Roadway Design Manual: Horizontal Alignment

Section 4: Horizontal Alignment

Overview

In the design of highway alignment, it is necessary to establish the proper relation between design speed and curvature. The two basic elements of horizontal curves are Curve Radius and Superelevation.

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General Considerations for Horizontal Alignment

There are a number of general considerations which are important in attaining safe, smooth flowing, and aesthetically pleasing facilities. These practices as outlined below are particularly applicable to high-speed facilities.

Flatter than minimum curvature for a certain design speed should be used where possible, retaining the minimum guidelines for the most critical conditions.
Compound curves should be used with caution and should be avoided on mainlanes where conditions permit the use of flat simple curves. Where compound curves are used, the radius of the flatter curve should not be more than 50 percent greater than the radius of the sharper curve for rural and urban open highway conditions. For intersections or other turning roadways (such as loops, connections, and ramps), this percentage may be increased to 100 percent.
Alignment consistency should be sought. Sharp curves should not follow tangents or a series of flat curves. Sharp curves should be avoided on high, long fill areas.
Reverse curves on high-speed facilities should include an intervening tangent section of sufficient length to provide adequate superelevation transition between the curves.
Broken-back curves (two curves in the same direction connected with a short tangent) should normally not be used. This type of curve is unexpected by drivers and is not pleasing in appearance.
Horizontal alignment and its associated design speed should be consistent with other design features and topography. Coordination with vertical alignment is discussed in Combination of Vertical and Horizontal Alignment in Section 5.

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Curve Radius

The minimum radii of curves are important control values in designing for safe operation. Design guidance for curvature is shown in Table 2-3 and Table 2-4: Horizontal Curvature of Highways without Superelevation¹

Anchor: #BGBJCCFITable 2-3: Horizontal Curvature of High-Speed Highways and Connecting Roadways with Superelevation
(US Customary [based on emax = 8%])
Design Speed (mph)	Usual Min.^1,2Radius of Curve (ft)	Absolute Min.^1,3 Radius of Curve (ft)
45	755	600
50	960	760
55	1490	965
60	1985	1205
65	2445	1485
70	3025	1820
75	3330	2215
80	4025	2675
(Metric [based on emax = 8%])
Design Speed (km/h)	Usual Min.^1,2 Radius of Curve (m)	Absolute Min.^1,3Radius of Curve (m)
70	220	175
80	290	230
90	470	305
100	650	395
110	830	500
120	1000	665
130	1250	830
¹For other maximum superelevation rates refer to AASHTO’s A Policy on Geometric Design of Highways and Streets. ² Applies to new location construction. For 3R or reconstruction, existing curvature equal to or flatter than absolute minimum values may be retained unless accident history indicates flattening curvature. ³ Absolute minimum values should be used only where unusual design circumstances dictate.

Anchor: #i1063544Table 2-3: (continued): Horizontal Curvature of High-Speed Highways and Connecting Roadways with Superelevation
(US Customary [based on emax = 6%])
Design Speed (mph)	Usual Min.^1,2 Radius of Curve (ft)	Absolute Min.^1,3 Radius of Curve (ft)
45	830	660
50	1055	835
55	1645	1065
60	2210	1340
65	2735	1660
70	3405	2050
75	3775	2510
80	4605	3060
(Metric [based on emax = 6%])
Design Speed (km/h)	Usual Min.^1,2 Radius of Curve (m)	Absolute Min.^1,3Radius of Curve (m)
70	250	195
80	320	250
90	520	335
100	720	435
110	930	560
120	1140	755
130	1430	950
¹For other maximum superelevation rates refer to AASHTO’s A Policy on Geometric Design of Highways and Streets. ² Applies to new location construction. For 3R or reconstruction, existing curvature equal to or flatter than absolute minimum values may be retained unless accident history indicates flattening curvature. ³ Absolute minimum values should be used only where unusual design circumstances dictate.

