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3-6 I A Policy on Geometric of Highways and Streets A strict application of the maximum relative gradient criterion provides runofflengths for four-lane undivided roadways that are double those for two-lane roadways; those for six-lane undivided roadways would be tripled. While lengths of this order may be considered desirable, it is often not practical to provide such lengths in design. On a purely empirical basis, it is recommended that minimum superelevation runoff lengths be adjusted downward to avoid excessive lengths for multilane roadways. The recommended adjustment factors are presented in Table 3-6. The adjustment factors listed in Table 3-6 are directly applicable to undivided streets and highways. Development of runoff for divided highways is discussed in more detail later in the subsection titled, "Axis of Rotation with a Median." The topic of runoff superelevation for turning roadway designs at intersections and through interchanges is discussed in Chapters 9 and 0, respectively. Table 3-6. Adjustment Factor for Number of lanes Rotated f.g Metric, @ iiii\!iii! tls.<ustomary length Increase length Increase Number of Adjustment Relative to One- Number of Adjustment Relative to One- lanes Rotated, Factor, * lane Rotated, lanes Rotated, Factor, * lane Rotated, n bw n bw (= n b w ) (= n b w ).00.0.00.0.5 0.83.5.5 0.83.5 0.75.5 0.75.5.5 0.70.75.5 0.70.75 3 0.67.0 3 0.67.0 3.5 0.64.5 3.5 0.64.5 One Lane Rotated Laoe Lane Two Lanes Rotated Three Lanes Rotated Lanes Normal Section Normal Section Laoe Lanes Rotated Lane ct Lanes Lanes Rotated Normal Section e±:j 3 Lanes 3 Lanes Rotated * b w =[ + 0.5 (nl -)]/n Typical minimum superelevation runofflengths are presented in Table 3-7. The lengths shown represent cases where one or two lanes are rotated about a pavement edge. The former case is found on two-lane roadways where the pavement is rotated about the centerline or on one-lane interchange ramps where the pavement rotation is about an edge line. The latter case is found on multilane undivided roadways where each direction is separately rotated about an edge line. Page 0

Table 3-7b. Superelevation Runoff Lr (tt) for Horizontal Curves U.$r Customary Vcr 5 mph Vd = 0 mph Vd = 5 mph Vd= 30 mph Vd= 35 mph Vd= 40 mph Vd=45 mph Vd= mph Vd= mph Vd= mph Vd= mph Vd= 70 mph Vd= 75 mph Vd= mph Number of Lanes Rotated. Note that ane rotated is typical for a -lane highway, lanes rotated is typical for a 4-lane highway, etc. (See Table 3-6.) e(%).5.0..4.6.8 3.0 3. 3.4 3.6 3.8 4.0 4. 4.4 4.6 4.8 5.0 5. 5.4 5.6 5.8 6.0 6. 6.4 6.6 6.8 7.0 7. 7.4 7.6 7.8 8.0 8. 8.4 8.6 8.8 9.0 9. 9.4 9.6 9.8 0.0 0. 0.4 0.6 0.8.0..4.6.8.0 3 3 34 37 40 43 46 49 5 6 68 7 74 77 83 86 89 9 95 98 0 05 08 4 7 0 3 6 9 3 35 38 4 45 48 5 54 57 63 66 69 7 75 78 8 85 35 46 5 69 74 78 83 88 9 97 0 06 5 0 5 9 34 38 43 48 5 57 6 66 7 75 85 89 94 98 03 08 7 6 3 35 40 45 49 54 63 68 7 77 4 3 36 39 4 45 49 5 6 68 7 75 78 8 88 9 94 97 0 04 07 0 4 7 0 3 6 30 33 36 39 43 46 49 5 56 59 6 69 7 75 78 8 85 88 9 95 37 49 54 63 68 73 78 83 88 9 97 0 07 7 6 3 36 4 46 5 56 6 70 75 85 90 95 99 04 09 4 9 4 9 34 38 43 48 53 63 68 7 77 8 9 6 34 38 4 45 48 5 6 69 7 75 79 8 86 89 96 99 03 06 0 3 7 0 3 7 