Rapid drainage system structure based on brachistochrone principle

Abstract

The invention discloses a rapid drainage system structure based on the brachistochrone principle, through systematic design and implementation of multiple steps, application of the brachistochrone principle and scientific calculation and optimization of a water flow path, the efficiency and adaptability of a drainage system are improved, the drainage system not only can efficiently meet the drainage requirement, but also can effectively meet the drainage requirement. The system can keep stable operation under the condition that the rainfall intensity is great, and through analogue simulation and real-time adjustment, the system can keep smooth drainage under various extreme weathers, the risk of roof water accumulation and overflow is reduced, the safety and durability of a building are greatly improved, and the service life of the building is prolonged. The drainage design not only stays on simple standard and experience calculation, but also ensures that the drainage system can efficiently and stably work under various climate and rainfall conditions through deep understanding of local climate and roof characteristics.

Description

Technical Field

[0001] The present application relates to the technical field of pump body processing equipment, and in particular to a rapid drainage system structure based on the brachistocentre principle. Background Art

[0002] As part of a building's drainage system, roof drainage systems are crucial for ensuring proper roof drainage and preventing water accumulation and leakage. In recent years, the architectural design community has placed increasing emphasis on the scientific nature and efficiency of roof drainage systems. This is particularly true for high-rise buildings and large public facilities, where the design and optimization of roof drainage systems are particularly crucial.

[0003] Traditional roof drainage designs often rely on simple outlet layouts and conventional gutter dimensions, lacking scientific analysis of factors such as roof elevation changes, water flow paths, and slopes. This can result in drainage systems failing to fully utilize their capacity, especially under extreme rainfall or complex roof structures. Drainage efficiency can be severely insufficient, even leading to roof flooding. Summary of the Invention

[0004] The main purpose of this application is to provide a rapid drainage system structure based on the brachistochrone principle to solve the problem proposed in the above background technology that traditional roof drainage design often relies on simple drainage outlet arrangement and conventional groove size, and lacks scientific analysis of factors such as roof elevation changes, water flow path, slope, etc.

[0005] To achieve the above objectives, this application provides the following technical solutions:

[0006] A rapid drainage system based on the brachistocentre principle is constructed, and the specific steps are as follows:

[0007] S1. Roof slope and drainage demand analysis: Analyze the amount of rainfall, rainfall intensity, and roof slope on the roof. Combined with local climate conditions and roof type, evaluate the roof drainage demand and the efficiency of the original drainage system.

[0008] S2. Apply the brachistocentre principle to optimize drainage paths. Based on this principle, optimize the roof drainage path and control point elevations. Through mathematical calculations and simulations, determine the fastest path for water flow from the roof to the drain outlet, ensuring that water can be effectively discharged in the shortest possible time.

[0009] S3. Drainage system design and drainage pipe layout. Based on the principle of the brachistocentre, design efficient drainage trenches, drainage pipes, and drainage outlets. Calculate the trench dimensions (GCC), pipe dimensions (GDC), and slope (GPD). The size and material of the drainage pipes must be appropriately selected based on factors such as rainfall intensity, roof area, and drainage volume to ensure smooth and unobstructed water flow.

[0010] S4. Drain outlets and optimal number: Based on the groove size GCC, pipe size GDC and slope GPD, the location and number of drain outlets should be reasonably arranged. Drain outlets should be set at the lowest point of the roof to ensure smooth drainage of water. By arranging multiple drain outlets, local drainage problems or excessive drainage pressure can be avoided.

[0011] S5. Optimize and adjust, simulating drainage effects under different rainfall intensities and durations. Based on the test results, timely adjust drainage pipes, drainage outlet locations and other design details to optimize the performance of the drainage system;

[0012] S6. According to the design plan, carry out the construction of the slope roof structure.

[0013] Preferably, in step S1, the evaluation of the roof drainage demand and the efficiency of the original drainage system is completed by the following steps:

[0014] S1.1. Collect and analyze local climate data to assess precipitation characteristics under different climate conditions. Also, consider the precipitation intensity distribution in the area where the roof is located to determine the drainage requirements of the roof under different seasons and precipitation conditions.

[0015] S1.2. Based on the drainage requirements obtained in step S1.1, analyze the distribution of water flow on the roof to determine whether the original drainage system can meet the roof drainage requirements.

[0016] Preferably, in step S1.1, local climate data including precipitation A, average temperature B and relative humidity C are obtained from a meteorological data website;

[0017] Through sensors, roof data including precipitation intensity D, roof drainage area E and drainage capacity F are obtained;

[0018] In step S1.1, the roof drainage demand PSX and the original drainage system efficiency YSP are calculated using the following formula. The specific calculation method is as follows:

[0019]

[0020] Where: A is the precipitation, E is the roof drainage area, D is the precipitation intensity, and F is the drainage capacity.

[0021] Preferably, in step S1.2, the specific analysis method is as follows:

[0022] When YSP>1, it means that the original drainage capacity can exceed the drainage demand;

[0023] When YSP=1, it means that the original drainage capacity can meet the drainage demand;

[0024] When YSP<1, it means that the original drainage capacity cannot meet the drainage demand.

[0025] Preferably, in step S2, the fastest path for water flow from the roof to the drain outlet is determined by the following steps:

[0026] S2.1. Analyze the roof geometry and water flow path, accurately measure the slope of the roof surface, the location of the drain outlet, and the elevation distribution on the roof. Use a digital elevation model and slope analysis tools to create a three-dimensional topographic map of the roof surface and determine the possible paths of water flow. According to the brachistocentre principle, water flows along the direction of the most dramatic change in roof elevation. Use mathematical formulas to calculate the fastest water flow path from each point on the roof to the drain outlet. Based on the elevation distribution and slope, combined with the movement patterns of water flow, identify the brachistocentre on the roof. Through algorithm optimization, these paths are calibrated as drainage paths, and their effectiveness is further verified through numerical simulation.

[0027] S2.2. Use computational fluid dynamics (CFD) simulation software to simulate water flow on the roof. Based on the brachistocentre principle, the flow from various points on the roof to the drain outlets is simulated. During the simulation, multiple rounds of optimization are performed to determine the optimal flow path by adjusting factors such as the roof geometry, gutter layout, and the number and location of drain outlets.

[0028] Preferably, in step S2.1, the slope value is calculated by the following formula:

[0029]

[0030] Where: Δh is the elevation change of a local area on the roof, and Δd is the horizontal distance between two adjacent points on the roof.

[0031] Preferably, in step S2.1, the elevation change Δh of the local area of ​​the roof is obtained using a digital elevation model. In this model, each position on the roof has a corresponding elevation value, and the elevation difference between adjacent points can be calculated;

[0032] In step S2.1, the horizontal distance Δd between two adjacent points on the roof is obtained by the following formula:

[0033]

[0034] Where: x1, y1 and x2, y2 are the coordinates of two points respectively.

[0035] Preferably, in step S2.1, the roof drainage route is calculated by the following formula:

[0036] LJ={x=r(θ-sinθ), y=r(1-cosθ)};

[0037] Where r is the radius of the cycloid, representing the scale of the path, θ is the angle variable, describing the angle change of the path, and the initial segment End

[0038] Preferably, in step S3, the groove size GCC, the pipe size GDC and the component slope GPD are calculated by the following formula;

[0039]

[0040] Where PSX is the roof drainage demand, YSP is the original drainage system efficiency, and Δh is the elevation change of the local area of ​​the roof.

[0041] Preferably, in step S4, the specific analysis method of the groove size GCC, the pipe size GDC and the slope GPD is as follows:

[0042] When one of the groove size GCC, pipe size GDC and slope GPD is greater than 1, it means that the corresponding data can exceed the drainage demand;

[0043] When one of the groove size GCC, pipe size GDC and slope GPD = 1, it means that the corresponding data can meet the drainage requirements;

[0044] When any one of the trench size GCC, pipe size GDC, and component slope GPD is less than 1, it means that the corresponding data cannot meet the drainage requirements.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] 1. Standardized drainage systems often rely on simplified calculations and fixed models, making it difficult to optimize them for different roof structures, climate conditions, and precipitation intensities. Through the systematic design and implementation of the six steps described above, the application of the brachistocentre principle, and the scientific calculation and optimization of water flow paths, the efficiency and adaptability of the drainage system have been improved. The drainage system not only efficiently meets drainage needs but also maintains stable operation under extremely high precipitation intensities. Through simulation and real-time adjustments, this system can maintain unimpeded drainage in various extreme weather conditions, reducing the risk of roof flooding and overflow, and significantly improving the safety and durability of buildings.

[0047] 2. Drainage design goes beyond simple standards and empirical calculations. Instead, it leverages a deep understanding of local climate and roof characteristics to ensure the drainage system can operate efficiently and stably under a variety of climate and precipitation conditions. This improvement significantly enhances the scientific and targeted nature of the drainage system, effectively preventing waterlogging in areas where the design isn't adapted to climate change, and further optimizing the performance of the entire roof drainage system.

[0048] 3. Calculate the horizontal distance between two adjacent points on the roof △ d (i.e., calculating horizontal distances through coordinate differences) further enhances drainage path accuracy. Traditional designs may overlook or simplify the actual spatial layout of the roof. However, accurate coordinate difference calculations more realistically reflect the geometry of the roof space, providing more accurate data support for drainage path planning. With this formula, each step in the drainage path calculation is based on detailed geometric relationships, ensuring efficient optimization of the water flow path.

[0049] 4. Using the cycloid formula to optimize drainage paths not only makes the design of the roof drainage system more scientific and systematic, but also significantly improves drainage efficiency. By precisely calculating the shortest path for water flow and dynamically adjusting the angle, water flow is ensured to follow the most appropriate path, preventing water accumulation. This optimization design method, based on the brachistochrone principle, ensures that the drainage system maintains efficient and stable drainage performance despite complex roof structures and changing climatic conditions, improving the overall drainage capacity and safety of the building.

[0050] 5. The calculations and analyses in steps S3 and S4 provide a precise, quantitative optimization solution for the drainage system design, ensuring its efficient operation while effectively avoiding the risk of resource waste or insufficient drainage. Compared to traditional empirical methods, this design approach, based on actual needs and efficiency calculations, is more adaptable to varying roof structures and climatic conditions, significantly improving the performance and reliability of the drainage system in practical applications. This innovative design approach also provides a scientific basis and practical guidance for future drainage system engineering designs, promoting technological advancement in the field of building drainage design. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 This is a step diagram of the application method. DETAILED DESCRIPTION

[0052] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0053] The terms "first", "second" and "third" in this application are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, a feature defined as "first", "second" and "third" may explicitly or implicitly include at least one of such features. In the description of this application, "multiple" means at least two, for example, two, three, etc., unless otherwise clearly and specifically defined. All directional indications in the embodiments of this application (such as up, down, left, right, front, back...) are only used to explain the relative positional relationship, movement, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not limited to the listed steps or units, but may optionally also include steps or units that are not listed, or may optionally also include other steps or units inherent to these processes, methods, products or devices.

