Section 08 - Performance Analysis - E - lower lift-to-drag ratio

[1]:
from AMAT.planet import Planet
from AMAT.vehicle import Vehicle
[2]:
import numpy as np
import matplotlib.pyplot as plt
[3]:
planet = Planet('URANUS')
planet.loadAtmosphereModel('../../../atmdata/Uranus/uranus-gram-avg.dat', 0 , 1 ,2, 3, heightInKmFlag=True)
planet.h_skip = 1000.0E3
planet.h_low  = 120e3
planet.h_trap = 100e3
[36]:
vehicle=Vehicle('Titania', 3200.0, 146 , 0.24, np.pi*4.5**2.0, 0.0, 1.125, planet)
vehicle.setInitialState(1000.0,-15.22,75.55,29.2877,88.687,-11.7 ,0.0,0.0)
vehicle.setSolverParams(1E-6)
# Set the guidance parameters described in the paper.
# See the function description for parameter details.

# Set max roll rate constraint to 30 deg/s
vehicle.setMaxRollRate(30.0)

# Set Ghdot = 83
# Set Gq = 9.0
# Set v_switch_kms = 16.0 :: this parameter is not really used, and should just be set to low value
# Set low_Alt_km = 120
# Set numPoints_lowAlt = 101
# Set hdot_threshold = -500 m/s
vehicle.setEquilibriumGlideParams(83.0, 9.0, 16.0, 120.0, 101, -500.0)

# Set target orbit parameters
# periapsis = 4000.0 km
# apoapsis = 550,000 km :: set slightly above target (500e3) to account for bias in targeting algorithm
# apoapsis tolerance = 10 km
vehicle.setTargetOrbitParams(4000.0, 550.0E3, 10.0E3)
[37]:
# Set path to atmfiles with randomly perturbed atmosphere files.
atmfiles = ['../../../atmdata/Uranus/perturbed/G-01.txt',
            '../../../atmdata/Uranus/perturbed/G-02.txt',
            '../../../atmdata/Uranus/perturbed/G-03.txt',
            '../../../atmdata/Uranus/perturbed/G-04.txt',
            '../../../atmdata/Uranus/perturbed/G-05.txt']
[38]:
vehicle.setupMonteCarloSimulation(1201, 200, atmfiles, 0, 1, 2, 3, 4, True, \
                                 -11.70, 0.10, 0.18, 0.013, 0.5, 0.1, 2400.0)