30 34 37 4 44 47 5 54 6 68 7 75 78 8 85 89 9 95 99 0 06 39 5 57 6 67 7 77 8 98 03 08 3 8 3 9 34 39 44 49 54 59 70 75 85 90 95 0 06 6 6 3 37 4 47 5 57 6 67 73 78 83 88 98 303 309 7 36 40 44 47 5 6 69 73 76 9 95 98 0 05 09 3 6 0 4 7 3 35 38 4 45 49 53 56 64 67 7 75 78 8 85 89 96 00 04 07 5 8 4 7 76 8 98 04 09 5 0 5 3 36 4 47 53 64 69 75 85 9 96 0 07 3 8 4 9 35 40 45 5 56 6 67 73 78 89 95 300 305 3 36 3 37 9 39 43 46 54 6 66 70 74 77 8 85 89 97 0 05 08 6 0 4 8 3 35 39 43 47 5 59 63 66 70 74 78 8 86 90 94 97 0 05 09 3 7 5 8 3 44 64 70 75 8 99 05 0 6 8 34 39 45 5 57 63 68 74 86 9 97 03 09 5 6 3 38 44 6 67 73 79 85 90 96 30 308 34 39 35 33 337 343 348 3 4 46 54 6 66 70 74 79 83 9 95 99 03 08 6 0 4 8 3 37 4 45 49 53 57 6 66 70 74 78 8 86 90 94 99 03 07 5 9 3 8 3 36 40 44 48 47 6 68 74 8 99 06 8 4 30 37 43 49 6 68 74 86 9 99 05 7 3 30 36 4 48 54 6 67 73 79 86 9 98 304 30 37 33 39 335 34 348 354 366 37 33 44 49 53 6 67 7 76 89 98 0 07 6 0 4 9 33 38 4 47 5 56 64 69 73 78 8 9 96 00 04 09 3 8 7 3 36 40 44 49 53 6 67 67 73 00 07 3 0 7 33 40 47 53 67 73 00 07 3 0 7 33 40 47 53 67 73 300 307 33 30 37 333 340 347 353 367 373 3 3 3 400 36 48 53 6 67 7 77 8 86 9 96 0 06 0 5 0 5 30 34 39 44 49 54 63 68 73 78 8 9 97 0 06 6 6 30 35 40 45 54 59 64 69 74 78 83 88 54 7 79 86 94 0 08 5 30 37 44 5 66 73 94 0 09 6 3 30 38 45 5 59 66 74 8 88 95 30 30 37 34 33 338 346 353 367 374 38 389 396 403 40 48 45 43 38 5 56 6 66 7 77 8 9 97 0 07 7 3 8 33 38 43 48 53 63 69 74 79 89 94 99 04 09 4 0 5 30 35 40 45 66 7 76 8 86 9 96 30 306 77 9 00 07 5 3 30 38 46 53 6 69 76 9 99 07 4 30 37 45 53 68 76 83 9 99 306 34 3 39 337 345 35 368 375 383 39 398 406 44 4 49 437 444 45 4 40 53 59 64 69 75 85 9 96 0 07 7 3 8 33 39 44 49 7 76 8 9 97 03 08 3 9 4 9 35 40 45 5 56 6 67 7 77 83 88 99 304 309 35 30 88 96 04 0 8 36 44 5 68 76 9 00 08 6 4 3 40 48 56 64 7 88 96 304 3 30 38 336 344 35 368 376 3 39 400 408 46 44 43 440 448 456 464 47 4 4 56 6 67 73 78 89 95 00 06 7 3 8 34 40 45 5 56 6 67 73 79 90 95 0 07 8 3 9 34 40 46 5 57 6 68 73 79 85 90 96 30 307 33 38 34 39 335 63 9 00 09 7 6 34 4 5 59 67 76 0 09 8 6 34 43 5 68 76 85 30 30 38 37 335 343 35 368 377 385 3 40 40 49 47 435 444 45 4 469 477 486 494 45 66 7 78 90 96 0 08 4 0 6 3 38 44 56 6 68 74 86 9 98 04 0 6 8 34 40 46 5 64 70 76 8 88 94 300 306 3 38 34 330 336 34 348 354 68 90 99 08 7 6 35 44 53 6 7 89 98 07 6 5 34 43 5 6 70 79 88 97 306 35 34 333 34 35 369 378 3 396 405 44 43 43 44 4 459 468 477 486 495 4 53 5 53 540 47 63 69 76 8 88 95 0 07 4 0 6 33 39 45 5 64 7 77 83 89 96 0 08 5 7 34 40 46 53 59 7 78 9 97 303 309 36 3 38 335 34 347 354 366 373 379 7 95 04 4 3 33 4 5 6 7 89 99 08 8 7 37 46 56 75 94 303 33 3 33 34 35 369 379 388 398 407 47 46 436 445 4 464 474 483 4 5 5 53 540 549 9 568 5 69 75 8 89 96 03 0 7 3 30 37 44 5 7 78 85 9 99 06 3 9 6 33 40 47 54 6 67 74 8 88 95 30 309 35 3 39 336 343 3 357 363 370 377 3 39 398 405 4 77 03 3 3 34 44 54 75 85 95 06 6 6 37 47 57 67 78 88 98 309 39 39 339 3 370 38 39 40 4 4 43 44 453 463 473 483 494 4 54 535 545 5 566 576 6 597 7 67 n ::r- OJ -0 r-t- ro w I m ro 3 ro r-tvi o-+> o ro VI oti' w en U Page

