Source Code for Module aerocalc.ssec

  1  #!/usr/bin/env python 
  2  # encoding: utf-8 
  3   
  4  # ############################################################################# 
  5  # Copyright (c) 2008, Kevin Horton 
  6  # All rights reserved. 
  7  # Redistribution and use in source and binary forms, with or without 
  8  # modification, are permitted provided that the following conditions are met: 
  9  # * 
 10  #     * Redistributions of source code must retain the above copyright 
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 12  #     * Redistributions in binary form must reproduce the above copyright 
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 15  #     * The name of Kevin Horton may not be used to endorse or promote products 
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 18  # THIS SOFTWARE IS PROVIDED BY KEVIN HORTON ``AS IS'' AND ANY EXPRESS OR 
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 28  # ############################################################################# 
 29  # 
 30  # version 0.10, 25 Apr 2008 
 31  # 
 32  # Version History: 
 33  # vers     date     Notes 
 34  # 0.10   25 Apr 08  First public release.  
 35  # ############################################################################# 
 36   
 37  """ 
 38  Various functions related to static source error correction. 
 39  """ 
 40   
 41  import airspeed as A 
 42  import math as M 
 43  import std_atm as SA 
 44  import unit_conversion as U 
 45   
 46  ############################################################################## 
 47  # 
 48  # TAS from GPS data. 
 49  # 
 50  ############################################################################## 
 51 -def gps2tas(GS, TK, verbose = 0): 
 52      """ 
 53      Returns true airspeed, given GPS groundspeed and track on at least 
 54      three legs (four legs preferred).  Uses the method developed by Doug 
 55      Gray - http://www.kilohotel.com/rv8/rvlinks/doug_gray/TAS_FNL4.pdf 
 56       
 57      GS and TK are lists of ground speed and track data. 
 58       
 59      Three legs: 
 60          If verbose = 0, then only TAS is returned. 
 61          If verbose = 1, then TAS, wind speed and direction are returned. 
 62          If verbose = 2, then TAS, wind speed and direction and the heading 
 63          for each leg are returned.  The wind speed and direction is  
 64          returned as a tuple, and the headings are returned as a tuple 
 65   
 66           
 67      Four legs: 
 68          Data from only three legs is sufficient to calculate TAS.  If data 
 69          four legs is entered, four different calculations are conducted, 
 70          using a different mix of three data points for each calculation. 
 71          If the data quality is high, the TAS and wind for all four  
 72          calculations will be similar.  The standard deviation on the TAS is 
 73          calculated - good quality data will have a standard deviation of 
 74          less than 1 kt. 
 75           
 76          If verbose = 0, then only TAS is returned. 
 77          If verbose = 1, then TAS and its standard deviation are returned. 
 78          If verbose = 2, then TAS, its standard deviation and the four wind 
 79          speeds and directions are returned (the winds are returned as a list 
 80          of four tuples) 
 81       
 82      Validated against sample data in four leg tab of NTPS GPS PEC spreadsheet: 
 83      http://www.ntps.edu/Files/GPS%20PEC.XLS 
 84       
 85      Examples: 
 86           
 87          Data for all examples: 
 88              >>> gs = [178, 185, 188, 184] 
 89              >>> tk = [178, 82, 355, 265] 
 90               
 91              Determine the TAS, given the above data from four runs: 
 92              >>> gps2tas(gs, tk) 
 93              183.72669557114619 
 94               
 95              Determine the TAS and standard deviation from the four calculations: 
 96              >>> gps2tas(gs, tk, verbose = 1) 
 97              (183.72669557114619, 0.82709634705928436) 
 98               
 99              Determine the TAS, standard deviation, and wind speed and direction 
100              for each calculation: 
101              >>> gps2tas(gs, tk, verbose = 2) 
102              (183.72669557114619, 0.82709634705928436, ((5.2608369270843056, 194.51673740323213), (3.5823966532035927, 181.52174627838372), (5.1495218164839995, 162.69803415599802), (6.4436728241320145, 177.94783081049718))) 
103   
104      """ 
105      # confirm GS and TK are valid lengths: 
106      if 2 < len(GS) < 5: 
107          pass 
108      else: 
109          raise ValueError, 'GS must be a list of three or four items' 
110           
111      if 2 < len(TK) < 5: 
112          pass 
113      else: 
114          raise ValueError, 'TK must be a list of three or four items' 
115       
116      if len(GS) != len(TK): 
117          raise ValueError, 'The ground speed and track arrays must have the same number of elements.' 