Small run N = 200

[39]:
vehicle.runMonteCarlo2(200, '../../../data/acta-astronautica/uranus-orbiter-probe/MCBXE')
RUN #: 1, SAMPLE #: 194, EFPA: -11.78, SIGMA: 0.44, LD: 0.18, APO : 491526.74
RUN #: 2, SAMPLE #: 190, EFPA: -11.63, SIGMA: -1.96, LD: 0.18, APO : 552012.89
RUN #: 3, SAMPLE #: 117, EFPA: -11.58, SIGMA: 0.96, LD: 0.16, APO : 512977.98
RUN #: 4, SAMPLE #: 72, EFPA: -11.84, SIGMA: 1.56, LD: 0.17, APO : 571313.31
RUN #: 5, SAMPLE #: 90, EFPA: -11.72, SIGMA: -0.32, LD: 0.19, APO : 527192.14
RUN #: 6, SAMPLE #: 10, EFPA: -11.69, SIGMA: -0.75, LD: 0.17, APO : 531266.12
RUN #: 7, SAMPLE #: 32, EFPA: -11.69, SIGMA: 0.70, LD: 0.20, APO : 531356.46
RUN #: 8, SAMPLE #: 5, EFPA: -11.79, SIGMA: 1.18, LD: 0.18, APO : 512413.03
RUN #: 9, SAMPLE #: 72, EFPA: -11.77, SIGMA: 0.31, LD: 0.17, APO : 585816.44
RUN #: 10, SAMPLE #: 133, EFPA: -11.66, SIGMA: -1.01, LD: 0.19, APO : 552269.58
RUN #: 11, SAMPLE #: 123, EFPA: -11.81, SIGMA: 0.74, LD: 0.17, APO : 536248.61
RUN #: 12, SAMPLE #: 100, EFPA: -11.70, SIGMA: -0.98, LD: 0.17, APO : 481788.66
RUN #: 13, SAMPLE #: 10, EFPA: -11.63, SIGMA: -0.84, LD: 0.18, APO : 509969.26
RUN #: 14, SAMPLE #: 120, EFPA: -11.74, SIGMA: 1.57, LD: 0.18, APO : 538552.87
RUN #: 15, SAMPLE #: 136, EFPA: -11.63, SIGMA: -0.73, LD: 0.17, APO : 527392.33
RUN #: 16, SAMPLE #: 134, EFPA: -11.62, SIGMA: 0.09, LD: 0.18, APO : 496944.94
RUN #: 17, SAMPLE #: 198, EFPA: -11.67, SIGMA: 0.78, LD: 0.22, APO : 519418.09
RUN #: 18, SAMPLE #: 107, EFPA: -11.56, SIGMA: -0.12, LD: 0.18, APO : 628793.63
RUN #: 19, SAMPLE #: 73, EFPA: -11.86, SIGMA: -0.19, LD: 0.18, APO : 528205.76
RUN #: 20, SAMPLE #: 137, EFPA: -11.70, SIGMA: -0.54, LD: 0.21, APO : 474351.34
RUN #: 21, SAMPLE #: 180, EFPA: -11.82, SIGMA: -1.03, LD: 0.18, APO : 562603.49
RUN #: 22, SAMPLE #: 194, EFPA: -11.82, SIGMA: 1.11, LD: 0.16, APO : 507516.70
RUN #: 23, SAMPLE #: 185, EFPA: -11.80, SIGMA: 1.02, LD: 0.18, APO : 528681.02
RUN #: 24, SAMPLE #: 32, EFPA: -11.74, SIGMA: -0.98, LD: 0.19, APO : 498700.93
RUN #: 25, SAMPLE #: 129, EFPA: -11.64, SIGMA: 1.17, LD: 0.17, APO : 521904.06
RUN #: 26, SAMPLE #: 193, EFPA: -11.65, SIGMA: -1.04, LD: 0.17, APO : 522931.81
RUN #: 27, SAMPLE #: 51, EFPA: -11.72, SIGMA: 0.45, LD: 0.17, APO : 539872.27
RUN #: 28, SAMPLE #: 123, EFPA: -11.83, SIGMA: 0.58, LD: 0.18, APO : 528962.48
RUN #: 29, SAMPLE #: 21, EFPA: -11.67, SIGMA: -0.16, LD: 0.19, APO : 553604.90
RUN #: 30, SAMPLE #: 111, EFPA: -11.59, SIGMA: -0.59, LD: 0.20, APO : 548119.52
RUN #: 31, SAMPLE #: 199, EFPA: -11.64, SIGMA: 0.14, LD: 0.18, APO : 536812.60
RUN #: 32, SAMPLE #: 8, EFPA: -11.69, SIGMA: 1.40, LD: 0.16, APO : 474302.65
RUN #: 33, SAMPLE #: 102, EFPA: -11.73, SIGMA: -0.80, LD: 0.17, APO : 508678.09
RUN #: 34, SAMPLE #: 64, EFPA: -11.59, SIGMA: -0.00, LD: 0.16, APO : 576679.99
RUN #: 35, SAMPLE #: 7, EFPA: -11.61, SIGMA: -0.94, LD: 0.17, APO : 551005.98
RUN #: 36, SAMPLE #: 75, EFPA: -11.73, SIGMA: -0.93, LD: 0.19, APO : 529560.24
RUN #: 37, SAMPLE #: 11, EFPA: -11.69, SIGMA: 1.79, LD: 0.18, APO : 519912.84
RUN #: 38, SAMPLE #: 115, EFPA: -11.66, SIGMA: -0.17, LD: 0.17, APO : 531801.14
RUN #: 39, SAMPLE #: 136, EFPA: -11.80, SIGMA: -0.16, LD: 0.16, APO : 490087.22
RUN #: 40, SAMPLE #: 3, EFPA: -11.75, SIGMA: 0.24, LD: 0.20, APO : 503692.54
RUN #: 41, SAMPLE #: 92, EFPA: -11.75, SIGMA: -0.05, LD: 0.19, APO : 487356.01
RUN #: 42, SAMPLE #: 169, EFPA: -11.78, SIGMA: 1.81, LD: 0.20, APO : 591959.65
RUN #: 43, SAMPLE #: 140, EFPA: -11.73, SIGMA: 0.68, LD: 0.20, APO : 520639.94
RUN #: 44, SAMPLE #: 6, EFPA: -11.73, SIGMA: -0.35, LD: 0.18, APO : 491871.83
RUN #: 45, SAMPLE #: 16, EFPA: -11.47, SIGMA: 1.60, LD: 0.18, APO : 564967.58
RUN #: 46, SAMPLE #: 108, EFPA: -11.69, SIGMA: 0.51, LD: 0.18, APO : 536687.19
RUN #: 47, SAMPLE #: 189, EFPA: -11.58, SIGMA: -1.86, LD: 0.17, APO : 577818.63
RUN #: 48, SAMPLE #: 6, EFPA: -11.80, SIGMA: -1.41, LD: 0.19, APO : 521152.82
RUN #: 49, SAMPLE #: 67, EFPA: -11.75, SIGMA: 0.95, LD: 0.17, APO : 485031.26
RUN #: 50, SAMPLE #: 2, EFPA: -11.60, SIGMA: -0.13, LD: 0.18, APO : 513910.86
RUN #: 51, SAMPLE #: 61, EFPA: -11.75, SIGMA: 0.86, LD: 0.18, APO : 504429.70
RUN #: 52, SAMPLE #: 196, EFPA: -11.70, SIGMA: -1.18, LD: 0.17, APO : 575392.51
