马赫角与马赫数关系的简洁推导

A Very Concise Derivation of Relationship between Mach Angle and Mach Number

根据物理学的理论，建立出了超声速小扰动传播的波动方程中与相互作用力相对应的项．采用频谱分析法得到了速度势的付里叶变换式，由此证明了超声速物体产生的马赫波的马赫角与马赫数所满足的关系式，并可得到与实验相符合的激波特性．

Bond et al in 1965[1] utilized physics fundamentals to derive the relationship bwtween Mach angle and Mach number. The first author developed the idca in Ref[1] further, and derived the above-mentioned relationship in a difftrcnt way [2]. Rof.[2] has been given relatively long reportage in both Engineering Index and International Acrosp:lcc Abstrilcts. In this paper the authors develop still further the idea of Ref.[1] and give a cleverer derivation .In the derivation by Bond et al a potential function was introduced in wave equation,but its pbyscial meaning was not discussed. Bond et al only said that potential function was related to the air pressure cxcrtcd On supersonic body. The authors deem that this air pressure is actually caused by collisions of air molecules with the surface of the oh.jcct, willch Icaal to a momentum transfer bctwccn it and air. Thus air pressure is related to mass flux density, which is an important concept introdueed by Laidau [3]. The authors, .after giving potential function of Bond et al physical meaning in terms of Landal's mass flux density. are able to derive the relationship between Mach angle and Mach number in a way much shorter tian that of Ref[2] and much much shorter than that of Ref.[1].