Dryer spreader system with product depth sensing

Abstract

Drying apparatus is provided that comprises a system for controlling the depth of particulate product that is deposited by a product spreader onto a conveyor that is configured to conduct the product into a dryer. The system includes an imaging device that can measure the depth of product within defined regions of the conveyor and a controller that compares information received from the imaging device with a predetermined depth profile and makes corrections to the speed of a product spreader as it travels across the defined regions of the conveyor.

Description

DRYER SPREADER SYSTEM WITH PRODUCT DEPTH SENSINGBACKGROUND OF THE INVENTIONRelated Applications

[0001] This application claims the priority benefit to U.S. Provisional Patent Application Serial No. 63 / 715,983 entitled DRYER SPREADER SYSTEM WITH PRODUCT DEPTH SENSING, filed November 4, 2024, the entire disclosure of which is incorporated herein by reference.Field of the Invention

[0002] Certain embodiments of the present invention are generally directed toward drying apparatus that can control the depth of a particulate product across a product conveyor in order to achieve uniform drying of the extruded product.Description of the Prior Art

[0003] During the production of certain comestible products, such as animal feeds or human foods, an initially dry formula typically containing protein, starch, and fats is first processed using an extruder or other cooking device to create a continuous stream of cooked product. The output from the extruder is normally too wet for packaging or storage (e.g., from about 20-40% by weight moisture), and thus must be dried. A dryer is positioned to receive the continuous stream of cooked, wet product, and to dry the product to a desired moisture level.

[0004] A variety of dryers have been used in the past to accomplish this moisture reduction, such as single or multiple pass horizontal dryers and vertical dryers. Horizontal dryers include a dryer housing with one or more internal conveyors leading from a wet product inlet to a dried product outlet. Similarly, vertical dryers have a series of stacked decks where product is initially processed in the uppermost deck and is then passed in serial order to the lower decks, leaving to a dried product outlet. In either case, ambient air is drawn into the dryer body and heated, either directly or indirectly, and is then circulatedfor contact with the product within the dryer body. In many instances, a cooler section is used with product dryers, in order to cool the product for downstream handling or packaging; such coolers do not utilize heated air, but merely circulate air through the dried product to lower the temperature thereof.

[0005] In the context of horizontal dryers, moist extruded product is loaded onto a conveyor that directs the extruded product into the dryer. This loading of product onto the conveyor can be accomplished via an automatic product dispensing system. However, a problem with conventional product loading systems is achieving optimal product distribution onto the conveyor so that regardless of product location on the conveyor, the product exiting the dryer is substantially uniform in moisture content. For instance, if the product depth on the outboard margins of the conveyor is less than the product depth of the innermost area of the convey, the moisture content of the outboard product upon exiting the dryer can tend to be substantially less than the product passing through the dryer in a more inboard position.

[0006] In some applications, the extruded products are required to have a moisture content not to exceed a certain level. Therefore, in order to ensure that maximum threshold is not exceeded, some quantity of the product may tend to be “overdried” thus having more moisture removed than is necessary. There can be several consequences of this over-drying. Over-drying can have impacts not only on product quality, but economic costs for the product manufacturer. Not only would the inefficient drying consume more energy, but as many of the extruded products are sold on a weight basis, the finished products will be less dense (having more moisture removed) thereby resulting in the generation of less revenue for the manufacturer.

[0007] Accordingly, there is a need in the art for a system for controlling product distribution on the conveyor that feeds into a dryer that can permit more efficient drying and more uniform moisture content of the product exiting the dryer.SUMMARY OF THE INVENTION

[0008] Embodiments of the present invention address the aforementioned problems by providing systems and methods for drying a particulate product.

[0009] In one particular embodiment, a drying system is provided that comprises a dryer, a product conveyor, a product spreader, an imaging device, and a controller. The dryer is configured to pass heated air through a bed of the particulate product to remove moisture therefrom. The product conveyor is configured to conduct the particulate product into the dryer. The product spreader is configured to deposit the particulate product onto the product conveyor. The product spreader has a delivery chute that is configured for lateral oscillation to distribute the particulate product onto the product conveyor between a pair of opposed conveyor side margins. The product conveyor is divided into a plurality of longitudinally extending zones located between the conveyor side margins. The imaging device is operable to measure a depth of particulate product deposited into each of the plurality of zones that has been deposited by the product spreader. The controller is operable to receive and process information from the imaging device related to the depth of the particulate product deposited into each of the zones and to adjust a speed of travel of the delivery chute across at least one of the plurality of zones to achieve a desired product depth within the one or more of the plurality of zones.

