A Simulation of Boom Length Effects For Drift Minimization

M. E. Teske, H. W. Thistle, J. W. Barry, B. Eav

ABSTRACT. The near-wake portion of the USDA Forest Service aerial application prediction model FSCBG is applied to a sensitivity study of the length of the spray boom relative to the length of the aircraft wingspan or helicopter rotor diameter. Building on extensive previous work, this study examines the predictions by the near-wake Lagrangian trajectory model of swath width, mean deposition within the spray block, and drift fraction downwind of the edge of the field. Ten aircraft and four BCPC droplet size distributions are used to simulate a typical agricultural application scenario. Findings from this study demonstrate the effects of varying boom length on downwind drift, the reduction of downwind drift with larger droplets, and the inherent ability of certain aircraft type to reduce downwind drift more easily than others. Model results indicate that a broad range of boom length (between 60 and 100% of aircraft wingspan or helicopter rotor diameter) recovers approximately the same levels of downwind drift, decreasing levels of mean deposition within the spray block, and increasing swath width between flight lines. The suggestoin that boom length should be less than 75% of wingspan or rotor diameter is perhaps based more on the anticipated position of the rolled-up vortices than on solid experimental evidence.

Keywords.Drift, Boom length, Aerial spraying, Sensitivity, Modeling.

Over the last 25 years the USDA Forest Service has been pursuing the development of computer models to predict the dispersion and deposition of aerially released spray material. The two current models available are AGDISP (Bilanin et al., 1989) and FSCBG (Teske et al., 1993). FSCBG (for Forest Service Cramer-Barry-Grim) predicts the transport and behavior of pesticide sprays released from aircraft, influenced by the aircraft wake and local atmospheric conditions, through downwind drift and deposition. The AGDISP (for AGricultural DISPersal) near-wake model, contained within FSCBG, solves a Lagrangian system of equations for the position and position variance of spray material released from each nozzle on the aircraft. The FSCBG far-wake model begins with the results of AGDISP at the top of the canopy or near the ground, and solves a Gaussian dispersion equation to recover ground deposition. The inclusion of AGDISP within FSCBG creates a powerful predictive tool for dispersal of spray material from multiple line sources. The model considers evaporation, canopy penetration, total accountancy and environmental fate.

FSCBG has undergone continued development, refinement, and enhancement over its lifetime (Dumbauld, Bjorklund and Saterlie, 1980; Bjorklund, Bowman and Dodd, 1988; Curbishley and Skyler, 1989; Teske and Curbishley, 1991, 1994). Model validation summaries may be found in Teske, Barry and Thistle (1994) and Teske, Thistle and Barry (1996). The near-wake portion of FSCBG (the AGDISP model) has been selected by the Spray Drift Task Force (SDTF), and renamed by them as AgDRIFT, for pesticide registration in the United States (Teske et al., 1997).

One of the areas in which predictive models can have great impact is in revealing trends in effects due to changes in input parameters. This is especially true in the case of complex problems, such as the aerial application of pesticides, where the wake formed by the aircraft creates a flow field superimposed over the ambient meteorological background, and into which spray material is released. The effects of different nozzles ejecting spray material (and the droplet size distributions produced), ambient wind speed, release height, evaporation, and any other parameter affecting this problem, have the possibility of significantly altering the downwind deposition pattern created by the typical spraying scenario.

Over the years practical experience (and some computer simulation support) has led to shorter boom lengths on aircraft, down from their original lengths (as far out as the wing or rotor blade tips) to 75% of the aircraft wingspan or helicopter rotor diameter. Ideally, the circulation load distribution on a wing or rotor blade will roll up into two distinct vortices, beginning at the wing or rotor blade tips and quickly moving inboard. For an elliptically loaded surface (encompassing most wings and rotor blades) the final vortex positions will be located 78.5% of the distance from the center of the wing or rotor blade to the tip (Donaldson and Bilanin, 1975). If boom lengths are less than this distance, the initial vertical velocity felt by the released spray material would be downward, and deposition should be enhanced. In less-clean configurations, such as those with winglets, the final vortex positions would be located more toward the wing or rotor blade tip (but never at the tip, which would result in unacceptably high drag effects), and the vortex strength would be correspondingly reduced (Betz, 1932). Quantifying boom length effect would require a careful field study or the use of a validated simulation model. Recently, the SDTF has validated the near-wake model within FSCBG with a series of field studies, wind tunnel measurements of droplet size distribution, and laboratory measurements of evaporation rate (Bird et al., 1997). With this validated model we may then make the sensitivity predictions needed for varying boom length, and compare results. These sensitivity predictions are presented here.

