Modeling Multirow Wind Barrier Density.
EOD = [[[sigma].sup.8].sub.N=1] OD/[N.sup.2] [square root] RS/H
EOD values were computed and correlated to total drag values. The relationship was then tested on additional barriers, and the resulting overall correlation ([r.sup.2] 0.92) was significant. Using the EOD equation, the wind barrier effects were computed for one to eight row (N) barriers, five optical densities, and three spacings between rows. EOD can be used to compute wind reduction patterns for the Revised Wind Erosion Equation (RWEQ) model. This permits the design of a wind barrier system (number of rows and plant density within each row) that will be most effective in reducing wind erosion for the farmer.
Keywords: Barrier effectiveness index, drag, equivalent optical density, wind erosion, wind reduction patterns, wind tunnel
Standing stubble, crop residues on the soil surface, or a soil surface roughened by tillage can increase drag, reduce wind shear, and control wind erosion. Strips of rail crops, shrubs or trees reduce wind speed and may protect the soil when the wind blows perpendicular to the strip or barrier (Black and Aase 1988; Chepil 1949). Barriers trap snow (Shaw 1988), protect farmsteads (Wight 1988), benefit wildlife (Capel 1988), or modify microclimate for downwind crops (Dickey 1988; Woodruff and Zingg 1952; Woodruff 1954). In regions with highly erodible soils, successful wind erosion control systems may utilize combinations of crop residues, soil roughness and wind barriers.
The technique of describing the optical density (OD) of single-stem barrier elements is relatively simple, but expressing the density of two to eight rows is not simple addition as reported by Bilbro and Stout (1999). With simple addition, four rows with 25% density would have the same effect as one row with 100% density. A method for computing OD for multirow barriers is needed to express the barrier effect on wind reduction patterns for the Revised Wind Erosion Equation model (RWEQ) (Fryrear et al. 1998b). The RWEQ wind erosion model was developed to incorporate new science (Fryrear et al. 1998a) in a model that improves estimates of erosion compared to the wind erosion equation (WEQ) (Woodruff and Siddoway 1965).
In WEQ, a barrier protects the leeward field for a distance of 10 times the height of the barrier. This assumption is correct for one wind speed, one barrier density, and one set of surface conditions. This assumption does not recognize the varying protected zones with different barrier densities, surface conditions, and wind speeds. Barriers divert the air flow upward, causing a drag on the wind, and lessening the drag on the soil surface (Woodruff 1954). Field drag plate measurements show a 50% reduction in surface drag at 10 H and a 20% reduction at 30 H (Bradley and Mulhearn 1983).
Slat fences have been used to simulate wind barrier effects in the field. Caution should be used in applying slat fence data to plant barriers (Hagen and Skidmore 1971) because slat fences are flat and plant barriers are composed of long, irregular cylinders. Depending on the shape of leaves and limbs, the drag coefficient of individual trees may vary from 0.3 to 1.0 but remains essentially constant for wind speeds less than 8 m [s.sup.-1] (17.9 mph) (Meroney 1968).
Drag coefficients for different barriers can be estimated using windward and leeward wind profiles (Woodruff et al. 1963). Determining drag coefficients of barriers from wind profiles is difficult because the exact wake depth cannot be measured when calculating momentum transfer (Hagen and Skidmore 1971).
Describing the wind reduction pattern downwind of a wind barrier challenges wind erosion scientists because the shape and size of the downwind protected zone varies with barrier density, barrier width, and soil surface conditions. To incorporate the influence of wind barriers into wind erosion models, the downwind protected zone must be described. The protected distance downwind has been described as 6-7 H (Chepil 1949), 9 H (Woodruff and Zingg 1952), or 12 H (Woodruff et al. 1963). The assumption of a 6-12 H protected distance downwind is valid for one wind speed, one barrier density and does not consider soil surface conditions between the barriers.
