Surveying With Construction Applications, 7th Edition Chapter 11 Highway Curves

TYPES OF HIGWAGH CURVES 1. SIMPLE. The simple curve is an arc of a circle (view A, fig. 11-1). 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 together and curving in the same direction (view B, fig. 11-1). 3. 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. 11-1). 4. SPIRAL. The spiral is a curve that has a varying radius. It is used on railroads and most modern 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. 11-1). Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

11.1 Route survey Highway and railroad route are chosen only after a complete and detailed study of all possible locations. Planning and route selection involve the use of the aerial imagery, satellite imagery, ground surveys and maps. The selected route must satisfied all design requirements with minimal social, environmental and financial impact. Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

The proposed central line is laid out in a series of straight lines (tangents) beginning at 0+00 (metric) and continue to the route terminal point. Each time the route change direction, the deflection angle between the back tangent and forward tangent is measured and recorded. Existing detail that has an effect on highway such as lakes, streams, trees, structure, existing roads and railroads. This details is measuring by (GPS) ground survey, aerial survey or by the two method. In addition, the surveyors determine elevations along the proposed route. This elevations is used to determine the horizontal and vertical alignment. Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

11.2 Circular Curves: General Background The point at which the alignment changes from straight to circular is known as the beginning of curve (BC). The BC is located distance T (subtangent) from the point of tangent intersection (PI). The length of the circular curve (L) depends on the central angle and the value of the radius (R). The point at which the alignment changes from circular back to tangent is known as the end of curve (EC). Because the curve is symmetrical about the PI, the EC is also located distance T from the PI. Recall from geometry that the radius of a circle is perpendicular to the tangent at the point of tangency. Therefore, the radius is perpendicular to the back tangent at the BC and to forward tangent at the EC. The terms BC and EC are also referred to by some agencies as the point of curve (PC) and the point of tangency (PT), respectively, and by others as the tangent to curve (TC) and the curve to tangent (CT), respectively. Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

FIGURE 11-1 Circular curve terminology. © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. • All Rights Reserved. Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

11.3 Circular Curve Geometry Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

External: In triangle BC-O-PI, O-PI= R+E R/((R+E) )=cos ∆/2 Midordinate: OB/R=cos∆/2 OB =R cos∆/2 But : OB= R-M R-M= R cos∆/2 M=R(1-cos∆/2 ) External: In triangle BC-O-PI, O-PI= R+E R/((R+E) )=cos ∆/2 E=R(1/cos ∆/2-1 ) E=R(sec∆/2-1 ) Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

FIGURE 11-2 Geometry of the circle. © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. • All Rights Reserved. Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

Many highway agencies use the concept of degree of curve (D). FIGURE 11-3 Relationship between the degree of curve (D) and the circle. L/2πR=∆/360 L =2πR(∆/360) Many highway agencies use the concept of degree of curve (D). Degree of curve (D) is defined to be that central angle subtended by 100 ft arc. D and R: D/360=100/2πR D= 5729.58/R Arc: L/100=∆/D L=100(∆/D) 4 © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. • All Rights Reserved. Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

FIGURE 11-4 Sketch for Example 11-1 FIGURE 11-4 Sketch for Example 11-1. Note: To aid in comprehension, the magnitude of the ∆ angle has been exaggerated in this section. © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. • All Rights Reserved. Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

FIGURE 11-5 Sketch for Example 11-2. © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. • All Rights Reserved. Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

FIGURE 11-6 Sketch for Example 11-3. Refer to Fig.11.6 You given the following information: ∆= 11o 21' 35" PI at14+87.33 D=6o Calculate the station of BC & EC. © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. • All Rights Reserved. Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

Solution: R=5729.58/D R= 954.93 ft T= R tan ∆/2 = 954.93 tan 5.679861o= 94.98 ft L=100(∆/D) =100*11.359722/6 = 189.33 ft PI at 14+ 87.33 -T 94.98 BC= 13 + 92.35 +L 1 89.33 EC = 15+ 81.68 Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

FIGURE 11-7 Field location for deflection angles. See Example 11-2. © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. • All Rights Reserved. Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

FIGURE 11-8 Curve arcs and chords. © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. • All Rights Reserved. Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

Compound Circular Curves compound circular curves are curves formed when of two (usually) or more circular arcs between two main tangents turn in the same direction and join at common tangent points Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

Reverse Curves Reverse curves are seldom used in highway or railway alignment. The instantaneous change indirection occurring at the point reverse curve (PRC) would cause discomfort and safety problems for all but the slowest of speeds. The reverse curve is particularly pleasing to the eye and is used with great success on park roads, form paths, waterway channels Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

FIGURE 11-16 Reverse curves. (a) Nonparallel tangents FIGURE 11-16 Reverse curves. (a) Nonparallel tangents. (b) Parallel tangents. © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. • All Rights Reserved. Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

Vertical Curves Vertical curves are used in highway and street vertical alignment to provide a gradual change between two adjacent grade line . Some highway and municipal agencies introduce vertical curves at every change in grade-line slope, whereas other agencies introduce vertical curves into the alignment only when the net change in slope direction exceeds a specific value (e.g., 1.5 percent or 2 percent). Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

FIGURE 11-17 Vertical curve terminology (profile view shown). © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. • All Rights Reserved. Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

FIGURE 11-18 Types of vertical curves. (a) Sag curve. (b) Crest curve. © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. • All Rights Reserved. Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

Spiral curve Spiral is a curve with a uniformly changing radius. Spirals are used in highway and railroad alignment to overcome abrupt change in direction that occurs when the alignment changes from a tangent to a circular curve, and versa. The length of the spiral curve is also used for the transition from normally crowned pavement to fully superelevated ( banked ) pavement. Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

FIGURE 11-22 Spiral curves. © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. • All Rights Reserved. Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

superelevation (general background) If a vehicle travels too fast on a horizontal curve, the vehicle may either skid off the road or overturn. The factors that cause this phenomenon are based on the radius of curvature and the velocity of the vehicle: The sharper the curve and the higher the velocity, the larger will be the centrifugal force requirement. Two factors can be called on to help stabilize the radius and velocity factors: (1) side friction, which is always present to some degree between the vehicle tires and the pavement, and (2) superelevation (e), which is a banking of the pavement toward the center of the curve. Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

Surveying With Construction Applications, 7th Edition Barry F. Kavanagh