Section 4: Horizontal Alignment
Anchor: #i1085865Overview
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 Rate.
Anchor: #i1085879General 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 highspeed facilities.
 Anchor: #FSYKGLYS
 Flatter than minimum curvature for a certain design speed should be used where possible, retaining the minimum guidelines for the most critical conditions. Anchor: #YEADLJWD
 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. Anchor: #ROSYVIDA
 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. Anchor: #OWCOWYFM
 Reverse curves on highspeed facilities should include an intervening tangent section of sufficient length to provide adequate superelevation transition between the curves. Anchor: #POVWPCYC
 Brokenback 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. Anchor: #ASEBJQWT
 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, Vertical Alignment.
Curve Radius
The minimum radii of curves are important control values in designing for safe operation. Design guidance for high speed or nonurban curvature is shown in Table 23 and Table 24; with and without superelevation respectively.
Design Speed (mph) 
Usual Min.^{1,2 }Radius of Curve (ft) 
Absolute Min.^{1,3} Radius of Curve (ft) 
[based on emax = 6%] 

45 
810 
643 
50 
1050 
833 
55 
1635 
1060 
60 
2195 
1330 
65 
2740 
1660 
70 
3390 
2040 
75 
3750 
2500 
80 
4575 
3050 
[based on emax = 8%] 

45 
740 
587 
50 
955 
758 
55 
1480 
960 
60 
1980 
1200 
65 
2445 
1480 
70 
3005 
1810 
75 
3315 
2210 
80 
4005 
2670 
^{1}For 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 crash history indicates flattening curvature. ^{3} Absolute minimum values should be used only where unusual design circumstances dictate. 
Design Speed (mph) 
6% Min. Radius (ft) 
8% Min. Radius (ft)^{} 

15 
868 
932 
20 
1580 
1640 
25 
2290 
2370 
30 
3130 
3240 
35 
4100 
4260 
40 
5230 
5410 
45 
6480 
6710 
50 
7870 
8150 
55 
9410 
9720 
60 
11100 
11500 
65 
12600 
12900 
70 
14100 
14500 
75 
15700 
16100 
80 
17400 
17800 
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.
Anchor: #BGBIIDDDSuperelevation Rate
As a vehicle traverses a horizontal curve, centrifugal force is counterbalanced 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 = V^{2}/15R (US Customary)
Where:
e = superelevation rate, in decimal format
f = side friction factor
V = vehicle speed, mph
R = curve radius, feet
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 LowSpeed Facilities. Although superelevation is advantageous for traffic operations, various factors often combine to make its use impractical in many builtup areas. These factors include the following:
 Anchor: #DSGPSHCA
 Wide pavement areas Anchor: #WIQELDUX
 Surface drainage considerations Anchor: #IUPMCXBW
 Frequency of cross streets and driveways, and Anchor: #CXSBTRJH
 Need to meet the grade of adjacent property.
For these reasons, horizontal curves on lowspeed streets in urban areas are frequently designed without superelevation, and centrifugal force is counteracted solely with side friction.
Table 25 shows the relationship of radius, superelevation rate, and design speed for lowspeed urban street design. For example, for a curve with normal crown (2 percent cross slope each direction), the designer may enter Table 25 with a given curve radius of 400 ft [110 m] and determine that through interpolation, the related design speed is approximately:
 Anchor: #AQNODTJD
 35 mph for positive crown condition, and Anchor: #IDUYWGMT
 32 mph for negative crown condition.
Table 25 should be used to evaluate existing conditions and may be used in design for constrained conditions, such as detours.
When superelevation is used on lowspeed streets, Table 25 should be used to determine design superelevation rate for specific curvature and design speed conditions. Given a design speed of 35 mph and a 400 ft radius curve, Table 25 indicates an approximate superelevation rate of 2.4 percent.
e(%) 
V = 15 mph R (ft) 
V = 20 mph R (ft) 
V = 25 mph R (ft) 
V = 30 mph R (ft) 
V = 35 mph R (ft) 
V = 40 mph R (ft) 
V = 45 mph R (ft) 

4.0 
54 
116 
219 
375 
583 
889 
1227 
3.0 
52 
111 
208 
353 
544 
821 
1125 
2.8 
51 
110 
206 
349 
537 
808 
1107 
2.6 
51 
109 
204 
345 
530 
796 
1089 
2.4 
51 
108 
202 
341 
524 
784 
1071 
2.2 
50 
108 
200 
337 
517 
773 
1055 
2.0 
50 
107 
198 
333 
510 
762 
1039 
1.5 
49 
105 
194 
324 
495 
736 
1000 
0 
47 
99 
181 
300 
454 
667 
900 
1.5 
45 
94 
170 
279 
419 
610 
818 
2.0 
44 
92 
167 
273 
408 
593 
794 
2.2 
44 
91 
165 
270 
404 
586 
785 
2.4 
44 
91 
164 
268 
400 
580 
776 
2.6 
43 
90 
163 
265 
396 
573 
767 
2.8 
43 
89 
161 
263 
393 
567 
758 
3.0 
43 
89 
160 
261 
389 
561 
750 
3.2 
43 
88 
159 
259 
385 
556 
742 
3.4 
42 
88 
158 
256 
382 
550 
734 
3.6 
42 
87 
157 
254 
378 
544 
726 
3.8 
42 
87 
155 
252 
375 
539 
718 
4.0 
42 
86 
154 
250 
371 
533 
711 
Notes:

