TY - JOUR
AU - Wing, Michael G.
AB - We describe a chip truck travel time prediction simulation model named CHIP-TRUCK. CHIP-TRUCK was developed using global positioning system (GPS) data from chip trucks that were transporting chipped biomass from forest operation sites on steep, single-lane roads. The model was developed based on maximum limiting speeds on a road segment as constrained by road grade, stopping sight distance, road alignment, and changes in driver behavior as road conditions transitioned. A two-pass simulation was used; the first-pass simulation calculated the maximum limiting speeds on each road segment and a second pass simulated driver speed adjustment between segments. Four cases were identified to emulate driver behavior to determine whether a driver will accelerate, decelerate, or continue at current speed. Acceleration and deceleration rates were determined through an optimization procedure that minimized deviations between observed times and modeled times. The model's accuracy for predicting travel time depended on acceleration and deceleration rates. An acceleration rate of 1.5 ft/second2 and deceleration rate of 9.5 ft/second2 gave the best fit for a loaded chip truck. These modeled travel times were within 5% of the observed times and represented an average speed of 19 miles per hour (mph). For an unloaded chip truck, an acceleration rate of 1.5 ft/second2 and deceleration rate of 6.5 ft/second2 gave the best fit. The modeled travel times for unloaded chip trucks were within 5% of the observed times with an average speed of 22 mph. CHIP-TRUCK can benefit operation managers in transportation planning applications involving steep terrain. biomass transport, chip truck, travel time, forest roads The transportation of wood and biomass resources from landing and other collection locations to processing and distribution sites is a substantial cost within the wood supply chain (Coulter et al. 2006, Sessions 2007, Sessions et al. 2010). Fuel, vehicle maintenance, and operator costs are only a fraction of the total transportation budget. Roads also require vigilance and maintenance and must also be monitored for potential negative impacts, such as sedimentation and slope failure (Murphy and Wing 2005). Several studies have found transportation of wood and biomass to be a major contributing factor to the delivered costs. Estimates of the portion of transportation costs fall between 20 and 50% of the delivered cost (Angus-Hankin et al. 1995, McDonald et al. 2001). Compacting materials either before or during loading is one method to reduce transportation costs. Optimization of travel routes can also help reduce costs. Chip trucks have been identified as the most cost-efficient mode of transporting biomass chips, provided the roads are suitable for the trucks. Trucks are generally built for highway use (Rawlings et al. 2004). The efficiency of chipped biomass transportation on forest roads depends on the ability of trucks pulling chip trucks to access forest supply points. Conventional chip trucks differ from roundwood trailers in that they have larger off-tracking around turns than stinger-steered log trucks along with lower clearance and a higher center of gravity, are often heavier, and must return to the forest pulling the unloaded trailer, which reduces gradeability for the unloaded vehicle (Sessions et al. 2010). Several studies and models have been developed to predict log truck travel times (Byrne et al. 1960, Botha et al. 1977, Jackson 1986, Schiess and Shen 1990, McCormack and Douglas 1992, Jalinier and Nader 1993, Shen 1993, Moll and Copstead 1996), but there have been limited studies to predict travel time of chip trucks over forest roads (Rawlings et al. 2004). We present a chip truck travel time prediction simulation model named CHIP-TRUCK. CHIP-TRUCK was developed using data collected through global positioning system (GPS) technology to track and monitor chip trucks that were exclusively used for transporting chipped biomass from forest operation sites in western Oregon. The GPS receivers used in this study collected location and speed information each second and provided a detailed assessment of chip truck movement. Data were collected on 4 separate days. A separate analysis was also conducted to validate and evaluate the accuracy of the data for the development of the model, by comparing measurements from three GPS receivers that were firmly mounted on the dashboard of each of the four chip trucks (Simwanda et al. 2011). Simulation models are classified as aggregate-correlative models or mechanistic models. Aggregate-correlative models are derived from empirical data and present their results in tabular or graphic form or regression formulas (Shen 1993). These models are limited in their applications: they assume that trucks are operating under steady conditions and that they are validated for the local conditions. The data are collected and cannot account for the components of the system, such as driver and/or road alignment (Shen 1993). Aggregate-correlative models, however, are efficient for large-scale or policy-level decisions (Watanatada et al. 1987, Shen 1993). Mechanistic models, on the other hand, are usually developed by simulation using a detailed description of the road alignment, truck parameters (e.g., engine, transmission, and weight), physical principles of motion, and some aspects of driver behavior (e.g., reaction times and maximum deceleration rates). Many