Horizontal Alignment and Superelevation

The horizontal alignment of a roadway should be designed to provide motorists with a facility for driving in a safe and comfortable manner. Adequate stopping sight distance should be furnished. Also, changes in direction should be accompanied by the use of curves and superelevation when appropriate in accordance with established guidelines. Some changes in alignment are slight and may not require curvature. Table 2.5 lists the maximum deflection angle which may be permitted without the use of a horizontal curve for each design speed shown. It is assumed that a motorist can easily negotiate the change in direction and maintain control over the vehicle without leaving the lane.

TABLE 2.4 Decision Sight Distance (DSD) for Design Speeds from 30 to 70 mi/h (48 to 113 km/h)

Decision sight distance, ft
Avoidance maneuver

Design speed, mi/h	A	B	C	D	E
30	220	490	450	535	620
35	275	590	525	625	720
40	330	690	600	715	825
45	395	800	675	800	930
50	465	910	750	890	1030
55	535	1030	865	980	1135
60	610	1150	990	1125	1280
65	695	1275	1050	1220	1365
70	780	1410	1105	1275	1445

• The avoidance maneuvers are as follows: A—rural stop; B—urban stop; C—rural speed/path/direction change; D—suburban speed/path/direction change; E—urban speed/path/direction change

• Decision sight distance (DSD) is calculated or measured using the same criteria as stopping sight distance: 3.50 ft (1.07 m) eye height and 2.00 ft (0.61 m) object height.

Conversions: 1 mi/h = 1.609 km/h, 1 ft = 0.305 m.

Source: Location and Design Manual, Vol. 1, Roadway Design, Ohio Department of

Transportation, with permission.

TABLE 2.5 Maximum Centerline Deflection Not Requiring a Horizontal Curve Design speed, mi/h Maximum deflection* 25 5°30′ 30 3°45′ 35 2°45′ 40 2°15′ 45 1°45′ 50 1°15′ 55 1°00′ 60 1°00′ 65 0°45′ 70 0°45′ Based on the following formulas: Design speed 50 mi/h or over: tan A = 1.0/V Design speed under 50 mi/h: tan A = 60/V2 where V = design speed, mi/h A = deflection angle

Conversions: 1 mi/h = 1.609 km/h, 1 ft = 0.305 m.

Note: The recommended minimum distance between consecutive horizontal deflections is:

200 ft where design speed > 45 mi/h 100 ft where design speed < 45 mi/h *Rounded to nearest 15 min.

Source: Location and Design Manual, Vol. 1, Roadway Design, Ohio Department of Transportation, with permission.

When centerline deflections exceed the values in Table 2.5, it is necessary to introduce a horizontal curve to assist the driver. Curves are usually accompanied by supereleva­tion, which is a banking of the roadway to help counteract the effect of centrifugal force on the vehicle as it moves through the curve. In addition to superelevation, cen­trifugal force is also offset by the side friction developed between the tires of the vehicle and the pavement surface. The relationship of the two factors when considering curvature for a particular design speed is expressed by the following equation:

U. S. units: e + f =	V2 15V	(2.1a)
SI units: e + f =	V2 127R	(2.1b)

where e = superelevation rate, ft per ft (m per m) of pavement width f = side friction factor V = design speed, mi/h (km/h)

R = radius of curve, ft (m)

In developing superelevation guidelines for use in designing roadways, it is necessary to establish practical limits for both superelevation and side friction factors. Several factors affect the selection of a maximum superelevation rate for a given highway. Climate must be considered. Regions subject to snow and ice should not be superelevated too sharply, because the presence of these adverse conditions causes motorists to drive slower, and side friction is greatly reduced. Consequently, vehicles tend to slide to the low side of the roadway. Terrain conditions are another factor. Flat areas tend to have rela­tively flat grades, and such conditions have little effect on superelevation and side friction factors. However, mountainous regions have steeper grades, which combine with super­elevation rates to produce steeper cross slopes on the pavement than may be apparent to the designer. Rural and urban areas require different maximum superelevation rates, because urban areas are more frequently subjected to congestion and slower-moving traffic. Vehicles operating at significantly less than design speeds necessitate a flatter maximum rate. Given the above considerations, a range of maximum values has been adopted for use in design. A maximum rate of 0.12 or 0.10 may be used in flat areas not subject to ice or snow. Rural areas where these conditions exist usually have a maximum rate of 0.08. A maximum rate of 0.06 is recommended for urban high-speed roadways, 50 mi/h (80 km/h) or greater, while 0.04 is used on low-speed urban roadways and temporary roads.

Various factors affect the side friction factors used in design. Among these are pavement texture, weather conditions, and tire condition. The upper limit of the side friction factor is when the tires begin to skid. Highway curves must be designed to avoid skidding conditions with a margin of safety. Side friction factors also vary with design speed. Higher speeds tend to have lower side friction factors. The result of various studies leads to the values listed in Table 2.6, which shows the side friction factors by design speed generally used in developing superelevation tables (Ref. 1).

Taking into account the above limits on superelevation rates and side friction factors, and rewriting Eq. (2.1), it follows that for a given design speed and maximum superelevation rate, there exists a minimum radius of curvature that should be allowed for design purposes:

V2

R. = ————— (2.2)

mn 15(e + f) v ‘

To allow a lesser radius for the design speed would require the superelevation rate or the friction factor to be increased beyond the recommended limit.

Highway design using U. S. Customary units defines horizontal curvature in terms of degree of curve as well as radius. Under this definition, the degree of curve is defined as the central angle of a 100-ft (30-m) arc using a fixed radius. This results in the following equation relating R (radius, ft) to D (degree of curve, degrees):

5729.6

R

Substituting in Eq. (2.2) gives the maximum degree of curvature for a given design speed and maximum superelevation rate:

Before presenting the superelevation tables, one final consideration must be addressed. Because for any curve, superelevation and side friction combine to offset the effects of centrifugal force, the question arises how much superelevation should be provided for curves flatter than the “maximum” allowed for a given design speed. The following five methods have been used over the years (Ref. 1):

Method 1. Superelevation and side friction are directly proportional to the degree of curve or the inverse of the radius.

Method 2. Side friction is used to offset centrifugal force in direct proportion to the degree of curve, for curves up to the point where fmax is required. For sharper curves, fmax remains constant and e is increased in direct proportion to the increasing degree of curvature until e is reached.

Method 3. Superelevation is used to offset centrifugal force in direct proportion to the degree of curve for curves up to the point where emax is required. For sharper curves, emax remains constant and f is increased in direct proportion to the increasing degree of curvature until f is reached.

Method 4. Method 4 is similar to method 3, except that it is based on average running speed instead of design speed.

Method 5. Superelevation and side friction are in a curvilinear relationship with the degree of curve (inverse of radius), with resulting values between those of method 1 and method 3.

Figure 2.8 shows a graphic comparison of the various methods. Method 5 is most commonly used on rural and high-speed [50 mi/h (80 km/h) or higher] urban high­ways. Method 2 is used on low-speed urban streets and temporary roadways.

Recommended minimum radii for a given range of design speeds and incremental superelevation rates are given in Tables 2.7 through 2.11, where each table represents

FIGURE 2.8 Methods of distributing superelevation and side friction. (a) Superelevation. (b) Corresponding friction factor at design speed. (c) Corresponding friction factor at running speed. (From A Policy on Geometric Design of Highways and Streets, American Association of State Highway and Transportation Officials, Washington, D. C., 2004, with permission)

TABLE 2.7 Minimum Radii for Design Speeds from 15 to 60 mi/ti (24 to 97 km/h) and Superelevation Rates to 4 Percent e (%) V, = 15 mi/h a R (ft) V. = 20 mi/h a R (ft) V, = 25 mi/h a R (ft) V, = 30 mi/h a R (ft) V. = 35 mi/h a R (ft) V. = 40 mi/h a Я (ft) V. = 45 mi/h a R (ft) V, = 50 mi/h a R (ft) V. = 55 mi/h a R (ft) V. = 60 mi/h a R (ft) 1.5 796 1410 2050 2830 3730 4770 5930 7220 8650 10300 2.0 506 902 1340 1880 2490 3220 4040 4940 5950 7080 2.2 399 723 1110 1580 2120 2760 3480 4280 5180 6190 2.4 271 513 838 1270 1760 2340 2980 3690 4500 5410 2.6 201 388 650 1000 1420 1930 2490 3130 3870 4700 2.8 157 308 524 817 1170 1620 2100 2660 3310 4060 3.0 127 251 433 681 982 1370 1800 2290 2860 3530 3.2 105 209 363 576 835 1180 1550 1980 2490 3090 3.4 88 175 307 490 714 1010 1340 1720 2170 2700 3.6 73 147 259 416 610 865 1150 1480 1880 2350 3.8 61 122 215 348 512 730 970 1260 1600 2010 4.0 42 86 154 250 371 533 711 926 1190 1500 Conversions: 1 mi/h = 1.609 km/h, 1 ft = 0.305 m. R = radius of curve Vd = design speed e = rate of superelevation Note: Use of emax = 4 percent should be limited to urban conditions. Source: A Policy on Geometric Design of Highways and Streets, American Association of State Highway and Transportation Officials, Washington, D. C., 2004, with permission.

TABLE 2.8 Minimum Radii for Design Speeds from 15 to 80 mi/h (24 to 129 km/h) and Superelevation Rates to 6 Percent e (%) Vd = 15 mi/h R (ft) Vd = 20 mi/h R (ft) Vd = 25 mi/h R (ft) Vd = 30 mi/h R (ft) Vd = 35 mi/h R (ft) Vd = 40 mi/h R (ft) Vd = 45 mi/h R (ft) 1.5 868 1580 2290 3130 4100 5230 6480 2.0 614 1120 1630 2240 2950 3770 4680 2.2 543 991 1450 2000 2630 3370 4190 2.4 482 884 1300 1790 2360 3030 3770 2.6 430 791 1170 1610 2130 2740 3420 2.8 384 709 1050 1460 1930 2490 3110 3.0 341 635 944 1320 1760 2270 2840 3.2 300 566 850 1200 1600 2080 2600 3.4 256 498 761 1080 1460 1900 2390 3.6 209 422 673 972 1320 1740 2190 3.8 176 358 583 864 1190 1590 2010 4.0 151 309 511 766 1070 1440 1840 4.2 131 270 452 684 960 1310 1680 4.4 116 238 402 615 868 1190 1540 4.6 102 212 360 555 788 1090 1410 4.8 91 189 324 502 718 995 1300 5.0 82 169 292 456 654 911 1190 5.2 73 152 264 413 595 833 1090 5.4 65 136 237 373 540 759 995 5.6 58 121 212 335 487 687 903 5.8 51 106 186 296 431 611 806 6.0 39 81 144 231 340 485 643 (Continued)

e	Vd = 50 mi/h	Vd = 55 mi/h	II o о 3 &	Vd = 65 mi/h	Vd = 70 mi/h	Vd = 75 mi/h	Vd = 80 mi/h
(%)	R (ft)	R (ft)	R (ft)	R (ft)	R (ft)	R (ft)	R (ft)
1.5	7870	9410	11100	12600	14100	15700	17400
2.0	5700	6820	8060	9130	10300	11500	12900
2.2	5100	6110	7230	8200	9240	10400	11600
2.4	4600	5520	6540	7430	8380	9420	10600
2.6	4170	5020	5950	6770	7660	8620	9670
2.8	3800	4580	5440	6200	7030	7930	8910
3.0	3480	4200	4990	5710	6490	7330	8260
3.2	3200	3860	4600	5280	6010	6810	7680
3.4	2940	3560	4250	4890	5580	6340	7180
3.6	2710	3290	3940	4540	5210	5930	6720
3.8	2490	3040	3650	4230	4860	5560	6320
4.0	2300	2810	3390	3950	4550	5220	5950
4.2	2110	2590	3140	3680	4270	4910	5620
4.4	1940	2400	2920	3440	4010	4630	5320
4.6	1780	2210	2710	3220	3770	4380	5040
4.8	1640	2050	2510	3000	3550	4140	4790
5.0	1510	1890	2330	2800	3330	3910	4550
5.2	1390	1750	2160	2610	3120	3690	4320
5.4	1280	1610	1990	2420	2910	3460	4090
5.6	1160	1470	1830	2230	2700	3230	3840
5.8	1040	1320	1650	2020	2460	2970	3560
6.0	833	1060	1330	1660	2040	2500	3050

Conversions: 1 mi/h = 1.609 km/h, 1 ft = 0.305 m.

R = radius of curve Vd = design speed e = rate of superelevation

Source: A Policy on Geometric Design of Highways and Streets, American Association of State Highway and Transportation Officials, Washington, D. C., 2004, with permission.

