annotate Common/Src/calc_crush.c @ 936:3029f0332f4f Evo_2_23

GNSS introduced power saving mode: In the previous implementation the modul always did a cold start. In the new one the power saving functions of the module are activated. The module will be switched to intervall mode while entering sleep. If the computer remains in sleep for a long time then the GNSS modul will be switchen of completly.
author Ideenmodellierer
date Sun, 08 Dec 2024 22:03:07 +0100 (6 days ago)
parents 8f8ea3a32e82
children
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38
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1 ///////////////////////////////////////////////////////////////////////////////
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2 /// -*- coding: UTF-8 -*-
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3 ///
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4 /// \file Common/Src/calc_crush.c
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5 /// \brief VPM Desaturation code
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6 /// \author Heinrichs Weikamp
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7 /// \date 2018
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8 ///
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9 /// $Id$
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10 ///////////////////////////////////////////////////////////////////////////////
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11 /// \par Copyright (c) 2014-2018 Heinrichs Weikamp gmbh
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12 ///
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13 /// This program is free software: you can redistribute it and/or modify
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14 /// it under the terms of the GNU General Public License as published by
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15 /// the Free Software Foundation, either version 3 of the License, or
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16 /// (at your option) any later version.
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17 ///
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18 /// This program is distributed in the hope that it will be useful,
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19 /// but WITHOUT ANY WARRANTY; without even the implied warranty of
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20 /// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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21 /// GNU General Public License for more details.
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22 ///
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23 /// You should have received a copy of the GNU General Public License
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24 /// along with this program. If not, see <http://www.gnu.org/licenses/>.
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25 //////////////////////////////////////////////////////////////////////////////
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26
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27 #include "calc_crush.h"
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28
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29 #include "decom.h"
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30 #include "math.h"
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31 #include "vpm.h"
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32
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33 /* Common Block Declarations */
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34 //#pragma warning(disable:1035)
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35
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36 const float SURFACE_TENSION_GAMMA = 0.0179f; //!Adj. Range: 0.015 to 0.065 N/m
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37 const float SKIN_COMPRESSION_GAMMAC = 0.257f; //!Adj. Range: 0.160 to 0.290 N/m
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38 const float UNITS_FACTOR = 10.1325f;
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39 const float WATER_VAPOR_PRESSURE = 0.493f; // (Schreiner value) based on respiratory quotien
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40 const float CRIT_VOLUME_PARAMETER_LAMBDA = 7500.0f; //!Adj. Range: 6500 to 8300 fsw-min
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41 const float GRADIENT_ONSET_OF_IMPERM_ATM = 8.2f; //!Adj. Range: 5.0 to 10.0 atm
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42 const float REGENERATION_TIME_CONSTANT = 20160.0f; //!Adj. Range: 10080 to 51840 min
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43 const float PRESSURE_OTHER_GASES_MMHG = 102.0f; //!Constant value for PO2 up to 2 atm
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44 const float CONSTANT_PRESSURE_OTHER_GASES = 102.0f * 10.1325f / 760.0f; // PRESSURE_OTHER_GASES_MMHG / 760. * UNITS_FACTOR;
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45
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46 const float HELIUM_TIME_CONSTANT[16] = {3.68695308808482E-001f,
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47 2.29518933960247E-001f,
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48 1.46853216220327E-001f,
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49 9.91626867753856E-002f,
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50 6.78890480470074E-002f,
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51 4.78692804254106E-002f,
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52 3.37626488338989E-002f,
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53 2.38113081607676E-002f,
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54 1.68239606932026E-002f,
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55 1.25592893741610E-002f,
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56 9.80544886914621E-003f,
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57 7.67264977374303E-003f,
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58 6.01220557342307E-003f,
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59 4.70185307665137E-003f,
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60 3.68225234041620E-003f,
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61 2.88775228329769E-003f};
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62
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63 const float NITROGEN_TIME_CONSTANT[16] = {1.38629436111989E-001f,
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64 8.66433975699932E-002f,
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65 5.54517744447956E-002f,
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66 3.74674151654024E-002f,
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67 2.56721177985165E-002f,
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68 1.80978376125312E-002f,
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69 1.27651414467762E-002f,
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70 9.00191143584345E-003f,
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71 6.35914844550409E-003f,
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72 4.74758342849278E-003f,
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73 3.70666941475907E-003f,
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74 2.90019740820061E-003f,
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75 2.27261370675392E-003f,
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76 1.77730046297422E-003f,
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77 1.39186180835330E-003f,
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78 1.09157036308653E-003f};
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79
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80 int onset_of_impermeability(SGas* pGas, float *starting_ambient_pressure,
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81 float *ending_ambient_pressure,
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82 float *rate,
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83 float* amb_pressure_onset_of_imperm,
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84 float* gas_tension_onset_of_imperm,
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85 float* initial_helium_pressure,
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86 float* initial_nitrogen_pressure,
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87 short i);
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88 int radius_root_finder (float *a, float *b, float *c, float *low_bound, float *high_bound, float *ending_radius);
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89 //void get_inert_gases_(SBuehlmann* input, ,short gas_id, float ambient_pressure_bar, float* fraction_nitrogen,float* fraction_helium );
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90 int vpm_repetitive_algorithm(SVpm* pVpm, float *surface_interval_time, float* initial_critical_radius_he, float* initial_critical_radius_n2);
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91
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92
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93
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94 /* =============================================================================== */
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95 /* NOTE ABOUT PRESSURE UNITS USED IN CALCULATIONS: */
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96 /* It is the convention in decompression calculations to compute all gas */
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97 /* loadings, absolute pressures, partial pressures, etc., in the units of */
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98 /* depth pressure that you are diving - either feet of seawater (fsw) or */
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99 /* meters of seawater (msw). This program follows that convention with the */
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100 /* the exception that all VPM calculations are performed in SI units (by */
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101 /* necessity). Accordingly, there are several conversions back and forth */
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102 /* between the diving pressure units and the SI units. */
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103 /* =============================================================================== */
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104 /* =============================================================================== */
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105 /* FUNCTION SUBPROGRAM FOR GAS LOADING CALCULATIONS - ASCENT AND DESCENT */
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106 /* =============================================================================== */
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107
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108 float schreiner_equation__2(float *initial_inspired_gas_pressure,
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109 float *rate_change_insp_gas_pressure,
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110 float *interval_time_minutes,