forest roads are designed and operated as single-lane roads because of low traffic density, sporadic use, and difficult topography. On these roads, the loaded trucks have the right of way, and unloaded trucks use the turnouts to permit the loaded trucks to pass, increasing the travel time for the unloaded trucks. The Byrne et al. (1960) model (BNG) provides a trip time multiplier for unloaded truck travel time based on traffic frequency. Later, simulation of traffic flow interaction on single-lane forest roads was attempted by Petropoulos (1971). More recent simulation models such as UWTRUCK (Shen 1993), OTTO (Jalinier and Nader 1993), and TRUCKSIM (McCormack 1990) ignore delay times of unloaded trucks in turnouts. The objectives of this study were to develop and validate a travel time prediction model for conventional chip trucks on single-lane forest roads using GPS technology for data collection. The performance of loaded and unloaded chip trucks in this study is restricted to single-lane forest roads. Our study is unique in its use of an exhaustive GPS database that captured the movement of multiple chip trucks across mountainous terrain to simulate travel times. It is also unique in that combinatorial optimization was used to find a best fit of driver acceleration and deceleration rates to fit the observed travel time data. Materials and Methods Our study was conducted on chip trucks that were exclusively transporting biomass from three harvesting operations on forestlands owned by Roseburg Forest Products Company in Dillard, Oregon, USA (Figure 1). The forest roads leading to all the operation sites included both native and unsealed aggregate sections and had a range of gradients from relatively level to 19% in the loaded direction (Table 1). Operations 1, 2, and 4 were situated about 12 miles south of Dillard. For identification and analysis purposes, these operation sites were separated into three components that we refer to as operations 1, 2, and 4. Each of these operations occurred in a different portion of the landscape and was selected based on the various forest canopy conditions that each exhibited. The forest road system associated with operation 1 was characterized by a forest canopy cover mixture of mature and young stands and open areas. The forest roads in operation 2 were characterized by more mature canopy cover than the open areas and almost no young forest canopy conditions. The forest roads in operation 4 had more open areas, very few young stands, and almost no mature forest canopy cover. Figure 1. View largeDownload slide Shaded relief image of operations 1–4. Figure 1. View largeDownload slide Shaded relief image of operations 1–4. Road characteristics of operations 1–4. Table 1. Road characteristics of operations 1–4. View Large Table 1. Road characteristics of operations 1–4. View Large Operation 3 was situated approximately 5 miles east of Lowell, Oregon. There were two smaller, recent clearcuts in the lands surrounding operation 3 roads. Standing forest in operation 3 also included young and mature stands. The forest roads leading to all the operation sites were single lane with turnouts and curve widening, included both paved and unpaved sections, and had a range of gradients from relatively level to 19%. All operations were carried out in 2009: operation 1 on July 30th and 31st, operation 2 on August 7th, operation 3 on August 11th and 12th, and operation 4 on August 26th and 27th. The weather conditions varied among the operations. Operation 1 had 82° F mean temperature, 52% mean humidity, and 6 miles per hour (mph) mean wind speed, operation 2 had 63° F mean temperature, 75% mean humidity, and 2 mph mean wind speed, and operation 4 had 73° F mean temperature, 55% mean humidity, and 4 mph mean wind speed. Operation 3 had 68° F mean temperature, 57% mean humidity, and mean wind speeds of 2 mph. GPS Receiver The GPS receiver used to record location and speed information on the chip trucks was a consumer-grade Visiontac VGPS-900 (Figure 2), which has a 51-channel MTK chipset with enhanced positioning system technology (up to 1.5-m accuracy with differential GPS [DGPS] support). The Visiontac VGPS-900 also comes with a MicroSD slot with support for up to 2 GB of storage capacity (about 25,000,000 locations, also referred to as waypoints). The measurement parameters recorded by this GPS receiver include date, time, latitude, longitude, altitude, speed, heading, fix mode, percent dilution of position (PDOP), horizontal dilution of precision (HDOP), and vertical dilution of precision (VDOP). We reported on the accuracy of this receiver in an earlier study (Simwanda et al. 2011). Figure 2. View largeDownload slide The Visiontac VGPS-900 GPS receiver. Figure 2. View largeDownload slide The Visiontac VGPS-900 GPS receiver. Tractors and Chip Trucks Trucks included the following: a 2007 Peterbilt (model 378SB) with a 500 horsepower (HP) Cummins ISX engine, an 18-speed transmission, and a 3.90 rear end ratio; a 1999 Peterbilt (model 379) with a 425 HP Cummins N14E engine, a 13-speed transmission, and a 3.70 rear end ratio; a 2009 Kenworth (model T800) with a 525 HP Cummins ISX engine, an 18-speed transmission, and a 4.10 rear end ratio; and a 2001 Kenworth (model T800) with a 550 HP Cat C15 engine, an 18-speed transmission, and a 3.70 rear end ratio. The chip trucks included three tandem axle 45-ft long live-floor chip trucks and one tri-axle 48-ft chip truck with a drop center. The