Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
Course and Distance Calculation  
Workbook  
Course and Distance Calculations  
1
1
1 Las Calderas Bay to Kingstown  
2 Georgetown to Speightstown  
3 Las Calderas Bay to Boca del Dragón  
4 St Georges to St Eustatius  
5 Kingston to Kingstown  
3
5
6
8
6 Bridgetown to Vieux Fort  
10  
12  
13  
15  
17  
19  
20  
22  
24  
26  
27  
7 Galeota Point to Paramaribo  
8 St Johns to Colon  
9 Maracaibo to Guayanilla  
10 Guantanamo Bay to Belize City  
11 San Juan to Bermuda  
12 Boca de Navios to Mona Passage  
13 Boca de Huevos to Windward Passage  
14 Galveston to Yucatan Channel  
15 Yucatan Channel to Boca del Dragon  
ETA Calculations  
Course and Distance Calculations  
1 Las Calderas Bay to Kingstown  
A ship is leaving from 18° 12.4’ N 70° 34.8’ W (Las Calderas Bay) to arrive at 13° 10’ N, 61° 17’  
W (Kingstown), what course does she need to make good, and what is the distance?  
1. Find the difference in latitude (D Lat)  
18° 12.4’ N -  
13° 10.0’ N  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
05° 02.4’ South  
Change to minutes  
(5 x 60) + 2 = 300 + 2 = 302’S  
2. Find the middle latitude  
302’/2 = 151  
151’/60 = 2.5°, [0.5 x 60 = 30’] = 2° 30’  
middle latitude = 13° 10’ N + 2° 30’ = 15° 40’ N  
3. Find the difference in longitude (D Long)  
70° 34.8’ W  
61° 17.0’ W  
09° 17.8’ East  
Change to minutes  
(9 x 60) + 18 = 540 + 18 = 558’ E  
4. Find the departure at the middle latitude (departure is difference of longitude in miles)  
Departure at the middle latitude  
= D Long x cosine of middle latitude  
= 558’ x cos 15° 40’  
Use a calculator, tables or website to find cosine of the middle latitude  
Departure at the middle latitude  
5. Find the course  
= D Long x cosine of middle latitude  
= 558’ x 0.96 = 536 miles  
Tangent of course  
= D Lat / Departure  
= 302 / 536  
= 0.5634  
Use a calculator, tables or website to find what angle has that tangent  
The angle with tangent 0.5634 is close to 29°  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
(remember that the D Lat was South and the D Long was East)  
S44°E = 90° + 29° = 119°T  
6. Find the distance  
Distance  
= D Lat / cosine course  
= 452 / cos 136°  
Use a calculator, tables or website to find cosine of the course  
Distance  
= D Lat / cosine course  
= 452 / 0.71934  
= 628 miles  
2 Georgetown to Speightstown  
1 A ship is leaving from 6° 54.0’ N 58° 12.0’ W (Georgetown) to arrive at 13° 15.0’ N 59° 37.0’ W  
(Speightstown), what course does she need to make good, and what is the distance?  
1. Find the difference in latitude (D Lat)  
13° 15.0’ N -  
06° 54.0’ N  
06° 21.0’ North  
Change to minutes  
(6 x 60) + 21 = 360 + 21 = 381’N  
2. Find the middle latitude  
381’/2 = 190  
190’/60 = 3.16° [0.16 x 60 = 10’] = 3° 10’  
middle latitude = 6° 54.0’ N + 3° 10’ = 10° 04’ N  
3. Find the difference in longitude (D Long)  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
59° 37.0’ W  
58° 12.0’ W  
01° 25.0’ West  
Change to minutes  
(1 x 60) + 25 = 60 + 25 = 85’ W  
4. Find the departure at the middle latitude (departure is difference of longitude in miles)  
Departure at the middle latitude  
= D Long x cosine of middle latitude  
= 85’ x cos 10° 04’  
Use a calculator, tables or website to find cosine of the middle latitude  
Departure at the middle latitude  
5. Find the course  
= D Long x cosine of middle latitude  
= 85’ x 0.98 = 83 miles  
Tangent of course  
= D Lat / Departure  
= 381 / 83  
= 4.5903  
Use a calculator, tables or website to find what angle has that tangent  
The angle with tangent 4.5903 is between 77° and 78°  
(remember that the D Lat was North and the D Long was East)  
N44°W = 270° + 78° = 348°T  
6. Find the distance  
Distance  
= D Lat / cosine course  
= 381 / cos 348°  
Use a calculator, tables or website to find cosine of the course  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
Distance  
= D Lat / cosine course  
= 381 / 0.9781  
= 373 miles  
3 Las Calderas Bay to Boca del Dragón  
A ship is leaving from 18° 12.4’ N 70° 34.8’ W (Las Calderas Bay) to arrive at 10° 40.3’ N 61°  
47.2’ W (Boca del Dragon), what course does she need to make good, and what is the  
distance?  
