When using the “backing in method,” the surveyor sets approximately one half the curve stations from the PC and the remainder from the PT. Two procedures for staking compound curves are described. It is the beginning of curve. The long chord is the chord from the PC to the PT. The surveyor may also use the values from table A-5 to compute the value of D. This is done by dividing the tabulated value of tangent, external, or middle ordinate for a l-degree curve by the given value of the limiting factor. Care must be taken when staking a curve in the field. The length of curve is the distance from the PC to the  PT measured along the curve. Another way to prevent getting this page in the future is to use Privacy Pass. The instrument should read 0° 00’ if the PC is sighted. In order to achieve a smooth change of direction when laying out vertical curves, the grade must be brought up through a series of elevations. The PC and PT are located by measuring off L1and L2. 0000006166 00000 n Arc definition. Occupy the PT, and sight the PI with one half of the I angle on the horizontal circle. (See figure 11.). Technically, the formulas for the arc definitions are not exact for the chord definition. Simple Curves Terminologies in Simple Curve. This gives the corrections to be applied if the curve was computed by the arc definition. Recognizing this fact, in the A.R.E.A. Basically, the two curves coincide up to the point where Δ = 15 degrees. This may also be done by tri-angulation when the PI is inaccessible. The point of curvature is the point where the circular curve begins. As the radius and length of curve increases, the tape becomes impractical, and the surveyor must use other methods. The surveyor may do this by field measurements or by scaling the distance and angle from the plan and profile sheet. Sight that station with the instruments telescope in the reverse position. At times, the surveyor may desire additional points, but this will depend on construction requirements. The tangent distance is the distance along the tangents from the PI to the PC or PT. Although this procedure has been set up as a method to avoid obstructions, it is widely used for laying out curves. The last station set before the PT should be C2 (16.33 feet from the PT), and its deflection should equal the angle measured in (1) above plus the last deflection, d2 (1° 14’). The same equation    is used to compute the length of a spiral between the  arcs of a compound curve. In some cases, the PT position will be specified, but Ts must still be measured for the computations. Solution- The domain of x lies n the first quadrant only. Any curve which does not cross itself is called as a Simple curve.

In this step, they are rounded off to the smallest reading of the instrument to be used in the field. Note that this reduces the rate of change. Depending upon the terrain and the needs of the project foremen, the surveyor may stake out the curve with shorter or longer chords than recommended.

The surveyor must use different formulas for railroad and airfield design. 10-chord spiral, when Δ does not exeed 45 degrees, are given on pages 28 and 29.

This may be accomplished as follows (figure 10): In some cases, the surveyor may have to use elements other than the radius as the limiting factor in determining the size of the curve. Stake the second curve in the same manner as the first. lie on the same side of their common tangent, and connect to form a continuous arc. The following steps explain the laying out of a compound curve between successive tangents. 0000001469 00000 n The  external  distance  bisects the interior angle at the PI. Table A-6 lists the tangent, external distance corrections (chord definition) for various angles of intersection and degrees of curve. This value varies as the square of the distance from the PVC or PVT and is computed using the formula: A parabolic curve presents a mirror image. The angle should equal one half of the I angle if the TS and ST are located properly. Compound Curves. The angle should equal 1° 40’ if the CS is located properly.

Continue along the forward tangent from PI a distance T2, and set PT2. If this happens, the surveyor must  determine  the degree of curve from the limiting factor. The larger the radius, the “flatter” the curve. 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. Compound Curve between Successive PIs. The remaining circular arc stations are set by subtracting their deflection angles from 360 degrees and measuring the corresponding chord distance from the previously set station.

By studying this course the surveyor learns to locate points using angles and distances. Similarly, there will be a subchord at the end of the curve from station 19+25 to the PT. Some engineers prefer to use a value of 5,730 feet for the radius of a l-degree curve, and the arc definition formulas. They are described as follows, and their abbreviations are given in parentheses.

