Using the tab on the beat, setting it an an angle of something like 6 or 8 degrees when well heeled, (*) reduces leeway.
* Earlier, I said "gives extra lift". That's nonsense. Let me try and explain properly what happens with a trim tab of the sort I am using here.
As Larry explains on the page explaining how to calculate fin area, as I explain on the foil sections and forces page, and as Will also explains on that page, the force produced by the fin balances the force produced by the sails. The required fin force is achieved by balancing or compromising on four things: the fin area, the leeway, boat speed, and the coefficient of lift. When sailing, fin area is fixed, and the boat speed is more or less given by the sails you are carrying and the wind. In order to balance the sail force, the required fin force is generated by leeway. The more leeway, the higher the coefficient of lift, and the more force produced. At a certain amount of leeway, the required fin force is achieved, and that's how the boat sails. The following diagram illustrates some sample data for a boat beating. We imagine 5 degrees of leeway and a course of 35 degrees with the apparent wind at 30 degrees.
In general, as the lift coefficient rises, so does the drag coefficient. Careful design and shaping of the section, however, can yield lower levels of drag at low leeway in exchange for higher drag at higher leeway. This is the 'drag bucket', the region of operation of the foil where drag stays more or less constant while lift rises linearly. For a symmetric section such as might be used on a rudder or fin, the drag bucket isn't very wide, perhaps from a coefficient of lift of around -0.2 or -0.3 to around +0.2 or +0.3 (giving a Cl range of around .4 or .6). The following graph gives an impression of a lift / drag curve for a symmetrical aerofoil section. The data points comprise lift and drag coefficients at various angles of attack (leeway) from -10 to +10 degrees. The drag bucket is shown as extending from a Cl of -0.3 to +0.3.
A lift coefficient of 0.2 or 0.3 is a little on the low side for our model boats, since we often find that a 'reasonable sized' fin on a Marblehead or IOM must generate a lift coefficient of 0.3 or 0.35 in a good breeze. The drag bucket region lift coefficients are particularly on the low side for "A" class boats, though. Because of the severe draught restriction imposed by the rating formula, "A" fins may need to operate comfortably at lift coefficients around 0.5 or 0.6, and as a result are known to be rather thick and have substantial area. The next graph shows a desired Cl of 0.3 just on the edge of the drag bucket, achieved at an angle of attack (leeway) of, say, 3 degrees.
An asymmetric section (see sail section lift), such as an aeroplane wing, has two advantages. The first is that it produces lift as a result of its curvature (in addition to the lift it produces due to its angle of attack). The second, connected to this, is that its drag bucket is not symmetrical, but the bucket as a whole moves towards higher angles of attack. (The drag bucket may also enlarge.) Such a drag bucket might start at Cl of 0.0, and extend to Cl of 0.6 or 0.7. Just the sort of thing needed for a "A" fin, and that is what the trim tab does -- it produces an asymmetric section which shifts the drag bucket into the range of Cl needed. The third graph illustrates the lift / drag curve for a cambered aerofoil section, where we see that the whole of the curve has been shifted to the right. There are two crucial features of this.
First, our desired Cl of 0.3 now sits right in the middle of the drag bucket. Second, this is achieved at an angle of attack of 0 degrees -- no leeway! OK, that's the theory. In practice, zero leeway is unlikely, but significantly reduced leeway is easily achieved.
The actual improvement in 'beta' -- how close to the wind you can sail -- depends upon the improvement in the lift to drag ratio given by moving the desired Cl into the drag bucket. We need to have a quick look at the 'Course Theorem', which says that beta depends upon the efficiency of the two components of the boat: its aerodynamics, and its hydrodynamics. Efficiency is measured by the lift to drag ratio, and 'eta' is the angle corresponding to that ratio, called the 'drag angle'. The course theorem says that beta equals the aero drag angle plus the hydro drag angle. Improve one or other of these drag angles, and you can sail closer to the wind. (We are talking total drag here, not just that due to the foil or sail. So drag from rigging, deck, etc will lower the aero efficiency, and drag from the hull, rudder, ballast, etc will lower hydro efficiency. While the fin alone, for example, might have a lift to drag ratio of 20 and a corresponding drag angle of around 3 degrees, lift to drag might drop to around 5 or 6 once the hull, rudder, and ballast drag is factored in, yielding a drag angle of around 10 degrees. Throw in the aero drag angle of around 25 degrees representing an aero lift to drag of around 2 and you have beta around 35 degrees -- pretty much the best an "A" Class can do to windward.)