Anchor: #BGBFHEDGTable 2-4: Horizontal Curvature of Highways without Superelevation¹
(US Customary)
Design Speed (mph)	Min. Radius (ft)
15	690
20	1220
25	1760
30	2410
35	3160
40	4010
45	4970
50	6030
55	7210
60	8500
65	9590
70	10750
75	12000
80	13340
(Metric)
Design Speed (km/h)	Min. Radius (m)
20	145
30	325
40	575
50	800
60	1100
70	1455
80	1800
90	2195
100	2685
110	3110
120	3650
130	4015
¹ Normal crown (2%) maintained (emax = 8%)

For high speed design conditions, the maximum deflection angle allowable without a horizontal curve is fifteen (15) minutes. For low speed design conditions, the maximum deflection angle allowable without a horizontal curve is thirty (30) minutes.

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Superelevation

As a vehicle traverses a horizontal curve, centrifugal force is counter-balanced by the vehicle weight component due to roadway superelevation and by the side friction between tires and surfacing as shown in the following equation:

e + f = V²/15R (US Customary)

Where:

e = superelevation rate, in decimal format
f = side friction factor
V = vehicle speed, mph
R = curve radius, feet

e + f = V²/127R (Metric)

Where:

e = superelevation rate, in decimal format
f = side friction factor
V = vehicle speed, km/h
R = curve radius, m

Superelevation transition is the general term denoting the change in cross slope from a normal crown section to the full superelevated section or vice versa. To meet the requirements of comfort and safety, the superelevation transition should be effected over a length adequate for the usual travel speeds. In general, the location of the transition in respect to the end of a simple (circular) curve should be such that two-thirds of the transition is outside the curve and one-third within the limits of the curve. This results in two-thirds of the full superelevation at the beginning of the curve. On curves which are spiraled, the transition usually is distributed over the length of the spiral curve. Care must be exercised in the transition, especially in curbed sections or on bridges, to avoid drainage problems and unsightly curb or bridge rail profiles.

Profiles of both gutters or pavement edges should be plotted to insure proper drainage and smoothness throughout transition sections, especially where these sections occur within vertical curvature of the profile grade line. Special care should be given to ensure that the zero cross slope in the superelevation transition does not occur at the flat portion of the crest or sag vertical curve. A plot of roadway contours can identify drainage problems in areas of superelevation transition.

A recommended and an alternate method for attaining superelevation is shown in Figure 2-1. Use of reverse parabolas as illustrated in the recommended method generally produces a gutter, pavement edge or bridge rail profile that is smooth, undistorted, and pleasing in appearance.

Figure 2-1. Methods for Attaining Superelevation. Click here to see a PDF of the image.

There are practical limits to the rate of superelevation. High rates create steering problems for drivers traveling at lower speeds, particularly during ice or snow conditions. On urban facilities, lower maximum superelevation rates may be employed since adjacent buildings, lower design speeds, and frequent intersections are limiting factors.

Although maximum superelevation is not commonly used on urban streets, if provided, maximum superelevation rates of 4 percent should be used. For urban freeways and all types of rural highways, maximum rates of 6 to 8 percent are generally used.

Superelevation on Low-Speed Facilities. Although superelevation is advantageous for traffic operations, various factors often combine to make its use impractical in many built-up areas. These factors include the following:

wide pavement areas
surface drainage considerations
frequency of cross streets and driveways
need to meet the grade of adjacent property
For this reason, horizontal curves on low-speed streets in urban areas are frequently designed without superelevation, and centrifugal force is counteracted solely with side friction.

shows the relationship of radius, superelevation rate, and design speed for low-speed urban street design. For example, for a curve with normal crown (2 percent cross slope each direction), the designer may enter Figure 2-2 given a curve radius of 350 ft [110 m] and determine that the related design speed is approximately:
34 mph [56 km/h] for positive crown condition
32 mph [52 km/h] for negative crown condition
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Figure 2-2. Relationship of Radius, Superelevation Rate, and Design Speed for Low-Speed Urban Street Design. Click here to see a PDF of the image.

Figure 2-2 should be used to evaluate existing conditions and may be used in design for constrained conditions, such as detours.

When superelevation is used on low-speed streets, Figure 2-2 should be used to determine design superelevation rate for specific curvature and design speed conditions. For US Customary units, given a design speed of 35 mph and a 350 ft radius curve, Figure 2-2 indicates an approximate superelevation rate of 3.5 percent. For Metric units, given a design speed of 50 km/h and a 80 m radius curve, Figure 2-2 indicates an approximate superelevation rate of 3.2 percent.

Length of superelevation transition on low-speed, two-lane streets with a normal crown and the axis of rotation about the centerline may be calculated using the following formula:

L = 47.2 (f)(V)/C (US Customary)

Where:

L = length of superelevation transition, ft
f = side friction factor
V = design speed, mph
C = rate of change of f, ft/sec³

L = 2.72(f)(V)/C (Metric)

Where:

L = length of superelevation transition, m
f = side friction factor
V = design speed, km/h
C = rate of change of f, m/sec³

Table 2-5 shows values of f, C, and L for two-lane roadways with the axis of rotation about the centerline. When the axis of rotation is about an outside edge of pavement, or for wider streets, increased lengths as permitted by conditions should be used. For example, where a two-lane pavement is to be rotated about the inside edge, the length of transition shown should be doubled. Also, for four- or six-lane pavements, all length values should be doubled or tripled, respectively.

Anchor: #i1063728Table 2-5: Minimum Radii and Superelevation Transition Lengths for Limiting Values of e and f for Low-Speed Urban Streets
(US Customary)
Design Speed (mph)	Max. e	Max. f	C	Min. R (ft)	Superelevation Transition Length¹, L (ft)
15	0.04	0.330	4.25	40	55
20	0.04	0.300	4.00	80	75
25	0.04	0.252	3.75	145	80
30	0.04	0.221	3.50	230	90
35	0.04	0.197	3.25	345	100
40	0.04	0.178	3.00	490	115
45	0.04	0.163	2.75	665	125

15	-0.02²	0.330	4.25	50	Not Required
20	-0.02²	0.300	4.00	90	Not Required
25	-0.02²	0.252	3.75	180	Not Required
30	-0.02²	0.221	3.50	300	Not Required
35	-0.02²	0.197	3.25	465	Not Required
40	-0.02²	0.178	3.00	675	Not Required
45	-0.02²	0.163	2.75	940	Not Required
¹ L based on two-lane roadway rotated about centerline. For rotation about a pavement edge, or for multilane streets, the design L is determined by multiplying the above tabulated L value times the number of lanes between the rotation axis and edge of pavement. Thus for 4 and 6 lane streets, with the axis of rotation about the centerline, the design L is double and triple, respectively, the tabulated L. ² Normal crown maintained.

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Table 2-5: Minimum Radii and Superelevation Transition Lengths for Limiting Values of e and f for Low-Speed Urban Streets
(Metric)
Design Speed (km/h)	Max. e	Max. f	C	Min. R (m)	Superelevation Transition Length¹, L (m)
20	0.04	0.350	1.25	10	15
30	0.04	0.312	1.20	20	20
40	0.04	0.252	1.15	45	25
50	0.04	0.214	1.10	80	25
60	0.04	0.186	1.05	125	30
70	0.04	0.163	1.00	190	30

20	-0.02²	0.350	1.25	10	Not Required
30	-0.02²	0.312	1.20	25	Not Required
40	-0.02²	0.252	1.15	55	Not Required
50	-0.02²	0.214	1.10	105	Not Required
60	-0.02²	0.186	1.05	175	Not Required
70	-0.02²	0.163	1.00	270	Not Required
¹ L based on two-lane roadway rotated about centerline. For rotation about a pavement edge, or for multilane streets, the design L is determined by multiplying the above tabulated L value times the number of lanes between the rotation axis and edge of pavement. Thus for 4 and 6 lane streets, with the axis of rotation about the centerline, the design L is double and triple, respectively, the tabulated L. ² Normal crown maintained.

Table 2-5 also shows minimum radii for a maximum superelevation of 4 percent and for normal crown. For curves with superelevation, it is possible to use this table to calculate the minimum desirable tangent length between two reverse curves of minimum radii. For curves with normal crown, transition length is not required.

