Mapua Institute of TechnologyIntramuros, Manila

School of Civil, Environmental and Geological Engineering

Surveying DepartmentCE121F/B2

FIELDWORK 6

LAYING OF A REVERSE CURVE USING TRANSIT AND TAPE

Submitted by:Pascual, Ma. Nadine Stephanie D.

GROUP NO. 9 Chief of Party: Vasquez, Clifford Dale

Date of Fieldwork: August 28, 2014Date of Submission: September 16, 2014

Submitted to:Engr. Bienvenido Cervantes

Data:

STATIONINCREMENTAL

CHORD

CENTRAL INCREMENTAL

ANGLEDEFLECTION

ANGLEOCCUPIED OBSERVED

14+104.6 14+120 15.4m 1.53˚ 00˚46’

14+140 20m 2˚ 01˚46’

14+160 20m 2˚ 02˚46’

14+180 20m 2˚ 03˚46’

14+200 20m 2˚ 04˚46’

14+220 20m 2˚ 05˚46’

14+240 20m 2˚ 06˚46’

14+260 20m 2˚ 07˚46’

14+280 20m 2˚ 08˚46’

14+300 20m 2˚ 09˚46’

14+320 20m 2˚ 10˚46’

14+340 20m 2˚ 11˚46’

14+360 20m 2˚ 12˚46’

14+380 20m 2˚ 13˚46’

14+400 20m 2˚ 14˚46’

14+420 20m 2˚ 15˚46’

14+480 20m 2˚ 16˚46’

14+500 20m 2˚ 17˚46’

14+520 20m 2˚ 18˚46’

14+524.6 4.6m 0.45˚ 19˚13’

14+524.6 14+540 15.4m 2.3˚ 01˚09’

14+560 20m 3˚ 02˚39’

14+580 20m 3˚ 04˚09’

14+600 20m 3˚ 05˚39’

14+640 20m 3˚ 07˚09’

14+660 20m 3˚ 08˚39’

14+680 20m 3˚ 10˚09’

14+700 20m 3˚ 11˚39’

14+720 20m 3˚ 13˚09’

14+740 20m 3˚ 14˚39’

14+760 20m 3˚ 16˚09’

14+764.6 4.6m 0.68˚ 16˚30’

Discussion:

Our professor, Engr. Bienvenido Cervantes gathered us for the discussion of the things we will do for the fieldwork 6. Also, he gave us the data we needed for the fieldwork. He gave us an adviced to compute all the necessary data in beforehand so it wouldn’t be a problem when we start accomplishing the fieldwork. After these, we went to the Surveying Department to borrow the instruments we will be utilizing for Laying of a Reverse Curve using theodolite and tape. These instruments were range poles, 30 meter tape, and theodolite. After that, we proceed to the South Parking lot to start plotting the points and create the reverse curve. The concept of the reverse curve was discussed before the fieldwork. We used a different data for this fieldwork.

The first curve was just easy to lay because it is similar with the previous fieldwork but the second was challenging because

we had to think of a way where we can lay the other curve by using the PC. We sight for the PC and set the vernier to zero then rotate it until the angle reaches 180° + the second intersection angle divided by two. After that, we sight for the intermediate points until the second curve was completed. Necessary computations were made after the fieldwork.

Photos:

Laying out and plotting of the reverse curve.

Setting up and sighting of the stations.Research Works:

PROPERTIES OF CURVES

The center line of a road consists of series of straight lines interconnected by curves that are used to change the alignment, direction, or slope of the road. Those curves that change the alignment or direction are known as horizontal curves, and those that change the slope are vertical curves.

The initial design is usually based on a series of straight sections whose positions are defined largely by the topography of the area. The intersections of pairs of straights are then connected by horizontal curves. Curves can be listed under three main headings, as follows: (1) Horizontal curve (2) Vertical curves Horizontal Curves

When a highway changes horizontal direction, making the point where it changes direction a point of intersection between two straight lines is not feasible. The change in direction would be too abrupt for the safety of modem, high-speed vehicles. It is therefore necessary to interpose a curve between the straight lines. The straight lines of a road are called tangents because the lines are tangent to the curves used to change direction.

