19A1. Definition. Compensation is the act
or process of counteracting a variable. In
connection with a submarine it refers to a
redistribution of ballast water to counteract
unsymmetrical moment arms and effect
balance about the center of buoyancy. It also
includes the addition or removal of ballast
to offset variations in the over-all weight of
the ship.

When submerged, a submarine may be
considered to be suspended from a single
point called the center of buoyancy. The condition of stable equilibrium requires that the
center of gravity be located in a vertical line
from the center of buoyancy downward. Following this natural law, a suspended body
will always assume this position. In the submarine, however, this result does not meet
the requirements necessary for stable equilibrium on an even keel.

The conditions necessary for equilibrium
at even keel follow the laws of the simple
balance. The products of the weights on each
side of the support times their moment arms,
or distance from the support, must be equal.
Before a submarine leaves port, it is
trimmed for surface operation by the

adjustment of ballast to compensate for any change
in the over-all weight since the last operation.
Further adjustment of the variable ballast is
ordered by the diving officer after submergence until perfect trim is obtained and the
men at the diving planes steady the ship on
an even keel. When the diving officer obtains
final trim, the amount of water in each variable ballast tank is recorded in the diving
book. On subsequent dives this trim is correct if conditions are the same. However,
conditions do not remain static for any extended periods and may change rapidly. On
long dives the variable ballast tank readings
should be recorded just prior to surfacing.
The weights that change on a ship are
those of personnel, torpedoes, provisions,
fresh water, lubricating oil, fuel oil, and air.
Most people, not familiar with submarines,
do not realize that the compressed air in the
air flasks weighs as much as 4 tons on some
submarines. These various changes affect the
fore-and-aft trim and also the total weight,
and must be counteracted by the manipulation of water ballast in the auxiliary and forward and after trim tanks. Compensation
therefore is nothing more than balancing;
the ship is balanced fore and aft and over-all.

B. COMPENSATION BY MOMENTS

19B1. General method of computing. The
proper distribution of ballast is ascertained
by consideration of the moment arms of the
various weights in question. The center of
gravity of the auxiliary tank is assumed to be
the center of gravity of the submarine, and
the moment arms are calculated from this
point to the center of gravity of the variable
weights. The table on the next page gives
some of these distances for feet-type submarines.

19B2. Examples. Some typical examples will
demonstrate the method of compensation by
moments.

In the following examples, it is assumed
that the ship is in perfect trim and two torpedoes are removed from the racks in the
forward torpedo room and placed on the
dock. It is desired to compensate by using
the forward trim tank and the auxiliary
tank.

Two torpedoes weigh 6,354 pounds. The
distance of the center of gravity of the forward torpedo racks from the center of the
auxiliary tank is 94.5 feet. The distance of
the center of gravity of the forward trim
tank from the center of auxiliary tank is
113.5 feet. The moment of two torpedoes
about the center of gravity is 6,354 X 94.5=

