Blade

The component blade includes three subcomponents, namely outer_shape_bem, elastic_properties_mb, and internal_structure_2d_fem. A fourth subfield lofted_shape is in progress.

All distributed quantities, such as blade chord or the thickness of a structural component, are expressed in terms of pair arrays grid and values, which must have a minimum length of two elements and the same size. grid is defined nondimensional between 0 (root) and 1 (tip) along the, possibly curved, reference_axis.

outer_shape_bem

outer_shape_bem consists of a dictionary containing the data for blade BEM-based aerodynamics.

            airfoil_position:
                grid: [0.0, 0.02, 0.15, 0.24517031675566095, 0.3288439506472435, 0.4391793464459161, 0.5376714071084352, 0.6382076569163737, 0.7717438522715817, 1.0]
                labels: [circular, circular, SNL-FFA-W3-500, FFA-W3-360, FFA-W3-330blend, FFA-W3-301, FFA-W3-270blend, FFA-W3-241, FFA-W3-211, FFA-W3-211]
            chord:
                grid: [0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 0.985, 0.99, 0.995, 1.0]
                values: [5.2, 5.208839941579524, 5.237887092263203, 5.293325313383697, 5.3673398548149205, 5.452092684226667, 5.5400317285038465, 5.621824261194381, 5.692531175149338, 5.74261089072697, 5.764836827022541, 5.756119529852528, 5.70309851275065, 5.604676021602162, 5.471559126660524, 5.322778014171772, 5.16648228816705, 5.019421327310202, 4.885807888739599, 4.767959675121795, 4.654566079625438, 4.54103105171191, 4.42817557762473, 4.316958876583997, 4.207880735790049, 4.101646187027423, 3.9987123353123564, 3.8994086760515647, 3.803172543681295, 3.7093894536544263, 3.6171117415725322, 3.525634918177657, 3.434082670567315, 3.341933111457596, 3.2486784477614132, 3.156109679927359, 3.0645800048338336, 2.9729926470824872, 2.8807051066906166, 2.786969376686517, 2.6910309386270574, 2.591965555977676, 2.4893236475052167, 2.383917231097341, 2.2759238162069977, 2.165466732053696, 2.0526250825584818, 1.9377533268191636, 1.819662967336163, 1.7799216728668075, 1.7077871948468315, 1.472482673397968, 0.5000000000000001]
            twist: &id002
                grid: [0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0]
                values: [0.27217629557079365, 0.27205736171561723, 0.26896980562529643, 0.26090151424382807, 0.24885698262522313, 0.23382423192614568, 0.21680513961749598, 0.1988727863224039, 0.18100767932828987, 0.16413076067279694, 0.1492522184680202, 0.1367143113540973, 0.12551282194274888, 0.11434749848233088, 0.10356776280240737, 0.0933068658568242, 0.0837118194006672, 0.07498970428955204, 0.06714203432398387, 0.06013256274855414, 0.053702278525950935, 0.047709665190988265, 0.04210143739978706, 0.03685595675838511, 0.03191153817565269, 0.027205903019809997, 0.022731811675977428, 0.018577762273585947, 0.014720912664231815, 0.011110140960669581, 0.00762759323174886, 0.00418280011853364, 0.0006925062977488528, -0.003016419809918337, -0.0071049531892497, -0.011874829529214339, -0.017440963696104015, -0.023047513564523475, -0.02833190814159476, -0.03288842847284285, -0.03641158408109318, -0.037768893627003246, -0.03797559234861602, -0.03761714725398, -0.036702695029715245, -0.035227785335510846, -0.033104414148684154, -0.030095161935387575, -0.026321748778324498, -0.021683756060763528]
            pitch_axis:
                grid: [0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0]
                values: [0.5045454545454545, 0.4900186808012221, 0.47270018284548393, 0.4540147730610375, 0.434647782591965, 0.4156278851950606, 0.3979378721273935, 0.38129960745617403, 0.3654920515699109, 0.35160780834472827, 0.34008443128769117, 0.3310670675965599, 0.3241031342163746, 0.3188472934612394, 0.3146895762675238, 0.311488897995355, 0.3088429219529899, 0.3066054031112312, 0.3043613335231313, 0.3018756624023877, 0.2992017656131912, 0.29648581499532917, 0.29397119399704474, 0.2918571873240831, 0.2901098902886204, 0.28880659979944606, 0.28802634398115073, 0.28784151044623507, 0.28794253614539367, 0.28852264941156663, 0.28957685074559625, 0.2911108045758606, 0.2930139151081327, 0.2952412111444283, 0.2977841397364215, 0.300565286724993, 0.3035753776130124, 0.30670446458784534, 0.30988253764299156, 0.3130107259708016, 0.31639042766652853, 0.32021109189825026, 0.32462311714967124, 0.329454188784972, 0.33463306413024474, 0.3401190402144396, 0.3460555975714659, 0.3527211856428439, 0.3600890296396286, 0.36818181818181805]
            reference_axis: &id001
                x:
                    grid: [0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0]
                    values: [0.0, 0.018400065266506227, 0.04225083661157623, 0.0713435070518306, 0.1036164118664373, 0.13698065932882636, 0.16947761902506267, 0.19850810716711273, 0.22314347791028566, 0.24053558565655847, 0.24886598803245524, 0.2502470372487695, 0.24941257744761433, 0.24756615214432298, 0.24481686563607896, 0.24130290560673967, 0.23698965095246982, 0.23242285078249267, 0.22531163517427788, 0.2110134548882222, 0.18623119147117725, 0.1479307251853749, 0.09847131457569316, 0.04111540547132665, -0.02233952894219675, -0.08884150619038655, -0.15891966620096387, -0.2407441175807782, -0.3366430472730907, -0.44693576549987823, -0.5680658106768092, -0.6975208703059096, -0.8321262196998409, -0.9699653368698024, -1.1090930486685822, -1.255144506570033, -1.4103667735456449, -1.5733007007462756, -1.7434963771088456, -1.9194542609028804, -2.1000907378795275, -2.285501961499942, -2.4756894577736315, -2.6734165188032692, -2.8782701025304545, -3.090085737186208, -3.308459127246535, -3.533712868740941, -3.7641269864926348, -4.0]
                y:
                    grid: [0.0, 1.0]
                    values: [0.0, 0.0]
                z:
                    grid: [0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0]
                    values: [0.0, 2.387755102040816, 4.775510204081632, 7.163265306122448, 9.551020408163264, 11.938775510204081, 14.326530612244898, 16.714285714285715, 19.10204081632653, 21.489795918367346, 23.877551020408163, 26.265306122448976, 28.653061224489797, 31.04081632653061, 33.42857142857143, 35.81632653061224, 38.20408163265306, 40.59183673469388, 42.979591836734684, 45.36734693877551, 47.75510204081632, 50.14285714285714, 52.53061224489795, 54.91836734693877, 57.30612244897959, 59.69387755102041, 62.08163265306122, 64.46938775510203, 66.85714285714285, 69.24489795918367, 71.63265306122447, 74.0204081632653, 76.40816326530611, 78.79591836734693, 81.18367346938776, 83.57142857142857, 85.95918367346938, 88.3469387755102, 90.73469387755102, 93.12244897959182, 95.51020408163265, 97.89795918367345, 100.28571428571428, 102.6734693877551, 105.0612244897959, 107.44897959183673, 109.83673469387753, 112.22448979591836, 114.61224489795919, 117.0]
airfoil_position'labelsArray of strings

The array labels specifies the names of the airfoils to be placed along the blade. The positions are specified in the field grid. The two arrays must share the same length and to keep an airfoil constant along blade span, this must be defined twice. The labels must match the names of the airfoils listed in the top level airfoils. In between airfoils, the recommended interpolation scheme for both coordinates and polars is the Piecewise Cubic Hermite Interpolating Polynomial (PCHIP), which is implemented in Matlab and in the Python library SciPy. Optionally, the field rthick.values can also be defined, see below.

chord.valuesArray of floats, m

The array values specifies the chord along blade span.

twist.valuesArray of floats, rad

The array values specifies the aerodynamic twist along blade span. In the example provided above, a json pointer &id002` is defined, which will be used to rotate composite layers in internal_structure_2d_fem. Remember, the unit of measure of the twist is not degrees!

pitch_axis.valuesArray of floats

The array values specifies the positions along blade span of the position of the airfoil in respect to the blade reference axis. A value of 0 means that the reference axis, around which the blade pitches and twists, crosses the airfoil at the leading edge, while a value of 1 corresponds to the trailing edge. Standard value oscillate between 0.5 for the blade root cylinder and 0.25. These are the values reported in the example.

rthick.valuesArray of floats

This array has recently been added to windIO to overcome the uncertainty in the interpolated distribution of relative thickness along blade span. It should match the field airfoil_position

reference_axisObject

The field reference_axis describes the three-dimensional shape of the reference axis of the blade via three sub-fields, namely x, y, and z. The three sub-fields contain the pairs of arrays grid and values. The former is nondimensional, while the latter is expressed in meters.

