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Dividing book shelves gradually equally (formula?)

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  • Dividing book shelves gradually equally (formula?)

    Im building a library for a lady and she wants a midcentury modern look. But i wanted to divide the shelves with 2 constraints. the top shelf will have a 10" cavity. the bottom cavity will be no greater than 13" with baseboard heating underneath. I am trying understand the formula for dividing the shelves on a gradual basis with 10 being the lesser and 13 being the larger.

  • #2
    To calculate spacing you'll need to account for either shelf thickness or nosing thickness if that is greater. Then overall height. Rather than progressive spacing I would make the bottom 2 or 3 shelves space the same. Top 2 or 3 shelves space the same. Remainder in the middle divide evenly. Or better yet, make the shelves adjustable and let your customer space them how she wants.

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    • #3
      I wanted to have a gradual decrease and all the shelves would be fixed. But I really wanted to know the understanding in the math of how to achieve this.

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      • #4
        Having a gradual increase in spacing is not considered a good idea by most, but here is the math for you:
        Assume the thickness of all shelves is zero and the individual heights are h1 through h7, so h1=10 and h7=13. The increase in height from each shelf to the next is delta, let's call it d.

        The height of each space is:
        h2=h1+d
        h3=h1+d+d
        h4=h1+d+d+d
        h5=h1+d+d+d+d
        h6=h1+d+d+d+d+d
        h7=h1+d+d+d+d+d+d

        Substituting in the last eq you get
        13=10+6d or d=0.5
        So the increment is half inch.
        Now to account for the thickness of the shelves you can either use the above and consider the heights to be center to center, or you can add the actual thickness of the shelves into the eq.(instead of zero). That will give you an increment for the shelf space heights not including the shelves themselves.

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