183

Distance in feet

Location

Torpedoes in forward tubes

118.00

Forward

Forward trim tank

113.50

Forward

WRT tank

98.50

Forward

Torpedoes in forward racks

94.50

Forward

Sanitary tank No. 1

77.50

Forward

Fresh water tanks No. 1 and No. 2

75.00

Forward

Normal fuel oil tank No. 1

68.50

Forward

Battery fresh water tank

67.00

Forward

Normal fuel oil tank No. 2

55.00

Forward

Battery fresh water tank

54.00

Forward

Negative tank

36.50

Forward

Sanitary tank No. 2

24.50

Forward

Stores

23.50

Forward

Fresh water tanks No. 3 and No. 1

19.50

Forward

4-inch magazine

15.50

Forward

Fuel ballast tanks No. 3A and No. 3B

15.00

Forward

Ammunition and refrigeration space

11.50

Forward

Safety tank

7.00

Forward

Auxiliary tank

0.00

Amidships

Battery fresh water tank

2.00

Aft

Battery fresh water tank

14.50

Aft

Reserve lube oil and sanitary tank No. 3

24.00

Aft

Fuel ballast tanks No. 5A and No. 5B

26.00

Aft

Lube oil tank No. 1

36.50

Aft

Main engine sumps No. 1 and No. 2

45.00

Aft

Clean fuel oil tank No. 1

50.00

Aft

Collecting and expansion tanks

62.50

Aft

Lube oil tank No. 2

64.00

Aft

Normal fuel oil tanks No. 6A and No. 6B

69.50

Aft

Main engine sumps No. 3 and No. 4

72.50

Aft

Clean fuel oil tank No. 2

76.50

Aft

Lube oil tank No. 4

80.50

Aft

Normal fuel oil tank No. 7

85.00

Aft

Lube oil tank No. 3

86.50

Aft

Motor and reduction gear sumps

92.50

Aft

Sanitary- tank No. 4

100.00

Aft

Torpedoes in after racks

115.00

Aft

WRT tank

121.00

Aft

Torpedoes in after tubes

139.00

Aft

After trim tank

140.00

Aft

184

600,453 pounds feet. To obtain the same
moment, using the forward trim tank, the
torpedo moment is divided by the distance
to the forward trim tank: 600,453 / 113.5 = 5,290
pounds.

Therefore 5,290 pounds are flooded into
the forward trim tank from the sea, preserving the fore-and-aft trim, but the total
weight of the ship would be 1,064 pounds
light. This amount, 1,064 pounds, is therefore flooded into the auxiliary tank from sea
and the trim is correct over-all and fore and
aft.

The process is the same in more complicated problems as illustrated below
A submarine in perfect trim takes
aboard 3 torpedoes in the forward racks.
Ten thousand gallons of fuel oil are taken
into each of the normal fuel oil tanks No. 1
and No. 2. Compensation is desired using the
forward trim and auxiliary tanks. Three
torpedoes, at 3,177 pounds each, weigh 9,531
pounds; fuel oil weighs approximately 7.13
pounds per gallon; sea water weighs 8.56
pounds per gallon. Using moment arms, it is
found that to compensate for the torpedoes,
the weight of sea water to be pumped from
forward trim tank to sea is:

W X 113.5=

9,531 X 94.5

W=

(9,531 X 94.5)/113.5 = 7,935 pounds

As 9,531 pounds were taken aboard, 1,596
pounds (9,531-7,935) must be pumped from
the auxiliary tank to the sea to maintain this
over-all weight. The 10,000 gallons of fuel
oil taken into fuel tank No. 1 displace 10,000
gallons of sea water. As the differential in
weight is 1.43 pounds per gallon, 14,800
pounds' ballast must be added. The amount
flooded into forward trim tank is:

W X 113.5=

14,300 X 68.5

W=

(14,300 X 68.5)/113.5 = 8,630 pounds

Therefore, 5,670 pounds {14,300-8.630}
are flooded into the auxiliary tank. The
weight used in the compensation for the No.
2 fuel tank is found to be:

W X 113.5=

14,300 X 55

W=

(14,300 X 55)/113.5 = 6,980 pounds

Therefore, 6,930 pounds are flooded into
the forward trim and 7,370 pounds (14,300 - 6,930) into the auxiliary. The vessel now has
the same trim fore and aft and over-all. In
actual practice, ballast is pumped or flooded
to the nearest point that can be read on the
gages.

The ballast disposal may be summarized
as shown in the following table:

FORWARD TRIM

AUXILIARY

OVER-ALL WEIGHT

In

Out

In

Out

In

Out

7,935

1,596

9,531

8,630

5,670

14,300

6,930

7,370

14,300

+15,560

-7,935

+13,040

-1,596

+9,531

-28,600

-7,935

-1,596

+9,531

+7,625

+11,444

-19,069

+7,625

+11,444

+19,069

-19,069

185

The over-all weight may be checked by
taking the algebraic sum of all weights added
to or taken from the ship, thus

Weights added (in pounds)

9,531

Torpedoes

142,600

Fuel oil

15,560

Ballast in forward trim

13,044

Ballast in auxiliary

+180,731

Weights subtracted (in pounds)

7,935

Out forward trim

1,596

Out auxiliary

171,200

Sea water from fuel tanks

+180,731

180,731 - 180,731 = 0 = net change in weight.