The smaller the radius of a circular curve, the sharper the

curve. For modern, high-speed highways, the curves must be flat, rather than sharp. The principal consideration in the design of a curve is the selection of the length of the radius or the degree of curvature. This selection is based on such considerations as the design speed of the highway and the sight distance as limited by headlights or obstructions.

The horizontal curve may be a simple circular curve or a compound curve. For a smooth transition between straight and a curve, a transition or easement curve is provided. The vertical curves are used to provide a smooth change in direction taking place in the vertical plane due to change of grade.

Types of Horizontal Curves There are four types of horizontal curves. They are described as follows:

A. Simple. The simple curve is an arc of a circle. The radius of the circle determines the sharpness or flatness of the curve. B. Compound. Frequently, the terrain will require the use of the compound curve. This curve normally consists of two simple curves joined together and curving in the same direction.

C. Reverse. A reverse curve consists of two simple curves joined together, but curving in opposite direction. For safety reasons, the use of this curve should be avoided when possible (view C, fig. 2).

D. Spiral. The spiral is a curve that has a varying radius. It is used on railroads and most modem highways. Its purpose is to provide a transition from the tangent to a simple curve or between simple curves in a compound curve (view D, fig. 2). Horizontal curve or Circular curves of constant radiusA simple circular curve shown in Fig., consists of simple arc of a circle of radius R connecting two straights lines, intersecting at PI, called the point of intersection (P.I.), having a deflection angle △. The distance E of the midpoint of the curve from P I is called the external distance. The arc length from T1 to T2 is the length of curve, and the chord T1T2 is called the long chord. The distance M between the midpoints of the curve and the long chord, is called the mid-ordinate. The distance T1 PI which is equal to the distance P IT2, is called the tangent length.

Elements of Horizontal Curves The elements of a circular curve are shown in figure 3. Each element is designated and explained as follows:

• Point of Intersection (PI). The point of intersection is the point where the back and forward tangents intersect. Sometimes, the point of intersection is designated as V (vertex). • Deflection Angle ( ). The central angle is the angle formed by two radii drawn from the center of the circle (O) to the PC and PT. The value of the central angle is equal to the I angle. Some authorities call both the intersecting angle and central angle either I or A. • Radius (R). The radius of the circle of which the curve is an arc, or segment. The radius is always perpendicular to back and forward tangents. • Point of Curvature (PC). The point of curvature is the point on the back tangent where the circular curve begins. It is sometimes designated as BC (beginning of curve) or TC (tangent to curve). • Point of Tangency (PT), The point of tangency is the point on the forward tangent where the curve ends. It is sometimes designated as EC (end of curve) or CT (curve to tangent). • Point of Curve. The point of curve is any point along the curve. Length of Curve (L) . The length of curve is the distance from the PC to the PT, measured along the curve.

• Tangent Distance (T). The tangent distance is the distance along the tangents from the PI to the PC or the PT. These distances are equal on a simple curve. • Long Cord (C). The long chord is the straight-line distance from the PC to the PT. Other types of chords are designated as follows: C The full-chord distance between adjacent stations (full, half, quarter, or one tenth stations) along a curve. • C1 The subchord distance between the PC and the first station on the curve. • C2 The subchord distance between the last station on the curve and the PT. • External Distance (E). The external distance (also called the external secant) is the distance from the PI to the midpoint of the curve. The external distance bisects the interior angle at the PI. • Middle Ordinate (M). The middle ordinate is the distance from the midpoint of the curve to the midpoint of the long chord. The extension of the middle ordinate bisects the central angle. • Degree of Curve. The degree of curve defines the sharpness or flatness of the curve.

Horizontal Curve Layout

(A) Rectangular Off sets From the Tangent /Coordinate/ Method This method is also suitable for short curve and, as in the previous method, no attempt is made to keep the chord of equal lengths.

(B) Polar Staking / Deflection Method/ Polar staking methods have become increasingly popular, especially with the availability of electronic tachometers. A simple method can be derived using the starting point of the circle Є is equal to the angle between the tangents and chord. For equal arc lengths the polar staking elements are determined with respect to the tangent. Vertical curves

Once the horizontal alignment has been determined, the vertical alignment of the section of highway can be addressed. Again, the vertical alignment is composed of a series of straight-line gradients connected by curves, normally parabolic in form. These vertical parabolic curves must therefore be provided at all changes in gradient. The curvature will be determined by the design speed being sufficient to provide adequate driver comfort with appropriate stopping sight distances provided.

