The Museum of HP Calculators

Tides for the HP-41

This program is Copyright © 2003 by Jean-Marc Baillard and is used here by permission.

This program is supplied without representation or warranty of any kind. Jean-Marc Baillard and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.

Overview

-Three programs are listed hereafter:

    1°)    "WL"    calculates the water level using the harmonic method.
    2°) "TIDE1"  gives the high tides or low tides using 5 tabular values.
    3°) "TIDE2"  yields these results more directly.
 

       1°)  Water Level
 

-The water level may be computed by a trigonometric series:       wl(t) = A₀ + A₁ cos ( V₁ - G₁ ) + ............ + A_i cos ( V_i - G_i ) + ..........
  where  A₀ = the mean sea level ;  A_i and G_i = the harmonic constituents of a port = constants.
             V_i  are linear combinations of astronomical arguments.
-The following program uses a few terms ( Sa ; Q1 ; O1 ; K1 ; N2 ; M2 ; S2 ; MN4 ; M4 ; MS4 )
-Under simplifying assumptions , 11 other terms are calculated ( namely: P1 ; o1 ; k1 ; 2N2 ; µ2 ; nu2 ; L2 ; K2 ; T2 ; m2 ; k2 )
-The results are good but not very accurate: errors can reach about 20cm.
-More than 100 sinusoidal functions would be needed to achieve full accuracy

-You can find other harmonic constituents at   http://co-ops.nos.noaa.gov/data_retrieve.shtml?input_code=100201001har
-For accurate tide predictions , cf also  www.shom.fr
 

Data Registers:             R00 = d = the number of days since 01/01/2000      R01 thru R06:  temp
                                   •   R07 thru R27 = the harmonic constituents of a port. These 21 registers are to be initialized before executing "WL"

Flags: /
Subroutine:  none if you have a Time-Module
                      "J0" otherwise  ( cf "Phases of the Moon for the HP-41" )
 

-The harmonic constituents of a few ports are listed below:  A_i  are given in millimeters and  G_i  in degrees.
 
 

Port  Latitude Longitude	A0=R07	A1=R08	A2=R09	A3=R10	A4=R11	A5=R12	A6=R13	A7=R14	A8=R15	A9=R16	A10=R17
Time Scale	/	G1=R18	G2=R19	G3=R20	G4=R21	G5=R22	G6=R23	G7=R24	G8=R25	G9=R26	G10=R27

 

Bombay    18°55'N    72°50'E	2520	43	41	201	425	287	1227	479	7	35	32
Time Scale = UT+5h30mn	/	33	58	52	56	327	345	25	296	332	43

-

Boston  42°21'N    71°02'W	1490	32	20	111	140	301	1345	219	0	20	9
Time Scale = UT-5h	/	131	110	119	132	300	326	356	0	98	118

-

Brest    48°23'N    04°30'W	4020	47	20	67	65	415	2040	746	19	54	34
Time Scale = UT+1h	/	243	294	342	89	119	138	178	117	164	239

-

Colombo    6°57'N    79°51'E	380	95	10	29	73	22	176	119	7	5	3
Time Scale = UT+5h30mn	/	308	82	59	36	31	50	100	269	169	258

-

Dakar   14°40'N     17°25'W	1010	87	12	38	63	91	461	166	0	10	6
Time Scale = UT	/	153	194	251	350	235	257	293	0	282	0

-

Dar Es-Salaam   6°49'S  39°19'E	1530	35	22	106	171	191	1074	536	4	11	7
Time Scale = UT+3h	/	311	30	43	42	86	111	156	250	316	31

-

Djibouti  11°35'N     43°09'E	1870	107	38	192	386	126	463	205	0	0	0
Time Scale = UT+3h	/	6	41	39	39	222	229	250	0	0	0

-

Hong-Kong  22°17'N   114°11'E	1380	100	54	289	359	85	404	162	8	25	17
Time Scale = UT+8h	/	215	225	249	299	250	268	299	268	333	19

-

Libreville     0°23'N      9°26'E	1290	90	6	17	95	120	595	193	9	28	17
Time Scale = UT+1h	/	282	126	328	8	140	146	176	34	82	148

