1. Field of Invention
The present inventive patent is a method for quantitative calculating lightning stroke frequency interception area of a building (including structure, for simplicity, hereinafter collectively called as building) under consideration of surrounding objects (which may be buildings, structures or any other facilities or arrangements higher above the ground), which is useful for the lightning protection industry, and for those related units, e.g., Engineering and Building Designing Institute, lightning prevention center of Weather Bureau of each province, lightning protection companies, lightning protection offices, to carry out lightning risk assessment, design, acceptance and detection of lightning protection device for buildings.
2. Description of Related Arts
Lightning stroke is a common natural disaster threatening the safety of buildings and humans. It requires for an estimation of annual lightning stroke frequency upon a building when one carries out lightning risk assessment, lightning protection design, and acceptance and detection of lightning protection device of the building, so as to reasonably classify its lightning protections level. According to the provision of the PRC standard GB50057-2010 “Design code for lighting protection of buildings” (hereinafter referred to as GB50057) implemented on Oct. 1, 2011, the formula is showed below:
N=k×Ng×Ae (formula 1)
In formula 1, N is an estimation of the annual number of lightning stroke to a building (unit: times/year); K is a correction factor, and generally is 1, without a numerical unit. Ng is the number of lightning strokes per square kilometer per year happened in the location of buildings, with a unit of times/square kilometer/year; it is generally converted according to a local number of thunderstorm day (according to GB50057, the conversion formula is that: Ng=0.1×Td, wherein, Td is a local annual average number of thunderstorm day) or obtained by the detection data according to the local lighting locating system. Ae is an equivalent area (hereinafter referred to as interception area (IA)) of the ground scope intercepting the same lightning stroke frequency (hereinafter referred to as interception scope (IS)) of the building, with a unit of square kilometer.
In generally, the two parameters, k and Ng, are relatively easy to determine, while the calculation process for Ae is relatively complicated. In the “Appendix A Estimation of annual lightning stroke frequency of a building” of the GB50057, it is stipulated that the equivalent area intercepting the same lightning stroke frequency of a building should be the area which is enlarged outward of its actual occupied area; as for a cuboid-shaped building, as shown in
Ae=[L×W+2(L+W)×D+πD2]×10−6 (formula 2)
In formula 2: L, W, D respectively refers to the length, width, and enlarged width (EW) of a cuboid building (unit: meter).
The EW D of a building, refers to the distance between the edge of the building and the edge of its IS, which depends on the height H (unit: meter) of the building. When the height H of the building is less than 100 meters, D is obtained by the following formula:
D=[H×(200−H)]1/2 (formula 3)
When the height H of the building is equal to or larger than 100 meters, D is obtained by the following formula:
D=H (formula 4)
The above are the provision in GB50057. In different standards or norms, the definitions of EW and IA are varied. For example, in GB21714.2-2008 “Lightning protection, part 2: Risk Management”, it is stipulated that regardless of how high the building is, the value of the EW is taken as three times of the height, i.e., D is obtained by the following formula:
D=3H (formula 5)
Correspondingly, in GB21714, IA is represented by Ad.
The different definitions of EW and IA have no effect on the independence and integrity of the present inventive patent. No matter which standard or norm is used to calculate the IA of a building, the basic principle of the present inventive patent is the same, but applying the corresponding formula of its EW of D.
To sum up, an IA of a cuboid-shaped building is calculated according to formula 2, with a plan view of its IS as shown in
The above describes a method for calculating an IA of an isolated building having no other objects around, but actually a building rarely exists alone. In the modern city, buildings are highly intensive, and the ISs of those adjacent buildings to will be affected by one another, as a result, in the “Appendix A Estimation of annual lightning stroke frequency of a building” of the GB50057, it also stipulates a calculating method for correcting the IA of the present building, when there are other buildings around, e.g., it is stipulated in item 3 that: “as the building is lower than 100 meters, and there are other higher buildings within the peripheral range of its 2D as well, . . . the equivalent area can be calculated by subtracting D×(the total length of all parallel side lengths of these buildings and those considered buildings in meters)×10−6 (km2)”; and it is stipulated in item 5 that: “as the building is equal to or higher than 100 meters, and there are other buildings having the same or less height within the peripheral range of its 2H, and without the protection range that the determined building is equal to the height (m) of the building in the form of ball radius, . . . the equivalent area can be calculated by subtracting (H/2)×(the total length of all parallel side lengths of these buildings and those considered buildings in meters)×10−6 (km2)”, etc.
