There seem to be two different situations that need to be considered. The first is when the boat is heeled (beating or reaching) and the fin is developing lift as well as drag. The second situation is when the fin is purely a drag appendage (on the run).
When heeled, the bulb and fin are angled towards the oncoming flow of water. This angle is the leeway angle; the boat must make leeway for the fin to develop lift, and counteract the force of the sail tending to push the boat off-course. While the fin is designed to act like a wing and develop lift with acceptable drag, the bulb is usually a simple torpedo shape and creates much more drag relative to its very small contribution to lift. No matter how the bulb is canted, there will always be a sideways flow over the bulb, and hence a component of drag.
We start by imagining a very light breeze, so the boat hardly heels at all. Nonetheless, it has drive, forward motion, and is thus making leeway. In this circumstance, canting the bulb simply mis-aligns it to the incident flow. So when heel angle is close to zero while beating, bulb cant should be close to zero while beating.
Next, we imagine a strong breeze. In fact, let's have the breeze so strong that, in our mind's eye at least, the boat has been knocked horizontal. In all other respects (this is just imagining, after all), let's have the boat "sailing normally", magically making normal leeway. In this circumstance, canting the bulb will help reduce its drag. In fact, canting the bulb by the leeway angle will minimise the bulb drag. It will not eliminate the bulb drag, of course, because there still is a sideways flow over the bulb as before. So when heel angle is 90 degrees, bulb cant could do with being set to the leeway angle.
So on the beat or the reach, it turns out that the bulb cant angle could do with being set equal to the boat's leeway angle times the sine of the heel angle. For example, imagine that our boat characteristically makes 4degrees of leeway in a good breeze, while heeled at 30 degrees. It would then be ideal to have the bulb canted by 4.sin(30) = 2 degrees. There are three questions which remain. What happens if the boat isn't heeling much? What happens if the boat trims down by the bows when heeled? What happens with the fin tip vortex?
If the boat isn't heeling much, the bulb cant set for, say, 30 degrees of heel would be inappropriate for a heel angle of, say, 10 degrees. Furthermore, the leeway angle would be lower as well, perhaps 2 or 3 degrees, so the ideal bulb cant here would be perhaps 2 x sin(10) = 0.35 degrees. This means that the bulb would be offering more drag than it might otherwise do. Two things make me think (without doing the maths!) that this might not be too bad. First thing is that the drag force is a function of the square of the speed. Other things being equal, I'd rather have the bulb aligned well to a faster flow and accept a degree of mis-alignment to a slower flow. (Bill Mullica disagrees, noting that he'd prefer to have minimum drag when the drive force is small, and allow drag to build up at higher wind speeds because the drive force can overcome that. The drive force produced by the sails is itself a function of the square of the speed as well, after all.) The second thing is that the bulk of the bulb drag is still a function of leeway, due to the sideways flow over the bulb, and the bulb cant only offers a pretty modest reduction in drag, just a fraction of this.
The second question concerns wide-transom boats. Note that we are not talking about wide beam boats here, although it is usually true that a wide beam boat also has a wide transom. When a wide transom boat heels, she trims down by the bows quite perceptibly (apparently called coupled pitch and heel). This puts her bulb at an angle to the oncoming flow in just the same way as described for a running boat in the next section. If the amount of bows-down trim is, say, 2 degrees, then the bulb could do with being canted up by 2 degrees to "neutralise" the trim change. (The bows-down trim change also apparently puts her fin at a lower angle of attack to the oncoming flow, but (an' this time I've done the maths!) that is just that - apparent. The boat must still develop an angle of attack that generates sufficient lift to balance the sail force, and in a wide transom design that simply means more leeway.) So the spreadsheet adds this bows-down trim angle to the angle derived from the earlier formula to give a suggested bulb cant. Note please that the spreadsheet assumes this bows-down trim is (already) in the vertical plane, not the plane of the hull. Most hydrostatic or hydrodynamic calculations are done relative to the axes of the boat, not the earth, and the trim these calculations give must be resolved into their vertical component by multiplying by COS(heel).
For beating and reaching, then, a narrow beam boat might have a suggested bulb cant of 2.25 degrees -- 2 due to heel and leeway, and 0.25 due to a very slight bows-down trim -- while a wide transom boat might have a suggested bulb cant of 3degrees -- 2 due to heel and leeway, and then due to a bows-down trim a further 1degree.
The third question involves the tip vortex of the fin in the vicinity of the bulb. As the fin develops lift, it also develops a span-wise flow. From the view at the "bottom" or high-pressure surface of the fin, the span-wise flow is towards the tip, and so a canted bulb would work well, better orienting the bulb nose with the local flow on the lower surface. However, from the "top" or low-pressure surface of the fin, the span-wise flow is away from the tip and towards the root, and so the canted bulb makes things worse for flow at the upper surface. The net effect is that modest bulb cant probably has little effect.
When the boat is running, the pressure of the wind on the sails makes the boat trim down by the bows. Carry too much sail, and the trim becomes excessive -- the boat pitch-poles or broaches uncontrollably. As far as I can see, the main reason the boat suddenly "lets go" and shows her rudder is that the bulb offers increasing drag until it is all too much and the bulb acts as a brake, tipping the boat forward as if she'd stubbed her toe. If the bulb were canted, however, the increasing drag could be postponed, and hence pitch-poling could be postponed.
