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3 ® ® ® u H ® ® U ® I ® ® ® ® R TREATING THE EFFECTS OF FILTER'DILUTION ON CIGARETTE DELIVERIES H. Hartung U ( 1~ M. ~1/ Wood

I I I r I I I I I 11 I THIS REPC7RT IS CONFIDENTIAL TO THE BUSINESS OF THE CWANYc IT SHWLD'BE CAREFULLY HANDLE-, IS NOT, TRANSFRABLE TO ANOTHER INDIVdDUAL,AND~ISNOT TO BE PHOTOCOPIE,D. If, tAersport has servedIta purpose and Is nolongx neadbdr please return It Imsedlately totAeCentral Fllbet tMResearch Center for record keeping purposes anddestruction. CHARGE NO. & TITLE: Project 1708: Physical and Chemical Properties of Tobacco TYPE REPORT: 0 ANNUAL Q SEMIANNUAL 0 COMPLETION SPECIAL DATE: PERIOD COVERED: REPORT TITLE: P'H~ILIP M~URRLS, U.S.A. RESEAR'CH CENITER R I C H M 0 N I D , V I R G I N I A Accession Nbmber: 82-271 Copy Number: Issued To: A MATH MODEL FOR TREATDNG THE EFFECTS~ OF FILTER DILUTIGT ON'CIGARETTE DELIVERIES BY APPROVED BY DISTRIBUTION: HI. Hartung F: Whidby M. /3'`• Wood ~ R. Dwyer W. Farone D. Fox ~ P. Gauviln B. Goodtlnan R. Greene I A. Kassr,-ani B. LaRoy W. Mokarry J. Sterrnller M. Waugh I I E KEYWORDS: Mathematical Ftodels, Filter Dilution, Filter Length, Puff Count, Tar, TPt11, Nicotine, Water, RTD,

I I I I I I I I t I t I- ABSTRACT Math models of the effects of filter dilution on cigarette puff count, tar, nicotine, water, TPM and' RTD are d'eveloped. The dependent parameters are ratios of deliivery reductions to dilution. These parameters are treated as linear func- tions of dilution and filter 1'ength. The model fits tows with fiber sizes ranging from 2.5 to 5 d.p.f.

IT I I i F I i t I F l I- F I L i L OBJECTIVE To develop mathematical models for treatingi filter dilution in computer modeliing systems used for cigarette design applications. DATA BASE The data used in this work were obtained from the N6w Products Develiopment Department, courtesy of Mr. Randall Greene. The data were from studies carried out several' years ago. Cigarettes were made using Marlboro blend, wrapper, flavors, casings and so-forth. Fi'lters were attached which were made from three different CA tow items and at three different lengths. A wide range of filter dilutiIons was obtained~ by varying the number and sizes of the dilution holes. The percent dilution was measured along with puff count, TPM, nicotine, water, tar and RTD. The resul'ts were reported, as percent red!ucti'on from the cigarettes with zero dilutioni. Since there was a puff count increase with, increasing diillu- tion, puff count changes were input as negative numbers so that all data would be in terms of percent reduction due to dilution. THEORY The assumptiion was made that the rati os of parameter reducti ons to dil uti on are linear functions of percent dilution and, filter length,: YZ = CRO + CR1 X1 + CZ2* X2 (1)1 where CQO CQI and CQ2 are model regres&ion coefficiients wi'th the iindex X running :from I to 6. Xl = percent dilution X2 = filter length Yl, =(~percent puff count reduction) T X1 Y2 = (percent tar reduction)' T X1 -2- L