-

Lisbon   38°42'N     09°08'W	2200	20	15	61	68	238	1150	401	0	77	48
Time Scale = UT+1h	/	33	277	334	73	89	106	136	0	303	342

-

Los Angeles  33°43'N   118°16'W	850	65	39	216	339	119	515	203	0	0	0
Time Scale = UT-8h	/	186	77	81	88	257	275	261	0	0	0

-

Madras    13°06'N    80°18'E	650	102	1	28	90	72	332	137	1	2	2
Time Scale = UT+5h30mn	/	221	86	313	341	235	243	279	77	102	179

-

Melbourne  37°52'S   144°55'E	560	0	10	70	90	40	240	60	0	10	0
Time Scale = UT+10h	/	0	88	96	135	14	64	198	0	95	0

-

Miami    25°46'N    80°08'W	380	88	6	33	41	84	365	73	0	0	0
Time Scale = UT-5h	/	199	214	199	170	219	236	255	0	0	0

-

Montevideo  34°55'S    56°13'W	640	53	31	78	23	55	136	38	19	39	13
Time Scale = UT-3h	/	314	104	139	315	352	30	106	147	181	268

-

Nassau  25°05'N     77°21'W	850	95	12	65	87	92	379	64	0	5	0
Time Scale = UT-5h	/	144	128	132	122	204	223	242	0	85	0

-

New-York  40°42'N    74°01'W	700	83	13	52	98	143	641	133	0	14	16
Time Scale = UT-5h	/	134	123	111	107	222	237	258	0	335	308

-

Oslo     59°55'N     10°44'E	150	137	8	21	3	32	112	36	0	19	12
Time Scale = UT+1h	/	185	223	287	222	99	136	97	0	21	117

-

Plymouth (GB) 50°22'N  4°11'W	3350	121	16	59	74	316	1691	603	51	144	95
Time Scale = UT	/	219	312	341	109	137	154	207	107	135	188

-

Port-au-Prince 18°33'N  72°21'W	180	74	0	41	70	33	145	42	0	0	0
Time Scale = UT-5h	/	164	0	145	154	242	249	260	0	0	0

-

Rio de Janeiro  22°53'S  43°10'W	690	27	26	92	62	26	318	179	20	48	31
Time Scale = UT-3h	/	21	110	104	144	174	93	88	224	96	186

-

Rotterdam  51°55'N     4°30'E	940	90	40	80	60	90	660	140	0	110	70
Time Scale = UT+1h	/	315	170	221	32	137	153	213	0	245	301

-

San Francisco 37°48'N  122°27'W	910	30	40	230	369	116	543	123	0	23	9
Time Scale = UT-8h	/	199	97	99	108	320	343	339	0	50	47

-

Singapore    1°16'N   103°51'E	1600	131	61	283	294	143	796	326	6	15	19
Time Scale = UT+8h	/	281	25	64	117	306	326	21	333	298	348

-

Seattle      47°36'N  122°20'W	2010	74	75	458	831	212	1060	258	0	21	10
Time Scale = UT-8h	/	289	143	144	157	113	140	158	0	92	120

-

Sydney (Aus)  33°51'S   151°14'E	910	33	25	96	147	111	518	131	1	4	3
Time Scale = UT+10h	/	61	54	82	121	222	239	264	132	149	149

-

Ushuaia    54°49'S    68°13'W	1100	45	34	155	199	148	560	64	6	16	8
Time Scale = UT-3h	/	66	349	13	59	114	154	163	299	346	67

-

Valparaiso  33°02'S    71°38'W	910	36	20	102	159	96	441	146	0	0	0
Time Scale = UT-4h	/	4	268	301	341	275	305	323	0	0	0

-

Vancouver  49°17'N   123°07'W	3060	0	89	470	860	179	940	230	0	0	0
Time Scale = UT-8h	/	0	134	154	169	144	164	186	0	0	0