Vertical curves should be simple in application and should result in a design that is safe and comfortable in operation, pleasing in appearance, and adequate for drainage. The major control for safe operation on crest vertical curves is the provision of ample sight distance for the design speed; while research has shown that vertical curves with limited sight distance do not necessarily experience safety problems, it is recommended that all vertical curves should be designed to provide at least stopping

sight distances. Wherever practical, more liberal stopping sight distances should be used. Furthermore, additional sight distance should be provided at decision points.

For driver comfort, the rate of change of grade should be kept within tolerable limits. This consideration is most important in sag vertical curves where gravitational and vertical centripetal forces act in opposite directions. Appearance also should be considered in designing vertical curves. A long curve has a more pleasing appearance than a short one; short vertical curves may give the appearance of a sudden break in the profile due to the effect of foreshortening.

The vertical offset from the tangent grade at any point along the curve is proportional of the vertical offset at the VPI, which is AL/800. The quantity L/A, termed “K”, is useful in determining the horizontal distance from the Vertical Point of Curvature (VPC) to the high point of Type I curves or to the low point of type III curves.

If the azimuth of the backward and the forward tangents are

given, the intersection angle I can be solved using:

I=azimuth of the forward tangent – azimuthof the backwardtangent

The tangent distance must be solve using:

T=R ∙ta n 12

The middle ordinate distance (M) can be computed using:

M=R ∙[1−co s 12 ]

The length of the curve (Lc) can be computed using:

Lc=πRI /180 ;when I is∈degreesLc=RI ;when I is∈radians

The station of PC can be computed using:

PC=PI−T

The station of PT can be found by:

PT =PI +Lc

The length of the first sub chord from PC, if PC is not exactly on a

full station (otherwise C1= a full chord length)

C1=First full stationon the curve−PC

The length of the last sub chord from PT, if PT is not exactly on a

full station (otherwise C2= a full chord length)

C 2=PT−last full stationon the curve

The value of the first deflection angle d1:

d 1=2 ∙sin−1 C12 R

The value of the last deflection angle d2:

d 2=2 ∙ sin−1 C 22 R

Incremental Chord and Tangent Offset Method

The tangent offset distance x1 must be solved using:

x1=c1∗co s( d 12 )

The tangent offset distance y1 must be solved using:

y 1=c 1∗sin ( d12 )

The tangent offset distances x2 must be solved using:

x2=c∗cos [d 1+D2 ]

The tangent offset distance y2 must be solved using:

y 2=c∗si n[ d1+D2 ]

The tangent offset distance x3, must be solved using:

x3=c∗cos [ D+D2 ]∨x3=c∗co s D

The tangent offset distance y3 must be solved using:

y 3=c∗si n [ D+D2 ]∨ y 3=c∗si n D

The tangent offset distance xn, must be solved using:

xn=c∗co s [d 2+D2 ]

The tangent offset distance yn, must be solved using:

yn=c∗si n[ d2+D2 ]

Conclusion:

From the fieldwork entitled Laying of a Reverse Curve using Theodolite and Tape, the following objectives had been achieved and accomplished. From laying of a simple and compound curve

by using the tape, we acquired the knowledge in laying a reverse curve with the use of the theodolite and tape. The theodolite is hard to set-up because we have to put all of the bubbles in the center for it to have a correct reading.

Aside from the first objective mentioned, we were able to master the skill in leveling, orienting and using the theodolite effectively. In addition to reviewing what we learned from Elementary Surveying, our Solid Mensuration skills were also improved as we analyzed different parts of the simple curve.

On the other hand, we can say that the fieldwork is a matter of computations. Hence, the most important thing is the practical application which in this case, the laying of the curve using the meter tape, two range poles, and the theodolite. From the data we have obtained, we can conclude that we have conducted the fieldwork well. This shows on the two near values of length of chord we have arrived from the actual and the computed. Moreover, the climax of this fieldwork is how we established the art of leading and following the designated and desired task on the group. In addition, responsibility is a very critical part of the performance in each member of the group.

With the things we learned, our minds worked harmoniously, thinking of the right way we can get more accurate results. These

field works are designed for students to utilize their minds and apply it in the simplest possible way that they can. Organization and proper knowledge of the activity is really a key to attaining precise outcomes.