The terrain in the operating area limits ground equipment. In the uphill situation, the machine horsepower is the limiting factor, while in the downhill situation, operator safety and production become the limiting factors. When yarding downhill, if the slope is too steep, the logs being yarded are very hard to control. This in turn causes production delays when the operator has to get out of the cab and free a hung up turn. The following table shows the conditions under which each piece of equipment can operate:

Table 5. Conditions under which each piece of equipment can operate.

Equipment Type	Uphill	Downhill
Wheeled Skidder	15%	25%
Tracked Skidder	20%	30%
Shovel	20%	35%
Feller-Buncher	20%	30%

As a rule of thumb 20% uphill, and 30% downhill was used as a cut off between ground based systems and cable systems.

Cable systems are limited less by the percent slope and more by shape of the ground. Cable systems are best suited for areas where the slopes were between 30% and 100+%. The major limiting factor is shape. A ground profile can be classified as concave, planar, or convex. The ideal ground profile is highly concave. This allows the cable system the greatest deflection, and therefore the highest payloads. The worst case profile is highly convex. This ground shape affords little or no deflection and therefore payloads tend to be uneconomical. In the planar case, deflection can usually be found, but most times this requires rigging a tailhold tree 30-50 feet high.

The major benefit of a helicopter system is that it doesn’t need road access into the unit. This can be a huge benefit in steep, remote areas where road building is too costly or physically unfeasible. The first limiting factor of this harvest system is its landing size requirement. A helicopter landing must be at least four acres in size. This is to accommodate both the landing/decking of logs as well as the refueling of helicopters. The second limiting factor for this system is external yarding distance. For helicopter yarding the maximum external yarding distance is approximately one mile.

We chose to look at seven different yarding systems. Each system was best suited for a particular terrain/distance combination. Below are the yarding systems and their design terrain/distance combination:

Table 6. Design terrain of each yarding system.

System	Typical EYD	Type of System
90 ft Tower	2000-4000 ft	Long Span
70 ft Tower	< 2000 ft	Conventional
52 ft Tower	< 2000 ft	Conventional & Long Span
40 ft Tower	< 2000 ft	Cable Thinning
Shovel	< 750 ft	Conventional
Tracked Skidder	< 500 ft	Conventional
Helicopter	< 5500 ft	Alternative

Shown below is a list of what components comprise each system:

Table 7. System components.

System	Yarder	Helicopter	Shovel	Skidder	Felling/Bucking
Cable	1	0	1	0	Manual/Manual
Shovel	0	0	2	0	Feller Buncher/Stroke Delimber
Tracked Skidder	0	0	1	2	Feller Buncher/Stroke Delimber
Helicopter	0	1	1	0	Manual/Manual

We have chosen to use the cycle time equation provided in the Caterpillar Performance Handbook, Edition 28. This equation takes into consideration the specifications of a 527 grapple skidder. The travel time is added to the given fixed times to find the time it takes for one cycle. The travel time can be found by dividing the length of the average skid trail by the travel speed of the skidder. This is calculated for the return empty and the haul load. Then the fixed times to maneuver the machines and to hook, unhook and deck logs provided in the handbook were added to the travel time to find the cycle time (the fixed time was given as 1.5 minutes). We then divided the volume per cycle by the cycle time to find the rate of production.

Travel Time (return empty) = (length of average skid trail) * (speed of skidder for return empty)

Travel Time (haul load) = (length of average skid trail) * (speed of skidder for haul road)

Fixed Times = (time to maneuver machines) + (time to hook) + (time to unhook) + (time to deck logs)

Cycle Time = travel time (return empty) + travel time (haul load) + fixed time

Production Rate = (volume per cycle) / (total cycle time)

The cycle time equation created by Ervin J. Brooks from the U.S. Forest Service was chosen for our analysis. The following five different equations were used in order to find the total cycle time:

Adverse Travel Empty (min) = .390283 + (0.002595 * distance)

Regeneration Loading Time (min) = 4.866 + (0.00000376 * pieces per load * payload weight)

Regeneration Move Time (sec) = 4.793 + (0.3049 * distance)

Favorable Travel Loaded (min) = 0.194106 + (0.003061 * distance)

Off Load (min) = 47.352151 + (0.543382 * grapple loads) – (3.609467 * pounds per board foot)

Originally, the equations for time spent traveling empty and time spent traveling loaded were separated into two categories: adverse and favorable grade. Also, the equations for loading time and moving time were divided into two categories: regeneration harvest and thinning harvest. For our analysis, it was assumed that we would be travelling empty on an adverse grade and traveling loaded on a favorable grade. It was also assumed that we would be dealing with a regeneration harvest.

Then, in order to find the total cycle time, the values of the previous five equations were added. The production rate was then calculated by dividing the log volume per cycle by the total cycle time as shown in the following equations:

Total Cycle Time = travel empty + load time + move time + travel loaded + off load

Production Rate = (volume per cycle) / (total cycle time)

The cycle time equation created by Penn Peters was chosen to model the cycle time for a swing yarder. The cycle time, turns per unit, number of corridors in unit and the total cycle time were calculated using the following equations. To clarify, the area of the rectangular corridor was assumed to be twice the average yarding distance times twice the lateral yarding distance.

