Surveying

Reconnaissance Survey

a survey made without the use of basic surveying equipment

Preliminary Survey

a survey made to pin and mark the points for construction

Final Survey

a survey used/undertaken during the construction phase

Intercepted arc

An inscribed angle is measured by one half its ______

One half

An inscribed angle is measured by ______ its intercepted arc.

Same or equal

Inscribed angles having the _______ intercepted arc are equal

Equal

Inscribed angles having the same or equal intercepted arc are ______

Tangent and a chord

An angle formed by a _____ is measured by one half its intercepted arc

Intercepted arc

An angle formed by a tangent and a chord is measured by one half its _____

Tangents

_____ from an external point of a circle are equal

Arc Basis

is the angle at the center subtended by an arc of 20m.

Chord Basis

is the angle at the center subtended by a chord of 20m.

D = 1145.916/R

Arc Basis

R = 10/sin(d/2)

Chord Basis

Circular curves

In highway or railroad construction, the curves most generally used presently are _____

simple, compound, reversed curves

Types of curves

Point of Curvature (PC)

point of tangency where the curve leaves the tangent

Point of Tangency (PT)

point of tangency where the curve meets the other tangent

Point of Intersection (PI)

point of where the two tangents meet

Central Angle (I)

angle of intersection of the tangents

Tangent Distance (T)

distance measured from PC or PT to the vertex or PI

Length of Curve (Lc)

arc length from PC to PT

Long Chord (C)

straight line drawn from PC to PT

Radius (R)

radius of the circular curve

External Distance (E)

distance measured from the vertex to the midpoint of the curve

Middle Ordinate (M)

measured from the midpoint of the curve to the midpoint of the chord

Tangent Distance (T)

=R(tan(I/2))

External Distance (E)

=R[(sec(I/2)-1]

Middle Ordinate (M)

=R[1-(cos(I/2)]

Long Chord (C)

=2R(sin(I/2))

Length of Curve (Lc)

=20I/D

Station PC

=Station PI-T

Station PT

Station PC+LC

Standard Format for Stationing

00+000.00

sec(I/2)

=1/cos(I/2)

First Subchord (C1)

=[first full station] - [station PC]

Last Subschord (C2)

=[station PC] - [last full station]

First subangle (d1)

=C1D/20

Last subangle

=C2D/20

Arc Basis

This is the method generally used in the highway practice.

compound curves

it consists two or more consecutive simple curves having different radius, but whose centers lie on the same side of the curve, likewise any two tangent at their meeting point.

different radius

compound curves consist two or more consecutive simple curves having __________, but whose centers lie on the same side of the curve, likewise any two tangent at their meeting point.

same side

compound curves consist two or more consecutive simple curves having different radius, but whose centers lie on the _________ of the curve, likewise any two tangent at their meeting point.

two or more

compound curves consist of _________ consecutive simple curves having different radius, but whose centers lie on the same side of the curve, likewise any two tangent at their meeting point.

consecutive

compound curves consist of two or more _________ simple curves having different radius, but whose centers lie on the same side of the curve, likewise any two tangent at their meeting point.

meeting point

compound curves consist of two or more consecutive simple curves having different radius, but whose centers lie on the same side of the curve, likewise any two tangent at their ________.

point of compound curvature

the point of the common tangent where the two curves join

angle of intersection of the compound curve

the angle of the intersection of the tangent

central angle of the first simple curve

subtended angle of the first curve

central angle of the second simple curve

subtended angle of the second curve

back tangent

distance from PC to PI

forward tangent

distance from PT to PI

vertex of the first simple curve

point of intersection of the first curve

vertex of the second simple curve

point of intersection of the second curve

common tangent

straight line from A to B

point of compound curvature

common point of tangency of the two joined simple curves