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Boat Displacement and Sail Area

Boat displacement is defined as the volume of water displaced by a boat afloat, and sail area is the total area of the boat's working sails.

Like speed, boat 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 Displacement/Length Ratio

Displacement/Length Ratio

Displacement/Length Ratio = D/(0.01L)3,

Where:

D is the boat displacement in tons (1 ton = 2,240lb)

L is the waterline length in feet.

An ultra-light racing yacht may have a D/L Ratio of 100 or so, a light cruiser/racer would be around 200, a medium displacement cruiser be around 300, while a Colin Archer type heavy-displacement cruiser may boast a D/L ratio of 400+.

displacement/length ratio chart

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 Sail Area/Displacement Ratio

Sail Area/Displacement Ratio

Sail Area/Displacement Ratio = SA/(DISPL)0.67,

Where:

SA is sail area in square feet

DISPL is boat displacement in cubic feet

Clearly then, performance is a function of both power and weight, or sail area and displacement.

sail area/displacement ratios chart

Sail Area/Displacement ratios range from around 14 for a lightly canvassed motor-sailor to 20 or so for an ocean racer.


Calculating Sail Area

luff perpendicular and j measurement

Mainsail Area

Calculating the area of the mainsail is simple. Afterall it's just a right-angled triangle, so:~

Area = (Base x Height)/2 = (Foot x Luff)/2

OK, it won't be spot if the sail has some roach, but it'll be near enough.

Foresail Area

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


and finally...

So to summarize, the criteria associated with good performance under sail are:

  • Waterline length: the longer the better, as wavemaking resistance is inversely proportional to waterline length.
  • Wetted area: the less the better, particularly in areas where light airs prevail, as hull drag is directly proportional to wetted area.
  • Boat Displacement: the lower the better, as the power requirement is directly proportional to displacement. Provided, of course, that light displacement doesn't come at the cost of structural integrity.
  • Sail area: the more the better, within reason, as power production is directly proportional to sail area. Having to reef early is much less frustrating than wishing you had an extra metre or so on the mast when the wind falls away.

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.


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