[0054] References to "embodiments" herein mean that a particular feature, structure, or characteristic described in connection with the embodiments may be included in at least one embodiment of the present application. The appearance of the phrase in various places in the specification does not necessarily refer to the same embodiment, nor does it constitute an independent or alternative embodiment that is mutually exclusive of other embodiments. It is understood, both explicitly and implicitly, by those skilled in the art that the embodiments described herein may be combined with other embodiments.

[0055] Example 1: Please refer to Figure 1 , a rapid drainage system construction based on the brachistocentre principle, the specific steps are as follows:

[0056] S1. Roof slope and drainage demand analysis: Analyze the amount of rainfall, rainfall intensity, and roof slope on the roof. Combined with local climate conditions and roof type, evaluate the roof drainage demand and the efficiency of the original drainage system.

[0057] S2. Apply the brachistocentre principle to optimize drainage paths. Based on this principle, optimize the roof drainage path and control point elevations. Through mathematical calculations and simulations, determine the fastest path for water flow from the roof to the drain outlet, ensuring that water can be effectively discharged in the shortest possible time.

[0058] S3. Drainage system design and drainage pipe layout. Based on the principle of the brachistocentre, design efficient drainage trenches, drainage pipes, and drainage outlets. Calculate the trench dimensions (GCC), pipe dimensions (GDC), and slope (GPD). The size and material of the drainage pipes must be appropriately selected based on factors such as rainfall intensity, roof area, and drainage volume to ensure smooth and unobstructed water flow.

[0059] S4. Drain outlets and optimal number: Based on the groove size GCC, pipe size GDC and slope GPD, the location and number of drain outlets should be reasonably arranged. Drain outlets should be set at the lowest point of the roof to ensure smooth drainage of water. By arranging multiple drain outlets, local drainage problems or excessive drainage pressure can be avoided.

[0060] S5. Optimize and adjust, simulating drainage effects under different rainfall intensities and durations. Based on the test results, timely adjust drainage pipes, drainage outlet locations and other design details to optimize the performance of the drainage system;

[0061] S6. According to the design plan, carry out the construction of the slope roof structure.

[0062] In this embodiment, step S1 effectively assesses the actual roof drainage requirements and the efficiency of the original drainage system by analyzing the roof slope, precipitation, precipitation intensity, and local climatic conditions. This process not only helps designers understand the drainage needs of roofs under different climatic conditions but also allows for a scientific estimation of drainage requirements based on roof type and precipitation intensity. This rational assessment ensures that the drainage system design meets the roof's drainage requirements in various climatic conditions, thereby avoiding waterlogging problems caused by inappropriate drainage system design.

[0063] In step S2, the fastest path for water flow from the roof to the drain outlet is determined through mathematical calculations and simulations, applying the brachistocentre principle. This optimization process minimizes water stagnation time, ensuring that water can be effectively drained from the roof in the shortest possible time. This optimization not only reduces water waste and resistance, but also improves drainage efficiency through precise path design, preventing water accumulation and backflow during drainage, thereby enhancing the overall performance of the roof drainage system.

[0064] In step S3, an efficient layout of drainage ditches, pipes, and outlets is designed based on the brachistocentric principle. By calculating the trench dimensions (GCC), pipe dimensions (GDC), and component slopes (GPD), the drainage system design is ensured to effectively handle varying rainfall intensities. Proper sizing ensures smooth operation of the drainage system, preventing water stagnation or blockage, and ensuring unimpeded flow under all rainfall conditions.

[0065] In step S4, based on the calculated trench dimensions GCC, pipe dimensions GDC, and component slope GPD, the optimal number and placement of drain outlets are designed. The placement of drain outlets should ensure smooth water flow and avoid localized water accumulation or excessive pressure. By providing multiple drain outlets, the design ensures even water distribution and reduces drainage problems in areas caused by insufficient or improperly positioned outlets. This optimized drain outlet layout significantly improves the reliability and stability of the drainage system.

[0066] In step S5, the drainage system is optimized by simulating drainage performance under varying precipitation intensities and durations. By analyzing the test results, designers can promptly adjust the location of drainage pipes and outlets, as well as other design details, to further improve the performance of the drainage system. This process ensures that the drainage system can cope with variable climate conditions and extreme weather in actual use, maintaining efficient drainage performance under varying precipitation intensities. This optimization makes the drainage system more adaptable and meets the drainage needs of different situations.

[0067] Step S6: Construct the sloped roof structure according to the design plan, ensuring the drainage system is tightly integrated with the building's structure and fully implementing the design plan. During construction, the correct installation of drainage pipes and outlets is crucial to ensuring the proper functioning of the system. This perfect integration of design and construction ensures the efficient operation of the entire drainage system, providing a solid foundation for roof drainage and ensuring that leaks and poor drainage are avoided during actual use.

[0068] Traditional drainage systems often rely on simplified calculations and fixed models, making it difficult to optimize them for different roof structures, climate conditions, and rainfall intensities. Through the systematic design and implementation of the six steps described above, the application of the brachistocentre principle, and the scientific calculation and optimization of water flow paths, the efficiency and adaptability of the drainage system have been improved. The drainage system not only efficiently meets drainage needs but also maintains stable operation even under extremely high rainfall intensities. Through simulation and real-time adjustments, this system can maintain unimpeded drainage in a variety of extreme weather conditions, reducing the risk of roof flooding and overflow, and significantly improving the safety and durability of buildings.

[0069] Example 2: Please refer to Figure 1 ,In step S1, the evaluation of the roof drainage demand and the efficiency of the original drainage system is completed through the following steps;

[0070] S1.1. Collect and analyze local climate data to assess precipitation characteristics under different climate conditions. Also, consider the precipitation intensity distribution in the area where the roof is located to determine the drainage requirements of the roof under different seasons and precipitation conditions.

[0071] S1.2. Based on the drainage requirements obtained in step S1.1, analyze the distribution of water flow on the roof to determine whether the original drainage system can meet the roof drainage requirements.

[0072] In this embodiment, the collection and analysis of local climate data, combined with specific precipitation intensity and volume, provides a more accurate and personalized assessment of roof drainage needs. This process overcomes the problem of traditional design often ignoring regional climate differences. By considering variations in different seasons and precipitation conditions, the drainage system design can cope with extreme weather conditions, avoiding reliance on a single precipitation criterion, thereby improving the system's adaptability and reliability.

[0073] Analyzing the distribution of water flow on the roof, combined with the characteristics of roof rainfall, can accurately assess the actual efficiency of the original drainage system. This step can identify localized drainage problems, redundant designs, or deficiencies in traditional designs, ensuring an optimized drainage system design. Traditional systems often use simple empirical rules to determine drainage capacity, but lack a comprehensive analysis of the specific roof structure and water flow dynamics. This step, through scientific analysis, can accurately assess the efficiency of the original drainage system, helping to promptly identify potential problems and identify areas for improvement.

[0074] Improvements to step S1 have enabled drainage design to move beyond simple standards and empirical calculations. Instead, they leverage a deeper understanding of local climate and roof characteristics to ensure the drainage system can operate efficiently and stably under a variety of climate and precipitation conditions. This improvement significantly enhances the scientific and targeted nature of the drainage system, effectively preventing waterlogging in local areas due to designs not adapted to climate change, and further optimizing the performance of the entire roof drainage system.

[0075] Example 3: Please refer to Figure 1 ,In step S1.1, local climate data including precipitation A, average temperature B and relative humidity C are obtained through the meteorological data website;

[0076] Through sensors, roof data including precipitation intensity D, roof drainage area E and drainage capacity F are obtained;

[0077] In step S1.1, the roof drainage demand PSX and the original drainage system efficiency YSP are calculated using the following formula. The specific calculation method is as follows:

[0078]

[0079] Where: A is the precipitation, E is the roof drainage area, D is the precipitation intensity, and F is the drainage capacity.

[0080] In this embodiment: local climate data (such as precipitation A, average temperature B, relative humidity C) is obtained through a meteorological data website, and combined with roof data (such as precipitation intensity D, roof drainage area E and drainage capacity F) for comprehensive analysis, which can provide an accurate localized climate condition assessment for drainage design. Traditional drainage design often relies on standardized climate data or empirical formulas, ignoring the climate differences in specific locations and the actual roof conditions. By utilizing the precise data from meteorological websites and sensors, the local climate and roof characteristics can be assessed more accurately, ensuring that the design plan is highly matched with actual needs, thereby avoiding the situation where the design is not adapted to the actual climate conditions and improving the reliability and stability of the system.

[0081] The formula for calculating roof drainage demand (PSX) and original drainage system efficiency (YSP) employs a scientific, quantitative approach to clearly calculate drainage demand. The formula (PSX = (A × E × D) / 1000 and YSP = F / PSX) effectively integrates key factors such as precipitation, roof area, precipitation intensity, and drainage capacity to systematically assess the roof's drainage demand and drainage system efficiency. This approach avoids the potential inefficiencies and inaccuracies of traditional empirical design. The quantitative assessment results help designers optimize drainage systems, ensuring adequate drainage capacity while avoiding overdesign and waste of resources.

[0082] This data-driven, scientifically calculated assessment approach provides a comprehensive understanding of drainage system requirements and capabilities, enabling more scientific and precise design solutions. Compared to traditional design methods, it significantly improves drainage system efficiency and adaptability, particularly in response to extreme rainfall events or specific climate conditions, demonstrating greater resilience and further enhancing the overall performance and reliability of roof drainage systems.

[0083] Example 4: Please refer to Figure 1 , in step S1.2, the specific analysis method is as follows:

[0084] When YSP>1, it means that the original drainage capacity can exceed the drainage demand;

[0085] When YSP=1, it means that the original drainage capacity can meet the drainage demand;

[0086] When YSP<1, it means that the original drainage capacity cannot meet the drainage demand.

[0087] In this embodiment: through clear YSP value (drainage system efficiency) analysis, designers can clearly understand the performance of the original drainage system when facing actual drainage needs. This quantitative way of evaluating the capacity of the drainage system is more intuitive and scientific than the traditional way of relying on experience or conventional design. Specifically, when YSP>1, it can clearly indicate that the original drainage capacity exceeds the drainage demand, indicating that the design scheme has redundant drainage capacity; when YSP=1, it means that the drainage system just meets the design requirements, indicating that the system design is appropriate; and when YSP<1, it clearly indicates that the drainage system is insufficient and cannot meet the actual drainage needs. This clear classification can help designers quickly identify and adjust the deficiencies in the system to ensure the rationality and effectiveness of the drainage design.

[0088] This analysis method, by comparing drainage capacity with drainage requirements, makes drainage system adjustments and optimization more precise and efficient. Traditionally, drainage system designs have relied on simple rules of thumb or single climate standards, easily overlooking localized drainage problems or overdesign. However, precise analysis of YSP values ​​allows designers to identify design redundancies or deficiencies, enabling timely optimization and adjustments to ensure efficient drainage system operation in all weather conditions.

