Optimized Weighting Method
OR "OVER ENGINEERED WEIGHTING METHOD"
Some people just want their chessmen to feel heavy. Triple weighted, quadruple weighted, the heavier, the better. However, for me, the purpose of weighting is to prevent the pieces from tipping and falling over. That reminded me of basic tipping calculations and how to find the tipping angle. The tipping point will occur when the CG (center of gravity) crosses the vertical line of the last point of contact of the base. A solid wood piece has a CG at the point shown.
Solid Wood Pawn-CG
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Solid Wood Pawn Tipping Angle
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To lower the CG, higher density material (lead) is added to the bottom of the piece, replacing the lower density material (wood/plastic). This rapidly lowers the CG, but we have to add more weight on top of the previous weight which lowers the CG at a slower and slower rate until the CG starts rising again. There is an optimum height of weight that will achieve the lowest CG.
I ran some iterative design experiments in CAD with a simple shaped weight. I varied the height of the weight in .010” inch increments and found which height achieved the lowest CG. I planned to pour molten lead into the exact shape of the cavity.
For the pawn, the theoretical optimized tipping angle was 75 degrees, measured from vertical. This was a 12% improvement over the maximum weight scenario and 39% reduction in weight. For a visual illustration of all scenarios I plotted the results.
The overlap is because I was changing two dimensions of the weight geometry.
I performed the same design study to all the pieces (pRNBQK) and made some drawings of the cavity dimensions.
Next, I needed a way to first create the cavity in the piece. I didn’t want to create the cavity before turning the outer profile because I didn’t think I would be able to locate the outer profile precisely with respect to the inner cavity. (Note: To turn a piece backward on the lathe to bore the cavity and turn the outer profile would ensure concentricity and position, but parting is difficult to do on the finial (top) of the piece. The very top of the piece needs to be sanded on the lathe to avoid imperfection.)
I decided to make custom collets for each piece size to hold the pieces backwards in the lathe after first turning the outer profile.
I performed the same design study to all the pieces (pRNBQK) and made some drawings of the cavity dimensions.
Next, I needed a way to first create the cavity in the piece. I didn’t want to create the cavity before turning the outer profile because I didn’t think I would be able to locate the outer profile precisely with respect to the inner cavity. (Note: To turn a piece backward on the lathe to bore the cavity and turn the outer profile would ensure concentricity and position, but parting is difficult to do on the finial (top) of the piece. The very top of the piece needs to be sanded on the lathe to avoid imperfection.)
I decided to make custom collets for each piece size to hold the pieces backwards in the lathe after first turning the outer profile.
Collets
I made these collets in 2018 from cherry and turned them after mounting them on arbor shanks so they would have better concentricity. Now that I have a 3D printer, I would definitely print the collets. The only compromise to the optimized cavity design was that I included a tapped thread at the top of the cavity to better retain the weight inside the piece. The weight could be removed by drilling a couple small holes in the bottom of the weight and using a pronged tool to unscrew the cast lead weight from the wooden piece. I believe Jaques of London used to do something similar (according to this chesspy video).
I ran into problems. The outer part of the weight cavity left the piece thickness very thin which caused splitting and there was difficulty to keep the molten lead from spilling. I was attempting to pour molten lead into the pieces with a medium sized cast iron pan. That resulted in over pouring and ruining pieces as the molten lead burned the outside of the piece. I found the most precise method for pouring lead was the Lee Pot. This is normally used for pouring lead fishing weights or reloading ammo.
A word on lead safety:
I did the melting and lead pouring outside or with the garage door open for ventilation. I wore gloves when handling the lead pieces.
A funny side story:
A friend knew I was scavenging lead and sent me a link to a government auction website that listed a “30 lb lead ingot”. I bid the minimum $10 on the item and won.
I ran into problems. The outer part of the weight cavity left the piece thickness very thin which caused splitting and there was difficulty to keep the molten lead from spilling. I was attempting to pour molten lead into the pieces with a medium sized cast iron pan. That resulted in over pouring and ruining pieces as the molten lead burned the outside of the piece. I found the most precise method for pouring lead was the Lee Pot. This is normally used for pouring lead fishing weights or reloading ammo.
A word on lead safety:
I did the melting and lead pouring outside or with the garage door open for ventilation. I wore gloves when handling the lead pieces.
