I have long admired Joshua Slocum's feat of circumnavigating the world - ever since picking up a second hand copy of his book for a dollar or two, more years ago than I care to remember. His was not a non-stop exercise, as the media demand today, but it took place in a different time, and a very different world. 1995 will be the centenary of his departure, on 24th April 1895, and his book is a reminder of the great changes in nations and manners since then.
But the nautical side was given at least as much attention, with everything from meteorology to the galley being covered. Slocum provided a good account of the design of the yacht, including a full body plan. After I started the Hullform project, Spray was one of the first designs entered - and it was the centrepiece on the cover of the first Hullform 3 manual.
Alan Dowd's article in the Spring 1994 edition of Australian Amateur Boatbuilder rekindled my interest in Spray's design. Joshua Slocum sang loudly in praise of the boat's virtues - and who would not feel that way, having been carried safely around the world in three years of navigation? But in the light of newer design trends, how would Spray compare to a more modern hull?
A PC-based hull design program is a good tool for probing such questions. All hull CAD programs allow the user to enter a representation of a design into the computer, and provide for fairing of hull lines and a range of scientific and engineering analyses.
The hydrostatic and dynamic characteristics of any design can be compared to reference designs, revealing its strengths and weaknesses. A lot of "what if"-ing can be pursued, to find out how it could have been improved.
Hullform, in particular, is well suited. Entry of existing offsets was one of the program's basic design objectives, and the hydrostatics analysis and reporting is pretty detailed in all versions. The professional versions also include hull drag estimates, based on a range of methods, and can present hydrostatic analyses in many more ways. With these versions' expanded 40 hull-line limit, there is no practical limit to the accuracy with which a design can be represented.
Figure 2. Body plan of Spray, as represented using Hullform.
Recreating Spray in computer terms was relatively easy - although there was no way to avoid keying in the many sets of transverse and vertical coordinates required. The design was entered using the sheerlines (the book showing the original sheerline, and Slocum's freeboard extension), keel and several waterlines in between. Offsets were measured in millimetres from the printed body plan, and these values were entered, unconverted, into the program. Scaling to real units was taken care of later, using the program's Edit, Multiply menu option.
The next stage was to fair the lines entered. This is always necessary, because the measurement error is usually larger than the amount of design error which gives an unfair hull. This led to a surprise - Spray was a good example of a well- faired hull.
Figure 1 is a copy of the program's line-fairing screen display. It shows the profile of the sheerline (vertical scale stretched) in the upper half, and its curvature in the lower half. Ignore the kink at the right end - this corresponds to the bowsprit. At transverse sections numbered 7 to 11, there is a rise-and-fall pattern, typical of measurement errors. However, overall, this line, like others extracted from the body plan, showed no major deviations from a smooth general trend. I wish I could say this about the one hull design I ever bought from a commercial designer!
Figure 1. Vertically-stretched profile and curvature trend of Spray's sheerline, as first entered into Hullform.
Smoothing the sheerline only involved telling the program to ignore the stem point, and to smooth sections 5 to 11. A smooth spline curve was fitted through the remainder of points on the sheerline, and the faired offsets at sections 5 to 11 replaced the initial estimates. On-screen, the smoothed offsets hardly moved, but the curvature lost all of its up-and-down steps.
After repeating this process for each hull line, the end result was a detailed representation of Spray (figure 2), to which Hullform's design analysis tools could be applied.
Figure 3. Spray's righting lever arm as a function of heel. This indicates that the righting moment increases up to a heel of about 45o, before decreasing again.
The first analysis showed an interesting point. Spray's rated displacement was not an exact value based on the waterline shown on the body plan. Joshua Slocum quoted a gross tonnage of 12.7 tons, while that calculated by Hullform was 14.5. I don't know the basis for the gross tonnage calculation, and it might have been rather simpler than we use today, or the body plan itself might be based on an incorrect waterline. Hullform's calculated mass displaced per foot of draft is 8.933 for Spray, indicating a sinkage difference of 2.4 inches - a significant discrepancy, even in 1895.
Being a fairly beamy and full hull, Spray showed good heeling stability. With a centre of gravity placed at the waterline, Hullform reported an upright stability of 1.68 ton foot per degree of heel - i.e., a mass of one ton placed one foot off the centreline (or 0.84 ton placed 2 feet off the centreline, etc) would heel the hull by one degree. Programs like the professional version of Hullform can display stability effects in more sophisticated ways than a simple numerical value, however - figure 3 shows a plot of righting lever arm (righting moment divided by displacement) for Spray.
