.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "gallery/plot_bicycle.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_gallery_plot_bicycle.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_gallery_plot_bicycle.py:


==============
Using Bicycles
==============

.. GENERATED FROM PYTHON SOURCE LINES 7-14

.. code-block:: Python

    import pprint
    from pathlib import Path

    import numpy as np
    import bicycleparameters as bp
    from bicycleparameters import Bicycle, tables








.. GENERATED FROM PYTHON SOURCE LINES 15-20

Loading Bicycle Data
====================

To load the data from one of the bicycles in the data folder, instantiate a
:py:class:`~bicycleparameters.main.Bicycle` object using the bicycle's name:

.. GENERATED FROM PYTHON SOURCE LINES 20-22

.. code-block:: Python

    bicycle = Bicycle('Stratos', pathToData='../data')





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Found the RawData directory: ../data/bicycles/Stratos/RawData
    Recalcuting the parameters.
    The glory of the Stratos parameters are upon you!




.. GENERATED FROM PYTHON SOURCE LINES 23-50

This will create an instance of the Bicycle class in the variable bicycle
based off of input data from the ``./bicycles/Stratos/`` directory. The
program first looks to see if there are any parameter sets in
``./bicycles/Stratos/Parameters/``. If so, it loads the data, if not it looks
for ``./bicycles/Stratos/RawData/StratosMeasurments.txt`` so that it can
generate the parameter set. The raw measurement file may or may not contain
the oscillation period data for the bicycle moment of inertia calculations.
If it doesn't then the program will look for the series of ``.mat`` files
need to calculate the periods. If no data is there, then you get an error.

There are other loading options::

    bicycle = Bicycle('Stratos', pathToData='..', forceRawCalc=True,
                         forcePeriodCalc=True)

The ``pathToData`` option allows you specify a directory other than the
current directory as your data directory. The ``forceRawCalc`` forces the
program to load ``./bicycles/Stratos/RawData/StratosMeasurments.txt`` and
recalculate the parameters regardless if there are any parameter files
available in ``./bicycles/Stratos/Parameters/``. The ``forcePeriodCalc``
option forces the period calculation from the ``.mat`` files regardless if
they already exist in the raw measurement file.

Exploring Bicycle Parameter Data
================================

The bicycle has a name:

.. GENERATED FROM PYTHON SOURCE LINES 50-52

.. code-block:: Python

    bicycle.bicycleName





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    'Stratos'



.. GENERATED FROM PYTHON SOURCE LINES 53-54

and a directory where its data is sourced:

.. GENERATED FROM PYTHON SOURCE LINES 54-56

.. code-block:: Python

    bicycle.directory





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    '../data/bicycles/Stratos'



.. GENERATED FROM PYTHON SOURCE LINES 57-60

The benchmark bicycle parameters from [Meijaard2007]_ are the fundamental
parameter set that is used behind the scenes for calculations. To access them
type:

.. GENERATED FROM PYTHON SOURCE LINES 60-63

.. code-block:: Python

    b_par = bicycle.parameters['Benchmark']
    pprint.pprint(b_par)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    {'IBxx': 0.3728775783567887+/-0.0015667031268957702,
     'IBxz': -0.03834761674810283+/-0.00041198945835815804,
     'IByy': 0.7171736482966189+/-0.0031346383690536894,
     'IBzz': 0.45472945576461815+/-0.0018865067694859123,
     'IFxx': 0.09156382237275022+/-0.00037264374475717767,
     'IFyy': 0.15678445500719673+/-0.0011443558970956002,
     'IHxx': 0.17684141949871102+/-0.0008247358323528924,
     'IHxz': -0.027331980252591023+/-0.000575667418054312,
     'IHyy': 0.14362051582791002+/-0.002481616129881456,
     'IHzz': 0.044632358231408514+/-0.00030908148376534593,
     'IRxx': 0.09387109992870839+/-0.000382033804274545,
     'IRyy': 0.1542264480253569+/-0.0011387182056513865,
     'c': 0.05626998711805831+/-0.0016271109815356594,
     'g': 9.81+/-0.01,
     'lam': 0.29496064358704177+/-0.003490658503988659,
     'mB': 7.22+/-0.02,
     'mF': 3.334+/-0.02,
     'mH': 3.04+/-0.02,
     'mR': 3.96+/-0.02,
     'rF': 0.340003929196009+/-0.00012242687930145795,
     'rR': 0.338477091115578+/-0.00011368210220849667,
     'w': 1.037+/-0.002,
     'xB': 0.32631503794489763+/-0.0032538862692938647,
     'xH': 0.9106573267080197+/-0.0037388403092143935,
     'zB': -0.48263958289208314+/-0.0026376802487648857,
     'zH': -0.7302812158759062+/-0.0024284656294034685}




