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Draft marks, by showing how low a ship is sitting in the water, make it possible to determine displacement.

The displacement or displacement tonnage of a ship is its weight. As the term indicates, it is measured indirectly, using Archimedes' principle, by first calculating the volume of water displaced by the ship, then converting that value into weight. Traditionally, various measurement rules have been in use, giving various measures in long tons.[1] Today, tonnes are more commonly used.[citation needed]

Ship displacement varies by a vessel's degree of load, from its empty weight as designed (known as "lightweight tonnage"[2]) to its maximum load. Numerous specific terms are used to describe varying levels of load and trim, detailed below.

Ship displacement should not be confused with measurements of volume or capacity typically used for commercial vessels and measured by tonnage: net tonnage and gross tonnage.

Calculation

[edit]
Shipboard stability computer programs can be used to calculate a vessel's displacement.

The process of determining a vessel's displacement begins with measuring its draft.[3] This is accomplished by means of its "draft marks". A merchant vessel has three matching sets: one mark each on the port and starboard sides forward, midships, and astern.[3] These marks allow a ship's displacement to be determined to an accuracy of 0.5%.[3]

The draft observed at each set of marks is averaged to find a mean draft. The ship's hydrostatic tables show the corresponding volume displaced.[4] To calculate the weight of the displaced water, it is necessary to know its density. Seawater (1,025 kg/m3) is more dense than fresh water (1,000 kg/m3);[5] so a ship will ride higher in salt water than in fresh. The density of water also varies with temperature.

Devices akin to slide rules have been available since the 1950s to aid in these calculations. Presently, it is done with computers.[6]

Displacement is usually measured in units of tonnes or long tons.[7]

Definitions

[edit]
In this 1940 photo, USS Aaron Ward, left, and USS Abel P. Upshur are destroyers of comparable size, but because the latter is more heavily loaded, it sits lower, displacing more water.

There are terms for the displacement of a vessel under specified conditions:

Loaded displacement

[edit]
  • Loaded displacement is the weight of the ship including cargo, passengers, fuel, water, stores, dunnage and such other items necessary for use on a voyage. These bring the ship down to its "load draft".[8]
  • Full load displacement and loaded displacement have almost identical definitions. Full load is defined as the displacement of a vessel when floating at its greatest allowable draft as approved by the load line assigning authority which is either the flag state (USCG etc) or a classification society (and designated by its "load line").[9] Warships have full load condition established through the Naval design process, and are exempt from commercial requirements laid out by flag state laws.[9]

Light displacement

[edit]
  • Light displacement (LDT) is defined as the weight of the ship excluding cargo, fuel, water, ballast, stores, passengers, crew, but with water in boilers to steaming level.[8]

Normal displacement

[edit]
  • Normal displacement is the ship's displacement "with all outfit, and two-thirds supply of stores, ammunition, etc., on board."[10]

Standard displacement

[edit]
  • Standard displacement, also known as "Washington displacement", is a specific term defined by the Washington Naval Treaty of 1922.[11] "It is the displacement of the ship complete, fully manned, engined, and equipped ready for sea, including all armament and ammunition, equipment, outfit, provisions and fresh water for crew, miscellaneous stores, and implements of every description that are intended to be carried in war, but without fuel or reserve boiler feed water on board."[11]
[edit]
  • A floating ship's displacement Fp and buoyancy Fb must be equal.
    A floating ship's displacement Fp and buoyancy Fb must be equal.
  • Greek philosopher Archimedes having his famous bath, the birth of the theory of displacement
    Greek philosopher Archimedes having his famous bath, the birth of the theory of displacement
  • A ship's hydrostatic curves. Lines 4 and 5 are used to convert from mean draft in meters to displacement in tonnes (table in Spanish).
    A ship's hydrostatic curves. Lines 4 and 5 are used to convert from mean draft in meters to displacement in tonnes (table in Spanish).

