Table of Contents

8.6.3 Crest Vertical Curves

Curvature of crest vertical curves is usually governed by sight distance requirements. However, the form of the road may dictate larger values to provide satisfactory appearance of the curve. These criteria are discussed below.

Crest vertical curves on undivided roads

Crest vertical curve lengths greater than the minimum are appropriate where they can be economically used or where they give a better fit to the topography. However, the quest for overtaking sight distance on vertical curves may be impractical and not always effective.

The level of service of an undivided road is improved if the vertical alignment provides a large proportion of overtaking opportunities. This is particularly true in the moderate traffic volume range. Therefore, it is desirable to provide for overtaking sight distance, where economically possible, to delay the need for carriageway duplication.

Examination of vertical curves along individual sections of roadway may give scope for increasing the proportion of the road providing overtaking opportunities as follows:

  • Where the available sight distance is less than the overtaking sight distance, an increase in the length of the vertical curve may permit the overtaking zones on each side of the crest to be extended, to allow limited overtaking over the crest.
  • Where the available sight distance is between the stopping sight distance and the overtaking sight distance, and it is not economically feasible to increase the length of the vertical curve to provide adequate overtaking, a decrease in the length of the vertical curve may enable the overtaking zones on each side of the crest to be extended. Stopping sight distance must still be available on the shortened vertical curve.

Additionally, many drivers refuse to pass on such curves despite adequate sight distance. It may be more appropriate to construct an auxiliary lane on a short vertical curve than to obtain overtaking sight distance by the use of a long vertical curve. Further, the provision of a short vertical curve in conjunction with longer approach and departure grades will result in more useable overtaking opportunities.

Appearance

At very small changes of grade, a vertical curve has little influence other than appearance of the profile and may be omitted – refer Section 8.6.7. At any significant change of grade, minimum vertical curves detract from the appearance. This is particularly evident on high standard roads.

Table 8.6 gives minimum K values for satisfactory appearance. Larger K value curves may be preferred where they can be used without conflicting with other design requirements, e.g. overtaking, drainage and where they give a better fit to the topography.

The designer should avoid unnecessarily large crest curves for longitudinal drainage reasons (to prevent water ponding near the apex). Large crest curves also increase the length of road subject to restricted sight distance. Designers should limit the length of crest curve that has less than 0.3% to 0.5% grade to about 30–50 m. Consideration should also be given to the provision of independently graded drains to facilitate drainage along crests or on otherwise flat grades.

The values in Table 8.6 are subjective approximations and therefore the lack of precision is intentional.

Table 8.6: Length of crest vertical curves – appearance criterion when S < L

Operating speed

(km/h)

Min. grade change requiring a crest vertical curve %(1)

Minimum length of crest vertical curve

(m)

Minimum K value(2)

S < L

401.020–3020–30
500.930–4033–44
600.840–5050–62
700.750–6071–86
800.660–80100–133
900.580–100160–200
1000.480–100200–250
1100.3100–150333–500
1200.2100–150333–500
1300.1100–150333–500
  1. In practice, crest vertical curves are provided at all changes of grade.
  2. Round resultant L values up to nearest 5 m. Values determined with SSD for reaction time = 2 sec and d = 0.36.

Sight distance criteria (crest)

The minimum crest vertical curve and K values are calculated using expressions from Appendix J, values of car stopping distance from Table 5.5, and formulae from Section 5.3 and Section 8.6.2.

Minimum crest vertical curve K values are shown in Table 8.7 for various operating speeds, reaction times, and vertical height constraints. Table 8.8 provides minimum crest vertical curve K values to satisfy intermediate sight distance.

Designers should be aware that there are economical and environmental considerations relating to the use of factors in Table 8.7, for example:

  • Generally it is only possible to use a value of d = 0.26 for ‘major highways and freeways’ at greenfield locations where topography permits an economic and environmentally sensitive design solution to be developed (i.e. flat terrain). This value should generally not be adopted for freeways or major highways in undulating or hilly terrain because of the relatively high cost involved and the greater visual and environmental impact. For these reasons, use of d = 0.26 (shaded area of Table 5.5) should only be used with the written approval of the relevant road agency when project objectives are being established.
  • Adoption of desirable minimum values for ‘most urban and rural road types’ (d = 0.36) is considered appropriate for most existing highway and freeway upgrades (brownfields locations) and where topography dictates that a solution using ‘desirable values for major highways and freeways’ criteria would produce an unacceptable solution (either economically or environmentally).
  • Appropriate design criteria for crest curves (sight distance) to be adopted in Table 8.7 for specific projects should be agreed to within a road agency when project objectives are being established.