[0010] According to another embodiment a method of drying a particulate product is provided. The particulate product is directed into a product spreader that has a delivery chute that is configured for lateral oscillation. The particulate product from the product spreader is deposited onto a product conveyor that is divided into a plurality of longitudinally extending zones located between a pair of opposed conveyor side margins. The depositing step includes oscillating the delivery chute across the plurality of zones. The depth of the particulate product deposited into each of the zones is measured with an imaging device that is operably connected to a controller. The controller processes information related to the depth of the particulate product deposited into each of the plurality of zones and adjusts a speed of travel of the delivery chute across at least one of the plurality of zones to achieve a desired product depth within the at least one of the plurality of zones. The particulate product located on the product conveyor is passed into a dryer where moisture is removed therefrom.BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 is a view of a drying apparatus in accordance with certain embodiments of the present invention;

[0012] Fig. 2 is a close-up view of the drying apparatus, in particular the product spreader, conveyor, and imaging device;

[0013] Fig. 3 depicts the product spreader and its oscillating movement during deposition of product onto the conveyor;

[0014] Fig. 4 is a side elevation view of the product spreader in operation depicting the positioning of the imaging device;

[0015] Fig. 5 is a schematic depiction of the division of the conveyor into zones;

[0016] Fig. 6 depicts the process for controlling the speed of spreader oscillation across individual zones and, accordingly, product bed depth; and

[0017] Fig. 7 is a chart depicting an exemplary spread shape factor curve.

[0018] While the drawings do not necessarily provide exact dimensions or tolerances for the illustrated components or structures, the drawings are to scale with respect to the relationships between the components of the structures illustrated in the drawings.DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

[0019] Cooking extruders can be used to prepare a wide range of comestible products such as human foods and animal feeds (e.g., pet feeds and aquatic feeds). These cooking extruders can be of a single or twin-screw variety in which a mixture of ingredients is processed, using thermal and / or mechanical energy inputs, and then passed through a restricted orifice die to create an extruded food product. The ingredients may generally contain quantities of starch, protein, and / or fat in desired amounts selected to meet nutritional requirements for the finished product. In some embodiments, the ingredients can be selected from the group consisting of grains (e.g., wheat, com, oats, soy), meat and meat by-products, ad various additives (e.g., vitamins, minerals, and colorants). The ingredients, or certain combinations of the ingredients, may also be processed in a preconditioner, before processing within the extruder, in which a portion of the starch fraction of the ingredients is at least partially gelatinized.

[0020] Upon exiting the extruder, the wet, cooked extruded product may have a moisture content that is higher than desired for the finished product. Therefore, at least a portion of the moisture within the extruded product must be removed before the product can be packaged. In certain embodiments, the extruded product can be immediately cut into pieces of desired size and dried. However, if the moisture content of the extruded product is too high, the product may first be extruded into ropes that are pre-dried and then cut. In one or more embodiments, the cut, extruded product has a moisture content of up to 50% by weight, or from 20-40% by weight before final drying.

[0021] Figure 1 depicts exemplary drying apparatus 10 that can be used to perform final drying of a particulate product, such as the aforementioned cut, extruded product. As used herein, the term “particulate product” refers to material that is in the form of pellets or having a pellet-like size, morsels, chunks, or granules and having a size amenable to processing within a forced-air dryer while remaining in place on the conveyor during passage through the dryer. Generally, this excludes smaller materials characterized as dust or fines which would be scattered from the conveyor by the forced air used within the dryer. The particulate product can comprise non-extruded and / or non-cooked products from which it is desirable to remove moisture. Examples of these alternate particulate products include fruits, vegetables, silica, nuts, tobacco, calcium, meat / jerky pieces. The particulate products can be formed from a larger product that is cut into pieces of a desired size, or they can exist naturally as a particulate material or they have been formed in an alternate way that does not involve size reduction by cutting. Preferably, the particulate products have a substantially uniform size as this tends to lead to more uniform drying, although this needs not always be the case. Drying apparatus 10 includes a dryer 12, a spreader 14, and a conveyor 16. Dryer 12 can be any dryer that is conventional in the art such as a horizontal single-pass or vertical multi-pass, fuel-fired convection dryer. The particulate product is delivered to the spreader 14, which in turn deposits the product onto conveyor 16. Conveyor 16 then transports the particulate product into the dryer 12.