A funny side story:
A friend knew I was scavenging lead and sent me a link to a government auction website that listed a “30 lb lead ingot”. I bid the minimum $10 on the item and won.
Auctioned Ingot from GovDeals
I was extremely excited because that would be a great deal and last me a long time. They told me to go pick up my item at the Oklahoma County Detention Center in downtown Oklahoma City. That seemed odd. When I arrived and told them why I was there, they looked confused when I mentioned the lead ingot but got someone to take me down a few floors to hopefully find it. The guard who was escorting me had to badge all the doors and elevator buttons to grant us access. There were some rough inmates going in and out. We came to what I believe was an evidence locker. I told the keeper I was there to pick up the lead ingot. He said “Wow, that lead ingot has been down here for 20 years.” We went over to the shelf where it was and when I saw it, I thought there’s no way that is lead. It was too massive to only weigh 30 lb. I told the evidence keeper my thoughts and he said I could take it if I wanted it. On the way back up and out, everyone gave me some strange looks as I carried the “lead” ingot. Once back home, I measured and modeled the ingot in CAD to try guessing the material by its actual weight and applying different material densities. I thought it was most likely aluminum but the actual weight was slightly heavier than the CAD, calculated weight. Then I thought, if this ingot was evidence in a crime, what if it was used to hide stolen jewelry by casting them into the middle of the ingot. The ingot could be full of diamonds, rubies, or even gold since it has a higher melting point than the aluminum, zinc, or pot metal. The ingot could be melted down and the stolen gems could be recovered. I took the ingot to the manufacturing plant where I work to ask if I could cut the ingot up on the bandsaw. I told the chief engineer my theory and hope that I was about to hit the jackpot. He was intrigued enough to watch me make the first cut. Nothing. I cut it twice in the thicker sections but no treasure was found. The only thing left to do would be to melt it down and pour it into smaller ingots to do a complete search. For now though, the piece of evidence remains unsolv-ed...
Even though I had a precise pouring method and thicker wall thickness, there were still challenges. Lead melts at 621 F (327 C) so any moisture left in the already dried wood is rapidly baked out. Sometimes a hissing noise was heard from the steam escaping. The bocote wood suffered a particularly annoying problem. The high resin content caused resin to bubble out of the outside profile of the piece. I made sure the lead did not get too far above its melting point while in the lee pot by checking it with an IR temp gun. Immediately after pouring the lead into the piece, I cooled the lead with an air nozzle.
After pouring the lead, the bottom was machined flat by holding the piece backwards in the collets a second time. The only trick was to load the piece in the collet to be square with the lathe. Otherwise the bottom of the piece would be at an angle. The other key was to wait until the lead had cooled completely so it would cut cleanly with a good surface finish instead of a rough, gummy finish.
Even though I had a precise pouring method and thicker wall thickness, there were still challenges. Lead melts at 621 F (327 C) so any moisture left in the already dried wood is rapidly baked out. Sometimes a hissing noise was heard from the steam escaping. The bocote wood suffered a particularly annoying problem. The high resin content caused resin to bubble out of the outside profile of the piece. I made sure the lead did not get too far above its melting point while in the lee pot by checking it with an IR temp gun. Immediately after pouring the lead into the piece, I cooled the lead with an air nozzle.
After pouring the lead, the bottom was machined flat by holding the piece backwards in the collets a second time. The only trick was to load the piece in the collet to be square with the lathe. Otherwise the bottom of the piece would be at an angle. The other key was to wait until the lead had cooled completely so it would cut cleanly with a good surface finish instead of a rough, gummy finish.
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Weighting the pieces in this manner was more work than originally turning the pieces out of wood, but the end result was worth it. You can put a wobbly spin on a piece, and it’s almost self-righting. I prioritized tipping angle over total weight in my optimization study but the truth is…these pieces are heavy!
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Maple King = 115g
Bocote King = 135g Maple Queen = 89g Bocote Queen = 102g Maple Bishop = 58g Bocote Bishop = 71g Maple Knight = 69g Bocote Knight = 74g Maple Rook = 69g Bocote Rook = 87g Maple Pawn = 28 g Bocote Pawn = 37g |
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Now I committed another treason against Dubrovnik chessmen history. I set up my Fischer Dubrovnik chessmen on my 1950 Dubrovnik Board. The pieces are so close to self-righting that I have to purposely lay each piece down on its side so I can close the box.
Building the 1950 Dubrovnik board/box is an article for another day...