THE AGDISP WAKE MODEL

The near-wake model is a Lagrangian model of the form: where Xj, Vi, and Ui are the ensemble-averaged ith components of droplet position, droplet velocity, and local fluid velocity, respectively. The fluctuating ith components of droplet position, droplet velocity, and local fluid velocity are xi, vi, and ui, respectively, gi = (0,0,-g) is gravity, and t is time. The mean square turbulence level is q2 = (u;u) + (vjvj) + (w;wj). K is a function of the mean relaxation time iJ) (the rime for Vi to approach U;) and the turbulent travel time Tt (the time for released material to pass through a typical eddy). Brackets ( ) indicate turbulent correlation. Equations 1 and 2 describe the mean flight path of a droplet, while equations 3-7 describe the spread of the droplet cloud. The AGDISP model is primarily concerned with deposition. Equations 1 and 2 are used to track the droplets to the ground, while equations 3-7 are employed to determine the resulting spatial distribution there. The Lagrangian approach assumes a neutrally buoyant background, and can be solved exactly if a small enough time step is used. The calculation of Ui near the aircraft is based on models described by Bilanin et al. (1989) from initial work by Reed (1953). For example, the aircraft wake flow field is controlled by a pair of counter-rotating vortices, described for an elliptically loaded wing by: 2 W " pasU- where W is aircraft weight, U_ is flight speed, s is semispan (one-half the aircraft wingspan or helicopter rotor diameter), pa is air density, and h is circulation strength. The vortices are located on either side of the aircraft or helicopter at a distance tts/4 from the center of the fuselage.

APPROACH

Previous work in this area includes initial studies of near-wake sensitivity (Teske, 1992; MacNichol, 1994), a general assessment of the importance of inputs into the FSCBG model (Teske and Barry, 1993), and a complete examination of the sensitivity of the near-wake model (Teske, 1996). These studies begin with a set of default conditions (for release height, wind speed, temperature, and relative humidity, for example), then vary each variable with all other variables held constant, toward the goal of spanning changes in the variables of interest. In several cases more than one variable is changed concurrently (for multiple effects). Unfortunately, a complete examination of the problem (with all variables changing randomly and accounted for) is out of the question, simply because of the staggering number of calculations that would be required.

However, it became clear-mostly from knowing which variables are more influential in the equations solving the problem, and from having observed the effects of specific variables in field situations-that certain variables are more important than others. Not surprisingly, these independent variables include (Teske and Barry, 1993) aircraft type, volume median diameter (droplet size distribution of the spray material produced by the nozzle), release height, wind speed, wind direction, spraying speed of the aircraft, aircraft weight, boom length, nonvolatile fraction of the released spray material, specific gravity of the tank mix, and temperature and relative humidity. Downwind distance is a dependent variable that is important when setting buffer distances.

Depending on the measure taken, or the default conditions assumed, any one of these variables can influence the deposition of the released spray material. Droplet size distribution, release height, and wind speed play important roles in the deposition problem (Bird et al., 1996), with boom length generally considered less important. It would seem useful, then, to quantify the effect of boom length, in an effort to understand why shorter boom lengths are considered better for controlling drift. To this end we develop near-wake predictions varying only boom length, for ten aircraft types and four droplet size distributions. These predictions are compared by developing the optimum swath width and corresponding mean deposition within the spray block, and drift fraction of applied spray material downwind of the edge of the field. Here the edge of the field is defined as a line parallel to the aircraft flight lines, located a specified swath displacement downwind of the farthest downwind flight line. The optimum swath width is obtained for a coefficient of variation (COV) of 0.3 for the deposition within the spray block, consistent with Parkin and Wyatt (1982), Spillman (1983), and Quantick (1985). Since swath displacement is assumed to change with swath width, both change for each change in model input conditions. We use 20 flight lines to represent the width of the spray block consistent with the Tier I assessment in AgDRIFT (Teske et al., 1997). Because optimum swath width varies with every model run, the actual spray block width sprayed will be different for every model run as well. The effects of the most upwind flight lines are assumed to be small when compared to the effects of the downwind flight lines closer to the edge of the field.

