RU2509288C1 - Method for remote determination of gradient of slope at control points of avalanche site using laser range finder - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: laser range finder mounted in a valley determines the distance to an arbitrary control point A on a slope (L₁), the probing angle (β₁) and the azimuth of the projection of the laser beam on the horizontal plane. The distance (L₂) and probing angle (β₂) for a second arbitrary (auxiliary) point B lying at a certain distance AB from the control point A on the slope are determined by moving the probing beam vertically downwards. The projection of the section AB on the horizontal plane and the height of the control point A from the auxiliary point B on the slope are determined using the found values L₁, L₂, β₁, and β₂, from the ratio of the sides and the angles of geometric figures (triangles) formed in the vertical plane, passing on the probing line. Further, the projection on the horizontal plane of the normal to the slope at control point A and the angle between said projection and the projection on the horizontal plane of the section AB, which connects the control point A and the auxiliary point B on the slope, are determined. The gradient of the slope is then calculated using a calculation relationship.

EFFECT: high accuracy of remote measurement of the gradient of a slope in avalanche sites, low labour input.

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Description

The present invention relates to the field of meteorology and glaciology, and in particular to methods for remote determination of the slope steepness in avalanche foci, and can be used to determine the thickness of the snow cover on the slopes to predict avalanche hazard and determine snow accumulation in the mountains.

The steepness of the slope is one of the most important morphometric characteristics of the relief. According to the definition, the steepness of the slope is a vertical angle formed by the direction of the slope of the mountain, ravine, riverbank, etc. with a horizontal plane at a given point, expressed in degrees.

There are various methods for determining the steepness of a slope in the mountains using a compass and a simple goniometer [1].

When determining the steepness of the slope, the simplest goniometer is most acceptable. It is a rigid base on which a protractor and a plumb are fixed with a load. When measuring the angle of inclination of the surface to the horizon, one of the sides of the base is set parallel to the surface of the slope and the slope relative to the protractor scale determines the slope of the slope at a given point.

A disadvantage of the known methods is that when using such devices as a compass and a goniometer, you can only get the average value of the measured value. Known methods are not acceptable for determining the steepness of the slope in the presence of deep snow cover on the slope, and even in the presence of serious danger associated with avalanches. In these cases, only remote measurements are needed.

The closest in technical essence to the claimed object is a method for remote determination of the parameters of the slope and snow cover in avalanche centers using a laser location. The objective of these surveys is to obtain high-precision digital models of the relief of the earth's surface and the surface of the snow cover [2].

The disadvantages of this method include the high cost of aircraft and the impossibility of its use in snowfalls, which complicates the implementation of the method for the purpose of active exposure.

The technical result expected from the use of the claimed method is to reduce labor costs for its implementation and increase the accuracy of remote measurement of the slope in avalanche foci using a laser rangefinder.

) в контрольной точке «А» и угол α между данной проекцией и проекцией на горизонтальную плоскость отрезка «АВ», соединяющего контрольную (А) и вспомогательную «В» точки на склоне, затем вычисляют крутизну склона (β) по формуле $$\beta =arctg\left[\frac{L_1\cdot \sin {\beta }_1-L_2\cdot \sin {\beta }_2}{(L_1\cdot \cos {\beta }_1-L_2\cdot \cos {\beta }_2)\cdot \cos \alpha }\right]$$

The technical result is achieved by the fact that in the known method for remote determination of the slope steepness at the control points of the avalanche site using a laser range finder, according to the invention, first, using a laser range finder located in the valley, the distance to an arbitrary control point “A” on the slope (L ₁ ) is determined , the sounding angle (β ₁ ) and the azimuth of the projection of the laser beam onto the horizontal plane (A ₁ ), then, by shifting the probe beam vertically downwards for the second arbitrary (auxiliary) point “B”, lying d at a certain distance "AB" from the control point "A" on the slope, determine the distance (L ₂ ) and the sounding angle (β ₂ ), then, using the found values of L ₁ , L ₂ , β ₁ and β ₂ , from the relation the sides and angles of geometric figures (triangles) formed in a vertical plane passing along the sensing line, determine the projection of the segment "AB" on the horizontal plane, and the height of the control point "A" from the auxiliary point "B" on the slope, then determine the projection on the horizontal plane of the normal to the slope ( $$\overline{n}$$

