Single-Node Orbital Thermal & Solder Fatigue Simulator
Integrate orbital temperature swings across sunlit and eclipse phases and estimate Engelmaier solder-joint fatigue cycles.
Show the data as a table
| Orbit time (min) | Node Temperature (°C) |
|---|---|
| 0 | — |
| 20 | 7 |
| 40 | −1 |
| 60 | −13 |
| 80 | −10 |
| 190 | — |
DETERMINISTIC PHYSICS & DATA METHODOLOGY
How This Calculator Works
Source modules: lib/physics/thermal.ts
Integrates the single-node radiative orbital energy balance over 14 consecutive orbits via fourth-order Runge–Kutta (RK4) to periodic steady state, then evaluates leadless solder-joint low-cycle thermal fatigue via the Engelmaier relation.
Governing Equations & Physical Model
m·c_p · dT/dt = ν(t)·[α·S₀·A/4 + α·S₀·a_E·F·A·max(cos θ, 0)] + ε·q_IR·F·A + Q_int − ε·σ·A·T⁴Integrates direct solar, Earth albedo (a_E = 0.30), Earth IR (q_IR = 237 W/m²) with spherical view factor F(h), and Stefan–Boltzmann emission (step Δt = 2 s).
N_f = ½ · (Δγ / (2·ε'_f))^(1/c), Δγ = (L_D · Δα · ΔT) / h_sEvaluated for a rigid package neutral-point distance L_D = 4 mm, standoff height h_s = 75 µm, CTE mismatch Δα = 10 ppm/K, and 15.1 cycles/day.
Inputs, Parameters & Units
| Parameter | Unit | Physical definition |
|---|---|---|
| m, A_tot | kg, cm² | Spacecraft thermal mass (c_p = 858 J/(kg·K) default) and radiating surface area. |
| α, ε | —, — | Surface-averaged solar absorptance and hemispherical infrared emittance. |
| Q_int | W | Continuous internal electronics dissipation at 525 km circular orbit (β = 0°). |
Assumptions & Validity Limits
- Treats the chassis and PCB stack as an isothermal lumped node; internal conduction gradients across nylon/stainless standoffs require multi-node analysis.
- Worst-case eclipse fraction is modelled at β = 0° (maximum cylindrical shadow duration).
Worked Default Reference Case
Periodic steady state at 525 km cycles between −16.0 °C at eclipse exit and +7.4 °C in sub-solar sunlight (ΔT = 23.4 K), yielding ~10,661 median Engelmaier solder cycles.
- Max sunlit temperature
- +7.4 °C
- Min eclipse temperature
- −16.0 °C
- Per-orbit thermal swing ΔT
- 23.4 K
- Engelmaier median cycles N_f
- 10,661 cycles