fixed points in survex

[John Halleck]

On Thu, 6 Feb 2003, Lev Bishop wrote:

> Date: Thu, 06 Feb 2003 03:37:35 -0500 (EST)
> From: Lev Bishop <lev.bishop@yale.edu>

  It is nice to see a literate post, from someone that appears
  to actually be familiar with the issues, as irrelevant as I
  may consider most of them to be in this context.

> To: Erin M. Lynch <elynch@cds.caltech.edu>
> Cc: survex@survex.com
> Subject: Re: fixed points in survex
> 
> Erin's message got me thinking. Thinking about the assumptions that 
> aven, survex, or the surveyors might be making regarding coordinate 
> systems and so on. I got kind of into it and maybe took things too far but 

  Yep.

> [...]

> Violated because: the positions of locations do not stay constant 
> in time. Reasons why not:
> 1) Tidal effects on the earth. The two sources of earth tides are the sun,
> causing effects of 17cm amplitude, and the moon, with 36cm (the next most
> influential body is venus, whose effects are less than 0.05% of the
> above). However, as long as our measurements cover an area of limited
> dimensions then the effects will be small. For example, over a 100km
> distance, the tides should come to less than a cm.

   Where does this figure come from?  It is higher than what I've been told.
   (Unless you mean "MUCH less than a cm".)

> [...]

> Assumption: the directions "north" and "down" are constant.
> 
> Violated because: the earth is ellipsoidal. At the 10^-5 level the earth
> is roughly an ellipsoid. The mean radius is about 6400km. The "down"  
> directions for 2 points on the surface of the earth and separated by 100km
> differ by almost a degree.

  Don't forget refraction.  Because the air closer to the ground 
  is denser than the air farther up, in isothermal conditions the the
  line of sight drops.  (Thereby making up somewhat for the curviture
  of the earth.

  If I remember aright, the earth curvature drops 1foot/mile, and
  the refraction drops line of sight 1/2 ft/mile, for a net APPARENT
  curviture of about 0.6 feet/mile.

> 
> NOTE: because the direction "north" is actually a direction which is 
> perpendicular to the direction "down" rather than just the direction 

  I'm not sure I agree with the argument of this paragraph.
  But private email is probably more suited for a discussion of this.

> parallel to the earth's axis (conventional or instantaneous) any errors in 
> measuring either the gravity direction or the axis direction will be 
> multiplied by tan(lattitude) when calculating "north". Ie a 1' deflection 

> [...]

> Final comment: My guess is that almost everything I've said so far is
> actually completely irrelevant because my feeling is that real cave
> surveys are actually dominated neither by random nor by systematic errors
> but rather by blunders/transcription errors.

  Or by the fact that angles are read to an accuracy much worse than most
  of the effects you mention.

> But maybe a few select people
> survey carefully enough, with backsights and other precautions to remove
> blunders, resurvey their loops when the closure error is too high, to make
> this message of more than purely academic interest.

  I've seen people who's data would tend to indicate that the blunder
  level is quite low for them.
 
> [...]

> Phew! Sorry that was so badly organised, but I couldn't face working it 
> into a more logical order. You can go back to ignoring me now.

  Not after that I can't.

> Lev