RUN #: 53, SAMPLE #: 61, EFPA: -11.66, SIGMA: 0.57, LD: 0.17, APO : 526394.75
RUN #: 54, SAMPLE #: 141, EFPA: -11.60, SIGMA: -1.17, LD: 0.21, APO : 565195.52
RUN #: 55, SAMPLE #: 148, EFPA: -11.85, SIGMA: -0.04, LD: 0.19, APO : 481697.23
RUN #: 56, SAMPLE #: 190, EFPA: -11.72, SIGMA: -0.66, LD: 0.19, APO : 514870.69
RUN #: 57, SAMPLE #: 93, EFPA: -11.67, SIGMA: -1.05, LD: 0.16, APO : 480341.62
RUN #: 58, SAMPLE #: 61, EFPA: -11.72, SIGMA: -2.14, LD: 0.19, APO : 546563.66
RUN #: 59, SAMPLE #: 134, EFPA: -11.63, SIGMA: -1.06, LD: 0.19, APO : 511642.88
RUN #: 60, SAMPLE #: 5, EFPA: -11.62, SIGMA: 2.51, LD: 0.20, APO : 505386.34
RUN #: 61, SAMPLE #: 101, EFPA: -11.88, SIGMA: -2.07, LD: 0.19, APO : 513683.99
RUN #: 62, SAMPLE #: 146, EFPA: -11.66, SIGMA: 1.37, LD: 0.19, APO : 526474.98
RUN #: 63, SAMPLE #: 72, EFPA: -11.72, SIGMA: -2.57, LD: 0.16, APO : 574252.00
RUN #: 64, SAMPLE #: 140, EFPA: -11.83, SIGMA: 0.32, LD: 0.18, APO : 563825.05
RUN #: 65, SAMPLE #: 120, EFPA: -11.53, SIGMA: 0.17, LD: 0.17, APO : 491554.53
RUN #: 66, SAMPLE #: 155, EFPA: -11.86, SIGMA: 0.63, LD: 0.18, APO : 529926.50
RUN #: 67, SAMPLE #: 161, EFPA: -11.81, SIGMA: -0.48, LD: 0.19, APO : 537378.79
RUN #: 68, SAMPLE #: 152, EFPA: -11.71, SIGMA: -1.04, LD: 0.16, APO : 509175.30
RUN #: 69, SAMPLE #: 148, EFPA: -11.57, SIGMA: -0.85, LD: 0.18, APO : 565935.22
RUN #: 70, SAMPLE #: 47, EFPA: -11.71, SIGMA: -0.94, LD: 0.19, APO : 508984.24
RUN #: 71, SAMPLE #: 63, EFPA: -11.73, SIGMA: -0.25, LD: 0.20, APO : 595279.54
RUN #: 72, SAMPLE #: 50, EFPA: -11.80, SIGMA: -0.71, LD: 0.19, APO : 588235.84
RUN #: 73, SAMPLE #: 107, EFPA: -11.82, SIGMA: 0.50, LD: 0.18, APO : 533524.08
RUN #: 74, SAMPLE #: 150, EFPA: -11.55, SIGMA: 1.28, LD: 0.19, APO : 564906.08
RUN #: 75, SAMPLE #: 51, EFPA: -11.81, SIGMA: 1.24, LD: 0.17, APO : 563292.85
RUN #: 76, SAMPLE #: 37, EFPA: -11.58, SIGMA: -0.44, LD: 0.17, APO : 553497.92
RUN #: 77, SAMPLE #: 180, EFPA: -11.74, SIGMA: -0.16, LD: 0.19, APO : 561928.21
RUN #: 78, SAMPLE #: 163, EFPA: -11.59, SIGMA: 1.23, LD: 0.19, APO : 520302.80
RUN #: 79, SAMPLE #: 5, EFPA: -11.64, SIGMA: -1.91, LD: 0.18, APO : 497086.72
RUN #: 80, SAMPLE #: 33, EFPA: -11.72, SIGMA: -0.14, LD: 0.17, APO : 510147.99
RUN #: 81, SAMPLE #: 143, EFPA: -11.63, SIGMA: -1.14, LD: 0.20, APO : 551720.59
RUN #: 82, SAMPLE #: 89, EFPA: -11.74, SIGMA: -0.64, LD: 0.16, APO : 517042.49
RUN #: 83, SAMPLE #: 84, EFPA: -11.58, SIGMA: 0.06, LD: 0.17, APO : 490438.35
RUN #: 84, SAMPLE #: 78, EFPA: -11.79, SIGMA: -0.55, LD: 0.18, APO : 556387.00
RUN #: 85, SAMPLE #: 132, EFPA: -11.74, SIGMA: 0.18, LD: 0.17, APO : 510387.61
RUN #: 86, SAMPLE #: 176, EFPA: -11.85, SIGMA: 0.20, LD: 0.19, APO : 566995.99
RUN #: 87, SAMPLE #: 38, EFPA: -11.43, SIGMA: 0.99, LD: 0.18, APO : 513973.84
RUN #: 88, SAMPLE #: 54, EFPA: -11.78, SIGMA: -0.50, LD: 0.18, APO : 533231.51
RUN #: 89, SAMPLE #: 117, EFPA: -11.49, SIGMA: 0.31, LD: 0.18, APO : 498282.78
RUN #: 90, SAMPLE #: 111, EFPA: -11.75, SIGMA: 1.03, LD: 0.18, APO : 495020.75
RUN #: 91, SAMPLE #: 33, EFPA: -11.72, SIGMA: 1.57, LD: 0.20, APO : 574586.40
RUN #: 92, SAMPLE #: 132, EFPA: -11.73, SIGMA: -1.68, LD: 0.19, APO : 462482.80
RUN #: 93, SAMPLE #: 36, EFPA: -11.86, SIGMA: 0.87, LD: 0.19, APO : 477859.13
RUN #: 94, SAMPLE #: 10, EFPA: -11.57, SIGMA: -0.15, LD: 0.18, APO : 520765.60
RUN #: 95, SAMPLE #: 117, EFPA: -11.57, SIGMA: 1.58, LD: 0.16, APO : 555568.10
RUN #: 96, SAMPLE #: 79, EFPA: -11.68, SIGMA: 0.28, LD: 0.18, APO : 539123.86
RUN #: 97, SAMPLE #: 182, EFPA: -11.92, SIGMA: -1.06, LD: 0.17, APO : 560416.35
RUN #: 98, SAMPLE #: 162, EFPA: -11.56, SIGMA: 1.11, LD: 0.16, APO : 525960.97
RUN #: 99, SAMPLE #: 79, EFPA: -11.68, SIGMA: -1.15, LD: 0.19, APO : 537797.55
RUN #: 100, SAMPLE #: 68, EFPA: -11.91, SIGMA: -0.50, LD: 0.18, APO : 540014.67
RUN #: 101, SAMPLE #: 166, EFPA: -11.66, SIGMA: -0.41, LD: 0.17, APO : 545120.47
RUN #: 102, SAMPLE #: 109, EFPA: -11.67, SIGMA: -0.60, LD: 0.18, APO : 525754.63
RUN #: 103, SAMPLE #: 89, EFPA: -11.74, SIGMA: 1.51, LD: 0.18, APO : 488336.11
RUN #: 104, SAMPLE #: 53, EFPA: -11.73, SIGMA: -0.41, LD: 0.18, APO : 494023.77
RUN #: 105, SAMPLE #: 135, EFPA: -11.70, SIGMA: 0.25, LD: 0.18, APO : 524809.05
RUN #: 106, SAMPLE #: 137, EFPA: -11.58, SIGMA: -1.79, LD: 0.19, APO : 511501.76
