SI: radian and steradian Mystery Cache

The International System of Units (SI), commonly known as the metric system, is the international standard for measurement. The SI plays an essential role in international commerce and is commonly used in scientific and technological research and development. This cache is part of the SI geoart that allows you to learn about the SI units. Visit the introduction cache to learn more about this geoart.

Plane Angle: radian (rad)

The radian is the SI unit for measuring angles. It is the standard unit of angular measure used in many areas of mathematics. An arc of a circle with the same length as the radius of that circle subtends an angle of 1 radian. The circumference subtends an angle of 2π radians.

Solid Angle: steradian (sr)

The steradian or square radian is the SI unit of solid angle. It is used in three-dimensional geometry, and is analogous to the radian. Whereas an angle in radians, projected onto a circle, gives a length on the circumference, a solid angle in steradians, projected onto a sphere, gives an area on the surface.

This Geocache

Most odometers work by counting wheel rotations. Using a properly inflated tire, the distance traveled during one radian of wheel rotation equals the radius of the wheel. If you ride a bicycle with 1 metre diameter wheels for 466.5 metres, how many radians do the wheels rotate? Let this number be ABC.

Think of the earth as a sphere with radius 6378 km. What’s the solid angle of Washington DC in the year 1801 in nanosteradians? Round as integer and add 2465 to get DEFG.

Final coordinates: N 39° 07.ABC W 077° 0D.EFG

You can validate your puzzle solution with certitude.

Cache container is a baby-nano with tiny log sheet. A pair of tweezers is mandatory for log retrieval. To conserve space, please omit the date and write the first two letters of your username only.

Some hides are located along a road without sidewalk. For your safety, please walk on the grass out of the car lanes, and avoid going at night without wearing a safety vest.

Lists of Caches in SI geoart

0. introduction
1. second and hertz
2. metre
3. kilogram
4. m/s and km/h
5. mole
6. radian and steradian
7. m/s² and newton
8. m² and pascal
9. joule and watt
10. ampere and coulomb
11. volt and farad
12. ohm
13. kelvin
14. candela, lumen, and lux
15. bushel
16. foreword & afterword
17. prize distribution