paa* 7 United States 

Department of $& 

Agriculture Stump-to-Mill Timber 

Forest Service Production Cost Equations 

Northeastern 

Station 

for Cable Logging 

Research Paper Eastern Hardwoods 

Chris B. LeDoux 
The Author 

Chris B. LeDoux is an industrial engineer with the USDA Forest Service, 

Northeastern Forest Experiment Station, Morgantown, West Virginia. - - -- - -- -- -p 

Manuscript received for publication 18 October 1984 

Abstract 

Logging cost simulators and data from logging cost studies have been 

assembled and converted into a series of equations that can be used to 

estimate the stump-to-mill cost of cable logging in mountainous terrain in 

the Eastern United States. These equations include the use of two small and 

four medium-size cable yarders and are appropriate for harvested trees 

ranging in diameter from 6 to 24 inches. Cost components can be determined 

easily with a hand calculator. A program that can be used with many desktop 

computers also is available that calculates the total stump-to-mill logging 

cost for specific logging conditions. 
Introduction 

Cost equations for stump-to-mill timber 

production were developed for logging hardwoods in 

the Eastern United States. The equations are 

applicable only to uphill skyline cable logging. They 

can be used for equipment selection, timber stand 

prescription planning, optimization of silvicultural 

decisions, break-even analysis, and silvicultural 

investment analysis. The equations summarized here 

include equipment that reflects nearly all of the 

conditions a logger or planner would encounter on 

steep, mountainous terrain in the Eastern United 

States. 

The equations were developed by using 1984 new 

equipment, labor, and fuel costs (Table 1); time and 

motion study data from ~aum~rasl andothers (Fisher 

and Peters 1983; Rossie 1983); USDA Forest Service 

regional timber appraisal guides; regression methods 

(Draper and Smith 1966); and simulation analysis 

(LeDoux and Butler 1981). Estimates of yield volume 

were derived from forest model plots.2 Presented 

here are specific cost equations for felling, limbing, 

bucking, yarding, loading, and hauling. The equations 

are exclusive of profit. 

l~aumgras, J. E. Time-study data for the Bitterroot 

Yarder. 1984. Unpublished report on file at the 

Northeastern Forest Experiment Station, 180 

Canfield St., P.O. Box 4360, Morgantown, West 

Virginia 26505. 

zone-acre forest model plot. (No date). 

Unpublished data on file at the Northeastern Forest 

Experiment Station, 180 Canfield St., P.O. Box 4360, 

Morgantown, West Virginia 26505. 

Because the data from which these equations 

were developed are generated by simulators, they do 

not have the degree of variability that one finds in 

empirical cost data. Therefore, the 112 values from 

the regressions are much higher than would result 

from regressions derived from sample data from 

actual field studies. The ~2 values indicate that the 

equations efficiently reproduce the simulator results. 

They do not demonstrate how well the simulation 

results compare with actual costs. 

Felling, Limbing, and Bucking Cost Equation 

Delay-free cost estimates (data points) for 

felling, limbing, and bucking with chain saws were 

developed for a range of diameters of harvested trees 

(Martin 1975). The stands chosen were from forest 

model plots of eastern hardwoods (Table 2). Each 

stand was thinned using a d/D ratio (arithmetic mean 

diameter of cut treeslarithmetic mean diameter of 

stand) of 1.0 to levels of 30 percent, 50 percent, and 

then clearcut. The trees cut from each treatment 

were bucked into log$ and the pooled data points 

(Table 3) used to develop a general equation for 

felling, limbing, and bucking cost by arithmetic mean 

diameter of cut trees: 

~L~DOUX, C. B. Hardwood log bucking simulator. 

1984. Unpublished computer program on file at the 

Northeastern Forest Experiment Station, 180 

Canfield St., P.O. Box 4360, Morgantown, West 

Virginia 26505. 

Table 1.-Hourly yarding costsa for six yarding systems 

Yarding 

system ~~ui~ment~ Labore sawsd Carriage Radio signale Total 

........................... Dollars/hr---------------------------- 

Bitterroot 6.26 13.00 2.65 0.61 1.09 23.61 

Appalachian 

Thinner 14.35 26.00 2.65 0.00 1.09 44.09 

Koller K-300 10.95 32.50 2.65 0.65 1.09 47.84 

Ecologger I 18.81 32.50 2.65 0.72 1.09 55.77 

Urus 1000-3 34.63 32.50 2.65 0.80 1.09 71.67 

Skylok 78 78.13 39.00 2.65 0.88 1.09 121.65 

aIncludes all new equipment (costs obtained from equipment dealers). 

b~ncludes depreciation, insurance, interest, operating costs (fuel, oil, lubricants, 

maintenance, repair, and taxes), and rigging. 

CRates obtained from cost guide for empirical appraisals, USDA Forest Service, 

Region 9, Amendment 112. 

d~hree chain saws. 

eThree transmitters. 
Table 2.-Stand data for forest model plots A2, 

B10, C8, D14, E13, F4, G4M, and H4M 

Forest 

model Average Merchantable Number of 

plot d.b.h.a volum eb trees/acreC 

Inches 

7.2 

8.1 

9.1 

11.6 

12.7 

16.8 

20.4 

24.0 

aTrees 5 inches or larger in d.b.h. included in the average. 

b~ogs less than 4 feet long and less than 4 inches 

top diameter not included as merchantable volume. 

CTrees 5 inches or larger in d.b.h. included. 

Table 3.-Log size parameters by bucking rule for 

forest model plots A2, B10, C8, D14, 

E13, F4, G4M, and H4M 

'Orest Bucking Log size Standard 

rule Mean plot Minimum Maximum deviation 
Yarding Cost Equations 

where: 

DBH = Arithmetic mean tree diameter at breast 

height, in inches 

LN = Natural logarithm 

Variable limits for DBH = 6 to 24 inches The limits on 

the variable diameter (DBH) should be observed carefully. 

Simulated, delay-free data points for yarding cost 

were developed for six uphill cable yarders under a 

wide range of diameters (DBH), volume cut per acre 

(VOAC), and average slope yarding distance (SYD). 

The stand and treatment conditions are identical to 

those used to develop data for felling, limbing, and 

bucking (Tables 2-3). The THIN (LeDoux and Butler 

1981) model and time-study data cited previously 

were used to develop the delay-free data points by 

making numerous simulations. The simulated data 

points were pooled by yarder to develop delay-free 

cost equations for each of the six yarders. Nonlinear 

multiple regression analysis was used to summarize 

the delay-free data points and the independent 

variables (Table 4). 

Table 4.-Simulated delay-free cost equations by yarder for forest 

model plots A2, B10, C8, D14, E13, F4, G4M, and H4M 

Yarder Equation R~ 

Skylok 78 $/ft3 = 0.090775 0.703 

+ 0.000071*(SYD)a 

+ 739.473795* (~/(VOAC*DBH) lb/c 

+ O.594844* (l/DBH) 

Appalachian $/ft3 = -0.089289 

Thinner + 81.991053* (l/VOAC) 

+ 0 .OOO269* (SYD) 

- 496.820821* (l/(VOAC*DBH)) 

+ 1.535553* (l/DBH) 

Urus 1000-3 $/ft3 = 0.203908 

- 0.000387* (DBH~) 

+ l3.160361* (l/VOAC) 

+ O.OOOl44* (SYD) 

Koller K-300 $/ft3 = 0.167004 

- 0.000343* (DBH~) 

+ 0.000146*(SYD) 

Ecologger I $/ft3 = 0 .TO7187 

- 0.050285 * (DBH) 

+ 0.001089*(~~~~) 

+ 33.lOlOl8* (l/VOAC) 

+ O.OOOl68* (SYD) 

- 2.095831*(1/DBH) 

aSYD = Average slope distance, feet; variable limits = 50 to 950. 

b~~~~ = Average volume removed per acre, cubic feet; variable 

limits = 780 to 6,871. 

CDBH = Average tree diameter at breast height, inches; variable 

limits = 7 to 9 for the Bitterroot; 7 to 16 for Koller K-300; 7 to 

24 for all others. 
The equations are yarder specific and rigged in 

the following uphill configurations: Skylok 784 rigged 

as a running skyline; Appalachian Thinner rigged as a 

jammer; Urus 1000-3 rigged as a standing skyline; 

Bitterroot rigged as a shotgun; Koller R-300 rigged as 

a shotgun; and the Ecologger I rigged as a live 

skyline. These types of equipment as rigged reflect 

most of the conditions a logger would encounter on 

steep terrain. Of course, there are many yarding 

machines to choose from so our equipment equations 

are not exclusive. 

Managers must be careful not to mismatch equipment with the size of logs to be removed. Mismatches can result in a combination of high costs and increased stand damage and safety hazards. The cost 

equations assume that the Koller K-300 will not be 

used in stands with trees larger than 16 inches and 

that the Bitterroot will not be used in stands where 

the average d.b.h. exceeds 9 inches. 

Loading Cost Equation 

Delay-free cost estimates (data points) for 

loading were developed with time-study data (Koger 

1982) for a range of diameters of harvested trees. 

The stand and treatment conditions are identical to 

those used to develop equations for felling, limbing, 

bucking, and yarding (Tables 2-3). These data points 

were used to develop the following equation: 

where: 

DBH = Arithmetic mean tree diameter at breast 

height, in inches 

Variable limits for DBH = 6 to 22 inches 

The delay-free cost equation for loading was 

developed from data that represent an average of 

several types of loading machine. Some adjustment 

maybe necessary if these equations are used for 

loading machines that are other than "average." 

4~he use of trade, firm, or corporation names in this 

paper is for the information and convenience of the 

reader. Such use does not constitute an official 

endorsement or approval by the U.S. Department of 

Agriculture or the Forest Service of any product or 

service to the exclusion of others that may be 

suitable. 

Hauling Cost Equation 

Empirical cost data from USDA Forest Service 

regional timber appraisal guides were used to develop 

an equation to predict log hauling costs for a range of 

truck classes operating on a range of road classes. 

The following equation was developed: 

$/ft3/haul mile = - 0.0071667 

+ 0.0008333*TC 

+ 0.0037629*RC 

R~ = 0.792 

where: 

TC = Truck class 

RC = Road class 

Truck class limits are: 

Class Body type 

5 Flat bed, 4x2, single axle 

4 Flat bed, 6x4, tandem axle 

3 Truck tractor 4x2, single axle with 

tandem trailer 

2 Truck tractor, 6x4, tandem axle with 

tandem trailer 

1 Truck tractor, 6x4, tandem axle with 

tandem 30-35 foot trailer wladditional 

15-20 foot trailer 

Road class limits are: 

Class Design speed 

(Mileslhour) 

The hauling cost equation for loading should not be 

used for other road or truck classes; to do so could 

result in gross errors. 
Move In and Out, Initial Rig Up and Down Logging Delays 

The delay-free cost estimates must be adjusted 

for delays. Data for estimating logging delay perI centages are sketchy. Delay percentage is the proportion of nonproductive time, One minus the proportion of nonproductive time is the proportion of 

productive time. For example, if the delay is 10 

percent, the proportion of nonproductive time is 0.1 ' and the portion of productive time is 0.9. Delay-free 

cost estimates are adjusted by dividing them by the 

proportion of productive time to obtain the respective cost with delay. The literature indicates ranges 

of delay percentages for each of the cost components 

detailed in this report. Delay percentages are summarized by component in Table 5. 

Delay-free costs should be adjusted for each component. For example, say a logger is estimating felling, bucking, and limbing costs for a hardwood stand 

with an average arithmetic tree diameter at breast 

height of 11.6 inches. Delay-free felling, bucking, 

limbing cost is: 

Adjusting delay-free cost with an average delay 

percentage of 0.20 (Table 5) = 0.158/(1-0.20) = I 0.158/0.80 or $0.197/ft3. Similar adjustments should 

be made for each cost component. The delay 

percentages summarized in Table 5 are not exclusive, 

so users may wish to substitute their own delay 

percentage based on experience or observation. 

I Table 5.-Delays for felling, bucking, limbing, 

yarding, loading, and hauling of eastern 

hardwoods, in percent 

Cost Delay 

component Average Minimum Maximum 

Felling, bucking, 

and limbing 0.20 0.07 0.47 

Yarding8 0.27 0.09 0.61 

Loading 0.08 0.02 0.19 

Hauling 0.17 0.04 0.36 

Both move in and out and initial rig up and down 

costs likely will change with tract size, volume removed, distance or move, and equipment being 

moved. The literature is essentially void of costs for 

cable yarding machines operating in eastern forests. 

The recommended approach is that individual users 

estimate these costs for specific conditions and then 

add them to those estimated with the component cost 

equations presented here. 

Using the Equations 

The cost equations in this report reflect average 

conditions typically encountered in logging operations 

on steep, mountainous terrain in the Eastern United 

States. These equations provide detailed stump-tomill cost estimates for thinning, partial cutting, shelterwood cutting, or clearcutting of hardwood stands 

in this region. The equations should be studied by 

potential users, compared with the current method of 

cost estimation, and used only within the limits of 

the conditions specified. 

The cost and delay equations were developed on a 

component-by-component basis to allow users maximum flexibility in making changes as needed. If 

users have other cost estimates that are more 

specific to their conditions, those estimates should be 

substituted for the respective cost or delay 

component. A BASIC computer program that 

calculates costs with these equations is available 

from the author.3 The program is specific to the 

Hewlett-Packard 98451' desktop computer. 

Application of the Costing Methodology 

To use these cost equations, the estimator will 

need to know the: (1) arithmetic mean tree d.b.h. to 

be harvested; (2) average volume cut per acre, in 

cubic feet; (3) average slope yarding distance, in 

feet; (4) yarder type (six to select from); (5) haul 

distance; (6) truck class; and (7) road class. These 

items can be obtained from inventory data and cruise 

data, and the logging plan for the tract in question. 

' - aDelay percentage includes road changing time and 

delay. 
Literature Cited 

Table 6 shows the stump-to-mill logging cost for a 

30-acre tract. In this example, yarding is done with a 

Koller K-300; the round-trip hauling distance is 40 

miles; the average slope yarding distance is 500 feet; 

the average volume removed is 1000 ft3/acre; the 

road class is 3 and the truck class is 3; and the average d.b.h. of cut trees is 10 inches. The values used 

for these variables are not representative of actual 

conditions but were selected to make this example 

easy to follow. 

Some adjustments to these estimated costs may 

be desirable depending on their intended use. The 

estimated costs do not include an allowance for 

profit and risk, but neither do they include 

recognition of the tax savings resulting from 

accelerated depreciation. 

Table 6. --Estimated logging costs for sample 

30-acre tract 

Operation Delay-free Average Costs with 

cost delay delay 

~ollarslf t Percent ~ollars/ft 3

Fell, limb, buck 0.175 20 0.219 

Yarding 

(Koller K-300) 0.206 27 0.282 

Loading 0.059 8 0.064 

Hauling 0.007 17 0.319 

Total cost/ft3 -- -- 0.884 

Draper, N. R.; Smith, H. Applied regression analysis. 

New York: John Wiley and Sons; 1966. 407 p. 

Fisher, E. L.; Peters, P. A. Analysis of eastern 

United States cable harvesting operations. Pap. 

No. 82-1602; St. Joseph, MI: American Society of 

Agricultural Engineers; 1983. 27 p. 

Koger, J. L. Factors affecting the production rates 

of chain saws. Tech. Note B39. Norris, TN: 

Tennessee Valley Authority; 1980; 26 p. 

Koger, J. L. Log loading methods and costs in the 

Tennessee Valley Region. Tech. Note B46. 

Norris, TN: Tennessee Valley Authority; 1982; 

36 p. 

LeDoux, C. B.; Butler, D. A. Simulating cable 

thinning in young-growth stands. For. Sci. 27(4): 

745-757; 1981. 

Martin, J. A. T-H-A-T-S. Timber harvesting and 

transport simulator. Res. Pap. NE-316. Upper 

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

Forest Service, Northeastern Forest Experiment 

Station; 1975; 32 p. 

Rossie, K. M. A case study of the Koller K-300 

yarder on a national forest timber sale in the 

Appalachian region. M.S. Thesis. Blacksburg, 

Virginia Polytechnical Institute and State 

University; 1983. 115 p. 
LeDoux, Chris B. Stump-to-mill timber production cost equations for cable 

logging eastern hardwoods. Res. Pap. NE-566. Broomall, PA:. U.S. Department 

of Agriculture, Forest Service, Northeastern Forest Experiment Station; 1985. 

6 P. 

Logging cost simulators and data from logging cost studies have been assembled 

and converted into a series of equations that can be used to estimate the 

stump-to-mill cost of cable logging in mountainous terrain in the Eastern 

United States. These equations include the use of two small and four mediumsize cable yarders and are appropriate for harvested trees ranging in diameter 

from 6 to 24 inches. Cost components can be determined easily with a hand 

calculator. A program that can be used with many desktop computers also is 

available that calculates the total stump-to-mill logging for specific logging 

conditions. 

ODC 377.2:66(74/75) 

Keywords: Cable'logging; yarding; stump-to-mill costs 

*U.S. GOVERNMENT PRINTING OFFICE:1985-505-028:20031 
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. 

0 Burlington, Vermont, in cooperation with the University of 

Vermont. 

0 Delaware, Ohio. 

0 Durham, New Hampshire, in cooperation with the University of 

New Hampshire. 

0 Hamden, Connecticut, in cooperation with Yale University. 

0 Morgantown, West Virginia, in cooperation with West Virginia 

University, Morgantown. 

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

Orono. 

0 Parsons, West Virginia. 

0 Princeton, West Virginia. 

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

New York College of Environmental Sciences and Forestry at 

Syracuse University, Syracuse. 

0 University Park, Pennsylvania, in cooperation with the 

Pennsylvania State University. 

0 Warren, Pennsylvania.