) at the control point "A" and the angle α between this projection and the projection onto the horizontal plane of the segment "AB" connecting the control (A) and auxiliary "B" points on the slope, then the slope slope (β) is calculated by the formula $$\beta =arctg\left[\frac{L_{\mathrm{one}}\cdot \sin {\beta }_{\mathrm{one}}-L_2\cdot \sin {\beta }_2}{(L_{\mathrm{one}}\cdot \cos {\beta }_{\mathrm{one}}-L_2\cdot \cos {\beta }_2)\cdot \cos \alpha }\right]$$

Where

L ₁ · cosβ ₁ -L ₂ · cosβ ₂ - the height of the control point "A" above the auxiliary point "B" on the slope;

L ₁ · sinβ ₁ -L ₂ · sinβ ₂ - the projection of the segment "AB" on the horizontal plane.

), затем с помощью угломера определяют угол α между данной проекцией и проекцией величины L₁ на горизонтальную плоскость.The technical result is also achieved by the fact that when determining the angle α, having previously shifted the probe beam from the control point “A” a certain horizontal distance to the left (or right), the distance “L _Z ” to the second, arbitrary auxiliary point “Z” on the slope is determined and the azimuth of the sounding of this point (A _z ), after which a projection onto the horizontal plane of the values L ₁ , L _Z and the segment “AZ” is built and, having drawn the perpendicular to the projection of the segment “AZ”, they find the projection onto the horizontal normal plane ( $$\overline{n}$$

), then using the goniometer determine the angle α between this projection and the projection of the value of L ₁ on the horizontal plane.

Figure 1 presents the sensing scheme of the control "A" and auxiliary "B" points on the slope.

Figure 2 presents the projection on the horizontal plane of the values of L ₁ L ₂ and the segment AZ connecting the control "A" and the auxiliary point "Z" lying on the same horizontal with the point "A".

» и отрезка «АВ», соединяющего контрольную «А» и вспомогательную точку «В» на склоне. Figure 3 presents a diagram of the calculation of the angle "α" between the projections on the horizontal plane of the normal " $$\overline{n}$$

"And the segment" AB "connecting the control" A "and the auxiliary point" B "on the slope.

In figure 1, the following notation:

AO - slope;

L ₁ and L ₂ - the distance measured by the laser range finder, respectively, to the control (A) and auxiliary (B) points on the slope;

β ₁ and β ₂ - the sounding angle of the points "A" and "B", respectively, on the slope;

AE - the height of the control point "A" from the auxiliary point "B" on the slope;

EB - the projection of the segment "AB" on the horizontal plane;

"X-x" - the horizontal passing through the control point "A" on the slope;

DC - the projection of the segment L ₁ on the horizontal plane;

KS - the projection of the segment L ₂ on the horizontal plane;

Z is an arbitrary auxiliary point lying at some distance from point "A" horizontally;

xx - horizontal.

In figure 2, the following notation:

Z ₁ is the projection of an arbitrary auxiliary point Z on the horizontal plane;

Z ₁ C is the projection of the distance L _Z on the horizontal plane;

A ₁ - azimuth of sounding points "A" and "B" on the slope;

A _z is the azimuth of the sounding of the auxiliary point "Z" on the slope;

- проекция нормали склона на горизонталь «x-x»; $$\overline{n}$$

- projection of the slope normal to the horizontal “xx”;

The arrow "N" indicates the direction to the North;

x ₁ -x ₂ is the horizontal projection (xx) on the horizontal plane.

In figure 3, the following notation:

EB - the projection of the segment "AB" on the horizontal plane;

» в горизонтальной плоскости;EM - the projection of the segment EB on the normal " $$\overline{n}$$

»In the horizontal plane;

AE - the height of the control point "A" relative to the auxiliary point "B" on the slope;

».α is the angle between the projections onto the horizontal plane of the segment "EB" and the normal " $$\overline{n}$$

".

The proposed method is implemented as follows:

1) Previously, in the valley at point “C”, from which the control point “A” is clearly visible on the slope (Fig. 1), a measurement system is installed (theodolite with a laser range finder).