tractor and trailer combinations included a tandem axle 45-ft long live-floor chip truck with 18- to 22-ft wheelbase tractors with three or four axles and a tri-axle 48-ft chip truck with a drop center combined with 18- to 22-ft wheelbase tractors with three or four axles (Figure 3). One of the axles on the four-axle tractors was a drop axle and was not used during the operations on forest roads. Table 2 shows the ranges of the average gross vehicle (loaded) weight and the tare (unloaded) weight of the tractor and chip truck combinations. Figure 3. View largeDownload slide Chip trucks used in the study: a tandem driving axle 20-ft tractor, drop axle in raised position, with a tandem axle 45-ft live-floor chip truck trailer (top); a tandem 18-ft tractor with a tri-axle 48-ft chip truck trailer with a drop center (middle); and a loaded chip truck on a single-lane forest road near Roseburg, Oregon (bottom). Figure 3. View largeDownload slide Chip trucks used in the study: a tandem driving axle 20-ft tractor, drop axle in raised position, with a tandem axle 45-ft live-floor chip truck trailer (top); a tandem 18-ft tractor with a tri-axle 48-ft chip truck trailer with a drop center (middle); and a loaded chip truck on a single-lane forest road near Roseburg, Oregon (bottom). Truck statistics. Table 2. Truck statistics. Vehicle weight: loaded (gross), 65,000–80,000 lbs; unloaded (tare), 30,000–34,000 lbs. View Large Table 2. Truck statistics. Vehicle weight: loaded (gross), 65,000–80,000 lbs; unloaded (tare), 30,000–34,000 lbs. View Large Data Collection and Preparation At least four chip trucks were used in each of the four operations and a set of three identical GPS units was placed within each chip truck. The operations were carried out on 7 separate days, and each chip truck made an average of three trips on each day. Data collection occurred during July and August 2009. Each GPS unit recorded an average of 60,000 points at 1-second intervals on each day, which created 5,040,000 points of chip truck location and speed information available for developing and testing the model. The GPS measurements were sieved using ESRI ArcGIS desktop 9.3.1 software so that all periods when the chip trucks were not in motion were removed from the databases. After sieving the GPS data, points were exported for processing to determine the geometry of the roads traversed by the chip truck using a script written in Visual Basic for Applications (VBA) programming language in Microsoft Excel 2007. First, to describe the road geometry, visual inspection was conducted in ArcGIS, and VBA was used to design a method to process the data points into separate road curves based on the change in the heading of each point recorded by the GPS receiver. A number was assigned to each road curve and road geometry parameters of curve radius, curve distance, and road gradient were determined using the GPS points on each separate road curve. Second, road geometry was derived from the GPS data using a curve-fitting procedure developed for this project. The curve-fitting procedure computed road geometry parameters of curve radius, curve distance, and road gradient on each separate road segment determined in the first step. Building the Model and Assumptions An attempt to develop an aggregate-correlative model using regression was made, but this was not possible because the data collected could not satisfy three statistical properties necessary for successful model building using linear regression models: normality, linearity, and homoscedasticity. Nonlinear transformations were also attempted, but these assumptions were still not satisfied. A two-part combined simulation and optimization model approach was therefore explored. The simulation phase predicts the travel time of the tractor and chip truck by determining the maximum (limiting) safe vehicle speed for each road section in the first pass and then uses the limit speeds to simulate the driver's actions (acceleration or deceleration) in the second pass. The model uses a least-squares optimization procedure to derive average acceleration and deceleration rates that most closely match modeled truck travel time to observed truck travel time. The simulation phase of the model begins with an approach similar to the vehicle performance simulation model UWTRUCK (Shen 1993). UWTRUCK uses a two-pass simulation procedure: a backward procedure that calculates the maximum allowable speeds of the truck from the end of the road to the beginning for each section of the road and a forward procedure that simulates the truck's performance by using the limiting speeds from the first pass to simulate the driver's reaction to road conditions ahead. We segmented the road database through an algorithm that processed GPS points into separate road sections/curves based on changes in direction and also through subsequent visual inspection in ArcGIS. The limiting speed for the truck on a road segment is calculated as the minimum of the maximum speeds limited by road grade, stopping sight distance (SSD), sliding, overturning, dust, and road roughness or regulatory limit (Sessions 2007). CHIP-TRUCK calculates the maximum limiting speeds on each road segment on a restricted set of parameters: road grade, SSD, and road curvature. The calculation of limiting speeds on each segment is similar to that presented by Byrne et al. (1960): the model first calculates the maximum speeds limited by road grade, SSD, and road alignment (sliding