Earth Curvature and Refraction

I have my data collector set to only record RAW data as measured (none).

Then when I reduce the RAW data in the office to generate coordinates, I have my PC software correct for curvature and refraction.

Just be sure it isn't doing it at both ends of the data process.

If your curious as to how much correction is being applied, reduce your data both ways and compare elevations. For a smaller sized landscape survey, you will more than likely not see any differences in elevations.

My newer textbook gives the formulas for correction in feet
h' = 0.667 (Miles)^2
= 0.0239 (feet/1000)^2
and in metric
h' = 78.5 (kilometers)^2 correction in millimeters

An older book gives slightly different factors, respectively:
0.57
0.021
67

The curvature would mean the earth's level surface is lower than horizontal. The refraction means your line of sight will be lower than horizontal, but not by as much as the curvature so it doesn't fully cancel out. That leaves the level surface h' below your line of sight. The formulas are reasonably good for the difference in typical conditions.

For a regional leveling network, more refined formulas would be used taking into account atmospheric conditions and changes in gravity.

Due to the squared term, the correction isn't much for a short sight, but grows quickly once you get to longer ones. A guideline is to approximately balance your backward and forward sights so the corrections cancel and you don't need to compute them, and to keep the sights to no more than 100 yards/meters so the corrections are small.

> I have my data collector set to only record RAW data as measured (none).
>
> Then when I reduce the RAW data in the office to generate coordinates, I have my PC software correct for curvature and refraction.
>
> Just be sure it isn't doing it at both ends of the data process.
>
> If your curious as to how much correction is being applied, reduce your data both ways and compare elevations. For a smaller sized landscape survey, you will more than likely not see any differences in elevations.

Total stations also are capable of making this correction. Most I have worked with are set to make the correction by the factory. As digger mentioned above making the corrections at both ends of the process should not be done. With current data collectors and software it is possible to apply the correction three times.

• ... 1 Total station
• ... 2 Data collector
• ... 3 Software

The result of this would be introducing error into all subsequent calculations.

A diagram to go with the formula given above.

In Survey Controller (not survey pro), the C & R correction is applied to displayed and computed data only. The raw values (HA, VA, Dist) are stored as raw, in fact the distances are stored with no corrections applied, not even PPM. Of course, the PPM info is stored in the dc file so that it can be applied.

So, if you have C & R turned on, and you just use computed N, E, and Z, then it will be applied to the elevation.

Not sure about Survey Pro, but I would assume it is similar.

One thing to be careful of...do not have the DC and the instrument both applying C & R.

Although I only use raw data in the office (uncorrected), I do like to have C & R turned on so that if I look at coordinates and elevations or differences in elevation, they are corrected when I am looking at them in the DC.

But, note that the refraction correction can vary a lot if you are close to the ground. The 0.13 )or 0.14) really only applies for sights that are up in the air, away from the ground.

Here is a graph that shows how it can vary by time of day and height above ground:

> I have my data collector set to only record RAW data as measured (none).
>
> Then when I reduce the RAW data in the office to generate coordinates, I have my PC software correct for curvature and refraction.
>
> Just be sure it isn't doing it at both ends of the data process.
>
> If your curious as to how much correction is being applied, reduce your data both ways and compare elevations. For a smaller sized landscape survey, you will more than likely not see any differences in elevations.

Aloha, Imaudigger:
I am just learning more about RAW data. My PLS said he only imports ASCII file with coordinates. So I also got into a habit of only importing coordinates. Just recently (two days ago) I took a look at the RAW data file in my DC. Wow! It shows everything I've done. From rebooting the app. to deleting point, renumbering points--everything!! Now, I understand why almost everyone here always talks about RAW data.

I digressed...I didn't realize the C&R are adjusted in several place. I checked my survey software--TraversePC, I didn't see any mention of C&R. I will check with their tech. support to confirm. Then I do need to verify if my TS applies it or not. All I know for now is, in my DC is is turned off.

I am a borderline OCD 😛 when I do anything. Always trying to do everything the best I am able. From what I've read so far...for my work C&R should not have significant impact. My longest traverse is about 800 feet. I think that is the only one leg in the entire 70 acres that long. It will be different of course once I get to the 300 acre parcel in the new future.

But I will do a test. I will apply it in DC then compare one without applying it.