Superelevation on High-Speed Facilities. Tables 2-6 and Table 2-7: Superelevation Rates for Horizontal Curves on High Speed Highways: Superelevation Rate, e (8%), for Design Speed of show superelevation rates (maximum 6 and 8 percent, respectively) for various design speeds and radii. These tables should be used for high-speed facilities such as rural highways and urban freeways.

Anchor: #i1249776Table 2-6: Superelevation Rates for Horizontal Curves on High-Speed Highways: Superelevation Rate, e (6%), for Design Speed of (US Customary)
Radius (ft)	15 mph	20 mph	25 mph	30 mph	35 mph	40 mph	45 mph	50 mph	55 mph	60 mph	65 mph	70 mph	75 mph	80 mph
23000	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC
20000	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC
17000	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC
14000	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC
12000	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	2.1
10000	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	2.1	2.3	2.5
8000	NC	NC	NC	NC	NC	NC	NC	NC	NC	RC	2.3	2.5	2.8	3.1
6000	NC	NC	NC	NC	NC	NC	NC	NC	2.2	2.6	2.9	3.2	3.6	4.0
5000	NC	NC	NC	NC	NC	NC	NC	2.2	2.6	3.0	3.4	3.7	4.2	4.7
4000	NC	NC	NC	NC	NC	NC	2.3	2.7	3.1	3.6	4.0	4.4	4.9	5.5
3500	NC	NC	NC	NC	NC	2.1	2.6	3.0	3.5	3.9	4.4	4.9	5.4	5.9
3000	NC	NC	NC	NC	NC	2.4	2.9	3.4	3.9	4.3	4.8	5.3	5.8	R_min= 3060ft
2500	NC	NC	NC	NC	2.3	2.8	3.3	3.8	4.3	4.8	5.3	5.8	R_min= 2510ft
2000	NC	NC	NC	2.2	2.8	3.3	3.8	4.3	4.9	5.4	5.8	R_min= 2050ft
1800	NC	NC	NC	2.4	3.0	3.6	4.1	4.6	5.1	5.6	6.0
1600	NC	NC	2.1	2.7	3.3	3.8	4.4	4.9	5.4	5.9	R_min= 1660ft
1400	NC	NC	2.3	2.9	3.6	4.1	4.7	5.2	5.7	6.0
1200	NC	NC	2.6	3.3	3.9	4.5	5.0	5.6	5.9	R_min= 1340ft
1000	NC	2.2	3.0	3.7	4.3	4.9	5.5	5.9	R_min= 1065ft
900	NC	2.4	3.2	3.9	4.5	5.1	5.7	6.0
800	NC	2.7	3.4	4.1	4.8	5.4	5.9	R_min = 835ft
700	NC	2.9	3.7	4.4	5.1	5.7	6.0
600	2.1	3.2	4.0	4.7	5.4	5.9	R_min= 660ft
500	2.4	3.6	4.3	5.1	5.7	R_min= 510ft
450	2.7	3.8	4.5	5.3	5.9
400	2.9	4.0	4.8	5.6	6.0
350	3.2	4.2	5.1	5.8	R_min= 380ft
300	3.5	4.5	5.4	6.0
250	3.8	4.8	5.7	R_min= 275ft
200	4.1	5.3	6.0
150	4.7	5.8	R_min= 185ft
100	5.5	R_min= 115ft
75	5.9
-	R_min= 65ft
NC = Normal Crown						RC = Reverse Crown			emax = 6%

Anchor: #i1284257Table 2-6 (continued): Superelevation Rates for Horizontal Curves on High-Speed Highways: Superelevation Rate, e (6%), for Design Speed of (Metric)
Radius (m)	20 km/h	30 km/h	40 km/h	50 km/h	60 km/h	70 km/h	80 km/h	90 km/h	100 km/h	110 km/h	120 km/h	130 km/h
7,000	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC
5,000	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC
3,000	NC	NC	NC	NC	NC	NC	NC	NC	NC	NC	2.3	2.5
2,500	NC	NC	NC	NC	NC	NC	NC	NC	RC	2.3	2.7	3.0
2,000	NC	NC	NC	NC	NC	NC	NC	2.1	2.5	2.8	3.3	3.7
1,500	NC	NC	NC	NC	NC	NC	2.2	2.7	3.1	3.6	4.2	4.7
1,400	NC	NC	NC	NC	NC	NC	2.4	2.8	3.3	3.8	4.4	5.0
1,300	NC	NC	NC	NC	NC	2.1	2.5	3.0	3.5	4.0	4.7	5.3
1,200	NC	NC	NC	NC	NC	2.2	2.7	3.2	3.7	4.2	5.0	5.6
1,000	NC	NC	NC	NC	2.1	2.6	3.1	3.6	4.2	4.8	5.6	6.0
900	NC	NC	NC	NC	2.3	2.8	3.4	3.9	4.5	5.1	5.8	R_min= 950m
800	NC	NC	NC	NC	2.5	3.1	3.6	4.2	4.9	5.4	6.0
700	NC	NC	NC	2.1	2.8	3.4	4.0	4.6	5.2	5.8	R_min= 755m
600	NC	NC	NC	2.4	3.1	3.8	4.3	5.0	5.6	6.0
500	NC	NC	2.1	2.8	3.5	4.2	4.8	5.4	5.9	R_min= 560m
400	NC	NC	2.5	3.3	4.0	4.7	5.3	5.9	R_min= 435m
300	NC	RC	3.1	3.9	4.6	5.4	5.9	R_min= 335m	-
250	NC	2.3	3.5	4.2	5.0	5.8	6.0	-
200	NC	2.8	3.9	4.7	5.5	6.0	R_min= 250m
175	NC	3.0	4.1	5.0	5.8	R_min= 195m
150	NC	3.3	4.4	5.3	6.0
140	NC	3.5	4.5	5.4	6.0
130	2.1	3.6	4.6	5.6	R_min= 135m
120	2.2	3.8	4.8	5.7
110	2.4	3.9	5.0	5.8
100	2.5	4.1	5.2	6.0
90	2.7	4.2	5.4	6.0
80	3.0	4.5	5.6	R_min= 90m
70	3.2	4.7	5.8	-	-	-	-	-	-	-	-	-
60	3.5	5.0	6.0	-	-	-	-	-	-	-	-	-
50	3.8	5.4	R_min= 55m	-	-	-	-	-	-	-	-	-
40	4.2	5.8	-	-	-	-	-	-	-	-	-	-
30	4.7	6.0	-	-	-	-	-	-	-	-	-	-
20	5.5	R_min= 30m	-	-	-	-	-	-	-	-	-	-
-	R_min= 15m	-	-	-	-	-	-	-	-	-	-	-
NC = Normal Crown					RC = Reverse Crown					emax = 6%