or overturning) on each road segment based on the road parameters and takes the lowest limiting speed. Unlike the UWTRUCK backward procedure, the CHIP-TRUCK simulation considers the effect of vertical alignment and sight distance on the truck's speed in the first pass along the road segment. This approach is used to prepare the model for the second-pass simulation, which models the driver's behavior based on the limiting speeds calculated in the first pass and does not consider any road parameters. The second pass calculates the allowable speeds by looking at one or two curves ahead and accelerating and decelerating as a driver would. The second pass looks ahead to simulate the driver's actions based on the limiting speeds on the previous curves and the limiting speed of the curves ahead. The acceleration and deceleration rates used by the model originate from a best-fitting optimization procedure described below (see Acceleration and Deceleration Rates section). The total travel time is calculated as the sum of time taken during acceleration and deceleration plus the time taken while traveling at the maximum allowable speeds. The formulas and logic used by the model simulation to predict the travel time are described in the following sections. Maximum Speed Limited by Road Alignment (Sliding or Overturning) The limiting speed of the vehicle around the horizontal curve, ft/second, can be calculated by considering vehicle weight, side friction force, centrifugal force, curve radius, side friction coefficient, and superelevation (Sessions 2007). The model assumes zero superelevation and uses the rollover criterion that determines the maximum speed on a horizontal curve based on the maximum lateral acceleration to prevent rollover (overturning). Douglas (1999) recommends maximum lateral acceleration, a, to prevent rollover to be limited to a design value of a = 0.15 g based on rollover tests by El-Gindy and Woodrooffe (1990). The a = 0.15 g rollover criterion provides results almost identical to those for the Byrne et al. (1960) recommended maximum lateral acceleration to prevent sliding on gravel roads of a = 0.16 g (Sessions 2009)     where F is the force (lb), m is the mass, a is acceleration rate (ft/second2), V is the velocity (ft/second), R is the curve radius (ft), and g is the standard gravity (ft/second2). Therefore, these rollover criteria would limit maximum truck velocity for a loaded truck on a road with zero superelevation to   where R is the radius of the horizontal curve in ft and g is the standard gravity of 32.174 ft/second2 (Sessions 2009). Maximum Speed Limited by Road Gradient The power required to move a vehicle along a road is the total power required to overcome grade resistance, rolling resistance, and air resistance (Byrne et al. 1960). We assume that air resistance is negligible for chip truck travel at low speeds on forest roads. Therefore, to find the maximum speed limited by road gradient, the model simulation first calculates the total force the chip truck has to overcome due to rolling and grade resistance using Equations 4 and 5    where gvw is the gross vehicle weight (lb), θ is the road gradient (degrees), and f is the coefficient of rolling resistance (lb/lb of normal force). Rolling resistance depends on the road surface type, type and condition of tires, and friction of wheel bearings (Byrne et al. 1960). Although the coefficient of rolling resistance of radial truck tires has been shown to increase slightly with speed (Wong 2001), we have assumed it to be constant at speeds typical of forest roads. All forest roads that were traversed during data collection were gravel, and studies in the past that determined the coefficient of rolling resistance for unsealed-aggregate roads recommended values ranging from 0.015 to 0.025 lb/lb (Byrne et al. 1960, Douglas 1999). This model assumes a constant coefficient rolling resistance of 0.02 lb/lb for all roads. The total force required by a vehicle to overcome resistive forces uphill is calculated by adding the grade resistance and the rolling resistance because both forces are opposing the moving direction of the vehicle. The total force required for a vehicle to overcome resistive forces downhill is calculated by subtracting the rolling resistance from the grade resistance because the grade resistance is supporting the vehicle's moving direction and the rolling resistance is opposing this movement. To calculate the speed limited by grade depends on the effective (wheel) horsepower (EHP), which is calculated using efficiencies of the gear transmissions. Sessions (1991) gives the common values of manual gear transmissions efficiencies: 0.90 for direct gears, 0.80 for other gears, and 0.75–0.85 for very high reduction gears. Douglas (1999) also gives a guide to drive train efficiencies based on the pulling vehicle configuration (number of wheels on the pulling tractor by number of drive wheels) and gear type. For a 6 × 4 vehicle Douglas (1999) suggests an efficiency of 0.85 for direct drives and 0.80 for other gears. The maximum net HP at the wheels depends on the operating conditions. Uphill travel depends on engine power output to the drive train to overcome power train energy losses, grade, rolling, and air resistances. Safe downhill travel depends on the power dissipation ability of the engine brake and power train energy losses to maintain a constant speed by dissipating the difference between grade assistance and the sum of