Spiromania #57
A puzzle cache. It uses both the VK notation which is common in this series as well as the XYxy coordinate system introduced in the previous cache. A review of that would be helpful. See the first link below.
XYxy and VK (essentially UTM) both use meters. The basic length in XYxy is called a "square" which is approximately 3 meters. A 3-meter by 3-meter square is also called a square. One might think that one could magically convert from one system to the other. Not so. Several excuses are listed in a paragraph below. The major problem is alignment. This is a consequence of the totally different approaches they take to locally flatten the earth. Recall that whereas XYxy uses a tiered wedding cake approach, UTM uses unrolled embedded cylindrical panels. See the figure above and the left one below. UTM's planes are over 30,000 times larger than those in XYxy. In XYxy one changes from plane or cell to another every couple of miles. See the center panel in the figure below which shows the four cells near the posted coordinates as well as the circle of radius two miles in which the solution has to lie.
So where's the cache? It's 1125 (VK) meters from the posted coordinates and 61 XYxy squares from a border. Although that might be enough to get the solution, some of the following information might be helpful.
Ed Sheehan and Gene Autry. During the recent ultra extravaganza for the Queen, the singer/songwriter Ed Sheehan sang one of hits, but not the one "xxxxx xx xxx xxxxxx" from 2019 which would provide a hint for this puzzle. The same title was used for a song written in 1939 that was sung by Gene Autry in a movie of the same name while he was harnessing his horse, Champion. It was also recorded by Frank Sinatra, Patsy Cline, George Strait, Asleep at the Wheel, et.al.
A mathematician, a surveyor, and an engineer were given the task to convert a location from UTM to XYxy. The mathematician first derived general equations in the XYZ ECEF (Earth Centered Earth Fixed) system for projecting a point on the best cylindrical panel approximation over any section of an oblate spheroid onto an m by n cell. The surveyor found a nearby benchmark and projected assuming one XYxy square was three meters. The engineer used the geocaching toolbox to convert the UTM to lat/lon and then the equations from the previous puzzle in this series to go from lat/lon to XYxy.
It's okay to be off-by-one.
- Round-off happens.
- Imprecision, e.g. too few decimals, e.g in 44° dd.dddd'. Using three rather than four decimal places for minutes can throw one off by a couple meters. Fortunately for this problem the fourth digits in the answer are 0 and 1.
- Counts can start at 0 or 1. In counting, one can easily get off by one anyway; at least I can.
- Squares are not exactly three meters long.
- The number of squares per 2.5 minutes longitude are either 1100 or 1101 in our vicinity. Let's use 1101 below 44 37.5' and 1100 above.
- Registration. UTM uses south-west corners; XYxy uses the center of the squares. See the figure on the right below.
- Alignment. Not just the jiggle at the 2.5 minutes latitude lines, but over the height of a cell the difference can be several meters because UTM and XYxy are skewed relative to the other.
You can check your work by entering N 44° mm.mmm' W 93° mm.mmm' into the geocaching.com checker at the left below or the corresponding w3w solution word5.word7.word7 in the certitude checker here.
You can validate your puzzle solution with certitude.
Click on the magnifying glass icon to enlarge the image.
Congrats to the first 10 solvers:
- 1. kcmcacher Thu, 9 Jun 2022 20:32:51
- 2. ctc128 Thu, 9 Jun 2022 23:18:14
- 3. toolrep1 Fri, 10 Jun 2022 9:35:06
- 4. salsman Sun, 12 Jun 2022 22:58:21
- 5. Boreal Walker Tue, 14 Jun 2022 12:06:35
- 6. PackADad Thu, 16 Jun 2022 14:30:09
- 7. pfalstad Thu, 30 Jun 2022 15:58:51
- 8. foundinthewild Wed, 6 Jul 2022 16:58:19
- 9. kkmk Sun, 17 Jul 2022 13:12:40
- 10. trista74 Thu, 4 Aug 2022 20:58:45