1. Find the difference in latitude (D Lat)  
18° 12.4’ N -  
10° 40.3’ N  
07° 32.1’ South  
Change to minutes  
(7 x 60) + 32 = 420 + 32 = 452’S  
2. Find the middle latitude  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
452’/2 = 226  
226’/60 = 3.76° [0.76 x 60 = 46’] = 3° 46’  
middle latitude = 10° 40.3’ N + 3° 46’ = 14° 26’ N  
3. Find the difference in longitude (D Long)  
70° 34.8’ W  
61° 47.2’ W  
08° 47.6’ East  
Change to minutes  
(8 x 60) + 48 = 480 + 48 = 528’ E  
4. Find the departure at the middle latitude (departure is difference of longitude in miles)  
Departure at the middle latitude  
= D Long x cosine of middle latitude  
= 528’ x cos 14° 26’  
Use a calculator, tables or website to find cosine of the middle latitude  
Departure at the middle latitude  
5. Find the course  
= D Long x cosine of middle latitude  
= 528’ x 0.97 = 512 miles  
Tangent of course  
= D Lat / Departure  
= 452 / 512  
= 0.8828  
Use a calculator, tables or website to find what angle has that tangent  
The angle with tangent 0.8828 is between 41° and 42°  
(remember that the D Lat was South and the D Long was East)  
S44°E = 90° + 42° = 132°T  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
6. Find the distance  
Distance  
= D Lat / cosine course  
= 452 / cos 132°  
Use a calculator, tables or website to find cosine of the course  
Distance  
= D Lat / cosine course  
= 452 / 0.6691  
= 676 miles  
4 St Georges to St Eustatius  
1 A ship is leaving from 12° 03.0’ N 61° 45.0’ W (St Georges) to arrive at 17° 29.0’ N 63° 00 .0’  
W (St Eustatius), what course does she need to make good, and what is the distance?  
1. Find the difference in latitude (D Lat)  
17° 29.0’ N -  
12° 03.0’ N  
05° 26.0’ North  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
Change to minutes  
(5 x 60) + 26 = 300 + 26 = 326’N  
2. Find the middle latitude  
326’/2 = 163  
163’/60 = 2.71° [0.71 x 60 = 43’] = 2° 43’  
middle latitude = 12° 03.0’ N + 2° 43’ = 14° 46’ N  
3. Find the difference in longitude (D Long)  
63° 00.0’ W  
61° 45.0’ W  
01° 15.0’ West  
Change to minutes  
(1 x 60) + 15 = 60 + 15 = 75’ W  
4. Find the departure at the middle latitude (departure is difference of longitude in miles)  
Departure at the middle latitude  
= D Long x cosine of middle latitude  
= 75’ x cos 14° 46’  
Use a calculator, tables or website to find cosine of the middle latitude  
Departure at the middle latitude  
5. Find the course  
= D Long x cosine of middle latitude  
= 75’ x 0.965 = 72 miles  
Tangent of course  
= D Lat / Departure  
= 326 / 72  
= 4.5277  
Use a calculator, tables or website to find what angle has that tangent  
The angle with tangent 4.5277 is between 77° and 78°  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
(remember that the D Lat was North and the D Long was West)  
N44°W = 270° + 78° = 348°T  
6. Find the distance  
Distance  
= D Lat / cosine course  
= 326 / cos 348°  
Use a calculator, tables or website to find cosine of the course  
Distance  
= D Lat / cosine course  
= 326 / 0.9781  
= 319 miles  
5 Kingston to Kingstown  
1 A ship is leaving from 17° 55.0’ N 76° 51.0’ W (Kingston) to arrive at 13° 08.0’ N 61° 15 .0’ W  
(Kingstown), what course does she need to make good, and what is the distance?  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
