5/8. ESTIMATING LOGGING UNIT COSTS
Page 1-2-3-4-5-6-7-8
5.1 Introduction
5.2 Felling and Bucking
5.3 Skidding
5.4 Loading
5.5 Truck Transport
5.6 Typical Stump to Mill Logging Systems
5.2 Felling and Bucking
5.3 Skidding
5.4 Loading
5.5 Truck Transport
5.6 Typical Stump to Mill Logging Systems
5.1 Introduction
Logging unit costs are estimated by dividing
machine rates by the production rates for the various logging activities.
Logging components considered here are felling, bucking, skidding, loading, and
transport.
5.2 Felling and Bucking
The major variables in felling and bucking are
the tree diameter and the number of bucking cuts after felling. An example of a
formula for the time to fell and buck a tree is
T = a + b D2 + c B
where T is the time per tree in minutes, b is
the minutes per unit diameter and the D is the diameter, c is the time per
bucking cut and B is the number of bucking cuts. The coefficient a is the time
per tree that is not related to diameter such as walking between trees or
preparing to cut. Sometimes terrain and brush are taken into account by using
equations of the form
T' = (1 + f) T
where f is an adjustment factor for terrain or
brush. The production rate, P, in cubic meters per hour is
P = V/T
where V is the volume per tree, m3, and T is the time per
tree, hr. The unit cost of felling is
UC = C/P
where C is the machine rate for felling and
bucking and P is the production rate.
EXAMPLE:
A power saw and operator cost $5.00 per hour and
the time to fall and buck a tree is
T = 4.0 + .005 D2 + 2.0 B
For a tree with volume 6 m3, dbh of 80 cm and 1
bucking cut
T = 4.0 + .005 (80)(80)
+ 2.0 (1) = 38.0 min = 0.63 hr
P = V/T = 6/0.63 = 9.5 m3 per hr
UC = 5/9.5 = $0.52 per m3
For a tree with volume 1.25 m3, dbh of 40 cm and 1
bucking cut
T = 4.0 + .005 (40) (40)
+ 2.0 (1) = 14.0 min = 0.23 hr
P = V/T = 1.25/.23 = 5.4
m3 per hr
UC = 5/5.4 = $0.93 per m3
5.3 Skidding
Skidding production is estimated by dividing the
volume per load by the time per round trip. The round trip time, T, is the sum
of the times for travel unloaded, hooking, travel loaded, and unhooking.
T = a N + b1 x1 +
b2 x2
where a is the combined time for hooking and
unhooking per log, b1 is the minutes per meter for unloaded
travel, b2 is the minutes per meter for loaded travel, x1 is
the distance from the landing to load pickup point and x2 is
the distance from the load pickup point to the landing. If the outhaul distance
and inhaul distance are the same, the roundtrip time can be expressed as
T = a N + b x
where b is the minutes per roundtrip distance
and x is the one-way distance. The coefficient b is calculated as
b = (V1+V2) / ( V1 V2)
where v1 is the travel speed
unloaded and v2 is the travel speed loaded.
EXAMPLE:
A skidder is bringing in 3 logs with a volume of
4 m3. The unloaded speed is 200 meters per minute and the loaded speed
is 100 meters per minute. The hook time is 1.5 minutes per log and the unhook
and decking time is 1.1 minutes per log. The skidding distance is 300 m. The
machine rate for the skidder and crew is $40 per hour.
T = (2.6) (3) + 300/200
+ 300/100 = 12.3 min = .21 hr
P = 4/.21 = 19.5 m3 per hour
UC = 40/19.5 = $2.05 per
m3
alternatively,
b = (200 + 100)/[(200)
(100)] = .015 min/m
T = (2.6) (3) + .015
(300) = 12.3 min
The cost of hooking, unhooking and decking is
UCF = (C/60) (aN)/V
UCF = (40/60) (2.6)
(3)/4 = $1.30 per m3
The cost per cubic meter of wood per unit
distance (measured one-way), UCV, is
UCV = (C/60) (b)/V
UCV = (40/60) (.015)/4 =
$0.0025/m3-m
At a skidding distance of 300 meters
UC = UCF + UCV = 1.3 +
(.0025) (300) = $2.05 per m3
The same method can be used to estimate the
skidding costs with agricultural tractors and trailers, animals, or with cable
systems.
