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## Section 5: Horizontal Alignment

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### Overview

It is necessary to establish the proper relation between design speed and curvature when designing roadway alignment. The two basic elements of horizontal curves are:

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### General Considerations for Horizontal Alignment

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

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• Flatter than minimum curvature for any particular design speed should be used where possible, while retaining the minimum guidelines for the most critical conditions;
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• Alignment consistency should be sought. Sharp curves should not follow long tangents or a series of flat curves;
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• Sharp curves should be avoided on long, high fills. It is difficult for drivers to perceive the extent of curvature and adjust their operation accordingly when the adjacent topography does not extend above the level of the roadway;
• Compound curves (two adjacent curves in the same direction with different radii) should be used with caution and should be avoided on mainlanes where conditions permit the use of simple curves. Where compound curves are used, the ratio of the flatter radius to the sharper radius should not exceed 3:2 (i.e., R1 should not exceed 1.5R2). For intersections or other turning roadways (such as loops, connections, and ramps), this ratio may be increased to 2:1 (i.e., R1 may be increased to 2R2);
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• Reverse curves (two adjacent curves in opposite directions) on high-speed facilities should include a tangent section of sufficient length to provide adequate superelevation transition between the curves;
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• Broken-back curves (two curves in the same direction with a short tangent between the curves) should be avoided if feasible. This configuration is unexpected by drivers, not pleasing in appearance, and more difficult for freight truck maneuverability; and
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• Horizontal alignment and its associated design speed should be consistent with other design features and topography. Coordination with vertical alignment is discussed in Chapter 2, Section 6, Combination of Vertical and Horizontal Alignment.
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The design of roadway curves should be based on an appropriate relationship between design speed and curvature as well as their joint relationships with superelevation rate and side friction. The minimum radii of curves are important control values in designing for safe operation. Design guidance for low-speed urban facilities (45-mph or less) is shown in Table 2-3. Design guidance for curvature of high-speed (50-mph or greater) or non-urban facilities is shown in Table 2-4 and Table 2-5 for maximum superelevation (emax) rates equal to 6 percent and 8 percent respectively.

For high-speed design conditions, the maximum allowable deflection angle without a horizontal curve is 30 minutes. For low-speed design conditions, the maximum allowable deflection angle without a horizontal curve is 1 degree.

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### Superelevation Rate

As a vehicle traverses a horizontal curve, it undergoes a centripetal acceleration that acts toward the center of the curve. Vehicle weight, roadway superelevation, and side friction between the tires and pavement surface sustain this acceleration. The equation that governs vehicle operation on a horizontal curve is:

Where:

e = superelevation rate, ft/ft

f = side friction factor

V = vehicle speed, mph

There are practical upper limits to the rate of superelevation. The Department normally uses a maximum superelevation rate of 6 percent. However, a maximum rate of 8 percent may be used where higher superelevation rates or sharper curves are desired. The recommended maximum for facilities where there is a regular occurrence of very-slow moving vehicles, whose operation might be affected by high superelevation rates is 6 percent. Use of 8 percent should be coordinated with the District Design Engineer prior to implementation and documented in the project files.

Superelevation Rates on Low-Speed Urban Facilities

Although superelevation is advantageous for traffic operations, various factors often combine to make its use impractical in many urban areas. These factors include the following:

For these reasons, horizontal curves on low-speed urban facilities are frequently designed with normal crown. The centripetal acceleration, in this case, is counteracted solely with side friction. The term “normal crown” (NC) represents an equal downward pavement cross-slope, typically 2 percent, on each side of the axis of rotation.

Low-speed urban facilities should be designed using normal crown, such that superelevation is not necessary where practical. This is accomplished by using the negative e-values from Table 2-3. However, when superelevation is needed, a maximum superelevation rate of 4 percent should be used. This is accomplished by using the positive e-values from Table 2-3 to determine the superelevation rate for specific curvature and design speed conditions.

Table 2-3 shows the relationship of radius, superelevation rate, and design speed for low-speed urban facility design and should be used to evaluate existing conditions or the need for superelevation for proposed conditions on low-speed urban facilities. This table may also be used for design of detour alignments in constrained conditions.

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• Example:

Given a design speed of 35 mph and a 400 ft radius curve, Table 2-3 indicates an approximate superelevation rate of 2.4 percent should be used.

For a normal crown section, the negative e-value (the slope on the outside of the curve) will always be the controlling value for a given design speed.

