Spacesuit Thermal Balance Calculator

Overview

A spacesuit in vacuum cannot dump heat by convection to air. Instead, it mainly exchanges heat by thermal radiation to its surroundings, while the astronaut’s body adds metabolic heat and the Sun (or other sources) can add incident radiation. Most EVA suits also include an active cooling system (for example, a liquid cooling and ventilation garment) that removes a roughly controllable amount of heat.

This calculator estimates a steady‑state (equilibrium) effective radiating-surface temperature for the suit given simple inputs. It is intended for education and rough scenario exploration (e.g., “How much does a whiter outer layer help?”), not mission planning or medical/safety decision‑making.

Inputs (what they mean)

• Metabolic heat, Q_m (W): internal heat generated by the astronaut. Light work might be a few hundred watts; heavy exertion can be higher.
• External radiation (irradiance), F (W/m²): incident radiant flux on the suit (often approximated by the solar constant near 1 AU, ~1361 W/m², when fully illuminated).
• Solar absorptivity, α (0–1): fraction of the incident irradiance that is absorbed as heat. Lower α means more reflective (less heating).
• Suit emissivity, ε (0–1): how effectively the suit radiates thermal energy compared with an ideal blackbody. Higher ε increases radiative cooling.
• Suit radiating area, A (m²): effective area that participates in absorbing external radiation and emitting IR. (This is a major simplification; real suits have view factors and orientation effects.)
• Cooling system capacity, Q_c (W): heat actively removed. Increasing Q_c reduces the radiative burden.
• Background temperature, T₀ (K): an effective “radiative environment” temperature representing what the suit “sees” (deep space ~3 K when the view is mostly cold space; near warm spacecraft or sunlit surfaces this can be much higher).

Model and formulas

The model treats the suit as a lumped surface at temperature T exchanging heat by radiation with an environment at T₀. The net radiated power is approximated with the Stefan–Boltzmann law:

Absorbed external radiation is modeled as:

Q_s = α · F · A

At steady state (equilibrium), incoming heat plus absorbed radiation minus active cooling equals net radiative loss:

Q_m + α F A − Q_c = σ ε A (T⁴ − T₀⁴)

Solving for T:

T = √√( T₀⁴ + (Q_m + α F A − Q_c) / (σ ε A) )

To express the result in Celsius:

T(°C) = T(K) − 273.15

How to interpret the results

The calculated temperature is best interpreted as an effective radiating surface temperature required for radiation to balance the net heat load under the stated assumptions. It is not a direct prediction of astronaut core temperature, skin temperature under garments, or local hot‑spot temperatures.

• Higher Q_m (more exertion) increases required radiative temperature unless offset by more cooling.
• Higher F and/or higher α increases absorbed heat (sunlit, darker surface) → higher temperature.
• Higher ε improves radiative heat rejection → lower temperature for the same heat load.
• Higher A spreads the same heat over more radiating area → lower temperature (all else equal).
• Higher T₀ reduces the radiative “temperature headroom” → higher equilibrium temperature for the same net load.

About the “risk” indicator

If the page displays a “risk score,” treat it as a simple heuristic tied to the computed equilibrium temperature, not a medical probability. Real heat strain depends on many factors (hydration, suit ventilation, work/rest cycles, sensor feedback, and operational constraints). For safety‑critical uses, defer to validated suit thermal models and operational flight rules.

Worked example

Suppose an astronaut is working moderately hard with:

• Q_m = 400 W
• F = 1361 W/m²
• α = 0.9
• ε = 0.8
• A = 2.0 m²
• Q_c = 300 W
• T₀ = 3 K

Absorbed external power:

Q_s = α F A = 0.9 × 1361 × 2.0 ≈ 2449.8 W

Net load that must be rejected by radiation:

Q_net = Q_m + Q_s − Q_c ≈ 400 + 2449.8 − 300 = 2549.8 W

Radiative term denominator:

σ ε A ≈ (5.670×10⁻⁸) × 0.8 × 2.0 ≈ 9.072×10⁻⁸ W/(m²·K⁴)

So:

T⁴ ≈ T₀⁴ + Q_net/(σ ε A) ≈ 0 + 2549.8 / (9.072×10⁻⁸) ≈ 2.81×10¹⁰

T ≈ (2.81×10¹⁰)^(1/4) ≈ 409 K ≈ 136 °C

This outcome indicates that with very high absorptivity and full solar loading, radiation alone would require an extremely high effective temperature to balance the heat—suggesting that either α must be much lower, the illuminated effective area must be smaller, cooling must be higher, the suit must be oriented/managed to reduce absorbed flux, or the environment differs from the assumed case. This illustrates why reflective outer layers and active cooling are essential.

Scenario comparison (typical directional effects)

Assumptions and limitations

• Steady-state only: ignores time-dependent heating/cooling, thermal inertia, and transient EVA operations.
• Uniform temperature: real suits have gradients and localized hot/cold spots.
• Orientation/view factors ignored: incident flux and radiating area depend strongly on pose, shadowing, and what fraction of the suit sees cold space vs nearby warm objects.
• Single “external radiation” term: lumps solar, reflected light (albedo), and IR from nearby bodies into a simplified representation (with T₀ as an additional knob).
• No conduction or convection paths: ignores heat exchange through tethers, contact with surfaces, or residual gas effects.
• Cooling capacity treated as fixed: actual cooling performance can vary with control settings, pump performance, heat exchanger limits, and water loop conditions.
• Not a safety tool: do not use for operational EVA planning, certification, or medical decisions.

References (concepts)

• Stefan–Boltzmann law (thermal radiation): σ ≈ 5.670374419×10⁻⁸ W·m⁻²·K⁻⁴
• Solar constant near 1 AU (order-of-magnitude incident solar irradiance): ~1361 W/m²