Engineering & Fluid Mechanics
Rosin-Rammler (RRSB) Particle Size Distribution Formula: Cumulative Retained & Passing %
Model pulverized coal, cement clinker, pharmaceutical sprays, and cyclone dusts using Rosin & Rammler’s 1933 Weibull sieve law R(d) = 100 * EXP(-(d / d_63.2)^n) and cumulative passing P(d) = 100 - R(d).
Six years before Weibull’s 1939 reliability paper: Rosin & Rammler’s 1933 pulverized-powder law!
Paul Rosin and Erich Rammler (1933, Journal of the Institute of Fuel — later formalized on double-log RRSB charts by Sperling and Bennett) discovered that cumulative mass percent RETAINED on a sieve of aperture d follows the stretched exponential law R(d) = 100 * EXP(-(d / d_char)^n), where characteristic size d_char (d_63.2) is the exact aperture at which R = 100 * EXP(-1) = 36.79% is retained (63.21% passing), and spread modulus n measures uniformity (higher n = narrower size distribution)!
For milled powder with characteristic size d_char = 300 um and spread index n = 1.85, a 450 um coarse screen retains R(450) = 12.04% (87.96% passing), whereas a finer 150 um screen retains R(150) = 75.78%!
| Sieve Aperture d (d_char = 300 um, n = 1.85) | Cumulative Retained R(d) % | Cumulative Passing P(d) % |
|---|---|---|
| Coarse Check Sieve d = 450 um | 12.04% Oversize | 87.96% Passing |
| Characteristic Size d = 300 um | 36.79% (= 100/e) | 63.21% Passing |
| Fine Sieve d = 150 um | 75.78% Oversize | 24.22% Passing |
Rosin-Rammler Cumulative Mass Retained Percentage R(d) = 100 * EXP(-(d / d_char)^n)
Computes oversize mass percent retained above aperture d (B2) given characteristic size d_char (B3) and uniformity index n (B4).
=IF(OR(B2 < 0, B3 <= 0, B4 <= 0), "Invalid Rosin-Rammler Parameters", ROUND(100 * EXP(-((B2 / B3) ^ B4)), 2))Rosin-Rammler Cumulative Mass Passing Percentage P(d) = 100 - R(d)
Computes undersize cumulative mass percent passing through sieve aperture d.
=IF(OR(B2 < 0, B3 <= 0, B4 <= 0), "Invalid Rosin-Rammler Parameters", ROUND(100 - 100 * EXP(-((B2 / B3) ^ B4)), 2))Try the example
Use the original values or change them to test your understanding.