1. Find the difference in latitude (D Lat)  
17° 55.0’ N -  
13° 08.0’ N  
04° 47.0’ South  
Change to minutes  
(4 x 60) + 47 = 240 + 47 = 287’S  
2. Find the middle latitude  
287’/2 = 144  
144’/60 = 2.4° [0.4 x 60 = 43’] = 2° 24’  
middle latitude = 13° 08.0’ N + 2° 43’ = 15° 51’ N  
3. Find the difference in longitude (D Long)  
76° 51.0’ W  
61° 15.0’ W  
15° 36.0’ East  
Change to minutes  
(15 x 60) + 36 = 900 + 36 = 936’ E  
4. Find the departure at the middle latitude (departure is difference of longitude in miles)  
Departure at the middle latitude  
= D Long x cosine of middle latitude  
= 936’ x cos 15° 51’  
Use a calculator, tables or website to find cosine of the middle latitude  
Departure at the middle latitude  
5. Find the course  
= D Long x cosine of middle latitude  
= 936’ x 0.965 = 903 miles  
Tangent of course  
= D Lat / Departure  
= 287 / 903  
= 0.3178  
Use a calculator, tables or website to find what angle has that tangent  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
The angle with tangent 0.3178 is between 17° and 18°  
(remember that the D Lat was North and the D Long was West)  
N44°W = 90° + 17° = 107°T  
6. Find the distance  
Distance  
= D Lat / cosine course  
= 287 / cos 107°  
Use a calculator, tables or website to find cosine of the course  
Distance  
= D Lat / cosine course  
= 287 / 0.3000  
= 956 miles  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
6 Bridgetown to Vieux Fort  
1 A ship is leaving from 13° 06.0’ N 59° 36.0’ W (Bridgetown) to arrive at 13° 42.0’ N 60° 59 .0’  
W (Vieux Fort), what course does she need to make good, and what is the distance?  
1. Find the difference in latitude (D Lat)  
13° 42.0’ N -  
13° 06.0’ N  
00° 36.0’ North  
Change to minutes  
(0 x 60) + 36 = 0 + 36 = 36’N  
2. Find the middle latitude  
36’/2 = 18  
middle latitude = 13° 06.0’ N + 0° 18’ = 13° 24’ N  
3. Find the difference in longitude (D Long)  
60° 59.0’ W  
59° 36.0’ W  
1° 23.0’ West  
Change to minutes  
(1 x 60) + 23 = 60 + 23 = 83’ W  
4. Find the departure at the middle latitude (departure is difference of longitude in miles)  
Departure at the middle latitude  
= D Long x cosine of middle latitude  
= 83’ x cos 13° 24’  
Use a calculator, tables or website to find cosine of the middle latitude  
Departure at the middle latitude  
5. Find the course  
= D Long x cosine of middle latitude  
= 83’ x 0.971 = 81 miles  
Tangent of course  
= D Lat / Departure  
= 36 / 81  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
= 0.4444  
Use a calculator, tables or website to find what angle has that tangent  
The angle with tangent 0.4444 is between 23° and 24°  
(remember that the D Lat was North and the D Long was West)  
N24°W = 270° + 24° = 294°T  
6. Find the distance  
Distance  
= D Lat / cosine course  
= 36 / cos 294°  
Use a calculator, tables or website to find cosine of the course  
Distance  
= D Lat / cosine course  
= 36 / 0.4067  
= 89 miles  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
7 Galeota Point to Paramaribo  
1 A ship is leaving from 10° 08.0’ N 61° 01.0’ W (Galeota Point) to arrive at 06° 09.0’ N 55° 15  
.0’ W (Paramaribo), what course does she need to make good, and what is the distance?  