The coordinate system is the one of BeamDyn of OpenFAST and it is shown in the figure below.

../_images/reference_axis.jpg

The consequences of this reference system is that standard wind turbine blades have positive twist inboard and close to zero or even slightly negative twist outboard, zero or negative x values for standard prebent blades, and positive y values for backward swept blades. The blade main direction is expressed along z, and total blade length must be computed integrating the fields x, y, and z three-dimensionally.

internal structure 2d_fem

The field internal_structure_2d_fem contains the data to describe the internal structure of standard wind turbine blades. This is a fairly sophisticated process and the ontology proposed in this work supports different definitions. On the top level, the field internal_structure_2d_fem has three sub-components, namely the reference_axis, which is usually defined equal to the reference_axis in the field outer_shape_bem, the webs, where the positions of the shear webs are defined, and the layers, which describe all internal layers in terms of name, material, thickness, number of plies n_plies, fiber_orientation (for composites), and position in the two-dimensional sections. Recently, the field joint was added to support blades that are segmented spanwise.

webs

The field webs consists of a list of entries, each representing a shear web defined in terms of name and position.

nameString

String that identifies the web.

The first (and usually most convenient) way to define the position of a shear web is by defining the fields rotation and offset_y_pa, which are distributed along span and are therefore described in terms of grid and values pairs.

               -  name: web0
                  rotation:
                      fixed: twist
                      grid: [0.0, 0.02, 0.04, 0.06, 0.08, 0.1, 0.125, 0.15, 0.1690340633511322, 0.18806812670226436, 0.20710219005339656, 0.22613625340452875, 0.24517031675566095, 0.2660887252285566, 0.2870071337014522, 0.30792554217434787, 0.3288439506472435, 0.350911029806978, 0.3729781089667125, 0.39504518812644707, 0.41711226728618156, 0.4391793464459161, 0.45887775857841995, 0.47857617071092373, 0.49827458284342757, 0.5179729949759314, 0.5376714071084352, 0.5577786570700229, 0.5778859070316106, 0.5979931569931983, 0.618100406954786, 0.6382076569163737, 0.657284256252832, 0.6763608555892903, 0.6954374549257486, 0.7145140542622068, 0.7335906535986652, 0.7526672529351234, 0.7717438522715817, 0.8, 0.8187500000000001, 0.8375, 0.85625, 0.875, 0.89375, 0.9125, 0.9312499999999999, 0.95, 0.975, 1.0]
                      values: [-0.27217629557079365, -0.2721151609261069, -0.2692829996121141, -0.26160974693508077, -0.25004194631128646, -0.23552614115701065, -0.21467775307891476, -0.19255079961979954, -0.1759878586013097, -0.16057133469540177, -0.14711714321398614, -0.1357292521960968, -0.12536451335231813, -0.11391930868991773, -0.10288584723243112, -0.09240330785216998, -0.08263112720589656, -0.07331222604686127, -0.06502804112954641, -0.05771742601208772, -0.05096319090575163, -0.04469782752454605, -0.03947910486050121, -0.03456265676425803, -0.0299081112103219, -0.025446129064633893, -0.02121583510652544, -0.01724217523108515, -0.013528184408954813, -0.01004307189737569, -0.006635163107666419, -0.0032467588547257582, 3.369564839038511e-05, 0.0035492823924747176, 0.007421594235148177, 0.011928778895197866, 0.017136732150624685, 0.0223974077244561, 0.027490996670335385, 0.03379973253909251, 0.036799280794358936, 0.037810153747541306, 0.037988462925127336, 0.03771818081838972, 0.036975584119978255, 0.03575998726335209, 0.03405925501568549, 0.03168024471993639, 0.027365297139775716, 0.021683756060763528]
                  offset_y_pa:
                      grid: [0.1, 0.975]
                      values: [-0.35, -0.35]
                  start_nd_arc:
                      grid: [0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0]
                      values: [0.20528324315541635, 0.2097556380134865, 0.214034201297075, 0.21859521544514496, 0.22544079600769645, 0.2600262599953903, 0.27325310403744485, 0.287036736327106, 0.29901531855266544, 0.31004427379885435, 0.31964630853682274, 0.327381221939197, 0.3332279257508938, 0.3404119921430249, 0.34536862450358796, 0.3483161845298215, 0.35087342593259435, 0.3541004018132578, 0.358143510233458, 0.36205656780675327, 0.3653808670486798, 0.3680072762780136, 0.37080869847411474, 0.37441862732222103, 0.3779001712687167, 0.3806367459556684, 0.382499122180323, 0.38387503752747754, 0.3856023866745639, 0.3873229946154009, 0.3888557122938616, 0.390149435947777, 0.39136648378757616, 0.3924310955228753, 0.39331444293528894, 0.39405844474889024, 0.3946944625752598, 0.3952672458224185, 0.3958134640671341, 0.39646716576057284, 0.3971471504083998, 0.39776245781144953, 0.39833240110413193, 0.39899014105047, 0.39981944363019767, 0.40090208432891433, 0.40224688844613343, 0.4037960986000614, 0.3131650477206493, 0.3090661411456019]
                  end_nd_arc:
                      grid: [0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0]
                      values: [0.7080802577208776, 0.7036455102335815, 0.7010488685736092, 0.7010884514333167, 0.7014967820188778, 0.6761888726465278, 0.6729065942397168, 0.6680497867709726, 0.6631623793152429, 0.6592024850579787, 0.6555258143570273, 0.6521844205829048, 0.6495084856532908, 0.6446894785290086, 0.6419750975110313, 0.641249573695285, 0.6405155416597471, 0.6386928766049896, 0.6359428243808779, 0.6331279745265908, 0.6308742184379281, 0.6292625886697967, 0.6273358867997892, 0.624391758073666, 0.6214725158861021, 0.6193781744502277, 0.618031171163369, 0.6168982314610834, 0.6153329183257642, 0.6137641313361158, 0.6124519759406767, 0.6114109925636344, 0.6104065498164664, 0.609385032345621, 0.6084107897293662, 0.6075786906771415, 0.6069950920595479, 0.6066337715002371, 0.606485952430602, 0.6062452813018124, 0.6058817873790933, 0.6053821435852097, 0.604819981036594, 0.6041148785485133, 0.6031834986262846, 0.601942851287227, 0.6003789528645205, 0.5985219881262099, 0.6892746108093417, 0.6929001625242511]
               -  name: web1
                  rotation:
                      fixed: twist
                      grid: [0.0, 0.02, 0.04, 0.06, 0.08, 0.1, 0.125, 0.15, 0.1690340633511322, 0.18806812670226436, 0.20710219005339656, 0.22613625340452875, 0.24517031675566095, 0.2660887252285566, 0.2870071337014522, 0.30792554217434787, 0.3288439506472435, 0.350911029806978, 0.3729781089667125, 0.39504518812644707, 0.41711226728618156, 0.4391793464459161, 0.45887775857841995, 0.47857617071092373, 0.49827458284342757, 0.5179729949759314, 0.5376714071084352, 0.5577786570700229, 0.5778859070316106, 0.5979931569931983, 0.618100406954786, 0.6382076569163737, 0.657284256252832, 0.6763608555892903, 0.6954374549257486, 0.7145140542622068, 0.7335906535986652, 0.7526672529351234, 0.7717438522715817, 0.8, 0.8187500000000001, 0.8375, 0.85625, 0.875, 0.89375, 0.9125, 0.9312499999999999, 0.95, 0.975, 1.0]
                      values: [-0.27217629557079365, -0.2721151609261069, -0.2692829996121141, -0.26160974693508077, -0.25004194631128646, -0.23552614115701065, -0.21467775307891476, -0.19255079961979954, -0.1759878586013097, -0.16057133469540177, -0.14711714321398614, -0.1357292521960968, -0.12536451335231813, -0.11391930868991773, -0.10288584723243112, -0.09240330785216998, -0.08263112720589656, -0.07331222604686127, -0.06502804112954641, -0.05771742601208772, -0.05096319090575163, -0.04469782752454605, -0.03947910486050121, -0.03456265676425803, -0.0299081112103219, -0.025446129064633893, -0.02121583510652544, -0.01724217523108515, -0.013528184408954813, -0.01004307189737569, -0.006635163107666419, -0.0032467588547257582, 3.369564839038511e-05, 0.0035492823924747176, 0.007421594235148177, 0.011928778895197866, 0.017136732150624685, 0.0223974077244561, 0.027490996670335385, 0.03379973253909251, 0.036799280794358936, 0.037810153747541306, 0.037988462925127336, 0.03771818081838972, 0.036975584119978255, 0.03575998726335209, 0.03405925501568549, 0.03168024471993639, 0.027365297139775716, 0.021683756060763528]
                  offset_y_pa:
                      grid: [0.1, 0.975]
                      values: [0.35, 0.35]
                  start_nd_arc:
                      grid: [0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0]
                      values: [0.20528324315541635, 0.2097556380134865, 0.214034201297075, 0.21859521544514496, 0.22544079600769645, 0.21049664507316915, 0.2221524829466206, 0.23489094260768295, 0.2464402901027729, 0.25704110608788355, 0.26610208870577773, 0.2731575064757129, 0.27811470862196863, 0.28363187347682567, 0.28684464332054505, 0.28819636059157144, 0.2891309058769609, 0.2903750579306535, 0.29226545725488406, 0.2942414364091017, 0.2957434998949183, 0.2966240162898488, 0.29743274073730547, 0.29872361977733936, 0.29987061080676763, 0.30037495151387633, 0.3001535023809019, 0.2994117591475181, 0.298827519553128, 0.2981070707230933, 0.2970548514754858, 0.2957385169642028, 0.29426155346364713, 0.29240890212879467, 0.2901619718691776, 0.2876315287799329, 0.2848624595040138, 0.2818820047526827, 0.2787099966471504, 0.2753600461183012, 0.2716467012515975, 0.2673799096461699, 0.26247590233736284, 0.25700603896247765, 0.25096216551166967, 0.24429441187125944, 0.23684302837967156, 0.22838339181634582, 0.3131650477206493, 0.3090661411456019]
                  end_nd_arc:
                      grid: [0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0]
                      values: [0.7080802577208776, 0.7036455102335815, 0.7010488685736092, 0.7010884514333167, 0.7014967820188778, 0.72644257193856, 0.7251577664798297, 0.72126525721117, 0.7165131474582784, 0.7128364931987339, 0.7096957702397008, 0.7071183083423042, 0.7054305232448042, 0.7021515188621643, 0.7009610615568496, 0.7015598004269967, 0.702584158734739, 0.7027824843897299, 0.7019583429960832, 0.7010163945237471, 0.7005850845804309, 0.7006799380712909, 0.7005868175868423, 0.6998365795372271, 0.6992426039535212, 0.6993988554511297, 0.7001942955932572, 0.7012212319673574, 0.7019864617769342, 0.7028820749437287, 0.7041382518976327, 0.7057052939823155, 0.7074485078117209, 0.7093898005592713, 0.7115965519922267, 0.7140900289099416, 0.7169370460528581, 0.7201287398105142, 0.7236820899656677, 0.7274079136833573, 0.731386467791719, 0.7356972916024903, 0.7405228051001613, 0.745836376011838, 0.751657201580099, 0.7580259971089817, 0.7650909530494675, 0.7730734039318857, 0.6892746108093417, 0.6929001625242511]
rotation.valuesArray of floats, rad

