2However, is the Bremen-Cog, an example of the Bremen-type shipbuilding method, a typical example of the vessels that traded across the open oceans with Iceland as documented in historical records? Is the Bremen-type ship of the archaeological record the oceangoing cog of 80-200 tonnes in the historical documents (Gardiner 2007) of the Hanseatic League?

3Ship technical calculations have in the past been employed in the analyses of the original qualities of an archaeological vessel, and hence its sphere of operation. While it is possible to determine various coefficients that can describe the form and the hydrostatic qualities for each individual vessel, only by quantifying these conditions can a basis be formed for a scientific analysis. When studying the hydrodynamic conditions, the problems are even greater. The results of these are dependent on several factors, and for new ships, a combination of experiments with scale models, tank tests and full-scale sea trials has made it possible to develop correlation factors that permit reasonably reliable predictions of performance to be made. However, such work on ancient ships has not been fully undertaken in order to corroborate the results (Crumlin-Pedersen, Trakadas 2003, p. 217–218).

1. Previous analyses of the Bremen-cog

4Previous analyses of the Bremen-Cog have included the rigging, which was designed by Hoheisel, a naval architect and technical director of the German Maritime Museum. Clausen, a student in ship engineering at Hamburg University, tested Hoheisel’s reconstructed rigging on a simplified model in a wind tunnel. Results indicated that the vessel could tack to windward, but tests were unable to include wave action or seaway. Redlin, a student at the Technical University of Berlin, tested the hull shape: he drew an idealised set of lines based on photogrammetry measurements, and calculated the stability for various cargo loads and resultant waterlines, concluding the vessel was stable while ballasted or loaded but unstable if unballasted with the rigging standing. Redlin calculated a minimum ballast of 26 tonnes, based on the Vejby cog in Denmark (Hoheisel 1994). Professor Postel at the Institute for Shipbuilding in Kiel undertook tank-towing tests, and his experiments indicated the model could not come above 90° to the true wind. Postel described the vessel as a “beam-wind sailor” provided it was ballasted and in calm waters (Hoffmann, Hoffmann 2009, p. 287-289).

Table 1: Comparison of the published versions of the Bremen-Cog

Version	Empty weight	Ballast tonnes	Cargo tonnes	Displacement tonnes	Draught
Lahn	60 tonnes	–	76 – 84	136 – 144	2.25 m
Hoheisel	55 tonnes	26	–	81	1.53 m
Hoheisel	55 tonnes	–	87	142	2.25 m
Jensen	–	–	–	139.23	2.25 m
Ubena von Bremen	40 tonnes	35	–	75	2.25 m
Kieler Hansekogge	38 tonnes	22	–	60	1.6 m
Roland von Bremen	100 tonnes	20	–	120	2.25 m

2. Available data sets

7The goal of the project changed from simply analysing the seafaring capabilities of the vessel to also examining the current form of the vessel on display, as well as attempting to distil several conflicting data sets into a valid hypothetical recons­truction to be used as the basis for detailed hydrodynamic and seakeeping analysis.

3. Methodology

8All of the available data sets were imported into Rhinoceros, a 3D CAD modelling software, and the original published Lahn drawings were converted into three-dimensional CAD models in order to compare with the various three-­dimensional digital documentation sets (fig. 1). This clearly illustrated the changing form of the hull shape over the 30 year period from the initial reconstruction to its shape when documented in 2014 (Tanner 2017a, p. 5-24). A series of cross sections (A-H) were taken at 2 m intervals along the keel, and the changing height of the sheer at each point is documented in table 2. This deformation and change in hull shape could possibly be explained by the steel structure, which is currently supporting the vessel in the museum, or by shrinkage of the exhibited timbers

Table 2: Changes in sheer heights over time

Position	A	B	C	D	E	F	G	H
Photogrammetry 1980	0	0	0	0	0	0	0	0
Lahn Drawing 1985	+32 mm	+15 mm	+23 mm	+86 mm	+82 mm	+66 mm	+19 mm	0 mm
3D scan 2011	No Data	– 46 mm	– 47 mm	– 117 mm	– 71 mm	– 104 mm	– 113 mm	– 79 mm
SFM Oct 2014	– 66 mm	– 58 mm	– 58 mm	– 141 mm	– 118 mm	– 135 mm	– 143 mm	– 92 mm
3D scan 2014	– 105 mm	– 103 mm	– 102 mm	– 169 mm	– 138 mm	– 156 mm	– 185 mm	– 99 mm

9While generating 3D models from Lahn’s drawings, it was realised that all of these drawings could not be reconciled into a single coherent three-dimensional model, as can be seen from the blue and green surfaces in figure 1. Additional discrepancies noted (fig. 2) include strake runs which appear very distorted when modelled three dimensionally, the transverse beam bolted 80 mm lower than the archaeological evidence suggests, the reverse camber to the castle deck, as well as the angled stern castle deck.

4. A new hypothetical reconstruction

11In a process similar to that used on the Drogheda boat, the Newport ship and the Poole Iron Age logboat (Berry et al. 2019; Tanner 2013a, 2013b), a digital model of every constituent part of the vessel was created using Rhinoceros 3D, with Lahn’s drawings and the archaeological data as reference. A series of fair curves were created to represent each strake. The length of each curve was fixed to match the archaeological evidence taken from the 3D scan data, and the curvature adjusted until fair, using Lahn’s drawings and the 3D scan data as a reference (fig. 3, top). Then, digital 3D models of the surviving hull elements were created and fitted to the evolving hull form (fig. 3, middle left). Next, the missing elements were extrapolated and modelled (fig. 3, bottom left) to create a more definitive hypothetical reconstruction combining all of the available data sets (fig. 3, bottom right). The revised hypothetical reconstruction based on the evidence resulted in a less full-bodied hull form, compared to Lahn’s reconstruction, particularly in the lower extremities, such as at Frame 10 (fig. 3, top left) where the revised shape was up to 20 cm narrower at the height of the fourth strake.

Table 3: Shrinkage measured between 1980 and 2014 scan dimensions

Location	Lahn measurement 1980	2014 laser scan dims.	Difference
Weather board @ F19	580 mm	527 mm	53 mm	9.1%
Strake 12 @ Frame 19	642 mm	604 mm	38 mm	5.9%
Strake 11 @ Frame 19	648 mm	609 mm	39 mm	6.0%
Strake 10 @ Frame 19	494 mm	457 mm	37 mm	7.5%
Strake 9 @ Frame 19	509 mm	465 mm	44 mm	8.6%
Weather board @ F23	574 mm	537 mm	37 mm	6.4%
Strake 12 @ Frame 23	635 mm	577 mm	58 mm	9.1%
Strake 11 @ Frame 23	649 mm	581 mm	68 mm	10.5%
Strake 10 @ Frame 23	505 mm	457 mm	48 mm	9.5%
Strake 9 @ Frame 23	515 mm	474 mm	41 mm	8.0%

5. Analysis of the hypothetical reconstruction

13The determination of a vessel’s capabilities is a complicated interaction between hydrodynamic and aerodynamic forces, dependant on many factors including flotation characteristics, static stability, dynamic stability, performance, environmental conditions, and seamanship. Past approaches to examining the Bremen-Cog’s seafaring or hydrodynamic capabilities have included tank and wind tunnel testing, which are limited (Crumlin-Pedersen, Trakadas 2003, p. 217-218), as well as full-scale replicas used for sea trials. However, the tests have produced conflicting results such as wind tunnel results indicating the vessel could tack to windward, while tank-towing tests indicated the model could not come above 90° to the true wind. The replicas all include modern additions, such as mechanical propulsion systems, watertight decks and other safety requirements. Hoheisel states the replica Kieler Hansekogge could sail at about 70° to the wind but would drift about 15 to 20° (Hoheisel 1994, p. 259), this would result in the vessel making little or no progress to weather as the resultant course to windward would be 90° or more.

6. Static Stability

16A digital analysis of the vessel was carried out using Orca3D to determine its resultant equilibrium flotation condition in various weight and draught configurations. As the original flotation configuration for the original vessel is not known, the vessel was first tested in both a bare hull and fully rigged configuration to establish a baseline. Results showed that the bare vessel, without mast or rigging, floats in a stable condition. However, once the mast and rigging are added, the vessel becomes unstable and would require the addition of internal ballast. The quantity of internal ballast needs to be enough to counteract the overturning tendencies of the vessel itself as well as counteracting additional heeling moments caused by wind loading or wave roll. Modern rules for the stability of ships are formulated by the International Maritime Organisation (IMO): Bureau Veritas (BV) is one such classification organisation founded in Antwerp in 1828; it was originally Belgian but is now a French company (Bureau Veritas 2012, p. 81-97). The stability testing carried out by Orca3D used the Bureau Veritas criteria and the resulting static stability flotation conditions are shown in table 4.

Table 4: Various draught and displacement results

Condition	Weight tonnes	Cargo tonnes	Displacement	Draught aft	Draught forward	Freeboard	Downflooding angle	GMt
Bare hull and superstructure	43.25	0	43.25	1.25 m	0.64 m	3.26 m	49.5°	0.39 m
Fully rigged – unballasted	47.29	The vessel with a negative metacentric height is unstable, resulting in an angle of loll* of 4.9°. Any slight heeling moment will capsize the ship.						– 0.29 m
Ballasted with 15 tonnes	62.29	0	62.29	1.49 m	0.95 m	2.97 m	44.7°	0.37 m
Draught set to 1.6 m (Hansekogge)	62.29	7.33	69.62	1.60 m	1.05 m	2.72 m	42.9°	0.34 m depending on cargo
Beams not submerged	62.29	45.01	107.30	2.06 m	1.54 m	2.72 m	35.32°	0.82 m depending on cargo
Draught set to 2.25 m	62.29	61.25	123.54	2.25 m	1.72 m	2.15 m	32.36°	0.86 m depending on cargo
Grågås Codex loading	62.29	108.01	170.30	2.77 m	2.17 m	1.74 m	24.21°	1.10 m depending on cargo
* Angle of loll is the state of a ship that is unstable when upright (i.e. has a negative metacentric height) and therefore takes on an angle of heel to either port or starboard. When this occurs, the vessel goes to neutral equilibrium, and the angle of heel at which it happens is called angle of loll.

7. Dynamic stability

17For lateral wind loading, the yard and sail were rotated as far as possible (36.3° in this case) in order to project the maximum possible surface area to a “beam-on” wind, representing a worst-case scenario wherein the sail was not released despite adverse winds. Orca3D uses this information to calculate a heeling moment, which is then applied to the vessel, in combination with wave roll action to determine the vessels resultant angle of heel and dynamic stability performance. Results from these tests indicated that 15 tonnes of internal ballast would be sufficient to satisfy the Marine Insurance Act (1906) and Bureau Veritas stability criteria. The term seaworthiness is a very broad one, as it not only includes the physical state of the vessel but also extends to other aspects and factors. Consequently, it is not easy to define seaworthiness in rigorous terms. A 13th-­century law defined a ship as seaworthy if it did not need to be bailed more than three times in 24 hours (Christensen 1968, p. 138-139). A medieval Icelandic law in the Grågås Codex states the minimum freeboard (F) of a cargo ship should be F=2D/5 where D = depth of hull amidships (Morken 1980, p. 178). In the case of the Bremen-Cog, this minimum freeboard would be F = 2 × 4.35 /5 = 1.74 m.

18The vessel was subsequently analysed in three flotation condi­tions: Condition A – fully rigged and ballasted with 15 tonnes; Condition B – with the protruding beam-ends not submerged, equating to a fully rigged ship, 15 tonnes of ballast and 45 tonnes of additional cargo; and Condition C – the Grågås Codex minimum freeboard condition, equating to a fully rigged ship, 15 tonnes of ballast and an additional 108 tonnes of cargo. For each flotation condition the vessel was then tested for various wind load and wave roll conditions using the Bureau Veritas criteria: the results are shown in Table 5.

	Wind strength	Power generated from sail area	Speed @ 70% efficient Sail	Speed @ 40% efficient Sail	Wind heel angle	Freeboard remaining	Gust heel angle 150% wind	Freeboard remaining
Condition A	Force 3	23.48 kW	7.45	6.75	7.98°	2.42 m	15.71°	1.92 m
	Force 4	32.04 kW	7.85	7.15	15.71°	1.92 m	26.01°	1.21 m
	Force 5	31.2 kW	7.80	7.1	15.80°	1.91 m	16.11°	1.20 m
	Force 6	55.9 kW	8.85	7.82	21.3°	1.53 m	32.4°	0.79m
Condition B	Force 3	23.48 kW	5.9	4.9	0.8°	1.54 m	4.47°	2.05 m
	Force 4	32.04 kW	6.5	5.5	4.47°	2.05 m	9.67°	1.76 m
	Force 5	31.2 kW	6.4	5.4	4.42°	2.05 m	9.60°	1.76 m
	Force 6	55.9 kW	7.4	6.4	6.84°	1.92 m	14.17°	1.49m
Condition C	Force 3	23.48 kW	4.85	4.00	0.76°	1.70 m	1.70°	1.63 m
	Force 4	32.04 kW	5.40	4.45	1.70°	1.63 m	3.89°	1.49 m
	Force 5	31.2 kW	5.35	4.40	1.65°	1.64 m	3.68°	1.50 m
	Force 6	55.9 kW	6.37	5.35	2.57°	1.57 m	5.71°	1.37 m

20Computational fluid dynamics is a potential approach to analyse both aero- and hydrodynamic interactions with a vessel, however, the calculation process is a static one and the vessel will require to be re-orientated for each changing environmental factor, and the computing requirements are large. An alternative approach was to use Unity3D, a real-time development platform that includes a built-in physics engine to handle calculations based on real world physics. Blocks of appropriate size were created to represent the wave height and length for both the Baltic Sea and Atlantic Ocean and the computer-­generated wind adjusted in order to create realistic sea conditions for both areas (fig. 4, top right). The digital model of the Bremen-Cog was then imported from Rhinoceros 3D to Unity, and with its characteristics set for Condition B (with the protruding beam ends not submerged, equating to a fully rigged ship, 15 tonnes of ballast and 45 tonnes of additional cargo), the physics engine applied a gravitational force on the vessel.

8. Conclusion

22The Bremen-Cog, based on its hull shape, if restricted to not having the through-hull beams submerged, can carry a cargo of 45 tonnes, potentially increased to 60 tonnes if the ballast were replaced with cargo. At 2.25 m draught, each of the replica ships sail with beams wholly or partially submerged and the rebates for hull planking on the beam ends would suggest they were constructed in such a manner as to prevent water ingress. Archaeological evidence such as Doel 1 (Vermeersch, Haneca 2015) or Aber Wrac’h (L’Hour, Veyrat 1989), and iconographic representations depicting cogs, clearly show triangular or wedge-shaped blocks of timber attached to the exterior of the hull, adjacent to the through-hull beam ends. As discussed by Vermeersch and Haneca (2015, p. 123), these hemi-conical elements should be referred to as fairing blocks rather than fenders, as their design appears more to guide objects past the exposed square beam-ends than to protect against side impact. Perhaps the fairing blocks and rebated treatment of the through-hull beams indicates that having the beam ends submerged was not considered an issue (Waldus et al. 2019, p. 477). If this were the case the vessel could be loaded much deeper, to the Grågås Codex laws, allowing a cargo capacity of over 100 tonnes while maintaining a freeboard of 1.74 m.

23The archaeological evidence for vessels of the Bremen-type shipbuilding method confirm the presence of such vessels all over the Baltic Sea and the southern North Sea (Abel et al. 1969; Crumlin-Pedersen 1979; Adams 1990; Ellmers 1994; Hoheisel 1994; Weski 1999; Adams, Rönnby 2002; von Arbin, Daly 2012; Hocker, Daly 2016; Waldus et al. 2019). It is obviously a vessel well suited to this activity, for if it were not, it simply would not have flourished to such an extent (Ellmers 1994). Ellmers also noted the need for increased cargo capacity due to expanding trade and cites a cog mentioned in AD 1241 with a cargo capacity of about 240 tonnes (Ellmers 1994, p. 38). Hocker (Hocker, Ward 2004, p. 75) says of the Bremen cog, “As deep-water cogs go, it is of medium size, at 24 m long, with a capacity of 40 lasts (about 120 m³, which is about 80 metric tons of rye). In fact, it is smaller than nearly all contemporary accounts would suggest was typical. Medieval documents show that some Hanseatic cogs exceeded 100 lasts by the 1240s and cogs of 150 lasts were known in the fifteenth century.”

24It is not possible to state whether a vessel of the Bremen-type ever successfully completed a voyage to Iceland, or crossed the exposed Bay of Biscay, en route to the Mediterranean. Certainly, the historical record suggests that ships termed “cogs” were known at least in the Mediterranean (Springmann, Schreier 2008), but this use of the term might not always correspond to the same archaeological definition. Perhaps the larger cogs suggested by Ellmers and Hocker might be better suited to voyages such as crossing the Atlantic to Iceland. One possibility could be the Ijsselcog (Waldus et al. 2019): with a midship height of 5.8 m it is over 1.5 m higher than the Bremen-Cog, and almost 3 m longer. The Bremen-Cog as tested had a cargo of 61.25 tonnes and ballast of 15 tonnes leaving a static freeboard of 2.15 m. A similar quantity of cargo on the Ijsselcog would leave a static freeboard of 3.95 m.

25The Bremen-Cog would, as a cargo vessel, appear to be well suited to transporting cargo along coastal routes and relatively short sea crossings, taking circa two to three days on the sheltered waters of northern Europe. However, its flat bottom, which would be prone to slamming in a high sea, combined with the overall hull shape and performance characteristics would not indicate a vessel ideally suited to operations on the high seas of the exposed North Atlantic. It is the opinion of the authors that ships with the characteristics and dimensions of the Bremen-Cog would not be the primary choice for such an adventure.