RU2166731C1 - Method for determining physical area of land - Google Patents

Abstract

FIELD: land management, in particular, geodesic works. SUBSTANCE: method involves determining average longitudinal and transverse angles of inclination of land or sections of land along lines mutually perpendicular and, as a rule, parallel to axes of abscissa and ordinates; calculating physical area from known formula through actually measured geodesic area, with total allowances being taken into account. Total allowances include corrections connected with transition to ellipsoid and to surface of middle mark of land, as well as relief changes. Method allows area of agricultural, municipal and other lands to be determined. EFFECT: increased efficiency and improved precision of determining area of lands.

Description

 The invention relates to the field of geodetic works in land management and can be used to determine the area of agricultural land, urban land, as well as other land uses.

или
P_э = P_г-ΔP_э,
здесь

где P_э - площадь на поверхности эллипсоида;
P_г - площадь в проекции Гаусса или геодезическая площадь;
Δ P_э - поправка за переход от поверхности проекции Гаусса к поверхности эллипсоида;
Y - среднее значение ординаты участка (расстояние от осевого меридиана до середины участка);
R - радиус эллипсоида для средней широты участка (в вычислении поправки обычно берут радиус шара).There is a method of determining the physical (actual) area by the coordinates of the boundary points of the land obtained in the system of the state reference geodetic network, according to topographic plans and maps, by introducing into the obtained area corrections for the transition from the Gaussian projection to the surface of the ellipsoid and then corrections for the "relief". (Sarmatov U.D. An analytical method for determining land use areas // Geodesy and Cartography, N 9, 1981, p. 16-19). The area obtained from plans and maps or from coordinates is always exaggerated and it is recalculated onto the surface of an ellipsoid by the formula:

or
P _e = P _g -ΔP _e
here

where P _e is the surface area of the ellipsoid;
P _g - area in the projection of Gauss or geodetic area;
Δ P _e - correction for the transition from the surface of the Gaussian projection to the surface of the ellipsoid;
Y is the average value of the ordinate of the site (the distance from the axial meridian to the middle of the site);
R is the radius of the ellipsoid for the average latitude of the plot (in calculating the corrections, the radius of the ball is usually taken).

или
P_н = P_э+ΔP_н
здесь

где P_н - площадь с учетом поправки за рельеф;
Δ P_н - поправка за переход с поверхности эллипсоида на поверхность средней отметки участка;
H - средняя высота (отметка) участка над поверхностью эллипсоида.For land plots located at a considerable distance (height) above the surface of the ellipsoid, the area is slightly reduced, therefore, a correction for the relief is introduced into it, expressed by the formula:

or
P _n = P _e + ΔP _n
here

where P _n - area adjusted for relief;
Δ P _n - correction for the transition from the surface of the ellipsoid to the surface of the average elevation of the site;
H is the average height (elevation) of the site above the surface of the ellipsoid.

Although the correction (Δ P _n ) is often called the relief correction, in fact it is not. More correctly, it should be called a correction for the average height (elevation) above the surface of the ellipsoid. The meaning of this amendment is that the surface of the ellipsoid moves to the level of the average elevation of the site and practically this surface of relevance will be a horizontal plane for any land plot drawn at the average elevation. The introduction of this amendment does not allow us to move to the physical (actual) area of the land plot, characterized by various forms of relief, such as, for example, a ravine, slope, hollow, hill, and so on, which are not taken into account in the values of the determined area.

 Thus, the considered method does not allow to determine the physical area of the land, which is its significant drawback.

или
P_ф = P_н+ΔP_ф,
здесь

где P_ф - физическая площадь;
Δ P_ф - поправка за рельеф;
ν - угол наклона плоскости земельного участка.There is a method of determining the physical area of a land plot that takes into account the terrain by introducing amendments for the angle of the plane of the plot (Maslov V.A., Yunusov A.G., Gorokhov G.N. Geodetic works in land management. M. - Nedra, 1990, p. . 32). In this method, adopted as a prototype, the physical area, taking into account the correction for the relief, is found by the formula:

or
P _f = P _n + ΔP _f ,
here

where P _f - physical area;
Δ P _f - correction for relief;
ν is the angle of inclination of the plane of the land.

 The physical area will always be larger than on the surface of an ellipsoid or on a horizontal plane.

 However, the scope of this method is extremely limited. It can only be used to determine the area of land with unilateral and uniform slope, which in reality is extremely rare.