RUN #: 107, SAMPLE #: 158, EFPA: -11.84, SIGMA: -0.05, LD: 0.16, APO : 514830.33
RUN #: 108, SAMPLE #: 38, EFPA: -11.59, SIGMA: 0.11, LD: 0.18, APO : 463683.01
RUN #: 109, SAMPLE #: 120, EFPA: -11.62, SIGMA: -1.57, LD: 0.21, APO : 534166.17
RUN #: 110, SAMPLE #: 162, EFPA: -11.70, SIGMA: -0.73, LD: 0.17, APO : 488512.41
RUN #: 111, SAMPLE #: 94, EFPA: -11.79, SIGMA: -0.29, LD: 0.17, APO : 486468.28
RUN #: 112, SAMPLE #: 86, EFPA: -11.94, SIGMA: 0.96, LD: 0.17, APO : 573478.35
RUN #: 113, SAMPLE #: 37, EFPA: -11.74, SIGMA: -0.82, LD: 0.17, APO : 551083.58
RUN #: 114, SAMPLE #: 1, EFPA: -11.62, SIGMA: 0.78, LD: 0.18, APO : 499462.33
RUN #: 115, SAMPLE #: 104, EFPA: -11.87, SIGMA: -0.49, LD: 0.15, APO : 515032.80
RUN #: 116, SAMPLE #: 153, EFPA: -11.68, SIGMA: -0.04, LD: 0.16, APO : 530134.79
RUN #: 117, SAMPLE #: 111, EFPA: -11.81, SIGMA: 0.08, LD: 0.18, APO : 542004.73
RUN #: 118, SAMPLE #: 165, EFPA: -11.86, SIGMA: 0.42, LD: 0.19, APO : 497855.40
RUN #: 119, SAMPLE #: 190, EFPA: -11.64, SIGMA: -0.85, LD: 0.18, APO : 535793.76
RUN #: 120, SAMPLE #: 81, EFPA: -11.70, SIGMA: -0.28, LD: 0.20, APO : 572600.91
RUN #: 121, SAMPLE #: 36, EFPA: -11.99, SIGMA: -0.14, LD: 0.17, APO : 551210.96
RUN #: 122, SAMPLE #: 19, EFPA: -11.73, SIGMA: -0.59, LD: 0.18, APO : 487576.32
RUN #: 123, SAMPLE #: 138, EFPA: -11.60, SIGMA: -1.21, LD: 0.17, APO : 506834.17
RUN #: 124, SAMPLE #: 27, EFPA: -11.84, SIGMA: 1.03, LD: 0.19, APO : 493896.31
RUN #: 125, SAMPLE #: 32, EFPA: -11.62, SIGMA: 0.57, LD: 0.19, APO : 515799.40
RUN #: 126, SAMPLE #: 54, EFPA: -11.83, SIGMA: -0.20, LD: 0.20, APO : 552330.89
RUN #: 127, SAMPLE #: 142, EFPA: -11.64, SIGMA: -0.17, LD: 0.16, APO : 542439.13
RUN #: 128, SAMPLE #: 17, EFPA: -11.71, SIGMA: 1.00, LD: 0.17, APO : 494607.35
RUN #: 129, SAMPLE #: 23, EFPA: -11.70, SIGMA: 0.74, LD: 0.18, APO : 547621.16
RUN #: 130, SAMPLE #: 17, EFPA: -11.69, SIGMA: -0.94, LD: 0.18, APO : 544791.12
RUN #: 131, SAMPLE #: 155, EFPA: -11.75, SIGMA: -1.08, LD: 0.18, APO : 489581.15
RUN #: 132, SAMPLE #: 137, EFPA: -11.78, SIGMA: 1.18, LD: 0.16, APO : 528818.81
RUN #: 133, SAMPLE #: 86, EFPA: -11.61, SIGMA: -0.16, LD: 0.17, APO : 549907.33
RUN #: 134, SAMPLE #: 1, EFPA: -11.64, SIGMA: 0.33, LD: 0.16, APO : 481473.61
RUN #: 135, SAMPLE #: 78, EFPA: -11.65, SIGMA: 1.32, LD: 0.18, APO : 517265.81
RUN #: 136, SAMPLE #: 170, EFPA: -11.59, SIGMA: -0.65, LD: 0.18, APO : 557250.58
RUN #: 137, SAMPLE #: 177, EFPA: -11.70, SIGMA: -1.05, LD: 0.19, APO : 477856.40
RUN #: 138, SAMPLE #: 89, EFPA: -11.65, SIGMA: 1.18, LD: 0.16, APO : 504012.53
RUN #: 139, SAMPLE #: 48, EFPA: -11.65, SIGMA: 0.24, LD: 0.18, APO : 544950.75
RUN #: 140, SAMPLE #: 187, EFPA: -11.81, SIGMA: -0.16, LD: 0.19, APO : 556991.45
RUN #: 141, SAMPLE #: 182, EFPA: -11.78, SIGMA: -1.34, LD: 0.17, APO : 558063.78
RUN #: 142, SAMPLE #: 109, EFPA: -11.79, SIGMA: 1.07, LD: 0.19, APO : 509364.80
RUN #: 143, SAMPLE #: 100, EFPA: -11.79, SIGMA: 1.43, LD: 0.18, APO : 544882.32
RUN #: 144, SAMPLE #: 161, EFPA: -11.72, SIGMA: 0.55, LD: 0.15, APO : 511087.21
RUN #: 145, SAMPLE #: 97, EFPA: -11.58, SIGMA: -0.52, LD: 0.17, APO : 533614.24
RUN #: 146, SAMPLE #: 138, EFPA: -11.71, SIGMA: 1.85, LD: 0.19, APO : 505655.11
RUN #: 147, SAMPLE #: 3, EFPA: -11.78, SIGMA: 2.27, LD: 0.18, APO : 523892.55
RUN #: 148, SAMPLE #: 84, EFPA: -11.87, SIGMA: -0.93, LD: 0.19, APO : 532988.74
RUN #: 149, SAMPLE #: 14, EFPA: -11.70, SIGMA: -0.69, LD: 0.18, APO : 492103.23
RUN #: 150, SAMPLE #: 64, EFPA: -11.55, SIGMA: 2.06, LD: 0.18, APO : 560215.58
RUN #: 151, SAMPLE #: 167, EFPA: -11.68, SIGMA: 0.20, LD: 0.17, APO : 556688.93
RUN #: 152, SAMPLE #: 184, EFPA: -11.82, SIGMA: 0.26, LD: 0.18, APO : 589944.43
RUN #: 153, SAMPLE #: 131, EFPA: -11.76, SIGMA: -0.76, LD: 0.18, APO : 525020.93
RUN #: 154, SAMPLE #: 171, EFPA: -11.75, SIGMA: -0.86, LD: 0.17, APO : 510048.37
RUN #: 155, SAMPLE #: 51, EFPA: -11.76, SIGMA: -2.12, LD: 0.18, APO : 518802.71
RUN #: 156, SAMPLE #: 112, EFPA: -11.63, SIGMA: 0.62, LD: 0.17, APO : 496097.58
RUN #: 157, SAMPLE #: 28, EFPA: -11.54, SIGMA: 1.95, LD: 0.17, APO : 522317.79
RUN #: 158, SAMPLE #: 134, EFPA: -11.70, SIGMA: 0.04, LD: 0.18, APO : 537658.50