Field and laboratory wind tunnel results agree that the leeward wind reductions are similar, irrespective of the wind speed (Woodruff and Zingg 1952; Bilbro and Fryrear 1997). An expression for computing reduction in wind speed using a barrier density index was developed by Bilbro and Fryrear (1997). The barrier density index is computed from barrier silhouette areas that include leaf area, stem length and diameter, and height of the plants. These data may be estimated for single stalk plants, but for branching plants, obtaining the plant data to compute barrier density index is difficult.
The leeward influence of a wind barrier can be expressed with a single number using the BEI (Fryrear 1963; Chepil and Woodruff 1963; Tibke 1988). The BEI index assumes a wind speed reduction at 30 H is more important than the same reduction at 5 H. A 10% reduction at 30 H is 0.10 x 30 = 3, and a 10% reduction at 5 H is 0.10 x 5 = 0.5.
The BEI equation is expressed as
BEI = 5 [1-V5H/Vo]10(1-V10H/V0] + 15[1-V15H/Vo]20[1-V20H/Vo]25
where [V.sub.0] = open wind velocity
V5H-V30H = wind velocities at 5 H, 10 H, 15 H, 20 H, 25H, and 30 H leeward
The empirical BET index does not reflect the impact of a barrier on wind erosion but does provide a single index to compare different barriers. The BET is similar to the Efficiency Index (EI) reported by Bilbro and Stout (1999). When comparing barriers, any number of wind speed reductions can be used as long as the same number and spacings are used for all barriers. The larger the BET the longer the downwind protected zone and/or the greater the reduction in wind speed.
The objective of this paper is to correlate field values of BET with total drag of simulated barriers in a laboratory wind tunnel. If the correlation is significant, then the wind tunnel drag for multirow barriers, barriers with rows with different optical densities, and barriers with variable spacing between the rows can be correlated with an expression of the equivalent optical density (EOD). For single row barriers, the optical density is equal to the EOD. For multirow barriers, the EOD can be used in place of the barrier density index or optical density to evaluate the leeward wind reduction patterns of complex barriers.
Percent of Upwind Velocity (PUV) calculated at a height of 0.62 m (2.03 ft) that is 0.03 to 0.4 of the barrier height, and photographs of wind barriers 1.4 to 19.8 m [4.6 to 64.9 ft] to develop a relationship between PUV and leeward distance (Sturrock 1969, 1972) (Figure 1). The optical density was determined by scanning photographs of the barriers and measuring optical density with a pseudo color leaf analysis system (Decagon model [AgVision.sup.2]). This technique has been used to derive optical density for natural barriers (Jensen 1954; Brown 1969; Maki and Allen 1978). The equation developed from Sturrock's data is
PUV= 100 [e.sup.-(OD)0.423(H)-1,098]
[r.sup.2] = 0.86
where PUV = percent of upwind velocity
OD = optical density
H = downwind distance in barrier heights
It is used in RWEQ (Fryrear et al. 1998b) to describe the influence of wind barriers on leeward wind reductions.
Field wind reduction patterns. Wind reduction patterns for one to eight row field barriers were measured in 1994 and 1995 (Bilbro and Stout 1999). The barriers consisted of cylindrical posts 1 m (3.28 ft) tall and 28 mm (1.1 in) in diameter in rows 1 m (3.28 ft) apart. The optical density within each row varied from 12.5% to 75%. All rows within a test had the same density. Only data for wind speeds at a height of 0.2 m (.66 ft) perpendicular to the barrier were included in the PUV analysis.
Laboratory wind tunnel drag. The Big Spring Dust and Drag wind tunnel is a suction type tunnel with a test section 1.2 m high, 0.5 m wide, and 2 m long (3.94 ft high, 1.64 ft wide, and 6.56 ft long). The height of the simulated barrier was 0.25 m (0.82 ft) and the diameter of each simulated barrier element was 7 mm (0.28 in). One, two, four, and eight row barriers were studied. The density within each row was 12.5%, 25%, 50%, 75%, or 100%. The spacing between rows was 0.25 H, 0.5 H, or 1.0 H. Spacing between field rows was 1 H and was not a variable in the field. No field data were available for row densities of 100%.