EXAMPLE:
A team of oxen brings in one log with a volume
of 0.8 m3. The unloaded speed is 30 meters per minute and the loaded speed
is 30 meters per minute. The hook time is 2 minutes and the unhooking and
watering time is 5 minutes. The skidding distance is 100 meters. The rate for
the oxen and driver is $3.00 per hour.
T = (7) + 100/30 +
100/30 = 13.7 min = .23 hr
P = .8/.23 = 3.48 m3 per hour
UC =3/3.48 = $0.86 per m3
5.4 Loading
Loading production is estimated by dividing the
volume per cycle by the minutes per cycle. The time per log for loading single
logs is often as simple as
T = a
where a is the time per cycle.
EXAMPLE:
A truck is being loaded by hydraulic knuckleboom
loader. It is loading 1.0 m3 logs individually at an average rate of 2 per minute. To
prepare for loading trucks, however, the loader spends 30 minutes per hour
sorting logs. What is the loading production rate and cost?
When the loader is actually loading logs, the
production rate is
P = (1.0)/.5 = 2.0 m3/min = 120 m3/hr
but the loading production per machine hour is
60 m3/hr.
The cost of log sorting can either be shown as a
reduced effective rate of log loading or as a separate sub unit cost of the
total logging unit cost. If the sorting cost is included in the loading cost,
the unit cost of loading is then
UC = 40/60 = $0.67 per m3
5.5 Truck Transport
The method of estimating truck production
depends upon the purpose of the analysis. If truck production is being
calculated for the purpose of determining the number of trucks needed for truck
haul, then the average truck load is divided by the total roundtrip time
including unloaded travel time, loading time, loaded travel time, and unloading
time. The calculation is similar to that for skidding with the roundtrip travel
time, T expressed as
T = a + b1 x1 +
b2 x2
where a is the combined time for loading and
unloading, b1 is the hours per km for unloaded travel, b2 is
the hours per km for loaded travel, x1 is the distance from the
landing to load pickup point and x2 is the distance from the
load pickup point to the landing. If the outhaul distance and inhaul distance
are the same, the roundtrip time can be expressed as
T = a + b x
where b is the hours per round trip km and x is
the one-way distance. The coefficient b is calculated as
b = (V1+V2) / ( V1 V2)
where v1 is the travel speed
unloaded and v2 is the travel speed loaded.
EXAMPLE:
A 22-ton truck carries an average of 30 m3 per trip. The haul
route is 35 km. The unloaded truck travels 40 km per hour and the loaded truck
travels 25 km per hour. The combined waiting and loading time is 30 min per
load and the combined waiting and unloading time is 20 min per load. The cost
per truck standing hour is $20 and the cost per truck running hour is $30. What
is the production per hour?
T = (30 + 20)/60 + 35/40
+ 35/25 = 3.11 hrs
P = 30/3.1 = 9.65 m3/hr
The "fixed" unit cost of truck standby
for loading and unloading is:
UFC = ($20/hr) (30 + 20
min)/60 min/hr/30 m3 = $0.56 per m3
The "variable" unit cost of truck
travel is:
UVC = ($30/hr) (35/40 hr
+ 35/25 hr)/30 m3 = $2.28 per m3
or expressed on a ton-km basis:
UVC = ($30/hr) (35/40 hr
+ 35/25 hr)/22 t/35 km = $.089 t-km
The total unit cost of truck haul is:
UC = UFC + UVC = 0.56 +
2.28 = 2.84 per m3
5.6 Typical Stump to Mill Logging Systems
To illustrate the use of machine rates (Section
3) and the production relationships discussed in this section, stump to mill
logging costs for three typical logging systems are shown. In each of these
examples, the stump to mill or water harvesting activities are listed along
with assumed machine rates and production data. The production data are then
converted into production per hour with the conversion method depending on the
form of the data. Unit costs for each activity and a stump to mill or water
cost is calculated.
