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Schematic of quantities for capstan equation An example of holding capstans and a powered capstan used to raise sails on a tall ship. The capstan equation [1] or belt friction equation, also known as Euler–Eytelwein formula [2] (after Leonhard Euler and Johann Albert Eytelwein), [3] relates the hold-force to the load-force if a flexible line ...
For thousands of years ship designers and builders of sailing vessels used rules of thumb based on the midship-section area to size the sails for a given vessel. The hull form and sail plan for the clipper ships, for example, evolved from experience, not from theory. It was not until the advent of steam power and the construction of large iron ...
Simpson's rules are used to calculate the volume of lifeboats, [6] and by surveyors to calculate the volume of sludge in a ship's oil tanks. For instance, in the latter, Simpson's 3rd rule is used to find the volume between two co-ordinates. To calculate the entire area / volume, Simpson's first rule is used. [7]
Ship stability is an area of naval architecture and ship design that deals with how a ship behaves at sea, both in still water and in waves, whether intact or damaged. Stability calculations focus on centers of gravity , centers of buoyancy , the metacenters of vessels, and on how these interact.
The Reynolds and Womersley Numbers are also used to calculate the thicknesses of the boundary layers that can form from the fluid flow’s viscous effects. The Reynolds number is used to calculate the convective inertial boundary layer thickness that can form, and the Womersley number is used to calculate the transient inertial boundary thickness that can form.
The coefficients within the major part of the region being integrated are one with non-unit coefficients only at the edges. These two rules can be associated with Euler–MacLaurin formula with the first derivative term and named First order Euler–MacLaurin integration rules. [8]
Hull speed can be calculated by the following formula: where is the length of the waterline in feet, and is the hull speed of the vessel in knots. If the length of waterline is given in metres and desired hull speed in knots, the coefficient is 2.43 kn·m −½.
The squat effect is the hydrodynamic phenomenon by which a vessel moving through shallow water creates an area of reduced pressure that causes the ship to increase its draft (alternatively decrease the underkeel clearance of the vessel in marine terms) and thereby be closer to the seabed than would otherwise be expected.