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.
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=


in feet
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

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:

 7,935 1,5969,531 
8,630 5,670  14,300
6,930 7,370  14,300
-7,935 -1,596   
+7,625 +11,444  -19,069

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)
142,600Fuel oil
15,560Ballast in forward trim
13,044Ballast in auxiliary
Weights subtracted (in pounds)
7,935Out forward trim
1,596Out auxiliary
171,200Sea water from fuel tanks
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.

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


Compensation by moments chart
Figure 19-1. Compensation by moments

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:


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.

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


Compensation by percentage chart
Figure 19-2. Compensation by percentage

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.

Fwd. Racks83 1/216 1/2  9,531 7,958 1,573  
No. 1 F.O.60 1/239 1/2 14,300 8,600 5,650   
No. 2 F.O.48 1/251 1/2 14,300 6,935 7,365   
    9,531 7,958 1,573   
    19,069 7,627 11,422   
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.

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Version 1.11, 16 July 2010