Kiwiprops™

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Speed - Displacement

To illustrate how important displacement is in determining motoring speed the following graph uses calculations from Dave Gerr's well know and respected Propeller Handbook.

These equations are for launches so do not deal with the generally substantial increases in area and consequently skin friction from the deep keels of most yachts.

Neither do they allow for the additional skin friction as a result of the greater hull immersion as displacement increases. These two factors will deliver greater reductions in vessel speed than shown on the graph below.

In this instance the power is held at 25 hp at the propeller and water line length at 30 feet - although again this may increase slightly with additional displacement and offer very small increases in vessel speed depending upon hull shape.

We started with the following equations from Dave Gerr's Handbook:

Speed to Length Ratio = Knots / Water Line Length^0.5

Horsepower Required = Displacement / ( 10.66 / Speed to Length )^3.0

Then re-arranging these equations to solve for Speed by Displacement we get:

Knots = ( 10.66 x WL^ 0.5) / (( Disp / Hp )^ 0.33)

By holding both Power and Water Line constant we can then get Knots as a function of Displacement - see graph below:

This is a reasonable guide as to how speed falls with increases in displacement for a 30 foot waterline vessel with 25 hp available at the propeller.

In the case of a catamaran one can imagine the vessel split amidships with each hull as a seperate vessel of half the displacement with the power of one engine again as a guide to motoring speed drop off with displacement.

Obviously the geneally easier driven hull form and lack of a deep keel with associated skin friction will deliver higher speeds for a " half " hull.