Dave Gerr - Boat Mechanical Systems Handbook-How to Design, Install, and Recognize Proper Systems in Boats

the momentum of the sloshing liquid reduce
stability due to “free-surface effect.” The nar-
rower a tank is in proportion to the beam of
a boat, the less the reduction in stability—-
the less the free-surface effect. For this rea-
son, tanks should generally be arranged to
be as narrow as practical athwartships. Wide
shallow tanks have the most free-surface ef-
fect for a given capacity and should be
avoided if possible.
As a rule, if a tank’s width is less than
20 percent of overall beam, and the capacity
of the tank is less than 12 percent of displace-
ment, you can neglect the free-surface effect
for pleasure-craft work. Sometimes, how-
ever, wide tanks are desirable to meet spe-
cific design goals. If so, be sure to divide up
the tanks into two or three separate tanks
athwartships. An example of this is in the
66-foot (20 m) Kingfisherdesign shown
Figure 5-4. Here it was advantageous to have
the fuel tanks running full width athwartships
aft of the master stateroom. In this case, the
main diesel tanks are divided into two sepa-
rate tanks at the centerline (with two addi-
tional smaller tanks low and outboard).
If you are doing a new design or a major
modification to tank size, location, or capac-
ity, whenever you have a tank wider than 20
percent of overall beam or with a capacity
greater than 12 percent of displacement, you
should calculate the reduction in stability and
use that reduced stability in all your other
stability work. (To be perfectly correct, you
should do this for all tanks in all boats; but it
generally isn’t required if the tanks are nar-
row and of modest capacity.)
Stability is evaluated in terms of GZ
(righting arm) and GM (distance to the meta-
center M from the VCG (vertical center of
gravity or G). If you know one, you can eas-
ily find the other for angles of heel up to
10 degrees using the following formula.

Formula 6-3. Stability

GZ =GM× sin q

or

GM =GZ ÷ sin q

Where

GZ =righting arm, ft. or m

GM =metacentric height, ft. or m

q =the angle of heel in degrees (qis

the Greek letter called theta)

Free-surface effect is evaluated using

the “free-surface GM correction” to find the

actual GM known as “effective GM,” after

allowing for the tank free surface. To deter-

mine effective GM, calculate boat GZ and GM

as usual, then apply the following formula.

Formula 6-4. Effective GM, or

Metacentric Height

Where

GMeff =GM effective, ft. or m

GMs =GM of the ship, prior to free-

surface calculation, ft. or m

GMred =GM reduction for each tank, ft.

or m

GMredT =total GM reduction for the

sum of all tanks, ft. or m

IL =moment of inertia of the plan area

of the surface of the tank about the

tank’s centerline, ft.^4 or m^4

∇s =displacement of ship, cu. ft. or m^3

rL =density of liquid in tank, lb./cu. ft.

or kg/m^3 , or specific gravity

rs =density of the water boat floats in

(usually seawater), lb./cu. ft. or kg/m^3 ,

or specific gravity

(ris the lowercase Greek letter rcalled

rho.)

(∑is the uppercase Greek letter Scalled

sigma. When used in a formula like

this, it means “sum.” So, in this case,

the sum of all “GMred.”)

NOTE:

The relationship is a ratio and can

be in any units of density as long as the same

units are used top and bottom.

Contrary to intuition, the total capac-

ity of the tank does not affect stability with

regard to free-surface effect, and neither

does the tank location (again, with regard

to free-surface effect). It doesn’t matter

how high or low, or how far inboard or out-

board the tank is located. Only the tank’s

individual fluid surface area contributes to

ρ

ρ

L

s

⎛

⎝⎜

⎞

⎠⎟

GMredT=∑GMred (of all tanks)

GM

IL

s

L

red

s

= (for each tank

∇

⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟

ρ

ρ

))

GMeff=−GMs GMredT

Chapter 6:Tank Capacity and Range

Formula 6-4.

Formula 6-3.