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111 const float *gas_time_constant,
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112 float *initial_gas_pressure)
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113 {
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114 /* System generated locals */
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115 float ret_val;
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116 float time_null_pressure = 0.0f;
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117 float time_rest = 0.0f;
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118 float time = *interval_time_minutes;
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119 /* =============================================================================== */
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120 /* Note: The Schreiner equation is applied when calculating the uptake or */
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121 /* elimination of compartment gases during linear ascents or descents at a */
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122 /* constant rate. For ascents, a negative number for rate must be used. */
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123 /* =============================================================================== */
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124 if( *rate_change_insp_gas_pressure < 0.0f)
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125 {
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126 time_null_pressure = -1.0f * *initial_inspired_gas_pressure / *rate_change_insp_gas_pressure;
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127 if(time > time_null_pressure )
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128 {
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129 time_rest = time - time_null_pressure;
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130 time = time_null_pressure;
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131 }
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132 }
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133 ret_val =
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134 *initial_inspired_gas_pressure +
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135 *rate_change_insp_gas_pressure *
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136 (time - 1.f / *gas_time_constant) -
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137 (*initial_inspired_gas_pressure -
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138 *initial_gas_pressure -
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139 *rate_change_insp_gas_pressure / *gas_time_constant) *
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140 expf(-(*gas_time_constant) * time);
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141
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142 if(time_rest > 0.0f)
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143 {
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144 ret_val = ret_val * expf(-(*gas_time_constant) * time_rest);
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145 }
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146
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147
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148 return ret_val;
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149 }; /* schreiner_equation__2 */
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150
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151 /* =============================================================================== */
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152 /* SUBROUTINE CALC_CRUSHING_PRESSURE */
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153 /* Purpose: Compute the effective "crushing pressure" in each compartment as */
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154 /* a result of descent segment(s). The crushing pressure is the gradient */
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155 /* (difference in pressure) between the outside ambient pressure and the */
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156 /* gas tension inside a VPM nucleus (bubble seed). This gradient acts to */
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157 /* reduce (shrink) the radius smaller than its initial value at the surface. */
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158 /* This phenomenon has important ramifications because the smaller the radius */
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159 /* of a VPM nucleus, the greater the allowable supersaturation gradient upon */
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160 /* ascent. Gas loading (uptake) during descent, especially in the fast */
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161 /* compartments, will reduce the magnitude of the crushing pressure. The */
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162 /* crushing pressure is not cumulative over a multi-level descent. It will */
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163 /* be the maximum value obtained in any one discrete segment of the overall */
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164 /* descent. Thus, the program must compute and store the maximum crushing */
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165 /* pressure for each compartment that was obtained across all segments of */
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166 /* the descent profile. */
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167
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168 /* The calculation of crushing pressure will be different depending on */
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169 /* whether or not the gradient is in the VPM permeable range (gas can diffuse */
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170 /* across skin of VPM nucleus) or the VPM impermeable range (molecules in */
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171 /* skin of nucleus are squeezed together so tight that gas can no longer */
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172 /* diffuse in or out of nucleus; the gas becomes trapped and further resists */
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173 /* the crushing pressure). The solution for crushing pressure in the VPM */
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174 /* permeable range is a simple linear equation. In the VPM impermeable */
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175 /* range, a cubic equation must be solved using a numerical method. */
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176
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177 /* Separate crushing pressures are tracked for helium and nitrogen because */
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178 /* they can have different critical radii. The crushing pressures will be */
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179 /* the same for helium and nitrogen in the permeable range of the model, but */
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180 /* they will start to diverge in the impermeable range. This is due to */
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181 /* the differences between starting radius, radius at the onset of */
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182 /* impermeability, and radial compression in the impermeable range. */
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183 /* =============================================================================== */
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184 int calc_crushing_pressure(SLifeData* lifeData, SVpm* vpm, float * initial_helium_pressure, float * initial_nitrogen_pressure, float starting_ambient_pressure,
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185 float rate )
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186 {
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187 /* System generated locals */
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188 static float r1, r2;
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189
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190 static float low_bound_n2,
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191 ending_radius_n2,
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192 gradient_onset_of_imperm_pa;
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193 static float low_bound_he,
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194 ending_radius_he,
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195 high_bound_n2,
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196 crushing_pressure_n2;
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197 short i;
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198 static float crushing_pressure_pascals_n2,
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199 gradient_onset_of_imperm,
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200 starting_gas_tension,
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201 high_bound_he,
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202 crushing_pressure_he,
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203 amb_press_onset_of_imperm_pa,
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204 crushing_pressure_pascals_he,
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205 radius_onset_of_imperm_n2,
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206 starting_gradient,
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207 radius_onset_of_imperm_he,
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208 ending_gas_tension;
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209
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210 static float ending_ambient_pressure_pa,
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211 a_n2,
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212 b_n2,
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213 c_n2,
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214 ending_gradient,
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215 gas_tension_onset_of_imperm_pa,
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216 a_he,
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217 b_he, c_he;
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218 static float amb_pressure_onset_of_imperm[16];
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219 static float gas_tension_onset_of_imperm[16];
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220
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221 static float helium_pressure_crush[16];
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222 static float nitrogen_pressure_crush[16];
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223
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224
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225 static float ending_ambient_pressure = 0;
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226
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227 ending_ambient_pressure = lifeData->pressure_ambient_bar * 10;
