United States 

Depadment of 

Agriculture 

The Weak Link 

Forest Service C Hand-he 

Northeastern Forest 

Experiment Station 

or Program 

Research 

Paper N E-510 Ross A. Phillips 

Penn A. Peters 

Gary D. Falk 
The Authors 

Ross A. Phillips is a research 

mechanicat engineer in the Forest 

Engineering Research Project, 

Northeastern Forest Experiment 

Station, Morgantown, West Virginia. 

He has a B.S. degree in Agriculture 

and a Bachelor of Agricultural 

Engineering degree from Ohio State 

University, an M.S. of Agricultural 

Engineering from the University of 

Missouri, and an MSE specializing 

in transportation from West Virginia 

University. He began his career with 

the USDA Forest Service in 1965. 

Penn A. Peters is Project 

Leader of the Forest Engineering 

Research Project, Northeastern Forest Experiment Station, Morgantown, West Virginia. He has a B.S. 

degree in Aerospace Engineering 

and a B.S. degree in Business Administration from the University of 

Minnesota. In 1969, he obtained an 

M.S. degree in Aerospace Engineering from the University of Washington. 

Gary D. Falk is a logging systems analyst on the Six Rivers National Forest, Eureka, California. 

When he worked on this manuscript, he was a research civil engineer with the Forest Engineering 

Research Project, Northeastern Forest Experiment Station, Morgantown, West Virginia. He has a B.S. 

degree in Civil Engineering from 

San Jose State University and an 

M.S. degree in Forest Engineering 

through the Advanced Logging System Training Program from Oregon 

State University. 

Abstract 

The Weak Link hand-held calculator program (HP-41C) quickly 

analyzes a system for logging production and costs. The production 

equations model conventional chain 

saw, skidder, loader, and tandemaxle truck operations in eastern 

mountain areas. Production of each 

function of the logging system may 

be determined so that the system 

may be balanced for minimum cost. 

The user supplies input data, and 

the program calculates cost rates 

for the various functions of logging. 

The final output is logging costs in 

dollars per M bf (thousand board 

feet). 

Manuscript received for publication 

30 October 1981 
Introduction 

The Weak Link Logging Systems Analyzer (Baumgras and Martin 1978) was accepted by users, 

probably because of the relative 

ease of making calculations for cost 

analysis of logging operations by 

the use of nomograms. Ease of use 

has been furthered by programming 

the formulas used in generating the 

Analyzer for solution by a programmable hand-held calculator, the 

Hewlett-Packard 41C.I 

The program described here 

solves the same problems as the 

Analyzer, but with greater speed. 

Consider the program a supplement 

to the Analyzer. The program requests input for which the Ana!yzer 

lists recommended values. If you do 

not have a copy, you may request 

The Weak Link Logging System 

Analyzer (GTR-NE-40) from National 

Technical Information Service, 5285 

Port Royal Road, Springfield, Virginia 22151, Accession Number PB 

80 218241, February 1982 cost: 

$9.00. 

Production equations used in 

the program are identical to those 

used in the Analyzer. They model 

conventional chain saw, skidder, 

loader, and tandem-axle truck operations in eastern mountain areas. 

Cost calculations in the program are 

different from those used in the 

Analyzer. Overhead in the Analyzer 

starts with the annual overhead 

which is reduced to overhead per 

shift. Overhead in the program must 

be input as a percentage of wages, 

percentage of average investment, 

or a percentage of depreciation. The 

latter inputs can be used to compare individual machines or to get a 

more accurate comparison of labor 

costs and machine costs. 

The use of trade, firm, or corporation 

names in this publication 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. 

The principal problems addressed by the Weak Link are manual felling, rubber-tired and crawler 

skidding operations, and trucking. 

Calculators give answers fast, so 

rapid estimates for logging costs 

can be obtained in the field. This 

program was written for the Hewlett-Packard 41C calculator and requires three extra memory modules 

or a quadmodule to hold the program (some 1700 bytes). The only 

other item needed for use is a 

knowledge of the units used in the 

program. The calculator prompts the 

operator for the needed data and 

then gives the answers on demand. 

This program is on magnetic 

cards. The card reader for the 

tip-41C calculator will load the program in less than a minute. The 

computer program described in this 

publication is available on request 

with the understanding that the U.S. 

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 information, please write: Engineering Research, Northeastern Forest Experiment Station, 180 Canfieid 

Street, Morgantown, WV 26505. If 

you want to obtain the program, 

send seven blank Hewlett-Packard 

magnetic cards. Features of the 

HP-41C are presented in Appendix 

A. A program list is provided in Appendix B. Nomenclature for keys 

and displays is given in Appendix C. 

First-Time User Instructions 

Depress the switch marked 

USER and then enter the program. 

USER appears on the view screen; 

neither PRGM nor ALPHA should 

appear. The alphabet is printed on 

the keys of the calculator along with 

symbols and numerals. The USER 

key activates the reassigned keys. 

The alphabet designates the keys to 

be used for this program when instructions call for pressing a key 

designated by a letter. 
Press A to start the program. 

An execution annunciator appears 

that somewhat resembles a bird flying across the screen, and PRGM 

appears while the program is running. The program prompts for various inputs. Three example problems 

are presented in this paper; problem 

1 will be worked in detail to illustrate the use of the program (Table 

1). Prompting notations can be 

changed to please the operator, so 

long as the total number of characters including blanks does not exceed 12. The program contains 

three input sections: felling, skidding, and trucking data. The calculator signals the end of each section. 

Felling Data 

The first prompt, DBH H, asks 

for two inputs. The first is diameter 

at breast height in inches, and the 

second is the height of the tree in 

logs (16-foot length). Use average 

values for the tract of timber being 

analyzed. Decimals of the input 

units may be used. The example 

uses 18 inches for the diameter and 

2 logs for the height. Key 18 into 

the calculator, then ENTER?, then 2, 

and then RIS. 