The test section of the tunnel floor [0.5 x 2 m (1.64 x 6.56 ft)] sits on a drag tray. All barriers were centered on and mounted directly to the drag tray. This allowed the measurement of total drag which included the drag on the tunnel floor plus the drag on the standing simulated barrier. The wind profile on the upwind edge of the test section duplicated the natural wind profile for a flat, smooth soil surface.
For each wind tunnel test, the free stream wind speed was controlled at 4, 6, 8, 10, and 12 m [S.sup.-1] (8.9, 13.4, 17.9, 22.4, and 26.8 mph) at a height of 0.52 (1.71 ft). For each test speed 30 drag readings were recorded. The drag force and wind speed results for each of the duplicated tests were expressed as:
[tau] = a [V.sup.b]
where = drag force (average of 30 readings) g [m.sup.-2]
a = coefficient which reflects barrier characteristics
V = wind speed at 0.52 m (1.71 ft) above tunnel floor m [s.sup.-1]
b = constant (assumed to be 2)
The field wind speed reduction results were expressed as BET for each combination of row density and number of rows (Table 1). The BET increased for increasing optical densities for the one row barrier. The one row, 75% density had the highest BEI. BET values did not follow a consistent pattern as the number of rows increased (Table 1). Part of the reason for the inconsistent pattern may be the downwind location of the PUV values. Traditionally, the distances downwind are measured from the downward edge of the barrier and are expressed in terms of the height of the barrier (H).
The field barrier systems in Table 1 were simulated in a laboratory wind tunnel and the field BET data were correlated to total drag data from a laboratory wind tunnel. The results were highly significant (Figure 2). The BET and drag increased in a non linear fashion. BEI increased rapidly until the BET value was about 15, but above 15 a small increase in BEI gave a large increase in drag. From these data it is possible to compute BEI from wind tunnel drag data.
As row number or optical density increased and the spacing between rows decreased, the "a" values increased (Table 2). The "a" coefficients in equation (3) were analyzed with AOV factorial analysis (Snedecor 1959) to determine if row spacing, row number, or density was significantly different (Table 3). The one row data were omitted because there were no between row spacing options for one row. Barrier density had a significant effect on drag, but row number or row spacings were not statistically significant at the 95% level.
The relationship between wind tunnel drag using equation (3) and barrier density was statistically significant. For barriers with more than two rows, the protected zone was primarily influenced by the density of the first upwind row. In describing the shape and size of the leeward protected zone, the reference point must be identified. The traditional reference point is the leeward row of the barrier not the upwind row.
For optical densities of 50% or less there was an increase in drag as the number of rows and optical density increased (Figure 3). With 100% density, the drag force decreased as the row number increased. The 100% density within a row is generally not feasible with plants, but the 100% density (solid row) data are included to support the fact that if there is 100% GD only one row is needed. Some grass barriers may approach 100% optical density, but they allow some air passage through the barrier (Black and Aase 1988; Bilbro and Fryrear 1997). A simple method of describing the equivalent density of multirow barriers is essential to correctly model the impact of a barrier on wind erosion.
Equivalent optical density (EOD). The term Equivalent Optical Density (EOD) is used to describe the optical density of a multirow barrier. The barrier may include different densities in each row and a variable spacing between the rows. The density of the first upwind row is very important. The spacing between rows and number of rows is less important. Lacking a proven model to test, the following equation was developed.
