Flat Fan Spray Research Articles

Evaluation of Dimilin for Rice Water Weevil Control, 1995

Abstract Dimilin was evaluated for control of adult rice water weevil at the Rice Research Station, Crowley, LA. Collectively levied plots, 5 X 20 ft, were arranged in a RBD with 4 blocks and 5 treatments with sub-sample nesting within the block X treatment effect. Fertilizer was incorporated pre-plant and applied broadcast 3 wk post-flood at 90 lb (13-13-13) and 50 lb (21-0-0) N-P-K/acre respectively. Plots were water seeded 29 May with pre-soaked ‘Cyprus’ rice at 138 lb seed/acre to Crowley silt loam and permanently flooded 8 Jun. Foliar applications of Dimilin 25 W were made at 0.25 or 0.125 lb (AI)/acre. Furadan 3 G was applied at RWW threshold (5 larvae/sample) at 0.6 lb (AI)/acre using a hand-held shaker. Dimilin 25 W applications were made using a CO2 backpack sprayer delivering 15 gpa at 16 psi with 80015VS flat-fan spray nozzles on a 3 ft boom. Rice water weevil eggs were counted from 5 randomly selected plants per plot beginning 2 d after flood then weekly until RWW threshold. Three randomly selected soil samples per plot were taken 26 Jun, 3 and 11 Jul using a 4 X 4 in core sampler. Individual samples were washed through a funnel, fitted with wire screen, into a 35-mesh screen sieve. Collected RWW larvae and pupae were floated in a saturated NaCl solution, and counted. Rough rice yield (lb/acre) was determined by hand-harvesting one random 3-ft2 sample per plot on 19 Sep. Moisture content of harvested grain was determined and standardized to 12% for determination of rough rice yield. RWW larval data were log transformed to improve normality. All data were subjected to ANOVA. Experimental and sampling error terms for the RWW larval data were tested for homogeneity of variances, and pooled error terms were used to test the treatment effect when appropriate. Protected least significant difference (LSD) was used for treatment mean separation.

Flame Cultivation as a Complement to Mechanical and Herbicidal Control of Weeds

ABSTRACT There is renewed interest in the practice of flame cultivation as a complement to mechanical cultivation and a partial or total replacement for herbicides in vegetable crops. This interest is fueled by three factors: (1) an increasingly negative public perception of herbicide use in vegetables, (2) a limited selection of herbicides labelled for vegetables, and (3) limited efficacy of some of the registered herbicides. Flame cultivation, in combination with mechanical cultivation, can replace or complement herbicides in some vegetable crops. Flame cultivation bursts plant cell walls as the weeds are heated. Most vegetable crops must be protected from the flame. This can be done with a height differential between weeds and crop, a water shield (water sprayed from a flat fan spray nozzle), or a physical shield. A field study involving flame cultivation of lima beans (Phaseolus limensis Macfady) and southern peas (Vigna unguiculata [L.] Walp.) has shown that multiple flame cultivations are effective ...

Calibration of Greenhouse Spray Chambers—The Importance of Dynamic Nozzle Patternation

In an attempt to refine calibration procedures for greenhouse spray chambers, the effects of an herbicide adjuvant, operating pressure, and travel speed on the static and dynamic spray patterns of single flat-fan hydraulic nozzle tips were studied. The volume output in the central 15 cm of the spray pattern (where target plants would ordinarily be positioned) was used as an indicator of the relative dosages received from both a tapered flat-fan tip (8001 VS) and an even-spray tip (8001 EVS). All tested variables significantly altered the spray pattern. Specifically, dynamic spray patterns differed from static patterns, and speed of travel affected the dynamic pattern for both tapered and even flat-fan sprays. Increasing the travel speed from 0.375 to 0.75 m/s reduced spray deposit in the central 15 cm of the spray pattern by up to 19% for water, and by up to 34% for water containing 0.1% v/v nonionic surfactant. Increasing surfactant concentration to 1% decreased the magnitude of the speed effect. Higher pressure sprays tended to reduce the effect of increased travel speeds. These results show that changes in physicochemical properties of the spray solution as well as air turbulence introduced by nozzle movement can affect the pesticide dosage to which a target plant is exposed in a spray chamber. For proper treatment comparison, delivery systems for greenhouse spray experiments should be calibrated with end-use spray liquids, operating pressures, and nozzle travel speeds.

