[Therion] Gradient out of range - does not process

[Martin Budaj]

Hi,

>> Theodolites are not really set up for doing traverses, for a loop of a
few hundred metres we have an mis-closure of about 1m.

Yes, theodolites are not really suitable for long traverses where the
angular errors accumulate. When using them it's essential to eliminate all
sources of error, most importantly errors in the instrument position (this
requires forced centering of the instruments, see e.g.
https://books.google.com/books?id=jPVxSDzVRP0C&pg=PA80&dq="centering,+forced").
Also it is essential to make traverse legs as long as possible when using
theodolite.

Here is a comparison (taken from a surveying textbook by Ryšavý, 1949) of
an error Δ in position of the last point on a traverse of length D, with an
average leg length S, and with a mean angle error α for theodolite and β
for compass (in radians):

Δ_theod ≃ ±α√(D³/(3S))
Δ_compass ≃ ±β√(D·S)

Which gives for e.g. D = 500 m, S = 10 m, α = ±20′′, β = ±3′

Δ_theod ≃ ±20 cm
Δ_compass ≃ ±6 cm

It's easy to check the formulas whether you should expect better results
using a theodolite or a compass depending on the length of traverse legs
and the precision of your instruments.

That’s an interesting anecdote, thanks Andrew. Conversely I had a surveyor
> complete a traverse around my house, a distance of about 60m from about 6
> legs, with a loop closure error of 3mm.


In our case we got a 3.4 cm error on a 95 m loop with 9 legs in a cave.


> So it would be useful to be able to incorporate Theodolite angular
> measurements into the Therion or Survex network with appropriately small
> standard deviations, notwithstanding Andrew’s observation in Wookey, but
> they would have to be treated differently to magnetic bearings.
> Can anyone suggest the mathematical approach for doing that?  Apologies
> that’s very lazy of me to ask!
>

Indeed, they should be treated very differently and something like
https://www.gnu.org/software/gama/ should be integrated to do it properly :(

I did consider using an approach similar to Andrew’s, ie to calibrate the
> Theodolite against a magnetic leg, but intuitively that seems to tie the
> measurement to the inaccuracy of a single leg losing the benefit of error
> reduction across multiple measurements of the magnetic field (which is what
> happens in a magnetic traverse). It feels that somehow we need to use both
> techniques at the same time, using the Theodolite to “lock” the angle
> between legs while using the compass to align the survey to North.
>

You can use a gyrotheodolite to combine both approaches :)

When using theodolite, always use multiple directions for orienting the
survey (shots to multiple distant points with known coordinates, the more
distant the better). I would hesitate to use magnetic legs for this purpose
(there is much uncertainty with the declination as the models are not
particularly precise, there is a daily variation of declination (up to 0.2
degrees!) and there might be local magnetic anomalies).

Martin
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