Chain sag inaccuracy

With a 20 pound sled at the top center of the work area each chain (or cable) will have about 33.26 pounds of tension. (reference)

David Lang and I have a bit of a long-running disagreement on the forces produced on the sled. The 66 pounds that he is referring to is the stall force for the motors - it’s what the motors are capable of producing; it is not the force on the chains in a static system at the top center. The actual tension in the chains (33.26 pounds) is easy to calculate and is explained quite clearly in this post.

In order for a 20 pound sled to put 66 pounds of force on the chains the internal chain angle would have to be about 162.55˚, that puts the sled just over 217mm (8.54 inches) above the top of the work piece. So it’s easy to see that the system should not see 66 pounds of force under normal operation. I do agree that there will be brief, momentary, spikes in the forces due to variables such as knots, sled friction, path direction change, dull bits, etc. but this will not be constant and therefor any error will also be momentary. (this math is assuming a 20 pound sled with motors that are 440mm above the workpiece and 2900mm apart)

I have not only done the math but I’ve also done real world tests with inline spring scales and come to the same conclusions (some of which is documented here).

Again, if anyone can show me how they are calculating 66 pounds per chain I would love to see the math. I could be wrong and I would be happy to concede if that’s the case. My math, real-world tests, and logic shows me ~33 pounds per chain, and I’ve shown all my work and explained the reasoning so hopefully someone can show me where I’m wrong if I’m wrong.

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