JP6944151B2 - How to install the tsunami fence and the tsunami fence - Google Patents

Description

The present invention relates to a tsunami fence for suppressing the momentum of a tsunami that overflows over the top of a breakwater at the time of the arrival of a tsunami and reducing the damage caused by the tsunami in the hinterland, and a method for installing the tsunami fence.

If a large tsunami occurs that exceeds the top of the breakwater, it can cause enormous damage in the hinterland. Therefore, as a countermeasure against a large tsunami, it is conceivable to construct a breakwater having a height dimension larger than the expected wave height of the tsunami.

Japanese Unexamined Patent Publication No. 2014-25219

However, when constructing a breakwater with a height higher than the wave height of the tsunami, there is a problem in terms of stability and a considerable cost will be incurred, and the top height will be raised for all existing breakwaters. If you try to do the construction, the construction cost will be enormous and it is not realistic.

The present invention is intended to solve such a problem in the prior art, and can be constructed only by simple and inexpensive construction, and can appropriately suppress the momentum of the tsunami and damage the tsunami in the hinterland. It is an object of the present invention to provide a tsunami fence that can effectively reduce the number of tsunamis and a method of installing the fence.

In the method of installing the tsunami fence of the present invention, half of the assumed tsunami height is ai, the height from the still water surface to the top of the breakwater is h0, the height of the tsunami fence is h1, and the top width of the breakwater. The value α of the installation position on the top of the breakwater is as follows, where B is B, the attenuation rate is β, and the water depth is d. A tsunami fence composed of a perforated plate with a shielding rate of 65 to 75% and a support column supporting the perforated plate having a shielding rate of 65 to 75% is placed on the top of the breakwater so as to satisfy the relational expressions (1) and (2). It is characterized by being installed.
(1) α ≧ (6ai-2h0-h1) / (1.2B)
(2) α ≦ 1-β × ai / B × (2 × h1 / d) ^1/2

In a breakwater of a typical scale, it is effective to set the value α of the installation position on the top of the breakwater within the range of 0.55 to 0.8.

Further, the tsunami fence according to the present invention is composed of a perforated plate having a shielding rate of 65 to 75% and a support column supporting the tsunami fence. When the height to the top of the breakwater is h0, the height of the tsunami fence is h1, the width of the top of the breakwater is B, the attenuation rate is β, and the water depth is d, the outer end of the top of the breakwater is 0, The feature is that the value α of the installation position on the top end of the breakwater with the inner end of the harbor as 1 is installed so as to satisfy the above relational expression (1) and the relational expression (2).

According to the method of installing the tsunami fence and the tsunami fence of the present invention, when a tsunami arrives at the breakwater, the momentum of the tsunami flowing over the top can be suppressed and the damage of the tsunami in the hinterland can be reduced. Further, by installing the tsunami fence so as to satisfy the above relational expressions (1) and (2), the problem of deterioration of the tsunami resistance stability of the breakwater and the problem of the occurrence of scouring are preferably solved. Can be done.

FIG. 1 is a cross-sectional view of a tsunami fence 1 and a breakwater 2 according to the present invention. FIG. 2 is an explanatory diagram of the increase in wave power [P +] when the tsunami fence is installed on the breakwater 2 of FIG. FIG. 3 is an explanatory diagram of an increase in resistance [P−] when the tsunami fence is installed on the breakwater 2 of FIG. FIG. 4 is an explanatory diagram of the horizontal movement distance [S] of the breakwater 2 of FIG. 1 until the water flow passing near the upper end of the tsunami fence 1 falls to the height of the top end 21. FIG. 5 is a graph showing the measurement results of wave power in the hydraulic experiment relating to the relational expression (1). FIG. 6 is a photograph of the flow condition of the water flow in the hydraulic experiment relating to the relational expression (2). FIG. 7 is a graph showing the measurement results of the landing point distance of the water flow in the hydraulic experiment relating to the relational expression (2).

Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. FIG. 1 is a cross-sectional view of a tsunami fence 1 or the like according to the present invention. The tsunami fence 1 is composed of a perforated plate having a shielding rate of 70% (± 5%) and a support column supporting the tsunami fence 1, and as shown in the figure, the breakwater 2 (basic mound on the seabed). It is installed on the top end 21 (position between the port outer end 22 and the port inner end 23) (installed on 3).