The rotation defines the angle between the chord line and the y axis and it has the opposite sign of the twist. For shear webs perpendicular to the chord line in the section(s) where twist is zero, it is easiest to simply use the keyword fixed: twist.

offset_y_pa.valuesArray of floats, m

The field offset_y_pa defines the distance in meters along the y axis between the pitch axis and the plane of the shear web. It is defined along y.

Blades with straight shear webs will always have the field rotation equal to the twist plus/minus a constant angle and, assuming a non-swept blade (zero values in the blade y reference axis), a linear field offset_y_pa.

The second approach to define the position of a shear web is by defining the fields start_nd_arc and end_nd_arc, which are also distributed along span and are therefore also described in terms of grid and values pairs.

               -  name: web0
                  rotation:
                      fixed: twist
                      grid: [0.0, 0.02, 0.04, 0.06, 0.08, 0.1, 0.125, 0.15, 0.1690340633511322, 0.18806812670226436, 0.20710219005339656, 0.22613625340452875, 0.24517031675566095, 0.2660887252285566, 0.2870071337014522, 0.30792554217434787, 0.3288439506472435, 0.350911029806978, 0.3729781089667125, 0.39504518812644707, 0.41711226728618156, 0.4391793464459161, 0.45887775857841995, 0.47857617071092373, 0.49827458284342757, 0.5179729949759314, 0.5376714071084352, 0.5577786570700229, 0.5778859070316106, 0.5979931569931983, 0.618100406954786, 0.6382076569163737, 0.657284256252832, 0.6763608555892903, 0.6954374549257486, 0.7145140542622068, 0.7335906535986652, 0.7526672529351234, 0.7717438522715817, 0.8, 0.8187500000000001, 0.8375, 0.85625, 0.875, 0.89375, 0.9125, 0.9312499999999999, 0.95, 0.975, 1.0]
                      values: [-0.27217629557079365, -0.2721151609261069, -0.2692829996121141, -0.26160974693508077, -0.25004194631128646, -0.23552614115701065, -0.21467775307891476, -0.19255079961979954, -0.1759878586013097, -0.16057133469540177, -0.14711714321398614, -0.1357292521960968, -0.12536451335231813, -0.11391930868991773, -0.10288584723243112, -0.09240330785216998, -0.08263112720589656, -0.07331222604686127, -0.06502804112954641, -0.05771742601208772, -0.05096319090575163, -0.04469782752454605, -0.03947910486050121, -0.03456265676425803, -0.0299081112103219, -0.025446129064633893, -0.02121583510652544, -0.01724217523108515, -0.013528184408954813, -0.01004307189737569, -0.006635163107666419, -0.0032467588547257582, 3.369564839038511e-05, 0.0035492823924747176, 0.007421594235148177, 0.011928778895197866, 0.017136732150624685, 0.0223974077244561, 0.027490996670335385, 0.03379973253909251, 0.036799280794358936, 0.037810153747541306, 0.037988462925127336, 0.03771818081838972, 0.036975584119978255, 0.03575998726335209, 0.03405925501568549, 0.03168024471993639, 0.027365297139775716, 0.021683756060763528]
                  offset_y_pa:
                      grid: [0.1, 0.975]
                      values: [-0.35, -0.35]
                  start_nd_arc:
                      grid: [0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0]
                      values: [0.20528324315541635, 0.2097556380134865, 0.214034201297075, 0.21859521544514496, 0.22544079600769645, 0.2600262599953903, 0.27325310403744485, 0.287036736327106, 0.29901531855266544, 0.31004427379885435, 0.31964630853682274, 0.327381221939197, 0.3332279257508938, 0.3404119921430249, 0.34536862450358796, 0.3483161845298215, 0.35087342593259435, 0.3541004018132578, 0.358143510233458, 0.36205656780675327, 0.3653808670486798, 0.3680072762780136, 0.37080869847411474, 0.37441862732222103, 0.3779001712687167, 0.3806367459556684, 0.382499122180323, 0.38387503752747754, 0.3856023866745639, 0.3873229946154009, 0.3888557122938616, 0.390149435947777, 0.39136648378757616, 0.3924310955228753, 0.39331444293528894, 0.39405844474889024, 0.3946944625752598, 0.3952672458224185, 0.3958134640671341, 0.39646716576057284, 0.3971471504083998, 0.39776245781144953, 0.39833240110413193, 0.39899014105047, 0.39981944363019767, 0.40090208432891433, 0.40224688844613343, 0.4037960986000614, 0.3131650477206493, 0.3090661411456019]
                  end_nd_arc:
                      grid: [0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0]
                      values: [0.7080802577208776, 0.7036455102335815, 0.7010488685736092, 0.7010884514333167, 0.7014967820188778, 0.6761888726465278, 0.6729065942397168, 0.6680497867709726, 0.6631623793152429, 0.6592024850579787, 0.6555258143570273, 0.6521844205829048, 0.6495084856532908, 0.6446894785290086, 0.6419750975110313, 0.641249573695285, 0.6405155416597471, 0.6386928766049896, 0.6359428243808779, 0.6331279745265908, 0.6308742184379281, 0.6292625886697967, 0.6273358867997892, 0.624391758073666, 0.6214725158861021, 0.6193781744502277, 0.618031171163369, 0.6168982314610834, 0.6153329183257642, 0.6137641313361158, 0.6124519759406767, 0.6114109925636344, 0.6104065498164664, 0.609385032345621, 0.6084107897293662, 0.6075786906771415, 0.6069950920595479, 0.6066337715002371, 0.606485952430602, 0.6062452813018124, 0.6058817873790933, 0.6053821435852097, 0.604819981036594, 0.6041148785485133, 0.6031834986262846, 0.601942851287227, 0.6003789528645205, 0.5985219881262099, 0.6892746108093417, 0.6929001625242511]
               -  name: web1
                  rotation:
                      fixed: twist
                      grid: [0.0, 0.02, 0.04, 0.06, 0.08, 0.1, 0.125, 0.15, 0.1690340633511322, 0.18806812670226436, 0.20710219005339656, 0.22613625340452875, 0.24517031675566095, 0.2660887252285566, 0.2870071337014522, 0.30792554217434787, 0.3288439506472435, 0.350911029806978, 0.3729781089667125, 0.39504518812644707, 0.41711226728618156, 0.4391793464459161, 0.45887775857841995, 0.47857617071092373, 0.49827458284342757, 0.5179729949759314, 0.5376714071084352, 0.5577786570700229, 0.5778859070316106, 0.5979931569931983, 0.618100406954786, 0.6382076569163737, 0.657284256252832, 0.6763608555892903, 0.6954374549257486, 0.7145140542622068, 0.7335906535986652, 0.7526672529351234, 0.7717438522715817, 0.8, 0.8187500000000001, 0.8375, 0.85625, 0.875, 0.89375, 0.9125, 0.9312499999999999, 0.95, 0.975, 1.0]