Cycle Time (min) = 4.443 + .00163 * AYD

Turns per Unit = (volume per acre * area of unit) / (turn volume)

Number of Corridors in Unit = (area of unit * 43560 sq. feet per acre) / (2 * LYD *2 * AYD)

Total Cycle Time = (cycle time / 60 minutes per hour) * (turns per unit)

In order to calculate the rigging time, it was assumed that one corridor change would take one half-hour. No initial set up time was assumed. However, the time per corridor change can easily be changed in the equation with a better time estimation. Also, any additional setup time can be added to this equation. The following equation was used:

Total Rigging Time = (.5 hours per corridor) * number of corridors in unit

Finally, the following equation was used in order to find the production rate of the swing yarder:

Production Rate = (volume per acre * area of unit) / (Total Yarding Time + Total Rigging Time)

The cycle time equation created by Penn Peters was chosen to model the cycle time for a 70-foot tower for both short span and long span analysis. Since cycle time in this equation is only dependent on AYD, no separate equation is used for long span analysis. The cycle time, turns per unit, area of corridor, number of corridors in the unit and the total cycle time were calculated using the following equations. To clarify, the area of the corridor was assumed to be the external distance EYD times the lateral yarding distance (LYD) for the case of a central yarding unit (fan-shaped) and EYD*2*LYD for the case of parallel settings.

1/12^th of the area of a circle with a radius of EYD.

Cycle Time (min) = 4.443 + .00163 * AYD

Turns per Unit = (volume per acre) * (area of unit) / (turn volume)

Area of Corridor

parallel setting = EYD*(2*LYD),

fan-shaped setting = EYD*(2*LYD)

Number of corridors in Unit = (area of unit * 43560 sq. feet per acre) / (Area of Corridor)

Total Cycle Time = (cycle time / 60 minutes per hour) * (turns per unit)

In order to calculate the rigging time, it was assumed that one corridor change would take .25 hours for short span analysis and .41666 hours for long span analysis. An initial set-up time of 6 hours was used. Again, the time per corridor change can easily be altered in the equation with a better time estimation. Also, any additional setup time can be added to this equation. The following rigging time equations were used:

Total Rigging Time (short span) = (number of corridors * .25 hours) + 6 hours

Total Rigging Time (long span) = (number of corridors * .41666 hours) + 6 hours

Finally, the following equation was used in order to find the production rate of the 70-foot tower:

Production Rate = (volume per acre * area of unit) / (Total Yarding Time + Total Rigging Time)

Binkley’s cycle time equation in the form that was presented in the paper, Comparing Long-Span vs. Conventional Skyline Design Options: Economics and Silvicultural Options by Peter Schiess and Weikko Jaross was used to model the long span cycle time for a 90-foot tower. The cycle time, turns per unit, number of corridors in the unit and the total cycle time was calculated using the following equations. To clarify, the area of the rectangular corridor was assumed to be twice the average yarding distance times twice the lateral yarding distance.

Cycle Time = 2.94608 + 0.00819 * (slope under skyline^♦♦) + (0.16345 * logs per turn) + (0.001277 * AYD) + (.003839 * LYD) + (.000001384 * LYD * vol per turn) + (.004127*vol per turn) + (10^(0.89995 + 0.0020715 * LYD))/10 + (10^(0.6147 +0.3169*(slope perpendicular to skyline^♦♦) + .09082 * logs per turn))/10

^♦♦ slope is to be entered as tenths of a percent (e.g. 80% should be entered as 8)

Turns per Unit = (volume per acre) * (area of unit) / (turn volume)

Number of corridors in Unit = (area of unit * 43560 sq. feet per acre) / (2 * AYD * 2 * LYD)

Total Cycle Time = (cycle time / 60 minutes per hour) * (turns per unit)

The rigging time was calculated using an equation from Weikko Jaross. This rigging time equation was based on information taken from the program Sky Appraisal and the rigging time equation that was derived from the data points from the Swiss Federal Forest Research Institute that was presented in the paper by Peter Schiess and Weikko Jaross.

Total Rigging Time = (EYD * 0.0115 + 3 * crew size + 19.5 * number of intermediate supports +10.5 * 2) * number of corridors –5*(number of corridors – 1)

Finally, the following equation was used in order to find the production rate of the 90-foot tower.

Production Rate = (volume per acre * area of unit) / (Total Yarding Time + Total Rigging Time)

By combining the equipment costing information with the production information we can obtain the contractor’s cost per unit volume and/or cost per day. This is particularly useful when reviewing timber sale bids. If the low bid is significantly lower than expected, it may be cause for further review.

In order to get the full range of values we analyzed each system based on a high, low, and average capital cost. This translated into a contractor with brand new, very used, and average machinery. In order to better estimate costs, we included all equipment, owning and operating, and overhead cost associated with a sale. To do this we determined all the equipment that is required for a "typical" timber sale. This equipment was combined into nine different systems. All tower systems included the tower, a shovel, and assumed manual felling/bucking. The shovel system included two shovels, a feller buncher, and a stroke delimber. Our tracked skidder system was defined as two skidders, a feller buncher, and a stroke delimber. The harvester system consisted of a harvester with processor head, a forwarder, and a shovel. Our helicopter system consisted of a logging helicopter, a crew/rigging helicopter, a shovel, and manual felling/bucking with no pre-bunching.

A spreadsheet was developed to find the total cost in dollars per day for each system. The World Forest Institute (WFI) Logging Cost Estimator was used to verify the spreadsheet results.

Our analysis took into account the fact that heavy equipment is only available to work a certain percentage of the time due to mechanical failures. Similarly, extreme hot or cold weather can halt a logging operation causing downtime. Therefore, the results are truly in dollars per "worked" day.

This cost analysis resulted in a total system cost per day. Below are the results of this analysis:

Table 8. Daily cost rates for various harvesting systems

System	Cost/Day
90 ft Tower	$3,795
70 ft Tower	$3,872
52 ft Tower	$3,860
40 ft Tower	$3,294
Shovel	$5,072
Tracked Skidder	$6,007
Harvester	$3,449
Helicopter	$15,445

A copy of spreadsheet used in this analysis can be found in the appendix.