This tsunami fence 1 can be expected to have the effect of suppressing the momentum of the tsunami that overflows over the top 21 and reducing the damage caused by the tsunami in the hinterland when the tsunami arrives at the breakwater 2. However, if the shielding rate of the perforated plate is less than 65%, the effect of sufficiently suppressing the momentum of the tsunami cannot be expected, and if it exceeds 75%, a problem in the strength of the tsunami fence 1 itself occurs, and Problems may also arise from the viewpoint of the stability of the breakwater 2. Therefore, it is effective to set the shielding rate within the range of 65 to 75%.

When a tsunami arrives, the breakwater receives a corresponding external force (wave force) in the horizontal direction, but in the breakwater 2 where the tsunami fence 1 is installed on the top 21, the breakwater 2 itself receives the wave. In addition to the force, the wave force received by the tsunami fence 1 also acts on the breakwater 2, so that the tsunami resistance stability of the breakwater 2 is reduced by that amount (the increase in the wave force in the horizontal direction when the tsunami fence is installed). There is a possibility that it will end up.

Further, when the tsunami fence 1 having a shielding rate of 65 to 75% is installed, the water flow of the tsunami is slowed down when passing over the top end 21, so that the inside of the harbor of the breakwater 2 (on the right side in FIG. 1). ), And if the installation position of the tsunami fence 1 is too close to the harbor inner end 23 of the breakwater 2, the water flow that has passed near the upper end of the tsunami fence 1 will be the breakwater 2. It will fall directly to the water surface inside the harbor (the water surface above the harbor inner part 31 of the foundation mound 3), and as a result, “scouring” may occur at the harbor inner part 31 of the foundation mound 3.

In the tsunami fence 1 of the present invention, the value [α] of the installation position on the top end 21 (the port outer end 22 of the top 21 shown in FIG. 1 is “0” and the port inner end 23 is “1”. , "Numerical values from 0 to 1") are installed so as to satisfy the following two relational expressions (1) and (2), which causes the above-mentioned problems (decrease in tsunami resistance stability, And the occurrence of scouring) can be solved suitably.
(1) α ≧ (6ai-2h0-h1) / (1.2B)
(2) α ≦ 1-β × ai / B × (2 × h1 / d) ^1/2

In the above relational expressions (1) and (2), [ai] is half the value of the assumed tsunami height (m), and [h0] is the height from the hydrostatic surface to the top 21 of the breakwater 2. (M) and [h1] are the height (m) of the tsunami fence 1, [B] is the top width (m) of the breakwater 2, [β] is the damping factor, and [d] is the water depth (). same as below).

When the tsunami fence 1 is installed at a position that satisfies the above relational expression (1), water that stays in the area outside the port (on the left side in FIG. 1) of the area on the crown 21 when the tsunami arrives. The water pressure due to the weight of the lump (vertically downward force to hold down the breakwater 2) (increase in resistance when installing the tsunami fence) acts on the breakwater 2 as described above. Can be reduced or canceled.

Further, when the tsunami fence 1 is installed at a position satisfying the above relational expression (2), all the water flow of the tsunami that has passed through the tsunami fence 1 will once fall on the top end 21 of the breakwater 2, and the water flow will be on the breakwater. It is possible to avoid falling directly to the water surface inside the harbor of 2 (the water surface above the harbor inner part 31 of the foundation mound 3), and as a result, “scouring” occurs at the harbor inner part 31 of the foundation mound 3. Can be preferably avoided.

Here, the significance of the above relational expressions (1) and (2) will be described in detail.

1. 1. Regarding relational expression (1) As described above, the wave force acting on the breakwater 2 with the tsunami fence 1 installed is the amount of increase in wave force when the tsunami fence is installed [P +] (see Fig. 2) compared to the breakwater without the tsunami fence. ), So if only this point is taken into consideration, there is a concern that the tsunami resistance stability will decrease when the tsunami fence 1 is installed. However, when the tsunami fence 1 is installed, the resistance of the breakwater 2 is increased by the water pressure due to the weight of the water mass WM (see FIG. 3) that stays in the area outside the harbor than the tsunami fence 1 in the area on the top 21. It is considered that the increase will occur, and the increase in resistance [P-] (see FIG. 3) when the tsunami fence is installed will increase in proportion to the value of the installation position [α] of the tsunami fence 1.