EOD = [[[sigma].sup.s].sub.N=1] [OD.sub.N]/[N.sup.2][square root]RS/H (4)
where EOD = equivalent optical density
ODN = optical density of row N
RS = spacing between rows in barrier height H
N = row number (in this study N is 1, 2, 3, 4, 5, 6, 7, 8)
H = barrier height
The OD data from Sturrock (1969, 1972) would provide an excellent test of equation (4), but the optical densities or spacings between rows are not given. As the number of rows increases beyond two, the influence of each additional row on the EOD rapidly decreased. As spacing between rows decreased, the EOD increased (Table 4). There may be scenarios where equation (4) may not be applicable, but when densities between adjacent rows vary by less than a factor of two the equation works well. With equation (4), the difference between EOD calculated for four rows and eight rows is small. This agrees with the BEI values from field barriers (Table 1). The relationship between EOD and wind tunnel drag for all densities except the 100% density is expressed as
Total drag = 81 + 17.369 (EOD)
[r.sup.2] = 0.92 (5)
Equation (5) shows a drag force of 81 g (0.18 lb) with a zero EOD (no barrier) (Figure 4). In this laboratory wind tunnel, the wind exerts a drag on the bare tunnel floor equal to the 81 g force (0.18 lb). When equation (5) was used for rows of 100% optical density, the drag results were consistent with the drag for other densities. Flow reversal in the laboratory wind tunnel with 100% dense barriers is probably the reason drag is less for the four and eight row 100% density barriers than for the 75% density. Flow reversal in the field is common as evidenced by snow drift patterns downwind of solid barriers.
The importance of the reference point used for computing BET is evident in Table 5. Since the density of the first upwind row on multirow barriers is extremely important, field wind speed data was reevaluated with the leeward protected zone of the barrier referenced from the upwind and downwind edges of the barrier (Table 5). The BET using the upwind row (UP) for a reference point is more than twice the BEI with the downwind row (DOWN) as a reference point for the four and eight row barriers. This may explain why the BET values decrease with four and eight row barriers with more than 25% density (Table 1).
The downwind BET data from the field plots was correlated with the EOD data from the laboratory wind tunnel.
BEI = 7.84 + 0.223 EOD [r.sup.2] = 0.66 (6)
Equation (6) was developed for EOD values between 12.5 and 115. The influence of a barrier on the leeward protected zone can be evaluated by computing EOD and using equation (6).
Additional wind tunnel tests were conducted on four row barriers with different densities to determine if the EOD [equation (4)] was suitable for barriers with mixed densities (Table 6). All of the EOD and drag force data are plotted in Figure 4. The results agree with the data used to test equation (4) and support the hypothesis that the EOD can be computed for complex barriers and the EOD used in equation (2) to describe the leeward protected zone. The final test should be the use of EOD in place of OD in equation (2) and then running RWEQ. The RWEQ considers wind direction and surface roughness in addition to barrier EOD in determining the effect of the barrier on wind erosion.
Using EOD to choose a wind barrier. The EOD is useful in evaluating the effect of number and spacing of rows and density within each row (Table 4). For example, a farmer must decide between using a two row sudan grass or an eight row corn stalk barrier. The sudan grass has an effective height of 0.7 m (2.30 ft) and an estimated row optical density of 50%. Corn height after harvest is 0.5 m (1.64). The corn has an optical density of 20% in the two outside rows and 10% in the six interior rows. There is 1 m (3.28 ft) spacing between all barrier rows.
For the sudan grass barrier, the EOD is expressed as
EOD = 50 + 50/[2.sup.2] [square root]1.0/0.7
50 + 10.5 = 60.5 (7)
The BEI using equation (6) is 21.3. Using equation (2) the percent upwind velocities at 5 H, 10 H, 15 H, 20 H, 25 H, and 30 H are 37.9%, 63.5%, 74.9%, 81.1%, 84.8%, and 87.3%, respectively (Figure 5). Using these values in equation (1) gives a BEI of 21.93.
For the corn barrier, the EOD is expressed as
20 + 10/[2.sup.2] [square root]1.0/0.5 + 10/[3.sup.2] [square root]1.0/0.5 + 10/[4.sup.2] [square root]1.0/0.5 + 10/[5.sup.2] [square root]1.0/0.5 + 10/[6.sup.2] [square root]1.0/0.5 + 10/[7.sup.2] [square root]1.0/0.5 + 10/[8.sup.2] [square root]1.0/0.5 = 23.8 (8)
The BEI using equation (6) is 13.1. With equation (2) the wind reductions at 5 H, 10 H, 15 H, 20 H, 25 H, and 30 H are 52.0%, 73.7%, 82.3%, 86.8%, 89.5%, and 91.2%, respectively (Figure 5). These values in equation (1) gives a BEI of 15.59.