MODEL INPUTS

The sensitivity study specifically focused on boom length; thus, we hold constant nearly all physical parameters in the near-wake model of FSCBG (as summarized in table 1), and vary only aircraft type, droplet size distribution, and boom length.

AIRCRAFT TYPE

Previous sensitivity studies examined several aircraft (both fixed-wing and helicopter). Here we concentrate on ten: four single-wing aircraft (Air Tractor AT-401, Air Tractor AT-502, Ayres Turbo Thrush S2R-G1/400, and Cessna AgHusky 188), two biplanes (Schweizer Ag-Cat G164B/450 and Stearman N2S-3), and four helicopters (Aerodyne Wasp, Bell 47G-3B-2A, Bell JetRanger 111206 B3, and Hiller 12E Soloy Turbo). Aircraft characteristics were taken from the FSCBG aircraft library, and confirmed by L. F. Bouse (1996, private communication). The aircraft parameters needed for the model are summarized in table 2.

Table 1. Default case conditions for the boom length sensitivity study
Parameter Value
Aircraft types As defined in table 2
Boom height 3.05 m
Wind speed 1.34 m/s
Wind direction 90o crosswind to flight line
Temperature 18.33oC
Relative humidity 60%
Droplet size distributions BCPC fine, medium, coarse, very coarse
Nonvolatile fraction 0.03
Application rate 100 L/ha
Number of flight lines 20
Boom length 40 to 120% wingspan or rotor diameter
Nozzle spacing 0.25 m
Swath width Optimized for COV = 0.3
Swath displacement 1.5 swath widths (BCPC fine)
1.0 swath widths (BCPC medium)
0.5 swath widths (BCPC coarse and very coarse)

Table 2. Characteristics for the ten aircraft used in the boom length sensitivity study
Characteristic Air Tractor Air Tractor Ayres Turbo
Value AT 401 AT-502 Thrush S2R-G 1/400
Wingspan (m) 14.94 15.24 14.48
Weight (N) 26690 29620 28700
Planform Area (m2) 27.31 27.87 32.50
Spraying Speed (m/s) 53.6 69.3 62.6
Biplane Distance (m) - - -
Propeller RPM 2000 2200 2000
Propeller Radius (m) 1.37 1.34 1.34

Characteristic Cessna Schweizer Stearman
Value AgHusky 188 Ag-Cat G164B/450 N2S-3
Wingspan (m) 12.70 12.96 9.80
Weight (N) 14910 22340 9560
Planform Area (mz) 19.20 36.40 26.94
Spraying Speed (m/s) 47.5 51.4 42.9
Biplane Distance (m) - 1.86 1.52
Propeller RPM 2700 2300 1950
Propeller Radius (m) 1.0 1.34 1.37

Characteristic Aerodyne Bell
Value Wasp 47G-3B-2A
Rotor Diameter (m) 10.60 11.32
Weight (N) 9300 10770
Rotor RPM 320 370
Spraying Speed (m/s) 27.7 25.9

Characteristic Bell Hiller
Value JetRanger 111 206 B3 12E Soloy Turbo
Rotor Diameter (m) 10.16 10.80
Weight (N) 9690 10550
Rotor RPM 384 394
Spraying Speed (m/s) 30.8 25.9

 

DROPLET SIZE DISTRIBUTION

Previous sensitivity studies used a wide variety of nozzle types to produce a breadth of droplet size distributions, with effort going into finding nozzle types (and their droplet size distributions) that span the distributions anticipated in aerial application. Here we make use of the four established BCPC (British Crop Protection Council) droplet size distributions (Doble et al., 1985; Southcombe, 1988; Parkin et al., 1994), representing the volume fraction average between the very fine and fine nozzle types (designated Fine), fine and medium nozzle types (designated Medium), medium and coarse nozzle types (designated Coarse), and coarse and very coarse nozzle types (designated Very Coarse). These droplet size distributions are plotted in figure 1. The Fine, Medium, Coarse and Very Coarse designations are those identified with the Tier I assessment in AgDRIFT (Teske et al., 1997), as are the swath displacements assumed here: 1 1 /2 swath widths for Fine, 1 swath width for Medium, and 1 /2 swath width for Coarse and Very Coarse. Nonvolatile fraction is assumed to be 0.03, again consistent with the Tier I assessment in AgDRIFT.

Figure 1
Figure 1-BCPC droplet size distributions.