See also

[edit]

References

[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Displacement (ship)

View on Grokipedia
from Grokipedia
In naval architecture, the displacement of a ship refers to the weight of the water displaced by the vessel when floating, which, by Archimedes' principle, equals the total weight of the ship and its contents. This measurement, typically expressed in metric tonnes, serves as a fundamental indicator of the ship's mass and buoyancy, influencing its design, stability, and load-carrying capacity. Displacement is calculated based on the volume of the submerged hull and the density of the surrounding water, with seawater (approximately 1.025 tonnes per cubic meter) requiring less volume to be displaced than freshwater (1 tonne per cubic meter) for the same weight. Ship displacement comprises two primary components: the , which is the mass of the empty vessel including its hull, machinery, and fixed equipment, and the deadweight, encompassing , , passengers, , and stores. The total or loaded displacement represents the full weight at maximum allowable draft, marked by load lines such as the Plimsoll line to ensure safety across different water conditions and seasons. Variations like light displacement (empty condition) and present displacement (current load) allow for precise assessment during operations, while specifically quantifies the ship's commercial carrying potential. In ship design and regulation, displacement is critical for determining draft—the vertical distance from the to the —directly affecting hydrostatic stability and performance. For instance, a vessel with a 25-foot draft might displace around 18,000 metric tonnes, guiding engineers in balancing hull form, , and safety margins. Historically rooted in ancient principles of flotation, modern applications extend to naval vessels, where standard displacement (fully manned, equipped, and armed but excluding fuel and reserve feedwater) standardizes comparisons across fleets.

Basic Concepts

Definition and Archimedes' Principle

In naval architecture, ship displacement refers to the total weight of the displaced by a floating vessel, which is precisely equal to the weight of the ship itself and its contents. This concept ensures that the vessel remains afloat in equilibrium, as the downward gravitational on the ship is balanced by the upward buoyant from the surrounding . Archimedes' principle, the foundational physical law underlying this phenomenon, states that any object partially or fully immersed in a experiences an upward buoyant equal to the weight of the displaced by the object's submerged volume. For a ship, this means the vessel sinks into the water until the weight of the displaced matches its own total weight, achieving . The principle applies universally to floating bodies, where the buoyant acts vertically upward through the center of —the of the displaced volume—preventing the ship from sinking under normal conditions. Discovered by the ancient Greek mathematician around 250 BCE in his treatise , the principle originated from investigations into the of irregular shapes, such as the famous crown density problem. Although laid the theoretical groundwork, its systematic application to emerged in the , when and Leonhard Euler integrated it into modern ship stability theory, enabling quantitative design for flotation and equilibrium. This principle is crucial for , load capacity, and overall design, as it dictates how much or fuel a vessel can carry without compromising , while also informing the hull form to maintain upright equilibrium against waves or shifts in weight. By ensuring the buoyant force counteracts the ship's weight, displacement prevents sinking and provides the basis for calculating safe operating limits, directly influencing structural integrity and seaworthiness. The basic equation for displacement, denoted as Δ (the weight of the ship), derives directly from and . The buoyant force FbF_b equals the weight of the displaced , given by Fb=ρVgF_b = \rho V g, where ρ\rho is the of the fluid (typically at approximately 1025 kg/m³), VV is the submerged volume of the hull, and gg is the acceleration due to gravity (about 9.81 m/s²). At equilibrium, the ship's weight W=mgW = mg (with mm as the ship's ) balances FbF_b, so Δ=ρVg\Delta = \rho V g. This formulation allows naval architects to compute displacement by measuring or estimating VV and adjusting for variations, such as between freshwater (ρ≈1000\rho \approx 1000 kg/m³) and saltwater. Δ=ρVg\Delta = \rho V g

