1The aim of this study was to evaluate the usefulness of computational fluid dynamics (CFD) in analysing archaeological digital boat models. Tangentially it was also a study of the ability of a maritime archaeologist, without a background in advanced mathematics, nautical engineering or physics, to utilise CFD. CFD is a mathematically based method of simulating fluid using a computer. It is utilised in a variety of industries to analyse the movement of fluid. One application for CFD is boat design. Several companies offer the possibility to study the flow of water around a hull and the flow of air around a sail to test the capabilities of said objects. This has obvious advantages for the study of archaeological boat remains, by allowing us to examine a digital model in a computational simulation. As our archaeological boat finds have hull shapes that would not be built, and so never analysed, today we need to carry out testing to understand their abilities, and their loading capacities.
2As archaeologists record and digitally preserve more and more boats (Ravn et al. 2011, p. 236), the possibility of taking our understanding of ancient boats further without the costs associated with a full-scale reconstruction is tantalising. Physical scale-model testing in tow tanks has been a possibility but such testing is quite expensive, time consuming, and the problems of scale for a small boat model add an extra element of imprecision (Milgram 1997, p. 640; Fassardi 2002). In the event that a full-scale reconstruction is planned and there is some doubt as to the shape of the hull, CFD could be used to analyse differing hypotheses before the building began. However, there is no guarantee that the optimal shape was necessarily the original shape. For seemingly non-optimal hulls, experiments with loading might show how the ship functioned.
3At the Norwegian Maritime Museum we have been digitally documenting boat finds for over a decade. Inspired by Roskilde (Bischoff 2016, p. 21), the Drogheda boat project (Schweitzer 2013, p. 30) and the Newport ship project (Jones 2007, 2008), we have been using FARO arms to digitally draw our boat parts, Rhino 3D to process our drawings, and Orca3D to analyse our hull forms (Bischoff 2016, p. 31; Tully, Tanner 2012). When we learned that Orca3D were teaming up with a CFD provider, Simerics, to analyse boat models, we approached them immediately. Simerics and Orca 3D kindly allowed us to use their simulation for free to analyse our Barcode 02 models.
4Between 2008 and 2009, an excavation, necessitated by the construction of a new high-rise development in the area, uncovered 13 shipwrecks in the old harbour of Oslo city (Gundersen 2012, p. 75-80). The largest and most complex of those ships was Barcode 02 (BC02). A model of the ship was constructed in 1:10 scale with 2D and 3D printed pieces made from digitally recorded 1:1 drawings of the boat parts. These drawings were made using FARO documentation in combination with the computer-aided design application software Rhinoceros 5.0 (Rhino 3D). The reconstructed ship contains 21 strakes, 32 rows of frames and is 14.5 m long, 6 m wide and 5.4 m high. The digital model of the boat is based on this physical scale model (fig. 1).
Fig. 1: Reconstruction of Barcode 02
Bottom part of the hull in pine, upper part in oak. The ship is 14.5 m long.
5The reason we choose Barcode 02 as a test for CFD is that it existed as two ships. The lower hull including the first 12 strakes and every second frame is made of pine taken from the northern part of the west coast of Norway and was felled in winter 1589/1590 (Kirchhefer 2015). This ship probably worked as a jekt carrying dry fish and grain along the west coast of Norway (Christensen 1989, p. 110-122). The rest of the ship is made of oak that was felled somewhere in the southern part of Norway or west coast of Sweden roughly between 1595 and 1602 (Daly 2014). The upper part has a ballast port on the portside and because of this our interpretation is that the ship was rebuilt for shipping timber from the east and south of Norway (Nymoen 2009, p. 105-106). We thought it would be interesting to try to reconstruct both of the ships and see how they act in water by using the CFD.
6Unfortunately, we did not have the resources to make a full 1:10 reconstruction of the lower hull. Instead, we adjusted the digital model. Some of the strakes were removed, while others were assigned the density of pine. We removed the foremast, and tipped the mainmast to stand straight. The shape of this hull will almost certainly not correspond perfectly with the shape of the original jekt. Nevertheless, for our purpose as a test for CFD, the digital model in pine will give us a lighter version of the reconstructed rebuilt boat with oak parts, and should act somewhat differently in the water.