Thanks!

> My newer textbook gives the formulas for correction in feet
> h' = 0.667 (Miles)^2
> = 0.0239 (feet/1000)^2
> and in metric
> h' = 78.5 (kilometers)^2 correction in millimeters
>
> An older book gives slightly different factors, respectively:
> 0.57
> 0.021
> 67
>
> The curvature would mean the earth's level surface is lower than horizontal. The refraction means your line of sight will be lower than horizontal, but not by as much as the curvature so it doesn't fully cancel out. That leaves the level surface h' below your line of sight. The formulas are reasonably good for the difference in typical conditions.
>
> For a regional leveling network, more refined formulas would be used taking into account atmospheric conditions and changes in gravity.
>
> Due to the squared term, the correction isn't much for a short sight, but grows quickly once you get to longer ones. A guideline is to approximately balance your backward and forward sights so the corrections cancel and you don't need to compute them, and to keep the sights to no more than 100 yards/meters so the corrections are small.

Aloha, Bill:
Thanks for explanations. I was planning to do trig. elevation with my TS. I wanted to carry the elevation while doing the traverse loop. I can apply this formula and see what the results are.

But it is not clear to me why there are two coefficients given by Survey Pro?

Aloha, Dallas: Thank you for pointing this out!!

Thanks Imaudigger! Aloha

> In Survey Controller (not survey pro), the C & R correction is applied to displayed and computed data only. The raw values (HA, VA, Dist) are stored as raw, in fact the distances are stored with no corrections applied, not even PPM. Of course, the PPM info is stored in the dc file so that it can be applied.
>
> So, if you have C & R turned on, and you just use computed N, E, and Z, then it will be applied to the elevation.
>
> Not sure about Survey Pro, but I would assume it is similar.
>
> One thing to be careful of...do not have the DC and the instrument both applying C & R.
>
> Although I only use raw data in the office (uncorrected), I do like to have C & R turned on so that if I look at coordinates and elevations or differences in elevation, they are corrected when I am looking at them in the DC.
>
> But, note that the refraction correction can vary a lot if you are close to the ground. The 0.13 )or 0.14) really only applies for sights that are up in the air, away from the ground.

Aloha, John: I just realize you answered my question to Bill why there are two options in Survey Pro. Could you please define how high is high from ground that it needs 0.13 or 0.14?

I like your approach of turning it on in the DC for accurate viewing then importing RAW data later. I am determine to only download raw data once I figure it out in the next couple days.

I know you use S6...does the S6 apply the C&R? I just recently traded-in my 5603 to a six years old but calibrated S6:-) Getting to know the gun now.

well, that (0.13) would really only apply if you were shooting hilltop to hilltop, with plenty of ground clearance in between.

For critical shots I do reciprocal observations, I have in the past for very critical work done simultaneous obs using two instruments. But that was to get millimeter accuracy across a river. The C&R correction cancels out for reciprocal. As long as conditions don't change much, near reciprocal works just as well. You can actually calculate the value of refraction if you observe from both ends.

Here are some errors in height versus errors in k (the coefficient of refraction):

D=100 m
dk=1.0, error in delta H: 0.8 mm
dk=2.0, error in delta H: 1.6 mm

D=300 m
dk=1.0, error in delta H: 7.0 mm
dk=2.0, error in delta H: 14.1 mm

D=500 m
dk=1.0, error in delta H: 19.6 mm
dk=2.0, error in delta H: 39.2 mm

or, in general,

And, it has been determined by tests that grazing sights (i.e. close to the ground) can result in a k from -3.0 to +4.0. So, using 0.13, or 0.14, or even 0.0 can result in about the same results. Keeping sight lengths short (<100 m), very little error will be introduced by using an incorrect k.

My S6 does not have a keyboard, so I don't know if there is any way to turn on C & R in the instrument. But, in the setup screen on the DC where you enter temperature and pressure there is a field for k. I always leave it at 0.14.

Aloha, John:
Looks like I need to run my level loop separately from my traverse loop and keep the distance within 100m.

Do you know if the S6 does the C&R correction?

Thanks you so much John! Aloha.

Yswami,

I've never used them, but if memory serves, 0.14 is for daylight shots and 0.20 is for nighttime shots. Why they would be different, I haven't a clue.

