Richard, I think you have misunderstood. All those photos appear to show the vane axis pointing directly fore and aft.

But you don't sail directly into the wind, do you?

Consider the least difficult scenario to understand. You are on a beam reach, and the vane axis is pointing directly athwartships. Now a wave rolls underneath the boat. On the face of the wave, she rolls to leeward, and as it passes, she rolls to windward. And so the angle of roll needs to be either added or subtracted from the angle of inclination when the boat is level. In one sense, they reinforce each other and apply more negative feedback. In the other sense, they tend to cancel each other. If the angle of inclination is zero to start with, then a roll to windward must result in an overall negative angle of inclination - and the vane becomes unstable. If there is some positive angle of incidence on the the vane axis, then the vane will only become unstable when this angle is surpassed by the angle of roll to windward. This is the simplest case. On other points of sail, the same principle applies, but we would need to get tangled up in some trigonometry to work out the actual angles.

This, in the end, is why vanes with a horizontal axis are unsatisfactory.  They will only work when they have an appreciable load to work against, so that they do not deflect too far during a roll to windward. And this is one of the reasons why they are totally unsatisfactory for driving a well balanced control surface. The Hebridean vane gear is perhaps more prone to this instability, but it will show up in all cases where there is a horizontal vane axis, to a greater or lesser extent. 

The Hebridean principle has one great  advantage over other servo pendulum gear geometries: that it greatly simplifies the primary linkage between vane and servo, and greatly simplifies the construction of the whole vane gear. It's true that the inclination of the power axis adds more negative feedback as the servo swings over, but all other pendulum gears do this anyway, by the way that the primary linkage is arranged relative to the power axis.

In reply, I can only quote the late lamented Professor C E M Joad:

"It all depends..."

... on the amount of balance on the servo blade

... on the amount of balance on the rudder

... whether there is a skeg

And doubtless some other variables. I don't suppose there's a simple answer to this. I do know that whenever my vane gets its axis "low end forward", it gets unstable and goes to its fullest travel in either direction.

John Fleming probably advocates a neutral helm because the angle through which the servo will swing is much smaller than for a horizontal axis pendulum, and so the ability to apply large quantities of weather helm is not there.

David Tyler wrote:

I've learned something more over the past few days: that a vane gear using the Hebridean principle must always be working so as to counteract weather helm - or must be fooled into thinking that it is.

If there is weather helm, the servo swings out to weather, and so the the vane turret tilts to leeward, thus putting some positive inclination onto the vane axis.

If there is lee helm, the servo swings to leeward and the vane turret tilts to windward, thus putting some negative inclination onto the vane axis, resulting in unstable steering.

Are you sure this is true of the original Hebridean design? I've not noticed it on mine, but I do usually have sine weather helm. John Fleming claims the Hebridean wants a neutral helm.

Weaverbird's helm is neutral, when sailing to windward in light conditions. Sometimes there is lee helm, and the steering goes haywire if I have the steering lines to the tiller at equal length. But if I shorten the lee side line, this induces a kind of artificial weather helm, and the steering becomes stable again.

I have a chain across my tiller that sits on a pin, allowing me to compensate for the helm while keeping the vane central. The pin often ends up at the mirror image position on the chain after a tack. See https://flic.kr/p/xR1Tuj

David,

So, in other words, the windvane gets positive feedback with a lee helm? I start to wonder if it would be better to separate the vane turret from the servo blade. With the vane turret fitted in the traditional way, fixed to the boat, you could still use the same servo blade with the 45° power axis. This axis will always produce negative feedback, and if you in addition tilt the vane axis a bit aft (preferably with an adjustable tilt angle), you should have a more stable system. That tilted power axis on the servo blade still appears to be a very good idea to me.

Arne

Ah.  That actually makes perfect sense. I was completely leaving effects of acceleration out of the equation.  On the ethereal frictionless plane, the gravitational acceleration and inclination would exactly cancel each other out, I believe, and the vane would not move one inch. The ethereal apparent wind would change, though - another factor I completely didn't think about.  Once all those dynamic effects come into play, it's pretty clear the solution is to become engineers and not physicists:  do what David's doing and make one. Trial it, tweak it.

And after studying the photos in your album, like Arne, I finally get how the thing works.  That was not an intuitive process.  I had to make a few small models out of crudely folded paper.  I have tough time picturing movement in three directions: the z-axis effects on the other two overwhelms my bio-neurolical video graphics card's capabilities.