Anchor: #CHDJFHHH

Section 4: Horizontal Alignment

Anchor: #i1085865

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 andAppendix A, Superelevation Rate.

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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, Vertical Alignment.
Anchor: #BGBHGEGC

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

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

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.



NOTE: Online users can view the metric version of this table in PDF format.

Anchor: #i1621441Table 2-4: Horizontal Curvature of Highways without Superelevation

Design Speed (mph)

6%

Min. Radius (ft)1

8%

Min. Radius (ft)1

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

1 Normal crown (2%) maintained



NOTE: Online users can view the metric version of this table in PDF format.

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: #BGBIIDDD

Superelevation Rate

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

NOTE: Online users can view the metric version of this equation in PDF format.

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 these reasons, horizontal curves on low-speed streets in urban areas are frequently designed without superelevation, and centrifugal force is counteracted solely with side friction.

Table 2-5 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 Table 2-5 with a given curve radius of 400 ft [110 m] and determine that through interpolation, the related design speed is approximately:

  • 35 mph for positive crown condition
  • 32 mph for negative crown condition

Table 2-5 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, Table 2-5 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 2-5 indicates an approximate superelevation rate of 2.4 percent.

Anchor: #i1321746Table 2-5: Minimum Radii and Superelevation for Low-Speed Urban Streets

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:

  1. Computed using Superelevation Distribution Method 2.
  2. Superelevation may be optional on low-speed urban streets.
  3. Negative superelevation values beyond -2.0% should be used for low type surfaces such as gravel, crushed stone, and earth. However, areas with intense rainfall may use normal cross slopes on high type surfaces of -2.5%.


NOTE: Online users can view the metric version of this table in PDF format.

Superelevation Rate on High-Speed Facilities. Tables 2-6 and 2-7 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: #i1431298Table 2-6: Minimum Radii for Design Superelevation Rates, Design Speeds, and emax = 6%

e

(%)

15 mph R (ft)

20 mph R (ft)

25 mph R (ft)

30 mph R(ft)

35mph R (ft)

40 mph R (ft)

45 mph R (ft)

50 mph R (ft)

55 mph R (ft)

60 mph R (ft)

65mph R (ft)

70 mph R (ft)

75 mph R (ft)

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



NOTE: Online users can view the metric version of this table in PDF format.

Anchor: #i1569750Table 2-7: Minimum Radii for Design Superelevation Rates, Design Speeds, and emax = 8%

e

(%)

Vd= 15mph R(ft)

Vd= 20mph R(ft)

Vd= 25mph R(ft)

Vd= 30mph R(ft)

Vd= 35mph R(ft)

Vd= 40mph R(ft)

Vd= 45mph R(ft)

Vd= 50mph R(ft)

Vd= 55mph R(ft)

Vd= 60mph R(ft)

Vd= 65mph R(ft)

Vd= 70mph R(ft)

Vd= 75mph R(ft)

Vd= 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



NOTE: Online users can view the metric version of this table in PDF format

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 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: #i1548651Table 2-8: Maximum Relative Gradient for Superelevation Transition

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.



NOTE: Online users can view the metric version of this table in PDF format.

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

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

Where:

LCT = 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”).

NOTE: Online users can view the metric version of this equation in PDF format.

Example determinations of superelevation transition shown in Figure 2-1.

Determination of Length of Superelevation
Transition. Click here to see a PDF of
the image. (click in image to see full-size image) Anchor: #SHEQIPOIgrtop

Figure 2-1. Determination of Length of Superelevation Transition. Click here to see a PDF of the image.

NOTE: Online users can view the metric version of this figure in PDF format.

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 (LCT) calculation is desirable, the length for multilane highways may become impractical for design purposes (e.g. drainage problems, avoiding bridges, accommodating merge/diverge condition). In such cases, an adjustment factor may be used to avoid excessive lengths such that the transition length formula becomes:

LCT = b[(CS)(W)]/G (US Customary and Metric)

where “b” is defined in Table 2-9

Anchor: #i1357549Table 2-9: Multilane Adjustment Factor1

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 discussion under “Axis of Rotation with a Median”.



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 2-10. When spiral curves are used, the transition usually is distributed over the length of the spiral curve.

Anchor: #i1550164Table 2-10: Portion of Superelevation Transition Located on the Tangent1

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, 2011, pg. 3-67).



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: #YWUECXWM

Superelevation Transition Type

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 2-1. 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 2-1 shows reverse parabolas over the full length of the transition. Alternative methods for developing smooth-edge 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: #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.

Where:

M = middle ordinate (ft)

S = stopping sight distance (ft) and,

R = radius (ft)

NOTE: Online users can view the metric version of this equation in PDF format.

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

(US). Stopping Sight Distance on Horizontal
Curves. Click here to see a PDF of
the image. (click in image to see full-size image) Anchor: #i1034244grtop

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

NOTE: Online users can view the metric version of this figure in PDF format.

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.

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