Tuesday, 6 October 2026

Sea or land? Calculating the bluestone route

This post goes with the short film Sea or land? and with a model anyone can run in a browser:

Calculating the bluestone route. (click to go to the model)

In short

Did the bluestones travel from the Preseli hills to Stonehenge by sea or over land? The model weighs the hard parts of the journey: distance, hills, time on the water, and lifting stones of several tonnes into and out of boats. Each can be turned up or down. For every setting, the model searches the ground for the easiest route; no route is drawn in advance and then fitted to the settings.

  • If boats are easy, the sea wins: down to Carmarthen Bay, then up the Bristol Channel to Avonmouth.
  • If loading and landing are hard work, the land wins, along the line of today's A40 through Llandovery, Brecon and Monmouth. On the most reasonable settings, this is the answer.
  • Many land routes are almost as easy, and all of them cross the Severn at one place: Newnham, below Gloucester.
  • The two Preseli outcrops, one high on the ridge and one lower down, give the same answer almost every time.
  • Keeping boats in sight of land, as Atkinson assumed, makes no difference.

None of this says where the stones actually went. Tides, weather, boats, crews and much else are left out. The model puts numbers on the argument, so that anyone can see what each assumption implies.

The question

Bluestone dolerites and rhyolites at Stonehenge have been matched to outcrops on the north side of Mynydd Preseli, among them Carn Goedog (Bevins, Ixer & Pearce 2014) and Craig Rhos-y-felin (Parker Pearson et al. 2015). Carn Goedog is 219 km from Stonehenge in a straight line. Proposed routes fall into two groups: by sea along the south Wales coast and up the Bristol Channel, as Atkinson proposed, or overland through south Wales and across the Severn. The overland case has been made here before, in The natural corridor for bluestones and Natural route analysis.

A least-cost model can compare the two only if water has a price. Make the sea free and the answer is the sea; make it a wall and the answer is the land. Published corridor work does the second: in Lewis (2024) the sea lies outside the cost surface. The question here is therefore: how cheap must water travel be, relative to hauling over land, before the cheapest route takes to the sea?

The model

The ground is OS Terrain 50, averaged onto a 200 m grid from Pembrokeshire to Hampshire and south to Land's End. Each step to a neighbouring cell is costed in metres of flat-ground hauling:

  • Overland: distance, plus 4 × metres climbed, plus 2.6 × metres descended.
  • On water: distance × m, the water cost. At m = 1 a kilometre on water costs the same as a kilometre on the flat; at 0.5, half as much.
  • Loading: an optional fixed charge T each time the load goes onto or off the water.

The climb weight of 4 corresponds to hauling against a friction coefficient of 0.25: if the force required scales as μ + gradient, the cost per metre scales as 1 + gradient/μ. Sea is any cell where most Terrain 50 posts lie below 0 m OD or where there are no posts offshore. Dijkstra's algorithm finds the cheapest route. A route counts as seaborne when at least 25% of it is on water, and as overland when no more than 10% is.

The order of work matters. First the settings were fixed: two outcrops, thirteen water costs, four loading charges, three climb weights and three rules for keeping to the coast, 936 combinations in all (468 from each outcrop). Then, for each combination, the model searched the whole cost surface and kept the cheapest route it found. No route was chosen or drawn beforehand: each one is simply the output for its settings, and different settings often return the same route. Because the full set is too slow to run in a browser, it was run in advance, and the model page looks up the stored result for whatever settings are selected. Scripts and full results are in the project repository.

Several other settings were tested and left off the page because they barely move the result. A climb weight anywhere from 1 to 16 puts the sea–land switch at m = 1.01–1.12. Closing slopes steeper than 1 in 10, or treating the main rivers as barriers or as waterways, leaves it at 1.03. Grids of 400, 200 and 100 m give 1.027, 1.030 and 1.037. Allowing 16 moves per cell instead of 8 raises it to 1.05–1.08.

The cheapest route: the A40


The cheapest route with water at 1 × flat ground and a charge of 25 km of hauling for each loading and each landing: Llandovery, Brecon, Monmouth, round the head of the Severn estuary. Model run, 200 m grid.

The model page opens with water at the same cost as the flat, a charge of 25 km of hauling for each loading and each landing, the standard climb weight, and boats kept in sight of land. On these settings the cheapest route never touches water. It runs from Carn Goedog up the Tywi to Llandovery, on to Brecon and Monmouth, and round the head of the Severn estuary: 256.5 km, the line of the A40. For the sea to win, water must be about 20% cheaper per kilometre than the flat (the switch lies between m = 0.79 and 0.81).

The loading charge decides this. Lifting a stone of several tonnes onto a boat and off again is not free, and without a charge the model lets a load hop on and off the water at no cost. With the charge, the land route avoids even a short ferry across the Severn. The right size of charge is open. Of the 117 settings per outcrop at each charge, the A40 is the answer in 9 with no charge, 24 at 10 km, 66 at 25 km and 80 at 50 km.

One crossing


Ground lying on some route within 1% (dark red), 2% (orange) or 5% (yellow) of the cheapest, from Carn Goedog, on the model page's default settings.

A single cheapest line overstates what the ground decides. A better measure is the band of near-cheapest routes: every cell on some route costing no more than 1%, 2% or 5% above the cheapest. For a 256 km route, 1% is about 2.5 km of hauling.

On the default settings the 1% band is 15–20 km wide from Preseli to Brecon and splits round the hills into a Teifi side and a Tywi side. The ground does not pick one valley. It does pick one crossing: every near-cheapest land route crosses the Severn at Newnham, about 12 km below Gloucester, where on a 200 m grid the estuary has narrowed to river width. The model charges nothing for crossing a river, so this marks where the estuary stops being sea in the terrain data, not a known ford or ferry. The historic lowest bridge was at Gloucester. East of the Severn the band widens again towards Stonehenge.