Table 8.9 provides the minimum size crest vertical curves for truck stopping sight distance. Guidance on truck stopping sight distance is provided in Section 5.2.3.

Table 8.7: Minimum size crest vertical curve (K value) for sealed roads (S < L)

Design speed
(km/h)

Based on stopping sight distance for a car(1)
h1 = 1.1 m h2 = 0.2 m

Absolute minimum values for specific road types and situations(2)
based on d = 0.46(3)(4)
Desirable minimum values for most urban and rural road types
based on d = 0.36
Values for major highways and freeways in flat terrain(8)
based on d = 0.26
RT = 1.5 s(5)RT = 2.0 sRT = 2.5 sRT = 1.5 s(5)RT = 2.0 sRT = 2.5 sRT = 2.0 sRT = 2.5 s
40 2.1 2.9 2.6 3.5 4.8
50 4.0 5.4 5.2 6.8 9.6
60 7.0 9.2 9.3 11.8 17.2
70 11.3 14.6 15.3 19.1 28.6
80 17.3 22.0 23.9 29.3 44.6
90 25.5 31.8 38.8 35.5 42.9 51.0 66.6 76.6
100 44.5 53.7 60.8 71.4 95.7 109.0
110 60.6 72.3 83.6 97.3 133.4 150.6
120 80.6 95.3 112.2 129.6 181.1 202.9
130 105.1 123.3 147.6 169.1 240.5 267.7
Minimum capability
provided by the crest
vertical curve size(6)
Car stopping at night(7)

d = 0.61 (dry road braking),

h1 = 0.65 m, h2 = 0.3 m.

d = 0.46, h1 = 0.65 m, h2=  0.5 m.

d = 0.53 (dry road braking), h1 = 0.65 m, h2 = 0.2 m.

d = 0.46, h1 = 0.65 m, h2 = 0.3 m.

d = 0.37, h1 = 0.65 m,
h2 = 0.2 m.
Truck stopping d = 0.29, h1 = 2.4 m, h2= 0.3 m. d = 0.25, h1 = 2.4 m, h2 = 0.2 m. d = 0.18, h1 = 2.4 m,
h2 = 0.2 m.
Truck stopping at night(7)d = 0.29, h1 = 1.05 m, h2= 1.25 m.

d = 0.29, h1 = 1.05 m, h2 = 0.6 m.

d = 0.26, h1 = 1.05 m,

h2 = 0.2 m.

  1. If the roadway is on a grade, adjust the stopping sight distance values by the process described in Note 5 of Table 5.5 to calculate the minimum size crest curve.
  2. These values are only suitable in constrained locations. Examples of this in Australia are:
    - lower volume roads
    - mountainous roads
    - lower speed urban roads
    - sighting over or around barriers.
  3. On any horizontal curve with a side friction factor greater than the desirable maximum value, reduce the coefficient of deceleration by 0.05 and calculate the crest curve size according to Equation 1 (Section 5.3) and Equation 18.
  4. Where deceleration values greater than 0.36 are used, minimum road widths for supplementary manoeuvre capability should be provided. For two‑lane, two‑way roads, a desirable minimum width of 12 m and a minimum of 9 m is applicable. This is especially important on horizontal curves with a side friction demand greater than the desirable maximum in Table 5.3.
  5. Reaction times of 1.5 s cannot be used in Western Australia. A 1.5 s reaction time is only to be used in constrained situations where drivers will be alert. Typical situations are given in Table 5.2. The general minimum reaction time is 2.0 s.
  6. These check cases define what stopping capability is provided for other combinations of driver and lighting conditions, to give designers confidence that reasonable capability is provided for these other conditions. The check cases assume the same combination of design speed and reaction time as those listed in the table, except:
    - where shown otherwise in the table
    - that the 120 km/h and 130 km/h speeds are not used for the truck cases.
  7. Many of the sight distances corresponding to the minimum crest size are greater than the range of most headlights (that is, 120–150 m). In addition, tighter horizontal curvature will cause the light beam to shine off the pavement (assuming 3° lateral spread each way).
  8. Green shaded area of Table 8.7 should only be used with the written approval of the relevant road agency when project objectives are being established.