.. GENERATED FROM PYTHON SOURCE LINES 64-66

.. code-block:: Python

    b_par['xB']





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    0.32631503794489763+/-0.0032538862692938647



.. GENERATED FROM PYTHON SOURCE LINES 67-71

The program automatically calculates the uncertainties in the parameters
based on the raw measurements or the uncertainties provided in the parameter
files. If you'd like to work with the pure values you can remove them from
the entire dictionary:

.. GENERATED FROM PYTHON SOURCE LINES 71-74

.. code-block:: Python

    b_par_pure = bp.io.remove_uncertainties(b_par)
    b_par_pure['xB']





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    0.32631503794489763



.. GENERATED FROM PYTHON SOURCE LINES 75-76

or any single uncertainity quantity's nominal value can be extracted with:

.. GENERATED FROM PYTHON SOURCE LINES 76-78

.. code-block:: Python

    b_par['xB'].nominal_value





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    0.32631503794489763



.. GENERATED FROM PYTHON SOURCE LINES 79-85

That goes the same for all values with uncertainties. Check out the
`uncertainties <http://packages.python.org/uncertainties>`_ package details
for more ways to manipulate the quantities.

If the bicycle was calculated from raw data measurements you can access them
by:

.. GENERATED FROM PYTHON SOURCE LINES 85-87

.. code-block:: Python

    pprint.pprint(bicycle.parameters['Measured'])





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    {'LhbF': np.float64(0.6552),
     'LhbR': np.float64(1.1014),
     'TcB1': 1.59880197567+/-6.3096072159e-06,
     'TcF1': 1.35366619175+/-5.30396954785e-06,
     'TcH1': 1.45406634451+/-1.95301826402e-05,
     'TcR1': 1.31217723331+/-7.33295949904e-06,
     'TtB1': 1.815949139+/-1.36701497554e-05,
     'TtB2': 1.58519804957+/-9.16825068389e-06,
     'TtB3': 1.66019943538+/-8.06563293967e-06,
     'TtF1': 0.801625248455+/-1.12728802487e-06,
     'TtH1': 1.01149389309+/-4.48284908821e-06,
     'TtH2': 0.525350778277+/-2.21244434089e-06,
     'TtH3': 1.08603695606+/-5.66372430716e-06,
     'TtP1': 1.89399317145+/-5.93377589066e-06,
     'TtR1': 0.811662317594+/-9.30058972579e-07,
     'aB1': 0.249+/-0.003,
     'aB2': -0.267+/-0.003,
     'aB3': -0.071+/-0.003,
     'aH1': 0.329+/-0.003,
     'aH2': -0.038+/-0.003,
     'aH3': 0.4+/-0.003,
     'alphaB1': 128.9+/-0.2,
     'alphaB2': 221.6+/-0.2,
     'alphaB3': 184.5+/-0.2,
     'alphaH1': 36.0+/-0.2,
     'alphaH2': 94.0+/-0.2,
     'alphaH3': 347.3+/-0.2,
     'dF': 27.772+/-0.01,
     'dP': 0.03+/-0.0001,
     'dR': 29.774+/-0.01,
     'f': 0.045+/-0.001,
     'g': 9.81+/-0.01,
     'gamma': 73.1+/-0.2,
     'hbb': np.float64(0.29),
     'lF': 0.297+/-0.001,
     'lP': 1.05+/-0.001,
     'lR': 0.2965+/-0.001,
     'lamst': np.float64(1.308996939),
     'lcs': np.float64(0.445),
     'lsp': np.float64(0.195),
     'lst': np.float64(0.48),
     'mB': 7.22+/-0.02,
     'mF': 3.334+/-0.02,
     'mH': 3.04+/-0.02,
     'mP': 5.56+/-0.02,
     'mR': 3.96+/-0.02,
     'nF': np.float64(13.0),
     'nR': np.float64(14.0),
     'w': 1.037+/-0.002,
     'whb': np.float64(0.58)}




