Astronomic North and Computer/Online Programs

TBC will give you geodetic north from state plane. Unless you've got some serious distances from an intersection point I don't see laplace and astronomic north changing the resulting answer from geodetic north.

@mightymoe I think you are right, but I don't have to do this a lot and I've never looked at what the differences could be for my area.  Thought about posting this question but was afraid it might derail the topic.  Just looking for software.

The NGS tool INVERSE/FORWARD will work if you want an open-source way to compute your bearings.

The inverse tool in TBC will return forward/backward/mean geodetic bearing in addition to grid bearing.

TBC also has single and double proportioning tools that will let you use planar or geodetic calcs.

It's been over 20 years since I had to double-proportion anything, but I did the proportion in lat/long and then converted the result to SPC.

@rover83 

Help me out. What is a mean geodetic bearing and how is it used?

@mathteacher 

I think they refer to the arithmetic mean of the forward and backward geodetic azimuths.  Those values can be rather different for a line that has some east-west component, but the difference would usually be negligible for an approximate north-south line.

Use DEFLEC18 from the NGS, I believe you will see some numbers in single seconds of deflection. 

Probably isn't going to mean much. You can get the results for a single location. 

@bill93 

That sounds right, but I don't know what that average means or how it can be useful.

The numbers that are used for LaPlace corrections were useful to drill down the calculations on long traverses. We could obtain them from the USGS office in Denver back when I was running long traverses. I never applied them to short measurements. 

@rover83 

Help me out. What is a mean geodetic bearing and how is it used?

(from the BLM Manual of Surveying Instructions)

@mightymoe Here's why I hate DEFLEC##, I forget which way to apply the correction (just a sample):

Output from DEFLEC18

Station Name            latitude       longitude       Xi      Eta     Hor_Lap
                        dd mm ss.sssss ddd mm ss.sssss arc-sec arc-sec arc-sec
USER LOCATION           35 55 19.02210 097 55 40.23510    1.99    2.16   -1.57

@rover83 

Thank you.

@mightymoe Here's why I hate DEFLEC##, I forget which way to apply the correction (just a sample):

Output from DEFLEC18

Station Name            latitude       longitude       Xi      Eta     Hor_Lap
                        dd mm ss.sssss ddd mm ss.sssss arc-sec arc-sec arc-sec
USER LOCATION           35 55 19.02210 097 55 40.23510    1.99    2.16   -1.57

LOL, same here, I don't remember how to use it. 

Can anyone confirm the following when using DEFLEC##:

ASTROAZ=GRIDAZ+CONVERGENCE-LAPLACE

This sign convention applies to north az, +CW. Right?

This is from an old readme file, deflec99, but I assume they wouldn't have changed it.

So yes, your formula is correct as far as the laplace correction is concerned

Per Mackie’s “The Elements of Astronomy for Surveyors” 9th Ed (1985) see pages 37-39.

To calculate a geodetic azimuth (Ag) from an astronomic azimuth (Aa) using the horizontal Laplace (n*tan(latitude)) one uses:

Ag = Aa - Laplace

The algebraic sign of the east longitudes in Mackie is positive and west are negative.   

Looking at the DEFLECTION 18 home page, I don’t find much detail much less how to apply the “Hor Lap” shown in the output. See copy of output showing this output below:

 The NGS Geodetic Glossary discusses this issue (algebraic sign of longitudes in computations) in their definition of the Laplace equation copied below:

@john-hamilton 

Good find. I remember seeing that note. It does not appear on the new model’s home page. It should be.

I find it amusing that the ending note in your screen capture includes mention that textbooks will show opposite signs evidently feeling no further explanation was necessary.

The bigger question is how will this apply to a double prorate? Even if there 10 seconds to deal with and a huge distance like 100', that's only .005'.

@mightymoe That is my thought as well. In the past probably no one was getting better than 1' accuracy, especially if they were using the altitude method