The required sail dimensions for calculating the area of any triangular sails are usually its height and the length of its foot. But that only works for mainsails and mizzens with no roach, and jibs with a 90 degree angle at the clew - and what about high-cut headsails, spinakers and cruising chutes? Read on...
Foresail and mainsail dimensions are universally referenced with the letters 'J', 'I', 'E' and 'P' approximating to the length of the foredeck, height of the mast, length of the boom and the height of the main sail - but more accurately defined further down this page.
Yacht designers need these sail dimensions to calculate thought provoking stuff such as the sail-area/displacement ratios of their creations, and sailmakers need them before they put scissors to sailcloth.
If our sailboat's sails were perfectly triangular then, as every schoolboy knows, their area would be 'half the height, times the base' - but with the possible exception of a mainsail with a straight luff, generally they're not. Here's how it works...
These are almost right-angled triangles except for the curvature of the leach (the 'roach') which increases the sail area.
It's usually calculated as:~
Area = (luff x foot)/1.8, or
Area = (P x E)/1.8, where:~
For the mizzen sails on ketches and yawls, 'P' and 'E' relate to the mizzen mast and boom.
For more heavily roached sails, the increased area can be accounted for by reducing the denominator in the formula to 1.6.
Clearly calculating sail areas isn't going to be an exact science...
For a working jib that fills the fore triangle - but no more - and with a foot that's parallel to the deck, then you've got a 'proper' right-angled triangular sail, whose area is:~
Area = (luff x foot)/2, or
Area = (I x J)/2, where:~
Genoas, by definition, have a clew which extends past the mast and are described by the amount by which they do so. For instance a 135% genoa has a foot 35% longer than 'J' and a 155% genoa 55% longer. Areas are calculated as follows:~
Area (135% genoa) = (1.44 x I x J)/2, and
Area (155% genoa) = (1.65 x I x J)/2
But these formulae don't work for a high-cut jib with a raised clew - unless you imagine the sail turned on its side such that the luff is the base and the luff perpendicular is the height.
It's still a simple calculation though, once you know the length of the luff perpendicular (LP), the sail area is:~
Area = (luff x luff perpendicular)/2, or
Area = (L x LP)/2, where:~
Much like calculating foresail areas, but with different multipliers for conventional spinnakers and asymmetric spinnakers...
Area = (1.8 x luff x foot), or
Area = (1.8 x I x J), where:~
Area = (1.65 x luff x foot), or
Area = (1.65 x I x J), where:~