Evaluation of Karate For Rice Water Weevil Control, 1996

Abstract Karate was evaluated for RWW control at the Rice Research Station, Crowley, LA. Plots, 5 X 20 ft, were arranged in a RB design with four blocks and seven treatments with sub-sample nesting within the block X treatment effect. Fertilizer was incorporated pre-plant and applied broadcast 3 wk post-flood at 90 lb (13-13-13) and 55 lb (21-0-0) N-P-K/acre respectively. Plots were water-seeded 21 May with pre-soaked ‘Cyprus’ rice at 130 lb seed/acre to Crowley silt loam and permanently flooded 28 May. Furadan 3G was applied 18 Jun at 0.6 lb(AI)/acre using a hand-held shaker. Karate applications were made using a CO2 backpack sprayer delivering 15 gpa at 28 psi with 10015VS flat-fan spray nozzles on a 3 ft boom. Three randomly selected soil samples per plot were taken 10, 17, 25 Jun using a 4 X 4 in core sampler. Individual samples were washed through a funnel, fitted with wire screen, into a 35 mesh screen sieve. Collected RWW larvae and pupae were floated in a saturated NaCl solution, and counted. Rough rice yield (lb/acre) was determined by harvesting the center 4 rows per plot using a Kubota combine 11 Sep. Moisture content of harvested grain was determined and standardized to 12% for determination of rough rice yield. All data were subjected to ANOVA. Experimental and sampling error terms for the RWW larval data were tested for homogeneity of variances, and pooled error terms were used to test the treatment effect when appropriate. Protected Least Significant Difference (LSD) was used for treatment mean separation at 0.05 probability level.

PRECISION BAND SPRAYING WITH MACHINE-VISION GUIDANCE AND ADJUSTABLE YAW NOZZLES

A system was developed for precision, ground-based application of foliar sprays to rows of small plants. Thesystem consisted of a machine-vision guidance system that positioned spray nozzles directly above each row of smallplants. An electrically actuated mechanical linkage rotated flat-fan spray nozzles about their central axes to vary the yawangle of the fans relative to the direction of travel. The nozzle rotation effectively changed the width of the spray patternrelative to the direction of travel and allowed the spray band to be adjusted to match the width of the target plants. Thesystem was evaluated on young stands of tomatoes and lettuce by measuring spray deposition on the plants andsurrounding soil. The precision system allowed spray application rates to be reduced by 66 to 80% and increased spraydeposition efficiency on the target plants by 2.5 to 3.7 times greater than conventional broadcast spraying. Nontargetdeposition on soil surfaces was reduced by 72% to 90%. Airborne displacement of spray liquid from the spray boom, asmeasured by collection strings surrounding the boom structure, was reduced by 62 to 93%. The reduction in displacementsuggested that spray drift from precision applications could be significantly less than that from conventional applications.

Evaluation of Guardian For Rice Water Weevil Control, 1995

Abstract Guardian was evaluated for RWW Control at the Rice Research Station, Crowley, LA. Collectively levied 5 X 20 ft plots were arranged in a RB design with 4 blocks and 4 treatments with sub-sample nesting within the block X treatment effect. Fertilizer was incorporated pre-plant and applied broadcast 3 wk post-flood at 90 lb (13-13-13) and 50 lb (21-0-0) N-P-K/acre respectively. Plots were water-seeded 29 May with pre-soaked ‘Cyrpus’ rice at 138 lb seed/acre to Crowley silt loam and permanently flooded 8 Jun. Foliar applications of Guardian were applied at 14.5 oz formulation/acre. Furadan 3G was applied at 0.6 lb (Al)/acre using a hand-held shaker when RWW larval density was at or above threshold (5 larvae/sample). Guardian applications were made using a CO2 backpack sprayer delivering 15 gpa at 16 psi with 80015VS flat-fan spray nozzles on a 3 ft boom. RWW eggs were counted from 5 randomly selected plants per plot beginning 2 days post-flood, then weekly until RWW threshold. Three randomly selected soil samples per plot were taken 26 Jun, and 3 and 11 Jul using a 4 X 4 in core sampler. Individual samples were washed through a funnel, fitted with wire screen, into a 35 mesh screen sieve. Collected RWW larvae and pupae were floated in a saturated NaCl solution, and counted. Rough rice yield (lb/acre) was determined by hand-harvesting one random 3 ft2 sample per plot on 19 Sep. Moisture content of harvested grain was determined and standardized to 12% for determination of rough rice yield. RWW larval data were log transformed and all data were subjected to analysis of variance using the GLM procedure of SAS. Experimental and sampling error terms for the RWW larval data were tested for homogeneity of variances, and pooled error terms were used to test the treatment effect when appropriate. Protected least significant difference (LSD) was used for treatment mean separation at 0.05 probability level.

