Wind Field Generator Overview ----------------------------- .. _fig-wind-module: .. figure:: wind_module.png :align: center :alt: Wind field creation dialogue in QBlade. 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. Turbulent Wind Field -------------------- .. _fig-turb-field: .. figure:: windfield.png :align: center :scale: 50% :alt: A turbulent wind field generated in QBlade. 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`). TurbSim Wind Fields ^^^^^^^^^^^^^^^^^^^ 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. .. _fig-turb-dia: .. figure:: turbsim_dialog.png :align: center :scale: 75% :alt: Turb sim wind field dialogue in QBlade. 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 (:math:`x`) direction. * **Grid Width**: Specifies box size in lateral (:math:`y`) direction. * **Grid Height**: Specifies box size in vertical (:math:`z`) direction. * **Grid Y Points**: Specifies spatial discretisation in :math:`y` direction. * **Grid Z Points**: Specifies spatial discretisation in :math:`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 :math:`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. Mann Wind Fields ^^^^^^^^^^^^^^^^ 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. .. _fig-mann-dia: .. figure:: mann_dialog.png :align: center :scale: 75% :alt: Mann wind field dialogue in QBlade. 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 (:math:`x`) direction. * **Grid Width**: Specifies box size in lateral (:math:`y`) direction. * **Grid Height**: Specifies box size in vertical (:math:`z`) direction. * **Grid Y Points**: Specifies spatial discretisation in :math:`y` direction (must be power of 2). * **Grid Z Points**: Specifies spatial discretisation in :math:`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 :math:`c` value (if ETM model chosen). **Mann Box Parameters** * **Alpha Epsilon**: The Mann model :math:`\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. Veers Wind Fields ^^^^^^^^^^^^^^^^^ 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. .. _fig-veers-dia: .. figure:: veers_dialog.png :align: center :scale: 75% :alt: Veers wind field dialogue in QBlade. 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 (:math:`x`) direction. * **Grid Height & Width**: Specifies box size in horizontal (:math:`y`) and vertical (:math:`z`) direction. * **Grid Y & Z Points**: Specifies spatial discretisation in :math:`y` and :math:`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). Importing Turbulent Wind Fields ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. _fig-import-wind: .. figure:: import_menu.png :align: center :scale: 75% :alt: Import options in the wind field menu. 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: Binary Wind Field File ********************** A wind field file in binary format (.bts) (see TurbSim Users Guide :footcite:`TurbSimGuide`) can be imported by simply reading the .bts file. Mann Model 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 and import the velocity components from these binary files directly. .. code-block:: console :caption: : Exemplary Mann (.man) format file ----------------------------------------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-variance TurbSim Input File ****************** A 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. .. code-block:: console :caption: : Exemplary TurbSim Input (.ipt) file !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 .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! ================================================== Uniform Wind Field ------------------ 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 be specified (see :doc:`../../theory/environment/wind/wind`). .. _fig-wind-pane: .. figure:: winddialog.png :align: center :scale: 80% :alt: Uniform wind field creation dialogue in QBlade. Specification of a uniform wind field within the turbine simulation dialogue. Hub Height File --------------- 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: .. code-block:: console :caption: : Exemplary Hub Height Format file 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::