# 5. ESTIMATING LOGGING UNIT COSTS

5.1 Introduction
5.2 Felling and Bucking
5.3 Skidding
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

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

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:

P = (1.0)/.5 = 2.0 m3/min = 120 m3/hr

The cost of log sorting can either be shown as a reduced effective rate of log loading or as a separate subunit 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 roundtrip km and x is the one-way distance. The coefficient b is calculated as

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

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.

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

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 Speedm/min (4)Outhaul Speedm/min (5)Load + Unloadmin/load (6)Delaymin/hr (7)ProductionData (8)m3/hr (9)\$/m3 Fell and cross cut 4.20 - - - - 4 trees/hr1.1 m3/tree 4.4 0.95 Skid 35.00 60 100 5 10 200 m skid2.2 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/load25 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.

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

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.

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 Speedm/min (4)Outhaul Speedm/min (5)Load + Unloadmin/load (6)Delaymin/hr (7)ProductionData (8)m3/hr (9)\$/m3 Fell and crosscut 5.30 - - - 15 90 cm dbh8 m3/tree 6.75 0.79 Crawler tractor 60.00 40 60 10 15 4 m3/load50 m skid 14.9 4.03 Rubber-tired skidder 45.00 80 100 3 10 4 m3/load500 m skid 14.0 3.21 Front-end loader 50.00 - - - 10 2 min/log4 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/load25 km/trip 13.3 3.01 Total 12.17