1. A symmetrical vertical summit curve has tangents of +6% and -4%.

If the stationing and

elevation of P.T. is 10 + 020 and 143.63 m. respectively, compute the elevation and

stationing of the highest point of the curve. Length of curve is 120m.

2. A -6% grade and a +2% grade intersect at STA 12 + 200 whose elevation is at 25.632 m.

The two grades are to be connected by a parabolic curve, 160 m long. Find the elevation

of the first quarter point on the curve.

3. Using arc basis, a 3.2 degree curve with central angle of 18 ° has a value of an external

distance equal to:

4. The offset distance of the simple curve from the P.T. to the tangent line passing through

the P.C. is equal to 120.20m. The simple curve has an angle of intersection of50 °. Find

the radius of the simple curve.

5. A descending grade of 4.2% intersects at an ascending grade of 3% at station12+325 at

elevation 14.2m These two grades are to be connected by a 260m vertical parabolic curve

. A reinforced concrete culvert pipe with its top 30cm below the subgrade. What will be

the invert elevation of the culvert?

6. The spiral easement curve has a length of spiral equal to 80m and the radius of the central

curve of the spiral curve is 192.84m. Compute the deflection angle at the end point of the

spiral.

7. The degree of curve of the central curve of a spiral easement curve is equal to 6°. If the

max. design velocity of the car passing thru the spiral curve is 75 kph, determine the

required length of spiral.

8. The length of the spiral curve is 82m and the radius of the central curve of the spiral

curve is 260m. Compute the length if throw.

9. A spiral easement curve has a length of 80m and the radius of the central curve is 200m.

Determine the max. velocity that a car could pass thru the spiral curve.

10. Determine the degree of simple curve whose central angle is 26° if the shortest distance

from the curve to the point of intersection of the tangents is 7.54m. Use arc basis.

11. The common tangent of a compound curve makes an angle of 12° from the tangent

passing thru the P.C. and 18° from the tangent passing thru the P.T. If the radius of the

second curve is 180 m, find the radius of the first curve if the length of the common

tangent is 70 m long.
12. The perpendicular distance between two parallel tangents of a reversed curve is 7.5 m.

and the length of the long chord is 65 m. Compute the common radius of the reversed

curve.

13. A +5.2% grade is followed by a -2% grade of a vertical summit parabolic curve at station

2 + 230 with an elevation of 194.60m. The parabolic curve is 450m. long.

a. Compute the length of curve per 1° change in grade

b. .Compute the elevation of the highest point of curve.

c. Compute the stationing of point C whose elevation is 185.35.

14. A horizontal curve is to be designed for a two-lane road in the proposed extension of

NLEX.

The following data as known:

Deflection angle = 40°

Tangent length = 134m

Coefficient of Friction = 0.12

Super elevation = 0.08

Compute the design speed in kph.

15. A vertical summit curve has its highest point of the curve at a distance of 48 m. from the

P.T. The back tangent has a grade of +6% and a forward tangent grade of -4%. If the

stationing of the P.T. is 10 + 100, determine the length of vertical summit curve in

meters.

16. On a railroad, a +0.8% grade meets a -0.4% grade at sta. 2 + 700 and elevation 30 m. The

maximum allowable change in grade per station is 0.2%. Determine the length of the

curve.

17. A vertical summit curve has tangent grades of +5% and -3.8%. The horizontal distance

from the P.C. to the highest point of the curve is 113.64 m. Determine the length of the

curve.

18. Compute the deflection angle at the end point of the spiral if the length of spiral is 80 m

with a degree of curve of the central curve of a spiral easement curve is 6.5° .
19. A spiral easement curve has a length of 100 m. with a central curve angle having a radius

of 300 m. Determine the offset distance from the tangent to the third quarter point of the

spiral.

20. A spiral easement curve has a length of 100 m. with a central curve angle having a radius

of 300 m. Determine the degree of spiral at the third quarter point.

21. A reversed curve of equal radii connects two parallel tangents 12m apart. The lenght of

chord from P.C. to P.T. is 140m. Determine the radius of the curve.