[0089] This YSP-based analysis method brings transparency and optimization to the design, allowing drainage system designs to better meet actual drainage needs while avoiding ineffective resource waste or over-design. This method can effectively improve the adaptability and reliability of drainage systems in complex roof structures or extreme climates, ultimately achieving significant improvements in drainage efficiency.

[0090] Example 5: Please refer to Figure 1 ,In step S2, the fastest path for water flow from the roof to the drain is determined through the following steps;

[0091] S2.1. Analyze the roof geometry and water flow path, accurately measure the slope of the roof surface, the location of the drain outlet, and the elevation distribution on the roof. Use a digital elevation model and slope analysis tools to create a three-dimensional topographic map of the roof surface and determine the possible paths of water flow. According to the brachistocentre principle, water flows along the direction of the most dramatic change in roof elevation. Use mathematical formulas to calculate the fastest water flow path from each point on the roof to the drain outlet. Based on the elevation distribution and slope, combined with the movement patterns of water flow, identify the brachistocentre on the roof. Through algorithm optimization, these paths are calibrated as drainage paths, and their effectiveness is further verified through numerical simulation.

[0092] S2.2. Use computational fluid dynamics (CFD) simulation software to simulate water flow on the roof. Based on the brachistocentre principle, the flow from various points on the roof to the drain outlets is simulated. During the simulation, multiple rounds of optimization are performed to determine the optimal flow path by adjusting factors such as the roof geometry, gutter layout, and the number and location of drain outlets.

[0093] In this embodiment, a digital elevation model and slope analysis tool are used to create a three-dimensional rooftop map and precisely measure the roof geometry, enabling a more accurate assessment of the distribution of water flow on the roof and the possible drainage paths. Traditional designs often rely on simplified assumptions or manually designed drainage paths, which can overlook the complexity of roof elevation and slope, leading to uneven water distribution and, in turn, poor drainage efficiency. By combining a digital elevation model with slope analysis tools, designers can accurately identify the natural flow direction of water, ensuring that it flows along the direction of the most dramatic roof slope change, thereby maximizing drainage efficiency.

[0094] By calculating the fastest water flow path through mathematical formulas and incorporating the laws of water motion, roof drainage paths can be precisely optimized. Traditional drainage designs typically employ simple flow distribution models, lacking scientific calculations of specific flow paths and velocities. By employing the principle of the brachistocentre (Brastel Descent Line) and combining it with actual roof elevation data, the optimal flow path can be clearly mapped out, avoiding unnecessary water stagnation or backflow. This precise flow path planning not only improves drainage efficiency but also reduces localized water accumulation caused by blockages.

[0095] The application of numerical simulation and computational fluid dynamics simulation software makes drainage path design more accurate and verifiable. Through multiple rounds of simulation optimization, designers can adjust multiple factors such as roof geometry, gutter layout, and the number and location of drain outlets to find the optimal drainage path. Traditional methods often rely on experience and manual adjustments, which may not be effective for complex roof structures and extreme precipitation conditions. However, simulation allows for comprehensive optimization based on different climate conditions and precipitation intensities, ensuring the efficiency and reliability of the drainage system in practical applications.

[0096] Step S2 utilizes advanced technologies such as digital modeling, mathematical calculations, and fluid simulation to make the drainage system design more scientific and precise. This improvement ensures the efficient operation of the roof drainage system under various complex conditions, significantly improving drainage capacity and avoiding the problems of localized drainage problems and uneven drainage in traditional designs. Through this systematic and optimized design approach, the drainage system is not only optimized in theory but also better adapted to changing climate conditions in practice, enhancing building safety.

[0097] Example 6: Please refer to Figure 1In step S2.1, the slope value is calculated using the following formula;

[0098]

[0099] Where: Δh is the elevation change of a local area on the roof, and Δd is the horizontal distance between two adjacent points on the roof.

[0100] In step S2.1, the elevation change Δh of the local area of ​​the roof is obtained using a digital elevation model. In this model, each location on the roof has a corresponding elevation value, and the elevation difference between adjacent points can be calculated;

[0101] In step S2.1, the horizontal distance Δd between two adjacent points on the roof is obtained by the following formula:

[0102]

[0103] Where: x1, y1 and x2, y2 are the coordinates of two points respectively.

[0104] In this embodiment: Traditional drainage system design often relies on simple average slopes or empirical estimates without considering the specific elevation changes in different areas of the roof. By using the formula PDZ = Δh / Δd, designers can accurately calculate the slope of each local area ( △ h is the elevation change, △ d is the horizontal distance), ensuring a scientific assessment of each area's drainage capacity. This precise calculation avoids uneven water flow or waterlogging caused by inaccurate elevation estimates in traditional methods.

[0105] Calculations based on the actual roof elevation changes and the horizontal distance between adjacent points provide a quantitative indicator to ensure that the drainage path conforms to the natural flow patterns of water. Traditional designs often overlook local elevation differences, which can lead to inappropriate drainage path designs. By accurately calculating the slope, designers can identify the most optimal flow path on the roof, thereby improving drainage efficiency.

[0106] Slope directly affects the speed and direction of water flow. By accurately calculating the slope of each area, we can ensure that water flows smoothly to the outlet, reducing the risk of water stagnation and backflow. Compared to traditional empirical design, this approach provides more precise drainage path planning, ensuring that water flows along the direction of the most dramatic slope changes, thereby maximizing drainage efficiency.

[0107] This allows drainage designs to be tailored to the specific conditions of different roof areas, allowing the drainage system to adapt to a variety of complex roof structures and elevation changes. By scientifically analyzing the slope of each local area, designers can fully account for elevation differences in the design, optimize water flow paths, and ensure that the drainage system can operate efficiently even in complex terrain.