Compensation may also be accomplished
by using the after trim tank. The ballast
to be pumped from the after trim tank, to
equal the 7,625 pounds pumped into the forward trim tank, is:

W X 140=

7,625 X 113.5

W=

(7,625 X 113.5)/140 = 6,182 pounds

Therefore 6,182 pounds out of the after
trim tank will maintain the fore-and-aft
trim. However the ship is now light over-all
and ballast must be added to the auxiliary
tank to compensate for the net loss of 19,069
pounds plus the amount pumped from after
trim. Total ballast added to the auxiliary
would be 19,069 + 6,182 = 25,251 pounds.

C. THE COMPENSATION CURVE

19C1. Description. A more convenient and
much shorter method than that given above
is by use of a compensation curve. The curve
shown in Figure 19-1 is for the submarine
herein described. As constructed, the center
of the auxiliary tank is the origin, as the
center of gravity of this tank is considered
coincident with the center of gravity of the
ship.

The center ordinate representing the
auxiliary tank is laid out in pounds. The axis
of abscissas is laid out in thousand-pound
feet. The curves for the various tanks are
drawn from the data available. A rapid and
accurate way to construct the curves is by
locating points as far from the center of
origin as possible and drawing the lines to
the point of origin.

The curves in Figure 19-1 are located as
follows:

The moment arm of the forward torpedo
tubes is 118 feet from the center of the auxiliary. The number of pounds required to
produce a moment of 200,000 pounds is

200,000 / 118 = 1,695

This point is located on the proper ordinate and the line drawn.

The forward trim tank curve is found in
like manner:

200,000 / 113.5 = 1,762

19C2. Use of curve. In using the curve, the
point is taken on the center ordinate that
represents the weight to be compensated. It
is projected to the line representing the location of the change. A line is dropped from
this point to the line of the forward or after
trim tank and from this intersection back to
the center ordinate. The point thus found
gives the number of pounds to be added or
taken from the trim tank to preserve the
fore-and-aft trim. If the line is dropped from
the intersection on the tank line to the base
line, the moment in thousand-pouted feet is
read directly.

As the summary of the changes in ballast to effect compensation is the algebraic
sum of the weight added to or taken from
the vessel, some care must be used to avoid
any confusion of signs. In the use of the
curves, all tanks and moment arms to the
right of the center ordinate are positive and
those to the left of the ordinate are negative.
Any weight added to or taken from the
vessel, which tends to depress the bow or
raise the stern, is positive. If the result of

186

Figure 19-1. Compensation by moments

187

the change in weight tends to produce a
counterclockwise rotation, the force is negative.

As the charts are laid out with the bow
to the right, any change which tends to rotate the boat clockwise about its center of
gravity is positive.

The preceding example in compensation
is worked out with the curve as follows:

Three torpedoes with a total weight of
9,531 pounds are placed in the forward racks.
Ten thousand gallons of fuel oil are poured
into the No. 1 fuel tank and 10,000 gallons
additional into the No. 2 fuel tank.

As the 9,531-pound weight of the torpedoes extended from the center ordinate
does not meet the torpedo rack curve, the
weight may be divided until the intersection
is on the chart. Dividing by 5 and extending
the 1,906 point to the rack curve and from
there down to the base line, the moment is
read as +180 thousand-pounds feet. Multiplying by 5 gives 900,000 as the moment of
the 3 torpedoes.

The fuel oil taken aboard displaces an
equal amount of sea water with the result
that 14,300 pounds are removed from each
of the two fuel tanks. The 14,300 pounds
extended runs off the chart, so 1/5, or 2,860,
is extended to intersect with the tank curves.
Doing this, and extending to the base line,

gives 196,000 for the No. 1 tank and 157,000
for the No. 2 tank. The moments for 14,300
pounds are 980,000 and 785,000.

Summarizing these moments:

+900.000

980,000

785,000

1,765,000

-1,765,000

+900,000

-865,000

This shows that the ship is light forward
and ballast must be flooded into the forward
trim tank to produce an 865,000-pound
moment.