Therefore, if the value of the installation position [α] of the tsunami fence 1 is set larger than the “certain value” (threshold value), the resistance increase [P-] may exceed the wave power increase [P +]. In this case, the problem of deterioration of tsunami resistance stability in the breakwater 2 due to the installation of the tsunami fence 1 can be suitably avoided. The relational expression (1) expresses the "threshold value" for this [α] in relation to the wave power increase [P +] and the resistance increase [P-], in other words, the resistance increase. This is a formulation of the conditions for the installation position [α] of the tsunami fence 1 required for the minute [P−] to exceed the wave power increase [P +].

The increase in wave force [P +] when the tsunami fence is installed is the wave pressure action height [η ^* ] (m) on the hydrostatic surface shown in FIG. 2, and the height from the hydrostatic surface to the top 21 of the breakwater 2 [h0]. ] (M), the height of the tsunami fence 1 [h1] (m), the wave pressure intensity at the still water surface [p1] (kN / m ² ), and the lifting pressure at the lower end of the front surface of the upright wall [pu] (kN / m). ^{It can be obtained from 2} ), and the increase in resistance [P-] when the tsunami fence is installed is the top width [B] (m) of the breakwater 2 and the height [h1] of the tsunami fence 1 shown in FIG. ] (M), the installation position of the tsunami fence 1 [α], the unit volume weight of seawater [ρ ₀ g] (kN / m ³ ), and the friction coefficient (the cason and the foundation mound 3 that make up the breakwater 2). It can be obtained from the friction coefficient with the rubble layer) [μ]. Then, by applying these to the condition “P−≧ P +” and arranging them, the relational expression (1) can be derived.

More specifically, the amount of increase in wave power [P +] when the tsunami fence is installed is as follows.
(3) P + = (((η ^* − (h0 + h1)) / η ^* × p1) + ((η ^* −h0) / η ^* × p1)) / 2 × h1

Here, assuming that "η ^* = 3.0ai", "p1 = 3.0ρ ₀ gai", and "pu = p1", these are substituted into the above equations and arranged as follows.
(4) P + = (6ai-2h0-h1) × ρ ₀ gh1 / 2

On the other hand, the increase in resistance [P-] when the tsunami fence is installed is as follows.
(5) P- = αB × ρ ₀ gh1 × μ

Then, under the condition "P-≥P +", the right side of the above equations (4) and (5) (in addition, in [μ] of the above equation (5), the caisson and the foundation mound 3 constituting the breakwater 2 are configured. By substituting the value of the general coefficient of friction "0.6" with the rubble layer) and rearranging them, the relational expression (1) "α ≧ (6ai-2h0-h1) / (1.2B) Can be derived.

In order to confirm the effectiveness of this relational expression (1), the inventor of the present invention conducted an experiment using a hydraulic experimental device capable of reproducing the tsunami phenomenon. Specifically, a model (about 1/50 scale) of the breakwater 2 and the foundation mound 3 on which the tsunami fence 1 was installed as shown in FIG. 1 was installed in the water tank of the hydraulic experiment device to reproduce the tsunami phenomenon. The wave force (tsunami combined wave force) acting on the tsunami fence 1 and the breakwater 2 was measured for each installation position of the tsunami fence 1.

Here, the height [h0] (see FIG. 2) from the still water surface to the top 21 of the breakwater 2 is 10.7 cm, the height [h1] of the tsunami fence 1 is 8 cm, and the width of the top of the breakwater 2 [B]. ] Was set to 30 cm. In addition, as tsunamis that spread to breakwaters 2 and the like, two types of tsunamis of different sizes, more specifically, "no overflow" tsunamis that do not exceed the tsunami fence 1 ([ai] is set to 8 cm in front of the breakwater). (Calculated value of [α] by relational expression (1) (recommended value): 0.48) and tsunami with "overflow" that overflows the tsunami fence 1 ([ai] is set to 10 cm in front of the breakwater) (Calculated value (recommended value) of [α] according to relational expression (1): 0.80) was synthesized.