00;00;00;00;00;00;00;00 3-54 A Policy on Geometric of Highways and Streets METRIC 6 4 0 «ai ""0 (9 o 0 Q) U C i:s u o.0 Q) OJ =< V = 0 v = K=7 v = K = v = 70 K = 7 v = K = 6 V=90 K = 39 v = 0 K = 74 ++--------------------------------------------+----- --- v = 30 km/h K = 4 ---------s = L _00_0 0-00_00- Drainage Maximum K = 5 - - - - -Computer S > L 00 00 300 400 0 0 Length of Crest Vertical Curve, L (m) 6 u.s. CUSTOMARY 4 «ai ""0 co (5 0 o Q) U C i:s u o.0 Q) OJ =< v = K = 5 v = 75 +-H+-++----------------r-------r=----+------K=3 V = mph K = 3 --------- S = L _0 0 _00_00_00- Drainage Maximum K = 67 - - - - - Computer S > L 00 400 0 0 000 00 400 0 0 000 Length of Crest Vertical Curve, L (ft) Figure 3-43. Controls for Crest Vertical Curves-Open Road Conditions Page

Chapter 3-Elements of I 3- Table 3-34. Controls for Crest Vertical Curves Based on Stopping Sight Distance Metric a,,': ", Speed (km/h) Stopping Sight Distance (m) Calculated 0 0 30,.., ;,, Rate of Vertical Curvature, Ka : u.s. Customary, Rate of Vertical Curvature, Ka Speed (mph) Stopping Sight Distance (tt) Calculated 0.6 5 3.0 3 35.9 0 5 6. 7 40 3.8 4 5. 6.4 7 30 00 8.5 9 85.0 35 9.0 9 70 05 6.8 7 40 305 43. 44 30 5.7 6 45. 6 90 38.9 39 45 83.7 00 85 5.0 5 495 3.5 4 0 0 73.6 74 570.6 5 0 95.0 95 645 9.8 30 85 3.4 4 70 730 46.9 47 75 3.6 3 90 383.7 3 Rate of vertical curvature, K, is the length of curve per percent algebraic difference in intersecting grades (A), K = L/A. The values of K derived above when S is less than L also can be used without significant error where S is greater than L. As shown in Figure 3-4, extension of the diagonal lines to meet the vertical lines for minimum lengths of vertical curves results in appreciable differences from the theoretical only where A is small and little or no additional cost is involved in obtaining longer vertical curves. For night driving on highways without lighting, the length of visible roadway is that roadway that is directly illuminated by the headlights of the vehicle. For certain conditions, the minimum stopping sight distance values used for design exceed the length of visible roadway. First, vehicle headlights have limitations on the distance over which they can project the light intensity levels that are needed for visibility. When headlights are operated on low beams, the reduced candlepower at the source plus the downward projection angle significantly restrict the length of visible roadway surface. Thus, particularly for highspeed conditions, stopping sight distance values exceed road-surface visibility distances afforded by the low-beam headlights regardless of whether the roadway profile is level or curving vertically. Second, for crest vertical curves, the area forward of the headlight beam's point of tangency with the roadway surface is shadowed and receives only indirect illumination. Since the headlight mounting height (typically about 0. m [.00 ft]) is lower than the driver eye height used for design (.08 m [3. ft]), the sight distance to an illuminated object is controlled by the height of the vehicle headlights rather than by the direct line of sight. Any object within the shadow zone must be high enough to extend into the headlight beam to be directly illuminated. On the basis of Equation 3-4, the bottom of the headlight beam is about 0.40 m [.30 ft] above the roadway at a distance ahead of the vehicle equal to the stopping sight distance. Although the vehicle headlight system does limit roadway Page 3