BOOM LENGTH

To capture the full range of effects possible with changes in boom length, we vary the boom length (as a percentage of aircraft wingspan or helicopter rotor diameter) as 40, 50, 60, 65, 75, 85, 95, 100, 110, and 120%. Nozzles were positioned 0.25 m apart.

A total of 400 runs was required to generate the results presented in this article. A typical result, for 65% boom length for the Cessna AgHusky 188, is shown in figure 2.

RESULTS

FSCBG model predictions were saved as ground deposition patterns of percentage of applied nonvolatile spray material released. From the ground deposition for a single flight line, we computed the optimum swath width (for COV = 0.3) and the corresponding mean deposition within the spray block, then set the swath displacement consistent with the BCPC droplet size distribution used, constructed the 20 flight line deposition pattern, and computed the drift fraction downwind of the edge of the field. With this construct the product of swath width with mean deposition will be approximately constant. Because each aircraft type (single-wing aircraft, biplanes, and helicopters) produce essentially the same patterns (Teske, 1998), we additionally averaged results across aircraft type. Swath width results are shown in figures 3 to 5, mean deposition results in figures 6 to 8, and drift fractions in figures 9 to 11.

Figure 2
Figure 2-The predicted deposition patterns from a Cessna AgHusky 188 with the aircraft characteristics given in table 2, for the default case conditions summarized in table 1 for 65 % boom length and one flight line. Swath widths are 21.0 m (BCPC Fine), 18.06 m (BCPC Medium), 14.99 m (BCPC Coarse), and 13.68 m (BCPC Very Coarse).

Figure 3
Figure 3-Single-wing aircraft swath width sensitivity (in percent of wingspan) to boom length (in percent of wingspan) for the BCPC droplet size distributions shown.

Figure 4
Figure 4-Biplane swath width sensitivity (in percent of wingspan) to boom length (in percent of wingspan) for the BCPC droplet size distributions shown.

Figure 5
Figure 5-Helicopter swath width sensitivity (in percent of rotor diameter) to boom length (in percent of rotor diameter) for the BCPC droplet size distributions shown.

Figure 6
Figure 6-Single-wing aircraft mean deposition sensitivity (in percent of applied) to boom length (in percent of wingspan) for the BCPC droplet size distributions shown.

For the most part all results trend correctly with regard to droplet size distribution; i.e., BCPC Fine recovers the largest swath widths, smallest mean depositions, and largest drift fractions. Swath width generally increases with boom length mean deposition decreases with boom length, and drift fraction remains fairly constant (except for BCPC Fine). The other trends are:

Figure 7
Figure 7-Biplane mean deposition sensitivity (in percent of applied) to boom length (in percent of wingspan) for the BCPC droplet size distributions shown.

Figure 8
Figure 8-Helicopter mean deposition sensitivity (in percent of applied) to boom length (in percent of rotor diameter) for the BCPC droplet size distributions shown.

Figure 9
Figure 9-Single-wing aircraft drift fraction sensitivity (in percent of applied) to boom length (in percent of wingspan) for the BCPC droplet size distributions shown.

Figure 10
Figure 10-Biplane drift fraction sensitivity (in percent of applied) to boom length (in percent of wingspan) for the BCPC droplet size distributions shown.

Figure 11
Figure 11-Helicopter drift fraction sensitivity (in percent of applied) to boom length (in percent of rotor diameter) for the BCPC droplet size distributions shown.

Two special features occur in these figures: the decrease in swath width (and corresponding increase in mean deposition) for boom lengths above 80% in helicopters, and the behavior of drift fraction for the BCPC Fine droplet size distribution. These features may be explained by realizing that for the release height considered here (3.05 m) the rolled-up vortices from the single-wing aircraft will be located closer to the ground than to the aircraft centerline. Spray material rotating around these vortices will encounter the ground before they are forced aloft on the outboard side of the vortices. This effect decreases swath width and increases mean deposition when boom lengths are small (pilots spray closer to the ground to take advantage of the preferential effect of the rotational motion induced on the released spray material by the vortices). Higher release heights may alter the results presented here, as more spray material would be entrained in the vortices, and be available for drift.

As boom length increases, more spray material is released closer to the vortex centers, spreading the spray material laterally and increasing swath width and decreasing mean deposition. When the boom length increases above 78.5%, spray material is released on the outboard side of the vortices; this material undergoes an additional one-half turn within the vortex before being directed toward the ground. Swath width continues to increase, and mean deposition continues to decrease.