Superelevation Rate on HighSpeed Facilities. Tables 26 and 27 show superelevation rates (maximum 6 and 8 percent, respectively) for various design speeds and radii. These tables should be used for highspeed facilities such as rural highways and urban freeways.
e (%) 
V_{d}= 15 mph R (ft) 
V_{d}= 20 mph R (ft) 
V_{d}= 25 mph R (ft) 
V_{d}= 30 mph R (ft) 
V_{d}= 35 mph R (ft) 
V_{d}= 40 mph R (ft) 
V_{d}= 45 mph R (ft) 
V_{d}= 50 mph R (ft) 
V_{d}= 55 mph R (ft) 
V_{d}= 60 mph R (ft) 
V_{d}= 65 mph R (ft) 
V_{d}= 70 mph R (ft) 
V_{d}= 75 mph R (ft) 
V_{d}= 80 mph R (ft) 

2.0 
614 
1120 
1630 
2240 
2950 
3770 
4680 
5700 
6820 
8060 
9130 
10300 
11500 
12900 
2.2 
543 
991 
1450 
2000 
2630 
3370 
4190 
5100 
6110 
7230 
8200 
9240 
10400 
11600 
2.4 
482 
884 
1300 
1790 
2360 
3030 
3770 
4600 
5520 
6540 
7430 
8380 
9420 
10600 
2.6 
430 
791 
1170 
1610 
2130 
2740 
3420 
4170 
5020 
5950 
6770 
7660 
8620 
9670 
2.8 
384 
709 
1050 
1460 
1930 
2490 
3110 
3800 
4580 
5440 
6200 
7030 
7930 
8910 
3.0 
341 
635 
944 
1320 
1760 
2270 
2840 
3480 
4200 
4990 
5710 
6490 
7330 
8260 
3.2 
300 
566 
850 
1200 
1600 
2080 
2600 
3200 
3860 
4600 
5280 
6010 
6810 
7680 
3.4 
256 
498 
761 
1080 
1460 
1900 
2390 
2940 
3560 
4250 
4890 
5580 
6340 
7180 
3.6 
209 
422 
673 
972 
1320 
1740 
2190 
2710 
3290 
3940 
4540 
5210 
5930 
6720 
3.8 
176 
358 
583 
864 
1190 
1590 
2010 
2490 
3040 
3650 
4230 
4860 
5560 
6320 
4.0 
151 
309 
511 
766 
1070 
1440 
1840 
2300 
2810 
3390 
3950 
4550 
5220 
5950 
4.2 
131 
270 
452 
684 
960 
1310 
1680 
2110 
2590 
3140 
3680 
4270 
4910 
5620 
4.4 
116 
238 
402 
615 
868 
1190 
1540 
1940 
2400 
2920 
3440 
4010 
4630 
5320 
4.6 
102 
212 
360 
555 
788 
1090 
1410 
1780 
2210 
2710 
3220 
3770 
4380 
5040 
4.8 
91 
189 
324 
502 
718 
995 
1300 
1640 
2050 
2510 
3000 
3550 
4140 
4790 
5.0 
82 
169 
292 
456 
654 
911 
1190 
1510 
1890 
2330 
2800 
3330 
3910 
4550 
5.2 
73 
152 
264 
413 
595 
833 
1090 
1390 
1750 
2160 
2610 
3120 
3690 
4320 
5.4 
65 
136 
237 
373 
540 
759 
995 
1280 
1610 
1990 
2420 
2910 
3460 
4090 
5.6 
58 
121 
212 
335 
487 
687 
903 
1160 
1470 
1830 
2230 
2700 
3230 
3840 
5.8 
51 
106 
186 
296 
431 
611 
806 
1040 
1320 
1650 
2020 
2460 
2970 
3560 
6.0 
39 
81 
144 
231 
340 
485 
643 
833 
1060 
1330 
1660 
2040 
2500 
3050 
e (%) 
V_{d}= 15mph R(ft) 
V_{d}= 20mph R(ft) 
V_{d}= 25mph R(ft) 
V_{d}= 30mph R(ft) 
V_{d}= 35mph R(ft) 
V_{d}= 40mph R(ft) 
V_{d}= 45mph R(ft) 
V_{d}= 50mph R(ft) 
V_{d}= 55mph R(ft) 
V_{d}= 60mph R(ft) 
V_{d}= 65mph R(ft) 
V_{d}= 70mph R(ft) 
V_{d}= 75mph R(ft) 
V_{d}= 80mph R(ft) 