[0108] Using a precise mathematical formula to calculate the slope value (PDZ) between two adjacent points (i.e., Δh / Δd), and by calculating the elevation difference and horizontal distance, the slope of each point on the roof can be more accurately assessed. This process allows designers to clearly understand the flow pattern and flow rate in each area of ​​the roof, ensuring that water flows along the direction of the most dramatic slope change, thereby improving the efficiency of the drainage system. Compared with traditional methods, this analysis based on specific elevation and geographic location provides a more detailed and quantitative drainage path assessment, avoiding localized water stagnation or poor drainage caused by rough designs.

[0109] By using a digital elevation model (DEM), an accurate elevation value can be assigned to each location on the roof. Traditional roof drainage design usually relies on simplified slopes or empirical formulas, lacking scientific analysis of local elevation differences. This high-precision digital elevation data can accurately describe the elevation changes of each local area of ​​the roof ( △ h). This allows the design of water flow paths to be based entirely on the actual topographic changes of the roof, rather than assumptions or simplified estimates, thereby ensuring that water flows along the most reasonable path and effectively improving the efficiency of the drainage system.

[0110] Using a formula to calculate the horizontal distance between two adjacent points, the distance between each calculation point can be accurately measured. This differs from the conventional design practice of roughly estimating or ignoring horizontal distances. By considering the coordinate differences (x1, y1 and x2, y2) of each point on the roof, the drainage path calculation is fully based on the actual geometry, further improving design accuracy.

[0111] Traditional drainage designs may fail to accurately account for elevation differences across different roof areas, leading to improper water flow path planning and potential localized waterlogging or poor flow. However, by obtaining the precise elevation of each point and calculating the horizontal distances between adjacent points, a digital elevation model ensures that drainage paths are scientifically optimized based on the roof's topography. This process ensures that water flows along the direction of the most dramatic slope change, minimizing stagnation or backflow, thereby optimizing the drainage system.

[0112] Digital elevation models allow designers to easily adjust and optimize roof drainage system designs, making them more flexible and adaptable, especially when faced with complex roof forms or changing climate conditions. By using highly accurate elevation data and horizontal distance calculations, designers can refine drainage paths based on the specific roof structure, avoiding drainage issues in localized areas caused by inadequate consideration of elevation changes.

[0113] By calculating the horizontal distance between two adjacent points on the roof △ d (i.e., calculating horizontal distances through coordinate differences) further enhances drainage path accuracy. Traditional designs may overlook or simplify the actual spatial layout of the roof. However, accurate coordinate difference calculations more realistically reflect the geometry of the roof space, providing more accurate data support for drainage path planning. With this formula, each step in the drainage path calculation is based on detailed geometric relationships, ensuring efficient optimization of the water flow path.

[0114] Example 7: Please refer to Figure 1 ,In step S2.1, the roof drainage route is obtained by calculating using the following formula;

[0115] LJ={x=r(θ-sinθ), y=r(1-cosθ)};

[0116] Where r is the radius of the cycloid, representing the scale of the path, θ is the angle variable, describing the angle change of the path, and the initial segment End

[0117] In this embodiment, the roof drainage route is calculated using a cycloid formula. This method, based on the principle of the brachistodes curve, ensures that water flows along the direction of the most dramatic roof elevation change. As a mathematical model describing a path, the cycloid provides the shortest drainage path for water flowing on a roof. This optimization method, by defining the radius r and angle variable θ of the cycloid, ensures maximum optimization of the flow direction and water velocity on the roof. Compared to traditional simple drainage path design methods, the cycloid model, through precise mathematical calculations, provides an optimal path that conforms to the laws of natural water flow, significantly improving drainage efficiency.

[0118] By using the angle variable θ in the cycloid model to describe the angle of the path, the water flow path can be more precisely adjusted, ensuring that the water flows along the optimal trajectory on the roof. Traditional designs often fail to adequately consider the impact of roof elevation changes, which limits the efficiency of the drainage path. The cycloid model, however, dynamically adjusts the path angle to ensure that the water always flows in the most appropriate drainage direction, minimizing water stagnation and reverse flow, thereby improving overall drainage effectiveness.

[0119] The initial segment θ = 0 - π / 2 and the terminal segment θ = π / 2 - π provide greater flexibility in path design, adapting to the specific needs of varying roof structures and drain outlet layouts. This flexibility allows the drainage path to be dynamically adjusted based on the specific roof shape and drainage requirements, avoiding the unsatisfactory drainage effects associated with fixed or simplified paths in traditional designs.

[0120] Using the cycloid formula to optimize drainage paths not only makes the design of the roof drainage system more scientific and systematic, but also significantly improves drainage efficiency. By precisely calculating the shortest path for water flow and dynamically adjusting the angle, water flow is ensured to follow the most appropriate path, preventing water accumulation. This optimization design method, based on the brachistocentre principle, ensures that the drainage system maintains efficient and stable drainage performance despite complex roof structures and changing climatic conditions, improving the overall drainage capacity and safety of the building.

[0121] Example 8: Please refer to Figure 1 In step S3, the groove size GCC, the pipe size GDC and the slope GPD are calculated by the following formula;

[0122]

[0123] Where PSX is the roof drainage demand, YSP is the original drainage system efficiency, and Δh is the elevation change of the local area of ​​the roof.

[0124] In step S4, the specific analysis method of the groove size GCC, the pipe size GDC and the slope GPD is as follows:

[0125] When one of the groove size GCC, pipe size GDC and slope GPD is greater than 1, it means that the corresponding data can exceed the drainage demand;

[0126] When one of the groove size GCC, pipe size GDC and slope GPD = 1, it means that the corresponding data can meet the drainage requirements;

[0127] When any one of the trench size GCC, pipe size GDC, and component slope GPD is less than 1, it means that the corresponding data cannot meet the drainage requirements.