                      values: [-0.27217629557079365, -0.2721151609261069, -0.2692829996121141, -0.26160974693508077, -0.25004194631128646, -0.23552614115701065, -0.21467775307891476, -0.19255079961979954, -0.1759878586013097, -0.16057133469540177, -0.14711714321398614, -0.1357292521960968, -0.12536451335231813, -0.11391930868991773, -0.10288584723243112, -0.09240330785216998, -0.08263112720589656, -0.07331222604686127, -0.06502804112954641, -0.05771742601208772, -0.05096319090575163, -0.04469782752454605, -0.03947910486050121, -0.03456265676425803, -0.0299081112103219, -0.025446129064633893, -0.02121583510652544, -0.01724217523108515, -0.013528184408954813, -0.01004307189737569, -0.006635163107666419, -0.0032467588547257582, 3.369564839038511e-05, 0.0035492823924747176, 0.007421594235148177, 0.011928778895197866, 0.017136732150624685, 0.0223974077244561, 0.027490996670335385, 0.03379973253909251, 0.036799280794358936, 0.037810153747541306, 0.037988462925127336, 0.03771818081838972, 0.036975584119978255, 0.03575998726335209, 0.03405925501568549, 0.03168024471993639, 0.027365297139775716, 0.021683756060763528]
                  offset_y_pa:
                      grid: [0.1, 0.975]
                      values: [0.35, 0.35]
                  start_nd_arc:
                      grid: [0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0]
                      values: [0.20528324315541635, 0.2097556380134865, 0.214034201297075, 0.21859521544514496, 0.22544079600769645, 0.21049664507316915, 0.2221524829466206, 0.23489094260768295, 0.2464402901027729, 0.25704110608788355, 0.26610208870577773, 0.2731575064757129, 0.27811470862196863, 0.28363187347682567, 0.28684464332054505, 0.28819636059157144, 0.2891309058769609, 0.2903750579306535, 0.29226545725488406, 0.2942414364091017, 0.2957434998949183, 0.2966240162898488, 0.29743274073730547, 0.29872361977733936, 0.29987061080676763, 0.30037495151387633, 0.3001535023809019, 0.2994117591475181, 0.298827519553128, 0.2981070707230933, 0.2970548514754858, 0.2957385169642028, 0.29426155346364713, 0.29240890212879467, 0.2901619718691776, 0.2876315287799329, 0.2848624595040138, 0.2818820047526827, 0.2787099966471504, 0.2753600461183012, 0.2716467012515975, 0.2673799096461699, 0.26247590233736284, 0.25700603896247765, 0.25096216551166967, 0.24429441187125944, 0.23684302837967156, 0.22838339181634582, 0.3131650477206493, 0.3090661411456019]
                  end_nd_arc:
                      grid: [0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0]
                      values: [0.7080802577208776, 0.7036455102335815, 0.7010488685736092, 0.7010884514333167, 0.7014967820188778, 0.72644257193856, 0.7251577664798297, 0.72126525721117, 0.7165131474582784, 0.7128364931987339, 0.7096957702397008, 0.7071183083423042, 0.7054305232448042, 0.7021515188621643, 0.7009610615568496, 0.7015598004269967, 0.702584158734739, 0.7027824843897299, 0.7019583429960832, 0.7010163945237471, 0.7005850845804309, 0.7006799380712909, 0.7005868175868423, 0.6998365795372271, 0.6992426039535212, 0.6993988554511297, 0.7001942955932572, 0.7012212319673574, 0.7019864617769342, 0.7028820749437287, 0.7041382518976327, 0.7057052939823155, 0.7074485078117209, 0.7093898005592713, 0.7115965519922267, 0.7140900289099416, 0.7169370460528581, 0.7201287398105142, 0.7236820899656677, 0.7274079136833573, 0.731386467791719, 0.7356972916024903, 0.7405228051001613, 0.745836376011838, 0.751657201580099, 0.7580259971089817, 0.7650909530494675, 0.7730734039318857, 0.6892746108093417, 0.6929001625242511]
start_nd_arc.valuesArray of floats

The field defines the nondimensional position along the arc of a 2D blade section, where 0 represents the trailing edge on the suction side and 1 the trailing edge on the pressure side. For flatback airfoils, the start (s = 0) and end (s = 1) nondimensional coordinate s is defined in the midpoint between suction and pressure sides. The shear webs have the field start_nd_arc on the suction side, so usually smaller than 0.5, which approximately correspond to the leading edge.

end_nd_arc.valuesArray of floats

On the opposite, the shear webs have the field end_nd_arc on the pressure side, so usually between 0.5 and 1.

../_images/web2.jpg

layers

The sub-field layers define the layers of the wind turbine blade. In most cases, these are layers of composite materials. Each layer is defined by the following entries.

nameString

String that identifies the layer.

materialString

String that identifies the material of the layer. The material and its properties must be defined in the top-level materials.

thicknessFloat, m

Dimensional thickness of the laminate, expressed in meters. This value is modeled constant along the section. To define ply drops along the 2D surface, the user is therefore required to define multiple layers, possibly ply by ply when many ply drops exist.

n_pliesInteger

In addition or in alternative to the dimensional thickness, the discrete number of plies of a composite laminate can be defined by the user. Notably, the ply thickness is a material property (not a layer property) and it is defined in the top-level field materials.

fiber_orientationFloat, rad

For composite laminates, the orientation of the fibers in radians can be specified. Looking from blade root, positive angles represent a rotation of the fibers towards the leading edge of the blade. Note that the angles are in respect to the cross section local reference system, not the reference system at blade root.