How much bulb cant do we need in this situation? First, as the boat trims bows down, the hull centre of buoyancy moves forward, until the moment arm of the change in CB (multiplied by the bulb weight) balances the sail force. Let's work an example, and have our IOM right at the very top of "A" suit on the run in 3.2 m/sec of wind. We assume that "A" suit is about 0.65 sq m of sail area, and that the boat is moving at her hull speed of around 1.2 m/sec. Assuming a coefficient of drag of about 1.9 (flat plate at 90 degrees to the wind), a dynamic pressure of about 0.60, and that the apparent wind is about 2 m/sec, the force on the sails is thus about 1.9 x 2 x 2 x 0.65 x 0.60 = 2.96 Newtons, 0.3 kg. If the centre of effort of the sails is, say, 800 mm above the CB, we have a pitching moment of 0.3 x 800 = 223 mm.kg. To counterbalance that, we have the bulb, 2.5 kg, whose CG needs to be about 90 mm behind the (new) CB to yield the same 223 mm.kg of righting moment. The CB thus needs to move forward by 90 mm. How much trim is required for this to happen?
It is time to use the spreadsheet. The second half of the spreadsheet calculates hull parameters when the boat is heeled, but has some additional calculations to calculate LCB change due to trim change. Setting the heel to 0 degrees, we try various small angles of trim such as -1 or -2 degrees to move the LCB forward the amount we want. For most of the designs I've played with, a trim change of around -2.5 degrees moved the LCB from station 5.16, say, to 4.28 -- a change of 88 mm. That'll do.
So, according to the spreadsheet, a trim of about -2.5 degrees produces the required change in CB to keep the rudder in the water. We should then cant the bulb by 2.5 degrees so that it offers minimum resistance on the run when at the top of "A" suit. Some questions remain. Do we need greater trim changes, and hence greater bulb cant, if the hull beam reduces or if it increases? What happens to drag with a fully canted bulb at lower speeds?
If beam increases or reduces, the spreadsheet (the hull lines are circular arcs, remember) suggests that, by and large, there is little difference in the trim needed to shift the LCB a given distance. For example, with a narrow hull, a trim of -2.8 degrees moved the LCB 90 mm, while a wide beam hull needed only -2.5 degrees. The difference is of the order of 10% or 12%, reflecting the fact that the wider-beam hull has a little more reserve buoyancy than a narrow beam. (Well, strictly speaking of course, the issue is "Where is the reserve buoyancy?", rather than "Is it a wide-beam hull?", as Larry Robinson has pointed out to me.)
OK, so we cant our bulb by 2.5 degrees on the run. What happens when the wind is blowing at a gentle apparent 1 m/sec? Sail forces would drop to around a quarter of their earlier values (wind speed halved), and so the LCB would move by about a quarter of the earlier value, about 23 mm, giving a quarter of the trim change, about -0.8 degrees. The bulb, canted at 2.5 degrees, will offer higher drag, now being inclined at around -1.7 degrees to the oncoming flow. As before (without doing the maths!), this might be a better deal (putting up with the drag due to -1.7 degrees angle of attack to an oncoming flow at 1 m/sec) than having no bulb cant (hence having to put up with -2.5 degrees angle of attack at 2 m/sec).
You know that it's up to you (as ever), and that the issue is one of compromise (again, as ever). It is encouraging to see that, for both upwind and downwind situations, we arrive at similar suggestions for bulb cant -- somewhere around 3 degrees if you can guarantee top-of-suit conditions. We also note that, for a wide transom design, we would like an extra 0.75 or 1 degree of cant for windward work, but a little less cant, around 0.25 degrees less, for downwind work. Shucks (grin).
If you can't guarantee top-of-suit conditions, then compromise is of course necessary. On the basis that I'd rather have the bulb mis-aligned at lower speeds than at higher speeds, I'd go for 2 degrees of bulb cant as an all-round number. Good luck!
Post-script: Now, recent experience at the Worlds in Croatia makes me think that bulb cant is probably more important than I originally thought in keeping the boat going on the run when hard-pressed, and not nose-diving. I'd now suggest 2.5 degrees of cant for an Ikon, though I saw more than one boat sporting 4 degrees. I'm also much clearer in my own mind that the excellent sea-keeping qualities of the TS2 are, in significant part, due to its bulb cant, which is 3 degrees or so as standard. Brad Gibson tells me that he has found that 2 degrees, my all-round number, works better for him when the wind is light, and that higher amount of cant only worked in the upper wind range. Brad's design is the Southern Cross 4, a narrow-beam boat.
Post-post-script: I've done some more research, and it seems that the required cant is very much more a function of whether you have a narrow or wide transom than I at first thought. If you have a wide transom, the boat will adopt a decided bows-down trim to windward, and this most certainly needs bulb cant to reduce the resulting increase in drag. So my suggestion of 3 degrees of cant is appropriate only for a wide transom design, such as the TS2. Two degrees would suit a narrow transom design (no matter what the beam). If you have a wide transom design and set the cant to 0 degrees because you thought the builder made an error, set it back to 3 degrees! If you have a narrow transom design (I'm being careful with the right words here -- we are talking transom, and not beam, please) and are wondering why it isn't flying with cant of 3 degrees, cut that back to 2 and try again.
Post-post-post-script: Giving your bulb some cant will, I am confident, improve your boat's handling and performance in the stronger winds, but will also hurt it in the lighter winds. Where you draw the line is dependent upon the kinds of winds you generally sail in. If you don't usually see anything above, say, 6 knots, then reduce the cant suggestions above by around 1 degree. Remember, please, we are talking about IOMs here. I have no real idea what the cant values should be for other classes.
©2011 Lester Gilbert