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228 for( i = 0; i < 16; i++)
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229 {
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230 helium_pressure_crush[i] = lifeData->tissue_helium_bar[i] * 10;
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231 nitrogen_pressure_crush[i] = lifeData->tissue_nitrogen_bar[i] * 10;
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232 }
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233
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234
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235
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236
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237
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238 /* loop */
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239 /* =============================================================================== */
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240 /* CALCULATIONS */
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241 /* First, convert the Gradient for Onset of Impermeability from units of */
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242 /* atmospheres to diving pressure units (either fsw or msw) and to Pascals */
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243 /* (SI units). The reason that the Gradient for Onset of Impermeability is */
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244 /* given in the program settings in units of atmospheres is because that is */
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245 /* how it was reported in the original research papers by Yount and */
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246 /* colleauges. */
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247 /* =============================================================================== */
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248
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249 gradient_onset_of_imperm = GRADIENT_ONSET_OF_IMPERM_ATM * UNITS_FACTOR;
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250 gradient_onset_of_imperm_pa = GRADIENT_ONSET_OF_IMPERM_ATM * 101325.0f;
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251
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252 /* =============================================================================== */
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253 /* Assign values of starting and ending ambient pressures for descent segment */
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254 /* =============================================================================== */
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255
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256 //starting_ambient_pressure = *starting_depth;
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257 //ending_ambient_pressure = *ending_depth;
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258
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259 /* =============================================================================== */
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260 /* MAIN LOOP WITH NESTED DECISION TREE */
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261 /* For each compartment, the program computes the starting and ending */
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262 /* gas tensions and gradients. The VPM is different than some dissolved gas */
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263 /* algorithms, Buhlmann for example, in that it considers the pressure due to */
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264 /* oxygen, carbon dioxide, and water vapor in each compartment in addition to */
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265 /* the inert gases helium and nitrogen. These "other gases" are included in */
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266 /* the calculation of gas tensions and gradients. */
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267 /* =============================================================================== */
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268
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269 crushing_pressure_he = 0.0f;
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270 crushing_pressure_n2 = 0.0f;
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271
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272 for (i = 0; i < 16; ++i) {
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273 starting_gas_tension = initial_helium_pressure[i] + initial_nitrogen_pressure[i] + CONSTANT_PRESSURE_OTHER_GASES;
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274 starting_gradient = starting_ambient_pressure - starting_gas_tension;
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275 ending_gas_tension = helium_pressure_crush[i] + nitrogen_pressure_crush[i] + CONSTANT_PRESSURE_OTHER_GASES;
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276 ending_gradient = ending_ambient_pressure - ending_gas_tension;
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277
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278 /* =============================================================================== */
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279 /* Compute radius at onset of impermeability for helium and nitrogen */
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280 /* critical radii */
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281 /* =============================================================================== */
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282
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283 radius_onset_of_imperm_he = 1.0f / (
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284 gradient_onset_of_imperm_pa /
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285 ((SKIN_COMPRESSION_GAMMAC -
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286 SURFACE_TENSION_GAMMA) * 2.0f) +
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287 1.0f / vpm->adjusted_critical_radius_he[i]);
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288 radius_onset_of_imperm_n2 = 1.0f / (
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289 gradient_onset_of_imperm_pa /
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290 ((SKIN_COMPRESSION_GAMMAC -
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291 SURFACE_TENSION_GAMMA) * 2.0f) +
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292 1.0f / vpm->adjusted_critical_radius_n2[i]);
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293
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294 /* =============================================================================== */
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295 /* FIRST BRANCH OF DECISION TREE - PERMEABLE RANGE */
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296 /* Crushing pressures will be the same for helium and nitrogen */
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297 /* =============================================================================== */
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298
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299 if (ending_gradient <= gradient_onset_of_imperm) {
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300 crushing_pressure_he = ending_ambient_pressure - ending_gas_tension;
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301 crushing_pressure_n2 = ending_ambient_pressure - ending_gas_tension;
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302 }
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303
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304 /* =============================================================================== */
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305 /* SECOND BRANCH OF DECISION TREE - IMPERMEABLE RANGE */
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306 /* Both the ambient pressure and the gas tension at the onset of */
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307 /* impermeability must be computed in order to properly solve for the ending */
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308 /* radius and resultant crushing pressure. The first decision block */
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309 /* addresses the special case when the starting gradient just happens to be */
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310 /* equal to the gradient for onset of impermeability (not very likely!). */
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311 /* =============================================================================== */
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312
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313 if (ending_gradient > gradient_onset_of_imperm) {
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314 if (starting_gradient == gradient_onset_of_imperm) {
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315 amb_pressure_onset_of_imperm[i] = starting_ambient_pressure;
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316 gas_tension_onset_of_imperm[i] = starting_gas_tension;
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317 }
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318
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319 /* =============================================================================== */
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320 /* In most cases, a subroutine will be called to find these values using a */
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321 /* numerical method. */
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322 /* =============================================================================== */
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323
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324 if (starting_gradient < gradient_onset_of_imperm) {
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325 onset_of_impermeability(&(lifeData->actualGas), &starting_ambient_pressure, &ending_ambient_pressure, &rate,
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326 amb_pressure_onset_of_imperm, gas_tension_onset_of_imperm,
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327 initial_helium_pressure, initial_nitrogen_pressure, i);
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328 }
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329
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330 /* =============================================================================== */
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331 /* Next, using the values for ambient pressure and gas tension at the onset */
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332 /* of impermeability, the equations are set up to process the calculations */
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333 /* through the radius root finder subroutine. This subprogram will find the */
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334 /* root (solution) to the cubic equation using a numerical method. In order */