TABLE 2.9 Minimum Radii for Design Speeds from 15 to 80 mi/h (24 to 129 km/h) and Superelevation Rates to 8 Percent e Vd = 15 mi/h Vd = 20 mi/h Vd = 25 mi/h Vd = 30 mi/h Vd = 35 mi/h II 4^ О 3 & Vd = 45 mi/h (%) R (ft) R (ft) R (ft) R (ft) R (ft) R (ft) R (ft) 1.5 932 1640 2370 3240 4260 5410 6710 2.0 676 1190 1720 2370 3120 3970 4930 2.2 605 1070 1550 2130 2800 3570 4440 2.4 546 959 1400 1930 2540 3240 4030 2.6 496 872 1280 1760 2320 2960 3690 2.8 453 796 1170 1610 2130 2720 3390 3.0 415 730 1070 1480 1960 2510 3130 3.2 382 672 985 1370 1820 2330 2900 3.4 352 620 911 1270 1690 2170 2700 3.6 324 572 845 1180 1570 2020 2520 3.8 300 530 784 1100 1470 1890 2360 4.0 277 490 729 1030 1370 1770 2220 4.2 255 453 678 955 1280 1660 2080 4.4 235 418 630 893 1200 1560 1960 4.6 215 384 585 834 1130 1470 1850 4.8 193 349 542 779 1060 1390 1750 5.0 172 314 499 727 991 1310 1650 5.2 154 284 457 676 929 1230 1560 5.4 139 258 420 627 870 1160 1480 5.6 126 236 387 582 813 1090 1390 5.8 115 216 358 542 761 1030 1320 6.0 105 199 332 506 713 965 1250 6.2 97 184 308 472 669 909 1180 6.4 89 170 287 442 628 857 1110 6.6 82 157 267 413 590 808 1050 6.8 76 146 248 386 553 761 990 7.0 70 135 231 360 518 716 933 7.2 64 125 214 336 485 672 878 7.4 59 115 198 312 451 628 822 7.6 54 105 182 287 417 583 765 7.8 48 94 164 261 380 533 701 8.0 38 76 134 214 314 444 587

e	Vd = 50 mi/h	Vd = 55 mi/h	II C О 3 &	Vd = 65 mi/h	Vd = 70 mi/h	Vd = 75 mi/h	Vd = 80 mi/h
(%)	R (ft)	R (ft)	R (ft)	R (ft)	R (ft)	R (ft)	R (ft)
1.5	8150	9720	11500	12900	14500	16100	17800
2.0	5990	7150	8440	9510	10700	12000	13300
2.2	5400	6450	7620	8600	9660	10800	12000
2.4	4910	5870	6930	7830	8810	9850	11000
2.6	4490	5370	6350	7180	8090	9050	10100
2.8	4130	4950	5850	6630	7470	8370	9340
3.0	3820	4580	5420	6140	6930	7780	8700
3.2	3550	4250	5040	5720	6460	7260	8130
3.4	3300	3970	4700	5350	6050	6800	7620
3.6	3090	3710	4400	5010	5680	6400	7180
3.8	2890	3480	4140	4710	5350	6030	6780
4.0	2720	3270	3890	4450	5050	5710	6420
4.2	2560	3080	3670	4200	4780	5410	6090
4.4	2410	2910	3470	3980	4540	5140	5800
4.6	2280	2750	3290	3770	4310	4890	5530
4.8	2160	2610	3120	3590	4100	4670	5280
5.0	2040	2470	2960	3410	3910	4460	5050
5.2	1930	2350	2820	3250	3740	4260	4840
5.4	1830	2230	2680	3110	3570	4090	4640
5.6	1740	2120	2550	2970	3420	3920	4460
5.8	1650	2010	2430	2840	3280	3760	4290
6.0	1560	1920	2320	2710	3150	3620	4140
6.2	1480	1820	2210	2600	3020	3480	3990
6.4	1400	1730	2110	2490	2910	3360	3850
6.6	1330	1650	2010	2380	2790	3240	3720
6.8	1260	1560	1910	2280	2690	3120	3600
7.0	1190	1480	1820	2180	2580	3010	3480
7.2	1120	1400	1720	2070	2470	2900	3370
7.4	1060	1320	1630	1970	2350	2780	3250
7.6	980	1230	1530	1850	2230	2650	3120
7.8	901	1140	1410	1720	2090	2500	2970
8.0	758	960	1200	1480	1810	2210	2670

Conversions: 1 mi/h = 1.609 km/h, 1 ft = 0.305 m. R = radius of curve Vd = design speed e = rate of superelevation Source: A Policy on Geometric Design of Highways and Streets, American Association of State Highway and Transportation Officials, Washington, D. C., 2004, with permission.

TABLE 2.10 Minimum Radii for Design Speeds from 15 to 80 mi/h (24 to 129 km/h) and Superelevation Rates to 10 Percent e Vd = 15 mi/h Vd = 20 mi/h Vd = 25 mi/h Vd = 30 mi/h Vd = 35 mi/h II 4^ О 3 & Vd = 45 mi/h (%) R (ft) R (ft) R (ft) R (ft) R (ft) R (ft) R (ft) 1.5 947 1680 2420 3320 4350 5520 6830 2.0 694 1230 1780 2440 3210 4080 5050 2.2 625 1110 1600 2200 2900 3680 4570 2.4 567 1010 1460 2000 2640 3350 4160 2.6 517 916 1330 1840 2420 3080 3820 2.8 475 841 1230 1690 2230 2840 3520 3.0 438 777 1140 1570 2060 2630 3270 3.2 406 720 1050 1450 1920 2450 3040 3.4 377 670 978 1360 1790 2290 2850 3.6 352 625 913 1270 1680 2150 2670 3.8 329 584 856 1190 1580 2020 2510 4.0 308 547 804 1120 1490 1900 2370 4.2 289 514 756 1060 1400 1800 2240 4.4 271 483 713 994 1330 1700 2120 4.6 255 455 673 940 1260 1610 2020 4.8 240 429 636 890 1190 1530 1920 5.0 226 404 601 844 1130 1460 1830 5.2 213 381 569 802 1080 1390 1740 5.4 200 359 539 762 1030 1330 1660 5.6 188 339 511 724 974 1270 1590 5.8 176 319 484 689 929 1210 1520 6.0 164 299 458 656 886 1160 1460 6.2 152 280 433 624 846 1110 1400 6.4 140 260 409 594 808 1060 1340 6.6 130 242 386 564 772 1020 1290 6.8 120 226 363 536 737 971 1230 7.0 112 212 343 509 704 931 1190 7.2 105 199 324 483 671 892 1140 7.4 98 187 306 460 641 855 1100 7.6 92 176 290 437 612 820 1050 7.8 86 165 274 416 585 786 1010 8.0 81 156 260 396 558 754 968 8.2 76 147 246 377 533 722 930 8.4 72 139 234 359 509 692 893 8.6 68 131 221 341 486 662 856 8.8 64 124 209 324 463 633 820 9.0 60 116 198 307 440 604 784 9.2 56 109 186 291 418 574 748 9.4 52 102 175 274 395 545 710 9.6 48 95 163 256 370 513 671 9.8 44 87 150 236 343 477 625 10.0 36 72 126 200 292 410 540 (Continued)