When more than two entries exist, press the RIS key after the last 

input; press the ENTER? key after 

each item in a series of entries except the last one. If only one item 

exists in the prompt, press only the 

RIS key. The letters RIS stand for 

run and stop. If the program is running, this key stops it. If the program is not running, the run command starts it again. The program 

has stops at appropriate places, but 

run must be manually executed. 

Table 1.-Fell, skid, and truck input data for Problems 1,2,3 

Input data Problem 1 Problem 2 Problem 3 

DBH (inches) 

H (16-foot logs) 

Vl (M bf) 

V2 (M bf) 

WT (minutes) 

$ PER HR? 

D (feet) 

SIS 

SIT 

LEVEL? 

UPHILL? 

BUNCH? 

DT (minutes) 

S A 

CAP (M bf) 

Dl (miles) 

02 (miles) 

D3 (miles) 

D4 (miles) 

TU (minutes) 

TD (minutes) 

TA 
The next prompt, V1 V2, asks 

for the volume of the tree and the 

volume per log, Use average values 

for the entire tract. The volume per 

log is the average volume per log 

loaded on the truck and is not necessarily the volume of the average 

16-foot log. The example gives an 

average value of 0.2 M bf (thousand 

board feet) per tree and an average 

value of 0.07 M bf per log. 

The next prompt, WT, asks for 

the average walking time, in minutes, from the tree just felled to the 

next tree. Slope influences walking 

time, which generally ranges from 

0.6 minutes to 1.4 minutes per tree. 

Use observed times on a similar logging job if possible, The example 

uses an average of 0.6 minutes to 

get to the next tree. 

The next prompt, $ PER HR?, 

asks if the feller gets paid by the 

hour. The alternative would be production pay or so much per M bf. A 

"yes" or "no" answers this prompt. 

Throughout the program use 1 for 

"yes" and @for "no". The example 

uses an hourly wage, thus enter 1. 

END FELL appears followed by D 

SIS SIT. 

Assignment of user keys permits entering the program at various 

locations. After pressing a user key 

other than A, the program will not 

proceed from one section to the 

next without pressing the proper 

user key. Limitations of reentering 

data are described later. 

Skidding Data 

The prompt D SIS SIT introduces skidding. D asks for the average skidding distance in feet; SIS, 

the average number of trees pulled 

by the rubber-tired skidder; and SIT, 

the average number of trees pulled 

by the crawler tractor. Example 

values are 2,000, 2, and 2. Information that does not apply to the desired answer will not affect the 

answer. Thus, if only rubber-tired 

skidders are used, the number of 

stems pulled by crawler tractors will 

have no effect on rubber-tired skidder production. 

After these entries, the prompt 

LEVEL? asks if the skidding will be 

along level terrain. It fequires a 

"yes'br "no" answer. If "noo"'is 

given, the prompt UPHILL? asks if 

the skidding will be uphill. If "no" 

for uphill, then downhill is left, however, if the operator replies "yes" to 

level, then the next prompt shows 

"BUNCH?". Again, use "yes" or 

"no". Bunching increases the skidder production. However, the program does not provide for the cost 

of the bunching machine as such, 

but a bunching tractor can be included with the skidders. This is explained later. In the example, downhill skidding with no bunching is 

specified. Therefore, enter LEVEL? 

= 9, UPHILL? = 9, and BUNCH? 

= 9. 

The next prompt, DT, requires a 

numerical value for skidding delay 

time in minutes per turn. The example uses 3.7 minutes delay time 

per Zurn. Average self-caused delay 

time generally ranges from slightly 

over 1 minute to less than 4 minutes, depending on the aggressiveness of the operator. Observation of 

the available operator will give the 

best input value. 

The next prompt, SA, asks for 

machine availability which represents the percentage of scheduled 

machine time that the machine is 

mechanically fit to do productive 

work. The example uses 0.85 for SA 

for skidding equipment. END SKID 

signals the end of skidding input. 

1 racking Data 

The first trucking data prompt, 

CAP, asks for the average truck 

capacity in M bf. The example uses 

2.5 M bf. The next prompt, Dl 02, 

asks for two distances in miles. Dl 

asks for the hauiing distance on a 

two-lane paved road; the example 

uses 20 miles. D2 asks for one-lane 

paved road distance; the example 

uses 10 miles. The next prompt, D3 

04, also asks for distance in miles. 

03 asks for distance on a one-tane 

gravel road and 04 asks for distance 

on a woods road. The example uses 

2 miles for each of these, The next 

prompt, TU TD, asks for truck unloading time in minutes and truck 

delay time in minutes. Delay time 

refers to delays caused by the 

driver. It does not refer to time 

spent waiting for some other piece 

of equipment or logs. The example 

uses 7 minutes unloading time and 

24 minutes delay time. Both times 

are averages from time studies. Of 

course, observed times of the concerned workers should be used. The 

last prompt, TA, asks for truck 

availability. The example uses 0.90. 

END TRUCK appears on the screen, 

and the next step is to get some 

answers. 

Production Output 

The first answer is UFPRO (unit 

felling production) = 1.43. This may 

be obtained by pressing B or MS. 

The value 1.43 is the number of M 

bf that one feller can cut in 1 hour, 

All production outputs are given in 

M bf per hour. Next, push RIS and 

USPRO (unit skidding production) = 1.25 appears. 

Pressing RIS again will display 

UTPRO = 1.05. This shows skidding 

production for crawler tractors. 

