The Way of Vertical Alignment Design

Once you designed a horizontal alignment for your highway section, it's time to design your vertical alignment.

First, let's talk about the actual geometry of a vertical alignment, and later, we will go into more depth on the actual design process.

Vertical alignment consists of straights connected by parabolic curves, which need to be provided at all changes in gradient. The parabolic curves can be divided into two groups: crest and sag curves. A crest curve is a curve used when the change in grade is negative, for example, hills. On the contrary, a sag curve is a curve used where the change in grade is positive, for example, valleys. Both types of curves are defined by three major points: Point of Vertical Curvature (PVC), Point of Vertical Intersection (PVI), and Point of Vertical Tangency (PVT). Please see Figure 1.0 for illustration.

The first red line, looking from left to right, defines the uphill straight (+) gradient, while the second (smaller) defines the downhill straight (-) gradient.

When designing a vertical alignment, a certain curvature based on the relevant standards should be followed (dependent on the design speed).

Let's revisit the table (Figure 2.0) from the CD109 Highways Link Design standard.

If you look at the vertical curvature section, you will see a letter K and a word K value for each sag and crest curve. Simply put, the K value tells us about the horizontal distance along which a 1 % change in grade occurs on the crest or a sag curve.

For example, for the design speed of 50 km/h, the desirable minimum K value of the crest curve is 10, and of the sag curve is 9. If this is not achievable, then if your design speed is in the BAND A, you can go one step below the desirable min crest K value of 6.5 in this particular case.

When designing a vertical alignment with a crest curve for a single carriageway up to the design speed of 120 km/h, you also need to be mindful of the full overtaking sight distance (FOSD). FOSD is measured from vehicle to vehicle, 1.05 - 2.00 m above the centre of the carriageway.

In regards to the sag curve design, the main factors to satisfy here are driver comfort and clearance from structures (such as bridges situated on sag curves). If you want to satisfy the driver's comfort, then the appropriate sag curve length will suffice. To calculate the most appropriate curve length, we can use the formula in Figure 3.0 below:

Let's calculate the length of the sag vertical curve (for the most driver's comfort) for a single carriageway road with a design speed of 85 km/h and A of 0.08 (descending gradient of 3 % with an ascending gradient of 5 %). Please take a look at the Figure 4.0.

After using the formula from Figure 3.0, we get L= 148.20 m (Figure 5.0).

It's worth mentioning that you will rarely be able to achieve this sag curve length (for 3 % descending and 5 % ascending gradient) in the real world, especially on a single-carriageway road.

Now, let's take a look at the sag curve length to satisfy the criterion clearance from structures.

Let's assume you have a bridge located within your sag curve with a clearance of 6.5 m. What will be the necessary sag curve length for a single carriageway road with a design speed of 85 km/h?

First, you need to determine your desired/minimum stopping sight distance for your design speed and then see whether it falls within the sag curve length.

For the design speed of 85 km/h, the desirable minimum SSD is 160 m. In order to determine whether the sight distance lies outside the sag curve length or not, you need to calculate the value e (vertical offset) as per Figure 6.0 below and then compare it to the driver's eye height of 1.05 m (assumed).

In our case, for p of 0.05 (ascending gradient), q of 0.03 (descending gradient) and L of 160 m, e equals 0.4 m. Since e < H1 (1.05 m - the driver's eye height) and S>L, our sight distance is greater than the curve length. Therefore, we can calculate the required length of the sag curve (clearance condition) using the formula below in Figure 7.0.

In our practical case we get Lm of 537 m.

CD109 requirements for vertical alignment design

CD109 states that for motorways, desirable maximum longitudinal gradient should be 3 %, for all-purpose dual carriageways 4 % and for all-purpose single carriageways 6 % with appropriate relaxations as per table 1.0 below.

On the other hand, the minimum longitudinal gradient should be 0.5 % (for drainage purposes) for kerbed roads.

Some practical tips for an efficient vertical alignment design

Here are some practical vertical alignment design tips from my experience:

• A very well-picked horizontal route can save you many headaches when designing a vertical alignment, such as balancing cuts & fills, staying within the max gradient threshold, etc. Always, if you have freedom, choose a horizontal route, which will result in minimal cut-and-fill quantities.
• Tie-in to the existing road is very important. You should never tie in with the straight gradient but rather with an appropriate sag or crest curve (with allowable gradient). Some councils require a 1:20 for a tie-in with the main access roads.
• Always design for two criteria: safety (sight distance) and comfort (sag or crest min curve length), as described here.
• When designing a vertical alignment of a road (centreline, curb return), a satisfactory longitudinal gradient (no less than 0.5 %) should be applied for drainage purposes.
• When dealing with the raised shared surfaces, the vertical offset is a function of the vertical alignment raise rather than a fixed gradient.
• Where possible, departures from standards and lengthy subject discussions with the overseeing agencies should be avoided for the sake of saving time & resources while progressing with the project.

If you want to learn more about highway and drainage engineering design tips please join the group Highway & Drainage Engineering Design in C3D & InfoDrainage Tips & Tricks.