手法を比較

	マッケイブ・チーレ法	ロジン・ラムラー分布	トロンプ曲線
分野	鉱山工学	鉱山工学	鉱山工学
系統	Process / pipeline	Process / pipeline	Process / pipeline
提唱年	1925	1933	1937
提唱者	Warren L. McCabe and Ernest W. Thiele	Paul Rosin and Erich Rammler	K. Tromp
種類	Graphical design method for distillation columns	Empirical probability distribution for crushed material fineness	Empirical model for size classifier performance
原典	McCabe, W. L., & Thiele, E. W. (1925). Graphical design of fractionating columns. Transactions of the American Institute of Chemical Engineers, 21, 30-60.	Rosin, P., & Rammler, E. (1933). The laws governing the fineness of powdered coal. Journal of the Institute of Fuel, 7, 29-36.	Tromp, K. (1937). Separation of fine particles from slurries by hydrocyclone. Colliery Guardian, 155(4), 251-256.
別名	McCabe-Thiele Diagram, Graphical Distillation Method	Rosin-Rammler Model, RRS Distribution, Weibull Distribution (particle size)	Partition Curve, Classification Efficiency Curve, Grade Recovery Curve
関連	3	3	3
概要	The McCabe-Thiele Method, introduced by Warren L. McCabe and Ernest W. Thiele in 1925, is a graphical technique for designing and analyzing distillation columns. It predicts the number of theoretical plates (stages) needed to achieve a desired separation between light and heavy components. While primarily a chemical engineering tool, it applies to liquid-vapor separation problems in mining operations such as mercury recovery and rare earth element refining.	The Rosin-Rammler Distribution, introduced by Paul Rosin and Erich Rammler in 1933, is an empirical probability distribution that describes the particle size distribution of ground or crushed materials. It characterizes fineness by two parameters: the characteristic size (d-prime) and the uniformity index (n). This distribution is remarkably accurate for mineral processing streams and is ubiquitous in comminution engineering.	The Tromp Curve, introduced by K. Tromp in 1937, is an empirical model that quantifies the performance of size classifiers (cyclones, screens, jigs) by showing the fraction of particles at each size that report to the target stream (overflow or underflow). It is universally used in mineral processing to evaluate classifier performance, design circuits, and diagnose operational problems.