One major problem with doing it the way you're suggesting is the plain piece of paper doesn't show you the rocks, shoals and other navigation hazards. So, while you may have some idea of how far you've run and such, it doesn't really help in terms of good navigation and avoiding the hazards without having to copy it over to the chart.
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You know what the first rule of sailing is? ...Love. You can learn all the math in the 'verse, but you take
a boat to the sea you don't love, she'll shake you off just as sure as the turning of the worlds. Love keeps
her going when she oughta fall down, tells you she's hurting 'fore she keens. Makes her a home.
—Cpt. Mal Reynolds, Serenity (edited)
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Still—DON'T READ THAT POST AGAIN.