From the BEI values, the sudan grass barrier is superior to the corn. The size of the protected zone depends on the surface conditions and the upwind velocity; however, for discussion purposes assume a 20% reduction (PUV = 80, Figure 5) is required to protect the soil. With the sudan grass, the protected zone is 13 x 0.7 m (2.3 ft) (effective height) or 9.1 m (29.8 ft). With the corn the protected zone is 7 x 0.5 m (1.64 ft) (effective height) or 3.5 m (11.48 ft). With the corn the protected zone is smaller than the width of the barrier [7 m (22.96 ft)], while the sudan grass [1 m (3.28 ft) wide] protects a distance seven times the barrier width. For this example, the sudan grass barrier would be much better.
Evaluating multirow barriers with EOD. Different densities in each row, or different spacings between rows can be evaluated for their effect on EOD using equation (4). For example, if four rows at 50% OD and spaced 1H apart are used, the EOD is 71 (Table 4). Using EOD = 71 in place of OD in equation (2) with a barrier height (H) of 1 m (3.28 ft), the PUV values are 34%, 60%, 72%, 79%, 83%, and 86% for H values of 5, 10, 15, 20, 25, 30, respectively . The BEL computed using equation (1) for this barrier is 24.1, and using equation (6) it is 23.6. If the rows have 25% density, the EOD from equation (4) is 36. With the PUV values of 45%, 69%, 79%, 84%, 87%, and 89%, the computed BEI is 18.8, and using equation (6) the BEI = 15.9. Considering that the BEI values from equation (1) are based on field wind speed reductions downwind and the BEI from equations (5) and (6) are from total drag measurements in a laboratory wind tunnel using simulated barriers, this is excellent agreement.
Evaluating multirow barriers with RWEQ97, a wind erosion model. For this example a 4.5 ha (9.9 ac) square field with no soil roughness or residues is considered. The soil is a sandy loam and the wind is always perpendicular to the barrier. Without a barrier system, the RWEQ97 (Fryrear et al., 1998) soil loss estimate is 83.8 kg [m.sup.-2] (373.8 t [ac.sup.-1]). With sudan grass barriers spaced perpendicular to the wind at 13.3 m, 30.3 m, or 60.6 m (43.6 ft, 99.4 ft, 198.4 ft) intervals, the RWEQ97 soil loss estimates are 6.3, 33.1, and 71.1 kg [m.sup.-2] (28.1, 147.6, and 319.8 t [ac.sup.-1]), respectively. With the corn barrier spaced 6.7 m or 30.3 m, the RWEQ97 soil loss estimates are 8.1 kg [m.sup.-2] and 65.7 kg [m.sup.-2], respectively. The corn barrier is very effective in reducing soil loss when properly spaced, but much less land would be required for the sudan grass barriers. Farmers may receive economic benefit from the eight rows of corn, so they would consider both the effectiveness in reducing e rosion and the economic return from the barrier strip before making any decision.
Field data on the protected zone downwind of multirow barriers were used to compute the BEI as a function of barrier optical density. Field barriers were simulated in a laboratory wind tunnel and total drag was measured. The total drag in the laboratory wind tunnel was correlated to the BEI from field studies. This made it possible to study various barrier characteristics in the laboratory wind tunnel and develop the equation below to compute the Equivalent Optical Density (EOD) for complex barriers using optical density (OD) of individual rows (N), barrier height (H), and spacing between rows (RS).
EOD = [[[sigma].sup.8].sub.N=1] [OD.sub.N]/[N.sup.2][square root]RS/H
The EOD values were correlated to total drag in the Big Spring Dust and Drag laboratory wind tunnel. The agreement between BEI from the field test and EOD values computed for additional tests not used to develop the relationship was significant. The EOD equation can be used to estimate density of complex multirow barriers. The EOD value can exceed 100, but this agrees with drag values from the laboratory wind tunnel. The EOD can be used to estimate wind reduction patterns and design the most effective barrier.
