Maximising shelf space in a given room

If the shelfs are 2-dimensional (meaning you don't worry about their height) and

rectangular with sides w,d (width, depth) , then

you want to maximize the expression 2w+2d , while minimizing wd. But I imagine

width is more important than depth (since more depth will not, in general,

allow you to store more books), so maybe you just want to maximize w , and

choosing d large-enough to store the books.

 

How much human access space would you specify? Also, is overhead and underfoot space considered?

 

Btw - with the overhead and underfoot question I considered the viewable requirement achievable with mirrors on ceiling and floor between shelves.

 

Please consider this solution. Determine the size required for a single person and a folded ladder to reach the ceiling - perhaps 2 sq ft? If the space is an even number of sq ft - construct 2' square shelves (accesible from 4 sides) on casters and extending from floor to ceiling. Fill the entire room with these shelves except for the human space and 1 additional 2' square space - this will allow you to move about through the room and utilize the ladder.

 

Only the simplest of real life situations can be solved by a single formula. Your problem is too complex for that. A practical way to approach your problem would be to write a computer program that tried a large number of configurations. You would have to specify the algorithms that determine if there is sufficient space for a human being to access the books conveniently and that is probably not a simple algorithm to write. You have to include other other practical considerations such as shelf length and shelf vertical spacing. Unless you are a metal worker, if you use metal shelves to have the advantage of the vertically thin shelf, you only find these made in certain lengths. If you use wood (or thin metal) you have the problem that a long shelf will sag. A clear space of 10 1/2 between shelves and a shelf depth of 10 inches is enough to accommodate most books but there will be a few bigger ones and if all your shelves have that spacing, the tall books would have to go on the top of the bookcase or on their sides.

Practical design problems are very interesting. Good designs are often compromises between several contradictory goals.