e Vd	= 50 mi/h	Vd = 55 mi/h	II o О 3 &	Vd = 65 mi/h	Vd = 70 mi/h	Vd = 75 mi/h	Vd = 80 mi/h
(%)	R (ft)	R (ft)	R (ft)	R (ft)	R (ft)	R (ft)	R (ft)
1.5	8280	9890	11700	13100	14700	16300	18000
2.0	6130	7330	8630	9720	10900	12200	13500
2.2	5540	6630	7810	8800	9860	11000	12200
2.4	5050	6050	7130	8040	9010	10100	11200
2.6	4640	5550	6550	7390	8290	9260	10300
2.8	4280	5130	6050	6840	7680	8580	9550
3.0	3970	4760	5620	6360	7140	7990	8900
3.2	3700	4440	5250	5930	6680	7480	8330
3.4	3470	4160	4910	5560	6260	7020	7830
3.6	3250	3900	4620	5230	5900	6620	7390
3.8	3060	3680	4350	4940	5570	6260	6990
4.0	2890	3470	4110	4670	5270	5930	6630
4.2	2740	3290	3900	4430	5010	5630	6300
4.4	2590	3120	3700	4210	4760	5370	6010
4.6	2460	2970	3520	4010	4540	5120	5740
4.8	2340	2830	3360	3830	4340	4900	5490
5.0	2240	2700	3200	3660	4150	4690	5270
5.2	2130	2580	3060	3500	3980	4500	5060
5.4	2040	2460	2930	3360	3820	4320	4860
5.6	1950	2360	2810	3220	3670	4160	4680
5.8	1870	2260	2700	3090	3530	4000	4510
6.0	1790	2170	2590	2980	3400	3860	4360
6.2	1720	2090	2490	2870	3280	3730	4210
6.4	1650	2010	2400	2760	3160	3600	4070
6.6	1590	1930	2310	2670	3060	3480	3940
6.8	1530	1860	2230	2570	2960	3370	3820
7.0	1470	1790	2150	2490	2860	3270	3710
7.2	1410	1730	2070	2410	2770	3170	3600
7.4	1360	1670	2000	2330	2680	3070	3500
7.6	1310	1610	1940	2250	2600	2990	3400
7.8	1260	1550	1870	2180	2530	2900	3310
8.0	1220	1500	1810	2120	2450	2820	3220
8.2	1170	1440	1750	2050	2380	2750	3140
8.4	1130	1390	1690	1990	2320	2670	3060
8.6	1080	1340	1630	1930	2250	2600	2980
8.8	1040	1290	1570	1870	2190	2540	2910
9.0	992	1240	1520	1810	2130	2470	2840
9.2	948	1190	1460	1740	2060	2410	2770
9.4	903	1130	1390	1670	1990	2340	2710
9.6	854	1080	1320	1600	1910	2260	2640
9.8	798	1010	1250	1510	1820	2160	2550
10.0	694	877	1090	1340	1630	1970	2370

Conversions: 1 mi/h = 1.609 km/h, 1 ft = 0.305 m.

R = radius of curve Vd = design speed e = rate of Superelevation

Source: A Policy on Geometric Design of Highways and Streets, American Association of State Highway and Transportation Officials, Washington, D. C., 2004, with permission.

TABLE 2.11 Minimum Radii for Design Speeds from 15 to 80 mi/h (24 to 129 km/h) and Superelevation Rates to 12 Percent e Vd = 15 mi/h Vd = 20 mi/h Vd = 25 mi/h Vd = 30 mi/h Vd = 35 mi/h II О 3 Vd = 45 mi/h (%) R (ft) R (ft) R (ft) R (ft) R (ft) R (ft) R (ft) 1.5 950 1690 2460 3370 4390 5580 6910 2.0 700 1250 1820 2490 3260 4140 5130 2.2 631 1130 1640 2250 2950 3750 4640 2.4 574 1030 1500 2060 2690 3420 4240 2.6 526 936 1370 1890 2470 3140 3900 2.8 484 863 1270 1740 2280 2910 3600 3.0 448 799 1170 1620 2120 2700 3350 3.2 417 743 1090 1510 1970 2520 3130 3.4 389 693 1020 1410 1850 2360 2930 3.6 364 649 953 1320 1730 2220 2750 3.8 341 610 896 1250 1630 2090 2600 4.0 321 574 845 1180 1540 1980 2460 4.2 303 542 798 1110 1460 1870 2330 4.4 286 512 756 1050 1390 1780 2210 4.6 271 485 717 997 1320 1690 2110 4.8 257 460 681 948 1260 1610 2010 5.0 243 437 648 904 1200 1540 1920 5.2 231 415 618 862 1140 1470 1840 5.4 220 395 589 824 1090 1410 1760 5.6 209 377 563 788 1050 1350 1690 5.8 199 359 538 754 1000 1300 1620 6.0 190 343 514 723 960 1250 1560 6.2 181 327 492 694 922 1200 1500 6.4 172 312 471 666 886 1150 1440 6.6 164 298 452 639 852 1110 1390 6.8 156 284 433 615 820 1070 1340 7.0 148 271 415 591 790 1030 1300 7.2 140 258 398 568 762 994 1250 7.4 133 246 382 547 734 960 1210 7.6 125 234 366 527 708 928 1170 7.8 118 222 351 507 684 897 1130 8.0 111 210 336 488 660 868 1100

e Vd	= 15 mi/h	Vd = 20 mi/h	Vd = 25 mi/h	Vd = 30 mi/h	Vd = 35 mi/h	II 4^ О 3 &	Vd = 45 mi/h
(%)	R (ft)	R (ft)	R (ft)	R (ft)	R (ft)	R (ft)	R (ft)
8.2	105	199	321	470	637	840	1070
8.4	100	190	307	452	615	813	1030
8.6	95	180	294	435	594	787	997
8.8	90	172	281	418	574	762	967
9.0	85	164	270	403	554	738	938
9.2	81	156	259	388	535	715	910
9.4	77	149	248	373	516	693	883
9.6	74	142	238	359	499	671	857
9.8	70	136	228	346	481	650	832
10.0	67	130	219	333	465	629	806
10.2	64	124	210	320	448	608	781
10.4	61	118	201	308	432	588	757
10.6	58	113	192	296	416	568	732
10.8	55	108	184	284	400	548	707
11.0	52	102	175	272	384	527	682
11.2	49	97	167	259	368	506	656
11.4	47	92	158	247	351	485	629
11.6	44	86	149	233	333	461	600
11.8	40	80	139	218	312	434	566
12.0	34	68	119	188	272	381	500