Anchor: #i1065227Table 2-7: Superelevation Rates for Horizontal Curves on High-Speed Highways: Superelevation Rate, e (8%), for Design Speed of(US Customary)
Radius (ft)	15 mph	20 mph	25 mph	30 mph	35 mph		40 mph	45 mph	50 mph	55 mph	60 mph	65 mph		70 mph	75 mph	80 mph
23000	NC	NC	NC	NC	NC		NC	NC	NC	NC	NC	NC		NC	NC	NC
20000	NC	NC	NC	NC	NC		NC	NC	NC	NC	NC	NC		NC	NC	NC
17000	NC	NC	NC	NC	NC		NC	NC	NC	NC	NC	NC		NC	NC	NC
14000	NC	NC	NC	NC	NC		NC	NC	NC	NC	NC	NC		NC	NC	NC
12000	NC	NC	NC	NC	NC		NC	NC	NC	NC	NC	NC		NC	NC	2.2
10000	NC	NC	NC	NC	NC		NC	NC	NC	NC	NC	NC		2.1	2.4	2.6
8000	NC	NC	NC	NC	NC		NC	NC	NC	NC	2.1	2.4		2.6	2.9	3.3
6000	NC	NC	NC	NC	NC		NC	NC	RC	2.4	2.7	3.1		3.4	3.8	4.3
5000	NC	NC	NC	NC	NC		NC	NC	2.4	2.8	3.2	3.6		4.1	4.5	5.1
4000	NC	NC	NC	NC	NC		RC	2.4	2.9	3.4	3.9	4.4		4.9	5.5	6.2
3500	NC	NC	NC	NC	NC		2.3	2.7	3.2	3.8	4.4	4.9		5.5	6.2	7.0
3000	NC	NC	NC	NC	2.1		2.6	3.1	3.7	4.3	5.0	5.6		6.3	7.0	7.8
2500	NC	NC	NC	NC	2.5		3.0	3.7	4.3	5.0	5.7	6.4		7.2	7.8	R_min= 2675ft
2000	NC	NC	NC	2.4	3.0		3.7	4.4	5.1	5.9	6.6	7.4		7.9	R_min= 2215ft	-
1800	NC	NC	NC	2.6	3.3		4.0	4.7	5.5	6.3	7.1	7.7		R_min= 1820ft	-	-
1600	NC	NC	2.2	2.9	3.6		4.4	5.2	5.9	6.7	7.5	8.0		-	-	-
1400	NC	NC	2.4	3.2	4.0		4.8	5.6	6.4	7.2	7.8	R_min= 1485ft		-	-	-
1200	NC	RC	2.8	3.6	4.5		5.4	6.2	7.0	7.7	R_min= 1205ft	-		-	-	-
1000	NC	2.4	3.3	4.2	5.1		6.0	6.8	7.6	8.0	-	-		-	-	-
900	NC	2.6	3.5	4.5	5.5		6.4	7.2	7.8	R_min= 965 ft	-	-		-	-	-
800	NC	2.9	3.9	4.9	5.9		6.8	7.6	8.0	-	-	-		-	-	-
700	NC	3.2	4.3	5.3	6.3		7.2	7.9	R_min= 760 ft	-	-	-		-	-	-
600	2.2	3.6	4.8	5.8	6.8		7.6	8.0	-	-	-	-		-	-	-
500	2.6	4.1	5.3	6.4	7.4		8.0	R_min= 600 ft	-	-	-	-		-	-	-
450	2.9	4.4	5.6	6.7	7.7		R_min= 465 ft	-	-	-	-	-		-	-	-
400	3.2	4.8	6.0	7.1	7.9		-	-	-	-	-	-		-	-	-
350	3.5	5.2	6.4	7.5	8.0		-	-	-	-	-	-		-	-	-
300	3.9	5.6	6.8	7.8	R_min= 350 ft		-	-	-	-	-	-		-	-	-
250	4.5	6.1	7.4	8.0	-		-	-	-	-	-	-		-	-	-
200	5.1	6.7	7.9	R_min= 250 ft	-		-	-	-	-	-	-		-	-	-
150	5.9	7.5	R_min= 170 ft	-	-		-	-	-	-	-	-		-	-	-
100	7.0	R_min= 105 ft	-	-	-		-	-	-	-	-	-		-	-	-
75	7.7	-	-	-	-		-	-	-	-	-	-		-	-	-
-	R_min= 60ft	-	-	-	-		-	-	-	-	-	-		-	-	-
NC = Normal Crown						RC = Reverse Crown							emax = 8%

