How Efficiently Does A Ship Sail Around The Globe?

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My previous blog post on sailing a ship around the globe raised an interesting question: how efficient is sailing a ship around the globe? I previously noted that the Suez Canal is not as beneficial as it could be (when sailing to/from Portsmouth) as France and Spain get in the way and sailing along the Mediterranean is inefficient regardless of the Suez Canal.

To this end, I wrote a simple script to compare the actual sailing times with the sailing times calculated by GST:

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#!/usr/bin/env python3

# Use the proper idiom in the main module ...
# NOTE: See https://docs.python.org/3.12/library/multiprocessing.html#the-spawn-and-forkserver-start-methods
if __name__ == "__main__":
    # Import standard modules ...
    import gzip
    import json
    import math
    import os

    # Import special modules ...
    try:
        import cartopy
        cartopy.config.update(
            {
                "cache_dir" : os.path.expanduser("~/.local/share/cartopy_cache"),
            }
        )
    except:
        raise Exception("\"cartopy\" is not installed; run \"pip install --user Cartopy\"") from None
    try:
        import numpy
    except:
        raise Exception("\"numpy\" is not installed; run \"pip install --user numpy\"") from None
    try:
        import PIL
        import PIL.Image
        PIL.Image.MAX_IMAGE_PIXELS = 1024 * 1024 * 1024                         # [px]
        import PIL.ImageDraw
    except:
        raise Exception("\"PIL\" is not installed; run \"pip install --user Pillow\"") from None
    try:
        import shapely
        import shapely.geometry
        import shapely.wkb
    except:
        raise Exception("\"shapely\" is not installed; run \"pip install --user Shapely\"") from None

    # Import my modules ...
    try:
        import pyguymer3
        import pyguymer3.geo
        import pyguymer3.image
    except:
        raise Exception("\"pyguymer3\" is not installed; run \"pip install --user PyGuymer3\"") from None

    # **************************************************************************

    # Define resolution ...
    res = "i"
    nLon = 3600                                                                 # [px]
    nLat = 1800                                                                 # [px]
    dLon = 360.0 / float(nLon)                                                  # [°/px]
    dLat = 180.0 / float(nLat)                                                  # [°/px]

    # Define speed ...
    speed = 20.0                                                                # [NM/hr]

    # Define starting location ...
    startingLon = -1.0                                                          # [°]
    startingLat = 50.5                                                          # [°]

    # Define combinations ...
    combs = [
        # Study convergence (changing just "nAng" and "prec") ...
        (2,  9, 5000,),
        (2, 17, 2500,),
        (2, 33, 1250,),
    ]

    # **************************************************************************

    # Load colour tables ...
    with open(f"{pyguymer3.__path__[0]}/data/json/colourTables.json", "rt", encoding = "utf-8") as fObj:
        cts = json.load(fObj)

    # Find the Shapefiles ...
    sfiles = [
        cartopy.io.shapereader.gshhs(
            level = 1,
            scale = res,
        ),
        cartopy.io.shapereader.gshhs(
            level = 5,
            scale = res,
        ),
        cartopy.io.shapereader.gshhs(
            level = 6,
            scale = res,
        ),
    ]

    print("Making axes ...")

    # Create axes ...
    lons = numpy.linspace(
        -180.0 + 0.5 * dLon,
        +180.0 - 0.5 * dLon,
        nLon,
        dtype = numpy.float64,
    )                                                                           # [°]
    lats = numpy.linspace(
        +90.0 - 0.5 * dLat,
        -90.0 + 0.5 * dLat,
        nLat,
        dtype = numpy.float64,
    )                                                                           # [°]

    # Check if the direct distance array exists ...
    if os.path.exists("directDist.bin"):
        # Load direct distance array ...
        directDist = numpy.fromfile(
            "directDist.bin",
            dtype = numpy.float64,
        ).reshape(nLat, nLon)                                                   # [m]
    else:
        # Create (and save) direct distance array ...
        directDist = numpy.zeros((nLat, nLon), dtype = numpy.float64)           # [m]
        for iLon in range(nLon):
            for iLat in range(nLat):
                try:
                    directDist[iLat, iLon], _, _ = pyguymer3.geo.calc_dist_between_two_locs(
                        startingLon,
                        startingLat,
                        lons[iLon],
                        lats[iLat],
                    )                                                           # [m]
                except:
                    print(f"WARNING: Failed to find distance to ({lons[iLon]:+.9f}°,{lats[iLat]:+.9f}°), skipping.")
                    directDist[iLat, iLon] = -1.0                               # [m]
        directDist.tofile("directDist.bin")

    # **************************************************************************

    # Loop over combinations ...
    for cons, nAng, prec in combs:
        print(f"Processing \"cons={cons:.2e}, nAng={nAng:d}, prec={prec:.2e}\" ...")

