be specified as shown by the wind field generator dialogue in :numref:`fig-veers-dia`. After these have been selected, clicking on the Create button automatically generates a wind field using the Veers method build into QBlade (see P. Veers :footcite:`veers1988`). The input parameters are described in detail in the following section.
Veers wind field dialogue in QBlade.
Main Parameters
These parameters dictate the spatial dimensions of the generated turbulent wind grid. A turbulent box is be generated which is then translated through the field of interest at the average velocity (defined below) as is consistent with Taylor's hypothesis for a turbulent flow :footcite:`BatchelorBook`.
- Name: The name of the wind field object.
- Ref. Wind Speed: The reference wind speed of this wind field.
- Seed: The random seed used to generate the wind field.
- Time: Determines the length of the generated turbulent box.
- Timestep: Specifies the discretisation in free stream (x) direction.
- Grid Height & Width: Specifies box size in horizontal (y) and vertical (z) direction.
- Grid Y & Z Points: Specifies spatial discretisation in y and z direction
- Center (Hub) Height: Specifies the vertical position of the box center.
Wind Parameters
These parameters specify the parameters and model inputs required for generation of the turbulent velocity field.
- Turbulence Intensity: The target turbulence intensity.
- Wind Profile Type: Specifies the model used to represent the atmospheric shear layer.
- Reference Height: Specifies the reference height of the aforementioned shear layer model.
- Shear Exponent: Specifies the shear exponent of the aforementioned shear layer model (if exponential model chosen).
- Roughness Length: Specifies the reference height of the aforementioned shear layer model (if logarithmic model chosen).
Import options in the wind field menu.
It is also possible to import externally generated three dimensional wind fields into QBlade, see :numref:`fig-import-wind`. Wind fields can be imported in three ways:
A wind field file in binary format (.bts) (see TurbSim Users Guide :footcite:`TurbSimGuide`) can be imported by simply reading the .bts file.
A Mann box can be imported through the Mann (.man) file format, shown below.
If the parameter IMPORTBOX is set to false, QBlade will automatically generate a Mann wind box with the parameters specified in the .man file.
If the parameter IMPORTBOX is set to true, QBlade will search for the (possibly externally generated) files:
- PREFIX _u.bin
- PREFIX _v.bin
- PREFIX _z.bin
An import the velocity components from these binary files directly.
----------------------------------------QBlade Mann Box Definition File--------------------------------------------
Generated with : QBlade EE v2.0.7.4_beta windows
Archive Format: 310024
Time : 13:53:10
Date : 14.07.2024
----------------------------------------Parameters-----------------------------------------------------------------
Windfield PREFIX - prefix of the .bin and other files generated
false IMPORTBOX - false: generate new box from parameters; true: try to find and read .bin files with prefix
120.000 HEIGHTBOX - height of the mann box center in [m]
630.000 XDIM_BOX - length of the mann box in [m]
240.000 YDIM_BOX - width of the mann box in [m]
240.000 ZDIM_BOX - height of the mann box in [m]
631 NX_BOX - number of points along length, must be power of 2 [-]
32 NY_BOX - number of points along width, must be power of 2 [-]
32 NZ_BOX - number of points along width, must be power of 2 [-]
120.000 REFHEIGHT - reference height for the BL profile in [m]
0 PROFILETYPE - BL profile type: 0- power law; 1 - logarithmic
0.200 PROFILEPARAM - power law exponent or roughness length
0.0660 ALPHA_EPSILON - Mann alpha-epsilon parameter
29.4000 L_MANN - Mann length scale [m]
3.9000 GAMMA - Mann gamma parameter
12345 SEED - turbulent seed
10.000 WINDSPEED - hub-height average wind speed
1 IEC_STANDARD - IEC standard 61400- (1, 2 or 3)
NTM IEC_WINDTYPE - IEC wind type (NTM, ETM, EWM1, EWM50 or ADDTURB
16.000 IEC_IREF - IEC I_ref value [-]
10.000 IEC_VAVE - IEC V_ave value [m/s]
50.000 IEC_VREF - IEC V_ref value [m/s]
5.600 IEC_B - IEC b value (or a in 61400-2) [m/s]
2.000 IEC_ETMC - IEC ETM c value [m/s]
true TURB_SCALING - enable turbulent scaling: 0 - OFF; 1 - ON
true HF_CORRECTION - enable high frequency correction: 0 - OFF; 1 - ON
1.000 X_FACTOR - scaling factor for x-variance
0.800 Y_FACTOR - scaling factor for y-variance
0.500 Z_FACTOR - scaling factor for z-varianceA TurbSim input file may be directly opened in QBlade. The input file (.inp) will then automatically be communicated to the TurbSim binary and the corresponding wind field is imported.
