Tacking

(This is based on my article that was published in issue #172 of the American Model Yachting Association's "Model Yachting" quarterly magazine.)

What is the rudder throw I should set on the boat? How should I feed the rudder in during a tack or turn?

Lift from the rudder

First, let's understand the hydrodynamics of a rudder. A rudder works like any wing or fin and steers the boat by generating lift when it is turned to an angle to the oncoming flow. It generates its maximum lift and maximum steering force at an angle of attack of somewhere between 8 and 16 degrees, depending upon its airfoil section. It is maximally efficient at somewhat lower angles of attack, its best lift-to-drag ratio is usually somewhere between 6 and 12 degrees. The lower numbers apply to thin rudders, perhaps 5% t/c, the higher to thicker rudders, perhaps 10% t/c.

Rudder throw

If a rudder works best at an angle of attack, a, of around 10 degrees, why would we want a throw of 45 degrees while tacking? It turns out that the angle of attack is to the local flow over the rudder, which is quite different from the local flow elsewhere over the hull. Figure 1 shows a boat in a turn, arranged so that the local flow over the fin is at approximately zero degrees. Because of the turn, at a distance L away from the fin (usually about half the boat length) the local flow over the rudder, shown as g, is given by Arcsin (L / r), around 35 degrees for a tight turn. If the rudder throw is 45 degrees, d, its angle of attack to the local flow is the 10 degrees we want. Ah!

Figure 1. Geometry of rudder action in a turn.

Local flow and turn radius

A little trigonometry computes the angle of the local flow at the rudder, given as Arcsin (L / r) -- the tighter the turn, the smaller its radius, and so the larger is the angle of local flow. Table 1 shows the different turn radii which would suit various rudder throws for a given angle of attack of 10 degrees. Note that these values apply to the fully developed turn and not at its start or end.

Rudder	Local	Turn
throw	flow	radius
d	g	r
(deg)	(deg)	(boat length)
15	5	5.74
20	10	2.88
25	15	1.93
30	20	1.46
35	25	1.18
40	30	1.00
45	35	0.87
50	40	0.78
55	45	0.71
60	50	0.65
65	55	0.61

Table 1. Local flow angle and turn radii to suit various rudder throws given a constant angle of attack of 10 degrees.

Looking at Table 1, it seems that the radius of the turn of around one boat length suits a rudder throw of 40 degrees. A rudder throw of 60 degrees implies the turn radius should be around two-thirds of a boat length. That is a tight turn! Brad Gibson recommends a maximum rudder throw of 45 degrees, while Graham Bantock recommends 55 degrees. I’ve had a look at Ken Binks’s boat, and I’d guess that his maximum throw is around 65 degrees. You might wonder if it is worth the trouble to arrange a maximum throw of 65 degrees, and Figure 2 aims to help out.

Figure 2. Turn radius versus rudder throw.

Time through a tack

You might think there is not much to choose between a turn radius of 1.18 boat lengths (rudder throw = 35 degrees) and one of, say, 0.71 (rudder throw = 55 degrees). They are both tight turns, after all. But a little thought will tell you that the time to execute the tack (or penalty turn) is in direct proportion to the turn radius -- that is, the length of the path that the boat follows is shorter the smaller the radius. On the assumption that the boat loses speed during a quick tack about as much for a 1.18 radius turn as a 0.71 radius turn, the boat will complete the tighter turn almost 40 percent faster, other things being equal.

Feeding the rudder

Do I just whack the stick over and hold the rudder at maximum throw all the time while tacking? Do I whack the rudder over and then ease it off during the tack? Or do I feed the rudder in during the tack? If so, when should I aim to hit maximum throw during the feed? And if I do feed it in, how quickly should I do that?

Figure 3 gives a simplified visualization of the hull and rudder positions through a tack. It is clear that the rudder must be fed in during the tack, so that it reaches and then maintains the optimum angle of attack to the oncoming flow of around 10 degrees as the boat turns. Whacking the rudder over to the stop immediately will simply stall the rudder, and, though it will give lift and thus turning force, drag will shoot through the roof.

Very roughly, it looks like I want to get the rudder to its maximum throw when the boat has passed through its turn by an angle equal to its set maximum throw angle. In Figure 3, the rudder shows a maximum throw of 45 degrees, and it ideally gets to that maximum about 45 degrees through the turn, that is, about half-way through a 90 degree tack. Very roughly, if maximum throw is 60 degrees, then I’ll want to hit the stick stop on the transmitter about two-thirds of the way through the tack or turn.

Figure 3. Rudder position during the tack

If you have a computer radio system, you might want to experiment with a programmed limit on your rudder rotation speed. Yeah, I know, you’ve just installed a fantastic new rudder servo that rotates through 60 degrees in 0.08 seconds, but that is way too fast if you just whack the stick over. My guess is to limit the servo rotation to around 50 degrees in 0.5 second — i.e. around 10 degrees per 0.1 second — and see how you get on. Put the program on a switch, of course, and use it only in clear water, otherwise your emergency steers on the start line and around the buoys may be compromised.

Summary

It might be strange to think of the rudder as generating lift during a turn, but in engineering terms that is exactly what it is doing. Depending on the tightness of the turn, the rudder might be at its full throw of 45 degrees to the hull centreline, but only acting at an angle of attack to the local water flow of around 10 degrees. It might seem that the rudder, fully deflected at 45 degrees, is producing a lot of drag, but that is not the case. It is producing the same amount of drag as it does with 10 degree deflection while going straight ahead. With an exceptionally tight turn, the rudder could be at 65 degrees full throw yet giving drag equivalent to 10 degrees deflection. The key is to feed the rudder in during the turn, in proportion to the tightness of the turn; as the turn tightens, feed more rudder.