Length, ft
Side (m) Bearing Latitude Departure
AV 955(291.1) 90° O +955.00
VB 800(243.8) 21°38' -743.65 +294.93
BO 2 1000(304.8) 68°22' -368.67 -929.56
Total ... ... -1112.32 +320.37- Express the latitudes and departures of the unknown sides In
terms of R 1 and A 1
Thus, for side O 2 O 1 : length = R 1 - 1000; bearing = A 1 ; latitude = -(R 1 - 1000) cos A 1 ; de-
parture = -(R 1 - 1000) sin A 1.
Also, for side O 1 A: length = ^ 1 bearing = O; latitude = R 1 departure = O. - Equate the sum of the latitudes and sum of the departures to
zero; express A 1 as a function of R 1
Thus, Slat - R 1 - (R 1 - 1000) cos A 1 - 1112.32 - O; cos A 1 = (R 1 - 1112.32V(IJ 1 - 1000),
or 1 - cos A 1 - 1 1232/(R 1 - 1000), Eq. a. Also, Sdep = -(R 1 - 1000) sin A 1 + 320.37 = O;
sin A 1 - 320.37/(^ 1 - 1000), Eq. b. - Divide Eq. a by Eq. b, and determine the central angles
Thus, (1 -cos AO/sin A 1 -tan
1
M 1 = 112.32/320.37;
1
M 1 = 19°19'13"; A 1 = 38°38'26";
A 2 = 680 22'-A 1 =29°43'34". - Substitute the value of A 1 in Eq. b to find R 1
Thus, R 1 = 1513.06 ft (461.181m). - Verify the foregoing results by analyzing triangle DEV
Thus, AD = R 1 tan
1
M 1 = 530.46 ft (161.684 m); DV= 955 - 530.46 = 424.54 ft (129.400
m); EB = R 2 tan
1
X 2 A 2 = 265.40 ft (80.894 m); VE = 800 - 265.40 - 534.60 ft (162.946 m);
DE = 530.46 + 265.40 = 795.86 ft (242.578 m). By the law of cosines, cos A = -(DF
2- VE
2
-DE
2
)/[2(DV)(VE); A = 68°22'. This is correct.
- VE
ANALYSIS OFA HIGHWAY
TRANSITION SPIRAL
A horizontal circular curve for a highway is to be designed with transition spirals. The PI
is at station 34 + 93.81, and the intersection angle is 52°48'. In accordance with the gov-
erning design criteria, the spirals are to be 350 ft (106.7 m) long and the degree of curve
of the circular curve is to be 6° (arc definition). The approach spiral will be staked by set-
ting the transit at the TS and locating 10 stations on the spiral by means of their deflection
angles from the main tangent. Compute all data needed for staking the approach spiral.
Also, compute the long tangent, short tangent, and external distance.
Calculation Procedure:- Calculate the basic values
In the design of a road, a spiral is interposed between a straight-line segment and a circu-
lar curve to effect a gradual transition from rectilinear to circular motion, and vice versa.
The type of spiral most frequently used is the clothoid, which has the property that the