If instead of making 35 degrees beta your yacht makes 33 degrees, that means you point two degrees higher. Doesn't sound a lot, but your yacht will climb to weather by around one boat length after beating for around 30 lengths relative to the other boats nearby... So, the fin does not need to have as much area, or be as thick, as might otherwise be the case.
SAILSetc designed and built my new keel. Around 25% smaller fin area, and around 20% thinner. The result is less drag. The trim tab accounts for around 20% of the total fin area.
I've been trying to find some basis for choosing '20%' as the tab size, but could find nothing, apart from the fact that almost all the NACA reports on flaps use or construct flaps that are 0.2c -- 20% of chord. It just seems to be the 'standard' size... The following graph is similar to that shown in Abbott & von Doenhoff, illustrating flap effectiveness depending upon flap size. Effectiveness is measured as the equivalent change in angle of attack for a given flap deflection. So, for example, a 0.2c flap has an effectiveness of approximately 0.45 -- every 1 degree of flap is equivalent to changing the angle of attack of the section by 0.45 degrees in terms of the lift generated.
Normal fin on left, fin with trim tab on right.
Another shot, showing the new fin on top of the old. The chord at the root (hull junction) of the new fin is pretty much the same as the chord that the old fin had at its tip (the ballast junction). The thickness to chord ratio is around 6.5%, so while the old fin was about 14 mm thick at the root tapering to 11 mm at the tip, the new fin is around 11 mm thick at the root tapering to around 8.5 mm at the tip.
You may notice the rather modest protrusion of the locating pins either side of the centre bolt in the above photo. They did an excellent job of locating, but not such a good job of resisting bulb twist when I went to empty the hull of bilge water. They allowed the bulb to shear away from the fin. The following photo of the disassembled keel shows the repaired fin with much more substantial pins, now located in the bulb. You can also see in the following two photos where the training edge was sawn off the original fin so as to turn it into a tab.
The trailing edge of the fin is carefully worked into a semi-circular groove and mated precisely to the leading edge of the tab.
The fin fits to the same style of ballast bulb as the old fin.
The following photos illustrate the tab operated at 8 degrees, pretty close to what would be 'maximum'. You can see that the resulting amount of camber induced into the fin section appears relatively modest. Modest, but completely effective at giving the very best lift to drag ratio from a lift coefficient right in the middle of the drag bucket.
The tab is controlled with a servo set up with a direct linkage, just like a rudder linkage.
To control the tab, the trick is to use a servo mix on the transmitter. On my Futaba 9CH, one of the knobs can set to give between 0 and around 12 degrees of throw on the tab. I dial in around 2 or 4 degrees for drifting conditions and light airs. 6 degrees for medium winds, and 8 or 10 for top of rig. Then, the knob setting is mixed to the servo through a three-position switch on the TX. When 'up', the switch sets the tab for starboard tack, when 'down' for port tack, and in the middle the mix is off.
There are two methods to command the trim. One method simply has the switch send 100% of the knob to the servo for starboard tack, and -100% for port tack.
The other method mixes the sheeting stick with the knob before it is sent through the switch. When the stick has the sheets fully in for beating, 100% of the knob is sent to the switch. As the stick moves to mid position for reaching, this is reduced to around 30% for a beam reach, and then reduced to 0% when the stick sheets out for the run.
Some early experimentation suggests that the tab allows the boat to point around 1 or 2 degrees higher, climbing around a boat length or two to windward after a beat of 50 or 60 lengths. I'm looking forward to trying this in a race!
Peter Humphreys has given me some very interesting comments.
