飛彈最省燃料水平轉彎之研究

A Study of Minimum-Fuel Horizontal Turns of Missiles

張文富(Wen-Fu Chang) ； 許棟龍(Dong-Long Sheu)

《中國航空太空學會學刊》 29卷2期 (1997/06) Pp. 123-129

https://doi.org/10.6124/TAASRC.199706_29(2).04

摘要

飛彈燃料之重量一般都佔其總重量的絕大部份，而飛彈在整個飛行的過程中，轉彎會消耗大量的燃料，因此本文特就轉彎問題，探討其最省燃料之軌跡。本文採用最佳化控制理論爲基礎，應用二階坡度演算法作反復運算以求數值解。根據最佳化理論推演得知，飛彈飛行的軌跡可分成推進弧、特異弧、滑翔弧三種。當起始條件與終端條件設定之後，在節省燃料的考量下，飛彈全程之飛行軌跡可能是上述三種弧的結合。因此，在兩種不同弧的交接處，限制條件及切換時間均是很重要的問題。爲証明理論分析之有效性，本文以一組典型之飛彈空氣動力數據，作爲數值計算範例。

關鍵字

飛行力學 ； 最佳飛行軌跡 ； 最佳控制

並列摘要

In general, the fuel weight of a missile is a predominant part of its total weight. Yet more essential is that, in the whole flight process of a missile, turns will consume a lot of fuel. Therefore, in this paper, the problem of turn is studied in order to determine a minimum-fuel trajectory. In this paper, the optimal control theory is used as a basis and the second-order gradient algorithm is applied to determine numerical solutions iteratively. According to the derivations using the optimal control theory, the flight trajectory of a missile may be decomposed into three types of arcs, i.e., boosting arc, singular arc, and coasting arc. For a minimum-fuel problem with a set of given initial conditions and final conditions, the whole trajectory of missile may be composed of these three arcs. Hence, at the joint of two different arcs, the determination of constraint conditions and the switching time is a very important problem. In order to validate the theoretical analysis, a set of typical aerodynamic coefficients of missile is adopted as an example of numerical computations.

並列關鍵字

minimum-fuel ； optimal flight trajectory ； optimal control ； flight mechanics