[0128] In this example, by using formulas to calculate GCC, GDC, and GPD, designers can more scientifically determine trench dimensions, pipe sizes, and slopes, thereby achieving precise drainage path design. Unlike traditional empirical methods, calculations based on roof drainage requirements (PSX) and original drainage system efficiency (YSP) enable more quantitative and optimized drainage system design. This precise parameter calculation avoids the over- or under-design issues common in traditional designs. By calculating specific values, it ensures that the drainage system accurately matches the roof's actual drainage needs.

[0129] By calculating the ratio of roof drainage requirements to drainage system efficiency, we can determine the optimal gutter size. This calculation method ensures that the gutter is neither oversized (causing waste) nor undersized (resulting in poor drainage). It provides a concrete, quantifiable basis for design, avoiding the miscalculations and lack of specificity that can occur in traditional designs.

[0130] The required pipe size is scientifically calculated using the proportional relationship between roof elevation changes and drainage requirements. This calculation method effectively determines the pipe size based on the actual roof topography (i.e., elevation changes) and drainage requirements, avoiding the traditional design situation where pipes are too small, resulting in poor drainage, or too large, resulting in wasteful resources.

[0131] By calculating the appropriate slope value, we can ensure that the slope of the drainage path is designed appropriately to increase the discharge rate of water. This calculation allows the slope design to be adjusted according to the specific drainage needs and system efficiency to achieve the optimal drainage effect.

[0132] By using clear criteria for parameter evaluation, designers can clearly determine whether the drainage system meets the roof drainage requirements. Compared to traditional empirical design, this evaluation method provides a more scientific evaluation method based on specific values ​​and actual needs.

[0133] When GCC, GDC, or GPD is greater than 1, it indicates that the design exceeds the drainage requirements. This standardized result avoids the risk of insufficient drainage system capacity while providing redundant drainage capacity to ensure the reliability of the drainage system in extreme weather or extremely high precipitation intensity.

[0134] When GCC, GDC or GPD is equal to 1, it means that the design solution just meets the drainage needs. This precise design ensures that the drainage system can work fully and effectively under normal precipitation conditions, avoiding overdesign or waste of resources.

[0135] When GCC, GDC or GPD is less than 1, it indicates that there are deficiencies in the drainage design and it cannot meet drainage requirements. This evaluation method can promptly identify design defects and avoid problems such as poor drainage and water accumulation in actual applications.

[0136] Compared to traditional methods, this analytical approach offers greater transparency and operability. Traditional designs often rely on experience and estimates, lacking precise standards to guide design. This approach, through scientific evaluation and standardized thresholds, can clearly demonstrate whether drainage designs meet requirements and provide targeted optimization directions. Furthermore, this approach emphasizes the adaptability and flexibility of drainage systems in different situations. Through quantitative analysis of gutter dimensions, pipe sizes, and slopes, design solutions can be adjusted based on specific roof characteristics and precipitation conditions, ensuring the system's stable operation under various conditions. Through scientific evaluation, designers can promptly adjust design elements such as drain outlet location and gutter size, enabling the drainage system to fully utilize its drainage capacity and avoiding the inefficient drainage caused by improper design in traditional methods.

[0137] The analysis method in step S4 provides a systematic and standardized evaluation approach for drainage system design, making the design more scientific and precise, avoiding the blind and empirical nature of traditional methods. By properly evaluating groove dimensions, pipe sizes, and slopes, the drainage system can better adapt to different roof structures and climate conditions, achieving efficient and reliable drainage performance, ultimately improving the safety and durability of the building.

[0138] The calculations and analyses in steps S3 and S4 provide a precise, quantitative optimization solution for drainage system design, ensuring efficient operation while effectively avoiding resource waste or the risk of insufficient drainage. Compared to traditional empirical methods, this design approach, based on actual needs and efficiency calculations, is more adaptable to varying roof structures and climatic conditions, significantly improving the performance and reliability of drainage systems in practice. This innovative design approach also provides a scientific basis and practical guidance for future drainage system engineering designs, promoting technological advancement in the field of building drainage design.

[0139] In addition, the functional units in the various embodiments of the present application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The above-mentioned integrated units can be implemented in the form of hardware or in the form of software functional units. The above is only an implementation method of the present application and does not limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made using the contents of the description and drawings of this application, or directly or indirectly used in other related technical fields, are also included in the patent protection scope of the present application.

[0140] The above detailed description of the specific embodiments of the invention is intended only as an example, and the present application is not limited to the specific embodiments described above. For those skilled in the art, any equivalent modifications or substitutions of the invention are also within the scope of the present application. Therefore, equivalent changes, modifications, and improvements made without departing from the spirit and scope of the present application should be included within the scope of the present application.