Either rubber-tired skidders or 

crawler tractors may be used in this 

program, or the combination may be 

used. After pressing RIS again, ULPRO = 3.62 appears. This indicates 

that the loader can load 3.62 M bf of 

logs per hour. This program assumes that the loader does not limit 

system production. After activating 

RIS again, UTRPRO = 0.50 appears. 

This readout concludes the series, 

and unit truck production equals 

0.50 M bf per hour. 

The program can be reentered 

at various places. Press B and the 

first of the unit production series 

appears. By using RIS, the entire 

series may be viewed. The user may 

write the answers for an overall view 

rather than use the calculator ta 

view the answers one at a time. If 

written, we suggest a tabular form 

with three columns added to facifitate the next step of balancing the 

production for the operation. The 
suggested format is shown in Table 

2; the production numbers for problem 1 correspond to the example. 

The next procedure may be obtained by pressing C. The prompt 

shows NF HID, which asks for the 

number of fellers and the hours per 

day that they work. The entry of 2 

fellers and 8 hours per day shows 

FPRO = 22.89, which indicates the 

felling production of 22.89 M bf per 

day with 2 workers. Hours per day 

may be changed for different production. These data are also recorded in Table 2. 

By pressing RIS, 22.89 appears 

and the number may be used with 

any arithmetical procedure such as 

division, addition, subtraction, and 

multiplication. The next press of RIS 

displays the prompt NS HID, or this 

prompt may be obtained by pressing D. The prompt NS HID asks for 

the number of rubber-tired skidding 

units and the hours per day that 

they are used. The entry of 2 units 

and 8 hours per day shows SPRO = 20.03, which indicates the skidding 

production of 20.03 M bf per 8 hour 

day with 2 rubber-tired skidders. 

Changing hours per day readily 

changes production, and the number of skidders also changes production. When the number of skidders change, remember to change 

the number of skidders in the cost 

section. 

By pressing RIS, the prompt NT 

HID asks for the number of units of 

skidding tractors and the hours per 

day that they work. Assume that only rubber-tired skidders are used 

and enter punits and (?I hours. In the 

event that only crawler tractors did 

the skidding, zero entries would be 

made for the rubber-tired skidders. 

Table 2.-Production by logging system functions 

Mbf Number 

Function unit of units Hourslday M bflday 

Felling 

Rubber-tired skidding 

Tractor skidding 

Total skidding 

Loading 

Trucking 

Felling 

Rubber-tired skidding 

Tractor skidding 

Total skidding 

Loading 

Trucking 

Felling 

Rubber-tired skidding 

Tractor skidding 

Total skidding 

Loading 

Trucking 

PROBLEM 1 

PROBLEM 2 

PROBLEM 3 

After inputting zeros and pressing 

RIS, the screen shows TPRO = 4). 88. Press RIS again, and S + TPRO = 20.03 shows on the screen. 

S + TPRO indicates the total daily 

skidding production. The next use 

of RIS shows 20.93. This number 

may be used as desired with the 

various arithmetical functions of the 

calculator. Previous numbers on the 

screen could not be acted upon 

directly. 
Continue with either RIS or E, 

and NTR HID asks for the number of 

trucks and the hours per day that 

they operate. The entry of 4 trucks 

at 10 hours per day shows TRPRO 

= 20.00 or 20 M bf per day for 

trucking production. Pressing RIS 

shows 20.00 on the screen. 

If the daily production of either 

felling, skidding, or trucking is substantially different from the others, 

this item may be recalculated for a 

different number of units or hours 

per day or both. Press C to reenter 

the program for felling production, 

D for skidding production, and E for 

trucking production. These three 

keys may be used in any order and 

as frequently as desired. Felling and 

skidding calculations give continuous answers. The truck calculations 

give incremental answers. Approximately 5 hours are required to make 

a trip with the sample input, Thus, 

both 6 and 9 hours give the same 

production for trucking with this example. Increased production shows 

at 10 hours, and the next increase 

will show at about 15 hours. Different trip conditions will change this 

incremental time. 

Our sample problem uses 2 

fellers for 8 hours and 2 skidders for 

8 hours. Note that by using 2 fellers 

for 7 hours the total production 

would be nearer even. Other factors 

may outweigh the precise balancing 

of total production. Working shorter 

hours may cause dissension among 

the workers, and a feller may be the 

owner's son-in-law. 

Cost lnput 

After production factors are 

closely balanced, start costing procedures to obtain the ultimate answer in dollars per M bf. Press F 

and FELL COSTS appears, followed 

by the prompt VC VS. This prompt 

asks for the initial cost and the salvage value of the equipment. Costs 

are usually known; salvage values 

must be estimated. The example 

uses an initial cost of $450 for saws 

and a salvage value of zero (Table 

3)' 

Table 3.-Cost input data for Problem 1 

Input data Fell Skid Load Truck 

vc ($1 

R 1 

vs ($1 

RM 

N (years) 

RR 

HRS PER YR 

NO OF PCS 

NO 

RATE ($/hour) 

NO 

RATE ($/Hour) 

RB 

RO 

SAPCOSTS ($lop. H R) 

SOPCOSTS ($IOP. H R) 

TOPCOSTS ($lop. H R) 

LOPCOSTS ($10 P. H R) 

TROPCOSTS ($lop. H R) 

The next prompt, RI RM, asks 

for interest rate and maintenance 

rate. They are multiplied by average 

investment to obtain annual interest 

charges and maintenance costs. 

Maintenance for saws includes files, 

spark plugs, and other minor items 

including other machine overhead. 

Use the best available value for both 

of these and enter as a decimal. The 

example uses 0.10 for interest and 

0.1 5 for maintenance. 

The next prompt, N, asks for 

the number of years of useful life of 

the machine or depreciation period. 

