=======================
Example EFH Jump Design
=======================

The following page describes how to construct a typical equivalent fall height
ski jump landing surface using the ``skijumpdesign`` API. Make sure to :ref:`install <install>`
the library first.

Approach
========

Start by creating a 20 meter length of an approach surface (also called the
in-run) which is flat and has a downward slope angle of 20 degrees. The
resulting surface can be visualized with the ``FlatSurface.plot()`` method.

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

   from skijumpdesign import FlatSurface

   approach_ang = -np.deg2rad(20)  # radians
   approach_len = 20.0  # meters

   approach = FlatSurface(approach_ang, approach_len)

   approach.plot()

Now that a surface has been created, a skier can be created. The skier can "ski"
along the approach surface using the ``slide_on()`` method which generates a
skiing simulation trajectory.

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

   from skijumpdesign import Skier

   skier = Skier()

   approach_traj = skier.slide_on(approach)

   approach_traj.plot_time_series()

Takeoff
=======

The takeoff ramp is constructed with a clothoid-circle-clothoid-flat surface to
transition from the approach parent slope angle to the desired takeoff angle, in this case 15
degrees.

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

   from skijumpdesign import TakeoffSurface

   takeoff_entry_speed = skier.end_speed_on(approach)

   takeoff_ang = np.deg2rad(15)

   takeoff = TakeoffSurface(skier, approach_ang, takeoff_ang,
                            takeoff_entry_speed, init_pos=approach.end)

   ax = approach.plot()
   takeoff.plot(ax=ax)

The trajectory of the skier on the takeoff can be examined also.

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

   takeoff_traj = skier.slide_on(takeoff, takeoff_entry_speed)

   takeoff_traj.plot_time_series()

Flight
======

Once the skier leaves the takeoff ramp at the maximum (design) speed they will be in flight. The
``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(takeoff, init_speed=takeoff_entry_speed)

   flight = skier.fly_to(approach, init_pos=takeoff.end,
                         init_vel=takeoff_vel)

   flight.plot_time_series()

The design speed flight trajectory can be plotted alongside the surfaces.

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

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

Landing Transition
==================

There is a single infinity of landing surfaces that satisfy the efh differential 
equation and provide the desired equivalent fall height. The algorithm selects 
the one of these that is closest to the parent slope, and hence is least expensive 
to build, but which still is able to transition back to the parent slope with 
slope continuity and simultaneously is constrained to experience limited normal acceleration. 
The final part of this step is to determine the landing transition curve which 
connects the optimum (cheapest) constant efh landing surface to the parent slope.

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

   from skijumpdesign import LandingTransitionSurface

   fall_height = 0.5

   landing_trans = LandingTransitionSurface(approach,
       flight, fall_height, skier.tolerable_landing_acc)

   ax = approach.plot()
   ax = takeoff.plot(ax=ax)
   ax = flight.plot(ax=ax, color='#9467bd')
   landing_trans.plot(ax=ax, color='#d62728')

Landing
=======

Finally, the equivalent fall height landing surface can be generated which
accommodates all takeoff speeds below the maximum takeoff (design) speed above.

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

   from skijumpdesign import LandingSurface

   slope = FlatSurface(approach_ang, np.sqrt(landing_trans.end[0]**2 +
                                             landing_trans.end[1]**2) + 1.0)


   landing = LandingSurface(skier, takeoff.end, takeoff_ang,
                            landing_trans.start, fall_height,
                            surf=slope)

   ax = approach.plot()
   ax = takeoff.plot(ax=ax)
   ax = flight.plot(ax=ax, color='#9467bd')
   ax = landing_trans.plot(ax=ax, color='#d62728')
   landing.plot(ax=ax, color='#2ca02c')

Entire Jump
===========

There is a convenience function for plotting the jump:

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

   from skijumpdesign import plot_jump

   plot_jump(slope, approach, takeoff, landing, landing_trans, flight)