The position of the layer in the 2D section can be specified in various ways. If nothing is defined, this assumes that the sub-field start_nd_arc is equal to 0 and the sub-field end_nd_arc is equal to 1. This means that the layer wraps the whole section, such as in the example below for the outer gelcoat. This definition of a layer should be used also for example for the outer shell skin, which typically wraps the whole section.

                  material: Gelcoat
                  thickness:
                      grid: [0.0, 1.0]
                      values: [0.001, 0.001]
                  start_nd_arc:
                      values: [0.0, 0.0]
                      grid: [0.0, 1.0]
                  end_nd_arc:
                      values: [1.0, 1.0]
                      grid: [0.0, 1.0]
                  fiber_orientation:
                      grid: [0.0, 1.0]
                      values: [0.0, 0.0]

The most convenient approach to define the position of spar caps mimics the definition of the shear webs, adding the width and side that define the width of the layer in meters and the side where the layer is located, either “pressure” or “suction”.

                  material: CarbonUD
                  thickness:
                      grid: [0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0]
                      values: [0.0001, 0.0019253427544743858, 0.005878030418028014, 0.012205741402763814, 0.02033847241410345, 0.029710037581228265, 0.03976076813427265, 0.04984579196655636, 0.059506919810752144, 0.06813475896247266, 0.07517917278251993, 0.08001633865143198, 0.08380373783594258, 0.08756302399896077, 0.09096088968367966, 0.09394183001092273, 0.09623412699697585, 0.0977753527026025, 0.09836307921598017, 0.0981999062871899, 0.09757657895482426, 0.09649171896998379, 0.09504926405790153, 0.09340609597066436, 0.09163396600383901, 0.08985822612692451, 0.08812902603702513, 0.08640958344856942, 0.08462830823429666, 0.08272111871184405, 0.08063005694324227, 0.07831036719824715, 0.07574643418843892, 0.07276138579954894, 0.06913218672253638, 0.06421642597820243, 0.05743129735425094, 0.0499439766596495, 0.04210164910682022, 0.03453603307614619, 0.027794810383669103, 0.022532572295399025, 0.01866188117363215, 0.015066576723923265, 0.011738804201119217, 0.008673947426939258, 0.006002632716771239, 0.0038861394151689125, 0.0022342962473922592, 0.0010000000000001236]
                  fiber_orientation:
                      grid: [0.0, 1.0]
                      values: [0.0, 0.0]
                  width:
                      grid: [0.0, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0]
                      values: [0.9, 0.9, 0.8999999988390655, 0.8999995100671728, 0.8999891507887757, 0.8998321453405057, 0.8986596837575513, 0.8916444980356923, 0.8645530713991059, 0.7694187536403974, 0.585345108782866, 0.294]
                  offset_y_pa:
                      grid: [0.0, 1.0]
                      values: [0.0, 0.0]
                  rotation:
                      fixed: twist
                      grid: [0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0]
                      values: [-0.27217629557079365, -0.27205736171561723, -0.26896980562529643, -0.26090151424382807, -0.24885698262522313, -0.23382423192614568, -0.21680513961749598, -0.1988727863224039, -0.18100767932828987, -0.16413076067279694, -0.1492522184680202, -0.1367143113540973, -0.12551282194274888, -0.11434749848233088, -0.10356776280240737, -0.0933068658568242, -0.0837118194006672, -0.07498970428955204, -0.06714203432398387, -0.06013256274855414, -0.053702278525950935, -0.047709665190988265, -0.04210143739978706, -0.03685595675838511, -0.03191153817565269, -0.027205903019809997, -0.022731811675977428, -0.018577762273585947, -0.014720912664231815, -0.011110140960669581, -0.00762759323174886, -0.00418280011853364, -0.0006925062977488528, 0.003016419809918337, 0.0071049531892497, 0.011874829529214339, 0.017440963696104015, 0.023047513564523475, 0.02833190814159476, 0.03288842847284285, 0.03641158408109318, 0.037768893627003246, 0.03797559234861602, 0.03761714725398, 0.036702695029715245, 0.035227785335510846, 0.033104414148684154, 0.030095161935387575, 0.026321748778324498, 0.021683756060763528]
                  side: suction
                  start_nd_arc:
                      grid: [0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0]
                      values: [0.17773570068243144, 0.18225456521002678, 0.18604187024451585, 0.1894208057544969, 0.19491682190018167, 0.2035111977739001, 0.21492220169188628, 0.22747556270503067, 0.23896542193889161, 0.24950552934239495, 0.2584881563049556, 0.2654445497010712, 0.27028298131884515, 0.2755557024298496, 0.27853854056668137, 0.2797315507100771, 0.2803739682779732, 0.28132580966028653, 0.2829133734335994, 0.2846153330288592, 0.2858639373398411, 0.28650712299101067, 0.2870579808532732, 0.2880476573408754, 0.2888847763645291, 0.2890483839399594, 0.2885148571593514, 0.28747185047725565, 0.28655673377511326, 0.28550374024630704, 0.28413177831399916, 0.28244810733149306, 0.2805381928509472, 0.27826960958187874, 0.27560086322100535, 0.27264537204392797, 0.26945777589404357, 0.2660506315331089, 0.26243484134157163, 0.2586163420238527, 0.2543899582712716, 0.2495513381795907, 0.24401076074009992, 0.23785709598249466, 0.23115648734884098, 0.22440217984963634, 0.21918975567204751, 0.2216384405804998, 0.23600864040444502, 0.16803069192449496]
                  end_nd_arc:
                      grid: [0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0]
                      values: [0.23283078562840126, 0.23725671081694624, 0.24202653234963417, 0.247769625135793, 0.25596477011521124, 0.2670315296506249, 0.28048290011103555, 0.29437392634069215, 0.3063549936044512, 0.3174275310624229, 0.32712628947371525, 0.33499966400533804, 0.34101471043413073, 0.34844368466828257, 0.3535744166911581, 0.35673959597583377, 0.35957391722047566, 0.3630666080812486, 0.3673827139153765, 0.37160185085425845, 0.37516772313169205, 0.37803473496404505, 0.38098180499218165, 0.38481135235881964, 0.38863638997089717, 0.3916685151753782, 0.3938905104917509, 0.3956414284923102, 0.397758719075737, 0.39986558160974367, 0.40170376953297604, 0.4033136983977561, 0.404877478949584, 0.40633831361987416, 0.4076804199064265, 0.4089325042764648, 0.41010190909865124, 0.4112187187281146, 0.4123082768703506, 0.41353055625835794, 0.4148270473923564, 0.41612027080389463, 0.41744580885705135, 0.4189290910545292, 0.4205732866622497, 0.42192677200808987, 0.4212416759086072, 0.4121166202755468, 0.39032145503685356, 0.4501015903667088]
width.valuesArray of floats, m

The field width defines the width in meters along the arc of the layer.

sideString

The field side is string that can be either suction or pressure, defining the side where a layer is defined.

../_images/layer1.jpg

To define reinforcements, the best way is usually to define the width, in meters, and the midpoint, named midpoint_nd_arc and defined nondimensional between 0 and 1. Converters should be able to look for the leading edge, marked as LE.

                  material: glass_uni
                  thickness:
                      grid: [0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0]
                      values: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0029970845481049565, 0.0029679300291545196, 0.0029387755102040823, 0.0029096209912536446, 0.0028804664723032065, 0.0028513119533527687, 0.002822157434402331, 0.002793002915451894, 0.0027638483965014577, 0.0027346938775510204, 0.002705539358600584, 0.0026763848396501467, 0.0026472303206997085, 0.002618075801749271, 0.0025889212827988335, 0.0025597667638483966, 0.0025306122448979598, 0.002501457725947523, 0.002472303206997085, 0.002443148688046647, 0.0024139941690962093, 0.0023848396501457733, 0.0023556851311953364, 0.002326530612244899, 0.0022973760932944614, 0.0022682215743440237, 0.0022390670553935855, 0.0022099125364431487, 0.002180758017492712, 0.002151603498542275, 0.0021224489795918376, 0.0020932944606413995, 0.0020641399416909617, 0.002034985422740525, 0.0020058309037900876, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
                  fiber_orientation:
                      grid: [0.0, 1.0]
                      values: [0.0, 0.0]
                  midpoint_nd_arc:
                      fixed: LE
                      grid: [0.0, 1.0]
                      values: [0.0, 0.0]
                  width:
                      grid: [0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0]
                      values: [0.0, 0.0, 0.0, 0.0, 0.0, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.7999735283820496, 0.7998325970130074, 0.7984778047921102, 0.7943075801410094, 0.7812145582381771, 0.7593886763210709, 0.7312551421192448, 0.7052091903532077, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
                  start_nd_arc:
                      grid: [0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0]
                      values: [0.4999993345962153, 0.4999993055719888, 0.499932025396804, 0.49976687374045037, 0.499500879329084, 0.4708880162401706, 0.4696375463788885, 0.4688948238131244, 0.46889663993404546, 0.46945061063220406, 0.469685612674169, 0.4694085927649272, 0.4688520073539291, 0.46805778158201233, 0.46739960537250774, 0.46682450560323396, 0.46604125884886216, 0.4648976952209234, 0.4636728750199575, 0.46264269587880497, 0.46178437131694283, 0.46094994262306743, 0.4598529712929675, 0.45831397033804844, 0.4566434908343083, 0.45512220135020276, 0.4537394322616389, 0.45233444473263756, 0.450734072230367, 0.4489892456923073, 0.4471695043754867, 0.44533446424407436, 0.44347055197928353, 0.44141748434749767, 0.43927892353515546, 0.4372963567402792, 0.4360580519757577, 0.4356503368324961, 0.43595347267011436, 0.4361472464495469, 0.4968399840020571, 0.4968399840020575, 0.49683998400205703, 0.4968399840020572, 0.496839984002057, 0.4968399840020573, 0.4968399840020573, 0.4968399840020572, 0.4968399840020571, 0.4968399840020574]
                  end_nd_arc:
                      grid: [0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0]
                      values: [0.4999993345962153, 0.4999993055719888, 0.499932025396804, 0.49976687374045037, 0.499500879329084, 0.527350533463926, 0.5279137227514656, 0.5283600359337124, 0.5287984814145428, 0.5298257232722289, 0.5306972866019554, 0.5312353610353866, 0.5317246554564051, 0.5328470991272861, 0.5340981619275982, 0.5352761013950177, 0.53644121346442, 0.537556182706223, 0.5387567332259816, 0.5399640450569376, 0.5411655142430326, 0.5423078199324314, 0.5433408149719972, 0.5443261436873322, 0.5453115918177466, 0.5463400957816862, 0.5474066796682162, 0.5484851807460195, 0.549580281386477, 0.5506442157931399, 0.5516779410145772, 0.5527705451918636, 0.553990704664652, 0.5552325111772755, 0.556459584068589, 0.5575784703047061, 0.5581394346315676, 0.5581381163648041, 0.5577264953339997, 0.5575327215545678, 0.4968399840020571, 0.4968399840020575, 0.49683998400205703, 0.4968399840020572, 0.496839984002057, 0.4968399840020573, 0.4968399840020573, 0.4968399840020572, 0.4968399840020571, 0.4968399840020574]
midpoint_nd_arc.valuesArray of floats