.. GENERATED FROM PYTHON SOURCE LINES 88-90

All parameter sets are stored in the parameter dictionary of the bicycle
instance, which is mutable. To modify a parameter type:

.. GENERATED FROM PYTHON SOURCE LINES 90-93

.. code-block:: Python

    bicycle.parameters['Benchmark']['mB'] = 50.0
    bicycle.parameters['Benchmark']['mB']





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    50.0



.. GENERATED FROM PYTHON SOURCE LINES 94-96

You can regenerate the parameter sets from the raw data stored in the
bicycle's directory by calling and resetting the parameters:

.. GENERATED FROM PYTHON SOURCE LINES 96-100

.. code-block:: Python

    par, extra = bicycle.calculate_from_measured()
    bicycle.parameters['Benchmark'] = par
    bicycle.parameters['Benchmark']['mB']





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    7.22+/-0.02



.. GENERATED FROM PYTHON SOURCE LINES 101-108

Basic Linear Model Analysis
===========================

The :py:class:`~bicycleparameters.main.Bicycle` object has some basic bicycle
analysis tools based on the linear Carvallo-Whipple bicycle model which has
been linearized about the upright configuration. For example, the canonical
coefficient matrices for the equations of motion can be computed:

.. GENERATED FROM PYTHON SOURCE LINES 108-111

.. code-block:: Python

    M, C1, K0, K2 = bicycle.canonical()
    M





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    array([[4.8773556938672025+/-0.023934341307719046,
            0.40791147549242046+/-0.008524955893962296],
           [0.40791147549242046+/-0.008524955893962296,
            0.20324563385641692+/-0.002358205055360836]], dtype=object)



.. GENERATED FROM PYTHON SOURCE LINES 112-114

.. code-block:: Python

    C1





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    array([[0.0, 4.852002528879055+/-0.024294894019445835],
           [-0.4888089303250309+/-0.0035871046725125507,
            0.7514232981989066+/-0.011819041279142298]], dtype=object)



.. GENERATED FROM PYTHON SOURCE LINES 115-117

.. code-block:: Python

    K0





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    array([[-8.178655065500777+/-0.028197632940217446,
            -0.7097919259369844+/-0.013158888467975648],
           [-0.7097919259369844+/-0.013158888467975648,
            -0.20633806986820977+/-0.005713958418318107]], dtype=object)



.. GENERATED FROM PYTHON SOURCE LINES 118-120

.. code-block:: Python

    K2





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    array([[0.0, 8.392121154615824+/-0.03139795630613271],
           [0.0, 0.7785916890571186+/-0.01280424781722948]], dtype=object)



.. GENERATED FROM PYTHON SOURCE LINES 121-123

as well as the state and input matrices for state space form at a particular
speed, here 1.34 m/s:

.. GENERATED FROM PYTHON SOURCE LINES 123-126

.. code-block:: Python

    A, B = bicycle.state_space(1.34)
    A





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    array([[0.0, 0.0, 1.0, 0.0],
           [0.0, 0.0, 0.0, 1.0],
           [16.324961318973738+/-0.03920451667799798,
            -2.3067790729148077+/-0.008241250090249008,
            -0.32389448988643155+/-0.005780051411844571,
            -1.1040117448741378+/-0.006841363234149875],
           [1.4953321687453922+/-0.15383983178776262,
            7.710369241737173+/-0.17069943546538485,
            3.87277321029708+/-0.03422655386074032,
            -2.7384015548749843+/-0.01336660103231202]], dtype=object)



.. GENERATED FROM PYTHON SOURCE LINES 127-129

.. code-block:: Python

    B





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    array([[0.0, 0.0],
           [0.0, 0.0],
           [0.24638537845620434+/-0.001697618784429188,
            -0.49449240979429593+/-0.007709061622436666],
           [-0.49449240979429593+/-0.007709061622436666,
            5.912595049141093+/-0.04018667284347065]], dtype=object)



.. GENERATED FROM PYTHON SOURCE LINES 130-132

You can calculate the eigenvalues and eigenvectors at any speed, e.g. 4.28
m/s, by calling:

.. GENERATED FROM PYTHON SOURCE LINES 132-134

.. code-block:: Python

    w, v = bicycle.eig(4.28)








.. GENERATED FROM PYTHON SOURCE LINES 135-136

eigenvalues:

.. GENERATED FROM PYTHON SOURCE LINES 136-138

.. code-block:: Python

    w





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    array([[-8.66347234+0.j        , -0.45211147+5.10373643j,
            -0.45211147-5.10373643j, -0.2133697 +0.j        ]])



.. GENERATED FROM PYTHON SOURCE LINES 139-140

eigenvectors:

.. GENERATED FROM PYTHON SOURCE LINES 140-142

.. code-block:: Python

    v





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    array([[[-0.00101381+0.j        ,  0.05594369-0.10482217j,
              0.05594369+0.10482217j,  0.85255206+0.j        ],
            [-0.11466133+0.j        , -0.0132583 -0.14966855j,
             -0.0132583 +0.14966855j,  0.47917718+0.j        ],
            [ 0.00878309+0.j        ,  0.50969192+0.33291314j,
              0.50969192-0.33291314j, -0.18190878+0.j        ],
            [ 0.99336529+0.j        ,  0.76986307+0.j        ,
              0.76986307-0.j        , -0.10224189+0.j        ]]])



.. GENERATED FROM PYTHON SOURCE LINES 143-150

The ``eig`` function also accepts a one dimensional array of speeds and
returns eigenvalues for all speeds. Note that uncertainty propagation into
the eigenvalue calculations is not supported yet.

The moment of inertia of the steer assembly (handlebar, fork and/or front
wheel) can be computed either about the center of mass or a point on the
steer axis, both with reference to a frame aligned with the steer axis:

.. GENERATED FROM PYTHON SOURCE LINES 150-152

.. code-block:: Python

    bicycle.steer_assembly_moment_of_inertia(aboutSteerAxis=True)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    handlebar cg distance 0.0415+/-0.0017

    array([[0.5399312058364284+/-0.0036287086418513004, 0.0+/-0,
            0.009214223478727322+/-0.001917537419751651],
           [0.0+/-0, 0.5789408520638009+/-0.0031152577644247338, 0.0+/-0],
           [0.00921422347872733+/-0.0019175374197516507, 0.0+/-0,
            0.14320609786788568+/-0.0010027929120792374]], dtype=object)



.. GENERATED FROM PYTHON SOURCE LINES 153-158

Plots
=====
You can plot the geometry of the bicycle and include the mass centers of the
various bodies, the inertia ellipsoids and the torsional pendulum axes from
the raw measurement data:

.. GENERATED FROM PYTHON SOURCE LINES 158-160

.. code-block:: Python

    _ = bicycle.plot_bicycle_geometry()




