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RE CEIVED 4A MAR 2 3 ~~? Date: 1 rch 1982 d M BL G T oo man o s ... . ,, ` '~. '°' R B ~EL1G&1~N rr. R..reene.. Fom: MK G ~ ;Subjecti''Cigaret'te Delivery as a Function of Butt Length~ L } . .~y~._~a .~.-a F~,~ „In .,response to a` September 1981 article in Beitrage Zur , Tabakforschung the chemical delivery of cigarettes were examined as a ry<s: hi ' ps , function of butt length. The authors claim that functional relations , ^?~~between deliivery and butt length might be used to correct cigarette ,~t,,.deliveries for data obtained using differing butt lengths. This would ,,permit direct comparisons of international delivery data of cigarettes smoked to differing butt lengths. Our analysis was made on puff by puff 'data from several different studies using the experimental computer : program PUFFER. This program allows use of puff by puff data rather than ;,„smoking cigarettes to various fixed butt lenghts. Results are shown, l graphicali~y followed b.y an analysis using the in-house statistica .i;,computer program LINEFIT.- The examination includes TPM, nicotine, C0, ;;;HCN, NO an&RCHO. The results show log scale fits for a linear funct'ion ~ of butt length for TPM and for nicotine, and show arithmetic scale fits ~ t''for C0 HCN NO and RCHO . ,, i" Analysis of puff bp puff data may take several forms. Plot 1 shows ;.TPM' delivery for three Saratoga cigarettes plotted against puff number ,,,;,(this data was obtained as part of a study of the effect of moisture on cigarette delivery.) This type of representation does not permit analysis of delivery versus butt length, nor does it visually show which, cigarette has the higher totall delivery. Plot 2 shows the same data plotted against a puff position calculated from the puff count, assuming a constant :cigarette burn rate. Plot 3 shows the total delivery to each puff ;_position (the iintegrate'd delivery). This analysis shows that the second code has the higher per puff delivery during the final puffs. It also ,,,;allows statistical analysis of the functional relationship between butt „,length and delivery. ty n~Arwarnin must accom a thiis techni ue and a er uff anal. sis. r,..., g P ny q ny P p y ,, .,First, most cigarettes burn fairly uniformly, but do occasionally burn —significantly faster or slower than the average as rod density'fluctuates. ' livery of that " This not only influences the puff position but the de ; particular portion of the rod. Secondly, puff by puff gas phase data is ; '.reported as the average of five ports for each run, where not all ";cigarettes have the same puff count. Suppose that the delivery of some .gas phase component was a linear arithmetilc functiion of puff position. Assuming that during the smoking two of five cigarettes took eight puffs and three cigarettes took nine puffs the data might look like that shown in Table 1. This data, showniin Plot 4 with the integrated data shown in j, Plot5, suggests that bothithe last and next to liast puffs are suspect; the last one being too low (since the delivery is divided by five puffs but only three cigarettes contributed),, and the next to the last one too high (since two contributing cigarettes were delivering as a function of •.their final butt position). Any analysis of actual delivery results therefore should also examine fitted lines omitting the final one or two puffs depending on the spread in puff count. Full analysis would also examine the significance of the first puffs where delivery is low since the coal has not fully formed. An analysis of this test data using the LINEFIT statistics program (Table 2) shows that the actual mean delivery has few significant relationhips with any type of equation, the best being the log of the .,