The practical range here probably 

would be 1 to 10 years, and the 

number of years influences the input for the following prompt, RR, 

which asks for the repair rate. Enter 

repair rate as a percentage of yearly 

depreciation, which could be quite 

low or could go over 100 percent depending on the equipment and 

operating conditions. For example, 

if the original costs is $2,500 with 

no salvage value, the depreciation 

period 5 years, and the estimated 

annual repair costs $200; then the 

annual depreciation is $500, and repair costs are 40 percent of the annual depreciation. Enter all percentages as decimals. For the example, 

use 1 year of life and 0.80 for the repair rate for chain saws. 

The next prompt, HRS PER YR, 

asks for the average number of 

hours of use per year. To estimate, 

use 40 hours per week for 50 weeks, 

which is 2,000 hours. Then consider 

time lost because of repairs and inclement weather. We used 1,800 

hours for the example. Of course, 

more than 2,000 hours could be 

worked by extending work weeks 

and the 8-hour day, or by double 

shift work. 

The next prompt, NO OF PCS, 

asks for the number of saws that fit 

in the above category; we used 2 for 

the example. Because many loggers 

with more than one saw have dlfferent models or at least one of the input factors differ from the other 

saws, the prompt VC VS shows. 

This starts the felling cost calculation again for other saws. 
After entering data for all of the 

saws, enter @for VC and $for VS. 

The prompt NO RATE then asks for 

the number of fellers and the dollars 

per hour that they are paid. Because 

different pay scale rates may be 

used, this prompt also repeats for 

as many times as needed. We used 

two workers at $5.75 per hour for 

the example. Use the same process 

to pass this loop as that used to 

pass the previous loop. After entering 2 and 5.75 enter @for the number of workers and @for the rate of 

pay and the prompt RB RO appears. 

This applies to all personnel and 

asks for the percentage of wages 

paid for benefits and the percentage 

of wages paid for overhead. Benefits include social security, paid 

vacations, holiday gifts, unemployment compensation, and other expenditures directly related to the individuals' payroll. Overhead includes pay for supervisors, foremen, 

payroll clerks, secretaries, office 

rent, and other items necessary to 

keep the woods crew operating. 

Show the portion of overhead costs 

allocated to felling in this entry. 

Values used for the example are 

0.30 for RB and 0.20 for RO. 

The next prompt, SAPCOSTS, 

asks for felling operating costs in 

dollars per hour for each saw. 

Operating costs include fuel, lubricants, and any other ongoing expense directly related to the equipment that was not included with 

maintenance. The example uses 

0.80. Pressing RIS again displays 

the value that was input for felling 

operating costs. Another press of 

RIS starts the skidding cost sequence, or press G to get the skidding cost sequence. 

SKID COSTS appears on the 

screen followed by the prompt VC 

VS, which asks for the cost value 

and the salvage value of a skidder. 

These values are $50,000 and $5,000. 

Continue to make inputs from data 

given in Table 3. The example contains two skidders with the same 

values. We used three workers-an 

operator for each skidder and a 

chokersetter. Values for the various 

workers accumulate so that extra 

costs pertaining to skidding may be 

entered. After the prompt SOPCOSTS, which asks for the skidder 

operating costs, has been answered 

and entered by RIS, TRACTOR 

COSTS appears on the screen followed by the prompt VC VS. This 

applies to skidding tractors. If the 

operation uses no skidding tractors, 

as in this sample problem, enter 

zero and zero for the prompts and 

NO RATE appears, which asks for 

the number of operators and their 

hourly rate. Again enter zero and 

zero and the prompt, RV RO appears. 

Because this asks for the percentage of wages for benefits and 

overhead, and no wages exist, zeros 

may be entered or any other number 

will give the same answer. The next 

prompt, TOPCOSTS, asks for the 

tractor operating costs, which are 

zero. When the operhtion uses a 

bunching tractor, it may be entered 

with the skidding tractors. Example 

number two (Table 4) uses tractors 

for skidding rather than rubber-tired 

skidders, so the zero values go in 

the rubber-tired skidder section. Example number three (Table 5) uses 

both a rubber-tired skidder and a 

tractor so enter values in both sections. 

Table 4.-Cost input data for Problem 2 

Input data Fell Skid Load Truck 

TR#1 TR#2 Bunch 

vc 6) 

VS($) R I 

RM 

N (years) 

RR 

HRS PERYR 

NO 0 PCS 

NO 

RATE ($/hour) 

NO 

RATE ($/hour) 

NO 

RATE ($/hour) 

RB 

RO 

SAPCOSTS ($lop. hour) 

SOPCOSTS ($lop. hour) 

TOPCOSTS ($lop. hour) 

LOPCOSTS (SOP. hour) 

TROPCOSTS ($lop. hour) 
Table 5.-Cost input data for Problem 3 Logging Cost 

Input data 

Skid 

Fell Load Truck 

Skidder Tractor -- 

vc (4) 

vs ($) RI 

RM 

N (years) 

RR 

HRS PER YR 

NO OF PCS 

NO 

RATE ($/hour) 

NO 

RATE ($/hour) 

RB 

RO 

SAPCOSTS ($lop. hour) 

SOPCOSTS ($lop. hour) 

TOPCOSTS ($lop. hour) 

LOPCOSTS ($lop. hour) 

TROPCOSTS ($lop. hour) 

Press H to start the load section and LOAD COSTS shows on 

the screen. The first prompt, VC VS, 

asks for cost value and salvage of 

the loader, and prompts follow the 

same sequences as that for felling 

and skidding equipment. 

Press I and TRUCK COSTS appears followed by the prompt VC 

VS. This sequence of prompts is the 

same as that for felling costs, skidding costs, and loading costs except for the last prompt, TROPCOSTS, which asks for truck operating costs. The four items of felling, 

skidding, loading, and trucking 

costs may be entered in any order. 

