Displacement (Δ)

What is Ship Displacement (Δ)?

Ship displacement (Δ) is the total weight of a vessel and represents the mass of water displaced by the hull at a given draft. Under static equilibrium, the ship’s displacement is equal to the weight of the ship and everything carried on board.

Definition

Displacement is related to the underwater volume of the hull through water density:

Δ = ρ · ∇

where ∇ is the submerged volume and ρ is the water density. Displacement is commonly expressed in metric tonnes.

Methods of estimating displacement

Displacement can be determined using several methods, depending on the stage of design or operation:

• Volume-based: Using known underwater volume and water density, typically from hydrostatic calculations.
• Geometric approximation: Using principal dimensions and the block coefficient (∇ ≈ L·B·T·C_B) during early design stages.
• Weight breakdown: Summing lightship, cargo, fuel, ballast, stores, and other weight components.
• TPC adjustment: Estimating changes in displacement due to small draft variations using tons per centimeter immersion.

Engineering significance

Displacement is a fundamental parameter in naval architecture and directly affects stability, trim, resistance, and propulsion requirements. Almost all hydrostatic and performance calculations are referenced to a specific displacement condition.

Because water density varies between fresh and seawater, displacement values must always be associated with the correct density and operating environment.

TPC and draft sensitivity

Tons per centimeter immersion (TPC) describes how much displacement changes for a small change in draft at a given waterline. It is draft-specific and closely related to the waterplane area.

TPC-based adjustments are appropriate for small draft changes but should not be used for large variations where hydrostatic properties change significantly.

Limitations and correct use

• Displacement is always associated with a specific draft and trim condition.
• Geometric approximations are suitable only for preliminary estimates.
• TPC adjustments assume locally linear hydrostatic behavior.
• Weight summation requires consistent weight definitions and margins.

Related calculators

Displacement is typically evaluated together with the following hull and stability parameters:

• Block Coefficient (CB) – used in early displacement estimates.
• Prismatic Coefficient (CP) – relates displacement to longitudinal volume distribution.
• Waterplane Coefficient (CWP) – directly affects TPC and draft sensitivity.
• Metacentric Height (GM) – stability parameter dependent on displacement.
• Trim Calculator – evaluates longitudinal balance at a given displacement.