        # **********************************************************************

        # Initialize images ...
        absDiff = numpy.full((nLat, nLon), 1.0e9, dtype = numpy.float64)        # [m]
        relDiff = numpy.full((nLat, nLon), 1.0e9, dtype = numpy.float64)        # [%]

        # **********************************************************************

        # Create short-hands ...
        # NOTE: Say that 40,000 metres takes 1 hour at 20 knots.
        freqLand = 24 * 40000 // prec                                           # [#]
        freqSimp = 40000 // prec                                                # [#]

        # Deduce directory name ...
        dname = f"res={res}_cons={cons:.2e}_tol=1.00e-10/nAng={nAng:d}_prec={prec:.2e}/freqLand={freqLand:d}_freqSimp={freqSimp:d}_lon={startingLon:+011.6f}_lat={startingLat:+010.6f}/limit"

        # Loop over sailing distances ...
        for sailingDist in range(5, 30005, 5):
            # Skip if this distance cannot exist (because the precision is too
            # coarse) and determine the step count ...
            if (1000 * sailingDist) % prec != 0:
                continue
            istep = ((1000 * sailingDist) // prec) - 1                          # [#]

            # Deduce file name and skip if it is missing ...
            fname = f"{dname}/istep={istep + 1:06d}.wkb.gz"
            if not os.path.exists(fname):
                continue

            # Load [Multi]LineString ...
            with gzip.open(fname, mode = "rb") as gzObj:
                limit = shapely.wkb.loads(gzObj.read())

            # Loop over lines ...
            for line in pyguymer3.geo.extract_lines(limit, onlyValid = False):
                # Loop over coordinates ...
                for lon, lat in line.coords:
                    # Deduce indices and skip if there isn't a direct distance ...
                    iLon = max(0, min(nLon - 1, math.floor((lon + 180.0) / dLon)))  # [px]
                    iLat = max(0, min(nLat - 1, math.floor(( 90.0 - lat) / dLat)))  # [px]
                    if directDist[iLat, iLon] < 0.0:
                        continue

                    # Update differences ...
                    delta = float(sailingDist * 1000) - directDist[iLat, iLon]  # [m]
                    absDiff[iLat, iLon] = min(
                        absDiff[iLat, iLon],
                        delta,
                    )                                                           # [m]
                    relDiff[iLat, iLon] = min(
                        relDiff[iLat, iLon],
                        delta / directDist[iLat, iLon],
                    )                                                           # [%]

        # **********************************************************************

        print(" > Cleaning arrays ...")

        # Remove pixels which are numerical noise (e.g., ones where it is
        # quicker to sail than go directly) ...
        numpy.place(absDiff, absDiff < 0.0, 0.0)                                # [m]
        numpy.place(relDiff, relDiff < 0.0, 0.0)                                # [%]

        print(f" > Maximum absolute value = {absDiff[absDiff < 1.0e9].max():.6e} m.")
        print(f" > Maximum relative value = {relDiff[relDiff < 1.0e9].max():.6e} %.")

        # **********************************************************************

        print(" > Scaling array ...")

        # Convert to useful units ...
        # NOTE: 1.0e9 / 1852.0 / speed = 26997.84017278618 ≥ 1.0e4
        absDiff /= 1852.0                                                       # [NM]
        absDiff /= speed                                                        # [hr]

        print(f" > Maximum absolute value = {absDiff[absDiff < 1.0e4].max():.6e} hr.")

        # **********************************************************************

        # NOTE: Maximum absolute value = 1.435046e+07 m.
        # NOTE: Maximum relative value = 1.276112e+01 %.
        # NOTE: Maximum absolute value = 3.874313e+02 hr.

        # NOTE: Maximum absolute value = 7.169781e+06 m.
        # NOTE: Maximum relative value = 3.577232e+00 %.
        # NOTE: Maximum absolute value = 1.935686e+02 hr.

        # **********************************************************************

        print(" > Making PNGs ...")

        # Create image ...
        absDiffImg = numpy.zeros((nLat, nLon, 3), dtype = numpy.uint8)
        for iLat in range(nLat):
            for iLon in range(nLon):
                if absDiff[iLat, iLon] < 1.0e4:
                    color = round(
                        min(
                            255.0,
                            255.0 * absDiff[iLat, iLon].astype(numpy.float64) / 200.0,
                        )
                    )
                    absDiffImg[iLat, iLon, :] = cts["rainbow"][color][:]
                else:
                    absDiffImg[iLat, iLon, :] = 255
        absDiffImg = PIL.Image.fromarray(absDiffImg)

        # Create image ...
        relDiffImg = numpy.zeros((nLat, nLon, 3), dtype = numpy.uint8)
        for iLat in range(nLat):
            for iLon in range(nLon):
                if relDiff[iLat, iLon] < 1.0e9:
                    color = round(
                        min(
                            255.0,
                            255.0 * relDiff[iLat, iLon].astype(numpy.float64) / 4.0,
                        )
                    )
                    relDiffImg[iLat, iLon, :] = cts["rainbow"][color][:]
                else:
                    relDiffImg[iLat, iLon, :] = 255
        relDiffImg = PIL.Image.fromarray(relDiffImg)