Anchor: #BGBJDCAHTable 2-7: Superelevation Rates for Horizontal Curves on High-Speed Highways: Superelevation Rate, e (8%), for Design Speed of(Metric)
Radius (m)	20 km/h	30 km/h	40 km/h	50 km/h		60 km/h	70 km/h	80 km/h	90 km/h	100 km/h		110 km/h	120 km/h	130 km/h
7,000	NC	NC	NC	NC		NC	NC	NC	NC	NC		NC	NC	NC
5,000	NC	NC	NC	NC		NC	NC	NC	NC	NC		NC	NC	NC
3,000	NC	NC	NC	NC		NC	NC	NC	NC	NC		2.1	2.4	2.6
2,500	NC	NC	NC	NC		NC	NC	NC	NC	2.1		2.4	2.9	3.1
2,000	NC	NC	NC	NC		NC	NC	NC	2.2	2.6		3.0	3.5	3.9
1,500	NC	NC	NC	NC		NC	NC	2.4	2.8	3.4		3.9	4.6	5.1
1,400	NC	NC	NC	NC		NC	2.1	2.5	3.0	3.6		4.1	4.9	5.4
1,300	NC	NC	NC	NC		NC	2.2	2.7	3.2	3.8		4.4	5.2	5.8
1,200	NC	NC	NC	NC		NC	2.4	2.9	3.4	4.1		4.7	5.6	6.3
1,000	NC	NC	NC	NC		2.2	2.8	3.4	4.0	4.8		5.5	6.5	7.4
900	NC	NC	NC	NC		2.4	3.1	3.7	4.4	5.2		6.0	7.1	7.9
800	NC	NC	NC	NC		2.7	3.4	4.1	4.8	5.7		6.6	7.6	R_min= 830m
700	NC	NC	NC	2.2		3.0	3.8	4.5	5.3	6.3		7.2	8.0	-
600	NC	NC	NC	2.6		3.4	4.3	5.1	6.0	6.9		7.7	R_min= 665m	-
500	NC	NC	2.2	3.0		3.9	4.9	5.8	6.7	7.6		8.0	-	-
400	NC	NC	2.7	3.6		4.7	5.7	6.6	7.5	8.0		R_min= 500m	-	-
300	NC	2.1	3.4	4.5		5.6	6.7	7.6	R_min= 305m	R_min= 395m		-	-	-
250	NC	2.5	4.0	5.1		6.2	7.4	7.9	-	-		-	-	-
200	NC	3.0	4.6	5.8		7.0	7.9	R_min= 230m	-	-		-	-	-
175	NC	3.4	5.0	6.2		7.4	8.0	-	-	-		-	-	-
150	NC	3.8	5.4	6.7		7.8	R_min= 175m	-	-	-		-	-	-
140	RC	4.0	5.6	6.9		7.9	-	-	-	-		-	-	-
130	2.2	4.2	5.8	7.1		8.0	-	-	-	-		-	-	-
120	2.3	4.4	6.0	7.4		R_min= 125m	-	-	-	-		-	-	-
110	2.5	4.7	6.3	7.6		-	-	-	-	-		-	-	-
100	2.7	5.0	6.6	7.8		-	-	-	-	-		-	-	-
90	3.0	5.2	6.9	7.9		-	-	-	-	-		-	-	-
80	3.3	5.5	7.2	8.0		-	-	-	-	-		-	-	-
70	3.6	5.9	7.5	R_min=80m		-	-	-	-	-		-	-	-
60	4.1	6.4	7.8	-		-	-	-	-	-		-	-	-
50	4.6	6.9	8.0	-		-	-	-	-	-		-	-	-
40	5.2	7.5	R_min=50m	-		-	-	-	-	-		-	-	-
30	5.9	8.0	-	-		-	-	-	-	-		-	-	-
20	7.1	R_min= 30m	-	-		-	-	-	-	-		-	-	-
-	R_min= 10m	-	-	-		-	-	-	-	-		-	-	-
NC = Normal Crown					RC = Reverse Crown						emax = 8%

Desirable design values for length of superelevation transition on high-speed facilities are based on using a given maximum relative gradient between profiles of the edge of traveled way and the axis of rotation. Table 2-8 shows recommended maximum relative gradient values. Transition length on this basis is directly proportional to the total superelevation, which is the product of the lane width and the change in cross slope.

