論圓錐幾何設計及尺度擴展對螺線管推進器效能之影響

Abstract

本篇研究建立在前人對於具有截面積梯度變化之線圈在地磁場中受力的理論框架上，驗證了微小尺寸推進器的有效性及磁矩梯度對受力提升的效果。然而，我們相信在更大尺度、增加電流強度，以及調整尺寸或梯度斜率等條件下，推進器的潛力將得到更大程度的發揮。 為了進一步驗證和拓展理論對受力大小的預測，我們運用商用模擬軟體Comsol-Multiphysics來模擬不同尺度下的實驗結果。透過這些模擬和實驗，我們成功驗證了線圈在地磁場中受力的理論並拓展了其受力大小的預測。 在實驗中，我們採用了具有更大截面積梯度變化的圓錐外型並調整更大的幾何尺寸和參數設置，這使我們成功地測量到了毫米牛頓等級的推力。然而，我們也針對鐵芯線圈於地磁場中受力的理論進行了修正。結果顯示，儘管圓錐具有較大的截面積梯度變化，但由於鐵芯材料與背景磁場的相互影響，推力將會降低。這種現象是因為鐵芯的幾何外型在磁場中呈現出更不均勻的分佈。儘管該理論修正在圓台的推力預測上存在較大的誤差，然而透過此修正因子，有助於未來更準確地考量材料和幾何特性，進而更準確地預測推力大小。 本篇研究的成果有助於深入瞭解推進器的性能及圓錐形狀對推力的影響。透過實驗和模擬的結果，我們成功拓展了推進器的潛力和應用範圍，並為未來的推進技術發展提供了有價值的參考。此外，無需推進劑的基於地磁場的超導螺線管推進器具有可持續性、資源節約、輕量、體積小、穩定推力及環境友好等優勢，為太空任務提供了高效、靈活和可持續的推進解決方案，推動外太空的探索和利用。

This study is based on the theoretical framework of the previous research on the force experienced by coils with cross-sectional area gradient variations in the geomagnetic field. It verifies small-sized thrusters' effectiveness and force enhancement due to magnetic moment gradients. However, the potential of the thruster will be further enhanced at larger scales, increased current intensity, and adjustments in size or gradient slope. To further validate and extend the theoretical predictions of force magnitude, we employed the commercial simulation software Comsol-Multiphysics to simulate experimental results at different scales. These simulations and experiments successfully validated the theoretical predictions of coil forces in the geomagnetic field and expanded their predicted force magnitudes. In the experiments, we used a cone-shaped geometry with more significant cross-sectional area gradient variations and adjusted the geometric size and parameters, enabling us to measure millinewton-level thrust. However, we also corrected the theoretical force predictions on the iron core coil in the geomagnetic field. The results showed that despite the cone's more considerable cross-sectional area gradient variations, it would reduce the force due to the mutual influence between the iron core material and the background magnetic field. This phenomenon arises from the non-uniform distribution of the iron core's geometry in the magnetic field. Although the theoretical corrections show more significant errors in force prediction for the frustum shape, incorporating this correction factor will aid in more accurately considering material properties and geometric characteristics for future force predictions. The findings of this study contribute to a deeper understanding of the thruster's performance and the impact of the cone-shaped design on thrust. By analyzing experimental and simulation results, we successfully explore the potential and application range of the thruster, providing valuable references for future propulsion technology development. Furthermore, the magnetically propelled superconducting coil thruster based on the geomagnetic field offers advantages such as sustainability, resource efficiency, lightweight, compact size, stable thrust, and environmental friendliness. This solution presents an efficient, flexible, and sustainable propulsion alternative for space missions, promoting exploration and utilization of outer space.