,-:- United States 

la ,& Deqartrnent of 

Agr~culture Simulated Yields for Managed 

Forest Service Northern Hardwood Stands 

Northeastern Forest 

Experiment Station Dale S. Solomon 

Research Paper 

N E-578 

William B. Leak 
The Authors 

Dale S. Solomon joined the Northeastern Forest Experiment Station in 

1962. He is engaged in mensurational research on the growth and yield of 

northern species in the Northeast at the Station's laboratory at Orono, 

Maine. 

William 6. Leak joined the Northeastern Station in 1956. He is engaged 

in silvicultural research at the Station's Forestry Sciences Laboratory at 

Durham, New Hampshire. 

Manuscript received for publication June 6, 1985. 

Abstract 

Board-foot and cubic-foot yields developed with the forest growth 

model SlMTlM are presented for northern hardwood stands grown with and 

without management. SlMTlM has been modified to include more accurate 

growth rates by species, a new stocking chart, and yields that reflect 

species values and quality classes. Treatments range from no thinning to 

intensive quality product management over a range of sites. 
Introduction 

Yield tables that show merchantable stand 

volumes by age are basic to the practice of even-age 

timber management. They provide estimates of future 

volumes that are useful in regulating the yields from a 

forest, estimating rotation ages, and calculating 

management options. 

Most yield tables are for fully stocked unmanaged 

stands. They were developed by measuring volumes in 

a series of well-stocked stands of different ages, and 

then graphing or regressing volume over age-usually 

for separate site classes. Although useful for extensive 

management, unmanaged stand yield tables cannot be 

used to estimate yields or rotations for managed or 

thinned stands. 

In the United States, few forest stands have been 

managed long enough for the development of managed 

yield tables for any forest type. The best alternative is 

computer simulation models. A computer model was 

developed for northern hardwoods in New England that 

included substantial data on stocking and growth 

response (Solomon 1977a,b,c). From this model, 

managed yield tables have been developed that show 

thinning and harvest yiel'ds (board feet and cubic feet) 

by species and quality classes for three site index 

classes and five thinning regimes. The species 

composition of the stands used to predict yields 

depicts northern hardwoods as composed of less than 

25 percent softwoods and approximately equal 

amounts of beech, birches, maples, and other 

associated hardwood species (Table 1). The merchantability limits were 4 inches inside bark for 5-inch-d.b.h. 

pulpwood and 6 or 8 inches inside bark at the smallest 

end for softwood and hardwood sawtimber, respectively. The log rule used was the International 114-inch 

saw kerf for 9.0-inch-d.b.h. softwood and 11 .O-inchd.b.h. hardwood sawlogs. 

The Model 

The original model was described for managed 

and unmanaged sapling (SIMSAP) and poletimbersawtimber (SIMTIM) northern hardwood stands 

(Solomon 1977a). The overall framework of the model 

continues to be a distance-independent average-stand 

model, though numerous changes have been made. 

Input consists of site index, specifications on the thinning regime, and the stand characteristics of age, 

basal area, quadratic mean stand diameter, and percent 

of basal area by size, species, and quality. The model 

projects all of these stand characteristics by positioning the stand within the northern hardwood stocking 

chart (Fig. 1) and relating stand development to 

stocking. The lines in Figure 1 are developed from 

trees within the main crown canopy of northern hardwood stands. The main crown canopy is defined as all 

trees on the plot that are not overtopped or suppressed. The revised model incorporates additional 

growth data, growth rates by species, a new stocking 

guide, and conversion to board feet and cubic feet. 

QUALITY LINE m l r r 

TREES PER ACRE 

Figure 1.-Stocking chart for northern hardwoods is based on trees in the main crown 

canopy. The A line is average maximum stocking. The B line is recommended minimum stocking for adequate growth response per acre. The C line defines the minimum amount of acceptable growing stock for a manageable stand. The quality line 

defines the stocking measure in young stands for maintaining quality development. 
The model SlMTlM is written in Fortran-77 and 

can be used interactively or by batch on any mainframe, microcomputer, or minicomputer that is 

MSlDOS compatible and has a minimum of 128K bytes 

of storage. Use of the model requires input for the 

following: 

Job No-Indicates number of jobs or different sets of 

stand conditions to be used as input (1 to 

999). 

Title-Eighty characters used to separate jobs and 

identify management to be conducted on 

each stand. 

Site-Site index of stand (site must be between 40 and 

80). 

POL'EN-Average number of trees per acre in stand (25 

to 1,500 trees). 

BA-Basal area in square feet to nearest hundredth 

square foot (20 to 130 ft2). 

POLED-Quadratic mean stand diameter to nearest 

tenth of an inch (4 to 20 inches). 

YEARS-Stand age in years. 

SPQU-List species composition by quality classes of 

I, II, or Ill in following order: beech, yellow 

birch, sugar maple, red maple, paper birchaspen, white ash, conifer, other. One quality 

class per line expressed to nearest tenth of 

a percent. 

SPQUC-Order of removal of species from the quality 

class 3 x 8 matrix. Numbers from 1 to 24 are 

arranged in priority of removal. 

THSPLT-Point in SPQUC for user to switch from 

complete species-quality class removal to 

proportional removal of remaining species 

quality classes. This maintains species composition and quality of species. 

ITHIN-Regulates thinning by basal area in stocking 

chart: 

0-No thinning 

1-Thin when stand reaches A line 

2-Thin when stand reaches user-specified basal 

area above B line. Enter amount of basal area 

above B line to begin thinning. 

QTH-Thinning to quality line in Figure 1: 

1-Thin to B line for all mean stand diameters. 

2-Thin to 80 ft2 up to 6-inch quadratic mean 

diameter, then thin to B line for stands with 

quadratic mean diameters greater than 6 

inches. 