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335 /* to do this efficiently, the equations are placed in the form */
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336 /* Ar^3 - Br^2 - C = 0, where r is the ending radius after impermeable */
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337 /* compression. The coefficients A, B, and C for helium and nitrogen are */
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338 /* computed and passed to the subroutine as arguments. The high and low */
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339 /* bounds to be used by the numerical method of the subroutine are also */
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340 /* computed (see separate page posted on Deco List ftp site entitled */
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341 /* "VPM: Solving for radius in the impermeable regime"). The subprogram */
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342 /* will return the value of the ending radius and then the crushing */
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343 /* pressures for helium and nitrogen can be calculated. */
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344 /* =============================================================================== */
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345
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346 ending_ambient_pressure_pa = ending_ambient_pressure / UNITS_FACTOR * 101325.0f;
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347 amb_press_onset_of_imperm_pa = amb_pressure_onset_of_imperm[i] / UNITS_FACTOR * 101325.0f;
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348 gas_tension_onset_of_imperm_pa = gas_tension_onset_of_imperm[i] / UNITS_FACTOR * 101325.0f;
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349 b_he = (SKIN_COMPRESSION_GAMMAC - SURFACE_TENSION_GAMMA) * 2.0f;
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350 a_he = ending_ambient_pressure_pa - amb_press_onset_of_imperm_pa + gas_tension_onset_of_imperm_pa
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351 + (SKIN_COMPRESSION_GAMMAC - SURFACE_TENSION_GAMMA) * 2.0f / radius_onset_of_imperm_he;
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352 /* Computing 3rd power */
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353 r1 = radius_onset_of_imperm_he;
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354 c_he = gas_tension_onset_of_imperm_pa * (r1 * (r1 * r1));
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355 high_bound_he = radius_onset_of_imperm_he;
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356 low_bound_he = b_he / a_he;
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357 radius_root_finder(&a_he, &b_he, &c_he, &low_bound_he, &high_bound_he, &ending_radius_he);
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358 /* Computing 3rd power */
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359 r1 = radius_onset_of_imperm_he;
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360 /* Computing 3rd power */
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361 r2 = ending_radius_he;
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362 crushing_pressure_pascals_he =
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363 gradient_onset_of_imperm_pa +
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364 ending_ambient_pressure_pa -
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365 amb_press_onset_of_imperm_pa +
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366 gas_tension_onset_of_imperm_pa *
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367 (1.0f - r1 * (r1 * r1) / (r2 * (r2 * r2)));
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368 crushing_pressure_he =
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369 crushing_pressure_pascals_he / 101325.0f * UNITS_FACTOR;
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370 b_n2 = (SKIN_COMPRESSION_GAMMAC - SURFACE_TENSION_GAMMA) * 2.0f;
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371 a_n2 = ending_ambient_pressure_pa -
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372 amb_press_onset_of_imperm_pa +
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373 gas_tension_onset_of_imperm_pa +
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374 (SKIN_COMPRESSION_GAMMAC - SURFACE_TENSION_GAMMA) *
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375 2.0f / radius_onset_of_imperm_n2;
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heinrichsweikamp
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376 /* Computing 3rd power */
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377 r1 = radius_onset_of_imperm_n2;
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378 c_n2 = gas_tension_onset_of_imperm_pa * (r1 * (r1 * r1));
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379 high_bound_n2 = radius_onset_of_imperm_n2;
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380 low_bound_n2 = b_n2 / a_n2;
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381 radius_root_finder(&a_n2,
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382 &b_n2,
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heinrichsweikamp
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383 &c_n2,
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heinrichsweikamp
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384 &low_bound_n2,
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385 &high_bound_n2,
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386 &ending_radius_n2);
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387
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388 /* Computing 3rd power */
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389 r1 = radius_onset_of_imperm_n2;
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heinrichsweikamp
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390 /* Computing 3rd power */
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391 r2 = ending_radius_n2;
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392 crushing_pressure_pascals_n2 =
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393 gradient_onset_of_imperm_pa +
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394 ending_ambient_pressure_pa -
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395 amb_press_onset_of_imperm_pa +
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396 gas_tension_onset_of_imperm_pa * (1.0f - r1 *
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397 (r1 * r1) / (r2 * (r2 * r2)));
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398 crushing_pressure_n2 = crushing_pressure_pascals_n2 / 101325.0f * UNITS_FACTOR;
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399 }
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400
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401 /* =============================================================================== */
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402 /* UPDATE VALUES OF MAX CRUSHING PRESSURE IN GLOBAL ARRAYS */
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403 /* =============================================================================== */
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404
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heinrichsweikamp
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405 /* Computing MAX */
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406 r1 = vpm->max_crushing_pressure_he[i];
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407 vpm->max_crushing_pressure_he[i] = fmaxf(r1, crushing_pressure_he);
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408 /* Computing MAX */
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409 r1 = vpm->max_crushing_pressure_n2[i];
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410 vpm->max_crushing_pressure_n2[i] = fmaxf(r1, crushing_pressure_n2);
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411 }
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412 return 0;
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413 } /* calc_crushing_pressure */
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414
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heinrichsweikamp
parents:
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415 /* =============================================================================== */
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heinrichsweikamp
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416 /* SUBROUTINE ONSET_OF_IMPERMEABILITY */
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417 /* Purpose: This subroutine uses the Bisection Method to find the ambient */
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418 /* pressure and gas tension at the onset of impermeability for a given */
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419 /* compartment. Source: "Numerical Recipes in Fortran 77", */
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420 /* Cambridge University Press, 1992. */
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421 /* =============================================================================== */
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422
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423 int onset_of_impermeability(SGas* pGas, float *starting_ambient_pressure,
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424 float *ending_ambient_pressure,
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425 float *rate,
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426 float* amb_pressure_onset_of_imperm,
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427 float* gas_tension_onset_of_imperm,
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428 float* initial_helium_pressure,
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429 float* initial_nitrogen_pressure,
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430 short i)
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431 {
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heinrichsweikamp
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432 /* Local variables */
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433 float time, last_diff_change, mid_range_nitrogen_pressure;
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434 short j;
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435 float gas_tension_at_mid_range,
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436 initial_inspired_n2_pressure,
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437 gradient_onset_of_imperm,
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438 starting_gas_tension,
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439 low_bound,
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heinrichsweikamp
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440 initial_inspired_he_pressure,
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441 high_bound_nitrogen_pressure,
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442 nitrogen_rate,
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heinrichsweikamp
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443 function_at_mid_range,