The measurement result of wave power is shown in the graph of FIG. The horizontal axis in this graph is the actual value of the installation position of the tsunami fence 1 on the top end 21 (see FIG. 1) (the port outer end 22 of the top 21 shown in FIG. 1 is “0”, and the port inner end. The numerical value of "0 to 1" where part 23 is "1") is the calculated value of [α] by the relational expression (1) ("0.48" and "0.48" in the case of a "no overflow" tsunami. In the case of a tsunami with "overflow", the value divided by "0.80") is shown. Specifically, "1" on the horizontal axis indicates that the actual value of the installation position of the tsunami fence 1 matches the calculated value (recommended value) of [α] according to the relational expression (1). "0.5" of the axis means that the tsunami fence 1 is installed at a position between the port outer end 22 and the position of the calculated value (recommended value) of [α] according to the relational expression (1). Shown. On the other hand, the vertical axis shows the rate of increase (%) of the "wave force acting on the tsunami fence 1 and the breakwater 2 when the tsunami fence 1 is installed" with respect to the "wave force acting on the breakwater 2 when the tsunami fence is not installed". There is.

As shown in the graph of FIG. 5, the calculated value (recommended value) of [α] by the relational expression (1) is used for both the “without overflow” tsunami and the “with overflow” tsunami. When the tsunami fence 1 is installed inside the port (on the right side in Fig. 1) from the position of, the wave power increase rate is within 3%, and practically, the wave power increase due to the installation of the tsunami fence 1 It is understood that the balance is such that the effects can be almost canceled. On the other hand, if the tsunami fence 1 is installed outside the port (on the left side in FIG. 1) from the position of the calculated value (recommended value) of [α] according to the relational expression (1), a large force acts during the tsunami action. It is considered that the breakwater 2 becomes unstable. From these experimental results, the validity and validity of the relational expression (1) were confirmed.

2. About relational expression (2) When a tsunami arrives at a breakwater where a tsunami fence is not installed on the top, the water flow of the tsunami passes over the top at a constant flow velocity and then from the inner end of the harbor at the top. It is discharged horizontally toward the space inside the harbor and falls on the water surface inside the harbor (a position away from the inner edge of the harbor to some extent) in a parabolic pattern.

On the other hand, when the tsunami fence 1 having a shielding rate of 65 to 75% is installed on the top 21 of the breakwater 2, the water flow of the tsunami is decelerated when passing over the top 21. The gradient of the water flow that is discharged from above the top to the space inside the harbor and falls is larger than when the tsunami fence is not installed, and falls to the water surface at a position closer to the inside end 23 of the harbor. Further, when the installation position of the tsunami fence 1 on the top end 21 is too close to the harbor inner end portion 23, the water flow passing near the upper end of the tsunami fence 1 (and above it) is the water surface inside the harbor of the breakwater 2. In this case, as described above, the possibility of "scouring" occurring in the harbor inner portion 31 (see FIG. 1) of the foundation mound 3 is increased.

However, it is considered that this problem can be avoided by setting the installation position of the tsunami fence 1 at a position sufficiently distant from the port inner end 23 to the port outer side. More specifically, by setting the value of the installation position [α] of the tsunami fence 1 to be smaller than the “certain value” (threshold value), the distance from the installation position of the tsunami fence 1 to the port inner end 23 is increased. , It becomes larger than the movement distance [S] (horizontal movement distance until falling to the height of the top end 21) (see FIG. 4) on the top end 21 of the water flow passing near the upper end of the tsunami fence 1. By setting as such, all the water flow of the tsunami that has passed through the tsunami fence 1 can be once dropped onto the top end 21 of the breakwater 2, and the water flow directly from the vicinity of the upper end of the tsunami fence 1 to the water surface inside the port of the breakwater 2. It is possible to avoid "scouring" of the foundation mound 3 due to falling.

The relational expression (2) expresses the "threshold" for this [α] in relation to the top width [B] of the breakwater 2, the height [h1] of the tsunami fence 1, and the like. The installation position of the tsunami fence 1 required for the distance from the installation position of 1 to the inner end 23 of the port to exceed the moving distance [S] on the top end 21 of the water flow that has passed near the upper end of the tsunami fence 1. It is a formulation of the condition of α]. This relational expression (2) can be obtained as follows.