1. Find the difference in latitude (D Lat)  
10° 08.0’ N -  
06° 09.0’ N  
03° 59.0’ South  
Change to minutes  
(3 x 60) + 59 = 180 + 59 = 239’S  
2. Find the middle latitude  
239’/2 = 120  
middle latitude = 6° 09.0’ N + 2° 00’ = 8° 09’ N  
3. Find the difference in longitude (D Long)  
61° 01.0’ W  
55° 15.0’ W  
5° 46.0’ East  
Change to minutes  
(5 x 60) + 46 = 300 + 46 = 346’ E  
4. Find the departure at the middle latitude (departure is difference of longitude in miles)  
Departure at the middle latitude  
= D Long x cosine of middle latitude  
= 346’ x cos 8° 09’  
Use a calculator, tables or website to find cosine of the middle latitude  
Departure at the middle latitude  
5. Find the course  
= D Long x cosine of middle latitude  
= 346’ x 0.99 = 343 miles  
Tangent of course  
= D Lat / Departure  
= 239 / 343  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
= 0.6968  
Use a calculator, tables or website to find what angle has that tangent  
The angle with tangent 0.6968 is between 34° and 35°  
(remember that the D Lat was South and the D Long was East)  
N24°W = 90° + 35° = 125°T  
6. Find the distance  
Distance  
= D Lat / cosine course  
= 239 / cos 125°  
Use a calculator, tables or website to find cosine of the course  
Distance  
= D Lat / cosine course  
= 239 / 0.5735  
= 417 miles  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
8 St Johns to Colon  
1 A ship is leaving from 17° 09.0’ N 61° 53.0’ W (St Johns) to arrive at 09° 30.0’ N 79° 57.0’ W  
(Colon), what course does she need to make good, and what is the distance?  
1. Find the difference in latitude (D Lat)  
17° 09.0’ N -  
09° 30.0’ N  
07° 39.0’ South  
Change to minutes  
(7 x 60) + 39 = 420 + 39 = 459’S  
2. Find the middle latitude  
459’/2 = 230  
middle latitude = 9° 30.0’ N + 3° 50’ = 13° 20’ N  
3. Find the difference in longitude (D Long)  
79° 57.0’ W  
61° 53.0’ W  
18° 04.0’ West  
Change to minutes  
(18 x 60) + 04 = 1080 + 04 = 1084’ W  
4. Find the departure at the middle latitude (departure is difference of longitude in miles)  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
Departure at the middle latitude  
= D Long x cosine of middle latitude  
= 1084’ x cos 13° 20’  
Use a calculator, tables or website to find cosine of the middle latitude  
Departure at the middle latitude  
5. Find the course  
= D Long x cosine of middle latitude  
= 1084’ x 0.97 = 1051 miles  
Tangent of course  
= D Lat / Departure  
= 459 / 1051  
= 0.4367  
Use a calculator, tables or website to find what angle has that tangent  
The angle with tangent 0.4367 is between 23° and 24°  
(remember that the D Lat was South and the D Long was East)  
S24°W = 270° - 24° = 246°T  
6. Find the distance  
Distance  
= D Lat / cosine course  
= 459 / cos 246°  
Use a calculator, tables or website to find cosine of the course  
Distance  
= D Lat / cosine course  
= 459 / 0.406737  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
= 1128 miles  
9 Maracaibo to Guayanilla  
1 A ship is leaving from 12° 28.0’ N 70° 43.0’ W (Maracaibo) to arrive at 17° 59.0’ N 66° 47.0’ W  
(Guayanilla), what course does she need to make good, and what is the distance?  