-

Vera Cruz  19°11'N    96°07'W	310	53	37	153	155	23	88	27	0	0	0
Time Scale = UT-6h	/	184	281	289	289	57	69	71	0	0	0

-

Washington  38°52'N    77°01'W	460	89	0	32	48	81	423	62	0	34	0
Time Scale = UT-5h	/	120	0	307	278	218	237	273	0	27	0

 

001  LBL "WL"
002  HR
003  24
004  /
005  X<>Y
006  1.012                If you don't have a Time Module, replace the 3 lines 06-07-08 by the 2 lines:     XEQ "J0"    +
007  DDAYS
008  -
009  LBL "T"
010  STO 00
011  DEG
012  .985647
013  *
014  STO 01
015  10
016  +
017  RCL 18
018  -
019  SIN
020  RCL 08
021  *
022  RCL 07
023  +
024  RCL 00
025  360
026  *
027  STO 02
028  RCL 01
029  +
030  STO 04
031  10
032  +
033  RCL 21
034  -
035  COS
036  RCL 11
037  *
038  +
039  RCL 04
040  .052954
041  RCL 00
042  *
043  STO 06
044  +
045  65
046  +
047  RCL 21
048  -
049  COS
050  RCL 11
051  *
052  7.4
053  /
054  -
055  RCL 02
056  ST+ 02
057  RCL 01
058  -
059  10
060  -
061  RCL 21
062  -
063  COS
064  RCL 11
065  *
066  3
067  /
068  +
069  RCL 04
070  ST+ 04
071  26.352793
072  RCL 00
073  *
074  STO 03
075  -
076  STO 05
077  53
078  -
079  RCL 20
080  -
081  COS
082  RCL 10
083  *
084  -
085  RCL 05
086  RCL 06
087  -
088  72
089  +
090  RCL 20
091  -
092  COS
093  RCL 10
094  *
095  5.3
096  /
097  -
098  RCL 05
099  13.064993
100  RCL 00
101  *
102  STO 05
103  -
104  2
105  -
106  RCL 19
107  -
108  COS
109  RCL 09
110  *
111  +
112  RCL 02
113  RCL 24
114  -
115  COS
116  RCL 14
117  *
118  +
119  RCL 04
120  20
121  +
122  RCL 24
123  -
124  COS
125  RCL 14
126  *
127  3.7
128  /
129  -
130  RCL 04
131  RCL 06
132  +
133  75
134  +
135  RCL 24
136  -
137  COS
138  RCL 14
139  *
140  12
141  /
142  +
143  RCL 04
144  RCL 03
145  -
146  STO 04
147  43.5
148  -
149  RCL 23
150  -
151  COS
152  RCL 13
153  *
154  -
155  RCL 04
156  RCL 06
157  -
158  8
159  -
160  RCL 23
161  -
162  SIN
163  RCL 13
164  *
165  27
166  /
167  -
168  RCL 04
169  RCL 05
170  +
171  5
172  -
173  RCL 23
174  -
175  SIN
176  RCL 13
177  *
178  35
179  /
180  -
181  RCL 02
182  RCL 01
183  -
184  3
185  +
186  RCL 24
187  -
188  COS
189  RCL 14
190  *
191  17
192  /
193  +
194  RCL 04
195  RCL 05
196  -
197  8
198  +
199  RCL 22
200  -
201  COS
202  RCL 12
203  *
204  +
205  RCL 04
206  RCL 05
207  ST+ X
208  -
209  60
210  +
211  RCL 22
212  -
213  COS
214  RCL 12
215  *
216  7.6
217  /
218  -
219  RCL 02
220  RCL 04
221  +
222  44
223  -
224  RCL 27
225  -
226  COS
227  RCL 17
228  *
229  -
230  RCL 04
231  ST+ X
232  STO 01
233  3
234  +
235  RCL 26
236  -
237  SIN
238  RCL 16
239  *
240  +
241  RCL 01
242  RCL 02
243  -
244  STO 06
245  3
246  +
247  RCL 22
248  -
249  SIN
250  RCL 12
251  *
252  6.3
253  /
254  +
255  RCL 05
256  RCL 06
257  +
258  41
259  +
260  RCL 22
261  -
262  COS
263  RCL 12
264  *
265  5.3
266  /
267  +
268  RCL 01
269  RCL 05
270  -
271  35
272  -
273  RCL 25
274  -
275  COS
276  RCL 15
277  *
278  -
279   E3
280  /
281  END