With the instrument at the PI, the instrumentman sights on the preceding PI and keeps the head tapeman on line while the tangent distance is measured. A compound curve consists of two (or more) circular curves between two main tangents joined at point of compound curve (PCC).Curve at PC is designated as 1 (R 1, L 1, T 1, etc) and curve at PT is designated as 2 (R 2, L 2, T 2, etc). It should be noted that for a given intersecting angle  or central angle, when using the arc definition, all the elements of the curve are inversely proportioned to the degree of curve. 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. 0000066579 00000 n Since their tangent lengths vary, compound curves fit the topography much better than simple curves. Rotate the telescope until 0° 00’ is read on the horizontal circle. The deflection angles for points 6, 7, 8, 9, and 10, with the instrument at point 5, are calculated with the use of table 2. The second is where the curve is  to be laid in between two successive tangents on the preliminary traverse. The surveyor should not waste too much time on preliminary work. The length of the chords varies with the degree of curve. However, the I angle still exists as in a simple curve. Table 2 is read as follows: with the instrument at any point, coefficients are obtained which, when multiplied by a1, give the deflection angles to the other points of the spiral. If the limiting factor is ≤ the D is rounded to the nearest ½ degree. Locate the PRC and measure m1 and m2. The external distance is the distance from the PI to the midpoint of the curve. This gives a tangent distance of 293.94 feet and an external distance of 99.79 feet for the chord definition. H�b`�zV�rA ��� �, �030�3�3. The extension of the middle ordinate bisects the central angle. Reverse curves are useful when laying out such things as pipelines, flumes, and levees. However, when a one-minute instrument is used to stake the curve, the surveyor may use them for either definition. Stake out as many stations from the PC as possible. There’s no learning curve – you’ll get a beautiful graph or diagram in minutes, turning raw data into something that’s both visual and easy to understand. For permissions beyond …

For example, the surveyor needs a reverse curve to connect two parallel tangents. Given the stationing of V1 The instrument is set up at the PC with the horizontal circle at 0°00’ on the PI. The resulting line-of-sight should intercept PI2. There are two definitions commonly in use for degree of curve, the arc definition and the chord definition. Once the length of curve is determined, the surveyor selects an appropriate station interval (SI). 0000005803 00000 n 0000036930 00000 n E = R {sec(∆/2) - 1} = 1000(sec 8o19') = 10.63 ft A common mistake made by students first studying circular curves to determine the station of the EC by adding the T distance to the PI. Set an offset PC at point Y by measuring from point Q toward point P a distance equal to the station of the PC minus station S. To set the PC after the obstacle has been removed, place the instrument at point Y, backsight point Q, lay off a 90-degree angle and a distance from Y to the PC equal to line PW and QS. Question: Calculate the area under the curve $${ y = \frac{1}{x^2}}$$ in the domain x = 1 to x = 2. Figure 2 shows the elements of a simple curve.

Therefore, the surveyor should compute to the nearest 0.5 degree. 0000063697 00000 n When unequal plus and minus tangent grades are encountered, the high or low point will fall on the side of the curve that has the flatter gradient. Road Curves to Right. Table A-5 is based on this definition. If the surveyor desires to place a stake at station 18+50,  a correction must be applied to the chords, since the distance from 18+00 through 18+50 to 19+00 is greater than the chord from 18+00 to 19+00.

Some of the examples of open curves are as follows. The surveyor can simplify the computation of simple curves by using tables.

The resulting line-of-sight should intercept PT2. This subchord will be 16,33 feet. The curve that is solved on page 6 had an I angle and degree of curve whose values were whole degrees.

The values are the same  as  those used to demonstrate the solution of a simple curve. The spiral is a curve with varying radius used on railroads and somemodern highways. The instrumentman now sights along the forward tangent to measure and set the ST. Set up the instrument at the TS, pointing on the PI, with 0°00’ on the horizontal circle. Grades G1 G2 are given as percentages of rise for 100 feet of horizontal distance. The surveyor either computes its value from the preliminary traverse station angles or measures it in the field. Surveyors often have to use a compound curve because  of the terrain. The spiral of the American Railway Engineering Association, known as the A.R.E.A.

These are usually the tangent T, external E, or middle ordinate M. When any limiting factor is given, it will usually be presented in the form of T equals some value x, T ≥ x or T ≤ x. Using these relationships, the deflection angles for the spirals and the circular arc are computed for the example spiral curve.

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