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heinrichsweikamp
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444 function_at_low_bound,
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heinrichsweikamp
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445 high_bound,
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heinrichsweikamp
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446 mid_range_helium_pressure,
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447 mid_range_time,
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448 ending_gas_tension,
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449 function_at_high_bound;
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heinrichsweikamp
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450
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451 float mid_range_ambient_pressure,
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452 high_bound_helium_pressure,
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453 helium_rate,
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454 differential_change;
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455 float fraction_helium_begin;
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456 float fraction_helium_end;
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457 float fraction_nitrogen_begin;
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heinrichsweikamp
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458 float fraction_nitrogen_end;
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heinrichsweikamp
parents:
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459 /* loop */
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heinrichsweikamp
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460 /* =============================================================================== */
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heinrichsweikamp
parents:
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461 /* CALCULATIONS */
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heinrichsweikamp
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462 /* First convert the Gradient for Onset of Impermeability to the diving */
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heinrichsweikamp
parents:
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463 /* pressure units that are being used */
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heinrichsweikamp
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464 /* =============================================================================== */
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465
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466 gradient_onset_of_imperm = GRADIENT_ONSET_OF_IMPERM_ATM * UNITS_FACTOR;
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467
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468 /* =============================================================================== */
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heinrichsweikamp
parents:
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469 /* ESTABLISH THE BOUNDS FOR THE ROOT SEARCH USING THE BISECTION METHOD */
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heinrichsweikamp
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470 /* In this case, we are solving for time - the time when the ambient pressure */
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heinrichsweikamp
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471 /* minus the gas tension will be equal to the Gradient for Onset of */
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heinrichsweikamp
parents:
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472 /* Impermeabliity. The low bound for time is set at zero and the high */
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heinrichsweikamp
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473 /* bound is set at the elapsed time (segment time) it took to go from the */
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heinrichsweikamp
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474 /* starting ambient pressure to the ending ambient pressure. The desired */
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heinrichsweikamp
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475 /* ambient pressure and gas tension at the onset of impermeability will */
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heinrichsweikamp
parents:
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476 /* be found somewhere between these endpoints. The algorithm checks to */
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heinrichsweikamp
parents:
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477 /* make sure that the solution lies in between these bounds by first */
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heinrichsweikamp
parents:
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478 /* computing the low bound and high bound function values. */
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heinrichsweikamp
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479 /* =============================================================================== */
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heinrichsweikamp
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480
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481 /*initial_inspired_he_pressure =
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482 (*starting_ambient_pressure - water_vapor_pressure) * fraction_helium[mix_number - 1];
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483 initial_inspired_n2_pressure =
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484 (*starting_ambient_pressure - water_vapor_pressure) * fraction_nitrogen[mix_number - 1];
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485 helium_rate = *rate * fraction_helium[mix_number - 1];
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486 nitrogen_rate = *rate * fraction_nitrogen[mix_number - 1];*/
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487 low_bound = 0.;
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488 high_bound = (*ending_ambient_pressure - *starting_ambient_pressure) / *rate;
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heinrichsweikamp
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489
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heinrichsweikamp
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490 //New
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491 decom_get_inert_gases( *starting_ambient_pressure / 10.0f, pGas, &fraction_nitrogen_begin, &fraction_helium_begin );
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492 decom_get_inert_gases(*ending_ambient_pressure / 10.0f, pGas, &fraction_nitrogen_end, &fraction_helium_end );
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493 initial_inspired_he_pressure = (*starting_ambient_pressure - WATER_VAPOR_PRESSURE) * fraction_helium_begin;
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494 initial_inspired_n2_pressure = (*starting_ambient_pressure - WATER_VAPOR_PRESSURE) * fraction_nitrogen_begin;
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495 helium_rate = ((*ending_ambient_pressure - WATER_VAPOR_PRESSURE)* fraction_helium_end - initial_inspired_he_pressure)/high_bound;
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496 nitrogen_rate = ((*ending_ambient_pressure - WATER_VAPOR_PRESSURE)* fraction_nitrogen_end - initial_inspired_n2_pressure)/high_bound;
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heinrichsweikamp
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497
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498 starting_gas_tension =
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499 initial_helium_pressure[i] +
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500 initial_nitrogen_pressure[i] +
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heinrichsweikamp
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501 CONSTANT_PRESSURE_OTHER_GASES;
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heinrichsweikamp
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502 function_at_low_bound =
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heinrichsweikamp
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503 *starting_ambient_pressure -
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heinrichsweikamp
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504 starting_gas_tension -
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heinrichsweikamp
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505 gradient_onset_of_imperm;
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heinrichsweikamp
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506 high_bound_helium_pressure =
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heinrichsweikamp
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507 schreiner_equation__2(&initial_inspired_he_pressure,
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heinrichsweikamp
parents:
diff changeset
508 &helium_rate,
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
509 &high_bound,
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heinrichsweikamp
parents:
diff changeset
510 &HELIUM_TIME_CONSTANT[i],
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
511 &initial_helium_pressure[i]);
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
512 high_bound_nitrogen_pressure =
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
513 schreiner_equation__2(&initial_inspired_n2_pressure,
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
514 &nitrogen_rate,
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heinrichsweikamp
parents:
diff changeset
515 &high_bound,
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
516 &NITROGEN_TIME_CONSTANT[i],
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
517 &initial_nitrogen_pressure[i]);
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heinrichsweikamp
parents:
diff changeset
518 ending_gas_tension =
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heinrichsweikamp
parents:
diff changeset
519 high_bound_helium_pressure +
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heinrichsweikamp
parents:
diff changeset
520 high_bound_nitrogen_pressure +
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heinrichsweikamp
parents:
diff changeset
521 CONSTANT_PRESSURE_OTHER_GASES;
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heinrichsweikamp
parents:
diff changeset
522 function_at_high_bound =
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heinrichsweikamp
parents:
diff changeset
523 *ending_ambient_pressure -
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
524 ending_gas_tension -
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heinrichsweikamp
parents:
diff changeset
525 gradient_onset_of_imperm;
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heinrichsweikamp
parents:
diff changeset
526 if (function_at_high_bound * function_at_low_bound >= 0.0f) {
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heinrichsweikamp
parents:
diff changeset