Coordinate along the arc of the midpoint of the layer.

Similar combinations can be constructed with the combination of width and start_nd_arc or end_nd_arc.

Finally, for composite layers belonging to the shear webs, a tag web should contain the name of the web. The layers are then modeled from leading edge to trailing edge in the order they were specified.

                  material: glass_biax
                  web: web0
                  thickness:
                      grid: [0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0]
                      values: [0.0, 0.0, 0.0, 0.0, 0.0, 0.00199639855942377, 0.001960384153661465, 0.0019243697478991601, 0.0018883553421368549, 0.0018523409363745498, 0.0018163265306122445, 0.0017803121248499399, 0.0017442977190876353, 0.0017082833133253304, 0.0016722689075630256, 0.0016362545018007207, 0.0016002400960384157, 0.0015642256902761102, 0.0015282112845138051, 0.0014921968787515003, 0.0014561824729891959, 0.0014201680672268908, 0.001384153661464586, 0.0013481392557022811, 0.001312124849939976, 0.001276110444177671, 0.0012400960384153662, 0.001204081632653061, 0.0011680672268907562, 0.0011320528211284512, 0.0010960384153661466, 0.0010600240096038413, 0.0010240096038415364, 0.0009879951980792314, 0.0009519807923169266, 0.0009159663865546219, 0.000879951980792317, 0.000843937575030012, 0.000807923169267707, 0.0007719087635054024, 0.0007358943577430975, 0.0006998799519807925, 0.0006638655462184875, 0.0006278511404561825, 0.0005918367346938778, 0.0005558223289315727, 0.0005198079231692679, 0.0, 0.0, 0.0]
                  fiber_orientation:
                      grid: [0.0, 1.0]
                      values: [0.0, 0.0]

elastic properties mb

The equivalent elastic properties of the blade are defined in elastic_properties_mb. Here, 6x6 stiffness and mass matrices are defined in the same reference system used by the solver BeamDyn of OpenFAST. Out of 36 entries of the matrices, given the symmetry, the yaml file requires the definition of only 21 values as inputs. These are defined row by row, so first the six elements of the first row, then the five elements of the second row, and so on finishing with the sixth element of the sixth row. For a blade without extra-diagonal, the stiffness and mass matrices look like this:

K = [Kflap, 0, 0, 0, 0, 0, Kedge, 0, 0, 0,0, EA, 0, 0, 0, EIedge, 0, 0, EIflap, 0, GJ]

M = [m, 0, 0, 0, 0, -mYcm, m, 0, 0, 0,mXcm, m, mYcm, -mXcm, 0, iedge, -icp, 0, iflap, 0, iplr]

where KShrEdg and KShrFlp are the edge and flap shear stiffnesses, respectively; EA is the extension stiffness; EIEdg and EIFlp are the edge and flap stiffnesses, respectively; GJ is the torsional stiffness, m is the mass density per unit span, Xcm and Ycm are the local coordinates of the sectional center of mass, iedge and iflap are the edge and flap mass moments of inertia per unit span, iplr is the polar moment of inertia per unit span, and finally icp is the sectional cross product of inertia per unit span. Please note that for beam-like structures iplr must be equal to iedge plus iflap.

