Many of the newer cruising sailboats in the 40-ft-and-up sizes are built with double headstays in the bow with one roller furling located behind another.

The forward roller-furling stay carries a big Genoa jib. The next stay aft carries a working jib.

Some boats also carry a third stay aft of the first two as a small blade staysail for storm conditions. Roller furling makes it easy to change these sails for a wide range of wind speeds.

During a recent squall, a new 40 footer had her rolled-up double headstays oscillating violently back and forth perpendicular to the wind direction, and the stays were shaking hard. This action was disconcerting to the boat’s owners, to say the least, so we decided to try to pinpoint the cause.

The wind was blowing 15 to 16 knots with gusts to 26 knots. The frequency of oscillation of each headstay was about 1.6 to 1.8 cycles/sec. The rolled sail formed a 6 to 7-in.-diameter cylinder. A pure guess of the amplitude of vibration put it at 10 to 12 in., side to side, for a total movement of about 20 to 24 in. This large amplitude or “rig pumping” was surprising because the wind was not that strong.

**The challenge was to model fluid flows in computational fluid dynamics (CFD) software to pinpoint the problem with the particular roller-furling configuration.**

The problem necessitates matching the physical case with a mathematical model. First, solving fluid-flow problems requires calculating the Reynolds number:

**Reynolds number = [air density (velocity) (diameter of furled sail)]/dynamic viscosity**

Next comes determining the drag coefficients. This is easy because drag coefficients for a cylinder in cross-flow versus the Reynolds number are given in just about every fluid-flow book. One publication not only gave the drag coefficients, it also showed the four flow regimes for a wide range of wind speeds. These regimes divide the drag coefficient versus Reynolds number curve into regions where the slope changes markedly to reflect actual physical changes in airflow.

For the first regime, flow around the furled jib is laminar. The flow pattern is symmetric and the Reynolds numbers for the 7-in.-diameter jib are less than 1. Back-calculating wind velocity from the Reynolds number equation gives about 7 in./hr for this geometry. As such, this regime is of no consequence to the cruising sailor.

Regime two flows around the furled jib and includes Reynolds numbers from 1 to 1,000. Here, a Reynolds number of 1,000 means the wind is only blowing at about 0.18 knots with the drag coefficient ranging from about 10 at the lower flows to 1 at the higher flows. A flow rate of 0.18 knots is also of no consequence. However, from a technical viewpoint, this is an interesting regime because these flows include Karman vortice trail patterns.

At first it seemed the Karman pattern rolled off the first headsail and hit the second rolled sail in its wake.

The resource publications also gave the relationship between the shedding frequency, the diameter of the cylinder or rolled sail, *D*, and the wind velocity, *V*:

**Karman Vortice Shedding frequency = 0.22 ( V/D)**

This relationship is dimensionless. The value 0.22 is independent of the choice of units and is known as the Strouhal number. What it means physically is the vortices shed at regular intervals 4.5-in. diameters apart (the inverse of 0.22). Picture an immersed cylinder moving through fluid shedding at regular intervals.

The Karman shedding frequency for 16 knots of free air velocity is 10 cycles/sec. It is 16 cycles/sec at 25 knots of air velocity — nearly 10 times higher than the observed frequency. It was clear that Karman vortices were not causing the rig pumping.

In regime three, the Reynolds numbers range from 1,000 to 50,0000. For the 7-in.-diameter furled jib, the calculated wind range is 0.18 to 80 knots. The drag coefficient remains fairly constant at 1 over this range. The flow pattern remains unsteady, perhaps as a carryover from regime two.

For the fourth regime, the fluid flow of the cylinder shape is almost a straight steady symmetrical pattern about the jib centerline. This is something no sailor wants to see because the velocities of more than 80 to 160 knots will probably destroy the furled jib.

This data is used in a simple model of the fluid dynamics of a furled jib.

The drag force is given by:

**Drag force = ½ Drag coefficient (projected area ) air density (velocity ^{2})**

For a 55-ft length of rolled jib in 70°F air, the drag force is 26 lbf in 16 knots and 64 lbf in 25 knots of wind. This is a large force for so little wind.

So what do these results mean for the average cruising sailor? When a rolled jib is about 6 to 7 in. in diameter, the flow velocity maximizes periodically 18 to 28 in. behind the jib. This happens to be the separation distance of some of the double headstay designs. Based on the one analysis, this appears to be a bad place to locate the second furler.

**Also read and visit —** **Blue Ridge Numerics**** | ****Patriot Engineering Co.**

**“Fundamentals of Heat and Mass Transfer,”** Third Edition, by Frank Incropera and David DeWitt, John Wiley & Sons, 1990.

**“Fundamentals of Momentum, Heat and Mass Transfer,” **By Welty, Wicks, & Wilson, John Wiley & Sons, 1969.

**“Mechanical Vibrations,”** by J. P. Den Hartog. This classic Dover Edition was first published in 1985 by General Publishing Company Ltd., Toronto, Canada. The original was published in 1935 by McGraw-Hill.