        # Create drawing objects ...
        absDiffDraw = PIL.ImageDraw.Draw(absDiffImg)
        relDiffDraw = PIL.ImageDraw.Draw(relDiffImg)

        # Loop over Shapefiles ...
        for sfile in sfiles:
            # Loop over records ...
            for record in cartopy.io.shapereader.Reader(sfile).records():
                # Loop over Polygons ...
                for poly in pyguymer3.geo.extract_polys(record.geometry, onlyValid = False, repair = False):
                    # Initialize list ...
                    coords = []                                                 # [px], [px]

                    # Loop over coordinates in exterior ring ...
                    for coord in poly.exterior.coords:
                        # Deduce location and append to list ...
                        x = max(0.0, min(float(nLon), (coord[0] + 180.0) / dLon))   # [px]
                        y = max(0.0, min(float(nLat), ( 90.0 - coord[1]) / dLat))   # [px]
                        coords.append((x, y))                                   # [px], [px]

                    # Draw exterior ring ...
                    absDiffDraw.line(coords, fill = (255, 255, 255), width = 1)
                    relDiffDraw.line(coords, fill = (255, 255, 255), width = 1)

        # Save PNG ...
        absDiffImg.save(f"../res={res}_cons={cons:.2e}_nAng={nAng:d}_prec={prec:.2e}_lon={startingLon:+011.6f}_lat={startingLat:+010.6f}_abs.png")
        pyguymer3.image.optimize_image(f"../res={res}_cons={cons:.2e}_nAng={nAng:d}_prec={prec:.2e}_lon={startingLon:+011.6f}_lat={startingLat:+010.6f}_abs.png", strip = True)

        # Save PNG ...
        relDiffImg.save(f"../res={res}_cons={cons:.2e}_nAng={nAng:d}_prec={prec:.2e}_lon={startingLon:+011.6f}_lat={startingLat:+010.6f}_rel.png")
        pyguymer3.image.optimize_image(f"../res={res}_cons={cons:.2e}_nAng={nAng:d}_prec={prec:.2e}_lon={startingLon:+011.6f}_lat={startingLat:+010.6f}_rel.png", strip = True)

              
You may also download “globalSailingEfficiency.py” directly or view “globalSailingEfficiency.py” on GitHub Gist (you may need to manually checkout the “main” branch).

Below are the three maps for the absolute (in)efficiency on a linear scale from 0 hours to 200 hours.

Download:
  1. 512 px × 256 px (0.1 Mpx; 117.6 KiB)
  2. 1,024 px × 512 px (0.5 Mpx; 385.2 KiB)
  3. 2,048 px × 1,024 px (2.1 Mpx; 1.2 MiB)
  4. 3,600 px × 1,800 px (6.5 Mpx; 667.8 KiB)
Download:
  1. 512 px × 256 px (0.1 Mpx; 117.5 KiB)
  2. 1,024 px × 512 px (0.5 Mpx; 387.4 KiB)
  3. 2,048 px × 1,024 px (2.1 Mpx; 1.3 MiB)
  4. 3,600 px × 1,800 px (6.5 Mpx; 454.3 KiB)
Download:
  1. 512 px × 256 px (0.1 Mpx; 116.5 KiB)
  2. 1,024 px × 512 px (0.5 Mpx; 384.7 KiB)
  3. 2,048 px × 1,024 px (2.1 Mpx; 1.2 MiB)
  4. 3,600 px × 1,800 px (6.5 Mpx; 436.0 KiB)

These show that sailing up to Basra (in Iraq) and Bangkok (in Thailand) add the most extra hours to your total sailing time. Now, if I plot the same data as a relative (in)efficiency on a linear scale from 0% to 4% then you will see that it is the Northern Mediterranean, with the least efficient being Venice (in Italy).

Download:
  1. 512 px × 256 px (0.1 Mpx; 107.0 KiB)
  2. 1,024 px × 512 px (0.5 Mpx; 315.9 KiB)
  3. 2,048 px × 1,024 px (2.1 Mpx; 907.3 KiB)
  4. 3,600 px × 1,800 px (6.5 Mpx; 196.3 KiB)
Download:
  1. 512 px × 256 px (0.1 Mpx; 103.6 KiB)
  2. 1,024 px × 512 px (0.5 Mpx; 303.5 KiB)
  3. 2,048 px × 1,024 px (2.1 Mpx; 875.8 KiB)
  4. 3,600 px × 1,800 px (6.5 Mpx; 194.1 KiB)
Download:
  1. 512 px × 256 px (0.1 Mpx; 101.6 KiB)
  2. 1,024 px × 512 px (0.5 Mpx; 297.6 KiB)
  3. 2,048 px × 1,024 px (2.1 Mpx; 853.6 KiB)
  4. 3,600 px × 1,800 px (6.5 Mpx; 186.1 KiB)