2) Then, using the laser range finder, determine the distance (L ₁ ) to the control point "A" on the slope, the azimuth (A ₁ ) and the sounding angle (β ₁ ).

3) Then, having shifted the probe beam by a certain distance AB vertically down (or up), determine the distance (L ₂ ) to an arbitrary auxiliary point (B) on the slope. The offset angle depending on the range is approximately 0.5-5 °.

4) Then, using the found values of the quantities L ₁ , L ₂ , β ₁ and β ₂ from the ratio of the sides and angles of the triangles formed in the vertical plane (Fig. 1), passing along the sensing line, determine the projection of the segment "AB" on the horizontal plane

EB = L ₁ cos β, -L ₂ cos β ₂

and the height of the control point "A" from the auxiliary point "B" on the slope according to the formula

AE = L ₁ · sinβ, -L ₂ · sinβ ₂ .

) в контрольной точке «А» и угол α между данной проекцией и проекцией на горизонтальную плоскость отрезка «АВ», соединяющего контрольную «А» и вспомогательную «В» точки на склоне. Для этого, предварительно сместив зондирующий луч от контрольной точки «А» на некоторое расстояние по горизонтали влево (или вправо), определяют расстояние «L_Z» до второй, произвольной вспомогательной точки «Z» на склоне и азимут зондирования этой точки (A_Z). После этого в соответствующем масштабе строят проекцию на горизонтальную плоскость величин L₁, L_Z и отрезка «AZ» (фиг.2). Затем по изложенной выше методике находят проекцию на горизонтальную плоскость нормали ( $$\overline{n}$$

) и с помощью угломера определяют угол α между данной проекцией и проекцией величины L₁ на горизонтальную плоскость.5) Then find the projection on the horizontal plane of the normal to the slope ( $$\overline{n}$$

) at the control point “A” and the angle α between this projection and the projection onto the horizontal plane of the segment “AB” connecting the control “A” and the auxiliary “B” of the point on the slope. To do this, having previously shifted the probe beam from the control point "A" to a certain horizontal distance to the left (or right), determine the distance "L _Z " to the second, arbitrary auxiliary point "Z" on the slope and the azimuth of sounding of this point (A _Z ) . After that, a projection on the horizontal plane of the values of L ₁ , L _Z and the segment "AZ" is constructed on an appropriate scale (figure 2). Then, according to the method described above, the projection onto the horizontal normal plane is found ( $$\overline{n}$$

) and using the protractor determine the angle α between this projection and the projection of the value of L ₁ on the horizontal plane.

6) After that, the slope of the slope is calculated at the control point "A" according to the above formula.

. $$\beta =arctg\left[\frac{L_{\mathrm{one}}\cdot \sin {\beta }_{\mathrm{one}}-L_2\cdot \sin {\beta }_2}{(L_{\mathrm{one}}\cdot \cos {\beta }_{\mathrm{one}}-L_2\cdot \cos {\beta }_2)\cdot \cos \alpha }\right]$$

.

An example of the method. As a result of sensing the control point "A" on the slope, the following results were obtained:

-distance to the control point L ₁ = 1800 m;

azimuth A ₁ = 120 °;

sounding angle β ₁ = 12 °.

After that, having shifted the probe beam a certain vertical distance down from point “A”, we chose an arbitrary auxiliary point “B” on the slope. As a result of sounding of this point “B” on the slope, the following results were obtained:

- distance to the auxiliary point L ₂ = 900 m;

- the sounding azimuth of the point "B" is equal to the azimuth of the sounding of the point "A" and is 120 °. In the text and in the figure, this azimuth is denoted by A ₁ );

sounding angle β = 9 °.

Then we found the projection on the horizontal plane of the segment AB according to the formula

EB = (L ₁ · cosβ ₁ -L ₂ · cosβ ₂ ) = 1800 · cos12-900 · cos9 = 871.75 m,

and the height of the control point "A" from the auxiliary point "B" on the slope according to the formula

AE = L ₁ · sinβ ₁ -L ₂ · sinβ ₂ = 1800 · sin12-900 · sin9 = 233.45 m.

