I find that the survey I am retracing is based on a east-west line which has been broken for curvature every six miles. What is the easiest way to calculate the angle difference at each six mile interval for a given latitude?
Where's Keith Williams when I need him?
> I find that the survey I am retracing is based on a east-west line which has been broken for curvature every six miles. What is the easiest way to calculate the angle difference at each six mile interval for a given latitude?
>
> Where's Keith Williams when I need him?
I think Keith, had that in his book, "Manual Of Surveying Instructions". (tic)
> I find that the survey I am retracing is based on a east-west line which has been broken for curvature every six miles. What is the easiest way to calculate the angle difference at each six mile interval for a given latitude?
>
> Where's Keith Williams when I need him?
I can't be sure at the moment since I'm out of town and away from ref material, but I took a class taught by Dennis Mouland and I think this is covered somewhere in the BLM manual. Is this work in west Texas?
> I find that the survey I am retracing is based on a east-west line which has been broken for curvature every six miles. What is the easiest way to calculate the angle difference at each six mile interval for a given latitude?
>
> Where's Keith Williams when I need him?
There's probably a calculator out there somewhere that does what you want, but here's the inverse:
http://www.csgnetwork.com/longlatdistance.html
Use it iteratively, inputting your latitude and an assumed Delta Longitude; see how close you get to six miles, and adjust. For example, it looks like 7.4' at 45 degrees lat.
According to old Barry from the first hit on the google search below it's 13.83ft for 6mi. at 30deg. of latitude. Pg556 of book/574 of the pdf.
https://www.google.com/#q=principles+and+applications+surveying+pdf
Seems like there used to be a better table/explanation in the 73 manual. Not seeing one in the new manual at a glance.
Steve
This should be a trivial exercise for any of the 1000's of Certified Federal Surveyors out there in the world?!!
You were all taught in infinite detail how to lay out a latitudinal arc? remember? so tell the guy, educate us....
Mouland, Scherler come forth...
jlq
Haven't done one in years, soooo we call it "cookbooking", where you have the instructions laid out in front of you:
but I prefer the tangent method, a few pages later.
Offset to Latitudinal curve = (0.6668)(distance in miles to west)(distance in miles to east)(tangent of latitude).
That's the easiest to do in the field and will match most early northwest surveys within reason.
It has gotten pretty simple if you have trimble or probably some other GPS software. They have a routine that calculates on a true bearing. And if you are trying to layout a curve between two existing found monuments that aren't exactly east-west you can simple prorate the lat, longs along the line.
Thank you
Thanks for the replies. Those links help. I've got Carlson and you'd think there is a routine for that.
Thank you
> I've got Carlson and you'd think there is a routine for that.
Aww, but now you will be able to check the button pushing.
Is it maybe this?
"Red Book," Table 11: "Convergence of Meridians, Six Miles Long and Six Miles Apart, and Differences of Latitude and Longitude." PP. 199 & ff. in 8th ed.
Cheers,
Henry
How about using CorpsCon for Lat/Lon to State Plane then do simple CoGo Inverses?
I haven't done it but will play with it tomorrow.
Six miles is about 6 min of Longitide. That should be easy.
Would like to have some solved answers from other methods as a comparison though.
Please post if possible.
Inverse from CorpsCon Values
103 102 101
*-------------------*-------------------*
101 34 00 00N 118 00 00 W
102 34 00 00N 118 06 00 W
103 34 00 00N 118 12 00 W
(6 min of Lon comes out here at 34N as 5.7 mi)
USFeet
Lat/Y Lon/X SF Conv
2311956.048 6031256.726 1.00002158 -0.96165576
2312479.291 6000950.682 1.00002158 -1.01660752
2313031.601 5970645.153 1.00002158 -1.07155927
Az Dist
101 - 102 270-59-20.9 30310.56
102 - 103 271-02-38.7 30310.56
Ang 180-03-17.8 (179-56-42.2)
BS101-OP102-FS103
PS formatting was ignored here by the Forum software.
Also, did nothing with Convergence angle on Az.
Don't even think it should be applied with this method
I used to look at this stuff
and when I did it, I'd look at the latitude at the beginning point. Then, in your case, I'd go 6 miles True West/East, review latitude, and adjust to the beginning latitude. I used Carlson also. I didn't find a routine, but whenever I ran True East/West, I always checked up with a new convergence factor. I was typically within a foot, but I wasn't looking at lines 30 miles long either. 🙂
I think this is the formula that I actually needed. Given a known point, in this case a found monument, heading due east for six sections.
ì 2 = asin( sin ì 1 ÜÉ cos ë« + cos ì 1 ÜÉ sin ë« ÜÉ cos ëü )
ëÈ2 = ëÈ1 + atan2( sin ëü ÜÉ sin ë« ÜÉ cos ì 1, cos ë« öÕ sin ì 1 ÜÉ sin ì 2 )
where ì is latitude, ëÈ is longitude, ëü is the bearing (clockwise from north), ë« is the angular distance d/R; d being the distance travelled, R the earthÛªs radius, and all angles are in radians.
Seems to be the right direction, just having trouble getting a solution on excel or my calculator. Digging deep to remember math principles I haven't used in a while.
The source website has a working version of the formula, unfortunately the precision is not quite sufficient for my needs. It stops at the nearest second of Lat and Long, whereas I would prefer an answer with the seconds to the thousandth.
NGS program Forward, checked with Inverse, calculates to 0.1 mm and lat-lon seconds to 5 places. You may need to iterate between them.
Pick your starting point and approximate end point. Inverse to find azimuth and distance. Correct distance and go Forward to better lat-lon. Correct latitude and Inverse to find azimuth and distance. Correct distance and Forward again.
Thank you, I will look at that.
I used the above formula to calculate a point and then checked it against Paden's cookbook link. My point was with 0.48 feet of where the cookbook said it would be (which I think is pretty tight over a 6 mile distance) and it was not too far from a point calculated by a surveyor in the 1960s. I still want another check to be confident in what I am doing. The area I am working in has the potential to be litigious and I want to be certain of my calcs.
And, the NGS program matches what I had previously calculated within 0.08' which I will attribute to a difference in rounding. Thanks again, Bill.
The only thing I don't understand is why my Latitude is slipping. I thought that if you start out on a given latitude and head due east, your latitude should stay the same?
My initial point is 32å¡00'00.5755"N 103å¡49'53.9675"W
Then E - 2710.185m to 32å¡00'00.5638"N 103å¡48'10.7147"W
Then E - 9652.019m to 32å¡00'00.4158"N 103å¡42'02.9915"W
My latitude seems to be heading south. If I am supposedly headed due east on a circle of latitude, why is the latitude changing when I calc the destination points? I'm missing something here.