By understanding the arguments and tiling scheme used by the project, you can access much larger and more detailed maps than by the default options. The basic options are:
1 is ultra-detailed, 24 is ultra-general (entire U.S.)
Relief view is scale 20 to 24
Image view is scale 10 to 16
Topo view is scale 11 to 17
The exact scale appears to be 200 pixels = (2^(S-13)) miles.
A parameter used in the map call but not tile image calls. This defines the size of the map, defined as the number of 200x200 pixel tiles displayed. It is this limitation of display which motivates setting up alternate views.
These are the 2-dimensional projections of the Earth's ellipsoid onto to plane, adjusted for each grid section. X is the "easting" coordinate, while Y is the "northing" coordinate. These are formed by Universal Transverse Mercator (UTM) projection, which is an algorithm of projecting the curved shape of the Earth onto flat two-dimensional maps. The ellipsoid of this projection is based on the North American Datum of 1983 (NAD83).
The projection of latitude and longitude to state plane coordinates is done by the SPCS83 program from the USGS. cf.
The UTM projection divides the Earth into sixty 6° wide bands of longitude called UTM zones, which are sequentially numbered from 1 beginning at the International Date Line. In North America, the UTM zones go from 10 (West Coast) to 19 (Maine). Algorithmically, the zone number is thus int(31+(longitude/6)), rounded down, where West longitude is considered negative.