Cryogenic Propellant Boil-Off Calculator

How the Boil-Off Calculation Works

The calculator is based on a simple energy balance: any heat that leaks into the tank must either warm the propellant or vaporize it. Under the assumption that the propellant remains near its saturation temperature, most of the heat goes into phase change. The rate at which mass is boiled off depends on how much heat arrives at the liquid surface and how much energy is required to vaporize each kilogram of propellant.

The main steps are:

1. Estimate the total heat leak into the tank from the insulation and surface area.
2. Convert that heat rate into energy per day.
3. Divide by the latent heat of vaporization to obtain daily mass loss.
4. Multiply by the number of days to get total mass loss, and compare to the initial tank mass.

Key Formulae

The instantaneous heat leak into the tank is modeled as:

Q = q"" × A

• Q is total heat leak into the tank (W).
• q"" is the average heat flux through the insulation (W/m²).
• A is the external tank surface area (m²).

The energy entering the tank over one day is then:

Eday = Q × 86 400 (J/day)

The latent heat of vaporization is usually given in kJ/kg. Converting to J/kg and dividing gives the daily boiled-off mass:

mday = Eday / L

• mday is the mass boiled off each day (kg/day).
• L is the latent heat of vaporization (J/kg).

In expanded form, with latent heat specified in kJ/kg:

Total boil-off over N days is:

mtotal = mday × N

Initial Tank Mass and Boil-Off Fraction

To understand how severe these losses are, the boil-off mass is compared against the initial propellant mass in the tank:

minitial = V × ρ

• minitial is the initial mass of liquid propellant (kg).
• V is the liquid volume in the tank (m³).
• ρ is the liquid density (kg/m³).

The total fraction boiled off over the storage period is then:

fractionboiloff = mtotal / minitial

Multiplying by 100 gives the percentage of the original load that has been lost.

Inputs Explained

The calculator fields correspond directly to the quantities in the equations above. Typical ranges are indicative and should be adjusted for your specific application.

Tank Volume (m³)

This is the internal volume actually filled with liquid propellant. It determines the total initial mass stored when combined with the liquid density. For upper-stage tanks, values might range from a few cubic metres up to several tens. Ground storage dewars can be hundreds of cubic metres or more.

Tank Surface Area (m²)

The external surface area of the tank through which heat is transferred. Area depends on geometry:

• Spherical tanks minimize area for a given volume, which helps reduce boil-off.
• Cylindrical tanks with hemispherical or elliptical ends are common in launch vehicles.
• Rectangular or horizontal vessels for ground storage often have higher area-to-volume ratios.

If you do not have an exact area, you can approximate it from design drawings or analytical geometry. The calculator assumes the specified area experiences the stated average heat flux.

Heat Leak (W/m²)

This is the average heat flux through the insulation into the tank. It is a lumped representation of all thermal paths (conduction, convection, radiation, supports, penetrations). Representative values include:

• Poor or minimal insulation: > 5 W/m²
• Typical multi-layer insulation (MLI) with vacuum: ~0.5–2 W/m²
• High-performance systems: < 0.5 W/m² under ideal conditions

Storage Duration (days)

The number of days the propellant remains in storage at approximately steady conditions. This might represent coast phases in space, ground holding time before launch, or long-term depot storage scenarios.

Latent Heat of Vaporization (kJ/kg)

The energy required to vaporize 1 kg of propellant at its boiling point without changing temperature. This value is specific to the fluid and its saturation temperature. Typical approximate values at near-atmospheric pressure include:

• Liquid hydrogen: ~446 kJ/kg
• Liquid oxygen: ~213 kJ/kg
• Liquid methane: ~510 kJ/kg

Use values appropriate to your pressure and temperature conditions when available from datasheets or handbooks.

Liquid Density (kg/m³)

The density of the liquid phase at the storage temperature. This determines how much mass is stored in each cubic metre of tank volume. Reference values at common conditions include:

• Liquid hydrogen: ~70 kg/m³
• Liquid oxygen: ~1 140 kg/m³
• Liquid methane: ~420–460 kg/m³

Accurate density values help the calculator produce realistic mass fractions, especially for partial fills or off-nominal temperatures.