RUN #: 159, SAMPLE #: 188, EFPA: -11.65, SIGMA: 0.53, LD: 0.18, APO : 499844.48
RUN #: 160, SAMPLE #: 183, EFPA: -11.64, SIGMA: 0.51, LD: 0.16, APO : 515892.92
RUN #: 161, SAMPLE #: 19, EFPA: -11.63, SIGMA: -1.16, LD: 0.20, APO : 567234.97
RUN #: 162, SAMPLE #: 41, EFPA: -11.78, SIGMA: -0.22, LD: 0.18, APO : 548506.44
RUN #: 163, SAMPLE #: 76, EFPA: -11.65, SIGMA: -0.81, LD: 0.18, APO : 587066.14
RUN #: 164, SAMPLE #: 90, EFPA: -11.72, SIGMA: -0.66, LD: 0.19, APO : 510333.90
RUN #: 165, SAMPLE #: 47, EFPA: -12.02, SIGMA: -1.17, LD: 0.17, APO : 419713.69
RUN #: 166, SAMPLE #: 113, EFPA: -11.60, SIGMA: -0.12, LD: 0.19, APO : 488143.86
RUN #: 167, SAMPLE #: 31, EFPA: -11.77, SIGMA: 0.20, LD: 0.17, APO : 596053.95
RUN #: 168, SAMPLE #: 12, EFPA: -11.66, SIGMA: -0.55, LD: 0.16, APO : 528943.56
RUN #: 169, SAMPLE #: 144, EFPA: -11.69, SIGMA: -0.88, LD: 0.18, APO : 530110.00
RUN #: 170, SAMPLE #: 173, EFPA: -11.73, SIGMA: 0.28, LD: 0.18, APO : 511546.42
RUN #: 171, SAMPLE #: 135, EFPA: -11.72, SIGMA: 2.21, LD: 0.18, APO : 480939.25
RUN #: 172, SAMPLE #: 133, EFPA: -11.72, SIGMA: 0.12, LD: 0.18, APO : 547914.70
RUN #: 173, SAMPLE #: 29, EFPA: -11.68, SIGMA: 0.09, LD: 0.17, APO : 501368.91
RUN #: 174, SAMPLE #: 151, EFPA: -11.56, SIGMA: 1.75, LD: 0.18, APO : 549628.92
RUN #: 175, SAMPLE #: 30, EFPA: -11.91, SIGMA: 1.48, LD: 0.19, APO : 520730.21
RUN #: 176, SAMPLE #: 61, EFPA: -11.65, SIGMA: 0.92, LD: 0.18, APO : 509436.02
RUN #: 177, SAMPLE #: 51, EFPA: -11.71, SIGMA: -1.55, LD: 0.18, APO : 533197.69
RUN #: 178, SAMPLE #: 14, EFPA: -11.73, SIGMA: -0.97, LD: 0.18, APO : 490860.80
RUN #: 179, SAMPLE #: 193, EFPA: -11.64, SIGMA: -0.73, LD: 0.19, APO : 547853.74
RUN #: 180, SAMPLE #: 24, EFPA: -11.68, SIGMA: 1.43, LD: 0.19, APO : 561798.19
RUN #: 181, SAMPLE #: 62, EFPA: -11.73, SIGMA: 0.87, LD: 0.17, APO : 514610.30
RUN #: 182, SAMPLE #: 38, EFPA: -11.82, SIGMA: -1.00, LD: 0.18, APO : 527914.46
RUN #: 183, SAMPLE #: 185, EFPA: -11.77, SIGMA: 0.18, LD: 0.17, APO : 488501.27
RUN #: 184, SAMPLE #: 127, EFPA: -11.66, SIGMA: 0.34, LD: 0.18, APO : 541226.13
RUN #: 185, SAMPLE #: 198, EFPA: -11.73, SIGMA: -0.18, LD: 0.17, APO : 517869.53
RUN #: 186, SAMPLE #: 190, EFPA: -11.61, SIGMA: 1.17, LD: 0.15, APO : 490728.37
RUN #: 187, SAMPLE #: 72, EFPA: -11.66, SIGMA: 0.09, LD: 0.19, APO : 518588.55
RUN #: 188, SAMPLE #: 196, EFPA: -11.85, SIGMA: -1.36, LD: 0.16, APO : 507235.90
RUN #: 189, SAMPLE #: 156, EFPA: -11.79, SIGMA: -0.37, LD: 0.19, APO : 499120.31
RUN #: 190, SAMPLE #: 43, EFPA: -11.77, SIGMA: -0.22, LD: 0.19, APO : 500487.67
RUN #: 191, SAMPLE #: 6, EFPA: -11.54, SIGMA: -1.69, LD: 0.18, APO : 535781.80
RUN #: 192, SAMPLE #: 194, EFPA: -11.57, SIGMA: -1.53, LD: 0.16, APO : 530677.27
RUN #: 193, SAMPLE #: 20, EFPA: -11.67, SIGMA: 0.24, LD: 0.16, APO : 575290.03
RUN #: 194, SAMPLE #: 170, EFPA: -11.69, SIGMA: 0.09, LD: 0.18, APO : 558777.59
RUN #: 195, SAMPLE #: 15, EFPA: -11.79, SIGMA: -0.94, LD: 0.19, APO : 597536.66
RUN #: 196, SAMPLE #: 79, EFPA: -11.49, SIGMA: -0.91, LD: 0.20, APO : 563795.79
RUN #: 197, SAMPLE #: 44, EFPA: -11.66, SIGMA: 0.23, LD: 0.18, APO : 553128.39
RUN #: 198, SAMPLE #: 8, EFPA: -11.77, SIGMA: 1.27, LD: 0.17, APO : 517033.99
RUN #: 199, SAMPLE #: 76, EFPA: -11.82, SIGMA: -1.32, LD: 0.18, APO : 497095.82
RUN #: 200, SAMPLE #: 80, EFPA: -11.82, SIGMA: -0.53, LD: 0.19, APO : 535946.90
[4]:
p1  = np.loadtxt('../../../data/acta-astronautica/uranus-orbiter-probe/MCBXE/terminal_periapsis_arr.txt')
x1  = np.loadtxt('../../../data/acta-astronautica/uranus-orbiter-probe/MCBXE/terminal_apoapsis_arr.txt')
y1  = np.loadtxt('../../../data/acta-astronautica/uranus-orbiter-probe/MCBXE/acc_net_g_max_arr.txt')
z1  = np.loadtxt('../../../data/acta-astronautica/uranus-orbiter-probe/MCBXE/q_stag_max_arr.txt')
h1  = np.loadtxt('../../../data/acta-astronautica/uranus-orbiter-probe/MCBXE/heatload_max_arr.txt')
u1  = np.loadtxt('../../../data/acta-astronautica/uranus-orbiter-probe/MCBXE/periapsis_raise_DV_arr.txt')
v1  = np.loadtxt('../../../data/acta-astronautica/uranus-orbiter-probe/MCBXE/apoapsis_raise_DV_arr.txt')
[6]:
fig, axes = plt.subplots(1, 2, figsize = (6.5, 3.25))
plt.rc('font',family='Times New Roman')
params = {'mathtext.default': 'regular' }
plt.rcParams.update(params)

