Hull Shape
The main guidance on the best hull shape is the Delft University of Technology series of tank tests on some 50 or more different hulls beginning in 1974 and continuing to the present. Papers by Gerritsma, Keuning and others at the Chesapeake Bay Yacht Symposia give most of the results but all the important conclusions and drag formulae are in the two yacht design books cited above. The tests were used to find the Residuary Resistance, loosely the wave drag plus some viscous separation components and any systematic errors from estimating the viscous resistance. The viscous resistance was estimated using the static wetted area, a representative Reynolds Number and the ITTC friction formula. This viscous resistance estimate was subtracted from the measured total drag to give the residuary Resistance. I tend to use the expression Wave Drag instead as I come from an aeronautical rather than marine background, but it’s the same thing.
The Residuary Resistance was measured over a range of Froude Numbers from 0.1 to 0.6 where the conventional “Hull Speed” is at about 0.4. The hull shapes have been characterised by a limited number of parameters including the Displacement/Length ratio, positions of the longitudinal centres of buoyancy and of flotation relative to length, the Prismatic Coefficient, Beam/Length, Displacement to wetted and waterplane areas, etc. For each Froude Number in 0.1 (0.05) 0.6, regression analysis has been used to find an expression for the ratio of Residuary Resistance to hull displacement as a linear function of eight parameters of the types above. The actual parameters used and the numbers from the regression analyses have varied over the years as the number of hulls tested has increased and better formulations have been developed. The ones in the books above are fairly recent and better than earlier ones. An important consideration in using these regressions is that the hull they are being applied to is within the range of hull form parameters of those tested at Delft. For a Footy Hull of almost any design this is unfortunately not so, as Footy hulls are in general rather wider for their length than the Delft hulls. However recent drag correlations, as above, seem to be robust enough to give a very plausible wave drag estimate, even slightly outside the official range, so these have been used. As always with fluid dynamics the answers are approximate, but the best you can do, and the final verdict is on the water in race conditions. The only real alternative is to attempt a CFD analysis using the Dawson or other approach, but this requires you to spend months writing your own program and has its own set of approximations and doubtful features so there is still no finality to it although the wave drag results it produces are quite plausible and could be true.
So, looking at the regressions and other data for guidance, around Fr = 0.4 or Hull Speed, the main conclusions are that for minimum drag we should have:
Prismatic coefficient, Cp = 0.6
Longitudinal Centre of Buoyancy, LCB = 3.6% behind the midship station.
Waterline Beam/Hull Draft, Bwl/Tc = 4
There was no guidance on the effect of Transom Beam/Max Beam or Beam/Length which were judged not very important.
However, the claimed optimum Cp of 0.6 at Hull Speed follows from an earlier regression analysis and does not follow from the one actually shown in Larsson et al. I have my doubts about it as trying to design a hull with that high a value it makes an already tubby boat look too barge-like. I prefer the recommendation of another author, Francis S Kinney in “Skene’s elements of yacht design”, who writes:
“The best sailboats today have prismatic coefficients between 0.55 and 0.49. Great importance is attached to this coefficient, because if it is larger than 0.55, the boat will be pretty much of a tub; and if it is less than 0.49, she will be so fine that she will suck up a horrible quarter wave.”
You can’t argue with prose like that, so the Iambus2 ended up with Cp = 0.56
The LCB was at 54.3% or 4.3% behind the midship station, which is as near the optimum as matters.
The Residuary Resistance was measured over a range of Froude Numbers from 0.1 to 0.6 where the conventional “Hull Speed” is at about 0.4. The hull shapes have been characterised by a limited number of parameters including the Displacement/Length ratio, positions of the longitudinal centres of buoyancy and of flotation relative to length, the Prismatic Coefficient, Beam/Length, Displacement to wetted and waterplane areas, etc. For each Froude Number in 0.1 (0.05) 0.6, regression analysis has been used to find an expression for the ratio of Residuary Resistance to hull displacement as a linear function of eight parameters of the types above. The actual parameters used and the numbers from the regression analyses have varied over the years as the number of hulls tested has increased and better formulations have been developed. The ones in the books above are fairly recent and better than earlier ones. An important consideration in using these regressions is that the hull they are being applied to is within the range of hull form parameters of those tested at Delft. For a Footy Hull of almost any design this is unfortunately not so, as Footy hulls are in general rather wider for their length than the Delft hulls. However recent drag correlations, as above, seem to be robust enough to give a very plausible wave drag estimate, even slightly outside the official range, so these have been used. As always with fluid dynamics the answers are approximate, but the best you can do, and the final verdict is on the water in race conditions. The only real alternative is to attempt a CFD analysis using the Dawson or other approach, but this requires you to spend months writing your own program and has its own set of approximations and doubtful features so there is still no finality to it although the wave drag results it produces are quite plausible and could be true.
So, looking at the regressions and other data for guidance, around Fr = 0.4 or Hull Speed, the main conclusions are that for minimum drag we should have:
Prismatic coefficient, Cp = 0.6
Longitudinal Centre of Buoyancy, LCB = 3.6% behind the midship station.
Waterline Beam/Hull Draft, Bwl/Tc = 4
There was no guidance on the effect of Transom Beam/Max Beam or Beam/Length which were judged not very important.
However, the claimed optimum Cp of 0.6 at Hull Speed follows from an earlier regression analysis and does not follow from the one actually shown in Larsson et al. I have my doubts about it as trying to design a hull with that high a value it makes an already tubby boat look too barge-like. I prefer the recommendation of another author, Francis S Kinney in “Skene’s elements of yacht design”, who writes:
“The best sailboats today have prismatic coefficients between 0.55 and 0.49. Great importance is attached to this coefficient, because if it is larger than 0.55, the boat will be pretty much of a tub; and if it is less than 0.49, she will be so fine that she will suck up a horrible quarter wave.”
You can’t argue with prose like that, so the Iambus2 ended up with Cp = 0.56
The LCB was at 54.3% or 4.3% behind the midship station, which is as near the optimum as matters.
| hull_shape.pdf |