Units and Measurement Scales

Ship displacement is typically expressed in three primary units: the long ton, used in UK and imperial systems and equivalent to 2,240 pounds (1,016.05 kilograms); the metric tonne, the SI unit defined as 1,000 kilograms (2,204.62 pounds); and the short ton, a general US unit equal to 2,000 pounds (907.18 kilograms). Conversion factors between these units are standard, with 1 long ton approximately equal to 1.016 metric tonnes or 1.12 short tons, facilitating international comparisons in naval and maritime documentation. Historically, displacement measurements evolved from 18th-century practices where a "" represented the weight of approximately 35 cubic feet of seawater, roughly aligning with the modern to account for the displaced water's mass under . This seawater-based ton gave way to more standardized units in the late 19th and early 20th centuries, driven by the need for consistency in international naval agreements, notably the 1922 , which specified limits in "tons" of standard displacement—interpreted as long tons for signatory nations like the and to ensure equitable warship sizing. In naval contexts, particularly for warships, long tons remain the conventional unit due to their alignment with historical British imperial standards and ease of conversion from seawater displacement volumes. Merchant shipping, by contrast, predominantly uses metric tonnes for displacement and related metrics, reflecting global adoption of the SI system for trade and logistics. A related but distinct scale is deadweight tonnage (DWT), measured in metric tonnes, which quantifies the maximum load a vessel can carry—including cargo, fuel, and provisions—without encompassing the ship's empty hull weight, unlike full displacement. The choice of scale is influenced by variations in water density, as displacement represents the equivalent weight of displaced water, which differs between saltwater (typically 1.025 g/cm³) and freshwater (1.000 g/cm³). In denser saltwater, a ship displaces a smaller volume for the same weight compared to freshwater, potentially requiring adjustments in reported values during transitions between bodies of water to maintain accuracy in load assessments. For example, the historic , a 104-gun , was recorded with a displacement of 3,500 in period documentation, equivalent to approximately 3,556 using modern conversions.
UnitEquivalent Weight (lbs)Equivalent Weight (kg)Common Context
2,2401,016.05Naval (/imperial)
2,204.621,000 (SI/global)
2,000907.18 (general)

Displacement Types

Light Displacement

Light displacement, also referred to as lightship or displacement, represents the of a ship in its empty but ready-to-sail condition, encompassing the hull, machinery, fixed equipment, outfitting, and essential liquids such as machinery fluids at operating levels, while excluding , , provisions, excess , , passengers, consumable liquids, and water ballast. This baseline measure establishes the inherent weight of the vessel without variable operational loads, serving as a foundational metric in grounded in of , where the ship's weight equals the volume of water displaced. The concept originated in the development of during the , building on earlier 17th-century practices of estimating ship weight at launch to compare hull efficiencies and ensure structural integrity independent of fluctuating loads like or . Key components included in light displacement typically comprise the structural hull, propulsion systems such as engines and boilers, fixed armament for warships, and minimal operational fluids, but exclude consumables beyond basic levels to maintain focus on permanent installations. For warships, this often incorporates installed weaponry but omits and stores, allowing designers to assess core performance without mission-specific variables. In practice, light displacement plays a critical role in initial ship design phases for predicting hydrodynamic performance, such as speed and stability, and in establishing regulatory standards for minimal operational weight to comply with and requirements. It enables engineers to evaluate baseline efficiency before adding variable elements, influencing choices in materials like versus aluminum, which can reduce displacement by up to 20-30% for equivalent strength due to aluminum's lower . Unlike deadweight tonnage, which quantifies the maximum variable load capacity including cargo, fuel, and provisions that a ship can carry, light displacement isolates the vessel's fixed mass, ensuring total displacement (light plus deadweight) provides a complete picture of loaded conditions. This distinction is essential for separating inherent design from operational payload, with light displacement forming the baseline counterpart to loaded displacement.