Chapter 3-Elements of I 3-59 METRIC 6 4 «0)- "'0 CO (5 0 o \ 0) 8 () c 0) 6 i:5 () o.0 4 0) 0) «\ \ K= 63 v = 30 km/h K = 73 S=L Drainage Maximum K = 5 Computed Values S > L 0 00 00 300 400 0 0 Length of Sag Vertical Curve, L (m) 6 u.s. CUSTOMARY 4 «oi "'0 (9 0 o 0) () C i:5 () Oro.0 0) 0) «S=L Drainage Maximum K = 67 Computed Values S > L V = K = 36 00 400 0 0 000 00 400 0 0 000 Length of Sag Vertical Curve, L (ft) Figure 3-44. Controls for Sag Vertical Curves-Open Road Conditions The effect on passenger comfort of the change in vertical direction is greater on sag than on crest vertical curves because gravitational and centripetal forces are combining rather than opposing forces. Comfort Page 4

Chapter 3-Elements of I 3-6 wherever practical, but special attention to drainage should be exercised where values of K in excess of 5 m [67 ft] per percent change in grade are used. Minimum lengths of vertical curves for flat gradients also are recognized for sag conditions. The values determined for crest conditions appear to be generally suitable for sags. Lengths of sag vertical curves, shown as vertical lines in Figure 3-44, are equal to 0.6 times the design speed in km/h [three times the design speed in mph]. Sag vertical curves shorter than the lengths computed from Table 3-36 may be justified for economic reasons in cases where an existing feature, such as a structure not ready for replacement, controls the vertical profile. In certain cases, ramps may also be designed with shorter sag vertical curves. Fixed-source lighting is desirable in such cases. For street design, some engineers accept design of a sag or crest where A is about percent or less without a length of calculated vertical curve. However, field modifications during construction usually result in constructing the equivalent to a vertical curve, even if short. Table 3-36. Controls for Sag Vertical Curves Metric a.- " t,,-','r. u.s. Customary Stopping Rate of Vertical Stopping Rate of Vertical Speed Sight Dis- Curvature, KG Speed Sight Dis- Curvature, KG (km/h) tance (m) Calculated (mph) tance (tt) Calculated 0 0. 3 5 9.4 0 30 35 5. 6 0 5 6.5 7 40 8.5 9 5 5.5 6. 3 30 00 36.4 37 85 7.3 8 35 49.0 49 70 05.6 3 40 305 63.4 64 30 9.4 30 45 78. 79 90 37.6 38 45 95.7 96 00 85 44.6 45 495 4.9 5 0 0 54.4 570 35.7 36 57 0 6.8 63 645 56.5 30 85 7.7 73 70 730.3 8 75 05.6 06 90 3.0 3 Rate of vertical curvature, K, is the length of curve (m) per percent algebraic difference intersecting grades (A), K =LIA. Sight Distance at Undercrossings Sight distance on the highway through a grade separation should be at least as long as the minimum stopping sight distance and preferably longer. of the vertical alignment is the same as at any other point on the highway except in some cases of sag vertical curves underpassing a structure as illustrated in Figure 3-45. While not a frequent concern, the structure fascia may cut the line of sight and limit the sight distance to less than otherwise is attainable. It is generally practical to provide the minimum length of sag vertical curve at grade separation structures, and even where the recommended grades are exceeded, Page 5