Near Coastal and Celestial examinations for inspected deck licenses over 200 gross tons will often include an ETA (Estimated Time of Arrival) problem. The more interesting of this type are trans-Pacific and therefore cross the International Date Line. The trick to these problems is not to think — not to think about the Date Line or the date or the direction of travel.  Instead, translate all times (departure, elapsed and arrival) through Greenwich.

For example:

Your vessel departs Yokohama from position Latitude 35º27.0’N, Longitude 139º39.0’E (Zone Description -9) at 1330 on 23 July, bound for Seattle at position Lat 47º36.0’N, Long 122º22.0’W (ZD +8). The distance by great circle is 4,245 miles and you estimate that you will average 13.6 knots. What is your estimated Zone Time of arrival?
A.  0438, 4 August
B.  2038, 4 August
C.  0438, 5 August
D.  1238, 5 August

Here is a format and step-by-step procedure to work any ETA that requires you to cross multiple time zones. These problems reward tidiness.

  1. Translate the Zone Time and Date of Departure Port to GMT and Date of Departure.
  2. Calculate the elapsed time of the voyage, including layovers, and apply it to GMT of Departure to find the GMT and Date of Arrival.
  3. Apply the reversed ZD (Zone Description) of the Arrival Port to GMT to find the ZT and Date of Arrival.

Those steps applied to this problem work as follows:

  1. Date & Zone Time of Departure Yokohama:                                       23 July 1330
    ZD Yokohama (-9)                                                                                                   -9
    GMT Departure:                                                                                       23 July 0430
  2. Calculate elapsed time of voyage:
    (Distance traveled is divided by the speed to find time in hours.)
    4245 miles ÷ 13.6 knots = 312.1323529 hours
    (Divide the hours by 24 to find the number of days.)
    312.1323529 ÷ 24 = 13.00551471 days         
    (Subtract the whole number of days from the calculator screen and record them)
    13.00551471 − 13 days = 0.00551471 days                                      +13 (days)
    (Multiply the percentage of an extra day by 24 to find how many hours it equals)
    0.00551471 × 24 = 0.132352941 hours                                              +0 (hours)
    (If your calculator has a button that converts decimal parts of hours and minutes to hours and minutes described in time (or arc), press it now. If not, record the hours (in this case, 0) and subtract them from the screen and convert the percentage of an hour to minutes by multiplying by 60.)

    0.132352941 × 60 = 8 minutes                                                             +08 (minutes)
    Total voyage: 13 days 00 hours 08 minutes
    Added to GMT Departure:                                                                    5 August 0438  
  3. Apply the reversed ZD of Seattle                                                                         –  8
    Date and Zone Time of Arrival in Seattle:                                         4 August 2038
    The answer is (B).

If the problem includes time for bunkering, transiting a canal or waiting for a pilot, add that time to the time found in Step 2.

Note:  Should you not remember the number of days in a given month, the Nautical Almanac (1981) has a calendar on Page 5. Leap years are years divisible by 4, except in the case of century years, which are only leap years if divisible by 400.

On the other hand, you could remember that:

Thirty days have September,
April, June and November;
Thirty-one the others date,
Except in Febuary, twenty-eight.
But in leap year we assign
February, twenty-nine.

Or you could use that most personal of calculators, your hands, particularly the knuckles. Beginning on the outside knuckle of the right (or left) hand, name the knuckle January, the declivity between knucKnuckleskles February, next knuckle March, dip April, next knuckle May, dip June, last knuckle July. Switch hands, new knuckle August, valley September, knuckle October, dip November, last knuckle December. The knuckle months have 31 days. The dip months have 30 days. And then there is February, which is different.


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