Given current global affairs, I decided it would be fun to calculate a Least Cost Path that bypasses the Strait of Hormuz while I teach myself QGIS. In GIS, a least-cost path assigns a 'cost' to each pixel in a raster and computes the path with the lowest cost using a pathfinding algorithm such as Dijkstra's.
From a 30m resolution Digital Terrain Model (image 2), slope (image 3) was calculated. From the slope, an Elevation Cost Multiplier raster was calculated by splitting the slope into 3 intervals: less than 3 percent, less than 10 %, and greater than 10 %.
These intervals were selected based on a New Pananamax lock length of 450m and a 10m elevation gain per lock (New Pananamax is 8.66m elevation gain per lock. Slopes of up to 10 percent could be tolerated over short distances but should be avoided. Slopes of greater than 10% are essentially impassable for a large ship canal and are heavily penalized.
**Formula IF elev <3 than (elev^2)/9 IF elev <10 than elev*2, else 100.
The Elevation raster is then multiplied by the Elevation Cost Multiplier raster to give the Cost Raster (image 4)
The Cost Raster is then used in the Least Cost Path tool in QGIS. The Start point is just west of the western screen edge between the Palm Islands, and the End point for the calculation is the red star near the eastern coast. Water was given a 0 cost, so the accumulated cost from the start and end point to any point on the coast is 0.
Does this path make sense?
The elevation profile at the end is the path dumped into Google. Earth Pro. It gives an average slope of 0.5% and a max slope of 4.5%. This is approximately 175km; some minor straightening reduces it to ~150km. These are both technically fine for a large canal. I do not think the 36 Locks required to ascend and 36 more to descend are reasonable for a real canal, but I am not a marine/civil/mega project Engineer.
When I started, I thought it would yield a result somewhere between ridiculous and ludicrous. As I looked at the results and and costs from the Suez and Panama expansions it started to seem a bit less rediculous. Panama spent about 500 million per lock, and Suez was about 8 billion for 35km of canal. Applying those numbers here, we have 150km x 2 for canal X 8/35 = 68.57 Billion for canal construction and 36 Billion for locks. An Economical 105 billion, probably less than the global Economy has lost in the last 2 months.
Data:
ESA global elevation model - Copernicus DEM GLO 30.
Political Boundaries - GeoBoundries.org
Tools:
QGIS
Google Earth Pro
TL;DR : Concept of a plan for a canal by-passing the Strait of Hormuz. derived from elevation and slope datas. (and rainbows)