22. The perpendicular distance between the two parallel tangents of a reversed curve is 8m

and the chord distance from the P.C. to the P.T. is equal to 30m. Compute the central

angle of the reversed curve.

23. What is the central angle in degrees of a curve whose radius is 200m and distance of the

midpoint of the curve P.I. is 14.20m?

24. A compound curve has a common tangent 520m long. The first curve passing through the

P.C. is a 3-degree curve with a central angle of 50 °. Find the length of the second curve

if its central angle is 35 ° .

25. An existing highway with bearing N. 20° E. Is to be connected to another highway with

bearing of N. 80 E by a 4° simple curve. What length of curve is required?

26. An 80-m spiral connects to a tangent with a 180-m radius circular curve. The maximum

velocity in kph that a car could pass through the curve without skidding is nearest to.

27. The offset distance from P.C to P.T of a simple curve is 18m. The angle of intersection of

the tangent is 24°. If the stationing of P.T is 45 + 158.32, what is the stationing of P.I.?

28. A grade of -5% is followed by a grade of +1%, the grade intersecting at the vertex (Sta.

10 + 060). The change of grade is restricted to 0.4% in 20m. Compute the length of the

vertical parabolic sag curve in meters.

29. A -6% grade and a +2% intersect at STA 12+200 whose elevation is at 14.375m. The two

grades are to be connected by a parabolic curve, 160m long. Find the elevation of the first

quarter point of the curve.

30. A 300m vertical parabolic sag curve are connected by tangent grades of -5% and +1%

which intersects at station 10+050 and elevation 374.50m.

a. Compute the length of curve per 1° change in grade.

 b. Compute the distance from the P.C. to the lowest point of the curve.

c. Compute the elevation of the lowest point of the curve.

31. A spiral easement curve has a length of 120 m with a central curve having a radius of 300

m. Determine the offset distance from the tangent to the third-quarter of the spiral.

32. 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 21°10’ and

15°20’, respectively. If the degree of the first curve is 3°30’, what is the degree of the

second curve?

33. The long chord of a compound curve is equal to 250 meters and the angles it makes with

the tangents equal to 8˚ and 10˚, respectively. Find the radii, R1 and R2 when the common

tangents is parallel to the long chord.

34. The angle of intersection of circular curve is 45˚30’ and its radius is 198.17 m. PC is at

Sta. 0 + 700. Compute the right angle offset from Sta. 0 + 736.58 on the curve to tangent

through PC.

35. A compound curve has a common tangent 84.5 m. long, which makes an angle of 16° and

20° with the tangents of the first and the second curves respectively. If the length of the

tangent of the first curve is 38.6 m, compute the radius of the second curve.

36. A symmetrical vertical summit curve has tangents of +4% and -2%. The allowable rate of

grade is 0.3% per meter station. Stationing and elevation of P.T. is at 10+020 and

142.63m respectively.

a. Compute the length of curve

b. Compute the distance of the highest point of curve from the P.C.

c. Compute the elevation of the highest point of curve.

37. A vertical parabolic sag curve of Lapulapu underpass has a grade of -4% followed by a

grade of +2% intersecting at station 12+150.60 at elevation 124.80m above the sea

level.The change of grade of the sag curve is restricted to 0.6%.

a. Compute the length of the curve.

b. Compute the elevation of the lowest point of the curve.

c. Compute the elevation at station 12+125.60.

38. A vertical summit parabolic curve has its P.I. at station 14+750 with elevation of 76.30m.

The grade of the back tangent is 3.4% and forward tangent of -4.8%.if the length of curve

is 300m.

a. Compute the location of the vertical curve turning point from the P.I.

b. Compute the elevation the vertical curve turning point in meters.

c. Compute the stationing of the vertical curve turning point.

39. A vertical summit parabolic curve has a vertical offset of 0.375m from the curve to the

grade tangent at station 10+050.The curve has a slope of +4% and -2% grades

intersecting at P.I. The offset distance of the curve at P.I. is equal to 1.5m. If the

stationing of the P.C is at 10+000.

a. Compute the required length of curve.

b. Compute the horizontal distance of the vertical curve turning point of intersection

of the grades.

c. Compute the elevation of the vertical curve turning point if the elevation of P.T. is

86.42m.