PBMAX-Paper birch removal: 

0-Paper birch mortality is removed between age 

80 and 100. Removal is shown in thinnings 

after age 70. 

1-User harvests paper birch. 

THDBH-Quadratic mean diameter to the nearest tenth 

of an inch for thinning to begin. 

XHARV-Quadratic mean diameter to the nearest tenth 

of an inch for final harvest. 

XROT-Maximum age in years for final harvest. 

IX-Any odd 9-digit random number used in mortality. 

INTRVL-Reports given at specified intervals (years). 

SAW-Percentage of sawtimber in stand. 

Stand Growth 

The amount of stocking, represented by the basal 

area, number of trees, and quadratic mean stand 

diameter, can be followed through time with the stocking chart (Fig. 1). The growth simulation within the 

model computes the number of trees per acre at both 

the A line and B line. The A line represents a fully 

stocked stand without any form of management. The B 

line is based on optimum stand growth from different 

northern hardwood growth studies. The number of 

trees at both the A line and the B line can be presented as a function of the natural logarithmic value of 

the quadratic mean stand diameter: 

where 

QMD = the diameter at breast height of the tree 

of average basal area. 

The C line represents a managed stand with 

minimum level of acceptable growing stock (sawlog 

potential) that will grow to the B line in 10 years. The 

quality line maintains a higher level of basal-area stocking for a smaller quadratic mean diameter. Thinning a 

stand to the quality line provides clear bole form on 

younger, smaller high-quality species. 

The stand growth components of accretion and 

ingrowth (ft21acrelyear) can be expressed as: 

Accretion = 2.153 + 0.005 (In BA) - 0.0076 (SAW) 

lngrowth = 3.200 - 0.643 (In BA) -' 0.0012 (SAW) 

where 

BA = Residual basal area in square feet 

SAW = Percentage of stanct in sawtimber-size 

trees 

Accretion = Dbh increment in basal area of trees 

present at the initial inventory, plus 

ingrowth accretion. ' 

lngrowth = Trees that grew larger than threshold 

size (5.0 inches) between inventories. 
The R2 values were 0.73 and 0.97; the standard 

errors of the mean were 0.0187 and 0.0138, respectively. These growth equations are based on information from managed stands of northern hardwoods 

(Marquis 1969; Solomon 1977b). The residual basal 

areas ranged from 20 to 100 ft2 for these stands that 

were 20 to 80 years old. The percentage of sawtimber 

ranged from zero to 60. Stand mortality increases as 

the basal area and mean stand diameter increase. 

Thus, as the stand grows from the B line to the A 

line, mortality increases. Our estimate of actual stand 

mortality is based on the assumption that mortality at 

minimum stocking (the B line) is zero, and that 

mortality of a stand above the B line is in some way 

proportional to its position between the A line and B 

line. 

BA - BAB 

Stand mortality = 

where 

BA = basal area of stand 

BAB = basal area at B line 

BAA = basal area at A line 

GG = gross growth 

BAGA = annual net basal-area growth at A line 

MF = mortality factor 

X = a random exponent between 1 and 1.5. 

When X = 1, mortality is computed in direct proportion to the position of the stand between'the A line 

and B line. When X is greater than 1, the mortality rate 

increases as the A line is approached and passed. The 

mortality factor (MF) ranged from - 2.5 for stands with 

basal areas of 60 ft2 or less up to 2.0 for stands with 

100 ft2 or more. 

Species Growth 

Stand growth provides the forest manager with an 

estimate of the growth.of northern hardwood stands. 

However, as species composition changes, the growth 

rate of any species may increase or decrease. Growth 

rates by species were computed and followed through 

the model as the user controls species composition 

(Marquis 1969; Solomon 1977b). Thus, stand growth, as 

computed from accretion, ingrowth, and mortality, is 

proportioned into species growth rate based on the 

residual basal area of.the stand, size class, and percent 

of species composition. Therefore, changing species 

composition does not change stand growth, but 

changes the amount of growth allotted to individual 

species. 

Yields 

The growth rates of the combined species were 

compared to the stand growth and calculated as boardfoot and cubic-foot yields at the time of harvest. Intermediate thinnings also are reported as a separate part 

of the total yield of the managed stand. Square feet of 

basal area is converted to both cubic feet and board 

feet based on the quadratic mean stand diameter (Leak 

1980). Thus, the yields by species are based on the percentage of a species in the total basal area. The cubic 

feet per square foot of basal area give the total cubic 

feet; similarly, the board feet per square foot give the 

board feet. Then the board feet divided by the board 

feetlcubic feet ratio gives the amount of cubic feet in 

the sawtimber yields. By subtracting this amount from 

the total yield, we can estimate amount of cubic feet in 

pulp, cull, or extra sawtimber. 

Thinning options 

The major species that made up the northern hardwood stand used to construct the model and 

presented in the yield tables were: 

Yellow birch-Betula alleghaniensis Britton 

Sugar maple-Acer saccharum Marsh. 

White ash-fraxinus americana L. 

Paper birch- Betula papyrifera Marsh. 

Other: 

Red maple-Acer rubrum L. 

Beech-~agus grandifolia Ehrh. 

Aspen-Populus tremuloides Michx. 

Conifer 

Hemlock- Tsuga canadensis (L.) Carr. ., 

Red spruce-Picea rubens Sarg. , 

To provide forest managers with examples of 

yields from northern hardwood stands, five thinning 

regimes were modeled: 

1. No thinning: The stands were allowed to develop 

naturally. 

2. Quality-line thinning (Fig. 1): Up to 6 inches quadratic mean diameter; stands that reached the A.line 

were thinned to 80 ft2 of residual basal areas: The 

higher basal area in the smaller sized and younger 
Results 

stand assured more height growth and increased 

natural pruning. Above 6 inches quadratic mean 

stand diameter, stands were thinned to B line 

whenever the basal area reached 30 ft2 above the B 

line (approximately two-thirds of the distance from 

B line to A line). 

3. 7-inch thinning: Stands were thinned to B line after 

mean stand diameter reached 7 inches and whenever the basal area exceeded the B line by 30 ft2. 

The delay in the start of thinning to 7 inches quadratic mean stand diameter allowed for an increase 

in merchantable-size products prior to the start of 

thinning. A comparison to the more frequent thinning methods can be made. 

4. 9-inch thinning: Stands were thinned to B line after 

quadratic mean stand diameter reached 9 inches 

and whenever the basal area exceeded the B line by 

30 ft2. The delay in the start of thinnings to 9 inches 

quadratic mean stand diameter allowed for an 

increase in merchantable size products prior to the 

start of thinnings. This thinning method might be 

used in remote areas or stands where frequent 

harvesting is not desirable. 

5. A-line thinning: Stands were thinned once to 

80 ft2 of residual basal area, between 5 and 6 inches 

mean stand diameter. Above 6 inches mean 

diameter, the stands were thinned to B line whenever the basal area reached the A line. 

All runs began at 4.0 inches mean stand diameter, 

91 ft2 of basal area per acre, and ages of 25, 30, and 35 

years, respectively, for site indexes 70, 60, and 50 feet 

(site index for sugar maple at breast-height age 50). 

Stands were grown to 18.0 inches quadratic mean 

stand diameter. 

Initial species composition varied by site index, 

based on available information on the relation of 

species to habitat (Leak 1978). The general form of the 

model recognizes three quality classes. Quality I stems 

are those with the potential to produce at least one 

sawlog now or in the future. Quality II stems are those 

with no sawlog potential. Quality Ill is cull. The proportion of basal area in potential quality I, II, and Ill steins 

was set at approximately 60, 30, and 10 percent, 

respectively (Table 1). To investigate yields from managed stands, quality II and Ill were combined. Also, to 

follow the yield by low- or high-value species, the highvalue species of white ash, sugar maple, yellow birch, 

and paper birch were analyzed separately. The lowvalue species were grouped into a single category of 

"other". 

The yield tables in both gross board feet and 

gross cubic feet by site index and thinning method are 

in Tables 6-21. In this section we provide general 

interpretations about the influence of thinning on yield 

and quality; no deductions were made for defect or 

cull. 

Cubic-foot production (thinned plus residual 

volumes) up to a quadratic mean diameter of 14 inches 

increased by approximately 30 to 50 percent by thinning compared to no thinning (Table 2). The amount of 

increase varied moderately with thinning intensity-the 

number of thinnings and the time of the first entry. By 

contrast, board-foot production up to 14 inches 

quadratic mean stand diameter was increased no more 

than 12 to 14 percent by thinning (Table 3). Almost no 

differences were observed among methods of management. One-third to one-half of the total cubic-foot or 

board-foot production comes from thinning. 

The important differences in productivity among 

thinning regimes became evident when the time 

required to reach a given quadratic mean stand 

diameter was taken into account. Mean annual increment in cubic feet (volume divided by years) up to 14 

inches mean stand diameter was increased by at least 

100 percent by quality-line thinning compared to no 

thinning; mean annual board-foot increment increased 

by about 50 to 100 percent (Table 3). Annual board-foot 

increments were about 20 to 40 percent greater under 

quality-line thinning than under A-line thinning, and 

cubic-foot yields were 30 to 60 percent greater. The 

response to thinning, expressed in percent, was 

greater on the poorer sites. 

Age of culmination of mean annual board-foot 

increment without thinning increased from about 100 

to 120 years as site index decreased from 70 to 50 feet; 

the corresponding mean stand diameter at the point of 

culmination decreased from 14 to 10 inches as site 

index decreased (Table 4). The thinning treatments 

resulted in a slight to moderate increase in culmination 

age and diameter for site index 50. Thinning slightly 

decreased culmination age for site 70, but increased 

the corresponding culmination diameter by as much as 

4 inches. On site 60, thinning increased culmination 

diameter slightly and, in most cases, caused a slight 

decrease in culmination age. Mean annual board-foot 

increment was increased through thinning by about 50 

to 100 percent on site 50, and by 25 to 50 percent on 

site 70; there were intermediate gains on site 60. 

Age of culmination of mean annual cubic-foot 

increment was less than 40 to 60 years under no thinning (Table 4). Culmination age and stand diameter 

were roughly doubled by thinning. Thinning increased 

mean annual increment by 40 to 60 percent, with the 

greatest increase on the better sites. However, lowintensity thinning methods had only a slight to moderate increase in mean annual increment. Culmination 
Lit lerature Cited 

ages for board-foot increment under any thinning 

method are only a little longer than those for cubicfoot increment. 

Stand value is reflected by the proportions of highvalue species and high-quality stems. On site index 50, 

the proportion of board-foot volume in high-value 

species and grade I stems changed from 11 percent 

without thinning to 14 percent with A-line thinning 

(Table 5). On sites 60 and 70, the proportion of highvalue basal area ranged from about 50 percent without 

thinning to about 75 percent with thinning. Differences 

among sites were substantial, primarily because 

species composition varied between sites. Although 

thinning produced a substantial increase in high-value 

yield on sites 60 and 70, differences among thinning 

regimes were not large. However, consideration should 

be given to the differences in species composition in 

Table 1. More yellow birch was in the species composition on site index 60 and more white ash was present 

on site index 70. 

Conclusion 

SlMTlM was used to develop a series of managed 

yield tables for even-aged northern hardwood stands 

over a range of thinning methods and site indexes. 

SlMTlM provides estimates of board-foot and cubicfoot yields by species and quality. 

lntensive thinning increased total mean annual 

yields by at least 100 percent for cubic-foot volumes, 

and by 50 to 100 percent for board-foot volumes. Thinning had little effect on rotation length (culmination of 

mean annual increment) for board-foot volume, but 

nearly doubled rotations for cubic-foot volume. 

Optimum rotations for intensively thinned stands 

ranged from about 80 to 90 years for cubic-foot production and 90 to 125 years for board-foot production on 

sites 70 to 50, respectively. Intensive thinning on sites 

60 and 70 raised the proportion of quality I high-value 

species from about 50 to 75 percent. 

The managed yield tables for northern hardwoods 

should prove useful to forest managers as well as 

those engaged in research on economic returns. An 

example of the program output is given in Table 21. 

The computer program described in this publication is available on request with the understanding 

that the US. Department of Agriculture cannot assure 

its accuracy, completeness, reliability, or suitability for 

any other purpose than that reported. The recipient 

may not assert any proprietary rights thereto nor represent it to anyone as other than a Government-produced 

computer program. For cost information, please 

write: Northeastern Forest Experiment Station, USDA 

Building-University of Maine, Orono, Maine 04469. 

Leak, W. B. Relationship of species and site index to 

habitat in the White Mountains of New Hampshire. 

Res. Pap. NE-397. Broomall, PA: U.S. Department of 

Agriculture, Forest Service, Northeastern Forest 

Experiment Station; 1978. 

Leak, William B. Rapid economic analysis of northern 

hardwood stand improvement options. Res. Note 

NE-296. U.S. Department of Agriculture, Forest 

Service, Northeastern Forest Experiment Station; 

1980. 

Marquis, David A. Thinning in young northern hardwoods: 5-year results. Res. Pap. NE-139. Upper 

Darby, PA: U.S. Department of Agriculture, Forest 

Service, Northeastern Forest Experiment Station; 

1969. 

Solomon, Dale S. A growth model of natural and silviculturally treated stands of even-aged northern hardwoods. USDA For. Serv. Gen. Tech. Rep. NE-36. 

Broomall, PA: US. Department of Agriculture, Forest 

Service, Northeastern Forest Experiment Station; 

1977a. 

Solomon, Dale S. The influence of stand density and 

structure on growth of northern hardwoods in New 

England. Res. Pap. NE-362. Broomall, PA: US. 

Department of Agriculture, Forest Service, Northeastern Forest Experiment Station; 1977b. 

Solomon, Dale S. Growth rates of northern hardwoods 

under uneven-age management. Northern Logger. 

25(8): 18, 38; 1977c. 
Table 1.-Initial species composition (at 4.0 inches mean d.6.h.) in percent of basal area, by site index and 

quality class 

Site Quality Yellow Sugar Red Paper White 

index classa Beech birch maple maple birch ash Conifer Other All 

-- 

aQuality class I: sawlog orveneer potential in at least one 16-foot log; class II: no veneer or sawlog potential; class Ill: cull trees. 

Table 2.-Residual and cumulative thinned volume per acre at 14 inches quadratic me&diameter (QMD),, 

by thinning method and site index 

Thinning 

Method No. 

No thinning 0 

Quality line 5 

7 inch 3 

9 inch 2 

A line 2 

Site index 50 

Begin 

QMD 

Thinned Residual All 

- - - - - - - - - - - - 2595 2595 

5.2 21 28 1738 3866 

7.1 1633 1990 3623 

9.1 1284 2069 3353 

5.2 1880 1485 3365 

Site index 60 Site index 70 

Thinned Residual All 

. - - - - - - - - - - - ,Ct31acre- ------- - 3102 3102 

2602 2011 4613 

1959 2369 4328 

1570 2374 3944 

1002 2991 3993 

Thinned Residual All 

..................... Board feetlacre ------------- ;- ------- 

No thinning 0 - - 10959 10959 - 13048 13048 - 15079 15079 

Quality line 5 5.2 4596 7502 12098 5633 8449 14082 6650 10139 16789 

7 inch 3 7.1 3928 8538 12466 4660 9957 14617 5790 11251 17041 

9 inch 2 9.1 3630 8789 12419 4517 9977 14494 5044 12025 17069 

A line 2 5.2 5572 6464 12036 1527 12573 14100 1722 14620 16342 

Table 3.-Years to reach 14 inches quadratic mean diameter and mean annual increment per acre, 

by thinning method and site index 

Site index 50 Site index 60 Site index 70 

Thinning 

method Board Cubic Board Cubic Board Cubic 

Years feet feet Years feet feet Years feet feet 

No thinning 236 46.4 11 .O 157 83.1 19.8 102 147.8 35.1 

Quality line 124 97.6 31.2 95 148.2 48.6 77 218.0 70.2 

7 inch 137 91 .O 26.4 101 144.7 42.9 80 213.0 62.3 

9 inch 154 80.6 21.8 110 131.8 35.9 86 198.5 53.5 

A line 181 66.5 18.6 119 118.5 33.6 88 185.7 52.4 
Table 4.-Approximatea mean annual increment (MAI) to the point of culmination in age 

and quadratic mean diameter (QMD) 

Thinn,ing 

method 

Ft3 

No thinning 21.8 

Quality line 30.9 

7 inch 25.2 

9 inch 21 .O 

A line 24.3 

Site 50 

Culmination 

Age QMD 

Years lnches 

< 59 < 6 

105 12 

119 12 

129 12 

98 10 

Site 60 - 

Culmination 

Age QMD - 

Years lnches 

< 49 < 6 

95 14 

101 14 

110 14 

78 10 

Site 70 

Culmination 

Age QMD 

Years lnches 

< 41 < 6 

77 14 

80 14 

86 14 

75 12 

Board Board Board 

feet Years Inches Feet Years inches feet Years Inches 

No thinning 46.3 120 10 85.8 114 12 147.8 102 14 

Quality line 97.6 124 14 148.2 95 14 227.3 92 18 

7 inch 91 .O 137 14 144.7 101 14 216.8 89 16 

9 inch 80.6 154 14 131.8 110 14 198.5 86 14 

A line 67.5 133 12 118.5 119 14 185.7 88 14 

aculmination determined directly from yield tables in this publication, without interpolation between age or diameter intervals; 

culmination is defined as the point where MA1 is within about 1 ft3 or 7 board feet of maximum. 

Table 5.-Percentage board-foot volume (thinned plus standing volume) at a quadratic mean diameter of 14 

inches in high-value and low-value speciesa and in quality classes I and Ilb, 

by thinning method and site index 

Site index 50 Site index 60 

High value Low value High value Low value 

Thinning 

method I II All I II All I I1 All I II All 

Nothinning 11 7 18 52 30 82 49 34 83 10 7 17 

Quality line 12 - 12 88 - 88 83 - 83 17 - 17 

7 inch 13 2 15 82 3 85 77 5 82 17 1 18 

9 inch 14 3 17 73 10 83 71 12 83 15 2 17 

A line 14 4 18 80 2 82 76 8 84 16 - 16 

Site index 70 

High value Low value 

I II All I I1 All 

a High-value species: white ash, sugar maple, yellow birch, and paper birch; low-value species: beech, red maple, conifers, and miscellaneous. 

b Quality class I: sawlog or veneer potential in at least one 16-foot log; class II: no sawlog or veneer potential (includes cull trees). 
Table &-Residual volumes per acre, by species and quality class (I and II), for no thinning and site index 50 

White ash Sugar maple Yellow birch Paper birch Other Combined 

Mean Residual - 

d.b.h. basal 

(inches) Age area I I I I I I I I I I I I I I I I I I All 

Years 
Table 7.-Residual volumes per acre, by species and quality class (I and 11) for no thinning and site index 60 

White ash ' Sugar maple Yellow birch Paper birch Other Combined 

Mean Residual 

d.b.h. basal 

(inches) Age area I I I I I I I I1 I I I I II . I I I All 

Years Ft2 

30 9 1 

49 102 

67 107 

87 110 

114 113 

157 116 

196 118 

230 119 

Board feetlacre----- - - - - - - 

484 357 285 

969 441 352 

1622 - - 

21 64 - - 

21 98 - - 

2225 - - 
Table 8.-Residual volumes per acre, by species and quality class (I and II) for no thinning and site index 70 

White ash Sugar maple Yellow birch Paper birch Other Combined 

Mean Residual 

d.b.h. basal 

(inches) Age area I I I I I I I I I I I I I I I I I I All 

Years Ft2 ..................... Ft3Iacre- -- - - ---- - - ----- - ---- 

-------- Board feetlacre----- 

- - - - - - 

134 436 291 

227 910 607 

361 1032 688 

559 - - 

571 - - 

58 1 - - 
Table 9.-Residual and cumulative thinneda volume per acre for quality-line thinning and site index 50 

White ash Sugar maple Yellow birch Paper birch Other Combined 

Mean Residual d.b~-,, basal Thin Residual Thin Residual Thin Residual Thin Residual Thin Residual Thin Residual -- (inches) area 

Aae I II I II I II I II I tl I II I II I II I II I II I II All I II All 

4 35 91 - - - - - - - - - - - - ------------ - - 65799- - - -- - 23 11 - 10 106 59 - 14 184 92 - 202 581 102 - 226 226 894 264 1158 

87465- - - - 13 11 23 - 54 69 97 - 99 106 182 - 356 304 694 - 522 490 1012 996 - 996 

10 8992 - - - - 13 11 36 - 54 69 143 - 99 106 135 - 356 304 1294 - 522 490 1012 1608 - 1608 

1210587 - - - - 24 11 36 - 99 69 140 - 142 106 - - 765 304 1549 - 1030 490 1520 1725 - 1725 

1412478 - - - - 37 11 34 - 149 69 131 - 142 106 - -1310 304 1573 - 1638 490 2128 1738 - 1738 

1614766 - - - - 50 11 29 - 199 69 111 - 142 106 - - 1905 304 1329 - 2296 490 2786 1469 - 1469 

1816282 - - - - 50 11 36 - 199 69 139 - 142 106 - - 1905 304 1659 - 2296 490 2786 1834 - 1834 

------------------- Board feellacre ..................... 4 35 91 - - - - - - - - - - - - ------ ------- - 6 57 99 - - - - - - - - - - -------- ------- - 87465- - - - 17 - 44 - 71 - 188 - 133 - 354 - 505 - 1386 - 726 - 726 1972 - 1972 

10 8992 - - - - 17 - 104 - 71 - 407 - 133 - 384 - 505 - 3799 - 726 - 726 4694 - 4694 

1210587 - - - - 50 - 129 - 200 - 506 - 254 - - -1707 - 5774 - 2211 - 2211 6409 - 6409 

1412478 - - - - 98 - 141 - 388 - 552 - 254 - - - 3856 - 6809 - 4596 - 4596 7502 - 7502 

16 147 66 - - - - 151. - 119 - 597 - 466 - 254 - - - 6433 - 5755 - 7435 - 7435 6340 - 6340 

18 162 82 - - - - 151 - 149 - 597 - 582 - 254 - - - 6433 - 7181 - 7435 - 7435 7912 - 791 2 

a Six thinnings at mean d.b.h. 5.2,6.0,7.8,10.0,12.7, and 15.9. 
Table 10.-Residual and cumulative thinneda volume per acre for quality-line thinning and site index 60 

White ash Sugar maple Yellow birch Paper birch Other Combined 

Mean Residual 

d.b.h. basal Thin Residual Thin Residual Thin Residual Thin Residual Thin Residual Thin Residual 

(inches) area 

Age I II I II I II I II I II I II I II I II I II I II I II All I II All 

Years Ft2 ---------------------Ft3/acw--------------------- 

4 30 91 - - ---- ---- ---- ---- ---- - - - 

6 48 93 - - 24 24 - 51 353 177 - 117 386 106 - 18 129 77 - 83 142 - - 269 269 1034 384 1418 

8 61 66 15 24 32 - 201 228 406 - 212 222 421 - 78 95 158 - 85 83 172 - 591 652 1243 1189 - 1189 

10 72 91 15 24 53 - 201 228 668 - 212 222 643 - 78 95 254 - 85 83 294 - 591 652 1243 1912 - 1912 

12 83 85 33 24 58 - 414 228 745 - 417 222 679 - 159 95 222 - 179 83 335 - 1202 652 1854 2039 - 2039 

14 95 75 55 24 63 - 701 228 81 1 - 678 222 738 - 207 95 33 - 309 83 366 - 1950 652 2602 201 1 - 201 1 

16 107 91 55 24 79 - 701 228 1004 - 678 222 913 - 207 95 - - 309 83 453 - 1950 652 2602 2449 - 2449 

18 119 78 81 24 67 - 1026 228 855 - 973 222 777 - 207 95 - - 455 83 386 - 2742 652 3394 2085 - 2085 

- -------------------Board feet/acre--------------------- 

4 3091 - - - - - - ---- - - - - - - - - ---- - - - - 6 48 93 - - ---- ---- - - - - - - - - ---- - - - - 8 61 66 23 - 58 - 305 - 756 - 319 - 783 - 119 - 293 - 129 - 321 - 895 - 895 2211 - 2211 

10 72 91 23 - 153 - 305 - 1910 - 319 - 1840 - 119 - 728 - 129 - 840 - 895 - 895 5471 - 5471 

12 83 85 73 - 213 - 927 - 2695 - 918 - 2454 -- 357 - 802 - 405 - 121 1 - 2680 - 2680 7375 - 7375 

14 95 75 162 - 268 - 2060 - 3408 - 1950 - 3100 - 546 - 1135 - 915 - 1538 - 5633 - 5633 8449 - 8449 

16 107 91 162 - 332 - 2060 - 4217 - 1950 - 3836 - 546 - - - 915 - 1904 - 5633 - 5633 10289 - 10289 

18 119 78 269 - 283 - 3424 - 3590 - 3191 - 3266 - 546 - - - 1530 - 1621 - 8960 - 8960 8760 - 8760 

aSix thinnings at mean d.b.h. 5.2,6.1,7.8, 10.2, 13.1, and 16.5. 
Table 11.-Residual and cumulative thinneda volume per acre for quality-line thinning and site index 70 

White ash Sugar maple Yellow birch Paper birch Other Combined 

Mean Residual 

d.b.h. basal Thin Residual Thin Residual Thin Residual Thin Residual Thin Residual Thin Residual 

(inches) area 

Ane I 11 I 11 I 11 I 11 I 11 1 11 I 11 I II I II I I ' I II All I II All 

Years Ft2 

4 25 91 

6 40 93 

8 50 67 

10 59 91 

12 68 85 

14 77 76 

16 85 92 

18 92 78 

aSix thinningsat mean d.b.h. 5.2,6.2, 7.9, 10.2, 13.1,and 16.6. 
Table 12.-Residual and cumulative thinneda volume per acre for 7-inch thinning and site index 50 

White ash 

Mean Residual 

d.b.h. basal Thin 

(inches) area 

Age I I1 

Years Ft2 

4 35 91 

6 59 103 

8 78 78 

10 95 75 

12 119 64 

14 137 89 

16 157 78 

18 177 94 

Sugar maple Yellow birch Paper birch Other Combined 

Residual Thin 

I I1 I II 

a Fourthinningsat mean d.b.h. 7.1, 9.1, 11.6,and 14.6. 

Residual Thin 

I II 

- - - - - - - 

- - 

- - 

4 67 

55 67 

116 67 

116 67 

181 67 

181 67 

Residual 

I II 

Thin 

I II 

-Ft3lacre--- 

- - - - 

8 129 

66 128 

66 128 

66 128 

66 128 

66 128 

Residual 

I II 

. - - - - - - - - - - 

- - 

177 106 

254 - 38 - - - - - - - - - 

Thin 

I il 

. - - - - - - - - 

- - - - 

21 340 

378 340 

878 340 

879 340 

1457 340 

1457 340 

Residual 

I II I 

Thin Residual 

All I II All 
Table 13.-Residual and cumulative thinneda volume per acre for 7-inch thinning and site index 60 

White ash Sugar maple Yellow birch Paper birch Other Combined 

Mean Residual 

d.b.h. basal Thin Residual Thin Residual Thin Residual Thin Residual Thin Residual Thin Residual 

(inches) area 

Aae I II I II I II I II I II I II I II I I1 I II I II I II All I II All 

Years 

30 

49 

64 

76 

90 

101 

114 

128 

Board feetiacre---- -- - - 

-- - - - - 153 416 

- 206 153 684 - 440 153 392 - 440 153 - - 440 153 - 

- 440 153 - 

aFourthinningsat mean d.b.h. 7.1,9.1, 11.7,and 14.9. 
Table 14.-Residual and cumulative thinneda volume per acre for 7-inch thinning and site index 70 

White ash Sugar maple Yellow birch Paper birch Other Combined 

Mean Residual 

d,b,h, basal Thin Residual Thin Residual Thin Residual Thin Residual Thin Residual Thin Residual 

(inches) area 

Ane I II I II I II I II I II I II I II I II I II I II I II All I II All 

42591 ---- -- --- - - - -- ---- --- 

6 41 103 - - 372 263 - - 334 218 - - 95 63 - - 150 100 - - 122 104 - 8 52 77 - 301 595 3 A 226 451 - - 67 128 - - 126 249 - - 114 194 - - 10 62 74 251 301 683 - 177 226 471 - 49 67 128 - 104 126 272 - 87 114 251 - 668 

12 72 94 251 301 976 - 177 226 659 - 49 67 171 - 104 126 383 - 87 114 448 - 668 

14 80 85 557 301 939 - 384 226 643 - 103 67 158 - 224 126 352 - 228 114 562 - 1496 

16 89 73 880 301 837 - 605 226 576 - 157 67 141 - 305 126 111 - 444 114 629 -2391 

18 97 88 880 301 994 - 605 226 684 - 157 67 168 - 305 126 35 - 444 114 886 - 2391 

-------------------Board feet/acre--------------------- 

42591 -- -- -- --- - - - -- ---- --- 

6 41 103 - - - - -- --- - - - -- ---- --- 

8 52 77 - 381 1096 5 - 285 830 - - 85 236 - - 159 458 - - 144 376 - - 10 62 74 634 391 1961 - 448 285 1352 - 125 85 368 - 263 159 782 - 231 144 752 - 1701 

12 72 94 634 391 3544 - 448 285 2392 - 125 85 620 - 263 159 1389 - 231 144 1692 - 1701 

14 80 85 1746 391 3947 - 1199 285 2703 - 320 85 665 - 699 159 1480 - 762 144 2456 - 4726 

16 89 73 3103 391 3519 - 2128 285 2420 - 549 85 593 - 1040 159 466 - 1707 144 2759 - 8527 

18 97 88 3103 391 4179 - 2128 285 2874 - 549 85 704 - 1040 159 146 - 1707 144 3899 - 8527 

a Four thinningsat mean d.b.h. 7.1,9.3, 12.1,and 15.3. 
Table 15.-Residual and cumulative thinneda volume per acre for 9-inch thinning and site index 50 

White ash Sugar maple Yellow birch Paper birch Other Combined 

Mean Residual 

d.b.h. basal Thin Residual Thin Residual Thin Residual Thin Residual Thin Residual Thin Residual - (inches) area , 

Age I 

Years Ft2 

4 35 91 - 

6 59 103 - 

8 83 107 - 

10 106 79 - 

12 129 71 - 

14 154 93 - 

16 172 80 - 

18 199 96 - 

II All I II All 

"Three thinnings at mean d.b.h. 9.0, 11.3, and 14.2. 
Table $6.-Residual and cumulative thinneda volume per acre for 9-inch thinning and site index 60 

White ash Sugar maple Yellow birch Paper birch Other Combined 

Mean Residual 

d.b.h. basal Thin Residual Thin Residuat Thin Residual Thin Residual Thin Residual Thin Residual 

(inches) area -- 

Age I II I II I II I II I II I II I II I II I II I II I II All I II All 

Years Ft2 ---------------------Ft3/am--------------------- 

aThreethinningsat mean d.b.h.9.1, 11.6,and 14.7. 
Table 17.-Residual and cumulative thinned" volume per acre for 9-inch thinning and site index 70 

White ash Sugar maple Yellow birch Paper birch Other Combined 

Mean Residual 

d.b.h. basal Thin Residual Thin Residual Thin Residual Thin Residual Residual Thin Residual Thin 

(inches) area 

Aae I II I II I II I II I II I I1 I II I II I II I II I II All I II All 

Years Ft2 

25 91 

41 103 

55 107 

67 79 

76 70 

86 91 

94 77 

104 92 

25 91 

41 103 

55 107 

67 79 

76 70 

86 91 

94 77 

104 92 

aThree thinningsat meand.b.h.9.1, 11.5,and 14.7. 
Table 18.-Residual and cumulative thinned' volume per acre (cubic-foot) for A-line thinning and site index 50 

White ash Sugar maple Yellow birch Paper birch Other Combined 

Mean Residual - 

d.b.h. basal Thin Residual Thin Residual Thin Residual Thin Residual Thin Residual Thin Residual 

(inches) area -- 

Age I 11 I I1 I II I II I II I II I II I II I II I II I II All I II All 

Years Ft2 

4 35 91 - 

6 57 92 - 

8 80 105 - 

10 98 89 - 

12 133 106 - 

14 181 64 - 

16 192 87 - 

18 217 102 - 

4 35 91 - 

6 57 92 - 

8 80 105 - 

10 98 89 - 

12 133 106 - 

14 181 64 - 

16 192 87 - 

18 217 102 - 

Board feetlacre----- -- - - 

-- - - 

134 - - 489 

- 89 229 73 

- 89 229 - 

- 89 229 - 

- 89 229 - 

- 89 229 - 

a Three thinnings at mean d.b.h. 5.2, 8.3, and 14.0 inches. 
Table 19.-Residual and cumulative thinneda volume per acre for A-line thinning and site index 60 

White ash Sugar maple Yellow birch Paper birch Other Combined 

Mean Residual 

d,b,h, basal Thin Residual Thin Residual Thin Residual Thin Residual Thin Residual Thin Residual 

(inches) area 

Aae I II I II I II I II I II I II I II I I1 I II I II I II All I II All 

Years Ft2 

4 30 91 

6 48 93 

8 65 105 

10 78 88 

12 94 103 

14 119 112 

16 141 76 

18 158 92 

a Three thinnings at mean d.b.h. 5.2,8.4, and 14.7 inches. 
Table 20.-Residual and cumulative thinneda volume per acre for A-line thinning and site index 70 

