RELEVANT RESEARCH

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.

In practically all modem highways, the curves are circular curves; that is, curves that form circular arcs. 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. That means they must be large-radius curves.

In highway work, the curves needed for the location or improvement of small secondary roads may be worked out in the field. Usually, however, the horizontal curves are computed after the route has been selected, the field surveys have been done, and the survey base line and necessary topographic features have been plotted. In urban work, the curves of streets are designed as an integral part of the preliminary and final layouts, which are usually done on a topographic map. In highway work, the road itself is the end result and the purpose of the design. But in urban work, the streets and their curves are of secondary importance; the best use of the building sites is of primary importance.

The principal consideration in the design of a curve is the selection of the length of the radius or the degree of curvature (explained later). This selection is based on such considerations as the design speed of the highway and the sight distance as limited by head-lights or obstructions (fig. 11-1). Some typical radii you may encounter are 12,000 feet or longer on an interstate highway, 1,000 feet on a major thorough-fare in a city, 500 feet on an industrial access road, and 150 feet on a minor residential street.

Figure 11-1.—Lines of sight.

TYPES OF HORIZONTAL CURVES

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

1. SIMPLE. The simple curve is an arc of a circle (view A, fig. 11-2). The radius of the circle determines the sharpness or flatness of the curve.

2. COMPOUND. Frequently, the terrain will require the use of the compound curve. This curve normally consists of two simple curves joined togetherand curving in the same direction (view B, fig. 11-2).

3. REVERSE. A reverse curve consists of two simple curves joined together, but curving in opposite direction. For safety reasons, the use of this curveshould be avoided when possible (view C, fig. 11-2).

4. 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. 11-2).

ELEMENTS OF A HORIZONTAL CURVE

The elements of a circular curve are shown in figure 11-3. Each element is designated and explained as follows:

PI POINT OF INTERSECTION. The point of intersection is the point where the back and for-ward tangents intersect. Sometimes, the point of intersection is designated as V (vertex).

I INTERSECTING ANGLE. The intersecting angle is the deflection angle at the PI. Its value is either computed from the preliminary traverse angles or measured in the field.

A CENTRAL ANGLE. The central angle is the angle formed by two radii drawn from the

Figure 11-2.—Horizontal curves.

Figure 11-3.—Elements of a horizontal curve.

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.

R    RADIUS. The radius of the circle of which the curve is an arc, or segment. The radius is always perpendicular to back and forward tangents.

PC    POINT OF CURVATURE. The point of curva-ture is the point on the back tangent where the circular curve begins. It is sometimes designated asBC (beginning of curve) or TC (tangent to curve).

PT    POINT OF TANGENCY, 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).

POC    POINT OF CURVE. The point of curve is any point along the curve.

L     LENGTH OF CURVE. The length of curve is the distance from the PC to the PT, measured along the curve.

T    TANGENT DISTANCE. 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.

LC    LONG CHORD. 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 adja-cent stations (full, half, quarter, or one-tenth stations) along a curve.

E    EXTERNAL DISTANCE. 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.

M    MIDDLE ORDINATE. 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.

D    DEGREE OF CURVE. The degree of curve defines the sharpness or flatness of the curve.

DEGREE OF CURVATURE

The last of the elements listed above (degree of curve) deserves special attention. Curvature may be expressed by simply stating the length of the radius of the curve. That was done earlier in the chapter when typical radii for various roads were cited. Stating the radius is a common practice in land surveying and in the design of urban roads. For highway and railway work, however, curvature is expressed by the degree of curve. Two definitions are used for the degree of curve. These definitions are discussed in the following sections.

DISCSUSSION

In this field work entitled Laying a simple curve by transit or theodolite (the incremental chord and deflection angle method) we ask to lay a simple curve on the field.

Honestly our group don’t start right away cause we keep on arguing on what scaling will be used , after 30 mins of arguing we agreed on 1:12m scaling because its perfectly fit to our space. the 1st thing we do is to lay the BT (back tangent) to find the point of intersection or the vertex after we find the PI me lay the FT (forward tangent) after we locate the FT we start laying the chord by using the given data and using deflection angle. Our professor said the normal full chord length in the Philippines is 20m so the central angle of is equal to .

For the computation of the deflection angle you can you this formula:

for the 2nd deflection angle and repeat this procedure to find all the deflection angle.

CONCLUSION

In this field work entitled Laying a simple curve by transit or theodolite (the incremental chord and deflection angle method), we lay a simple curve using a theodolite as primary surveying instrument and by the use of the incremental chord and deflection angle.I therefore conclude that knowing the instrument well will help you finish your work easily and knowing the use of the deflection angle will help you lay a simple curve it a less percent error.

