Buoyancy Force Calculator v1

Subject

Buoyancy is the positive (anti-gravity) or negative (pro-gravity) force in a body suspended in a fluid dependent upon their relative densities.

The density of the body is not the density of the material(s) from which it is made, but its total mass divided by its total displaced volume.

The fluid may be a liquid, e.g. for submarines, or a gas, e.g. an airship.

With sufficiently accurate data it is possible to predict the level (depth or altitude) at which a buoyant object will settle.

Buoyancy provides four calculation options that have been tailored for; submarines, airships, helium-filled balloons and hot-air balloons.

Buoyancy calculates the lift capacity of a buoyant body including the effects of body and fluid density variations and compression due to pressure changes with depth and altitude.

For help using this calculator see Technical Help

Buoyancy Calculator - Options

Liquid

An object (or body) immersed in a liquid will float if it is less dense than the surrounding water. It will sink if it is denser than the surrounding water and it will settle mid-depth if the liquid and object densities are equal. The density of a liquid increases with depth (due to pressure) and the density of a body also increases with depth (due to compression). If the increase in density of the body is more gradual than that of the surrounding liquid their densities (the object and the liquid) may equalise on the way down, at which point the body will stop sinking.

You enter:	and the buoyancy calculator will provide:
Object volume Object mass Object compressibility Liquid volume Liquid density Liquid compressibility Liquid depth Atmospheric pressure Gravitational acceleration	Buoyancy Displaced volume Settle depth Liquid depth increase Density @ depth

Airships

An airship is filled with a gas significantly lighter (less dense) than air in order to generate lift. If the combined weight of the airship (gas and structure) and its cargo equate to a density lighter than the surrounding air, the airship will rise to an altitude where the densities equalise, at which point the airship will cease to rise any further and will hover (or fly).

You enter:	and the buoyancy calculator will provide:
Altitude Internal pressure Common temperature Internal volume Gas constant for internal gas Gas constant for atmospheric gas	Lift capacity

Helium Filled Balloon

A balloon is filled with a gas significantly lighter (less dense) than air in order to generate lift. If the combined weight of the balloon, its pressurised gas and its cargo together equate to a density lighter than the surrounding air, the balloon will rise to an altitude where the densities equalise or the balloon bursts, whichever occurs first.

You enter:	and the buoyancy calculator will provide:
Mass carried Inflated strain Burst strain Balloon diameter (flat) Balloon wall thickness Balloon material density Flexural modulus Inflation air pressure Inflated air density Fill gas density Base-line height	Balloon diameter at inflation strain Balloon density at inflation strain Balloon diameter at burst strain Balloon density at burst strain Burst altitude Air pressure at burst altitude Air density at burst altitude Hover altitude Air pressure at hover altitude Air density at hover altitude Quantity of fill gas

Hot Air Balloon

The air in an open envelope (a balloon) is heated to a temperature that reduces its density to less than the surrounding air. The balloon will then rise to an altitude where its effective density (including its own mass and cargo) is equal to the density of the surrounding air, at which point the balloon will cease to rise any further and will hover (or float).

You enter:	and the buoyancy calculator will provide:
Altitude Inside temperature Outside temperature Balloon major diameter Balloon height Fabric weight Basket weight Ambient air pressure Gas constant for air Base-line height	Lift Carrying capacity

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