Near-cheapest band with water at 2 × flat ground and no loading charge. Bands as above.

With water at twice the cost of the flat and no loading charge, the band runs straighter and funnels instead to the short crossing at Beachley–Aust. Either way the model identifies a crossing place, not a single line through Wales.

The sea's case


Share of the cheapest route on water as the water cost changes (Carn Goedog, 200 m grid, no loading charge). The route flips at m = 1.03.

Without a loading charge the balance is almost exactly even. The route switches from sea to land at m = 1.03 for both outcrops: the sea wins whenever a kilometre on water costs no more than about a kilometre on the flat.

The reason is geography. The Bristol Channel lies almost on the straight line from Preseli to Stonehenge, and at the switch the last sea route and the first land route are both 238.9 km long. Climbing adds about 2% to the sea route and about 9% to an all-land route, so the hills of south Wales hardly count. What decides the outcome is the cost of water relative to the flat, and a terrain model cannot supply that.


Water at half the cost of the flat, no loading charge: the route boards in Carmarthen Bay and lands at Avonmouth. Model run, 200 m grid.

With water at half the cost of the flat and no loading charge, the route from Carn Goedog walks 15–20 km to Carmarthen Bay, boards near Pendine, sails up the Bristol Channel and lands at Avonmouth: 259 km, 61% on water.


Water at twice the cost of the flat, no loading charge: the route walks and crosses the Severn at Beachley–Aust. Model run, 200 m grid.

At twice the cost it walks: up the Tywi, across the coalfield valleys towards Newport, over the shortest Severn crossing (3.5 km, Beachley to Aust) and on through Bath: 238 km, 1.5% on water. That route holds up to water at ten times the cost of the flat. The A40 line takes over only when loading is charged or water is very dear.

Two outcrops

Carn Goedog sits on the ridge at about 290 m OD, 9 km from the sea at Newport Bay. Craig Rhos-y-felin lies in the valley below at about 80 m, 6 km from the same bay. Across 468 combinations of settings the two agree on sea or land in all but two, and the switch is the same. They differ when water is cheap. At a fifth of the cost of the flat, the route from Craig Rhos-y-felin goes north to Newport Bay and round St David's Head (345 km), while the route from Carn Goedog walks south to Carmarthen Bay (260 km). Over the whole set, Craig Rhos-y-felin goes round the north 100 times and Carn Goedog 80.

Keeping to the coast

Atkinson's sea route assumed boats kept close inshore, in sight of land. The model tests this by closing sea cells. Under the in-sight rule a sea cell stays open only if land shows above the horizon from a boat with an eye height of 2 m, that is, within 3.57 × (√2 + √H) km of land H metres high. A stricter rule closes all sea more than 2 km from land.

Staying in sight of land changes nothing: from every stretch of sea these routes use, land is above the horizon, even round Land's End. Limits of 20 and 10 km also leave the switch unchanged, and 5 km moves it slightly, only with a loading charge (to 0.77–0.78). The 2 km limit lowers it to 0.94–0.97 without a charge and 0.67–0.68 with one, because a voyage hugging the shore is longer. In the Bristol Channel land is never far away, so keeping to the coast hardly affects the choice.

Round Land's End?

With the whole coast open, a route north to Newport Bay and round St David's Head and Land's End wins only when water costs about a tenth of the flat or less. At a twentieth it sails 685 km and lands at Southampton Water. Within 2 km of land it is never the cheapest route.

What the model leaves out

  • Tides, currents, weather, seasons, and the risk of losing a stone at sea or on land.
  • How the stones were moved: no boats, rafts, sledges, rollers or crew sizes are modelled.
  • Vegetation, woodland and wetland. OS Terrain 50 is today's land surface.
  • Soft or flooded valley floors, and the cost of crossing rivers. Valleys still attract routes because they are flat: 15.6% of the default land route lies in the main river corridors, which cover 2.2% of the land in the frame.
  • Mid-Holocene sea level. By then relative sea level around the Bristol Channel was within a few metres of today's (Shennan, Bradley & Edwards 2018), not tens of metres lower as in the early Holocene. Most of these coasts are steep, so a few metres barely moves the shoreline on a 200 m grid. The Severn levels near Avonmouth and Weston-super-Mare are the exception, where the tidal edge may have lain some way inland. That changes where a stone could come ashore, not whether water beats land.
  • Any claim that the cheapest route is the one used.

What follows

Once loading and landing cost something, the cheapest way from Preseli to Stonehenge is overland on the A40 line, through a broad band across Wales and a single crossing of the Severn at Newnham. Without that cost the ground cannot choose: sea and land routes are almost the same length, and the break-even sits at water costing about the same as the flat. Whether Neolithic water transport of a multi-tonne stone, loading and landing included, was cheaper than that is a question for experiment and for the archaeology of boats and landing places, not for elevation data. The model makes the price explicit and lets anyone change it: try the model.

Notes on the film

Every route in the film is a model run on the 200 m grid with 8 moves per cell, drawn as the model gives it, over an OS Terrain 50 hillshade. The near-cheapest band uses the model page's default settings. The switch chart shows the share of each cheapest route on water for 22 water costs. In the film, "boat 2× easier" means m = 0.5, "same effort" means m = 1, and "if loading boats is hard" means a charge of 25 km of hauling for each loading and each landing. The music is original, generated for the film.

Sources

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