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Rosin-Rammler Plots In size analysis tests the data originally appears as the percent weight of the original sample that is retained in each size fraction. If the increments of sizing are chosen so the particle size doubles as the size openings get larger coal data plotted as a bar chart which typically results in a slightly skewed “bell” or Gaussian distribution curve as shown in figure 2 ¹ .
The most common method of plotting size analysis data for coal is to use the Rosin-Rammler equation.
Where R = % of material retained x = the particle size in mm k = absolute size constant n = size distribution constant Note, only square hole screen sizes are used.
For your convenience click below for SGS' specifically designed Rosin-Rammler process plot points graph templates:
Figure 2. Rosin-Rammler Plot of same data
As can be seen the Rosin-Rammler plot gives a good straight line representation of the original data. The x-axis is on log scale with the particle sizes plotted at their square hole mm equivalent. The y-axis is a probability distribution based on the Rosin-Rammler formula. The slope of this Rosin-Rammler line is “n” in the equation. It represents the width of the size distribution curve of figure 2 and thus is similar to sigma in the Gaussian distribution equation. The absolute size constant “k” represents the most common particle size in the coal and is thus the peak of the particle distribution curve in figure 2. The value of “k” is the size at which the line crosses “R” equal to 36.79 (the blue dashed line on the plot). The Rosin-Rammler equation was originally derived in the 1920’s from theoretical considerations, which will not be covered here.² But two assumptions made in the derivation of the formula should be noted. One is that each of the particles in the size distribution is formed by breakage of a larger particle, and each larger particle has been broken into at least ten smaller particles. Thus a size reduction of approximately two is required for the curve to be theoretically correct. The second is the formula should only be used when no screen or size separation has occurred.
¹ Rosin-Rammler Charts and Their Application to Size Distribution Problems, E. C. Winegartner, Exxon Research and Engineering Company Baytown, Texas ² The derivation of the Rosin-Rammler equation is explained by W. S. Landers and W. T. Reid, “A Graphical Form for Applying the Rosin and Rammler Equation to the Size Distribution of Broken Coal,” U.S.B.M. Information Circular 7343, 1946. |
Equation 1