Flame Cultivation for Controlling Weeds

Flame “cultivation” for weed control was developed about 50 years ago. The practice was very popular with Southern cotton farmers through the 1950s and 1960s, but lost favor when petroleum prices rose drastically in the 1970s. There is now a new interest in the practice of flame cultivation as a partial or total replacement for herbicides in vegetable crops. This interest is fueled by three factors: 1) an increasingly negative public perception of herbicides on vegetables, 2) a very limited selection of herbicides labeled for vegetables, and 3) limited efficacy of some of the herbicides that are registered. Flame cultivation, in combination with mechanical cultivation, can replace or supplement herbicides in some vegetable crops. The mode of action of flame cultivation is the bursting of cell walls in the weeds as the weeds are heated by a carefully directed LP gas flame. With most vegetable crops, the crop plants must be protected in some manner. This can be done with a water shield (flat fan water spray), height differential between weeds and crop, physical shield, etc. Much of the early work on flame cultivation of vegetables was done with sweet corn. Work is now underway on flame cultivation of lima beans and southernpeas, where multiple flame cultivations have proven effective at controlling weeds for which no herbicide is available.

Small Plot Assessment of Insecticides Against the Sugarcane Borer, 1995

Abstract Fifteen insecticide treatments were evaluated for control of SCB at St. Gabriel Research Station, St. Gabriel, LA. A RCB design with 5 replications was used in a field of first ratoon sugarcane. Insecticide treatments were applied to 3-row plots (0.05 acre) using a CO2 sprayer mounted on an ATV (all terrain vehicle) on 7 and 28 Jul, and 25 Aug. Three 8005 flat fan spray tips per 6 ft width of row at 35 psi delivered 20 gpa. Initial treatment was made when the SCB infestation exceeded the economic threshold (5% of the stalks containing live larvae in the leafsheaths); succeeding applications occurred when reinfestations began to appear in the Guthion/Baythroid treatment. Prior to the initiation of the experiment, 1 application of Lorsban 15G was broadcast (15.0 lb/acre) to suppress red imported fire ant predation on SCB larvae (Jun 13). SCB damage was assessed by counting the bored intemodes, moth emergence holes, and total number of intemodes per stalk from 75 randomly selected stalks of sugarcane (15 stalks/plot) in each treatment (20 Oct). All of the Confirm treatments were applied with Triton CS-7 at 0.125% v/v. Following ANOV, separation of means was by LSD.

Small Plot Insecticide Trial Against SCB, 1994

Abstract Control of the SCB was evaluated in a RCB design (4 replications) of plant cane at the St Gabriel Research Station, St Gabriel, LA. Insecticide treatments were applied over the sugarcane canopy with a CO2 backpack sprayer on 22 Jul, 8, and 26 Aug when the SCB infestation exceeded the economic threshold (5% of the stalks containing live larvae in the leafsheaths). Four 0.004 flat fan spray tips per 6 ft width of row at 32 psi applied 20.1 gal of finished formulation/acre. Prior to the initiation of the experiment, 2 applications of Lorsban 15G were made (15 lb/acre each) to suppress red imported fire ant predation on SCB larvae (10 May and 9 Jun). Due to weather conditions the timing of the first application was delayed 12 days. The three Rohm & Haas (RH-2485, RH-0345 and Confirm) treatments were applied with Triton CS-7 at 0.125% vol/vol, and the Condor treatment was applied with Kinetic, at a rate of 0.125% vol/vol. SCB damage was assessed by counting the bored internodes, exit holes, and total number of internodes from 80 randomly selected stalks of sugarcane (20 stalks/replication) in each treatment (18 Oct). Following ANOVA, separation of means was by LSD.

