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Trimaran Performance vs Hull Form

QUESTION: If I build a multihull with straight sides of plywood to make construction easier, how much performance would I lose compared to a more ideal shape?

ANSWER: OK, let's first take a hypothetical case in order to have some figures to work with. Let's assume the straight sided hull goes down in a Vee with a small flat area on the bottom, somewhat like the Vee-hull of a James Wharram catamaran.

Now let's compare that to the shape with a semi-circular bottom that has the minimum wetted surface. Superimposed, the two might look like this (picture on right). Although I might refer to this simple shape as 'a Vee-hull', the shape I prefer actually has a small bottom flat in order to provide useful buoyancy lower down.
See also the article on relative virtues of flat panel shapes.

Right away, for the same displacement, one can see that the Vee hull has significantly more draft, is narrower at the waterline and will have more underwater (wetted) surface. In practice, the Vee hull is likely to be 10% heavier in construction, but that might only mean say 5% required increase in overall displacement as the deadweight (crews, supplies etc.) could be considered the same.

Now we need to look at how a boat's resistance varies with its speed and this is much related to its length. About 140 years ago, a William Froude discovered that up to a Speed/Length ratio (SLR)* of about 1, resistance is mostly made up of frictional resistance and in such a case, would be directly proportional to the wetted surface. From a SLR of 1 to about 1.8, there's a major spike in hull resistance due to waves made by the hull through the water and the wetted surface resistance, although still there, takes a more minor role.

Once over the SLR of about 1.8, then the wetted surface again becomes the predominant resistance (although again, some wave resistance is still present). Now for different boat lengths, let's make a table to see what speeds we are talking about.

Waterline Boat Length SLR = 1 SLR = 1.8
FEET KNOTS KNOTS
20'
30'
40'
50'
60'
4.47
5.48
6.32
7.07
7.75
  8.05
  9.86
11.38
12.73
13.94

*SLR = speed (in knots) divided by the square root of Waterline Length (ft)

So, both below the speed given for SLR=1 and above the speed given for SLR=1.8, the resistance would be directly affected by the roughly 20% increase in the wetted surface for the Vee shape and if we add in the 5% weight penalty, this could go to about 24%. (While these percentages might apply for speeds well under SLR of 0.5 or well over 2.5, they would in fact be somewhat less than that at the SLRs listed, as not all the resistance would be due to friction on the surface.)

But between the two values listed, wave resistance grows to a peak at around SLR=1.4 and at this point, the narrower beam of the Vee hulls could lower wave resistance enough to offset the frictional resistance and therefore be quite efficient in the relatively narrow range between the two speeds listed above for each length.

Of course, there are other aspects to consider too—like having less interior space at the waterline with the V-hull and also, that the V-hull would sink about 20% more for each 100 lbs of extra weight loaded on. The extra depth of a Vee hull is sometimes used as a longitudinal keel to resist lateral drift and that 'might' annul the need for a dagger board or centerboard, although such deeper fins are clearly more efficient for sailing upwind.

But if you're content to sail in the speed range indicated by the table and can accept the other compromises, then there's definitely a case for using V-hulls and keeping it simple. Outside of that, expect speeds at least 10% slower at the low end and even more at the higher end beyond SLR of 2.5.

Of course, even 'ideal hulls' are seldom perfectly semi-circular and the total resistance also depends on many other things, such as the hull ends and even air resistance etc., but this gives a general idea of speed performance for such differing hull shapes, assuming all other factors are alike and comparable. On another aspect, the deeper V-hulls will also have more directional stability but in turn, be harder to tack—helpful for long trips but not for short tacking.

Such V-hulls are seldom used for the center hull of a trimaran as they offer so little space. However, they have been used for easy-to-build catamarans and trimaran amas, for owners ready to accept the performance sacrifices noted above. Their use for the main hull of a small day-trimaran (say under 19') might also be justified for the sake of easy building, when their relative loss of space would not really be an issue.

Recent tests on a small prototype trimaran with this deep vee hull form and flat bottom, demonstrated that performance can be surprisingly good and some of what is lost through increased wetted surface is indeed made up by the slimmer form. While this may not be true at very low speeds (below say 3 kt), the flat of bottom may give enough dynamic lift over at least part of the hull length to offset the theoretically greater surface, and show that the higher speeds of a light trimaran will not be as adversely affected by this deep box form as first thought.

Editors Note: For this reason, this simple-to-build form was chosen for the new W17 that has since proven to perform very well indeed. The added resistance at the very low end (say under 4 k) will still be there and will need some imaginative boat trimming and added light-wind sail area to overcome. But at more common higher speeds, this boat, especially when built to design weight, is proving that the flat underbody surface can indeed offer a very clean type of dynamic lift that is closer to surface skiing and surfing than conventional planing and W17 owners will likely be calling this 'oiling', as it reportedly feels 'like the boat was running on oil'. Even with the very moderate cruising rig, a speed of 14.9 k has already been recorded (by GPS) in this mode, so this is impressive and promises to offer lots of fun. So for this particular design at least, the high end restriction of a Veed hard chine hull has been overcome by the narrower hull, the flat of bottom and its design profile.
Compared to a round bilge, the deeper hull also offers additional lateral resistance, so the dagger board wetted surface can be slightly reduced for another small speed gain.

Note: Please note that percentages given are general indications only, as the calculation of wave making resistance for a specific hull shape is virtually impossible due to the constantly changing forms of associated wave formations and waves themselves. Comparative results can best be made by testing one boat against another, either in controlled tank tests (see photo) or through comparison of full-size boats. By contrast, frictional resistance can be calculated, based on well documented results of past tests with various surfaces. But frictional resistance is only part of the total, though as noted, will be significant at both low and high speeds. However, the actual speeds at which frictional resistance is most predominant, will still vary between different hull forms, their proportions and length. No one said it was easy ;-)


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