40. A symmetrical parabolic curve summit curves connects two grades of +6% and -4%. It is

to pass through a point “P” on the curve at station 25+140 having an elevation of

98.134m. If the elevation of the grade intersection is 100m with stationing of 25+160.

a. Compute the length of the curve.

b. Compute the stationing of the highest point of the curve.

c. Compute the elevation of the station 25+120 on the curve.

41. A -3% grade meets a +5% grade at a vertex (Elev. 146.24) directly under an overpass

bridge whose underside is at elev. 152.74, and carries another road across the grades at

right angles.

a. What is the longest parabolic curve that can be used to connect the two grades and

the same time provide at least 5m pf clearance under the bridge at its center line?

b. If the underside of the bridge is level and is 12m. wide, find the actual clearance

at the left edge of the bridge.

c. If the underside of the bridge is level and is 12m. wide, find the actual clearance

at the right edge of the bridge.

42. A descending grade of 4.2% intersects an ascending grade of 3% at sta. 12+325 at

elevation 14.2m. These two grades are to be connected by a 260m vertical parabolic

curve. A reinforced concrete culvert pipe with overall diameter of 105cm is to be

constructed with its top 30cm blow the subgrade. What will be the invert elevation of the

culvert?

43. A -6% grade and a +12% grade intersects at station 12+200 whose elevation is at

14.375m. The two grades are to be connected by a parabolic curve, 160m long. Find the

elevation of the first quarter point on the curve.

44. A -6% grade and a +12% grade intersects at station 12+200 whose elevation is at

25.632m. The two grades are to be connected by a parabolic curve, 160m long. Find the

elevation of the first quarter point on the curve.

45. A grade descending at the rate of -4% intersects another grade ascending at the rate of

+8% at station 2+0000, elevation 100m. A vertical curve is to connect the two such that

the curve will clear a boulder located at station 1+980, elevation 101.34m.

a. Determine the necessary length of the curve.

b. Determine the station of the location of a sewer to be laid out.

c. Compute the elevation of station where the sewer is to be place.

46.

a. A vertical summit curve has tangent grades of +5% and -3.8%. If the radius of the

vertical summit curve is 2200m, determine the length of the tangent of the summit

curve.

b. The radius of the sag vertical curve is equal to 1500m. If it has tangent grades of -

2.8% and +2.2%, determine the length of the vertical sag curve.

c. A vertical summit curve has a radius of 227.73m and tangent grades of +5% and -

3.8%. How far is the highest point of the curve from the P.C.?

47.

a. A vertical sag curve has tangent grades of -3% and +2%. If the length of the

vertical sag curve is 120m, determine the raduis of the vertical sag curve.

b. A parabolic summit curve, designed for the extension of SCTEX (Subic-Clark-

Tarlac Expressway) has a back tangent grade of +4.5%. The parabolic summit
 curve has a length and radius of 600m and 7500m respectively. Compute the

forward tangent grade neede to satisfy these conditions.

c. A vertical sag curve have tangent grades of -1.8% and +3.2%. If the design speed

of the vertical sag curve is 90 kph, determine the radius of the vertical sag curve.

48. The P.C. of a vertical parabolic curve is at station 2+000 of elevation 50.40m and the

grade of the P.C. is +3.2%. The elevation of station 2+060 is 51.50m. What is the

elevation of station 2+106?

49. A vertical curve has an upgrade of 2.5% and is followed with a downgrade of 1.5%. If the

rate of change of grade is 0.05% per 20m chain, compute the value of the constant K used

for the computations of the tangent correction per 20m length of curve.

50. A grade of -5% is followed by a grade of +1%, the grades intersecting at station 10+050

of elevation 374.50m. The change of grade is restricted to 0.4% in 20m.

a. Compute the length of vertical parabolic sag curve.

b. How far is the lowest point of the curve from the P.T.?

c. What is the elevation at station 10+000?