(Continued)

TABLE 2.11 Minimum Radii for Design Speeds from 15 to 80 mi/h (24 to 129 km/h) and Superelevation Rates to 12 Percent (Continued) e Vd = 50 mi/h Vd = 55 mi/h Vd = 60 mi/h Vd = 65 mi/h Vd = 70 mi/h Vd = 75 mi/h Vd = 80 mi/h (%) R (ft) R (ft) R (ft) R (ft) R (ft) R (ft) R (ft) 1.5 8370 9990 11800 13200 14800 16400 18100 2.0 6220 7430 8740 9840 11000 12300 13600 2.2 5640 6730 7930 8920 9980 11200 12400 2.4 5150 6150 7240 8160 9130 10200 11300 2.6 4730 5660 6670 7510 8420 9380 10500 2.8 4380 5240 6170 6960 7800 8700 9660 3.0 4070 4870 5740 6480 7270 8110 9010 3.2 3800 4550 5370 6060 6800 7600 8440 3.4 3560 4270 5030 5690 6390 7140 7940 3.6 3350 4020 4740 5360 6020 6740 7500 3.8 3160 3790 4470 5060 5700 6380 7100 4.0 2990 3590 4240 4800 5400 6050 6740 4.2 2840 3400 4020 4560 5130 5750 6420 4.4 2700 3240 3830 4340 4890 5490 6120 4.6 2570 3080 3650 4140 4670 5240 5850 4.8 2450 2940 3480 3960 4470 5020 5610 5.0 2340 2810 3330 3790 4280 4810 5380 5.2 2240 2700 3190 3630 4110 4620 5170 5.4 2150 2590 3060 3490 3950 4440 4980 5.6 2060 2480 2940 3360 3800 4280 4800 5.8 1980 2390 2830 3230 3660 4130 4630 6.0 1910 2300 2730 3110 3530 3990 4470 6.2 1840 2210 2630 3010 3410 3850 4330 6.4 1770 2140 2540 2900 3300 3730 4190 6.6 1710 2060 2450 2810 3190 3610 4060 6.8 1650 1990 2370 2720 3090 3500 3940 7.0 1590 1930 2290 2630 3000 3400 3820 7.2 1540 1860 2220 2550 2910 3300 3720 7.4 1490 1810 2150 2470 2820 3200 3610 7.6 1440 1750 2090 2400 2740 3120 3520 7.8 1400 1700 2020 2330 2670 3030 3430 8.0 1360 1650 1970 2270 2600 2950 3340

e Vd	= 50 mi/h	Vd = 55 mi/h	Vd = 60 mi/h	Vd = 65 mi/h	Vd = 70 mi/h	Vd = 75 mi/h	Vd = 80 mi/h
(%)	R (ft)	R (ft)	R (ft)	R (ft)	R (ft)	R (ft)	R (ft)
8.2	1320	1600	1910	2210	2530	2880	3260
8.4	1280	1550	1860	2150	2460	2800	3180
8.6	1240	1510	1810	2090	2400	2740	3100
8.8	1200	1470	1760	2040	2340	2670	3030
9.0	1170	1430	1710	1980	2280	2610	2960
9.2	1140	1390	1660	1940	2230	2550	2890
9.4	1100	1350	1620	1890	2180	2490	2830
9.6	1070	1310	1580	1840	2130	2440	2770
9.8	1040	1280	1540	1800	2080	2380	2710
10.0	1010	1250	1500	1760	2030	2330	2660
10.2	980	1210	1460	1720	1990	2280	2600
10.4	951	1180	1430	1680	1940	2240	2550
10.6	922	1140	1390	1640	1900	2190	2500
10.8	892	1110	1350	1600	1860	2150	2460
11.0	862	1070	1310	1560	1820	2110	2410
11.2	831	1040	1270	1510	1780	2070	2370
11.4	799	995	1220	1470	1730	2020	2320
11.6	763	953	1170	1410	1680	1970	2280
11.8	722	904	1120	1350	1620	1910	2230
12.0	641	807	1000	1220	1480	1790	2130

Conversions: 1 mi/h = 1.609 km/h, 1 ft = 0.305 m. R = radius of curve Vd = design speed e = rate of superelevation

Source: A Policy on Geometric Design of Highways and Streets, American Association of State Highway and Transportation Officials, Washington, D. C., 2004, with permission.

a different maximum superelevation rate. Table 2.7 shows values for a maximum rate of 0.04; Table 2.8, for 0.06; Table 2.9, for 0.08; Table 2.10, for 0.10; and Table 2.11, for 0.12. Method 5 was used to calculate the minimum radius for each superelevation rate less than the maximum rate in each design speed column in the tables.

The superelevation rates on low-speed urban streets are set using method 2 described above, in which side friction is used to offset the effect of centrifugal force up to the maximum friction value allowed for the design speed. Superelevation is then introduced for sharper curves. The design data in Table 2.12, based on method 2 and a maximum superelevation rate of 0.04, can be used for low-speed urban streets and temporary roads. The design data in Table 2.13 can be used for a wider range of design speeds and superelevation rates.

In attempting to apply the recommended superelevation rates for low-speed urban roadways, various factors may combine to make these rates impractical to obtain. These factors include wide pavements, adjacent development, drainage conditions, and frequent access points. In such cases, curves may be designed with reduced or no superelevation, although crown removal is the recommended minimum.

Effect of Grades on Superelevation. On long and fairly steep grades, drivers tend to travel somewhat slower in the upgrade direction and somewhat faster in the downgrade direction than on level roadways. In the case of divided highways, where each pavement can be superelevated independently, or on one-way roadways such as ramps, this ten­dency should be recognized to see whether some adjustment in the superelevation rate would be desirable and/or feasible. On grades of 4 percent or greater with a length of 1000 ft (305 m) or more and a superelevation rate of 0.06 or more, the designer may adjust the superelevation rate by assuming a design speed 5 mi/h (8 km/h) less in the upgrade direction and 5 mi/h (8 km/h) greater in the downgrade direction, provided that the assumed design speed is not less than the legal speed. On two-lane, two-way roadways and on other multilane undivided highways, such adjustments are less feasible, and should be disregarded.