527 //printf("\nERROR! ROOT IS NOT WITHIN BRACKETS");
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heinrichsweikamp
parents:
diff changeset
528 }
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heinrichsweikamp
parents:
diff changeset
529
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
530 /* =============================================================================== */
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heinrichsweikamp
parents:
diff changeset
531 /* APPLY THE BISECTION METHOD IN SEVERAL ITERATIONS UNTIL A SOLUTION WITH */
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heinrichsweikamp
parents:
diff changeset
532 /* THE DESIRED ACCURACY IS FOUND */
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heinrichsweikamp
parents:
diff changeset
533 /* Note: the program allows for up to 100 iterations. Normally an exit will */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
534 /* be made from the loop well before that number. If, for some reason, the */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
535 /* program exceeds 100 iterations, there will be a pause to alert the user. */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
536 /* =============================================================================== */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
537
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heinrichsweikamp
parents:
diff changeset
538 if (function_at_low_bound < 0.0f) {
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heinrichsweikamp
parents:
diff changeset
539 time = low_bound;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
540 differential_change = high_bound - low_bound;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
541 } else {
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heinrichsweikamp
parents:
diff changeset
542 time = high_bound;
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heinrichsweikamp
parents:
diff changeset
543 differential_change = low_bound - high_bound;
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heinrichsweikamp
parents:
diff changeset
544 }
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
545 for (j = 1; j <= 100; ++j) {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
546 last_diff_change = differential_change;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
547 differential_change = last_diff_change * 0.5f;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
548 mid_range_time = time + differential_change;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
549 mid_range_ambient_pressure = *starting_ambient_pressure + *rate * mid_range_time;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
550 mid_range_helium_pressure =
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
551 schreiner_equation__2(&initial_inspired_he_pressure,
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
552 &helium_rate,
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
553 &mid_range_time,
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
554 &HELIUM_TIME_CONSTANT[i],
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
555 &initial_helium_pressure[i]);
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
556 mid_range_nitrogen_pressure =
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
557 schreiner_equation__2(&initial_inspired_n2_pressure,
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
558 &nitrogen_rate,
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
559 &mid_range_time,
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
560 &NITROGEN_TIME_CONSTANT[i],
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
561 &initial_nitrogen_pressure[i]);
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heinrichsweikamp
parents:
diff changeset
562 gas_tension_at_mid_range =
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
563 mid_range_helium_pressure +
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
564 mid_range_nitrogen_pressure +
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
565 CONSTANT_PRESSURE_OTHER_GASES;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
566 function_at_mid_range =
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
567 mid_range_ambient_pressure -
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
568 gas_tension_at_mid_range -
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
569 gradient_onset_of_imperm;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
570 if (function_at_mid_range <= 0.0f) {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
571 time = mid_range_time;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
572 }
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
573 if (fabs(differential_change) < .001f ||
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
574 function_at_mid_range == 0.0f) {
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heinrichsweikamp
parents:
diff changeset
575 goto L100;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
576 }
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
577 }
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
578 //printf("\nERROR! ROOT SEARCH EXCEEDED MAXIMUM ITERATIONS");
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heinrichsweikamp
parents:
diff changeset
579
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
580 /* =============================================================================== */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
581 /* When a solution with the desired accuracy is found, the program jumps out */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
582 /* of the loop to Line 100 and assigns the solution values for ambient */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
583 /* pressure and gas tension at the onset of impermeability. */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
584 /* =============================================================================== */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
585
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
586 L100:
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heinrichsweikamp
parents:
diff changeset
587 amb_pressure_onset_of_imperm[i] = mid_range_ambient_pressure;
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heinrichsweikamp
parents:
diff changeset
588 gas_tension_onset_of_imperm[i] = gas_tension_at_mid_range;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
589 return 0;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
590 } /* onset_of_impermeability */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
591
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
592
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
593 /* =============================================================================== */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
594 /* SUBROUTINE RADIUS_ROOT_FINDER */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
595 /* Purpose: This subroutine is a "fail-safe" routine that combines the */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
596 /* Bisection Method and the Newton-Raphson Method to find the desired root. */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
597 /* This hybrid algorithm takes a bisection step whenever Newton-Raphson would */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
598 /* take the solution out of bounds, or whenever Newton-Raphson is not */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
599 /* converging fast enough. Source: "Numerical Recipes in Fortran 77", */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
600 /* Cambridge University Press, 1992. */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
601 /* =============================================================================== */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
602
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
603 int radius_root_finder (float *a,
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
604 float *b,
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
605 float *c,
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
606 float *low_bound,
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
607 float *high_bound,
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
608 float *ending_radius)
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
609 {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
610 /* System generated locals */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
611 float r1, r2;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
612
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
613 /* Local variables */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
614 float radius_at_low_bound,
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
615 last_diff_change,
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
616 function,
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
617 radius_at_high_bound;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
618 short i;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
619 float function_at_low_bound,
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
620 last_ending_radius,
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
621 function_at_high_bound,
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
622 derivative_of_function,
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
623 differential_change;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
624
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
625 /* loop */
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heinrichsweikamp
parents:
diff changeset
626 /* =============================================================================== */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
627 /* BEGIN CALCULATIONS BY MAKING SURE THAT THE ROOT LIES WITHIN BOUNDS */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
628 /* In this case we are solving for radius in a cubic equation of the form, */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
629 /* Ar^3 - Br^2 - C = 0. The coefficients A, B, and C were passed to this */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
630 /* subroutine as arguments. */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
631 /* =============================================================================== */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
632
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
633 function_at_low_bound =
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
634 *low_bound * (*low_bound * (*a * *low_bound - *b)) - *c;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
635 function_at_high_bound =
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
636 *high_bound * (*high_bound * (*a * *high_bound - *b)) - *c;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
637 if (function_at_low_bound > 0.0f && function_at_high_bound > 0.0f) {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
638 // printf("\nERROR! ROOT IS NOT WITHIN BRACKETS");
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
639
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
640 }
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
641
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