5.6.1 Plantation Large Wood
Assume clear felling of a pine plantation is
being planned. An estimate is being made of the stump-to-mill harvesting costs
for one possible alternative for the operation. The roads are already in place.
The activities are:
1. Fell, delimb, and cross cut with power saw.
2. Skid to roadside using a rubber-tired
skidder.
3. Load truck trailer using a self-loading
truck.
4. Transport by truck to the mill.
Machine rates (col 2) and production data (col
7) for this example are shown in Table 5.1. The machine rates for the various
labor-equipment combinations of cutter with power saw, rubber-tired skidder
with operator and helper, and truck driver with self-loading truck are
developed using the techniques from Chapter 3. Production estimates are made
from experience, available formulas or tables, or short time studies (Appendix
B). A good source of felling, skidding and loading production for large
plantation wood can be found in Planning Roads and Harvesting Systems by
FAO, 1977.
The formula used for the hourly production
calculation (Table 5.2, col 8) depends upon the information available. On the
following pages production calculations are shown for various harvesting
activities. For the felling, delimbing and cross cutting:
P = 4 trees/hr × 1.1 m3 per tree = 4.4 m3 per hour.
For skidding the logs to the landing by rubber
tired skidder:
T = 5 + 200 m/(60 m/min)
+ 200 m/(100 m/min) = 10.33 min
Assume we have observed about 10 min per hour
are involved in unplanned delays so we can either increase the average time per
trip to
T = 10.33 min × (60/50)
= 12.4 min per trip including delays
or we can reduce the effective hour from 60
minutes per hour to 50 minutes per hour:
P = 2.2 m3/load × 50 min/10.33 min
per trip = 10.6 m3/hr
For loading the truck trailers a short time
study indicates the time per log is 30 sec with an average log size of 0.55 m3. The loader only spends
about 30 minutes per hour loading trucks and the remainder of the time decking
and sorting logs. We have two choices here. We could reduce the loading rate to
create a "sorting and loading production" rate or we could keep the
two production rates separate. A combined sorting and loading rate is used in
Table 5.1.
P (loading only) = .55 m3/log × 2 log/min × 60
min/hr = 66 m3/hr
P (sorting and loading) = 66 m3/hr/2 = 33 m3 per hr
For truck transport to the mill yard:
T (standing) = 45 min per trip = .75 hr
P (standing) = 20 m3/load/.75 hr = 26.7 m3/hr
T (traveling) = 25 km/20 km/hr + 25 km/25 km/hr
= 2.25 hr
P (traveling) = 20 m3/load/2.25 hr = 8.9 m3/hr
After the machine rates and production rates
have been derived, the individual unit costs can be calculated (Table 5.1, col
9). The stump-to-mill cost for this harvesting alternative is $9.58 per m3. Road reconstruction or
road maintenance costs should be added, if appropriate, using the techniques
from Chapter 4.
Table 5.1 Large Wood
Plantation Harvesting Example
(1)
Activity |
(2)
Cost
$/hr |
(3)
Inhaul Speed m/min |
(4)
Outhaul Speed m/min |
(5)
Load + Unload min/load |
(6)
Delay min/hr |
(7)
Production Data |
(8)
m3/hr |
(9)
$/m3 |
Fell and cross cut
|
4.20
|
-
|
-
|
-
|
-
|
4 trees/hr
1.1 m3/tree |
4.4
|
0.95
|
Skid
|
35.00
|
60
|
100
|
5
|
10
|
200 m skid
2.2 m3/load |
10.6
|
3.29
|
Load
|
40.00
|
-
|
-
|
-
|
30
|
2 logs/min
.55 m3/log |
33.0
|
1.21
|
Truck standing
|
20.00
|
-
|
-
|
45
|
-
|
20 m3/load
|
26.7
|
0.75
|
Truck traveling
|
30.00
|
20
km/h
|
25
km/h
|
-
|
-
|
20 m3/load
25 km/trip |
8.9
|
3.38
|
Total
|
9.58
|
5.6.2 Plantation Small Wood
Assume thinning of a young pine plantation is
being planned. An estimate is being made of the stump-to-mill harvesting costs
for one possible alternative for the operation. The roads are already in place.
