As mentioned in the section on the organisation of the guild, it was natural to utilise the professional skills and interests of the members. The aim was to gain as much knowledge as possible about the Hjortspring boat, its original shipbuilders and finally, through them, about the community that had created the boat.
We were fortunate to have some members who had experience in fluid mechanics, strength calculations and computerised geometry, so already during the preparation of the boat building, the design group started analysing the boat as mentioned earlier. Here we will show some of the calculations that are important for assessing the sailing characteristics. As a starting point, the design team used the drawing that the Norwegian marine engineer Fr. Johannessen had made in connection with the publication of Rosenberg's book about the Hjortspring find.
G. Rosenberg: Hjortspringfundet (The Hjortspring discovery).
Hydrostatics and dynamics
Here are a few of the many calculations that were performed.
A full description can be found in foredrag 2 from the Gdansk symposium.
For example, if the boat is loaded with 2.5 tonnes, it will sink 30 cm.
Drawing: HSBL.
The wetted surface of the boat, a quantity used when calculating boat speed, was also calculated.
At a draught of 30 cm, corresponding to the weight of 2.5 tonnes mentioned above, the wetted surface of the boat will be 15 m².
Drawing: HSBL.
By calculating the centre of buoyancy and centre of gravity, the boat's sensitivity to uneven loading was calculated. It turned out that the boat could be expected to be very unstable, a fact that proved to be true in the sailing tests.
The power required to propel the boat at different speeds was also calculated. This power is particularly dependent on the wetted surface, its roughness and the length of the boat's waterline. The achievable speed of the boat had been the subject of a heated discussion at a couple of member meetings. Only the president of the guild trusted the abilities of our predecessors so much that he claimed the boat could reach a speed of 8 knots (15 km/hour). A bet was made. However, the calculations could not settle it. Sailing was needed.
But back to the calculations.
At 8 knots, the 20 paddlers need a net power of 2.5 kW or 125 watts each. This equates to 0.2 hp per paddle.
Drawing: HSBL.
Strength calculations
It was also interesting to calculate the load on the boat from the load, buoyancy and wave action. However, a structure as complicated as a boat with its double-curved surfaces is difficult to analyse without using very extensive computer calculations. As we did not have access to a large enough computer, we had to simplify the starting point for the calculations.
We therefore considered the boat as a beam tapered at both ends without taking into account that a boat, when loaded, can expand or contract the width of the hull (like a pea pod).
The boat is loaded by external forces from the weight of the boat itself, the weight of the cargo (crew with equipment) and finally from the buoyancy forces. The first two act downwards, while the last one acts upwards. These external forces will be in equilibrium. These forces were considered to be single forces attacking the boat from a distance of 1 metre above it.
When considering the strength of ships, it is common practice to calculate it in three different modes:
It was also interesting to calculate the load on the boat from the load, buoyancy and wave action. However, a structure as complicated as a boat with its double-curved surfaces is difficult to analyse without using very extensive computer calculations. As we did not have access to a large enough computer, we had to simplify the starting point for the calculations.
We therefore considered the boat as a beam tapered at both ends without taking into account that a boat, when loaded, can expand or contract the width of the hull (like a pea pod).
The boat is loaded by external forces from the weight of the boat itself, the weight of the cargo (crew with equipment) and finally from the buoyancy forces. The first two act downwards, while the last one acts upwards. These external forces will be in equilibrium. These forces were considered to be single forces attacking the boat from a distance of 1 metre above it.
When considering the strength of ships, it is common practice to calculate it in three different modes:
- In still waters
- Riding a wave amidships
- Riding on two waves with the tops at the bow and stern
You use a standard wave with a length equal to the water length of the boat and a height of 1/10 of the wavelength.
The resulting forces from weight, load and buoyancy are shown below.
It can be seen that in such a wave the boat will be loaded to keel hogging.
Drawing: HSBL.
For the three load cases, in calm water, with the top of the standard wave amidships and with the two tops of the standard wave at each end of the boat, the tensile, compressive and shear stresses were calculated. The latter were greater at the bottom seam than the seam's permissible displacement when the boat was travelling in standard waves (13 m wave length and a wave height of 0.65 m).
Wear and tear on the seam was therefore to be expected when travelling in waves. At the same wave size, the bows would vibrate in the vertical direction with a movement of 30 mm. These calculations do not take into account the expected favourable effect of the tension rope but also the weak sewing seams.
We must remember that the calculations are based on the shape of the boat as described by Johannessen. However, Tilia had a slightly shorter waterline due to the more curved keel line. The impact of this change on the stresses was not assessed in these calculations.
Sources
- Hvad Haanden former er Aandens Spor.
- Symposiums: Paper 2: Theoretical Performance and initial Test Results