7While CFD itself is complex, the Orca 3D/Simerics simulation is straightforward to use. Each simulation takes about 48 hours to reach completion. Once a model has had a successful hydrostatic analysis in Orca 3D it can be uploaded to the Simerics simulation. This upload function is built into the Orca 3D tabs in Rhino. When uploading the model you can specify which speeds you wish your model to run at. You can also specify whether you would like to run a “resistance” (drag) test or a “propulsion” test. The propulsion test was designed primarily with propellers in mind so all of the completed test runs in this paper are the results of resistance tests. You can choose between salt or fresh water. There is also an option to indicate that you are analysing a displacement hull. The fluid modelled in the simulation is still water, moved only by the boat being dragged through it.
8There are two forms of output from the simulations: animations and graphs. The animations show the dynamic pressure on the hull, the free surface elevation (wake) (fig. 2), the streamlines around the part of the hull that is out of the water, and the flow of water around the hull. Colour gradations display the changes in pressure on the hull and to the height of the waves. The ranges for the output are automatically set but are also adjustable, so if you want to show comparative simulations you can ensure that the ranges match. The graphs (fig. 3) numerically display the heave and pitch of the boat, the effective power, the resistance, and the forward velocity. It is also possible to export the graph data to an Excel file for further comparison. As with the animations, the ranges for the graphs are automatically set, so if you want to show comparative data you must adjust the ranges to ensure they are the same.
Fig. 2: Plan view of Barcode 02 being dragged through the water in the Simerics CFD simulation
The free surface elevation or wake is visible.
Fig. 3: Side view of Barcode 02 being dragged through the water at 12 knots in the Simerics CFD simulation.
9The animations provided the most compelling results (fig. 4). It was possible to see the hull in action, cutting through the water. The simulation allows for moving the viewpoint in all directions. With a side view, you can see the waves displaced by the bow of the boat curling along the side of the hull and expelled at the aft end. To evaluate the animation function, we ran simulations at speeds from 3 to 12 knots. There is a method to estimate the top speed of a hull, using the Froude number or speed-length ratio to estimate the number of waves along the length of a hull (Marchaj 1964, p. 250-251) (table 1). For this model, the Froude number of 0.4 and the speed-length ratio of 1.34 are reached at 8.46 knots. In the simulations run up to 7 knots the waves were mere ripples, but from 8 knots and up the water displaced became more dramatic. At 12 knots, the freeboard was cut in half by the waves formed at the bow of the boat. A side view also shows the boat heaving and pitching and the resultant changes in sinkage and trim that occur at speed. A pale silhouette of the boat shows the model’s position before the drag test began. With a view from above or below the boat, it is possible to see the wake that forms as the boat is dragged through the water. It is also possible to zoom in to any area of the hull to see how the dynamic pressure is distributed.
Fig. 4: Example of the Simerics graph output showing heave and pitch
Table 1: Froude numbers and speed-length ratio for the oak and pine model, with a displacement of 36,472 kgf, run through the Simerics CFD simulation between 3 knts and 12 knts.
Velocity |
3knts |
4knts |
5knts |
6knts |
7knts |
8knts |
9knts |
10knts |
11knts |
12knts |
Fr |
0.142 |
0.189 |
0.237 |
0.284 |
0.331 |
0.378 |
0.426 |
0.473 |
0.520 |
0.568 |
S\L ratio |
0.47 |
0.63 |
0.79 |
0.95 |
1.11 |
1.27 |
1.42 |
1.58 |
1.74 |
1.90 |
10The simulations showed that Barcode 02 moved through the water without creating excessive bow waves up to 7 knots: less waves mean less resistance moving through the water (Manen, Oossanen 1988, p. 15). With 7 knots being the highest speed without this obvious sign of wave-making resistance, we decided to use 7 knots to evaluate the graph output from the simulation. Four models were run through the simulation to provide a basis of comparison. Two of the models were based on what we theorised the original version of Barcode 02 was like. It had a displacement of 4,216 kg: to that a cargo of timber, crew and provisions (25,847 kg) was added, which gave it a displacement of 30,063 kg. Another version of this model was run with an extra 8,000 kg.of ballast, giving it an overall displacement of 38,063 kg. The second pair of models was based on Barcode 02 as it had been found, with additional strakes and a deck. It had a displacement of 10,305 kg: to that a cargo of timber, crew and provisions was added (26,167 kg), which gave it a displacement of 36,472 kg. A second version of this model was also run with an extra 8,000 kg.of ballast, giving that an overall displacement of 44,472 kg. The mass and geometry of each Barcode 02 model that was run through the simulation can be seen in table 2, here changes to the mass and geometry can be seen with each model. It should be noted that the CFD simulation could only run if the transverse (T) centre of gravity was manually changed to 0 m. For more thorough analyses of the model, a range of speeds and loadings would have been analysed, but time constraints dictated that only one speed and four loadings could be analysed for this study.
