Chapter 4 - Elements of Design

4.2. Horizontal Alignment

4.2.2. Types of Curves

The following types of curves are discussed in this section:

• circular curves
• compound curves
• reverse curves
• spiral curves
• broken back curves
• curves with small deflection angles
• minimum length of horizontal curve
• alignment changes without horizontal curves

Circular Curves

GDOT typically uses the arc definition of the circular curve. Under this definition, the curve is defined by the degree of curve (Da), which is the central angle formed when two radial lines at the center of the curve intersect two points on the curve that are 100-ft. apart, measured along the arc of the curve.

Da = 18,000 / (Π * R)

Where:      Da = Degree of Curve (degrees)              

               R = Radius of Curve ( ft.)

                           

L = (100 * I) / Da

Where:            L = Length of Curve ( ft.)

                        Da = Degree of Curve (degrees)

                        I = Total deflection of curve (degrees)  

Compound Curves

Compound curves involve two horizontal curves of different radii sharing a common point for their point of tangent (PT) and point of curve (PC), respectively. For open highways, compound curves between connecting tangents shall be used only where existing topographic controls make a single simple curve impractical. The use of compound curves on two-way facilities shall be avoided. When compound curves are used, the radius of the flatter curve shall not exceed the radius of the sharper curve by more than 50% (a ratio of 1.5: 1).

Guidance regarding compound curves falls into two categories:

• Roadways (excluding ramps), one-way or two-way - The use of compound curves whose radii ratio exceeds 1.5:1 shall require a design variance.

  

• Ramps - A ratio as great as 1.75:1 may be used on one-way interchange ramps, where compound curves are more common. Ratios between 1.75:1 and the AASHTO 2.0:1 absolute maximum shall require a design variance. Ratios greater than 2.0:1 are strongly discouraged and shall require a design exception. The compound radii ratio criteria is only applicable when the curve radii decreases from one curve to the next in the direction of travel.

Reverse Curves

Any abrupt reversal in alignment shall be avoided. A reversal in alignment can be suitably designed by including a sufficient length of tangent between the two curves to provide adequate superelevation transitions. See Section 4.4. Combined Horizontal and Vertical Alignments for additional discussion of superelevation transition lengths.

The tangent distance between reverse curves shall be the distance (based on the appropriate gradient or ratio) to rotate from 2/3 of the full superelevation rate of the first curve to 2/3 of the full superelevation rate of the second curve.  For roadways with design speeds less than or equal to 45 mph, a minimum tangent of 100-ft. shall be provided between reverse curves, even if superelevation is not required.  

With or without superelevation, extreme physical constraints may dictate the use of a reverse curve with a 0-ft. length tangent (the PT of the first curve and the PC of the second curve are at the same location). In this case, the 0% cross slope point shall be placed at the shared PT/PC and use the best possible superelevation transition ratio. Where it is impractical to provide a tangent length capable of incorporating the superelevation runoff lengths and the tangent run out lengths of both superelevated curves, the 0% cross slope point shall be placed at a point derived from the best possible superelevation transition ratio between the two curves (not necessarily the center of the tangent). For an expanded discussion of superelevation refer to Section 4.4. Combined Horizontal and Vertical Alignments.

The goal of the designer shall be to provide the proper transition length on all projects.  However, in certain circumstances, a minimum tangent length between curves may be necessary.  For reverse curves on a roadway with a design speed less than or equal to 45 mph, the use of tangent lengths between 0-ft. and 100-ft. shall require a design variance.

On higher-speed roadways (design speeds greater than 45 mph), curves that do not require superelevation are so flat that no tangent between the curves is necessary. However, wherever practical, a 150-ft. minimum tangent shall be introduced between reverse curves. On higher-speed roadways with curves requiring superelevation, a tangent length suitable for accommodating the necessary superelevation transition shall be provided (see Section 4.4. Combined Horizontal and Vertical Alignments). For reverse curves on a roadway with a design speed greater than 45 mph, the use of tangent lengths less than those calculated by AASHTO procedures shall require a design exception.

Spiral Curves

Spiral curves are generally not utilized on Georgia roadways, except in special cases. For overlay or widening projects, existing spiral curves may remain. For roadways to be re-constructed, existing spiral curves are to be replaced with simple curves, unless existing property improvements or other controls make this impractical. Refer to the AASHTO Green Book Chapter 3, Elements of Design, for additional information on spiral curves.

Railroads typically utilize spiral curves at the beginning and end of each simple horizontal curve. A project involving a railroad crossing and possibly track relocation may require the use of spiral curves. For additional information related to the design of railroad alignments (including spiral curves), refer to the American Railway Engineering and Maintenance-of-Way Association (AREMA) Manual for Railway Engineering.  The current edition of this manual (in full or individual chapters) may be ordered online at: http://www.AREMA.org.

Broken-Back Curves

Successive curves in the same direction that are separated by a short tangent are known as broken-back curves. GDOT defines this short tangent as one with a length less than:

15*V    for design speeds less than or equal to 45 mph, or

30*V   for design speeds greater than 45 mph.

In these equations, V is the design speed in mph.

Broken-back curves are very undesirable from both an operational and an appearance standpoint. While it may not be feasible or practical in some situations to completely eliminate broken-back curves, every effort shall be made to avoid this type of alignment if possible by separating, combining, or compounding curves in the same direction.

Curves with Small Deflection Angles

A short horizontal curve with a small deflection angle (less than five degrees) may appear as a kink in the roadway. As a minimum, curves shall be at least 100-ft. in length for every one degree of central angle.

Minimum Length of Horizontal Curve

The minimum length of horizontal curve shall be in accordance with the following:

L = 15*V          

Where:              L = minimum curve length (ft.)

                               V = design speed (mph)

On high-speed controlled-access facilities that use large-radius curves, the minimum length of horizontal curve shall be in accordance with the following: 

L = 30*V          

Where:              L = minimum curve length (ft.)

                       V = design speed (mph) 

Alignment Changes without Horizontal Curves

There may be instances where existing constraints will make it impractical to utilize horizontal curves which maintain the minimum length criteria specified in the first seven cases cited in Section 4.2.1. Horizontal Alignment General Considerations. Right-of-way, cost, or environmental constraints could be prohibitive on widening, reconstruction, maintenance, safety, and 3R projects in both urban and rural settings.

When situations warrant, slight deflection angles may be introduced to (or maintained on) the roadways horizontal alignment. These angles shall be very slight so that they do not adversely affect safety or operations. Acceptable angles of deflection will depend on the design speed of the facility. Table 4.1. Maximum Horizontal Alignment Deflection without Use of a Curve lists the maximum angle of horizontal deflection for roadways in Georgia.

 

Table 4.1. Maximum Horizontal Alignment Deflection without Use of a Curve
Design Speed (MPH)	Maximum Angle of Horizontal Deflection (minutes)
15 20 25 30 35 40 45 50 55 60 65 70 75 80	120 90 60 45 40 35 30 25 20 18 16 14 12 10

 

 

 

 

 

 

 

 

 

 

 

 

The use of horizontal curves is preferable to deflection angles. Curves shall be utilized wherever practical. However, there are cases where small deflections are acceptable. For example, as shown in Table 4.1, an existing deflection angle up to 14 minutes (imperceptible to the eye) on an interstate widening project (design speed 70 mph) may be maintained.

At intersections with an all-way stop condition (with no foreseeable signalization) and some form of constraint, there may be a break in the roadway alignment as much as five degrees (at the centerline crossing in the intersection), provided intersection sight distance is maintained in all directions.