'~~~ ~ c~ .. v ... . ~ rx Pa$e a~ ~ "A ;;r :; ~delivery .~`r, ,Subtracting the last puff improves the fits significantly particularlg for the liriear arithmetic function. The integrated delivery is best represented by an equatiori u'sirig "the log of the butt length..',•: . Puff by puff TPM delivery is usuall+y collected on~20 ports using a Ysingle pad-for each puff. Since a single integer puff count is reported, no problems are encountered in estimating puff position from puff number 'fbther than the natural variation in individual rod burn rates. The raw ;,data is"shown'in,Plots 6 and 7 for TPM and nicotine respectively. -Plot's 8' ~and 9'sh bth itgtd dl ,owonerae&an raweivery as a function of butt length, ~i~i'or these two components. '-The shape of the integrated delivery at'various ~butt lengths appears to be logarithmetic. An analysis of the integrated ~i'data sh i 3 thth b ownn Table showsa teest line through the data includes " th lf th btt lth eog oeueng ~ J y'`"°Puff by+puff :gasphase `data is presentlp'I collected on, five ' rts po Wuaing "a'p redetermined butt length The delivery for each puff ad . numbern ~the puff counts are reported. Since the puff counts are non-integer 4,'vl adul' by at l auesn .sualy varyeast one puff, the analysis of delivery :versus puff position for gas phase components requires more data sets. `P'lots 10 thorugh 13 show the integrated deliveries for CO, HCN, NO and RCHO respectively on Monitor 201cigarettes. Plots 14 through 17 show the "ra dtf th waa oese components and illustrate the problem with the final puff, where the total analyzed delivery is divided by five cigarettes '"regardless of how many cigarettes actually contributed. The LINEFIT f`'ana],y'sis of the four gas components are given in Tables 4'through 7. The e'',high F-val'ues in each case indicate an arithmetic linear fit for both the _integrated delivery and the actual delivery with the last puff omitted. `These preliminary results~are in conflict with the Beitrage article :,;•Fi:_Yor nicotine and CO. The authors report log scale fits for their delivery `~,at various butt lengths for TPM and C0 and an arithmetic scale filt for inicotine.";'Total HCN (gas phase and particulate delivery summed) they ._report can fit either log or arithmetic scales. An additional report on analysis of particulate data for several Monitor cigarettes is in ;.;progress. Current experiments are underway with gas phase analysis of :-'Monitor 22. . In these experiments rods will be smoked to an integer puff count, extinguished, and the five individual butt lengths measured. This may ' serve to`eliminate some of the error in estimating puff position from puff count. . t ' `A~ 4 ti '.., j r'` I ~v SiF r F,~ . _ C. C. ° rdD`r; R B ''Seligman ;fz`_ ;.hr3 Mr LF Meyer r ;. ... Mr. P.N~. Gauvin -° Dr. W.A. Geiszler '' '. i Mr WG Houck ... c~a ?' :Ms. C.C. Bri'ght ~ !'rt?' a!-tlti'I f ° 'xt f ~: . _ . . . . ~ .. . . ~ ~?.

Page 3 TABLE 1~. CALCULATED PER PUFF DELIVERY - LINEAR FUNCTION OF PUFF POSITION EQUATION: Delivery --0.03041 * Puff Position + 3.1681 Eight Puff Model Butt 85.-00 ~ :. 76.86 68.71 60.57 52.43- 44.29 36.14 28.00 Del (2X) 0.6 1.2000, 0.8 1.6855 1.1 2.1717 1 .3 2.6572 1 .6 3.1428' 1.8 3.6283 2.1 4.1145 2.3 4.6000, Nine Puff Model 'Butt Del (3X) SUMI MEAN 85.00 0.6 1.8000 3.0000 0.6 77.88 0.8 2.4371 4.1226 0.8' 7,0.75 1.0 3.0750 -5.2467, 1.0. 63.63 1.2 3.7121 6.3693 1.3 56.50 1.4 4.3500 7.4928 1.5 49.38 1.7 4.9871 8.6154 1.7 42.25 1.9 5.6250 9.7395 1.9 35.13 2.1 6.262'1 10.862 2.2 28.00 2.3 6.9000 6.9000 1.4 LINEAR CORRELATIONS VERSUS BUTT LENGTH Eight Nine Mean W/o Last Puff C.C.(r) -0.9991 -0.9990 -0.8441 -0.9986 . Slope -0.03041 -0.03041 -0.02246 -0.03175 Intercept . 3.1681 3.1626 2.6466 3.2819 INTEGRATED DATA Eight Puff Mod el Nine Puff Model Mean Butt Delivery Butt Delivery De livery 85.00 0.6 85.00 0.6 a.6 76.86 1.4 77.88 1.4 1.4 68.71 2.5 70.75 2.4 2.4 60.57 3.8 63.63. 3.6 3.7 -52.43 5.4 56.50 5.0 5.2 44.29 7.2 49.38 6.7 6.9. 36.14 9.3 4,2 . 25 8.6 8. 8~ 28.-00 11.6 35.13 10.7 11.0 28.00 13.0 12.4