( 387 bytes / SIZE 028 )
 
 
 

STACK	INPUTS	OUTPUTS
Y	Date	/
X	hh.mnss	water level (m)

Example:     Calculate the water level in Seattle on   11/11/2003  at 14h45mn  ( local time = UT-8h )

-First, we initialize registers R07 to R27   ( 2010 STO 07   74 STO 08   75 STO 09 ...................  92  STO 26  120  STO 27 )

-Then,  11.112003 ENTER^
            14.45         XEQ "WL"   yields   2.75m    ( in 24 seconds )

    ( Key in  2003.1111 instead of  11.112003  if you are using "J0" )

-Similar computations produce the following results:
 
 

time	0h	1h	2h	3h	4h	5h	6h	7h	8h	9h	10h	11h	12h	13h	14h	15h	16h	17h	18h	19h	20h	21h	22h	23h	24h
wl	-0.35	-0.06	0.56	1.35	2.15	2.82	3.28	3.48	3.43	3.18	2.82	2.49	2.31	2.34	2.54	2.82	3.03	3.08	2.91	2.52	1.93	1.23	0.52	-0.05	-0.34

 

 Water Level - SEATTLE - 11/11/2003
          |
          |                      -   -
          |               -               -                                           -
          |          -                          -                        -                      -
          |       -                                      -     -                                    -
          |     -                                                                                       -
          |   -                                                                                            -
          |  -                                                                                               -
    ----|----------------------------------|----------------------------------|------ ( local time = UT-8h )
         0h                                              12h                                               24h
 
 
 

       2°) Tides  ( with 5 tabular values )
 

-   "TIDE1"  uses 5 tabular water levels  wl(t₁)  wl(t₂)  wl(t₃)  wl(t₄)  wl(t₅)  where    t₅ - t₄  =  t₄ - t₃  =  t₃ - t₂  =  t₂ - t₁  =  h   ( equally spaced abcissas )
-The extremum of a polynomial of degree 4 is found by an iterative method.
 

Data Registers:             R00 and  R28 thru R32:  temp  ;   R07 thru R27 are undisturbed.

                                    •   R01 =  wl(t₁)
                                    •   R02 =  wl(t₂)
                                    •   R03 =  wl(t₃)      these 5 registers are to be initialized before executing "TIDE1"
                                    •   R04 =  wl(t₄)
                                    •   R05 =  wl(t₅)

Flags: /
Subroutine:  /
 
 

01  LBL "TIDE1"
02  STO 28
03  X<>Y
04  STO 00
05  CLX
06  STO 06
07  RCL 05
08  RCL 01
09  -
10  RCL 02
11  RCL 04
12  -
13  ST+ X
14  +
15  STO 29
16  CHS
17  LASTX
18  3
19  *
20  -
21  STO 30
22  RCL 01
23  RCL 05
24  +
25  RCL 02
26  RCL 04
27  +
28  16
29  *
30  -
31  RCL 03
32  30
33  *
34  +
35  STO 31
36  RCL 03
37  24
38  *
39  -
40  RCL 02
41  RCL 04
42  +
43  12
44  *
45  +
46  STO 32
47  LBL 01
48  RCL 32
49  ST+ X
50  RCL 06
51  *
52  RCL 29
53  3
54  *
55  +
56  RCL 06
57  X^2
58  *
59  RCL 30
60  +
61  RCL 31
62  /
63  ENTER^
64  X<> 06
65  -
66  ABS
67   E-4
68  X<Y?
69  GTO 01
70  RCL 06
71  RCL 06
72  RCL 06
73  RCL 32
74  *
75  RCL 29
76  ST+ X
77  +
78  *
79  RCL 31
80  -
81  *
82  RCL 30
83  ST+ X
84  +
85  *
86  24
87  /
88  RCL 03
89  +
90  RCL 00
91  RCL 06
92  2
93  +
94  *
95  HMS
96  RCL 28
97  HMS+
98  END

