Bruce Number

We have previously discussed the SA/D ratio (Sail Area to Displacement) and the D/L Ratio (Displacement to length.

Let’s talk about another ratio that is often used in comparing yachts: the Bruce Number.

This number is calculated as the ratio of the square root of the sail area of the boat (mainsail + foretriangle) divided by the cube root of its displacement.

The Bruce Number, (or the Bruce Roberts Formula), is used by yacht designers as in insight into the relative stability (and thus seaworthiness) of a yacht. It’s named after Bruce Roberts, a famous naval architect who made the formula famous.

The formula used for the Bruce Number in this calculator is:

Bno. = Bruce Number
SA = Total Sail Area in square feet
D = Displacement of Boat in pounds

A bigger Bruce Number suggests more stability, while a lower Bruce Number suggests less stability.

The Bruce Number shouldn’t be used in isolation. The shape of the hulls, weight distribution, center of gravity (eg flybridge versus aft-helm cats), boom height and sail plan are also important considerations when thinking about a yacht’s stability and seaworthiness.