118           
119      if len(GS) == 3: 
120          result = gps2tas3(GS, TK, verbose) 
121          return result 
122      else: 
123          gs_data_sets, tk_data_sets, results = [], [], [] 
124           
125          gs_data_sets.append([GS[0], GS[1], GS[2]]) 
126          gs_data_sets.append([GS[1], GS[2], GS[3]]) 
127          gs_data_sets.append([GS[2], GS[3], GS[0]])       
128          gs_data_sets.append([GS[3], GS[0], GS[1]]) 
129   
130          tk_data_sets.append([TK[0], TK[1], TK[2]]) 
131          tk_data_sets.append([TK[1], TK[2], TK[3]]) 
132          tk_data_sets.append([TK[2], TK[3], TK[0]])       
133          tk_data_sets.append([TK[3], TK[0], TK[1]]) 
134           
135          for (gs, tk) in zip (gs_data_sets, tk_data_sets): 
136              results.append(gps2tas3(gs, tk, 2)) 
137           
138          ave_TAS = 0 
139          ave_wind_x = 0 
140          ave_wind_y = 0 
141          sum2_TAS = 0 
142           
143          for item in results: 
144              ave_TAS +=item[0] 
145              sum2_TAS += item[0] ** 2 
146              ave_wind_x += item[1][0] * M.sin(M.pi * item[1][1] / 180.) 
147              ave_wind_y += item[1][0] * M.cos(M.pi * item[1][1] / 180.) 
148   
149          ave_TAS /= 4. 
150          std_dev_TAS = M.sqrt((sum2_TAS - 4 * ave_TAS ** 2) / 3) 
151          ave_wind_x /= 4 
152          ave_wind_y /= 4. 
153          ave_wind_speed = M.sqrt(ave_wind_x ** 2 + ave_wind_y ** 2) 
154          ave_wind_dir = (720. - (180. / M.pi * M.atan2(ave_wind_x, ave_wind_y))) % 360 
155          # return results 
156           
157          if verbose == 0: 
158              return ave_TAS 
159          elif verbose == 1: 
160              return ave_TAS, std_dev_TAS 
161          elif verbose == 2: 
162              return ave_TAS, std_dev_TAS, ((results[0][1][0], results[0][1][1]),(results[1][1][0], results[1][1][1]),(results[2][1][0], results[2][1][1]),(results[3][1][0], results[3][1][1])) 
163          else: 
164              raise ValueError, 'The value of verbose must be equal to 0, 1 or 2' 
165   
166   
167 -def gps2tas3(GS, TK, verbose=0): 
168      """ 
169      Returns true airspeed, given GPS groundspeed and track on three legs. 
170      Uses the method developed by Doug Gray: 
171      http://www.kilohotel.com/rv8/rvlinks/doug_gray/TAS_FNL4.pdf 
172       
173      GS and TK are arrays of ground speed and track data. 
174       
175      If verbose = 0, then only TAS is returned. 
176      If verbose = 1, then TAS, wind speed and wind direction are returned. 
177      If verbose = 2, then TAS, wind speed and direction and the heading for 
178      each leg are returned.  The wind speed and direction is returned as a  
179      tuple, and the headings are returned as a tuple 
180   
181      Validated against sample in Doug Gray's paper. 
182       
183      Examples: 
184       
185      """ 
186      x, y, b, m, hdg = [], [], [], [], [] 
187   
188      for (gs, tk) in zip(GS, TK): 
189          x.append(gs * M.sin(M.pi * (360. - tk) / 180.)) 
190          y.append(gs * M.cos(M.pi * (360. - tk) / 180.)) 
191       
192      m.append(-1 * (x[1] - x[0]) / (y[1] - y[0])) 
193      m.append(-1 * (x[2] - x[0]) / (y[2] - y[0])) 
194       
195      b.append((y[0] + y[1]) / 2 - m[0] * (x[0] + x[1]) / 2) 
196      b.append((y[0] + y[2]) / 2 - m[1] * (x[0] + x[2]) / 2) 
197       
198      wind_x = (b[0] - b[1]) / (m[1] - m[0])  
199      wind_y = m[0] * wind_x + b[0] 
200       
201      wind_speed = M.sqrt(wind_x ** 2 + wind_y ** 2) 
202      wind_dir = (540. - (180. / M.pi * M.atan2(wind_x, wind_y))) % 360. 
203       
204      TAS = M.sqrt((x[0] - wind_x) ** 2 + (y[0] - wind_y) ** 2) 
205       
206      if verbose >= 2: 
207          hdg.append((540. - (180. / M.pi * M.atan2(wind_x - x[0], wind_y - y[0]))) % 360.) 
208          hdg.append((540. - (180. / M.pi * M.atan2(wind_x - x[1], wind_y - y[1]))) % 360.) 
209          hdg.append((540. - (180. / M.pi * M.atan2(wind_x - x[2], wind_y - y[2]))) % 360.) 
210           
211          return TAS, (wind_speed, wind_dir), (hdg[0], hdg[1], hdg[2]) 
212   
213      elif verbose == 1: 
214          return TAS, (wind_speed, wind_dir) 
215      elif verbose == 0: 
216          return TAS 
217      else: 
218          raise ValueError, 'The value of verbose must be equal to 0, 1 or 2' 
219   
220   
221 -def main(): 
222          pass 
223   
224   
225  if __name__ == '__main__': 
226          main() 
227