!TurbSim Input File. Valid for TurbSim from OpenFAST v2.4.0. Generated with QBlade QBlade IH v2.0.7-release_candidate_beta windows on 15.05.2024 at 17:22:58
---------Runtime Options-----------------------------------
False Echo - Echo input data to <RootName>.ech (flag)
12345 RandSeed1 - First random seed (-2147483648 to 2147483647)
RANLUX RandSeed2 - Second random seed (-2147483648 to 2147483647) for intrinsic pRNG, or an alternative pRNG: "RanLux" or "RNSNLW"
False WrBHHTP - Output hub-height turbulence parameters in binary form? (Generates RootName.bin)
False WrFHHTP - Output hub-height turbulence parameters in formatted form? (Generates RootName.dat)
False WrADHH - Output hub-height time-series data in AeroDyn form? (Generates RootName.hh)
True WrADFF - Output full-field time-series data in TurbSim/AeroDyn form? (Generates Rootname.bts)
False WrBLFF - Output full-field time-series data in BLADED/AeroDyn form? (Generates RootName.wnd)
False WrADTWR - Output tower time-series data? (Generates RootName.twr)
False WrFMTFF - Output full-field time-series data in formatted (readable) form? (Generates RootName.u, RootName.v, RootName.w)
False WrACT - Output coherent turbulence time steps in AeroDyn form? (Generates RootName.cts)
True Clockwise - Clockwise rotation looking downwind? (used only for full-field binary files - not necessary for AeroDyn)
0 ScaleIEC - Scale IEC turbulence models to exact target standard deviation? [0=no additional scaling; 1=use hub scale uniformly; 2=use individual scales]
--------Turbine/Model Specifications-----------------------
24 NumGrid_Z - Vertical grid-point matrix dimension
24 NumGrid_Y - Horizontal grid-point matrix dimension
0.1000 TimeStep - Time step [seconds]
63.0000 AnalysisTime - Length of analysis time series [seconds] (program will add time if necessary: AnalysisTime = MAX(AnalysisTime, usableTimeLabel+GridWidth/MeanHHWS) )
63.0000 usableTimeLabel - Usable length of output time series [seconds] (program will add GridWidth/MeanHHWS seconds)
120.0001 HubHt - Hub height [m] (should be > 0.5*GridHeight)
240.00 GridHeight - Grid height [m]
240.00 GridWidth - Grid width [m] (should be >= 2*(RotorRadius+ShaftLength))
0.0 VFlowAng - Vertical mean flow (uptilt) angle [degrees]
0.0 HFlowAng - Horizontal mean flow (skew) angle [degrees]
--------Meteorological Boundary Conditions-------------------
"IECKAI" TurbModel - Turbulence model ("IECKAI"=Kaimal, "IECVKM"=von Karman, "GP_LLJ", "NWTCUP", "SMOOTH", "WF_UPW", "WF_07D", "WF_14D", "TIDAL", or "NONE")
"unused" UserFile - Name secondary input file for user-defined spectra or time series inputs
"1-ED3" IECstandard - Number of IEC 61400-x standard (x=1,2, or 3 with optional 61400-1 edition number (i.e. "1-Ed2") )
"A" IECturbc - IEC turbulence characteristic ("A", "B", "C" or the turbulence intensity in percent) ("KHTEST" option with NWTCUP model, not used for other models)
"NTM" IEC_WindType - IEC turbulence type ("NTM"=normal, "xETM"=extreme turbulence, "xEWM1"=extreme 1-year wind, "xEWM50"=extreme 50-year wind, where x=wind turbine class 1, 2, or 3)
2.00 ETMc - IEC Extreme Turbulence Model "c" parameter [m/s]