Loaded Displacement

Loaded displacement represents the maximum total weight of a ship when fully laden to its designed capacity, encompassing the vessel's light displacement plus all consumable and transportable loads such as , fuel, passengers, , provisions, water, and stores, limited by the load line to ensure safe immersion in water. This measure defines the ship's operational upper limit, balancing capacity with structural and stability constraints. Regulatory frameworks, notably the Plimsoll line established under the United Kingdom's Merchant Shipping Act of 1876, mandate load line markings on hulls to indicate the maximum allowable draft in varying conditions, densities, and seasons, thereby preventing overloading and reducing the risk of vessels becoming unseaworthy "coffin ships." The added components to achieve loaded displacement typically include diverse types like bulk commodities or standardized containers for commercial ships, water to maintain trim and stability during voyages, provisions and freshwater for onboard personnel, and—in naval applications—full complements of and to support extended missions. Loaded displacement plays a pivotal role in stability assessments, where it informs calculations of the and righting moments to verify the vessel remains upright under full load conditions, directly impacting ratings by quantifying operational risks. Additionally, it influences and fees, as many authorities levy charges based on the corresponding draft or displacement to account for infrastructure strain from deeper drafts. For instance, the RMS Titanic had a loaded displacement of 52,310 long tons at its design draft of 34 feet 7 inches, significantly higher than its light displacement of approximately 39,000 long tons, underscoring how excessive loading beyond safe limits could compromise stability and contribute to catastrophic overload risks. This metric relates directly to (DWT), defined as the difference between loaded and light displacement, quantifying the total carrying capacity for cargo, fuel, ballast, and provisions without exceeding regulatory limits.

Normal Displacement

Normal displacement represents the weight of a ship under typical operational or service conditions, encompassing the light displacement augmented by approximately 50-70% of fuel capacity, standard crew provisions, average stores, and partial loads of cargo or ammunition for routine duties. This measure provides a balanced assessment of the vessel's mass when engaged in standard cruising or peacetime activities, excluding extremes like empty holds or maximum combat provisioning. In contrast to standard displacement, which excludes fuel for treaty comparisons, normal displacement includes partial fuel and stores to reflect average operations. The concept emerged in early 20th-century US naval architecture to enable practical assessments of warships in cruising trim. Key components typically include full operational armament for readiness, but limited to non-combat quantities of , alongside the full complement of crew and essential equipment, reflecting a state of practical preparedness without excess. In practice, normal displacement informs critical applications such as sea trials for speed and handling, estimates of fuel consumption over extended voyages, and cross-national fleet assessments for . For instance, the had a normal displacement of 2,050 long tons, in contrast to 2,500 long tons at full load, influencing attainable speeds of up to 35 knots and operational ranges exceeding 3,000 nautical miles. This configuration underscores how from full loads reduces performance metrics like and . While the definition aligns broadly across vessel types, variations exist between and naval ships; applications often emphasize partial commercial for economic viability, whereas naval uses prioritize combat-oriented inclusions like reserve munitions to maintain tactical edge. Loaded displacement serves as the upper boundary for such routine states, invoked only during exceptional emergencies.

Standard Displacement

Standard displacement refers to the weight of a naval vessel, measured in long tons (2,240 pounds per ton), when it is complete, fully manned, engined, and equipped ready for sea, including all armament, , , outfit, provisions, for the crew, miscellaneous stores, and implements intended for , but excluding and reserve feed water on board. This definition was established to provide a consistent basis for comparing sizes without the variability introduced by loads, which could differ based on operational status. The concept was formalized in the 1922 Washington Naval Treaty, signed by the United States, the British Empire, France, Italy, and Japan, to curb the naval arms race following World War I by imposing standardized limits on warship construction. Under the treaty, capital ships were capped at 35,000 tons standard displacement, while cruisers (other than capital ships or aircraft carriers) were limited to 10,000 tons, ensuring equitable comparisons across signatories. It was later refined in the 1936 London Naval Treaty, which retained the core definition but adjusted limits, such as allowing an "escalator clause" for increased displacement up to 45,000 tons for capital ships if any signatory exceeded gun caliber restrictions. Unlike normal displacement, which includes a partial fuel load (typically two-thirds) for assessing average operational conditions, standard displacement specifies zero fuel to emphasize structural and armament capacity. In practice, standard displacement served as a key regulatory tool for naval , influencing design baselines and enforcing historical limits to prevent escalation. For instance, the Iowa-class battleships, designed under the 's escalator provisions, had a standard displacement of 45,000 long tons, compared to a full load displacement exceeding 58,000 long tons when including , , and other consumables, demonstrating how treaty constraints shaped hull and machinery sizing while allowing for greater operational loads. Although less prevalent after the with the decline of formal arms limitation treaties, standard displacement remains referenced in some modern naval specifications, such as U.S. analyses of foreign fleets and the Montreux Convention's restrictions on warships transiting the .