Start the final sequence of the 

program by pressing J, and the 

prompt AC PRO shows, which asks 

for actual production. Enter the lowest figure obtained from the daily 

production values for felling, skidding, or trucking. Use the lowest 

figure because the other functions 

of harvesting will slow down to 

meet this low production functionthe weak link. Because the trucking 

production was low with 20 M bf per 

day, enter 20 for the example. After 

pressing RIS, FELL = 8.04 appears 

which is the actual felling costs in 

dollars per tvl bf. The assumption is 

made that reducing the output of 

the felling operation would not reduce any of the costs. Pressing RIS 

shows SKID = 25.06, which indicates the skidding costs. The next 

display LOAD = 5.88 is the loading 

cost followed by TRUCK = 33.58, 

the trucking costs. The next step 

obtained by pressing RIS shows 

TOTAL = 72.56, which indicates 

that the total logging cost is $72.56 

per M bf (Table 6). The next use of 

RIS gives 72.56, which may be used 

for calculations. This step ends the 

calculations. 

Table 6,-Logging cost by function as determined 

by weak link producton 

Function Problem 1 Problem 2 Problem 3 

AC PRO (M bflday) 

FCOST ($IM bf) 

FELL ($IM bf) 

SKID ($IM bf) 

LOAD 

TRUCK ($IM bf) 

TOTAL ($IM bf) 72.56 63.84 79.84 
YES 

! 

PRODUCTION A INUMBER OF UNITS I -1 HOURS PER DAY I 

- YES CHANGE 3 

COSTS 

PRODUCTION COSTS 

$/ MBF I 

Figure 1.-Flow diagram for weak link hand-held computer program 
Reentering Data 

The program user may want to 

change some inputs and calculate 

the effect on production and cost 

without reentering data for the 

whole program. The instructions for 

reentering data are organized by the 

following categories: (1) daily production; (2) hours per day; (3) owning, operating, and labor costs; and 

(4) fell, skid, and truck input data. In 

addition to the desired change, it 

may be necessary to reenter some 

data because of the structures of 

the program. Specific instructions 

follow. 

Daily Production 

The daily production is entered 

as AC PRO in the calculation of logging system costs (J). In the weak 

link method of determining costs, 

AC PRO is the minimum daily production achieved by either felling, 

skidding, or trucking production. 

The following example illustrates 

the reentering of data for AC PRO. 

In Problem 1, the minimum 

daily production of 20 M bf per day 

resulted in felling costs of $8.04 per 

M bf. To determine how much additional felling cost we were incurring 

because production was limited to 

20 M bf per day when fellers had the 

capability of producing 22.89 M bf 

per day, we pressed J, entered 22.89 

for AC PRO to get the optimum felling costs. Felling costs = $7.09 per 

M bf indicating that if the rest of 

the system had been capable of producing 22.89 M bf per day, felling 

costs could be reduced by $0.95 per 

M bf. Changes to AC PRO (J) can be 

made without reentering data for 

other keys. 

Hours Per Day 

The daily production that can 

be obtained can be adjusted by 

changing the working hours per day 

for felling, skidding, and trucking. 

Data for hours per day can be reentered by pressing C for felling, D 

for skidding, or E for trucking. After 

reentering data, press J and reenter 

actual production to obtain results. 

The number of units working could 

also be changed, but the appropriate cost data should also be reentered to reflect the additional 

costs associated with additional 

units. This applies only to item 

changes such as skidders. 

Owning, Operating, and Labor Costs 

Data can be reentered for owning, operating, and labor costs by 

pressing the appropriate key: F for 

felling costs, G for skidding costs, 

H for loading costs, or I for trucking 

costs. Data do not have to be reentered for any other keys. For example, if felling labor rates increased, press F, enter the data required (even enter values that have 

not changed). When finished, press 

J and reenter actual production to 

obtain results. 

Fell, Skid, and Truck Input Data 

K, L, and M allow you to reenter 

data that affect the unit felling, skidding, and the trucking production 

per hour, respectively. The data that 

can be reentered by pressing K, L, 

and M are inputs DBH through TA 

shown in Table 1. Rules for reentering data in K, L, or M: 

(1) If variables DBH, Hi WT, or $ 

PER HR? are changed, reenter 

data in K. 

(2) If variables V, D, SIS, S/T, LEVEL?, UPHILL?, BUNCH?, DT, 

and SA are changed, reenter 

data in K and L. 

(3) If variables V2, CAP, Dl, 02, 03, 

04, TU, TD, or TA are changed, 

reenter data in K and M. 

When data have been reentered, 

complete the problem by pressing 

B, C, D, E, (F, G, H, and I, if required) and J. 

Literature Cited 

Baumgras, John E.; Martin, A. Jeff. 

The weak link logging systems 

analyzer. 1978; USDA For. Serv. 

Gen. Tech. Rep. NE-40.63 p. 
Appendix A 

Cat~ulator Description 

The hand-held Hewlett-Packard 

41C contains programmable capabilities and a reasonably extensive 

storage. The calculator was designed for easy entrance of program 

storage. The program may be entered by direct programming, which 

is relatively simple, or through magnetic cards. Magnetic cards offer 

quick recovery of the program after 

some interruption such as using another program. The calculator's continuous memory holds the program 

as long as the storage space is not 

used for something else and even 

when the calculator is turned off. 

The reader will also transfer a program to magnetic cards. 

Visual prompting for data 

shows on the visual display of the 

calculator so the program can readily be used at logging sites or any 

other place where a quick answer 

would be desirable. The operator 

needs to remember the abbreviations displayed and the units for the 

data to be entered. 

