Counterweight calculation "lesson"

I’m designing my counterweight system for my frame and thought I would check out some older threads on the subject so I don’t reinvent the wheel. Lots of great stuff out there and I especially liked the attention to avoiding gear backlash (i.e. keep the counterweight tension less than the sled tension)
which @dlang mentioned …genius! I did notice some systems were using a moveable pulley and it wasn’t clear to me if the mechanical advantage was being taken into account? Anyways, I thought I’d post this in hopes it might help others when deciding how much weight to use. Perhaps a better way to look at this is from a tension perspective. i.e., how much TENSION works best on the slack side of the motor, and then go ahead and design the system based off of that figure. I don’t mean to offend anyone if this is second nature to you but I used to train employees on overhead and mobile cranes and you would be surprised how many people get messed up with this. This is not necessarily intuitive for most people.

In the picture below, the right side has a 2# weight hanging directly from the motor sprocket. Obviously the mechanical advantage is 1:1 or 2# of tension on the chain. The problem here is you might need to dig a hole in your floor! In my case, I’m probably going to run mine up and take advantage of a high ceiling and just do a 1:1 arrangement, but “upside down”.

In the left example, the chain end is attached on the beam. The motor will have to pull 10" of chain to raise the weight 5" (no hole in floor required). The mechanical advantage is 2:1 and the tension is therefore reduced to 1# on the slack side of motor and 1# on the attachment side of the moving sprocket. Each part of chain is supporting 1/2 of the 2# counterweight. If we did a block and tackle arrangement (more than 1 pulley at the load) and there were lets say 4 parts of rope at the moveable pulley we would divide the weight by 4 and the tension on the slack side of the motor would be 1/4 the counterweight value, so you would have to add 4 times the counterweight than the tension you desire at the slack side of the motor to achieve your goal.

Also, with a fixed pulley (attached to a beam for example) the pulley is simply changing direction of travel. The mechanical advantage is only calculated on a moveable pulley/sprocket that is moving with the load. Hope this helps someone in the future.

The tension on the sled side of the motor will change depending on “share of the load” and chain angle, but thats a separate lesson for another day. Jerry