[0022] As can be seen in Fig. 2, spreader 14 comprises a product chute 18 having an inlet 20 that is configured to receive particulate product delivered to it, such as from an airlock or other pneumatic conveying system 21. The product then travels through aspout section 22 from which it is dispensed onto the conveyor 16. Spreader 14 is configured for oscillating movement so that product 23 can be distributed across the width of the conveyor 16. See, Fig. 3. In one or more embodiments, a gear motor 24 driven by a variable frequency drive (VFD) is used to control the oscillation of the spreader 14. As explained in greater detail below, the VFD is used to control the speed at which the chute 18 traverses above the conveyor 16 affecting the depth of the product that is deposited on the conveyor.

[0023] In one or more embodiments, conveyor 16 comprises a motor-driven belt that extends past a dryer air curtain 26 and into dryer 12. The belt can be formed from a stainless steel wire mesh or a polyester screen. Alternatively, the conveyor 16 can comprise one or more metal trays. In particular embodiments, conveyor 16 can extend the length of the dryer 12 thereby conducting the particulate product through the dryer to a dryer exit (not shown). Alternatively, conveyor 16 can be configured to transfer the particulate product onto a different conveyor system located inside the dryer 12. Conveyor 16 further comprises a pair of opposed side margins 28, 30 that cooperatively define the width of the conveyor.

[0024] In one or more embodiments, the conveyor 16 is divided into a plurality of longitudinally extending zones 32 located between the conveyor side margins 28, 30. See, e.g., Fig. 5. The term “divided” as used herein does not necessarily imply that a structural or physical partitioning of the conveyor 16 is performed. Rather, the conveyor can be virtually segmented into zones 32, which as explained below, are used to create regions of product depth analysis and setting the speed at which the chute 18 moves across the conveyor 16.

[0025] As can be seen in Fig. 5, the plurality of zones is defined by an essentially rectilinear margin 34 and an essentially curvilinear margin 36. Each of margins 34 and 36 terminate at side margins 28, 30, and preferably at the same points on each side margin. The length of rectilinear margin 34 is set by the width of the conveyor 16, whereas the length of curvilinear margin 36 generally corresponds with an arc along which the spout 22 of chute 18 travels during spreader oscillation. As depicted, in certain embodiments, each of zone 32 comprises a segment 38 of rectilinear margin 34 having essentially an equivalent length. Thus, in preferred embodiments, if the conveyor has a width X andis divided into 10 zones, the width of each zone (and the length of segment 38) equals X - 10. However, the length of segment 40 of curvilinear margin 36, corresponding to a particular segment 38, varies depending upon the location of segment 40 along curvilinear margin 36.

[0026] Together, segments 38 and 40 of each zone are used to define an arc ratio value for each of zones 32. The arc ratio is the ratio between the length of segment 40 (the arc length) to the length of segment 38 (i.e., the horizontal length). These ratios can be normalized so that the outermost zones have an arc ratio of 1, and the arc ratios decrease as the center of the conveyor 16 is approached. The arc ratio represents an amount of time that the spreader’s spout 22 spends over each zone. Thus, the spreader’s spout 22 spends more time over the outermost zones due to the nature of oscillation of the chute 18, and less time over the more interior zones.

[0027] Turning to Fig. 4, drying apparatus 10 further comprises an imaging device 42 positioned in an elevated position having a field of view that includes conveyor 16, and in particular, the plurality of zones 32. The imaging device 42 is operable to measure a depth of particulate product deposited into each of the plurality of zones 32 by the spreader 14. In certain embodiments, the imaging device 42 comprises a light detection and ranging (LiDAR) sensor, an ultrasound sensor, or a digital camera, with a LiDAR sensor being preferred. An exemplary LiDAR sensor that may be used in connection with the present invention is the MRS 1000 LiDAR sensor available from SICK AG, Waldkirch, Germany. In certain embodiments, the imaging device 42 is positioned above the conveyor 16 and has a field of view of substantially the entire extent of the conveyor located between the spreader spout 22 and the dryer air curtain 26. However, it is within the scope of the present invention for the imaging device 42 to be mounted in any location in which a portion of the conveyor having the particulate product loaded thereon is within view. For example, the imaging device 42 could be located within the dryer 12, just inside of the air curtain 26. The imaging device 42 may be adjustably mounted above the conveyor 16 in order to fine tune the device’s field of view.

[0028] The drying apparatus 10 further comprises a controller 44 that can monitor and control various aspects of the drying apparatus operation. In particular, controller 44 comprises programmable logic controller (PLC) that includes at least a processor andassociated memory that is configured to receive and store inputs related to operational conditions associated with drying apparatus 10, such as spreader oscillation speed, imaging data, dryer temperature, heater fuel flow, and product moisture content. The controller may also include some form of user interface that may be located on the drying apparatus itself or remote from the drying apparatus, such as in a plant control room.

[0029] The controller 44 can also receive inputs from an operator regarding the dimensions of each of zones 32, the arc ratio for each zone, and spread shape factor for each zone. The shape factor is a percentage change from the product bed depth average for a particular zone. For certain dryers and product combinations, it can be more desirable and lead to more efficient drying for the depth of particulate product to be different depending upon zone location on the conveyor. For instance, in some dryer / product combinations, it is desirable for the depth of particulate product to be greater in the outer-most zones and less in the inner zones. This is depicted in Fig. 7. A shape factor of 1.1, such as appears for zones 1 and 10, means that the depth of product in zones 1 and 10 is 10% greater than the average product depth across all zones. A shape factor of 0.95, such as for zones 3-8, means that the depth of product in that zone is 5% less than the average product depth across all zones. Note, the average shape factor across all zones must equal 1. Thus, the shape factor profile for zones 1-10 has a concave or bathtub-like shape with the outermost ends having a greater shape factor and the inner zones. It is noted that the shape factor is a parameter specific for a particular drying operation. The shape factor may have a concave profile such as depicted in Fig. 7. Alternatively, the shape factor may be crowned or convex toward the center of the conveyor thereby presenting predetermined shape factor that is larger for the zones closest to the center of the conveyor than for any other of the plurality of zones. Still further, the predetermined shape factor can be flat or of a constant value across the width of the conveyor indicating a constant product depth across the width of the conveyor, or of any customized shape that leads to the desired drying of the product. Generally, the shape factor represents a target or optimal profile for product depth across all 10 zones for a particular drying operation. The spread shape factor is set by the dryer operator and generally is not altered during the run of a particular productthrough the dryer. The controller 44 may be programmed with certain preset shape factor configurations, such as concave, flat, or convex. The dryer operator may simply select one of the preset shape factors or create a custom shape factor profile.

[0030] One particularly important function of controller 44 is to adjust the speed at which the oscillating spreader travels across individual zones based upon the depth of product within each zone as measured by the imaging device 42. In order to accomplish this, the controller is configured to compare the measured zone bed depth with a mathematical product of the average measured bed depth across all zones and the zone shape factor. This comparison results in the generation of an arc ratio correction factor which, if the correction factor exceeds a predetermined threshold, is used to calculate a corrected arc ratio. The controller 44 uses the corrected arc ratio to adjust the VFD which speeds up or slows down, whichever the case may be, the spreader as it travels across a particular zone. These comparisons and calculations are described in further detail below.

[0031] Apparatus as described herein can be used to dry a particulate product to a desired moisture level. In particular, methods for ensuring that the particulate product are deposited on product conveyor 16 according to a predetermined depth and profile. Figure 6 generally describes a method for accomplishing this objective. As the particulate product is deposited onto conveyor 16 from the spout 22 of delivery chute 18, imaging device 42 measures the bed depth within each of zones 32 (step 46). The imaging device 42 can be programmed to continuously take product bed depth measurements across the width of conveyor 16. This can result in a large quantity of data points that is preferably condensed before being acted upon by a PLC controller. In one embodiment, step 46 includes utilizing a gateway processor, such as a Phoenix Axioline Controller, to collect the measurements from imaging device 42 and condense that data into an average bed depth measurement for a particular zone over a given time (e.g., a 5-minute rolling average). This information is sent to controller 42 for processing. Controller 42 determines the average bed depth across all conveyor zones. The spreader arc ratios and spread shape factors for all zones are provided by the operator.

[0032] The controller 42 compares the measured zone bed depths (which may be a rolling bed depth average) to the mathematical product of the average bed depth and the zone shape factor (step 48). The controller 42 then determines if the difference between the measured zone bed depths and the mathematical product exceed a predetermined threshold or tolerance level (e.g., + / - 10%, 5%, or 1% of the mathematical product) (step 50). If the difference does not exceed the tolerance level, no change is made to the spreader arc ratio values (step 52) However, if the difference does exceed the tolerance level, the controller 42 computes corrected arc ratio values that can be used by the controller to adjust the speed at which the chute 18 travels across the individual zones in order to alter the bed depth within the individual zones (step 54).

[0033] The corrected arc ratio, Ac, for a particular zone is calculated by multiplying the previous or original arc ratio, Ao, by a correction factor, CF. CF is calculated by dividing the zone’s measured bed depth, DM, by the product of the average bed depth, DA, and the zone’s shape factor, Fs. It is noted that the shape factor can be an optional variable and need not always be taken into account, particularly if a uniform product depth across the conveyor’s width is desired (i.e., the shape factor would be 1 in such a scenario). Therefore, the formula for calculating the corrected arc ratio, Ac, is represented by equations (1) and (2).CF= [DM(DAX Fs)] (1)Ac=Aox Cp (2)

[0034] Controller 42 uses the corrected arc ratio values to increase the speed of the chute 18 as it traverses a particular zone in the case in which the controller seeks to reduce the product bed depth within the zone, or to decrease the speed of the chute 18 as it traverses a zone in the case in which the controller seeks to increase the product bed depth within a particular zone. In either instance, after the determination is made and any resulting corrected arc ratios calculated, the controller can set a timer, the lapsing of which causes the imaging device 42 to re-measure the zone bed depths (step 46) and the process repeats. In certain embodiments, the process is repeated at a cycle interval of every 1 to 10 minutes, every 2 to 8 minutes, every 3 to 7 minutes, or about every 5minutes. However, it is within the scope of the invention for any suitable time interval between cycles to be used, including nearly continuous measuring of bed depth and real time correction of arc ratio values.

[0035] In addition to being used to measure bed depths for purposes of maintaining a desired spread shape factor, imaging device 42 can also be used to acquire information that could indicate other problems associated with operation of drying apparatus 10, including providing warnings related to poor product spread due to spreader malfunction. In the absence of the surveillance provided by imaging device 42, an operator would need to always be physically present with drying apparatus 10 in order to promptly detect any such malfunctions. However, embodiments of the present invention allow drying apparatus 10 to be monitored remotely and notifications of detected malfunctions can be delivered and acted upon in real time.EXAMPLE

[0036] The following is an example of product depth measurement as deposited on a conveyor by an oscillating spreader and the calculation of corrected arc ratios in furtherance of achieving a desired spread shape factor for the various conveyor zones. It is to be understood, however, that this example is provided by way of illustration, and nothing therein should be taken as a limitation upon the overall scope of the invention.

[0037] In this example, the process for correcting how a particulate product is deposited onto a conveyor by an oscillating spreader is explored. The conveyor has been divided into 10 zones 32 as depicted in Fig. 5. The arc ratios for each zone are listed in Fig. 5 and in Table 1, below. The arc ratios are values that have been calculated as set forth in the description above. In addition, spread shape factors have been selected based upon an optimal profde for the characteristics of the particulate product and dryer apparatus to be used. These shape factors are listed in Table 2, below.Table 1

[0038] A run of product through a product spreader is performed. The depth of product deposited onto the conveyor is measured with an imaging device, such as a LiDAR camera. The measured product depths by zone are reported in Table 2.Table 2

[0039] As can be seen, the measured bed depths do not correspond with expectations for bed depth based upon the spread shape factor. For example, in zone 10, based upon a shape factor of 1.1, it would be expected that the bed depth should be 10% greater than average in that zone. However, the measured bed depth is almost 80% greater than the average depth across all zones. Therefore, some correction to spreader speed across at least zone 10 is required in order to achieve the desired spread shape factor.

[0040] A corrected spreader arc ratio, which can then be used by the dryer controller to adjust the speed of spreader travel across any given zone, is then calculated as described previously herein. The corrected spreader arc ratios are listed in Table 3. Estimations can then be made as to expected bed depths in each zone once adjustments to the spreader have been made. These corrected bed depths are also provided in Table 3.Table 3

[0041] After a predetermined period of time, actual bed depths of product being deposited into the conveyor zones can be re-measured, compared to the desired shape factor, and additional corrected spreader arc ratios can be calculated. Thus, spreader operation canbe continuously monitored and adjusted so that optimal product bed depth can be maintained during drying of the particulate product.

Claims

We claim :

1. A system for drying a particulate product comprising: a dryer configured to pass heated air through the particulate product to remove moisture therefrom; a product conveyor configured to conduct the particulate product into the dryer; a product spreader configured to deposit the particulate product onto the product conveyor, the product spreader having a delivery chute that is configured for lateral oscillation to distribute the particulate product onto the product conveyor between a pair of opposed conveyor side margins, the product conveyor being divided into a plurality of longitudinally extending zones located between the conveyor side margins; an imaging device operable to measure a depth of particulate product deposited into each of the plurality of zones that has been deposited by the product spreader; and a controller operable to receive and process information from the imaging device related to the depth of the particulate product deposited into each of the zones and to adjust a speed of travel of the delivery chute across at least one of the plurality of zones to achieve a desired product depth within the one or more of the plurality of zones.

2. The system of claim 1, wherein the imaging device is a LiDAR sensor, an ultrasound sensor, or a digital camera.

3. The system of claim 1, wherein the imaging device is positioned above the product conveyor.

4. The system of claim 1, wherein the controller is configured to compare the measured depth of particulate product deposited into each of the plurality of zones with a mathematical product of an average bed depth across all of the plurality of zones and a predetermined shape factor for each of the plurality of zones and calculate an arc ratio correction factor.

5. The system of claim 4, wherein the predetermined shape factor is larger for the zones closest to the conveyor side margins than for any other of the plurality of zones.

6. The system of claim 4, wherein the predetermined shape factor is larger for the zones closest to the center of the conveyor than for any other of the plurality of zones.

7. The system of claim 4, wherein the predetermined shape factor is constant across the width of the conveyor.

8. The system of claim 4, wherein the controller is further configured to calculate a corrected arc ratio for each of the plurality of zones by multiplying the shape factor by the arc ratio correction factor.

9. The system of claim 8, wherein the controller is operable to adjust the speed of travel of the delivery chute across the at least one of the plurality of zones based upon the calculated arc ratio for the at least one of the plurality of zones.

10. A method of drying a particulate product comprising: directing the particulate product into a product spreader, the product spreader having a delivery chute that is configured for lateral oscillation; depositing the particulate product from the product spreader onto a product conveyor, the product conveyor being divided into a plurality of longitudinally extending zones located between a pair of opposed conveyor side margins, wherein the depositing step includes oscillating the delivery chute across the plurality of zones; measuring the depth of the particulate product deposited into each of the zones with an imaging device, the imaging device being operably connected to a controller;processing with the controller information received from the imaging device related to the depth of the particulate product deposited into each of the plurality of zones and adjusting a speed of travel of the delivery chute across at least one of the plurality of zones to achieve a desired product depth within the at least one of the plurality of zones; passing the particulate product located on the product conveyor into a dryer; and removing moisture from the particulate product within the dryer.

11. The method of claim 10, wherein the measuring the depth of the particulate product comprises scanning the plurality of zones with a LiDAR sensor, an ultrasound sensor, or a digital camera.

12. The method of claim 10, wherein the processing information with the controller comprises comparing the measured depth of particulate product deposited into each of the plurality of zones with a mathematical product of an average bed depth across all of the plurality of zones and a predetermined shape factor for each of the plurality of zones and calculating an arc ratio correction factor.

13. The method of claim 12, wherein the predetermined shape factor is larger for the zones closest to the conveyor side margins than it is for any other of the plurality of zones.

14. The method of claim 12, wherein the predetermined shape factor is larger for the zones closest to the center of the conveyor than for any other of the plurality of zones.

15. The method of claim 12, wherein the predetermined shape factor is constant across the width of the conveyor.

16. The method of claim 12, further comprising calculating a corrected arc ratio for at least one of the plurality of zones by multiplying the shape factor by the arc ratio correction factor.

17. The method of claim 16, wherein the adjusting the speed of travel of the delivery chute across one or more of the plurality of zones is based upon the calculated arc ratio for the at least one of the plurality of zones.

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