51. A vertical summit has its highest point of the curve at a distance 48 m from the P.T. The

back tangent has a grade of +6% and a forward grade of -4%. The curve passes thru point

A on the curve at station 25 + 140. The elevation of the grade intersection is 100m at

station 25 + 160.

a. Compute the length of the curve

b. Compute the stationing of P.T

c. Compute the elevation of point A on the curve.

52. A symmetrical summit curve has tangents of +4% and -2%. The allowable rate of change

of grade is 0.3% per meter station. Stationing and elevation of P.T is at 10 + 020 and

142.63m respectively.

a. Compute the length of curve.

b. Compute the distance of the highest point of the curve from the P.C.

c. Compute the elevation of the highest point of curve.

53. A vertical symmetrical sag curve has a descending grade of -4.2% and an ascending

grade of +3% intersecting at station 10+020, whose elevation is 100m.The two grade

lines are connected by a 260m vertical parabolic sag curve .

 a. At what distance from the P.C is the lowest point of the curve located?

b. What is the vertical offset of the parabolic curve to the point of intersection of

the tangent grades.

c. If a 1m diameter Culvert is placed at the lowest point of the curve with the top

of the culvert buried 0.60m below the subgrade, what will be the elevation of the

invert of the culvert?

54. A horizontally laid circular pipe culvert having an elevation of its top to be 26.0m crosses

at right angles under a proposed 120m high way parabolic curve. The point of

intersection of the grade lines is at station 5+216 and its elevation is 27.0m while the

culvert is located at station 5+228.The backward tangent has a grade of 3% and the grade

of the forward tangent is -1.6%.

a. Compute the stationing of the highest point of the curve.(ans 5+234.26)

b. Compute the elevation of the highest point of curve.(ans.26.378m)

c. Under the conditions,what will be the depth of cover the pipe.(ans.0.368m)

55. A vertical highway curve is to pass through a railway t grade.The crossing must be at

station 4+210 and at elevation 220.82m.The initial grade of the highway is +2% and

meets a -3% grade at station 4+135 at an elevation of 223.38m. The rate of change must

not exceed 2%.

a. What length of curve will meet these conditions?

b. What is stationing of the highest point of the curve?(ans.4+108.545)

c. What is the elevation of the highest point of the curve?(ans.221.794m)

56. A symmetrical parabolic summit curve connect two grades of +6% and -4%. It is to pass

point through a point "P" the stationing of which is 35+280 and the elevation is 193.13m.

If the elevation of the grade intersection is 200m with stationing of 35+330.

a. Determine the length of the curve.

b. Determine the stationing and elevation of P.C.

c. Determine the stationing and elevation of P.T.

57. An underpass crossing a reinforce concrete bridge along a shaw blvd. has a downward

garde of 4% meeting an upward grade of 8% at the vertex V at elevation 70m and

 stationing of 7+700 , exactly underneath the center line of the bridge having a width of

10m. If the required minimum clearance under the bridge is 5m and the elevation of the

bottom of the bridge is 78.10m.

a. Determine the length of the vertical parabolic curve that shall connect the two

tangents.

b. Determine the stationing of the point where a catch basin will be placed.

c. Determine the elevation of the point where a catch basin will be placed.

58. A symmetrical parabolic curve passes through point A whose elevation is 23.23m at a

distance of 54m from the P.C. The elevation of the P.C at station 4+100 is 22.56m. The

grade of the back tangent is +2% and the length of curve is 120m.

a. Compute the grade of the forward tangent.

b. Compute the stationing of the highest point of the curve.

c. Compute the elevation of the highest point of the curve.

59. 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 P.C. is at the station 8+780 and has elevation of 110m. An outcrop

is found at station 6+800 has an elevation of 108.40m.

a. Compute the height of fill needed to cover the outcrop.

b. Compute the elevation of curve at station 6+820.

c. Compute the elevation of the highest point of the curve.

