.. _analyze jump:

=========================
Example: Analyze Jump EFH
=========================

The following page describes how to analyze an existing or hypothetical ski
jump landing surface by calculating it's equivalent fall height using the
``skijumpdesign`` :ref:`API <API>`. Make sure to :ref:`install <install>` the
library first.

Load Data
=========

Start by loading data of a ski jump surface's horizontal and vertical
coordinates measured in meters. The resulting surface can be visualized with
the :meth:`~skijumpdesign.surfaces.Surface.plot` method. Create a tuple for the
takeoff point coordinates, and a variable for the takeoff angle. Data for this
example is taken from a jump measured with a level and tape measure and
translated into horizontal (x) and vertical (y) components. The sample surface
below was collected from a real slope and jump.

.. plot::
   :include-source: True
   :context:
   :width: 600px

   from skijumpdesign import Surface
   import numpy as np

   takeoff_ang = 10  # degrees
   takeoff_point = (0, 0)  # meters

   x_ft = [-232.3,-203.7,-175.0,-146.3,-117.0,-107.4,-97.7,-88.0,-78.2,
           -68.5,-58.8,-49.1,-39.4,-34.5,-29.7,-24.8,-19.8,-17.8,-15.8,
           -13.8,-11.8,-9.8,-7.8,-5.9,-3.9,-2.0,0.0,0.0,0.0,2.0,3.9,5.9,
           7.9,9.9,11.9,13.9,15.9,17.9,19.9,21.9,23.9,25.8,27.8,29.7,
           31.5,33.4,35.2, 37.0,38.8,43.3,47.8,52.3,56.8,61.5,66.2,70.9,
           75.7,80.6,85.5,88.4,88.4] # feet

   y_ft = [55.5,46.4,37.7,29.1,22.2,19.7,17.2,14.8,12.5,10.2,7.7,5.2,
           2.9,1.8,0.7,-0.2,-1.0,-1.2,-1.4,-1.6,-1.7,-1.6,-1.5,-1.3,
           -1.0,-0.4,0.0,0.0,0.0,-0.3,-0.8,-1.0,-1.4,-1.4,-1.5,-1.5,-1.5,
           -1.5,-1.6,-1.8,-2.0,-2.4,-2.9,-3.5,-4.2,-5.0,-5.8,-6.7,-7.5,
           -9.8,-12.0,-14.2,-16.2,-18.1,-19.8,-21.4,-22.9,-24.0,-25.0,
           -25.6,-25.6] # feet

   x = np.asarray(x_ft)*0.3048 # convert to meters
   y = np.asarray(y_ft)*0.3048 # convert to meters

   measured_surf = Surface(x, y)

   measured_surf.plot()

Now that a surface has been created, a skier can be created. The skier can
"ski" along the surface by extracting the data in the array before takeoff and
using the :meth:`~skijumpdesign.skiers.Skier.slide_on` method which generates a
skiing simulation trajectory.

.. plot::
   :include-source: True
   :context: close-figs
   :width: 600px

   from skijumpdesign import Skier

   x_beforetakeoff = x[x<=takeoff_point[0]]
   y_beforetakeoff = y[x<=takeoff_point[0]]

   before_takeoff = Surface(x_beforetakeoff, y_beforetakeoff)

   skier = Skier()

   beforetakeoff_traj = skier.slide_on(before_takeoff)

   beforetakeoff_traj.plot_time_series()

Flight
======

Once the skier leaves the takeoff ramp at the maximum (design) speed they will
be in flight. The :meth:`~skijumpdesign.skiers.Skier.fly_to` method can be used
to simulate this longest flight trajectory.

.. plot::
   :include-source: True
   :context: close-figs
   :width: 600px

   takeoff_vel = skier.end_vel_on(before_takeoff)

   flight = skier.fly_to(measured_surf, init_pos=before_takeoff.end,
                         init_vel=takeoff_vel)

   flight.plot_time_series()

The design speed flight trajectory can be plotted in addition to the surface.

.. plot::
   :include-source: True
   :context: close-figs
   :width: 600px

   ax = measured_surf.plot()
   flight.plot(ax=ax, color='#9467bd')

Calculate Equivalent Fall Height
================================

The equivalent fall height of the landing surface is calculated at constant
intervals relative to the provided takeoff point or start of the surface.

.. plot::
   :include-source: True
   :context: close-figs
   :width: 600px

   dist, efh, speeds = measured_surf.calculate_efh(
       np.deg2rad(takeoff_ang), takeoff_point,skier, increment=1.0)

There is a convenience function for plotting the calculated efh.

.. plot::
   :include-source: True
   :context: close-figs
   :width: 600px

   from skijumpdesign.functions import plot_efh

   plot_efh(measured_surf, takeoff_ang, takeoff_point, skier=skier,
            increment=1.0)