Superelevation Methods. There are three basic methods for developing superelevation on a crowned pavement leading into and coming out of a horizontal curve. Figure 2.9 shows each method. In the most commonly used method, case I, the pavement edges are revolved about the centerline. Thus, the inner edge of the pavement is depressed by half of the superelevation and the outer edge raised by the same amount. Case II shows the pavement revolved about the inner or lower edge of pavement, and case III shows the pavement revolved about the outer or higher edge of pavement. Case II can be used where off-road drainage is a problem and lowering the inner pavement edge cannot be accommodated. The superelevation on divided roadways is achieved by revolving the pavements about the median pavement edge. In this way, the outside (high side) roadway uses case II, while the inside (low side) roadway uses case III. This helps control the amount of “distortion” in grading the median area.

Superelevation Transition. The length of highway needed to change from a normal crowned section to a fully superelevated section is referred to as the superelevation transition. This length is shown as X in Fig. 2.9, which also shows the various other elements described below. The superelevation transition is divided into two parts: the tangent runout, and the superelevation runoff.

The tangent runout (T in Fig. 2.9) is the length required to remove the adverse pavement cross slope. As is shown for case I of Fig. 2.9, this is the length required to raise the outside edge of pavement from a normal cross slope to a half-flat section. The superelevation runoff (L in Fig. 2.9) is the length required to raise the outside

TABLE 2.12 Superelevation Rates and Runoff Lengths (ft) for Horizontal Curves on Low-Speed Urban Streets Based on a Maximum Superelevation Rate of 4 Percent

Design speed, mi/h

20 25 30 35 40 45

Conversions: 1 mi/h = 1.609 km/h, 1 ft = 0.305 m.

Source: Location and Design Manual, Vol. 1, Roadway Design, Ohio Department of Transportation, with

permission.

TABLE 2.13 Runoff Lengths (ft) for Horizontal Curves with Design Speeds from 15 to 80 mi/h (24 to 129 km/h) and Superelevation Rates to 12 Percent Based on One Lane Rotated about the Centerline e Vd = 15 mi/h Vd = 20 mi/h Vd = 25 mi/h Vd = 30 mi/h Vd = 35 mi/h II О 3 Vd = 45 mi/h (%) L (ft) L (ft) L (ft) Lr (ft) L (ft) Lr (ft) L (ft) 1.5 0 0 0 0 0 0 0 2.0 31 32 34 36 39 41 44 2.2 34 36 38 40 43 46 49 2.4 37 39 41 44 46 50 53 2.6 40 42 45 47 50 54 58 2.8 43 45 48 51 54 58 62 3.0 46 49 51 55 58 62 67 3.2 49 52 55 58 62 66 71 3.4 52 55 58 62 66 70 76 3.6 55 58 62 65 70 74 80 3.8 58 62 65 69 74 79 84 4.0 62 65 69 73 77 83 89 4.2 65 68 72 76 81 87 93 4.4 68 71 75 80 85 91 98 4.6 71 75 79 84 89 95 102 4.8 74 78 82 87 93 99 107 5.0 77 81 86 91 97 103 111 5.2 80 84 89 95 101 108 116 5.4 83 88 93 98 105 112 120 5.6 86 91 96 102 108 116 124 5.8 89 94 99 105 112 120 129 6.0 92 97 103 109 116 124 133 6.2 95 101 106 113 120 128 138 6.4 98 104 110 116 124 132 142 6.6 102 107 113 120 128 137 147 6.8 105 110 117 124 132 141 151 7.0 108 114 120 127 135 145 156 7.2 111 117 123 131 139 149 160 7.4 114 120 127 135 143 153 164 7.6 117 123 130 138 147 157 169 7.8 120 126 134 142 151 161 173 8.0 123 130 137 145 155 166 178 8.2 126 133 141 149 159 170 182 8.4 129 136 144 153 163 174 187 8.6 132 139 147 156 166 178 191 8.8 135 143 151 160 170 182 196 9.0 138 146 154 164 174 186 200 9.2 142 149 158 167 178 190 204 9.4 145 152 161 171 182 194 209 9.6 148 156 165 175 186 199 213 9.8 151 159 168 178 190 203 218 10.0 154 162 171 182 194 207 222 10.2 157 165 175 185 197 211 227 10.4 160 169 178 189 201 215 231 10.6 163 172 182 193 205 219 236 10.8 166 175 185 196 209 223 240 11.0 169 178 189 200 213 228 244 11.2 172 182 192 204 217 232 249 11.4 175 185 195 207 221 236 253 11.6 178 188 199 211 225 240 258 11.8 182 191 202 215 228 244 262 12.0 185 195 206 218 232 248 267 (Continued)

TABLE 2.13 Runoff Lengths (ft) for Horizontal Curves with Design Speeds from 15 to 80 mi/h (24 to 129 km/h) and Superelevation Rates to 12 Percent Based on One Lane Rotated about the Centerline (Continued) e V = 50 mi/h Vd = 55 mi/h Vd = 60 mi/h Vd = 65 mi/h Vd = 70 mi/h Vd = 75 mi/h Vd = 80 mi/h (%) Lr (ft) Lr (ft) Lr (ft) Lr (ft) Lr (ft) Lr (ft) Lr (ft) 1.5 0 0 0 0 0 0 0 2.0 48 51 53 56 60 63 69 2.2 53 56 59 61 66 69 75 2.4 58 61 64 67 72 76 82 2.6 62 66 69 73 78 82 89 2.8 67 71 75 78 84 88 96 3.0 72 77 80 84 90 95 103 3.2 77 82 85 89 96 101 110 3.4 82 87 91 95 102 107 117 3.6 86 92 96 100 108 114 123 3.8 91 97 101 106 114 120 130 4.0 96 102 107 112 120 126 137 4.2 101 107 112 117 126 133 144 4.4 106 112 117 123 132 139 151 4.6 110 117 123 128 138 145 158 4.8 115 123 128 134 144 152 165 5.0 120 128 133 140 150 158 171 5.2 125 133 139 145 156 164 178 5.4 130 138 144 151 162 171 185 5.6 134 143 149 156 168 177 192 5.8 139 148 155 162 174 183 199 6.0 144 153 160 167 180 189 206 6.2 149 158 165 173 186 196 213 6.4 154 163 171 179 192 202 219 6.6 158 169 176 184 198 208 226 6.8 163 174 181 190 204 215 233 7.0 168 179 187 195 210 221 240 7.2 173 184 192 201 216 227 247 7.4 178 189 197 207 222 234 254 7.6 182 194 203 212 228 240 261 7.8 187 199 208 218 234 246 267 8.0 192 204 213 223 240 253 274 8.2 197 209 219 229 246 259 281 8.4 202 214 224 234 252 265 288 8.6 206 220 229 240 258 272 295 8.8 211 225 235 246 264 278 302 9.0 216 230 240 251 270 284 309 9.2 221 235 245 257 276 291 315 9.4 226 240 251 262 282 297 322 9.6 230 245 256 268 288 303 329 9.8 235 250 261 273 294 309 336 10.0 240 255 267 279 300 316 343 10.2 245 260 272 285 306 322 350 10.4 250 266 277 290 312 328 357 10.6 254 271 283 296 318 335 363 10.8 259 276 288 301 324 341 370 11.0 264 281 293 307 330 347 377 11.2 269 286 299 313 336 354 384 11.4 274 291 304 318 342 360 391 11.6 278 296 309 324 348 366 398 11.8 283 301 315 329 354 373 405 12.07 288 306 320 335 360 379 411 Conversions: 1 mi/h = 1.609 km/h, 1 ft = 0.305 m. Source: A Policy on Geometric Design of Highways and Streets, American Association of State Highway and Transportation Officials, Washington, D. C., 2004, with permission.