First, the maximum flow velocity [V0] of the tsunami water flow in the horizontal direction can be expressed as follows from the "long wave theory".
(6) V0 = ai × (g / d) ^1/2

The flow velocity [V1] of the water flow after passing through the tsunami fence 1 is expressed as follows by multiplying [V0] by the damping factor [β] due to the passage of the tsunami fence 1.
(7) V1 = β · V0 = β × ai × (g / d) ^1/2

Therefore, the moving distance [S] on the top end 21 of the water stream passing near the upper end of the tsunami fence 1 is as follows from the parabolic equation.
(8) S = V1 · (2 x h1 / g) ^1/2 = β x ai x (2 x h1 / d) ^1/2

In order to temporarily drop all the tsunami water flow that has passed through the tsunami fence 1 onto the top end 21 of the breakwater 2, as described above, the distance from the installation position [α] of the tsunami fence 1 to the port inner end 23 is required. It is necessary to exceed the moving distance [S] on the top end 21 of the water flow that has passed near the upper end of the tsunami fence 1, and this condition is "αB" (the port outer end 22 of the top end 21) shown in FIG. The sum of "S" (the distance traveled on the top 21 of the water stream that passed near the upper end of the tsunami fence 1) is "B" (the sky of the breakwater 2). It is synonymous with being smaller than (edge width) (the following equation).
(9) αB + S ≦ B

Then, from the above equations (8) and (9), the relational expression (2) “α ≦ 1-β × ai / B × (2 × h1 / d) ^1/2 ” can be obtained.

In order to confirm the effectiveness of this relational expression (2), the inventor of the present invention conducted an experiment using a hydraulic experimental device capable of reproducing the tsunami phenomenon. Specifically, a model (about 1/50 scale) of the breakwater 2 and the foundation mound 3 on which the tsunami fence 1 was installed as shown in FIG. 1 was installed in the water tank of the hydraulic experiment device to reproduce the tsunami phenomenon. The flow conditions at each installation position of the tsunami fence 1 were photographed.

Here, the height [h1] of the tsunami fence 1 (see FIG. 4) was set to 8 cm, and the overflow depth of the tsunami was set to 8 cm (calculated value (recommended value) of [α] according to the relational expression (2): 0. .82). Regarding the installation position of the tsunami fence 1, the actual values of [α] were set to "0.5", "0.75", and "1".

As shown in FIG. 6 (1), the actual value of [α] was set to “0.5”, and as shown in FIG. 6 (2), the actual value of [α] was set to “0.75”. In the case (in each case, the condition “α ≦ 0.82” according to the relational expression (2) in this case is satisfied), the water flow passing through the tsunami fence 1 lands on the top 21 (see FIG. 4) of the breakwater 2. bottom. On the other hand, as shown in FIG. 6 (3), when the actual value of [α] is set to “1” (the condition “α ≦ 0.82” according to the relational expression (2) in this case is not satisfied), the water flow. Fell directly onto the foundation mound.

Further, for each installation position of the tsunami fence 1, the landing point distance of the water flow after passing through the tsunami fence 1 (from the harbor inner end 23 of the breakwater 2 shown in FIG. 1 to the harbor inner side of the breakwater 2 (right side in FIG. 1). The distance to the landing point on the water surface) was measured. Here, the height [h1] of the tsunami fence 1 (see FIG. 4) was set to 10 cm, and the overflow depth of the tsunami was set to 10 cm. The measurement result is shown in the graph of FIG.

The horizontal axis in the graph of FIG. 7 is the actual value of the installation position of the tsunami fence 1 on the top end 21 (see FIG. 1) (the port outer end 22 of the top 21 shown in FIG. 1 is “0”, and the port inner end. The value obtained by dividing the numerical value of "from 0 to 1", where the part 23 is "1", by the calculated value (recommended value) of [α] according to the relational expression (2) is shown. On the other hand, the vertical axis shows the rate of change (%) of the "water landing point distance when the tsunami fence is installed" with respect to the "water landing point distance when the tsunami fence is not installed".

As shown in the graph of FIG. 7, when the tsunami fence 1 is installed inside the port (on the right side in FIG. 1) from the position of the calculated value (recommended value) of [α] according to the relational expression (2) (FIG. 7). When the value on the horizontal axis of 7 exceeds "1"), the water flow falls to the area remarkably close to the inner end of the harbor 23 (see FIG. 1) of the breakwater 2, and the problem of "scouring" occurs in the foundation mound 3. It turns out that it may occur. On the other hand, when the tsunami fence 1 is installed outside the port (on the left side in FIG. 1) from the position of the calculated value (recommended value) of [α] according to the relational expression (2) (the numerical value on the horizontal axis in FIG. 7 is " If it is "1 or less"), the landing point distance does not decrease so much from the landing point distance when the tsunami fence is not installed. Therefore, it is considered that there is no particular problem regarding "scouring". From these experimental results, the validity and validity of the relational expression (2) were confirmed.

