R = 300 ft
△ = 74°46′36″
Tangent distance, T =?
Length of curve, L =?
Long chord, C =?
External distance, E =?
Middle ordinate, M =?
T = R tan ∆2= 300 tan 74.782= 229.284 ft
L = πR∆180= 3.14 ×300×74.78180= 391.348 ft
C = 2R sin ∆2= 2(300) sin 74.782=364.342 ft
E = (Rcos∆2)-R= (300cos74.782)-300= 77.586 ft
M = R (1-cos∆2) = 300 (1-cos74.782) = 61.643 ft
(a) Control points
There are three types of control points. They are the
1. PC = Point of content
2. PI = Point of intersection
3. PT = Point of tangent
Two factors need to be taken into account when establishing horizontal control points.
1. The control points should be located throughout the site in order that all the design points can be fixed from at least two or three of them so that the work can be independently checked.
2. The design points must be set out to the accuracy stated in the specifications
Setting PC and PT
With the instrument at the PI, the instrument man sights on the preceding PI and keeps the head tape man on line while the tangent distance is measured. A stake is set on line and marked to show the PC and its station value. The instrument man now points the instrument on the forward PI, and the tangent distance is measured to set and mark a stake for the PT.
Laying Out Curve from PC
The procedure for laying out a curve from the PC is described as follows. Note that the procedure varies depending on whether the road curves to the left or to the right
(b) The procedures for producing large horizontal curves used in road construction are the following.
1) Setting out with theodolite and tape
2) Setting out with two theodolites
3) Setting-out using EDM
4) Setting-out using coordinates
5) Setting out with two tapes (method of offsets)
6) Setting out by offsets with sub-chords
7) Setting out with inaccessible intersection point
8) Setting out with theodolite at an intermediate point on the curve