2.0 
676 
1190 
1720 
2370 
3120 
3970 
4930 
5990 
7150 
8440 
9510 
10700 
12000 
13300 
2.2 
605 
1070 
1550 
2130 
2800 
3570 
4440 
5400 
6450 
7620 
8600 
9660 
10800 
12000 
2.4 
546 
959 
1400 
1930 
2540 
3240 
4030 
4910 
5870 
6930 
7830 
8810 
9850 
11000 
2.6 
496 
872 
1280 
1760 
2320 
2960 
3690 
4490 
5370 
6350 
7180 
8090 
9050 
10100 
2.8 
453 
796 
1170 
1610 
2130 
2720 
3390 
4130 
4950 
5850 
6630 
7470 
8370 
9340 
3.0 
415 
730 
1070 
1480 
1960 
2510 
3130 
3820 
4580 
5420 
6140 
6930 
7780 
8700 
3.2 
382 
672 
985 
1370 
1820 
2330 
2900 
3550 
4250 
5040 
5720 
6460 
7260 
8130 
3.4 
352 
620 
911 
1270 
1690 
2170 
2700 
3300 
3970 
4700 
5350 
6050 
6800 
7620 
3.6 
324 
572 
845 
1180 
1570 
2020 
2520 
3090 
3710 
4400 
5010 
5680 
6400 
7180 
3.8 
300 
530 
784 
1100 
1470 
1890 
2360 
2890 
3480 
4140 
4710 
5350 
6030 
6780 
4.0 
277 
490 
729 
1030 
1370 
1770 
2220 
2720 
3270 
3890 
4450 
5050 
5710 
6420 
4.2 
255 
453 
678 
955 
1280 
1660 
2080 
2560 
3080 
3670 
4200 
4780 
5410 
6090 
4.4 
235 
418 
630 
893 
1200 
1560 
1960 
2410 
2910 
3470 
3980 
4540 
5140 
5800 
4.6 
215 
384 
585 
834 
1130 
1470 
1850 
2280 
2750 
3290 
3770 
4310 
4890 
5530 
4.8 
193 
349 
542 
779 
1060 
1390 
1750 
2160 
2610 
3120 
3590 
4100 
4670 
5280 
5.0 
172 
314 
499 
727 
991 
1310 
1650 
2040 
2470 
2960 
3410 
3910 
4460 
5050 
5.2 
154 
284 
457 
676 
929 
1230 
1560 
1930 
2350 
2820 
3250 
3740 
4260 
4840 
5.4 
139 
258 
420 
627 
870 
1160 
1480 
1830 
2230 
2680 
3110 
3570 
4090 
4640 
5.6 
126 
236 
387 
582 
813 
1090 
1390 
1740 
2120 
2550 
2970 
3420 
3920 
4460 
5.8 
115 
216 
358 
542 
761 
1030 
1320 
1650 
2010 
2430 
2840 
3280 
3760 
4290 
6.0 
105 
199 
332 
506 
713 
965 
1250 
1560 
1920 
2320 
2710 
3150 
3620 
4140 
6.2 
97 
184 
308 
472 
669 
909 
1180 
1480 
1820 
2210 
2600 
3020 
3480 
3990 
6.4 
89 
170 
287 
442 
628 
857 
1110 
1400 
1730 
2110 
2490 
2910 
3360 
3850 
6.6 
82 
157 
267 
413 
590 
808 
1050 
1330 
1650 
2010 
2380 
2790 
3240 
3720 
6.8 
76 
146 
248 
386 
553 
761 
990 
1260 
1560 
1910 
2280 
2690 
3120 
3600 
7.0 
70 
135 
231 
360 
518 
716 
933 
1190 
1480 
1820 
2180 
2580 
3010 
3480 
7.2 
64 
125 
214 
336 
485 
672 
878 
1120 
1400 
1720 
2070 
2470 
2900 
3370 
7.4 
59 
115 
198 
312 
451 
628 
822 
1060 
1320 
1630 
1970 
2350 
2780 
3250 
7.6 
54 
105 
182 
287 
417 
583 
765 
980 
1230 
1530 
1850 
2230 
2650 
3120 
7.8 
48 
94 
164 
261 
380 
533 
701 
901 
1140 
1410 
1720 
2090 
2500 
2970 
8.0 
38 
76 
134 
214 
314 
444 
587 
758 
960 
1200 
1480 
1810 
2210 
2670 
Superelevation Transition Length
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.
Desirable design values for length of superelevation transition are based on using a given maximum relative gradient between profiles of the edge of traveled way and the axis of rotation. Table 28 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.
Design Speed (mph) 
Maximum Relative Gradient%^{1} 
Equivalent Maximum Relative Slope 
15 
0.78 
1:128 
20 
0.74 
1:135 
25 
0.70 
1:143 
30 
0.66 
1:152 
35 
0.62 
1:161 
40 
0.58 
1:172 
45 
0.54 
1:185 
50 
0.50 
1:200 
55 
0.47 
1:213 
60 
0.45 
1:222 
65 
0.43 
1:233 
70 
0.40 
1:250 
75 
0.38 
1:263 
80 
0.35 
1:286 
^{1} Maximum 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 equation:
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 28: Maximum Relative Gradient for Superelevation Transition).
Example determinations of superelevation transition shown in Figure 22.
Figure 22. Determination of Length of Superelevation Transition.
As the number of lanes to be transitioned increases, the length of superelevation transition increases proportionately with the increased width. While strict adherence to the length (L_{CT}) calculation is desirable, the length for multilane highways may become impractical for design purposes (e.g. drainage problems, avoiding bridges, accommodating merge/diverge condition). A minimum length L_{CT}, can be calculated using adjustment factors as shown in Table 29, such that the transition length formula becomes:
L_{CT} = b[(CS)(W)]/G (US Customary and Metric)
where “b” is defined in Table 29
Number of Lanes Rotated 
Adjustment Factor (b) 