( 135 bytes / SIZE 033 )
 
 
 

STACK	INPUTS	OUTPUTS
Y	h	water level
X	t1 ( hh.mnss )	hh.mnss

 

Example:    With    wl(5) = 2.82  STO 01
                               wl(6) = 3.28  STO 02
                               wl(7) = 3.48  STO 03
                               wl(8) = 3.43  STO 04
                               wl(9) = 3.18  STO 05

   1  ENTER^
   5  XEQ "TIDE1"  yields    7.1654   ( in 6 seconds )
                              X<>Y   3.4898

-Thus, there is a high tide at 7h17mn and the corresponding water level = 3.49m  ( error = 15 minutes )
 
 

       3°) Tides ( without tabular values )
 

-The following program calculates 3 water levels.
-Then, it finds the extremum of the parabola thus defined and its abscissa replaces one of the 3 first abscissas.
-The process is repeated until the difference between 2 abscissas is smaller than E-4 day ( line 65 )
 

Data Registers:             R28 thru R33:  temp  (  R07 thru R27 are undisturbed  )

Flags: /
Subroutine:  "T" ( line 9 of the program "WL")
            (  and "J0" & "DT" if you don't have a Time Module - cf "Phases of the Moon for the HP-41" )
 
 

01  LBL "TIDE2"
02  HR
03  24
04  /
05  X<>Y
06  1.012
07  DDAYS                If you don't have a Time Module, replace the 3 lines 06-07-08 by the 2 lines:     XEQ "J0"    +
08  -
09  STO 29
10  XEQ "T"
11  STO 31
12  RCL 00
13  .01
14  -
15  STO 28
16  XEQ "T"
17  STO 30
18  .02
19  ST+ 00
20  LBL 01
21  RCL 00
22  VIEW X
23  XEQ "T"
24  STO 32
25  RCL 31
26  -
27  RCL 00
28  RCL 29
29  -
30  /
31  RCL 31
32  RCL 30
33  -
34  RCL 29
35  RCL 28
36  -
37  /
38  -
39  RCL 28
40  RCL 00
41  -
42  /
43  STO 33
44  RCL 29
45  RCL 00
46  -
47  *
48  +
49  RCL 33
50  ST+ X
51  X#0?
52  /
53  RCL 00
54  +
55  X<> 00
56  X<> 29
57  STO 28
58  RCL 32
59  X<> 31
60  STO 30
61  RCL 00
62  RCL 29
63  -
64  ABS
65   E-4
66  X<Y?
67  GTO 01
68  RCL 00
69  XEQ "T"
70  RCL 00
71  ENTER^
72  INT
73  X>Y?
74  DSE X
75  LBL 02
76  ST- Y
77  1.012
78  X<>Y
79  DATE+                If you don't have a Time Module, replace the 4 lines 77-78-79-80 by  XEQ "DT"  RCL 01  X<> Z  and add  STO 01 after line 69
80  X<>Y
81  24
82  *
83  HMS
84  RCL 33
85  X#0?
86  SIGN
87  RDN
88  CLD
89  END

( 154 bytes / SIZE 034 )
 
 
 

STACK	INPUTS	OUTPUTS
T	/	+1  or  -1 *
Z	/	water level
Y	Date	Date
X	approximate time	hh.mnss

*  +1  means "High Tide"
     -1  ------ "Low Tide"

Example:    Once again , in Seattle , on 11/11/2003  near 7 AM

     11.112003    ENTER^
       7                 XEQ "TIDE2"  produces  7.1718    ( in 2mn26s )    ( the successive d-approximations are displayed )
                               RDN                         11.112003
                               RDN                           3.4915
                               RDN                            1

-Thus, there is a high tide at 7h17mn and the corresponding water level = 3.49m  ( exact time = 7h02mn according to the "Shom" )

    ( Key in  2003.1111 instead of  11.112003  if you are using "J0" & "DT" )

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