default ProfileType - Wind profile type ("JET";"LOG"=logarithmic;"PL"=power law;"H2L"=Log law for TIDAL spectral model;"IEC"=PL on rotor disk, LOG elsewhere; or "default")
"unused" ProfileFile - Name of the file that contains user-defined input profiles
120.00 RefHt - Height of the reference wind speed [m]
10.00 URef - Mean (total) wind speed at the reference height [m/s] (or "default" for JET wind profile)
default ZJetMax - Jet height [m] (used only for JET wind profile, valid 70-490 m)
default PLExp - Power law exponent [-] (or "default")
default Z0 - Surface roughness length [m] (or "default")
--------Non-IEC Meteorological Boundary Conditions------------
default Latitude - Site latitude [degrees] (or "default")
0.05 RICH_NO - Gradient Richardson number
default UStar - Friction or shear velocity [m/s] (or "default")
default ZI - Mixing layer depth [m] (or "default")
default PC_UW - Hub mean u'w' Reynolds stress (or "default")
default PC_UV - Hub mean u'v' Reynolds stress (or "default")
default PC_VW - Hub mean v'w' Reynolds stress (or "default")
--------Spatial Coherence Parameters----------------------------
default SCMod1 - u-component coherence model ("GENERAL","IEC","API","NONE", or "default")
default SCMod2 - v-component coherence model ("GENERAL","IEC","API","NONE", or "default")
default SCMod3 - w-component coherence model ("GENERAL","IEC","API","NONE", or "default")
default InCDec1 - u-component coherence parameters [-, m^-1] ("a b" in quotes or "default")
default InCDec2 - v-component coherence parameters [-, m^-1] ("a b" in quotes or "default")
default InCDec3 - w-component coherence parameters [-, m^-1] ("a b" in quotes or "default")
default CohExp - Coherence exponent for general model [-] (or "default")
--------Coherent Turbulence Scaling Parameters-------------------
"path/to/coh_events/eventdata" CTEventPath - Name of the path where event data files are located
"Random" CTEventFile - Type of event files ("LES", "DNS", or "RANDOM")
true Randomize - Randomize the disturbance scale and locations? (true/false)
1.0 DistScl - Disturbance scale (ratio of wave height to rotor disk). (Ignored when Randomize = true.)
0.5 CTLy - Fractional location of tower centerline from right (looking downwind) to left side of the dataset. (Ignored when Randomize = true.)
0.5 CTLz - Fractional location of hub height from the bottom of the dataset. (Ignored when Randomize = true.)
30.0 CTStartTime - Minimum start time for coherent structures in RootName.cts [seconds]
==================================================
NOTE: Do not add or remove any lines in this file!
==================================================A uniform wind field is specified directly within the Wind Input Type of the turbine simulation dialogue, shown in :numref:`fig-wind-pane` (see :doc:`../simulation/simulation`). The necessary input parameters including velocity, horizontal inflow angle and directional shear are defined here. In the case that the atmospheric boundary layer is to be modelled, this can be selected with the wind shear type radio button. The corresponding shear parameters can then by specified (see :doc:`../../theory/environment/wind/wind`).
Specification of a uniform wind field within the turbine simulation dialogue.