NOTE: The diagrams below show positioning of the superelevation transition for both simple curves and spiral curves. Only one of these conditions would exist for a given transition.

LEGEND: X = Length of superelevation transition.

L = Length of superelevation runoff.

T = Tangent runout R = Crown removal

G = Equivalent slope rate of Change of outside pavement edge compared to the control line In each case. (See Table 2.13 for values.)

N = Normal cross slope S = Full superelevation rate

FIGURE 2.9 Superelevation transition between tangent and simple or spiral curves for three cases. (From Location and Design Manual, Vol. 1, Roadway Design, Ohio Department of Transportation, with permission) edge of pavement from a half-flat section to a fully superelevated section. The length of transition required to remove the pavement crown (R in Fig. 2.9) is generally equal to twice the T distance.

The minimum superelevation transition length X should be equal in feet to 3 times the design speed in miles per hour. This includes the tangent runout (T) as previously described. The reason to specify this minimum is to avoid the appearance of a “kink” in
the roadway that a shorter transition would provide. The distance is approximately equal to that traveled by a vehicle in 2 s at design speed. This requirement does not apply to low-speed roadways, temporary roads, superelevation transitions near intersec­tions, or transitions between adjacent horizontal curves (reverse or same direction) where normal transitions would overlap each other. In these cases, the minimum transi­tion length is determined by multiplying the edge of pavement correction by the equiv­alent slope rate (G) shown in Table 2.14. The rate of change of superelevation should be constant throughout the transition X. Some agencies use a flatter rate of transition through the T or R sections than that recommended in Table 2.14, an acceptable but unnecessary practice.

The values given for Lr in Tables 2.12 and 2.13 are based on one 12-ft (3.66-m) lane revolved about the centerline. Table 2.14 shows methods of calculating L when more lanes are revolved about the centerline. In the equations in Table 2.14, L is sub­stituted for Lr. In addition to the terms described in Fig. 2.9, two additional ones are used. W is the width from the point of revolution to the outside edge of pavement. For example, if three 12-ft (3.66-m) lanes are revolved about the lane edge between lanes 2 and 3, then W = 3 X 12 = 36 ft (11 m); the wider section of pavement is used for the width. B is an adjustment factor for multilane pavements to allow for some reduction in the superelevation transition for roads other than interstates, freeways, expressways, and ramps. Section (a) in Table 2.14 lists the equivalent slope rate values G for the various design speeds. Section (b) provides the multilane adjustments factors B for the speeds. Section (c) calculates the value of the overall transition length X based on the values given in (a) and (b) along with a given W and S for each case in Fig. 2.9. Finally, section (d) tests the values calculated to ensure that the minimum transition length discussed in this section is provided. Values for X, L, and T can be lengthened if necessary to achieve a 2-s transition time.

Superelevation Position. Figure 2.9 shows the recommended positioning of the proposed superelevation transition in relationship to the horizontal curve. For those curves with spirals, the transition from adverse crown removal to full superelevation should occur within the limits of the spiral. In other words, the spiral length should equal the L value, usually rounded to the nearest 25 ft (7.6 m).

For simple curves without spirals, the L transition should be placed so that 50 to 70 percent of the maximum superelevation rate is outside the curve limits (point of curvature PC to point of tangency PT). It is recommended that whenever possible, two-thirds of the full superelevation rate be present at the PC and PT. See the case diagrams in Fig. 2.9 for a graphic presentation of the recommended positioning.

Profiles and Elevations. Breakpoints at the beginning and end of the superelevation transition should be rounded to obtain a smooth profile. One suggestion is to use a “vertical curve” on the edge of the pavement profile with a length in feet equal to the design speed in mi/h (i. e., 45 ft for 45 mi/h). The final construction plans should have the superelevation tables or pavement details showing the proposed elevations at the centerline, pavement edges, and, if applicable, lane lines or other breaks in the cross slopes. Pavement or lane widths should be included where these widths are in transition. Pavement edge profiles should be plotted to an exaggerated vertical profile within the limits of the superelevation transitions to check calculations and to determine the location of drainage basins. Adjustments should be made to obtain smooth profiles. Special care should be taken in determining edge elevations in a transition area when the profile grade is on a vertical curve.

Superelevation between Reverse Horizontal Curves. When two horizontal curves are in close proximity to each other, the superelevation transitions calculated independently

TABLE 2.14 Superelevation Notes for Adjusting Runoff Lengths in Tables 2.12 and 2.13 (a) Maximum relative gradients for profiles between the edge of pavement and the centerline or reference line Design speed, mi/h Relative gradient Equivalent slope rate, G 20 0.74 135:1 25 0.70 143:1 30 0.66 152:1 35 0.62 161:1 40 0.58 172:1 45 0.54 185:1 50 0.50 200:1 55 0.47 213:1 60 0.45 222:1 65 0.43 233:1 70 0.40 250:1

(b) Transition length adjustment factors for wide pavements Number of lanes B for interstates, freeways, B for from point of rotation expressways, and ramps other roadways 1.0 1.00 1.00 1.5 1.00 0.83 2.0 1.00 0.75 2.5 1.00 0.70 3.0 1.00 0.67 3.5 1.00 0.64 (c) Calculate X, L, T Case I Cases II and III X = BW(S + N)G X = BWSG L = BWSG L = BW(S — N/2)G T = BWNG T = BW(N/2)G (d) Check for 2-second minimum transition

(Note: D is the linear ft equivalent of the design speed in mi/h. For example, D = 60 ft for 60 mi/h)

If X > 3D, then the values for X, L, and T from section (c) are valid.