fig.tight_layout()
plt.subplots_adjust(wspace=0.30)

axes[0].hist(x1/1000.0, bins=10, color='xkcd:periwinkle')
axes[0].set_xlabel('Apoapsis altitude x '+r'$10^3$'+', km', fontsize=12)
axes[0].set_ylabel('Number of cases', fontsize=12)

axes[0].tick_params(direction='in')
axes[0].yaxis.set_ticks_position('both')
axes[0].xaxis.set_ticks_position('both')
axes[0].tick_params(axis='x',labelsize=12)
axes[0].tick_params(axis='y',labelsize=12)


axes[1].plot(p1, x1/1000.0, 'bo', markersize=5, mfc='None')

axes[1].set_xlabel('Periapsis altitude, km',fontsize=12)
axes[1].set_ylabel('Apoapsis altitude x '+r'$10^3$'+', km', fontsize=12)


axes[1].tick_params(direction='in')
axes[1].yaxis.set_ticks_position('both')
axes[1].xaxis.set_ticks_position('both')
axes[1].tick_params(axis='x',labelsize=12)
axes[1].tick_params(axis='y',labelsize=12)

for ax in axes:
    ax.xaxis.set_tick_params(direction='in', which='both')
    ax.yaxis.set_tick_params(direction='in', which='both')
    ax.xaxis.set_tick_params(width=1, length=8)
    ax.yaxis.set_tick_params(width=1, length=8)
    ax.xaxis.set_tick_params(width=1, length=6, which='minor')
    ax.yaxis.set_tick_params(width=1, length=6, which='minor')
    ax.xaxis.grid(which='major', color='k', linestyle='dotted', linewidth=0.5)
    ax.xaxis.grid(which='minor', color='k', linestyle='dotted', linewidth=0.0)
    ax.yaxis.grid(which='major', color='k', linestyle='dotted', linewidth=0.5)
    ax.yaxis.grid(which='minor', color='k', linestyle='dotted', linewidth=0.0)

    for axis in ['top', 'bottom', 'left', 'right']:
        ax.spines[axis].set_linewidth(2)

plt.show()
../../_images/acta-aa-notebooks_uranus-orbiter-probe_08-performance-analysis-E-lower-lift-to-drag-ratio_10_0.png

Remove cases which did not capture

[7]:
del_index1 = np.where(x1 < 0)
del_index1
[7]:
(array([], dtype=int64),)

No cases failed to capture. Nothing to delete.

[44]:
fig, axes = plt.subplots(1, 2, figsize = (6.5, 3.25))
plt.rc('font',family='Times New Roman')
params = {'mathtext.default': 'regular' }
plt.rcParams.update(params)

fig.tight_layout()
plt.subplots_adjust(wspace=0.30)

axes[0].hist(x1/1000.0, bins=20, color='xkcd:periwinkle')
axes[0].set_xlabel('Apoapsis altitude x '+r'$10^3$'+', km', fontsize=12)
axes[0].set_ylabel('Number of cases', fontsize=12)

axes[0].tick_params(direction='in')
axes[0].yaxis.set_ticks_position('both')
axes[0].xaxis.set_ticks_position('both')
axes[0].tick_params(axis='x',labelsize=12)
axes[0].tick_params(axis='y',labelsize=12)


axes[1].plot(p1, x1/1000.0, 'bo', markersize=5, mfc='None')

axes[1].set_xlabel('Periapsis altitude, km',fontsize=12)
axes[1].set_ylabel('Apoapsis altitude x '+r'$10^3$'+', km', fontsize=12)


axes[1].tick_params(direction='in')
axes[1].yaxis.set_ticks_position('both')
axes[1].xaxis.set_ticks_position('both')
axes[1].tick_params(axis='x',labelsize=12)
axes[1].tick_params(axis='y',labelsize=12)

for ax in axes:
    ax.xaxis.set_tick_params(direction='in', which='both')
    ax.yaxis.set_tick_params(direction='in', which='both')
    ax.xaxis.set_tick_params(width=1, length=8)
    ax.yaxis.set_tick_params(width=1, length=8)
    ax.xaxis.set_tick_params(width=1, length=6, which='minor')
    ax.yaxis.set_tick_params(width=1, length=6, which='minor')
    ax.xaxis.grid(which='major', color='k', linestyle='dotted', linewidth=0.5)
    ax.xaxis.grid(which='minor', color='k', linestyle='dotted', linewidth=0.0)
    ax.yaxis.grid(which='major', color='k', linestyle='dotted', linewidth=0.5)
    ax.yaxis.grid(which='minor', color='k', linestyle='dotted', linewidth=0.0)

    for axis in ['top', 'bottom', 'left', 'right']:
        ax.spines[axis].set_linewidth(2)

plt.show()
../../_images/acta-aa-notebooks_uranus-orbiter-probe_08-performance-analysis-E-lower-lift-to-drag-ratio_14_0.png
[8]:
print("--------------------------------------------------------------------------------------------------------")

print("Parameter              |      Min.     0.13-percentile      Mean      99.87-percentile      Max")
print("--------------------------------------------------------------------------------------------------------")
print("Apoapsis altitude, km  |    " + str(round(np.min(x1))) + "          " +  str(round(np.percentile(x1, 0.13))) +\
                                                                "         " +  str(round(np.average(x1))) +
                                                                "          " +  str(round(np.percentile(x1, 99.87)))+\
                                                                "          " +  str(round(np.max(x1))))
print("Periapsis altitude, km |       " + str(round(np.min(p1))) + "             " +  str(round(np.percentile(p1, 0.13))) +\
                                                                "            " +  str(round(np.average(p1))) +
                                                                "             " +  str(round(np.percentile(p1, 99.87)))+\
                                                                "             " +  str(round(np.max(p1))))
print("Peak deceleration, g   |       " + str(round(np.min(y1), 2)) + "           " +  str(round(np.percentile(y1, 0.13), 2)) +\
                                                                "           " +  str(round(np.average(y1), 2)) +
                                                                "            " +  str(round(np.percentile(y1, 99.87), 2))+\
                                                                "           " +  str(round(np.max(y1), 2)))