Reassignment of key functions 

of the calculator facilitates entering 

the program at any program location 

so that input may be changed quickly and the answers may be obtained 

without going through the whole 

program. 

The calculator signals for low 

batteries when BAT appears in the 

lower left side of the viewscreen. 

This signal indicates the need for a 

battery change. Old batteries may 

cause erratic functions of a program, even before the calculator indicates a need for battery change. 

Appendix B 

Weak Link HP-41C Program List 

User Keys: 

11 "START" 41 ENTER? 

12 "UPRO" 42 RCLZ 

13 "FPRO" 43 ST0 33 

14 "SKPRO" 44 X<>Y 

15 "TRPRO" 45 * 

21 "FCOSTS" 

22 "SCOSTS" 

23 "LCOST" 

24 "TRCOSTS" 

25 "ACOST" 

32 "FELL" 

33 "SKID" 

34 "TRUCK" 

01 LBL "START" 

02 XEQ "FELL" 

03 XEQ "SKID" 

04 XEQ "TRUCK" 

05 XEQ "UPRO" 

06 LBL "FPRO" 

07 "NFHID" 

08 PROMPT 

09 ST0 17 

10 * 

11 RCL@ 

12 * 

13 "FPRO=" 

14 XEQ "AP" 

15 RTN 

16 LBL "SKPRO" 

17 "NSHID" 

18 PROMPT 

19 ST015 

20 * 

21 RCLN 

22 * 

23 "SPRO = " 

24 XEQ "AP" 

25 "NT HID" 

26 PROMPT 

27 ST0 31 

28 * 

29 RCLR 

30 * 

31 "TPRO=" 

32 XEQ "AP 

33 + 

34 "S+TPRO=" 

35 XEQ "AP" 

36 RTN 

37 LBL "TRPRO'" 

38 "MTR HID" 

39 PROMPT 

40 ST0 18 

46 GSTX 

47 RCL@ 

48 * 

49 RCL 22 

50 

7- 1 I 

51 LASTX 

52 X<>Y 

53 INT 

54 * 

55 RCL 33 

56 * 

57 "TRPRO=" 

58 XEQ "AP" 

59 RTN 

60 LBL " FCOSTS" 

61 "FELL COSTS" 

62 XEQ "25" 

63 ST0 25 

64 "SAPCOSTS" 

65 PROMPT 

66 ST0 26 

67 RTN 

68 LBL "SCOSTS" 

69 "SKID COSTS" 

70 XEQ "Z5" 

71 ST0 23 

72 "SOPCOSTS" 

73 PROMPT 

74 ST0 24 

75 "TRACTOR COS 

76 XEQ "Z5" 

77 ST0 Q18 

78 "TOPCOSTS" 

79 PROMPT 

80 ST0 16 

81 RTN 

82 LBL " LCOST" 

83 "LOAD COSTS" 

84 XEQ "Z5" 

85 ST0 32 

86 " LOPCOSTS" 

87 PROMPT 

88 ST0 27 

89 RTN 

90 LBL TRCOSTS" 

91 "TRUCK COSTS" 

92 XEQ"Z5" 

93 ST0 28 

94 "TROPCOSTS" 

TS" 

95 PROMPT 

96 ST0 39 

97 RTN 

98 LBL "ZS" 

99 AVlEW 

loo g, 

101 ST0 Q)Q) 

102 XEQ "OWN1" 

103 XEQ "LAB1" 

104 RCLQ)@ 

105 RTN 

106 LBLCiOWN1" 

107 "VC VS" 

108 PROMPT 

109 X=Y? 

110 RTN 

111 - 112 ST029 

113 LASTX 

114 "RI RM" 

115 PROMPT 

116 + 

117 * 

118 LASTX 

119 'IN" 

120 PROMPT 

121 ST129 

122 1 

123 + 

124 * 

125 2 

126 1 

127 1 

128 + 

129 "RR" 

130 PROMPT 

131 + 

132 ST * 29 

133 X<>Y 

134 ST + 29 

135 "HRS PERYR" 

136 PROMPT 

137 ST129 

138 "NO OF PCS" 

139 PROMPT 

140 ST * 29 

141 RCL 29 

142 ST + $41 

143 Q) 

144 ST0 29 

145 GTO "OWN1" 

146 LBL "LAB1" 

147 "NO RATE" 

148 PROMPT 

149 X=@ 

150 GTO "LAB2" 

151 * 

152 ST + 29 

153 GTO "LAB1" 

154 LBL"LAB2" 
155 "RB RO" 

156 PROMPT 

157 1 

158 + 

159 X<>Y 

160 1 

161 + 

162 * 

163 RCL29 

164 * 

165 ST+ @Q) 

166 RTN 

167 LBLiiACOST" 

168 "AC PRO" 

169 PROMPT 

170 ST0 Q)@ 

171 FC?Q)l 

172 GTO "Z1" 

173 RCL 25 

174 RCL17 

175 * 

176 RCLQ)4) 

177 1 

178 RCL26 

179 RCL01 

180 1 

181 + 

182 GTO "23" 

183 LBL"Z1" 

184 "FCOST" 

185 PROMPT 

186 LBLiiZ3" 

187 ST0 29 

188 "FELL=" 

189 XEQ "AP" 

190 RCL1S 

191 X=Q)3 

192 GTOiiZ2" 

193 RCL23 

194 * 

195 RCLQ)Q) 

196 1 

197 RCL 24 

198 RCLW 

199 1 

200 + 

201 LBLiiZ2" 

202 RCL31 

203 X=@ 

204 GTO "24" 

205 RCL @ 

206 * 

207 RCL Q)Q) 

208 1 

209 RCL 16 

210 RCL@ 

211 1 

212 + 

213 LBL "24" 

214 + 

215 "SKID=" 

