**Displacement (nautical). **It is the weight of the boat and the weight of the volume of water displaced by the hull, including all submerged appendages. According to the Archimedes principle , it can be said that displacement, in general, is the weight of the volume of the liquid dislodged by the ship in a certain float.

## Summary

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- 1 Displacement calculation
- 1 Ship Displacement
- 2 Calculation of displacement with hydrostatic curves
- 3 Calculation of the ship’s displacement
- 3.1 List correction
- 3.2 Density shift correction
- 3.3 Correction to displacement by seat or NEMOTO correction.
- 3.4 Density correction

- 4 Table relating Motor Power to Displacement

- 2 Sources

## Displacement calculation

The calculation of the maximum displacement is done with the boat ready to go sailing, with all its equipment and fixed installations, with the heaviest engines for which it is designed, with full fuel and drinking water tanks, and the maximum number authorized persons, (75 Kgs per person), security elements, fire, rescue and navigation.

Depending on the load, the displacement can be, in addition to the maximum:

- a)
**Displacement in thread**: - b)
**Displacement in ballast**: - c)
**Displacement under load**:

The ‘ *Carriage* is the difference between the displacement in ballast and the displacement at maximum load.

The **Dead Weight** (PM) is the difference between the displacement at maximum load and the displacement in thread, that is, the maximum weight that the ship can load.

### Ship Displacement

Displacement is defined as; Δ = submerged · γmar, and represents the weight of the water displaced by this volume (Archimedean Principle). The unit used is tons and, in the Anglo-Saxon system, long tons. From the point of view of the theory of the ship they are distinguished:

Thread displacement, Δr (in English, lightweight displacement): is the weight of the ship as delivered by the shipyard; that is, without fuel, supplies, provisions or crew.

Standard displacement, Light displacement, Δe It is the weight of the complete ship, in addition to equipment ( boats , navigation instruments , etc.) plus crew with their luggage, liquids in circulation, food, ammunition (in warships), water sweet and lubricating oil. Fuel and reserve water for boilers would be excluded .

Displacement in ballast, Δl: is the weight of the threaded ship plus everything necessary for it to navigate (fuel, drinking water, supplies and supplies), but without load.

Maximum displacement, Δm: is the weight that it reaches when submerged up to the line of maximum load (sea water in summer of the Plimsoll brand). The “displacement” data of a ship, unless otherwise specified, refers to the maximum displacement.

The difference between the maximum displacement and the thread displacement is called the “gross tonnage” or “deadweight tonnage”, TPM. Thus, the deadweight tonnage includes the weight of the cargo, including passengers and crew, and that of the consumables (fuel, food, drinking water …) mentioned above.

The difference between the maximum displacement and the ballast displacement is known as ‘cargo capacity’, which indicates the weight of the cargo that can be carried on that ship. It is not routinely used by shippers and shipping agents.

### Displacement calculation with hydrostatic curves

Hydrostatic curves, are the curves that reflect the behavior of the hull of a ship for the different drafts (load states). They are called the right hull because they are calculated for the righting condition. They are made by the shipyard and delivered to the captainfor application in the calculation of the initial transverse stability of a ship. Undoubtedly, for this purpose, the most significant curve is the one that determines the height of the transverse metacenter (Figure 1 curve). Other curves are used in the final draft and seat calculations. The vertical parameter curves are referred to the base line or top edge of the keel. The curves of longitudinal parameters, (longitudinal position of the center of the hull, etc.) are referred to either the master section or the perpendicular aft.

### Ship displacement calculation

The calculation of the displacement of the ship is based on the value of the average draft for the waterline parallel to the keel, this occurs when the ship is in equal waters and the drafts are read on the respective perpendiculars.

The stern perpendicular is the vertical line that passes through the axis of the rudder stock, if it is hung or through the stern face of the stern trim. The length between perpendiculars is the horizontal distance between both lines measured parallel to the keel. Now this displacement is subject to a series of corrections:

#### Heel correction

The average is made between the drafts read at each end. If you only read the draft in one of the fore and aft bands and in the two bands in the center we calculate the list value:

And with this value we correct the drafts of the calculated heads (it is necessary to know the sleeve plane in the area where the draft has been read). With these operations we have already applied the first correction. The marks of the drafts often do not coincide in the respective perpendiculars (bow, stern), so when reading the marked scale there is a difference with what would correspond to the scale in perpendiculars , this phenomenon appears when the ship is in ballast, for its correction it is necessary to proceed as follows: We calculate the longitudinal inclination

