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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 initially 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 least 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 little wider flat bottom in order to provide useful buoyancy lower down - see later.
See also the article on relative virtues of flat panel shapes.

Right away, for the same displacement, one can see that the boxy hull has more draft, is narrower at the waterline but 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 double the dry weight.

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 (for a typical multihull), there's an increase 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 a SLR of about 3.0, the wetted surface is again on the increase (although wave resistance is still significant).  So for different boat lengths, here are the speeds we are talking about.

Waterline Boat Length SLR = 1 SLR = 3.0
FEET KNOTS KNOTS

16'

20'
30'
40'

4.00

4.47
5.48
6.32

12.00 

13.42
16.43
18.97

*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=3.0, the majority of resistance would be directly affected by the roughly 20% increase in the wetted surface for the Vee or Box shape and if we add in the 5% weight penalty, this could go to about 24%. (While these percentages might also apply for speeds well under SLR of 0.5 or over 3.5, they would in fact be somewhat less than that at the SLRs listed, as not all the resistance would be due to surface friction)

But between the two values listed, wave resistance grows to a peak at around SLR=1.8 (for the average multihull) 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 range between the two speeds listed above for each length.   The box or Vee'd shape would also offer less leeway and that will also help to compensate.

If we widen the hull at the bottom, the sides can become more vertical and this more box-like section can further lower the wave-making compared to the Vee-section we started out with, as it disturbs the passing waves even less.

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 15% more for each 100 lbs of extra weight loaded on. The extra draft 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, which is surprisingly broad, and can accept the other compromises, there's definitely a case for using the box hulls and keeping it simple. Outside of that, expect speeds at around 10% slower at the low end and similar at the higher end beyond SLR of 3.5.

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.

True 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. However, the more box-hull can be justified for the sake of easy building. and at least offers more foot space than the narrow Vee'd for a main hull.

Recent tests (2009) on a small prototype trimaran with this Box-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 low speeds (below say 4 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 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 for a significant speed range above that, this boat, especially when built to design weight, is proving that the flat underbody surface can indeed offer a very clean running hull with some dynamic lift at higher speeds that some W17 owners are calling 'oiling', as it reportedly feels 'like the boat is 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 boxy hard chine hull has been overcome by the relatively narrow hull, the flat of bottom and its low-rocker design profile.
Compared to a round bilge, the box-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, is most significant at both low and high speeds. However, the actual speeds at which frictional resistance is most predominant, will also vary between different hull forms, their proportions and length. No one said it was easy ;-)

 

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