rolling resistance and air resistances. During downhill movement, the rolling resistance, air resistance, and internal efficiencies aid engine braking. To determine the EHP for uphill and downhill movement in the model, Equation 6 was solved for EHP using the average fastest speed at the steepest grade and the vehicle weight from the data collected during the study. Based on the comparison to empirical data collected during the study, a maximum of 400 HP was estimated as available for uphill travel. Similarly, for downhill travel, a maximum engine dissipation capacity of 300 HP was established. These EHPs also represent 80 and 60% of the gross HP of the chip trucks used in the study, respectively, which was generally 500 HP. These percentages compare well with the gear transmission efficiencies given by Sessions (1991) and Douglas (1999). Because we have the EHP and the force, the grade-limited speed on the curve is calculated using Equation 6  Maximum Speed Limited by SSD The American Association of State Highway and Transportation Officials (1984) defines sight distance as the length of the roadway ahead that is visible to the driver. The objective is to provide a sufficient sight distance for the driver to safely stop his or her vehicle before reaching objects obstructing the forward motion (Sessions 2007). The safe speed on single-lane roads, for which this model is developed, is limited by the sight distance that permits two trucks approaching each other to stop without colliding or one truck to stop without hitting an obstruction in the road (Byrne et al. 1960). The model simulation calculates SSD as a function of the curve radius (R) and the middle ordinate (M) as developed by Byrne et al. (1960),  The curve radius is used in the equation based on the assumption that the vehicle speeds depend on the radius of the curve (Byrne et al. 1960, Jackson 1986). The middle ordinate is calculated using the height above the road at which the line of sight is tangent to the back slope. After the SSD is determined, the velocity for two vehicles approaching each other is derived from Equation 8  where V0 is the vehicle speed (ft/second), μ is the coefficient of friction, f is the coefficient of rolling resistance (lb/lb), and T is the reaction time (seconds). Solving for V (in mph) gives   The derivation of Equation 9 assumes 3 seconds as the driver's reaction time and a combined coefficient of friction plus coefficient of rolling resistance of 0.4 that is typical of many graveled forest roads (Byrne et al. 1960, Douglas 1999). Modeling Driver's Behavior and Travel Time Modeling driver's behavior is one of the most difficult steps in the development of vehicle simulation models. Drivers vary considerably in operation patterns and their responses to changing road conditions are dependent on the driver's experience and other factors. In the truck performance simulation program OTTO, Jalinier and Courteau (1993) carried out tests using more than 60 drivers to develop the results to derive five driving techniques: fastest driver (A), slowest driver (B), highest consumption (C), lowest consumption (D), and reference driver (E). A driver technique is selected as one of the inputs to the model to incorporate driver behavior simulation in the model. Other models have emulated driver's behaviors through simulating gear shifting in relation to engine revolutions per minute (RPMs), engine torque, engine HP, and road conditions. Truck simulations need detailed control logic to emulate the more important aspects of this highly discretionary driver behavior and the two most important functions are gear shifting and precautionary braking (McCormack 1990). In a log truck performance simulator TRUCKSIM, McCormack (1990) modeled the driver's behavior using gear shifting (upshift or downshift) during simulation that was initiated whenever engine RPM changed based on user-defined limits. This model uses a conceptually similar method in emulating the driver's behavior but does not use the engine properties (HP and RPM) and gear shifting approach of others (McCormack and Canberra 1990, Shen 1993). During travel, it is not likely that the driver of the truck will reach maximum speed on all curves based on the limiting speeds on the road curves before and ahead. The driver will either accelerate or decelerate to ensure that he or she reaches the next curve at a slower or maximum limiting speed. To determine whether a driver will reach the maximum speed or not, four cases are checked (Figure 4). The four cases are applied in the model to determine whether the driver will accelerate, decelerate, or continue at the current speeds. In case I, the driver can either accelerate, reach the maximum limit speed on the road curve and start decelerating before the next curve [case I(a)] or the driver can accelerate, reach the highest nonlimiting speed and immediately start decelerating before the next curve [case I(b)]. In case II, the driver can either enter a road curve at the maximum limit speed, travel at that speed for some time, and decelerate before the next curve [case II(a)] or the driver can just be decelerating throughout the curve [case II(b)]. In case III, the driver can either enter a road curve, accelerate to the maximum limit speed, and travel at that speed until he or she reaches the next curve [case III(a)], or the driver can just be accelerating throughout the curve [case III(b)]. In case IV, the driver can travel at the maximum