Hi Victor.  Langstroth Hoffman-type frames, as commonly supplied in USA,
are designed so that when the frames are crowded together, they are
automatically spaced at 1 3/8".  Normally there will be some room left over
at each side of the hive body as well.
 
>Maybe my math is in error but I calculate 10 frame spacing to be 1.475
>inches and 9 frame spacing to be 1.62 inches.
OK, but IME the brood frames are best not spread evenly across the box.
 
With 10 frames the end-bar shoulders are butting right up against each
other.  This leaves some extra space at the sides.
 
With 9 frames, there is a bit of a gap between adjacent frame-shoulders,
and again you end up with some space at the sides.
 
[If, instead, one uses 9 frames along with a dummy board or two, then the
frames are right up tight against each other (as with 10), and the dummy
board goes between the first frame and the adjacent hive wall.  This can be
advantageous, but then you have to have dummies -- another piece of
equipment to worry about].
 
In honey supers, on the other hand, the combs are evenly spread out across
the box; that's maybe how you get the 1.62".(?)   Also depends on your hive
body inside measurements, too, which can vary considerably, as Allen has
noted. ---------JG