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Plotting a Course in Advance

The marteloio was an excellent tool for recovering a course, but it could also be used to plot a course in advance.

As Michael states the problem (page icon 47a):

"My destination is 100 miles to the levante. How far do I want to go by levante sirocho such that the destination would be in the direction tramontana al griego, and how far from my destination would I be at that time?"

Click to enlarge the diagram
Plotting a Course in Advance
Click to enlarge the marteloio table
The marteloio table

For this problem, it is helpful to remember that levante sirocho (east southeast) is 2 quarters off the intended course, and the quarter of tramontana al griego (north by northeast) is 7 quarters off the intended course.

  • a) First leg of the voyage

    Michael begins by calculating the distance he has to sail on the first leg of his journey (AC). While he had no technical name for this part of a journey, he did have a simple rule.

    Here, "combined winds" means the combined quarters of the winds on the voyage out and on the ritorno.

    To make the calculation:

    • 1] Michael takes the alargar for the second wind from the table. The value is 98.

    • 2] Michael stipulates the ritorno of the combined winds. He gives the value as 101 over 5.

      While Michael provides no explanation for this, the reason is that the total of the combined quarter winds is 9. There is no value for 9 quarters in the table. It so happens trigonometrically, however, that once the number of quarters passes 8, the ritorno values work their way back up the column of values given in the table, so that 9 is the same as 7, 10 is the same as 6, and so on. The rule for quarters above 9 would be to subtract the second wind from the total quarters.

    • 3] Michael can now calculate the distance he must sail by levante sirocho before making his turn:

      He would have to sail 9948 over 50 miles along the first wind to make the turn toward the destination.

  • b) The ritorno

    Michael's second task was to calculate the ritorno leg of the course. He has a rule for this calculation.

    To make the calculation:

    • 1] Michael takes the values from the table. The table value of alargar for the first wind of 2 quarters is 38. Note that he had always calculated the real value of alargar in his previous problems. The ritorno for 9 quarters is the same as the ritorno for 7 quarters, or 101 over 5.

    • 2] Michael can now calculate the ritorno:

      Michael would have to sail 3838 over 50 miles on the second leg of his journey to reach his destination.

See how Michael recovers a course or deals with multiple course changes.