1. Find the difference in latitude (D Lat)  
17° 59.0’ N -  
12° 28.0’ N  
05° 31.0’ North  
(5 x 60) + 31 = 300 + 31 = 331’N  
2. Find the middle latitude  
331’/2 = 165  
middle latitude = 12° 28.0’ N + 2° 45’ = 15° 13’ N  
3. Find the difference in longitude (D Long)  
70° 43.0’ W  
66° 47.0’ W  
03° 56.0’ East  
Change to minutes  
(3 x 60) + 56 = 180 + 56 = 236’ E  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
4. Find the departure at the middle latitude (departure is difference of longitude in miles)  
Departure at the middle latitude  
= D Long x cosine of middle latitude  
= 236’ x cos 15° 13’  
Use a calculator, tables or website to find cosine of the middle latitude  
Departure at the middle latitude  
5. Find the course  
= D Long x cosine of middle latitude  
= 236’ x 0.96 = 227 miles  
Tangent of course  
= D Lat / Departure  
= 331 / 227  
= 1.4581  
Use a calculator, tables or website to find what angle has that tangent  
The angle with tangent 1.4581 is between 55° and 56°  
(remember that the D Lat was South and the D Long was East)  
N24°E = 90° - 56° = 034°T  
6. Find the distance  
Distance  
= D Lat / cosine course  
= 331 / cos 034°  
Use a calculator, tables or website to find cosine of the course  
Distance  
= D Lat / cosine course  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
= 331 / 0.82  
= 404 miles  
10 Guantanamo Bay to Belize City  
1 A ship is leaving from 19° 50.0’ N 75° 11.0’ W (Guantanamo Bay) to arrive at 17° 31.0’ N 88°  
05.0’ W (Belize City), what course does she need to make good, and what is the distance?  
1. Find the difference in latitude (D Lat)  
19° 50.0’ N -  
17° 31.0’ N  
02° 19.0’ South  
(2 x 60) + 19 = 120 + 19 = 139’S  
2. Find the middle latitude  
139’/2 = 70  
middle latitude = 17° 31.0’ N + 1° 10’ = 18° 41’ N  
3. Find the difference in longitude (D Long)  
88° 05.0’ W  
75° 11.0’ W  
12° 54.0’ West  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
Change to minutes  
(12 x 60) + 54 = 720 + 54 = 774’ W  
4. Find the departure at the middle latitude (departure is difference of longitude in miles)  
Departure at the middle latitude  
= D Long x cosine of middle latitude  
= 236’ x cos 18° 41’  
Use a calculator, tables or website to find cosine of the middle latitude  
Departure at the middle latitude  
5. Find the course  
= D Long x cosine of middle latitude  
= 774’ x 0.95 = 735 miles  
Tangent of course  
= D Lat / Departure  
= 139 / 735  
= 0.1891  
Use a calculator, tables or website to find what angle has that tangent  
The angle with tangent 0.1891 is between 10° and 11°  
(remember that the D Lat was South and the D Long was West)  
N24°E = 270° - 11° = 259°T  
6. Find the distance  
Distance  
= D Lat / cosine course  
= 139 / cos 259°  
Use a calculator, tables or website to find cosine of the course  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
Distance  
= D Lat / cosine course  
= 139 / 0.19  
= 732 miles  
11 San Juan to Bermuda  
1 A ship is leaving from 18° 31.0’ N 66° 06.0’ W (San Juan) to arrive at 32° 15.0’ N 64° 53.0’ W  
(Bermuda), what course does she need to make good, and what is the distance?  
1. Find the difference in latitude (D Lat)  
32° 15.0’ N -  
18° 31.0’ N  
13° 44.0’ North  
(13 x 60) + 44 = 780 + 44 = 824’ N  
2. Find the middle latitude  
824’/2 = 412  
middle latitude = 18° 31.0’ N + 6° 52’ = 25° 23’ N  
3. Find the difference in longitude (D Long)  
66° 06.0’ W  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
64° 53.0’ W  
1° 13.0’ East  
Change to minutes  
(1 x 60) + 13 = 60 + 13 = 73’ E  
4. Find the departure at the middle latitude (departure is difference of longitude in miles)  
Departure at the middle latitude  
= D Long x cosine of middle latitude  
= 73’ x cos 25° 23’  
Use a calculator, tables or website to find cosine of the middle latitude  
Departure at the middle latitude  
5. Find the course  
= D Long x cosine of middle latitude  
= 73’ x 0.9 = 66 miles  
Tangent of course  
= D Lat / Departure  
= 824 / 66  
= 12.4848  
Use a calculator, tables or website to find what angle has that tangent  
The angle with tangent 12.4848 is between 85° and 86°  
(remember that the D Lat was North and the D Long was East)  
N85°E = 090° - 85° = 005°T  
6. Find the distance  
Distance  
= D Lat / cosine course  
= 824 / cos 005°  
Use a calculator, tables or website to find cosine of the course  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
Distance  
= D Lat / cosine course  
= 824 / 0.99  
= 832 miles  
12 Boca de Navios to Mona Passage  
1 A ship is leaving from 10° 42.0’ N 61° 44.0’ W (Boca de Navios) to arrive at 18° 06.0’ N 67°  
35.0’ W (Mona Passage), what course does she need to make good, and what is the distance?  
