Compound curves are horizontal curves in highway and railway engineering that consist of two or more simple circular arcs of different radii, joined together and curving in the same direction, with a common tangent at their point of connection. They are used when site conditions or alignment constraints make a single-radius curve impractical, allowing a smoother transition between tangents while fitting the roadway within limited right-of-way or difficult terrain.
Two simple curves are connected together as physical obstructions do not permit the use of a single circular curve. The radius of the first curve is 400m while that of the second is 300m. The angles of intersection of the first and second curves are 36º and 50º, respectively. The stationing of PC is 4+509. Determine the following:
a. Length of the common tangent
b. Stationing of PT
c. Stationing of the vertex
d. Length of the common chord
The long chord from the PC to the PT of a compound curve is 300 meters long and the angles it makes with the longer and shorter tangents are 12º and 15º respectively. If the common tangent is parallel to the long chord.
a. Find the radius of the first curve.
b. Find the radius of the second curve.
c. If the stationing of PC is 10+204.30, find the stationing of PT.
A compound curve connects three tangents having azimuths of 254º, 270º, and 280º, respectively. The length of the chord is 320m long measured from the PC to the PT of the curve, and it is parallel to the common tangent having an azimuth of 270º. If the stationing of PT is 6+520:
a. Determine the total length of the curve.
b. Determine the stationing of the PCC.
c. Determine the stationing of PC.
The common tangent AB of a compound curve is 76.42m with an azimuth of 268º30', the vertex V being inacessible. The azimuths of the tangents AV and VB were measured to be 247º50' and 282º50', respectively. The stationing at A is 10+010.46 and the degree of the first curve is 4º based on the 20m chord. Use chord basis.
a. Compute the stationing of PCC
b. Compute the radius of the second curve
c. Compute the stationing of PT
d. Compute the length of the common chord.
Additional board-style practice items for this topic.
The common tangent AB of a compound curve is 76.42m with an azimuth of 268º30', the vertex V being inaccessible. The azimuth of the tangents AV and VB was measured to be 247º50'; and 282º50' respectively. The stationing at A is 10+010.46 and the degree of the first curve is 4º based on the 20m chord. Use chord basis.
Compute the stationing of PCC
Compute the radius of the second curve
Compute the stationing of PT
Compute the length of the common chord
Solution pending in psadquestions/q496.json.
The long chord from the PC to the PT of a compound curve is 300 meters long and the angle it makes with the longer and shorter tangents are 12º and 15º respectively. If the common tangent is parallel to the long chord,
Find the radius of the first curve.
Find the radius of the second curve
If the stationing of PC is 10+204.30, find the stationing of PT
Solution pending in psadquestions/q497.json.
A compound curve connects three tangents having azimuths of 254º, 270º, and 280º, respectively. The length of the chord measured from the PC to the PT of the curve is 320m, and this chord is parallel to the common tangent. If the stationing of the PT is 6+520
Determine the total length of the curve
Determine the stationing of the PCC
Determine the stationing of the PC
Solution pending in psadquestions/q498.json.
An unsymmetrical parabolic curve has a forward tangent of -8% and a back tangent of +5%. The length of curve on the left side of the curve is 40m long while that of the right side is 60m long. The PC is at station 6+780 and has an elevation of 110m. An outcrop is found at station 6+800 and has an elevation of 108.4m
Compute the height of fill needed to cover the outcrop.
Compute the elevation of curve at station 6+820.
Compute the elevation of the highest opint of the curve.
Solution pending in psadquestions/q505.json.
Two simple curves are connected together as physical obstructions do not permit the use of a single circular curve. The radius of the first curve is 400m, while that of the second is 300m. The angles of intersection of the first and second curves are 36º and 50º, respectively. The stationing of PC is 4+509. Determine the following:
Length of the common tangent
Stationing of PT
Stationing of the vertex
Length of the common chord
Solution pending in psadquestions/q584.json.
The perpendicular distance between two parallel tangents of a reversed curve is 7.5m, and the length of the long chord is 65m. Compute the common radius of the reversed curve.