Anchor: #BGBCIFEDTable 2-8: Maximum Relative Gradient for Superelevation Transition
(US Customary)			(Metric)
Design Speed (mph)	Maximum Relative Gradient%1	Equivalent Maximum Relative Slope	Design Speed (km/h)	Maximum Relative Gradient%1	Equivalent Maximum Relative Slope
15	0.78	1:128	20	0.80	1:125
20	0.74	1:135	30	0.75	1:133
25	0.70	1:143	40	0.70	1:143
30	0.66	1:152	50	0.65	1:150
35	0.62	1:161	60	0.60	1:167
40	0.58	1:172	70	0.55	1:182
45	0.54	1:185	80	0.50	1:200
50	0.50	1:200	90	0.47	1:213
55	0.47	1:213	100	0.44	1:227
60	0.45	1:222	110	0.41	1:244
65	0.43	1:233	120	0.38	1:263
70	0.40	1:250	130	0.35	1:286
75	0.38	1:263
80	0.35	1:286
¹Maximum relative gradient for profile between edge of traveled way and axis of rotation.

Transition length, L, for a multilane highway can be calculated using the following formula:

L_CT = [(CS)(W)]/G (US Customary)

Where:

L_CT = calculated transition length (ft)
CS = percent change in cross slope of superelevated pavement,
W = distance between the axis of rotation and the edge of traveled way (ft),
G = maximum relative gradient ( Table 2-8: Maximum Relative Gradient for Superelevation Transition).

L_CT = [(CS)(W)]/G (Metric)

Where:

L_CT = calculated transition length (m)
CS = percent change in cross slope of superelevated pavement,
W = distance between the axis of rotation and the edge of traveled way (m),
G = maximum relative gradient (Table 2-8: Maximum Relative Gradient for Superelevation Transition)

There are certain transition lengths which should be provided, as a minimum, for reasons of general appearance and to avoid undesirably abrupt edge of pavement profiles. This transition length, L_AP, approximates the distance traveled in two (2) seconds at the design speed.

L_AP= 2.93 V_D (US Customary)

Where:

L_AP = the transition length for appearance and profiles (ft) and
V_D = design speed (mph)

L_AP= 0.56 V_D (Metric)

Where:

L_AP= the transition length for appearance and profiles (m) and
V_D = design speed (km/h)

To calculate the length of superelevation transition for any width pavement and superelevation rate, the designer should determine which pavement edge controls, and calculate both L_CT and L_AP. The greater of L_CT or L_AP should be used.

Example determinations of superelevation are shown in Figure 2-3.

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Figure 2-3. Determination of Length of Superelevation Transition. Click US Customary or Metric to see a PDF of the image.

Whenever the calculated “desirable” value for length of superelevation transition controls but is impractical to provide, the length used should be as near as practical to the calculated desirable value.

Whenever reverse curves are closely spaced and superelevation transition lengths overlap, L values should be adjusted to prorate change in cross slope and to insure that roadway cross slopes are in the proper direction for each horizontal curve. More detailed information regarding superelevation may be found in AASHTO's A Policy on Geometric Design of Highways and Streets.

Anchor: #i1086199

Sight Distance on Horizontal Curves

Where an object off the pavement, such as a bridge pier, bridge railing, median barrier, retaining wall, building, cut slope or natural growth restricts sight distance, the minimum radius of curvature is determined by the stopping sight distance.

The following equation applies only to the circular curves longer than the stopping sight distance for the pertinent design speed. For example, with a 50 mph [80 km/h] design speed and a curve with a 1150 ft [350 m] radius, a clear sight area with a middle ordinate of a approximately 20 ft [6.0 m] is needed for stopping sight distance.

M = middle ordinate (ft)
S = stopping sight distance (ft) and,
R = radius (ft)

Where:

M = middle ordinate (m)
S = stopping sight distance (m)
R = radius (m)

Figure 2-4 provides a graph illustrating the required offset where stopping sight distance is less than the length of curve (S<L).

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Figure 2-4. (US). Stopping Sight Distance on Horizontal Curves. Click US Customary or Metric to see a PDF of the image.

In cases where complex geometries or discontinuous objects cause sight obstructions, graphical methods may be useful in determining available sight distance and associated offset requirements. Graphical methods may also be used when the circular curve is shorter than the stopping sight distance.

To check horizontal sight distance on the inside of a curve graphically, sight lines equal to the required sight distance on horizontal curves should be reviewed to ensure that obstructions such as buildings, hedges, barrier railing, high ground, etc., do not restrict sight below that required in either direction