Coasting Arc (Coasting Arc)

Editor Source: 胡敏, 肖金伟, 张天天, 陶雪峰 (2026) "面向中高轨小卫星批量部署的轨道转移飞行器任务规划"

Website: https://cislunarspace.cn

Definition

A coasting arc refers to the flight segment where, during low-thrust orbit transfer, when thrust efficiency falls below a set threshold, the engine shuts down and the spacecraft coasts on inertia.

Coasting arcs and thrust arcs together constitute the basic flight modes for low-thrust orbit transfer. By reasonably setting the proportion of coasting arcs, a flexible trade-off between propellant consumption and transfer time can be achieved.

Physical Mechanism

Thrust Efficiency Determination

The efficiency parameters defined by 胡敏等 (2026) determine whether to enter a coasting arc:

Absolute Efficiency Parameter:

ηa=min⁡α,β(Q˙)min⁡θ(min⁡α,β(Q˙))\eta_a = \frac{\min_{\alpha, \beta}(\dot{Q})}{\min_\theta(\min_{\alpha, \beta}(\dot{Q}))}

Relative Efficiency Parameter:

ηr=min⁡α,β(Q˙)−max⁡θ(min⁡α,β(Q˙))min⁡θ(min⁡α,β(Q˙))−max⁡θ(min⁡α,β(Q˙))\eta_r = \frac{\min_{\alpha, \beta}(\dot{Q}) - \max_\theta(\min_{\alpha, \beta}(\dot{Q}))}{\min_\theta(\min_{\alpha, \beta}(\dot{Q})) - \max_\theta(\min_{\alpha, \beta}(\dot{Q}))}

Coasting Arc Switching Logic

The judgment formula for thrust on or off:

u={[0,0],ηr≤ηrel or ηa≤ηabsTmax[α∗,β∗],otherwiseu = \begin{cases} [0, 0], & \eta_r \leq \eta_{rel} \text{ or } \eta_a \leq \eta_{abs} \\ T_{max}[\alpha^*, \beta^*], & \text{otherwise} \end{cases}

When relative or absolute efficiency falls below the set threshold, the engine shuts down and enters the coasting phase.

Propellant-Time Trade-off

Trade-off Mechanism

The introduction of coasting arcs decouples propellant from time:

Optimization ObjectiveEfficiency ThresholdCoasting Arc ProportionCharacteristics
Time minimizationηrel=0,ηabs=0\eta_{rel}=0, \eta_{abs}=0NoneFull maximum thrust
Propellant minimizationHigher thresholdMoreTrade time for propellant
Trade-off modeMedium thresholdModeratePropellant-time compromise

Simulation Results

Simulation results from 胡敏等 (2026) verify the trade-off effect of coasting arcs:

Mission ObjectivePropellant Mass (kg)Transfer Time (d)
Time minimization96.4932.87
Propellant minimization76.0737.55
Propellant-time trade-off85.1235.87

Propellant savings approximately 21%, time increase approximately 14%.

Value in Batch Deployment

Mission Configuration Flexibility

The coasting arc mechanism provides powerful configuration flexibility for batch deployment missions:

  • Flexible selection of optimization objectives based on mission requirements
  • When propellant budget is limited, mission duration can be extended by increasing coasting arcs
  • Multiple trade-off solutions provide diverse options for mission decision-making

Q-law Controller Adaptation

The Q-law controller automatically identifies low thrust efficiency intervals and shuts down the engine:

  • Real-time calculation of efficiency parameters for current state
  • Automatic switching between thrust arcs and coasting arcs
  • Adaptive control without manual intervention

Coasting Arc and Mass Discontinuity

The combination of coasting arc strategy and mass discontinuity characteristics:

  • In later mission phases when OTV mass is lighter, the same thrust produces greater acceleration
  • Efficiency parameters automatically reflect this change
  • Systematic optimization of propellant consumption across the entire mission profile

References

  • 胡敏, 肖金伟, 张天天, 陶雪峰. 面向中高轨小卫星批量部署的轨道转移飞行器任务规划[J]. 航天器工程, 2026, 25(3): 634-646.
  • Narayanaswamy S, Damaren C J. Equinoctial Lyapunov control law for low-thrust rendezvous[J]. Journal of Guidance, Control, and Dynamics, 2023, 46(4): 781-795.