Spacing between adjacent rows becomes more important when density within a row is 50% or greater. Eight rows with 50% density and spaced 0.25 H apart have the same EOD as two rows with 75% density and spaced 0.5 H apart. Some farmers would prefer the wider barrier because the wider barrier fits their equipment while other farmers may prefer the narrow barrier because it requires less land. The EOD equation can be used to test the effect of row spacing within the barrier and variable densities between rows within the barrier on the protected zone downwind. The protected distance downwind as a function of wind velocity, barrier height, and EOD can then be computed using the equation below.
PUV 100 [e.sup.-[(EOD).sup.0.423] [(H).sup.-1.098]]
With a clear understanding of the parameters responsible for controlling wind erosion, the optimum number of rows in a barrier and the desired density in each row can be evaluated to customize barrier design to the unique needs of each farmer.
Donald Fryrear is a research engineer for Custom Products and retired research engineer for the USDA ARS James D. Bibiro is a retired research agronomist for the USDA ARS. Charles E Yates is an engineering technician and Ernest G. Berry is an agricultural science research technician for the USDA ARS.
Reference to a proprietary product or company is for specific information only and not to imply approval or recommendation of the product by the USDA ARS.
The authors would like to express their appreciation to Cathy Lester for her contributions and review of this report.
Bilbro, J.D. and D.W. Fryrear. 1997. Comparative performance of forage sorghum, grain sorghum, kenaf, switchgrass, and slat-fence wind barriers in reducing wind velocity. Journal of Soil and Water Conservation 52 (6):447-452.
Bilbro, J.D. and J.E. Stout. 1999. Wind velocity patterns as modified by plastic pipe windbarriers. Journal of Soil and Water Conservation 54 (3):551-556.
Black, A.L. and J.K. Asse. 1988. The use of perennial herbaceous barriers for water conservation and protection of soils and crops. Agriculture Ecosystems and Environment 22/23:135-148.
Bradley, E.F. and P.J. Mulhearn. 1983. Development of velocity and shear stress distribution in the wake of a porous shelter belt. Journal of Wind Engineering and Industrial Aerodynamics 15:145-156.
Brown, K.W. 1969. Mechanisms of windbreak influence on microclimate, evapotranspiration, and photosynthesis of the sheltered crop. p 254 in Horticulture Progress Report No. 71. Lincoln: University of Nebraska Agricultural Experiment Station.
Capel, S.W. 1988. Design of windbreaks for wildlife in the Great Plains of North America. Agriculture, Ecosystems, and Environment 22/23:337-348.
Chepil, W.S. 1949. Wind erosion control with shelterbelts in North China. American Society Agronomy Journal 41:127.
Chepil, W.S. and N.P. Woodruff 1963. The physics of wind erosion and its control. Advances in Agronomy 15:211-302.
Dickey, D.L. 1988. Crop water use and water conservation benefits from windbreaks. Agriculture, Ecosystems, and Environment 22/23:381-392.
Fryrear, D.W. 1963. Annual crops as windbarriera. Transactions of the American Society of Agricultural Engineers 6:340-342, 352.
Fryrear, D.W., A. Saleh, and J.D. Bilbro. 1998a. A single event wind erosion model. . Transactions of the American Society of Agricultural Engineers 41 (5):1369-1374.
Fryrear, D.W., A. Saleh, J.D. Bilbro, H. Schomberg, J.E. Stout, and T.M. Zobeck. 1998b. Revised wind erosion equation (RWEQ). Wind Erosion and Water Conservation Research Unit. USDA ARS, Southern Plains Area Cropping Systems Research Laboratory Technical Bull. No. 1.
Hagen, L.J. and E.L. Skidmore. 1971. Windbreak drag as influenced by porosity. Transactions of the American Society of Agricultural Engineers 14 (3):464-465.
Hagen, L.J., E.L. Skidmore, P.L. Miller, and J.D. Kipp. 1981. Simulation of effect of wind barriers on airflow. Transactions of the American Society of Agricultural Engineers 24:1002-1008.