The helicopter results show a decrease in swath width (and corresponding increase in mean deposition) for boom lengths above 78.5%. Helicopter vortices are rolled up near the rotor blades, at a vertical location considerably higher than the spray boom itself. The resulting vortices lift the smaller spray droplets aloft, rather than forcing them to deposit as in the single-wing aircraft case. This effect results in higher drift fraction and lower swath width, as less material deposits beneath the helicopter to define the optimum swath. Mean deposition must increase to accommodate COV = 0.3. The downwash effect experienced under the helicopter rotor blades is quickly replaced by single-wing aircraft-like vortices (within a distance of two rotor diameters behind the helicopter). This downwash effect augments the deposition of spray material released close to the centerline of the helicopter.

The biplane vortical field is far more complicated than either the single-wing aircraft or the helicopter, because of the presence of a second pair of vortices above the first pair, and the mutual action of the vortices on either side of the aircraft centerline to rotate around each other. In this rotation process released spray material is swept into the vortices, and larger levels of drift fraction result.

Overall, as boom length increases, more spray material should become entrained in the vortices, and drift fraction should increase. However, figures 9 to 11 illustrate the presence of a distinct local maximum in the drift fraction for the BCPC Fine droplet size distribution (less so or not at all for the other three droplet size distributions). This behavior is a reflection of the technique used to set the swath displacement (as a fraction of swath width). Increasing swath width increases swath displacement, which moves the edge of the field further downwind from the farthest downwind flight line, encompassing more deposited material and eventually causing drift fraction to decrease. A different definition of swath width (such as the assumption of a constant value throughout the calculations) would have generated different results. The results presented here clearly show the impact of tying swath displacement to swath width as suggested in the Tier I assessment in AgDRIFT (Teske et al., 1997).

From these results we may infer the following:

CONCLUSIONS AND RECOMMENDATIONS

This FSCBG near-wake sensitivity study on boom length suggests that no consensus can be reached on boom length, as it will inevitably be a compromise between spray project cost (number of flight lines needed to cover the spray block) and minimum acceptable coverage within the spray block. Results shown here could not confirm the need to reduce boom lengths below the current practice of 75% of aircraft wingspan or helicopter rotor diameter. However, model predictions suggest that biplanes generate twice the drift of single-wing aircraft when spraying close to the ground, and that the BCPC Fine droplet size distribution drifts a factor of two to four times more than BCPC Medium.

Confirmation of these results, especially for biplanes, would require a carefully controlled field trial, with witness cards to record deposition from booms of varying length. Unfortunately, the resources needed for such a definitive test may not be forthcoming from any source known to the authors.

 

REFERENCES

Betz, A. 1932. Behavior of Vortex Systems. NACA TM 713. National Advisory Committee on Aeronautics, Langley, Va.

Bilanin, A. J., M. E. Teske, J. W. Barry, and R. B. Ekblad. 1989. AGDISP: The aircraft spray dispersion model, code development and experimental validation. Transactions of the ASAE 32(1):327-334.

Bird, S. L., D. M. Esterly, and S. G. Perry. 1996. Off-target deposition of pesticides from agricultural aerial spray applications. J. Environ. Qual. 25(5):1095-1104.

Bird, S. L., S. G. Perry, S. L. Ray, M. E. Teske, and P. N. Scherer. 1997. An evaluation of AgDRIFT for use in aerial applications. Draft Report. National Exposure Research Laboratory, Ecosystem Division, Office of Research and Development, U.S. Environmental Protection Agency, Athens, Ga.

Bjorklund, J. R., C. R. Bowman, and G. C. Dodd. 1988. User manual for the FSCBG aircraft spray and dispersion model version 2.0. Report FPM 88-5. Davis, Calif.: USDA Forest Service.

Curbishley, T. B., and P. J. Skyler. 1989. Forest service aerial spray computer model-FSCBG (PC) user manual for ver. 3.04. Report FPM 89-1. USDA Forest Service: Davis, Calif.

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Donaldson, C. duP., and A. J. Bilanin. 1975. Vortex wakes of conventional aircraft. AGARDograph 204. Technical Editing and Reproduction Ltd., London, England.

Dumbauld, R. K., J. R. Bjorklund, and S. F. Saterlie. 1980. Computer model for predicting aircraft spray dispersion and deposition above and within forest canopies: Users manual for the FSCBG computer program. Report 80-1 I . Davis, Calif.: USDA Forest Service.