            six_x_six:
                reference_axis: *id001
                twist: *id002
                stiff_matrix:
                    grid: [0.0, 0.01, 0.02, 0.03, 0.04, 0.05, 0.075, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.95, 1.0]
                    values:
                       -  [6740375994.200792, 2653738.5919261174, 0.0, 0.0, 0.0, 148446683.0081474, 6729088765.395921, 0.0, 0.0, 0.0, 38985021.66520424, 46051081603.60474, -1092494742.1422234, 18829097.30285156, 0.0, 149629012637.96594, -22581466.165237263, 0.0, 149729095916.4146, 0.0, 87489183048.03288]
                       -  [6384592445.510168, -376400.6474385026, 0.0, 0.0, 0.0, -93807158.54721366, 6388480690.310746, 0.0, 0.0, 0.0, 16608264.93565775, 43751344063.19816, 582609637.8397082, 3336008.299362885, 0.0, 142328864112.50156, -232559270.06092423, 0.0, 143137826352.7965, 0.0, 83285587642.82162]
                       -  [6033428473.028316, -5351360.127132061, 0.0, 0.0, 0.0, -302258358.414727, 6055417688.515367, 0.0, 0.0, 0.0, 5594870.114677965, 41569662567.47037, 2071574619.5397494, -39669072.53786528, 0.0, 135212838311.38753, -606773042.4005727, 0.0, 137008541712.70963, 0.0, 79106159653.8364]
                       -  [5399937528.5606785, 2545105.3701622505, 0.0, 0.0, 0.0, -376430490.9109713, 5758216767.868562, 0.0, 0.0, 0.0, 19709135.853905857, 38669982721.7398, 2739604966.9813576, -139140684.30100253, 0.0, 123284345388.39743, -1348337968.6178887, 0.0, 119514275124.89417, 0.0, 69973323042.1117]
                       -  [4800672070.892391, 6445969.845348487, 0.0, 0.0, 0.0, -410026336.0979204, 5468722459.955154, 0.0, 0.0, 0.0, 28462348.93837689, 36038990116.73735, 3310499851.237116, -201959858.66306534, 0.0, 112223397786.61401, -2131730557.8957243, 0.0, 104365370041.97543, 0.0, 61533150488.50107]
                       -  [4245595846.60386, 6455163.702384659, 0.0, 0.0, 0.0, -423187047.4596364, 5195984070.294925, 0.0, 0.0, 0.0, 35814075.943787806, 33746441410.19616, 3921047165.837773, -248900545.30290735, 0.0, 102686583994.11134, -2938603122.299237, 0.0, 91978034767.20616, 0.0, 54135840079.7236]
                       -  [3015180949.0747685, -6056529.370011804, 0.0, 0.0, 0.0, -335581833.17485225, 4552086385.17254, 0.0, 0.0, 0.0, 53346766.10196565, 29212071034.730743, 5225114500.366909, -316621483.96654403, 0.0, 82456226297.96957, -4823615805.899531, 0.0, 68686121530.687454, 0.0, 38418612295.439545]
                       -  [2419253237.9808803, 113285786.00360973, 0.0, 0.0, 0.0, -235382612.4995677, 3985354344.8681536, 0.0, 0.0, 0.0, 87781196.91790846, 27339201435.297394, 8519455804.023233, -518317006.6590065, 0.0, 72781368868.39719, -6133557676.831683, 0.0, 52263394041.374664, 0.0, 25428346793.25849]
                       -  [936314786.8968203, 80833117.672499, 0.0, 0.0, 0.0, 110222775.82612513, 2314391966.661147, 0.0, 0.0, 0.0, 102518319.262035, 22665764106.85165, 10699908369.669474, -252339646.012082, 0.0, 54125167812.039314, -4839685559.488184, 0.0, 27988353518.859665, 0.0, 8076640558.8585005]
                       -  [459476847.22473943, 50723215.96362021, 0.0, 0.0, 0.0, 44624062.11459313, 963021463.3416004, 0.0, 0.0, 0.0, 63418511.854790874, 20450235425.96102, 9176487472.148022, -318201927.73381317, 0.0, 39196915729.85904, -3395447917.8743534, 0.0, 21820483410.15772, 0.0, 2768066330.973254]
                       -  [281350049.44872, 19062499.890864983, 0.0, 0.0, 0.0, 39788481.558390185, 480065126.665447, 0.0, 0.0, 0.0, 35649958.00142443, 20473859852.028965, 9004633626.168808, -370375609.629183, 0.0, 35299428705.26732, -1524671060.6524186, 0.0, 15615256841.106361, 0.0, 1026128471.8607168]
                       -  [224644322.01692382, 4177613.4992410876, 0.0, 0.0, 0.0, 22822651.106314287, 346901262.38535905, 0.0, 0.0, 0.0, 26944490.484182574, 21366371296.473003, 8306288511.852894, -349173302.5918751, 0.0, 31051165577.557346, -615674444.313989, 0.0, 13362814423.387623, 0.0, 627053086.269001]
                       -  [187672692.57290956, -2993741.656823819, 0.0, 0.0, 0.0, 14817252.655003047, 324078740.9094225, 0.0, 0.0, 0.0, 22977520.67687867, 21785402237.03918, 7885934214.420893, -281941707.05108696, 0.0, 26088284004.54947, -91553134.31292474, 0.0, 10663481378.13921, 0.0, 461211585.49078345]
                       -  [161609316.90177184, -3309906.622644328, 0.0, 0.0, 0.0, 14196051.945945216, 317531903.30316025, 0.0, 0.0, 0.0, 19104038.48691781, 21621041012.04207, 6912268845.2773905, -151464382.0873222, 0.0, 22217425410.95908, -10375272.853503438, 0.0, 8537806429.681531, 0.0, 364794590.1572093]
                       -  [137969183.99018735, -2612569.6184869376, 0.0, 0.0, 0.0, 10110737.414443506, 309152872.5553294, 0.0, 0.0, 0.0, 15276680.601082614, 20779461548.755814, 6380607368.417731, -81958836.22604564, 0.0, 18717308525.793583, 2259343.50512368, 0.0, 6549534664.533833, 0.0, 285660364.09887934]
                       -  [116600478.4523859, -1443459.826543158, 0.0, 0.0, 0.0, 9756447.07571729, 303218881.82122993, 0.0, 0.0, 0.0, 12426129.212282114, 19923519424.805744, 5510503208.482732, -145792800.15431416, 0.0, 15586807919.093891, -28845801.840308778, 0.0, 4893346064.323091, 0.0, 220544333.37495336]
                       -  [97422515.98334335, -997091.0381108759, 0.0, 0.0, 0.0, 7650615.789120105, 292909738.469172, 0.0, 0.0, 0.0, 11590547.025402421, 18925122694.713356, 4939813431.154279, -215770838.70957416, 0.0, 12739863625.745161, -43922352.51904449, 0.0, 3604017503.6991744, 0.0, 168037150.44173867]
                       -  [81358328.95851956, 122590.70890719072, 0.0, 0.0, 0.0, 7709138.634627286, 300285135.273037, 0.0, 0.0, 0.0, 12779793.365596209, 17539655765.235256, 3340368066.1970086, -299940988.574154, 0.0, 8379809772.736287, -29747619.287767652, 0.0, 2655217532.05773, 0.0, 128226839.00696014]
                       -  [67080158.82424255, 1150059.0011940901, 0.0, 0.0, 0.0, 8354890.671745444, 334604810.69196564, 0.0, 0.0, 0.0, 15336313.590033066, 15853197990.946262, 1772039285.1553001, -358354291.37689996, 0.0, 4637021573.468788, -2424421.8976960694, 0.0, 1917970315.4393296, 0.0, 95377930.58201036]
                       -  [55553240.58366735, 1941394.5823109567, 0.0, 0.0, 0.0, 8124277.187599225, 376257910.10373855, 0.0, 0.0, 0.0, 18041654.778164484, 14061229868.525568, 1013471013.85025, -411634704.48295814, 0.0, 2889083609.8505793, -12258851.347575188, 0.0, 1351951128.6929338, 0.0, 71456369.55600888]
                       -  [44994384.56866734, 2180662.5761736603, 0.0, 0.0, 0.0, 7061108.353385276, 395913126.7681885, 0.0, 0.0, 0.0, 19527620.335504133, 11003024089.793188, 625226575.7818947, -386594144.7272241, 0.0, 1877272361.936434, -15695344.266583264, 0.0, 838106592.74152, 0.0, 52519301.176315226]
                       -  [36509915.3832926, 2151842.3143516458, 0.0, 0.0, 0.0, 6124281.751202558, 375210610.3003366, 0.0, 0.0, 0.0, 17825049.8174219, 7310260724.863415, 354179115.2888132, -261309728.4735774, 0.0, 1099701983.6863494, -6469059.311161065, 0.0, 466233432.88131785, 0.0, 38106482.51374478]
                       -  [27272722.33611301, 993432.1718194059, 0.0, 0.0, 0.0, 3331136.312449322, 239673891.33303756, 0.0, 0.0, 0.0, 10738401.632739767, 4521289678.947009, 266089109.4029744, -148760396.98544225, 0.0, 683571619.6771157, -4841801.236680448, 0.0, 243066553.44047254, 0.0, 23330158.861795776]
                       -  [19745236.354008205, 510321.8004162957, 0.0, 0.0, 0.0, 1832045.8991628585, 144312493.8658793, 0.0, 0.0, 0.0, 6016948.89773326, 2675615584.13509, 184789087.68407992, -79832450.74825534, 0.0, 420297066.7672982, -4125365.2248271434, 0.0, 113253467.97005808, 0.0, 13417874.462175902]
                       -  [9179700.675681142, 307950.61736175837, 0.0, 0.0, 0.0, 1267110.0781497026, 86939021.67477001, 0.0, 0.0, 0.0, 3396279.8195240535, 1203040036.154266, 137345812.75625196, -31896540.37930602, 0.0, 231512293.70712498, -3561131.725327512, 0.0, 36395660.02090348, 0.0, 6805118.090718728]
                       -  [931474.1817045894, 232415.29456365184, 0.0, 0.0, 0.0, 106353.52899654783, 15879263.61054028, 0.0, 0.0, 0.0, 117375.6660814398, 118283403.93224278, 1168848.1431805997, -795943.4168930704, 0.0, 1384839.7699354952, -26483.691742438405, 0.0, 186239.91293931668, 0.0, 71452.33631373737]