Note: Combinations of design speed and reaction times not shown in this table are generally not used.

Table 8.8: Minimum size crest vertical curve (K value) for sealed roads to satisfy intermediate sight distance (S < L)

Design speed
(km/h)

Based on intermediate sight distance for cars(1)

K value

h1 = 1.1 m
h2 = 1.25 m
d = 0.36(2)

RT = 2 sRT = 2.5 s
50
60
70 36.4
80 55.8
90 81.8 97.2
100 115.9 136.2
110 159.4 185.6
120 214.0 247.0
130 281.4 322.4
Minimum capability provided
by the crest vertical curve size(3)
Car stopping at nightDrivers will see the glow from oncoming headlights well before they need to start braking.
Truck stoppingd = 0.23, h1 = 2.4 m, h2 = 2.4 m.
Truck stopping at nightDrivers will see the glow from oncoming headlights well before they need to start braking.
  1. If the roadway is on a grade, adjust the stopping sight distance values by the process described in Note 5 of Table 5.5 to calculate the minimum size crest curve.
  2. In constrained locations on one-lane, two-way roads, a coefficient of deceleration of 0.46 may be used. For any horizontal curve with a side friction factor greater than the desirable maximum value for cars (in constrained locations on one‑lane, two‑way roads), use a coefficient of deceleration of 0.41. The resultant crest curve size can then be calculated according to Equation 1 (Section 5.3) and Equation 18.
  3. These check cases define what stopping capability is provided for other combinations of driver and lighting conditions, to give designers confidence that reasonable capability is provided for these other conditions. The check cases assume the same combination of design speed and reaction time as those listed in the table, except that the 120 km/h and 130 km/h speeds are not used for the truck cases.

Notes:

  • Combinations of design speed and reaction times not shown in this table are generally not used.
  • The K values in this table are derived by using Equation 18, using double the calculated sight distance as discussed in Section 5.8.
  • RT is reaction time.

Table 8.9: Minimum size crest vertical curve (K value) to satisfy truck stopping sight distance for sealed roads (S < L)

Design speed (km/h)

Truck stopping sight distance K value

h1 = 2.4 m and h2 = 0.2 m

RT=1.5 sRT=2.0 sRT=2.5 s
40 2 2 3
50 4 5 6
60 7 8 10
70 11 14 17
80 18 22 25
90 27 32 37
100 46 53
110 64 73

Note: RT is reaction time.

Hidden dip grading

On long lengths of straight alignment, particularly in slightly rolling country, hidden dips should be avoided wherever possible. At times, in periods of high glare or poor visibility, and because of the foreshortening effect due to the level of the eye, an illusion of apparent continuity of pavement omitting the dip is sometimes created.

Hidden dips contribute to overtaking manoeuvre crashes, the overtaking driver being deceived by the view of highway beyond the dip free of opposing vehicles. Even with shallow dips, this type of road profile is disconcerting because the driver cannot be sure whether or not there is an oncoming vehicle or obstacles on the road (such as stock) hidden beyond the crest. This type of profile can be avoided by appropriate horizontal curvature or by more gradual grades made possible by heavier cuts and fills.

It is preferred that the entire pavement surface is visible in these cases. However, if there is no alternative, a maximum depression of 60 mm below the driver’s line of sight may be tolerated. Guidance on the limited depth of depression gives confidence to drivers, and road edge guide posts at close intervals provide an acceptable method.

Floodways

The longitudinal grade on the approach to floodways must be carefully designed to:

  • avoid discomfort to the occupants of vehicles
  • provide stopping sight distance to the pavement level in a short floodway
  • ensure that drivers are not mislead regarding the extent and depth of the floodway.

The vertical curves should be designed in accordance with the comfort criteria described in Section 8.6.4. For floodways, it is important that drivers can see the presence of water on the road and the sight distance should be checked to ensure that stopping sight distance is achieved to the road pavement (object height = 0.0 m) to enable drivers to see debris on the road or washouts.

In flat country, the presence of the floodway must be obvious to the driver and a relatively short, sharp entrance to the floodway section (within the comfort criterion) should be provided. It is also essential to avoid more than one level in a floodway. That is, once the driver has entered the floodway with water across it, there must be no deeper water at some point further along the floodway. This type of design is misleading to drivers and can result in a dangerous situation.