In [14]:
%matplotlib notebook

import pandas as pd
import numpy as np
import matplotlib

from matplotlib import pyplot as plt
import seaborn as sns

Out[14]:
<matplotlib.legend.Legend at 0x7f64ec77fb00>
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')

Out[87]:
$$V_{tip(HF)} = R_R\Omega$$
In [ ]:
def hover_flight_tip_speed(rotor_radius, rotor_frequency):

In [86]:
latexmath('V_{tip(FF)} = R_R\Omega + V_{\infty} \sin \psi')

Out[86]:
$$V_{tip(FF)} = R_R\Omega + V_{\infty} \sin \psi$$
In [89]:
def forward_flight_tip_speed(freestream_airspeed,blade_azimuth_angle,rotor_radius, rotor_frequency):

In [85]:
latexmath('A = \pi R_R^2')

Out[85]:
$$A = \pi R_R^2$$
In [ ]:
def rotor_disk_area(rotor_radius):

In [84]:
latexmath(r'C_T = \frac{T}{A R_R^2 \Omega^2 \rho}')

Out[84]:
$$C_T = \frac{T}{A R_R^2 \Omega^2 \rho}$$
In [ ]:
def rotor_thrust_coefficent(rotor_thrust,rotor_area, rotor_radius, rotor_frequency, air_density):

In [58]:
IFrame('https://upload.wikimedia.org/wikipedia/commons/e/e5/VTOL_DiscLoad-LiftEfficiency.svg',width=450,height=450)

Out[58]:
In [96]:
airspeed = np.linspace(0, 150, 151)
rotor_frequency = 1

print(tip_speed_matrix)

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59.26427609,  59.08422667,  59.00341551,  59.03059973,
59.16283352,  59.38578729,  59.67530053,  60.        ]), array([ 60.        ,  60.64939894,  61.22842543,  61.67433296,
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55.81416761,  56.92893644,  58.37650265,  60.        ]), array([ 60.        ,  61.94819682,  63.68527628,  65.02299887,
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69.69400266,  69.96584493,  69.15773327,  67.35723911,
64.75947393,  61.6459459 ,  58.3540541 ,  55.24052607,
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51.62833522,  53.85787287,  56.75300531,  60.        ]), array([ 60.        ,  63.57169416,  66.75633984,  69.20883126,
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41.58233748,  46.48732032,  52.85661168,  60.        ]), array([ 60.        ,  67.46808779,  74.12689239,  79.254829  ,
82.29620612,  82.92144334,  81.06278651,  76.92164995,
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36.55933861,  42.80204404,  50.90841486,  60.        ]), array([ 60.        ,  69.41628461,  77.81216867,  84.27782787,
88.11260771,  88.9009503 ,  86.55742647,  81.33599341,
73.8024744 ,  64.77324312,  55.22675688,  46.1975256 ,
38.66400659,  33.44257353,  31.0990497 ,  31.88739229,
35.72217213,  42.18783133,  50.58371539,  60.        ]), array([ 60.        ,  69.74098408,  78.42638138,  85.11499435,
89.08200798,  89.89753479,  87.4731998 ,  82.07171732,
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37.92828268,  32.5268002 ,  30.10246521,  30.91799202,
34.88500565,  41.57361862,  50.25901592,  60.        ]), array([ 60.        ,  70.06568355,  79.04059409,  85.95216083,
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37.19255877,  31.61102687,  29.10588072,  29.94859176,
34.04783917,  40.95940591,  49.93431645,  60.        ]), array([ 60.        ,  70.39038301,  79.65480681,  86.7893273 ,
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36.45683486,  30.69525355,  28.10929622,  28.97919149,
33.2106727 ,  40.34519319,  49.60961699,  60.        ]), array([ 60.        ,  70.71508248,  80.26901952,  87.62649378,
91.99020878,  92.88728827,  90.22051978,  84.27888905,
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31.53633974,  39.11676777,  48.96021805,  60.        ]), array([ 60.        ,  71.36448142,  81.49744494,  89.30082674,
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30.69917326,  38.50255506,  48.63551858,  60.        ]), array([ 60.        ,  71.68918089,  82.11165766,  90.13799322,
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29.86200678,  37.88834234,  48.31081911,  60.        ]), array([ 60.        ,  72.01388036,  82.72587037,  90.9751597 ,
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26.51334087,  35.43149149,  47.01202123,  60.        ]), array([  60.        ,   73.31267824,   85.18272122,   94.32382561,
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29.83531966,   22.45329361,   19.14003579,   20.2545891 ,
25.67617439,   34.81727878,   46.68732176,   60.        ]), array([  60.        ,   73.63737771,   85.79693393,   95.16099209,
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24.83900791,   34.20306607,   46.36262229,   60.        ]), array([  60.        ,   73.96207718,   86.41114665,   95.99815857,
101.68421144,  102.8531332 ,   99.37825305,   91.63612816,
80.4657379 ,   67.07756738,   52.92243262,   39.5342621 ,
28.36387184,   20.62174695,   17.1468668 ,   18.31578856,
24.00184143,   33.58885335,   46.03792282,   60.        ]), array([  60.        ,   74.28677665,   87.02535936,   96.83532504,
102.6536117 ,  103.84971769,  100.29402637,   92.37185207,
80.94168529,   67.24216197,   52.75783803,   39.05831471,
27.62814793,   19.70597363,   16.15028231,   17.3463883 ,
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103.62301197,  104.84630219,  101.2097997 ,   93.10757598,
81.41763269,   67.40675656,   52.59324344,   38.58236731,
26.89242402,   18.7902003 ,   15.15369781,   16.37698803,
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104.59241223,  105.84288668,  102.12557303,   93.84329989,
81.89358008,   67.57135115,   52.42864885,   38.10641992,
26.15670011,   17.87442697,   14.15711332,   15.40758777,
21.490342  ,   31.74621522,   45.06382442,   60.        ]), array([  60.        ,   75.26087505,   88.8679975 ,   99.34682448,
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25.4209762 ,   16.95865365,   13.16052883,   14.4381875 ,
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In [ ]: