Confusion over Board size.

https://www.chess.com/forum/view/chess-equipment/a-system-for-sizing-chess-pieces-and-boards-long

DD,

Let me know if you're having any troubles wading through my write up that baddogno linked to above.

I've taken the dimensions you referenced in your OP and worked out the scaling and deviation factors for use on a 2.12", 2.25", and 2.36" chess board.

The scaling factor is merely the ratio of a piece's diameter to the size of the square. So a 1.75" diameter king on a 2.25" chess board would have a scaling factor of 1.75"/2.25" = 77.8%.

The deviation factor was something I came up with to measure how close a set was to my preferred scaling factors of 76.5% for the king, and 58.6% for the pawn. The lower the deviation factor, the closer a set is to these ratios. I try and select sets and matching boards so that the deviation factor is less than 5.9. Once the scaling factors get over 10 or so, the sets start looking fairly disproportioned.

For reference, here is a summary of the USCF guidelines for matching king diameters and chess boards.

This, of course, only outlines the acceptable dimensions for USCF tournament play. You're free to use whatever set up you find pleasing to the eye.

I hope this helps.

Lou

DD,

Thanks, I'm glad a few others are finding this info helpful. Funny how things work out, the second (2.25") board just happened to have the best (lowest) deviation factor (Df)! That would be my first choice as well, all else being equal. Since the deviation factors between the 2.25" and 2.36" boards are so close as to be inconsequential, other factors might come into play, such as the size of one or more of the back rank pieces, the spatial design of the set, and of course, personal preference.   

To illustrate, I've created an Inventory spreadsheet of all my chess sets, covering five board sizes, (partial view below) which includes dimensions and the scaling & deviation factors for each set.

As mentioned above, I try and keep the deviation factor for each set around 5.9 or below, where possible. The average deviation factor of the 16 sets in the spreadsheet below is (3.3).

For comparison,

(1)  An original (1849) 4.4" Jaques Staunton set has a deviation factor (Df) of 7.3 on a 2.5" board.

(2)  The new 95mm FIDE Championship set (the one with the funny looking knights) has a Df of 2.9 on a 50mm board (and 9.7 on a 55mm board).

(3)  And the 3.6" Chess Bazaar Dubrovnik set has a Df of 3.2 on a 2.125" board.

The point I've been trying to make is that a well balanced chess set requires pawns that are proportionately scaled of the rest of the set. Having a beautifully matched back row and undersized pawns is like having a massive bodybuilder with skinny legs! Like many things in life, it all comes down to a question of balance.