Jensen, M. 1954. Shelter effect: Investigations into the aerodynamics of shelter and its effects on climate and crops. P 263. Copenhagen: The Danish Technical Press.
Maki, T. and L.H. Allen Jr. 1978. Turbulence characteristics of a single line pine tree windbreak. In: Proceedings of Soil and Crop Science Society 33:81-92.
Meroney, R.N. 1968. Characteristics of wind and turbulence in and above model forests. Journal of Applied Meteorology 7 (5):780-787.
Shaw, D.L. 1988. Crop water use and water conservation benefits from windbreaks. Agriculture, Ecosystems, and Environment 22/23:351-362.
Snedecor, G.W. 1959. Statistical methods applied to experiments in agriculture and biology. P 534. Ames: Iowa State College Press.
Sturrock, J.W. 1969. Aerodynamic studies of shelrerbelts in New Zealand-1: low to medium height shelterbelts in mid-Canterbury. New Zealand Journal of Science 12:754-776.
Sturrock, J.W. 1972. Aerodynamic studies of shelterbelts in New Zealand-2: medium-height to tall shelterbelts in mid-Canterbury. New Zealand Journal of Science 15:113-140.
Tibke, G. 1988. Basic principles of wind erosion control. Agriculture, Ecosystems, and Environment 22/23:103-122.
Wight, B. 1988. Farmstead windbreaks. Agriculture, Ecosystems and Environment 22/23:261-280.
Woodruff, N.P. 1954. Shelterbelt and surface barrier effects on wind velocities, evaporation, house heating, snowdrifting. P 27. Kansas Agricultural Experiment Station Technical Bull. No. 77.
Woodruff, N.P. and A.W. Zingg. 1952. Wind-tunnel studies of fundamental problems related to windbreaks. Washington, D.C.: U.S. Department of Agriculture (USDA). P 25USDA SCS Technical Pub. No. 112.
Woodruff, N.P., D.W. Fryrear, and L. Lyles. 1963. Engineering, similitude and momentum transfer principles applied to shelterbelt studies. Transactions of the American Society of Agricultural Engineers 6 (1):41-47.
Woodruff, N.P. and F.H. Siddoway. 1965. A wind erosion equation. Soil Science Society of America. 29 (5):602-608.
Summary of Barrier Effectiveness Index (BEI) values from field study of stimulated stalks (1 m tall, 28 mm diameter) positioned in 1, 2, 4, and 8 rows with for densities. Number of Rows Optical Density of each row, % 12.5 25 50 75 BEI 1 4.3 10.1 19.6 32.8 2 8.0 17.6 22.8 27.7 4 13.6 22.1 32.2 32.3 8 16.1 20.1 21.1 22.0
Summary of "a" coeffieients for the drag equation t = aV2 for laboratory wind tunnel drag tests of 1, 2, 4, and 8 row barriers with 12.5%, 25%, 50%, and 100% densities and between row spacings (RS) of 0.25, 0.5, and 1H. Ninety-six of the r2 values were 0.99 or larger and all were 0.96 or larger.
Number Row Optical Density, % of Rows Spacing H 12.5 25 50 75 100 1 0.0010 0.0018 0.0047 0.0111 0.0182 2 0.25 0.0017 0.0033 0.0075 0.0150 0.0200 2 0.50 0.0016 0.0034 0.0077 0.0137 0.0197 2 1.00 0.0016 0.0032 0.0074 0.0136 0.0184 4 0.25 0.0026 0.0054 0.0100 0.0158 0.0197 4 0.50 0.0029 0.0053 0.0100 0.0138 0.0182 4 1.00 0.0028 0.0054 0.0098 0.0149 0.0153 8 0.25 0.0040 0.0082 0.0125 0.0164 0.0181 8 0.50 0.0045 0.0082 0.0123 0.0155 0.0150 8 1.00 0.0047 0.0082 0.0128 0.0.157 0.0134
Factorial analysis of the "a" coefficients in Equation 4 with "b" = 2 from the laboratory wind tunnel drag data (Table 2) for 2, 4, or 8 rows of 12.5%, 25%, 50%, 75%, and 100% density. Spacing between adjacent rows is 0.25, 0.5, or 1.0 H.