TABLE 2. LINEFIT ANALYSIS - LINEAR TEST MODEL ANALYSIS OF MEAN DELIVERY Y = b + m ~ X Y = b + m / X 1/Y =b+m*X :1/Y =b+m/X Y = b + m * ln(X) ln(Y) = b + m * X ,ln(Y)-= b + m * ln(X) ANALYSIS OF MEAN DELIVERY MINUS LAST PUFF Y = b + m * X Y ='b+ m /X ~ 1 = b + m X 1/Y =b+m/X Y = b + m * ln(X) ln(Y) = b+m*X ln(Y )~ = b + m ~ ln(X Model Intcp Slope R-SQ F-Value 2.647 -0.0225 .71253 17•4 0.508 43.42 .44559 5.6 -0.119 . 0.017 .72235 18.2 1.495 -32.27 .42853 5.2 5.615 -1.066_ .59280 10.2 1_.302 -0.019 .74703 20.7 3.736 -0 . 877 .60997 10.9 Intcp 3.281 -0.0318 -0.314_ 93•46 -0.484 0.0225 1.959 -60.52 8.652 -1.79 1.758 -0.0253 5.913 -1 . 40 .99712 2077.6 .94215 97.7 .88332 45.4 .69929 14.0 .98466 385.1 .96929 189.4 .91556 65.1 ANALYSIS OF INTEGRATED DATA Intcp Slope R-SQ F-Value Y =b+m*X- .Y =b+m/X 1/Y =b+m~X 1/Y =b+m/X Y = b + m * ln(X) ln (Y ) = b + m * X ln(Y ) = b + m * ln(X) 17.98 -0.2152 .98280 400.1 -4.55 517.73 .95102 135.9 -0.772 0.02092 .63292 12.1 1.216 -40.25 .39155 ;4.5 50.58 -11.26 .99333 1042.2 4.253 . -&. 0503 .93502 100.7 11.31 . -2.491 .84541 38.3

TABLE 3.LINEI'IT ANALYSIS - SARATOGA 120's ANALYSIS'OF SARATOGA TPM DATA - INTEGRATED DELIVERY Model Intcp Slope R-SQ F-Value Y = b + m~ X 23..22 -0. i 958 .97303 1226. 5 Y = b + m/ X -5.429 919.2 .94592 594.7 1/Y = b + m* X -0.629 0.01196 .46327 29.3 1/Y = b + m/ X 0.9430 -43 . 78 .27397 12.8 Y= b + m * ln(X) 69.48 -14.32 .98481 2203.7 ln(Y )= b + m* X 4.462 -0. 0347' - .88995 274.9 ln(Y ) = b + m * ln(X) 12.03 -2. 394 .79801 134.3 ANALYSIS OF SARATOGA NICOTINE DATA - INTEGI3AjFD _DELIVE_RY Model Intcp Slope R-SQ F-Value Y*= b + m*•X 1.541 -0 . 0130 . 91326 358.0 Y = b + m / X -0.363 61 .05 .88513 262.0 1/Y' = b + m~ X -9. 996 0.1892 .49026 32.7 1/Y = b + m/ X 1 4.88 -692.3 .28962 13.9 'Y b + m * in(X) 4.616 -0.952 .92296 407.3 ln(Y )= b + m * X 1 .771 -0. 0354 .87324 234.2 ln(Y )= b + m * 1-n(X) 9.454 -2.430 .78136 121 .5 Page 5

