[Therion] sd for a vertical pole

[Olly Betts]

On Wed, Sep 07, 2022 at 10:56:00AM +0100, Tarquin Wilton-Jones via Therion wrote:
> > In Therion, this generates an error "invalid quantity -- plumb".
> > 
> > sd length 0.001 metres
> > sd plumb 0.125 degrees
> > gps surveystart 2.000 - DOWN
> 
> I wrote a bunch of tests. Therion is missing the required "sd plumb"
> functionality, and has no equivalent. I have filed this as:
> https://github.com/therion/therion/issues/445
> 
> The only workaround is to use:

Another workaround is to process your centreline data directly with
cavern and point therion at the resultant .3d file.  However, if you
have existing centreline data in therion format that would require
converting it which is probably too annoying.

> sd length 0.001 metres
> sd clino 0.125 degrees
> gps surveystart 2.000 - -90
> 
> but this will then generate a warning from Cavern saying that the
> compass bearing may not be omitted. (It will still work, however.)

Not sure what therion generates to feed to cavern in this case, but
presumably this gets handled as having a compass reading of 0, so
it doesn't give you the symmetric situation you want.

Setting the compass SD high probably won't give you the symmetric
situation either.

As you concluded modelling this as a plumb is the best approach
in Survex.  The plumb error is assumed to be a small angle from the
vertical since the main error component is assumed to be linear in the
length of the leg.

I'm not sure if those assumptions are entirely justified, but having
the error increase with length seems appropriate as on longer plumbs the
end tends to wander over a larger area and the period of oscillation for
a pendulum increases with length (proportional to sqrt(length) if you
assume the string is weightless, or if you assume the whole pendulum is
rigid, neither of which are going to be entirely true for a plumb in a
cave).

It might be interesting to experiment to see what the plumb reading
error actually looks like with increasing length (perhaps down a
stairwell in a tall building).

Anyway, the main error from your spirit level on the stick will also be
a small angle from the vertical.

Cheers,
    Olly