I would say 5 family series JD or larger, not sure what that is in other brands. HP is rather irrelevant when it comes to loader work but I would say 50hp plus.
I have a 4 series and with big round bales I wish I had a bigger tractor for stability reasons. I suppose a 4 series would do it but would be pushing its limits.
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Pallet forks on a 6x4 round bale, around 1200lbs maybe more, I haven’t bought another that big since and don’t plan to.
I have around 30psi in my front tires and 12psi in the rears, you can see how stressed the front tires were on that bale.