As 865 is off the chart it is divided by
5. Projecting upward from 173 on the base
line to the forward trim tank curve and then
left to the center ordinate, the amount is read
as 1,520. Multiplying by 5 gives 7,600 pounds
as the amount to be flooded into the forward
trim tank.

As 9,531 pounds were added to the vessel
and 28,600 pounds were lost as a result of the
displacement of sea water by the fuel oil,
the net loss in over-all weight is 28,600 - 9,531 = 19,069 pounds. Since 7,600 pounds
were added to the forward trim tank,
11,469 pounds must be flooded into the auxiliary tank to maintain the original over-all
trim.

D. COMPENSATION BY PERCENTAGE

19D1. Description. Another type of compensation curve may be constructed using
percentages (Figure 19-2). The center of the
auxiliary tank is the origin. This ordinate
is laid off in percent, 0 to 100. The base,
or line of abscissas, is laid off in feet and
the relative locations of the centers of gravity of the different tanks are indicated. Lines
are drawn from the 100-percent point in the
center ordinate to the locations of the forward and after trim tanks.

19D2. Use of curve. This curve is used by
projecting the point, indicating the tank in
which the change in weight is made, up to an
intersection with the percentage curve. This
intersection gives the percentage of the

weight which must be pumped out of or
flooded into the variable tanks to correct the
fore-and-aft trim and over-all weight. This
intersection is projected to the center ordinate. This point gives the percentage of the
weight in question which must be pumped
out of or flooded into the auxiliary tank.
When projected to the corresponding trim
tank scale it gives the percentage of weight
to be flooded into or pumped out of the trim
tank.

The previous example may be worked
out with this curve as follows:

Weight in forward torpedo racks is
9.531 pounds

Weight out (net) No. 1 fuel tank is
11,300 pounds

188

Figure 19-2. Compensation by percentage

189

Weight out (net) No. 2 fuel tank is
14,300 pounds

The forward torpedo rack intersection
with the forward trim tank line shows that
83.5 percent of the 9,531 pounds should come
out of the trim tank and the remainder, 16.5
percent, out of the auxiliary.

7,958 pounds out of trim tank.

1,573 pounds out of auxiliary.

The 14,300 pounds out of No. 1 fuel tank
reads 60.5 percent or 8,650 in the trim tank,
the remaining 39.5 percent of 5,650 in the
auxiliary tank.

The 14,300 pounds out of No. 2 fuel tank
reads 48.5 percent or 6,935 pounds in the
trim tank, the remaining 51.5 percent or 7,365
pounds in the auxiliary.

SUMMARY

TANK OR SPACE

PERCENT

WEIGHT CHANGE

FORWARD TRIM

AUXILIARY

AFTER TRIM

F.T.

AUX.

A.T.

Lighter

Heavier

In

Out

In

Out

In

Out

Fwd. Racks

83 1/2

16 1/2

9,531

7,958

1,573

No. 1 F.O.

60 1/2

39 1/2

14,300

8,600

5,650

No. 2 F.O.

48 1/2

51 1/2

14,300

6,935

7,365

28,600

9,531

15,585

7,958

13,015

9,531

7,958

1,573

19,069

7,627

11,422

11,442

19,069

Pumping 7,627 pounds into the forward
trim from the sea and flooding 11,442 pounds
into the auxiliary, trims the ship fore and
aft and over-all. Pumping and flooding to
the nearest 50 pounds, as is the practice,
the figures would be 11,500 pounds into the
auxiliary and 7,600 pounds into the forward
trim. The ship is 27 pounds lighter forward
and 31 pounds heavy over-all.

If the location of the weight change is
in the after part of the ship, compensation is
effected by using the after trim tank and the
auxiliary tank.

The computations necessary for any
problem in compensation may be quickly and
easily made by the use of either of the curves.
It is of the utmost importance, however, that
extreme care be used to include all the weight
changes and to get them in the proper columns. Small mistakes in the case of some
tanks may make a large error in the final
trim. For example, a 100-pound mistake in
the weight change in the forward trim tank
has the same effect on the fore-and-aft trim
as a 1,040-pound change in the ammunition
and refrigeration space.