Each ship has a plane in which the distance for each draft can be calculated between the corresponding perpendicular and the draft scale marked on the ship. Once the distance for the calculated draft is known, the correction to be applied depends on the seat and the position of the scale with respect to the perpendiculars, since it can be at the bow or stern (normally at the bow the draft scale is aft of the perpendicular and aft to bow.) In many ships, the shapes of the stem and the codaste do not allow the tracing of these lines, so the draft scales must be marked in the possible areas, outside the perpendiculars, in these cases, once that we read the marks, a correction must be applied to the values obtained, the value of which depends on the ship’s seat Cpr = Draft read at the bow Cpp = Broth read at the stern x = Correction at the bow draft y = Correction at the stern draft dx = Scale distance from draft to pp. bow dy = Draft scale distance to pp. aft Seat A = Cpp- Cpr (+ Apopante, – Aproante) Epp = Length between perpendiculars. We calculate the longitudinal inclination:

The values of the corrections to the readings are: 1.-for the bow draft

2.- For the aft draft

#### Density shift correction

The displacement of the ship is equal to the weight of the water occupied by its hull, and its value is the volume of the hull multiplied by the specific weight of the water in which the ship floats. The specific weight of fresh water at 4º Centigrade is 1, so a liter of water at that temperature weighs 1 kg. 4ºC is the temperature at which the density of fresh water is the highest. The ship’s hydrostatic curves allow calculating its displacement, for any draft, with the ship in equal waters and for a water density equal to 1,025 tons. per m3. which is the average density of the North Atlantic. The density value varies with salinity and temperature. If we drink fresh water at 4ºC, its specific weight is 1 but at 15ºC it is 0.99999, so a cubic meter of fresh water at 4ºC weighs 1,000 kg. but at 15ºC its weight is 999.13 kg. Steps to follow Reading the bow, stern, center port and starboard draft Determination of the density of the water where the ship floats Calculation of the sea water temperature. -We calculate the correction:

d = distance between perpendicular and draft scale Signs: In forward draft correction: + if positive seat (scale forward of perpendicular) + if negative seat (scale aft of perpendicular) – if negative seat (scale forward of perpendicular) – yes positive seat (scale aft of perpendicular) In the aft draft the corrections have the same previous signs. We apply the calculated corrections to the corrected heel drafts and we will have the drafts in perpendiculars. In some cases the longitudinal inclination is calculated instead of with the length between perpendiculars with the distance between marks of drafts, since the calculated seat corresponds to the position of the scales, if we do so, the distance between marks is:

d1 bow distance, and d2 aft distance from respective scales to the perpendiculars. With these data we calculate

With the draft read in the middle, if we have a difference with the previous one, it is because the ship has a ruff draft. If the draft is read in the middle> medium draft is ruffled If the draft is read in the middle <half draft. This situation causes a difference in the value of the submerged volume calculated in the hydrostatic curves, which are built for the ship with flat floats.

#### Correction to displacement by seat or NEMOTO correction.

When calculating the corrected displacement a value is obtained, but the Engineer Nemoto found that if the Bonjean curves were used to determine the displacement of the ship, whenever there was a seat, a difference appeared, with the displacement calculated by the Bonjean curves being greater than that obtained in hydrostatics with medium draft. The reason for this difference is given by the irregular shapes of the ship in the fore and aft fines. Applying a series of equations according to Taylor’s method, and integrating according to the length of the ship, he found the difference in displacement, which is obtained by applying the following formula that bears his name:

A = Seat in meters ΔMu Difference between the values of the unit moment of seat calculated in curves with Cm + 0.5 and Cm-0.5 The value of this correction comes in tons and is always positive.

#### Density correction

The hydrostatic curves of the ship give us the value of the displacement with the average draft when the ship floats in fresh water of density 1 and in salty water of density 1,025 Tn / m3 When the value of the density does not coincide with one of the indicated values To calculate the real value of the displacement, we take samples of seawater and measure the value of its density. Calculated this value the displacement corrected for density is:

**Unit Moment Calculation** We have defined the unit seating moment as the longitudinal heeling moment that must be applied to the boat, measured in tons x meter, to produce an alteration of 1 cm. As I have previously commented, it is intuitively evident that this magnitude will depend on the displacement of the boat (equivalently, on its average draft). It will be obtained, therefore, from the hydrostatic curves of the boat for each state of load. Now, we can easily deduce a useful expression for M _{u} in terms of the longitudinal metacentric height GM _{L} that we introduced when studying longitudinal static stability. Not surprisingly, M _{u} can relate to GM _{L}since, as indicated by the equation tgθL.p = GG ‘/ GM _{L} , GM _{L} determines the longitudinal heel produced and, in turn, the longitudinal heel is the one that causes the alteration. Thus, we have previously seen that the alteration a and the longitudinal list θL are related by the equation tgθ _{L} = a / E, where E is the length between perpendiculars. Therefore, combining these equations we find the following result:

in which we have also made use of the value GG ‘= pxd _{l} / Δ for the displacement caused in the center of gravity when the weight p is transferred longitudinally a distance d _{l} . That transfer has produced a heeling pair whose moment is obviously pxd _{l,} so the previous equation is telling us that the heeling moment necessary to produce an alteration a is M _{esc} = ax Δ x GM _{I} / E. Since the unit seating moment M _{u} is defined as the moment necessary to produce an alteration at 1 cm, it will be given by the value of M _{esc} that in the previous equation produces an a = 1 cm = 0.01 meters. That is to say,

equation in which GM _{L} and E will be measured in meters, Δ in tons and the result for M _{u} will be in tons x meter. This equation will allow us to obtain the longitudinal metacentric height GM _{L} from the value of M _{u} obtained from the hydrostatic curves, entering with the displacement Δ that the boat has in the circumstances in which it is found. **Shape** coefficients Total, block or block coefficient (Cb) is the relationship between the volume of the hull of a hull and the parallelepiped that contains it (L = Length, M = Beam and H = Draft). (Upper figure). Cb = Vol. Of fairing / Vol. Of the parallelepiped = Vc / (L x M x H)

**Float coefficient** It is defined as the float coefficient (Cf) to the relationship between the area of the float plane (upper figure in light blue) and the area of the rectangle that surrounds it. Cf = Floatation area / Rectangle area = Af / (L x M) Prismatic or longitudinal coefficient C _{p} is defined as the ratio between the volume of the hull and the volume of a cylinder whose base has the same area as the master section. Cp = Fairing volume / Cylinder volume = Vc / (Am x L)

Master section coefficient Master section coefficient Cm is defined as the relation between the area of the master section and the rectangle that surrounds it. Cm = Master section area / Rectangle area = Am / (M x H) **Tons per centimeter of immersion** Tons per centimeter of immersion or TPC is the mass in tons that must be added to a vessel, applied to the center of gravity of a ship, to achieve an increase of one centimeter in the average draft. The new float plane remains parallel to the initial one. Since the hull of a ship is not a parallelogram, the value of the TPC coefficient varies depending on the average draft considered. This draft variation is equal to the weight of the hull slice whose base is the floatation area, A _{f}initial and its height of one centimeter (volume of the slice) by the specific weight of the water in which the boat is floating. In the case of seawater with a specific weight of 1,025 t / m ^{3,} we would have

where A _{f} is the float area. Units are shown in red. The TPC coefficient is proportional to the floatation area, so the larger the vessel, the greater the TPC value. It is very common to find for ships built in Saxon countries with the concept tons per inch, the concept is the same, but it should be noted that it refers to English tons and not metric tons. An English ton or short ton is equivalent to 907.18474 kg. Knowing this value allows us to calculate with relative ease the amount of load to be rigged to undo a boat that requires a decrease in draft by a certain number of centimeters.

Slice volume

### Table Relating Engine Power to Displacement

Ship displacement in Tons. | Power required in CV-HP |

two | 9 |

3 | 12.2 |

4 | 15.5 |

5 | 18.8 |

6 | 22.5 |

7 | 25.8 |

8 | 29 |

9 | 32.3 |

10 | 35.6 |

eleven | 39.8 |

12 | 44.1 |

13 | 47.3 |

These motor power values have to be taken as the necessary power on the shaft, so an increase of 10-15% would be admissible as a consideration of the motor brake power, which is what the manufacturer will provide us. The results of our spreadsheet together with the compilation of documentation that we have carried out to develop this article, lead us to think that we can fairly reliably apply a very general and easy to calculate general rule, with which to determine the boat quickly and without Too many complications, which is the power needed for most series sailboats. THE EASY RULE It consists of multiplying by 4 CV the tons of displacement of the sailboatfor which we want to know the necessary power. This value will give us an approximate engine power that will allow us to navigate at 75% of the maximum engine power, and thus obtain a cruising speed according to the expectations of our waterline. Obviously this rule has to be taken according to a fairly standard type of sailboat, with a conventional hull shape and dead work. For any boat with unusual characteristics it will be necessary to evaluate some variation.