How to implement on the ground the main components (start, middle, end points) of a circular curve with known radius R, tangent to two main alignments E1 and E2, where node K (intersecting point of the two main tangents) is not accessible to occupy.

How to implement on the ground the main components (start, middle, end points) of a circular curve with known radius R, tangent to two main alignments E1 and E2, by occupying node K (intersecting point of the two main tangents).

Determine the length between two points A and B by measuring two side lengths from a third occupied point C and the included angle c. Points A and B are visible from point C, but interrupted between each other.

Calculate the volume included between a horizontal plane, a ramp (inclination 1:m, side slopes 1:n) and a vertical wall using Simpson’s rule.

Calculate the coordinates of a known point P in an orthogonal coordinate system to a reference orthogonal coordinate system preserving shapes (angles) during transformation, in 2-D space.

Determine the elevation and grade value of an unknown point K which lies along a profile vertical curve (convex in this example).

*Commonly in profile vertical curves, a parabola is applied as an approximation to circular curve, considering that for large radius values and target precision, these elements practically coincide.

Determine the elevation of an unknown point X which lies between two known points A and B along an alignment tangency. The profile of tangency AB is also a tangent.

Determine the coordinates of an unknown point M (impossible to occupy) visible from two (2) previously surveyed reference stations A, B of a control baseline, only by observing angles α and β subtended by lines of sight from stations A and B to the intersected point M. Intersection technique is commonly implemented when the unknown point to be observed is inaccessible during a survey.

Calculate the maximum offset value ΔΖmax of an extrusion or intrusion detail from a reference plane (mainly flat object) so that the maximum error on the image plane due to radial shift does not exceed a certain limit Δρmax. (optical axis perpendicular to object plane)

Determine water content w and unit weight γsat of a sandy soil sample when it becomes saturated, at the same void ratio.