limit speed throughout the curve. Table 3 contains the nomenclature for the chip truck speeds and curve distances covered as used in Figure 4 and equations for all of the cases. All equations used to calculate the velocities, time taken, acceleration (or deceleration), and distances are derived from Equations 10 and 11. The model has a built in “look ahead feature” that determines which one of the four cases to apply on the current curve. To begin, the model uses this feature to look at the cases that apply to one or two curves ahead to ensure that there is a correct transition from Vfn to Vin from one curve to the next. The acceleration and deceleration rates used in the model were determined through a least-squares method that searched for the combination of a1 and a2 that gave the best fit to the observed travel time data collected and gave the model the best travel time prediction     Figure 4. View largeDownload slide Cases determining the conditions for accelerating and decelerating of a chip truck on a road curve. Figure 4. View largeDownload slide Cases determining the conditions for accelerating and decelerating of a chip truck on a road curve. Key parameters for chip truck speeds, time, and curve distances as used in Figure 4 and equations for the four cases. Table 3. Key parameters for chip truck speeds, time, and curve distances as used in Figure 4 and equations for the four cases. View Large Table 3. Key parameters for chip truck speeds, time, and curve distances as used in Figure 4 and equations for the four cases. View Large Case I Case I applies when Vmax is greater than Vin and Vfn. In this case, it is assumed that the chip truck will either accelerate for a distance S1 to Vmax and move at the same limiting speed for some time before it decelerates for a distance S2 to Vfn [case I(a)] or it will accelerate for a distance S1 to Vmin and immediately decelerate for a distance S2 to Vfn [case I(b)]. The curve distance determines whether the chip truck will accelerate to Vmax or Vmin. To check which situation applies S1 and S2 for case I(a) are calculated using Equations 12 and 13    Because the sum of S1 and S2 in case I(a) is less than S (Figure 4), it is assumed that if the sum of S1 and S2 is greater than S then case I(b) applies, otherwise case I(a) applies. If case I(a) applies, travel time on the curve is calculated as the sum of T1, T2, and TVmax. T1, T2, and TVmax for case I(a) are calculated using Equations 14–16      If case I(b) applies, then Vmin is calculated through Equation 18 and the total time on the curve is calculated as the sum of T1 and T2. For case I(b), S1, S2, T1, and T2 are calculated by replacing Vmax with Vmin in Equations 12, 13, 14, and 15, respectively. Equation 17 is derived from sum of S1 and S2. Since S = S1 + S2; therefore,   Solving for Vmin gives Equation 18  Case II Case II applies when the chip truck reaches a curve at Vmax but has to decelerate at some point because Vfn is less than Vmax. In this case, it is assumed that in case II(a) the chip truck will move at Vmax for the distance S1 and then decelerate for a distance S2 or as in case II(b), it will immediately start decelerating as soon as it reaches the curve for the entire distance S. To check which situation applies, S2 is calculated through Equation 13, and if it is greater than S, then case II(b) applies; otherwise case II(a) applies. If case II(a) applies, the total time taken on the curve is calculated as the sum of T2 (Equation 15) and TVmax is calculated using Equation 16 without S2. If case II(b) applies, it means that the chip truck should have entered the curve with a slower speed than Vmax. Thus, in the model simulation, Vin is recalculated backwards (Equation 19) using Vfn to determine the speed the chip truck should have started with, given the available S for deceleration. The total time taken on the curve is calculated using Equation 14 by replacing Vmax with Vback.   Case III Case III applies when the chip truck enters a curve with Vin less than Vmax and Vfn equal to or greater than Vmax. The assumption in this case is that the chip truck will both accelerate to Vmax for a distance S1 and move at Vmax for a distance S2 [case III(a)] before the next curve or it will accelerate for the entire distance S until it enters the next curve [case III(b)]. To check which case applies, S1 is calculated through Equation 11 and if it is greater than S, then case II(b) applies; otherwise case II(a) applies. If case II(a) applies, then the total time taken on the curve is calculated as the sum of T1 (Equation 14) and TVmax is calculated using Equation 16 without S1. If case II(b) applies, it means the chip truck cannot accelerate to Vmax, given the available distance S, and, therefore, the model simulation calculates the speed (Vfront) that the chip truck will be able to accelerate to through the distance S using Vin (Equation 20). The total time taken on the curve is calculated using Equation 15 by replacing Vmax with Vfront  Case IV Case IV assumes that the chip truck enters a curve with Vin equal to Vmax and Vfn equal to or greater than Vmax. The assumption under this case is that the truck driver can maintain the speed at Vmax but cannot accelerate until he or she enters the next curve. Therefore, the model simulation assumes that the truck driver maintains the speed at Vmax. The total time taken on the curve is calculated by dividing S by Vmax. Turnouts Because loaded trucks were assumed to have