Here, when the preferable installation range (recommended value) of the tsunami fence according to the present invention is calculated using the above relational expressions (1) and (2) and the numerical values relating to the breakwater of a typical scale, for example. A tsunami fence with a water depth [d] of 10 m, a height [h0] from the still water surface to the top 21 of the breakwater 2, a breakwater 2 with a top width [B] of 15 m, and a height [h1] of 4 m. Assuming that the height of the tsunami [2ai] is 8 m when installing 1, it is effective to set [α] to "0.55 or more" according to the relational expression (1). , It is effective to set [α] to “0.8 or less” according to the relational expression (2).

1: Tsunami fence,
2: Breakwater,
21: Top,
22: Outer end of the harbor,
23: Inner end of the harbor,
3: Basic mound,
31: Inside the harbor,
α: Value of tsunami fence installation position on the top,
ai: Half the height of the assumed tsunami,
B: Breakwater top width,
d: Water depth,
h1: Height of tsunami fence,
h0: Height from the still water surface to the top of the breakwater,
η ^* : Wave pressure action height on the hydrostatic surface,
P +: Increased wave power when the tsunami fence is installed,
P-: Increased resistance when installing a tsunami fence,
p1: Wave pressure intensity on the hydrostatic surface,
pu: Lifting pressure at the lower end of the front of the upright wall,
S: Distance traveled above the top of the stream,
V0: Maximum flow velocity of horizontal tsunami water flow,
V1: Flow velocity of water flow after passing through the tsunami fence

Claims (3)

Half the height of the assumed tsunami is ai, the height from the still water surface to the top of the breakwater is h0, the height of the tsunami fence is h1, the width of the top of the breakwater is B, and the water flow after passing the tsunami fence. When the attenuation rate obtained by dividing the flow velocity of the tsunami water flow in the horizontal direction by the maximum flow velocity of the tsunami water flow is β and the water depth is d,
The value α of the installation position on the top of the breakwater, where 0 is the outer end of the breakwater and 1 is the inner end of the harbor, satisfies the following relational expressions (1) and (2). As described above, a method for installing a tsunami fence, which comprises installing a tsunami fence composed of a perforated plate having a shielding rate of 65 to 75% and a support column supporting the tsunami fence on the top end of the breakwater.
(1) α ≧ (6ai-2h0-h1) / (1.2B)
(2) α ≦ 1-β × ai / B × (2 × h1 / d) ^1/2 When installing a tsunami fence with a height of 4 m on a breakwater with a water depth of 10 m, a height from the still water surface to the top of the breakwater of 5 m, and a width of the top of 15 m, the height of the tsunami is assumed to be 8 m. In this case, the value α of the installation position on the top of the breakwater with 0 at the outer end of the breakwater and 1 at the inner end of the harbor should be within the range of 0.55 to 0.8. A method of installing a tsunami fence, which comprises installing a tsunami fence composed of a perforated plate having a shielding rate of 65 to 75% and a support column supporting the tsunami fence on the top end of the breakwater. A perforated plate shielding rate is 65% to 75%, post and tsunami fence that consists by supporting it is, a the installed breakwater on the top end,
Half the height of the assumed tsunami is ai, the height from the still water surface to the top of the breakwater is h0, the height of the tsunami fence is h1, the width of the top of the breakwater is B, and the water flow after passing the tsunami fence. When the attenuation rate obtained by dividing the flow velocity of the tsunami water flow in the horizontal direction by the maximum flow velocity of the tsunami water flow is β and the water depth is d,
The value α of the installation position on the top of the breakwater, where 0 is the outer end of the breakwater and 1 is the inner end of the harbor, satisfies the following relational expressions (1) and (2). A breakwater characterized by the installation of a tsunami fence .
(1) α ≧ (6ai-2h0-h1) / (1.2B)
(2) α ≦ 1-β × ai / B × (2 × h1 / d) ^1/2

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