Field Test of a Pathogenic Virus Against Scb, 1994

Abstract Season long control of the SCB was evaluated in a RCB design (5 replications) of plant cane at the St Gabriel Research Station, St Gabriel, LA. Two biological treatments were compared to that of an insecticide treatment and an untreated control. All treatments were applied over the sugarcane canopy with a CO2 backpack sprayer on 20 Jul, 10 Aug, and 1 Sept when the SCB infestation exceeded the economic threshold (5% of the stalks containing live larvae in the leafsheaths). Four 0.004 flat fan spray tips per 6 ft width of row at 32 psi applied 20.1 gpa of finished formulation. Prior to the initiation of the experiment, 2 applications of Lorsban 15G were made (15 lb/acre each) to suppress red imported fire ant predation on SCB larvae (10 May and 9 Jun). The two Crop Genetics International treatments were applied with Plyac at a rate of 6 oz/100 gallons and powdered skim milk at 0.5% wt:vol. SCB damage was assessed by counting the bored internodes, exit holes, and total number of internodes from 100 randomly selected stalks of sugarcane (20 stalks/replication) in each treatment (18 Oct). Analysis of variance was conducted and separation of means was by LSD.

Drift Predictions in the Near Nozzle Region of a Flat Fan Spray

Previous work concerned with modelling spray drift from agricultural flat fan nozzles has used random-walk approaches to predict individual droplet trajectories in the region close to the nozzle and further downwind. Work reported here has extended this approach such that droplets are tracked in three dimensions in the near nozzle region and then a two-dimensional random-walk is used to predict trajectories further downwind. Model predictions were validated against wind tunnel drift experiments. Measurements in a wind tunnel with a 110° flat fan nozzle operating with a flow rate of 0·61 min -1 at a pressure of 3·0 bar, gave volumes of airborne spray 2·0 m downwind of the nozzle of 5·2% of the nozzle output with the spray fan oriented at right angles to the direction of airflow at a speed of 2-0 m s -1 and 0·6% when the spray fan was aligned with the direction of the airflow at a speed of 2·0 m s -1. The model gave drift percentages of 7·5% and 2·8% for the same conditions, and also over-predicted drift for all remaining angles of nozzle orientation. These results suggest that further work is required to: (1) account for the air interactions associated with spray formation processes from a flat fan nozzle; (2) examine the interactions between wind speed and the forward motion of the sprayer.

Small Plot Insecticide Trials, 1993

Abstract Season-long control of the SCB in plant care was evaluated in a RCBD study with 5 replications at the St Gabriel Research Station, St Gabriel, LA. Insecticide treatments were applied over the sugarcane canopy with a CO2 backpack sprayer on 30 Jul, 19 Aug, and 16 Sep when the SCB infestation exceeded the economic threshold (5% of the stalks containing live larvae in the leafsheaths). Four 0.004 flat fan spray tips per 6 ft width of row at 2.25 kg/cm2 applied 188 liters of finished formulation/ha. In addition to an untreated check, 2 granular insecticide treatments were applied using a 400 ml shaker jar calibrated to deliver the designated amount of formulation to the top of the sugarcane canopy 30 Jul, 19 Aug, and 16 Sep. Prior to the initiation of the experiment, 2 applications of Lorsban 15G were made (7.8 kg formulated product/ha each) to suppress red imported fire ant predation (10 May and 6 Jul). The 4 Rohm & Haas treatments were applied with Triton CS-7 at 0.25% v/v, and the Javelin treatment was applied with Kinetic, at a rate of 0.25% v/v. SCB damage was assessed by counting the bored internodes, exit holes, and total number of internodes from 100 randomly-selected stalks of sugarcane (20 stalks/replication) in each treatment on 19 and 21 Oct. Separation of means was by LSD.

Deposition characteristics and biological effectiveness of fungicides applied to winter wheat and the hazards of drift when using different types of hydraulic nozzles

Hydraulic-fan cone, low-pressure fan and two-chamber cone nozzles were used at 1.5, 3.0 and 6.0 bar (150, 300 and 600 kPa) to deliver 140, 200 and 3001 ha −1 respectively of a fungicide spray to control mildew and yellow rust in winter wheat. No significant differences in biological effect were obtained although fan nozzles deposited significantly more on the upper parts of the stems, and two-chamber cone nozzles deposited less on the flag leaf and on the upper part of the stems. Because of their higher deposit and more even distribution, fan nozzles should be preferred, operated at a pressure of 1.5–3 bar to deliver a spray volume of 140–190 lha −1 at 7 km h −1 and to obtain an acceptable biological effect. Higher pressure (6 bar) and volume rates gave no improvement in fungicide performance. Adding a surfactant or penetration oil did not change the volume median diameter or proportion of spray liquid in droplets < 150 μm. Less drift was found when using two-chamber cone nozzles at 3 bar than with flat-fan spray nozzles at 1.5 bar. It is concluded that the two-chamber cone nozzle is useful for fungicide application when drift must be avoided.

