#!/usr/bin/env python
# coding: utf-8

# In[14]:


get_ipython().run_line_magic('matplotlib', 'notebook')

import pandas as pd
import numpy as np
import matplotlib

from matplotlib import pyplot as plt
import seaborn as sns


# In[50]:


from IPython.display import Math as latexmath
from IPython.display import IFrame


# * 6 Tip mounted Turbojets + 1 turboshaft in tail to power tail rotor
# * 3 rotors with diameter of 120m
# * Empty weight 200,000kg
# * Gross weight 453,000kg
# * 60 rpm (according to Jay Spensers book Vertical Challenge. The Hiller Aircraft Story from Jay P. Spenser. ISBN 0-295-97203-3 and also the Air Tug video)
# * Circumference = 383.02m
# so tips are 383m/s
# sea level speed of sound is 344 m/s
# Tips are supersonic...

# $$ 
# Takeoff\; Gross\; Weight = W_0 \\
# Blade\; Position(Azimuth\; Angle)\; = \psi \\ 
# Rotor\; Tip\; Speed\; (Hovering\; Flight)\; = V_{tip(HF)}\\
# Rotor\; Tip\; Speed\; (Forward\; Flight)\; = V_{tip(FF)}\\
# Freestream\; Air\; Speed\; = V_{\infty}\\
# Rotor\; Rotation\; Frequency\; = \Omega\\
# Rotor\; Radius\; = R_R\\
# Rotor\; Hub\; Radius\; = R_H\\
# Rotor\; Thrust\; = T\\
# Rotor\; Thrust\; Coefficient\; = C_T\\
# Rotor\; Disk\; Area\; = A\\
# Air\; Density\; = \rho\\
# Rotor\; Disk\; Power\; Loading\; = PL\\
# Rotor\; Disk\; Loading\; = DL\\
# $$

# In[87]:


latexmath('V_{tip(HF)} = R_R\Omega')


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def hover_flight_tip_speed(rotor_radius, rotor_frequency):
    return rotor_radius*rotor_frequency


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latexmath('V_{tip(FF)} = R_R\Omega + V_{\infty} \sin \psi')


# In[89]:


def forward_flight_tip_speed(freestream_airspeed,blade_azimuth_angle,rotor_radius, rotor_frequency):
    return (rotor_radius*rotor_frequency)+(freestream_airspeed*np.sin(blade_azimuth_angle))


# In[85]:


latexmath('A = \pi R_R^2')


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def rotor_disk_area(rotor_radius):
    return np.pi*rotor_radius**2


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latexmath(r'C_T = \frac{T}{A R_R^2 \Omega^2 \rho}')


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def rotor_thrust_coefficent(rotor_thrust,rotor_area, rotor_radius, rotor_frequency, air_density):
    return rotor_thrust/(air_density*rotor_area*(rotor_frequency**2)*(rotor_radius**2))


# In[58]:


IFrame('https://upload.wikimedia.org/wikipedia/commons/e/e5/VTOL_DiscLoad-LiftEfficiency.svg',width=450,height=450)


# In[96]:


airspeed = np.linspace(0, 150, 151)
rotor_frequency = 1
rotor_radius = 60
blade_azimuth_angles = np.linspace(0, 2*np.pi, 20)
tip_speed_matrix = [forward_flight_tip_speed(a ,blade_azimuth_angles,rotor_radius, rotor_frequency) for a in airspeed]



print(tip_speed_matrix)


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