1. Find the difference in latitude (D Lat)  
18° 06.0’ N -  
10° 42.0’ N  
07° 24.0’ North  
(7 x 60) + 24 = 420 + 24 = 444’ N  
2. Find the middle latitude  
444’/2 = 222  
middle latitude = 10° 42.0’ N + 3° 42’ = 14° 24’ N  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
3. Find the difference in longitude (D Long)  
67° 06.0’ W  
61° 44.0’ W  
05° 22.0’ West  
Change to minutes  
(5 x 60) + 22 = 300 + 22 = 322’ W  
4. Find the departure at the middle latitude (departure is difference of longitude in miles)  
Departure at the middle latitude  
= D Long x cosine of middle latitude  
= 322’ x cos 14° 24’  
Use a calculator, tables or website to find cosine of the middle latitude  
Departure at the middle latitude  
5. Find the course  
= D Long x cosine of middle latitude  
= 322’ x 0.97 = 321 miles  
Tangent of course  
= D Lat / Departure  
= 444 / 321  
= 1.383  
Use a calculator, tables or website to find what angle has that tangent  
The angle with tangent 1.383 is between 54° and 55°  
(remember that the D Lat was North and the D Long was West)  
N54°W = 270° + 54° = 324°T  
6. Find the distance  
Distance  
= D Lat / cosine course  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
= 444 / cos 324°  
Use a calculator, tables or website to find cosine of the course  
Distance  
= D Lat / cosine course  
= 444 / 0.8  
= 555 miles  
13 Boca de Huevos to Windward Passage  
1 A ship is leaving from 10° 42.0’ N 61° 42.0’ W (Boca de Huevos) to arrive at 19° 00.0’ N 75°  
32.0’ W (Windward Passage), what course does she need to make good, and what is the  
distance?  
1. Find the difference in latitude (D Lat)  
19° 00.0’ N -  
10° 42.0’ N  
08° 18.0’ North  
(8 x 60) + 18 = 480 + 18 = 498’ N  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
2. Find the middle latitude  
498’/2 = 249  
middle latitude = 10° 42.0’ N + 4° 09’ = 14° 51’ N  
3. Find the difference in longitude (D Long)  
75° 32.0’ W  
61° 42.0’ W  
13° 50.0’ West  
Change to minutes  
(13 x 60) + 50 = 780 + 50 = 830’ W  
4. Find the departure at the middle latitude (departure is difference of longitude in miles)  
Departure at the middle latitude  
= D Long x cosine of middle latitude  
= 830’ x cos 14° 51’  
Use a calculator, tables or website to find cosine of the middle latitude  
Departure at the middle latitude  
5. Find the course  
= D Long x cosine of middle latitude  
= 830’ x 0.96 = 797 miles  
Tangent of course  
= D Lat / Departure  
= 498 / 797  
= 0.6248  
Use a calculator, tables or website to find what angle has that tangent  
The angle with tangent 0.6248 is 32°  
(remember that the D Lat was North and the D Long was West)  
N32°W = 270° + 32° = 302°T  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
6. Find the distance  
Distance  
= D Lat / cosine course  
= 498 / cos 302°  
Use a calculator, tables or website to find cosine of the course  
Distance  
= D Lat / cosine course  
= 498 / 0.53  
= 939 miles  
14 Galveston to Yucatan Channel  
1 A ship is leaving from 29° 10.0’ N 94° 41.0’ W (Galveston) to arrive at 21° 44.0’ N 85° 36.0’ W  
(Yucatan Channel), what course does she need to make good, and what is the distance?  
