Formula 6-5b. Moment of Inertia of a
Rectangular Plane Area (Metric)
I =bh^3 ÷12
Where (for evaluating tank free surface)
b =the length of the tank fore-and-aft, m
h =the width of the tank athwartships, m
In our case, the diesel tanks are 2.743 m
long by 2.073 m wide athwartships. Thus the
moment of inertia of each tank is
I =2.743 m× (2.073 m)^3 ÷ 12 =2.036 m^4
Then
Multiply by 2 for both diesel tanks =
0.0552 m GMred (diesel)
The water tanks are 0.762 m long by 1.981
m wide athwartships. Thus the moment of
inertia for each tank is
I =0.762 m× (1.981 m)^3 ÷ 12 =0.494 m^4
Then
Multiply by 2 for both water tanks =
0.01574 m GMred (water)
Now
and
This is the loss in stability due to free-
surface effect and can be translated into
reduced GZ or RM using the preceding rela-
tionship between GZ and GM.
In our case, stability after free-surface
effect is
GZ 1°=1.02 m GM× sin 1°=0.0178 m
RM 1°=0.0178 m GZ 1°× 62,588 kg
Disp. =1,114 kgm
This is a reduction in righting moment of
6% due to free-surface effect.
Free-Surface Effect and
Loading Conditions
Keep in mind that the free-surface reduc-
tion changes for various conditions of load-
ing (for different displacements). Using
boat displacement to the DWL (or to the
expected flotation waterline at^2 / 3 load) is
adequate for most work on small craft; for
commercial projects, however, carefully
tabulated GMs for different loading condi-
tions will be required. Performing stability
calculations for all reasonable conditions of
loading and flooding are detailed and time-
consuming. Usually, these should be con-
ducted using a software package, such as
GHS, intended for this purpose; however,
you need to understand the concept of free-
surface effect to interpret the results
correctly.
GMeff=−1.091 m GMs 0.071 m GMredT=1.02 m
GM 0.0552 m GM
0.01574 m G
redT= red (diesel)
+ MMred (water)=0.071 m
GM
0.494 m
61.05 m
1.000
1.028
red
4
= 3
⎛
⎝⎜
⎞
⎠⎟
⎛
⎝⎜
⎞
⎠⎟⎟
=0.00787 m
(for each water tank)
GM
2.036 m
61.05 m
0.852
1.028
red
4
= 3
⎛
⎝⎜
⎞
⎠⎟
⎛
⎝⎜
⎞⎞
⎠⎟
=0.0276 m
(for each diesel tank)
Chapter 6:Tank Capacity and Range
Formula 6-5b.