As you would expect for a hull of Spray's fishing-boat origins, the design shows no respect for the aims of the racing yacht designer. By Slocum's comments, her full ends drew comment even at the turn of the century. (Figure 4 shows well the full shape of the hull)
Figure 4. The prismatic coefficient - the ratio of the displacement of the hull (form shown at the top), to the displacement of a hull of fixed cross section equal to the top hull's maximum, and of the same waterline length (shown at the bottom)
In naval architecture, the fullness of a design is measured by a range of shape coefficients. The commonest is the prismatic coefficient, measuring the ratio of the displaced volume to the product of the maximum immersed cross- sectional area and the waterline length. (See figure 4) A "full" hull more closely fills the latter volume, giving a large prismatic coefficient. Typical values are in the range 0.5 to 0.6.
In general, a hull with a small prismatic coefficient will perform better in light winds, while one with a larger coefficient will be faster in strong winds.
This effect is due to the wave-making contribution to drag. As the hull travels through the water, the shape of the hull sides generates waves. Waves forming along the whole length of the hull are the dominant source of drag at high speeds. For a full hull, whose sides are straighter than those of a hull with slender ends, the long waves are reduced in size. This makes wave drag less at the top of the hull's speed range.
Hullform's analysis showed a prismatic coefficient of 0.65 - much larger than most racing yachts. Significantly, another design in the Hullform library, a 19th century schooner form approximating the U.S. design "Pride of Baltimore", showed a coefficient in the normal range (0.57). Clearly, some hulls at the time were put together with performance in mind - but not Spray's.
As a comparison exercise, I created a reference design matching closely the displacement, waterline length and waterline beam of Spray, but with finer ends. It had a prismatic coefficient of 0.60, at the upper end of the normal range.
Of Hullform's five drag estimation options, the most appropriate is probably the "Gerritsma" scheme. This uses a mathematical best-fit curve, based on drag variations for a set of similar yacht models (the "Standfast series"). For a yacht of Spray's length, it gives valid drag estimates for speeds up to about 8 knots.
The Gerritsma estimates agreed well with the normal connection between drag and prismatic coefficient. At 6 knots, Spray showed a total drag of 0.176 tons, while the reference hull's drag was only 0.106 tons. This looks terrible for Spray, but we must not forget that wave drag changes very quickly with speed. For a drag of 0.106 tons, Spray is indicated as travelling at 5.3 knots.
But at higher speeds, the relationship changed. This brings up the question of Spray's actual operating speed. Joshua Slocum quotes one passage of 2700 miles in 23 days - an average of about 5 knots. By the above, it seems that most of the time Spray was operating well out of her best regime. Was there any realistic condition in which she would have performed the better?
To find this, we need some estimate of the hull's driving force. For downwind sailing, this is easy - just multiply the wind pressure by the sail area. The would be some errors in estimating sail force coefficient and area, but these are of little significance given the dramatic change of drag with hull speed. So, estimating a sail area of about 120 square metres, and a wind speed in the sail of 8 metres per second (about 16 knots), we can calculate a driving force of roughly 0.46 tons.
The Gerritsma estimates suggest that for this driving force, both Spray and the reference hull would have been running at 7.4 knots. Spray had clearly made up ground. The true wind in these conditions would have been the sum of hull speed and the 16 knots, so we can say that when winds became fresh - as they often do in the trade wind zones - Spray would have come into her own.
Of course, there is more to speed through the water than a fixed sail area and the hull's drag. A good sail-carrying capacity can readily compensate for a fuller hull. We can measure this capacity using a design's heeling and pitching stability measures - the first of these being crucial on windward and crosswind headings, the second being important when running downwind. Spray's heeling stability has already been described. Pitching stability is traditionally expressed as the moment required to change to relative trim of bow and stern by a small distance (usually one centimetre or one inch).
In comparison to Spray's heeling stability measure of 1.68 ton foot per degree, the reference hull showed a slightly smaller value, of 1.59. This was an expected result, since the reference hull had the same beam and waterline length, but was finer at its ends. With less surface of boat on the water, there was less to hold it level. But the difference was small - about 6%.
The pitching stability analysis showed the same sort of result, Spray having a "moment to change trim" of 1.02 ton foot per inch, the reference hull having a value of 0.89. The difference was rather larger, at 14%.
With 14% extra sail carrying capacity, Spray should really be allowed 14% extra driving force, for downwind sailing - which would push her speed with a 16 knot apparent wind to 7.6 knots.
So it is possible that Joshua Slocum was correct, in his own terms. Spray was a good sail platform, and her extra sail carrying capacity may have compensated partly for the shape of the hull, particularly downwind. In any rating scheme except IMS, she would have paid a heavy penalty for additional acreage up top - but then, I don't think that was to much in Slocum's mind, running before fresh trade winds in the middle of the Pacific Ocean.