Calculation and Determination

Volume-Based Methods

Volume-based methods for determining ship displacement rely on calculating the submerged volume of the hull and multiplying it by the of the surrounding , yielding the displacement as Δ=ρ×V\Delta = \rho \times V, where Δ\Delta is the displacement, ρ\rho is the , and VV is the underwater volume. This approach stems from that a ship's weight equals the weight of the water it displaces, allowing indirect computation from geometric data. These methods are foundational in for design and verification phases, applicable to various displacement types by selecting the appropriate draft corresponding to light or loaded conditions. Key techniques involve deriving the submerged volume from ship plans or models. Hydrostatic curves, plotted against draft, provide displacement values directly for even keel conditions, enabling quick estimation at different immersion levels. For more detailed computation, integration of hull offsets—measurements of the hull's shape at stations along its length—allows volume estimation by summing sectional areas. Modern practices increasingly use software to compute VV precisely from digital hull representations. Specialized tools facilitate these calculations for irregular hull forms. Bonjean curves plot the immersed cross-sectional areas at each station as functions of draft, from which volumes and centers of can be derived by graphical or . , a method, approximates the volume by dividing the hull length into equal intervals and applying weighted sums of sectional areas: V=h3(A0+4A1+2A2+4A3+⋯+An)V = \frac{h}{3} (A_0 + 4A_1 + 2A_2 + 4A_3 + \dots + A_n), where hh is the interval length and AiA_i are the areas; this parabolic approximation offers higher accuracy than simpler trapezoidal methods for typical ship hulls. Accurate application requires precise draft measurements at the bow, , and midship to account for trim, along with the local —typically 64 lb/ft³ for saltwater and 62.4 lb/ft³ for freshwater—to convert to weight. Without these, errors in Δ\Delta can arise from environmental variations. For a simple illustrative example, consider a rectangular with length L=100L = 100 ft, beam B=30B = 30 ft, and draft d=5d = 5 ft in saltwater; the submerged approximates as V=L×B×d=15,000V = L \times B \times d = 15,000 ft³, yielding Δ=64×15,000=960,000\Delta = 64 \times 15,000 = 960,000 lb (or approximately 429 long tons). This rectangular approximation suits basic pontoon-like vessels but underestimates for flared or V-shaped hulls, where full integration is needed. These methods assume , where the ship floats steadily without dynamic effects; inaccuracies emerge in wavy conditions or significant trim, potentially requiring adjustments or empirical corrections.