ANALYSIS - CO DELIVERY - MONITOR 20 ACTUAL DELIVERY - 6 SETS .Y=b+m*X = b + m / X (Y = b + m * X ;1/Y = b + m / X = (X b + m * X ln(Y ) .ln (Y ) = b + m * ln ( X Intcp 2.539 -0~.00958 .73787 2.8 2.075 -4. 33G ..00156 0.1 0.510 0.00297 ~7.00880 0.5 0.487 .9,893 .01452 0.8 2.866 -0.219 .00948 0.5 .0.835 -0 . 0045 .02149 1.1 0.714 -0.034,6 -/( .00044 0.02 ACTUAL DELIVERY - 6 Intcp 'Y=b+m*X Y = b + m / X 1/Y =b+m*X 1/Y =b+m/X 'Y = b + m * ln(X) ln(Y) = b + m * X ' ln (Y ) = b + m * ln (X ). SETS - MINUS LAST PU'FF' 4.178 -0.0335 .69006 102.4 0.538 90.82 .51510 48.3 -0.443 0.0169 .30433 20.1 1.340 - -42.92 .19901 11.4 9.509 -1 . 809 .60381 70.1 1.964 -0.0210 .53409 52.7 5.232 -1.116 .45253 38.0 INTEGRATED DELIVERY.- 6 SETS Model Intcp Slope R-SQ F-Value Y = b + m ~ X 28.81 -0 . 337 0 .99075 5570.9 Y = b + m / X -6 .692 833.0 .89748 455.2 1/Y =b+m*X -0.751 0.0184 .36590 30.0 1/Y =b+m/X 1.021 -36.86 .21750 14.5 Y = b + m * ln(X) 80.36 -17.73 .96617 1485.3 l (Y) b * X 0 6 6 6 n = + m 4.94 -0.0531 .83 3 5.8 2 ln(Y ) = b + m * ln(X) 12.50 -2.65 '.73567 144.7

. A& . .%. TABLE' 5. LINEFIT ANALYSIS - HCN DELIVERY - MONITOR 20 ACTUAL DELIVERY - 5 SETS Model Intcp Slope R-SQ F-Value Y = b + m * X 41.03 -0.284 .29047 17.6 Y = b + m / X 16.91 403.6 .08693 4.1 1/Y = b + m * X -0.0122 0.0011 .19985 10.7 1/Y =b+m/X 0.0882 -1 . 816 .07575 3.5 Y = b + m * ln(X) 72.40 -11.92 .18033 9.5 ln(Y) =b+m * X 3.976 -0.01,52 _ .27'902 16.6 In(Y) = b + m * ln(X)~ 5.656 -0.638 ~ .17424 9.t ACTUAL DELIVERY - 5 SETS' - MINUS LAST PUFF Model Intcp Slope R-S'Q F-Value Y = b + m * X 58.97 -0.546 .85189 218.6 Y = b + m / X -1.680 1554.5 .69692 87.4 1/Y=b+m*X -0.0575 0.0018 .35410 20.8 1/Y=b+m/X 0.1345 -4.698 .24395 12.3 Y.=b+m* ln(X)) 148.9 -30 . 22 .78286 137.0 ln(Y) = b + m * X 4.801, -0 . 027 2 .67378 7 8. 5 ln(Y ) = b + m * ln(X). 9.153 -1 • 474 .59448 55.7 INTEGRATED DELIVERY - 5 SETS Model Intcp S'lope R-SQ F-Value Y = b+ m ~ X 351.1 -4 .195 .97345 157 6. 8 Y = b + m / X -9 4. 3 10547.6 .91259 448.9 1/Y = b + m * X -0.0712 0.00174 .36093 24.3 1/Y = b + m / X 0.0964 -3.502 .21757 12.0 Y = b + m * ln(X) 1000.2 -222.6 .96560 1207.2 ln(Y)'=b+m*X 7.535 -0.0562 .85560 254.8 ln(Y), = b + m * ln(X) 15 . 61 -2 . 828 .76241 1 38 . 0 Page 7

