Okay, maybe this isn't exactly a contest to see how well various posters can chain. Actually, it's a contest to see who can best estimate the systematic errors in the distances that the survey party who ran the Travis/Hays County line in Central Texas in 1954 made in their chaining.
The object of the exercise is to estimate the actual distance from the 18-Mile Post to the end of the line at record chainage station 36M+67.2 vrs. (M = Miles and 36 vrs. = 100 US Survey Feet in Texas). It isn't a rigged question. I haven't tied that monument in yet, so I don't know myself.
Here's the County Line Marker at 30M+734.5
Here are the observations:
From 32M+1329.0 to 30M+734.5:
12,211.39 ft. Record
12,205.67 ft. Actual
From 32M+1329.0 to 18M+1775.8:
72,678.89 ft. Record
72,636.28 ft. Actual
From 32M+1329.0 to 18M
77,611.67 ft. Record
77,564.71 ft. Actual
From 32M+1329.0 to 17M
82,891.67 ft. Record
82,841.09 ft. Actual
So what would you expect the distance from 32M+1329.0 to 36M+67.2 to actually be? I'll probably actually measure the distance, so the closest estimate will be eventually known.
> So what would you expect the distance from 32M+1329.0 to 36M+67.2 to actually be? I'll probably actually measure the distance, so the closest estimate will be eventually known.
17,604.4'
Kent
I'm sure you have more data, so I'll play your game with the LIMITED data provided by you.
It would appear that you have a fairly constant scale factor (local one obviously) that could be calculated and applied. It seems fairly uniform with the exception of 32+1329 to 18+1775, however, the scale factors I calculate to more distant objects based on your measurements are more in line, leading me to believe that there is a blunder in that monument set at 18M+1775.8. For this reason, I've thrown out that one leaving only three for me to play with.
That being said, 32+1329 to 17+00 yields 0.9993898, and 32+1329 to 18+00 = 0.9993949, and 32+1329 to 30+734.5 = 0.9995315 for an average of 0.9994387.
Based on your data, the call distance from 32+1329.0 to 36+67.2 should be 17,615.00 feet and with the application of my nifty scale factor, I would estimate that the actual distance would be around 17,605.12 feet.
Now, tell me what I didn't know from the data and I'll probably change my way of thinking. 😉
Alan
Only missed you by 0.72' in 17000. That's like 1: in 24,000. I can live with that.
🙂
17,606.12
Alan
> Only missed you by 0.72' in 17000. That's like 1: in 24,000. I can live with that.
>
> 🙂
Kris,
I chose a different outlier than you. Let's just split the difference, shall we? 🙂
Alan
Works for me bud!
I wish I knew a little more about the terrain, but tossing that aside, I'll throw out a calculated guesstimate of 17605.04'
Like Carl, I would really want to know if the terrain was different in each segment and choose accordingly.
Lacking that information, the best estimate is taken from the longest distance, since they all have the same starting point and the longest one averages in all the other data. The others tell you something about consistency, but add no information about a short chain. That gets an estimate of 17,604.25
Here are the NAD83 latitudes and longitudes of various of the monuments, along with their NAVD88 elevations:
17M 30-11-57.673124 97-57-12.955436 1008.93
18M 30-11-24.438863 97-56-26.580543 954.25
30M+734.5 30-04-32.401788 97-46-52.808944 707.95
32M+1329.0 30-03-15.377424 97-45-05.803030 758.58
The line runs through rolling terrain, some in cleared fields and some that had to be cut (which it was).
My guess is 17605.03'
> My guess is 17605.03'
Taking the "Price is Right" approach?
😉
Rounding differences I suppose. I would venture to say we used the same method though.
> Rounding differences I suppose. I would venture to say we used the same method though.
No, I came up with a calculated distance of about 0.09' shorter, and did a little head figgerin' and threw something down (I honestly did). I was just picking anyway. Good luck to ya!
🙂
Chaining Contest (Actually Not a Math Puzzle)
Today, among other things, we tied in the terminal monument on the Travis/Hays County line, nominally at station 36Miles+67.2vrs. The position of the monument plotted on the North side of an old cemetery at the community of Niederwald, an area settled in the late 19th century mostly by German immigrants. There may have been a couple of non-Germanic surnames on the stones in the cemetery, but there weren't many.
The monument itself was described by Travis County Surveyor M.O. Metcalfe in 1954 as "concrete monument 12" top by 24" base of a pyramidal type construction about 2-1/2' above the ground with Bronze plate in top". What I found was what I'd describe as Punchmark at Center of 3-3/4 in. dia. Bronze Tablet in 12" x 12" Top of Truncated Pyramidal Concrete Monument, 2.35 ft. above ground, with 24" x 24" Base, the NE face with the letter "T" cast into it, the SE with the letter "C", and the Southwest with the letter "H". However, as you can see, this fairly substantial monument was leaning well out of plumb.
By the way, just to the left of the frame is the bed of the Old San Antonio Road, the road from San Antonio to Nacogdoches that was originally opened during the Spanish colonial period. The raised road bed dates from before 1940, but well after the Texas Revolution.
Here's another view of the listing terminal monument.
Some of the stones in the cemetery also had pronounced lists. My suspicion is that the county line monument had probably been undermined by ants on one side and had settled. One corner of the monument was still at grade.
The edges of the monument were chamferred, so I located the points at the intersections of the faces at the base of the monument. This diagram shows both the punchmark on the tablet (Pt.199) and the center of the base (Pt.222), 0.31 ft. apart.
I'm going to consider Pt.222 to be the best estimate of the original position of the monument until someone rights it (and hopefully treats the soil under it for ants).
Oh, the distance from the monument at 32M+1329.0vrs to this monument at 36M+67.2vrs?
The distance to Pt.222 at the center of the base of the monument is 17,613.69 ft. Mr. Metcalfe reported chaining the distance as 17,615.0 ft. in 1954.
Chaining Contest (Actually Not a Math Puzzle)
> Oh, the distance from the monument at 32M+1329.0vrs to this monument at 36M+67.2vrs?
>
> The distance to Pt.222 at the center of the base of the monument is 17,613.69 ft. Mr. Metcalfe reported chaining the distance as 17,615.0 ft. in 1954.
Well that was a bust!
Next contest, please.
Closest estimate? Not happy with how far off, but I'll pat my own back...
Chaining Contest (Actually Not a Math Puzzle)
> > The distance to Pt.222 at the center of the base of the monument is 17,613.69 ft. Mr. Metcalfe reported chaining the distance as 17,615.0 ft. in 1954.
>
> Well that was a bust!
>
> Next contest, please.
I'm going to have to look at Mr. Metcalfe's fieldbooks for that work to try to figure out why the chaining on the last 3.33 miles of the line was as good as it was. My first guess is temperature was a factor. I don't think that they made any temperature corrections in their ordinary work, so they may have lucked out and chained those 3.33 miles at close to standard temperature, the rest hotter (although temperature alone wouldn't account for the shortening on the other invervals of the line that I mentioned.
Chaining Contest (Actually Not a Math Puzzle)
Kent,
I applaud your restraint from entering a guess. Perhaps next time I'll follow suit. 🙂