Though these calculation methods are given in GB50057, the definition is not clear enough, and the stipulation is not specific enough as well. For example, it stipulates that, “as those buildings are not within the protection scope of the considered buildings . . . ”, then how to determine that whether a building is located within the protection scope of another building? If a part of the building is located within the protection scope of the considered buildings, then how to calculate? For another example, a calculation parameter is frequently mentioned in GB50057 that “the total length of all parallel side lengths of these buildings and those considered buildings in meters”, but as for a circular building or a building that is not parallel with the considered building, then how to calculate? No specific definition or stipulation is made in GB50057 for those situations.
Meanwhile, the calculation methods given in GB50057 are inadequately to considered for a variety of complicated situations, such as: where the difference between the present building and other building in height merely features two options that “same with or less than” and “higher than”. No matter how higher it is, there is just one option that “higher than”, and the obtained calculation results are the same. As for the difference of distance between the present building and other building, there are merely two options that “within the range of 2D” and “within the range of 2H”; as long as it is within such range, no matter how far it is, the calculation results are the same. Apparently, the calculation results of same height are unable to reflect the wide variety of height and distance among different buildings.
Moreover, the calculation methods given in GB50057, greatly require human to determine and select different items, formulas and corresponding parameters, while in the case of a large number of buildings with complicated shapes, the probability of error is large.
In short, the calculation methods given in GB50057 are given from the qualitative viewpoint, and are not conducive for the establishment of mathematical model, and feature difficulty in operation, high error probability, poor calculation accuracy, and actually is unable to meet the requirement of daily work in reality.
In such situation, by studying, GAO Lei provides a method for calculating lightning stroke frequency interception area of a building under consideration of surrounding objects scientifically and reasonably. The method is given from a quantitative viewpoint, and is easy for calculation by establishing mathematical model. According to developed software by this method, once the user completes the measurement and model establishment of the present building and the surrounding buildings, the remaining calculations can be done automatically by the software, which is convenient for use, and the calculation results are accurate as well.
Buildings are rarely alone, and for most buildings, there more or less exists other buildings or structures around, and the interception scopes (ISs) of them would overlap to some extent (by using a concept of mathematics, the ISs of different buildings have intersections); as a result, when one calculates an interception area (IA) of a building (hereinafter referred to as the present building (TPB)), the calculation result is undoubtedly unscientific if its surrounding buildings are not taken into consideration. So, when considering its surrounding buildings, it is an issue that how to calculate lightning stroke frequency interception area (IS) of TPB.
From
To be specific, for TPB, project each point (referred to as the present point (PP), with a height assumed to be H) on the peripheral edges of its top surface (which top surface may be horizontal or slope surface, and a building may have a number of top surfaces) to the surrounding ground according to its own EW D (D is determined by H, and might feature varied specific definitions in various standards or provisions), so as to obtain a respective circular projection region on the ground. For adjacent points, the projection regions may be overlapped (i.e., have intersection).
Similarly, one can project each sideline at the peripheral edges of the top surface to the surrounding ground according to its own EW D. The essence of that is to integrate the projection region of each PP on the sideline, to obtain the projection region of the sideline. The integration refers to that, if one point on the ground locates within the projection region of any PP on the sideline, the point should be considered being located within the projection region of the sideline; accordingly, the projection region of the sideline is obtained (by using a concept of mathematics, the projection region of the sideline may be understood as an union set of the projection region of each PP). If the sideline is horizontal, the shape of the projection region on the ground is similar to a capsule, as shown in
Similarly, one can also project the whole top surface to the surrounding ground according to its own EW D. Its essence is to integrate the projection region of each sideline of the top surface and vertical projection of the top surface itself on the ground, while the specific shapes of the obtained projection region vary over the shape and the height of a top surface.