Weight-Based Formulas

Weight-based formulas for ship displacement involve aggregating the masses of individual components, such as hull structure, machinery, outfit, , , and consumables, to determine the total weight that the vessel displaces when floating. This method is particularly valuable during the and verification phases, where weights are estimated from blueprints, specifications, and parametric models before physical . Unlike volume-derived approaches, it directly accounts for the actual mass distribution, ensuring balance between and deadweight elements. In the design phase, light displacement (Δ_light) is calculated as the sum of fixed component weights, including hull steel, systems, and outfitting, often using estimates for structural elements like Δ_light ≈ ∫ (hull material density × volume) over the hull form. Loaded displacement then incorporates deadweight (Δ_deadweight), defined as the mass of , , , , provisions, and stores, yielding total displacement Δ = Δ_light + Δ_deadweight. These sums rely on detailed breakdowns, with reserves typically allocated at 2-5% of light displacement to account for uncertainties. Component weights are estimated parametrically for precision; for instance, structural weight may use Mc = 1.36 × k × E × (B/C1)^{0.5} × 0.7, where k is a structural coefficient, E is Lloyd's Equipment Numeral, B is beam, and C1 is the block coefficient at 80% depth, while propulsion weight follows Mmp = (P_B / RPM)^{0.84}, with P_B as brake power and RPM as engine revolutions. Outfit weight can be approximated as Mai = C0 × Lpp × B, using an outfit coefficient C0, length between perpendiculars Lpp, and beam B. Deadweight components include payload Mu = ζu × Δ_deadweight (ζu as cargo coefficient) and fuel Mcomb = (k_M × A × b_c × P_B × v) / 1000, incorporating safety factor k_M, autonomy A, specific fuel rate b_c, and speed v. These parametric relations, derived from regression on historical data, facilitate iterative design balance. To refine weight estimates, naval architects incorporate hydrostatic coefficients like the block coefficient Cb = V / ( × B × d), where V is underwater , is , B is beam, and d is draft; this aids in cross-checking weight sums against volume-based predictions without direct integration. Such refinements ensure consistency, as discrepancies may indicate errors in component assumptions. methods serve as a complementary verification tool in this context. Historical weight-based formulas from the often employed empirical rules approximating displacement from principal dimensions, reflecting limited computational tools. In W. H. White's A Manual of Naval Architecture (), displacement volume for merchant cargo ers was estimated as ∇ ≈ 0.65–0.78 × L × B × D (in cubic feet), where L is at load line, B is extreme breadth, and D is mean draft, converted to tons by dividing by 35 ( volume per ); this yielded Δ ≈ (0.65–0.78 × L × B × D) / 35 for typical . These rules, based on observed data from iron and steam vessels, provided rough guidance for builders. A representative example is an with a displacement of approximately 50,000 metric tonnes, comprising hull (about 30,000 tonnes), machinery and outfit (15,000 tonnes), and reserves (5,000 tonnes); adding 100,000 metric tonnes of cargo and consumables results in a loaded displacement of 150,000 metric tonnes, aligning with operational deadweight capacities for such vessels. Accuracy of weight-based formulas in the design phase typically ranges from ±2-5%, depending on the detail level and margins applied (e.g., 15% in preliminary design reducing to 3% in detailed stages); modern CAD software enhances precision by automating calculations for complex geometries, reducing errors below 2% in advanced simulations.

Practical Measurement Techniques

Practical measurement techniques for ship displacement involve empirical methods applied to completed vessels to verify theoretical calculations and ensure operational . One primary technique is the draft survey, which determines displacement by measuring the ship's immersion in water. Surveyors take draft readings at multiple points—typically the bow, , and midships—using marked lines on the hull to establish the mean draft, which is then used to compute the underwater volume and total displacement via hydrostatic tables provided by the . To account for variable loads, tools such as gauges measure the level of liquids in tanks, allowing adjustments for fuel, , and consumables that affect the overall weight. For lightship displacement, load cells installed on drydock supports directly weigh the vessel after pumping out all variables and accounting for residual weights like fixed equipment. Hydrostatic tables, derived from the ship's design data, convert the observed mean draft into displacement values, incorporating factors like water density. For loaded ships, the procedure involves conducting the draft survey before and after cargo operations, then subtracting known cargo, fuel, and stores weights from the total displacement to isolate the ship's base weight. In lightship conditions, all removable items are offloaded or emptied, and residues are weighed precisely to confirm the empty hull mass. Another key technique is the inclining experiment, performed in near-lightship condition, where controlled weights are shifted transversely to induce a small heel, measuring the resulting angle with pendulums or modern inclinometers to determine the metacentric height and verify the vertical center of gravity position, thereby confirming the displacement. Modern advancements include and systems for scanning the hull to create precise 3D models, enabling accurate volume calculations independent of water immersion, particularly useful for verifying hull form during refits. GPS-integrated draft sensors provide real-time, automated readings at multiple hull points, compensating for dynamic effects like motion in waves. Historically, in the , draft was assessed manually by observing the hull's immersion against strakes or rudimentary marks, often leading to overloading; post-World War II, the () standardized procedures through SOLAS regulations, mandating inclining tests for stability verification. Common error sources in these measurements include tidal variations affecting draft readings and the in shallow waters, which reduces apparent draft due to increased pressure; corrections are applied using adjustments for trim (longitudinal inclination) and (transverse tilt) based on observed angles and hydrostatic data. For example, the US Navy conducts inclining tests on Forrest Sherman-class destroyers to confirm lightship displacement of approximately 2,800 long tons, ensuring the center of gravity aligns with design parameters for safe operations.

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