Two-node Model

Author: CislunarSpace
Site: https://cislunarspace.cn

Definition

The two-node model simplifies the stratospheric airship thermodynamic system into two lumped-parameter nodes: the skin node representing external structure and the helium node representing internal gas. This model trades precision for computational efficiency, suitable for rapid iteration in initial design.

Model Structure

Node	Component	Temperature
Node 1	Skin (Envelope)	$T_{skin}$
Node 2	Helium	$T_{He}$

Mathematical Equations

Skin Energy Balance

C_{skin}\frac{dT_{skin}}{dt} = Q_{ext} - h_{int}A_{int}(T_{skin} - T_{He}) - h_{ext}A_{ext}(T_{skin} - T_{air})

Helium Energy Balance

C_{He}\frac{dT_{He}}{dt} = h_{int}A_{int}(T_{skin} - T_{He}) + Q_{int}

Application Scenarios

Suitable	Not Suitable
Initial design rapid estimation	Detailed performance analysis
Preliminary controller design	Extreme condition analysis
Parameter sensitivity analysis	Local hot-spot prediction
Steady-state equilibrium calculation	Fine transient response analysis

References

Jones J A. Simplified Thermal Model for High Altitude Airship Analysis[R]. MIT, 2023.
Wang H. Thermodynamic Analysis of Stratospheric Airship[J]. Journal of Aerospace Power, 2025.