Earlier quoted context omitted.
The space question is interesting. The most common Mac mini rack mount enclosure holds 2 minis in 1ru. I think at amazon's scale they could probably get 4 minis in 1ru with some custom cooling. how dense do you think instances are on average in the amazon datacenters?
Why would you not put them on their side and stack them like hard drives? You'd get way more density that way then trying to figure out how to make it fit in 1u for no reason. You could even stack multiple rows deep to get more density.
19 mod 7.7 = 3.6, 3.6 x 1.4 = 5.04 in^2
Presumably the greater waste of bottom side down is in higher number of shelves?