MacNichol, A. Z. 1994. Spray Drift Task Force aircraft sensitivity study. Technical Note 93-20. Continuum Dynamics, Inc., Princeton, N.J.

Parkin, C. S., A. J. Gilbert, E. S. E. Southcombe, and C. J. Marshall. 1994. British Crop Protection Council scheme for the classification of pesticide application equipment by hazard. Crop Protection 13(4):281-285.

Parkin, C. S., and J. C. Wyatt. 1982. The determination of flightlane separations for the aerial application of pesticides. Crop Protection 1(3):309-321.

Quantick, H. R. 1985. Aviation in Crop Protection, Pollution and Insect Control, 256-270. Collins: London, England.

Reed, W. H. 1953. An analytical study of the effect of airplane wake on the lateral dispersion of aerial sprays. NACA TN 3032. National Advisory Committee on Aeronautics, Langley, Va.

Southcombe, E. S. E. 1988. The coding and selection of agricultural spraying nozzles. In Proc. U. S. Agricultural Research Institute Workshop on Improving On-Target Placement of Pesticides, Reston, Va.

Spillman, J. J. 1983. Lane separation determination. Lecture notes for short course on aerial application of pesticides. Vol. II: Cranfield Institute of Technology.

Teske, M. E. 1992. Spray drift task force sensitivity analysis. Technical Note 91-04. Continuum Dynamics, Inc., Princeton, N.J.

___________. 1996. Evaluation of the FSCBG aerial spray model's near-wake sensitivity to selected input parameters. Report FHTET 96-30. USDA Forest Service, Davis, Calif.

___________. 1998. FSCBG model sensitivity predictions of spray boom length. Report FHTET 98-04. USDA Forest Service, Ft. Collins, Colo.

Teske, M. E., and J. W. Barry. 1993. Parametric sensitivity in aerial application. Transactions of the ASAE 36(I ):27-33.

Teske, M. E., J. W. Barry, and H. W. Thistle. 1994. Aerial spray drift modeling. In Environmental Modeling Vol. II: Computer Models and Software for Simulating Environmental Pollution and its Adverse Effects, ed. P. Zannetti, 11-42. Southampton, England: Computational Mechanics Publications.

Teske, M. E., S. L. Bird, D. M. Esterly, S. L. Ray, and S. G. Perry. 1997. A user's guide to AgDRIFT: A tiered approach for the assessment of spray drift of pesticides. Technical Note 95-10. Continuum Dynamics, Inc., Princeton, N.J.

Teske, M. E., J. E Bowers, J. E. Rafferty, and J. W. Barry. 1993. FSCBG: An aerial spray dispersion model for predicting the fate of released material behind aircraft. Environ. Toxicol. & Chemistry 12(3):453-464.

Teske, M. E., and T. B. Curbishley. 1991. Forest service aerial spray computer model FSCBG ver. 4.0 user manual. Report FPM 91-I. USDA Forest Service, Davis, Calif. ___________. 1994. Forest service aerial spray computer model FSCBG 4.3 user manual extension. Report FPM 94-10. USDA Forest Service, Davis, Calif.

Teske, M. E., H. W. Thistle, and J. W. Barry. 1996. Topics in aerial spray drift modeling. In Environmental Modeling Vol. III: Computer Methods and Sqftware,for Simulating Environmental Pollution and its Adverse Effects, ed. P. Zannetti, 17-53. Southampton, England: Computational Mechanics Publications.

Article was submitted for publication in September 1997; reviewed and approved for publication by the Power & Machinery Div. of ASAE in April 1998. Presented as ASAE Paper No. 97-1071.

The authors are Milton E. Teske, ASAE Member Engineer, Senior Associate, Continuum Dynamics, Inc., Princeton, N.J.; Harold W. Thistle, ASAE Member, Program Leader, USDA Forest Service, Ft. Missoula, Missoula, Mont.; John W. Barry, USDA Forest Service (retired), 3123 Beacon Bay Place, Davis, Calif.; and Bov Eav, Director, USDA Forest Service Northeast Research Station, Radnor, Pa. Corresponding author: Milton E. Teske, Continuum Dynamics, Inc., PO Box 3073, Princeton, NJ 08543; tel: (609) 734-9282; fax: (609) 7349286; e-mail: milt@cdiprinceton.com.

Transactions of the ASAE

VOL. 41(3):545-551 © 1998 American Society of Agricultural Engineers 0001-2351/98/4103-545

 


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