.. image-sg:: /gallery/images/sphx_glr_plot_bicycle_001.png
   :alt: Stratos Bicycle Geometry
   :srcset: /gallery/images/sphx_glr_plot_bicycle_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 161-162

A Bode plot for any input output pair can be generated with:

.. GENERATED FROM PYTHON SOURCE LINES 162-164

.. code-block:: Python

    _ = bicycle.plot_bode(3.0, 1, 2)




.. image-sg:: /gallery/images/sphx_glr_plot_bicycle_002.png
   :alt: Steer Torque to Roll Rate
   :srcset: /gallery/images/sphx_glr_plot_bicycle_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 165-167

For visualization of the linear analysis you can plot the root loci of the
real and imaginary parts of the eigenvalues as a function of speed:

.. GENERATED FROM PYTHON SOURCE LINES 167-170

.. code-block:: Python

    speeds = np.linspace(0., 10., num=100)
    _ = bicycle.plot_eigenvalues_vs_speed(speeds)




.. image-sg:: /gallery/images/sphx_glr_plot_bicycle_003.png
   :alt: Stratos Eigenvalues vs Speed
   :srcset: /gallery/images/sphx_glr_plot_bicycle_003.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 171-172

You can also compare the eigenvalues of two or more bicycles:

.. GENERATED FROM PYTHON SOURCE LINES 172-175

.. code-block:: Python

    yellowrev = Bicycle('Yellowrev', pathToData='../data')
    _ = bp.plot_eigenvalues([bicycle, yellowrev], speeds)




.. image-sg:: /gallery/images/sphx_glr_plot_bicycle_004.png
   :alt: Eigenvalues vs Speed
   :srcset: /gallery/images/sphx_glr_plot_bicycle_004.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Found the RawData directory: ../data/bicycles/Yellowrev/RawData
    Looks like you've already got some parameters for Yellowrev, use forceRawCalc to recalculate.




.. GENERATED FROM PYTHON SOURCE LINES 176-180

Tables
======
You can generate reStructuredText tables of the bicycle parameters with the
``Table`` class:

.. GENERATED FROM PYTHON SOURCE LINES 180-184

.. code-block:: Python

    tab = tables.Table('Benchmark', False, (bicycle, yellowrev))
    rst = tab.create_rst_table()
    print(rst)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    +----------+------------------+------------------+
    |          | Stratos          | Yellowrev        |
    +==========+=========+========+=========+========+
    | Variable | v       | sigma  | v       | sigma  |
    +----------+---------+--------+---------+--------+
    | c        | 0.056   | 0.002  | 0.180   | 0.002  |
    +----------+---------+--------+---------+--------+
    | g        | 9.81    | 0.01   | 9.81    | 0.01   |
    +----------+---------+--------+---------+--------+
    | IBxx     | 0.373   | 0.002  | 0.2254  | 0.0009 |
    +----------+---------+--------+---------+--------+
    | IBxz     | -0.0383 | 0.0004 | 0.0179  | 0.0001 |
    +----------+---------+--------+---------+--------+
    | IByy     | 0.717   | 0.003  | 0.388   | 0.005  |
    +----------+---------+--------+---------+--------+
    | IBzz     | 0.455   | 0.002  | 0.2147  | 0.0009 |
    +----------+---------+--------+---------+--------+
    | IFxx     | 0.0916  | 0.0004 | 0.0852  | 0.0003 |
    +----------+---------+--------+---------+--------+
    | IFyy     | 0.157   | 0.001  | 0.147   | 0.002  |
    +----------+---------+--------+---------+--------+
    | IFzz     | 0.0916  | 0.0004 | NA      | NA     |
    +----------+---------+--------+---------+--------+
    | IHxx     | 0.1768  | 0.0008 | 0.1475  | 0.0006 |
    +----------+---------+--------+---------+--------+
    | IHxz     | -0.0273 | 0.0006 | -0.0172 | 0.0005 |
    +----------+---------+--------+---------+--------+
    | IHyy     | 0.144   | 0.002  | 0.120   | 0.002  |
    +----------+---------+--------+---------+--------+
    | IHzz     | 0.0446  | 0.0003 | 0.0294  | 0.0004 |
    +----------+---------+--------+---------+--------+
    | IRxx     | 0.0939  | 0.0004 | 0.0877  | 0.0004 |
    +----------+---------+--------+---------+--------+
    | IRyy     | 0.154   | 0.001  | 0.149   | 0.001  |
    +----------+---------+--------+---------+--------+
    | IRzz     | 0.0939  | 0.0004 | NA      | NA     |
    +----------+---------+--------+---------+--------+
    | lam      | 0.295   | 0.003  | 0.339   | 0.003  |
    +----------+---------+--------+---------+--------+
    | mB       | 7.22    | 0.02   | 3.31    | 0.02   |
    +----------+---------+--------+---------+--------+
    | mF       | 3.33    | 0.02   | 1.90    | 0.02   |
    +----------+---------+--------+---------+--------+
    | mH       | 3.04    | 0.02   | 2.45    | 0.02   |
    +----------+---------+--------+---------+--------+
    | mR       | 3.96    | 0.02   | 2.57    | 0.02   |
    +----------+---------+--------+---------+--------+
    | rF       | 0.3400  | 0.0001 | 0.3419  | 0.0001 |
    +----------+---------+--------+---------+--------+
    | rR       | 0.3385  | 0.0001 | 0.3414  | 0.0001 |
    +----------+---------+--------+---------+--------+
    | w        | 1.037   | 0.002  | 0.985   | 0.002  |
    +----------+---------+--------+---------+--------+
    | xB       | 0.326   | 0.003  | 0.412   | 0.004  |
    +----------+---------+--------+---------+--------+
    | xH       | 0.911   | 0.004  | 0.919   | 0.005  |
    +----------+---------+--------+---------+--------+
    | zB       | -0.483  | 0.003  | -0.618  | 0.004  |
    +----------+---------+--------+---------+--------+
    | zH       | -0.730  | 0.002  | -0.816  | 0.002  |
    +----------+---------+--------+---------+--------+




.. GENERATED FROM PYTHON SOURCE LINES 185-264

Which renders in Sphinx like:

+----------+------------------+------------------+
|          | Stratos          | Yellowrev        |
+==========+=========+========+=========+========+
| Variable | v       | sigma  | v       | sigma  |
+----------+---------+--------+---------+--------+
| IBxx     | 0.373   | 0.002  | 0.2254  | 0.0009 |
+----------+---------+--------+---------+--------+
| IBxz     | -0.0383 | 0.0004 | 0.0179  | 0.0001 |
+----------+---------+--------+---------+--------+
| IByy     | 0.717   | 0.003  | 0.388   | 0.005  |
+----------+---------+--------+---------+--------+
| IBzz     | 0.455   | 0.002  | 0.2147  | 0.0009 |
+----------+---------+--------+---------+--------+
| IFxx     | 0.0916  | 0.0004 | 0.0852  | 0.0003 |
+----------+---------+--------+---------+--------+
| IFyy     | 0.157   | 0.001  | 0.147   | 0.002  |
+----------+---------+--------+---------+--------+
| IHxx     | 0.1768  | 0.0008 | 0.1475  | 0.0006 |
+----------+---------+--------+---------+--------+
| IHxz     | -0.0273 | 0.0006 | -0.0172 | 0.0005 |
+----------+---------+--------+---------+--------+
| IHyy     | 0.144   | 0.002  | 0.120   | 0.002  |
+----------+---------+--------+---------+--------+
| IHzz     | 0.0446  | 0.0003 | 0.0294  | 0.0004 |
+----------+---------+--------+---------+--------+
| IRxx     | 0.0939  | 0.0004 | 0.0877  | 0.0004 |
+----------+---------+--------+---------+--------+
| IRyy     | 0.154   | 0.001  | 0.149   | 0.001  |
+----------+---------+--------+---------+--------+
| c        | 0.056   | 0.002  | 0.180   | 0.002  |
+----------+---------+--------+---------+--------+
| g        | 9.81    | 0.01   | 9.81    | 0.01   |
+----------+---------+--------+---------+--------+
| lam      | 0.295   | 0.003  | 0.339   | 0.003  |
+----------+---------+--------+---------+--------+
| mB       | 7.22    | 0.02   | 3.31    | 0.02   |
+----------+---------+--------+---------+--------+
| mF       | 3.33    | 0.02   | 1.90    | 0.02   |
+----------+---------+--------+---------+--------+
| mH       | 3.04    | 0.02   | 2.45    | 0.02   |
+----------+---------+--------+---------+--------+
| mR       | 3.96    | 0.02   | 2.57    | 0.02   |
+----------+---------+--------+---------+--------+
| rF       | 0.3400  | 0.0001 | 0.3419  | 0.0001 |
+----------+---------+--------+---------+--------+
| rR       | 0.3385  | 0.0001 | 0.3414  | 0.0001 |
+----------+---------+--------+---------+--------+
| w        | 1.037   | 0.002  | 0.985   | 0.002  |
+----------+---------+--------+---------+--------+
| xB       | 0.326   | 0.003  | 0.412   | 0.004  |
+----------+---------+--------+---------+--------+
| xH       | 0.911   | 0.004  | 0.919   | 0.005  |
+----------+---------+--------+---------+--------+
| zB       | -0.483  | 0.003  | -0.618  | 0.004  |
+----------+---------+--------+---------+--------+
| zH       | -0.730  | 0.002  | -0.816  | 0.002  |
+----------+---------+--------+---------+--------+

Adding a Rigid Rider
====================
The program also allows one to add the inertial affects of a rigid rider to
the Whipple bicycle model.

Rider Data
----------
You can provide rider data in one of two ways, much in the same way as the
bicycle. If you have the inertial parameters of a rider, e.g. Jason, simply
add a file into the ``./riders/Jason/Parameters/`` directory. Or if you have
raw measurements of the rider add the two files to
``./riders/Jason/RawData/``. The `yeadon documentation`_ explains how to
collect the data for a rider.

.. _yeadon documentation: http://packages.python.org/yeadon

Adding a Rider
--------------
To add a rider key in:

.. GENERATED FROM PYTHON SOURCE LINES 264-266

.. code-block:: Python

    bicycle.add_rider('Jason')





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    There is no rider on the bicycle, now adding Jason.
    No parameter files found, calculating the human configuration.
    /home/docs/checkouts/readthedocs.org/user_builds/bicycleparameters/checkouts/stable/bicycleparameters/rider.py:338: RuntimeWarning: The iteration is not making good progress, as measured by the 
     improvement from the last five Jacobian evaluations.
      solution = fsolve(zero, guess)
    Joint angle A1A2extension = 0.0021339788477382124 pi-rad is out of range. Must be between -1.0 and 0.0 pi-rad.
    Joint angle B1B2extension = 0.0021339788477382124 pi-rad is out of range. Must be between -1.0 and 0.0 pi-rad.




.. GENERATED FROM PYTHON SOURCE LINES 267-276

The program first looks for a parameter for for Jason sitting on the Stratos
and if it can't find one, it looks for the raw data for Jason and computes
the inertial parameters. You can force calculation from raw data with::

   bicycle.add_rider('Jason', reCalc=True)

Exploring the rider
-------------------
The bicycle has a few new attributes now that it has a rider:

.. GENERATED FROM PYTHON SOURCE LINES 276-278

.. code-block:: Python

    bicycle.hasRider





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    True



.. GENERATED FROM PYTHON SOURCE LINES 279-281

.. code-block:: Python

    bicycle.riderName





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    'Jason'