Effect of Selected Soil Insecticides on Corn Rootworms, 1991

Abstract Soil insecticides were applied at planting time at 4 locations 2 May (Urbana), 9 May (Monmouth), 10 May (DeKalb), and 22 May (Bondville). The experimental design was a randomized complete block with 4 replications. Each treatment was applied to a single 100-ft row; rows were 30 inches apart. Granular insecticides were metered through Noble units mounted on each of the planter units (John Deere, 7000 series, 4-row Max-Emerge planter). Granules were applied in-furrow or in a 7-inch band ahead of the firming wheels and incorporated into the soil. Liquid application of Lorsban 4 E was delivered at planting in a 7- to 10-inch band with extended range flat fan spray tips (XR Tee Jet 8004VS) mounted ahead of the firming wheels and turned perpendicular to the row for band applications. Later, the liquid was incorporated into the soil. The liquid was applied with a compressed-air system calibrated to deliver 11.5 gal/acre at 20 psi at a speed of 5 mph. Five roots were evaluated for damage in each plot using the Iowa State 1-6 scale. Stand counts were determined by recording the number of plants per 17.4 linear ft of row on 4 Jun at Urbana, 5 Jun at DeKalb and Monmouth, and 6 Jun at Bondville.

Planting-Time Versus Rescue Insecticide Treatments for Black Cutworm Control, 1991

Abstract Corn was planted in 30 inch rows on 28 May. A randomized complete block design was used, and each treatment was replicated 5 times. Each plot was 4 rows wide × 50 ft long. Insecticides applied at planting-time and as rescue treatments were evaluated for the control of BCW in artificial infestations of corn plants (plants infested 6 Jun) within 36-ft2 barrier arenas. Granular insecticides were metered through Noble units mounted on each of the planter units and applied in-furrow or in a 7-inch band ahead of the firming wheels on the planter. Band treatments were incorporated into the soil with spring tines attached to the planter. The planting-time liquid insecticides (41.1 gpa) were applied in a 10-inch band at 30 psi and a speed of 5 mph with 8004E Teejet even flat nozzles. Rescue treatments were broadcast on 7 Jun with XR8004 Teejet extended range flat fan spray tips mounted on a 10-ft boom by a 3-point hitch to the rear of a tractor. A compressed-air system was calibrated to deliver 36.3 gpa at a pressure of 40 psi and a speed of 3 mph. The cumulative number of cut plants in each barrier was determined 1, 6, and 10 days after rescue treatments were applied (DAT). These dates corresponded to corn seedling growth stages 2-3, 4, and 5, respectively. The condition of the plants cut by BCW larvae was also determined at 10 DAT; that is, cut plants were classified as either “dead” or “recovered” from earlier cutting.

Control of Rice Water Weevil with Carbofuran, 1991

Abstract Carbofuran was evaluated for control of RWW at Stuttgart (Crowley silt loam soil) and Keiser (Sharkey silt clay soil), AR. The experimental design was a randomized complete block with 4 replications. Plot size was 9 rows with 17.8 cm spacing × 4.88 m. At Stuttgart, rice ('Newbonnet') was drill-seeded at 123.2 kg seed/ha 25 Apr and emerged 6 May. Propanil at 4.48 kg (AI)/ha and thiobencarb at 2.24 kg (AI)/ha were applied 16 May. Plots were temporarily flooded 17 May and permanently flooded 30 May. Urea at 151.2 kg/ha was applied in a 3-way split of 84 kg/ha 30 May and 33.6 kg/ha each on 10 and 22 Jul. Carbofuran 4 F was sprayed 30 May with a CO2-powered backpack sprayer equipped with Tee Jet 8002 flat fan spray tips. Carbofuran 3 C and fertilizer granules (33.6 kg/ha) coated with carbofuran 4 F were applied with a hand-held shaker 13 Jun. At Keiser, rice ('Alan') was drill-seeded at 100.8 kg seed/ha 23 May and emerged 5 Jun. Propanil at 4.48 kg (AI)/ha and thiobencarb at 3.36 kg (AI)/ha were applied 14 Jun. Urea at 151.2 kg/ha was applied in a 3-way split of 84 kg/ha 25 Jun and 33.6 kg/ha each on 7 and 26 Jul. Carbofuran 4 F, 3 G, and coated fertilizer granules were applied on 24 Jun with the same equipment as at Stuttgart. On 20 and 27 Jun at Stuttgart and on 16 and 25 Jul at Keiser, 5, 10.2 cm diam by 10.2 cm deep, soil cores were removed from each plot. Soil and plant roots were washed into 40-mesh screens. Screens were immersed in salt water and RWW larvae and pupae were recovered and counted. Plots were harvested with a small plot combine.