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• Example:

Given a design speed of 45 mph and 1,050-ft radius curve, Table 2-3 indicates that a normal crown of 2 percent cross slope in each direction should be used.

Anchor: #i1321746Table 2-3: Minimum Radii and Superelevation Rates1 for Low-Speed Urban Facilities

Design Speed

e (%)

15 mph R (ft)

20 mph R (ft)

25 mph R (ft)

30 mph R (ft)

35 mph R (ft)

40 mph R (ft)

45 mph R (ft)

-4.02

54

116

219

375

583

889

1,227

-3.02

52

111

208

353

544

821

1,125

-2.82

51

110

206

349

537

808

1,107

-2.62

51

109

204

345

530

796

1,089

-2.52,3

51

109

203

343

527

790

1,080

-2.42

51

108

202

341

524

784

1,071

-2.22

50

108

200

337

517

773

1,055

-2.0

50

107

198

333

510

762

1,039

-1.54,5

49

105

194

324

495

736

1,000

-1.04,5

48

103

189

316

480

711

964

-0.54,5

48

101

185

308

467

688

931

05,6

47

99

181

300

454

667

900

0.55

46

97

177

293

441

646

871

1.05

45

95

174

286

430

627

844

1.55

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. See AASHTO's A Policy on Geometric Design of Highways and Streets for the different types of Superelevation Distribution Methods.
2. Normal crown values beyond -2.0% should be used for surfaces such as gravel, crushed stone, and earth.
3. Areas with paved surfaces that receive more frequent rainfall events with high intensities and greater depths than other areas may use 2.5% normal crown.
4. For the purpose of evaluating existing conditions, normal crown values up to -1.5% may be used.
5. Values ranging from -1.5% to +1.5% should only be used in special circumstances such as intersections.
6. 0% is provided for information purposes only and should not be used for design.

Superelevation Rate on High-Speed or Non-Urban Facilities

Table 2-4 and 2-5 show superelevation rates (maximum 6 percent and 8 percent, respectively) for various design speeds and radii. These tables should be used for high-speed or non-urban facilities. For multi-lane facilities, particularly where wide medians are used, the radius applies to the inside edge of the innermost travel lane.

Anchor: #i1431298Table 2-4: Minimum Radii and Superelevation Rates1for High-Speed or Non-Urban Facilities, emax = 6%

Design Speed

e (%)

15 mph R (ft)

20 mph R (ft)

25 mph R (ft)

30 mph R (ft)

35 mph R (ft)

40 mph R (ft)

45 mph R (ft)

50 mph R (ft)

55 mph R (ft)

60 mph R (ft)

65 mph R (ft)

70 mph R (ft)

75 mph R (ft)

80 mph R (ft)

