Proper use of fiber ropes on capstans and bitts

Ropes are commonly tensioned by capstans on merchant and navy ships as well as on shore. Here the term capstan means any cylinder around which a rope is wrapped, including wrapping heads, bitts and bollards. Improper use of ropes on capstans can cause injuries and fatalities. When a rope is wrapped around a capstan, it is held by friction. The ratio of effective tension to back tension is a function of the number of turns on the capstan and of the friction coefficient between the rope and the capstan. If insufficient turns are applied, the rope cannot be held by back tension. If too many turns are applied, then the rope cannot be released by relaxing back tension. This paper discusses the capstan formula, which relates friction coefficient and number of turns to the ratio of effective tension to back tension. The formula is not new or original. But it is not widely known and has not published before in a form accessible and usable by merchant and navy personnel, advisors and consultants. The capstan formula can help understand the loss of tension which occurs when a rope passes around a cylinder. It can be used to calculate the friction coefficient of a rope against a surface, and with that information, it can then be used to calculate the loss of tension in other similar circumstances.