TABLE 6. LINEFIT ANALYSIS - N0 DELIVERY - MONITOR 20 ACTUAL DELIVERY - 6 SETS Model Intcp Slope R-SQ F-Value Y=b+m *X 33.91 -0.0223 .00173 0.1 ~ Y = b + m / X 38 . 49 -301 . 0 .q467 3 2.5 1/Y=b+m~X 0.0528 ' -0.00029 .06105 3.4 1/Y=b+m/X 0.00842 1.422 .21422 14.2 Y = b + m * ln(g) 23.12 2.38 .00696 0.4 ln(Y)' = b + m * X 3.277 0.00254 .01257 0.7 . ln(Y )~ = b + m * ln(X 2.303 _ 0.280 .05376 3.0 ACTUAL DELIVERY - 6 SETS - MINUS LAST PUFF Model Y = b + m Y = b + m 1/Y = b + 1/Y = b + Y = b + m ln(Y ) = b ln(Y ) = b Intcp Slope R-SQ F=Value 56.26 -&. 348 .70604 110.5 18.05 964.6 .54660 55.5 0.00751 0.00037 .50279 46.5 0.0473 -&.982 .35967 25.8 -112.6 -19.02 .63179 78.9 4.207 -0.0110 .62459 76.5 5.965 -0~.596 .54796 55.8 INTEGRATED DELIVERY - 6 SETS Y = b + m ~ X 464.5 -5.281 .99171 6218.4 Y = b + m / X -91 .48 13033.9 .89566 446.4 1/Y=b+m*X -0.0217 0.00059 .56066 66.4 .1/Y =b+m/X 0.0358 -1 .217 .35486 28.6 Y =b+m* ln(X) 1271 . 3 -277 . 6 .96547 1453.9 ln(Y) = b + m * X 7.353 -0.0441 .88254 3K.7 ln(Y) = b + m * ln(X) 13.69 -2.217 .78732 192.5 :; P age 8 . f

TABLE 7. LINEFIT ANALYSIS - RCHO' DELIVERY - MONITOR 20 Mode l Y = b + m * X Y = b + m / X 1/Y = b + m * X 1/Y=b+m/X ln(Y ) = b + m * (~X ln(Y ) = b + m * ln(X) ACTUAL DELIVERY - 5SETS Intcp Slope R-SQ F-Value 108.5 -0.280 .04504 2.0 94 • 71 -1 13 . 9 .00111 0.05 0.0110 0.00001 .00322 0.1 0.00964 0.11183 .03200 1.4 1 19. 2 -6 . 693 .00909 0.4 4.615 -0 . 0022 .01714 0.7 4.533 -0.0113• .00016 0.007 ACTUAL DELIVERY - 5 SETS - MINUS'LAST PUFF Model Intcp Slope R-SQ F-Value Y = b + m * X 160.8 -1 .04 .72763 101 . 5 Y = b + m / X 44.30 3007.0 .61048 59.6 .1/Y =b+m~X 0.-0021 0. 00014 .49402 37 .1i 1/Y =b+m/X 0.0178 -0.396 .37395 22.7 Y = b + m * ln(X) 333•8 -58.05 .67627 79.4 ln(Y) = b + m * X 5.277 -0. 0119 .63345 65.7 ln{Y ) = b + m * ln(~X). 7.215 -0 . 653 .57421 51 . 2 INTEGRATED DELIVERY - 5 SETS .Model Intcp Slope R-SQ F-Value Y = b + m * X 1296.8 -14.79 .98397 2640.0 Y = b + m / X -265.8 36768.7 .90112 391.9 1/Y =b+m*X -0 . 00798 .00022 . 541,86 50 . 9! 1/Y =b+m/X 0.0131 -0.447 .34346 22.5 Y = b + m * ln(X) 3567.0 -7801.1 . 96418 1157.5 ln (Y ) = b + m * X 8.385, -0 . 0443, .87956 314.0 ln(Y ) = b + m * ln(X) 14.777' -2 . 235 .78753 159.4 Page 9

:. L I V 'E R ~Y 3 2.5 -~ 2 ~ 1. 5 .J 1 ~ 0.5 .~ Saratoga TPM Vs Puff Number Raw Data °---A 5R9-1 (7%o.v.) 13 ---S SR9-2 (13%o. v . ) ¢--'0 9R9-3 (21%o . v . ) . 6 6 .PUFF NUMBER t0 . 12 --e 14