["Followup-To:" header set to rec.boats.cruising.]
On 2004-03-12, Wayne.B wrote:
On Fri, 12 Mar 2004 15:42:16 GMT, "Skip Gundlach"
u wrote:
The latter - like two vang hardware setups, at the end of the boom, one each
to the opposite sides of the cabin roof - and, I suppose, you could go one
better and put them on the genny rail if it had a hook place, or a slotted
toe rail, if that's what you have (ours doesn't) for the widest dispersion
of downhaul capability.

======================

The best place for the vang in my opinion is from the boom (about 25%
out from the gooseneck) leading down to the mast, just above the cabin
top. This requires some fairly rugged fittings on both boom and mast
but the vang tacks and jibes automatically with no intervention
needed.
[...]

At the risk of mentioning some mathematics (gasp!), I'ts interesting
to analyze some loads. Here goes:

First let the boom have length B, and the goosneck-to-vang-attachment
point have length 1. (Use meters, or feet, or some other imaginary unit
to make this be 1, OK?)

Suppose that the force on the boom is entirely applied at the ends
(as it is, say, in my Tornado, where there's a cringle at the tack
and something that looks a little like a headboard at the clew; this
is attached to a little traveller that runs along the boom. The remainder
of the foot of the sail is not attached ot the boom at all. This
is also, to some degree, the case for my old sloop, where the foot
of the main has a substantial shelf in it, so that the sail is more
or less tangent to the cylinderical boom over most of its length, excepting
the ends). Suppose the force at the clew end, upwards, is F.

The forces from the vang are decomposed into vertical (pulling down
on the boom), called G_v, and horizontal, trying to push the boom forward,
called G_h. At the mast attachment points, the forces are opposite:
G_v pulling "up" on the mast, and G_h trying to rip the into-the-mast
bolts out along their axes.

The attachment point is at a fraction u of the way from the goosneck
to the clew. In Wayne's example above, u is 0.25.

Because the boom looks like a lever,

F * b = G_v * u * b; so

G_v = (1/u) * F. (1)

Since 0 = u = 1, it's clear that G_v is generally larger than F.

Because the triangle formed by the boom, vang, and mast has the
vang as its hypotenuse, a little vector filddling shows that

G_h/G_v = (u* b) / 1

so we get

G_h = u * b ( (1/u) * F [see equation 1]
= b * F

The horizontal force on the boom is independent of the attachment
point.

The total force on the vang is i

sqrt(G_h^2 + G_v^2) = (F/u) * sqrt(1 + b^2)

Note, then, that as u gets small, this goes up insanely large.
In fact it's clear that from a loading point of view, u = 1 is
optimal.

From a convenience point of view, it has some drawbacks -- that
diagonal line trying to take your head off during a jib being one of them!

By the way, once you attach the vang, when you pull the back end of the boom
up with a force of F, the goosneck of the boom is pushed DOWN with
a force of F (1-u)/u. (Think of a see-saw with the boom-to-vang joint
as the fulcrum). If you use a lot of downhaul, maybe this means
you don't have to work so hard (unless u = 1).

There's also the matter of deflection of the boom resulting from
applying these forces at various points. If you've got a skinny
boom that's really loaded mostly in compression, and designed for
that sort of load, you could easily bust it using a u of 0.1;
I haven't worked out the details, but it's clear that u = 1.0
presents no bending moment on the boom at all (although it still
tends to tack off your head during a jibe).

My recommendation, based on all this?

1. Get the bottom of the vang as low as possible.
2. Get the top of the vang as far aft as you can for
convenience and safety. Remember that 1/u rule: 25% of
the boom gives 4F loading; 33% of the boom gives 3F loading,
etc.
3. If your setup cannot handle this, consider what we do in trying
to support tall masts: instead of running a wire to the masthead
directly, we run two of them -- lowers and uppers -- and it
works somewhat better. It's possible that a "double vang"
system could work where a single one failed. (It'd have
to be custom made, of course...)

-John Hughes