The activities are:
1. Fell and cross cut with bowsaw.
2. Delimb with axe.
3. Skid to roadside using a hand-guided sulky.
4. Manually load agricultural trailers.
5. Forward by tractor to a transfer yard and
unload using tilt-bed trailers.
6. Load truck trailer using small hydraulic
grapple.
7. Transport by truck to the mill.
Machine rates (col 2) and production data (col.
7) for this example are shown in Table 5.2. The machine rates for the various
labor-equipment' combinations of cutter, worker with sulky, loader, tractor
operator with tractor and trailer, operator with hydraulic loader, and driver
with truck and trailer are developed using the techniques from Chapter 3.
Production estimates are made from experience, available formulas or tables, or
short time studies (Appendix B). A good source of felling, skidding and loading
production rates for small plantation wood can be found in Harvesting
Man-Made Forests in Developing Countries by FAO, 1976.
The formula used for the hourly production
calculation (Table 5.2, col. 8) depends upon the information available. The
analyst must be flexible in the approach to converting the production data to
production units per hour. Two of the production calculations are shown below.
For the felling, delimbing and cross cutting:
P = 5 trees × .1 m3 per tree = 0.5 m3 per hour.
For the manual forwarding operation using the
hand-guided sulky:
T = 1 + 50 m/(10 m/min)
+ 50 m/(10 m/min) = 11.0 min/trip
P = (45 min/hr)/(11
min/trip) × .1 m3/trip = 0.41 m3/hr
Table 5.2 Small Wood
Plantation Harvesting Example
(1)
Activity |
(2)
Cost $/hr |
(3)
Inhaul Speed m/min |
(4)
Outhaul Speed m/min |
(5)
Load + Unload min/load |
(6)
Delay min/hr |
(7)
Production Data |
(8)
m3/hr |
(9)
$/m3 |
Bowsaw fell axe delimb
|
1.00
|
-
|
-
|
-
|
-
|
5 trees/hr
.1 m3/tree |
0.5
|
2.00
|
Manual sulky forward
|
1.10
|
10
|
10
|
1
|
15
|
.1 m3/load
50 m skid |
0.4
|
2.68
|
Manual load
|
1.00
|
-
|
-
|
-
|
-
|
30 logs/hr
.033 m3/log |
1.0
|
1.00
|
Tractor standing
|
9.00
|
-
|
-
|
45
|
-
|
3 m3/load
|
4.0
|
2.25
|
Tractor traveling
|
15.00
|
50
|
60
|
-
|
-
|
3 m3/load
1000 m forward |
4.9
|
3.05
|
Load truck
|
20.00
|
-
|
-
|
-
|
-
|
8 load/hr
3 m3/load |
24.0
|
0.83
|
Truck standing
|
20.00
|
-
|
-
|
45
|
-
|
15 m3/load
|
20.0
|
1.00
|
Truck traveling
|
30.00
|
20
km/h
|
25
km/h
|
-
|
-
|
15 m3/load
25 km/trip |
6.7
|
4.50
|
Total
|
17.31
|
5.6.3 Tropical High Forest
Assume that selective harvest of tropical high
forest is being planned. An estimate is being made of the stump-to-raft
harvesting costs for one possible alternative for the operation. Costs for
roads and unloading dock are not included. The activities are:
1. Fell, delimb, and, cross-cut with power saw.
2. Skid along low standard skid trails to the
high standard skid trail using a crawler tractor and deck logs for later
swinging by rubber-tired skidder to road side.
3. Swing by rubber-tired skidder to road side
and deck.
4. Load by front-end loader on to
truck-trailers.
5. Transport by truck to water. Logs are
unloaded by releasing the trailer stakes.
Machine rates (col. 2) and production data (col.
7) for this example are shown in Table 5.3. The machine rates for the various
labor-equipment combinations of cutter and helper with power saw, crawler
tractor with operator and helper, rubber-tired skidder with operator and
helper, front-end loader with helper, and truck driver with self-loading truck
are developed using the techniques from Chapter 3. Production estimates are
made from experience, available formulas or tables, or short time studies
(Appendix B). A good source of felling, skidding, loading, and transport rates
for tropical high forest can be found in Logging and Log Transport in
Tropical High Forest by FAO, 1974.