NC3,4

868

1,580

2,290

3,130

4,100

5,230

6,480

7,870

9,410

11,100

12,600

14,100

15,700

17,400

RC3,4

614

1,120

1,630

2,240

2,950

3,770

4,680

5,700

6,820

8,060

9,130

10,300

11,500

12,900

2.2

543

991

1,450

2,000

2,630

3,370

4,190

5,100

6,110

7,230

8,200

9,240

10,400

11,600

2.4

482

884

1,300

1,790

2,360

3,030

3,770

4,600

5,520

6,540

7,430

8,380

9,420

10,600

2.6

430

791

1,170

1,610

2,130

2,740

3,420

4,170

5,020

5,950

6,770

7,660

8,620

9,670

2.8

384

709

1,050

1,460

1,930

2,490

3,110

3,800

4,580

5,440

6,200

7,030

7,930

8,910

3.0

341

635

944

1,320

1,760

2,270

2,840

3,480

4,200

4,990

5,710

6,490

7,330

8,260

3.2

300

566

850

1,200

1,600

2,080

2,600

3,200

3,860

4,600

5,280

6,010

6,810

7,680

3.4

256

498

761

1,080

1,460

1,900

2,390

2,940

3,560

4,250

4,890

5,580

6,340

7,180

3.6

209

422

673

972

1,320

1,740

2,190

2,710

3,290

3,940

4,540

5,210

5,930

6,720

3.8

176

358

583

864

1,190

1,590

2,010

2,490

3,040

3,650

4,230

4,860

5,560

6,320

4.0

151

309

511

766

1,070

1,440

1,840

2,300

2,810

3,390

3,950

4,550

5,220

5,950

4.2

131

270

452

684

960

1,310

1,680

2,110

2,590

3,140

3,680

4,270

4,910

5,620

4.4

116

238

402

615

868

1,190

1,540

1,940

2,400

2,920

3,440

4,010

4,630

5,320

4.6

102

212

360

555

788

1,090

1,410

1,780

2,210

2,710

3,220

3,770

4,380

5,040

4.8

91

189

324

502

718

995

1,300

1,640

2,050

2,510

3,000

3,550

4,140

4,790

5.0

82

169

292

456

654

911

1,190

1,510

1,890

2,330

2,800

3,330

3,910

4,550

5.2

73

152

264

413

595

833

1,090

1,390

1,750

2,160

2,610

3,120

3,690

4,320

5.4

65

136

237

373

540

759

995

1,280

1,610

1,990

2,420

2,910

3,460

4,090

5.6

58

121

212

335

487

687

903

1,160

1,470

1,830

2,230

2,700

3,230

3,840

5.8

51

106

186

296

431

611

806

1,040

1,320

1,650

2,020

2,460

2,970

3,560

6.0

39

81

144

231

340

485

643

833

1,060

1,330

1,660

2,040

2,500

3,050

Notes:

1. Computed using Superelevation Distribution Method 5. See AASHTO's A Policy on Geometric Design of Highways and Streets for the different types of Superelevation Distribution Methods.
• The term "NC" (normal crown) represents an equal downward cross-slope, typically 2%, on each side of the axis of rotation.
• The minimum curve radii for normal crown are suitable up to 3.0%.
• 3.0% normal crown should only be used when 3 or more lanes are sloped in the same direction.
• 1.5% or flatter normal crown should only be used for the design of special circumstance, such as table-topping intersections, or the evaluation of existing conditions.
2. The term "RC" (reverse crown) represents a curve where the downward, or adverse, cross-slope should be removed by superelevating the entire roadway at the normal cross-slope rate.
3. For curve radii falling between normal crown and reverse crown, rather than interpolation a superelevation rate equal to the normal crown should typically be used.

Anchor: #i1569750Table 2-5: Minimum Radii and Superelevation Rates1for High-Speed or Non-Urban Facilities, emax = 8%

Design Speed

e

(%)

15 mph R(ft)

20 mph R(ft)

25 mph R(ft)

30 mph R(ft)

35 mph R(ft)

40 mph R(ft)

45 mph R(ft)

50 mph R(ft)

55 mph R(ft)

60 mph R(ft)

65 mph R(ft)

70 mph R(ft)

75 mph R(ft)

80 mph R(ft)