If X < 3D, then recalculate X, L, and T as follows:

Case I	Cases II and III
X = 3D	X = 3D
L = 3D[S/(N + S)]	L = 3D[(2S — N)/2S]
T = 3D[N/(N + S)]	T = 3D(N/2S)

Conversion: 1 mi/h = 1.609 km/h.

General notes:

1. The Lr in Tables 2.12 and 2.13 is the same as L in Table 2.14 and is based on a two-lane 24-ft pavement revolved about the centerline.

2. Adjustments to L for varying two-lane pavement widths can be made by direct proportion. For a 20-ft pave­ment revolved about the centerline, L’ = L(20/24).

3. Determination of X, L, and T when more than one lane is revolved about the centerline (or other reference line, such as a baseline or edge of pavement) is shown in part (c). Values for G and B in the formulas are given in parts (a) and (b), respectively. The value for W is the pavement width from the point of rotation to the farthest edge.

4. The minimum length of superelevation transition (X) as discussed in the text is the distance traveled in 2 s. This number can be rounded off to a figure in feet equal to 3 times the design speed. In part (d) the calculated X value is compared to the value of 3D, where D is the linear feet equivalent of the design speed in miles per hour. If the value of 3D is larger, X is set equal to this value and L and T are adjusted accordingly.

5. The L value is also the recommended spiral length where spirals are used.

Source: Location and Design Manual, Vol. 1, Roadway Design, Ohio Department of Transportation, with

permission.

may overlap each other. In these cases, the designer should coordinate the transitions to provide a smooth and uniform change from the full superelevation of the first curve to the full superelevation of the second curve. Figure 2.10 shows two diagrams sug­gesting ways in which this may be accomplished. In both diagrams each curve has its own L value (L1, L2) depending on the degree of curvature, and the superelevation is revolved about the centerline.

PAV	‘EMENT REVOLVED ABC LI	3UT THE CENTERLINE L2	—
JL.	-50Lito. TOLi,	.50L2to. T0L2	—— .—————— ——
	D.
—	PT«		® PCI	—_______ d) 2 ———————-
S.-5 Ut SIMPLE CURVES

PA	VEMENT REVOLVED ABOUT THE CENTERLINE . L3	—
LI		L2
	D
CS«I	ST[1]I		TS		SC*2
SPIRAL CURVES

LEGEND:

(A) — Centerline Pavement (D — Outside EP. Curve I,

Inside EP. Curve 2 E. P.=Edge of Pavement

© — Inside EP, Curve I, Outside EP. Curve 2 Si, S2 = Superelevation Rates: Curves I & 2 Li, L2 = Superelevation Transition Lengths: Curves I <t 2 D = Distance between Curves

L3 = Total Superelevation Transition between Spiral Curves

FIGURE 2.10 Superelevation transition between reverse horizontal curves, simple or spiral. (From Location and Design Manual, Vol. 1, Roadway Design, Ohio Department of Transportation, with permission)

The top diagram involves two simple curves. In the case of new or relocated align­ment, the PT of the first curve and the PC of the second curve should be separated by enough distance to allow a smooth, continuous transition between the curves at a rate not exceeding the G value for the design speed (Table 2.14). This requires that the distance be not less than 50 percent nor greater than 70 percent of L1 + L2. Two-thirds is the rec­ommended portion. When adapting this procedure to existing curves where no alignment revision is proposed, the transition should conform as closely as possible to the above cri­teria. When the available distance between the curves is less than 50 percent of L1 + L2, the transition rate may be increased and/or the superelevation rate at the PT or PC may be set to less than 50 percent of the full superelevation rate.

The lower diagram involves two spiral curves. Where spiral transitions are used, the spiral-to-tangent (ST) point of the first curve and the tangent-to-spiral (TS) transi­tion of the second curve may be at, or nearly at, the same location, without causing superelevation problems. In these cases, the crown should not be reestablished as shown in Fig. 2.9, but instead, both pavement edges should be in continual transition between the curves, as shown in the lower diagram of Fig. 2.10. The total superelevation transition length is the distance between the curve-to-spiral (CS) point of the first curve and spiral-to-curve (SC) point of the second curve.

Spiral Transitions. When a motor vehicle enters or leaves a circular horizontal curve, it follows a transition path during which the driver makes adjustments in steering to account for the gain or loss in centrifugal force. For most curves, the average driver can negotiate this change in steering within the normal width of the travel lane. However, combinations of higher speeds and sharper curvature may cause the driver to move into an adjacent travel lane while accomplishing the change. To prevent this occurrence, the designer should use spirals to smooth out transitions.

There are several advantages to using spiral transitions for horizontal curves:

• They provide an easy-to-follow path for the driver to negotiate.

• They provide a convenient area in which to place the superelevation transition.

• They provide an area where the pavement width can be transitioned when required for curve widening.

• They provide a smoother appearance to the driver.

The Euler spiral is the one most commonly used in highway design. The degree of curve varies gradually from zero at the tangent end to the degree of the circular arc at the curve end. By definition, the degree of curve at any point along the spiral varies directly with the length measured along the spiral. In the case where a spiral transition connects two simple curves, the degree of curve varies directly from that of the first circular arc to that of the second circular arc. As a general guideline, spirals should be used on roadways where the design speed is 50 mi/h (80 km/h) or greater and the degree of curvature exceeds the values given in Table 2.15 for various design speeds listed.

Horizontal Alignment Considerations. The following items should be considered when establishing new horizontal alignment: •

TABLE 2.15 Maximum Curve without a Spiral Design speed, mi/h Design speed, km/h Max. degree of curve Min. radius, ft Min. radius, m 50 80 4°30′ 1273 388 55 88 3°45′ 1528 466 60 96 3°00′ 1910 582 65 105 2°30′ 2292 699 70 113 2°15′ 2546 776 Source: Location and Design Manual, Vol. 1, Roadway Design, Ohio Department of Transportation, with permission.

• Tangents and/or flat curves should be provided on high, long fills.

• Compound curves should be used only with caution.

• Abrupt alignment reversals should be avoided.

• Two curves in the same direction separated by a short tangent (broken-back or flat — back curves) should be avoided.