use of the network response Re: 'fix' vertical?

[Warren Family]

I think there's another way to do this which exploits the response of 
the network on being forced to accommodate a fake leg, and avoids the 
clunky [to me :-)] use of a small value of the standard deviation to 
constraint the height difference.

First - solve the network as it stands and calculate ∆X, ∆Y and ∆Z 
between the two stations at the two sumps.  I use capital letter here to 
distinguish these values from the fake leg displacements added below.

Next, using *data cartesian, introduce a fake leg between the two 
stations with displacements ∆x = ∆X and ∆y = ∆Y, but with ∆z as yet 
unspecified.

The key idea is that there will be /some/ value of ∆z for the fake leg 
for which, after network is re-solved, the sump stations are level in 
altitude (∆Z = 0).  The challenge is to find this value.  I think such 
an approach is equivalent to adding a hard constraint z1 = z2 into the 
underlying math problem, and distributing the error optimally (in the 
survex sense).

Also, given the way the underlying problem of distributing the 
misclosure error is set up as a least-squares problem [yes!?], the 
change in the relative sump heights (∆∆Z as it were) is likely to be 
linear in the vertical displacement ∆z of the added leg. Assuming this 
is the case, one only needs one more calculation, for instance at ∆z =0, 
to find the value of ∆z which makes ∆Z = 0.  I'll post an answer later 
when I've had a chance to work through the math and perhaps try a small 
example, unless someone beats me to it!

Patrick



On 01/11/2022 15:54, Andrew Atkinson wrote:
> Instead of using 0 for clino you can use LEVEL, equivalent to up/down for plumps search for "Deal with Plumbs or Legs Across Static Water" in
>
> https://survex.com/docs/manual/svxhowto.htm
>
> You'll still need to do the SD part.
> Andrew