print("Peak heat rate, W/cm2  |       " + str(round(np.min(z1))) + "           " +  str(round(np.percentile(z1, 0.13))) +\
                                                                "           " +  str(round(np.average(z1))) +
                                                                "            " +  str(round(np.percentile(z1, 99.87)))+\
                                                                "            " +  str(round(np.max(z1))))

print("Peak heat load, kJ/cm2 |        " + str(round(np.min(h1))) + "            " +  str(round(np.percentile(h1, 0.13))) +\
                                                                "            " +  str(round(np.average(h1))) +
                                                                "             " +  str(round(np.percentile(h1, 99.87)))+\
                                                                "             " +  str(round(np.max(h1))))
print("Periapsis raise dV, m/s|      " + str(round(np.min(u1), 2)) + "          " +  str(round(np.percentile(u1, 0.13), 2)) +\
                                                                "          " +  str(round(np.average(u1), 2)) +
                                                                "           " +  str(round(np.percentile(u1, 99.87), 2))+\
                                                                "           " +  str(round(np.max(u1), 2)))

print("Apoapsis corr. dV, m/s |     " + str(round(np.min(v1), 2)) + "         " +  str(round(np.percentile(v1, 0.13), 2)) +\
                                                                "           " +  str(round(np.average(v1), 2)) +
                                                                "          " +  str(round(np.percentile(v1, 99.87), 2))+\
                                                                "          " +  str(round(np.max(v1), 2)))

print("--------------------------------------------------------------------------------------------------------")

--------------------------------------------------------------------------------------------------------
Parameter              |      Min.     0.13-percentile      Mean      99.87-percentile      Max
--------------------------------------------------------------------------------------------------------
Apoapsis altitude, km  |    419714          430778         527364          620707          628794
Periapsis altitude, km |       166             166            191             210             211
Peak deceleration, g   |       7.0           7.02           8.03            9.88           10.0
Peak heat rate, W/cm2  |       1634           1634           1750            1887            1888
Peak heat load, kJ/cm2 |        206            206            221             231             231
Periapsis raise dV, m/s|      56.01          56.71          65.75           78.78           80.59
Apoapsis corr. dV, m/s |     -57.04         -51.62           20.76          122.95          136.54
--------------------------------------------------------------------------------------------------------
[9]:
fig, axes = plt.subplots(1, 2, figsize = (6.75, 3.5))
plt.rc('font',family='Times New Roman')
params = {'mathtext.default': 'regular' }
plt.rcParams.update(params)

fig.tight_layout()
plt.subplots_adjust(wspace=0.30)

axes[0].axvline(x=550.0, linewidth=1.5, color='k', linestyle='dashed')
axes[0].hist(x1/1000.0, bins=10, color='xkcd:periwinkle')
axes[0].set_xlabel('Apoapsis altitude x '+r'$10^3$'+', km', fontsize=12)
axes[0].set_ylabel('Number of cases', fontsize=12)

axes[0].tick_params(direction='in')
axes[0].yaxis.set_ticks_position('both')
axes[0].xaxis.set_ticks_position('both')
axes[0].tick_params(axis='x',labelsize=12)
axes[0].tick_params(axis='y',labelsize=12)


axes[1].plot(p1, x1/1000.0, 'bo', markersize=5, mfc='None')
axes[1].axhline(y=550.0, linewidth=1.5, color='k', linestyle='dashed')

axes[1].set_xlabel('Periapsis altitude, km',fontsize=12)
axes[1].set_ylabel('Apoapsis altitude x '+r'$10^3$'+', km', fontsize=12)


axes[1].tick_params(direction='in')
axes[1].yaxis.set_ticks_position('both')
axes[1].xaxis.set_ticks_position('both')
axes[1].tick_params(axis='x',labelsize=12)
axes[1].tick_params(axis='y',labelsize=12)

for ax in axes:
    ax.xaxis.set_tick_params(direction='in', which='both')
    ax.yaxis.set_tick_params(direction='in', which='both')
    ax.xaxis.set_tick_params(width=1, length=8)
    ax.yaxis.set_tick_params(width=1, length=8)
    ax.xaxis.set_tick_params(width=1, length=6, which='minor')
    ax.yaxis.set_tick_params(width=1, length=6, which='minor')
    ax.xaxis.grid(which='major', color='k', linestyle='dotted', linewidth=0.5)
    ax.xaxis.grid(which='minor', color='k', linestyle='dotted', linewidth=0.0)
    ax.yaxis.grid(which='major', color='k', linestyle='dotted', linewidth=0.5)
    ax.yaxis.grid(which='minor', color='k', linestyle='dotted', linewidth=0.0)

    for axis in ['top', 'bottom', 'left', 'right']:
        ax.spines[axis].set_linewidth(2)

plt.savefig('../../../data/acta-astronautica/uranus-orbiter-probe/periapsis-vs-apoapsis-XE.png', dpi= 300,bbox_inches='tight')
plt.savefig('../../../data/acta-astronautica/uranus-orbiter-probe/periapsis-vs-apoapsis-XE.pdf', dpi=300,bbox_inches='tight')
plt.savefig('../../../data/acta-astronautica/uranus-orbiter-probe/periapsis-vs-apoapsis-XE.eps', dpi=300,bbox_inches='tight')


plt.show()
../../_images/acta-aa-notebooks_uranus-orbiter-probe_08-performance-analysis-E-lower-lift-to-drag-ratio_16_0.png
[10]:
fig, axes = plt.subplots(1, 2, figsize = (6.75, 3.5))
plt.rc('font',family='Times New Roman')
params = {'mathtext.default': 'regular' }
plt.rcParams.update(params)

fig.tight_layout()
plt.subplots_adjust(wspace=0.30)

axes[0].plot(y1, z1, 'ro', markersize=5, mfc='None')
axes[0].axhline(y=np.percentile(z1, 99.87), linewidth=1.5, color='k', linestyle='dotted')
axes[0].axvline(x=np.percentile(y1, 99.87), linewidth=1.5, color='k', linestyle='dotted')
axes[0].set_xlabel('Peak deceleration, Earth g', fontsize=12)
axes[0].set_ylabel('Peak stagnation-point heat rate, '+r'$W/cm^2$', fontsize=12)
axes[0].tick_params(direction='in')
axes[0].yaxis.set_ticks_position('both')
axes[0].xaxis.set_ticks_position('both')
axes[0].tick_params(axis='x',labelsize=12)
axes[0].tick_params(axis='y',labelsize=12)