Claims

1. A rapid drainage system structure based on the brachistocentre principle, characterized by: The specific steps are as follows: S1. Roof slope and drainage demand analysis: Analyze the amount of rainfall, rainfall intensity, and roof slope on the roof. Combined with local climate conditions and roof type, evaluate the roof drainage demand and the efficiency of the original drainage system. S2. Apply the brachistocentre principle to optimize drainage paths. Based on this principle, optimize the roof drainage path and control point elevations. Through mathematical calculations and simulations, determine the fastest path for water flow from the roof to the drain outlet, ensuring that water can be effectively discharged in the shortest possible time. S3. Drainage system design and drainage pipe layout. Based on the principle of the brachistocentre, design efficient drainage trenches, drainage pipes, and drainage outlets. Calculate the trench dimensions (GCC), pipe dimensions (GDC), and slope (GPD). The size and material of the drainage pipes must be appropriately selected based on factors such as rainfall intensity, roof area, and drainage volume to ensure smooth and unobstructed water flow. S4. Drain outlets and optimal number: Based on the groove size GCC, pipe size GDC and slope GPD, the location and number of drain outlets should be reasonably arranged. Drain outlets should be set at the lowest point of the roof to ensure smooth drainage of water. By arranging multiple drain outlets, local drainage problems or excessive drainage pressure can be avoided. S5. Optimize and adjust, simulating drainage effects under different rainfall intensities and durations. Based on the test results, timely adjust drainage pipes, drainage outlet locations and other design details to optimize the performance of the drainage system; S6. According to the design plan, carry out the construction of the slope roof structure.

2. The rapid drainage system structure based on the brachistocentre principle according to claim 1 is characterized in that: In step S1, the evaluation of the roof drainage demand and the efficiency of the original drainage system is completed through the following steps; S1.

1. Assess precipitation characteristics under different climatic conditions by collecting and analyzing local climate data. Also, determine the drainage requirements of the roof under different seasons and precipitation conditions, taking into account the distribution of precipitation intensity in the area where the roof is located. S1.

2. Based on the drainage requirements obtained in step S1.1, analyze the distribution of water flow on the roof to determine whether the original drainage system can meet the roof drainage requirements.

3. The rapid drainage system structure based on the brachistocentre principle according to claim 2 is characterized in that: In step S1.1, local climate data including precipitation A, average temperature B and relative humidity C are obtained from the meteorological data website; Through sensors, roof data including precipitation intensity D, roof drainage area E and drainage capacity F are obtained; In step S1.1, the roof drainage demand PSX and the original drainage system efficiency YSP are calculated using the following formula. The specific calculation method is as follows: Where: A is the precipitation, E is the roof drainage area, D is the precipitation intensity, and F is the drainage capacity.

4. The rapid drainage system structure based on the brachistocentre principle according to claim 3 is characterized in that: In step S1.2, the specific analysis method is as follows: When YSP>1, it means that the original drainage capacity can exceed the drainage demand; When YSP=1, it means that the original drainage capacity can meet the drainage demand; When YSP<1, it means that the original drainage capacity cannot meet the drainage demand.

5. The rapid drainage system structure based on the brachistocentre principle according to claim 4 is characterized in that: In step S2, the fastest path for water flow from the roof to the drain is determined through the following steps: S2.

1. Analyze the roof geometry and water flow path, accurately measure the roof surface slope, the location of the drain outlet, and the elevation distribution on the roof. Utilize a digital elevation model and slope analysis tools to create a three-dimensional topographic map of the roof surface and determine the likely flow path. Based on the brachistodes principle, water flows along the direction of the most dramatic roof elevation change. Utilize mathematical formulas to calculate the fastest flow path from each point on the roof to the drain outlet. Based on the elevation distribution and slope, combined with the laws of water flow, identify the brachistodes on the roof. Through algorithmic optimization, these paths are calibrated as drainage paths, and their effectiveness is further verified through numerical simulation. S2.

2. Use computational fluid dynamics simulation software to simulate the water flow on the roof. Based on the principle of the brachistodes curve, the flow process of water from various points on the roof to the drain outlet is simulated. During the simulation process, multiple rounds of optimization are performed by adjusting factors such as the roof geometry, the layout of the drainage grooves, and the number and location of the drain outlets to obtain the optimal water flow path.

6. The rapid drainage system structure based on the brachistocentre principle according to claim 5 is characterized in that: In step S2.1, the slope value is calculated using the following formula: Where: Δh is the elevation change of a local area on the roof, and Δd is the horizontal distance between two adjacent points on the roof.

7. The rapid drainage system structure based on the brachistocentre principle according to claim 6 is characterized in that: In step S2.1, the elevation change Δh of the local area of ​​the roof is obtained using a digital elevation model. In this model, each location on the roof has a corresponding elevation value, and the elevation difference between adjacent points can be calculated; In step S2.1, the horizontal distance Δd between two adjacent points on the roof is obtained by the following formula: Where: x1, y1 and x2, y2 are the coordinates of two points respectively.

8. The rapid drainage system structure based on the brachistocentre principle according to claim 7 is characterized in that: In step S2.1, the roof drainage route is calculated using the following formula; LJ={x=r(θ-sinθ), y=r(1-cosθ)}; Where r is the radius of the cycloid, representing the scale of the path, θ is the angle variable, describing the angle change of the path, and the initial segment End 9. The rapid drainage system structure based on the brachistocentre principle according to claim 8, characterized in that: In step S3, the groove size GCC, the pipe size GDC and the component slope GPD are calculated by the following formula; Where PSX is the roof drainage demand, YSP is the original drainage system efficiency, and Δh is the elevation change of the local area of ​​the roof.

10. The rapid drainage system structure based on the brachistocentre principle according to claim 9, characterized in that: In step S4, the specific analysis method of the groove size GCC, the pipe size GDC and the slope GPD is as follows: When one of the groove size GCC, pipe size GDC and slope GPD is greater than 1, it means that the corresponding data can exceed the drainage demand; When one of the groove size GCC, pipe size GDC and slope GPD = 1, it means that the corresponding data can meet the drainage requirements; When any one of the trench size GCC, pipe size GDC, and component slope GPD is less than 1, it means that the corresponding data cannot meet the drainage requirements.

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