Table 2: Mass and geometry of each Barcode 02 model before the CFD simulations were run
Pine model, full loading |
Displacement |
30,063. 586 kgf |
Waterplane values |
Vol. [m^3] |
Wetted surface [m^2] |
Overall dimensions [m] |
Waterline dimensions [m] |
Hull form coefficients |
Centre of buoyancy [m] |
Centre of gravity [m] |
LCF:5.968m |
29.305 |
60.665 |
Loa:13.919 |
Lwl:11.946 |
Cb:0.281 |
L: 6.037 |
L:6.048 |
TCF:0.012m |
|
|
Boa: 5.962 |
Bwl: 5.1 |
Cp: 0.580 |
T: 0.019 |
T:0.015 |
Awp:41.844m^2 |
|
D: 4.417 |
T: 1.71 |
Cx: 0.485 |
V: -0.761 |
V:-0.311 |
|
|
|
|
|
Cvp:0.410 |
|
|
|
|
|
|
|
Cwp:0.687 |
|
|
|
Pine model, full loading, and ballast |
Displacement 38,063.586 kgf 38,063.586 kgf |
Waterplane values |
Vol. [m^3] |
Wetted surface [m^2] |
Overall dimensions [m] |
Waterline dimensions [m] |
Hull form coefficients |
Centre of buoyancy [m] |
Centre of gravity [m] |
LCF:5.99m |
37.103 |
66.431 |
Loa:13.919 |
Lwl:12.154 |
Cb: 0.308 |
L:6.142 |
L:6.144 |
TCF:0.011m |
|
|
Boa: 5.962 |
Bwl:5.301 |
Cp: 0.594 |
T:0.018 |
T:0.017 |
Awp:44.642m^2 |
|
D: 4.417 |
T: 1.868 |
Cx: 0.519 |
V:-0.653 |
V:-0.508 |
|
|
|
|
|
Cvp:0.445 |
|
|
|
|
|
|
|
Cwp:0.693 |
|
|
Oak and pine model, full loading |
Displacement 36,472.033 kgf 36,472.033 kgf |
Waterplane values |
Vol. [m^3] |
Wetted surface [m^2] |
Overall dimensions [m] |
Waterline dimensions [m] |
Hull form coefficients |
Centre of buoyancy [m] |
Centre of gravity [m] |
LCF:6.176m |
35.551 |
65.414 |
Loa:14.328 |
Lwl:12.158 |
Cb: 0.291 |
L:6.236 |
L:6.253 |
TCF:0.018m |
|
|
Boa:6.205 |
Bwl:5.275 |
Cp: 0.565 |
T:0.023 |
T:0.019 |
Awp:44.355m^2 |
|
D:5.389 |
T: 1.865 |
Cx: 0.505 |
V:-1.078 |
V:-0.466 |
|
|
|
|
|
Cvp:0.430 |
|
|
|
|
|
|
|
Cwp:0.692 |
|
|
|
Oak and pine model, full loading, and ballast |
Displacement 44,472.033 kgf 44,472.033 kgf |
Waterplane values |
Vol. [m^3] |
Wetted surface [m^2] |
Overall dimensions [m] |
Waterline dimensions [m] |
Hull form coefficients |
Centre of buoyancy [m] |
Centre of gravity [m] |
LCF:5.945m |
43.349 |
70.843 |
Loa:14.328 |
Lwl:12.327 |
Cb: 0.322 |
L:6.101 |
L:6.104 |
TCF:0.013m |
|
|
Boa:6.205 |
Bwl:5.439 |
Cp: 0.602 |
T:0.021 |
T:0.018 |
Awp:46.729m^2 |
|
D:5.389 |
T: 2.007 |
Cx: 0.535 |
V:-0.569 |
V:-0.299 |
|
|
|
|
|
Cvp:0.462 |
|
|
|
|
|
|
|
Cwp:0.697 |
|
|
The values were calculated using Orca3D.