axes[1].plot(z1, h1, 'go', markersize=5, mfc='None')
axes[1].axhline(y=np.percentile(h1, 99.87), linewidth=1.5, color='k', linestyle='dotted')
axes[1].axvline(x=np.percentile(z1, 99.87), linewidth=1.5, color='k', linestyle='dotted')
axes[1].set_xlabel('Peak stagnation-point heat rate, '+r'$W/cm^2$', fontsize=12)
axes[1].set_ylabel('Peak stagnation-point heat load, '+r'$kJ/cm^2$', fontsize=12)
axes[1].tick_params(direction='in')
axes[1].yaxis.set_ticks_position('both')
axes[1].xaxis.set_ticks_position('both')
axes[1].tick_params(axis='x',labelsize=12)
axes[1].tick_params(axis='y',labelsize=12)



for ax in axes:
    ax.xaxis.set_tick_params(direction='in', which='both')
    ax.yaxis.set_tick_params(direction='in', which='both')
    ax.xaxis.set_tick_params(width=1, length=8)
    ax.yaxis.set_tick_params(width=1, length=8)
    ax.xaxis.set_tick_params(width=1, length=6, which='minor')
    ax.yaxis.set_tick_params(width=1, length=6, which='minor')
    ax.xaxis.grid(which='major', color='k', linestyle='dotted', linewidth=0.5)
    ax.xaxis.grid(which='minor', color='k', linestyle='dotted', linewidth=0.0)
    ax.yaxis.grid(which='major', color='k', linestyle='dotted', linewidth=0.5)
    ax.yaxis.grid(which='minor', color='k', linestyle='dotted', linewidth=0.0)

    for axis in ['top', 'bottom', 'left', 'right']:
        ax.spines[axis].set_linewidth(2)

plt.savefig('../../../data/acta-astronautica/uranus-orbiter-probe/heat-rate-vs-g-load-XE.png', dpi= 300,bbox_inches='tight')
plt.savefig('../../../data/acta-astronautica/uranus-orbiter-probe/heat-rate-vs-g-load-XE.pdf', dpi=300,bbox_inches='tight')
plt.savefig('../../../data/acta-astronautica/uranus-orbiter-probe/heat-rate-vs-g-load-XE.eps', dpi=300,bbox_inches='tight')


plt.show()
../../_images/acta-aa-notebooks_uranus-orbiter-probe_08-performance-analysis-E-lower-lift-to-drag-ratio_17_0.png
[11]:
fig, axes = plt.subplots(1, 2, figsize = (6.75, 3.5))
plt.rc('font',family='Times New Roman')
params = {'mathtext.default': 'regular' }
plt.rcParams.update(params)

fig.tight_layout()
plt.subplots_adjust(wspace=0.30)


axes[0].hist(u1, bins=10, color='xkcd:periwinkle')
axes[0].axvline(x=np.percentile(u1, 99.87), linewidth=1.5, color='k', linestyle='dotted')
axes[0].set_xlabel('Periapse raise '+r'$\Delta V$'+', m/s', fontsize=12)
axes[0].set_ylabel('Number of cases', fontsize=12)
axes[0].tick_params(direction='in')
axes[0].yaxis.set_ticks_position('both')
axes[0].xaxis.set_ticks_position('both')
axes[0].tick_params(axis='x',labelsize=12)
axes[0].tick_params(axis='y',labelsize=12)

axes[1].hist(v1, bins=10, color='xkcd:orange')
axes[1].axvline(x=np.percentile(v1, 99.87), linewidth=1.5, color='k', linestyle='dotted')
axes[1].set_xlabel('Apoapsis correction '+r'$\Delta V$'+', m/s', fontsize=12)
axes[1].set_ylabel('Number of cases', fontsize=12)
axes[1].tick_params(direction='in')
axes[1].yaxis.set_ticks_position('both')
axes[1].xaxis.set_ticks_position('both')
axes[1].tick_params(axis='x',labelsize=12)
axes[1].tick_params(axis='y',labelsize=12)



for ax in axes:
    ax.xaxis.set_tick_params(direction='in', which='both')
    ax.yaxis.set_tick_params(direction='in', which='both')
    ax.xaxis.set_tick_params(width=1, length=8)
    ax.yaxis.set_tick_params(width=1, length=8)
    ax.xaxis.set_tick_params(width=1, length=6, which='minor')
    ax.yaxis.set_tick_params(width=1, length=6, which='minor')
    ax.xaxis.grid(which='major', color='k', linestyle='dotted', linewidth=0.5)
    ax.xaxis.grid(which='minor', color='k', linestyle='dotted', linewidth=0.0)
    ax.yaxis.grid(which='major', color='k', linestyle='dotted', linewidth=0.5)
    ax.yaxis.grid(which='minor', color='k', linestyle='dotted', linewidth=0.0)

    for axis in ['top', 'bottom', 'left', 'right']:
        ax.spines[axis].set_linewidth(2)

plt.savefig('../../../data/acta-astronautica/uranus-orbiter-probe/prm-arm-maneuvers-XE.png', dpi= 300,bbox_inches='tight')
plt.savefig('../../../data/acta-astronautica/uranus-orbiter-probe/prm-arm-maneuvers-XE.pdf', dpi=300,bbox_inches='tight')
plt.savefig('../../../data/acta-astronautica/uranus-orbiter-probe/prm-arm-maneuvers-XE.eps', dpi=300,bbox_inches='tight')


plt.show()
../../_images/acta-aa-notebooks_uranus-orbiter-probe_08-performance-analysis-E-lower-lift-to-drag-ratio_18_0.png
[12]:
def percent_between(a, lower, upper, closed_left=True, closed_right=True):
    """
    Finds the percentage of values between a range for a numpy array

    Parameters
    ----------
    a: np.ndarray
      numpy array to calculate percentage
    lower: int, float
      lower bound
    upper: int, float
      upper bound
    closed_left:
      closed left bound ( > vs >= )
    closed_right:
      closed right bound ( < vs <= )
    """
    l = np.greater if not closed_left else np.greater_equal
    r = np.less if not closed_right else np.less_equal

    c = l(a, lower) & r(a, upper)
    return np.count_nonzero(c) / float(a.size)
[13]:
percent_between(x1, -1e9, 0)
[13]:
0.0
[51]:
percent_between(x1, 500e3, 600e3)
[51]:
0.78
[52]:
percent_between(x1, 450e3, 650e3)
[52]:
0.995
[53]:
percent_between(x1, 350e3, 750e3)
[53]:
1.0