White ash Sugar maple Yellow birch Paper birch Other Combined 

Mean Residual 

d,b,h, basal Th~n Residual Thin Residual Thin Residual Thin Residual Thin Residual Thin Res~dual 

(inches) area -- 

Aae I II I II I II I II I II I II I II I II I I1 I II I II All I II All 

- 

aThree thinnings at mean d.b.h. 5.2,8.4, and 16.3. 
Table 21.-Example of model output at the end of poletimber-sawtimber-harvest phase for a typical northern hardwood stand 

Quality-line thinning Stand Number 1 started with: Site = 60 

Number of treeslacre = 1,050 

Basal arealacre = 91 .OO 

Quadratic mean diameter = 4.0 

Age of stand = 30; percent sawtimber = 15 

Species 

Quality 

class BE YB SM RM PB A WA CON OTHER TOTAL 

1 7.0% 23.0% 22.0% 1.0% 5.0% 1.0% 0.0% 0.0% 59.0% 

FT2 6.4 20.9 20.0 0.9 4.5 0.9 0.0 0.0 53.7 

ORDER OF SPECIES CLASS REMOVAL BY PRIORITY 

24 20 17 23 18 19 21 22 16 12 9 15 10 11 13 .14 8 4 

1 7 5 2 3 6 

ITHIN = 2, thin when stand reaches 30. FT2 above the B line 

THINNING SPLOT NUMBER: 17 

Q-LINE THINNING (THIN TO 80 FT2) WILL BE USED UPTO DIAMETER 6 INCHES 

OPERATOR CONTROLS PAPER BIRCH REMOVAL PRIORITY 

DIAMETER AT WHICH THINNING STARTED = 5.0 

ROTATION AGE = 400 

HARVEST DIAMETER = 18.0 

THINNING NO. 1 

Number of trees = 132.401 Quadratic mean diameter = 5.19 BA = 19.45 

Species 

Quality 

class BE YB SM RM PBA WA CON OTHER TOTAL 

Mean diameter for age 49 = 6.096 A-line number of trees present = 520.4 next yr = 504.7 

Number of trees in stand = 460.79 B~line number of trees present = 303.4 next yr = 294.1 

Basal area of stand = 93.40 BA at A line = 101.37 

Percent sawtimber = 0 BA at B line = 59.07 

Table 21. (continued) 
Harvest Yield in Percent 

Species 

Quality 

class BE YB SM RM PBA WA CON OTHER TOTAL 

I 15.2% 37.3% 41.0% 3.3% 0.0% 3.2% 0.0% 0.0% 100.0% 

FT2 11.8 29.0 31.9 2.6 0.0 2.5 0.0 0.0 77.7 

FT3 1 316.2 777.3 854.3 69.5 0.0 67.2 0.0 0.0 2084.4 

BF 1328.8 3266.8 3590.5 292.0 0.0 282.6 0.0 0.0 8760.5 

Total Yield from Thinnings 

Species 

Quality 

class BE YB SM RM PB A WA CON OTHER TOTAL 

Total Yield 

Species 

Quality 

class BE YB SM RM PB A WA CON OTHER TOTAL 

FT2 28.0 72.1 76.9 6.2 10.2 6.0 

FT3 1 687.4 1751.1 1880.5 152.7 207.1 147.7 

BF 2579.1 6458.9 7016.0 571.1 545.5 552.6 

FT2 3.8 11.5 11.6 0.0 5.1 1.6 

FT3 2 53.2 168.9 176.4 0.0 77.1 23.7 

BF 0.0 0.0 0.0 0.0 0.0 0.0 

FT2 1 .O 3.9 3.7 0.0 1.3 0.0 

FT3 3 13.3 53.7 51.2 0.0 18.2 0.0 

BF 0.0 0.0 0.0 0.0 0.0 0.0 

The total harvest per acre (including thinnings) is: 

Basal area: 244. 164 Cubic feet: 5,478.480 Board feet: 17,723.145 
Solomon, Dale S.; Leak, William 6. Simulated yields for managed northern hardwood stands. Res. Pap. NE-578. 

Broomall, PA: U.S. Department of Agriculture, Forest 

Service, Northeastern Forest Experiment Station; 1986. 24 p. 

Board-foot and cubic-foot yields developed with the 

forest growth model SlMTlM are presented for northern hardwood stands grown with and without management. SlMTlM 

has been modified to include more accurate growth rates by 

species, a new stocking chart, and yields that reflect species 

values and quality classes. Treatments range from no thinning 

to intensive quality product management over a range of 

sites. 

ODC: 524.37:62 

Keywords: yields; northern hardwoods; growth; model 

*U.S. GOVERNMENT PRINTING OFFICE:1986-505-026:20043 
Headquarters of the Northeastern Forest Experiment Station are in 

Broomall, Pa. Field laboratories are maintained at: 

Amherst, Massachusetts, in cooperation with the University of 

Massachusetts. 

Berea, Kentucky, in cooperation with Berea College. 

Burlington, Vermont, in cooperation with the University of 

Vermont. 

Delaware, Ohio. 

Durham, New Hampshire, in cooperation with the University of 

New Hampshire. 

Hamden, Connecticut, in cooperation with Yale University. 

Morgantown, West Virginia, in cooperation with West Virginia 

University, Morgantown. 

Orono, Maine, in cooperation with the University of Maine, 

Orono. 

Parsons, West Virginia. 

Princeton, West Virginia. 

Syracuse, New York, in cooperation with the State University of 

New York College of Environmental Sciences and Forestry at 

Syracuse University, Syracuse. 

University Park, Pennsylvania, in cooperation with the 

~enns~lvaiia State University. 

Warren, Pennsylvania.