Solution pending in psadquestions/q752.json.
A simple curve of a railroad has a degree of 6 degrees and a length of 140 m. What is the central angle of the curve? Use chord basis.
Solution pending in psadquestions/t1197.json.
A 5-degree simple curve is has a central angle of 50°. From the center of the curve, a line is drawn intersecting the tangent through PT at an angle of 60°, and passing through a point E on the curve. What is the length of the curve from E to PT?
Solution pending in psadquestions/t1201.json.
The common tangent AB of a compound curve is 82.38 m. The angles the common tangent makes with the tangents through PC and PT of the compound curve are 21° 10' and 15° 20', respectively. If the degree of the first curve is 3° 30', what is the radius of the second curve?
Solution pending in psadquestions/t1213.json.
Two tangents AV and BV are connected by a compound curve, where A is at PC, B is at PT, and V is at PI. Chord AB is 350 m long, angle VAB is 30°, angle VBA = 41°. The radius of the curve through PC is 100 m. What is the radius of the other curve in meters?
Solution pending in psadquestions/t1214.json.
The long chord of a compound curve makes an angle of 20° and 38°, respectively with the tangents. The common tangent of the compound curve is parallel to the long chord that is 185 meters long.
What is the radius of the smaller curve?
What is the radius of the bigger curve?
What is the length of the curve?
Solution pending in psadquestions/t1215.json.
A reversed curve consist of two curves of equal radius. The curve is to connect two parallel roads that are 60 meters apart. The length of the common tangent is 180 meters.
What is the angle of intersection of the curve?
What is the radius of the curve?
What is the length of the curve from PC to PT?
Solution pending in psadquestions/t1219.json.
A central curve having a degree of 6 has a spiral curve 100 m long on two sides. At what comfortable speed can a car travel along the spiral? Use arc basis.
Solution pending in psadquestions/t1232.json.
A car traveling at 130 kph locks up it wheel and skids up a 3% incline before crashing into a stationary massive concrete pedestal and coming to a complete stop. The skid marks leading up to the pedestal are 90 m long. The coefficient of friction between the tires and the road is 0.35.
How far would the car have skidded if it had not hit the pedestal?
What was the speed of the car at impact?
Solution pending in psadquestions/t1265.json.
A levee built on level ground is parallel to a river channel. The width of the levee on the top is 10 m. The side slope of the river side is 3:1 and on the land side is 2:1. The levee is 4.5 m high at its center. What is the volume of the levee (in m^3) if it is 2.5 km long?
Solution pending in psadquestions/t1284.json.
To determine the traffic density on a single-lane highway, a surveillance was made to measure the occupancy on a 400-m stretch of the highway. Ten vehicles pass the stretch. From the aerial photograph, the lengths (in meters) of each vehicle were found as follows: 3.5, 6.3, 4.2, 5.4, 3.4, 3.6, 6.1, 7.2, 5.1, & 3.8.
What is the occupancy rate in m per kilometer.
What is the average length of vehicles in meters.
What is the traffic density in vehicles per kilometer?
Solution pending in psadquestions/t1316.json.
The average speed per lane of a freeway is 60 kph. The average length of cars moving on that lane is 5.3 m. The PIEV (perception, identification, emotion and volition) time is 1.1 second.
What is the required center-to-center spacing of vehicles, in meters.
What is the traffic density in vehicles per kilometer.
What is the minimum time headway per vehicle in seconds?
Solution pending in psadquestions/t1319.json.
A location on a coast or shore containing one or more harbors where ships can dock and transfer people or cargo to or from land.
Solution pending in psadquestions/t1333.json.
A structure on the shore of a harbor where ships may dock to load and unload cargo or passengers.
Solution pending in psadquestions/t1335.json.
A compound curve has the following data: $I_1 = 28°$, $I_2 = 38°$, $R_1 = 380$ m., $R_2 = 220$ m. If P.C. is at sta. 20 + 100. Compute the length of the common tangent.
A compound curve has component central angles 28° and 36°. Find the total central angle.
Answer: The total central angle is 64°.