NC2,4

932

1,640

2,370

3,240

4,260

5,410

6,710

8,150

9,720

11,500

12,900

14,500

16,100

17,800

RC3,4

676

1,190

1,720

2,370

3,120

3,970

4,930

5,990

7,150

8,440

9,510

10,700

12,000

13,300

2.2

605

1,070

1,550

2,130

2,800

3,570

4,440

5,400

6,450

7,620

8,600

9,660

10,800

12,000

2.4

546

9,59

1,400

1,930

2,540

3,240

4,030

4,910

5,870

6,930

7,830

8,810

9,850

11,000

2.6

496

872

1,280

1,760

2,320

2,960

3,690

4,490

5,370

6,350

7,180

8,090

9,050

10,100

2.8

453

796

1,170

1,610

2,130

2,720

3,390

4,130

4,950

5,850

6,630

7,470

8,370

9,340

3.0

415

730

1,070

1,480

1,960

2,510

3,130

3,820

4,580

5,420

6,140

6,930

7,780

8,700

3.2

382

672

985

1,370

1,820

2,330

2,900

3,550

4,250

5,040

5,720

6,460

7,260

8,130

3.4

352

620

911

1,270

1,690

2,170

2,700

3,300

3,970

4,700

5,350

6,050

6,800

7,620

3.6

324

572

845

1,180

1,570

2,020

2,520

3,090

3,710

4,400

5,010

5,680

6,400

7,180

3.8

300

530

784

1,100

1,470

1,890

2,360

2,890

3,480

4,140

4,710

5,350

6,030

6,780

4.0

277

490

729

1,030

1,370

1,770

2,220

2,720

3,270

3,890

4,450

5,050

5,710

6,420

4.2

255

453

678

955

1,280

1,660

2,080

2,560

3,080

3,670

4,200

4,780

5,410

6,090

4.4

235

418

630

893

1,200

1,560

1,960

2,410

2,910

3,470

3,980

4,540

5,140

5,800

4.6

215

384

585

834

1,130

1,470

1,850

2,280

2,750

3,290

3,770

4,310

4,890

5,530

4.8

193

349

542

779

1,060

1,390

1,750

2,160

2,610

3,120

3,590

4,100

4,670

5,280

5.0

172

314

499

727

991

1,310

1,650

2,040

2,470

2,960

3,410

3,910

4,460

5,050

5.2

154

284

457

676

929

1,230

1,560

1,930

2,350

2,820

3,250

3,740

4,260

4,840

5.4

139

258

420

627

870

1,160

1,480

1,830

2,230

2,680

3,110

3,570

4,090

4,640

5.6

126

236

387

582

813

1,090

1,390

1,740

2,120

2,550

2,970

3,420

3,920

4,460

5.8

115

216

358

542

761

1,030

1,320

1,650

2,010

2,430

2,840

3,280

3,760

4,290

6.0

105

199

332

506

713

965

1,250

1,560

1,920

2,320

2,710

3,150

3,620

4,140

6.2

97

184

308

472

669

909

1,180

1,480

1,820

2,210

2,600

3,020

3,480

3,990

6.4

89

170

287

442

628

857

1,110

1,400

1,730

2,110

2,490

2,910

3,360

3,850

6.6

82

157

267

413

590

808

1,050

1,330

1,650

2,010

2,380

2,790

3,240

3,720

6.8

76

146

248

386

553

761

990

1,260

1,560

1,910

2,280

2,690

3,120

3,600

7.0

70

135

231

360

518

716

933

1,190

1,480

1,820

2,180

2,580

3,010

3,480

7.2

64

125

214

336

485

672

878

1,120

1,400

1,720

2,070

2,470

2,900

3,370

7.4

59

115

198

312

451

628

822

1,060

1,320

1,630

1,970

2,350

2,780

3,250

7.6

54

105

182

287

417

583

765

980

1,230

1,530

1,850

2,230

2,650

3,120

7.8

48

94

164

261

380

533

701

901

1,140

1,410

1,720

2,090

2,500

2,970

8.0

38

76

134

214

314

444

587

758

960

1,200

1,480

1,810

2,210

2,670

Notes:

1. Computed using Superelevation Distribution Method 5. See AASHTO's A Policy on Geometric Design of Highways and Streets for the different types of Superelevation Distribution Methods.
• The term "NC" (normal crown) represents an equal downward cross-slope, typically 2%, on each side of the axis of rotation.
• The minimum curve radii for normal crown are suitable up to 3.0%.
• 3.0% normal crown should only be used when 3 or more lanes are sloped in the same direction.
• 1.5% or flatter normal crown should only be used for the design of special circumstance, such as table-topping intersections, or the evaluation of existing conditions.
2. The term "RC" (reverse crown) represents a curve where the adverse, or negative, cross-slope should be removed by superelevating the entire roadway at the normal cross-slope rate.
3. For curve radii falling between normal crown and reverse crown, a superelevation rate equal to the normal crown should typically be used.

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 occur over a length adequate for the usual travel speeds. Transition lengths should also account for potential future traveled way widening, including widening associated with the ultimate typical section in a schematic.

Desirable design values for length of superelevation transition are based on a given maximum relative gradient between profiles of the edge of traveled way and the axis of rotation. Table 2-6 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 2-6: Maximum Relative Gradient (G) for Superelevation Transition

Design Speed (mph)

(%)

Equivalent Maximum Relative Slope (run:rise)

15

0.89

1:112

20

0.80

1:125

25

0.73

1:137

30

0.67

1:150

35

0.62

1:162

40

0.57

1:175

45

0.53

1:187

50

0.50

1:200

Note:

1. Maximum relative gradient for profile between edge of traveled way and axis of rotation.

Desirable transition length, LCT can be calculated using the following equation:

Where:

LCT = Calculated desirable transition length, ft

CS = Change in cross slope of superelevated pavement, percent

W = distance between the axis of rotation and the edge of traveled way, ft

G = maximum relative gradient ( Table 2-6).