642 /* =============================================================================== */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
643 /* Next the algorithm checks for special conditions and then prepares for */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
644 /* the first bisection. */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
645 /* =============================================================================== */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
646
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
647 if (function_at_low_bound < 0.0f && function_at_high_bound < 0.0f) {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
648 //printf("\nERROR! ROOT IS NOT WITHIN BRACKETS");
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
649
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
650 }
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
651 if (function_at_low_bound == 0.0f) {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
652 *ending_radius = *low_bound;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
653 return 0;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
654 } else if (function_at_high_bound == 0.0f) {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
655 *ending_radius = *high_bound;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
656 return 0;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
657 } else if (function_at_low_bound < 0.0f) {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
658 radius_at_low_bound = *low_bound;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
659 radius_at_high_bound = *high_bound;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
660 } else {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
661 radius_at_high_bound = *low_bound;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
662 radius_at_low_bound = *high_bound;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
663 }
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
664 *ending_radius = (*low_bound + *high_bound) * .5f;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
665 last_diff_change = (r1 = *high_bound - *low_bound, fabs(r1));
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
666 differential_change = last_diff_change;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
667
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
668 /* =============================================================================== */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
669 /* At this point, the Newton-Raphson Method is applied which uses a function */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
670 /* and its first derivative to rapidly converge upon a solution. */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
671 /* Note: the program allows for up to 100 iterations. Normally an exit will */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
672 /* be made from the loop well before that number. If, for some reason, the */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
673 /* program exceeds 100 iterations, there will be a pause to alert the user. */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
674 /* When a solution with the desired accuracy is found, exit is made from the */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
675 /* loop by returning to the calling program. The last value of ending */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
676 /* radius has been assigned as the solution. */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
677 /* =============================================================================== */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
678
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
679 function =
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
680 *ending_radius * (*ending_radius * (*a * *ending_radius - *b)) - *c;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
681 derivative_of_function =
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
682 *ending_radius * (*ending_radius * 3.0f * *a - *b * 2.0f);
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
683 for (i = 1; i <= 100; ++i) {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
684 if (((*ending_radius - radius_at_high_bound) * derivative_of_function - function) *
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
685 ((*ending_radius - radius_at_low_bound) * derivative_of_function - function) >= 0.0f
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
686 || (r1 = function * 2.0f, fabs(r1)) >
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
687 (r2 = last_diff_change * derivative_of_function, fabs(r2))) {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
688 last_diff_change = differential_change;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
689 differential_change =
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
690 (radius_at_high_bound - radius_at_low_bound) * .5f;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
691 *ending_radius = radius_at_low_bound + differential_change;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
692 if (radius_at_low_bound == *ending_radius) {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
693 return 0;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
694 }
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
695 } else {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
696 last_diff_change = differential_change;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
697 differential_change = function / derivative_of_function;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
698 last_ending_radius = *ending_radius;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
699 *ending_radius -= differential_change;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
700 if (last_ending_radius == *ending_radius) {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
701 return 0;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
702 }
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
703 }
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
704 if (fabs(differential_change) < 1e-12) {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
705 return 0;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
706 }
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
707 function =
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
708 *ending_radius * (*ending_radius * (*a * *ending_radius - *b)) - *c;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
709 derivative_of_function =
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
710 *ending_radius * (*ending_radius * 3.0f * *a - *b * 2.0f);
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
711 if (function < 0.0f) {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
712 radius_at_low_bound = *ending_radius;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
713 } else {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
714 radius_at_high_bound = *ending_radius;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
715 }
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
716 }
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
717 // printf("\nERROR! ROOT SEARCH EXCEEDED MAXIMUM ITERATIONS");
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
718 return 0;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
719 } /* radius_root_finder */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
720
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
721
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
722
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
723
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
724 void vpm_init(SVpm* pVpm, short conservatism, short repetitive_dive, long seconds_since_last_dive)
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
725 {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
726
51
8f8ea3a32e82 Resolved warnings pointing to possible invalid memory access
Ideenmodellierer
parents: 38
diff changeset
727 float critical_radius_n2_microns = 0.82; /* be conservative in case of an unexpected parameter value */
8f8ea3a32e82 Resolved warnings pointing to possible invalid memory access
Ideenmodellierer
parents: 38
diff changeset
728 float critical_radius_he_microns = 0.72;
38
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
729 float initial_critical_radius_n2[16];
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
730 float initial_critical_radius_he[16];
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
731 int i = 0;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
732 float surface_time = seconds_since_last_dive / 60;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
733 pVpm->repetitive_variables_not_valid = !repetitive_dive;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
734 //pVpm->vpm_conservatism = conservatism;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
735 switch(conservatism)
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
736 {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
737 case 0:
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
738 critical_radius_n2_microns=0.55; //!Adj. Range: 0.2 to 1.35 microns
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
739 critical_radius_he_microns=0.45; //!Adj. Range: 0.2 to 1.35 microns
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
740 break;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
741 case 1:
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
742 critical_radius_n2_microns=0.58;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
743 critical_radius_he_microns=0.48;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
744 break;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
745 case 2:
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
746 critical_radius_n2_microns=0.62;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
747 critical_radius_he_microns=0.52;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
748 break;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
749 case 3:
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
750 critical_radius_n2_microns=0.68;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
751 critical_radius_he_microns=0.58;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
752 break;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
753 case 4:
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
754 critical_radius_n2_microns=0.75;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
755 critical_radius_he_microns=0.65;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
756 break;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
757 case 5:
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
758 critical_radius_n2_microns=0.82;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
759 critical_radius_he_microns=0.72;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
760 break;
51
8f8ea3a32e82 Resolved warnings pointing to possible invalid memory access
Ideenmodellierer
parents: 38
diff changeset
761 default:
8f8ea3a32e82 Resolved warnings pointing to possible invalid memory access
Ideenmodellierer
parents: 38
diff changeset
762 critical_radius_n2_microns=0.82;
