After the total deflection has been decided, the surveyor determines the angles for each station on the curve.

Figure 17 illustrates this procedure. To solve a simple curve, the surveyor must know three parts. The third is the degree of curve, which is given in the project specifications or computed using one of the elements limited by the terrain (see section II). In the cubic spiral, the lengths have been considered as measured along the spiral curve itself, but measurements in the field must be taken by chords.

L is the distance around the arc for the arc definition, or the distance along the chords for the chord definition. It provides a transition from the tangent to a simple curve or between simple curves in a compound curve. Thus, L = 4.8 stations would be extended to 5 stations, and the value of r computed from r = Δ G/L. Grades G1 G2 are given as percentages of rise for 100 feet of horizontal distance. In this case, the surveyor locates the curve elements by using the following steps (figure 6). The tapemen measure the standard chord (25 feet) from the previously set station (16+50) while the instrument man keeps the head tapeman on line to set station 16+75. The remaining spiral stations are set by subtracting their deflection angles from 360 degrees and measuring 25 feet from the previously set station. The remaining stations are set by continuing to subtract their deflection angles from 360  degrees and setting the results on the horizontal circles. To solve a simple curve, the surveyor must know three elements. The surveyor normally determines elevation for vertical curves for the beginning (point of vertical curvature or PVC), the end (point of vertical tangency or PVT), and all full stations.

To obtain the required accuracy, the surveyor should convert values to five decimal places.

The external distance is the distance from the PI to the midpoint of the curve.

$\text{Sta PT} = \text{Sta } V_1 - T_1 + L_{c1} + L_{c2}$. In some cases, the PT position will be specified, but Ts must still be measured for the computations. Calculating Deflection Angles Following are the procedures for calculating the deflection angles and staking the spiral. Substituting into the length formula gives.

First and Second Differences. Special Cases.

For example, given a limiting tangent T ≤ 45 feet and I = 20°20’, the T for a l-degree curve from table A-5 is 1,027.6 and D = 1,027.6/45.00 = 22.836°.

0000000895 00000 n When it is impossible to stake the entire curve from the PC, the surveyor must use an adaptation of the above procedure.

Since the ends of the chords lie on the circumference of the curve, the surveyor defines the arc in the field.

To convert these values to the chord definition, the surveyor uses the values in table A-5. The station number simply becomes the distance from the beginning of the project. Compute T2, the tangent of the second curve. Recognizing this fact, in the A.R.E.A.

The surveyor indicates it as one of the stations on the preliminary traverse. Obtain I1, I2, and distance AB from the field data. Surveyors often have to use a compound curve because  of the terrain. Measure line y, the distance from the PI to the fixed point.

Set the remaining stations by using their deflections and chord distances as if computed from the PC or by computing the deflections in reverse order from the PT. If you are at an office or shared network, you can ask the network administrator to run a scan across the network looking for misconfigured or infected devices. Stake the first curve as described on pages 14 and 15. Since the degree of curve by arc definition is inversely proportional to the other functions of the curve, the values for a one-degree curve are divided by the degree of curve to obtain the element desired. practice, the surveyor should compute the value of Vm using both formulas, since working both provides a check on the Vm, the elevation of the PVC, and the elevation of the PVT. Unlike other online graph makers, Canva isn’t complicated or time-consuming. is brought into harmony with field practice. Table A-5 is based on this definition.

Measure Ts to locate the PT as the point where the curve is to join the forward tangent. trailer << /Size 32 /Info 7 0 R /Root 10 0 R /Prev 123834 /ID[<07841d4e69f26018db4456c9da036e7c><44768c50ece8a3f661ca982acbaedc4b>] >> startxref 0 %%EOF 10 0 obj << /Type /Catalog /Pages 6 0 R /Metadata 8 0 R /PageLabels 5 0 R >> endobj 30 0 obj << /S 48 /L 111 /Filter /FlateDecode /Length 31 0 R >> stream In  engineering  construction,  the  surveyor  often inserts a transition curve, also known as a spiral curve, between a circular curve  and  the  tangent  to  that curve. C = 2R sin (∆/2) = 2 x 1000 x sin 8o 19' = 289.29 ft. M=R{ 1 - Cos (∆/2)} = 1000(l - cos 8o 19') = 10.52'.

Continue along the forward tangent from PI a distance T2, and set PT2. 0000002247 00000 n The first and second differences are determined as a check. For example, 0+00 indicates the beginning of  the  project. When this happens, they should form a pattern.

Check the location of PI1 and PI2 by either measuring the distance between the two PIs and comparing the measured distance to the computed length of line AB, or by placing the instrument at PI1, sighting the PI, and laying off I1.

From table 1, when D = 4° and V = 60 mph, the value for Ls is 250 feet.

Compute D2 according to the formulas on pages 11 through 13. In fig. The PC and PT are located by measuring off L1and L2. Angle dp is the angle at the center of the curve between point P and the PT, which is equal to two times the difference between the deflection at P and one half of I. Sight the TS with the instrument telescope in the reverse position.

The angle to the PT is measured if the PT can be seen.

Compound Curve between Successive PIs. Select one of the stations (for example, “P”) on the curve, so that a line PQ, parallel to the tangent line AV, will clear the obstacle at the PC. The point of tangency is the end of the curve. They are sometimes used on canals, but only with extreme caution, since they make the canal difficult to navigate and contribute to erosion.

Point of Intersection (PI) The point of intersection marks the point where the back and forward tangents intersect. The angle should equal one half of the I angle if the TS and ST are located properly. The larger the radius, the “flatter” the curve.

For example, a 300-foot curve could not be staked at 100- foot intervals but could be staked at 10-, 25-, 30-, 50-, or 75-foot intervals. Two different circles are involved in comparing two curves with the same degree of curve. Since the total of the deflection angles should be one half of the I angle, a problem arises when the I angle contains an odd number of minutes and the instrument used is a one- minute instrument. This subchord will be 16,33 feet.

Chord Definition. Using a chord 30.48 meters long, the surveyor computes R by the formula. The resulting line-of-sight should intercept PI2.

.

Measure p, the perpendicular distance between tangents.

Follow the steps for inaccessible PC to set lines PQ and QS.

.

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