216 XEQ "AP" 

217 RCL 29 

218 + 

219 RCL32 

220 8 

221 * 

222 RCL Q)$ 

223 1 

224 RCL 27 

225 RCLQ)7 

226 1 

227 + 

228 "LOAD = " 

229 XEQ "AP" 

230 + 

231 RCL28 

232 RCL 18 

233 * 

234 RCL (be 235 1 

236 RCL 34) 

237 RCL 10 

238 1 

239 + 

240 "TRUCK = " 

241 XEQ "AP" 

242 + 

243 "TOTAL = " 

244 XEQ "AP" 

245 STOP 

246 LBL "FELL" 

247 "BDH H" 

248 PROMPT 

249 ST0 12 

250 RDN 

251 ST0 11 

252 "V1 V2" 

253 PROMPT 

254 ST0 14 

255 RDN 

256 ST0 13 

257 CF81 

258 RCL 11 

259 ,3184 

260 * 

261 RCL 12 

262 ,4719 

263 * 

264 -k 

265 3.0349 

266 - 267 ST0 $1 

268 2.5 

269 + 

270 "WT" 

271 PROMPT 

272 + 

273 ST0 19 

274 "$ PER HR?" 

275 PROMPT 

276 X#Q)3 

277 XEQ "AI" 

278 RCL 19 

279 1IX 

280 ST0 4)2 

281 RCLl1 

282 .244$5 

283 * 

284 RCL 12 

285 1.71424 

286 * 

287 + 

288 5.24374 

289 - 290 ST + Q)1 

291 RCLQjl 

292 1IX 

293 ST0 01 

294 RCL 13 

295 6Q) 

296 * 

297 ST * (B1 

298 ST * $2 

299 "END FELL" 

300 AVlEW 

301 RTN 

302 LBL "SKID" 

303 " D SIS SIT" 

304 PROMPT 

305 ST0 21 

306 RON 

307 ST0 28 

308 RDN 

309 ST0 19 

310 .4)@ 

311 * 

312 2.18224 

313 + 

314 STOB 

315 3.15239 

316 + 

317 ST0 $5 

318 RCL2Q) 

319 XEQ "BI" 

320 ST + 03 

321 RCL21 

322 XEQ "BI" 

323 ST + $5 

324 "LEVEL?" 

325 PROMPT 

326 X=@? 

327 GTOiiDI" 

328 .98651 

329 ST + $3 

330 ST + 6)5 

331 GT0"FI" 

332 LBL "Dl" 

333 "UPHILL?" 

334 PROMPT 

335 x=p 

336 GTO "FI" 

337 1.4376 

338 ST + 03 

339 ST + $5 

340 LBL "FI" 

341 "BUNCH?" 

342 PROMPT 

343 X#@? 

344 XEQ "GI" 

345 '"T" 

346 PROMPT 

347 ENTERt 

348 ENTERt 

349 RCL 03 

350 + 

351 1IX 

352 ST0 QI 

353 X<>Y 

354 RCL@ 

355 + 

356 1IX 

357 ST0 $6 

358 RCL B)3 

359 1lX 

360 ST0 $3 

361 RCLR 

362 1IX 

363 ST0 $5 

364 RCL21 

365 RCL 13 

366 6Q) 

367 * 

368 * 

369 ST *$5 

370 ST * $6 

371 LASTX 

372 RCL 24) 

373 * 

374 ST * 91. 

375 ST * @3 

376 "SAW 

377 PROMPT 

378 ST * $4 

379 ST * Qkj 

380 "END SKID" 

381 AVIEW 

382 RTN 

383 LBL "TRUCK" 

384 "CAP" 

385 PROMPT 

386 ST0 22 

387 RCL 14 

388 1 

389 1.m 

390 * 

391 4.6 

392 + 

393 ST0 07 

394 4) 

395 ST0 1Q) 

396 "Dl D2" 

397 PROMPT 

398 X#@? 

399 XEQ "AT" 

400 X<>Y 

401 Xfp 

402 XEQ "BT" 

403 "03 D4" 

404 PROMPT 

405 X#@? 

406 XEQ "CT" 

407 X<>Y 

408 XPQY! 

439 XEQ " DT" 

410 "TU TD" 

411 PROMPT 

412 + 

413 RCL Q)7 

414 + 

415 RCL1Q) 

416 + 

417 1IX 

418 STO@ 

419 RCLQ)7 

420 1IX 

421 ST0 Q)7 

422 RCL 1Q) 

423 1IX 

424 ST0 1Q) 

425 RCL 22 

426 6Q) 

427 * 

428 ST * Blf 

429 ST * 14) 

430 "TA" 

431 PROMPT 

432 * 

433 ST * @ 

434 "END TRUCK" 

435 AVIEW 

436 RTN 

437 LBLiiAT" 

438 5 

439 * 

440 3.1 

441 + 

442 ST+ 1Q) 

443 RTN 

444 LBLiiBT" 

445 3.1 75 

446 * 

447 11.125 

448 + 

449 ST + lQ) 

450 RTN 

451 LBLiiCT" 

452 19.64 

453 * 

454 5.96 

455 + 

456 ST+ 10 

457 RTN 

458 LBL "DT" 

459 7.742 

460 * 

461 7.68 

462 + 

463 ST + 1$ 

464 RTN 

465 LBLiiAI" 

466 SF 01 

467 X<>Y 

468 RCL 1 1 

469 .@28 

470 * 

471 .484 

472 - 473 ST + $1 

474 + 

475 1 

476 + 

477 ST0 19 

478 RTN 

479 LBLiiBI" 

480 RCL 13 

481 1.42 

482 * 

483 1.924 

484 + 

485 * 

486 RTN 

487 LBL"GIU 

488 RCL 2% 

489 XEQ "HI" 

490 ST - 4)3 

491 RCL21 

492 XEQ "HI" 

493 ST - $5 

494 RTN 

495 LBLiiHI" 

496 1.395 

497 * 

498 .32 

499 - 500 RTN 

501 LBL ''UPRO" 

502 "UFPRO=" 