The user has more modelling freedom when a hub-height wind file is used. This type of file can either be created manually or by using the IEC wind tool :footcite:`IECwindtool`. This allows the specification of the velocity field at the hub height as a function of time. QBlade interpolates the time between the starting time of the file and the point where the predefined wind velocity profile (EOG in this case) should start. If the user specified simulation time exceeds the ending time in the hub-height file, QBlade will create a constant wind field with the parameters from the last entry of the hub-height file until the end of the simulation. An exemplary hubheight input file that described an extreme operating gust (EOG) at 20m/s is shown below:
Time Wind Horiz. Vert. LinH. Vert. LinV. Gust
Speed Dir Speed Shear Shear Shear Speed
0.000 20.000 0.000 0.000 0.000 0.200 0.000 0.000
60.000 20.000 0.000 0.000 0.000 0.200 0.000 0.000
60.100 20.000 0.000 0.000 0.000 0.200 0.000 -0.000
60.200 20.000 0.000 0.000 0.000 0.200 0.000 -0.004
60.300 20.000 0.000 0.000 0.000 0.200 0.000 -0.012
60.400 20.000 0.000 0.000 0.000 0.200 0.000 -0.028
60.500 20.000 0.000 0.000 0.000 0.200 0.000 -0.054
60.600 20.000 0.000 0.000 0.000 0.200 0.000 -0.092
60.700 20.000 0.000 0.000 0.000 0.200 0.000 -0.144
60.800 20.000 0.000 0.000 0.000 0.200 0.000 -0.209
60.900 20.000 0.000 0.000 0.000 0.200 0.000 -0.289
61.000 20.000 0.000 0.000 0.000 0.200 0.000 -0.384
61.100 20.000 0.000 0.000 0.000 0.200 0.000 -0.493
61.200 20.000 0.000 0.000 0.000 0.200 0.000 -0.614
61.300 20.000 0.000 0.000 0.000 0.200 0.000 -0.747
61.400 20.000 0.000 0.000 0.000 0.200 0.000 -0.889
61.500 20.000 0.000 0.000 0.000 0.200 0.000 -1.037
61.600 20.000 0.000 0.000 0.000 0.200 0.000 -1.188
61.700 20.000 0.000 0.000 0.000 0.200 0.000 -1.338
61.800 20.000 0.000 0.000 0.000 0.200 0.000 -1.485
61.900 20.000 0.000 0.000 0.000 0.200 0.000 -1.622
62.000 20.000 0.000 0.000 0.000 0.200 0.000 -1.748
62.100 20.000 0.000 0.000 0.000 0.200 0.000 -1.856
62.200 20.000 0.000 0.000 0.000 0.200 0.000 -1.944
62.300 20.000 0.000 0.000 0.000 0.200 0.000 -2.007
62.400 20.000 0.000 0.000 0.000 0.200 0.000 -2.041
62.500 20.000 0.000 0.000 0.000 0.200 0.000 -2.043
62.600 20.000 0.000 0.000 0.000 0.200 0.000 -2.011
62.700 20.000 0.000 0.000 0.000 0.200 0.000 -1.942
62.800 20.000 0.000 0.000 0.000 0.200 0.000 -1.834
62.900 20.000 0.000 0.000 0.000 0.200 0.000 -1.686
63.000 20.000 0.000 0.000 0.000 0.200 0.000 -1.498
63.100 20.000 0.000 0.000 0.000 0.200 0.000 -1.271
63.200 20.000 0.000 0.000 0.000 0.200 0.000 -1.005
63.300 20.000 0.000 0.000 0.000 0.200 0.000 -0.703
63.400 20.000 0.000 0.000 0.000 0.200 0.000 -0.366
63.500 20.000 0.000 0.000 0.000 0.200 0.000 0.000
63.600 20.000 0.000 0.000 0.000 0.200 0.000 0.393
63.700 20.000 0.000 0.000 0.000 0.200 0.000 0.807
63.800 20.000 0.000 0.000 0.000 0.200 0.000 1.237
63.900 20.000 0.000 0.000 0.000 0.200 0.000 1.678
64.000 20.000 0.000 0.000 0.000 0.200 0.000 2.124
64.100 20.000 0.000 0.000 0.000 0.200 0.000 2.568
64.200 20.000 0.000 0.000 0.000 0.200 0.000 3.003
64.300 20.000 0.000 0.000 0.000 0.200 0.000 3.425