1. Find the difference in latitude (D Lat)  
29° 10.0’ N -  
21° 44.0’ N  
07° 26.0’ South  
(7 x 60) + 26 = 420 + 26 = 446’ S  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
2. Find the middle latitude  
446’/2 = 223  
middle latitude = 21° 44.0’ N + 2° 43’ = 24° 27’ N  
3. Find the difference in longitude (D Long)  
95° 41.0’ W  
85° 36.0’ W  
10° 05.0’ East  
Change to minutes  
(10 x 60) + 05 = 600 + 05 = 605’ E  
4. Find the departure at the middle latitude (departure is difference of longitude in miles)  
Departure at the middle latitude  
= D Long x cosine of middle latitude  
= 605’ x cos 24° 27’  
Use a calculator, tables or website to find cosine of the middle latitude  
Departure at the middle latitude  
5. Find the course  
= D Long x cosine of middle latitude  
= 605’ x 0.91 = 551 miles  
Tangent of course  
= D Lat / Departure  
= 446 / 551  
= 0.8094  
Use a calculator, tables or website to find what angle has that tangent  
The angle with tangent 0.8094 is 39°  
(remember that the D Lat was South and the D Long was East)  
S32°E = 090° + 39° = 129°T  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
6. Find the distance  
Distance  
= D Lat / cosine course  
= 446 / cos 129°  
Use a calculator, tables or website to find cosine of the course  
Distance  
= D Lat / cosine course  
= 446 / 0.63  
= 708 miles  
15 Yucatan Channel to Boca del Dragon  
1 A ship is leaving from 21° 44.0’ N 85° 36.0’ W (Yucatan Channel) to arrive at 10° 40.3’ N 61°  
47.2’ W (Boca del Dragon), what course does she need to make good, and what is the  
distance?  
1. Find the difference in latitude (D Lat)  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
21° 44.0’ N -  
10° 40.0’ N  
11° 04.0’ South  
(11 x 60) + 04 = 660 + 04 = 664’ S  
2. Find the middle latitude  
664’/2 = 332  
middle latitude = 10° 40.0’ N + 5° 32’ = 16° 12’ N  
3. Find the difference in longitude (D Long)  
85° 36.0’ W  
61° 47.0’ W  
23° 49.0’ East  
Change to minutes  
(23 x 60) + 49 = 1380 + 49 = 1429’ E  
4. Find the departure at the middle latitude (departure is difference of longitude in miles)  
Departure at the middle latitude  
= D Long x cosine of middle latitude  
= 1429’ x cos 16° 12’  
Use a calculator, tables or website to find cosine of the middle latitude  
Departure at the middle latitude  
5. Find the course  
= D Long x cosine of middle latitude  
= 1429’ x 0.96 = 1372 miles  
Tangent of course  
= D Lat / Departure  
= 664 / 1372  
= 0.4840  
Use a calculator, tables or website to find what angle has that tangent  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
The angle with tangent 0.8094 is 26°  
(remember that the D Lat was South and the D Long was East)  
S32°E = 090° + 26° = 116°T  
6. Find the distance  
Distance  
= D Lat / cosine course  
= 664 / cos 116°  
Use a calculator, tables or website to find cosine of the course  
Distance  
= D Lat / cosine course  
= 664 / 0.4384  
= 1515 miles  
Document Title  
Document no.  
Author  
Coastal Navigation Workbook 3 Instructors  
OPS-WI-005  
J Farray  
Doc owner  
Revision  
D Villafana  
Rev. 01  
Reviewed by  
Next review  
D Villafana  
Approved by  
Approved on  
D Villafana  
31/08/2025  
ETA Calculations  
Santo Domingo to St Vincent  
Guyana to Barbados  
Santo Domingo to Trinidad  
Grenada to St Eustatius  
Jamaica to St Vincent  
Barbados to St Lucia  
Trinidad to Suriname  
Antigua to Panama  
Venezuela to Puerto Rico  
Cuba to Belize  
San Juan to Bermuda  
Boca de Navios to Mona Passage  
Boca de Huevos to Windward Passage  
Galveston to Yucatan Channel  
Yucatan Channel to Boca del Dragon