Cornu Spirals Mystery Cache

A puzzle cache so the cache is not located at the given coordinates which are at the center of the map on the left below. The center is at VK7560020400, which is short for UTM: 15T E 475600 N 4920400. The map on the right shows the units which are in kilometers now with center (0,0). The cache is located at the center of one of the eyes of one of the spirals. Maybe you can spot the spiral that's a little different.

"Doodles" of Cornu decided to send a message back to her home planet by scarfing some Cornu spirals into the earth in rural Rice County in such a way that you could see them from space but not from the ground. She titled her crop spiral piece "Oodles of Doodles". The message to her people is encoded by the shape, size, color, position and orientation of the spirals. The two basic shapes are shown in the figures below. The one on the left is called a clockwise spiral because as the spirals spiral inward they spiral clockwise. Its reflection, shown on the right, is termed counter-clockwise as the spirals spiral counter-clockwise. Notice in each case that the centers of the eyes are located at plus or minus 45°, and √ 2 kilometers away from each other. In the map on the right above notice that the center of each spiral is at a point with integer coordinates in kilometers.

Perhaps you've spotted the special spiral already. It contains her signature and the cache is at one of it's eyes. It's not the full-sized counterclockwise one smack-dab in the middle of the map. It's one of the smaller ones that have been rotated. To be precise, it has been scaled down by a factor of 2/3, and rotated clockwise by 39.5 degrees.

To account for rounding differences note that your easting should should end in 5 and your northing in 0. Enter the correct location of the cache into the coordinate checker in the form VKeeee5nnnn0 and you will receive the corresponding lat/lon coords and a hint on the hide.

You can validate your puzzle solution with certitude.

More than you need to know: Cornu spirals were earlier studied by Leonard Euler and Johann Bernoulli, esp. as they occurred in diffraction. Their parametric equations involve Fresnel integrals. Of special interest is the smooth transition of the curvature from the line to that of a circle leading Cornu and others to apply them to railroads, racetracks and highways.

The first ten solvers are:
1.      rickrich        Thu, 17 Aug 2017 15:17:27
2.      ctc128  Thu, 17 Aug 2017 18:39:04
3.      pfalstad        Thu, 17 Aug 2017 23:38:57
4.      foundinthewild  Sat, 19 Aug 2017 19:28:26
5.      PackADad        Fri, 15 Sep 2017 18:21:48
6.      salsman Fri, 3 Nov 2017 21:06:46
7.      pcc322  Tue, 14 Nov 2017 19:31:06
8.      PA-20   Wed, 29 Nov 2017 9:10:24
9.      fish2007        Mon, 8 Jan 2018 19:27:56
10.     Dragon Eye      Fri, 19 Jan 2018 8:08:24