                inertia_matrix:
                    grid: [0.0, 0.01, 0.02, 0.03, 0.04, 0.05, 0.075, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.95, 1.0]
                    values:
                       -  [3127.4021155424143, 0.0, 0.0, 0.0, 0.0, 73.93195471060494, 3127.4021155424143, 0.0, 0.0, 0.0, -0.23227931035313248, 3127.4021155424143, -73.93195471060494, 0.23227931035313248, 0.0, 10167.976322208995, 1.0683130734106165, 0.0, 10166.284427210068, 0.0, 20334.260749419092]
                       -  [2964.7325318133635, 0.0, 0.0, 0.0, 0.0, -39.689341530367614, 2964.7325318133635, 0.0, 0.0, 0.0, -0.1696455253166024, 2964.7325318133635, 39.689341530367614, 0.1696455253166024, 0.0, 9670.817488009772, -0.9133955577605082, 0.0, 9677.506658278195, 0.0, 19348.32414628797]
                       -  [2805.1273323852683, 0.0, 0.0, 0.0, 0.0, -140.75148902158406, 2805.1273323852683, 0.0, 0.0, 0.0, 2.405715769683996, 2805.1273323852683, 140.75148902158406, -2.405715769683996, 0.0, 9183.723741815673, -6.143364484361837, 0.0, 9189.979166446146, 0.0, 18373.702908261756]
                       -  [2591.1367835087917, 0.0, 0.0, 0.0, 0.0, -186.50710374919134, 2591.1367835087917, 0.0, 0.0, 0.0, 8.850322233785226, 2591.1367835087917, 186.50710374919134, -8.850322233785226, 0.0, 8366.670547933158, -30.1760176639648, 0.0, 7913.55513775584, 0.0, 16280.22568568902]
                       -  [2389.1154059162695, 0.0, 0.0, 0.0, 0.0, -225.67253185892582, 2389.1154059162695, 0.0, 0.0, 0.0, 12.729809187017585, 2389.1154059162695, 225.67253185892582, -12.729809187017585, 0.0, 7605.999205249705, -51.13814800535637, 0.0, 6778.707874270462, 0.0, 14384.707079520182]
                       -  [2203.52246956623, 0.0, 0.0, 0.0, 0.0, -266.66982245842087, 2203.52246956623, 0.0, 0.0, 0.0, 15.77615497545956, 2203.52246956623, 266.66982245842087, -15.77615497545956, 0.0, 6947.021691181144, -69.34293642402783, 0.0, 5816.730513104689, 0.0, 12763.75220428584]
                       -  [1793.5621800535478, 0.0, 0.0, 0.0, 0.0, -349.63893753405364, 1793.5621800535478, 0.0, 0.0, 0.0, 21.32062998431816, 1793.5621800535478, 349.63893753405364, -21.32062998431816, 0.0, 5542.22198919525, -103.28185672319495, 0.0, 3914.596828171232, 0.0, 9456.81881736644]
                       -  [1694.5071226473444, 0.0, 0.0, 0.0, 0.0, -525.4310002430254, 1694.5071226473444, 0.0, 0.0, 0.0, 33.63149776511567, 1694.5071226473444, 525.4310002430254, -33.63149776511567, 0.0, 4883.611585776837, -159.42251092667695, 0.0, 2785.9557474336307, 0.0, 7669.567333210458]
                       -  [1050.5041617289855, 0.0, 0.0, 0.0, 0.0, -610.1711896797851, 1050.5041617289855, 0.0, 0.0, 0.0, 24.488449094119666, 1050.5041617289855, 610.1711896797851, -24.488449094119666, 0.0, 3320.886520496825, -109.41235764515795, 0.0, 956.3088698304845, 0.0, 4277.195390327287]
                       -  [668.8389205216013, 0.0, 0.0, 0.0, 0.0, -519.3241440864526, 668.8389205216013, 0.0, 0.0, 0.0, 20.275144559753706, 668.8389205216013, 519.3241440864526, -20.275144559753706, 0.0, 2253.558667409682, -74.25657502591736, 0.0, 476.36366817186706, 0.0, 2729.9223355815425]
                       -  [531.0612749513001, 0.0, 0.0, 0.0, 0.0, -469.18731596545734, 531.0612749513001, 0.0, 0.0, 0.0, 18.40686653041935, 531.0612749513001, 469.18731596545734, -18.40686653041935, 0.0, 1848.5783850624332, -51.00047866730059, 0.0, 268.55950272107657, 0.0, 2117.1378877835145]
                       -  [483.98515809475083, 0.0, 0.0, 0.0, 0.0, -429.5473703129163, 483.98515809475083, 0.0, 0.0, 0.0, 15.24938260415129, 483.98515809475083, 429.5473703129163, -15.24938260415129, 0.0, 1564.7359685439142, -34.07084223757462, 0.0, 204.06774305708595, 0.0, 1768.8037116010007]
                       -  [458.0838867335805, 0.0, 0.0, 0.0, 0.0, -387.99790618434287, 458.0838867335805, 0.0, 0.0, 0.0, 12.541536147390817, 458.0838867335805, 387.99790618434287, -12.541536147390817, 0.0, 1286.7175819089484, -23.38641910057473, 0.0, 154.74717074687635, 0.0, 1441.4647526558301]
                       -  [433.8716017058155, 0.0, 0.0, 0.0, 0.0, -345.8892017251126, 433.8716017058155, 0.0, 0.0, 0.0, 9.385100666405265, 433.8716017058155, 345.8892017251126, -9.385100666405265, 0.0, 1076.1432859614897, -18.75152324183863, 0.0, 120.1630106896849, 0.0, 1196.3062966511723]
                       -  [404.9178066535816, 0.0, 0.0, 0.0, 0.0, -311.07188808957676, 404.9178066535816, 0.0, 0.0, 0.0, 7.475763615859694, 404.9178066535816, 311.07188808957676, -7.475763615859694, 0.0, 895.7513821150329, -15.603626309920882, 0.0, 90.50849177530833, 0.0, 986.2598738903342]
                       -  [377.73123303078404, 0.0, 0.0, 0.0, 0.0, -272.8500883723055, 377.73123303078404, 0.0, 0.0, 0.0, 7.8155616062122695, 377.73123303078404, 272.8500883723055, -7.8155616062122695, 0.0, 735.407926823897, -13.644216263894043, 0.0, 66.51587194758397, 0.0, 801.9237987714802]
                       -  [350.48434003585845, 0.0, 0.0, 0.0, 0.0, -237.97949220138435, 350.48434003585845, 0.0, 0.0, 0.0, 8.182976209383485, 350.48434003585845, 237.97949220138435, -8.182976209383485, 0.0, 593.1078000418055, -11.662250592755035, 0.0, 48.3879168461972, 0.0, 641.4957168880029]
                       -  [307.3478250743852, 0.0, 0.0, 0.0, 0.0, -164.7291992520334, 307.3478250743852, 0.0, 0.0, 0.0, 7.95168602738849, 307.3478250743852, 164.7291992520334, -7.95168602738849, 0.0, 389.10967484563156, -7.836966520296293, 0.0, 35.22217015645534, 0.0, 424.3318450020865]
                       -  [260.2653356372791, 0.0, 0.0, 0.0, 0.0, -93.43468152003294, 260.2653356372791, 0.0, 0.0, 0.0, 7.292661316519065, 260.2653356372791, 93.43468152003294, -7.292661316519065, 0.0, 215.46936888932268, -4.176133069084764, 0.0, 25.215546621059765, 0.0, 240.68491551038218]
                       -  [223.94256194555769, 0.0, 0.0, 0.0, 0.0, -57.93504767403098, 223.94256194555769, 0.0, 0.0, 0.0, 7.223037382444947, 223.94256194555769, 57.93504767403098, -7.223037382444947, 0.0, 131.65454148509653, -2.6421037604616724, 0.0, 17.745330077956677, 0.0, 149.39987156305426]
                       -  [179.58407067190126, 0.0, 0.0, 0.0, 0.0, -38.0523975504382, 179.58407067190126, 0.0, 0.0, 0.0, 6.572357722853001, 179.58407067190126, 38.0523975504382, -6.572357722853001, 0.0, 84.64962149907886, -1.7996118776795522, 0.0, 11.271194923324614, 0.0, 95.92081642240376]
                       -  [129.3080054809469, 0.0, 0.0, 0.0, 0.0, -23.226025130813625, 129.3080054809469, 0.0, 0.0, 0.0, 4.71916228979406, 129.3080054809469, 23.226025130813625, -4.71916228979406, 0.0, 51.45480233093064, -1.0405277605856154, 0.0, 6.684580575763557, 0.0, 58.13938290669439]
                       -  [84.45573745266202, 0.0, 0.0, 0.0, 0.0, -16.39546225863475, 84.45573745266202, 0.0, 0.0, 0.0, 2.8210572700220213, 84.45573745266202, 16.39546225863475, -2.8210572700220213, 0.0, 31.507539581364625, -0.6232077662449509, 0.0, 3.616337664050583, 0.0, 35.1238772454151]
                       -  [54.70473032506861, 0.0, 0.0, 0.0, 0.0, -11.033185396820333, 54.70473032506861, 0.0, 0.0, 0.0, 1.6418254028409995, 54.70473032506861, 11.033185396820333, -1.6418254028409995, 0.0, 19.31985607950643, -0.36848755076490375, 0.0, 1.78333715736047, 0.0, 21.103193236866915]
                       -  [34.44992885232661, 0.0, 0.0, 0.0, 0.0, -8.119492797706668, 34.44992885232661, 0.0, 0.0, 0.0, 0.916505016263078, 34.44992885232661, 8.119492797706668, -0.916505016263078, 0.0, 12.262821999907853, -0.24956166062622986, 0.0, 0.7573836161406937, 0.0, 13.020205616048557]
                       -  [5.394970691335722, 0.0, 0.0, 0.0, 0.0, -0.1588859366089294, 5.394970691335722, 0.0, 0.0, 0.0, 0.036961089182658016, 5.394970691335722, 0.1588859366089294, -0.036961089182658016, 0.0, 0.09373427692288798, -0.0022768326051883147, 0.0, 0.007180810431802968, 0.0, 0.10091508735469075]

Lofted Shape

This is work in progress. lofted_shape will consist of a dictionary containing the 3D points describing the outer lofted shape of the blade