hp41programs

Tides for the HP-41

Overview

    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.
and 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 ( Registers R07 thru R27 are to be initialized before executing "WL" )

R01 thru R06: temp

• R07 thru R27 = the harmonic constituents of the port.

Flags: /
Subroutine: none if you have a Time-Module
"J0" otherwise ( cf "Julian & Gregorian Calendars 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

-If you don't have a Time Module, replace lines 06-07-08 by: XEQ "J0" +

01 LBL "WL"
02 HR
03 24
04 /
05 X<>Y
06 1.012
07 DDAYS
08 -
09 LBL "T"
10 STO 00
11 DEG
12 .985647
13 *
14 STO 01
15 10
16 +
17 RCL 18
18 -
19 SIN
20 RCL 08
21 *
22 RCL 07
23 +
24 RCL 00
25 360
26 *
27 STO 02
28 RCL 01
29 +
30 STO 04
31 10
32 +
33 RCL 21
34 -
35 COS
36 RCL 11
37 *
38 +
39 RCL 04
40 .052954
41 RCL 00
42 *
43 STO 06
44 +
45 65
46 +
47 RCL 21

48 -
49 COS
50 RCL 11
51 *
52 7.4
53 /
54 -
55 RCL 02
56 ST+ 02
57 RCL 01
58 -
59 10
60 -
61 RCL 21
62 -
63 COS
64 RCL 11
65 *
66 3
67 /
68 +
69 RCL 04
70 ST+ 04
71 26.352793
72 RCL 00
73 *
74 STO 03
75 -
76 STO 05
77 53
78 -
79 RCL 20
80 -
81 COS
82 RCL 10
83 *
84 -
85 RCL 05
86 RCL 06
87 -
88 72
89 +
90 RCL 20
91 -
92 COS
93 RCL 10
94 *

95 5.3
96 /
97 -
98 RCL 05
99 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: /
Subroutines: /

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 "Julian & Gregorian Calendars for the HP-41" )

-If you don't have a Time Module:

replace lines 77-78-79-80 by XEQ "DT" RCL 01 X<> Z
add STO 01 after line 69
and replace lines 06-07-08 by: XEQ "J0" +

01 LBL "TIDE2"
02 HR
03 24
04 /
05 X<>Y
06 1.012
07 DDAYS
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+
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 for a "High Tide" , -1 for a "Low Tide"

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

     11.112003    ENTER^
       7                 XEQ "TIDE2" >>>> 7.1718             ( the successive d-approximations are displayed )    ---Execution time = 2m26s---
                               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" )