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O / CONSIDERATIONS ON ChECKERBOAKD PAT7E~H5 ~Q If we consider a cigaretLe with a line of bu±n additive extendinc down i the length cf the cigarette (Eig. l], we can segment this ]ins ~nto either short or longer segments and displace evc:y seco:d segment 7 (Figs. 2 and 3). For segment length L random cigarette cross sections f Figure 3 will leave remaining segment portions v,ith average len§th of L/2. This corresponds to the paper burn line at %he siart o£ a pu££, with the remainder o£ the segment being open for ventilation of the puff. Taking ")%he treated length as N ~m, ve~ti!ation eliectiveness io~ one r~ndom ~,pu££ is L/2N. Thus, it is obviou~ t~at the longer segFcnts are far more effective¸ £~r ventilation than the shcrt secmen:s. Since the ~rea around.the.p~per burn li:~c2is a hi9h pressure drop a~ea duxlng a puffj a veotllatlorl hole of i m:[l ar£a at the paDe/ burn line shold provide much less ventllation than tho ~ame size ventila~ on hol~ ~rther removed. Now let u5 ccnsider the remote ve~tilatlorl ~reah~ defined as ventilation at least one mm away from the paper burn line. Usin9 the mode] above, this ~ill be (L-1)/~ i~ pcsitive and otherwise zero. Ventilation e£fectiven~s :o: one random puff is then (L-l~/2N. For 43 mm of %rested area and segmenls o£ unit widths and varying lengths we can construct the following table. L L/2N ~ i00 (L-I~4 x lOD I ~iI 1.16 " C.00 - ~ 2 mm 2.33 1.16 : 3 mrrL 3.49 2.33 t.~ 4 m~: 4.65 3.49 5 mm 5.82 4.65 Our current C~iECK£R~JARD pattern h~s large 2~ x 2~ rm': checks and a number o£ ~maller check~. Tho inrge che~_ks give holes cf about 2 x 2 mm during bu2ning, so inc~'~.asing the length by one m~ should increase the ef{eciivene~s ~ m t.16 to 2.33, or a ]Qo;~ iccreasc ( (L-l)/2?r ~asis). Using the "%_~{r°,rL/2~ basis, we stil± find a 50~ inc:_~se in effectiveaess. Irc~ea~ing the width o£ a check will give a ?roportional increase in ~ean ventilation with no change in effecLiveness DR ~X~I~ arl 31e~ treated basis.