64.400 20.000 0.000 0.000 0.000 0.200 0.000 3.825
64.500 20.000 0.000 0.000 0.000 0.200 0.000 4.198
64.600 20.000 0.000 0.000 0.000 0.200 0.000 4.539
64.700 20.000 0.000 0.000 0.000 0.200 0.000 4.841
64.800 20.000 0.000 0.000 0.000 0.200 0.000 5.101
64.900 20.000 0.000 0.000 0.000 0.200 0.000 5.314
65.000 20.000 0.000 0.000 0.000 0.200 0.000 5.477
65.100 20.000 0.000 0.000 0.000 0.200 0.000 5.587
65.200 20.000 0.000 0.000 0.000 0.200 0.000 5.642
65.300 20.000 0.000 0.000 0.000 0.200 0.000 5.642
65.400 20.000 0.000 0.000 0.000 0.200 0.000 5.587
65.500 20.000 0.000 0.000 0.000 0.200 0.000 5.477
65.600 20.000 0.000 0.000 0.000 0.200 0.000 5.314
65.700 20.000 0.000 0.000 0.000 0.200 0.000 5.101
65.800 20.000 0.000 0.000 0.000 0.200 0.000 4.841
65.900 20.000 0.000 0.000 0.000 0.200 0.000 4.539
66.000 20.000 0.000 0.000 0.000 0.200 0.000 4.198
66.100 20.000 0.000 0.000 0.000 0.200 0.000 3.825
66.200 20.000 0.000 0.000 0.000 0.200 0.000 3.425
66.300 20.000 0.000 0.000 0.000 0.200 0.000 3.003
66.400 20.000 0.000 0.000 0.000 0.200 0.000 2.568
66.500 20.000 0.000 0.000 0.000 0.200 0.000 2.124
66.600 20.000 0.000 0.000 0.000 0.200 0.000 1.678
66.700 20.000 0.000 0.000 0.000 0.200 0.000 1.237
66.800 20.000 0.000 0.000 0.000 0.200 0.000 0.807
66.900 20.000 0.000 0.000 0.000 0.200 0.000 0.393
67.000 20.000 0.000 0.000 0.000 0.200 0.000 0.000
67.100 20.000 0.000 0.000 0.000 0.200 0.000 -0.366
67.200 20.000 0.000 0.000 0.000 0.200 0.000 -0.703
67.300 20.000 0.000 0.000 0.000 0.200 0.000 -1.005
67.400 20.000 0.000 0.000 0.000 0.200 0.000 -1.271
67.500 20.000 0.000 0.000 0.000 0.200 0.000 -1.498
67.600 20.000 0.000 0.000 0.000 0.200 0.000 -1.686
67.700 20.000 0.000 0.000 0.000 0.200 0.000 -1.834
67.800 20.000 0.000 0.000 0.000 0.200 0.000 -1.942
67.900 20.000 0.000 0.000 0.000 0.200 0.000 -2.011
68.000 20.000 0.000 0.000 0.000 0.200 0.000 -2.043
68.100 20.000 0.000 0.000 0.000 0.200 0.000 -2.041
68.200 20.000 0.000 0.000 0.000 0.200 0.000 -2.007
68.300 20.000 0.000 0.000 0.000 0.200 0.000 -1.944
68.400 20.000 0.000 0.000 0.000 0.200 0.000 -1.856
68.500 20.000 0.000 0.000 0.000 0.200 0.000 -1.748
68.600 20.000 0.000 0.000 0.000 0.200 0.000 -1.622
68.700 20.000 0.000 0.000 0.000 0.200 0.000 -1.485
68.800 20.000 0.000 0.000 0.000 0.200 0.000 -1.338
68.900 20.000 0.000 0.000 0.000 0.200 0.000 -1.188
69.000 20.000 0.000 0.000 0.000 0.200 0.000 -1.037
69.100 20.000 0.000 0.000 0.000 0.200 0.000 -0.889
69.200 20.000 0.000 0.000 0.000 0.200 0.000 -0.747
69.300 20.000 0.000 0.000 0.000 0.200 0.000 -0.614
69.400 20.000 0.000 0.000 0.000 0.200 0.000 -0.493
69.500 20.000 0.000 0.000 0.000 0.200 0.000 -0.384
69.600 20.000 0.000 0.000 0.000 0.200 0.000 -0.289
69.700 20.000 0.000 0.000 0.000 0.200 0.000 -0.209
69.800 20.000 0.000 0.000 0.000 0.200 0.000 -0.144
69.900 20.000 0.000 0.000 0.000 0.200 0.000 -0.092
70.000 20.000 0.000 0.000 0.000 0.200 0.000 -0.054
70.100 20.000 0.000 0.000 0.000 0.200 0.000 -0.028
70.200 20.000 0.000 0.000 0.000 0.200 0.000 -0.012
70.300 20.000 0.000 0.000 0.000 0.200 0.000 -0.004
70.400 20.000 0.000 0.000 0.000 0.200 0.000 -0.000
70.500 20.000 0.000 0.000 0.000 0.200 0.000 0.000.. footbibliography::