 Using this method to determine the physical area of land with various landforms having different slopes of the surfaces is impossible, since it will give only approximate results, which is the main disadvantage of this method.

или
P_ф = P_н+ΔP_ф,
здесь

где P_ф - физическая площадь участка или секции;
P_н - площадь, исправленная за переход на поверхность эллипсоида и за переход к поверхности, отнесенной к средней отметке участка;
Δ P_ф - поправка к площади за рельеф;
ν₁ - средний продольный угол наклона земельного участка (или его секции);
ν₂ - средний поперечный угол наклона земельного участка (или его секции).The technical problem to which the invention is directed is to increase the accuracy of determining the physical area of land plots. The problem is solved in that, in contrast to the known method adopted for the prototype, determine the average longitudinal and transverse angles of inclination of the land plot or its sections along lines mutually perpendicular and, as a rule, parallel to the abscissa and ordinates, and the physical area is calculated by the formula:

or
P _f = P _n + ΔP _f ,
here

where P _f - the physical area of the site or section;
P _n - area corrected for the transition to the surface of the ellipsoid and for the transition to the surface referred to the average elevation of the site;
Δ P _f - correction to the area for the relief;
ν ₁ is the average longitudinal angle of inclination of the land plot (or its section);
ν ₂ - the average transverse angle of inclination of the land (or its section).

Средние продольные и поперечные углы наклона определяются по линиям, расположенным перпендикулярно друг другу. Углы находятся по формуле:

где h - превышения, определенные по горизонталям плана (карты) для каждой из линий;
d - горизонтальные проложения линий, определенные по плану (карте).The formula for calculating the physical area of a land plot can be converted to:

The average longitudinal and transverse angles of inclination are determined by lines perpendicular to each other. The angles are found by the formula:

where h is the excess determined by the horizontal plan (map) for each of the lines;
d - horizontal lines laid out according to plan (map).

где Σν_пр - сумма продольных углов наклона;
Σν_{поп =} - сумма поперечных углов наклона;
n - число углов (или линий);
Конкретное число линий, по которым определяются средние углы наклона, зависит от размеров участка и частоты сменяемости форм рельефа на нем. Чем меньше участок, тем с большей точностью его поверхность будет аппроксимирована поверхностями, образованными взаимно перпендикулярными линиями, а следовательно, с большей точностью будет определена его физическая площадь. При значительных размерах участка его необходимо разбивать на секции с однородными продольными и поперечными уклонами.The average tilt angles are found by the formulas:

where Σν _etc. - the amount of longitudinal inclination angles;
Σν _{pop =} - the sum of the transverse angles of inclination;
n is the number of angles (or lines);
The specific number of lines by which the average inclination angles are determined depends on the size of the site and the frequency of change of relief forms on it. The smaller the area, the more accurately its surface will be approximated by surfaces formed by mutually perpendicular lines, and therefore, its physical area will be determined with greater accuracy. With significant dimensions of the site, it must be divided into sections with uniform longitudinal and transverse slopes.

В случаях, когда учитывать ту или иную поправку нет необходимости по причине ее пренебрежимо малой величины, в общей формуле соответственная часть поправки (в скобках) вырождается в ноль.In cases where on any line intended to determine the angle of inclination, its changes are observed in individual sections, this line is divided into sections and the angles of inclination are determined in sections, and then the angle of inclination for the entire line is calculated as the arithmetic mean value. The method of determining the area is implemented both in traditional methods and in the automated determination of a digital terrain model. For the convenience of practical application, we bring the formula for calculating the physical area to the form in which it is calculated through the directly measured geodetic area, taking into account the total correction, taking into account the transition to the surface of the ellipsoid and to the surface of the average elevation of the site, as well as for the influence of the relief. The formula is:

In cases where it is not necessary to take into account one or another amendment because of its negligible value, in the general formula the corresponding part of the amendment (in brackets) degenerates to zero.

 The method can be applied in all cases of determining the area of land.

Claims (1)

A method for determining the physical area of a land plot by introducing an amendment for the relief, characterized in that the average longitudinal and transverse angles of inclination of the land or its sections are determined by mutually perpendicular lines, and then the land area is calculated by the formula

where R _f - the physical area of the land;
R _g - the geodetic area of the land;
υ ₁ and υ ₂ - respectively, the average longitudinal and transverse angles of inclination;
Y is the average value of the ordinate of the site (the distance from the axial meridian to the middle of the site);
R is the radius of the earth's ellipsoid for the middle latitude of the site;
H - average height (mark) of the site.