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

Figure 2-2. 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 (LCT) calculation is desirable, the length for multi-lane facilities may become impractical for design purposes (e.g., drainage problems, avoiding bridges, accommodating merge/diverge condition). A minimum length (LCT), can be calculated using adjustment factors as shown in Table 2-7, such that the transition length formula becomes:

where “b” is defined in Table 2-7. In the case of one lane being rotated, “b” is 1.0, such that LCT (min) = LCT (des)

Anchor: #i1357549Table 2-7: Multilane Adjustment Factor1

Number of Lanes Rotated

(n)

(b)

1.5

0.83

2

0.75

2.5

0.70

3

0.67

3.5

0.64

Note:

1. These adjustment factors are directly applicable to undivided facilities. For divided facilities where the axis of rotation is not the edge of traveled way, see AASHTO’s A Policy on Geometric Design of Highways and Streets.

Anchor: #EFCGXLVU

### Superelevation Transition Placement

The transition with respect to the termini of a simple (circular) curve should be placed to minimize lateral acceleration and the vehicle's lateral motion. The recommended allocation of superelevation transition on the tangent, preceding or following a curve, is provided on Table 2-8. For superelevation on bridge structures, it is preferred to begin/end superelevation at the bridge bent line. When spiral curves are present on an existing facility and alignment modifications aren't practical, refer to AASHTO’s A Policy on Geometric Design of Highways and Streets for transition distribution.

Anchor: #i1550164Table 2-8: 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

Note:

1. These values are recommendations based on prevailing research. A value between 0.7 and 0.9 for all speeds and rotated widths is considered acceptable. Refer to AASHTO’s A Policy on Geometric Design of Highways and Streets for additional information.

Care must be exercised in designing the length and location of the superelevation transition. Pavement surfaces should be modeled to ensure proper drainage, especially near the high or low portions of Type I or III vertical curves (see Figure 2-5 for curve types). A plot of roadway contours may assist with the verification of grades and identification of drainage problems in areas of superelevation transition. Desirably, a minimum profile grade line (PGL) of 0.5 percent and minimum edge-of-pavement (EOP) profile grade of 0.2 percent (0.5 percent for curbed roadways) should be maintained throughout the transition section. At a minimum, either criterion should be met.

Whenever reverse curves are closely spaced and superelevation transition lengths overlap, transition lengths (LCT) should be adjusted to ensure that roadway cross slopes are in the proper direction for each horizontal curve. For proposed construction of new facilities, the tangent section between reverse curves should be of sufficient length such that minimum transition lengths for each transition do not overlap.

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### Superelevation Transition Type

Linear or reverse parabolic transitions may be used for attaining superelevation. Where appearance is a factor (e.g., curbed sections and retaining walls) use of reverse parabolic is recommended. This produces an outer edge profile that is smooth, undistorted, and pleasing in appearance. However, for bridges, linear transitions are generally preferred for constructability, ride quality, and lower cost. Notate the transition type in the plans to ensure the transition is properly constructed.

Figure 2-2 shows reverse parabolic and linear transitions over the full length of the transition. Refer to AASHTO’s A Policy on Geometric Design of Highways and Streets for alternative methods for developing smooth-edge profiles over the length of the transition.

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### Sight Distance on Horizontal Curves

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

The following equation applies only to circular curves longer than the stopping sight distance (S<L) for the pertinent design speed. For example, with a 50-mph design speed and a curve with a 1,150-ft radius, a clear sight area with a horizontal sight line offset (HSO) of approximately 20-ft is needed for stopping sight distance.

Where:

HSO = horizontal sight line offset, ft

S = stopping sight distance (Table 2-1), ft

R = radius at centerline of inner most travel lane, ft

This method for calculating HSO is only exact when both the vehicle and sight obstruction are located within the horizontal curve. When the vehicle or sight obstruction are located outside of the horizontal curve (i.e. S>L) this method will result in an HSO slightly larger than required. In many instances the resulting additional clearance will not be significant. In some cases, the design should be checked either by using graphical procedures or computational methods to verify HSO. NHCRP 910 provides computational methods for verifying HSO.

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, and high ground do not restrict the sight distance required in either direction. Figure 2-3 illustrates a graphical approach to determining horizontal sight distance in a curve.

Figure 2-3. Diagram Illustrating Components for Determining Horizontal Sight Distance. Source: AASHTO's A Policy on Geometric Design of Highways and Streets

Where sufficient stopping sight distance is not available because a railing, longitudinal barrier or other features constitutes a sight obstruction, alternative designs should be considered. Potential alternatives include: (1) increasing the offset to the obstruction or (2) increasing the radius. However, the alternative should not incorporate a shoulder width on the inside of the curve in excess of 12-ft because of the concern that drivers will use wider shoulders as a passing or travel lane.