Dave

> Yswami,
>
> I've never used them, but if memory serves, 0.14 is for daylight shots and 0.20 is for nighttime shots. Why they would be different, I haven't a clue.
>
> Dave

Aloha, Dave: Thank you for chiming in. Now that I have better understanding what C&R is...I think I'll keep my distance within 330ft. Then I don't have think about the adjustment.
Aloha.

Refraction varies with air temp. and pressure. The values in the formulas are for average conditions. Unless your sights are very long those values should be OK. When we did sun and start shots by the altitude method we used tables to look up corrections to the vertical angle based on atomospheric conditions.

You don't need to run the loops separately, you just have to record perhaps more information when running your horizontal traverse.

I would highly suggest recording the data in a field book and calculating your elevations by hand the first time, so you have a handle on what the software is doing AND you have a way to check the results.

For elevations only, Record:
Inst. HI, Foresight HT, Slope Distance, F1 and F2 Zenith angles.
Move ahead
Measure the same looking at your backsight.

Your foresight and backsight lengths are equal so curvature cancels out.

Now it comes down to limiting your leg lengths due to sighting errors.

Depending on your accuracy requirements,refraction errors may not be worth considering.

Multiply the COS of your adjusted zenith angle (converted to decimal degrees) by the slope distance, plus your HI, minus your HT, gives you the difference between marks.

Average the foresight and backsight difference to use in your elevation calculations.

> Refraction varies with air temp. and pressure. The values in the formulas are for average conditions. Unless your sights are very long those values should be OK. When we did sun and start shots by the altitude method we used tables to look up corrections to the vertical angle based on atomospheric conditions.

Aloha, Tom:
I am religious about entering the temperature and pressure. C&R my attempt to refine my field work. Thanks!

> You don't need to run the loops separately, you just have to record perhaps more information when running your horizontal traverse.
>
> I would highly suggest recording the data in a field book and calculating your elevations by hand the first time, so you have a handle on what the software is doing AND you have a way to check the results.
>
> For elevations only, Record:
> Inst. HI, Foresight HT, Slope Distance, F1 and F2 Zenith angles.
> Move ahead
> Measure the same looking at your backsight.
>
> Your foresight and backsight lengths are equal so curvature cancels out.
>
> Now it comes down to limiting your leg lengths due to sighting errors.
>
> Depending on your accuracy requirements,refraction errors may not be worth considering.
>
> Multiply the COS of your adjusted zenith angle (converted to decimal degrees) by the slope distance, plus your HI, minus your HT, gives you the difference between marks.
>
> Average the foresight and backsight difference to use in your elevation calculations.

Aloha, Imaudigger:
Thank you so much for the detailed step by step procedure! I am planning to do small loop manually before attempting to do the larger loop. Your steps above are very straight forward.

My accuracy requirement is self imposed. I do want to maintain high standards for what I do. That way if I slip, I won't fall to far down!

I hope you don't mind clarifying a bit more for me...

If I were to do both loops together I do have to sacrifice my horizontal traverse distance in favor of the vertical. Right? We are talking about reducing from 800 feet to perhaps 300 feet. Then I do have to balance the foresight and the backsight.

Right now I have about 35 inter visible control points set for the 70 acres. I will post few pictures tomorrow.

I want to traverse along through this point then learn how to apply Lease Square adjustment. Ambitious I am! 🙂 Hence I am refining my field work procedures to eliminate all the systematic errors as much as possible.

Thank you so much again for taking the time to guide me along!

Aloha

> If I were to do both loops together I do have to sacrifice my horizontal traverse distance in favor of the vertical. Right? We are talking about reducing from 800 feet to perhaps 300 feet. Then I do have to balance the foresight and the backsight.

I would pretty much never give up an 800-foot shot just to balance FS and BS. I'd keep the 800-footer and, if vertical is a big concern, shoot it both ways with as little time lapse as is practical in order to get the same atmospheric conditions for both shots. The C+R errors will effectively cancel out.

I recently had to transfer vertical across a river in 3 places. Distances ranged from 630 to 750 feet. The differences between the reciprocal mark height calculations at the 3 sites was between 0.02 and 0.03 foot.

Edit: I used a Leica T2000 on one side and the Geodimeter GDM640 on the other. Both are nominally 1-second guns.