1.5 
0.83 
2 
0.75 
2.5 
0.70 
3 
0.67 
3.5 
0.64 
^{1} These adjustment factors are directly applicable to undivided streets and highways. For divided highways where the axis of rotation is not the edge of travel, see AASHTO’s A Policy on Geometric Design of Highways and Streets. 
Anchor: #EFCGXLVU
Superelevation Transition Placement
The location of the transition in respect to the termini of a simple (circular) curve should be placed to minimize lateral acceleration and the vehicle's lateral motion. The appropriate allocation of superelevation transition on the tangent, either preceding or following a curve, is provided on Table 210. When spiral curves are used, the transition usually is distributed over the length of the spiral curve.
Design Speed (mph) 
No. of Lanes Rotated 



1.0 
1.5 
2.0  2.5 
3.0  3.5 
15  45 
0.80 
0.85 
0.90 
0.90 
50  80 
0.70 
0.75 
0.80 
0.85 
^{1} These values are desirable and should be followed as closely as possible when conditions allow. A value between 0.6 and 0.9 for all speeds and rotated widths is considered acceptable. (AASHTO’s A Policy on Geometric Design of Highways and Streets). 
Care must be exercised in designing the length and location of the transition. Profiles of both gutters or pavement edges should be plotted relative to the profile grade line to insure proper drainage, 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 near the flat portion of the crest or sag vertical curve. A plot of roadway contours can identify drainage problems in areas of superelevation transition. See "Minimum Transition Grades" section of AASHTO's A Policy on Geometric Design of Highways and Streets for further discussion on potential drainage problems and effective means to mitigate them.
Whenever reverse curves are closely spaced and superelevation transition lengths overlap, L values should be adjusted to prorate change in cross slope and to ensure that roadway cross slopes are in the proper direction for each horizontal curve.
Anchor: #YWUECXWMSuperelevation Transition Type
Linear superelevation transition may be used. Where appearance is a factor (e.g. curbed sections and retaining walls) use of reverse parabolas is recommended for attaining superelevation as shown in Figure 22. This produces an outer edge profile that is smooth, undistorted, and pleasing in appearance. Sufficient information needs to be in the plans to ensure the parabolic design is properly constructed.
Figure 22 shows reverse parabolas over the full length of the transition. Alternative methods for developing smoothedge profiles over the length of the transition are given in the section "Design of Smooth Profiles for Traveled Way Edges" of AASHTO's A Policy on Geometric Design of Highways and Streets.
Anchor: #i1086199Sight 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.
Where:
M = middle ordinate (ft)
S = stopping sight distance (ft) and,
R = radius (ft)
Figure 23 provides a graph illustrating the required offset where stopping sight distance is less than the length of curve (S<L).
Figure 23. (US). Stopping Sight Distance on Horizontal Curves.
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.
Where sufficient stopping sight distance is not available because a railing or a longitudinal barrier constitutes a sight obstruction, alternative designs should be considered. The alternatives are: (1) increase the offset to the obstruction, (2) increase the radius, or (3) reduce the design speed. However, the alternative selected should not incorporate shoulder widths on the inside of the curve in excess of 12 ft [3.6 m] because of the concern that drivers will use wider shoulders as a passing or travel lane.