503 ARCL@ 

504 XEQ ''BPP" 

505 "USPRO = " 

506 ARCLQI 

507 XEQ "BP" 

508 "UTPRO = " 

509 ARCLe 

510 XEQ "BP" 

51 1 "ULPRO = " 

512 ARCL $7 

513 XEQ ''BPP" 

514 "UTRPRO=" 

515 ARCL @ 

516 AVIEW 

517 RTN 

518 LBL "AP" 

519 ARCLX 

520 LBLUBP'" 

521 AVIEW 

522 STOP 

523 RTN 

524 END. 
Appendix C 

Nomenclature for Keys and Displays 

USER-ready for use of reass~gned 

keys (M bflSc hedu led 

hours) 

PRG M - prog ram 

ALPHA-alphabet designates 

DBH H-diameter at breast height 

(inches)- height of the 

trees (no, of 16-ft. logs). 

RIS-runlstop, use for data entry 

V1 -average volume per tree (M bf) 

V2-average volume per log (M bf) 

WT-average walking time from tree 

felled to the next tree (minutes) 

$ PER HR?-salary at hourly rate, 

yes or no 

END FELL-input for felling completed 

D SIS SIT 

D-average skidding distance 

(feet) 

SIS-number of stems pulled by 

the rubber-tired skidder 

SIT-number of stems pulled by 

crawler-tractor 

LEVEL?-yes or no 

UPHILL?-yes or no 

BUNCH?-yes or no 

DT-delay time per turn (minutes) 

SA-machine availability 

CAP-average truck capacity (M bf) 

Dl-distance of hauling in miles on 

paved road (2 lane) 

D2-distance of hauling in miles on 

paved road (1 lane) 

D3-distance of hauling in miles on 

a one-lane gravelled road 

D4-distance of hauling in miles on 

a woods road 

TU TD-truck unloading time (minutes)-truck delay time 

(minutes) 

TA-truck availability 

END TRUCK-input for trucking 

completed 

UFPRO-unit felling production (M 

bflSc heduied hour) 

USPRO-unit rubber-tired skidding 

production (M bflscheduled hour) 

UTPRO-unit tractor skidding 

production (M bflscheduled hour) 

ULPRO-unit loading production (M 

bflSc heduled hour) 

UTRPRO-unit trucking production 

M bflscheduled hour) 

NF HID-number of fellers and the 

hours per day that they 

work 

FPRO-felling production per day 

(M bf) NS HID-number of rubber-tired 

skidding units and the 

hours per day they work 

SPRO-skidding production per day 

with rubber-tired skidders (M bf) 

NT HID-number of units of skidding tractors and the 

hours per day they 

work 

TPRO-skidding production per day 

with tractors (M bf) 

S + TPRO-skidding production per 

day (M bf) 

FELL COSTS 

VC-cost value ($) 

VS-salvage value ($) 

RI RM- interest rate-maintenance 

rate (based on average investment) 

N-number of'years of useful life 

RR-rate of repairs (based on depreciation) 

HRS PER YR-average number of 

hours of use per year 

NO OF PCS-number of pieces 

VC VS-(t he second time) starts 

data over for next category 

as equipment variations 

NO RATE-number of workers-rate 

of pay per hour 

RB RO-percentage of wages paid 

FOR BENEFITS-percentage 

of wages paid for overhead 

SAPCOSTS-saw operating costs 

($/hour) 

SKID COSTS 

VC-cost value ($) 

VS-salvage value ($) 

SOPCOSTS-skidder operating 

costs ($/hour) 

TRACTORCOSTS 

VC-cost value ($) 

VS-salvage value ($) 

NO RATE-number of operatorshourly rate 

RB RQ-percentage sf wages paid 

for benef its-percentage of wages paid for overhead 

TOPCOSTS- tractor operating 

costs ($/hour) 

LOAD COSTS 

VC-cost value ($) 

VS-salvage cost ($) 

TROPCOSTS- truck operating costs 

($/hour) 

AC PRO-actual production (M 

bflday) 

FELL-actual felling costs 

($IM bf) 

SKID-skidding costs ($IM bf) 

LOAD-loading costs ($IM bf) 

TRUCK-trucking costs ($IM bf) 

TOTAL-total logging costs ($IM bf) 
Phillips, Ross A.; Peters, Penn A.; Falk, Gary D. The weak link 

HP-41C hand-held calculator program. Broomall, PA: Northeast. For. Exp. Stn.; 1982; USDA For. Sew. Res. Pap. NE-510. 

12 p. 

Describes a hand-held calculator program (HP-41C) that 

quickly analyzes a system for logging production and costs. 

The program models conventional chain saw, skidder, loader, 

and tandem-axle truck operations in eastern mountain areas. 

The program calculates production of each function of the 

logging system from user-supplied input. System production 

equals the lowest production of any function-the weak link. 

Costs of each function are calculated to obtain logging costs 

in dollars per M bf. 

Keywords: Harvesting costs, logging, hand-held calculator, 

timber production, forest engineering. 
Headguarters of the Northeastern Forest Experiment Station are in 

Broomall, Pa. Field laboratories are maintained at: 

* Amherst, Massachusetts, in cooperation with the University of 

Mshusetts. * 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 

* Hamden, Connecticut, in cooperation with Yak 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 

Pemsylvania State University. 

@ Warren, Pennsylvania. 

* U . S . CaVERNMENT PRINTING OFFICE : 1982-505-0 12 : 3 1