Update 19 Apr 2010: Peter mentioned that he has tried a trim tab but it didn't seem to work for him. This puzzled me until I revisited the 'course theorem', illustrated earlier. The ability to point better or to climb to weather better depends upon the efficiency, the lift to drag ratios, of the rig and the foils. Putting a trim tab on a fin will only improve efficiency if the fin section has been designed to have a drag bucket. That's because the effect of the trim tab is to move the operating condition of the fin well into the drag bucket. A trim tab won't improve efficiency on an 'ordinary' fin, and won't help you climb to weather. That might be what Peter found...
Curiously, a trim tab won't change upwind performance either on a fin which does have a drag bucket, but which is of such an area that it usually operates within its drag bucket anyway. For example, if the fin has been sized so that it needs only generate Cl = 0.2 when heeled at 30 degrees, it is probably operating within its bucket, and does not get to be any more efficient if it operates in the centre of the bucket... Hmmm! What the trim tab does permit, of course, is a reduction in fin area and hence thickness; and in this case it should yield its promised benefits.
Update 26 Apr 2010: I raced Marie II at the third PRACC event at Fleetwood on Sunday (http://radioaclass.wordpress.com/2010/04/30/wyre-trophy-pracc-3-report/). Conditions gave us 'A' rig all day, with heel angles between 15 and 25 degrees, very occasionally 30 or 35 degrees. So, medium airs then. We managed a beat up the lake for around 600 ft or 200 m, for the first several races needing only one tack, and as the wind veered needing three or four tacks. An excellent time and place to throw in 2 or 4 or 6 or 8 or 10 or 12 degrees of trim tab and see what happened... I ended up 5th, out of a fleet of 14 which ranged from world class to clubman boats.
First, the good news. The tab worked pretty much as expected, helping me point higher than everyone else with the exception of the event winner Derek Priestley whose pointing I could match but not beat. Not too surprising, perhaps, because Derek's boat also runs with a trim tab.
Now the other news... While I was able to point higher on the beat, I did not necessarily achieve better VMG. Second to fourth places went to Brad Gibson, John Taylor, and Ken Binks. They sailed lower but faster, and while I could sometimes get ahead, sometimes I couldn't. Towards the end of the event, I think I began to see a pattern, which was that I really did need to match my tab setting to the wind strength. While 10 or 12 degrees produced outstanding pointing, VMG was slow. I had to force myself to try 4 and 2 degrees (almost negligible to the naked eye!) when heeled at 15 or 10 degrees in order to keep up. And, with heel of 20 or 25, I began to settle on tab settings of 6 or 8 degrees as getting close to optimum. So, more experimentation needed.
I tried to explore the interaction with helm balance and tab setting, and I thought there was some connection. If the boat was exactly balanced with, say 8 degrees of tab, she developed a touch of lee helm as I tabbed back to 2 degrees. Conversely, if she was balanced on 2 degrees, she developed very modest weather helm with 10 degrees of tab. And, it seemed to me that if she had a little weather helm while the tab setting was, say, 6 or 8 degrees, this hurt her VMG more than I would have expected from such a small amount of weather helm. I didn't get the same feeling, though, when sailing with a touch of lee helm. It simply needed more concentration from me to correct the helm carefully and promptly, but VMG didn't seem to suffer. So, more experimentation needed here as well, but I'm thinking that I'll have to work hard at maintaining neutral balance in order to get the most out of the tab.
On the run, I couldn't say whether the lower area, thinner fin was helping. It must have been helping, of course, but I don't know that I ever made up (or lost) places on the run because of it, whereas I could always claw my way back into 4th or 5th place from last off the starting line by the end of the second beat with better pointing.
And finally, the gotchas -- the times when I was distracted and did not throw the Tx switch to the correct side for port or starboard tack, or centre it for the run. Curiously, I never noticed my errors on the run. I completed one 600 ft run not knowing I had sailed with 8 degrees of tab all the way. On the beat, the effect was pretty dramatic, but sometimes I never noticed immediately, thinking instead that I had hit a series of headers whose timing coincided exactly with my tacks (smile). So more experience needed there then!
©2011 Lester Gilbert