# **2.1 Routing Data**

Plotting the road network, while informative about its extent, does not permit a rigorous assessment of its efficiency. Routing engines<sup>4</sup> provide more precise information on how cars can use the network to get from A to B. In my case, A and B could be anywhere on the continent. Two approaches invite themselves to choose points: (1) using a uniform spatial grid and taking the cell centroids, or (2) selecting the centers of important cities/places. In this paper, I employ both approaches, but for spatial analysis, the grid approach is more suitable. Hence, I begin with it.

Accurate spatial analysis at the continental scale warrants using an equally spaced grid. Discrete Global Grid Systems (DGGS) provide these via hierarchical tessellation of cells partitioning the globe. Sahr et al. (2003) propose the Icosahedral Snyder Equal Area Aperture 3 Hexagon (ISEA3H) as a good general-purpose Geodesic DGGS. The grid is implemented as part of the DGGRID C++ library (Sahr, 2022), accessed via the ’dggridR’ R package (Barnes, 2020). To limit complexity, I choose a resolution 9 ISEA3H grid, with a cell area of 2591.4km<sup>2</sup> and a centroid spacing of 50.28km. Partitioning the African mainland and Madagascar with this grid yields 12,016 cells.

Figure 3: Grid Cell Centroids and OSRM Route Starting and End Points Grid Centroids (Inaccessible Cells in Grey) Actua ~~l~~ Route Starting/Destination Points _<u>Notes:</u>_ <u>Figure shows centroids of 50.28km ISEA3H grid</u> (LHS) <u>and the nearest road segment to each centroid (RHS).</u> To compute a large number of routes, I configure a server with the Open Source Routing Machine (OSRM)<sup>5</sup> and a copy of the Africa OSM from the 5th of June 2023, and compute fastest car routes between all cell centroids. This amounts to 12,016<sup>2</sup> _−_ 12,016 = 144,372,240 routes, for which I obtain both the road distance in _m_ and the estimated travel time in minutes. OSRM ’snaps’ cell centroids to the nearest road, yielding divergent route start/endpoints. Figure 3 shows the outcome of this process. For some cells in the Sahara, the Congo Basin, and Madagascar, colored in light grey on the left-hand side (LHS), OSRM cannot find the nearest road and returns ’NA’. For many further cells, the nearest road snapped to is outside of the cell, as shown on the RHS.

I clean the data by first mapping inaccessible cells to the nearest route start/endpoints. I then follow Graff (2024) in adding the spherical centroid-start/end distance to all routes. This increases the length of routes by 0.53% on average. I also adjust travel time estimates by assuming a travel speed of 10km/h on these straight passages, increasing travel time by 3.4% on average.<sup>6</sup>

> 4Large computer programs used for navigating (routing) through digitized transport networks.

> 5A high-performance open routing engine in C++ optimized for OSM. Website: https://project-osrm.org/.

> 6In this regard I differ from Graff (2024), which assumes walking speed of 4km/h. My main reason is that the centroid of such cells is unlikely of economic significance, and assuming a travel speed of 4km/h increases travel time by 8.5% on average, whereas assuming 10km/h only increases travel time by 3.4% on average. Furthermore, since most cells where the distance between the cell centroid and the route stating/endpoints is large are in the Sahara, I believe that motorized transport with specialized vehicles (4x4) is possible.

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