CALCULATORS / MARINE AND UNDERWATER DEVICES

Ballast and neutral-buoyancy sizing calculator

Added dense ballast to cancel an existing positive buoyancy; includes ballast displacement.

marine-ballast.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

Scenario	masskg
	2.33855
	1.87084

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

ballast mass budget2.34 kg✓ passes

BASELINE INPUTS

excessBuoyancy20 NfluidDensity1000 kg/m^3ballastDensity7800 kg/m^3gravity9.81 m/s^2

CALCULATED

mass2.3386 kg

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Ballast and neutral-buoyancy sizing
# Scope: Added dense ballast to cancel an existing positive buoyancy; includes ballast displacement.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

excessBuoyancy = 20 N
fluidDensity = 1000 kg/m^3
ballastDensity = 7800 kg/m^3
gravity = 9.81 m/s^2

mass := excessBuoyancy/(gravity*(1-fluidDensity/ballastDensity)) [kg]

check ballast mass budget: mass <= 3 kg

scenario alternative: excessBuoyancy = 16 N

Calculated from your source · not saved

Baseline · Baseline

ballast mass budget2.34 kg ✓ passes

alternative · alternative

ballast mass budget1.87 kg ✓ passes

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

mass: mass = excessBuoyancy/(gravity*(1-fluidDensity/ballastDensity)) [kg]

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

excess buoyancy: 20 N
fluid density: 1000 kg/m^3
ballast density: 7800 kg/m^3
gravity: 9.81 m/s^2

Calculated

mass: 2.33855 kg

Assumptions and limits

Added dense ballast to cancel an existing positive buoyancy; includes ballast displacement.

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Ballast and neutral-buoyancy sizing. Inputs: displacement; dry mass; water density; ballast material. Outputs: ballast mass; reserve buoyancy. Model scope: Hydrostatics and calibrated hydrodynamic coefficients. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

Inputs: displacement, dry mass, water density, ballast material
Outputs: ballast mass, reserve buoyancy
Modes: calculate, compare, sweep
Drawing: Hull and underwater load diagram

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS