Method for determining unloading range of screw ship unloader based on multi-factor material surface height calculation

Abstract

The application discloses a spiral ship unloader unloading range determination method based on multi-factor material surface height calculation and belongs to the technical field of overall size design of spiral ship unloaders. It comprises the following steps: step 1, a material surface height calculation model is established based on multi-factors and is used for determining the highest / lowest material surface height; step 2, the positions of a cargo hold near a sea side and a shore side are determined; step 3, based on the highest / lowest material surface height in step 1 and the positions of the cargo hold near the sea side and the shore side in step 2, the unloading range is finally obtained. Under the condition of considering the influence of multi-factors, the application effectively reflects the change of the material surface height in each hold of a bulk carrier during the working process of the spiral ship unloader, thereby accurately calculating the unloading range that the spiral ship unloader should meet under each design condition and providing an important design basis for the reasonable design of the overall size of the spiral ship unloader.

Description

Technical Field

[0001] This invention relates to a method for determining the unloading range of a screw unloader based on multi-factor material level height calculation, and belongs to the technical field of overall size design of screw unloaders. Background Technology

[0002] In the overall dimensional design of screw unloaders, the surface of bulk material in the cargo hold of a bulk carrier is called the material surface. Using the wharf level as a reference plane, the horizontal position of the material surface is usually characterized by its height. During the operation of the screw unloader, the material surface height is constantly changing due to numerous factors, including ship type characteristics, unloading sequence, unloading cycles, unloading rate per cycle, unloading draft of the bulk carrier, ballast draft of the bulk carrier, wharf water level, and bulk material density. During this period, there will be both the highest and lowest material surfaces. The unloading range of the screw unloader is encompassed by the two sides of the bulk carrier's cargo hold, the highest material surface, and the lowest material surface. Accurate calculation of the unloading range is one of the important conditions for the reasonable overall dimensional design of the screw unloader.

[0003] In existing studies on unloading range, the methods for determining the position on both sides of the cargo hold are basically consistent and undisputed. The difficulty lies in determining the highest and lowest material level heights.

[0004] The empirical formula method, after long-term use and verification by relevant enterprises, has basically met most overall dimensional design requirements and demonstrated high accuracy. However, because the empirical formula method is a specific formula given only considering factors such as ship type characteristics, unloading draft of bulk carriers, and wharf water level, it can only describe the minimum material level. Therefore, the screw unloader designed under this method cannot effectively cope with unloading situations with different unloading sequences, unloading cycles, unloading rates per cycle, and bulk material densities. In actual production, there have been cases where the overall dimensional design of the screw unloader does not meet the requirements due to different unloading cycles.

[0005] The literature calculation method, proposed by researchers in related fields, is a specific formula given under the consideration of many factors, including unloading sequence, unloading rounds, unloading rate per round, and bulk density. Although it can effectively deal with different design situations of unloading sequence, unloading rounds, unloading rate per round, and bulk density, this method can only describe two specific material level heights: the highest material level and the lowest material level. It cannot reflect the changes in material level height in each hold of the bulk carrier during the operation of the screw unloader. Furthermore, this method ignores the characteristics of the ship type, leading to doubts about the accuracy of the formula. Summary of the Invention

[0006] The technical problem to be solved by this invention is to provide a method for determining the unloading range of a screw unloader based on multi-factor material level height calculation. This method ensures the accuracy of the calculation of the highest and lowest material level heights. Furthermore, it requires a method for calculating the material level height that simultaneously considers the influence of multiple factors such as ship type characteristics, unloading sequence, unloading rounds, unloading rate per round, unloading draft of bulk carriers, ballast draft of bulk carriers, wharf water level, and bulk material density. This method is used to determine the unloading range of the screw unloader under various design conditions, thereby ensuring that the overall dimensions of the screw unloader meet various operational requirements.

[0007] The technical problem to be solved by this invention is achieved by the following technical solution:

[0008] The method for determining the unloading range of a screw unloader based on multi-factor material level height calculation includes the following steps:

[0009] Step 1: Based on multiple factors, establish a material surface height calculation model to determine the highest / lowest material surface height, i.e.:

[0010]

[0011] Where: Y S This indicates the material level height when the screw unloader is working; d max Indicates the maximum draft of the bulk carrier; DWT indicates the maximum load capacity of the bulk carrier; ρ indicates the bulk density of the bulk material; B DX L represents the equivalent width of the cargo hold cross-section; H ξ represents the length of a single cargo hold on a bulk carrier; ξ represents the unloading rate, which is the ratio of the unloaded cargo to the total unloaded cargo, 0 ≤ ξ ≤ 1; n represents the number of cargo holds on the bulk carrier; j represents the j-th unloading round; w represents the w-th unloading round; a j Indicates the unloading rate in round j; a w Represents the unloading rate in round w; i represents the i-th cargo hold; h S This represents the distance h from the water level at the wharf to the wharf's reference plane. S At the high water level of the dock H and the low water level at the wharf L Between; B indicates the width of the bulk carrier; h SD This indicates the height of the double bottom at the mid-longitudinal section line.

[0012] When 0.025B + 0.042d max When +0.3 ≥ min{0.76, B / 20}, h SD It is 0.025B + 0.042d max +0.3 meters,

[0013] When 0.025B + 0.042d max When +0.3 < min{0.76, B / 20}, h SDThe minimum value is {0.76, B / 20} meters.

[0014] Step 2: Determine the position of the cargo hold on the seaward side, i.e.: Z1+BW ds Determine the position of the cargo hold on the berth side, i.e.: Z1+W ds Where: Z1 represents the minimum distance between the bulk carrier and the quayside; B represents the bulk carrier's beam; W ds This indicates the side width of a bulk carrier, ranging from 0.6 to 1.2 meters.

[0015] Step 3: Based on the highest / lowest material level height in Step 1 and the cargo hold positions on the seaward and shoreward sides in Step 2, the final unloading range is obtained, i.e.:

[0016]

[0017] Where: Y Smax Y indicates the maximum material level height during the operation of the screw unloader; Smin Y indicates the minimum material level height during the operation of the screw unloader; S The equation representing the calculation of the material level height during operation of the screw unloader in step 1 above; X L Indicates the position of the cargo hold on the seaward side; X R Z1 indicates the position of the cargo hold on the quayside; B indicates the minimum distance between the bulk carrier and the quayside; W indicates the bulk carrier's beam; W indicates the minimum distance between the bulk carrier and the quayside. ds This indicates the side width of a bulk carrier, ranging from 0.6 to 1.2 meters.

[0018] As a preferred example, in step 1, the material level calculation model is established according to the following method:

[0019] Step 1.1: Establish an ideal unloading model based on multiple factors;

[0020] Step 1.2: Simplify the cargo hold shape to obtain a simplified cargo hold model;

[0021] Step 1.3: Introduce the regression equations for the unloading draft and ballast draft of the bulk carrier to obtain the relationship equation between the unloading operation of the screw unloader and the change in the draft of the bulk carrier, namely:

[0022] d ξ =d j +(d B -d max +DWT 0.3682 / 6.0359)ξ;

[0023] Where: d j =d max -DWT 0.3682 ·ξ / 6.0359;

[0024] Where: d j Indicates the unloading draft of a bulk carrier; d B Indicates the ballast draft of a bulk carrier; d ξ The equation representing the relationship between the unloading operation of the screw unloader and the change in the draft of the bulk carrier; d max ξ represents the maximum draft of the bulk carrier; DWT represents the maximum load capacity of the bulk carrier; ξ represents the unloading rate, which is the ratio of the unloaded cargo to the total cargo, 0≤ξ≤1;

[0025] Step 1.4, based on the unloading model in Step 1.1, the simplified cargo hold model in Step 1.2, and the regression and relational equations in Step 1.3, yields:

[0026]

[0027] Where: Y S This indicates the material level height when the screw unloader is working; d max Indicates the maximum draft of the bulk carrier; DWT indicates the maximum load capacity of the bulk carrier; ρ indicates the bulk density of the bulk material; B DX L represents the equivalent width of the cargo hold cross-section; H ξ represents the length of a single cargo hold on a bulk carrier; ξ represents the unloading rate, which is the ratio of the unloaded cargo to the total unloaded cargo, 0 ≤ ξ ≤ 1; n represents the number of cargo holds on the bulk carrier; j represents the j-th unloading round; w represents the w-th unloading round; a j Indicates the unloading rate in round j; a w Represents the unloading rate in round w; i represents the i-th cargo hold; h S This represents the distance h from the water level at the wharf to the wharf's reference plane. S At the high water level of the dock H and the low water level at the wharf L Between; B indicates the width of the bulk carrier; h SD This indicates the height of the double bottom at the mid-longitudinal section line, when 0.025B + 0.042d max When +0.3 ≥ min{0.76, B / 20}, h SD It is 0.025B + 0.042d max +0.3 meters,

[0028] When 0.025B + 0.042d max When +0.3 < min{0.76, B / 20}, h SD The value is min{0.76, B / 20} meters.

[0029] As a preferred example, in step 1.1, the multiple factors include unloading order, unloading rounds, and unloading rate per round; the unloading model is established according to the following method:

[0030] Step 1.1.1: Ensure that the bulk carrier meets stability and strength requirements in each unloading step, i.e., the unloading sequence, unloading rounds, and unloading rate per round are configured reasonably to prevent changes in the hull's heel and stern due to roll or trim, maintaining a stable buoyancy.

[0031]

[0032] Where: d a Indicates the draft of the bow in the longitudinal direction; d m Indicates the midship draft in the longitudinal direction; d f Δd represents the draft of the stern in the longitudinal direction; h It represents the difference in draft between any two symmetrical points on either side of the central line of symmetry in the horizontal direction.

[0033] Step 1.1.2: The unloading and ballasting processes of a bulk carrier begin and end simultaneously, and both are linearly related to the unloading rate, i.e.:

[0034] d ξ =(k j +k B )ξ+c j +c B ;

[0035] Where: d ξ The equation representing the relationship between the unloading operation of the screw unloader and the change in the draft of the bulk carrier is the same as the equation in step 1.3 above. ξ Equal; k j k represents the slope coefficient of the unloading draft regression equation. B ξ represents the slope coefficient of the ballast draft regression equation; ξ represents the unloading rate, which is the ratio of the unloaded cargo to the total cargo volume, 0≤ξ≤1; c j c represents the constant in the unloading draft regression equation; B The constant representing the ballast draft regression equation;

[0036] Step 1.1.3: The bulk carrier's materials are uniform and its structure is symmetrical along the length and beam of the ship. All cargo holds on board have the same shape, size, and capacity. The unloading process within the same hold is uniform, and the material level decreases horizontally.

[0037]

[0038] Where: Δρ b Δl represents the difference in material density between any structural locations on a bulk carrier. b ΔY represents the dimensional difference of the structure at any symmetrical position on either side of the beam centerline of a bulk carrier. S This indicates the height difference between any material surface positions within the same cargo hold.

[0039] As a preferred example, in step 1.2, the simplified cargo hold model is established according to the following method:

[0040] Step 1.2.1: Based on the typical cargo hold type of a dry bulk carrier, the cargo hold shape is simplified. The cross-sectional area S1 of the original octagonal cargo hold is:

[0041]

[0042] Step 1.2.2: Keeping the cross-sectional area S1 unchanged, simplify the cargo hold cross-section to a quadrilateral to obtain the equivalent width B of the cargo hold cross-section. DX for:

[0043]

[0044] Wherein: H D B indicates the depth of the bulk carrier; W indicates the width of the bulk carrier. ds This indicates the side beam of a bulk carrier, ranging from 0.6 to 1.2 meters; B H This indicates the maximum width of the cargo hold, designated as B-2W. ds Meters; b indicates the width of the cargo hold hatch, which is 0.4B to 0.7B meters; B DB θ1 represents the width of the double bottom between the two bottom side compartments, which is b + (4~8) meters; θ1 represents the inclination angle of the top side compartment ramp, 30°≤θ1≤90°; θ2 represents the inclination angle of the bottom side compartment ramp, 35°≤θ2≤50°; H CZ This indicates the height of the vertical plate of the top side compartment, which is 0.7 to 0.8 meters; h SD This indicates the height of the double bottom at the mid-longitudinal section line.

[0045] When 0.025B + 0.042d max When +0.3 ≥ min{0.76, B / 20}, h SD It is 0.025B + 0.042d max +0.3 meters;

[0046] When 0.025B + 0.042d max When +0.3 < min{0.76, B / 20}, h SD The value is min{0.76, B / 20} meters.

[0047] As a preferred example, in step 1.3, the regression equations for the unloading draft and ballast draft of the bulk carrier are used to obtain the relationship equation between the unloading operation of the screw unloader and the change in the draft of the bulk carrier, specifically:

[0048] Step 1.3.1, the unloading draft regression equation is as follows: d j =d max -DWT 0.3682 ·ξ / 6.0359;

[0049] The ballast draft regression equation is as follows:

[0050] Where: d j Indicates the unloading draft of a bulk carrier; d B Indicates the ballast draft of a bulk carrier; d max ξ represents the maximum draft of the bulk carrier; DWT represents the maximum load capacity of the bulk carrier; ξ represents the unloading rate, which is the ratio of the unloaded cargo to the total cargo, 0≤ξ≤1;

[0051] Step 1.3.2, the relationship between the unloading operation of the screw unloader and the change in the draft of the bulk carrier is as follows:

[0052] d ξ =d j +(d B -d max +DWT 0.3682 / 6.0359)ξ;

[0053] Where: d j Indicates the unloading draft of a bulk carrier; d B Indicates the ballast draft of a bulk carrier; d ξ The equation representing the relationship between the unloading operation of the screw unloader and the change in the draft of the bulk carrier; d max ξ represents the maximum draft of the bulk carrier; DWT represents the maximum load capacity of the bulk carrier; ξ represents the unloading rate, which is the ratio of the unloaded cargo to the total cargo, 0≤ξ≤1.

[0054] A computing device includes a processor and a memory for storing a processor-executable program, wherein when the processor executes the program stored in the memory, it implements the method described above.

[0055] A storage medium storing a program that, when executed by a processor, implements the method described above.

[0056] The beneficial effects of this invention are as follows: Considering multiple factors such as ship type characteristics, unloading sequence, unloading rounds, unloading rate per round, unloading draft of bulk carriers, ballast draft of bulk carriers, wharf water level, and bulk material density, this invention effectively reflects the changes in material level in each hold of a bulk carrier during the operation of the screw unloader. This allows for accurate calculation of the unloading range that the screw unloader should meet under various design conditions, solving the problems of insufficient accuracy and difficulty in rationally designing for different design conditions in current calculation methods. It provides an important design basis for the rational design of the overall dimensions of the screw unloader. Attached Figure Description

[0057] Figure 1 This is a schematic diagram showing the relevant dimensions and unloading range of the bulk carrier in this invention;

[0058] Figure 2 This is a simplified diagram of the cargo hold of a bulk carrier in this invention;

[0059] Figure 3 This is a curve showing the cargo level of a 50,000 DWT bulk carrier in this invention. Detailed Implementation

[0060] To facilitate a clear understanding of the technical means, creative features, objectives, and effects of this invention, the invention will be further described below in conjunction with specific illustrations and embodiments.

[0061] The unloading draft regression equation, cited in (On the estimation method of draft of unloaded bulk carriers. Yang Yang, Yang Xingyan. China Harbor Construction, 2014, 0(5): 19-20), is based on the regression analysis of the unloading draft of 1051 bulk carriers with a tonnage range of 7500 tons to 375000 tons, and meets the 75% confidence level.

[0062] The ballast draft regression equation, cited in (Statistical Study on Ballast and Operating Draft of Ships Based on Actual Ship Data. Ma Xiaobo. Dalian Maritime University, 2017), is obtained by regression analysis on the ballast draft status of 1031 bulk carriers with a tonnage range of 10,000 tons to 300,000 tons, and meets the 50% confidence level.

[0063] This invention addresses the problem of unreasonable overall size design of screw unloaders under complex design conditions, based on the insufficient accuracy of existing unloading range calculation methods and the difficulty in making reasonable designs for different design conditions.

[0064] Example 1

[0065] Taking a 50,000 DWT bulk carrier as an example, its unloading process consists of two rounds. The unloading rate in the first round is 60%, and the unloading rate in the second round is 40%. The change curve of its cargo level is as follows: Figure 3 As shown.

[0066] by Figure 3 Example of cargo level height in each hold under medium-high water level conditions (solid line):

[0067] During the first round of unloading, when the i-th compartment is unloaded, the corresponding unloading rate segment A... 1i B 1i The curve represents the change in the height of the unloading surface in the compartment; A 1i A 1(i+1) The curve represents the change in the material level in the unloaded tank; B 1(i-1) B 1i The curve represents the change in the material level in the unloaded hold. During the second round of unloading, A 2i B 2i The curve represents the change in the height of the unloading surface in the compartment; A2i A 2(i+1) The curve represents the change in the material level in the unloaded tank; B 2(i-1) B 2i The curve represents the change in the material level in the unloaded tank. The low water level condition (dashed line) is similar.

[0068] The highest material level condition is determined to be A. 15 Under this condition, the wharf water level is at the design high level, the other four compartments have completed the first round of unloading, and the remaining compartment has not yet started the first round of unloading; the minimum material level condition is determined to be b. 21 Under this condition, the water level at the wharf is at the designed low level. The other four compartments have completed the first round of unloading, and the remaining compartment has completed the second round of unloading.

[0069] The cargo hold's position on the seaward side is: Z1+BW ds The position of the cargo hold on the shore side is obtained as: Z1+W ds Where Z1 represents the minimum distance between the bulk carrier and the quayside; B represents the bulk carrier's beam; W ds This indicates the side width of a bulk carrier, ranging from 0.6 to 1.2 meters.

[0070] Based on the highest and lowest material levels and the positions of the bulk carrier's cargo holds on both sides, the unloading range of the screw unloader was finally determined:

[0071] The equivalent width of the cargo hold cross-section is:

[0072]

[0073] The material level height during the operation of the screw unloader is:

[0074]

[0075] The horizontal position of the highest material level is:

[0076]

[0077] The horizontal position of the lowest material level is:

[0078]

[0079] The vertical position of the cargo hold on the seaward side is: X L =Z1+BW ds =1 + 32.3 - 0.8 = 32.5 meters;

[0080] The vertical position of the cargo hold on the shore side is: X R =Z1+W ds =1 + 0.8 = 1.8 meters.

[0081] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments, and various changes and modifications can be made without departing from the spirit and scope of the invention, all of which fall within the scope of the claims. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for determining the unloading range of a spiral ship unloader based on multi-factor material surface height calculation, characterized in that: The method comprises the following steps: Step 1, based on multiple factors, establish a material surface height calculation model for determining the highest / lowest material surface height, i.e.: ; wherein: represents the material surface height when the spiral ship unloader is working; represents the maximum draft of the bulk carrier; represents the maximum loading capacity of the bulk carrier; represents the bulk material bulk density; represents the equivalent width of the cross section of the cargo hold; represents the length of a single cargo hold of the bulk carrier; represents the unloading rate, i.e. the ratio of the unloaded amount of the cargo to the total amount, ; represents the number of cargo holds of the bulk carrier; represents the unloading of the first round; represents the unloading of the second round; represents the unloading rate of the first round; represents the unloading rate of the second round; represents the th cargo hold; represents the distance from the wharf water level to the wharf reference plane, and is between the wharf high water level and the wharf low water level ; represents the bulk carrier type width; represents the double bottom height at the center longitudinal centerline, When time, for rice; When time, for rice; Step 2, determining the position of the cargo hold side close to the sea, namely: Step 3, determining the position of the cargo hold side close to the shore, namely: Wherein: represents the minimum distance between the bulk carrier and the shore side of the wharf; represents the bulk carrier type width; represents the bulk carrier side width, which is 0.6-1.2 meters; Step 3, based on the highest / lowest material level in step 1 and the location of the cargo hold side close to the sea and the cargo hold side close to the shore in step 2, the final unloading range is obtained, that is: ； wherein: represents the maximum material surface height when the screw unloader is working; represents the minimum material surface height when the screw unloader is working; represents the material surface height calculation equation when the screw unloader described in step 1 is working; represents the position of the cargo hold close to the sea side; represents the position of the cargo hold close to the shore side; represents the minimum distance between the bulk carrier and the shore side of the wharf; represents the bulk carrier type width; represents the bulk carrier side width, which is 0.6-1.2 meters.

2. The method for determining the unloading range of a spiral ship unloader based on multi-factor material surface height calculation according to claim 1, characterized in that: In step 1, the material level calculation model is established according to the following method: Step 1.1, based on multiple factors, an ideal unloading model is established; Step 1.2, a simplified cargo hold model is obtained by simplifying the shape of the cargo hold; Step 1.3, the regression equation of the unloading draft and the ballast draft of the bulk carrier is introduced to obtain the relationship equation between the unloading work of the spiral ship unloader and the change of the draft of the bulk carrier, that is: ； wherein: ; ; denotes the unloading draft of the bulk carrier; denotes the ballast draft of the bulk carrier; denotes the equation of the relationship between the unloading work of the screw unloader and the draft change of the bulk carrier; denotes the maximum draft of the bulk carrier; denotes the maximum loading capacity of the bulk carrier; denotes the unloading rate, i.e. the ratio of the unloading amount of the cargo to the total amount, ; Step 1.4, based on the unloading model in step 1.1, the simplified cargo hold model in step 1.2, and the regression equation and the relationship equation in step 1.3, the equation in step 1 of claim 1 is obtained.

3. The method for determining the unloading range of a spiral ship unloader based on multi-factor material surface height calculation according to claim 2, characterized in that: In step 1.1, the unloading model is established according to the following method: Step 1.1.1, ensure that the bulk carrier meets the stability and strength in each unloading step, that is, the unloading sequence, unloading round and unloading rate configuration of the bulk carrier are reasonable, so that the hull of the bulk carrier does not cause the change of the floating state of the transverse and longitudinal inclination, and the heave of the positive floating state is maintained, that is: ； wherein: denotes the bow draft in the longitudinal direction; denotes the midship draft in the longitudinal direction; denotes the stern draft in the longitudinal direction; denotes the draft difference of any symmetrical points on both sides of the center line of symmetry in the transverse direction; Step 1.1.2, the unloading process and the ballast process of the bulk carrier are started and ended at the same time, and both have a linear relationship with the unloading rate, that is: ； wherein: represents the relationship between the unloading work of the spiral ship unloader and the change of the draft of the bulk carrier, i.e. the equation in step 1.3 of claim 2 ; represents the slope coefficient of the unloading draft regression equation; represents the slope coefficient of the ballast draft regression equation; represents the unloading rate, i.e. the ratio of the unloading amount of the cargo to the total amount, ; represents the constant of the unloading draft regression equation; represents the constant of the ballast draft regression equation; Step 1.1.3, the materials of the bulk carrier are uniform and the structure is symmetrical along the length and width of the ship, the shapes, sizes and capacities of each cargo hold on the ship are completely consistent, the unloading process in the same hold is uniform, and the material level is horizontally lowered, that is: ； wherein: represents the difference in material density between arbitrary structural positions of a bulk carrier; represents the difference in dimension of the structure at arbitrary symmetric positions on either side of the centerline of the bulk carrier type; represents the difference in height between arbitrary positions of a cargo hold.

4. The method for determining the unloading range of a spiral ship unloader based on multi-factor material surface height calculation according to claim 2, characterized in that: In step 1.2, the simplified cargo hold model is established according to the following method: Step 1.2.

1. Simplify the shape of the cargo hold according to the typical cargo hold type of dry bulk carriers, the original octagonal cargo hold cross-sectional area is: ； Step 1.2.2, maintaining cross-sectional area Without loss of generality, the cargo hold cross-section is simplified to a quadrilateral, resulting in the equivalent width of the cargo hold cross-section is: ； wherein: represents the depth of the bulk carrier type; represents the width of the bulk carrier type; represents the side width of the bulk carrier, and is 0.6-1.2 meters; represents the maximum width of the cargo hold, and is meters; represents the hatch width of the cargo hold, and is meters; represents the width of the double bottom between two bottom side holds, and is meters; represents the inclination angle of the inclined plate of the top side hold, ; represents the inclination angle of the inclined plate of the bottom side hold, ; represents the height of the vertical plate of the top side hold, and is 0.7-0.8 meters; represents the height of the double bottom at the center longitudinal line, When time, for rice; When time, for m.

5. A computing device, comprising: The program is executed by the processor to realize the spiral ship unloader unloading range determination method based on the multi-factor material level calculation as claimed in any one of claims 1-4.

6. A storage medium storing a program, characterized by comprising: The program is executed by the processor to realize the spiral ship unloader unloading range determination method based on the multi-factor material level calculation as claimed in any one of claims 1-4.

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