the right of way, no delays are included for loaded trucks. If unloaded trucks encounter loaded trucks, either by sight or by radio communication, the unloaded truck uses the turnout. This requires decelerating to a stop and accelerating when leaving the turnout. In this model, the number of turnouts used by unloaded truck is specified exogenously. Acceleration and Deceleration Rates The model's accuracy for predicting travel was highly dependent on the acceleration and deceleration rates. Travel time results from using the limiting velocities on each segment greatly underestimated travel time over the route; i.e., the velocities were too high. Overestimations of travel speeds based on simulations to the limits of truck performance have been observed by others (Moll and Copstead 1996). We used a combination of simulation and optimization to identify the average acceleration and deceleration values that would produce the closest fit between the observed and modeled travel times. Our approach was to minimize the sum of the squared deviations between the observed and modeled roads based on the performance of several different drivers over a randomly selected road and then to use the derived acceleration and deceleration rates to compare modeled travel times to observed travel times for trucks operating on the remaining roads in our database. The model had two dependent decision variables, average driver acceleration and deceleration rates. To evaluate the objective function, the travel time for each of 12 trips to operating sites along a sample road was simulated for a trial acceleration and deceleration rate. A range of acceleration rates from 1 to 5 ft/second2 and deceleration rates from 1 to 10 ft/second2 were evaluated. These ranges represent physically possible acceleration and deceleration rates for loaded and unloaded chip trucks (Botha et al. 1977). The maximum suggested comfortable deceleration rates for logging trucks based on travel speed ranged from 12 ft/second2 at 10 mph to 9 ft/second2 at 30 mph (Botha et al. 1977). The least-squares estimates were done separately for the loaded and unloaded trips (Figures 5 and 6). We calculated percent differences and prediction percentages to check the accuracy of the modeled travel times. The percent differences between the modeled and observed travel times were calculated using Equation 21 (Moll et al. 1996)   For the loaded chip truck, an acceleration rate of 1.5 ft/second2 and deceleration rate of 9.5 ft/second2 gave the best fit. The modeled travel times for the loaded chip truck were within 5% of the observed values for the 12 trips. For the unloaded chip truck, an acceleration rate of 1.5 ft/second2 and deceleration rate of 6.5 ft/second2 gave the best fit. The average speed for the loaded truck was 19 mph. The modeled travel times for the unloaded chip trucks were also within 5% of the observed values for the 12 trips. The average speed for the unloaded truck was 22 mph. Figure 6 shows an example of a speed profile for modeled and observed speeds after using the derived acceleration and deceleration rates. Without the use of transition acceleration and deceleration rates, the modeled travel speeds would have been much higher times with modeled times only 60% of observed travel times. Figure 5. View largeDownload slide Results showing the best fit of CHIP-TRUCK modeled travel times and the observed travel times taken by the loaded chip trucks for 12 trips (shown as 1–12) over the test road. Figure 5. View largeDownload slide Results showing the best fit of CHIP-TRUCK modeled travel times and the observed travel times taken by the loaded chip trucks for 12 trips (shown as 1–12) over the test road. Figure 6. View largeDownload slide Results showing the best fit of CHIP-TRUCK modeled travel times and the observed travel times taken by unloaded chip trucks for 12 trips (shown as 1–12) over the test road. Figure 6. View largeDownload slide Results showing the best fit of CHIP-TRUCK modeled travel times and the observed travel times taken by unloaded chip trucks for 12 trips (shown as 1–12) over the test road. Model Validation The coefficients for acceleration rate and deceleration rate were applied to a total of 33 trips on three other roads. The roads were part of the four operations and are referred to as roads 1 to 4, respectively. The maximum difference between the observed and modeled time for the loaded truck (Figure 7) was 36% with a mean difference of 14%. The largest differences were for road 3, which had the shortest distance where the average modeled travel time was almost 21% less than the observed times. We do note that on road 2, all but one time was overestimated, and all but one time was underestimated on road 3. We believe that this result may reflect the various operation patterns of the different drivers on those particular trips. It might also be that on these trips the drivers did not react to the changing road conditions with consistency. They might have been driving faster or slower than they usually do because of factors that cannot be simulated by the model. For the unloaded chip trucks, the maximum difference between the observed and modeled time for the loaded truck (Figure 8) was generally 28% with a mean difference of 10%. Figure 7. View largeDownload slide CHIP-TRUCK modeled travel times compared with observed travel times for each loaded chip truck road trip. Figure 7. View largeDownload slide CHIP-TRUCK modeled travel times