After constructing the projections of the values of L ₁ , L ₂ and the segment “AZ” on the horizontal scale, using the protractor, we found the angle α = 30 degrees.

Knowing the value of the angle α, we found the slope of the slope

$$\beta =arctg\left[\frac{L_{\mathrm{one}}\cdot \sin {\beta }_{\mathrm{one}}-L_2\cdot \sin {\beta }_2}{(L_{\mathrm{one}}\cdot \cos {\beta }_{\mathrm{one}}-L_2\cdot \cos {\beta }_2)\cdot \cos \alpha }\right]=arctg\frac{233.45}{871.75\cdot 0.86}=17.43\text{hail}\text{.}$$

For the case when the beam of the laser rangefinder is shifted upward from the control point, the calculations are carried out in a similar way, assuming that the auxiliary (upper) point is the control and the lower point is the auxiliary, which simplifies the calculation procedure.

The proposed method, unlike the known ones, significantly reduces the complexity of operations and increases the accuracy of remote measurement of the slope exposure in avalanche sites using a laser range finder.

Information sources

1. Aleshin V.M., Serebryannikov A.V. Tourist topography (section Measuring the heights and steepness of slopes on the ground). - M.: Profizdat, 1985, - 160 p.

2. Boyko ES Using the method of airborne laser location when assessing snow accumulation in mountain conditions // Materials of the VI international conference. “Laser scanning and digital aerial photography. Today and tomorrow". - M., 2006. P.29-30. - PROTOTYPE.

3. Alekseev A. A. Mountain building and mountainous terrain (a guide for instructors and teachers of tourism), second edition. - M., 2002, - 40 s.

Claims (2)

1. The method for remote determination of the slope steepness at the control points of the avalanche site using a laser range finder, characterized in that using a laser range finder located in the valley, first determine the distance to an arbitrary control point "A" on the slope (L ₁ ), the sounding angle ( β ₁₎ and the bearing projection of the laser beam on the horizontal plane (A _1), then, the probe beam is displaced vertically downward to an arbitrary second (auxiliary) point "B", lying at a distance "AB" from the reference point "A a slope, determining the distance (L ₂₎ and the sensing angle (β _2), then use the results values of L _1, L _2, β ₁ and β ₂ of the aspect ratio and angle of geometric shapes (triangles) formed in a vertical plane , passing along the sensing line, determine the projection of the segment "AB" on the horizontal plane and the height of the control point "A" from the auxiliary point "B" on the slope, then determine the projection on the horizontal plane of the normal slope ( $$\overline{n}$$

) at the control point "A" and the angle α between this projection and the projection onto the horizontal plane of the segment "AB" connecting the control (A) and auxiliary "B" points on the slope, then the slope slope (β) is calculated by the formula $$\beta =arctg\left[\frac{L_{\mathrm{one}}\cdot \sin {\beta }_{\mathrm{one}}-L_2\cdot \sin {\beta }_2}{(L_{\mathrm{one}}\cdot \cos {\beta }_{\mathrm{one}}-L_2\cdot \cos {\beta }_2)\cdot \cos \alpha }\right]$$

where
L ₁ · sinβ ₁ -L ₂ · sinβ ₂ - the height of the control point "A" above the auxiliary point "B" on the slope;
L ₁ · cosβ ₁ -L ₂ · cosβ ₂ - the projection of the segment "AB" on the horizontal plane. 2. The method for remote determination of the steepness of the slope at the control points of the avalanche source according to claim 1, characterized in that when determining the projection onto the horizontal plane of the normal ( $$\overline{n}$$

) angle α, having previously shifted the probe beam from the control point "A" to a certain horizontal distance to the left (or right), determine the distance "L _Z " to the second arbitrary auxiliary point "Z" on the slope and the azimuth of sounding of this point (A _z ) then the projection on the horizontal plane of the values L ₁ , L _Z and the segment “AZ” is constructed and, having drawn the perpendicular to the projection of the segment “AZ”, the projection on the horizontal normal plane is found ( $$\overline{n}$$

), then using the protractor measure the angle α between this projection and the projection of the value of L ₁ on the horizontal plane.

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