I installed a 12k winch on my Kioti DK45 HSE at the 3PH using a purpose built portable winch mount for a 2" receiver I had laying around. Ran 0 or 1 gauge cable from the standard tractor battery back to the winch using Anderson QD type mounts. Exact same setups I use in my 1996 Jeep GC and 2015 Ram 2500 diesel. I have never had any power problems for relatively short pulls in getting out an old Ford tractor at max. single line pull that was mud bogged to the frame at the bottom of a hill or a myriad of large oak trees needing directional coaxing or other "projects" using a single battery. Of course multiple batteries and high amp. alternators would be a nice option.
On the tractor the winch was used to pull trees towards the direction I wanted them to fall versus their natural leaning path, regardless of how the chainsaw cuts were made. Had some heavy leaners that required mechanical persuasion.
Use large, solid rubber tire chocks if unable to chain down the tractor against the pull for the heavy pulls. Heavy duty, non solid tire chocks have always worked okay on my 9k winch but failed miserably on the 12k winch. Long story for the failed chocks in the pic involving wife at the tractor with winch remote and me at the tree cutting and providing directions.
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