Interpreting the Results

When you run the calculation, you can expect outputs along the following lines (exact field names may differ):

• Daily boil-off mass (kg/day): how much propellant is lost in a typical day under the assumed constant heat leak.
• Total boil-off mass (kg): the integrated mass lost over the requested storage duration.
• Initial propellant mass (kg): how much liquid was stored at the start, based on volume and density.
• Total boil-off percentage (%): the fraction of the original load lost, useful for quick comparisons.

Small percentages (e.g., < 1% over the full storage period) usually indicate that insulation and tank sizing are adequate for many missions. Higher percentages may signal the need for better insulation, shorter storage times, active cooling, or larger tanks to reduce the area-to-volume ratio.

Worked Example

Consider a liquid hydrogen upper-stage tank with these approximate parameters:

• Tank volume: 100 m³
• Tank surface area: 200 m²
• Heat leak: 2 W/m²
• Storage duration: 30 days
• Latent heat of vaporization (LH₂): 446 kJ/kg
• Liquid density (LH₂): 70 kg/m³

Step 1: Total Heat Leak

Q = q"" × A = 2 × 200 = 400 W

Step 2: Energy per Day

Eday = 400 × 86 400 ≈ 3.46 × 107 J/day

Step 3: Convert Latent Heat

L = 446 kJ/kg = 446 000 J/kg

Step 4: Daily Boil-Off Mass

mday = 3.46 × 107 / 446 000 ≈ 77.6 kg/day

Step 5: Total Boil-Off Over 30 Days

mtotal = 77.6 × 30 ≈ 2 330 kg

Step 6: Initial Mass and Fraction Lost

minitial = 100 × 70 = 7 000 kg

fractionboiloff = 2 330 / 7 000 ≈ 0.33, or about 33% of the initial load over 30 days.

This example illustrates how even modest heat fluxes can produce substantial losses over long storage periods, especially for low-density, high-performance propellants like liquid hydrogen.

Comparison of Illustrative Scenarios

The table below compares three simplified scenarios using the same 100 m³ hydrogen tank, but with different insulation performance and storage durations. These values are illustrative only; real systems require detailed analysis.

Notice how reducing heat flux from 2 W/m² to 0.5 W/m² (a factor of 4) reduces both daily and total boil-off by roughly the same factor. This proportional relationship holds as long as other assumptions remain valid.

Assumptions and Limitations

The calculator intentionally simplifies the physics to keep the method transparent and easy to apply. Key assumptions include:

• Constant heat flux: The average heat leak per unit area is assumed constant over time and uniformly distributed across the tank surface.
• Steady-state temperature: The propellant is assumed to remain near its saturation temperature, so nearly all incoming heat goes into vaporization rather than warming the liquid.
• Uniform liquid properties: Density and latent heat are treated as fixed values, independent of small temperature and pressure variations.
• No active refrigeration: Systems such as cryocoolers or subcooling loops are not modeled. Any such hardware that removes heat would reduce actual boil-off relative to the estimate.
• No stratification or sloshing: The liquid is treated as a well-mixed bulk fluid, with no thermal gradients, slosh-induced mixing, or stratified layers.
• Vent system behavior simplified: The details of pressure control, venting, and recondensation are not included; all vaporized mass is assumed to be lost.
• Idealized geometry: Penetrations, supports, feedlines, and structural attachments are not explicitly modeled, even though they can contribute additional heat leaks.

Because of these simplifications, the results should be viewed as approximate. They are well suited for quick trades (e.g., “What if I halve the heat leak?”) and concept-level sizing, but detailed mission design should use more comprehensive thermal models or experimental data.

Practical Tips and Further Reading

When using this calculator for engineering work or educational purposes, consider the following tips:

• Use fluid property values from reliable handbooks or databases appropriate to your storage pressure.
• Estimate heat leak based on insulation type, thickness, and test data if available. Simple worst-case values can be chosen when no data exist.
• Explore sensitivity by varying one parameter at a time (heat flux, area, duration) to see which design choices offer the largest reduction in boil-off.
• For long-duration depots or high-value missions, cross-check estimates with detailed thermal analysis tools or experimental measurements.

For deeper coverage of cryogenic storage and boil-off physics, consider standard references such as cryogenics textbooks, rocket propulsion handbooks, or aerospace thermal design guides from recognized organizations. These sources discuss more advanced topics like stratification, pressure control strategies, and active re-liquefaction systems.