Definitions of Plane Surveying
Below are five definitions from various civil engineering forums or textbooks, and from Wikipedia, which specify that the Earth's alleged curvature is ignored for surveying projects to 260 sq kilometers (or approximately 100 sq. miles), or more specifically, to assume the Earth is a FLAT plane! So if professional civil engineers and surveyors are trained to ignore over 20 meters (66.6 feet) of curvature to 260 sq kilometers, at what point are they trained to factor the Earth's alleged curvature? Know an engineer?
Civil Engineers Forum:
Plane Surveying  Methods of Surveying
"Plane surveying is the survey in which the earth surface is assumed to be plane and the curvature of the earth is ignored. The plane surveys extend only over small areas and the lines connecting any two points on the surface of the earth are treated as straight lines and the angles between such lines are taken as plane angles. In dealing with plane surveys, knowledge of plane geometry and trigonometry is required. Surveys covering an area up to 260 km² may be treated as plane surveys. It is to be noted that the difference in length between the arc and the subtended chord on the earth surface for a distance of 18.2 km is only 0.1 m."
Scope and Use of Plane Surveying:
"Plane surveys are carried out for engineering projects on sufficiently large scale to determine relative positions of individual features of the earth surface. Plane surveys are used for the layout of highways, railways, canals, fixing boundary pillars, construction of bridges, factories etc. The scope and use of plane surveys is very wide. For majority of engineering project, plane surveying is the first step to execute them. Plane surveys are basically needed for proper, economical and accurate planning of all engineering projects and their practical significance cannot be overestimated."
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https://civilengineersforum.com/planesurveying/
WIKIPEDIA:
Plane and Geodetic Surveying:
"Based on the considerations and true shape of the earth, surveying is broadly classified into two types."
"Plane surveying assumes the earth is flat. Curvature and spheroidal shape of the earth is neglected. In this type of surveying all triangles formed by joining survey lines are considered as plane triangles. It is employed for small survey works where errors due to the earth's shape are too small to matter."
"In geodetic surveying the curvature of the earth is taken into account while calculating reduced levels, angles, bearings and distances. This type of surveying is usually employed for large survey works. Survey works up to 100 square miles (260 sq kilometers) are treated as plane and beyond that are treated as geodetic. In geodetic surveying necessary corrections are applied to reduced levels, bearings and other observations."
https://en.wikipedia.org/wiki/Surveying#Plane_and_geodetic_surveying
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More links here:
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Definition of Plane Survey:
"The type of survey in which curvature of earth is not taken into account,as the survey is extend over small areas, is known as the Plane Survey."
https://www.civilengineeringterms.com/surveyinglevelling/planesurveying/;
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Method of Surveying in Civil Engineering:
"Plane surveying is conducted by state agencies as well as private agencies. As we know earth is spherical in shape but its diameter is big enough to consider plane in small dimensions. It is that type of surveying in which the mean surface of the earth is considered as a plane and the spheroidal shape is neglected. Plane surveying is done of the area of survey is less than 250 km2."
https://theconstructor.org/surveying/surveyingprinciplesmethodscivilengineering/13048/;
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Classification and Types of Civil Engineering Survey:
Plane Surveying:

When radius of curvature of the earth is not taken into account.

Small area and small distances are covered

Degree of accuracy is comparatively low.

American survey put 250 km2 for treating survey as Plane, but controlling factor should be degree of precision rather than extent of area.
https://www.aboutcivil.org/typesclassificationofsurveying.html
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