Modelling Link Gradients
The latest in Multimodal’s series of technical blogs for microsimulation modelling focuses on the calculating and modelling of link gradients.
As with all of our technical posts, we acknowledge that these are not ‘set-in-stone’ methodologies and other techniques and processes may exist. However, we want to share our current processes to encourage feedback and improvement, as well as providing some guidance for those looking for a starting point on specific modelling methodologies.
When developing a base VISSIM model, there is a need to review the gradients on the critical* links and include gradients which may have an impact** on the power and acceleration / deceleration profiles of all vehicle types modelled.
*Multimodal’s definition of ‘critical’ links includes grade-separated junction (GSJ) off and on-slips and other links which are a key part of the base model, or have the potential to be a key part of any future testing . A more refined definition cannot be given as those links deemed ‘critical’ will be depend on the nature, size and complexity of the network modelled.
**Multimodal’s definition of ‘impact’ is for any road gradient which is over 3% for a minimum distance of 100m .
From the PTV VISSIM Help documentation, the maximum acceleration and maximum deceleration profiles in VISSIM are affected as follows:
-0.1 m/s² per gradient percent incline (the maximum accelerating power decreases when the deceleration power increases)
+0.1 m/s² per gradient percent decline (the maximum accelerating power increases when the deceleration power decreases).
First up, reviewing the existing network
Up until very recently, Multimodal used the website Doogal (www.doogal.co.uk/RouteElevation.php) to review road gradients. This allowed users to draw sections of route and then the associated elevation and gradient was shown (see examples in Figure 1 below).
Figure 1 – Doogal Gradient Examples
However, a recent change by Google to the Pricing Structure has meant that access through Doogal for gradient calculations now requires a Google API code.
As a workaround to this, Multimodal now use Mapometer (https://gb.mapometer.com/), which is commonly used by cyclists and other sports enthusiasts for route planning. In much the same way as Doogal, sections can be manually drawn to identify the elevation and gradients, as shown in Figure 2.
Figure 2 – Mapometer Gradient Examples
So how are these calculated for VISSIM?
Having produced gradient graphs for all the GSJ off and on-slips, along with the models’ critical links, the next step is to convert these into VISSIM gradients.
Taking the off-slip example from Figure 2, this can be broken down into 5 main sections as shown in Figure 3.
Figure 3 – Off-Slip Gradient Sections
The sections allow gradients to be calculated based on the scale on the right hand side, which are then converted into VISSIM gradients by using the end gradient figure* for each section, as shown below.
*It is acknowledged that there are more mathematical methods for producing a more accurate gradient percentages. However, by taking the end-point over small sections, the modelling of on-street gradients is able to be undertaken in a quick, simple and justifiable manner.
How are these modelled in VISSIM?
So, having defined the section lengths and the associated gradients, the next stage is to split the associated VISSIM links on the off-slip to replicate each of the sections and then apply the specific gradients to the links in the ‘Other’ tab within Link Attributes (as shown in Figures 4 and 5 below).
Figure 4 – Split Link Sections in VISSIM
Figure 5 – Applying Gradients to Specific Links using ‘Other’ Tab
This process can then be repeated for all sections where gradients are required to be modelled.
This methodology of modelling link gradients has allowed Multimodal to develop microsimulation models which take into account gradients on the more critical links in the network and the potential impacts associated with them through the power and acceleration / deceleration profiles.
It is acknowledged that this is not the only methodology for modelling gradients, but we feel it does provide a quick, simple and justifiable method in developing more realistic base models for validation.
As with other modelling elements, if more site specific data is available to evidence and justify adjustments to the gradient percentages used, then these should be considered and documented as part of the model development exercise.