228 



TIMBER TRENDS IN THE UNITED STATES 



Cutting rates. — Cutting rates were used to distribute 

 the total allocated sawtimber cut (as described in the 

 section on The Outlook for Timber Supply) by 2-inch 

 diameter class. Cutting rates, by 2-inch diameter classes, 

 were determined in the West by the ratio between the 

 number of trees cut during a year and the inventory of 

 trees at the beginning of the year. In the East where the 

 cut is from young-growth timber, cutting rates were set 

 as the ratios between numbers of trees cut during a year 

 and the net growth in numbers of trees in each 2-inch 

 d.b.h. class. These cutting rates were determined from 

 utilization studies, from stump counts on initial surveys, 

 and from tallies of trees cut during the period between 

 remeasurement of permanent plots. Cutting rates by 

 diameter class were usually curved to remove irregularities. 



In the East cutting rates for 1962 were varied annually 

 by a constant rate to approximate the following rates by 

 2000. 



D.b.h. Softwoods Hardwoods 



6 0.75 0.50 



8 .90 .80 



10 1.00 .90 



12 + 1.00 1.00 



For example, in 1962 the cutting rate for 6-inch softwoods 



in the South was 34.8 percent of the net growth. The 

 AC factor is: 



AC = -^%--^^^ = + .0109 



Cutting rates used to distribute the softwood in the South 

 cut by size of timber expressed as a proportion of net 

 growth were as follows: 



D.b.h. class 1962 1980 2000 



6 0.348 0.538 0.750 



8 .484 .681 .900 



10 .574 .776 1.000 



12 .687 .835 1.000 



14 .662 .822 1.000 



16 .667 .825 1.000 



18 .701 .842 1.000 



20 .714 .849 1.000 



22+ .899 .947 1.000 



The higher cutting rate for 12-inch trees than for 14-inch 

 trees reflects an overlap of heavy cutting for both pulp- 

 wood and saw logs. 



Sapling ingrowth. Ingrowth of saplings was defined as 

 the number of trees that grew to be 1.0 inch or larger 

 during the year of estimate. This was computed as 

 shown in equation 3 under sapling mortality. In the 

 illustration for East Gulf Softwoods, ingrowth was 

 664,735,000 trees per year (column 6). 



For planted ingrowth it was assumed that for each 

 1,000 seedlings distributed to landowners 600 would 

 survive to enter the 1.0 inch and larger stands in 5 years 

 in the South, and in 7 years elsewhere. During the period 

 1958-62, for example, the average annual area planted 

 in the South was 1,262,029 acres. It was assumed that 

 if this rate of planting continued, plantations would 

 contribute 757 million trees to the annual ingrowth. 



Net volume per tree. Average volumes per tree in 

 board feet and cubic feet, by 2-inch diameter class, were 

 based on data from the most recently completed forest 

 survey. It was assumed that volumes per tree would 

 remain constant throughout the updating and projecting 

 computations. 



Forest areas. Inventory and input factors were entered 

 in terms of numbers of trees per acre of commercial forest 

 land in the West and per acre of softwood and hardwood 

 types in the East. All computations were first made on 

 a per-acre basis for the output years, and then multiplied 

 by the forest areas in each section to obtain estimates of 

 total growth and inventory. It was assumed that areas 

 would remain constant throughout the projection period 

 except in the South where it was assumed that the shift 

 from softwood to hardwood types would continue at the 

 rate prevailing over the past 10 years. These projected 

 areas in acres were as follows: 



Year 



1953. 



1963 



1970 



1980 



1990 



2000 



Softwood 



Hardwood 



Commercial 



type 



type 



forest area 



81,591 



112,765 



194,356 



80.609 



120,460 



201,069 



79,933 



121,136 



201,069 



78,965 



122,104 



201,069 



77,993 



123,076 



201,069 



77,017 



124,052 



201,069 



Computations 



The following programed computations were used with the above input data to obtain estimates of growth and 

 inventory in each of the output years, as follows: 



1. Number of trees at the end = Number of trees at the ± 



of the year beginning of the year 



2. Change in number of trees = Net growth 



during the year 



3. Net growth = Potential increase 



:The change in number 



of trees during the year 

 -Timber cut 



4. Potential increase 



5. Ingrowth 



6. Ingrowth rate 



7. Stand-structure quotient 



8. Accumulative inventory 



9. Outgrowth 



10. Mortality 



11. Mortality rate 



= Ingrowth 



= Ingrowth rate 



= Antilog of 



= Accumulative inventory 

 in the next smaller 

 stand size 



= Sum of all trees x.O 

 inches and larger, for 

 example, number of 

 trees 1.0 inch and 

 larger, 3.0 inches and 

 larger, 5.0 inches and 

 larger, etc. 



= Ingrowth into the next 

 larger stand size 



= Number of trees at the 

 beginning of the year 



= Number of trees that 

 die during the year 



— Mortality 



— Outgrowth 



X Accumulative inventory 



Logarithm of the stand 



structure quotient 



^Accumulative inventory 



— Growth on 

 mortality 



— Growth on 

 timber cut 



X Average annual — 1 

 radial growth 



X Mortality rate 



-f- Number of trees at the 

 beginning of the year 