By integrating the individual projection region of each top surface of TPB, the obtained whole projection region is an IS of TPB on the ground, which is called the present interception scope (TPIS), and its area is the IA of TPB, which is called the present interception area.
In a three-dimensional space, there exists a virtual space body, which is composed by top surfaces and the IS of TPB and line segments projecting from the top surfaces to the IS. This space body is called the present interception body (TPIB).
To be specific, TPIB is encircled by a top surface (i.e., each top surface of TPB, which may be horizontal, or inclined), a bottom surface (i.e., the IS of TPB on the ground) and a side face (the side face consists of the projection lines at the outmost and links the periphery of the top surface and the periphery of the bottom surface together); wherein the side face is generally combined by conical surfaces and slope surfaces. For example, as for an interception body (IB) of a cylindrical building, the top surface is circular, the bottom surface is circular as well, the side face is a taper surface of full 360 degree, and the whole shape is a flat conoid, as shown in
The processing principle of the side face is that: side faces are always located at the outermost and at the upper side. That means: in the case that side faces and top surfaces intersect one another, the side faces at the outermost and at the upper side are the side faces of the whole IB, while the side faces at the inner side and at the lower side are wrapped inside the IB, and are no longer considered as the side face. For building tops with a large inclination or located at a relative lower position (for example, the roof of annex buildings of a tall building), the whole or a part of the top surfaces may be wrapped inside the IB and no longer be considered as the top surface.
The above is the process of establishing TPIB.
According to the above method, one can perform the same process on each other building around TPB, to obtain their own IB. The distant other building can be disregarded, if its IS on the ground does not overlap with that of TPB. Therefore, the so-called the other buildings (TOBs) herein, are just those buildings having influence on the IA of TPB. There may be more than one TOB, which are distributed around TPB.
The different definitions of EW D may affect the number of TOBs. Undoubtedly, when defining the EW by using formula 5, the number of TOBs will be larger than that is defined by using formula 4.
After the other building (TOB) is determined, the individual IB of each TOB is integrated to form an integration (the union set of each IB), which is called the other interception body (TOIB), and its IS is called the other interception scope (TOIS). The meaning of the integration herein is that: if a space point is located within the interception body (IB) of any TOB, then it is a point belongs to TOIB, and thus TOIB is obtained. Since there may be more than one TOB which are distributed around TPB, the shape of TOIB may be complicated and even unconnected. However, same with TPIB, TOIB is encircled by top surfaces, bottom surfaces and side faces, wherein, the side face is generally combined by taper surfaces and slope surfaces, and the side face or the top surface may intersect one another, by this time, the outermost and the upper sides become the side face of the whole IB.
TPIB and TOIB are obtained above. Hereinafter, the IA of TPB will be calculated accordingly.
In some special cases, S0 or S may be zero. For example, if TPB is relative low, while TOB is relative high, and both are very close as well, at this time, TPIS is completely located within TOIS (being its subset), then S0 is zero. If TPB is isolated (there is no other building around), at this time, there are no intersection between TPIS and TOIS, then S is zero. Even under such cases, the calculation method of the present patent is still available.
Since the overlapped IS is shared by TPB and TOB, then if S is larger than zero, the area of S can be divided into two parts, S1 and S2, in which S1 belongs to TPB and S2 belongs to TOB.
As shown in
There are two methods for calculating S1, which will be introduced respectively as follows:
First method, which is called volume-quantitative method
The periphery ring line of the overlapped IS moves upwards vertically to cut TPIB and TOIB respectively, as shown in
S1=S×V1/(V1+V2)
The volume-quantitative method is scientific and reasonable, and is our key recommended method. However, such method has a small disadvantage that: since S1 is calculated by a quantitative method, it is unable to clearly divide the boundary between TPIS and TOIS. Accordingly, the following method can be used to supplement.