Y3 = (percent TPM reduction~) = X1 = (percent Nicotine reduction) : X~l Y5 = (percent Hi20 reduction) : X1 Y6 = (percent RTD reducti on) : X1 The rati os of percent reducti on to percent di,lluti on were used because the reducti oni must extrapol ate to zero as di l uti oni approaches zero and a di rect pro- portionality seems to: be a reasonable first approximati,on. The use of these ratios was ultimately justified by the results obtained,, of course. This formu- lation is consistent with the formalisms and conventions developed for "Cig;arette Modeling Theory" by H. A. Hartung.' Iin parti~cullar, the calibratiion method descriibed previously (see page 9, ref. 1), is directly appllicable to these Y's. ~ For undiluted cigarettes, strictly speaking, the Y parameters are undefined because X1 is zero. This does not make any difference when prediicting pu~ff count, tar or other delivery parameters directly. Consider, for example, P = the puff count at a finite dilution level and Po = the puff count at zero diil'lution. Percent Puff count reduction = (Po - P)100 (,2) ~ P o C; (Po-P),100. Yl P'oX1 (3) ~ Then rearranging this gives the predicted pu~ff count: ,~ W= P o (1- h 1001~ (4) ~ such that P = Po when X'1 = 0 no matter what happens to Y1. . I~t is important to note that the factor (Po-P') i's a small difference between l arge numbers when di l uti on (X 1) i s l ow. Hence, rel atiively llarge errors i n the Y-parameters should be expected at llow, dilutions. Also, the zero dilution points must be excluded when regressing,tol fit function, (1) because the Y-parameters are undefined when X1=1. -3- i I I I i i I I I I I I L L L L L

I I i i I I I I I I t I I I L L L RESULTS Data points and model contour lines are shawn in Fiigure 1. This shows that Y data and the contours are straiight li!nes. As expected, the scatter of points and lines increases as zero diilution is approached'.. Figures 2, 3, and 4 show the same data andl contours pl otted~ as actuall percent reductions rather than ratios. In these figures the scatter between points and lines is reasonable over the entire range of dillutions. A' summary of the modeling system as installed in a public filie on the R&D computer system is provided in Appendix I. CONCLUiSIONS A good model of dilution effects on cigarette deliveries has been developed. This shouldl be added to existiing computer modeling systems to obtain better treatments of di liuti on effects. REFERENCE 1H. A. Ha~rtwng, "Cigarette Modeling Theory", Special Report 82-208, August 16, 11982. -4- L

Figure 1. Model Contours and Y data 0 In 25 50 DILUTION 0 J ~ C) W ~ 75 0 ^ 0 _e t _ -+~ ~+ N N N H N 25 50 QILUTION 0 0+ vo 0 O O 25 50 75 DILUTION F2GI.CHT 'm'm P~ 'wMM Room "mm Ii/m" r-- r r- rt-r r- -- J ~ ~ ~ W cr- //Or/4 Pr+ -ea +--- +- + ++ + 00 . 8 .± •00 . Y . . •. ~ N ~4 0 'k N -- F- -- . .. --- 25 50 DILUTION N -1 75 ..r, ...r~ "mmm~ .mmml "--1

r... r""' f'_.. r"-' r-.M rmm ~ P~" ~ pmok .... .nw am" ••" .•" mm'1 ""1 '.R.'1 Figure 2.. •Tov+r 5.046 Test data and contours. Z 0 ~_- ~ ~ 0 W ~ f-- Z ~ O U ~ ~ ~ ~ 0 0 i 0 N M 25 50 75 DILUTION 0 to tn N 25 50 75 DILUTION GTB4OVOOnT z O ~ U ~ ~ W ~ U Z 0 to 0 to 0 v 4] N 25 50 75 D I LUT ION 0 0 25 50 75 DILUTION 0 to T z 0 0 v ~ U / ~ / ~ / W / . ~ 0 N O 25 50 75 25 50 75 DILUTION DILUTION F=G2.CHT

z 0 F-- U ~ ~ W ~ 0 to to N Figure 3. Tow 3.446 Test data and contours 25 50 75 D I LUT I ON 0 V- d N Mg40VnOOT z 0 r- EJ ~ ~ W or_ ~ F- ~ 0 O N 25 50 DILUTION 75 1 --+-~ 25 50 75 25 50 75 DILUTION DILUTION F2G3.CHT

11,/0SZ8Z TAR REDIUCTION 34 68 Gr O N!C REiDUCTIOiN 7 34 N : 102 61 N U *+ \ CU 0 V U RTD REDUCT IlON 20 40 160 N cn r C ~ O Z v+ 0 m PUFF COUNT REDUCTION -20 -10 0 m ,%I .+. 1 V LA I