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Sailing performance of the shnjaka

Perhaps every one, who owned a sailing boat, more then once gave some thought as to what her sailing performance depend upon? Is it not possible to improve it somehow? Maybe Pomor fishermen just had to put an extra keel or a centerboard to make their shnjakas tack a lot closer into the wind? The following formula can be derived from simple trigonometrical considerations:

Here V - velocity of the wind with respect to still water, U - true velocity of the boat, with allowance for her side drifting, also with respect to water, and a - angle between these two vectors. By Q we denote aerodynamic fineness, the ratio of the sail's "lift", acting transversely to the wind direction, to the "drag" in direction of the wind. Similarly, С is hydrodynamic fineness, the ratio between the hulls "lift" (this is the force that counteracts sideways drifting) and water drag, in opposition to the boat's true velocity. Our formula is correct within the approximation of low boat speed and strong wind, U << V. Ratio of the distance that the vessel can gain against wind at one tack, to the distance it must go transversely to the wind, is denoted K. It can be named "tacking fineness" of the vessel, it is equal to the cotangent of smallest achievable angle a between the vessel's course direction and wind direction.

As one can easily see from this formula, while the product QC is below unity, the tacking fineness is negative and the vessel cannot gain against wind at all, it can only sail down before the wind. Tacking fineness K can be improved both by improving aerodynamic and hydrodynamic finenesses; but, whatever high is one of these latter, tacking fineness cannot surpass the other, lower one of them. For example, if we have a flatbottom hull of low hydrodynamic performance (she is not built to counteract sideways drift), then it does not make sense to perfect her rigging and add sail area. All the same she will remain incapable of beating against wind. And conversely, if we have small sail and primitive rigging, neither deep keel nor centerboard would help. Optimal boat has these both finesses about equal, and the lower one of them must be attended first.

In good weather shnjaka can beat as close-hauled as a = 60^o-70^o against wind, so her tacking fineness is ctg 60^o - 70^o, or in average about 0.4. But how can one find out, which of Q or C is retarding shnjaka's tacking fineness? Is it her imperfect rigging, or imperfect lines of the hull? Luckily, there exist a simple way for direct measurement of aerodynamic fineness, without any special equipment, it is shown on the drawing below:

On condition of steady and even wind, (and in absence of water currents!) the vessel is to be moored by just one long line, allowing some freedom of movement. Sail is to be tacked and trimmed to make the vessel lie as high into the wind as possible, to achieve maximal angle b that mooring line makes with the wind direction. Here F is bulk aerodynamic force, whose parallel to the wind component is "drag" D, and transverse component is "lift" L; naturally, force application point must lie on straight prolongation of the mooring line. By this scheme, the desired aerodynamic fineness Q can be found as tangent of the angle b. Wind direction as well as mooring line direction can be easily obtained by means of a compass.

Thus determined Q for the shnjaka turned out around tg 50^o - tg 60^o , i.e. 1.45 in average. One can use quite similar technique to get the hydrodynamic fineness С - a vessel is to be moored on a river with steady current, with sail down, preferably in absence of any wind at all. In this case one must obtain the maximal angle between water current direction (by compass) and mooring line. For the shnjaka this measurement was not yet completed, but, judging by the above formulae, her hydrodynamic fineness С must amount to something like 1.5 - and this value is close enough to her Q (~1.45). So shnjaka has nearly optimal combination of sail and hull.

Doubtless, this optimum was practically found by generations of Pomor boatbuilders, after building and testing of countless boats with different proportions and lines. Any further improvement of shnjaka's performance would require simultaneous refinement in both lines and rigging, which was apparently impossible without serious sacrifices in seaworthiness and lightness to row, as well as deepening of the draft and other disadvantages at fishing.

This is to be pointed out, that ratio of shnjaka's sail area (~27 m²) to displacement (1.5-2 tons without cargo) is about 15 m² per ton, like in a modern yacht; shnjaka's keel area is above 2.5 m² - also by no means smaller then in a yacht of similar displacement. Therefore shnjaka's performance should be compared to that of a modern yacht, in some special conditions like sailing straight before light breeze the former can even outsail the latter. Let alone the advantage of small draft (some 0.5m) and ability to enter shallow waters and go ashore at almost any spot.

Many historical sources state that shnjakas were not so seaworthy, and were dangerous in a storm. In a sudden squall they could capsize, and could be swamped by high seas. In autumn 2003 I did not test the replica in a storm, actually, I never once reefed the sail. Nevertheless, I got the impression that in a squall it can become dangerous indeed, one must watch out and reduce the sail in good time. And reefing of the sail will unavoidably damage tacking fineness, so the boat might become incapable of gaining against wind any more, in which case the danger of being cast upon some rocks increases immensely. On the whole, the danger of being wrecked on rocks seems a lot more actual than floundering in open sea - since tacking performance can be also impaired by any minor trouble with tackle, rigging, rudder, etc. Anyway, good reliable anchors must be always at hand, all the more so when the crew is too few to row against wind in emergency.

Most rigging systems build up a strong careen torque when sailing close hauled. But square sail has an advantage at this point (among its numerous drawbacks) -- it can be set to produce a lift, like a kite. Theoretically, it can be trimmed so that straight prolongation of the lift vector would pass through hydrodynamic pressure center at the vessel's keel -- this would reduce heeling torque to zero, whatever the wind's strength and sail area.

Wind pressure on sail and hydrodynamic pressure on keel constitute careen torque;
Sail is set like a kite, hydrodynamic pressure center lies on prolongation of the lift vector, torque is absent (provided that the vessel is on level keel).