TOTAL PER CENT OF WASTE IN LOG 55 



Corrections for Saw Kerfs of Different Widths. Since the per cent of 

 waste caused by saw kerf applies directly to the residual volume of logs 

 after subtracting the waste for slabbing and edging, the effect of using 

 a saw of greater or lesser width than that used in constructing the rule 

 can be found in terms of a per cent of the values of the log rule. This 

 flat correction can then be applied if desired, to correct timber estimates, 

 convert the log rule into one which eliminates over-run from saw kerf, 

 or correct the scale of logs to coincide more closely with sawed output. 



For instance, the above rule would utilize 1 — .158 or 84.2 per cent of the net 

 cubic contents of the cylinder. A saw cutting a j-inch kerf, with the same allowance 

 for shrinkage, calls for the formula, 



i+A .3125 



= 23.8 per cent, 



l+i+fe 1-3125 



giving 72.6 per cent utilized. The values expressed by the log rule made for the 



§-inch kerf must now be taken as 100 per cent to which the correction will apply. 



76.2 



Then gives 90.5 per cent. The second rule requires values equaling 90.5 per 



84 . 2 



cent of the first, or a straight reduction of 9.5 per cent. 



That this conversion can be accurately made was demonstrated on diagrams by 



H. D. Tiemann, who found that the possible error was less than one-half of one 



per cent.^ 



54. Total Per Cent of Waste in a Log. The total per cent of waste in 

 a log is the sum of the waste from slabbing and edging, or surface waste, 

 and from saw kerf. The proportion of this total waste represented 

 respectively by slabbing and by sawdust will depend upon which of 

 these deductions is made first, and whether the sawdust made in slabbing 

 and edging is included as part of the waste in slabs and edgings, or is 

 counted as part of the waste in sawdust. If the deduction for sawdust 

 is made first, it will include a fixed per cent of the cubic volume of the 

 log. If on the other hand, the slab waste is first deducted as a ring or 

 collar of a given thickness, the subsequent deduction for saw kerf, 

 although the per cent is the same, applies only to the residual volume of 

 the log. 



The total per cent of waste, and its distribution between these two factors is 

 illustrated in table VIL Let slab waste equal a ring f-inch in thickness or a 

 reduction of 1.5 inches in diameter. Sawdust, for J-inch kerf, equals 20 per cent. 

 The per cent of waste will vary with diameter of logs, as shown : 



In column 2 the per cent of waste is seen to be approximately one-half as great 

 for 20-inch logs as for 10-inch logs. 



1 Proc. Soc. of Am. Foresters, Vol. V, 1909, p. 29. 