Source df SS F- value Rows (R) 2 0.00041 0.582 Spacing (S) 2 0.00069 0.973 Density (D) 4 0.00671 4.674 [**] R x S 4 0.00147 1.037 R x D 8 0.00399 1.415 S x D 8 0.00291 1.034 R x S x D 16 0.00569 1.010 Error 45 0.01585 (**.)Statistically significant at the 0.01 probability level. EOD values for different numbers of rows, spacings between rows, and different row optical densities using Equation 4 Number of Row Optical Density, % Rows Spacing 12.5 25 50 75 100 1 0 12.5 25 50 75 100 2 .25 18 38 75 113 150 2 .50 17 34 68 102 135 2 1 16 31 63 94 125 3 .25 21 43 86 129 172 3 .50 19 38 74 113 151 3 1 17 34 68 102 136 4 .25 23 46 92 139 185 4 .50 20 40 79 120 160 4 1 18 36 71 107 142 6 .25 24 50 99 149 198 6 .50 21 42 84 127 170 6 1 19 37 75 112 149 8 .25 25 51 103 154 206 8 .50 21 44 86 131 175 8 1 19 38 76 115 153
Barrier Effectiveness Index (BEI) values for 1, 2, 4, and 8 row field barriers with 12.5%, 25%, 50%, or 75% density in each row. The EOD values are computed using Equation 4. BEI values are computed with reference to downwind or upwind edge of the barrier.
Number of Rows OD EOD Barrier Effectiveness Index in Barrier % % Down Up 1 12.5 12.5 4.3 4.3 1 25.0 25.0 10.1 10.1 1 50.0 50.0 19.6 19.6 1 75.0 75.0 32.8 32.8 2 12.5 16.0 8.0 8.8 2 25.0 31.0 17.6 19.1 2 50.0 62.0 22.8 25.6 2 75.0 94.0 27.7 31.6 4 12.5 19.0 13.6 17.8 4 25.0 36.0 22.1 29.5 4 50.0 71.0 32.2 44.6 4 75.0 106.0 32.3 46.8 8 12.5 19.0 16.1 34.4 8 25.0 38.0 20.1 52.1 8 50.0 78.0 21.1 58.3 8 75.0 115.0 22.0 60.6 Total DRAG values from laboratory wind tunnel tests and EOD values using Equation 4 for four row barriers with different densities in the rows and H = 1 meter. Optical Density Row Spacing, m of individual rows 0.25 0.5 1.0 in 4-row barrier EOD DRAG EOD DRAG EOD % % g/[m.sup.2] % g/[m.sup.2] % 25- 12.5- 12.5- 12.5 35.6 475 32.5 494 30.3 25- 12.5- 12.5- 25 37.2 599 33.6 598 31.1 50- 25 -25 -25 71.2 1040 65.0 1002 60.6 50- 25 -25 -50 74.3 1204 67.2 1178 62.2 75- 50 -50 -50 117.4 1862 105.0 1849 96.2 75- 50 -50 -75 120.5 2041 107.2 1998 97.7 Optical Density of individual rows in 4-row barrier DRAG % g/[m.sup.2] 25- 12.5- 12.5- 12.5 517 25- 12.5- 12.5- 25 617 50- 25 -25 -25 1019 50- 25 -25 -50 1194 75- 50 -50 -50 1795 75- 50 -50 -75 1960
|Printer friendly Cite/link Email Feedback|
|Author:||Fryrear, D.W.; Bilbro, J.D.; Yates, C.E.; Berry, E.G.|
|Publication:||Journal of Soil and Water Conservation|
|Article Type:||Statistical Data Included|
|Date:||Jun 22, 2000|
|Previous Article:||Spatial Prediction and Uncertainty Analysis of Topographic Factors for the Revised Universal Soil Loss Equation (RUSLE).|
|Next Article:||A modest proposal for the year 2001: we can control greenhouse gases and feed the world ... with proper soil management.|