Second method, which is called height-qualitative method
Since TPIB and TOIB have an intersection, a boundary line could be drawn between them, which is called the interception scope boundary (TISB), with its two sides being called as the present side (TPS) and the other side (TOS), respectively. TPS is close to TPB, and TOS is close to TOB, as shown in
The definition of TISB is that: for any point of TPS of the boundary, the height of TPIB at such point is no lower than the height of TOIB at such point; for any point of TOS of the boundary, the height of TOIB at such point is no lower than the height of TPIB at such point; for any point on the boundary, TPIB and TOIB features same height at such point. According to such definition, the boundary may be straight line, curved line, or other forms. The overlapped IS is divided into two parts by TISB, with the area of the part at TPS being S1, and the area of the part at TOS being S2, as shown in
According to the above definition, one can draw the boundary line, and calculate S1 and S2 as well. To be specific, the overlapped IS is divided into grids according to a certain size, then respectively calculate the height of TPIB (h1) and the height of TOIB (h2) at each grid node. According to the height difference between h1 and h2, the process is listed respectively as follows:
If h1 is higher than h2, the node position is located at TPS of the boundary, and the grid area is counted into S1;
If h1 is lower than h2, the node position is located at TOS of the boundary, and the grid area is counted into S2;
If h1 is identical to or substantially identical to h2, the point is the point at TISB, and the point need to be drawn;
After processing each grid node sequentially in this way, final accumulation values of S1 and S2 are obtained; and the points on the boundary are drawn sequentially to form TISB finally.
Generally, the calculation result by using the height-qualitative method is the same with that by using the volume-quantitative method. Furthermore, the height-qualitative method may clearly draw a boundary line between TPIS and TOIS, and be convenient to showcase the specific IS of a building. However, in some special cases, the height-qualitative method has problems, such as, if two buildings have relative large height difference, and are close together, and the IS of the lower building is a subset of the IS of the higher building, as shown in
S1 can be obtained by the above two methods (the volume-quantitative method or the height-qualitative method). Finally, by adding S0 to S1, it is the lightning stroke frequency interception area of a building under consideration of surrounding objects
The above is the main content of the present inventive patent.
Generally, the shape of an IB is relative complicated, and it is impossible to obtain accurate S0, S, V1 and V2 by a way of hand calculation, thus it is preferred to calculate by using computer programming. Though the principle is the same, both the manner and process of a specific programming may be varied according to personal habits. Hereinafter, a simplest embodiment is list, which comprises the following steps:
Step 1: measuring TPB and TOB surrounded, to acquire the related information of direction, shape, size, height and the like, which are inputted into a to computer by modeling. If it is unclear whether a building is TOB, one should input the surrounding buildings as many as possible, that is the wider the region is, the better it is.
Step 2: by using computer programming, the whole region including the IS of all buildings is divided into grids according to a certain size, and the height of each grid node of TPIB and TOIB is calculated and is stored into a multi-dimensional array; the array at least has three dimensions, wherein the two dimensions are used to represent plane coordinates, and the other dimension is used to represent a height of an IB on the coordinate point; the more finer the divided grid is, the more the number of the grids is, the larger the scale of the array is, the more accurate the calculation result is, and the longer time the calculation needs as well.
Step 3: by using computer programming, scanning each grid node in the whole region, to respectively acquire the height h1 of TPIB and h2 of TOIB at this point, as shown in
If h1 is zero, performing no operation;
If h1 is larger than zero, h1/(h1+h2) of such grid area is accumulated into the IA of TPB, such as: assume that h1=3 m, h2=7 m, then 30% (i.e., 3/10) of the grid area is added; assume that h2=0, then 100% of the grid area is added.
Step 4: performing the process on the area of each grid of the whole region in this way, the accumulative value is finally obtained, that is the lightning stroke frequency interception area of TPB under consideration of surrounding objects.
Number | Date | Country | Kind |
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201210182588.8 | Jun 2012 | CN | national |
Filing Document | Filing Date | Country | Kind |
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PCT/CN2013/075412 | 5/9/2013 | WO | 00 |