Boat displacement is defined as the weight of the volume of water displaced by a floating object, and sail area is the total area of a boat's working sails.
Like speed, displacement doesn't mean much unless compared to waterline length,so you need to take a look at the Displacement/Length Ratio to compare the relative heaviness of boats no matter what their size.
Similarly, sail area doesn't tell you much about a boat's likely performance unless compared to its displacement, which is why we have the Sail Area/Displacement Ratio.
Let's take a look at both of these displacement related ratios in turn...
The formula for calculating the Displacement/Length Ratio is:
An ultra-light racing yacht may have a D/L Ratio of 80 or so, a light cruiser/racer would be around 140, a moderate displacement cruiser be around 230, a heavy displacement boat will be around 320 while a Colin Archer type super- heavy displacement cruiser may boast a D/L ratio of 400+.
As immersed volume and displacement are proportional, a heavy displacement yacht will have to heave aside a greater mass of water than its light displacement cousin.
Or put another way, the lower D/L Ratio vessel will have a lower resistance to forward motion than the higher D/L ratio vessel, and will be quicker as a result.
That's a longwinded way of saying that the greater the mass, the greater the power required to shift it.
That power is of course derived from the force of the wind acting upon the sails, and the greater the sail area the greater the power produced for a given wind strength.
The formula for calculating the Sail Area/Displacement Ratio is:
Clearly then, performance is a function of both power and weight, or sail area and displacement.
Sail Area/Displacement ratios range from around 14 for a lightly canvassed motor-sailor to 20 or so for an ocean racer.
Calculating the area of the mainsail is simple. After all, it's just a right-angled triangle so:~
Area = (Base x Height)/2 = (Foot x Luff)/2
OK, it won't be spot on if the sail has some roach, but it'll be near enough. Having said that, for a fully-battened, heavily roached sail you could add 10 to 15% to be more accurate.
The foresail would be just as easy if it exactly fitted the fore-triangle but usually the sail will be high-cut or will overlap the mast - or both.
So the calculation becomes:~
Sail Area = (luff perpendicular x luff)/2
For more on this subject, take a look at Understanding Sail Dimensions...
So to summarize, the criteria associated with good performance under sail are:
But performance in an offshore cruising sailboat isn't just about speed. Whilst, as part of the deal for getting their hands on the silverware, a racing crew will cheerfully accept the high degree of attentiveness needed to keep a twitchy racing machine on her feet, a cruising sailor most definitely won't.
For us, a degree of speed will be readily sacrificed for a boat that's easy on the helm, and which rewards its crew with a gentler motion and more comfortable ride.
And whilst talking of comfort, Ted Brewer's 'Comfort Ratio' has much to to with Boat Displacement.