.. GENERATED FROM PYTHON SOURCE LINES 282-283

inertial parmeters of the rider

.. GENERATED FROM PYTHON SOURCE LINES 283-285

.. code-block:: Python

    pprint.pprint(bicycle.riderPar)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    {'Benchmark': {'IBxx': np.float64(9.360297604528963),
                   'IBxz': np.float64(0.01640061915204971),
                   'IByy': np.float64(9.840351664496836),
                   'IBzz': np.float64(2.5154561357221947),
                   'mB': np.float64(83.50000000000001),
                   'xB': np.float64(0.4642273125970131),
                   'yB': np.float64(0.0),
                   'zB': np.float64(-1.0232877173495207)}}




.. GENERATED FROM PYTHON SOURCE LINES 286-287

this is a yeadon.human object representing the Jason

.. GENERATED FROM PYTHON SOURCE LINES 287-289

.. code-block:: Python

    bicycle.human





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    <yeadon.human.Human object at 0x71240435f620>



.. GENERATED FROM PYTHON SOURCE LINES 290-295

.. code-block:: Python

    try:
        bicycle.human.print_properties()
    except:
        pass





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Mass (kg):

    83.50000

    COM in global frame from bottom center of pelvis (Ls0) (m):

    [[ 0.     ]
     [-0.19658]
     [ 0.08129]]

    Inertia tensor in global frame about human's COM (kg-m^2):

    [[9.84035 0.      0.     ]
     [0.      9.3603  0.0164 ]
     [0.      0.0164  2.51546]]





.. GENERATED FROM PYTHON SOURCE LINES 296-298

The bicycle parameters now reflect that a rigid rider has been added to the
bicycle frame:

.. GENERATED FROM PYTHON SOURCE LINES 298-300

.. code-block:: Python

    bicycle.parameters['Benchmark']['mB']





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    90.72000000000001+/-0.02



.. GENERATED FROM PYTHON SOURCE LINES 301-316

At this point, the uncertainties don't necessarily offer much information for
any of the parameters that are functions of the rider, because we do not have
a good idea of the uncertainty in the human inertia calculations in the
Yeadon method.

Analysis
--------
The same linear analysis can be performed now that a rider has been added,
albeit the reported values and graphs will reflect the fact that the bicycle
frame has the added inertial effects of the rider.

Plots
-----
The bicycle geometry plot now reflects that there is a rider on the bicycle
and displays a simplified depiction:

.. GENERATED FROM PYTHON SOURCE LINES 316-318

.. code-block:: Python

    _ = bicycle.plot_bicycle_geometry()




.. image-sg:: /gallery/images/sphx_glr_plot_bicycle_005.png
   :alt: Stratos Bicycle Geometry
   :srcset: /gallery/images/sphx_glr_plot_bicycle_005.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 319-320

The Bode plot reflects the changes:

.. GENERATED FROM PYTHON SOURCE LINES 320-322

.. code-block:: Python

    _ = bicycle.plot_bode(3.0, 1, 2)




.. image-sg:: /gallery/images/sphx_glr_plot_bicycle_006.png
   :alt: Steer Torque to Roll Rate
   :srcset: /gallery/images/sphx_glr_plot_bicycle_006.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 323-324

The eigenvalue plot reflects the changes:

.. GENERATED FROM PYTHON SOURCE LINES 324-325

.. code-block:: Python

    _ = bicycle.plot_eigenvalues_vs_speed(speeds)



.. image-sg:: /gallery/images/sphx_glr_plot_bicycle_007.png
   :alt: Stratos Eigenvalues vs Speed
   :srcset: /gallery/images/sphx_glr_plot_bicycle_007.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 1.335 seconds)


.. _sphx_glr_download_gallery_plot_bicycle.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_bicycle.ipynb <plot_bicycle.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_bicycle.py <plot_bicycle.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_bicycle.zip <plot_bicycle.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_