compared with observed travel times for each loaded chip truck road trip. Figure 8. View largeDownload slide CHIP-TRUCK modeled travel times compared with observed travel times for each unloaded chip truck road trip. Figure 8. View largeDownload slide CHIP-TRUCK modeled travel times compared with observed travel times for each unloaded chip truck road trip. Discussion and Future Work Combining simulation and optimization into a chip truck travel time model provided the ability to combine physical performance relationships with driver behavior. The development of the model differs from previous simulation approaches in that driver behavior is simulated based on calculating an average rate of acceleration and deceleration that best fits the observed travel times. Moll et al. (1996) found differences up to 50% between modeled and observed travel times using the OTTO and UWTRUCK models in log truck tests on several US national forests. In their tests, the BNG model gave the best overall comparison on the national forest tests. In our model, the first-pass simulation that determined the limiting speeds for each segment was very similar to the BNG method. However, if we had not included the second pass simulating acceleration and deceleration, we would have greatly overestimated travel speeds. Thus, chip truck performance on mountainous forest roads appears slower than log truck performance on forest roads. Our model predicts the travel time for chip trucks transporting biomass on forest roads and can be used as a template by forest transport managers for planning purposes. The required input data include both truck specifications and road conditions. Road conditions include the total number of curves and the length, radius, and road gradient on each road curve. In addition, road surface type and road width are required. We made an effort to reduce the amount of input data required from the user but acknowledge that some effort will be required in collecting these data. The methodology for estimating travel time by empirically fitting acceleration and deceleration rates is preliminary but appears to be initially promising. We encourage others to examine the approach we used and to consider incorporating different approaches or additional characteristics. The sensitivity of travel time to parameters affecting the limiting speed per segment could be explored. If our limiting speeds were too high, then acceleration and deceleration rates and overall travel time would be affected. In this study, only acceleration and deceleration rates were the decision variables during the least-squares optimization procedure. We could also have included the first-pass variables directly into the optimization procedure so that we could have simultaneously solved for some first-pass coefficients at the same time as the acceleration and deceleration rates. For example, driver reaction times for stopping distances and the coefficient of friction around curves, which is partially based on driver comfort, have been set exogenously. Both of these coefficients could have been allowed to vary over ranges. Acknowledgments: We thank Jason Reed, the owner of Reed's Fuel and Trucking Company (Springfield, OR), and Terrain Tamers Chip Hauling, Inc. (Dillard, OR), for allowing Matamyo Simwanda to ride with their drivers and allowing access to their chip trucks for data collection. Literature Cited American Association of State Highway and Transportation Officials. 1984. A policy on geometric design of highways and streets . American Association of State Highway and Transportation Officials, Washington, DC. 1087 p. Angus-Hankin C. Stokes B. Twaddle A.. 1995. The transportation of fuelwood from forest to facility. Biomass Bioenergy  9( 1–5): 191– 203. Google Scholar CrossRef Search ADS   Botha J. Follette J. Sullitruck E. van Deventer D.. 1977. Link investment strategy model . Institute of Transportation Studies, Res. Rep. UCB-ITS-RR-77-4, Univ. of California, Berkeley, CA. 76 p. Byrne J. Nelson R. Googins P.. 1960. Logging road handbook . USDA For. Serv., Agri. Handbk. 183, Washington, DC. 65 p. Coulter E.D. Sessions J. Wing M.G.. 2006. Scheduling forest road maintenance using the analytic hierarchy process and heuristics. Silva Fenn . 40( 1): 143– 160. Google Scholar CrossRef Search ADS   Douglas R. 1999. Transportation of raw natural resources products from roadside to mill . Univ. of New Brunswick, Fredericton, NB, Canada. 202 p. El-Gindy M. Woodrooffe J.. 1990. Study of roll-over threshold and directional stability of log hauling trucks . Ottawa Division of Mechanical Engineering, Tech. Rep. 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Sessions J.. 2011. Evaluating global positioning system accuracy for forest biomass transportation tracking within varying forest canopy. West. J. Appl. For . 26( 4): 165– 173. Watanatada T. Dhareshwar A.M. Rezende-Lima P.R.S.. 1987. Vehicle speeds and operating costs. Models for road planning and management . The Highway Design and Maintenance Standards Series, World Bank, Washington, DC. 461 p. Wong J.Y. 2001. Theory of ground vehicles , 3rd ed. John Wiley, New York. 528 p. Copyright © 2015 Society of American Foresters
TI - Modeling Biomass Transport on Single-Lane Forest Roads
JF - Forest Science
DO - 10.5849/forsci.14-059
DA - 2015-08-01
UR - https://www.deepdyve.com/lp/springer-journals/modeling-biomass-transport-on-single-lane-forest-roads-644CUISdu0
SP - 763
EP - 773
VL - 61
IS - 4
DP - DeepDyve
ER -