8f8ea3a32e82 Resolved warnings pointing to possible invalid memory access
Ideenmodellierer
parents: 38
diff changeset
763 critical_radius_he_microns=0.72;
8f8ea3a32e82 Resolved warnings pointing to possible invalid memory access
Ideenmodellierer
parents: 38
diff changeset
764 break;
38
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
765 }
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
766
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
767 for (i = 0; i < 16; ++i) {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
768 initial_critical_radius_n2[i] = critical_radius_n2_microns * 1e-6f;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
769 initial_critical_radius_he[i] = critical_radius_he_microns * 1e-6f;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
770 }
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
771
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
772
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
773
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
774 if( (surface_time > 0)
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
775 && (!pVpm->repetitive_variables_not_valid) )
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
776 //&& (pVpm->decomode_vpm_plus_conservatism_last_dive > 0)
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
777 //&& (pVpm->decomode_vpm_plus_conservatism_last_dive - 1 == pVpm->vpm_conservatism))
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
778 {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
779 vpm_repetitive_algorithm(pVpm, &surface_time,initial_critical_radius_he, initial_critical_radius_n2);
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
780 }
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
781 else
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
782 {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
783 //Kein gültiger Wiederholungstauchgang
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
784 for (i = 0; i < 16; ++i) {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
785 pVpm->adjusted_critical_radius_n2[i] = initial_critical_radius_n2[i];
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
786 pVpm->adjusted_critical_radius_he[i] = initial_critical_radius_he[i];
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
787 }
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
788 pVpm->repetitive_variables_not_valid = 0;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
789 }
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
790 for (i = 0; i < 16; ++i) {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
791 pVpm->max_crushing_pressure_he[i] = 0.0f;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
792 pVpm->max_crushing_pressure_n2[i] = 0.0f;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
793 pVpm->max_actual_gradient[i] = 0.0f;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
794 pVpm->adjusted_crushing_pressure_he[i] = 0.0f;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
795 pVpm->adjusted_crushing_pressure_n2[i] = 0.0f;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
796 pVpm->initial_allowable_gradient_he[i] = 0.0f;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
797 pVpm->initial_allowable_gradient_n2[i] = 0.0f;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
798 }
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
799 pVpm->max_first_stop_depth_save = 0;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
800 pVpm->depth_start_of_deco_zone_save = 0;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
801 pVpm->run_time_start_of_deco_zone_save = 0;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
802 pVpm->deco_zone_reached = 0;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
803 }
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
804
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
805 /* =============================================================================== */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
806 /* SUBROUTINE VPM_REPETITIVE_ALGORITHM */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
807 /* Purpose: This subprogram implements the VPM Repetitive Algorithm that was */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
808 /* envisioned by Professor David E. Yount only months before his passing. */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
809 /* =============================================================================== */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
810 int vpm_repetitive_algorithm(SVpm* pVpm, float *surface_interval_time, float* initial_critical_radius_he, float* initial_critical_radius_n2)
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
811 {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
812 /* Local variables */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
813 static float max_actual_gradient_pascals;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
814 //static float initial_allowable_grad_n2_pa, initial_allowable_grad_he_pa;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
815 static short i;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
816 static float adj_crush_pressure_n2_pascals,
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
817 new_critical_radius_n2,
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
818 adj_crush_pressure_he_pascals,
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
819 new_critical_radius_he;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
820
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
821 /* loop */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
822 /* =============================================================================== */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
823 /* CALCULATIONS */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
824
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
825 /* by hw 160215 */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
826 /* IN: */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
827 /* pVpm->max_actual_gradient[i] */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
828 /* pVpm->initial_allowable_gradient_n2[i] */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
829 /* pVpm->initial_allowable_gradient_he[i] */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
830 /* pVpm->adjusted_crushing_pressure_he[i] */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
831 /* pVpm->adjusted_crushing_pressure_n2[i] */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
832 /* OUT: */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
833 /* pVpm->adjusted_critical_radius_n2[i] */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
834 /* pVpm->adjusted_critical_radius_he[i] */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
835 /* =============================================================================== */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
836
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
837 for (i = 0; i < 16; ++i) {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
838 max_actual_gradient_pascals = pVpm->max_actual_gradient[i] / UNITS_FACTOR * 101325.0f;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
839 adj_crush_pressure_he_pascals = pVpm->adjusted_crushing_pressure_he[i] / UNITS_FACTOR * 101325.0f;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
840 adj_crush_pressure_n2_pascals = pVpm->adjusted_crushing_pressure_n2[i] / UNITS_FACTOR * 101325.0f;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
841 /*
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
842 initial_allowable_grad_he_pa =
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
843 pVpm->initial_allowable_gradient_he[i] / UNITS_FACTOR * 101325.0f;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
844 initial_allowable_grad_n2_pa =
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
845 pVpm->initial_allowable_gradient_n2[i] / UNITS_FACTOR * 101325.0f;
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
846 */
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
847 if (pVpm->max_actual_gradient[i] > pVpm->initial_allowable_gradient_n2[i])
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
848 {
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
849 new_critical_radius_n2 =
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
850 SURFACE_TENSION_GAMMA * 2.0f *
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
851 (SKIN_COMPRESSION_GAMMAC - SURFACE_TENSION_GAMMA) /
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
852 (max_actual_gradient_pascals * SKIN_COMPRESSION_GAMMAC -
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
853 SURFACE_TENSION_GAMMA * adj_crush_pressure_n2_pascals);
5f11787b4f42 include in ostc4 repository
heinrichsweikamp
parents:
diff changeset
854
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855 pVpm->adjusted_critical_radius_n2[i] =
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856 initial_critical_radius_n2[i]
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857 + (initial_critical_radius_n2[i] - new_critical_radius_n2)
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858 * exp(-(*surface_interval_time) / REGENERATION_TIME_CONSTANT);
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859
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860 } else {
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861 pVpm->adjusted_critical_radius_n2[i] =
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862 initial_critical_radius_n2[i];
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863 }
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864 if (pVpm->max_actual_gradient[i] > pVpm->initial_allowable_gradient_he[i])
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865 {
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866 new_critical_radius_he =
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867 SURFACE_TENSION_GAMMA * 2.0f *
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868 (SKIN_COMPRESSION_GAMMAC - SURFACE_TENSION_GAMMA) /
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869 (max_actual_gradient_pascals * SKIN_COMPRESSION_GAMMAC -
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870 SURFACE_TENSION_GAMMA * adj_crush_pressure_he_pascals);
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871
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872 pVpm->adjusted_critical_radius_he[i] =
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873 initial_critical_radius_he[i]
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874 + ( initial_critical_radius_he[i] - new_critical_radius_he)
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875 * exp(-(*surface_interval_time) / REGENERATION_TIME_CONSTANT);
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876 } else {
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877 pVpm->adjusted_critical_radius_he[i] =
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878 initial_critical_radius_he[i];
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879 }
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880 }
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881 return 0;
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882 } /* vpm_repetitive_algorithm */