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Monty Mariner > Articles > Various Constants and formulae

Various Constants and formulae

POUNDS PER INCH IMMERSION (PPI):

The weight required to sink the yacht one inch.

It is calculated by multiplying the LWL area by 5.333 for sea water or 5.2 for fresh.

The PPI usually increases as the hull sinks into the water as the LWL area is also increasing

due to the shape of the hull above water.

MOMENT TO TRIM 1 INCH (MTI):

The MTI is the moment, expressed in foot-pounds,

that will change the fore and aft trim of the yacht one inch.

For a displacement hull, the MTI is, roughly (but close enough for all practical purposes),

0.35 times the square of the waterline area divided by the WL beam, or:

For example; a boat has a LWL Area of 165 sq ft and a Beam WL of 8 feet.

The MTI is 0.35 x 165 x 165 /8 = 1191 ft-lbs., say 1200 for rough figuring.

Now you hang a 100 pound dink 18 feet abaft the CB. You’ve added 1800 ft-lbs of aft moment

so the boat will trim 1800/1200 = 1.5 inches down by the stern.

However, the boat does trim about its CF and, as that is usually abaft amidships, the stern will move less than the bow. You might find that she trims 5/8″ down by the stern, and 7/8″ up by the bow, making a total trim change of 1.5 inches.

Obviously on a cat things are slightly different.

once the new waterline area is calculated you can apply the figures to SA/D

(taking into account the new displacement with the gear onboard)..

this gives a reasonable view of the potential change.. mainly a monohull formula though

SAIL AREA/DISPLACEMENT RATIO:

The SA/D ratio is the sail area in sq ft. divided by the displacement in cubic ft to the 2/3 power,

or SA/D*0.667

Ratios below 14 are suited for motor sailers,

from 14-17 for ocean cruisers and

from 16-18 for typical coastal cruisers.

Ratios over 18-20 are seen on racing dinghies, inshore racers and ocean racing yachts.

The more extreme screamers can have very high SA/D ratios indeed; A 60 foot design boat, had a SA/D ratio, based on 100% fore triangle, of well over 30, depending on her displacement at the moment.

Her displacement varied widely as she could carry 8,000 pounds of water ballast in tanks on the windward side

DISPLACEMENT/LENGTH RATIO:

Displacement in Tons / (0.01*Waterline Length)3

The D/L ratio is a non-dimensional figure derived from the displacement in tons (of 2240 lbs)

divided by 0.01 LWL cubed, or Dt/(.01 LWL)3.

It allows us to compare the displacement of boats of widely different LWL.

Some examples of various D/L ratios follow, but are generalities only,

as there is often a wide range within each type.

BOAT TYPE D/L RATIO:

Light racing multihull 40-50

Ultra light ocean racer 60-100

Very light ocean racer 100-150

Light cruiser/racer 150-200

Light cruising auxiliary 200-250

Average cruising auxiliary 250-300

Heavy cruising auxiliary 300-350

Very heavy cruising auxiliary 350-400

>300 best for GRP  >400 best for Steel

Maximum Speed

1.4*sq root of waterline length (ft)

Ave speed / day

20* sq root of waterline length (ft)

Wave Length

5.12*(time in secs between crests)2

Wave Speed

3.03*time in secs between crests

Volume below waterline (in cu ft)

Wt in Tons * 35

[35 (34.973) cu ft of Seawater weighs 1 Ton]

[1 cu ft of Seawater weighs 64 lbs]

USYRC’s ‘Capsize Risk Factor’

Beam / ( Disp / (.9*64)) ^.333

(Values less than 2 are good).

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