Circulation, Planform, Bubbles

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The discussion of two-dimensional sail theory in these pages matches most wind tunnel experiments, where the cambered foil is tested without wind gradient or end effects. When the "cambered foil" or sail is tested as a three-dimensional entity, a rather different picture emerges.

Upwash

The first feature to note is that, when a sail is set at an angle of attack to the apparent wind, the actual angle at which the local wind meets the luff is somewhat different from the nominal angle of attack.

Streamlines over sail

As the wind approaches the sail, it is lifted into a local upwash at the luff. The green dashed line shows the angle of this upwash, which creates a local angle of attack considerably greater than the nominal angle of attack. The blue dotted line shows the sail's entry angle. The entry angle is normally more or less oriented towards the local upwash, rather than towards the apparent wind at some distance from the sail. The end result is an "effective" angle of attack to the local wind, whose value is not at all known, simply because the details of the local wind at the luff is not known. Actual observation of a sail suggests that the sail shape changes with the wind strength and direction in a way that tends to maintain some sort of optimum "effective" entry.

Triangular planform

The second feature is that the upwash along a foil with a triangular planform increases quite dramatically towards the pointed tip. An ideal "elliptical" planform does not show this feature, and neither does a moderately tapered planform. This upwash means that the tip of a triangular foil is very prone to stalling, unless it is set with some wash-out -- that is, twist.

Increasing upwash

According to Marchaj, the need for twist in a sail has much less to do with the wind gradient, and much more to do with the upwash along a triangular planform. Unfortunately, the amount of this upwash is not readily calculated by simple methods. It depends upon the lift being generated by the sail; if the sail is operating with a relatively small coefficient of lift, there is little increase in upwash. Conversely, if the lift being generated by the sail is being maximised, then the increase in upwash will be at a maximum and the need for twist is at a maximum.

Tip vortex & mast-top burgee

The increasing upwash towards the sail head produces a tip vortex, a natural consequence of the lift produced by the sail. The tip vortex is felt quite strongly by the mast-top burgee, and so the burgee indicates an apparent incident wind which is several degrees abeam of the "real" wind. (Thanks to Mikko Brummer of WB Sails for pointing this out.) The tip vortex may have added 5 degrees to the apparent wind angle, depending on the vortex strength, that is, upon the amount of lift being produced by the sails.

Luff bubble

The inability to determine the theoretically "optimum" twist in the sail may be thought to be a minor difficulty. After all, on the water, one refers to the tell tales to see if the sail is set correctly. Er, not quite so straightforward...

The third feature to note is that, contrary to the impression given in the above diagrams, flow over the leeward side of the sail is not smooth and attached. Instead, under most conditions, a leeward "bubble" forms at the luff, and the air flow only re-attaches to the sail at some point aft of the luff.

Luff bubble

The bubble is believed to act like the rounded leading edge of a thick foil, and forms because the air cannot follow the sharp edge of the sail luff and remain attached when the sail is set at normal operating angles of attack. The "Theodorsen" angle of ideal entry, when there is no leeward bubble because the sail entry angle exactly matches the locally incident upwashed wind, does not provide maximum lift from the sail, only minimum drag. The sail is usually sheeted more tightly than the ideal Theodorsen angle in order to provide maximum lift, even though drag is thereby increased. In fact, wind tunnel tests seem to show that maximum lift is generated when virtually the whole of the sail is covered in a leeward bubble! (Mikko is unconvinced, pointing out that the flow separation at the leech is a different phenomenon from the flow separation at the luff, and that the tests mentioned applied to a Finn sail, which may not be representative of the sails in which we are interested.)

Tell tales

The implication of this is that a nicely streaming leeward tell-tale may not be "best", because the prior questions are "Just how big do you want your luff bubble?" and "Where has the tell tale been positioned?"

Tell tales around bubble

The diagram shows, let us imagine, a luff bubble that gives good lift with acceptable drag. Tell tale number 3 is streaming nicely, number 2 is twirling and lifting, while number 1 is lifting and reversing. If you had your tell tale in number 1's position, you would immediately ease the sheet, thinking your sail had stalled. On the other hand, if your tell tale was in number 3's position, you might tighten the sheet further, thinking the sail had not reached its optimum sheeting angle. I "explored" this problem with some telltales on my Rod Carr No.1 jib. The first set of telltales told real "tales", indicating that the jib was hopelessly stalled even as I powered away on a very satisfactory tack. The solution was to move the rags back; the original position had put them too close to the luff, where they lifted and flapped almost regardless of my sheeting angle.  More on the Telltales page and the Boundary layer page, where I note that these ideas really only apply to No.1 rig at lower wind speeds.  In lower rigs and higher wind speeds, the bubble shortens and so the tell-tales need to be closer to the luff.

2005-12-18


2011 Lester Gilbert