60. A forward tangent having a slope of -4% intersects the back tangent having a slope of

+7% at point V at stations 6+300 having an elevation of 230m. It is required to connect

the two tangents with an unsymmetrical parabolic curve that shall pass through point A

on the curve having an elevation of 227.57m at stations 6+270. The length of curve is

60m on the side of the back tangent.

a. Determine the length of the curve on the side of the forward tangent.

b. Determine the stationing of the highest point of the curve.

c. Determine the elevation of the highest point of the curve.

61. A -3% grade meets a +5% grade near an underpass. In order to maintain the minimum

clearance allowed under the bridge and at the same time introduce a vertical transition

curve in the grade line, it is necessary to use a curve that lies 200m on the side of the
 vertex of straight grade and 100m on the other. The station of the beginning of the curve

(200m side) is 10+000 and its elevation is 228m.

a. Determine the elevation at station 10+040.

b. If the uphill edge of the underside of the bridge is at station 10+220 and at

elevation 229.206m, what is the vertical clearance under the bridge at this point?

c. Determine the stationing of the lowest point of the curve.

62. A roadway goes form tangent alignment to a 250m circular curve by means of an 80m

long spiral transition curve. The deflection angle between the tangent is 45®. Use

formulas to compute Xs, Ys p, and k. assume that the station of the P.I. measured along

the back tangent, is 250 + 00, and compute the stations of the TS, SC, CS, and ST.

63. The tangent of a spiral curve has a azimuths of 226® and 221® respectively. The

minimum length of spiral is 40m. With a minimum super elevation at 0.10 m/m width of

roadway. The maximum velocity to pass over the curve is 70kph. Assume width of

roadway to be 9m.

a. Determine the degree of simple curve.

b. Determine the length of spiral at each ends of simple curve.

c. Determine the super elevation of the first 10m from S.C on the spiral.

64. A simple curve having a radius of 250m connects two tangents intersecting at an angle of

50®. It is to be replaced by another curve having 80m, spiral at its ends such that the

point of tangency shall be the same.

a. Determine the radius of the new circular curve

b. Determine the distance that the curve will nearer the vertex.

c. Determine the central angle of the circular curve

d. Determine the deflection angle at the end point of the spiral

e. Determine the offset from tangent at the end point of the spiral

f. Determine the distance along the tangent at the midpoint of the spiral.

65. The two tangents of a simple curve have azimuth of 270˚ and 10˚ respectively. If has a

radius of 320 m. it is required to change this curve to spiral curve that will have value if

p=2.5m, b=30m as shown on the figure.

a. Determine the distance on which the new curve must be moved from the vertex.

b. Determine the value of “y”.

 c. Determine the external distance from T.S to the P.C of the simple curve. If DE is

parallel to h.

66. Two tangents having azimuths of 240˚ and 282˚ are connected by an 80m spiral curve

with a 6˚ circular curve. The width of the roadway is 10m if the design velocity is 60kph.

a. Determine the super-elevation at quarter points.

b. Determine the deflection angle at the end point (S.C)

c. Determine the external distance.

67. A spiral curve was laid out in a certain portion of the Manila-Cavite Coastal road. It has a

length of spiral of 80m and an angle of intersection of two tangents of 40%. If the degree

of curve is degrees, determine the following elements of the spiral curve to be laid out:

a. Length of long and short tangent.

b. External distance

c. Length of throw

d. Maximum velocity that a car could pass thru the curve without skidding.

68. An Easement Spiral curve has a design speed of 100kph. The radius of the central angle

is 360m with a permissible super-elevation of 0.07.

a. Compute the centrifugal acceleration so as not to cause discomfort to the driver in

m/sec.

b. Compute the length of the transition curve to limit the centrifugal acceleration.

c. Compute the length of the short tangent of the transition curve.

69. The length of a spiral curve is 80m with a radius of 280 at the central curve.

a. Determine the offset distance from the tangent on the first quadrant point of the

spiral.

b. Compute the length of throw for the spiral curve

c. What is the maximum velocity that a car could pass thru the easement curve?

