According to Chataigner and Barge (2008), a reconstructed Neolithic log-boat with a load of 100kg of obsidian travelled at an average speed of 4 km/h on the Mediterranean Sea. This result indicates that in prehistoric times, boats were somewhat slower than walking.
In her study on social interaction in Michigan, Howey (2007) assigns high priority to travelling on water. Whereas non-forested areas that are easy to walk and see through are assigned a cost value of 30, the cost value of major rivers is only 5. Canoe travel along the shoreline of the Great Lakes is considered twice as costly as river canoeing and traversing small lakes is avoided by choosing a high cost value (65) for these areas. Forested wetlands, i.e. waterways often obstructed by vegetation, are given a lower cost (25) than non-forested areas, easy to walk/see through. This model reflects the fact that Historic Native American Trails frequently follow major river networks and run along the shorelines of the Great Lakes.
Drennan (1984) describes cargo dugout boats in Mesoamerica lowlands and South America. They are at least 8m long, and the carrying capacity is one ton or more. He assumes that a cargo boat with a load of 780kg carries four paddlers who expend the same amount of energy as porters. Moreover, rafts could be used for downstream travel. Drennan notes that dugout boats covered about 20km per day upstream and 40km downstream on a sluggish river. In his view, these calculations are more subject to errors because more variables are involved than in overland transport.
In his investigation of the spatial pattern of flat-top pyramidal mounds (1000–1600 AD) in the southern Appalachians, Livingood calculates LCPs that take canoe travel into account. Canoe travel time requirements are estimated on the basis of historic and modern canoe speeds adjusted according to the current. He comes to the conclusion that 'probably any value between 3.5 and 5 km/hr could be defended, with a range between 4 and 4.5 km/hr the most likely' (2012, 180) and for his calculations he uses 4 km/hr plus or minus the speed of the current.
Bevan (2011) analyses travel in Bronze Age Crete, starting at Knossos, and compares the time required to get to points on the island by walking only and combined maritime and pedestrian routes. He notes that travelling speed at sea depends on many factors, including the mode of propulsion (rowing, paddling, or sailing), wind and current variations, time of day and season as well as the risk the navigator is willing to take. Assuming a speed of 10 km/h on sea, most points that are not in the hinterland of Knossos can be reached more rapidly using combined sea and land routes.
Rahn (2005) refers to a study which calculated that in Roman times, land transport of bulk material was 28 times as costly as sea transport. In his study on transport during Roman times in Germania, Kunow (1980, 19–23) notes that ships with a load of 15 tons could be hauled upstream by one horse or 7 to 8 people, whereas the average load of wagons pulled by two oxen was only about 262kg. According to Kunow, the typical load of a river boat was in the range of 3 to 7 tons, whereas Roman seagoing cargo ships were able to carry heavier loads, maybe 100 tons or more. Kunow also presents the transport costs as issued in the Edict of Maximum Prices in 301 AD by the Roman Emperor Diocletian. According to this edict, transport on rivers was 3.9 to 7.8 times as expensive as transport on sea ships. But the expenses for transport on wagons were more than 10 times as high as river transport, if the costs for upstream and downstream movements are averaged. On the basis of this data, Kunow argues that in Roman times, long-distance trade focused on the sea and rivers even if this included extensive detours – although the Roman road network was quite advanced.
Kunow (1980, 22) refers to a study on early medieval cargo ships at sea, which covered about 53 to 69km each day when stopping at night and 109 to 137km without a night break. According to a publication referenced by Kunow (1980, 21), the average speed of draught boats was 15 to 17km a day during medieval and early modern times. Kunow assumes a downstream speed on the River Rhine of 50 to 60km a day, which could be increased by rowing. In medieval England, the road system is considered to be the basic means of transport for most goods. Nevertheless, river transport was important, especially for heavy or bulky cargo. Most of the populous towns were located on navigable water, and the decline of some towns has been explained in the context of a lack of accessibility by boat (Hindle 2002, 60).
A cost function that assigns 1 to land and 0.67 to water travel may create an LCP which switches the means of transportation repeatedly, which is counter-intuitive. Such a model assumes that a boat or ship is readily available whenever needed and ignores embarkation and disembarkation costs. Wheatley and Gillings (2002, 156–7) solve this problem by modelling a navigable river as a transportation opportunity flanked by barriers.