Assuming the various production data in Table
5.3 the details of converting data to hourly production rates are shown below.
For the felling, delimbing and cross cutting we
might use a formula adapted from production studies such as:
P = 6 + .1 [DBH - 40 ] -
N m3 per hr.
where DBH = the diameter at breast height (cm)
N = number of cross cuts
made
If the average tree is 90 cm, has 8 m3 of usable wood and
requires 2 bucking cuts, the production per 60 min hour would be:
P = 6 + .1 [90 - 40] - 2
= 9 m3 per hour
Adjusting for a 45 min effective hour we would
have
P = 9 × 45/60 = 6.75 m3 per hour
For breaking the logs out of their beds and
skidding by crawler tractor to the main skid trail, the time is estimated as:
T = 10 + 50 m/(40 m/min)
+ 50 m/(60 m/min) = 12.1 min
Assume we have observed about 15 min per hour
are involved in unplanned delays so we can either increase the average time per
trip to
T = 12.1 min × (60/45) =
16.1 min/trip
including delays or we can reduce the effective
from 60 minutes per hour to 45 minutes per hour:
P = 4 m3/load × 45 min/(12.1
min/trip) = 14.9 m3/hr
For hooking the logs and swinging by
rubber-tired skidder, the time is estimated as:
T = 3 + 500 m/(80 m/min)
+ 500 m/(100 m/min) = 14.25 min
Assume we have observed about 10 min per hour
are involved in unplanned delays, so we increase the average time per trip to
T = 14.25 min × (60/50)
=17.1 min per trip including delays.
or we can reduce the effective from 60 minutes
per hour to 50 minutes per hour:
P = 4 m3/load × 50 min/14.25 min
per trip = 14.0 m3/hr
For loading the truck-trailers a short time
study indicates the time per log is 2 minutes with an average log size of 4 m3 and
an estimated delay of 10 minutes per hour.
P (loading) = 4 m3/log × 1 log/2 min × 50
min/hr = 100 m3/hr
For transport by truck to the log dump we divide
the trip into traveling time and standing time:
T (standing) = 45 min per trip = .75 hr
P (standing) = 30 m3/load/.75 hr = 40.0 m3/hr
T (traveling) = 25 km/20 km/hr + 25 km/25 km/hr
= 2.25 hr
P (traveling) = 30 m3/load/2.25 hr = 13.3 m3/hr
After the machine rates and production rates
have been derived, the individual unit costs can be calculated (Table 5.3, col
9). The stump-to-water cost for this harvesting alternative is $12.17 per m3. Skid trail, road,
landing, log dump construction and road maintenance costs should be added, if
appropriate, using the techniques from Chapter 4.
Table 5.3 Tropical High
Forest Harvesting Example
(1)
Activity |
(2)
Cost $/hr |
(3)
Inhaul Speed m/min |
(4)
Outhaul Speed m/min |
(5)
Load + Unload min/load |
(6)
Delay min/hr |
(7)
Production Data |
(8)
m3/hr |
(9)
$/m3 |
Fell and crosscut
|
5.30
|
-
|
-
|
-
|
15
|
90 cm dbh
8 m3/tree |
6.75
|
0.79
|
Crawler tractor
|
60.00
|
40
|
60
|
10
|
15
|
4 m3/load
50 m skid |
14.9
|
4.03
|
Rubber-tired skidder
|
45.00
|
80
|
100
|
3
|
10
|
4 m3/load
500 m skid |
14.0
|
3.21
|
Front-end loader
|
50.00
|
-
|
-
|
-
|
10
|
2 min/log
4 m3/log |
100.0
|
0.50
|
Truck standing
|
25.00
|
-
|
-
|
45
|
-
|
30 m3/load
|
40.0
|
0.63
|
Truck traveling
|
40.00
|
20
km/h
|
25
km/h
|
-
|
-
|
30 m3/load
25 km/trip |
13.3
|
3.01
|
Total
|
12.17
|
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