70. The central curve of an easement curve is on a 5° curve. Spiral easement curve has a

length of throw equal to 1.02m at the T.S

a. Compute the required length of the spiral curve.

b. Determine the velocity of the car passing thru this curve so that it will not exceed

the minimum centrifugal acceleration of 0.50m/sec.

 c. What is the length of the long tangent of a spiral easement curve if the distance

along the tangent up to S.C is 73.60m long

71. A car is approaching an easement curve having a rate of centrifugal acceleration of

0.5161 m/sec so as not to cause discomfort to the passengers. The length of a spiral curve

is 80m long.

a. Compute the velocity of the approaching car in kph.

b. Compute the required radius of the central curve of the easement curve to limit

the centrifugal acceleration.

c. Compute the length of the long tangent of the spiral curve if the distance along the

tangent from T.S to S.C is 79.30m long.

72. The spiral angle at the S.C of the spiral easement curve is equal to 11.46°, with a radius

of 200m for the central curve.

a. Compute the length of throw at the T.S.

b. Compute the length of the long tangent of the spiral easement curve if the distance

along the tangent from the T.S to S.C is 79.20m.

c. Compute the value of the centrifugal acceleration in m/sec.

73. The design speed of a car passing thru an easement curve is equal to 80kph. The radius of

the central curve of the spiral curve is equal to 260m long.

a. Compute the value of the rate of centrifugal acceleration in m/sec for this speed

b. Compute the length of the spiral curve based on the centrifugal acceleration

c. Compute for the length of the throw

74. The tangents of a spiral curve forms an angle of intersection of 25° at staion 2+058.

Design speed is 80km/hr. For a radius of a central curve of 300m and a length of spiral of

52.10m.

a. Find the stationing at the point where the spiral starts

b. Find the stationing of the start of central curve

c. Find the length of the central curve

75. A simple curve having a degree of curve equal to 4°30' has a central angle of 50°50'. It is

required to replace the simple curve to another circular curve by connecting a transition

curve (spiral) at each ends by maintaining the radius of old curve is moved away 5m from

the intersection point.

 a. Determine the central angle of the new circular curve.

b. Compute the tangent distance Ts of the curve spiral.

c. What is the maximum velocity that a car could pass thru the curve without

skidding.

76. A simple curve having a radius of 600m has an angle of intersection of its tangents equal

to 40°30'. This curve is to be replaced by one of smaller radius so as to admit a 100m

spiral at each end. The deviation of the new curve from the old curve at thier midpoint is

0.50m towards the intersection of the tangent.

a. Determine the radius of the central curve.

b. Determine its central angle.

c. If the stationing of the intersection of the tangents is 10+820.94, determine the

stationing of the T.S of the spiral curve.

77. As the transition curve are used to build up super elevation gradually, the radius of

curvature should increase gradually from infinity to that of the circular curve, so as to

enable convenient handling of the steering wheel to eliminate the shock due to the

increase in centrifugal force and the radius of the curvature should be inversely

proportional to the length such that the rate of change of centrifugal acceleration should

not cause discomfort to the driver. If a car approaches the easement curve at a speed

90kph and the permissible value of super elevation for the easement curve is 0.07.

a. Compute the centrifugal acceleration of the car, so that it will not give discomfort

to the driver.

b. Compute the radius of curvature of the easement curve for a length of transition

curve of 120m to limit the centrifugal acceleration.

c. Compute the lateral friction in the easement curve.

78. If a vehicle travelling along a tangent meets the circular arc, the full impact of

centrifugal side thrust is suddenly experienced, because of this the steering angle must be

changed instantaneously, otherwise the vehicle will not be able to follow the circular

path. Obviously no driver can be expected to keep up to such a situation at every curve

and the vehicle will be subjected to shock and the passengers subjected to sway. The

situation can be greatly improved by providing transition curves. If a car approaches the
transition curves at a rate of centrifugal acceleration of 0.50m/sec with a degree of curve

of 5’ on the central curve.

a. Compute the velocity of the car as it approaches the transition curve.

b. Compute the spiral angle of transition curve at the S.C.

c. Compute the length of the short tangent on the transition curve.