Twist due to wind gradient

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A while back, I developed a spreadsheet to analyse the wind gradient.

The closer to the water, the slower the wind.  This is the wind gradient, caused by friction between the wind and the water surface and its waves.  This is one reason why the sail must twist, allowing its angle of attack to remain relatively constant to the apparent wind as that apparent wind frees off with increasing height above the water.

I've been assuming that the twist needed in my mainsail and jib due to the wind gradient was about 4 or 5 degrees, and have set that ever since.  A recent issue of "Seahorse" magazine (December 2002) had an article about the "twisted flow wind tunnel" at the University of Auckland.  Something caught my eye:

"When sailing upwind, the twist [due to the wind gradient] is very small.  However the difference [...] when sailing downwind can be large."

Really?  I decided to construct a spreadsheet to illustrate this.  The result was simply stunning.  When hard on the wind, twist needed due to the wind gradient is about 4 degrees, no problem.  With the wind abeam, however, twist needed due to the wind gradient is about 12 degrees.  Wow!  This is shown in the following graph.

I keep adding "...twist due to wind gradient", because the other requirement for twist is dictated by the vortex being shed at the head of the sail.  The stronger this vortex, the more "washout" the sail needs, and this depends upon the lift being generated by the sail.  In light airs, lift will be modest, the vortex will be small, and the requirement for twist due to lift will be modest.  As the wind picks up, the lift generated by the sail increases (think increasing lift coefficient here), the vortex strength increases, and more twist is needed if you are not to stall the head of the sail.

Wind speed about 4.7 m/s at top of mast, IOM "A" rig, boat sailing at "hull" speed

The spreadsheet (about 33kb) takes the wind gradient (on the assumption that waves get uniformly rougher as wind speed increases) and applies it at various heights up the mast.  You can change the heights to look at the wind, the wind speed, and other assumptions about the speed of the boat.  Look at the "Wind gradient" page for more details.

The graph shows that twist needs to come back down to zero when on a dead run.  Now, how to achieve that on an IOM?  I've tilted my gooseneck axis (see the "Gooseneck" page) so that it takes the twist out of the mainsail as the boom swings out, but the graph says this is wrong -- I should be increasing twist in a controlled way up to a beam reach, and only after that should twist be decreased.

I've been speaking about twist so far, as a convenient way of measuring how to get the sail angled better towards the apparent wind.  The real issue, of course, is entry angle rather than twist.  Entry angle measures how well the sail's leading edge is oriented towards the wind.  The point here is that, by varying the draft of the sail, we can vary the entry angle without changing the twist.  Sail draft, and hence entry angle, is controlled by the basic sail shape and the placement of the seams, by the outhauls on the booms, by mast bend for the main, by jibstay sag for the jib, and by the gooseneck axis offset for the main.


2011 Lester Gilbert