Overall, this fieldwork helps us to master the use of theodolite and fully understand the concept and theory about simple curve that we can you as a guide to our future fieldwork that concerns about simple curve.

GROUP NO. 5 CHIEF OF PARTY/LEADER: SAMSON, NORMAINE G.

MEMBERS

1. Sarmiento, Mark Angelo D. 4. 2. Sevilla, Quennie Haidee R. 5.3. Tantoco, Czarlette May J. 6.

FIELD WORK NO. 1LAYING OF A SIMPLE CURVE BY TRANSIT AND TAPE

(THE INCREMENTAL CHORD AND DEFLECTION ANGLE METHOD)

OBJECTIVE:

1. To be able to lay a simple curve by deflection angle.2. To master the skill in leveling, orienting and using the transit

effectiveness.

INSTRUMENTS:

1. 2 range poles2. chalk (for pavements)3. 50 meter tape4. theodolite

PROCEDURE:

1. The professor gives the ff. data:R= 143.24mBackward Tangent direction: 65°Forward Tangent direction: 125°Station of the Vertex: 10+074mAdopt Full chord length of 20m

2. The student compute the elements of the simple curve using the following formulas: if the azimuth of the backward and forward tangents are given, the intersection angle I can be solve using:

I = azimuth of the forward tangent - azimuth of the backward tangent

The tangent distance must be solved using:

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

The length of the curve (Lc) can be computed using (provided that I is converted to radians):

The long chord (C) can be solved using:

The station of PC can be computed using:

The station of PT can be found by:

The length of the first sub chord from PC, if PC is not exactly on a full station (otherwise C1 = a full chord length)

The length of the last sub chord from PT, if PT is not exactly on full station (otherwise C2 – a full chord length)

The value of the first deflection angle d1:

The value of the last deflection angle d2:

3. Set up the transit/theodolite over the vertex V, level the instrument and sight/locate PC and PT using the computed length of the tangent segments. Mark the position of PC and PT by chalk if on pavements.

4. Transfer the instrument over PC, level and start locating points of the curve using the following procedures:

a. Initialize the horizontal venier by setting to zero reading. Tighten the upper clamp and adjust it with the upper tangent screw.

b. Using the telescope, sight the vertex or PI with the vernier still at zero reading.

c. Tighten the lower clamp and focus it using the lower tangent screw.d. With the lower tangent screw already tight, loosen the upper clamp

and start to measure half the first deflection angle. Mark the direction with a range pole. Along this line, using a marking pin/chalk, mark point A measured with a tape the length of the first sub chord.

e. Locate the next point B, a full chord length from point A but this time intersecting the line sighted at an angle of half positioned over station PC.

f. Proceed in locating other points on the curve following step e until you cover all full chord stations on the entire length of the curve.

g. Measure the distance C2 and from the last full station on the curve and intersecting the line of sight with a deflection angle equal to half the intersection angle, mark the last point as PT.

5. Check the position of PT by determining the length of PC from PT and compare it to the computed total length of the chord of the simple curve.

FINAL DATA SHEETFIELD WORK 1 LAYING A SIMPLE CURVE BY TRANSIT AND TAPE

(THE INCREMENTAL CHORD AND DEFLECTION ANGLE METHOD)

DATE: MAY 12, 2010 GROUP NO.5TIME: 12:00 - 4:30 PM LOCATION:MIT

CampusWEATHER: Sunny PROFESSOR: Engr.

Cervantes

DATE SUPPLIED

R= 143.24mBackward Tangent direction: 65°Forward Tangent direction: 125°Station of the Vertex: 10+074mAdopt Full chord length of 20m

INCREMENTAL

CHORD

CENTRALINCREMENT

ALANGLE

DEFLECTION

ANGLE FROM BACK

TANGENT

- - -

0.725m 3.48 1.74

OCCUPIED

OBSERVE

D

STATION

9 + 931

9 + 940

-

1.67m 8 5.74

1.67m 8 9.74

1.67m 8 13.74

1.67m 8 17.74

1.67m 8 21.74

1.67m 8 25.74

1.17m 2.912 28.65

COMPUTED LENGTH OF THE CHORD: 143.24m

ACTUAL LENGTH OF THE CHORD: 142.98m

COMPUTATION

Given:

d=

P.T = PC + C

I=

9 + 960

9 + 980

10 + 000

10 + 040

10 + 020

10 + 060

10 + 074

For 1st central angle:

For last central angle;

PICTURE