Predicting the transverse volume distribution under an agricultural spray boom

The volume distribution of spray below individual agricultural flat-fan spray nozzles was fitted to a truncated normal distribution. This expresses the parameters as a function of the spray liquid pressure, the boom height and the nozzle orifice size. This model was used to predict the transverse distribution below an agricultural spray boom.

Control of Cotton Aphid, 1989

Abstract Five chemical treatments and an untreated control were compared in 6 row by 1,254-ft plots of cotton grown on 38-inch rows on a commercial farm located near Robstown, TX. All treatments were applied on 4 May and were replicated 3 times in a randomized complete block design. Tractor mounted spray equipment was calibrated to deliver a total spray volume of 10 gal/acre through 2, size 8002 nozzle tips/row at 38 psi. Flat fan spray tips were used due to the wind speed (15-28 mph) and the small size of plants (pinhead square stage). However, wind was blowing exactly parallel with the treatd rows, thus drift between plots was minimal. Insecticide efficacy was measured by (1) counting the no. of aphids on 20 randomly chosen individual plant “key leaves” from the center 2 rows of each plot (the “key leaf was the third leaf down the main stem from the terminal; usually it is the highest fully expanded leaf on the plant), (2) hand harvest of 13.75 row-ft subplots on 10 and 18 Jul at 3 sites from the center 2 rows of each plot, and (3) evaluation of cotton fiber properties. Harvested seed cotton was ginned on a 10-saw Eagle laboratory machine. Lint samples were sent to the International Center for Textile Research and Development, Lubbock, TX for fiber analysis on a High Volume Instrument Tester manufactured by Motion Control.

Effects of application methods, spray volumes, pressures and herbicide rates on weed control in spring cereals

Herbicides were sprayed in spring cereals with conventional and low pressure hydraulic flat-fan spray nozzles and rotary atomizers. The biological effects were measured on weeds and oats. In addition, some spray retention studies were performed. Conventional flat-fan spray nozzles at a spraying pressure of 2 or 4 bar (200 or 400 kPa) gave the best effect. There was no difference in effect between spray volumes of 125 1/ha and 250 1/ha. In most field situations, 200 kPa and 125 1/ha should be preferred. However, when the spray volume is reduced from 250 to 125 1/ha, the droplet size decreases and the drift hazard increases. Where great care has to be taken, the use of conventional flat-fan spray or low-pressure nozzles at 100 kPa and 250 1/ha may be a compromise between effect and safety.

Semiempirical Analysis of Liquid Fuel Distribution Downstream of a Plain Orifice Injector Under Cross-Stream Air Flow

An improved semiempirical analysis is presented for the liquid fuel distribution downstream of a plain orifice fuel injector under a cross-stream air flow of uniform high velocity and constant ambient temperature. The analysis is based on a simplified “flat-fan spray” model (ε–ψ model). A ε–ψ model is proposed which assumes that the fuel injected through the orifice forms a flat-fan liquid sheet with an average fan angle 2ψ0. Once the droplets have been formed, the trajectory of individual droplets determines the fuel distribution downstream. The validity of the analysis is confirmed by comparison of calculations based on the ε–ψ model and test data obtained from fuel distribution experiments under cross-stream air flow of ambient temperature. The agreement is shown to be very good. The semiempirical analysis presented offers a very useful approach in the preliminary design of the fan air flow path portion of turbofan afterburners.