Table 3: Data output from computational fluid dynamics analysis of four versions of the Barcode 02 digital model
Pine model, full loading |
Displacement 30,063.586 kgf |
Forward velocity [knot] |
Dynamic sinkage [cm] |
Heave up [cm] |
Heave down [cm] |
Dynamic trim by bow [deg] |
Pitch by stern [deg] |
Pitch by bow [deg] |
Effective power (EHP) [N-m/s] |
Total resistance [N] |
7.00 |
– 38.42 |
0.06 |
– 0.11 |
0.19 |
– 0.01 |
0.01 |
12366.40 |
3434.05 |
|
Pine model, full loading, and ballast |
Displacement 38,063.586 kgf |
Forward velocity [knot] |
Dynamic sinkage [cm] |
Heave up [cm] |
Heave down [cm] |
Dynamic trim unchanged [deg] |
Pitch by stern [deg] |
Pitch by bow [deg] |
Effective power (EHP) [N-m/s] |
Total resistance [N] |
7.00 |
– 59.03 |
0.19 |
– 0.26 |
0 |
– 0.01 |
0.02 |
13796.90 |
3831.30 |
|
Oak and pine model, full loading |
Displacement 36,472.033 kgf |
Forward velocity [knot] |
Dynamic sinkage [cm] |
Heave up [cm] |
Heave down [cm] |
Dynamic trim by stern [deg] |
Pitch by stern [deg] |
Pitch by bow [deg] |
Effective power (EHP) [N-m/s] |
Total resistance [N] |
7.00 |
– 60.01 |
0.26 |
– 0.26 |
– 0.45 |
– 0.03 |
0.02 |
9963.45 |
2766.77 |
|
Oak and pine model, full loading, and ballast |
|
Forward velocity [knot] |
Dynamic sinkage [cm] |
Heave up [cm] |
Heave down [cm] |
Dynamic trim by stern [deg] |
Pitch by stern [deg] |
Pitch by bow [deg] |
Effective power (EHP) [N-m/s] |
Total resistance [N] |
7.00 |
– 44.41 |
0.42 |
– 0.56 |
– 0.21 |
– 0.04 |
0.03 |
10827.30 |
3006.66 |
11Using CFD is a time consuming endeavour. Not only because each run takes 48 hours but also due to the amount of runs that must occur to get a full picture of the capabilities of any one boat. It is essential to make a detailed plan in advance. Plan what speeds you intend to run. Make a plan to incrementally change the trim of the boat. Establishing what range of trim you will test is probably faster to start in Orca 3D. There you can experiment to establish a range that Orca 3D calculates as stable. Record the initial trim of the boat and the resultant dynamic trim of the boat. Record the initial freeboard of the boat and the resultant freeboard due to the dynamic sinkage of the boat. Keep all related data together, weight cost reports and stability reports from Orca 3D, videos and graphs from Simerics. Decide on a range for your videos and graphs in advance so that everything is easily comparable. Make a video of at least a side view and a plan view for each run. All of this information should be combined to give a full and rounded report on the testing of a boat.
12The CFD study has shown the resistance and dynamic pressure exerted on the hull at 7 knots, which raises the possibility that the rebuild added to the sailing capabilities of Barcode 02. These changes in resistance are probably a result of the change in sinkage, trim and waterline length. The sinkage also shows the depth limitations the sailors of Barcode 02 would have to take into account, as well as the freeboard should it be carrying a heavy load.
13There is other information we could find out about Barcode 02. Computational fluid dynamics offers an array of possibilities for the study of boats. Even within the Simerics simulation, there were aspects of analysis not included in this study. There is a possibility of studying yaw angles. There is also, theoretically, a way to move the force of propulsion into the sails. Other CFD simulations analyse the capabilities of sails and the ability of boats to move through and with waves. The use of CFD to study any archaeological boat would be interesting but a library of results from all of the digitally recorded boats would yield a wealth of information. It would give us a more in-depth understanding of the capabilities of ships from different eras. In so doing, we would have one more, small, piece of the puzzle that is trying understanding the past through material objects.
14Due to time constraints, this is a rough study of the use of CFD to analyse digitally recorded archaeological ship finds. More simulations are needed with different loadings and speeds to attain a clearer picture of the Barcode 02 models. While the results here pertaining to Barcode 02 are not conclusive, CFD shows one way forward in how we can interpret our ship finds. Computational fluid dynamics is complex in and of itself, but CFD is an accessible tool. While a background in engineering or physics would be helpful, results are attainable for anyone. Interpreting the results and extrapolating meaning from them is a subject that requires more examination.